diff --git a/.github/workflows/python-release.yml b/.github/workflows/python-release.yml
index 57411c197..a672ae10d 100644
--- a/.github/workflows/python-release.yml
+++ b/.github/workflows/python-release.yml
@@ -220,6 +220,7 @@ jobs:
             PATH=$HOME/.cargo/bin:$HOME/.pecos/deps/llvm-14/bin:$PATH
             LLVM_SYS_140_PREFIX=$HOME/.pecos/deps/llvm-14
             MACOSX_DEPLOYMENT_TARGET=13.2
+            SDKROOT=$(xcrun --show-sdk-path)
           CIBW_BEFORE_ALL_MACOS: |
             curl -sSf https://sh.rustup.rs | sh -s -- -y
             source $HOME/.cargo/env
@@ -287,6 +288,7 @@ jobs:
             PATH=$HOME/.cargo/bin:$HOME/.pecos/deps/llvm-14/bin:$PATH
             LLVM_SYS_140_PREFIX=$HOME/.pecos/deps/llvm-14
             MACOSX_DEPLOYMENT_TARGET=13.2
+            SDKROOT=$(xcrun --show-sdk-path)
           CIBW_BEFORE_ALL_MACOS: |
             source $HOME/.cargo/env 2>/dev/null || { curl -sSf https://sh.rustup.rs | sh -s -- -y && source $HOME/.cargo/env; }
             if [ ! -d "$HOME/.pecos/deps/llvm-14/bin" ]; then
diff --git a/.github/workflows/python-version-consistency.yml b/.github/workflows/python-version-consistency.yml
index 65989d385..16bd806e9 100644
--- a/.github/workflows/python-version-consistency.yml
+++ b/.github/workflows/python-version-consistency.yml
@@ -3,46 +3,28 @@ name: Python Version Consistency Check
 on:
   push:
     paths:
+      - 'pyproject.toml'
       - 'python/**/pyproject.toml'
+      - 'scripts/check_python_workspace.py'
+      - '.github/workflows/python-version-consistency.yml'
   pull_request:
     paths:
+      - 'pyproject.toml'
       - 'python/**/pyproject.toml'
+      - 'scripts/check_python_workspace.py'
+      - '.github/workflows/python-version-consistency.yml'
 
 jobs:
-  check_versions:
+  check_python_workspace:
     runs-on: ubuntu-latest
     steps:
       - name: Checkout code
         uses: actions/checkout@v6
 
-      - name: Check version consistency
-        run: |
-          # Find all pyproject.toml files in the python/ directory
-          PYPROJECT_FILES=$(find python -name pyproject.toml)
+      - name: Set up Python
+        uses: actions/setup-python@v6
+        with:
+          python-version: "3.11"
 
-          # Initialize variables
-          FIRST_VERSION=""
-          INCONSISTENT=false
-
-          # Check each pyproject.toml file
-          for file in $PYPROJECT_FILES; do
-            VERSION=$(grep -oP 'version = "\K[^"]+' $file)
-
-            if [ -z "$FIRST_VERSION" ]; then
-              FIRST_VERSION=$VERSION
-              echo "Reference version: $FIRST_VERSION (from $file)"
-            elif [ "$VERSION" != "$FIRST_VERSION" ]; then
-              echo "Inconsistent version found in $file: $VERSION"
-              INCONSISTENT=true
-            else
-              echo "Consistent version found in $file: $VERSION"
-            fi
-          done
-
-          # Exit with error if versions are inconsistent
-          if [ "$INCONSISTENT" = true ]; then
-            echo "Error: Inconsistent versions found across pyproject.toml files"
-            exit 1
-          else
-            echo "Success: All pyproject.toml files have consistent versions"
-          fi
+      - name: Check Python workspace metadata
+        run: python scripts/check_python_workspace.py
diff --git a/.typos.toml b/.typos.toml
index 05b3f16f9..716e3bb44 100644
--- a/.typos.toml
+++ b/.typos.toml
@@ -40,3 +40,5 @@ egative = "egative"
 agger = "agger"
 # Ruff rule code prefix (flake8-copyright)
 CPY = "CPY"
+# Abbreviation for "undetectable" in fault enumeration debug output
+UNDET = "UNDET"
diff --git a/Cargo.lock b/Cargo.lock
index 3f9b368ea..167eb8a3f 100644
--- a/Cargo.lock
+++ b/Cargo.lock
@@ -85,6 +85,15 @@ version = "0.1.6"
 source = "registry+https://github.com/rust-lang/crates.io-index"
 checksum = "4b46cbb362ab8752921c97e041f5e366ee6297bd428a31275b9fcf1e380f7299"
 
+[[package]]
+name = "ansi_term"
+version = "0.12.1"
+source = "registry+https://github.com/rust-lang/crates.io-index"
+checksum = "d52a9bb7ec0cf484c551830a7ce27bd20d67eac647e1befb56b0be4ee39a55d2"
+dependencies = [
+ "winapi",
+]
+
 [[package]]
 name = "anstream"
 version = "1.0.0"
@@ -121,7 +130,7 @@ version = "1.1.5"
 source = "registry+https://github.com/rust-lang/crates.io-index"
 checksum = "40c48f72fd53cd289104fc64099abca73db4166ad86ea0b4341abe65af83dadc"
 dependencies = [
- "windows-sys 0.60.2",
+ "windows-sys 0.61.2",
 ]
 
 [[package]]
@@ -132,7 +141,7 @@ checksum = "291e6a250ff86cd4a820112fb8898808a366d8f9f58ce16d1f538353ad55747d"
 dependencies = [
  "anstyle",
  "once_cell_polyfill",
- "windows-sys 0.60.2",
+ "windows-sys 0.61.2",
 ]
 
 [[package]]
@@ -254,9 +263,9 @@ dependencies = [
 
 [[package]]
 name = "assert_cmd"
-version = "2.2.1"
+version = "2.2.2"
 source = "registry+https://github.com/rust-lang/crates.io-index"
-checksum = "39bae1d3fa576f7c6519514180a72559268dd7d1fe104070956cb687bc6673bd"
+checksum = "2aa3a22042e45de04255c7bf3626e239f450200fd0493c1e382263544b20aea6"
 dependencies = [
  "anstyle",
  "bstr",
@@ -284,6 +293,17 @@ version = "1.1.2"
 source = "registry+https://github.com/rust-lang/crates.io-index"
 checksum = "1505bd5d3d116872e7271a6d4e16d81d0c8570876c8de68093a09ac269d8aac0"
 
+[[package]]
+name = "atty"
+version = "0.2.14"
+source = "registry+https://github.com/rust-lang/crates.io-index"
+checksum = "d9b39be18770d11421cdb1b9947a45dd3f37e93092cbf377614828a319d5fee8"
+dependencies = [
+ "hermit-abi 0.1.19",
+ "libc",
+ "winapi",
+]
+
 [[package]]
 name = "autocfg"
 version = "1.5.0"
@@ -355,7 +375,7 @@ dependencies = [
  "rand 0.10.1",
  "rand_xoshiro 0.8.0",
  "rapidhash",
- "wide 1.3.0",
+ "wide 1.4.0",
 ]
 
 [[package]]
@@ -364,7 +384,7 @@ version = "0.72.1"
 source = "registry+https://github.com/rust-lang/crates.io-index"
 checksum = "993776b509cfb49c750f11b8f07a46fa23e0a1386ffc01fb1e7d343efc387895"
 dependencies = [
- "bitflags",
+ "bitflags 2.11.1",
  "cexpr",
  "clang-sys",
  "itertools 0.13.0",
@@ -438,6 +458,12 @@ version = "0.9.1"
 source = "registry+https://github.com/rust-lang/crates.io-index"
 checksum = "b71798fca2c1fe1086445a7258a4bc81e6e49dcd24c8d0dd9a1e57395b603f51"
 
+[[package]]
+name = "bitflags"
+version = "1.3.2"
+source = "registry+https://github.com/rust-lang/crates.io-index"
+checksum = "bef38d45163c2f1dde094a7dfd33ccf595c92905c8f8f4fdc18d06fb1037718a"
+
 [[package]]
 name = "bitflags"
 version = "2.11.1"
@@ -503,6 +529,24 @@ version = "0.1.0"
 source = "registry+https://github.com/rust-lang/crates.io-index"
 checksum = "38c99613cb3cd7429889a08dfcf651721ca971c86afa30798461f8eee994de47"
 
+[[package]]
+name = "bp"
+version = "0.1.0"
+source = "git+https://github.com/yuewuo/mwpf?tag=v0.2.12#b8444428f999457208c4b0956f3f1c745a0ec2d5"
+dependencies = [
+ "float-cmp",
+ "rand 0.8.6",
+]
+
+[[package]]
+name = "bs58"
+version = "0.5.1"
+source = "registry+https://github.com/rust-lang/crates.io-index"
+checksum = "bf88ba1141d185c399bee5288d850d63b8369520c1eafc32a0430b5b6c287bf4"
+dependencies = [
+ "tinyvec",
+]
+
 [[package]]
 name = "bstr"
 version = "1.12.1"
@@ -584,9 +628,9 @@ dependencies = [
 
 [[package]]
 name = "cargo-platform"
-version = "0.3.2"
+version = "0.3.3"
 source = "registry+https://github.com/rust-lang/crates.io-index"
-checksum = "87a0c0e6148f11f01f32650a2ea02d532b2ad4e81d8bd41e6e565b5adc5e6082"
+checksum = "dd0061da739915fae12ea00e16397555ed4371a6bb285431aab930f61b0aa4ba"
 dependencies = [
  "serde",
  "serde_core",
@@ -614,9 +658,9 @@ checksum = "37b2a672a2cb129a2e41c10b1224bb368f9f37a2b16b612598138befd7b37eb5"
 
 [[package]]
 name = "cc"
-version = "1.2.60"
+version = "1.2.62"
 source = "registry+https://github.com/rust-lang/crates.io-index"
-checksum = "43c5703da9466b66a946814e1adf53ea2c90f10063b86290cc9eb67ce3478a20"
+checksum = "a1dce859f0832a7d088c4f1119888ab94ef4b5d6795d1ce05afb7fe159d79f98"
 dependencies = [
  "find-msvc-tools",
  "jobserver",
@@ -624,12 +668,6 @@ dependencies = [
  "shlex",
 ]
 
-[[package]]
-name = "cesu8"
-version = "1.1.0"
-source = "registry+https://github.com/rust-lang/crates.io-index"
-checksum = "6d43a04d8753f35258c91f8ec639f792891f748a1edbd759cf1dcea3382ad83c"
-
 [[package]]
 name = "cexpr"
 version = "0.6.0"
@@ -725,6 +763,21 @@ dependencies = [
  "libloading 0.8.9",
 ]
 
+[[package]]
+name = "clap"
+version = "2.34.0"
+source = "registry+https://github.com/rust-lang/crates.io-index"
+checksum = "a0610544180c38b88101fecf2dd634b174a62eef6946f84dfc6a7127512b381c"
+dependencies = [
+ "ansi_term",
+ "atty",
+ "bitflags 1.3.2",
+ "strsim 0.8.0",
+ "textwrap",
+ "unicode-width 0.1.14",
+ "vec_map",
+]
+
 [[package]]
 name = "clap"
 version = "4.6.1"
@@ -744,16 +797,16 @@ dependencies = [
  "anstream",
  "anstyle",
  "clap_lex",
- "strsim",
+ "strsim 0.11.1",
 ]
 
 [[package]]
 name = "clap_complete"
-version = "4.6.2"
+version = "4.6.5"
 source = "registry+https://github.com/rust-lang/crates.io-index"
-checksum = "3ff7a1dccbdd8b078c2bdebff47e404615151534d5043da397ec50286816f9cb"
+checksum = "e0a7a9bfdb35811f9e59832f0f05975114d2251b415fb534108e6f34060fd772"
 dependencies = [
- "clap",
+ "clap 4.6.1",
 ]
 
 [[package]]
@@ -800,7 +853,7 @@ checksum = "af491d569909a7e4dee0ad7db7f5341fef5c614d5b8ec8cf765732aba3cff681"
 dependencies = [
  "serde",
  "termcolor",
- "unicode-width",
+ "unicode-width 0.2.2",
 ]
 
 [[package]]
@@ -827,7 +880,7 @@ checksum = "d64e8af5551369d19cf50138de61f1c42074ab970f74e99be916646777f8fc87"
 dependencies = [
  "encode_unicode",
  "libc",
- "unicode-width",
+ "unicode-width 0.2.2",
  "windows-sys 0.61.2",
 ]
 
@@ -879,6 +932,15 @@ dependencies = [
  "winapi",
 ]
 
+[[package]]
+name = "cpp_demangle"
+version = "0.4.5"
+source = "registry+https://github.com/rust-lang/crates.io-index"
+checksum = "f2bb79cb74d735044c972aae58ed0aaa9a837e85b01106a54c39e42e97f62253"
+dependencies = [
+ "cfg-if",
+]
+
 [[package]]
 name = "cpufeatures"
 version = "0.2.17"
@@ -899,27 +961,27 @@ dependencies = [
 
 [[package]]
 name = "cranelift-assembler-x64"
-version = "0.130.2"
+version = "0.131.1"
 source = "registry+https://github.com/rust-lang/crates.io-index"
-checksum = "adc822414b18d1f5b1b33ce1441534e311e62fef86ebb5b9d382af857d0272c9"
+checksum = "f8628cc4ba7f88a9205a7ee42327697abc61195a1e3d92cfae172d6a946e722e"
 dependencies = [
  "cranelift-assembler-x64-meta",
 ]
 
 [[package]]
 name = "cranelift-assembler-x64-meta"
-version = "0.130.2"
+version = "0.131.1"
 source = "registry+https://github.com/rust-lang/crates.io-index"
-checksum = "8c646808b06f4532478d8d6057d74f15c3322f10d995d9486e7dcea405bf521a"
+checksum = "d582754487e6c9a065a91c42ccf1bdd8d5977af33468dac5ae9bec0ce88acb3e"
 dependencies = [
  "cranelift-srcgen",
 ]
 
 [[package]]
 name = "cranelift-bforest"
-version = "0.130.2"
+version = "0.131.1"
 source = "registry+https://github.com/rust-lang/crates.io-index"
-checksum = "7b5996f01a686b2349cdb379083ec5ad3e8cb8767fb2d495d3a4f2ee4163a18d"
+checksum = "fb59c81ace12ee7c33074db7903d4d75d1f40b28cd3e8e6f491de57b29129eb9"
 dependencies = [
  "cranelift-entity",
  "wasmtime-internal-core",
@@ -927,9 +989,9 @@ dependencies = [
 
 [[package]]
 name = "cranelift-bitset"
-version = "0.130.2"
+version = "0.131.1"
 source = "registry+https://github.com/rust-lang/crates.io-index"
-checksum = "523fea83273f6a985520f57788809a4de2165794d9ab00fb1254fceb4f5aa00c"
+checksum = "f25c06993a681be9cf3140798a3d4ac5bec955e7444416a2fdc87fda8567285d"
 dependencies = [
  "serde",
  "serde_derive",
@@ -938,9 +1000,9 @@ dependencies = [
 
 [[package]]
 name = "cranelift-codegen"
-version = "0.130.2"
+version = "0.131.1"
 source = "registry+https://github.com/rust-lang/crates.io-index"
-checksum = "d73d1e372730b5f64ed1a2bd9f01fe4686c8ec14a28034e3084e530c8d951878"
+checksum = "27b61f95c5a211918f5d336254a61a488b36a5818de47a868e8c4658dce9cccc"
 dependencies = [
  "bumpalo",
  "cranelift-assembler-x64",
@@ -966,9 +1028,9 @@ dependencies = [
 
 [[package]]
 name = "cranelift-codegen-meta"
-version = "0.130.2"
+version = "0.131.1"
 source = "registry+https://github.com/rust-lang/crates.io-index"
-checksum = "b0319c18165e93dc1ebf78946a8da0b1c341c95b4a39729a69574671639bdb5f"
+checksum = "0b85aa822fce72080d041d7c2cf7c3f5c6ecdea7afae68379ba4ef85269c4fa5"
 dependencies = [
  "cranelift-assembler-x64-meta",
  "cranelift-codegen-shared",
@@ -979,24 +1041,24 @@ dependencies = [
 
 [[package]]
 name = "cranelift-codegen-shared"
-version = "0.130.2"
+version = "0.131.1"
 source = "registry+https://github.com/rust-lang/crates.io-index"
-checksum = "9195cd8aeecb55e401aa96b2eaa55921636e8246c127ed7908f7ef7e0d40f270"
+checksum = "833eb9fc89326cd072cc19e96892f09b5692c0dfe17cd4da2858ba30c2cd85c0"
 
 [[package]]
 name = "cranelift-control"
-version = "0.130.2"
+version = "0.131.1"
 source = "registry+https://github.com/rust-lang/crates.io-index"
-checksum = "8976c2154b74136322befc74222ab5c7249edd7e2604f8cbef2b94975541ffb9"
+checksum = "9d005320f487e6e8a3edcc7f2fd4f43fcc9946d1013bf206ea649789ac1617fc"
 dependencies = [
  "arbitrary",
 ]
 
 [[package]]
 name = "cranelift-entity"
-version = "0.130.2"
+version = "0.131.1"
 source = "registry+https://github.com/rust-lang/crates.io-index"
-checksum = "6038b3147c7982f4951150d5f96c7c06c1e7214b99d4b4a98607aadf8ded89d1"
+checksum = "5e62ef34c6e720f347a79ece043e8584e242d168911da640bac654a33a6aaaf5"
 dependencies = [
  "cranelift-bitset",
  "serde",
@@ -1006,9 +1068,9 @@ dependencies = [
 
 [[package]]
 name = "cranelift-frontend"
-version = "0.130.2"
+version = "0.131.1"
 source = "registry+https://github.com/rust-lang/crates.io-index"
-checksum = "4cbd294abe236e23cc3d907b0936226b6a8342db7636daa9c7c72be1e323420e"
+checksum = "dfa2ad00399dd47e7e7e33cb1dc23b0e39ed9dcd01e8f026fc37af91655031b8"
 dependencies = [
  "cranelift-codegen",
  "log",
@@ -1018,15 +1080,15 @@ dependencies = [
 
 [[package]]
 name = "cranelift-isle"
-version = "0.130.2"
+version = "0.131.1"
 source = "registry+https://github.com/rust-lang/crates.io-index"
-checksum = "b5a90b6ed3aba84189352a87badeb93b2126d3724225a42dc67fdce53d1b139c"
+checksum = "02c51975ed217b4e8e5a7fd11e9ec83a96104bdff311dddcb505d1d8a9fd7fc6"
 
 [[package]]
 name = "cranelift-native"
-version = "0.130.2"
+version = "0.131.1"
 source = "registry+https://github.com/rust-lang/crates.io-index"
-checksum = "c3ec0cc1a54e22925eacf4fc3dc815f907734d3b377899d19d52bec04863e853"
+checksum = "f9b1889e00da9729d8f8525f3c12998ded86ea709058ff844ebe00b97548de0e"
 dependencies = [
  "cranelift-codegen",
  "libc",
@@ -1035,9 +1097,9 @@ dependencies = [
 
 [[package]]
 name = "cranelift-srcgen"
-version = "0.130.2"
+version = "0.131.1"
 source = "registry+https://github.com/rust-lang/crates.io-index"
-checksum = "948865622f87f30907bb46fbb081b235ae63c1896a99a83c26a003305c1fa82d"
+checksum = "d5a8f82fd5124f009f72167e60139245cd3b56cfd4b53050f22110c48c5f4da1"
 
 [[package]]
 name = "crc"
@@ -1050,9 +1112,9 @@ dependencies = [
 
 [[package]]
 name = "crc-catalog"
-version = "2.4.0"
+version = "2.5.0"
 source = "registry+https://github.com/rust-lang/crates.io-index"
-checksum = "19d374276b40fb8bbdee95aef7c7fa6b5316ec764510eb64b8dd0e2ed0d7e7f5"
+checksum = "217698eaf96b4a3f0bc4f3662aaa55bdf913cd54d7204591faa790070c6d0853"
 
 [[package]]
 name = "crc32fast"
@@ -1073,7 +1135,7 @@ dependencies = [
  "anes",
  "cast",
  "ciborium",
- "clap",
+ "clap 4.6.1",
  "criterion-plot",
  "itertools 0.13.0",
  "num-traits",
@@ -1178,6 +1240,12 @@ dependencies = [
  "memchr",
 ]
 
+[[package]]
+name = "cute"
+version = "0.3.0"
+source = "registry+https://github.com/rust-lang/crates.io-index"
+checksum = "45e700c2d1c3feea9b695e79b2dfeeb93040556a58c556fae23f71b1e6b449fd"
+
 [[package]]
 name = "cxx"
 version = "1.0.194"
@@ -1214,7 +1282,7 @@ version = "1.0.194"
 source = "registry+https://github.com/rust-lang/crates.io-index"
 checksum = "d0956799fa8678d4c50eed028f2de1c0552ae183c76e976cf7ca8c4e36a7c328"
 dependencies = [
- "clap",
+ "clap 4.6.1",
  "codespan-reporting",
  "indexmap 2.14.0",
  "proc-macro2",
@@ -1259,7 +1327,7 @@ dependencies = [
  "ident_case",
  "proc-macro2",
  "quote",
- "strsim",
+ "strsim 0.11.1",
  "syn 2.0.117",
 ]
 
@@ -1434,9 +1502,9 @@ dependencies = [
 
 [[package]]
 name = "digest"
-version = "0.11.2"
+version = "0.11.3"
 source = "registry+https://github.com/rust-lang/crates.io-index"
-checksum = "4850db49bf08e663084f7fb5c87d202ef91a3907271aff24a94eb97ff039153c"
+checksum = "f1dd6dbb5841937940781866fa1281a1ff7bd3bf827091440879f9994983d5c2"
 dependencies = [
  "block-buffer 0.12.0",
  "const-oid",
@@ -1471,7 +1539,7 @@ dependencies = [
  "libc",
  "option-ext",
  "redox_users 0.5.2",
- "windows-sys 0.60.2",
+ "windows-sys 0.61.2",
 ]
 
 [[package]]
@@ -1491,7 +1559,7 @@ version = "0.3.1"
 source = "registry+https://github.com/rust-lang/crates.io-index"
 checksum = "1e0e367e4e7da84520dedcac1901e4da967309406d1e51017ae1abfb97adbd38"
 dependencies = [
- "bitflags",
+ "bitflags 2.11.1",
  "objc2",
 ]
 
@@ -1646,7 +1714,7 @@ source = "registry+https://github.com/rust-lang/crates.io-index"
 checksum = "39cab71617ae0d63f51a36d69f866391735b51691dbda63cf6f96d042b63efeb"
 dependencies = [
  "libc",
- "windows-sys 0.52.0",
+ "windows-sys 0.61.2",
 ]
 
 [[package]]
@@ -1657,13 +1725,12 @@ checksum = "9f1f227452a390804cdb637b74a86990f2a7d7ba4b7d5693aac9b4dd6defd8d6"
 
 [[package]]
 name = "filetime"
-version = "0.2.27"
+version = "0.2.28"
 source = "registry+https://github.com/rust-lang/crates.io-index"
-checksum = "f98844151eee8917efc50bd9e8318cb963ae8b297431495d3f758616ea5c57db"
+checksum = "2d5b2eef6fafbf69f877e55509ce5b11a760690ac9700a2921be067aa6afaef6"
 dependencies = [
  "cfg-if",
  "libc",
- "libredox",
 ]
 
 [[package]]
@@ -1718,6 +1785,15 @@ dependencies = [
  "miniz_oxide",
 ]
 
+[[package]]
+name = "float-cmp"
+version = "0.10.0"
+source = "registry+https://github.com/rust-lang/crates.io-index"
+checksum = "b09cf3155332e944990140d967ff5eceb70df778b34f77d8075db46e4704e6d8"
+dependencies = [
+ "num-traits",
+]
+
 [[package]]
 name = "fnv"
 version = "1.0.7"
@@ -1766,7 +1842,7 @@ dependencies = [
  "cc",
  "cfg-if",
  "chrono",
- "clap",
+ "clap 4.6.1",
  "core_affinity",
  "derivative",
  "lazy_static",
@@ -2117,7 +2193,7 @@ version = "0.3.2"
 source = "registry+https://github.com/rust-lang/crates.io-index"
 checksum = "b89c83349105e3732062a895becfc71a8f921bb71ecbbdd8ff99263e3b53a0ca"
 dependencies = [
- "bitflags",
+ "bitflags 2.11.1",
  "gpu-descriptor-types",
  "hashbrown 0.15.5",
 ]
@@ -2128,7 +2204,7 @@ version = "0.2.0"
 source = "registry+https://github.com/rust-lang/crates.io-index"
 checksum = "fdf242682df893b86f33a73828fb09ca4b2d3bb6cc95249707fc684d27484b91"
 dependencies = [
- "bitflags",
+ "bitflags 2.11.1",
 ]
 
 [[package]]
@@ -2166,7 +2242,10 @@ version = "0.15.5"
 source = "registry+https://github.com/rust-lang/crates.io-index"
 checksum = "9229cfe53dfd69f0609a49f65461bd93001ea1ef889cd5529dd176593f5338a1"
 dependencies = [
+ "allocator-api2",
+ "equivalent",
  "foldhash 0.1.5",
+ "rayon",
 ]
 
 [[package]]
@@ -2184,9 +2263,26 @@ dependencies = [
 
 [[package]]
 name = "hashbrown"
-version = "0.17.0"
+version = "0.17.1"
 source = "registry+https://github.com/rust-lang/crates.io-index"
-checksum = "4f467dd6dccf739c208452f8014c75c18bb8301b050ad1cfb27153803edb0f51"
+checksum = "ed5909b6e89a2db4456e54cd5f673791d7eca6732202bbf2a9cc504fe2f9b84a"
+dependencies = [
+ "foldhash 0.2.0",
+]
+
+[[package]]
+name = "heapz"
+version = "1.1.4"
+source = "git+https://github.com/yuewuo/mwpf?tag=v0.2.12#b8444428f999457208c4b0956f3f1c745a0ec2d5"
+
+[[package]]
+name = "heck"
+version = "0.3.3"
+source = "registry+https://github.com/rust-lang/crates.io-index"
+checksum = "6d621efb26863f0e9924c6ac577e8275e5e6b77455db64ffa6c65c904e9e132c"
+dependencies = [
+ "unicode-segmentation",
+]
 
 [[package]]
 name = "heck"
@@ -2200,6 +2296,15 @@ version = "0.5.0"
 source = "registry+https://github.com/rust-lang/crates.io-index"
 checksum = "2304e00983f87ffb38b55b444b5e3b60a884b5d30c0fca7d82fe33449bbe55ea"
 
+[[package]]
+name = "hermit-abi"
+version = "0.1.19"
+source = "registry+https://github.com/rust-lang/crates.io-index"
+checksum = "62b467343b94ba476dcb2500d242dadbb39557df889310ac77c5d99100aaac33"
+dependencies = [
+ "libc",
+]
+
 [[package]]
 name = "hermit-abi"
 version = "0.5.2"
@@ -2218,6 +2323,25 @@ version = "0.2.1"
 source = "registry+https://github.com/rust-lang/crates.io-index"
 checksum = "dfa686283ad6dd069f105e5ab091b04c62850d3e4cf5d67debad1933f55023df"
 
+[[package]]
+name = "highs"
+version = "1.6.1"
+source = "git+https://github.com/yuewuo/mwpf?tag=v0.2.12#b8444428f999457208c4b0956f3f1c745a0ec2d5"
+dependencies = [
+ "highs-sys",
+ "log",
+]
+
+[[package]]
+name = "highs-sys"
+version = "1.14.2"
+source = "registry+https://github.com/rust-lang/crates.io-index"
+checksum = "11a9fa9dea5b5f277075460b695db30ad7e5ce28554f2dd27c312c640acd101f"
+dependencies = [
+ "bindgen",
+ "cmake",
+]
+
 [[package]]
 name = "html-escape"
 version = "0.2.13"
@@ -2379,9 +2503,9 @@ dependencies = [
 
 [[package]]
 name = "hybrid-array"
-version = "0.4.10"
+version = "0.4.12"
 source = "registry+https://github.com/rust-lang/crates.io-index"
-checksum = "3944cf8cf766b40e2a1a333ee5e9b563f854d5fa49d6a8ca2764e97c6eddb214"
+checksum = "9155a582abd142abc056962c29e3ce5ff2ad5469f4246b537ed42c5deba857da"
 dependencies = [
  "typenum",
 ]
@@ -2575,9 +2699,9 @@ dependencies = [
 
 [[package]]
 name = "idna_adapter"
-version = "1.2.1"
+version = "1.2.2"
 source = "registry+https://github.com/rust-lang/crates.io-index"
-checksum = "3acae9609540aa318d1bc588455225fb2085b9ed0c4f6bd0d9d5bcd86f1a0344"
+checksum = "cb68373c0d6620ef8105e855e7745e18b0d00d3bdb07fb532e434244cdb9a714"
 dependencies = [
  "icu_normalizer",
  "icu_properties",
@@ -2591,7 +2715,6 @@ checksum = "bd070e393353796e801d209ad339e89596eb4c8d430d18ede6a1cced8fafbd99"
 dependencies = [
  "autocfg",
  "hashbrown 0.12.3",
- "rayon",
  "serde",
 ]
 
@@ -2602,7 +2725,8 @@ source = "registry+https://github.com/rust-lang/crates.io-index"
 checksum = "d466e9454f08e4a911e14806c24e16fba1b4c121d1ea474396f396069cf949d9"
 dependencies = [
  "equivalent",
- "hashbrown 0.17.0",
+ "hashbrown 0.17.1",
+ "rayon",
  "serde",
  "serde_core",
 ]
@@ -2616,7 +2740,7 @@ dependencies = [
  "console",
  "portable-atomic",
  "rayon",
- "unicode-width",
+ "unicode-width 0.2.2",
  "unit-prefix",
  "web-time",
 ]
@@ -2681,25 +2805,15 @@ version = "2.12.0"
 source = "registry+https://github.com/rust-lang/crates.io-index"
 checksum = "d98f6fed1fde3f8c21bc40a1abb88dd75e67924f9cffc3ef95607bad8017f8e2"
 
-[[package]]
-name = "iri-string"
-version = "0.7.12"
-source = "registry+https://github.com/rust-lang/crates.io-index"
-checksum = "25e659a4bb38e810ebc252e53b5814ff908a8c58c2a9ce2fae1bbec24cbf4e20"
-dependencies = [
- "memchr",
- "serde",
-]
-
 [[package]]
 name = "is-terminal"
 version = "0.4.17"
 source = "registry+https://github.com/rust-lang/crates.io-index"
 checksum = "3640c1c38b8e4e43584d8df18be5fc6b0aa314ce6ebf51b53313d4306cca8e46"
 dependencies = [
- "hermit-abi",
+ "hermit-abi 0.5.2",
  "libc",
- "windows-sys 0.52.0",
+ "windows-sys 0.61.2",
 ]
 
 [[package]]
@@ -2743,9 +2857,9 @@ checksum = "8f42a60cbdf9a97f5d2305f08a87dc4e09308d1276d28c869c684d7777685682"
 
 [[package]]
 name = "jiff"
-version = "0.2.23"
+version = "0.2.24"
 source = "registry+https://github.com/rust-lang/crates.io-index"
-checksum = "1a3546dc96b6d42c5f24902af9e2538e82e39ad350b0c766eb3fbf2d8f3d8359"
+checksum = "f00b5dbd620d61dfdcb6007c9c1f6054ebd75319f163d886a9055cec1155073d"
 dependencies = [
  "jiff-static",
  "log",
@@ -2756,9 +2870,9 @@ dependencies = [
 
 [[package]]
 name = "jiff-static"
-version = "0.2.23"
+version = "0.2.24"
 source = "registry+https://github.com/rust-lang/crates.io-index"
-checksum = "2a8c8b344124222efd714b73bb41f8b5120b27a7cc1c75593a6ff768d9d05aa4"
+checksum = "e000de030ff8022ea1da3f466fbb0f3a809f5e51ed31f6dd931c35181ad8e6d7"
 dependencies = [
  "proc-macro2",
  "quote",
@@ -2767,18 +2881,32 @@ dependencies = [
 
 [[package]]
 name = "jni"
-version = "0.21.1"
+version = "0.22.4"
 source = "registry+https://github.com/rust-lang/crates.io-index"
-checksum = "1a87aa2bb7d2af34197c04845522473242e1aa17c12f4935d5856491a7fb8c97"
+checksum = "5efd9a482cf3a427f00d6b35f14332adc7902ce91efb778580e180ff90fa3498"
 dependencies = [
- "cesu8",
  "cfg-if",
  "combine",
- "jni-sys 0.3.1",
+ "jni-macros",
+ "jni-sys 0.4.1",
  "log",
- "thiserror 1.0.69",
+ "simd_cesu8",
+ "thiserror 2.0.18",
  "walkdir",
- "windows-sys 0.45.0",
+ "windows-link",
+]
+
+[[package]]
+name = "jni-macros"
+version = "0.22.4"
+source = "registry+https://github.com/rust-lang/crates.io-index"
+checksum = "a00109accc170f0bdb141fed3e393c565b6f5e072365c3bd58f5b062591560a3"
+dependencies = [
+ "proc-macro2",
+ "quote",
+ "rustc_version",
+ "simd_cesu8",
+ "syn 2.0.117",
 ]
 
 [[package]]
@@ -2821,9 +2949,9 @@ dependencies = [
 
 [[package]]
 name = "js-sys"
-version = "0.3.95"
+version = "0.3.98"
 source = "registry+https://github.com/rust-lang/crates.io-index"
-checksum = "2964e92d1d9dc3364cae4d718d93f227e3abb088e747d92e0395bfdedf1c12ca"
+checksum = "67df7112613f8bfd9150013a0314e196f4800d3201ae742489d999db2f979f08"
 dependencies = [
  "cfg-if",
  "futures-util",
@@ -2911,9 +3039,9 @@ checksum = "b3a6a8c165077efc8f3a971534c50ea6a1a18b329ef4a66e897a7e3a1494565f"
 
 [[package]]
 name = "libc"
-version = "0.2.185"
+version = "0.2.186"
 source = "registry+https://github.com/rust-lang/crates.io-index"
-checksum = "52ff2c0fe9bc6cb6b14a0592c2ff4fa9ceb83eea9db979b0487cd054946a2b8f"
+checksum = "68ab91017fe16c622486840e4c83c9a37afeff978bd239b5293d61ece587de66"
 
 [[package]]
 name = "libloading"
@@ -2947,10 +3075,7 @@ version = "0.1.16"
 source = "registry+https://github.com/rust-lang/crates.io-index"
 checksum = "e02f3bb43d335493c96bf3fd3a321600bf6bd07ed34bc64118e9293bdffea46c"
 dependencies = [
- "bitflags",
  "libc",
- "plain",
- "redox_syscall 0.7.4",
 ]
 
 [[package]]
@@ -2993,6 +3118,12 @@ dependencies = [
  "semver",
 ]
 
+[[package]]
+name = "lnexp"
+version = "0.2.1"
+source = "registry+https://github.com/rust-lang/crates.io-index"
+checksum = "f98924c778103b33dcf6beb1af911977e5d65c6cae74b45e133b3c90bd6db948"
+
 [[package]]
 name = "lock_api"
 version = "0.4.14"
@@ -3066,6 +3197,12 @@ dependencies = [
  "libc",
 ]
 
+[[package]]
+name = "maplit"
+version = "1.0.2"
+source = "registry+https://github.com/rust-lang/crates.io-index"
+checksum = "3e2e65a1a2e43cfcb47a895c4c8b10d1f4a61097f9f254f183aee60cad9c651d"
+
 [[package]]
 name = "matrixmultiply"
 version = "0.3.10"
@@ -3091,6 +3228,12 @@ dependencies = [
  "rustix",
 ]
 
+[[package]]
+name = "min_max_macros"
+version = "0.1.1"
+source = "registry+https://github.com/rust-lang/crates.io-index"
+checksum = "131a74fe105e2662ce9646e3a3af4c0eeb19bc0e5936852bf81341bfc415b9f2"
+
 [[package]]
 name = "minimal-lexical"
 version = "0.2.1"
@@ -3118,15 +3261,63 @@ dependencies = [
  "windows-sys 0.61.2",
 ]
 
+[[package]]
+name = "more-asserts"
+version = "0.3.1"
+source = "registry+https://github.com/rust-lang/crates.io-index"
+checksum = "1fafa6961cabd9c63bcd77a45d7e3b7f3b552b70417831fb0f56db717e72407e"
+
+[[package]]
+name = "mwpf"
+version = "0.2.12"
+source = "git+https://github.com/yuewuo/mwpf?tag=v0.2.12#b8444428f999457208c4b0956f3f1c745a0ec2d5"
+dependencies = [
+ "base64",
+ "bp",
+ "cfg-if",
+ "chrono",
+ "ciborium",
+ "clap 4.6.1",
+ "derivative",
+ "flate2",
+ "getrandom 0.2.17",
+ "hashbrown 0.15.5",
+ "heapz",
+ "highs",
+ "itertools 0.14.0",
+ "lazy_static",
+ "lnexp",
+ "maplit",
+ "more-asserts",
+ "num-bigint",
+ "num-rational",
+ "num-traits",
+ "parking_lot",
+ "pheap",
+ "prettytable-rs",
+ "priority-queue 2.7.0",
+ "rand 0.8.6",
+ "rand_xoshiro 0.6.0",
+ "serde",
+ "serde-wasm-bindgen",
+ "serde_json",
+ "serde_variant",
+ "slp",
+ "sugar",
+ "tempfile",
+ "thread-priority",
+ "urlencoding",
+]
+
 [[package]]
 name = "naga"
-version = "29.0.1"
+version = "29.0.3"
 source = "registry+https://github.com/rust-lang/crates.io-index"
-checksum = "aa2630921705b9b01dcdd0b6864b9562ca3c1951eecd0f0c4f5f04f61e412647"
+checksum = "0dd91265cc2454558f659b3b4b9640f0ddb8cc6521277f166b8a8c181c898079"
 dependencies = [
  "arrayvec 0.7.6",
  "bit-set 0.9.1",
- "bitflags",
+ "bitflags 2.11.1",
  "cfg-if",
  "cfg_aliases",
  "codespan-reporting",
@@ -3361,6 +3552,7 @@ dependencies = [
  "num-bigint",
  "num-integer",
  "num-traits",
+ "serde",
 ]
 
 [[package]]
@@ -3379,7 +3571,7 @@ version = "1.17.0"
 source = "registry+https://github.com/rust-lang/crates.io-index"
 checksum = "91df4bbde75afed763b708b7eee1e8e7651e02d97f6d5dd763e89367e957b23b"
 dependencies = [
- "hermit-abi",
+ "hermit-abi 0.5.2",
  "libc",
 ]
 
@@ -3398,7 +3590,7 @@ version = "0.3.2"
 source = "registry+https://github.com/rust-lang/crates.io-index"
 checksum = "2a180dd8642fa45cdb7dd721cd4c11b1cadd4929ce112ebd8b9f5803cc79d536"
 dependencies = [
- "bitflags",
+ "bitflags 2.11.1",
  "dispatch2",
  "objc2",
 ]
@@ -3415,7 +3607,7 @@ version = "0.3.2"
 source = "registry+https://github.com/rust-lang/crates.io-index"
 checksum = "e3e0adef53c21f888deb4fa59fc59f7eb17404926ee8a6f59f5df0fd7f9f3272"
 dependencies = [
- "bitflags",
+ "bitflags 2.11.1",
  "objc2",
  "objc2-core-foundation",
 ]
@@ -3426,7 +3618,7 @@ version = "0.3.2"
 source = "registry+https://github.com/rust-lang/crates.io-index"
 checksum = "a0125f776a10d00af4152d74616409f0d4a2053a6f57fa5b7d6aa2854ac04794"
 dependencies = [
- "bitflags",
+ "bitflags 2.11.1",
  "block2",
  "objc2",
  "objc2-foundation",
@@ -3438,7 +3630,7 @@ version = "0.3.2"
 source = "registry+https://github.com/rust-lang/crates.io-index"
 checksum = "96c1358452b371bf9f104e21ec536d37a650eb10f7ee379fff67d2e08d537f1f"
 dependencies = [
- "bitflags",
+ "bitflags 2.11.1",
  "objc2",
  "objc2-core-foundation",
  "objc2-foundation",
@@ -3447,12 +3639,12 @@ dependencies = [
 
 [[package]]
 name = "object"
-version = "0.38.1"
+version = "0.39.1"
 source = "registry+https://github.com/rust-lang/crates.io-index"
-checksum = "271638cd5fa9cca89c4c304675ca658efc4e64a66c716b7cfe1afb4b9611dbbc"
+checksum = "2e5a6c098c7a3b6547378093f5cc30bc54fd361ce711e05293a5cc589562739b"
 dependencies = [
  "crc32fast",
- "hashbrown 0.16.1",
+ "hashbrown 0.17.1",
  "indexmap 2.14.0",
  "memchr",
 ]
@@ -3565,7 +3757,7 @@ checksum = "2621685985a2ebf1c516881c026032ac7deafcda1a2c9b7850dc81e3dfcb64c1"
 dependencies = [
  "cfg-if",
  "libc",
- "redox_syscall 0.5.18",
+ "redox_syscall",
  "smallvec",
  "windows-link",
 ]
@@ -3578,9 +3770,9 @@ checksum = "57c0d7b74b563b49d38dae00a0c37d4d6de9b432382b2892f0574ddcae73fd0a"
 
 [[package]]
 name = "pastey"
-version = "0.2.1"
+version = "0.2.2"
 source = "registry+https://github.com/rust-lang/crates.io-index"
-checksum = "b867cad97c0791bbd3aaa6472142568c6c9e8f71937e98379f584cfb0cf35bec"
+checksum = "c5a797f0e07bdf071d15742978fc3128ec6c22891c31a3a931513263904c982a"
 
 [[package]]
 name = "pbr"
@@ -3653,6 +3845,7 @@ dependencies = [
  "ndarray 0.17.2",
  "pecos-build",
  "pecos-decoder-core",
+ "pecos-pymatching",
  "thiserror 2.0.18",
 ]
 
@@ -3661,7 +3854,7 @@ name = "pecos-cli"
 version = "0.2.0-dev.0"
 dependencies = [
  "assert_cmd",
- "clap",
+ "clap 4.6.1",
  "clap_complete",
  "env_logger",
  "log",
@@ -3735,6 +3928,8 @@ version = "0.2.0-dev.0"
 dependencies = [
  "anyhow",
  "ndarray 0.17.2",
+ "pecos-random",
+ "rayon",
  "thiserror 2.0.18",
 ]
 
@@ -3746,16 +3941,33 @@ dependencies = [
  "pecos-decoder-core",
  "pecos-fusion-blossom",
  "pecos-ldpc-decoders",
+ "pecos-mwpf",
  "pecos-pymatching",
  "pecos-relay-bp",
  "pecos-tesseract",
+ "pecos-uf-decoder",
+]
+
+[[package]]
+name = "pecos-eeg"
+version = "0.2.0-dev.0"
+dependencies = [
+ "pecos-core",
+ "pecos-qec",
+ "pecos-quantum",
+ "pecos-random",
+ "pecos-simulators",
+ "rayon",
+ "serde_json",
+ "smallvec",
+ "thiserror 2.0.18",
 ]
 
 [[package]]
 name = "pecos-engines"
 version = "0.2.0-dev.0"
 dependencies = [
- "bitflags",
+ "bitflags 2.11.1",
  "bitvec",
  "bytemuck",
  "dyn-clone",
@@ -3779,7 +3991,7 @@ dependencies = [
  "pecos-random",
  "pecos-simulators",
  "rand 0.10.1",
- "wide 1.3.0",
+ "wide 1.4.0",
 ]
 
 [[package]]
@@ -3812,6 +4024,7 @@ dependencies = [
  "fusion-blossom",
  "ndarray 0.17.2",
  "pecos-decoder-core",
+ "serde_json",
  "thiserror 2.0.18",
 ]
 
@@ -3898,6 +4111,21 @@ dependencies = [
  "thiserror 2.0.18",
 ]
 
+[[package]]
+name = "pecos-lindblad"
+version = "0.2.0-dev.0"
+dependencies = [
+ "approx 0.5.1",
+ "num-complex 0.4.6",
+ "pecos-qec",
+ "pecos-quantum",
+ "proptest",
+ "rand 0.10.1",
+ "serde",
+ "serde_json",
+ "thiserror 2.0.18",
+]
+
 [[package]]
 name = "pecos-llvm"
 version = "0.2.0-dev.0"
@@ -3909,11 +4137,23 @@ dependencies = [
  "pecos-core",
 ]
 
+[[package]]
+name = "pecos-mwpf"
+version = "0.2.0-dev.0"
+dependencies = [
+ "mwpf",
+ "ndarray 0.17.2",
+ "pecos-decoder-core",
+ "serde_json",
+ "thiserror 2.0.18",
+]
+
 [[package]]
 name = "pecos-neo"
 version = "0.2.0-dev.0"
 dependencies = [
  "criterion",
+ "num-complex 0.4.6",
  "num_cpus",
  "pecos-core",
  "pecos-engines",
@@ -4035,15 +4275,17 @@ dependencies = [
  "ndarray 0.17.2",
  "pecos-core",
  "pecos-decoder-core",
+ "pecos-num",
  "pecos-quantum",
  "pecos-random",
  "pecos-simulators",
  "rand 0.10.1",
  "rand_core 0.10.1",
  "rayon",
+ "serde_json",
  "smallvec",
  "thiserror 2.0.18",
- "wide 1.3.0",
+ "wide 1.4.0",
 ]
 
 [[package]]
@@ -4099,7 +4341,9 @@ dependencies = [
  "num-complex 0.4.6",
  "pecos-core",
  "pecos-num",
+ "pecos-random",
  "pecos-simulators",
+ "serde_json",
  "smallvec",
  "tket",
 ]
@@ -4113,7 +4357,7 @@ dependencies = [
  "rand_xoshiro 0.8.0",
  "random_tester",
  "rapidhash",
- "wide 1.3.0",
+ "wide 1.4.0",
 ]
 
 [[package]]
@@ -4136,6 +4380,7 @@ dependencies = [
  "dirs",
  "libc",
  "log",
+ "nalgebra",
  "ndarray 0.17.2",
  "num-complex 0.4.6",
  "parking_lot",
@@ -4161,6 +4406,7 @@ dependencies = [
  "pecos-wasm",
  "pyo3",
  "rand 0.10.1",
+ "rayon",
  "serde_json",
  "tempfile",
 ]
@@ -4184,9 +4430,18 @@ version = "0.2.0-dev.0"
 dependencies = [
  "num-complex 0.4.6",
  "pecos-core",
+ "pecos-eeg",
+ "pecos-neo",
+ "pecos-qec",
+ "pecos-quantum",
+ "pecos-random",
  "pecos-simulators",
  "pecos-stab-tn",
  "pyo3",
+ "rayon",
+ "serde",
+ "serde_json",
+ "smallvec",
 ]
 
 [[package]]
@@ -4206,7 +4461,7 @@ name = "pecos-selene-core"
 version = "0.2.0-dev.0"
 dependencies = [
  "anyhow",
- "clap",
+ "clap 4.6.1",
  "pecos-core",
  "pecos-simulators",
  "selene-core 0.2.1",
@@ -4249,7 +4504,7 @@ name = "pecos-selene-stabilizer"
 version = "0.2.0-dev.0"
 dependencies = [
  "anyhow",
- "clap",
+ "clap 4.6.1",
  "pecos-core",
  "pecos-simulators",
  "selene-core 0.2.1",
@@ -4269,6 +4524,7 @@ dependencies = [
 name = "pecos-simulators"
 version = "0.2.0-dev.0"
 dependencies = [
+ "nalgebra",
  "num-complex 0.4.6",
  "paste",
  "pecos-core",
@@ -4277,7 +4533,7 @@ dependencies = [
  "rand 0.10.1",
  "rayon",
  "smallvec",
- "wide 1.3.0",
+ "wide 1.4.0",
 ]
 
 [[package]]
@@ -4311,6 +4567,16 @@ dependencies = [
  "thiserror 2.0.18",
 ]
 
+[[package]]
+name = "pecos-uf-decoder"
+version = "0.2.0-dev.0"
+dependencies = [
+ "fastrand",
+ "pecos-decoder-core",
+ "pecos-random",
+ "rayon",
+]
+
 [[package]]
 name = "pecos-wasm"
 version = "0.2.0-dev.0"
@@ -4405,6 +4671,14 @@ dependencies = [
  "serde",
 ]
 
+[[package]]
+name = "pheap"
+version = "0.3.0"
+source = "git+https://github.com/yuewuo/mwpf?tag=v0.2.12#b8444428f999457208c4b0956f3f1c745a0ec2d5"
+dependencies = [
+ "num-traits",
+]
+
 [[package]]
 name = "phf_shared"
 version = "0.11.3"
@@ -4426,12 +4700,6 @@ version = "0.3.33"
 source = "registry+https://github.com/rust-lang/crates.io-index"
 checksum = "19f132c84eca552bf34cab8ec81f1c1dcc229b811638f9d283dceabe58c5569e"
 
-[[package]]
-name = "plain"
-version = "0.2.3"
-source = "registry+https://github.com/rust-lang/crates.io-index"
-checksum = "b4596b6d070b27117e987119b4dac604f3c58cfb0b191112e24771b2faeac1a6"
-
 [[package]]
 name = "plotters"
 version = "0.3.7"
@@ -4580,7 +4848,7 @@ checksum = "0d22152487193190344590e4f30e219cf3fe140d9e7a3fdb683d82aa2c5f4156"
 dependencies = [
  "arrayvec 0.5.2",
  "typed-arena",
- "unicode-width",
+ "unicode-width 0.2.2",
 ]
 
 [[package]]
@@ -4593,6 +4861,20 @@ dependencies = [
  "syn 2.0.117",
 ]
 
+[[package]]
+name = "prettytable-rs"
+version = "0.10.0"
+source = "registry+https://github.com/rust-lang/crates.io-index"
+checksum = "eea25e07510aa6ab6547308ebe3c036016d162b8da920dbb079e3ba8acf3d95a"
+dependencies = [
+ "csv",
+ "encode_unicode",
+ "is-terminal",
+ "lazy_static",
+ "term",
+ "unicode-width 0.1.14",
+]
+
 [[package]]
 name = "priority-queue"
 version = "1.4.0"
@@ -4623,6 +4905,30 @@ dependencies = [
  "toml_edit",
 ]
 
+[[package]]
+name = "proc-macro-error"
+version = "1.0.4"
+source = "registry+https://github.com/rust-lang/crates.io-index"
+checksum = "da25490ff9892aab3fcf7c36f08cfb902dd3e71ca0f9f9517bea02a73a5ce38c"
+dependencies = [
+ "proc-macro-error-attr",
+ "proc-macro2",
+ "quote",
+ "syn 1.0.109",
+ "version_check",
+]
+
+[[package]]
+name = "proc-macro-error-attr"
+version = "1.0.4"
+source = "registry+https://github.com/rust-lang/crates.io-index"
+checksum = "a1be40180e52ecc98ad80b184934baf3d0d29f979574e439af5a55274b35f869"
+dependencies = [
+ "proc-macro2",
+ "quote",
+ "version_check",
+]
+
 [[package]]
 name = "proc-macro2"
 version = "1.0.106"
@@ -4647,9 +4953,9 @@ dependencies = [
 
 [[package]]
 name = "profiling"
-version = "1.0.17"
+version = "1.0.18"
 source = "registry+https://github.com/rust-lang/crates.io-index"
-checksum = "3eb8486b569e12e2c32ad3e204dbaba5e4b5b216e9367044f25f1dba42341773"
+checksum = "3d595e54a326bc53c1c197b32d295e14b169e3cfeaa8dc82b529f947fba6bcf5"
 
 [[package]]
 name = "proptest"
@@ -4659,7 +4965,7 @@ checksum = "4b45fcc2344c680f5025fe57779faef368840d0bd1f42f216291f0dc4ace4744"
 dependencies = [
  "bit-set 0.8.0",
  "bit-vec 0.8.0",
- "bitflags",
+ "bitflags 2.11.1",
  "num-traits",
  "rand 0.9.4",
  "rand_chacha 0.9.0",
@@ -4672,9 +4978,9 @@ dependencies = [
 
 [[package]]
 name = "pulley-interpreter"
-version = "43.0.2"
+version = "44.0.1"
 source = "registry+https://github.com/rust-lang/crates.io-index"
-checksum = "7ec12fe19a9588315a49fe5704502a9c02d6a198303314b0c7c86123b06d29e5"
+checksum = "b9326e3a0093d170582cf64ed9e4cf253b8aac155ec4a294ff62330450bbf094"
 dependencies = [
  "cranelift-bitset",
  "log",
@@ -4684,9 +4990,9 @@ dependencies = [
 
 [[package]]
 name = "pulley-macros"
-version = "43.0.2"
+version = "44.0.1"
 source = "registry+https://github.com/rust-lang/crates.io-index"
-checksum = "36f7d5ef31ebf1b46cd7e722ffef934e670d7e462f49aa01cde07b9b76dca580"
+checksum = "00c6433917e3789605b1f4cd2a589f637ff17212344e7fa5ba99544625ba52c7"
 dependencies = [
  "proc-macro2",
  "quote",
@@ -4844,7 +5150,7 @@ source = "registry+https://github.com/rust-lang/crates.io-index"
 checksum = "5d7aeb420f81a3c9e632e70cf19a36bfeec45e25a749230c1e99c95486946f9f"
 dependencies = [
  "approx 0.5.1",
- "clap",
+ "clap 4.6.1",
  "derive_more 1.0.0",
  "env_logger",
  "itertools 0.13.0",
@@ -5099,16 +5405,7 @@ version = "0.5.18"
 source = "registry+https://github.com/rust-lang/crates.io-index"
 checksum = "ed2bf2547551a7053d6fdfafda3f938979645c44812fbfcda098faae3f1a362d"
 dependencies = [
- "bitflags",
-]
-
-[[package]]
-name = "redox_syscall"
-version = "0.7.4"
-source = "registry+https://github.com/rust-lang/crates.io-index"
-checksum = "f450ad9c3b1da563fb6948a8e0fb0fb9269711c9c73d9ea1de5058c79c8d643a"
-dependencies = [
- "bitflags",
+ "bitflags 2.11.1",
 ]
 
 [[package]]
@@ -5161,7 +5458,7 @@ checksum = "de2c52737737f8609e94f975dee22854a2d5c125772d4b1cf292120f4d45c186"
 dependencies = [
  "allocator-api2",
  "bumpalo",
- "hashbrown 0.17.0",
+ "hashbrown 0.17.1",
  "log",
  "rustc-hash 2.1.2",
  "smallvec",
@@ -5253,9 +5550,9 @@ checksum = "19b30a45b0cd0bcca8037f3d0dc3421eaf95327a17cad11964fb8179b4fc4832"
 
 [[package]]
 name = "reqwest"
-version = "0.13.2"
+version = "0.13.3"
 source = "registry+https://github.com/rust-lang/crates.io-index"
-checksum = "ab3f43e3283ab1488b624b44b0e988d0acea0b3214e694730a055cb6b2efa801"
+checksum = "62e0021ea2c22aed41653bc7e1419abb2c97e038ff2c33d0e1309e49a97deec0"
 dependencies = [
  "base64",
  "bytes",
@@ -5308,7 +5605,7 @@ version = "0.12.1"
 source = "registry+https://github.com/rust-lang/crates.io-index"
 checksum = "4147b952f3f819eca0e99527022f7d6a8d05f111aeb0a62960c74eb283bec8fc"
 dependencies = [
- "bitflags",
+ "bitflags 2.11.1",
  "once_cell",
  "serde",
  "serde_derive",
@@ -5381,6 +5678,12 @@ dependencies = [
  "unicode-ident",
 ]
 
+[[package]]
+name = "rustc-demangle"
+version = "0.1.27"
+source = "registry+https://github.com/rust-lang/crates.io-index"
+checksum = "b50b8869d9fc858ce7266cce0194bd74df58b9d0e3f6df3a9fc8eb470d95c09d"
+
 [[package]]
 name = "rustc-hash"
 version = "1.1.0"
@@ -5408,18 +5711,18 @@ version = "1.1.4"
 source = "registry+https://github.com/rust-lang/crates.io-index"
 checksum = "b6fe4565b9518b83ef4f91bb47ce29620ca828bd32cb7e408f0062e9930ba190"
 dependencies = [
- "bitflags",
+ "bitflags 2.11.1",
  "errno",
  "libc",
  "linux-raw-sys",
- "windows-sys 0.52.0",
+ "windows-sys 0.61.2",
 ]
 
 [[package]]
 name = "rustls"
-version = "0.23.38"
+version = "0.23.40"
 source = "registry+https://github.com/rust-lang/crates.io-index"
-checksum = "69f9466fb2c14ea04357e91413efb882e2a6d4a406e625449bc0a5d360d53a21"
+checksum = "ef86cd5876211988985292b91c96a8f2d298df24e75989a43a3c73f2d4d8168b"
 dependencies = [
  "aws-lc-rs",
  "once_cell",
@@ -5443,9 +5746,9 @@ dependencies = [
 
 [[package]]
 name = "rustls-pki-types"
-version = "1.14.0"
+version = "1.14.1"
 source = "registry+https://github.com/rust-lang/crates.io-index"
-checksum = "be040f8b0a225e40375822a563fa9524378b9d63112f53e19ffff34df5d33fdd"
+checksum = "30a7197ae7eb376e574fe940d068c30fe0462554a3ddbe4eca7838e049c937a9"
 dependencies = [
  "web-time",
  "zeroize",
@@ -5453,9 +5756,9 @@ dependencies = [
 
 [[package]]
 name = "rustls-platform-verifier"
-version = "0.6.2"
+version = "0.7.0"
 source = "registry+https://github.com/rust-lang/crates.io-index"
-checksum = "1d99feebc72bae7ab76ba994bb5e121b8d83d910ca40b36e0921f53becc41784"
+checksum = "26d1e2536ce4f35f4846aa13bff16bd0ff40157cdb14cc056c7b14ba41233ba0"
 dependencies = [
  "core-foundation",
  "core-foundation-sys",
@@ -5469,7 +5772,7 @@ dependencies = [
  "security-framework",
  "security-framework-sys",
  "webpki-root-certs",
- "windows-sys 0.52.0",
+ "windows-sys 0.61.2",
 ]
 
 [[package]]
@@ -5504,8 +5807,8 @@ checksum = "aaeee6f84153fd6f62507fc22bfe9499c8485075b44186dcbb918166ef75116f"
 dependencies = [
  "fixedbitset 0.5.7",
  "foldhash 0.1.5",
- "hashbrown 0.14.5",
- "indexmap 1.9.3",
+ "hashbrown 0.15.5",
+ "indexmap 2.14.0",
  "ndarray 0.16.1",
  "num-traits",
  "petgraph 0.8.3",
@@ -5626,7 +5929,7 @@ version = "3.7.0"
 source = "registry+https://github.com/rust-lang/crates.io-index"
 checksum = "b7f4bc775c73d9a02cde8bf7b2ec4c9d12743edf609006c7facc23998404cd1d"
 dependencies = [
- "bitflags",
+ "bitflags 2.11.1",
  "core-foundation",
  "core-foundation-sys",
  "libc",
@@ -5707,6 +6010,17 @@ dependencies = [
  "serde_derive",
 ]
 
+[[package]]
+name = "serde-wasm-bindgen"
+version = "0.6.5"
+source = "registry+https://github.com/rust-lang/crates.io-index"
+checksum = "8302e169f0eddcc139c70f139d19d6467353af16f9fce27e8c30158036a1e16b"
+dependencies = [
+ "js-sys",
+ "serde",
+ "wasm-bindgen",
+]
+
 [[package]]
 name = "serde_core"
 version = "1.0.228"
@@ -5760,13 +6074,23 @@ dependencies = [
  "serde_core",
 ]
 
+[[package]]
+name = "serde_variant"
+version = "0.1.3"
+source = "registry+https://github.com/rust-lang/crates.io-index"
+checksum = "0a0068df419f9d9b6488fdded3f1c818522cdea328e02ce9d9f147380265a432"
+dependencies = [
+ "serde",
+]
+
 [[package]]
 name = "serde_with"
-version = "3.18.0"
+version = "3.20.0"
 source = "registry+https://github.com/rust-lang/crates.io-index"
-checksum = "dd5414fad8e6907dbdd5bc441a50ae8d6e26151a03b1de04d89a5576de61d01f"
+checksum = "e72c1c2cb7b223fafb600a619537a871c2818583d619401b785e7c0b746ccde2"
 dependencies = [
  "base64",
+ "bs58",
  "chrono",
  "hex",
  "indexmap 1.9.3",
@@ -5781,9 +6105,9 @@ dependencies = [
 
 [[package]]
 name = "serde_with_macros"
-version = "3.18.0"
+version = "3.20.0"
 source = "registry+https://github.com/rust-lang/crates.io-index"
-checksum = "d3db8978e608f1fe7357e211969fd9abdcae80bac1ba7a3369bb7eb6b404eb65"
+checksum = "b90c488738ecb4fb0262f41f43bc40efc5868d9fb744319ddf5f5317f417bfac"
 dependencies = [
  "darling",
  "proc-macro2",
@@ -5827,7 +6151,7 @@ checksum = "446ba717509524cb3f22f17ecc096f10f4822d76ab5c0b9822c5f9c284e825f4"
 dependencies = [
  "cfg-if",
  "cpufeatures 0.3.0",
- "digest 0.11.2",
+ "digest 0.11.3",
 ]
 
 [[package]]
@@ -5855,6 +6179,22 @@ version = "0.3.9"
 source = "registry+https://github.com/rust-lang/crates.io-index"
 checksum = "703d5c7ef118737c72f1af64ad2f6f8c5e1921f818cdcb97b8fe6fc69bf66214"
 
+[[package]]
+name = "simd_cesu8"
+version = "1.1.1"
+source = "registry+https://github.com/rust-lang/crates.io-index"
+checksum = "94f90157bb87cddf702797c5dadfa0be7d266cdf49e22da2fcaa32eff75b2c33"
+dependencies = [
+ "rustc_version",
+ "simdutf8",
+]
+
+[[package]]
+name = "simdutf8"
+version = "0.1.5"
+source = "registry+https://github.com/rust-lang/crates.io-index"
+checksum = "e3a9fe34e3e7a50316060351f37187a3f546bce95496156754b601a5fa71b76e"
+
 [[package]]
 name = "similar"
 version = "2.7.0"
@@ -5863,9 +6203,9 @@ checksum = "bbbb5d9659141646ae647b42fe094daf6c6192d1620870b449d9557f748b2daa"
 
 [[package]]
 name = "siphasher"
-version = "1.0.2"
+version = "1.0.3"
 source = "registry+https://github.com/rust-lang/crates.io-index"
-checksum = "b2aa850e253778c88a04c3d7323b043aeda9d3e30d5971937c1855769763678e"
+checksum = "8ee5873ec9cce0195efcb7a4e9507a04cd49aec9c83d0389df45b1ef7ba2e649"
 
 [[package]]
 name = "slab"
@@ -5892,6 +6232,20 @@ dependencies = [
  "version_check",
 ]
 
+[[package]]
+name = "slp"
+version = "0.2.0"
+source = "git+https://github.com/yuewuo/mwpf?tag=v0.2.12#b8444428f999457208c4b0956f3f1c745a0ec2d5"
+dependencies = [
+ "num-bigint",
+ "num-rational",
+ "num-traits",
+ "pest",
+ "pest_derive",
+ "rayon",
+ "structopt",
+]
+
 [[package]]
 name = "smallvec"
 version = "1.15.1"
@@ -5918,7 +6272,7 @@ source = "registry+https://github.com/rust-lang/crates.io-index"
 checksum = "3a766e1110788c36f4fa1c2b71b387a7815aa65f88ce0229841826633d93723e"
 dependencies = [
  "libc",
- "windows-sys 0.60.2",
+ "windows-sys 0.61.2",
 ]
 
 [[package]]
@@ -5927,7 +6281,7 @@ version = "0.4.0+sdk-1.4.341.0"
 source = "registry+https://github.com/rust-lang/crates.io-index"
 checksum = "d9571ea910ebd84c86af4b3ed27f9dbdc6ad06f17c5f96146b2b671e2976744f"
 dependencies = [
- "bitflags",
+ "bitflags 2.11.1",
 ]
 
 [[package]]
@@ -5970,12 +6324,42 @@ dependencies = [
  "precomputed-hash",
 ]
 
+[[package]]
+name = "strsim"
+version = "0.8.0"
+source = "registry+https://github.com/rust-lang/crates.io-index"
+checksum = "8ea5119cdb4c55b55d432abb513a0429384878c15dde60cc77b1c99de1a95a6a"
+
 [[package]]
 name = "strsim"
 version = "0.11.1"
 source = "registry+https://github.com/rust-lang/crates.io-index"
 checksum = "7da8b5736845d9f2fcb837ea5d9e2628564b3b043a70948a3f0b778838c5fb4f"
 
+[[package]]
+name = "structopt"
+version = "0.3.26"
+source = "registry+https://github.com/rust-lang/crates.io-index"
+checksum = "0c6b5c64445ba8094a6ab0c3cd2ad323e07171012d9c98b0b15651daf1787a10"
+dependencies = [
+ "clap 2.34.0",
+ "lazy_static",
+ "structopt-derive",
+]
+
+[[package]]
+name = "structopt-derive"
+version = "0.4.18"
+source = "registry+https://github.com/rust-lang/crates.io-index"
+checksum = "dcb5ae327f9cc13b68763b5749770cb9e048a99bd9dfdfa58d0cf05d5f64afe0"
+dependencies = [
+ "heck 0.3.3",
+ "proc-macro-error",
+ "proc-macro2",
+ "quote",
+ "syn 1.0.109",
+]
+
 [[package]]
 name = "strum"
 version = "0.25.0"
@@ -6043,6 +6427,18 @@ version = "2.6.1"
 source = "registry+https://github.com/rust-lang/crates.io-index"
 checksum = "13c2bddecc57b384dee18652358fb23172facb8a2c51ccc10d74c157bdea3292"
 
+[[package]]
+name = "sugar"
+version = "0.2.0"
+source = "registry+https://github.com/rust-lang/crates.io-index"
+checksum = "616a397f08825a805c27d9a18afcd17d953aee58c1637d078cc1791e1e3e22c1"
+dependencies = [
+ "cute",
+ "maplit",
+ "min_max_macros",
+ "vec_box",
+]
+
 [[package]]
 name = "syn"
 version = "1.0.109"
@@ -6118,7 +6514,7 @@ dependencies = [
  "getrandom 0.4.2",
  "once_cell",
  "rustix",
- "windows-sys 0.52.0",
+ "windows-sys 0.61.2",
 ]
 
 [[package]]
@@ -6147,6 +6543,15 @@ version = "0.5.1"
 source = "registry+https://github.com/rust-lang/crates.io-index"
 checksum = "8f50febec83f5ee1df3015341d8bd429f2d1cc62bcba7ea2076759d315084683"
 
+[[package]]
+name = "textwrap"
+version = "0.11.0"
+source = "registry+https://github.com/rust-lang/crates.io-index"
+checksum = "d326610f408c7a4eb6f51c37c330e496b08506c9457c9d34287ecc38809fb060"
+dependencies = [
+ "unicode-width 0.1.14",
+]
+
 [[package]]
 name = "thiserror"
 version = "1.0.69"
@@ -6187,6 +6592,20 @@ dependencies = [
  "syn 2.0.117",
 ]
 
+[[package]]
+name = "thread-priority"
+version = "1.2.0"
+source = "registry+https://github.com/rust-lang/crates.io-index"
+checksum = "cfe075d7053dae61ac5413a34ea7d4913b6e6207844fd726bdd858b37ff72bf5"
+dependencies = [
+ "bitflags 2.11.1",
+ "cfg-if",
+ "libc",
+ "log",
+ "rustversion",
+ "winapi",
+]
+
 [[package]]
 name = "time"
 version = "0.3.47"
@@ -6302,9 +6721,9 @@ dependencies = [
 
 [[package]]
 name = "tket-json-rs"
-version = "0.8.2"
+version = "0.8.3"
 source = "registry+https://github.com/rust-lang/crates.io-index"
-checksum = "f94cdded1cb82aaf9e0c2508762753f72c60ce8c068853b8ecc6c1bcd21644b9"
+checksum = "d411ed63c40c69f147fb2ecfae59bc9c8e15aee1f0d916fb07f37465a7a4b2e9"
 dependencies = [
  "derive_more 2.1.1",
  "serde",
@@ -6337,9 +6756,9 @@ dependencies = [
 
 [[package]]
 name = "tokio"
-version = "1.52.1"
+version = "1.52.3"
 source = "registry+https://github.com/rust-lang/crates.io-index"
-checksum = "b67dee974fe86fd92cc45b7a95fdd2f99a36a6d7b0d431a231178d3d670bbcc6"
+checksum = "8fc7f01b389ac15039e4dc9531aa973a135d7a4135281b12d7c1bc79fd57fffe"
 dependencies = [
  "bytes",
  "libc",
@@ -6427,20 +6846,20 @@ dependencies = [
 
 [[package]]
 name = "tower-http"
-version = "0.6.8"
+version = "0.6.10"
 source = "registry+https://github.com/rust-lang/crates.io-index"
-checksum = "d4e6559d53cc268e5031cd8429d05415bc4cb4aefc4aa5d6cc35fbf5b924a1f8"
+checksum = "68d6fdd9f81c2819c9a8b0e0cd91660e7746a8e6ea2ba7c6b2b057985f6bcb51"
 dependencies = [
- "bitflags",
+ "bitflags 2.11.1",
  "bytes",
  "futures-util",
  "http",
  "http-body",
- "iri-string",
  "pin-project-lite",
  "tower",
  "tower-layer",
  "tower-service",
+ "url",
 ]
 
 [[package]]
@@ -6506,9 +6925,9 @@ checksum = "bc7d623258602320d5c55d1bc22793b57daff0ec7efc270ea7d55ce1d5f5471c"
 
 [[package]]
 name = "typenum"
-version = "1.19.0"
+version = "1.20.0"
 source = "registry+https://github.com/rust-lang/crates.io-index"
-checksum = "562d481066bde0658276a35467c4af00bdc6ee726305698a55b86e61d7ad82bb"
+checksum = "40ce102ab67701b8526c123c1bab5cbe42d7040ccfd0f64af1a385808d2f43de"
 
 [[package]]
 name = "typetag"
@@ -6558,6 +6977,12 @@ version = "1.13.2"
 source = "registry+https://github.com/rust-lang/crates.io-index"
 checksum = "9629274872b2bfaf8d66f5f15725007f635594914870f65218920345aa11aa8c"
 
+[[package]]
+name = "unicode-width"
+version = "0.1.14"
+source = "registry+https://github.com/rust-lang/crates.io-index"
+checksum = "7dd6e30e90baa6f72411720665d41d89b9a3d039dc45b8faea1ddd07f617f6af"
+
 [[package]]
 name = "unicode-width"
 version = "0.2.2"
@@ -6620,9 +7045,9 @@ checksum = "06abde3611657adf66d383f00b093d7faecc7fa57071cce2578660c9f1010821"
 
 [[package]]
 name = "uuid"
-version = "1.22.0"
+version = "1.23.1"
 source = "registry+https://github.com/rust-lang/crates.io-index"
-checksum = "a68d3c8f01c0cfa54a75291d83601161799e4a89a39e0929f4b0354d88757a37"
+checksum = "ddd74a9687298c6858e9b88ec8935ec45d22e8fd5e6394fa1bd4e99a87789c76"
 dependencies = [
  "getrandom 0.4.2",
  "js-sys",
@@ -6630,6 +7055,18 @@ dependencies = [
  "wasm-bindgen",
 ]
 
+[[package]]
+name = "vec_box"
+version = "1.0.0"
+source = "registry+https://github.com/rust-lang/crates.io-index"
+checksum = "c5283fc94a1cd6b5199f707a4b4d7f885b9457d430d111c68a07d3e3d199fb2b"
+
+[[package]]
+name = "vec_map"
+version = "0.8.2"
+source = "registry+https://github.com/rust-lang/crates.io-index"
+checksum = "f1bddf1187be692e79c5ffeab891132dfb0f236ed36a43c7ed39f1165ee20191"
+
 [[package]]
 name = "version_check"
 version = "0.9.5"
@@ -6672,11 +7109,11 @@ checksum = "ccf3ec651a847eb01de73ccad15eb7d99f80485de043efb2f370cd654f4ea44b"
 
 [[package]]
 name = "wasip2"
-version = "1.0.2+wasi-0.2.9"
+version = "1.0.3+wasi-0.2.9"
 source = "registry+https://github.com/rust-lang/crates.io-index"
-checksum = "9517f9239f02c069db75e65f174b3da828fe5f5b945c4dd26bd25d89c03ebcf5"
+checksum = "20064672db26d7cdc89c7798c48a0fdfac8213434a1186e5ef29fd560ae223d6"
 dependencies = [
- "wit-bindgen",
+ "wit-bindgen 0.57.1",
 ]
 
 [[package]]
@@ -6685,14 +7122,14 @@ version = "0.4.0+wasi-0.3.0-rc-2026-01-06"
 source = "registry+https://github.com/rust-lang/crates.io-index"
 checksum = "5428f8bf88ea5ddc08faddef2ac4a67e390b88186c703ce6dbd955e1c145aca5"
 dependencies = [
- "wit-bindgen",
+ "wit-bindgen 0.51.0",
 ]
 
 [[package]]
 name = "wasm-bindgen"
-version = "0.2.118"
+version = "0.2.121"
 source = "registry+https://github.com/rust-lang/crates.io-index"
-checksum = "0bf938a0bacb0469e83c1e148908bd7d5a6010354cf4fb73279b7447422e3a89"
+checksum = "49ace1d07c165b0864824eee619580c4689389afa9dc9ed3a4c75040d82e6790"
 dependencies = [
  "cfg-if",
  "once_cell",
@@ -6703,9 +7140,9 @@ dependencies = [
 
 [[package]]
 name = "wasm-bindgen-futures"
-version = "0.4.68"
+version = "0.4.71"
 source = "registry+https://github.com/rust-lang/crates.io-index"
-checksum = "f371d383f2fb139252e0bfac3b81b265689bf45b6874af544ffa4c975ac1ebf8"
+checksum = "96492d0d3ffba25305a7dc88720d250b1401d7edca02cc3bcd50633b424673b8"
 dependencies = [
  "js-sys",
  "wasm-bindgen",
@@ -6713,9 +7150,9 @@ dependencies = [
 
 [[package]]
 name = "wasm-bindgen-macro"
-version = "0.2.118"
+version = "0.2.121"
 source = "registry+https://github.com/rust-lang/crates.io-index"
-checksum = "eeff24f84126c0ec2db7a449f0c2ec963c6a49efe0698c4242929da037ca28ed"
+checksum = "8e68e6f4afd367a562002c05637acb8578ff2dea1943df76afb9e83d177c8578"
 dependencies = [
  "quote",
  "wasm-bindgen-macro-support",
@@ -6723,9 +7160,9 @@ dependencies = [
 
 [[package]]
 name = "wasm-bindgen-macro-support"
-version = "0.2.118"
+version = "0.2.121"
 source = "registry+https://github.com/rust-lang/crates.io-index"
-checksum = "9d08065faf983b2b80a79fd87d8254c409281cf7de75fc4b773019824196c904"
+checksum = "d95a9ec35c64b2a7cb35d3fead40c4238d0940c86d107136999567a4703259f2"
 dependencies = [
  "bumpalo",
  "proc-macro2",
@@ -6736,9 +7173,9 @@ dependencies = [
 
 [[package]]
 name = "wasm-bindgen-shared"
-version = "0.2.118"
+version = "0.2.121"
 source = "registry+https://github.com/rust-lang/crates.io-index"
-checksum = "5fd04d9e306f1907bd13c6361b5c6bfc7b3b3c095ed3f8a9246390f8dbdee129"
+checksum = "c4e0100b01e9f0d03189a92b96772a1fb998639d981193d7dbab487302513441"
 dependencies = [
  "unicode-ident",
 ]
@@ -6755,22 +7192,22 @@ dependencies = [
 
 [[package]]
 name = "wasm-encoder"
-version = "0.245.1"
+version = "0.246.2"
 source = "registry+https://github.com/rust-lang/crates.io-index"
-checksum = "3f9dca005e69bf015e45577e415b9af8c67e8ee3c0e38b5b0add5aa92581ed5c"
+checksum = "61fb705ce81adde29d2a8e99d87995e39a6e927358c91398f374474746070ef7"
 dependencies = [
  "leb128fmt",
- "wasmparser 0.245.1",
+ "wasmparser 0.246.2",
 ]
 
 [[package]]
 name = "wasm-encoder"
-version = "0.246.2"
+version = "0.248.0"
 source = "registry+https://github.com/rust-lang/crates.io-index"
-checksum = "61fb705ce81adde29d2a8e99d87995e39a6e927358c91398f374474746070ef7"
+checksum = "ac92cf547bc18d27ecc521015c08c353b4f18b84ab388bb6d1b6b682c620d9b6"
 dependencies = [
  "leb128fmt",
- "wasmparser 0.246.2",
+ "wasmparser 0.248.0",
 ]
 
 [[package]]
@@ -6791,7 +7228,7 @@ version = "0.244.0"
 source = "registry+https://github.com/rust-lang/crates.io-index"
 checksum = "47b807c72e1bac69382b3a6fb3dbe8ea4c0ed87ff5629b8685ae6b9a611028fe"
 dependencies = [
- "bitflags",
+ "bitflags 2.11.1",
  "hashbrown 0.15.5",
  "indexmap 2.14.0",
  "semver",
@@ -6799,11 +7236,11 @@ dependencies = [
 
 [[package]]
 name = "wasmparser"
-version = "0.245.1"
+version = "0.246.2"
 source = "registry+https://github.com/rust-lang/crates.io-index"
-checksum = "4f08c9adee0428b7bddf3890fc27e015ac4b761cc608c822667102b8bfd6995e"
+checksum = "71cde4757396defafd25417cfb36aa3161027d06d865b0c24baaae229aac005d"
 dependencies = [
- "bitflags",
+ "bitflags 2.11.1",
  "hashbrown 0.16.1",
  "indexmap 2.14.0",
  "semver",
@@ -6812,35 +7249,35 @@ dependencies = [
 
 [[package]]
 name = "wasmparser"
-version = "0.246.2"
+version = "0.248.0"
 source = "registry+https://github.com/rust-lang/crates.io-index"
-checksum = "71cde4757396defafd25417cfb36aa3161027d06d865b0c24baaae229aac005d"
+checksum = "aa4439c5eee9df71ee0c6efb37f63b1fcb1fec38f85f5142c54e7ed05d33091a"
 dependencies = [
- "bitflags",
+ "bitflags 2.11.1",
  "indexmap 2.14.0",
  "semver",
 ]
 
 [[package]]
 name = "wasmprinter"
-version = "0.245.1"
+version = "0.246.2"
 source = "registry+https://github.com/rust-lang/crates.io-index"
-checksum = "5f41517a3716fbb8ccf46daa9c1325f760fcbff5168e75c7392288e410b91ac8"
+checksum = "6e41f7493ba994b8a779430a4c25ff550fd5a40d291693af43a6ef48688f00e3"
 dependencies = [
  "anyhow",
  "termcolor",
- "wasmparser 0.245.1",
+ "wasmparser 0.246.2",
 ]
 
 [[package]]
 name = "wasmtime"
-version = "43.0.2"
+version = "44.0.1"
 source = "registry+https://github.com/rust-lang/crates.io-index"
-checksum = "efb1ed5899dde98357cfdcf647a4614498798719793898245b4b34e663addabf"
+checksum = "372db8bbad8ec962038101f75ab2c3ffcd18797d7d3ae877a58ab9873cd0c4bd"
 dependencies = [
  "addr2line",
  "async-trait",
- "bitflags",
+ "bitflags 2.11.1",
  "bumpalo",
  "cc",
  "cfg-if",
@@ -6857,7 +7294,7 @@ dependencies = [
  "serde_derive",
  "smallvec",
  "target-lexicon",
- "wasmparser 0.245.1",
+ "wasmparser 0.246.2",
  "wasmtime-environ",
  "wasmtime-internal-core",
  "wasmtime-internal-cranelift",
@@ -6872,11 +7309,12 @@ dependencies = [
 
 [[package]]
 name = "wasmtime-environ"
-version = "43.0.2"
+version = "44.0.1"
 source = "registry+https://github.com/rust-lang/crates.io-index"
-checksum = "4172382dcc785c31d0e862c6780a18f5dd437914d22c4691351f965ef751c821"
+checksum = "1e15aa0d1545e48d9b25ca604e9e27b4cd6d5886d30ac5787b57b3a2daf85b57"
 dependencies = [
  "anyhow",
+ "cpp_demangle",
  "cranelift-bforest",
  "cranelift-bitset",
  "cranelift-entity",
@@ -6886,22 +7324,23 @@ dependencies = [
  "log",
  "object",
  "postcard",
+ "rustc-demangle",
  "serde",
  "serde_derive",
  "sha2 0.10.9",
  "smallvec",
  "target-lexicon",
- "wasm-encoder 0.245.1",
- "wasmparser 0.245.1",
+ "wasm-encoder 0.246.2",
+ "wasmparser 0.246.2",
  "wasmprinter",
  "wasmtime-internal-core",
 ]
 
 [[package]]
 name = "wasmtime-internal-core"
-version = "43.0.2"
+version = "44.0.1"
 source = "registry+https://github.com/rust-lang/crates.io-index"
-checksum = "9a3820b174f477d2a7083209d1ad5353fcdb11eaea434b2137b8681029460dd3"
+checksum = "8f2c7fa6523647262bfb4095dbdf4087accefe525813e783f81a0c682f418ce4"
 dependencies = [
  "hashbrown 0.16.1",
  "libm",
@@ -6910,9 +7349,9 @@ dependencies = [
 
 [[package]]
 name = "wasmtime-internal-cranelift"
-version = "43.0.2"
+version = "44.0.1"
 source = "registry+https://github.com/rust-lang/crates.io-index"
-checksum = "d1679d205caf9766c6aa309d45bb3e7c634d7725e3164404df33824b9f7c4fb7"
+checksum = "98c032f422e39061dfc43f32190c0a3526b04161ec4867f362958f3fe9d1fe29"
 dependencies = [
  "cfg-if",
  "cranelift-codegen",
@@ -6928,7 +7367,7 @@ dependencies = [
  "smallvec",
  "target-lexicon",
  "thiserror 2.0.18",
- "wasmparser 0.245.1",
+ "wasmparser 0.246.2",
  "wasmtime-environ",
  "wasmtime-internal-core",
  "wasmtime-internal-unwinder",
@@ -6937,9 +7376,9 @@ dependencies = [
 
 [[package]]
 name = "wasmtime-internal-fiber"
-version = "43.0.2"
+version = "44.0.1"
 source = "registry+https://github.com/rust-lang/crates.io-index"
-checksum = "f1e505254058be5b0df458d670ee42d9eafe2349d04c1296e9dc01071dc20a85"
+checksum = "d8dd76d80adf450cc260ba58f23c28030401930b19149695b1d121f7d621e791"
 dependencies = [
  "cc",
  "cfg-if",
@@ -6952,9 +7391,9 @@ dependencies = [
 
 [[package]]
 name = "wasmtime-internal-jit-debug"
-version = "43.0.2"
+version = "44.0.1"
 source = "registry+https://github.com/rust-lang/crates.io-index"
-checksum = "1c2e05b345f1773e59c20e6ad7298fd6857cdea245023d88bb659c96d8f0ea72"
+checksum = "ab453cc600b28ee5d3f9495aa6d4cb2c81eda40903e9287296b548fba8b2391d"
 dependencies = [
  "cc",
  "wasmtime-internal-versioned-export-macros",
@@ -6962,9 +7401,9 @@ dependencies = [
 
 [[package]]
 name = "wasmtime-internal-jit-icache-coherence"
-version = "43.0.2"
+version = "44.0.1"
 source = "registry+https://github.com/rust-lang/crates.io-index"
-checksum = "b86701b234a4643e3f111869aa792b3a05a06e02d486ee9cb6c04dae16b52dab"
+checksum = "6a1859e920871515d324fb9757c3e448d6ed1512ca6ccdff14b6e016505d6ada"
 dependencies = [
  "cfg-if",
  "libc",
@@ -6974,9 +7413,9 @@ dependencies = [
 
 [[package]]
 name = "wasmtime-internal-unwinder"
-version = "43.0.2"
+version = "44.0.1"
 source = "registry+https://github.com/rust-lang/crates.io-index"
-checksum = "f63558d801beb83dde9b336eb4ae049019aee26627926edb32cd119d7e4c83cd"
+checksum = "f1dfe405bd6adb1386d935a30f16a236bd4ef0d3c383e7cbbab98d063c9d9b73"
 dependencies = [
  "cfg-if",
  "cranelift-codegen",
@@ -6987,9 +7426,9 @@ dependencies = [
 
 [[package]]
 name = "wasmtime-internal-versioned-export-macros"
-version = "43.0.2"
+version = "44.0.1"
 source = "registry+https://github.com/rust-lang/crates.io-index"
-checksum = "737c4d956fc3a848541a064afb683dd2771132a6b125be5baaf95c4379aa47df"
+checksum = "2a9b9165fc45d42c81edfe3e9cb458e58720594ad5db6553c4079ea041a4a581"
 dependencies = [
  "proc-macro2",
  "quote",
@@ -6998,22 +7437,22 @@ dependencies = [
 
 [[package]]
 name = "wast"
-version = "246.0.2"
+version = "248.0.0"
 source = "registry+https://github.com/rust-lang/crates.io-index"
-checksum = "fe3fe8e3bf88ad96d031b4181ddbd64634b17cb0d06dfc3de589ef43591a9a62"
+checksum = "acc54622ed5a5cddafcdf152043f9d4aed54d4a653d686b7dfe874809fca99d7"
 dependencies = [
  "bumpalo",
  "leb128fmt",
  "memchr",
- "unicode-width",
- "wasm-encoder 0.246.2",
+ "unicode-width 0.2.2",
+ "wasm-encoder 0.248.0",
 ]
 
 [[package]]
 name = "wat"
-version = "1.246.2"
+version = "1.248.0"
 source = "registry+https://github.com/rust-lang/crates.io-index"
-checksum = "4bd7fda1199b94fff395c2d19a153f05dbe7807630316fa9673367666fd2ad8c"
+checksum = "d75cd9e510603909748e6ebab89f27cd04472c1d9d85a3c88a7a6fc51a1a7934"
 dependencies = [
  "wast",
 ]
@@ -7038,9 +7477,9 @@ checksum = "323f4da9523e9a669e1eaf9c6e763892769b1d38c623913647bfdc1532fe4549"
 
 [[package]]
 name = "web-sys"
-version = "0.3.95"
+version = "0.3.98"
 source = "registry+https://github.com/rust-lang/crates.io-index"
-checksum = "4f2dfbb17949fa2088e5d39408c48368947b86f7834484e87b73de55bc14d97d"
+checksum = "4b572dff8bcf38bad0fa19729c89bb5748b2b9b1d8be70cf90df697e3a8f32aa"
 dependencies = [
  "js-sys",
  "wasm-bindgen",
@@ -7067,12 +7506,12 @@ dependencies = [
 
 [[package]]
 name = "wgpu"
-version = "29.0.1"
+version = "29.0.3"
 source = "registry+https://github.com/rust-lang/crates.io-index"
-checksum = "72c239a9a747bbd379590985bac952c2e53cb19873f7072b3370c6a6a8e06837"
+checksum = "bb3feacc458f7bee8bc1737149b42b6c731aa461039a4264a67bb6681646b250"
 dependencies = [
  "arrayvec 0.7.6",
- "bitflags",
+ "bitflags 2.11.1",
  "bytemuck",
  "cfg-if",
  "cfg_aliases",
@@ -7097,14 +7536,14 @@ dependencies = [
 
 [[package]]
 name = "wgpu-core"
-version = "29.0.1"
+version = "29.0.3"
 source = "registry+https://github.com/rust-lang/crates.io-index"
-checksum = "1e80ac6cf1895df6342f87d975162108f9d98772a0d74bc404ab7304ac29469e"
+checksum = "02da3ad1b568337f25513b317870960ef87073ea0945502e44b864b67a8c77b7"
 dependencies = [
  "arrayvec 0.7.6",
  "bit-set 0.9.1",
  "bit-vec 0.9.1",
- "bitflags",
+ "bitflags 2.11.1",
  "bytemuck",
  "cfg_aliases",
  "document-features",
@@ -7130,42 +7569,42 @@ dependencies = [
 
 [[package]]
 name = "wgpu-core-deps-apple"
-version = "29.0.0"
+version = "29.0.3"
 source = "registry+https://github.com/rust-lang/crates.io-index"
-checksum = "43acd053312501689cd92a01a9638d37f3e41a5fd9534875efa8917ee2d11ac0"
+checksum = "62e51b5447e144b3dbba4feb01f80f4fa21696fa0cd99afb2c3df1affd6fdb28"
 dependencies = [
  "wgpu-hal",
 ]
 
 [[package]]
 name = "wgpu-core-deps-emscripten"
-version = "29.0.0"
+version = "29.0.3"
 source = "registry+https://github.com/rust-lang/crates.io-index"
-checksum = "ef043bf135cc68b6f667c55ff4e345ce2b5924d75bad36a47921b0287ca4b24a"
+checksum = "3487cd6293a963bc5c0c0396f6a2192043c50003c07f4efdccbad3d90ec9d819"
 dependencies = [
  "wgpu-hal",
 ]
 
 [[package]]
 name = "wgpu-core-deps-windows-linux-android"
-version = "29.0.0"
+version = "29.0.3"
 source = "registry+https://github.com/rust-lang/crates.io-index"
-checksum = "725d5c006a8c02967b6d93ef04f6537ec4593313e330cfe86d9d3f946eb90f28"
+checksum = "1bfb01076d0aa08b0ba9bd741e178b5cc440f5abe99d9581323a4c8b5d1a1916"
 dependencies = [
  "wgpu-hal",
 ]
 
 [[package]]
 name = "wgpu-hal"
-version = "29.0.1"
+version = "29.0.3"
 source = "registry+https://github.com/rust-lang/crates.io-index"
-checksum = "89a47aef47636562f3937285af4c44b4b5b404b46577471411cc5313a921da7e"
+checksum = "31f8e1a9e7a8512f276f7c62e018c7fa8d60954303fed2e5750114332049193f"
 dependencies = [
  "android_system_properties",
  "arrayvec 0.7.6",
  "ash",
  "bit-set 0.9.1",
- "bitflags",
+ "bitflags 2.11.1",
  "block2",
  "bytemuck",
  "cfg-if",
@@ -7206,13 +7645,14 @@ dependencies = [
  "wgpu-types",
  "windows",
  "windows-core",
+ "windows-result",
 ]
 
 [[package]]
 name = "wgpu-naga-bridge"
-version = "29.0.1"
+version = "29.0.3"
 source = "registry+https://github.com/rust-lang/crates.io-index"
-checksum = "7b4684f4410da0cf95a4cb63bb5edaac022461dedb6adf0b64d0d9b5f6890d51"
+checksum = "59c654c483f058800972c3645e95388a7eca31bf9fe1933bc20e036588a0be02"
 dependencies = [
  "naga",
  "wgpu-types",
@@ -7220,11 +7660,11 @@ dependencies = [
 
 [[package]]
 name = "wgpu-types"
-version = "29.0.1"
+version = "29.0.3"
 source = "registry+https://github.com/rust-lang/crates.io-index"
-checksum = "ec2675540fb1a5cfa5ef122d3d5f390e2c75711a0b946410f2d6ac3a0f77d1f6"
+checksum = "a9bcc31518a0e9735aefebedb5f7a9ef3ed1c42549c9f4c882fa9060ceaac639"
 dependencies = [
- "bitflags",
+ "bitflags 2.11.1",
  "bytemuck",
  "js-sys",
  "log",
@@ -7244,9 +7684,9 @@ dependencies = [
 
 [[package]]
 name = "wide"
-version = "1.3.0"
+version = "1.4.0"
 source = "registry+https://github.com/rust-lang/crates.io-index"
-checksum = "c9479f84a757f819cfab37295955906479181395de83add28f74975fde083141"
+checksum = "9a7714cd0430a663154667c74da5d09325c2387695bee18b3f7f72825aa3693a"
 dependencies = [
  "bytemuck",
  "safe_arch 1.0.0",
@@ -7274,7 +7714,7 @@ version = "0.1.11"
 source = "registry+https://github.com/rust-lang/crates.io-index"
 checksum = "c2a7b1c03c876122aa43f3020e6c3c3ee5c05081c9a00739faf7503aeba10d22"
 dependencies = [
- "windows-sys 0.52.0",
+ "windows-sys 0.61.2",
 ]
 
 [[package]]
@@ -7384,15 +7824,6 @@ dependencies = [
  "windows-link",
 ]
 
-[[package]]
-name = "windows-sys"
-version = "0.45.0"
-source = "registry+https://github.com/rust-lang/crates.io-index"
-checksum = "75283be5efb2831d37ea142365f009c02ec203cd29a3ebecbc093d52315b66d0"
-dependencies = [
- "windows-targets 0.42.2",
-]
-
 [[package]]
 name = "windows-sys"
 version = "0.52.0"
@@ -7420,21 +7851,6 @@ dependencies = [
  "windows-link",
 ]
 
-[[package]]
-name = "windows-targets"
-version = "0.42.2"
-source = "registry+https://github.com/rust-lang/crates.io-index"
-checksum = "8e5180c00cd44c9b1c88adb3693291f1cd93605ded80c250a75d472756b4d071"
-dependencies = [
- "windows_aarch64_gnullvm 0.42.2",
- "windows_aarch64_msvc 0.42.2",
- "windows_i686_gnu 0.42.2",
- "windows_i686_msvc 0.42.2",
- "windows_x86_64_gnu 0.42.2",
- "windows_x86_64_gnullvm 0.42.2",
- "windows_x86_64_msvc 0.42.2",
-]
-
 [[package]]
 name = "windows-targets"
 version = "0.52.6"
@@ -7477,12 +7893,6 @@ dependencies = [
  "windows-link",
 ]
 
-[[package]]
-name = "windows_aarch64_gnullvm"
-version = "0.42.2"
-source = "registry+https://github.com/rust-lang/crates.io-index"
-checksum = "597a5118570b68bc08d8d59125332c54f1ba9d9adeedeef5b99b02ba2b0698f8"
-
 [[package]]
 name = "windows_aarch64_gnullvm"
 version = "0.52.6"
@@ -7495,12 +7905,6 @@ version = "0.53.1"
 source = "registry+https://github.com/rust-lang/crates.io-index"
 checksum = "a9d8416fa8b42f5c947f8482c43e7d89e73a173cead56d044f6a56104a6d1b53"
 
-[[package]]
-name = "windows_aarch64_msvc"
-version = "0.42.2"
-source = "registry+https://github.com/rust-lang/crates.io-index"
-checksum = "e08e8864a60f06ef0d0ff4ba04124db8b0fb3be5776a5cd47641e942e58c4d43"
-
 [[package]]
 name = "windows_aarch64_msvc"
 version = "0.52.6"
@@ -7513,12 +7917,6 @@ version = "0.53.1"
 source = "registry+https://github.com/rust-lang/crates.io-index"
 checksum = "b9d782e804c2f632e395708e99a94275910eb9100b2114651e04744e9b125006"
 
-[[package]]
-name = "windows_i686_gnu"
-version = "0.42.2"
-source = "registry+https://github.com/rust-lang/crates.io-index"
-checksum = "c61d927d8da41da96a81f029489353e68739737d3beca43145c8afec9a31a84f"
-
 [[package]]
 name = "windows_i686_gnu"
 version = "0.52.6"
@@ -7543,12 +7941,6 @@ version = "0.53.1"
 source = "registry+https://github.com/rust-lang/crates.io-index"
 checksum = "fa7359d10048f68ab8b09fa71c3daccfb0e9b559aed648a8f95469c27057180c"
 
-[[package]]
-name = "windows_i686_msvc"
-version = "0.42.2"
-source = "registry+https://github.com/rust-lang/crates.io-index"
-checksum = "44d840b6ec649f480a41c8d80f9c65108b92d89345dd94027bfe06ac444d1060"
-
 [[package]]
 name = "windows_i686_msvc"
 version = "0.52.6"
@@ -7561,12 +7953,6 @@ version = "0.53.1"
 source = "registry+https://github.com/rust-lang/crates.io-index"
 checksum = "1e7ac75179f18232fe9c285163565a57ef8d3c89254a30685b57d83a38d326c2"
 
-[[package]]
-name = "windows_x86_64_gnu"
-version = "0.42.2"
-source = "registry+https://github.com/rust-lang/crates.io-index"
-checksum = "8de912b8b8feb55c064867cf047dda097f92d51efad5b491dfb98f6bbb70cb36"
-
 [[package]]
 name = "windows_x86_64_gnu"
 version = "0.52.6"
@@ -7579,12 +7965,6 @@ version = "0.53.1"
 source = "registry+https://github.com/rust-lang/crates.io-index"
 checksum = "9c3842cdd74a865a8066ab39c8a7a473c0778a3f29370b5fd6b4b9aa7df4a499"
 
-[[package]]
-name = "windows_x86_64_gnullvm"
-version = "0.42.2"
-source = "registry+https://github.com/rust-lang/crates.io-index"
-checksum = "26d41b46a36d453748aedef1486d5c7a85db22e56aff34643984ea85514e94a3"
-
 [[package]]
 name = "windows_x86_64_gnullvm"
 version = "0.52.6"
@@ -7597,12 +7977,6 @@ version = "0.53.1"
 source = "registry+https://github.com/rust-lang/crates.io-index"
 checksum = "0ffa179e2d07eee8ad8f57493436566c7cc30ac536a3379fdf008f47f6bb7ae1"
 
-[[package]]
-name = "windows_x86_64_msvc"
-version = "0.42.2"
-source = "registry+https://github.com/rust-lang/crates.io-index"
-checksum = "9aec5da331524158c6d1a4ac0ab1541149c0b9505fde06423b02f5ef0106b9f0"
-
 [[package]]
 name = "windows_x86_64_msvc"
 version = "0.52.6"
@@ -7617,9 +7991,9 @@ checksum = "d6bbff5f0aada427a1e5a6da5f1f98158182f26556f345ac9e04d36d0ebed650"
 
 [[package]]
 name = "winnow"
-version = "1.0.1"
+version = "1.0.2"
 source = "registry+https://github.com/rust-lang/crates.io-index"
-checksum = "09dac053f1cd375980747450bfc7250c264eaae0583872e845c0c7cd578872b5"
+checksum = "2ee1708bef14716a11bae175f579062d4554d95be2c6829f518df847b7b3fdd0"
 dependencies = [
  "memchr",
 ]
@@ -7633,6 +8007,12 @@ dependencies = [
  "wit-bindgen-rust-macro",
 ]
 
+[[package]]
+name = "wit-bindgen"
+version = "0.57.1"
+source = "registry+https://github.com/rust-lang/crates.io-index"
+checksum = "1ebf944e87a7c253233ad6766e082e3cd714b5d03812acc24c318f549614536e"
+
 [[package]]
 name = "wit-bindgen-core"
 version = "0.51.0"
@@ -7682,7 +8062,7 @@ source = "registry+https://github.com/rust-lang/crates.io-index"
 checksum = "9d66ea20e9553b30172b5e831994e35fbde2d165325bec84fc43dbf6f4eb9cb2"
 dependencies = [
  "anyhow",
- "bitflags",
+ "bitflags 2.11.1",
  "indexmap 2.14.0",
  "log",
  "serde",
diff --git a/Cargo.toml b/Cargo.toml
index ce3e865cd..5cdaae24b 100644
--- a/Cargo.toml
+++ b/Cargo.toml
@@ -70,7 +70,7 @@ tket-qsystem = { version = "0.23", default-features = false }
 hugr-core = "=0.25.6"
 
 # --- WebAssembly ---
-wasmtime = { version = "43", default-features = false, features = [
+wasmtime = { version = "44", default-features = false, features = [
   "cranelift",
   "runtime",
   "wat",
@@ -151,12 +151,16 @@ assert_cmd = "2"
 criterion = "0.8"
 paste = "1"
 random_tester = "0.1"
+proptest = "1"
 
 # --- ZX calculus ---
 quizx = "0.3"
 
 # --- Decoder libraries ---
 fusion-blossom = "0.2"
+mwpf = { git = "https://github.com/yuewuo/mwpf", tag = "v0.2.12", default-features = false, features = [
+  "f64_weight",
+] }
 relay-bp = "0.2"
 # ndarray 0.16 for relay-bp compat (relay-bp uses ndarray 0.16, PECOS uses 0.17)
 ndarray-016 = { package = "ndarray", version = "0.16" }
@@ -177,6 +181,8 @@ pecos-cuquantum-sys = { version = "0.2.0-dev.0", path = "crates/pecos-cuquantum-
 pecos-decoder-core = { version = "0.2.0-dev.0", path = "crates/pecos-decoder-core" }
 pecos-decoders = { version = "0.2.0-dev.0", path = "crates/pecos-decoders" }
 pecos-engines = { version = "0.2.0-dev.0", path = "crates/pecos-engines" }
+pecos-eeg = { version = "0.2.0-dev.0", path = "exp/pecos-eeg" }
+pecos-stab-tn = { version = "0.2.0-dev.0", path = "exp/pecos-stab-tn" }
 pecos-experimental = { version = "0.2.0-dev.0", path = "exp/pecos-experimental" }
 pecos-foreign = { version = "0.2.0-dev.0", path = "crates/pecos-foreign" }
 pecos-fusion-blossom = { version = "0.2.0-dev.0", path = "crates/pecos-fusion-blossom" }
@@ -184,7 +190,9 @@ pecos-gpu-sims = { version = "0.2.0-dev.0", path = "crates/pecos-gpu-sims" }
 pecos-hugr = { version = "0.2.0-dev.0", path = "crates/pecos-hugr" }
 pecos-hugr-qis = { version = "0.2.0-dev.0", path = "crates/pecos-hugr-qis" }
 pecos-ldpc-decoders = { version = "0.2.0-dev.0", path = "crates/pecos-ldpc-decoders" }
+pecos-lindblad = { version = "0.2.0-dev.0", path = "exp/pecos-lindblad" }
 pecos-llvm = { version = "0.2.0-dev.0", path = "crates/pecos-llvm" }
+pecos-mwpf = { version = "0.2.0-dev.0", path = "crates/pecos-mwpf" }
 pecos-neo = { version = "0.2.0-dev.0", path = "exp/pecos-neo" }
 pecos-num = { version = "0.2.0-dev.0", path = "crates/pecos-num" }
 pecos-phir = { version = "0.2.0-dev.0", path = "crates/pecos-phir" }
@@ -203,6 +211,7 @@ pecos-rslib = { version = "0.2.0-dev.0", path = "python/pecos-rslib" }
 pecos-rslib-llvm = { version = "0.2.0-dev.0", path = "python/pecos-rslib-llvm" }
 pecos-simulators = { version = "0.2.0-dev.0", path = "crates/pecos-simulators" }
 pecos-tesseract = { version = "0.2.0-dev.0", path = "crates/pecos-tesseract" }
+pecos-uf-decoder = { version = "0.2.0-dev.0", path = "crates/pecos-uf-decoder" }
 pecos-wasm = { version = "0.2.0-dev.0", path = "crates/pecos-wasm" }
 pecos-zx = { version = "0.2.0-dev.0", path = "exp/pecos-zx" }
 
@@ -220,6 +229,14 @@ lto = true        # Link-time optimization (same as "fat")
 codegen-units = 1 # Single codegen unit for better optimization
 strip = true      # Strip debug symbols for smaller binaries
 
+# Profiling profile: release optimizations but keeps debug info for perf/samply.
+# Use with: cargo build --profile profiling
+# Or: maturin develop --profile profiling
+[profile.profiling]
+inherits = "release"
+strip = false
+debug = 1            # line tables only — minimal size impact
+
 # Native profile: release + CPU-specific optimizations
 # Use with: cargo build --profile native
 # Build scripts detect this via PROFILE=native env var and add --march=native for C++ code
@@ -238,4 +255,4 @@ multiple-crate-versions = "allow"
 # Physics/math code uses short, domain-standard variable names (sx/sz, x/z/r/s/p)
 similar-names = "allow"
 many-single-char-names = "allow"
-too-many-lines = "allow"          # ~114 hits across 11 crates -- sim algorithms, tests, benchmarks
+too-many-lines = "allow"         # ~114 hits across 11 crates -- sim algorithms, tests, benchmarks
diff --git a/Justfile b/Justfile
index 7033955a0..c05a2600f 100644
--- a/Justfile
+++ b/Justfile
@@ -195,7 +195,7 @@ test mode="release": (rstest mode) pytest
 
 # Fix formatting and linting issues (or: just lint check)
 [group('lint')]
-lint mode="fix":
+lint mode="fix": python-workspace-check
     #!/usr/bin/env bash
     set -euo pipefail
     # Detect CUDA: only use --all-features when CUDA toolkit is available
@@ -245,6 +245,11 @@ lint mode="fix":
 check:
     cargo check --workspace --all-targets
 
+# Check Python workspace metadata
+[group('lint')]
+python-workspace-check:
+    @uv run python scripts/check_python_workspace.py
+
 # Run cargo clippy (CUDA-aware: uses --all-features only when CUDA is available)
 [group('lint')]
 clippy:
diff --git a/README.md b/README.md
index a1fa04841..d77865ba2 100644
--- a/README.md
+++ b/README.md
@@ -82,6 +82,7 @@ For OpenQASM, PHIR, or other formats, see the [documentation](#documentation). F
 For tutorials, API reference, and advanced features:
 
 - [Getting Started Guide](docs/user-guide/getting-started.md) — Installation, first simulation, next steps
+- [PECOS Concepts](docs/user-guide/pecos-concepts.md) — Detectors, observables, tracked operators, gates, and noise
 - [Simulators Guide](docs/user-guide/simulators.md) — Choosing the right backend
 - [Noise Model Builders](docs/user-guide/noise-model-builders.md) — Adding realistic noise
 - [Decoders Guide](docs/user-guide/decoders.md) — Quantum error correction decoding
diff --git a/crates/benchmarks/README.md b/crates/benchmarks/README.md
index 7424d17bc..52c525056 100644
--- a/crates/benchmarks/README.md
+++ b/crates/benchmarks/README.md
@@ -22,3 +22,26 @@ Alternatively, run manually with:
 ```bash
 RUSTFLAGS="-C target-cpu=native" cargo bench -p benchmarks
 ```
+
+## Fault Catalog Benchmarks
+
+The fault-catalog suite covers rotated surface-code memory circuits at
+distances 3, 5, 7, 9, and 11. It measures structural catalog construction,
+noise re-parameterization, raw-mechanism materialization, and noise-sweep
+strategies.
+
+```bash
+# Full fault-catalog suite
+just bench native "" "fault_catalog/"
+
+# Structural construction only
+just bench native "" "fault_catalog/from_circuit"
+
+# Compare direct rebuild, cloned parameterization, and mutable with_noise sweeps
+just bench native "" "fault_catalog/noise_sweep"
+```
+
+For parameter sweeps that do not need to keep independent catalog snapshots,
+prefer building one structural catalog and calling `with_noise()` for each
+noise point. Use `parameterized()` when the code needs independent catalogs
+alive at the same time.
diff --git a/crates/benchmarks/benches/benchmarks.rs b/crates/benchmarks/benches/benchmarks.rs
index d32dad430..d496fa89b 100644
--- a/crates/benchmarks/benches/benchmarks.rs
+++ b/crates/benchmarks/benches/benchmarks.rs
@@ -21,6 +21,7 @@ mod modules {
     pub mod dem_builder;
     pub mod dem_sampler;
     pub mod dod_statevec;
+    pub mod fault_catalog;
     pub mod quizx_eval;
     pub mod stab_vec;
     // TODO: pub mod hadamard_ops;
@@ -44,6 +45,7 @@ mod modules {
     pub mod stabilizer_sims;
     pub mod state_vec_sims;
     pub mod surface_code;
+    pub mod tick_circuit_layout;
     pub mod trig;
 }
 
@@ -57,9 +59,9 @@ use modules::sparse_stab_vs_cpp;
 use modules::stab_mps_vs_stab_vec;
 use modules::{
     allocation_overhead, cpu_stabilizer_comparison, dem_builder, dem_sampler, dod_statevec,
-    measurement_sampling, native_statevec_comparison, noise_models, pecos_neo_comparison,
-    quizx_eval, rng, set_ops, sparse_stab_w_vs_y, sparse_state_vec, stab_vec, stabilizer_sims,
-    state_vec_sims, surface_code, trig,
+    fault_catalog, measurement_sampling, native_statevec_comparison, noise_models,
+    pecos_neo_comparison, quizx_eval, rng, set_ops, sparse_stab_w_vs_y, sparse_state_vec, stab_vec,
+    stabilizer_sims, state_vec_sims, surface_code, tick_circuit_layout, trig,
 };
 
 fn all_benchmarks(c: &mut Criterion) {
@@ -72,6 +74,7 @@ fn all_benchmarks(c: &mut Criterion) {
     dem_builder::benchmarks(c);
     dem_sampler::benchmarks(c);
     dod_statevec::benchmarks(c);
+    fault_catalog::benchmarks(c);
     #[cfg(feature = "gpu-sims")]
     gpu_influence_sampler::benchmarks(c);
     measurement_sampling::benchmarks(c);
@@ -87,6 +90,7 @@ fn all_benchmarks(c: &mut Criterion) {
     sparse_stab_vs_cpp::benchmarks(c);
     sparse_stab_w_vs_y::benchmarks(c);
     surface_code::benchmarks(c);
+    tick_circuit_layout::benchmarks(c);
     #[cfg(feature = "stab-tn")]
     stab_mps_vs_stab_vec::benchmarks(c);
     trig::benchmarks(c);
diff --git a/crates/benchmarks/benches/modules/dem_sampler.rs b/crates/benchmarks/benches/modules/dem_sampler.rs
index b46a2feac..42353ae76 100644
--- a/crates/benchmarks/benches/modules/dem_sampler.rs
+++ b/crates/benchmarks/benches/modules/dem_sampler.rs
@@ -11,30 +11,17 @@
 // the License.
 
 //! DEM Sampler benchmarks for threshold estimation.
-//!
-//! These benchmarks measure the performance of the DEM-based sampling
-//! infrastructure used for fast error threshold estimation.
-//!
-//! # Benchmarks
-//!
-//! - **DEM Sampler - Original vs Columnar**: Compare row-major vs column-major sampling
-//! - **DEM Sampler - Statistics**: Compare statistics-only methods
-//! - **DEM Sampler - Scaling**: How different methods scale with DEM size
-
-use std::str::FromStr;
 
 use criterion::{BenchmarkId, Criterion, Throughput, measurement::Measurement};
-use pecos_qec::fault_tolerance::dem_builder::{DemSamplerBuilder, ParsedDem};
+use pecos_qec::fault_tolerance::dem_builder::DemSamplerBuilder;
 use pecos_qec::fault_tolerance::propagator::DagFaultAnalyzer;
 use pecos_quantum::DagCircuit;
 use pecos_random::PecosRng;
 use std::hint::black_box;
 
 pub fn benchmarks<M: Measurement>(c: &mut Criterion<M>) {
-    bench_sampler_comparison(c);
-    bench_statistics_comparison(c);
-    bench_optimization_comparison(c);
-    bench_parsed_dem_sampling(c);
+    bench_sampler(c);
+    bench_statistics(c);
 }
 
 /// Create a realistic DEM sampler from a surface-code-like circuit.
@@ -45,48 +32,40 @@ fn create_surface_code_sampler(
     // Create a simplified surface code circuit
     let num_data = distance * distance;
     let num_ancilla = num_data - 1;
+    let total_qubits = num_data + num_ancilla;
 
     let mut dag = DagCircuit::new();
 
-    // Initialize data qubits
-    for q in 0..num_data {
-        dag.pz(&[q]);
-        dag.h(&[q]);
-    }
+    // Prep all qubits
+    let all_qubits: Vec<usize> = (0..total_qubits).collect();
+    dag.pz(&all_qubits);
 
     // Syndrome extraction rounds
-    for _round in 0..rounds {
-        // Initialize ancillas
-        for a in 0..num_ancilla {
-            dag.pz(&[num_data + a]);
-        }
-
-        // Entangle ancillas with data (simplified pattern)
+    let ancilla_qubits: Vec<usize> = (num_data..total_qubits).collect();
+    for _ in 0..rounds {
+        dag.h(&ancilla_qubits);
         for a in 0..num_ancilla {
-            let ancilla = num_data + a;
-            let d1 = a % num_data;
-            let d2 = (a + 1) % num_data;
-            dag.cx(&[(ancilla, d1)]);
-            dag.cx(&[(ancilla, d2)]);
-        }
-
-        // Measure ancillas
-        for a in 0..num_ancilla {
-            dag.mz(&[num_data + a]);
+            let data_q = a.min(num_data - 1);
+            dag.cx(&[(data_q, num_data + a)]);
         }
+        dag.h(&ancilla_qubits);
+        dag.mz(&ancilla_qubits);
+        dag.pz(&ancilla_qubits);
     }
 
-    // Build influence map and sampler
+    // Measure data qubits
+    let data_qubits: Vec<usize> = (0..num_data).collect();
+    dag.mz(&data_qubits);
+
+    // Build influence map
     let analyzer = DagFaultAnalyzer::new(&dag);
     let influence_map = analyzer.build_influence_map();
 
-    // Create detector definitions (one per ancilla measurement)
-    let num_measurements = num_ancilla * rounds;
+    // Build DEM sampler with simple detectors
+    let num_measurements = num_ancilla * rounds + num_data;
     let mut detector_records = Vec::new();
     for i in 0..num_measurements.min(50) {
-        // Limit to 50 detectors for benchmark
         #[allow(clippy::cast_possible_wrap, clippy::cast_possible_truncation)]
-        // i < 50, fits in i32
         detector_records.push(vec![-(i as i32 + 1)]);
     }
 
@@ -95,48 +74,31 @@ fn create_surface_code_sampler(
         .with_detector_records(detector_records)
         .with_observable_records(vec![])
         .build()
+        .expect("Failed to build DEM sampler")
 }
 
-/// Benchmark comparing original row-major vs columnar sampling.
-fn bench_sampler_comparison<M: Measurement>(c: &mut Criterion<M>) {
-    let mut group = c.benchmark_group("DEM Sampler - Original vs Columnar");
+/// Benchmark sampling with different circuit sizes.
+fn bench_sampler<M: Measurement>(c: &mut Criterion<M>) {
+    let mut group = c.benchmark_group("DEM Sampler - Batch");
 
-    // Test with different circuit sizes
     for (distance, rounds) in [(3, 2), (5, 3)] {
         let sampler = create_surface_code_sampler(distance, rounds);
         let num_mechanisms = sampler.num_mechanisms();
         let num_detectors = sampler.num_detectors();
 
-        // Test different shot counts
         for shots in [1_000, 10_000, 100_000] {
             let label = format!("d{distance}_r{rounds}_{shots}");
-
             group.throughput(Throughput::Elements((num_mechanisms * shots) as u64));
 
-            // Original row-major sampling
-            group.bench_with_input(BenchmarkId::new("row_major", &label), &(), |b, ()| {
+            group.bench_with_input(BenchmarkId::new("sample_batch", &label), &(), |b, ()| {
                 let mut rng = PecosRng::seed_from_u64(42);
                 b.iter(|| {
                     let result = sampler.sample_batch(shots, &mut rng);
                     black_box(result)
                 });
             });
-
-            // Columnar sampling (accurate - one random per shot per mechanism)
-            group.bench_with_input(
-                BenchmarkId::new("columnar_accurate", &label),
-                &(),
-                |b, ()| {
-                    let mut rng = PecosRng::seed_from_u64(42);
-                    b.iter(|| {
-                        let result = sampler.sample_batch_columnar_accurate(shots, &mut rng);
-                        black_box(result)
-                    });
-                },
-            );
         }
 
-        // Print info
         println!(
             "  d={distance} r={rounds}: {num_mechanisms} mechanisms, {num_detectors} detectors"
         );
@@ -145,261 +107,29 @@ fn bench_sampler_comparison<M: Measurement>(c: &mut Criterion<M>) {
     group.finish();
 }
 
-/// Benchmark comparing statistics methods.
-fn bench_statistics_comparison<M: Measurement>(c: &mut Criterion<M>) {
+/// Benchmark statistics methods.
+fn bench_statistics<M: Measurement>(c: &mut Criterion<M>) {
     let mut group = c.benchmark_group("DEM Sampler - Statistics");
 
     let sampler = create_surface_code_sampler(5, 3);
     let num_mechanisms = sampler.num_mechanisms();
 
-    for shots in [10_000, 100_000, 1_000_000] {
+    for shots in [10_000, 100_000] {
         let label = format!("{shots}shots");
-
         group.throughput(Throughput::Elements((num_mechanisms * shots) as u64));
 
-        // Original statistics (row-major)
         group.bench_with_input(
-            BenchmarkId::new("row_major", &label),
+            BenchmarkId::new("sample_statistics", &label),
             &shots,
             |b, &shots| {
                 let mut rng = PecosRng::seed_from_u64(42);
                 b.iter(|| {
-                    let result = sampler.sample_statistics_row_major(shots, &mut rng);
+                    let result = sampler.sample_statistics_with_rng(shots, &mut rng);
                     black_box(result)
                 });
             },
         );
-
-        // Columnar statistics
-        group.bench_with_input(BenchmarkId::new("columnar", &label), &shots, |b, &shots| {
-            let mut rng = PecosRng::seed_from_u64(42);
-            b.iter(|| {
-                let result = sampler.sample_statistics_columnar(shots, &mut rng);
-                black_box(result)
-            });
-        });
-    }
-
-    group.finish();
-}
-
-/// Benchmark comparing all optimization methods.
-fn bench_optimization_comparison<M: Measurement>(c: &mut Criterion<M>) {
-    let mut group = c.benchmark_group("DEM Sampler - Optimizations");
-
-    // Use a realistic surface code sampler
-    let sampler = create_surface_code_sampler(5, 3);
-    let num_mechanisms = sampler.num_mechanisms();
-
-    let shots = 100_000;
-    group.throughput(Throughput::Elements((num_mechanisms * shots) as u64));
-
-    // Baseline: current columnar_accurate
-    group.bench_function("columnar_accurate", |b| {
-        let mut rng = PecosRng::seed_from_u64(42);
-        b.iter(|| {
-            let result = sampler.sample_batch_columnar_accurate(shots, &mut rng);
-            black_box(result)
-        });
-    });
-
-    // SIMD u64x4 version
-    group.bench_function("simd_u64x4", |b| {
-        let mut rng = PecosRng::seed_from_u64(42);
-        b.iter(|| {
-            let result = sampler.sample_batch_columnar_simd(shots, &mut rng);
-            black_box(result)
-        });
-    });
-
-    // Geometric skip version (fastest for low error rates)
-    group.bench_function("geometric", |b| {
-        let mut rng = PecosRng::seed_from_u64(42);
-        b.iter(|| {
-            let result = sampler.sample_batch_columnar_geometric(shots, &mut rng);
-            black_box(result)
-        });
-    });
-
-    group.finish();
-
-    // Also compare statistics methods
-    let mut stats_group = c.benchmark_group("DEM Sampler - Stats Optimizations");
-    stats_group.throughput(Throughput::Elements((num_mechanisms * shots) as u64));
-
-    stats_group.bench_function("stats_columnar", |b| {
-        let mut rng = PecosRng::seed_from_u64(42);
-        b.iter(|| {
-            let result = sampler.sample_statistics_columnar(shots, &mut rng);
-            black_box(result)
-        });
-    });
-
-    stats_group.bench_function("stats_simd", |b| {
-        let mut rng = PecosRng::seed_from_u64(42);
-        b.iter(|| {
-            let result = sampler.sample_statistics_simd(shots, &mut rng);
-            black_box(result)
-        });
-    });
-
-    stats_group.bench_function("stats_geometric", |b| {
-        let mut rng = PecosRng::seed_from_u64(42);
-        b.iter(|| {
-            let result = sampler.sample_statistics_geometric(shots, &mut rng);
-            black_box(result)
-        });
-    });
-
-    stats_group.bench_function("stats_auto", |b| {
-        let mut rng = PecosRng::seed_from_u64(42);
-        b.iter(|| {
-            let result = sampler.sample_statistics_with_rng(shots, &mut rng);
-            black_box(result)
-        });
-    });
-
-    stats_group.bench_function("stats_parallel", |b| {
-        b.iter(|| {
-            let result = sampler.sample_statistics_parallel(shots, 42);
-            black_box(result)
-        });
-    });
-
-    stats_group.finish();
-
-    // Benchmark parallel scaling with larger DEM
-    bench_parallel_scaling(c);
-}
-
-/// Benchmark parallel scaling with different DEM sizes.
-fn bench_parallel_scaling<M: Measurement>(c: &mut Criterion<M>) {
-    let mut group = c.benchmark_group("DEM Sampler - Parallel Scaling");
-
-    let shots = 100_000;
-
-    // Test with different circuit sizes
-    for (distance, rounds) in [(3, 2), (5, 3), (7, 5)] {
-        let sampler = create_surface_code_sampler(distance, rounds);
-        let num_mechanisms = sampler.num_mechanisms();
-        let label = format!("d{distance}_r{rounds}_{num_mechanisms}mech");
-
-        group.throughput(Throughput::Elements((num_mechanisms * shots) as u64));
-
-        // Sequential geometric (baseline)
-        group.bench_with_input(BenchmarkId::new("sequential", &label), &(), |b, ()| {
-            let mut rng = PecosRng::seed_from_u64(42);
-            b.iter(|| {
-                let result = sampler.sample_statistics_geometric(shots, &mut rng);
-                black_box(result)
-            });
-        });
-
-        // Parallel
-        group.bench_with_input(BenchmarkId::new("parallel", &label), &(), |b, ()| {
-            b.iter(|| {
-                let result = sampler.sample_statistics_parallel(shots, 42);
-                black_box(result)
-            });
-        });
-
-        // Auto (should pick geometric for low p)
-        group.bench_with_input(BenchmarkId::new("auto", &label), &(), |b, ()| {
-            let mut rng = PecosRng::seed_from_u64(42);
-            b.iter(|| {
-                let result = sampler.sample_statistics_with_rng(shots, &mut rng);
-                black_box(result)
-            });
-        });
     }
 
     group.finish();
 }
-
-/// Create a synthetic DEM string for benchmarking.
-fn create_synthetic_dem(num_mechanisms: usize, num_detectors: usize, prob: f64) -> String {
-    use std::fmt::Write;
-
-    let mut dem = String::new();
-
-    for i in 0..num_detectors {
-        writeln!(dem, "detector({i}, 0, 0) D{i}").unwrap();
-    }
-
-    for i in 0..num_mechanisms {
-        let d1 = i % num_detectors;
-        let d2 = (i + 1) % num_detectors;
-        let d3 = (i + 2) % num_detectors;
-
-        match i % 3 {
-            0 => writeln!(dem, "error({prob}) D{d1}").unwrap(),
-            1 => writeln!(dem, "error({prob}) D{d1} D{d2}").unwrap(),
-            _ => writeln!(dem, "error({prob}) D{d1} D{d2} D{d3}").unwrap(),
-        }
-    }
-
-    dem
-}
-
-/// Benchmark `ParsedDem` sampling (used by equivalence testing).
-fn bench_parsed_dem_sampling<M: Measurement>(c: &mut Criterion<M>) {
-    let mut group = c.benchmark_group("ParsedDem - Sampling");
-
-    let medium_dem = create_synthetic_dem(50, 24, 0.01);
-    let complex_dem = create_synthetic_dem(200, 96, 0.01);
-
-    let dems: [(&str, &str); 3] = [
-        (
-            "simple",
-            "error(0.01) D0\nerror(0.01) D1\nerror(0.01) D0 D1",
-        ),
-        ("medium", &medium_dem),
-        ("complex", &complex_dem),
-    ];
-
-    let shots = 50_000;
-
-    for (name, dem_str) in &dems {
-        let dem = ParsedDem::from_str(dem_str).expect("failed to parse DEM");
-        let num_mechanisms = dem.mechanisms.len();
-
-        group.throughput(Throughput::Elements((num_mechanisms * shots) as u64));
-
-        group.bench_with_input(BenchmarkId::new("sample_batch", *name), &(), |b, ()| {
-            let mut rng = PecosRng::seed_from_u64(42);
-            b.iter(|| {
-                let result = dem.sample_batch(shots, &mut rng);
-                black_box(result)
-            });
-        });
-    }
-
-    group.finish();
-}
-
-#[cfg(test)]
-mod tests {
-
-    #[test]
-    fn test_sampler_creation() {
-        let sampler = create_surface_code_sampler(3, 1);
-        assert!(sampler.num_mechanisms() > 0);
-    }
-
-    #[test]
-    fn test_columnar_matches_row_major() {
-        let sampler = create_surface_code_sampler(3, 1);
-
-        // Sample with row-major
-        let mut rng1 = PecosRng::seed_from_u64(42);
-        let stats1 = sampler.sample_statistics(1000, &mut rng1);
-
-        // Sample with columnar
-        let mut rng2 = PecosRng::seed_from_u64(42);
-        let stats2 = sampler.sample_statistics_columnar(1000, &mut rng2);
-
-        // Statistics should be similar (not exact due to different RNG consumption order)
-        // Just verify both produce reasonable results
-        assert!(stats1.total_shots == stats2.total_shots);
-    }
-}
diff --git a/crates/benchmarks/benches/modules/fault_catalog.rs b/crates/benchmarks/benches/modules/fault_catalog.rs
new file mode 100644
index 000000000..58f428eac
--- /dev/null
+++ b/crates/benchmarks/benches/modules/fault_catalog.rs
@@ -0,0 +1,476 @@
+// Copyright 2026 The PECOS Developers
+//
+// Licensed under the Apache License, Version 2.0 (the "License"); you may not use this file except
+// in compliance with the License. You may obtain a copy of the License at
+//
+//     https://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software distributed under the License
+// is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express
+// or implied. See the License for the specific language governing permissions and limitations under
+// the License.
+
+//! Parameterized fault-catalog benchmarks.
+//!
+//! These benchmarks cover the Rust-side sweep path before doing packed
+//! performance work:
+//! - structural catalog construction from a `TickCircuit`,
+//! - applying a concrete noise point with `with_noise`,
+//! - projecting the richer catalog into raw-measurement mechanisms, and
+//! - amortized noise sweeps compared with direct concrete catalog builds.
+
+use criterion::{BatchSize, BenchmarkId, Criterion, Throughput, measurement::Measurement};
+use pecos_qec::SurfaceCode;
+use pecos_qec::fault_tolerance::fault_sampler::{
+    FaultCatalog, StochasticNoiseParams, build_fault_catalog, build_fault_table,
+};
+use pecos_quantum::{Attribute, TickCircuit, TickMeasRef};
+use std::hint::black_box;
+
+const DISTANCES: &[usize] = &[3, 5, 7, 9, 11];
+const SWEEP_NOISES: &[StochasticNoiseParams] = &[
+    StochasticNoiseParams {
+        p1: 0.00005,
+        p2: 0.0005,
+        p_meas: 0.0005,
+        p_prep: 0.0005,
+    },
+    StochasticNoiseParams {
+        p1: 0.0001,
+        p2: 0.001,
+        p_meas: 0.001,
+        p_prep: 0.001,
+    },
+    StochasticNoiseParams {
+        p1: 0.0002,
+        p2: 0.002,
+        p_meas: 0.002,
+        p_prep: 0.002,
+    },
+    StochasticNoiseParams {
+        p1: 0.0005,
+        p2: 0.005,
+        p_meas: 0.005,
+        p_prep: 0.005,
+    },
+];
+
+#[derive(Debug)]
+struct MemoryCircuit {
+    circuit: TickCircuit,
+    distance: usize,
+    rounds: usize,
+    num_measurements: usize,
+    num_detectors: usize,
+    num_observables: usize,
+}
+
+#[derive(Debug)]
+struct CatalogShape {
+    locations: usize,
+    alternatives: usize,
+}
+
+pub fn benchmarks<M: Measurement>(c: &mut Criterion<M>) {
+    bench_from_circuit(c);
+    bench_with_noise(c);
+    bench_to_mechanisms(c);
+    bench_noise_sweeps(c);
+}
+
+fn bench_from_circuit<M: Measurement>(c: &mut Criterion<M>) {
+    let mut group = c.benchmark_group("fault_catalog/from_circuit");
+
+    for memory in surface_memory_circuits() {
+        let shape = catalog_shape(&memory.circuit);
+        group.throughput(Throughput::Elements(as_u64(shape.locations)));
+        group.bench_with_input(bench_id(&memory, &shape), &memory, |b, memory| {
+            b.iter(|| {
+                black_box(FaultCatalog::from_circuit(black_box(&memory.circuit)))
+                    .expect("surface memory circuit should be supported")
+            });
+        });
+    }
+
+    group.finish();
+}
+
+fn bench_with_noise<M: Measurement>(c: &mut Criterion<M>) {
+    let mut group = c.benchmark_group("fault_catalog/with_noise");
+    let noise = representative_noise();
+
+    for memory in surface_memory_circuits() {
+        let shape = catalog_shape(&memory.circuit);
+        group.throughput(Throughput::Elements(as_u64(shape.locations)));
+        group.bench_with_input(bench_id(&memory, &shape), &memory, |b, memory| {
+            b.iter_batched(
+                || {
+                    FaultCatalog::from_circuit(&memory.circuit)
+                        .expect("surface memory circuit should be supported")
+                },
+                |mut catalog| {
+                    catalog.with_noise(black_box(&noise));
+                    black_box(catalog)
+                },
+                BatchSize::SmallInput,
+            );
+        });
+    }
+
+    group.finish();
+}
+
+fn bench_to_mechanisms<M: Measurement>(c: &mut Criterion<M>) {
+    let mut group = c.benchmark_group("fault_catalog/to_mechanisms");
+    let noise = representative_noise();
+
+    for memory in surface_memory_circuits() {
+        let shape = catalog_shape(&memory.circuit);
+        group.throughput(Throughput::Elements(as_u64(shape.alternatives)));
+        group.bench_with_input(bench_id(&memory, &shape), &memory, |b, memory| {
+            b.iter_batched(
+                || {
+                    let mut catalog = FaultCatalog::from_circuit(&memory.circuit)
+                        .expect("surface memory circuit should be supported");
+                    catalog.with_noise(&noise);
+                    catalog
+                },
+                |catalog| black_box(catalog.to_mechanisms()),
+                BatchSize::SmallInput,
+            );
+        });
+    }
+
+    group.finish();
+}
+
+fn bench_noise_sweeps<M: Measurement>(c: &mut Criterion<M>) {
+    let mut group = c.benchmark_group("fault_catalog/noise_sweep");
+
+    for memory in surface_memory_circuits() {
+        let shape = catalog_shape(&memory.circuit);
+        let id = bench_label(&memory, &shape);
+        group.throughput(Throughput::Elements(as_u64(
+            shape.locations * SWEEP_NOISES.len(),
+        )));
+
+        group.bench_with_input(
+            BenchmarkId::new("direct_catalog_sweep", id.clone()),
+            &memory,
+            |b, memory| {
+                b.iter(|| {
+                    let mut total_locations = 0usize;
+                    let mut total_alternatives = 0usize;
+                    for noise in SWEEP_NOISES {
+                        let catalog = build_fault_catalog(black_box(&memory.circuit), noise)
+                            .expect("surface memory circuit should be supported");
+                        total_locations += catalog.locations.len();
+                        total_alternatives += count_alternatives(&catalog);
+                    }
+                    black_box((total_locations, total_alternatives))
+                });
+            },
+        );
+
+        group.bench_with_input(
+            BenchmarkId::new("parameterized_catalog_sweep", id.clone()),
+            &memory,
+            |b, memory| {
+                b.iter(|| {
+                    let structural = FaultCatalog::from_circuit(black_box(&memory.circuit))
+                        .expect("surface memory circuit should be supported");
+                    let mut total_locations = 0usize;
+                    let mut total_alternatives = 0usize;
+                    for noise in SWEEP_NOISES {
+                        let catalog = structural.parameterized(noise);
+                        total_locations += catalog.locations.len();
+                        total_alternatives += count_alternatives(&catalog);
+                    }
+                    black_box((total_locations, total_alternatives))
+                });
+            },
+        );
+
+        group.bench_with_input(
+            BenchmarkId::new("mutable_catalog_sweep", id.clone()),
+            &memory,
+            |b, memory| {
+                b.iter(|| {
+                    let mut catalog = FaultCatalog::from_circuit(black_box(&memory.circuit))
+                        .expect("surface memory circuit should be supported");
+                    let mut total_locations = 0usize;
+                    let mut total_alternatives = 0usize;
+                    for noise in SWEEP_NOISES {
+                        catalog.with_noise(black_box(noise));
+                        total_locations += catalog.locations.len();
+                        total_alternatives += count_alternatives(&catalog);
+                    }
+                    black_box((total_locations, total_alternatives))
+                });
+            },
+        );
+
+        group.bench_with_input(
+            BenchmarkId::new("direct_raw_mechanism_sweep", id.clone()),
+            &memory,
+            |b, memory| {
+                b.iter(|| {
+                    let mut total_mechanisms = 0usize;
+                    let mut total_alternatives = 0usize;
+                    for noise in SWEEP_NOISES {
+                        let mechanisms = build_fault_table(black_box(&memory.circuit), noise)
+                            .expect("surface memory circuit should be supported");
+                        total_mechanisms += mechanisms.len();
+                        total_alternatives += mechanisms
+                            .iter()
+                            .map(|mechanism| mechanism.alternatives.len())
+                            .sum::<usize>();
+                    }
+                    black_box((total_mechanisms, total_alternatives))
+                });
+            },
+        );
+
+        group.bench_with_input(
+            BenchmarkId::new("parameterized_raw_mechanism_sweep", id.clone()),
+            &memory,
+            |b, memory| {
+                b.iter(|| {
+                    let structural = FaultCatalog::from_circuit(black_box(&memory.circuit))
+                        .expect("surface memory circuit should be supported");
+                    let mut total_mechanisms = 0usize;
+                    let mut total_alternatives = 0usize;
+                    for noise in SWEEP_NOISES {
+                        let catalog = structural.parameterized(noise);
+                        let mechanisms = catalog.to_mechanisms();
+                        total_mechanisms += mechanisms.len();
+                        total_alternatives += mechanisms
+                            .iter()
+                            .map(|mechanism| mechanism.alternatives.len())
+                            .sum::<usize>();
+                    }
+                    black_box((total_mechanisms, total_alternatives))
+                });
+            },
+        );
+
+        group.bench_with_input(
+            BenchmarkId::new("mutable_raw_mechanism_sweep", id),
+            &memory,
+            |b, memory| {
+                b.iter(|| {
+                    let mut catalog = FaultCatalog::from_circuit(black_box(&memory.circuit))
+                        .expect("surface memory circuit should be supported");
+                    let mut total_mechanisms = 0usize;
+                    let mut total_alternatives = 0usize;
+                    for noise in SWEEP_NOISES {
+                        catalog.with_noise(black_box(noise));
+                        let mechanisms = catalog.to_mechanisms();
+                        total_mechanisms += mechanisms.len();
+                        total_alternatives += mechanisms
+                            .iter()
+                            .map(|mechanism| mechanism.alternatives.len())
+                            .sum::<usize>();
+                    }
+                    black_box((total_mechanisms, total_alternatives))
+                });
+            },
+        );
+    }
+
+    group.finish();
+}
+
+fn surface_memory_circuits() -> Vec<MemoryCircuit> {
+    DISTANCES
+        .iter()
+        .map(|&distance| {
+            build_rotated_z_memory_circuit(distance, distance)
+                .expect("surface memory circuit should build")
+        })
+        .collect()
+}
+
+fn representative_noise() -> StochasticNoiseParams {
+    StochasticNoiseParams {
+        p1: 0.0001,
+        p2: 0.001,
+        p_meas: 0.001,
+        p_prep: 0.001,
+    }
+}
+
+fn bench_id(memory: &MemoryCircuit, shape: &CatalogShape) -> BenchmarkId {
+    BenchmarkId::from_parameter(bench_label(memory, shape))
+}
+
+fn bench_label(memory: &MemoryCircuit, shape: &CatalogShape) -> String {
+    format!(
+        "d{}_r{}_m{}_det{}_obs{}_loc{}_alt{}",
+        memory.distance,
+        memory.rounds,
+        memory.num_measurements,
+        memory.num_detectors,
+        memory.num_observables,
+        shape.locations,
+        shape.alternatives,
+    )
+}
+
+fn catalog_shape(circuit: &TickCircuit) -> CatalogShape {
+    let catalog =
+        FaultCatalog::from_circuit(circuit).expect("surface memory circuit should be supported");
+    CatalogShape {
+        locations: catalog.locations.len(),
+        alternatives: count_alternatives(&catalog),
+    }
+}
+
+fn count_alternatives(catalog: &FaultCatalog) -> usize {
+    catalog
+        .locations
+        .iter()
+        .map(|location| location.faults.len())
+        .sum()
+}
+
+fn build_rotated_z_memory_circuit(distance: usize, rounds: usize) -> Result<MemoryCircuit, String> {
+    let code = SurfaceCode::rotated(distance)?;
+    let num_data = code.num_data_qubits();
+    let x_ancilla_offset = num_data;
+    let z_ancilla_offset = x_ancilla_offset + code.num_x_stabilizers();
+
+    let x_ancilla = |idx: usize| x_ancilla_offset + idx;
+    let z_ancilla = |idx: usize| z_ancilla_offset + idx;
+
+    let mut circuit = TickCircuit::new();
+    let data_qubits: Vec<usize> = (0..num_data).collect();
+    circuit.tick().pz(&data_qubits);
+
+    let mut x_round_measurements: Vec<Vec<TickMeasRef>> = Vec::with_capacity(rounds);
+    let mut z_round_measurements: Vec<Vec<TickMeasRef>> = Vec::with_capacity(rounds);
+
+    for _round in 0..rounds {
+        let x_ancillas: Vec<usize> = (0..code.num_x_stabilizers()).map(x_ancilla).collect();
+        let z_ancillas: Vec<usize> = (0..code.num_z_stabilizers()).map(z_ancilla).collect();
+
+        circuit.tick().pz(&x_ancillas);
+        circuit.tick().pz(&z_ancillas);
+        circuit.tick().h(&x_ancillas);
+
+        for check in code.x_stabilizers() {
+            let ancilla = x_ancilla(check.index);
+            for data in check.qubits() {
+                circuit.tick().cx(&[(ancilla, data)]);
+            }
+        }
+
+        for check in code.z_stabilizers() {
+            let ancilla = z_ancilla(check.index);
+            for data in check.qubits() {
+                circuit.tick().cx(&[(data, ancilla)]);
+            }
+        }
+
+        circuit.tick().h(&x_ancillas);
+
+        let x_refs = circuit.tick().mz(&x_ancillas);
+        let z_refs = circuit.tick().mz(&z_ancillas);
+        x_round_measurements.push(x_refs);
+        z_round_measurements.push(z_refs);
+    }
+
+    let final_data_measurements = circuit.tick().mz(&data_qubits);
+    let num_measurements = circuit.num_measurements();
+
+    let mut detectors: Vec<Vec<i32>> = Vec::new();
+
+    for &meas_ref in z_round_measurements[0]
+        .iter()
+        .take(code.num_z_stabilizers())
+    {
+        detectors.push(relative_records(num_measurements, &[meas_ref]));
+    }
+
+    for round in 1..rounds {
+        for (&current, &previous) in x_round_measurements[round]
+            .iter()
+            .zip(x_round_measurements[round - 1].iter())
+            .take(code.num_x_stabilizers())
+        {
+            detectors.push(relative_records(num_measurements, &[current, previous]));
+        }
+        for (&current, &previous) in z_round_measurements[round]
+            .iter()
+            .zip(z_round_measurements[round - 1].iter())
+            .take(code.num_z_stabilizers())
+        {
+            detectors.push(relative_records(num_measurements, &[current, previous]));
+        }
+    }
+
+    let last_round = rounds - 1;
+    for check in code.z_stabilizers() {
+        let mut refs = vec![z_round_measurements[last_round][check.index]];
+        refs.extend(
+            check
+                .qubits()
+                .into_iter()
+                .map(|q| final_data_measurements[q]),
+        );
+        detectors.push(relative_records(num_measurements, &refs));
+    }
+
+    let logical_z_refs: Vec<TickMeasRef> = code
+        .logical_z()
+        .data_qubits
+        .iter()
+        .map(|&q| final_data_measurements[q])
+        .collect();
+    let observables = vec![relative_records(num_measurements, &logical_z_refs)];
+
+    circuit.set_meta(
+        "num_measurements",
+        Attribute::String(num_measurements.to_string()),
+    );
+    circuit.set_meta("detectors", Attribute::String(records_json(&detectors)));
+    circuit.set_meta("observables", Attribute::String(records_json(&observables)));
+
+    Ok(MemoryCircuit {
+        circuit,
+        distance,
+        rounds,
+        num_measurements,
+        num_detectors: detectors.len(),
+        num_observables: observables.len(),
+    })
+}
+
+fn relative_records(num_measurements: usize, refs: &[TickMeasRef]) -> Vec<i32> {
+    let num_measurements = i32::try_from(num_measurements).expect("measurement count fits in i32");
+    refs.iter()
+        .map(|meas_ref| {
+            i32::try_from(meas_ref.record_idx).expect("measurement record index fits in i32")
+                - num_measurements
+        })
+        .collect()
+}
+
+fn records_json(records: &[Vec<i32>]) -> String {
+    let entries: Vec<String> = records
+        .iter()
+        .map(|records| {
+            let values = records
+                .iter()
+                .map(i32::to_string)
+                .collect::<Vec<_>>()
+                .join(",");
+            format!(r#"{{"records":[{values}]}}"#)
+        })
+        .collect();
+    format!("[{}]", entries.join(","))
+}
+
+fn as_u64(value: usize) -> u64 {
+    u64::try_from(value).expect("benchmark size fits in u64")
+}
diff --git a/crates/benchmarks/benches/modules/gpu_influence_sampler.rs b/crates/benchmarks/benches/modules/gpu_influence_sampler.rs
index ecb305548..27f218c6e 100644
--- a/crates/benchmarks/benches/modules/gpu_influence_sampler.rs
+++ b/crates/benchmarks/benches/modules/gpu_influence_sampler.rs
@@ -20,7 +20,7 @@
 
 use criterion::{BenchmarkId, Criterion, Throughput, measurement::Measurement};
 use pecos_gpu_sims::{GpuInfluenceMapData, GpuInfluenceSampler};
-use pecos_qec::fault_tolerance::noisy_sampler::{NoisySampler, UniformNoiseModel};
+use pecos_qec::fault_tolerance::dem_builder::DemSampler;
 use pecos_qec::fault_tolerance::{DagFaultInfluenceMap, InfluenceBuilder};
 use pecos_quantum::DagCircuit;
 use std::hint::black_box;
@@ -105,31 +105,44 @@ fn build_influence_maps(
     circuit: &DagCircuit,
     num_data: usize,
 ) -> (DagFaultInfluenceMap, GpuInfluenceMapData) {
-    let logical_qubits: Vec<usize> = (0..num_data).collect();
-    let builder = InfluenceBuilder::new(circuit).with_logical_z(logical_qubits);
+    let tracked_pauli_qubits: Vec<usize> = (0..num_data).collect();
+    let builder = InfluenceBuilder::new(circuit).with_z(&tracked_pauli_qubits);
     let influence_map = builder.build();
 
     let (
         num_loc,
         num_det,
-        num_log,
+        num_dem_outputs,
         det_off_x,
         det_data_x,
         det_off_y,
         det_data_y,
         det_off_z,
         det_data_z,
-        log_off_x,
-        log_data_x,
-        log_off_y,
-        log_data_y,
-        log_off_z,
-        log_data_z,
+        dem_output_offsets_x,
+        dem_output_data_x,
+        dem_output_offsets_y,
+        dem_output_data_y,
+        dem_output_offsets_z,
+        dem_output_data_z,
     ) = influence_map.export_csr();
 
     let gpu_map = GpuInfluenceMapData::from_csr(
-        num_loc, num_det, num_log, det_off_x, det_data_x, det_off_y, det_data_y, det_off_z,
-        det_data_z, log_off_x, log_data_x, log_off_y, log_data_y, log_off_z, log_data_z,
+        num_loc,
+        num_det,
+        num_dem_outputs,
+        det_off_x,
+        det_data_x,
+        det_off_y,
+        det_data_y,
+        det_off_z,
+        det_data_z,
+        dem_output_offsets_x,
+        dem_output_data_x,
+        dem_output_offsets_y,
+        dem_output_data_y,
+        dem_output_offsets_z,
+        dem_output_data_z,
     );
 
     (influence_map, gpu_map)
@@ -155,11 +168,11 @@ fn bench_cpu_vs_gpu_surface_codes<M: Measurement>(c: &mut Criterion<M>) {
         group.throughput(Throughput::Elements(u64::from(num_shots)));
 
         // CPU benchmark
-        let noise = UniformNoiseModel::depolarizing(p_error);
-        let mut cpu_sampler = NoisySampler::new(&cpu_map, noise, seed);
+        let probs = vec![p_error; cpu_map.locations.len()];
+        let cpu_sampler = DemSampler::from_influence_map(&cpu_map, &probs);
 
         group.bench_with_input(BenchmarkId::new("CPU", &label), &(), |b, ()| {
-            b.iter(|| black_box(cpu_sampler.sample(num_shots as usize)));
+            b.iter(|| black_box(cpu_sampler.sample_statistics(num_shots as usize, seed)));
         });
 
         // GPU benchmark
@@ -196,11 +209,11 @@ fn bench_gpu_sampler_shot_scaling<M: Measurement>(c: &mut Criterion<M>) {
         group.throughput(Throughput::Elements(u64::from(num_shots)));
 
         // CPU benchmark
-        let noise = UniformNoiseModel::depolarizing(p_error);
-        let mut cpu_sampler = NoisySampler::new(&cpu_map, noise, seed);
+        let probs = vec![p_error; cpu_map.locations.len()];
+        let cpu_sampler = DemSampler::from_influence_map(&cpu_map, &probs);
 
         group.bench_with_input(BenchmarkId::new("CPU", &label), &num_shots, |b, &shots| {
-            b.iter(|| black_box(cpu_sampler.sample(shots as usize)));
+            b.iter(|| black_box(cpu_sampler.sample_statistics(shots as usize, seed)));
         });
 
         // GPU benchmark
diff --git a/crates/benchmarks/benches/modules/tick_circuit_layout.rs b/crates/benchmarks/benches/modules/tick_circuit_layout.rs
new file mode 100644
index 000000000..cf020824c
--- /dev/null
+++ b/crates/benchmarks/benches/modules/tick_circuit_layout.rs
@@ -0,0 +1,314 @@
+// Copyright 2026 The PECOS Developers
+//
+// Licensed under the Apache License, Version 2.0 (the "License"); you may not use this file except
+// in compliance with the License. You may obtain a copy of the License at
+//
+//     https://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software distributed under the License
+// is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express
+// or implied. See the License for the specific language governing permissions and limitations under
+// the License.
+
+//! `TickCircuit` batched layout benchmarks.
+//!
+//! These benchmarks measure the current batched `TickCircuit` access patterns:
+//! - direct `TickCircuit` traversal,
+//! - explicit batched `TickCircuit` traversal, and
+//! - direct vs `CircuitExecutor` simulator execution.
+
+use criterion::{BenchmarkId, Criterion, Throughput, measurement::Measurement};
+use pecos_core::gate_type::GateType;
+use pecos_quantum::{Gate, QubitId, TickCircuit};
+use pecos_simulators::{CircuitExecutor, CliffordGateable, SparseStab};
+use std::hint::black_box;
+
+const DISTANCES: &[usize] = &[3, 5, 7, 9, 11];
+const AMORTIZED_SHOTS: usize = 64;
+
+#[derive(Clone)]
+struct LayoutSpec {
+    label: String,
+    num_qubits: usize,
+    gate_count: usize,
+    tick_circuit: TickCircuit,
+}
+
+pub fn benchmarks<M: Measurement>(c: &mut Criterion<M>) {
+    let specs = DISTANCES
+        .iter()
+        .map(|&distance| {
+            let rounds = distance;
+            let tick_circuit = build_surface_like_tick_circuit(distance, rounds);
+            let num_qubits = surface_like_num_qubits(distance);
+            let gate_count = tick_circuit.gate_count();
+            LayoutSpec {
+                label: format!("d{distance}_r{rounds}"),
+                num_qubits,
+                gate_count,
+                tick_circuit,
+            }
+        })
+        .collect::<Vec<_>>();
+
+    bench_traversal(c, &specs);
+    bench_execution(c, &specs);
+    bench_amortized_execution(c, &specs);
+}
+
+fn bench_traversal<M: Measurement>(c: &mut Criterion<M>, specs: &[LayoutSpec]) {
+    let mut group = c.benchmark_group("tick_circuit_layout/traversal");
+
+    for spec in specs {
+        group.throughput(Throughput::Elements(spec.gate_count as u64));
+        group.bench_with_input(
+            BenchmarkId::new("tick_circuit_iter_gates", &spec.label),
+            spec,
+            |b, spec| {
+                b.iter(|| black_box(traverse_tick_circuit(black_box(&spec.tick_circuit))));
+            },
+        );
+        group.bench_with_input(
+            BenchmarkId::new("tick_circuit_gate_batches", &spec.label),
+            spec,
+            |b, spec| {
+                b.iter(|| black_box(traverse_tick_circuit_batched(black_box(&spec.tick_circuit))));
+            },
+        );
+    }
+
+    group.finish();
+}
+
+fn bench_execution<M: Measurement>(c: &mut Criterion<M>, specs: &[LayoutSpec]) {
+    let mut group = c.benchmark_group("tick_circuit_layout/execution_one_shot");
+
+    for spec in specs {
+        group.throughput(Throughput::Elements(spec.gate_count as u64));
+        group.bench_with_input(
+            BenchmarkId::new("tick_circuit_direct", &spec.label),
+            spec,
+            |b, spec| {
+                b.iter(|| {
+                    black_box(run_tick_circuit_direct(
+                        black_box(&spec.tick_circuit),
+                        spec.num_qubits,
+                    ))
+                });
+            },
+        );
+        group.bench_with_input(
+            BenchmarkId::new("circuit_executor", &spec.label),
+            spec,
+            |b, spec| {
+                b.iter(|| {
+                    black_box(run_tick_circuit_executor(
+                        black_box(&spec.tick_circuit),
+                        spec.num_qubits,
+                    ))
+                });
+            },
+        );
+    }
+
+    group.finish();
+}
+
+fn bench_amortized_execution<M: Measurement>(c: &mut Criterion<M>, specs: &[LayoutSpec]) {
+    let mut group = c.benchmark_group("tick_circuit_layout/execution_amortized_64_shots");
+
+    for spec in specs {
+        let throughput = spec.gate_count.saturating_mul(AMORTIZED_SHOTS);
+        group.throughput(Throughput::Elements(throughput as u64));
+        group.bench_with_input(
+            BenchmarkId::new("tick_circuit_direct", &spec.label),
+            spec,
+            |b, spec| {
+                b.iter(|| {
+                    let mut total = 0usize;
+                    for _ in 0..AMORTIZED_SHOTS {
+                        total = total.wrapping_add(run_tick_circuit_direct(
+                            black_box(&spec.tick_circuit),
+                            spec.num_qubits,
+                        ));
+                    }
+                    black_box(total)
+                });
+            },
+        );
+        group.bench_with_input(
+            BenchmarkId::new("circuit_executor", &spec.label),
+            spec,
+            |b, spec| {
+                b.iter(|| {
+                    let mut total = 0usize;
+                    for _ in 0..AMORTIZED_SHOTS {
+                        total = total.wrapping_add(run_tick_circuit_executor(
+                            black_box(&spec.tick_circuit),
+                            spec.num_qubits,
+                        ));
+                    }
+                    black_box(total)
+                });
+            },
+        );
+    }
+
+    group.finish();
+}
+
+fn build_surface_like_tick_circuit(distance: usize, rounds: usize) -> TickCircuit {
+    let num_data = distance * distance;
+    let plaquettes = (distance - 1) * (distance - 1);
+    let x_ancilla_start = num_data;
+    let z_ancilla_start = x_ancilla_start + plaquettes;
+    let total_qubits = surface_like_num_qubits(distance);
+
+    let mut circuit = TickCircuit::new();
+    let data_qubits = (0..num_data).collect::<Vec<_>>();
+    let ancilla_qubits = (num_data..total_qubits).collect::<Vec<_>>();
+    let x_ancillas = (x_ancilla_start..z_ancilla_start).collect::<Vec<_>>();
+    let all_qubits = (0..total_qubits).collect::<Vec<_>>();
+
+    circuit.tick().pz(&all_qubits);
+    circuit.tick().h(&data_qubits);
+
+    for _ in 0..rounds {
+        circuit.tick().pz(&ancilla_qubits);
+        circuit.tick().h(&x_ancillas);
+
+        for neighbor in 0..4 {
+            let pairs = surface_like_pairs_for_neighbor(distance, neighbor);
+            add_disjoint_cx_layers(&mut circuit, total_qubits, pairs);
+        }
+
+        circuit.tick().h(&x_ancillas);
+        circuit.tick().mz(&ancilla_qubits);
+    }
+
+    circuit.tick().mz(&data_qubits);
+    circuit
+}
+
+fn surface_like_num_qubits(distance: usize) -> usize {
+    let num_data = distance * distance;
+    let plaquettes = (distance - 1) * (distance - 1);
+    num_data + 2 * plaquettes
+}
+
+fn surface_like_pairs_for_neighbor(distance: usize, neighbor: usize) -> Vec<(usize, usize)> {
+    let num_data = distance * distance;
+    let plaquettes_per_type = (distance - 1) * (distance - 1);
+    let x_ancilla_start = num_data;
+    let z_ancilla_start = x_ancilla_start + plaquettes_per_type;
+    let mut pairs = Vec::with_capacity(2 * plaquettes_per_type);
+
+    for row in 0..(distance - 1) {
+        for col in 0..(distance - 1) {
+            let plaquette = row * (distance - 1) + col;
+            let x_ancilla = x_ancilla_start + plaquette;
+            let z_ancilla = z_ancilla_start + plaquette;
+            let data = match neighbor {
+                0 => row * distance + col,
+                1 => (row + 1) * distance + col,
+                2 => row * distance + col + 1,
+                3 => (row + 1) * distance + col + 1,
+                _ => unreachable!("neighbor index is in 0..4"),
+            };
+
+            pairs.push((x_ancilla, data));
+            pairs.push((data, z_ancilla));
+        }
+    }
+
+    pairs
+}
+
+fn add_disjoint_cx_layers(
+    circuit: &mut TickCircuit,
+    num_qubits: usize,
+    mut remaining: Vec<(usize, usize)>,
+) {
+    while !remaining.is_empty() {
+        let mut used = vec![false; num_qubits];
+        let mut layer = Vec::new();
+        let mut next = Vec::new();
+
+        for (control, target) in remaining {
+            if !used[control] && !used[target] {
+                used[control] = true;
+                used[target] = true;
+                layer.push((control, target));
+            } else {
+                next.push((control, target));
+            }
+        }
+
+        circuit.tick().cx(&layer);
+        remaining = next;
+    }
+}
+
+fn traverse_tick_circuit(circuit: &TickCircuit) -> usize {
+    let mut total = 0usize;
+    for (tick_idx, tick) in circuit.iter_ticks() {
+        total = total.wrapping_add(tick_idx);
+        for gate in tick.gate_batches() {
+            total = total.wrapping_add(gate.num_gates());
+            total = total.wrapping_add(gate.qubits.len());
+        }
+    }
+    total
+}
+
+fn traverse_tick_circuit_batched(circuit: &TickCircuit) -> usize {
+    let mut total = 0usize;
+    for (tick_idx, batch) in circuit.iter_gate_batches_with_tick() {
+        total = total.wrapping_add(tick_idx);
+        total = total.wrapping_add(batch.num_gates());
+        total = total.wrapping_add(batch.qubits.len());
+    }
+    total
+}
+
+fn run_tick_circuit_direct(circuit: &TickCircuit, num_qubits: usize) -> usize {
+    let mut sim = SparseStab::new(num_qubits);
+    let mut measurement_count = 0usize;
+
+    for (_tick_idx, tick) in circuit.iter_ticks() {
+        for gate in tick.gate_batches() {
+            measurement_count += execute_gate_direct(&mut sim, gate);
+        }
+    }
+
+    measurement_count
+}
+
+fn execute_gate_direct<S: CliffordGateable>(sim: &mut S, gate: &Gate) -> usize {
+    match gate.gate_type {
+        GateType::PZ | GateType::QAlloc => {
+            sim.pz(&gate.qubits);
+            0
+        }
+        GateType::H => {
+            sim.h(&gate.qubits);
+            0
+        }
+        GateType::CX => {
+            let pairs = gate
+                .qubits
+                .chunks_exact(2)
+                .map(|pair| (pair[0], pair[1]))
+                .collect::<Vec<(QubitId, QubitId)>>();
+            sim.cx(&pairs);
+            0
+        }
+        GateType::MZ | GateType::MeasureFree => sim.mz(&gate.qubits).len(),
+        other => panic!("unsupported benchmark gate type: {other:?}"),
+    }
+}
+
+fn run_tick_circuit_executor(circuit: &TickCircuit, num_qubits: usize) -> usize {
+    let mut sim = SparseStab::new(num_qubits);
+    CircuitExecutor::new(circuit).run(&mut sim).len()
+}
diff --git a/crates/pecos-chromobius/Cargo.toml b/crates/pecos-chromobius/Cargo.toml
index f945d9a24..6b1528949 100644
--- a/crates/pecos-chromobius/Cargo.toml
+++ b/crates/pecos-chromobius/Cargo.toml
@@ -13,6 +13,7 @@ description = "Chromobius color code decoder for PECOS"
 
 [dependencies]
 pecos-decoder-core.workspace = true
+pecos-pymatching.workspace = true
 ndarray.workspace = true
 thiserror.workspace = true
 cxx.workspace = true
diff --git a/crates/pecos-chromobius/build_chromobius.rs b/crates/pecos-chromobius/build_chromobius.rs
index 75a27a1dc..dd2d0bf94 100644
--- a/crates/pecos-chromobius/build_chromobius.rs
+++ b/crates/pecos-chromobius/build_chromobius.rs
@@ -59,7 +59,33 @@ pub fn build() -> Result<()> {
     let manifest = Manifest::find_and_load_validated()?;
     let chromobius_dir = ensure_dep_ready("chromobius", &manifest)?;
     let stim_dir = ensure_dep_ready("stim", &manifest)?;
-    let pymatching_dir = ensure_dep_ready("pymatching", &manifest)?;
+    // PyMatching headers and compiled objects come from pecos-pymatching via cargo metadata.
+    // This avoids compiling a second copy of PyMatching sources which would cause
+    // duplicate symbol errors at link time.
+    let pymatching_include = env::var("DEP_PYMATCHING_PECOS_PYMATCHING_INCLUDE").map_or_else(
+        |_| {
+            // Fallback: download and use directly (for standalone builds)
+            ensure_dep_ready("pymatching", &manifest)
+                .expect("pymatching dependency")
+                .join("src")
+        },
+        PathBuf::from,
+    );
+    let stim_include = env::var("DEP_PYMATCHING_PECOS_STIM_INCLUDE").map_or_else(
+        |_| {
+            ensure_dep_ready("stim", &manifest)
+                .expect("stim dependency")
+                .join("src")
+        },
+        PathBuf::from,
+    );
+    let stim_dir_for_header = env::var("DEP_PYMATCHING_PECOS_STIM_DIR").map_or_else(
+        |_| ensure_dep_ready("stim", &manifest).expect("stim dependency"),
+        PathBuf::from,
+    );
+    let pymatching_lib_dir = env::var("DEP_PYMATCHING_PECOS_LIB_DIR")
+        .ok()
+        .map(PathBuf::from);
 
     // Apply compatibility patches for newer Stim version
     chromobius_patch::patch_chromobius_for_newer_stim(&chromobius_dir)?;
@@ -67,21 +93,34 @@ pub fn build() -> Result<()> {
     // Generate amalgamated stim.h if needed
     build_stim::generate_amalgamated_header(&stim_dir)?;
 
-    // Build using cxx
-    build_cxx_bridge(&chromobius_dir, &stim_dir, &pymatching_dir)?;
+    // Build using cxx -- only chromobius and stim sources, NOT pymatching
+    build_cxx_bridge(
+        &chromobius_dir,
+        &stim_dir,
+        &pymatching_include,
+        &stim_include,
+        &stim_dir_for_header,
+        pymatching_lib_dir.as_deref(),
+    )?;
 
     Ok(())
 }
 
-fn build_cxx_bridge(chromobius_dir: &Path, stim_dir: &Path, pymatching_dir: &Path) -> Result<()> {
+fn build_cxx_bridge(
+    chromobius_dir: &Path,
+    stim_dir: &Path,
+    pymatching_include: &Path,
+    stim_include: &Path,
+    stim_dir_for_header: &Path,
+    pymatching_lib_dir: Option<&Path>,
+) -> Result<()> {
     let chromobius_src_dir = chromobius_dir.join("src");
     let stim_src_dir = stim_dir.join("src");
-    let pymatching_src_dir = pymatching_dir.join("src");
 
-    // Find essential source files
+    // Find essential source files -- only chromobius and stim, NOT pymatching.
+    // PyMatching objects come from pecos-pymatching (linked, not compiled here).
     let chromobius_files = collect_chromobius_sources(&chromobius_src_dir)?;
     let stim_files = build_stim::collect_stim_sources(&stim_src_dir);
-    let pymatching_files = collect_pymatching_sources(&pymatching_src_dir)?;
 
     // Build the cxx bridge first to generate headers
     let mut build = cxx_build::bridge("src/bridge.rs");
@@ -101,18 +140,17 @@ fn build_cxx_bridge(chromobius_dir: &Path, stim_dir: &Path, pymatching_dir: &Pat
         build.file(file);
     }
 
-    // Add PyMatching files
-    for file in pymatching_files {
-        build.file(file);
-    }
+    // PyMatching objects are provided by pecos-pymatching -- NOT compiled here.
+    // We only need headers for compilation, not source files.
 
     // Configure build
     build
         .std("c++20")
         .include(&chromobius_src_dir)
         .include(&stim_src_dir)
-        .include(stim_dir) // For amalgamated stim.h
-        .include(&pymatching_src_dir)
+        .include(stim_dir_for_header) // For amalgamated stim.h
+        .include(pymatching_include) // PyMatching headers (from pecos-pymatching)
+        .include(stim_include) // Stim headers
         .include("include")
         .include("src")
         .define("CHROMOBIUS_BRIDGE_EXPORTS", None);
@@ -173,6 +211,12 @@ fn build_cxx_bridge(chromobius_dir: &Path, stim_dir: &Path, pymatching_dir: &Pat
 
     build.compile("chromobius-bridge");
 
+    // Link against pecos-pymatching's compiled PyMatching objects
+    if let Some(lib_dir) = pymatching_lib_dir {
+        println!("cargo:rustc-link-search=native={}", lib_dir.display());
+        println!("cargo:rustc-link-lib=static=pymatching-bridge");
+    }
+
     // On macOS, link against the system C++ library
     if target.contains("darwin") {
         println!("cargo:rustc-link-search=native=/usr/lib");
@@ -193,19 +237,6 @@ fn collect_chromobius_sources(chromobius_src_dir: &Path) -> Result<Vec<PathBuf>>
     Ok(files)
 }
 
-fn collect_pymatching_sources(pymatching_src_dir: &Path) -> Result<Vec<PathBuf>> {
-    let mut files = Vec::new();
-
-    // PyMatching sparse_blossom implementation files
-    let sparse_blossom_dir = pymatching_src_dir.join("pymatching/sparse_blossom");
-    if sparse_blossom_dir.exists() {
-        collect_cc_files_filtered(&sparse_blossom_dir, &mut files)?;
-    }
-
-    info!("Found {} PyMatching source files", files.len());
-    Ok(files)
-}
-
 fn collect_cc_files_filtered(dir: &Path, files: &mut Vec<PathBuf>) -> Result<()> {
     for entry in fs::read_dir(dir)? {
         let entry = entry?;
diff --git a/crates/pecos-chromobius/pecos.toml b/crates/pecos-chromobius/pecos.toml
index 4c4f5c34d..0d19b9545 100644
--- a/crates/pecos-chromobius/pecos.toml
+++ b/crates/pecos-chromobius/pecos.toml
@@ -4,19 +4,16 @@
 version = 1
 
 [dependencies.chromobius]
-version = "35e289570fdc1d71e73582e1fd4e0c8e29298ef5"
-url = "https://github.com/quantumlib/chromobius/archive/35e289570fdc1d71e73582e1fd4e0c8e29298ef5.tar.gz"
-sha256 = "da73d819e67572065fd715db45fabb342c2a2a1e961d2609df4f9864b9836054"
+version = "acd09febcd6d4c9001b4d708507c8bfb10e4322e"
+url = "https://github.com/quantumlib/chromobius/archive/acd09febcd6d4c9001b4d708507c8bfb10e4322e.tar.gz"
+sha256 = "4aff65fbf3e5a4ed2974f9a48b772274ffa6129daa4b82bfc4182808cbe6360f"
 description = "Color code decoder"
 
-[dependencies.pymatching]
-version = "2b72b2c558eec678656da20ab6c358aa123fb664"
-url = "https://github.com/oscarhiggott/PyMatching/archive/2b72b2c558eec678656da20ab6c358aa123fb664.tar.gz"
-sha256 = "1470520b66ad7899f85020664aeeadfc6e2967f0b5e19ad205829968b845cd70"
-description = "MWPM decoder"
+# PyMatching is NOT downloaded here -- pecos-pymatching provides the compiled
+# objects and headers via cargo metadata (links = "pymatching-pecos").
 
 [dependencies.stim]
-version = "bd60b73525fd5a9b30839020eb7554ad369e4337"
-url = "https://github.com/quantumlib/Stim/archive/bd60b73525fd5a9b30839020eb7554ad369e4337.tar.gz"
-sha256 = "2a4be24295ce3018d79e08369b31e401a2d33cd8b3a75675d57dac3afd9de37d"
+version = "213275795e49027772bea7c610b6aac3a80583e1"
+url = "https://github.com/quantumlib/Stim/archive/213275795e49027772bea7c610b6aac3a80583e1.tar.gz"
+sha256 = "b63c4ae94494a8819d440757776cf80a829ec1e30454fa7c9b0f670e981938ab"
 description = "Stabilizer simulator for QEC"
diff --git a/crates/pecos-cli/src/cli.rs b/crates/pecos-cli/src/cli.rs
index f7e14a19f..7d2d5d2bf 100644
--- a/crates/pecos-cli/src/cli.rs
+++ b/crates/pecos-cli/src/cli.rs
@@ -11,6 +11,7 @@
 
 pub mod cuda_cmd;
 pub mod cuquantum_cmd;
+pub mod env_cmd;
 pub mod gpu_cmd;
 pub mod info;
 pub mod install_cmd;
diff --git a/crates/pecos-cli/src/cli/env_cmd.rs b/crates/pecos-cli/src/cli/env_cmd.rs
new file mode 100644
index 000000000..4f8007142
--- /dev/null
+++ b/crates/pecos-cli/src/cli/env_cmd.rs
@@ -0,0 +1,130 @@
+// Copyright 2026 The PECOS Developers
+//
+// Licensed under the Apache License, Version 2.0 (the "License"); you may not use this file except
+// in compliance with the License. You may obtain a copy of the License at
+//
+//     https://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software distributed under the License
+// is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express
+// or implied. See the License for the specific language governing permissions and limitations under
+// the License.
+
+//! Implementation of the `env` subcommand.
+//!
+//! Prints the build environment variables for the current platform. This is
+//! the single source of truth for platform-specific build configuration.
+//! CI workflows, Justfile recipes, and `pecos python build` should all derive
+//! their environment from this command.
+//!
+//! Usage:
+//!   eval $(pecos env)           # bash/zsh — set variables in current shell
+//!   pecos env --format json     # machine-readable output
+//!   pecos env --show            # human-readable display
+
+use std::collections::BTreeMap;
+use std::fmt::Write;
+
+/// Collect the build environment for the current platform.
+///
+/// Returns a map of environment variable names to values. Only includes
+/// variables that PECOS needs to set — does not duplicate the entire shell
+/// environment.
+pub fn collect_env() -> BTreeMap<String, String> {
+    let mut env = BTreeMap::new();
+
+    // LLVM
+    if let Some(llvm_path) = pecos_build::llvm::find_llvm_14(None) {
+        let llvm_str = llvm_path.display().to_string();
+        env.insert("LLVM_SYS_140_PREFIX".into(), llvm_str);
+
+        // Add LLVM bin to PATH
+        let bin_path = llvm_path.join("bin");
+        if bin_path.exists() {
+            let current_path = std::env::var("PATH").unwrap_or_default();
+            env.insert(
+                "PATH".into(),
+                format!("{}:{current_path}", bin_path.display()),
+            );
+        }
+    }
+
+    // macOS-specific
+    #[cfg(target_os = "macos")]
+    {
+        // SDKROOT — needed for bindgen/clang to find system headers
+        if std::env::var("SDKROOT").is_err()
+            && let Ok(output) = std::process::Command::new("xcrun")
+                .args(["--show-sdk-path"])
+                .output()
+            && output.status.success()
+        {
+            let sdk = String::from_utf8_lossy(&output.stdout).trim().to_string();
+            if !sdk.is_empty() {
+                env.insert("SDKROOT".into(), sdk);
+            }
+        }
+
+        // Deployment target
+        env.insert("MACOSX_DEPLOYMENT_TARGET".into(), "13.2".into());
+    }
+
+    // CUDA
+    if let Some(cuda_path) = pecos_build::cuda::find_cuda() {
+        env.insert("CUDA_PATH".into(), cuda_path.display().to_string());
+    }
+
+    // cuQuantum
+    if let Some(cuquantum_path) = pecos_build::cuquantum::find_cuquantum() {
+        env.insert(
+            "CUQUANTUM_ROOT".into(),
+            cuquantum_path.display().to_string(),
+        );
+    }
+
+    env
+}
+
+/// Print environment in shell-eval format: `export KEY="VALUE"`
+pub fn print_shell(env: &BTreeMap<String, String>) {
+    for (key, value) in env {
+        println!("export {key}=\"{value}\"");
+    }
+}
+
+/// Print environment in JSON format.
+pub fn print_json(env: &BTreeMap<String, String>) {
+    let mut out = String::from("{\n");
+    for (i, (key, value)) in env.iter().enumerate() {
+        let escaped = value.replace('\\', "\\\\").replace('"', "\\\"");
+        let _ = write!(out, "  \"{key}\": \"{escaped}\"");
+        if i + 1 < env.len() {
+            out.push(',');
+        }
+        out.push('\n');
+    }
+    out.push('}');
+    println!("{out}");
+}
+
+/// Print environment in human-readable format.
+pub fn print_show(env: &BTreeMap<String, String>) {
+    if env.is_empty() {
+        println!("No PECOS-specific environment variables needed.");
+        return;
+    }
+    println!("PECOS build environment:");
+    for (key, value) in env {
+        println!("  {key}={value}");
+    }
+}
+
+/// Run the env subcommand.
+pub fn run(format: &str) {
+    let env = collect_env();
+    match format {
+        "json" => print_json(&env),
+        "show" => print_show(&env),
+        _ => print_shell(&env),
+    }
+}
diff --git a/crates/pecos-cli/src/cli/python_cmd.rs b/crates/pecos-cli/src/cli/python_cmd.rs
index 565f6aa73..c37cac0ad 100644
--- a/crates/pecos-cli/src/cli/python_cmd.rs
+++ b/crates/pecos-cli/src/cli/python_cmd.rs
@@ -3,7 +3,7 @@
 use pecos_build::Result;
 use pecos_build::errors::Error;
 use std::fs;
-use std::path::PathBuf;
+use std::path::{Path, PathBuf};
 use std::process::Command;
 
 /// Run the python subcommand
@@ -118,6 +118,8 @@ fn run_build(profile: &str, rustflags: Option<&str>, cuda: bool) -> Result<()> {
             }
         );
 
+        remove_stale_extension_artifacts(&repo_root, profile, crate_name)?;
+
         let maturin = venv_bin.join("maturin");
         let mut cmd = Command::new(&maturin);
         cmd.args(["develop", "--uv"]);
@@ -149,6 +151,16 @@ fn run_build(profile: &str, rustflags: Option<&str>, cuda: bool) -> Result<()> {
             cmd.env("LIBRARY_PATH", "/usr/lib");
         }
 
+        // Apply PECOS build environment (SDKROOT, LLVM, CUDA, etc.)
+        // This is the single source of truth — same logic as `pecos env`.
+        let build_env = super::env_cmd::collect_env();
+        for (key, value) in &build_env {
+            // Don't override PATH — we already set it above with venv
+            if key != "PATH" {
+                cmd.env(key, value);
+            }
+        }
+
         let status = cmd.status();
         match status {
             Ok(s) if s.success() => {}
@@ -192,3 +204,112 @@ fn run_build(profile: &str, rustflags: Option<&str>, cuda: bool) -> Result<()> {
         ))),
     }
 }
+
+fn cargo_profile_dir(profile: &str) -> &'static str {
+    if matches!(profile, "release" | "native") {
+        "release"
+    } else {
+        "debug"
+    }
+}
+
+fn extension_library_filename(crate_name: &str) -> String {
+    let module_name = crate_name.replace('-', "_");
+
+    #[cfg(target_os = "windows")]
+    {
+        format!("{module_name}.dll")
+    }
+
+    #[cfg(target_os = "macos")]
+    {
+        format!("lib{module_name}.dylib")
+    }
+
+    #[cfg(all(unix, not(target_os = "macos")))]
+    {
+        format!("lib{module_name}.so")
+    }
+}
+
+fn extension_artifact_candidates(
+    repo_root: &Path,
+    profile: &str,
+    crate_name: &str,
+) -> [PathBuf; 3] {
+    let filename = extension_library_filename(crate_name);
+    let target_dir = repo_root.join("target");
+    let profile_dir = target_dir.join(cargo_profile_dir(profile));
+
+    [
+        profile_dir.join(&filename),
+        profile_dir.join("deps").join(&filename),
+        target_dir.join("maturin").join(&filename),
+    ]
+}
+
+fn remove_stale_extension_artifacts(
+    repo_root: &Path,
+    profile: &str,
+    crate_name: &str,
+) -> Result<()> {
+    let [profile_artifact, deps_artifact, maturin_staging_artifact] =
+        extension_artifact_candidates(repo_root, profile, crate_name);
+
+    for path in [profile_artifact, deps_artifact] {
+        match fs::metadata(&path) {
+            Ok(metadata) if metadata.is_file() && metadata.len() == 0 => {
+                println!(
+                    "Removing zero-byte extension artifact before rebuild: {}",
+                    path.display()
+                );
+                fs::remove_file(path)?;
+            }
+            Ok(_) => {}
+            Err(err) if err.kind() == std::io::ErrorKind::NotFound => {}
+            Err(err) => return Err(err.into()),
+        }
+    }
+
+    match fs::metadata(&maturin_staging_artifact) {
+        Ok(metadata) if metadata.is_file() => {
+            println!(
+                "Removing stale maturin staging artifact before rebuild: {}",
+                maturin_staging_artifact.display()
+            );
+            fs::remove_file(maturin_staging_artifact)?;
+        }
+        Ok(_) => {}
+        Err(err) if err.kind() == std::io::ErrorKind::NotFound => {}
+        Err(err) => return Err(err.into()),
+    }
+
+    Ok(())
+}
+
+#[cfg(test)]
+mod tests {
+    use super::*;
+
+    #[test]
+    fn cargo_profile_dir_maps_native_to_release() {
+        assert_eq!(cargo_profile_dir("debug"), "debug");
+        assert_eq!(cargo_profile_dir("release"), "release");
+        assert_eq!(cargo_profile_dir("native"), "release");
+    }
+
+    #[test]
+    fn extension_artifact_candidates_use_python_module_name() {
+        let repo = PathBuf::from("/repo");
+        let candidates = extension_artifact_candidates(&repo, "debug", "pecos-rslib-llvm");
+        let filename = extension_library_filename("pecos-rslib-llvm");
+
+        assert!(filename.contains("pecos_rslib_llvm"));
+        assert_eq!(candidates[0], repo.join("target/debug").join(&filename));
+        assert_eq!(
+            candidates[1],
+            repo.join("target/debug/deps").join(&filename)
+        );
+        assert_eq!(candidates[2], repo.join("target/maturin").join(&filename));
+    }
+}
diff --git a/crates/pecos-cli/src/cli/rust_cmd.rs b/crates/pecos-cli/src/cli/rust_cmd.rs
index 8cfbbaec3..a891d97f7 100644
--- a/crates/pecos-cli/src/cli/rust_cmd.rs
+++ b/crates/pecos-cli/src/cli/rust_cmd.rs
@@ -373,6 +373,8 @@ fn run_test(release: bool, include_ffi: bool) -> Result<()> {
     println!("Testing workspace packages...");
     // runtime = sim + qasm + phir (format parsers)
     // hugr = qis (includes llvm) + hugr compilation
+    // pecos-cli is excluded here and tested separately below with --features=runtime
+    // to ensure the pecos binary has PHIR/QIS support for integration tests.
     let mut args: Vec<&str> = vec!["test", "--workspace", "--features=runtime,hugr"];
 
     for crate_name in FFI_CRATES {
@@ -384,6 +386,8 @@ fn run_test(release: bool, include_ffi: bool) -> Result<()> {
         "--exclude",
         "pecos-cuquantum", // Requires cuQuantum SDK, test separately if available
         "--exclude",
+        "pecos-cli", // Test separately with --features=runtime (see below)
+        "--exclude",
         "pecos-decoders",
         "--exclude",
         "pecos-gpu-sims", // Always exclude from workspace test, test separately if GPU available
@@ -397,6 +401,22 @@ fn run_test(release: bool, include_ffi: bool) -> Result<()> {
         return Err(Error::Config("cargo test (workspace) failed".to_string()));
     }
 
+    // Test pecos-cli separately with --features=runtime.
+    // cargo test --workspace --features=runtime overwrites the pecos binary
+    // WITHOUT runtime features (cargo feature unification bug), so the CLI
+    // integration tests that invoke `cargo_bin!("pecos")` would get a broken
+    // binary. Testing separately ensures the binary is built correctly.
+    println!("Testing pecos-cli with runtime features...");
+    let mut cli_args: Vec<&str> = vec!["test", "-p", "pecos-cli", "--features=runtime"];
+    if !release_flag.is_empty() {
+        cli_args.push(release_flag);
+    }
+    if !run_cargo_command(&cli_args) {
+        return Err(Error::Config(
+            "cargo test (pecos-cli with runtime) failed".to_string(),
+        ));
+    }
+
     // Test cuQuantum if SDK is available (requires both CUDA and cuQuantum)
     if probe_cuquantum_availability() {
         println!("cuQuantum runtime available - testing pecos-cuquantum");
diff --git a/crates/pecos-cli/src/main.rs b/crates/pecos-cli/src/main.rs
index 3e58d5619..27f203b7e 100644
--- a/crates/pecos-cli/src/main.rs
+++ b/crates/pecos-cli/src/main.rs
@@ -112,6 +112,21 @@ enum Commands {
         #[command(subcommand)]
         command: DepsCommands,
     },
+    /// Print build environment variables for the current platform
+    ///
+    /// Use `eval $(pecos env)` in bash/zsh to set variables in the current
+    /// shell. All platform-specific build configuration (LLVM paths, SDKROOT,
+    /// CUDA, cuQuantum) is detected and printed.
+    ///
+    /// Example: eval $(pecos env)
+    /// Example: pecos env --format show
+    /// Example: pecos env --format json
+    Env {
+        /// Output format: shell (default), json, show
+        #[arg(long, default_value = "shell")]
+        format: String,
+    },
+
     /// Set up build environment (detect and install missing dependencies)
     ///
     /// Interactively checks for LLVM, CUDA, and cuQuantum and offers to
@@ -677,6 +692,7 @@ fn main() -> Result<(), Box<dyn std::error::Error>> {
         Commands::Llvm { command } => cli::llvm_cmd::run(command.clone())?,
         Commands::Selene { command } => cli::selene_cmd::run(command.clone())?,
         Commands::Deps { command } => cli::manifest_cmd::run(command.clone())?,
+        Commands::Env { format } => cli::env_cmd::run(format),
         Commands::Setup {
             yes,
             no,
diff --git a/crates/pecos-core/src/channel.rs b/crates/pecos-core/src/channel.rs
new file mode 100644
index 000000000..8109b0766
--- /dev/null
+++ b/crates/pecos-core/src/channel.rs
@@ -0,0 +1,322 @@
+// Copyright 2026 The PECOS Developers
+//
+// Licensed under the Apache License, Version 2.0 (the "License"); you may not use this file except
+// in compliance with the License.You may obtain a copy of the License at
+//
+//     https://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software distributed under the License
+// is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express
+// or implied. See the License for the specific language governing permissions and limitations under
+// the License.
+
+//! Symbolic quantum-channel namespace.
+//!
+//! Constructors in this module return [`ChannelExpr`]. Use this namespace for
+//! physical noise, open-system maps, and other CPTP processes:
+//!
+//! ```
+//! use pecos_core::channel::*;
+//!
+//! let noise = Depolarizing(0.001, 0) & BitFlip(0.01, 1);
+//! ```
+//!
+//! Ideal gates can be lifted into this level with [`from_gate`]. Unitary
+//! operations and ideal gates are not noise, but they are valid channels when a
+//! channel-level expression is needed.
+
+use crate::op::Op;
+use crate::qubit_support::overlapping_qubits;
+use crate::{GateExpr, PauliString, QubitId, UnitaryRep, op};
+use std::ops::{BitAnd, Mul};
+
+pub use crate::op::ChannelExpr;
+
+fn channel_from_op(op: Op) -> ChannelExpr {
+    op.into_channel()
+}
+
+/// Lifts a unitary expression to the channel level.
+#[must_use]
+pub fn from_unitary(unitary: impl Into<UnitaryRep>) -> ChannelExpr {
+    ChannelExpr::Unitary(unitary.into())
+}
+
+/// Lifts an ideal gate expression to the channel level.
+#[must_use]
+pub fn from_gate(gate: impl Into<GateExpr>) -> ChannelExpr {
+    ChannelExpr::Gate(gate.into())
+}
+
+impl From<UnitaryRep> for ChannelExpr {
+    fn from(unitary: UnitaryRep) -> Self {
+        ChannelExpr::Unitary(unitary)
+    }
+}
+
+impl From<PauliString> for ChannelExpr {
+    fn from(pauli: PauliString) -> Self {
+        ChannelExpr::Unitary(UnitaryRep::from(pauli))
+    }
+}
+
+impl From<GateExpr> for ChannelExpr {
+    fn from(gate: GateExpr) -> Self {
+        ChannelExpr::Gate(gate)
+    }
+}
+
+/// Single-qubit depolarizing channel.
+#[allow(non_snake_case)]
+#[must_use]
+pub fn Depolarizing(p: f64, qubit: impl Into<QubitId>) -> ChannelExpr {
+    channel_from_op(op::Depolarizing(p, qubit))
+}
+
+/// Dephasing channel.
+#[allow(non_snake_case)]
+#[must_use]
+pub fn Dephasing(p: f64, qubit: impl Into<QubitId>) -> ChannelExpr {
+    channel_from_op(op::Dephasing(p, qubit))
+}
+
+/// Bit-flip channel.
+#[allow(non_snake_case)]
+#[must_use]
+pub fn BitFlip(p: f64, qubit: impl Into<QubitId>) -> ChannelExpr {
+    channel_from_op(op::BitFlip(p, qubit))
+}
+
+/// Bit-phase-flip channel.
+#[allow(non_snake_case)]
+#[must_use]
+pub fn BitPhaseFlip(p: f64, qubit: impl Into<QubitId>) -> ChannelExpr {
+    channel_from_op(op::BitPhaseFlip(p, qubit))
+}
+
+/// General single-qubit Pauli channel.
+#[allow(non_snake_case)]
+#[must_use]
+pub fn PauliChannel(px: f64, py: f64, pz: f64, qubit: impl Into<QubitId>) -> ChannelExpr {
+    channel_from_op(op::PauliChannel(px, py, pz, qubit))
+}
+
+/// Two-qubit depolarizing channel.
+#[allow(non_snake_case)]
+#[must_use]
+pub fn Depolarizing2(p: f64, q0: impl Into<QubitId>, q1: impl Into<QubitId>) -> ChannelExpr {
+    channel_from_op(op::Depolarizing2(p, q0, q1))
+}
+
+/// Amplitude damping channel.
+#[allow(non_snake_case)]
+#[must_use]
+pub fn AmplitudeDamping(gamma: f64, qubit: impl Into<QubitId>) -> ChannelExpr {
+    channel_from_op(op::AmplitudeDamping(gamma, qubit))
+}
+
+/// Phase damping channel.
+#[allow(non_snake_case)]
+#[must_use]
+pub fn PhaseDamping(lambda: f64, qubit: impl Into<QubitId>) -> ChannelExpr {
+    channel_from_op(op::PhaseDamping(lambda, qubit))
+}
+
+/// Erasure channel.
+#[allow(non_snake_case)]
+#[must_use]
+pub fn Erasure(prob: f64, qubit: impl Into<QubitId>) -> ChannelExpr {
+    channel_from_op(op::Erasure(prob, qubit))
+}
+
+/// Leakage channel.
+#[allow(non_snake_case)]
+#[must_use]
+pub fn Leakage(rate: f64, qubit: impl Into<QubitId>) -> ChannelExpr {
+    channel_from_op(op::Leakage(rate, qubit))
+}
+
+impl BitAnd for ChannelExpr {
+    type Output = ChannelExpr;
+
+    fn bitand(self, rhs: ChannelExpr) -> ChannelExpr {
+        let overlap = overlapping_qubits(self.qubits(), rhs.qubits());
+        assert!(
+            overlap.is_empty(),
+            "tensor product requires disjoint channel support; overlapping qubits: {overlap:?}"
+        );
+        ChannelExpr::Tensor(vec![self, rhs])
+    }
+}
+
+impl BitAnd<&ChannelExpr> for ChannelExpr {
+    type Output = ChannelExpr;
+
+    fn bitand(self, rhs: &ChannelExpr) -> ChannelExpr {
+        self & rhs.clone()
+    }
+}
+
+impl BitAnd<ChannelExpr> for &ChannelExpr {
+    type Output = ChannelExpr;
+
+    fn bitand(self, rhs: ChannelExpr) -> ChannelExpr {
+        self.clone() & rhs
+    }
+}
+
+impl BitAnd<&ChannelExpr> for &ChannelExpr {
+    type Output = ChannelExpr;
+
+    fn bitand(self, rhs: &ChannelExpr) -> ChannelExpr {
+        self.clone() & rhs.clone()
+    }
+}
+
+impl BitAnd<GateExpr> for ChannelExpr {
+    type Output = ChannelExpr;
+
+    fn bitand(self, rhs: GateExpr) -> ChannelExpr {
+        self & ChannelExpr::Gate(rhs)
+    }
+}
+
+impl BitAnd<ChannelExpr> for GateExpr {
+    type Output = ChannelExpr;
+
+    fn bitand(self, rhs: ChannelExpr) -> ChannelExpr {
+        ChannelExpr::Gate(self) & rhs
+    }
+}
+
+impl Mul for ChannelExpr {
+    type Output = ChannelExpr;
+
+    fn mul(self, rhs: ChannelExpr) -> ChannelExpr {
+        ChannelExpr::Compose(vec![self, rhs])
+    }
+}
+
+impl Mul<&ChannelExpr> for ChannelExpr {
+    type Output = ChannelExpr;
+
+    fn mul(self, rhs: &ChannelExpr) -> ChannelExpr {
+        self * rhs.clone()
+    }
+}
+
+impl Mul<ChannelExpr> for &ChannelExpr {
+    type Output = ChannelExpr;
+
+    fn mul(self, rhs: ChannelExpr) -> ChannelExpr {
+        self.clone() * rhs
+    }
+}
+
+impl Mul<&ChannelExpr> for &ChannelExpr {
+    type Output = ChannelExpr;
+
+    fn mul(self, rhs: &ChannelExpr) -> ChannelExpr {
+        self.clone() * rhs.clone()
+    }
+}
+
+impl Mul<GateExpr> for ChannelExpr {
+    type Output = ChannelExpr;
+
+    fn mul(self, rhs: GateExpr) -> ChannelExpr {
+        self * ChannelExpr::Gate(rhs)
+    }
+}
+
+impl Mul<ChannelExpr> for GateExpr {
+    type Output = ChannelExpr;
+
+    fn mul(self, rhs: ChannelExpr) -> ChannelExpr {
+        ChannelExpr::Gate(self) * rhs
+    }
+}
+
+#[cfg(test)]
+mod tests {
+    use super::*;
+    use crate::gate;
+
+    #[test]
+    fn noise_constructors_return_channel_expr() {
+        assert!(matches!(Depolarizing(0.1, 0), ChannelExpr::MixedUnitary(_)));
+        assert!(matches!(Dephasing(0.1, 0), ChannelExpr::MixedUnitary(_)));
+        assert!(matches!(BitFlip(0.1, 0), ChannelExpr::MixedUnitary(_)));
+        assert!(matches!(BitPhaseFlip(0.1, 0), ChannelExpr::MixedUnitary(_)));
+        assert!(matches!(
+            PauliChannel(0.1, 0.2, 0.3, 0),
+            ChannelExpr::MixedUnitary(_)
+        ));
+        assert!(matches!(
+            Depolarizing2(0.1, 0, 1),
+            ChannelExpr::MixedUnitary(_)
+        ));
+        assert!(matches!(
+            AmplitudeDamping(0.1, 0),
+            ChannelExpr::AmplitudeDamping { .. }
+        ));
+        assert!(matches!(
+            PhaseDamping(0.1, 0),
+            ChannelExpr::PhaseDamping { .. }
+        ));
+        assert!(matches!(Erasure(0.1, 0), ChannelExpr::Erasure { .. }));
+        assert!(matches!(Leakage(0.1, 0), ChannelExpr::Leakage { .. }));
+    }
+
+    #[test]
+    #[should_panic(expected = "Depolarizing2 requires distinct qubits")]
+    fn channel_namespace_two_qubit_channel_rejects_repeated_qubit() {
+        let _ = Depolarizing2(0.1, 0, 0);
+    }
+
+    #[test]
+    fn ideal_gate_lifts_to_channel_expr() {
+        let channel = from_gate(gate::MZ(0));
+        assert!(matches!(
+            channel,
+            ChannelExpr::Gate(GateExpr::Measure { .. })
+        ));
+    }
+
+    #[test]
+    fn channel_tensor_and_composition_stay_channel_level() {
+        let tensor = Depolarizing(0.1, 0) & BitFlip(0.2, 1);
+        assert!(matches!(tensor, ChannelExpr::Tensor(parts) if parts.len() == 2));
+
+        let sequence = AmplitudeDamping(0.1, 0) * PhaseDamping(0.2, 0);
+        assert!(matches!(sequence, ChannelExpr::Compose(parts) if parts.len() == 2));
+    }
+
+    #[test]
+    #[should_panic(expected = "tensor product requires disjoint channel support")]
+    fn channel_tensor_rejects_overlapping_qubits() {
+        let _ = Depolarizing(0.1, 0) & BitFlip(0.2, 0);
+    }
+
+    #[test]
+    #[should_panic(expected = "tensor product requires disjoint channel support")]
+    fn channel_tensor_rejects_partial_overlap_with_multi_qubit_support() {
+        let _ = Depolarizing2(0.1, 0, 2) & BitFlip(0.2, 2);
+    }
+
+    #[test]
+    fn channel_tensor_uses_sparse_support_not_dense_span() {
+        let tensor = Depolarizing2(0.1, 0, 2) & BitFlip(0.2, 1);
+        assert!(matches!(tensor, ChannelExpr::Tensor(ref parts) if parts.len() == 2));
+        assert_eq!(tensor.qubits(), vec![0, 1, 2]);
+    }
+
+    #[test]
+    fn gate_channel_combinations_promote_to_channel_level() {
+        let tensor = gate::H(0) & Depolarizing(0.1, 1);
+        assert!(matches!(tensor, ChannelExpr::Tensor(parts) if parts.len() == 2));
+
+        let sequence = Depolarizing(0.1, 0) * gate::MZ(0);
+        assert!(matches!(sequence, ChannelExpr::Compose(parts) if parts.len() == 2));
+    }
+}
diff --git a/crates/pecos-core/src/clifford.rs b/crates/pecos-core/src/clifford.rs
index cd767989e..a92cd72f3 100644
--- a/crates/pecos-core/src/clifford.rs
+++ b/crates/pecos-core/src/clifford.rs
@@ -10,36 +10,37 @@
 // or implied. See the License for the specific language governing permissions and limitations under
 // the License.
 
-//! Named Clifford gate primitives.
+//! Clifford gate namespace.
 //!
-//! The base Clifford gates (single-qubit and two-qubit), analogous to [`Pauli`]
-//! for the Pauli group. The 24 single-qubit elements form a closed group with
-//! fast composition via lookup. Two-qubit gates are the standard entangling primitives.
-//!
-//! # Example
+//! This module provides the [`Clifford`] enum (named gate primitives) and
+//! re-exports [`CliffordRep`] with free constructors for the Heisenberg-picture
+//! representation. Use `use pecos_core::clifford::*` for Clifford-level work:
 //!
 //! ```
-//! use pecos_core::clifford::Clifford;
-//! use pecos_core::Pauli;
-//! use pecos_core::Sign;
+//! use pecos_core::clifford::*;
 //!
-//! let h = Clifford::H;
-//! let (sign, p) = h.conjugate(Pauli::X);
-//! assert_eq!(p, Pauli::Z);
-//! assert_eq!(sign, Sign::PlusOne);
+//! // Constructors return CliffordRep (composable Heisenberg-picture gates)
+//! let layer = CX(0, 1) * H(0);
 //!
-//! // Two-qubit gates
-//! let cx_rep = Clifford::CX.on_qubits(0, 1);
-//! assert!(cx_rep.is_valid());
+//! // The Clifford enum provides named gate primitives with Pauli conjugation
+//! let h = Clifford::H;
+//! let (sign, p) = h.conjugate(pecos_core::Pauli::X);
+//! assert_eq!(p, pecos_core::Pauli::Z);
 //! ```
 
-use crate::clifford_rep::CliffordRep;
 use crate::gate_type::GateType;
 use crate::unitary_rep::UnitaryRep;
 use crate::{Angle64, Pauli, QubitId, Sign};
 use std::fmt;
 use std::ops::Mul;
 
+// Re-export CliffordRep and its constructors so `use pecos_core::clifford::*` works.
+pub use crate::clifford_rep::CliffordRep;
+pub use crate::clifford_rep::constructors::{
+    CX, CY, CZ, F, F2, F2dg, F3, F3dg, F4, F4dg, Fdg, G, Gdg, H, H2, H3, H4, H5, H6, ISWAP,
+    ISWAPdg, Id, SWAP, SX, SXX, SXXdg, SXdg, SY, SYY, SYYdg, SYdg, SZ, SZZ, SZZdg, SZdg,
+};
+
 /// Named Clifford gate primitive.
 ///
 /// Includes all 24 single-qubit Clifford gates and the standard two-qubit gates.
@@ -984,6 +985,12 @@ mod tests {
         }
     }
 
+    #[test]
+    #[should_panic(expected = "SWAP requires distinct qubits")]
+    fn test_2q_on_qubits_rejects_repeated_qubit() {
+        let _ = Clifford::SWAP.on_qubits(0, 0);
+    }
+
     #[test]
     fn test_on_qubits_noncontiguous() {
         let rep = Clifford::CX.on_qubits(0, 3);
diff --git a/crates/pecos-core/src/clifford_rep.rs b/crates/pecos-core/src/clifford_rep.rs
index f65e428b7..efb7bb4f5 100644
--- a/crates/pecos-core/src/clifford_rep.rs
+++ b/crates/pecos-core/src/clifford_rep.rs
@@ -19,7 +19,7 @@
 //!
 //! ```
 //! use pecos_core::clifford_rep::CliffordRep;
-//! use pecos_core::unitary_rep::{X, Z};
+//! use pecos_core::unitary::{X, Z};
 //!
 //! // Hadamard swaps X <-> Z
 //! let h = CliffordRep::h(0);
@@ -29,6 +29,7 @@
 //! ```
 
 use crate::pauli::algebra::i;
+use crate::qubit_support::{assert_distinct_qubits, overlapping_qubits};
 use crate::unitary_rep::UnitaryRep;
 use crate::{Pauli, PauliString, Phase, QuarterPhase};
 use rand::RngExt;
@@ -70,6 +71,27 @@ impl CliffordRep {
         self.num_qubits
     }
 
+    /// Returns qubits where this Clifford acts non-trivially.
+    ///
+    /// This is the operator support, not the tableau span. Identity action on
+    /// spectator qubits is omitted.
+    #[must_use]
+    pub fn support_qubits(&self) -> Vec<usize> {
+        let mut support = Vec::new();
+        for q in 0..self.num_qubits {
+            let x_image = self.x_image(q);
+            let z_image = self.z_image(q);
+            if *x_image != PauliString::x(q) || *z_image != PauliString::z(q) {
+                support.push(q);
+                support.extend(x_image.qubits());
+                support.extend(z_image.qubits());
+            }
+        }
+        support.sort_unstable();
+        support.dedup();
+        support
+    }
+
     /// Returns how X on the given qubit transforms.
     #[must_use]
     pub fn x_image(&self, qubit: usize) -> &PauliString {
@@ -186,7 +208,7 @@ impl CliffordRep {
     ///
     /// ```
     /// use pecos_core::clifford_rep::CliffordRep;
-    /// use pecos_core::unitary_rep::{X, Z};
+    /// use pecos_core::unitary::{X, Z};
     ///
     /// let h = CliffordRep::h(0);
     /// let stabilizer = X(0) & Z(1);
@@ -551,6 +573,7 @@ impl CliffordRep {
     ///     `X_t` -> `X_t`,     `Z_t` -> `Z_c` `Z_t`
     #[must_use]
     pub fn cx(control: usize, target: usize) -> Self {
+        assert_distinct_qubits("CX", [control, target]);
         let num_qubits = control.max(target) + 1;
         let mut cliff = Self::identity(num_qubits);
 
@@ -569,6 +592,7 @@ impl CliffordRep {
     ///     `X_1` -> `Z_0` `X_1`, `Z_1` -> `Z_1`
     #[must_use]
     pub fn cz(q0: usize, q1: usize) -> Self {
+        assert_distinct_qubits("CZ", [q0, q1]);
         let num_qubits = q0.max(q1) + 1;
         let mut cliff = Self::identity(num_qubits);
 
@@ -587,6 +611,7 @@ impl CliffordRep {
     ///       `X_1` -> `X_0`, `Z_1` -> `Z_0`
     #[must_use]
     pub fn swap(q0: usize, q1: usize) -> Self {
+        assert_distinct_qubits("SWAP", [q0, q1]);
         let num_qubits = q0.max(q1) + 1;
         let mut cliff = Self::identity(num_qubits);
 
@@ -606,6 +631,7 @@ impl CliffordRep {
     ///     `X_t` -> `Z_c` `X_t`, `Z_t` -> `Z_c` `Z_t`
     #[must_use]
     pub fn cy(control: usize, target: usize) -> Self {
+        assert_distinct_qubits("CY", [control, target]);
         let num_qubits = control.max(target) + 1;
         let mut cliff = Self::identity(num_qubits);
 
@@ -624,6 +650,7 @@ impl CliffordRep {
     /// SXX gate (sqrt XX): XI -> XI, IX -> IX, ZI -> -YX, IZ -> -XY
     #[must_use]
     pub fn sxx(q0: usize, q1: usize) -> Self {
+        assert_distinct_qubits("SXX", [q0, q1]);
         let num_qubits = q0.max(q1) + 1;
         let mut cliff = Self::identity(num_qubits);
         cliff.z_images[q0] = -(PauliString::y(q0) & PauliString::x(q1));
@@ -634,6 +661,7 @@ impl CliffordRep {
     /// SXX† gate: XI -> XI, IX -> IX, ZI -> YX, IZ -> XY
     #[must_use]
     pub fn sxxdg(q0: usize, q1: usize) -> Self {
+        assert_distinct_qubits("SXXdg", [q0, q1]);
         let num_qubits = q0.max(q1) + 1;
         let mut cliff = Self::identity(num_qubits);
         cliff.z_images[q0] = PauliString::y(q0) & PauliString::x(q1);
@@ -644,6 +672,7 @@ impl CliffordRep {
     /// SYY gate (sqrt YY): XI -> -ZY, IX -> -YZ, ZI -> XY, IZ -> YX
     #[must_use]
     pub fn syy(q0: usize, q1: usize) -> Self {
+        assert_distinct_qubits("SYY", [q0, q1]);
         let num_qubits = q0.max(q1) + 1;
         let mut cliff = Self::identity(num_qubits);
         cliff.x_images[q0] = -(PauliString::z(q0) & PauliString::y(q1));
@@ -656,6 +685,7 @@ impl CliffordRep {
     /// SYY† gate: XI -> ZY, IX -> YZ, ZI -> -XY, IZ -> -YX
     #[must_use]
     pub fn syydg(q0: usize, q1: usize) -> Self {
+        assert_distinct_qubits("SYYdg", [q0, q1]);
         let num_qubits = q0.max(q1) + 1;
         let mut cliff = Self::identity(num_qubits);
         cliff.x_images[q0] = PauliString::z(q0) & PauliString::y(q1);
@@ -668,6 +698,7 @@ impl CliffordRep {
     /// SZZ gate (sqrt ZZ): XI -> YZ, IX -> ZY, ZI -> ZI, IZ -> IZ
     #[must_use]
     pub fn szz(q0: usize, q1: usize) -> Self {
+        assert_distinct_qubits("SZZ", [q0, q1]);
         let num_qubits = q0.max(q1) + 1;
         let mut cliff = Self::identity(num_qubits);
         cliff.x_images[q0] = PauliString::y(q0) & PauliString::z(q1);
@@ -678,6 +709,7 @@ impl CliffordRep {
     /// SZZ† gate: XI -> -YZ, IX -> -ZY, ZI -> ZI, IZ -> IZ
     #[must_use]
     pub fn szzdg(q0: usize, q1: usize) -> Self {
+        assert_distinct_qubits("SZZdg", [q0, q1]);
         let num_qubits = q0.max(q1) + 1;
         let mut cliff = Self::identity(num_qubits);
         cliff.x_images[q0] = -(PauliString::y(q0) & PauliString::z(q1));
@@ -688,6 +720,7 @@ impl CliffordRep {
     /// iSWAP gate: XI -> ZY, IX -> YZ, ZI -> IZ, IZ -> ZI
     #[must_use]
     pub fn iswap(q0: usize, q1: usize) -> Self {
+        assert_distinct_qubits("ISWAP", [q0, q1]);
         let num_qubits = q0.max(q1) + 1;
         let mut cliff = Self::identity(num_qubits);
         cliff.x_images[q0] = PauliString::z(q0) & PauliString::y(q1);
@@ -700,6 +733,7 @@ impl CliffordRep {
     /// G gate: XI -> IX, IX -> XI, ZI -> XZ, IZ -> ZX
     #[must_use]
     pub fn g(q0: usize, q1: usize) -> Self {
+        assert_distinct_qubits("G", [q0, q1]);
         let num_qubits = q0.max(q1) + 1;
         let mut cliff = Self::identity(num_qubits);
         cliff.x_images[q0] = PauliString::x(q1);
@@ -714,6 +748,7 @@ impl CliffordRep {
     /// Both X images have opposite signs from iSWAP (the Z images are the same).
     #[must_use]
     pub fn iswapdg(q0: usize, q1: usize) -> Self {
+        assert_distinct_qubits("ISWAPdg", [q0, q1]);
         let num_qubits = q0.max(q1) + 1;
         let mut cliff = Self::identity(num_qubits);
         cliff.x_images[q0] = -(PauliString::z(q0) & PauliString::y(q1));
@@ -889,11 +924,22 @@ impl Mul<&CliffordRep> for &CliffordRep {
 
 // --- BitAnd trait: & operator for tensor product ---
 
+fn assert_disjoint_clifford_support(lhs: &CliffordRep, rhs: &CliffordRep) {
+    let lhs_support = lhs.support_qubits();
+    let rhs_support = rhs.support_qubits();
+    let overlap = overlapping_qubits(lhs_support, rhs_support);
+    assert!(
+        overlap.is_empty(),
+        "tensor product requires disjoint Clifford support; overlapping qubits: {overlap:?}"
+    );
+}
+
 impl BitAnd for CliffordRep {
     type Output = CliffordRep;
 
     /// Tensor product of two `CliffordReps` acting on disjoint qubits.
     fn bitand(self, rhs: CliffordRep) -> CliffordRep {
+        assert_disjoint_clifford_support(&self, &rhs);
         // Since compose auto-extends with identity on extra qubits,
         // and these CliffordReps act on disjoint qubits, composing gives the tensor.
         self.compose(&rhs)
@@ -904,6 +950,7 @@ impl BitAnd<&CliffordRep> for CliffordRep {
     type Output = CliffordRep;
 
     fn bitand(self, rhs: &CliffordRep) -> CliffordRep {
+        assert_disjoint_clifford_support(&self, rhs);
         self.compose(rhs)
     }
 }
@@ -912,6 +959,7 @@ impl BitAnd<CliffordRep> for &CliffordRep {
     type Output = CliffordRep;
 
     fn bitand(self, rhs: CliffordRep) -> CliffordRep {
+        assert_disjoint_clifford_support(self, &rhs);
         self.compose(&rhs)
     }
 }
@@ -920,6 +968,7 @@ impl BitAnd<&CliffordRep> for &CliffordRep {
     type Output = CliffordRep;
 
     fn bitand(self, rhs: &CliffordRep) -> CliffordRep {
+        assert_disjoint_clifford_support(self, rhs);
         self.compose(rhs)
     }
 }
@@ -981,13 +1030,13 @@ impl From<&PauliString> for CliffordRep {
 
 /// Free-standing constructor functions for Clifford gates.
 ///
-/// These mirror the `pecos_core::pauli::constructors` module, providing
-/// ergonomic gate creation and composition via the `*` operator.
+/// These are re-exported through `pecos_core::clifford`, providing ergonomic
+/// gate creation and composition via the `*` operator.
 ///
 /// # Examples
 ///
 /// ```
-/// use pecos_core::clifford_rep::constructors::*;
+/// use pecos_core::clifford::*;
 ///
 /// // H * SZ * H = SX (sqrt-X)
 /// let sx = H(0) * SZ(0) * H(0);
@@ -1879,6 +1928,61 @@ mod tests {
         assert_eq!(cliff.apply(&z1), composed.apply(&z1));
     }
 
+    #[test]
+    fn clifford_tensor_accepts_disjoint_support() {
+        let tensor = CliffordRep::h(0) & CliffordRep::sz(1);
+
+        assert_eq!(tensor.apply(&PauliString::x(0)), PauliString::z(0));
+        assert_eq!(tensor.apply(&PauliString::z(0)), PauliString::x(0));
+        assert_eq!(tensor.apply(&PauliString::x(1)), PauliString::y(1));
+        assert_eq!(tensor.apply(&PauliString::z(1)), PauliString::z(1));
+    }
+
+    #[test]
+    #[should_panic(expected = "tensor product requires disjoint Clifford support")]
+    fn clifford_tensor_rejects_overlapping_support() {
+        let _ = CliffordRep::h(0) & CliffordRep::sz(0);
+    }
+
+    #[test]
+    fn support_qubits_omits_identity_spectators() {
+        assert!(CliffordRep::identity(10).support_qubits().is_empty());
+        assert_eq!(CliffordRep::h(3).extended_to(10).support_qubits(), vec![3]);
+        assert_eq!(
+            CliffordRep::cx(0, 2).extended_to(5).support_qubits(),
+            vec![0, 2]
+        );
+    }
+
+    #[test]
+    fn clifford_tensor_accepts_interleaved_disjoint_support() {
+        let tensor = CliffordRep::cx(0, 2) & CliffordRep::h(1);
+
+        assert!(tensor.is_valid());
+        assert_eq!(tensor.support_qubits(), vec![0, 1, 2]);
+        assert_eq!(
+            tensor.apply(&PauliString::x(0)),
+            PauliString::x(0) & PauliString::x(2)
+        );
+        assert_eq!(
+            tensor.apply(&PauliString::z(2)),
+            PauliString::z(0) & PauliString::z(2)
+        );
+        assert_eq!(tensor.apply(&PauliString::x(1)), PauliString::z(1));
+    }
+
+    #[test]
+    #[should_panic(expected = "tensor product requires disjoint Clifford support")]
+    fn clifford_tensor_rejects_nonadjacent_partial_overlap() {
+        let _ = CliffordRep::cx(0, 2) & CliffordRep::z(2);
+    }
+
+    #[test]
+    #[should_panic(expected = "SWAP requires distinct qubits")]
+    fn clifford_two_qubit_gate_rejects_repeated_qubit() {
+        let _ = CliffordRep::swap(2, 2);
+    }
+
     #[test]
     fn test_clifford_enum_on_qubit() {
         use crate::clifford::Clifford;
diff --git a/crates/pecos-core/src/gate.rs b/crates/pecos-core/src/gate.rs
new file mode 100644
index 000000000..985c0cff3
--- /dev/null
+++ b/crates/pecos-core/src/gate.rs
@@ -0,0 +1,553 @@
+// Copyright 2026 The PECOS Developers
+//
+// Licensed under the Apache License, Version 2.0 (the "License"); you may not use this file except
+// in compliance with the License.You may obtain a copy of the License at
+//
+//     https://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software distributed under the License
+// is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express
+// or implied. See the License for the specific language governing permissions and limitations under
+// the License.
+
+//! Ideal circuit-operation namespace.
+//!
+//! Constructors in this module return [`GateExpr`]. Use this namespace when
+//! the operation is an intended ideal circuit operation, including unitary
+//! gates, preparation, measurement, and reset:
+//!
+//! ```
+//! use pecos_core::gate::*;
+//!
+//! let layer = H(0) & MZ(1);
+//! let sequence = PZ(0) * H(0) * MZ(0);
+//! ```
+//!
+//! For automatic promotion across all levels, use [`crate::op`]. For physical
+//! noise and open-system maps, use [`crate::channel`].
+
+use crate::op::Op;
+use crate::qubit_support::overlapping_qubits;
+use crate::unitary_rep::{QubitPairs, Qubits};
+use crate::{Angle64, PauliString, QubitId, UnitaryRep, op, unitary_rep};
+use std::ops::{BitAnd, Mul};
+
+pub use crate::op::{Basis, GateExpr};
+
+fn gate_from_op(op: Op) -> GateExpr {
+    op.into_gate()
+        .expect("gate namespace constructors are gate-convertible")
+}
+
+/// Lifts a unitary expression to the ideal gate level.
+#[must_use]
+pub fn from_unitary(unitary: impl Into<UnitaryRep>) -> GateExpr {
+    GateExpr::Unitary(unitary.into())
+}
+
+impl From<UnitaryRep> for GateExpr {
+    fn from(unitary: UnitaryRep) -> Self {
+        GateExpr::Unitary(unitary)
+    }
+}
+
+impl From<PauliString> for GateExpr {
+    fn from(pauli: PauliString) -> Self {
+        GateExpr::Unitary(UnitaryRep::from(pauli))
+    }
+}
+
+macro_rules! unitary_1q {
+    ($name:ident) => {
+        #[allow(non_snake_case)]
+        #[must_use]
+        pub fn $name(qubit: impl Into<QubitId>) -> GateExpr {
+            from_unitary(unitary_rep::$name(qubit))
+        }
+    };
+}
+
+macro_rules! unitary_1q_plural {
+    ($name:ident) => {
+        #[allow(non_snake_case)]
+        #[must_use]
+        pub fn $name(qubits: impl Into<Qubits>) -> GateExpr {
+            from_unitary(unitary_rep::$name(qubits))
+        }
+    };
+}
+
+macro_rules! op_1q {
+    ($name:ident) => {
+        #[allow(non_snake_case)]
+        #[must_use]
+        pub fn $name(qubit: impl Into<QubitId>) -> GateExpr {
+            gate_from_op(op::$name(qubit))
+        }
+    };
+}
+
+macro_rules! op_2q {
+    ($name:ident) => {
+        #[allow(non_snake_case)]
+        #[must_use]
+        pub fn $name(q0: impl Into<QubitId>, q1: impl Into<QubitId>) -> GateExpr {
+            gate_from_op(op::$name(q0, q1))
+        }
+    };
+}
+
+macro_rules! unitary_2q {
+    ($name:ident) => {
+        #[allow(non_snake_case)]
+        #[must_use]
+        pub fn $name(q0: impl Into<QubitId>, q1: impl Into<QubitId>) -> GateExpr {
+            from_unitary(unitary_rep::$name(q0, q1))
+        }
+    };
+}
+
+macro_rules! unitary_2q_plural {
+    ($name:ident) => {
+        #[allow(non_snake_case)]
+        #[must_use]
+        pub fn $name(pairs: impl Into<QubitPairs>) -> GateExpr {
+            from_unitary(unitary_rep::$name(pairs))
+        }
+    };
+}
+
+unitary_1q!(I);
+unitary_1q_plural!(Is);
+unitary_1q!(X);
+unitary_1q_plural!(Xs);
+unitary_1q!(Y);
+unitary_1q_plural!(Ys);
+unitary_1q!(Z);
+unitary_1q_plural!(Zs);
+unitary_1q!(H);
+unitary_1q_plural!(Hs);
+unitary_1q!(SX);
+unitary_1q_plural!(SXs);
+op_1q!(SXdg);
+unitary_1q!(SY);
+unitary_1q_plural!(SYs);
+op_1q!(SYdg);
+unitary_1q!(SZ);
+unitary_1q_plural!(SZs);
+op_1q!(SZdg);
+op_1q!(H2);
+op_1q!(H3);
+op_1q!(H4);
+op_1q!(H5);
+op_1q!(H6);
+op_1q!(F);
+op_1q!(Fdg);
+op_1q!(F2);
+op_1q!(F2dg);
+op_1q!(F3);
+op_1q!(F3dg);
+op_1q!(F4);
+op_1q!(F4dg);
+unitary_1q!(T);
+unitary_1q_plural!(Ts);
+op_1q!(Tdg);
+
+unitary_2q!(CX);
+unitary_2q_plural!(CXs);
+unitary_2q!(CY);
+unitary_2q_plural!(CYs);
+unitary_2q!(CZ);
+unitary_2q_plural!(CZs);
+unitary_2q!(SWAP);
+unitary_2q_plural!(SWAPs);
+op_2q!(SXX);
+op_2q!(SXXdg);
+op_2q!(SYY);
+op_2q!(SYYdg);
+unitary_2q!(SZZ);
+unitary_2q_plural!(SZZs);
+op_2q!(SZZdg);
+op_2q!(ISWAP);
+op_2q!(ISWAPdg);
+op_2q!(G);
+op_2q!(Gdg);
+
+/// Rotation around X axis: exp(-i theta/2 X).
+#[allow(non_snake_case)]
+#[must_use]
+pub fn RX(angle: Angle64, qubit: impl Into<QubitId>) -> GateExpr {
+    from_unitary(unitary_rep::RX(angle, qubit))
+}
+
+/// Rotations around X on multiple qubits.
+#[allow(non_snake_case)]
+#[must_use]
+pub fn RXs(angle: Angle64, qubits: impl Into<Qubits>) -> GateExpr {
+    from_unitary(unitary_rep::RXs(angle, qubits))
+}
+
+/// Rotation around Y axis: exp(-i theta/2 Y).
+#[allow(non_snake_case)]
+#[must_use]
+pub fn RY(angle: Angle64, qubit: impl Into<QubitId>) -> GateExpr {
+    from_unitary(unitary_rep::RY(angle, qubit))
+}
+
+/// Rotations around Y on multiple qubits.
+#[allow(non_snake_case)]
+#[must_use]
+pub fn RYs(angle: Angle64, qubits: impl Into<Qubits>) -> GateExpr {
+    from_unitary(unitary_rep::RYs(angle, qubits))
+}
+
+/// Rotation around Z axis: exp(-i theta/2 Z).
+#[allow(non_snake_case)]
+#[must_use]
+pub fn RZ(angle: Angle64, qubit: impl Into<QubitId>) -> GateExpr {
+    from_unitary(unitary_rep::RZ(angle, qubit))
+}
+
+/// Rotations around Z on multiple qubits.
+#[allow(non_snake_case)]
+#[must_use]
+pub fn RZs(angle: Angle64, qubits: impl Into<Qubits>) -> GateExpr {
+    from_unitary(unitary_rep::RZs(angle, qubits))
+}
+
+/// Two-qubit XX rotation: exp(-i theta/2 XX).
+#[allow(non_snake_case)]
+#[must_use]
+pub fn RXX(angle: Angle64, q0: impl Into<QubitId>, q1: impl Into<QubitId>) -> GateExpr {
+    from_unitary(unitary_rep::RXX(angle, q0, q1))
+}
+
+/// XX rotations on multiple qubit pairs.
+#[allow(non_snake_case)]
+#[must_use]
+pub fn RXXs(angle: Angle64, pairs: impl Into<QubitPairs>) -> GateExpr {
+    from_unitary(unitary_rep::RXXs(angle, pairs))
+}
+
+/// Two-qubit YY rotation: exp(-i theta/2 YY).
+#[allow(non_snake_case)]
+#[must_use]
+pub fn RYY(angle: Angle64, q0: impl Into<QubitId>, q1: impl Into<QubitId>) -> GateExpr {
+    from_unitary(unitary_rep::RYY(angle, q0, q1))
+}
+
+/// YY rotations on multiple qubit pairs.
+#[allow(non_snake_case)]
+#[must_use]
+pub fn RYYs(angle: Angle64, pairs: impl Into<QubitPairs>) -> GateExpr {
+    from_unitary(unitary_rep::RYYs(angle, pairs))
+}
+
+/// Two-qubit ZZ rotation: exp(-i theta/2 ZZ).
+#[allow(non_snake_case)]
+#[must_use]
+pub fn RZZ(angle: Angle64, q0: impl Into<QubitId>, q1: impl Into<QubitId>) -> GateExpr {
+    from_unitary(unitary_rep::RZZ(angle, q0, q1))
+}
+
+/// ZZ rotations on multiple qubit pairs.
+#[allow(non_snake_case)]
+#[must_use]
+pub fn RZZs(angle: Angle64, pairs: impl Into<QubitPairs>) -> GateExpr {
+    from_unitary(unitary_rep::RZZs(angle, pairs))
+}
+
+/// Toffoli gate (CCX).
+#[allow(non_snake_case)]
+#[must_use]
+pub fn CCX(c0: impl Into<QubitId>, c1: impl Into<QubitId>, target: impl Into<QubitId>) -> GateExpr {
+    from_unitary(unitary_rep::CCX(c0, c1, target))
+}
+
+/// Prepare a qubit in the requested basis eigenstate.
+#[must_use]
+pub fn prep(basis: Basis, qubit: impl Into<QubitId>) -> GateExpr {
+    GateExpr::Prep {
+        basis,
+        qubit: qubit.into().0,
+    }
+}
+
+/// Measure a qubit in the requested basis.
+#[must_use]
+pub fn measure(basis: Basis, qubit: impl Into<QubitId>) -> GateExpr {
+    GateExpr::Measure {
+        basis,
+        qubit: qubit.into().0,
+    }
+}
+
+/// Reset a qubit to the requested basis eigenstate.
+#[must_use]
+pub fn reset(basis: Basis, qubit: impl Into<QubitId>) -> GateExpr {
+    GateExpr::Reset {
+        basis,
+        qubit: qubit.into().0,
+    }
+}
+
+/// Prepare qubit in the |0> state.
+#[allow(non_snake_case)]
+#[must_use]
+pub fn PZ(qubit: impl Into<QubitId>) -> GateExpr {
+    prep(Basis::Z, qubit)
+}
+
+/// Prepare qubit in the |+> state.
+#[allow(non_snake_case)]
+#[must_use]
+pub fn PX(qubit: impl Into<QubitId>) -> GateExpr {
+    prep(Basis::X, qubit)
+}
+
+/// Prepare qubit in the Y-basis +1 eigenstate.
+#[allow(non_snake_case)]
+#[must_use]
+pub fn PY(qubit: impl Into<QubitId>) -> GateExpr {
+    prep(Basis::Y, qubit)
+}
+
+/// Measure qubit in the Z basis.
+#[allow(non_snake_case)]
+#[must_use]
+pub fn MZ(qubit: impl Into<QubitId>) -> GateExpr {
+    measure(Basis::Z, qubit)
+}
+
+/// Measure qubit in the X basis.
+#[allow(non_snake_case)]
+#[must_use]
+pub fn MX(qubit: impl Into<QubitId>) -> GateExpr {
+    measure(Basis::X, qubit)
+}
+
+/// Measure qubit in the Y basis.
+#[allow(non_snake_case)]
+#[must_use]
+pub fn MY(qubit: impl Into<QubitId>) -> GateExpr {
+    measure(Basis::Y, qubit)
+}
+
+/// Reset qubit to |0>.
+#[allow(non_snake_case)]
+#[must_use]
+pub fn Reset(qubit: impl Into<QubitId>) -> GateExpr {
+    reset(Basis::Z, qubit)
+}
+
+impl BitAnd for GateExpr {
+    type Output = GateExpr;
+
+    fn bitand(self, rhs: GateExpr) -> GateExpr {
+        let overlap = overlapping_qubits(self.qubits(), rhs.qubits());
+        assert!(
+            overlap.is_empty(),
+            "tensor product requires disjoint gate support; overlapping qubits: {overlap:?}"
+        );
+        GateExpr::Tensor(vec![self, rhs])
+    }
+}
+
+impl BitAnd<&GateExpr> for GateExpr {
+    type Output = GateExpr;
+
+    fn bitand(self, rhs: &GateExpr) -> GateExpr {
+        self & rhs.clone()
+    }
+}
+
+impl BitAnd<GateExpr> for &GateExpr {
+    type Output = GateExpr;
+
+    fn bitand(self, rhs: GateExpr) -> GateExpr {
+        self.clone() & rhs
+    }
+}
+
+impl BitAnd<&GateExpr> for &GateExpr {
+    type Output = GateExpr;
+
+    fn bitand(self, rhs: &GateExpr) -> GateExpr {
+        self.clone() & rhs.clone()
+    }
+}
+
+impl Mul for GateExpr {
+    type Output = GateExpr;
+
+    fn mul(self, rhs: GateExpr) -> GateExpr {
+        GateExpr::Compose(vec![self, rhs])
+    }
+}
+
+impl Mul<&GateExpr> for GateExpr {
+    type Output = GateExpr;
+
+    fn mul(self, rhs: &GateExpr) -> GateExpr {
+        self * rhs.clone()
+    }
+}
+
+impl Mul<GateExpr> for &GateExpr {
+    type Output = GateExpr;
+
+    fn mul(self, rhs: GateExpr) -> GateExpr {
+        self.clone() * rhs
+    }
+}
+
+impl Mul<&GateExpr> for &GateExpr {
+    type Output = GateExpr;
+
+    fn mul(self, rhs: &GateExpr) -> GateExpr {
+        self.clone() * rhs.clone()
+    }
+}
+
+#[cfg(test)]
+mod tests {
+    use super::*;
+
+    #[test]
+    fn namespace_constructors_return_gate_expr() {
+        assert!(matches!(
+            MZ(3),
+            GateExpr::Measure {
+                basis: Basis::Z,
+                qubit: 3
+            }
+        ));
+        assert!(matches!(
+            MX(4),
+            GateExpr::Measure {
+                basis: Basis::X,
+                qubit: 4
+            }
+        ));
+        assert!(matches!(
+            MY(5),
+            GateExpr::Measure {
+                basis: Basis::Y,
+                qubit: 5
+            }
+        ));
+        assert!(matches!(
+            PZ(0),
+            GateExpr::Prep {
+                basis: Basis::Z,
+                qubit: 0
+            }
+        ));
+        assert!(matches!(
+            PX(1),
+            GateExpr::Prep {
+                basis: Basis::X,
+                qubit: 1
+            }
+        ));
+        assert!(matches!(
+            PY(2),
+            GateExpr::Prep {
+                basis: Basis::Y,
+                qubit: 2
+            }
+        ));
+    }
+
+    #[test]
+    fn unitary_constructor_lifts_to_gate_level() {
+        assert!(matches!(H(0), GateExpr::Unitary(_)));
+        assert!(matches!(T(0), GateExpr::Unitary(_)));
+        assert!(matches!(CX(0, 1), GateExpr::Unitary(_)));
+        assert_eq!(I(7).qubits(), vec![7]);
+    }
+
+    #[test]
+    #[should_panic(expected = "CX requires distinct qubits")]
+    fn gate_namespace_two_qubit_gate_rejects_repeated_qubit() {
+        let _ = CX(0, 0);
+    }
+
+    #[test]
+    #[should_panic(expected = "RZZ requires distinct qubits")]
+    fn gate_namespace_two_qubit_rotation_rejects_repeated_qubit() {
+        let _ = RZZ(Angle64::QUARTER_TURN, 1, 1);
+    }
+
+    #[test]
+    #[should_panic(expected = "CCX requires distinct qubits")]
+    fn gate_namespace_three_qubit_gate_rejects_repeated_qubit() {
+        let _ = CCX(0, 1, 1);
+    }
+
+    #[test]
+    fn gate_tensor_and_composition_stay_gate_level() {
+        let tensor = H(0) & MZ(1);
+        assert!(matches!(tensor, GateExpr::Tensor(parts) if parts.len() == 2));
+
+        let sequence = PZ(0) * H(0) * MZ(0);
+        assert!(matches!(sequence, GateExpr::Compose(parts) if parts.len() == 2));
+    }
+
+    #[test]
+    #[should_panic(expected = "tensor product requires disjoint gate support")]
+    fn gate_tensor_rejects_overlapping_qubits() {
+        let _ = H(0) & MZ(0);
+    }
+
+    #[test]
+    #[should_panic(expected = "tensor product requires disjoint gate support")]
+    fn gate_tensor_rejects_partial_overlap_with_multi_qubit_support() {
+        let _ = CX(0, 2) & H(2);
+    }
+
+    #[test]
+    fn gate_tensor_uses_sparse_support_not_dense_span() {
+        let tensor = CX(0, 2) & MZ(1);
+        assert!(matches!(tensor, GateExpr::Tensor(ref parts) if parts.len() == 2));
+        assert_eq!(tensor.qubits(), vec![0, 1, 2]);
+    }
+
+    #[test]
+    fn gate_namespace_plural_helpers_match_tensor_forms() {
+        let cxs = CXs([(0, 1), (2, 3)]);
+        assert!(matches!(cxs, GateExpr::Unitary(_)));
+        assert_eq!(cxs.qubits(), vec![0, 1, 2, 3]);
+
+        let rzzs = RZZs(Angle64::QUARTER_TURN, [(0, 1), (2, 3)]);
+        assert!(matches!(rzzs, GateExpr::Unitary(_)));
+        assert_eq!(rzzs.qubits(), vec![0, 1, 2, 3]);
+
+        let tensor = CX(0, 1) & CX(2, 3);
+        assert!(matches!(tensor, GateExpr::Tensor(_)));
+        assert_eq!(tensor.qubits(), vec![0, 1, 2, 3]);
+    }
+
+    #[test]
+    fn gate_namespace_plural_helpers_reject_overlapping_support() {
+        fn assert_tensor_overlap_panic(f: impl FnOnce() + std::panic::UnwindSafe) {
+            let err = std::panic::catch_unwind(f).expect_err("expected tensor overlap panic");
+            let message = err
+                .downcast_ref::<String>()
+                .map(String::as_str)
+                .or_else(|| err.downcast_ref::<&str>().copied())
+                .unwrap_or("<non-string panic>");
+            assert!(
+                message.contains("tensor product requires disjoint"),
+                "unexpected panic message: {message}"
+            );
+        }
+
+        assert_tensor_overlap_panic(|| {
+            let _ = CXs([(0, 1), (1, 2)]);
+        });
+        assert_tensor_overlap_panic(|| {
+            let _ = RZZs(Angle64::QUARTER_TURN, [(0, 2), (2, 3)]);
+        });
+    }
+}
diff --git a/crates/pecos-core/src/gate_type.rs b/crates/pecos-core/src/gate_type.rs
index fe3a03de9..2c2c94386 100644
--- a/crates/pecos-core/src/gate_type.rs
+++ b/crates/pecos-core/src/gate_type.rs
@@ -108,8 +108,24 @@ pub enum GateType {
     /// Free/deallocate a qubit
     QFree = 136,
     Idle = 200,
+    /// Meta-gate: tracked-Pauli annotation for fault tracking.
+    ///
+    /// This gate carries a Pauli string but has no effect on quantum state.
+    /// Its position in the circuit determines which faults can flip the tracked Pauli
+    /// (only faults before this node are relevant). The propagator uses it as a
+    /// backward propagation start point.
+    ///
+    /// The Pauli string is encoded in `params`: each param encodes
+    /// `qubit * 4 + pauli_type` where `pauli_type` is 1=X, 2=Y, 3=Z.
+    TrackedPauliMeta = 210,
     MeasCrosstalkGlobalPayload = 218,
     MeasCrosstalkLocalPayload = 219,
+    /// Typed channel operation embedded in an annotated/noisy circuit.
+    ///
+    /// The concrete channel payload is stored on [`crate::Gate`], not in the
+    /// numeric gate type. Ideal circuits should not contain this gate type; it
+    /// represents compiled noise annotations or explicit channel placement.
+    Channel = 220,
     /// Custom/unrecognized gate type, with actual name stored in metadata
     Custom = 255,
 }
@@ -164,6 +180,8 @@ impl From<u8> for GateType {
             200 => GateType::Idle,
             218 => GateType::MeasCrosstalkGlobalPayload,
             219 => GateType::MeasCrosstalkLocalPayload,
+            210 => GateType::TrackedPauliMeta,
+            220 => GateType::Channel,
             255 => GateType::Custom,
             _ => panic!("Invalid gate type ID: {value}"),
         }
@@ -171,6 +189,15 @@ impl From<u8> for GateType {
 }
 
 impl GateType {
+    /// Returns true if this gate type is a meta-gate (annotation, not physical).
+    ///
+    /// Meta-gates have a position in the DAG but do not affect quantum state
+    /// and should not create fault locations or receive noise.
+    #[must_use]
+    pub const fn is_meta(self) -> bool {
+        matches!(self, GateType::TrackedPauliMeta)
+    }
+
     /// Returns the number of angle parameters this gate type requires
     ///
     /// # Returns
@@ -212,10 +239,12 @@ impl GateType {
             | GateType::MeasureFree
             | GateType::MeasCrosstalkGlobalPayload
             | GateType::MeasCrosstalkLocalPayload
+            | GateType::Channel
             | GateType::PZ
             | GateType::QAlloc
             | GateType::QFree
-            | GateType::Custom => 0,
+            | GateType::Custom
+            | GateType::TrackedPauliMeta => 0,
 
             // Gates with one parameter
             GateType::RX
@@ -277,7 +306,13 @@ impl GateType {
             | GateType::Idle
             | GateType::MeasCrosstalkGlobalPayload
             | GateType::MeasCrosstalkLocalPayload
-            | GateType::Custom => 1,
+            | GateType::Custom
+            // TrackedPauliMeta and Channel are variable-arity but return 1
+            // here because gate validation checks
+            // `is_multiple_of(quantum_arity())` and any count is a multiple
+            // of 1. The actual qubit count is in the gate.
+            | GateType::Channel
+            | GateType::TrackedPauliMeta => 1,
 
             // Two-qubit gates
             GateType::CX
@@ -303,6 +338,29 @@ impl GateType {
         }
     }
 
+    /// Returns the number of gates represented by a command with `qubit_count`
+    /// qubits.
+    ///
+    /// Most gate commands are batchable: a command with 4 qubits and arity 2
+    /// represents two gates. Payload/meta gates are annotations, not physical
+    /// gates. Variable-arity custom/channel gates are counted as one
+    /// command-level gate.
+    #[must_use]
+    pub const fn num_gates(self, qubit_count: usize) -> usize {
+        if matches!(
+            self,
+            GateType::MeasCrosstalkGlobalPayload
+                | GateType::MeasCrosstalkLocalPayload
+                | GateType::TrackedPauliMeta
+        ) {
+            return 0;
+        }
+        if matches!(self, GateType::Custom | GateType::Channel) {
+            return 1;
+        }
+        qubit_count / self.quantum_arity()
+    }
+
     /// Returns the number of angle parameters this gate type requires.
     ///
     /// This is separate from `classical_arity()` which includes all classical parameters.
@@ -404,7 +462,9 @@ impl fmt::Display for GateType {
             GateType::Idle => write!(f, "Idle"),
             GateType::MeasCrosstalkGlobalPayload => write!(f, "MeasCrosstalkGlobalPayload"),
             GateType::MeasCrosstalkLocalPayload => write!(f, "MeasCrosstalkLocalPayload"),
+            GateType::Channel => write!(f, "Channel"),
             GateType::Custom => write!(f, "Custom"),
+            GateType::TrackedPauliMeta => write!(f, "TrackedPauli"),
         }
     }
 }
@@ -466,6 +526,8 @@ impl std::str::FromStr for GateType {
             "QALLOC" => Ok(GateType::QAlloc),
             "QFREE" => Ok(GateType::QFree),
             "IDLE" => Ok(GateType::Idle),
+            "TRACKEDPAULI" | "TRACKEDPAULIMETA" | "TP" => Ok(GateType::TrackedPauliMeta),
+            "CHANNEL" => Ok(GateType::Channel),
             _ => Err(format!("Unknown gate type: {s}")),
         }
     }
@@ -501,6 +563,7 @@ mod tests {
         assert_eq!(GateType::Idle as u8, 200);
         assert_eq!(GateType::MeasCrosstalkGlobalPayload as u8, 218);
         assert_eq!(GateType::MeasCrosstalkLocalPayload as u8, 219);
+        assert_eq!(GateType::Channel as u8, 220);
         assert_eq!(GateType::Custom as u8, 255);
 
         assert_eq!(GateType::from(0u8), GateType::I);
@@ -527,6 +590,7 @@ mod tests {
         assert_eq!(GateType::from(200u8), GateType::Idle);
         assert_eq!(GateType::from(218u8), GateType::MeasCrosstalkGlobalPayload);
         assert_eq!(GateType::from(219u8), GateType::MeasCrosstalkLocalPayload);
+        assert_eq!(GateType::from(220u8), GateType::Channel);
         assert_eq!(GateType::from(255u8), GateType::Custom);
     }
 
@@ -544,6 +608,7 @@ mod tests {
         assert_eq!(GateType::from_str("SXXdg").unwrap(), GateType::SXXdg);
         assert_eq!(GateType::from_str("SYY").unwrap(), GateType::SYY);
         assert_eq!(GateType::from_str("SYYdg").unwrap(), GateType::SYYdg);
+        assert_eq!(GateType::from_str("Channel").unwrap(), GateType::Channel);
         assert_eq!(GateType::from_str("SWAP").unwrap(), GateType::SWAP);
         assert_eq!(GateType::from_str("CCX").unwrap(), GateType::CCX);
 
@@ -590,6 +655,7 @@ mod tests {
         assert_eq!(GateType::MeasureFree.classical_arity(), 0);
         assert_eq!(GateType::MeasCrosstalkGlobalPayload.classical_arity(), 0);
         assert_eq!(GateType::MeasCrosstalkLocalPayload.classical_arity(), 0);
+        assert_eq!(GateType::Channel.classical_arity(), 0);
         assert_eq!(GateType::PZ.classical_arity(), 0);
         assert_eq!(GateType::QAlloc.classical_arity(), 0);
         assert_eq!(GateType::QFree.classical_arity(), 0);
@@ -626,6 +692,7 @@ mod tests {
         assert_eq!(GateType::Idle.quantum_arity(), 1);
         assert_eq!(GateType::MeasCrosstalkGlobalPayload.quantum_arity(), 1);
         assert_eq!(GateType::MeasCrosstalkLocalPayload.quantum_arity(), 1);
+        assert_eq!(GateType::Channel.quantum_arity(), 1);
 
         // Two-qubit gates
         assert_eq!(GateType::CX.quantum_arity(), 2);
@@ -634,6 +701,41 @@ mod tests {
         assert_eq!(GateType::RZZ.quantum_arity(), 2);
     }
 
+    #[test]
+    fn test_num_gates() {
+        assert_eq!(GateType::H.num_gates(4), 4);
+        assert_eq!(GateType::CX.num_gates(4), 2);
+        assert_eq!(GateType::CCX.num_gates(6), 2);
+        assert_eq!(GateType::Custom.num_gates(2), 1);
+        assert_eq!(GateType::Channel.num_gates(2), 1);
+        assert_eq!(GateType::TrackedPauliMeta.num_gates(3), 0);
+        assert_eq!(GateType::MeasCrosstalkGlobalPayload.num_gates(3), 0);
+        assert_eq!(GateType::MeasCrosstalkLocalPayload.num_gates(3), 0);
+    }
+
+    #[test]
+    fn test_tracked_pauli_meta_gate_type_contract() {
+        assert_eq!(
+            "TrackedPauli".parse::<GateType>().unwrap(),
+            GateType::TrackedPauliMeta
+        );
+        assert_eq!(
+            "TrackedPauliMeta".parse::<GateType>().unwrap(),
+            GateType::TrackedPauliMeta
+        );
+        assert_eq!(
+            "TP".parse::<GateType>().unwrap(),
+            GateType::TrackedPauliMeta
+        );
+
+        assert_eq!(GateType::TrackedPauliMeta.to_string(), "TrackedPauli");
+        assert_eq!(GateType::TrackedPauliMeta as u8, 210);
+        assert!(GateType::TrackedPauliMeta.is_meta());
+        assert_eq!(GateType::TrackedPauliMeta.classical_arity(), 0);
+        assert_eq!(GateType::TrackedPauliMeta.quantum_arity(), 1);
+        assert_eq!(GateType::TrackedPauliMeta.num_gates(4), 0);
+    }
+
     #[test]
     fn test_is_parameterized() {
         // Non-parameterized gates
diff --git a/crates/pecos-core/src/gates.rs b/crates/pecos-core/src/gates.rs
index c48fa72a3..c03830714 100644
--- a/crates/pecos-core/src/gates.rs
+++ b/crates/pecos-core/src/gates.rs
@@ -4,8 +4,11 @@
 //! gate operation with its type, qubits, and parameters.
 
 use crate::Angle64;
+use crate::ChannelExpr;
+use crate::MeasId;
 use crate::QubitId;
 use crate::gate_type::GateType;
+use crate::qubit_support::duplicate_qubits;
 use smallvec::SmallVec;
 
 /// Stack-allocated qubit buffer for gates (up to 4 qubits inline).
@@ -20,6 +23,10 @@ pub type GateAngles = SmallVec<[Angle64; 3]>;
 /// Most gates have 0-1 non-angle parameters.
 pub type GateParams = SmallVec<[f64; 2]>;
 
+/// Measurement result identities for measurement gates.
+/// Empty for non-measurement gates. One entry per qubit for MZ/MX/MY.
+pub type GateMeasIds = SmallVec<[MeasId; 1]>;
+
 /// Flat gate command representation for quantum operations
 ///
 /// Clean, flat representation of quantum gate commands
@@ -45,6 +52,17 @@ pub struct Gate {
     /// The qubits the gate acts on.
     /// Stack-allocated for up to 4 qubits.
     pub qubits: GateQubits,
+    /// Measurement result identities (one per qubit for measurement gates).
+    ///
+    /// Assigned at circuit construction time, carried through all
+    /// transformations. Empty for non-measurement gates.
+    /// Follows the MLIR SSA pattern: defined once, referenced everywhere.
+    pub meas_ids: GateMeasIds,
+    /// Typed channel payload for `GateType::Channel`.
+    ///
+    /// This is `None` for ideal circuit gates. It is populated only for
+    /// annotated/noisy circuits that explicitly carry channel operations.
+    pub channel: Option<ChannelExpr>,
 }
 
 /// Legacy quantum gate representation for `ByteMessageBuilder` compatibility
@@ -67,6 +85,8 @@ impl Gate {
             angles: angles.into(),
             params: params.into(),
             qubits: qubits.into(),
+            meas_ids: GateMeasIds::new(),
+            channel: None,
         }
     }
 
@@ -97,7 +117,66 @@ impl Gate {
     #[inline]
     #[must_use]
     pub fn num_gates(&self) -> usize {
-        self.num_qubits() / self.quantum_arity()
+        self.gate_type.num_gates(self.num_qubits())
+    }
+
+    /// Returns true if `self` and `other` can be represented as one batched gate
+    /// command by concatenating qubit and measurement-id payloads.
+    ///
+    /// Batch-compatible gates are identical except for disjoint qubit support
+    /// and, for measurement gates, their corresponding measurement ids.
+    #[must_use]
+    pub fn can_batch_with(&self, other: &Self) -> bool {
+        if self.gate_type != other.gate_type
+            || self.angles != other.angles
+            || self.params != other.params
+            || self.channel != other.channel
+        {
+            return false;
+        }
+
+        if matches!(
+            self.gate_type,
+            GateType::Custom
+                | GateType::Channel
+                | GateType::TrackedPauliMeta
+                | GateType::MeasCrosstalkGlobalPayload
+                | GateType::MeasCrosstalkLocalPayload
+        ) {
+            return false;
+        }
+
+        if self.qubits.iter().any(|q| other.qubits.contains(q)) {
+            return false;
+        }
+
+        let self_has_meas_ids = !self.meas_ids.is_empty();
+        let other_has_meas_ids = !other.meas_ids.is_empty();
+        if self_has_meas_ids != other_has_meas_ids {
+            return false;
+        }
+        if self_has_meas_ids
+            && (self.meas_ids.len() != self.qubits.len()
+                || other.meas_ids.len() != other.qubits.len())
+        {
+            return false;
+        }
+
+        true
+    }
+
+    /// Appends a compatible gate command into this batch.
+    ///
+    /// # Panics
+    ///
+    /// Panics if `other` is not batch-compatible with `self`.
+    pub fn append_batch(&mut self, other: Self) {
+        assert!(
+            self.can_batch_with(&other),
+            "cannot batch incompatible gate commands"
+        );
+        self.qubits.extend(other.qubits);
+        self.meas_ids.extend(other.meas_ids);
     }
 
     /// Helper function to flatten qubit pairs into a `GateQubits` buffer
@@ -116,6 +195,36 @@ impl Gate {
         Self::simple(GateType::Custom, qubits)
     }
 
+    /// Create a typed channel operation for an annotated/noisy circuit.
+    #[must_use]
+    pub fn channel(channel: ChannelExpr) -> Self {
+        let qubits = channel
+            .qubits()
+            .into_iter()
+            .map(QubitId)
+            .collect::<GateQubits>();
+        Self {
+            gate_type: GateType::Channel,
+            angles: GateAngles::new(),
+            params: GateParams::new(),
+            qubits,
+            meas_ids: GateMeasIds::new(),
+            channel: Some(channel),
+        }
+    }
+
+    /// Returns the typed channel payload when this is a channel operation.
+    #[must_use]
+    pub fn channel_expr(&self) -> Option<&ChannelExpr> {
+        self.channel.as_ref()
+    }
+
+    /// Returns true when this gate carries a channel payload.
+    #[must_use]
+    pub fn is_channel(&self) -> bool {
+        self.gate_type == GateType::Channel
+    }
+
     /// Create Identity gate on multiple qubits
     #[must_use]
     pub fn i(qubits: &[impl Into<QubitId> + Copy]) -> Self {
@@ -917,6 +1026,9 @@ impl Gate {
     #[inline]
     #[must_use]
     pub fn classical_arity(&self) -> usize {
+        if self.is_channel() {
+            return 0;
+        }
         self.gate_type.classical_arity()
     }
 
@@ -928,6 +1040,9 @@ impl Gate {
     #[inline]
     #[must_use]
     pub fn quantum_arity(&self) -> usize {
+        if self.is_channel() {
+            return self.qubits.len().max(1);
+        }
         self.gate_type.quantum_arity()
     }
 
@@ -935,6 +1050,9 @@ impl Gate {
     #[inline]
     #[must_use]
     pub fn is_parameterized(&self) -> bool {
+        if self.is_channel() {
+            return false;
+        }
         self.gate_type.is_parameterized()
     }
 
@@ -942,6 +1060,9 @@ impl Gate {
     #[inline]
     #[must_use]
     pub fn is_single_qubit(&self) -> bool {
+        if self.is_channel() {
+            return self.qubits.len() == 1;
+        }
         self.gate_type.is_single_qubit()
     }
 
@@ -949,6 +1070,9 @@ impl Gate {
     #[inline]
     #[must_use]
     pub fn is_two_qubit(&self) -> bool {
+        if self.is_channel() {
+            return self.qubits.len() == 2;
+        }
         self.gate_type.is_two_qubit()
     }
 
@@ -956,6 +1080,9 @@ impl Gate {
     #[inline]
     #[must_use]
     pub fn angle_arity(&self) -> usize {
+        if self.is_channel() {
+            return 0;
+        }
         self.gate_type.angle_arity()
     }
 
@@ -970,7 +1097,47 @@ impl Gate {
     /// Returns an error if:
     /// - The number of angles doesn't match the gate's angle arity
     /// - The number of qubits is not a multiple of the gate's quantum arity
+    /// - Any qubit is repeated within the gate command
     pub fn validate(&self) -> Result<(), String> {
+        if self.is_channel() {
+            let Some(channel) = &self.channel else {
+                return Err("GateType::Channel requires a channel payload".to_string());
+            };
+            if !self.angles.is_empty() || !self.params.is_empty() || !self.meas_ids.is_empty() {
+                return Err(
+                    "Channel gates cannot carry angle, parameter, or measurement-id payloads"
+                        .to_string(),
+                );
+            }
+            let expected = channel
+                .qubits()
+                .into_iter()
+                .map(QubitId)
+                .collect::<GateQubits>();
+            if self.qubits != expected {
+                return Err(format!(
+                    "Channel gate qubits {:?} do not match channel payload qubits {:?}",
+                    self.qubits, expected
+                ));
+            }
+            return Ok(());
+        }
+        if self.channel.is_some() {
+            return Err("Only GateType::Channel can carry a channel payload".to_string());
+        }
+        if self.gate_type == GateType::Custom {
+            let duplicates = duplicate_qubits(self.qubits.iter().map(|q| q.0));
+            if !duplicates.is_empty() {
+                return Err(format!(
+                    "Gate {:?} requires distinct qubits within one gate command; duplicated qubits: {:?}",
+                    self.gate_type, duplicates
+                ));
+            }
+            if !self.meas_ids.is_empty() {
+                return Err("Custom gates cannot carry measurement-id payloads".to_string());
+            }
+            return Ok(());
+        }
         // Check angle parameters
         if self.angles.len() != self.angle_arity() {
             return Err(format!(
@@ -989,6 +1156,41 @@ impl Gate {
                 self.qubits.len()
             ));
         }
+        let expected_params = self.classical_arity() - self.angle_arity();
+        if self.params.len() != expected_params {
+            return Err(format!(
+                "Gate {:?} expected {} non-angle parameters, got {}",
+                self.gate_type,
+                expected_params,
+                self.params.len()
+            ));
+        }
+        let duplicates = duplicate_qubits(self.qubits.iter().map(|q| q.0));
+        if !duplicates.is_empty() {
+            return Err(format!(
+                "Gate {:?} requires distinct qubits within one gate command; duplicated qubits: {:?}",
+                self.gate_type, duplicates
+            ));
+        }
+        let is_measurement = matches!(
+            self.gate_type,
+            GateType::MZ | GateType::MeasureLeaked | GateType::MeasureFree
+        );
+        if is_measurement {
+            if !self.meas_ids.is_empty() && self.meas_ids.len() != self.qubits.len() {
+                return Err(format!(
+                    "Measurement gate {:?} expected measurement-id count to be 0 or {}, got {}",
+                    self.gate_type,
+                    self.qubits.len(),
+                    self.meas_ids.len()
+                ));
+            }
+        } else if !self.meas_ids.is_empty() {
+            return Err(format!(
+                "Gate {:?} cannot carry measurement-id payloads",
+                self.gate_type
+            ));
+        }
         Ok(())
     }
 }
@@ -1041,6 +1243,83 @@ mod tests {
         assert!(measure_gate.angles.is_empty());
     }
 
+    #[test]
+    fn test_channel_gate_creation_and_validation() {
+        use crate::channel::{Dephasing, Depolarizing};
+
+        let gate = Gate::channel(Depolarizing(0.25, 0));
+        assert_eq!(gate.gate_type, GateType::Channel);
+        assert_eq!(gate.qubits.as_slice(), &[QubitId::from(0)]);
+        assert!(gate.channel_expr().is_some());
+        assert!(gate.validate().is_ok());
+
+        let two_qubit_channel = Depolarizing(0.1, 0) & Dephasing(0.2, 1);
+        let two_qubit_gate = Gate::channel(two_qubit_channel);
+        assert_eq!(
+            two_qubit_gate.qubits.as_slice(),
+            &[QubitId::from(0), QubitId::from(1)]
+        );
+        assert_eq!(two_qubit_gate.quantum_arity(), 2);
+        assert_eq!(two_qubit_gate.num_gates(), 1);
+        assert!(two_qubit_gate.is_two_qubit());
+        assert!(two_qubit_gate.validate().is_ok());
+    }
+
+    #[test]
+    fn test_num_gates_counts_batched_gates() {
+        assert_eq!(Gate::h(&[0, 1, 2, 3]).num_gates(), 4);
+        assert_eq!(Gate::cx(&[(0, 1), (2, 3)]).num_gates(), 2);
+        assert_eq!(Gate::ccx(&[(0, 1, 2), (3, 4, 5)]).num_gates(), 2);
+
+        assert_eq!(
+            Gate::custom(vec![QubitId::from(0), QubitId::from(1)]).num_gates(),
+            1
+        );
+        assert_eq!(
+            Gate::simple(
+                GateType::TrackedPauliMeta,
+                vec![QubitId::from(0), QubitId::from(1)]
+            )
+            .num_gates(),
+            0
+        );
+        assert_eq!(Gate::meas_crosstalk_global_payload(&[0, 1]).num_gates(), 0);
+    }
+
+    #[test]
+    fn test_gate_batch_compatibility_and_append() {
+        let mut h0 = Gate::h(&[0]);
+        let h1 = Gate::h(&[1]);
+        assert!(h0.can_batch_with(&h1));
+        h0.append_batch(h1);
+        assert_eq!(h0.qubits.as_slice(), &[QubitId::from(0), QubitId::from(1)]);
+        assert_eq!(h0.num_gates(), 2);
+
+        assert!(!Gate::h(&[0]).can_batch_with(&Gate::h(&[0])));
+        assert!(
+            !Gate::rz(Angle64::from_turns(0.25), &[0])
+                .can_batch_with(&Gate::rz(Angle64::from_turns(0.5), &[1]))
+        );
+        assert!(
+            !Gate::custom(vec![QubitId::from(0)])
+                .can_batch_with(&Gate::custom(vec![QubitId::from(1)]))
+        );
+    }
+
+    #[test]
+    fn test_measurement_batch_compatibility_preserves_measurement_ids() {
+        let mut m0 = Gate::mz(&[0]);
+        m0.meas_ids.push(MeasId(4));
+        let mut m1 = Gate::mz(&[1]);
+        m1.meas_ids.push(MeasId(5));
+
+        assert!(m0.can_batch_with(&m1));
+        m0.append_batch(m1);
+
+        assert_eq!(m0.qubits.as_slice(), &[QubitId::from(0), QubitId::from(1)]);
+        assert_eq!(m0.meas_ids.as_slice(), &[MeasId(4), MeasId(5)]);
+    }
+
     #[test]
     fn test_two_qubit_gate_vec_variants() {
         // Test CX with _vec variant - much more convenient when you have a flat list
@@ -1079,6 +1358,45 @@ mod tests {
         let _ = Gate::cx_vec(&[0, 1, 2]);
     }
 
+    #[test]
+    fn test_gate_validate_rejects_repeated_qubits_within_pair() {
+        let err = Gate::cx(&[(0, 0)]).validate().unwrap_err();
+        assert!(err.contains("requires distinct qubits"));
+        assert!(err.contains("[0]"));
+    }
+
+    #[test]
+    fn test_gate_validate_rejects_repeated_qubits_across_batched_pairs() {
+        let err = Gate::swap(&[(0, 1), (1, 2)]).validate().unwrap_err();
+        assert!(err.contains("requires distinct qubits"));
+        assert!(err.contains("[1]"));
+    }
+
+    #[test]
+    fn test_gate_validate_rejects_repeated_qubits_in_three_qubit_gate() {
+        let err = Gate::ccx(&[(0, 1, 1)]).validate().unwrap_err();
+        assert!(err.contains("requires distinct qubits"));
+        assert!(err.contains("[1]"));
+    }
+
+    #[test]
+    fn test_gate_validate_rejects_repeated_qubits_in_parameterized_two_qubit_gates() {
+        let angle = Angle64::from_turns(0.25);
+        let kak_angles = [[Angle64::ZERO; 3]; 2];
+        let interaction = [Angle64::ZERO; 3];
+
+        let cases = [
+            Gate::rzz(angle, &[(2, 2)]),
+            Gate::rxxryyrzz(angle, angle, angle, &[(3, 3)]),
+            Gate::u2q(kak_angles, interaction, kak_angles, &[(4, 4)]),
+        ];
+
+        for gate in cases {
+            let err = gate.validate().unwrap_err();
+            assert!(err.contains("requires distinct qubits"), "{err}");
+        }
+    }
+
     #[test]
     #[should_panic(expected = "SZZ gate requires an even number of qubits")]
     fn test_szz_vec_odd_qubits() {
@@ -1291,4 +1609,83 @@ mod tests {
         );
         assert!(multi_cx_gates.validate().is_ok()); // Multiple CX gates
     }
+
+    #[test]
+    fn test_gate_validation_rejects_duplicate_qubits_for_batched_commands() {
+        let duplicate_x = Gate::x(&[0, 0]);
+        let err = duplicate_x.validate().unwrap_err();
+        assert!(err.contains("requires distinct qubits"));
+        assert!(err.contains("[0]"));
+
+        let duplicate_mz = Gate::mz(&[1, 1]);
+        let err = duplicate_mz.validate().unwrap_err();
+        assert!(err.contains("requires distinct qubits"));
+        assert!(err.contains("[1]"));
+    }
+
+    #[test]
+    fn test_gate_validation_checks_non_angle_parameters_and_measurement_ids() {
+        let missing_idle_duration = Gate::new(
+            GateType::Idle,
+            Vec::<Angle64>::new(),
+            Vec::<f64>::new(),
+            vec![QubitId::from(0)],
+        );
+        assert!(
+            missing_idle_duration
+                .validate()
+                .unwrap_err()
+                .contains("expected 1 non-angle parameters, got 0")
+        );
+
+        let mut measured = Gate::mz(&[0, 1]);
+        measured.meas_ids.push(MeasId(0));
+        assert!(
+            measured
+                .validate()
+                .unwrap_err()
+                .contains("expected measurement-id count to be 0 or 2, got 1")
+        );
+
+        let mut non_measurement = Gate::x(&[0]);
+        non_measurement.meas_ids.push(MeasId(0));
+        assert!(
+            non_measurement
+                .validate()
+                .unwrap_err()
+                .contains("cannot carry measurement-id payloads")
+        );
+    }
+
+    #[test]
+    fn test_channel_gate_validation_rejects_stale_payloads() {
+        use crate::channel::{BitFlip, Depolarizing};
+
+        let mut stale_qubits = Gate::channel(Depolarizing(0.25, 0));
+        stale_qubits.qubits = vec![QubitId::from(1)].into();
+        assert!(
+            stale_qubits
+                .validate()
+                .unwrap_err()
+                .contains("do not match channel payload qubits")
+        );
+
+        let mut stale_angles = Gate::channel(BitFlip(0.1, 0));
+        stale_angles.angles.push(Angle64::from_turns(0.25));
+        assert!(
+            stale_angles
+                .validate()
+                .unwrap_err()
+                .contains("cannot carry angle, parameter, or measurement-id payloads")
+        );
+
+        let mut channel_payload_on_ideal_gate = Gate::x(&[0]);
+        channel_payload_on_ideal_gate.channel = Some(BitFlip(0.1, 0));
+        assert!(
+            channel_payload_on_ideal_gate
+                .validate()
+                .unwrap_err()
+                .contains("Only GateType::Channel can carry a channel payload")
+        );
+    }
 }
diff --git a/crates/pecos-core/src/lib.rs b/crates/pecos-core/src/lib.rs
index 7007492af..68127d0d4 100644
--- a/crates/pecos-core/src/lib.rs
+++ b/crates/pecos-core/src/lib.rs
@@ -27,10 +27,12 @@ pub mod gate_registry;
 pub mod gate_type;
 pub mod gates;
 pub mod index_set;
+pub mod meas_id;
 pub mod pauli;
 pub mod phase;
 pub mod prelude;
 pub mod qubit_id;
+mod qubit_support;
 pub mod rng;
 pub mod sets;
 pub mod signal;
@@ -46,6 +48,7 @@ pub use bitset::BitSet;
 pub use duration::{TimeScale, TimeUnits};
 pub use element::Element;
 pub use index_set::IndexSet;
+pub use meas_id::MeasId;
 pub use phase::GlobalPhase;
 pub use phase::quarter_phase::QuarterPhase;
 pub use phase::sign::Sign;
@@ -69,8 +72,12 @@ pub use gate_registry::{
     AngleSource, ConcreteStep, DecompStep, GateDefinition, GateDefinitionBuilder, GateRegistry,
     GateSignature,
 };
-pub use gates::{Gate, GateAngles, GateParams, GateQubits};
+pub use gates::{Gate, GateAngles, GateMeasIds, GateParams, GateQubits};
 pub use pauli::pauli_bitmap::PauliBitmap;
+pub use pauli::pauli_bitmask::{
+    BitmaskStorage, Conjugated, PauliBitmask, PauliBitmaskGeneric, PauliBitmaskSmall,
+    PauliBitmaskVec,
+};
 pub use pauli::pauli_sparse::PauliSparse;
 pub use pauli::pauli_string::{ParsePauliStringError, PauliString};
 pub use pauli::{Pauli, PauliOperator};
@@ -84,22 +91,32 @@ pub use circuit_diagram::{
     DiagramStyleBuilder, FamilyPalette, FillPattern, GraphStyle, GraphStyleBuilder, blend_hex,
 };
 
-// UnitaryRep algebra
+// --- Algebraic-level namespaces ---
+//
+// Each level is a module whose glob import gives the user the constructors and
+// types for that algebraic level:
+//
+//   use pecos_core::pauli::*;     // I, X, Y, Z, Xs, Ys, Zs -> PauliString
+//   use pecos_core::clifford::*;  // H, CX, CZ, SWAP, ... -> CliffordRep
+//   use pecos_core::unitary::*;   // T, RZ, CCX, ... -> UnitaryRep
+//   use pecos_core::gate::*;      // MZ, PZ, Reset, ... -> GateExpr
+//   use pecos_core::channel::*;   // Depolarizing, PauliChannel, ... -> ChannelExpr
+//   use pecos_core::op::*;        // MZ, PZ, Depolarizing, ... -> Op (promoted)
+
+pub mod unitary;
 pub use unitary_rep::{Is, Unitary, UnitaryRep};
 
-// PauliString constructors (primary user-facing API for Pauli algebra)
 pub use pauli::constructors::{I, X, Xs, Y, Ys, Z, Zs};
 
-// Clifford base type (single-qubit Clifford group element)
 pub mod clifford;
 pub use clifford::Clifford;
 
-// Cross-type algebraic operators (Pauli * Clifford -> CliffordRep, etc.)
+pub mod channel;
+pub mod gate;
 pub mod gate_algebra;
 
-// Unified gate algebra with automatic type promotion
 pub mod op;
-pub use op::{Basis, ChannelExpr, Level, Op};
+pub use op::{Basis, ChannelExpr, GateExpr, Level, Op};
 
 // Signals
 pub use signal::Signal;
diff --git a/crates/pecos-core/src/meas_id.rs b/crates/pecos-core/src/meas_id.rs
new file mode 100644
index 000000000..4a6f71fb0
--- /dev/null
+++ b/crates/pecos-core/src/meas_id.rs
@@ -0,0 +1,68 @@
+// Copyright 2026 The PECOS Developers
+//
+// Licensed under the Apache License, Version 2.0
+
+//! Measurement result identity.
+//!
+//! Each measurement gate (MZ, MX, etc.) produces a `MeasId` — a unique
+//! identifier for that measurement's outcome. Assigned once at circuit
+//! construction time, carried through all transformations (`TickCircuit` →
+//! `DagCircuit` → `InfluenceMap` → DEM). Never reassigned.
+//!
+//! This follows the MLIR SSA pattern: the value is defined at one point
+//! and referenced everywhere. Detectors reference `MeasId` values
+//! directly instead of fragile position-dependent offsets.
+//!
+//! Metadata (qubit, basis, coordinates, labels) lives in a side table,
+//! not on the `MeasId` itself. The hot path (DEM builder, sampler,
+//! decoder) works with `MeasId` only.
+
+use std::fmt;
+
+/// Unique identity of a measurement result.
+///
+/// Lightweight (pointer-sized), `Copy`, directly usable as an array index.
+/// Analogous to [`QubitId`](crate::QubitId) but for measurement outcomes.
+///
+/// # Example
+///
+/// ```
+/// use pecos_core::MeasId;
+///
+/// let m0 = MeasId(0);
+/// let m1 = MeasId(1);
+/// assert_ne!(m0, m1);
+///
+/// // Direct array indexing
+/// let mut outcomes = vec![false; 10];
+/// outcomes[m0.0] = true;
+/// ```
+#[derive(Debug, Clone, Copy, PartialEq, Eq, PartialOrd, Ord, Hash)]
+pub struct MeasId(pub usize);
+
+impl MeasId {
+    /// The underlying index.
+    #[inline]
+    #[must_use]
+    pub fn index(self) -> usize {
+        self.0
+    }
+}
+
+impl fmt::Display for MeasId {
+    fn fmt(&self, f: &mut fmt::Formatter<'_>) -> fmt::Result {
+        write!(f, "m{}", self.0)
+    }
+}
+
+impl From<usize> for MeasId {
+    fn from(v: usize) -> Self {
+        Self(v)
+    }
+}
+
+impl From<MeasId> for usize {
+    fn from(m: MeasId) -> Self {
+        m.0
+    }
+}
diff --git a/crates/pecos-core/src/op.rs b/crates/pecos-core/src/op.rs
index 30a967c2e..0062d7c8e 100644
--- a/crates/pecos-core/src/op.rs
+++ b/crates/pecos-core/src/op.rs
@@ -12,20 +12,20 @@
 
 //! Unified quantum operation algebra with automatic type promotion.
 //!
-//! [`Op`] wraps four algebraic levels — [`PauliString`], [`CliffordRep`],
-//! [`UnitaryRep`], and [`Channel`] — and automatically promotes to the
+//! [`Op`] wraps five algebraic levels — [`PauliString`], [`CliffordRep`],
+//! [`UnitaryRep`], [`GateExpr`], and [`ChannelExpr`] — and automatically promotes to the
 //! tightest level that can represent a combination.
 //!
 //! # Promotion Hierarchy
 //!
 //! ```text
-//! Pauli  ⊂  Clifford  ⊂  Unitary  ⊂  Channel
+//! Pauli  ⊂  Clifford  ⊂  Unitary  ⊂  Gate  ⊂  Channel
 //! ```
 //!
 //! Combining two `Op` values via tensor (`&`) or composition (`*`) promotes
 //! to the maximum level of the operands. The first three levels support full
-//! algebraic operations including adjoint (`dg()`). The Channel level supports
-//! tensor and composition but not adjoint.
+//! algebraic operations including adjoint (`dg()`). The Gate and Channel levels
+//! support tensor and composition but not adjoint.
 //!
 //! # Examples
 //!
@@ -44,12 +44,17 @@
 //! let u = X(0) & H(3) & T(5);
 //! assert!(u.is_unitary());
 //!
-//! // Adding a measurement promotes to Channel
-//! let ch = H(0) & MZ(1);
+//! // Adding a measurement promotes to Gate
+//! let g = H(0) & MZ(1);
+//! assert!(g.is_gate());
+//!
+//! // Adding a noise channel promotes to Channel
+//! let ch = g & Depolarizing(0.01, 2);
 //! assert!(ch.is_channel());
 //! ```
 
 use crate::clifford_rep::CliffordRep;
+use crate::qubit_support::{assert_distinct_qubits, overlapping_qubits};
 use crate::unitary_rep::{PhaseValue, UnitaryRep};
 use crate::{Angle64, PauliString, QubitId};
 use std::fmt;
@@ -61,7 +66,7 @@ pub use crate::unitary_rep::phase;
 
 /// Unified quantum operation with automatic level promotion.
 ///
-/// Wraps one of four algebraic levels and promotes to the tightest
+/// Wraps one of five algebraic levels and promotes to the tightest
 /// level when combined via `&` (tensor) or `*` (composition).
 ///
 /// The Clifford variant stores both a [`CliffordRep`] (for efficient Clifford
@@ -74,7 +79,10 @@ pub enum Op {
     Clifford(CliffordRep, UnitaryRep),
     /// General unitary level: expression tree.
     Unitary(UnitaryRep),
-    /// Channel level: non-unitary quantum operations (measurements, preparations).
+    /// Gate level: ideal circuit operations such as unitary gates, preparation,
+    /// measurement, and reset.
+    Gate(GateExpr),
+    /// Channel level: general CPTP maps and noise/decoherence operations.
     Channel(ChannelExpr),
 }
 
@@ -84,22 +92,69 @@ pub enum Level {
     Pauli = 0,
     Clifford = 1,
     Unitary = 2,
-    Channel = 3,
+    Gate = 3,
+    Channel = 4,
+}
+
+/// Error returned by fallible tensor-product constructors when supports overlap.
+#[derive(Debug, Clone, PartialEq, Eq)]
+pub struct TensorProductError {
+    overlapping_qubits: Vec<usize>,
 }
 
-/// A non-unitary quantum operation expression.
+impl TensorProductError {
+    /// Qubits touched by both operands.
+    #[must_use]
+    pub fn overlapping_qubits(&self) -> &[usize] {
+        &self.overlapping_qubits
+    }
+}
+
+impl fmt::Display for TensorProductError {
+    fn fmt(&self, f: &mut fmt::Formatter<'_>) -> fmt::Result {
+        write!(
+            f,
+            "tensor product requires disjoint operator support; overlapping qubits: {:?}",
+            self.overlapping_qubits
+        )
+    }
+}
+
+impl std::error::Error for TensorProductError {}
+
+/// An ideal circuit operation expression.
 ///
-/// Channels include measurements, preparations, noise channels (Kraus
-/// operators), and their compositions. They compose and tensor like
-/// unitaries but are not invertible.
+/// Gate expressions represent operations that can appear in an ideal circuit
+/// block: unitaries, preparations, measurements, resets, and their tensor or
+/// sequential combinations. Measurement record allocation is owned by the
+/// surrounding circuit representation, not by this expression.
 #[derive(Debug, Clone, PartialEq)]
-pub enum ChannelExpr {
+pub enum GateExpr {
+    /// A unitary operation lifted to the gate level.
+    Unitary(UnitaryRep),
     /// Prepare qubit in a given basis eigenstate.
     Prep { basis: Basis, qubit: usize },
-    /// Measure qubit (produces classical bit).
+    /// Measure qubit in a given basis (produces a classical outcome).
     Measure { basis: Basis, qubit: usize },
+    /// Reset qubit to the given basis eigenstate.
+    Reset { basis: Basis, qubit: usize },
+    /// Tensor product of gate expressions.
+    Tensor(Vec<GateExpr>),
+    /// Sequential composition: apply first element, then second, etc.
+    Compose(Vec<GateExpr>),
+}
+
+/// A general quantum channel expression.
+///
+/// Channels include noise/decoherence maps, mixed unitaries, lifted ideal
+/// gates, and their compositions. They compose and tensor like unitaries but
+/// are not generally invertible.
+#[derive(Debug, Clone, PartialEq)]
+pub enum ChannelExpr {
     /// A unitary operation lifted to the channel level.
     Unitary(UnitaryRep),
+    /// An ideal gate expression lifted to the channel level.
+    Gate(GateExpr),
     /// Mixed-unitary channel: ρ → `Σ_k` `p_k` `U_k` ρ `U_k`†.
     ///
     /// Each entry is `(probability, unitary)` with probabilities summing to 1.
@@ -121,10 +176,6 @@ pub enum ChannelExpr {
     /// replaced by the maximally mixed state and an erasure flag is raised.
     /// This is a heralded error — the location of the error is known.
     Erasure { prob: f64, qubit: usize },
-    /// Reset channel: ρ → |0⟩⟨0| regardless of input state.
-    ///
-    /// Kraus operators: K₀ = |0⟩⟨0|, K₁ = |0⟩⟨1|.
-    Reset { qubit: usize },
     /// Leakage channel: qubit transitions to a non-computational state
     /// with probability `rate`.
     ///
@@ -155,6 +206,15 @@ fn cliff(cr: CliffordRep, ur: UnitaryRep) -> Op {
     Op::Clifford(cr, ur)
 }
 
+fn require_disjoint_support(lhs: &[usize], rhs: &[usize]) -> Result<(), TensorProductError> {
+    let overlapping_qubits = overlapping_qubits(lhs.iter().copied(), rhs.iter().copied());
+    if overlapping_qubits.is_empty() {
+        Ok(())
+    } else {
+        Err(TensorProductError { overlapping_qubits })
+    }
+}
+
 // --- Core methods ---
 
 impl Op {
@@ -165,6 +225,7 @@ impl Op {
             Op::Pauli(_) => Level::Pauli,
             Op::Clifford(..) => Level::Clifford,
             Op::Unitary(_) => Level::Unitary,
+            Op::Gate(_) => Level::Gate,
             Op::Channel(_) => Level::Channel,
         }
     }
@@ -184,11 +245,25 @@ impl Op {
         matches!(self, Op::Unitary(_))
     }
 
+    #[must_use]
+    pub fn is_gate(&self) -> bool {
+        matches!(self, Op::Gate(_))
+    }
+
     #[must_use]
     pub fn is_channel(&self) -> bool {
         matches!(self, Op::Channel(_))
     }
 
+    /// Extracts the inner `GateExpr`, if at the Gate level.
+    #[must_use]
+    pub fn as_gate(&self) -> Option<&GateExpr> {
+        match self {
+            Op::Gate(gate) => Some(gate),
+            _ => None,
+        }
+    }
+
     /// Extracts the inner `ChannelExpr`, if at the Channel level.
     #[must_use]
     pub fn as_channel(&self) -> Option<&ChannelExpr> {
@@ -235,34 +310,48 @@ impl Op {
     }
 
     /// Consumes and returns the inner `CliffordRep`.
-    /// Pauli promotes to Clifford. Returns `None` for Unitary/Channel (cannot demote).
+    /// Pauli promotes to Clifford. Returns `None` for Unitary/Gate/Channel (cannot demote).
     #[must_use]
     pub fn into_clifford(self) -> Option<CliffordRep> {
         match self {
             Op::Pauli(ps) => Some(CliffordRep::from(ps)),
             Op::Clifford(cr, _) => Some(cr),
-            Op::Unitary(_) | Op::Channel(_) => None,
+            Op::Unitary(_) | Op::Gate(_) | Op::Channel(_) => None,
         }
     }
 
     /// Consumes and returns a `UnitaryRep`.
-    /// Returns `None` for Channel (cannot demote).
+    /// Returns `None` for Gate/Channel (cannot demote).
     #[must_use]
     pub fn into_unitary(self) -> Option<UnitaryRep> {
         match self {
             Op::Pauli(ps) => Some(UnitaryRep::from(ps)),
             Op::Clifford(_, ur) | Op::Unitary(ur) => Some(ur),
+            Op::Gate(_) | Op::Channel(_) => None,
+        }
+    }
+
+    /// Consumes and returns a `GateExpr`. Unitary and lower levels promote to
+    /// `GateExpr::Unitary`; Channel cannot demote.
+    #[must_use]
+    pub fn into_gate(self) -> Option<GateExpr> {
+        match self {
+            Op::Pauli(ps) => Some(GateExpr::Unitary(UnitaryRep::from(ps))),
+            Op::Clifford(_, ur) | Op::Unitary(ur) => Some(GateExpr::Unitary(ur)),
+            Op::Gate(gate) => Some(gate),
             Op::Channel(_) => None,
         }
     }
 
     /// Consumes and returns a `ChannelExpr`. Always succeeds:
-    /// lower levels promote to `ChannelExpr::Unitary`.
+    /// unitary and lower levels promote to `ChannelExpr::Unitary`; Gate
+    /// promotes to `ChannelExpr::Gate`.
     #[must_use]
     pub fn into_channel(self) -> ChannelExpr {
         match self {
             Op::Pauli(ps) => ChannelExpr::Unitary(UnitaryRep::from(ps)),
             Op::Clifford(_, ur) | Op::Unitary(ur) => ChannelExpr::Unitary(ur),
+            Op::Gate(gate) => ChannelExpr::Gate(gate),
             Op::Channel(ch) => ch,
         }
     }
@@ -280,44 +369,105 @@ impl Op {
     }
 
     /// Promotes this `Op` to at least the Unitary level.
-    /// Returns `None` if at Channel level (cannot demote).
+    /// Returns `None` if at Gate or Channel level (cannot demote).
     #[must_use]
     pub fn to_unitary_level(self) -> Option<Op> {
         match self {
             Op::Pauli(ps) => Some(Op::Unitary(UnitaryRep::from(ps))),
             Op::Clifford(_, ur) | Op::Unitary(ur) => Some(Op::Unitary(ur)),
-            Op::Channel(_) => None,
+            Op::Gate(_) | Op::Channel(_) => None,
         }
     }
 
+    /// Promotes this `Op` to the Gate level.
+    #[must_use]
+    pub fn to_gate_level(self) -> Option<Op> {
+        self.into_gate().map(Op::Gate)
+    }
+
     /// Promotes this `Op` to the Channel level.
     #[must_use]
     pub fn to_channel_level(self) -> Op {
         Op::Channel(self.into_channel())
     }
 
+    /// Returns the tensor product of two operations.
+    ///
+    /// This is the fallible form of the `&` operator. Tensor products require
+    /// disjoint qubit support; use `*` for sequential composition on the same
+    /// qubits.
+    ///
+    /// # Errors
+    ///
+    /// Returns [`TensorProductError`] when the two operations touch any of the
+    /// same qubits.
+    pub fn try_tensor(self, rhs: Op) -> Result<Op, TensorProductError> {
+        require_disjoint_support(&self.qubits(), &rhs.qubits())?;
+        Ok(self.tensor_unchecked(rhs))
+    }
+
+    fn tensor_unchecked(self, rhs: Op) -> Op {
+        let max_level = self.level().max(rhs.level());
+        match max_level {
+            Level::Pauli => {
+                let a = self.into_pauli().expect("max_level is Pauli");
+                let b = rhs.into_pauli().expect("max_level is Pauli");
+                Op::Pauli(&a & &b)
+            }
+            Level::Clifford => {
+                let (cr_a, ur_a) = match self {
+                    Op::Pauli(ps) => pauli_to_cliff_pair(ps),
+                    Op::Clifford(cr, ur) => (cr, ur),
+                    _ => unreachable!(),
+                };
+                let (cr_b, ur_b) = match rhs {
+                    Op::Pauli(ps) => pauli_to_cliff_pair(ps),
+                    Op::Clifford(cr, ur) => (cr, ur),
+                    _ => unreachable!(),
+                };
+                cliff(cr_a.compose(&cr_b), ur_a & ur_b)
+            }
+            Level::Unitary => {
+                let a = self.into_unitary().expect("max_level is Unitary");
+                let b = rhs.into_unitary().expect("max_level is Unitary");
+                Op::Unitary(a & b)
+            }
+            Level::Gate => {
+                let a = self.into_gate().expect("max_level is Gate");
+                let b = rhs.into_gate().expect("max_level is Gate");
+                Op::Gate(GateExpr::Tensor(vec![a, b]))
+            }
+            Level::Channel => {
+                let a = self.into_channel();
+                let b = rhs.into_channel();
+                Op::Channel(ChannelExpr::Tensor(vec![a, b]))
+            }
+        }
+    }
+
     /// Returns the adjoint (dagger) of this expression.
     ///
     /// # Panics
-    /// Panics if called on a Channel-level `Op` (channels are not invertible).
+    /// Panics if called on a Gate-level or Channel-level `Op` (not generally invertible).
     #[must_use]
     pub fn dg(&self) -> Op {
         match self {
             Op::Pauli(ps) => Op::Pauli(ps.clone()),
             Op::Clifford(cr, ur) => cliff(cr.inverse(), ur.dg()),
             Op::Unitary(ur) => Op::Unitary(ur.dg()),
+            Op::Gate(_) => panic!("dg() is not defined for Gate-level operations"),
             Op::Channel(_) => panic!("dg() is not defined for Channel-level operations"),
         }
     }
 
-    /// Returns the adjoint if this is a unitary-level operation, `None` for channels.
+    /// Returns the adjoint if this is a unitary-level operation, `None` for gates/channels.
     #[must_use]
     pub fn try_dg(&self) -> Option<Op> {
         match self {
             Op::Pauli(ps) => Some(Op::Pauli(ps.clone())),
             Op::Clifford(cr, ur) => Some(cliff(cr.inverse(), ur.dg())),
             Op::Unitary(ur) => Some(Op::Unitary(ur.dg())),
-            Op::Channel(_) => None,
+            Op::Gate(_) | Op::Channel(_) => None,
         }
     }
 
@@ -326,8 +476,15 @@ impl Op {
     pub fn qubits(&self) -> Vec<usize> {
         match self {
             Op::Pauli(ps) => ps.qubits(),
-            Op::Clifford(cr, _) => (0..cr.num_qubits()).collect(),
+            Op::Clifford(cr, ur) => {
+                let mut qs = cr.support_qubits();
+                qs.extend(ur.qubits());
+                qs.sort_unstable();
+                qs.dedup();
+                qs
+            }
             Op::Unitary(ur) => ur.qubits(),
+            Op::Gate(gate) => gate.qubits(),
             Op::Channel(ch) => ch.qubits(),
         }
     }
@@ -339,6 +496,71 @@ impl Op {
     }
 }
 
+// --- GateExpr methods ---
+
+impl GateExpr {
+    /// Returns the set of qubit indices this gate expression acts on.
+    #[must_use]
+    pub fn qubits(&self) -> Vec<usize> {
+        let mut qs = Vec::new();
+        self.collect_qubits(&mut qs);
+        qs.sort_unstable();
+        qs.dedup();
+        qs
+    }
+
+    fn collect_qubits(&self, out: &mut Vec<usize>) {
+        match self {
+            GateExpr::Prep { qubit, .. }
+            | GateExpr::Measure { qubit, .. }
+            | GateExpr::Reset { qubit, .. } => {
+                out.push(*qubit);
+            }
+            GateExpr::Unitary(ur) => {
+                out.extend(ur.qubits());
+            }
+            GateExpr::Tensor(parts) | GateExpr::Compose(parts) => {
+                for part in parts {
+                    part.collect_qubits(out);
+                }
+            }
+        }
+    }
+}
+
+impl fmt::Display for GateExpr {
+    fn fmt(&self, f: &mut fmt::Formatter<'_>) -> fmt::Result {
+        match self {
+            GateExpr::Unitary(ur) => write!(f, "{ur:?}"),
+            GateExpr::Prep { basis, qubit } => write!(f, "P{basis:?}({qubit})"),
+            GateExpr::Measure { basis, qubit } => write!(f, "M{basis:?}({qubit})"),
+            GateExpr::Reset {
+                basis: Basis::Z,
+                qubit,
+            } => write!(f, "Reset({qubit})"),
+            GateExpr::Reset { basis, qubit } => write!(f, "Reset{basis:?}({qubit})"),
+            GateExpr::Tensor(parts) => {
+                for (i, part) in parts.iter().enumerate() {
+                    if i > 0 {
+                        write!(f, " & ")?;
+                    }
+                    write!(f, "{part}")?;
+                }
+                Ok(())
+            }
+            GateExpr::Compose(parts) => {
+                for (i, part) in parts.iter().enumerate() {
+                    if i > 0 {
+                        write!(f, " * ")?;
+                    }
+                    write!(f, "{part}")?;
+                }
+                Ok(())
+            }
+        }
+    }
+}
+
 // --- ChannelExpr methods ---
 
 impl ChannelExpr {
@@ -354,18 +576,18 @@ impl ChannelExpr {
 
     fn collect_qubits(&self, out: &mut Vec<usize>) {
         match self {
-            ChannelExpr::Prep { qubit, .. }
-            | ChannelExpr::Measure { qubit, .. }
-            | ChannelExpr::AmplitudeDamping { qubit, .. }
+            ChannelExpr::AmplitudeDamping { qubit, .. }
             | ChannelExpr::PhaseDamping { qubit, .. }
             | ChannelExpr::Erasure { qubit, .. }
-            | ChannelExpr::Reset { qubit }
             | ChannelExpr::Leakage { qubit, .. } => {
                 out.push(*qubit);
             }
             ChannelExpr::Unitary(ur) => {
                 out.extend(ur.qubits());
             }
+            ChannelExpr::Gate(gate) => {
+                out.extend(gate.qubits());
+            }
             ChannelExpr::MixedUnitary(ops) => {
                 for (_, ur) in ops {
                     out.extend(ur.qubits());
@@ -383,9 +605,8 @@ impl ChannelExpr {
 impl fmt::Display for ChannelExpr {
     fn fmt(&self, f: &mut fmt::Formatter<'_>) -> fmt::Result {
         match self {
-            ChannelExpr::Prep { basis, qubit } => write!(f, "P{basis:?}({qubit})"),
-            ChannelExpr::Measure { basis, qubit } => write!(f, "M{basis:?}({qubit})"),
             ChannelExpr::Unitary(ur) => write!(f, "{ur:?}"),
+            ChannelExpr::Gate(gate) => write!(f, "{gate}"),
             ChannelExpr::MixedUnitary(ops) => {
                 write!(f, "MixedUnitary[")?;
                 for (i, (p, ur)) in ops.iter().enumerate() {
@@ -405,7 +626,6 @@ impl fmt::Display for ChannelExpr {
             ChannelExpr::Erasure { prob, qubit } => {
                 write!(f, "Erasure({prob}, {qubit})")
             }
-            ChannelExpr::Reset { qubit } => write!(f, "Reset({qubit})"),
             ChannelExpr::Leakage { rate, qubit } => {
                 write!(f, "Leakage({rate}, {qubit})")
             }
@@ -445,37 +665,7 @@ impl BitAnd for Op {
     type Output = Op;
 
     fn bitand(self, rhs: Op) -> Op {
-        let max_level = self.level().max(rhs.level());
-        match max_level {
-            Level::Pauli => {
-                let a = self.into_pauli().expect("max_level is Pauli");
-                let b = rhs.into_pauli().expect("max_level is Pauli");
-                Op::Pauli(&a & &b)
-            }
-            Level::Clifford => {
-                let (cr_a, ur_a) = match self {
-                    Op::Pauli(ps) => pauli_to_cliff_pair(ps),
-                    Op::Clifford(cr, ur) => (cr, ur),
-                    _ => unreachable!(),
-                };
-                let (cr_b, ur_b) = match rhs {
-                    Op::Pauli(ps) => pauli_to_cliff_pair(ps),
-                    Op::Clifford(cr, ur) => (cr, ur),
-                    _ => unreachable!(),
-                };
-                cliff(cr_a.compose(&cr_b), ur_a & ur_b)
-            }
-            Level::Unitary => {
-                let a = self.into_unitary().expect("max_level is Unitary");
-                let b = rhs.into_unitary().expect("max_level is Unitary");
-                Op::Unitary(a & b)
-            }
-            Level::Channel => {
-                let a = self.into_channel();
-                let b = rhs.into_channel();
-                Op::Channel(ChannelExpr::Tensor(vec![a, b]))
-            }
-        }
+        self.try_tensor(rhs).unwrap_or_else(|err| panic!("{err}"))
     }
 }
 
@@ -510,6 +700,11 @@ impl Mul for Op {
                 let b = rhs.into_unitary().expect("max_level is Unitary");
                 Op::Unitary(a * b)
             }
+            Level::Gate => {
+                let a = self.into_gate().expect("max_level is Gate");
+                let b = rhs.into_gate().expect("max_level is Gate");
+                Op::Gate(GateExpr::Compose(vec![a, b]))
+            }
             Level::Channel => {
                 let a = self.into_channel();
                 let b = rhs.into_channel();
@@ -573,6 +768,7 @@ impl Neg for Op {
             Op::Pauli(ps) => Op::Pauli(-ps),
             Op::Clifford(cr, ur) => cliff(cr, -ur),
             Op::Unitary(ur) => Op::Unitary(-ur),
+            Op::Gate(_) => panic!("negation is not defined for Gate-level operations"),
             Op::Channel(_) => panic!("negation is not defined for Channel-level operations"),
         }
     }
@@ -594,6 +790,9 @@ impl Mul<Op> for ImaginaryUnit {
             Op::Pauli(ps) => Op::Pauli(self * ps),
             Op::Clifford(cr, ur) => cliff(cr, self * ur),
             Op::Unitary(ur) => Op::Unitary(self * ur),
+            Op::Gate(_) => {
+                panic!("phase multiplication is not defined for Gate-level operations")
+            }
             Op::Channel(_) => {
                 panic!("phase multiplication is not defined for Channel-level operations")
             }
@@ -617,6 +816,9 @@ impl Mul<Op> for NegImaginaryUnit {
             Op::Pauli(ps) => Op::Pauli(self * ps),
             Op::Clifford(cr, ur) => cliff(cr, self * ur),
             Op::Unitary(ur) => Op::Unitary(self * ur),
+            Op::Gate(_) => {
+                panic!("phase multiplication is not defined for Gate-level operations")
+            }
             Op::Channel(_) => {
                 panic!("phase multiplication is not defined for Channel-level operations")
             }
@@ -637,19 +839,22 @@ impl Mul<&Op> for NegImaginaryUnit {
 /// Applies the global phase e^{i*angle} to the operation.
 ///
 /// # Panics
-/// Panics if applied to a Channel-level operation.
+/// Panics if applied to a Gate-level or Channel-level operation.
 impl Mul<Op> for PhaseValue {
     type Output = Op;
 
     fn mul(self, rhs: Op) -> Op {
         match rhs {
+            Op::Gate(_) => {
+                panic!("phase multiplication is not defined for Gate-level operations")
+            }
             Op::Channel(_) => {
                 panic!("phase multiplication is not defined for Channel-level operations")
             }
             other => {
                 let ur = other
                     .into_unitary()
-                    .expect("non-Channel Op is convertible to Unitary");
+                    .expect("non-Gate/non-Channel Op is convertible to Unitary");
                 Op::Unitary(self * ur)
             }
         }
@@ -702,6 +907,18 @@ impl From<UnitaryRep> for Op {
     }
 }
 
+impl From<GateExpr> for Op {
+    fn from(gate: GateExpr) -> Op {
+        Op::Gate(gate)
+    }
+}
+
+impl From<ChannelExpr> for Op {
+    fn from(channel: ChannelExpr) -> Op {
+        Op::Channel(channel)
+    }
+}
+
 // --- Display ---
 
 impl fmt::Display for Op {
@@ -710,6 +927,7 @@ impl fmt::Display for Op {
             Op::Pauli(ps) => write!(f, "{ps}"),
             Op::Clifford(cr, _) => write!(f, "{cr}"),
             Op::Unitary(ur) => write!(f, "{ur:?}"),
+            Op::Gate(gate) => write!(f, "{gate}"),
             Op::Channel(ch) => write!(f, "{ch}"),
         }
     }
@@ -1179,13 +1397,13 @@ pub fn CCX(c0: impl Into<QubitId>, c1: impl Into<QubitId>, target: impl Into<Qub
     Op::Unitary(crate::unitary_rep::CCX(c0, c1, target))
 }
 
-// --- Gate constructors — Channel level ---
+// --- Gate constructors — Gate level ---
 
 /// Prepare qubit in the |0> state (Z-basis preparation).
 #[allow(non_snake_case)]
 #[must_use]
 pub fn PZ(qubit: impl Into<QubitId>) -> Op {
-    Op::Channel(ChannelExpr::Prep {
+    Op::Gate(GateExpr::Prep {
         basis: Basis::Z,
         qubit: qubit.into().0,
     })
@@ -1195,17 +1413,27 @@ pub fn PZ(qubit: impl Into<QubitId>) -> Op {
 #[allow(non_snake_case)]
 #[must_use]
 pub fn PX(qubit: impl Into<QubitId>) -> Op {
-    Op::Channel(ChannelExpr::Prep {
+    Op::Gate(GateExpr::Prep {
         basis: Basis::X,
         qubit: qubit.into().0,
     })
 }
 
+/// Prepare qubit in the Y-basis +1 eigenstate.
+#[allow(non_snake_case)]
+#[must_use]
+pub fn PY(qubit: impl Into<QubitId>) -> Op {
+    Op::Gate(GateExpr::Prep {
+        basis: Basis::Y,
+        qubit: qubit.into().0,
+    })
+}
+
 /// Measure qubit in the Z basis (computational basis measurement).
 #[allow(non_snake_case)]
 #[must_use]
 pub fn MZ(qubit: impl Into<QubitId>) -> Op {
-    Op::Channel(ChannelExpr::Measure {
+    Op::Gate(GateExpr::Measure {
         basis: Basis::Z,
         qubit: qubit.into().0,
     })
@@ -1215,12 +1443,22 @@ pub fn MZ(qubit: impl Into<QubitId>) -> Op {
 #[allow(non_snake_case)]
 #[must_use]
 pub fn MX(qubit: impl Into<QubitId>) -> Op {
-    Op::Channel(ChannelExpr::Measure {
+    Op::Gate(GateExpr::Measure {
         basis: Basis::X,
         qubit: qubit.into().0,
     })
 }
 
+/// Measure qubit in the Y basis.
+#[allow(non_snake_case)]
+#[must_use]
+pub fn MY(qubit: impl Into<QubitId>) -> Op {
+    Op::Gate(GateExpr::Measure {
+        basis: Basis::Y,
+        qubit: qubit.into().0,
+    })
+}
+
 // --- Noise channel constructors ---
 
 /// Single-qubit depolarizing channel: ρ → (1−p)ρ + (p/3)(XρX + `YρY` + `ZρZ`).
@@ -1341,6 +1579,7 @@ pub fn Depolarizing2(p: f64, q0: impl Into<QubitId>, q1: impl Into<QubitId>) ->
     assert!((0.0..=1.0).contains(&p), "probability p must be in [0, 1]");
     let a = q0.into();
     let b = q1.into();
+    assert_distinct_qubits("Depolarizing2", [a.0, b.0]);
     let p15 = p / 15.0;
     let paulis_1q = [
         unitary_rep::I,
@@ -1405,7 +1644,8 @@ pub fn Erasure(prob: f64, qubit: impl Into<QubitId>) -> Op {
 #[allow(non_snake_case)]
 #[must_use]
 pub fn Reset(qubit: impl Into<QubitId>) -> Op {
-    Op::Channel(ChannelExpr::Reset {
+    Op::Gate(GateExpr::Reset {
+        basis: Basis::Z,
         qubit: qubit.into().0,
     })
 }
@@ -1521,6 +1761,18 @@ mod tests {
         assert!(op.is_clifford());
     }
 
+    #[test]
+    fn clifford_tensor_uses_actual_support_not_span() {
+        let op = H(0) & SZ(3);
+        let cr = op.as_clifford().unwrap();
+
+        assert_eq!(op.qubits(), vec![0, 3]);
+        assert_eq!(cr.apply(&PauliString::x(0)), PauliString::z(0));
+        assert_eq!(cr.apply(&PauliString::z(0)), PauliString::x(0));
+        assert_eq!(cr.apply(&PauliString::x(3)), PauliString::y(3));
+        assert_eq!(cr.apply(&PauliString::z(3)), PauliString::z(3));
+    }
+
     #[test]
     fn pauli_unitary_tensor_promotes() {
         let op = X(0) & T(3);
@@ -1539,6 +1791,131 @@ mod tests {
         assert!(op.is_unitary());
     }
 
+    #[test]
+    fn try_tensor_reports_overlapping_qubits() {
+        let err = X(0).try_tensor(Z(0)).unwrap_err();
+        assert_eq!(err.overlapping_qubits(), &[0]);
+    }
+
+    #[test]
+    fn try_tensor_rejects_mixed_level_overlaps() {
+        let cases = [
+            ("pauli-clifford", X(0), H(0), vec![0]),
+            ("pauli-unitary", X(0), T(0), vec![0]),
+            ("pauli-gate", X(0), MZ(0), vec![0]),
+            ("pauli-channel", X(0), Depolarizing(0.01, 0), vec![0]),
+            ("clifford-gate", H(0), MZ(0), vec![0]),
+            ("gate-channel", MZ(0), Depolarizing(0.01, 0), vec![0]),
+            ("partial-multi-qubit", CX(0, 2), H(2), vec![2]),
+        ];
+
+        for (name, lhs, rhs, expected_overlap) in cases {
+            let err = lhs.try_tensor(rhs).unwrap_err();
+            assert_eq!(
+                err.overlapping_qubits(),
+                expected_overlap.as_slice(),
+                "{name}"
+            );
+        }
+    }
+
+    #[test]
+    fn tensor_operator_panics_are_consistent_across_levels() {
+        fn assert_overlap_panic(f: impl FnOnce() + std::panic::UnwindSafe, expected: &str) {
+            let err = std::panic::catch_unwind(f).expect_err("expected tensor overlap panic");
+            let message = if let Some(message) = err.downcast_ref::<String>() {
+                message.as_str()
+            } else if let Some(message) = err.downcast_ref::<&str>() {
+                message
+            } else {
+                panic!("unexpected non-string panic payload");
+            };
+            assert!(
+                message.contains("tensor product requires disjoint operator support"),
+                "{message}"
+            );
+            assert!(message.contains(expected), "{message}");
+        }
+
+        assert_overlap_panic(
+            || {
+                let _ = X(0) & Z(0);
+            },
+            "[0]",
+        );
+        assert_overlap_panic(
+            || {
+                let _ = H(0) & T(0);
+            },
+            "[0]",
+        );
+        assert_overlap_panic(
+            || {
+                let _ = T(0) & MZ(0);
+            },
+            "[0]",
+        );
+        assert_overlap_panic(
+            || {
+                let _ = MZ(0) & Depolarizing(0.01, 0);
+            },
+            "[0]",
+        );
+        assert_overlap_panic(
+            || {
+                let _ = CX(0, 2) & Depolarizing(0.01, 2);
+            },
+            "[2]",
+        );
+    }
+
+    #[test]
+    fn try_tensor_accepts_mixed_level_disjoint_support() {
+        assert!((X(0).try_tensor(H(1))).unwrap().is_clifford());
+        assert!((H(0).try_tensor(T(1))).unwrap().is_unitary());
+        assert!(
+            (MZ(0).try_tensor(Depolarizing(0.01, 1)))
+                .unwrap()
+                .is_channel()
+        );
+    }
+
+    #[test]
+    #[should_panic(expected = "tensor product requires disjoint operator support")]
+    fn pauli_tensor_rejects_overlapping_qubits() {
+        let _ = X(0) & Z(0);
+    }
+
+    #[test]
+    #[should_panic(expected = "tensor product requires disjoint operator support")]
+    fn clifford_tensor_rejects_overlapping_qubits() {
+        let _ = H(0) & SZ(0);
+    }
+
+    #[test]
+    #[should_panic(expected = "tensor product requires disjoint operator support")]
+    fn gate_tensor_rejects_overlapping_qubits() {
+        let _ = H(0) & MZ(0);
+    }
+
+    #[test]
+    #[should_panic(expected = "tensor product requires disjoint operator support")]
+    fn channel_tensor_rejects_overlapping_qubits() {
+        let _ = H(0) & Depolarizing(0.01, 0);
+    }
+
+    #[test]
+    #[should_panic(expected = "SWAP requires distinct qubits")]
+    fn op_two_qubit_gate_rejects_repeated_qubit() {
+        let _ = SWAP(0, 0);
+    }
+
+    #[test]
+    #[should_panic(expected = "Depolarizing2 requires distinct qubits")]
+    fn op_two_qubit_channel_rejects_repeated_qubit() {
+        let _ = Depolarizing2(0.01, 2, 2);
+    }
+
     // --- Composition promotion ---
 
     #[test]
@@ -1589,8 +1966,9 @@ mod tests {
     }
 
     #[test]
-    fn into_unitary_none_for_channel() {
+    fn into_unitary_none_for_gate_and_channel() {
         assert!(MZ(0).into_unitary().is_none());
+        assert!(Depolarizing(0.01, 0).into_unitary().is_none());
     }
 
     // --- Level promotion ---
@@ -1613,8 +1991,9 @@ mod tests {
     }
 
     #[test]
-    fn to_unitary_level_none_for_channel() {
+    fn to_unitary_level_none_for_gate_and_channel() {
         assert!(MZ(0).to_unitary_level().is_none());
+        assert!(Depolarizing(0.01, 0).to_unitary_level().is_none());
     }
 
     // --- Adjoint ---
@@ -1763,6 +2142,8 @@ mod tests {
     fn level_ordering() {
         assert!(Level::Pauli < Level::Clifford);
         assert!(Level::Clifford < Level::Unitary);
+        assert!(Level::Unitary < Level::Gate);
+        assert!(Level::Gate < Level::Channel);
     }
 
     // --- From conversions ---
@@ -1900,44 +2281,60 @@ mod tests {
         assert!(b.is_clifford());
     }
 
-    // --- Channel level ---
+    // --- Gate level ---
 
     #[test]
-    fn channel_level() {
-        assert!(MZ(0).is_channel());
-        assert!(MX(0).is_channel());
-        assert!(PZ(0).is_channel());
-        assert!(PX(0).is_channel());
+    fn gate_level() {
+        assert!(MZ(0).is_gate());
+        assert!(MX(0).is_gate());
+        assert!(MY(0).is_gate());
+        assert!(PZ(0).is_gate());
+        assert!(PX(0).is_gate());
+        assert!(PY(0).is_gate());
     }
 
     #[test]
-    fn channel_tensor_stays_channel() {
+    fn gate_tensor_stays_gate() {
         let op = MZ(0) & MZ(1);
-        assert!(op.is_channel());
+        assert!(op.is_gate());
     }
 
     #[test]
-    fn channel_compose_stays_channel() {
+    fn gate_compose_stays_gate() {
         let op = PZ(0) * MZ(0);
-        assert!(op.is_channel());
+        assert!(op.is_gate());
     }
 
     #[test]
-    fn unitary_channel_tensor_promotes() {
+    fn unitary_gate_tensor_promotes() {
         let op = H(0) & MZ(1);
-        assert!(op.is_channel());
+        assert!(op.is_gate());
     }
 
     #[test]
-    fn pauli_channel_tensor_promotes() {
+    fn non_clifford_unitary_gate_tensor_promotes_to_gate_tensor() {
+        let op = T(0) & MZ(1);
+        assert!(op.is_gate());
+        assert!(matches!(op, Op::Gate(GateExpr::Tensor(parts)) if parts.len() == 2));
+    }
+
+    #[test]
+    fn pauli_gate_tensor_promotes() {
         let op = X(0) & MZ(1);
-        assert!(op.is_channel());
+        assert!(op.is_gate());
     }
 
     #[test]
-    fn unitary_channel_compose_promotes() {
+    fn unitary_gate_compose_promotes() {
         let op = H(0) * MZ(0);
-        assert!(op.is_channel());
+        assert!(op.is_gate());
+    }
+
+    #[test]
+    fn non_clifford_unitary_gate_compose_promotes_to_gate_compose() {
+        let op = T(0) * MZ(0);
+        assert!(op.is_gate());
+        assert!(matches!(op, Op::Gate(GateExpr::Compose(parts)) if parts.len() == 2));
     }
 
     #[test]
@@ -1950,12 +2347,21 @@ mod tests {
     }
 
     #[test]
-    fn into_clifford_none_for_channel() {
+    fn into_gate_promotes_unitaries_and_keeps_gates() {
+        assert!(X(0).into_gate().is_some());
+        assert!(H(0).into_gate().is_some());
+        assert!(T(0).into_gate().is_some());
+        assert!(MZ(0).into_gate().is_some());
+        assert!(Depolarizing(0.01, 0).into_gate().is_none());
+    }
+
+    #[test]
+    fn into_clifford_none_for_gate() {
         assert!(MZ(0).into_clifford().is_none());
     }
 
     #[test]
-    fn try_dg_none_for_channel() {
+    fn try_dg_none_for_gate() {
         assert!(MZ(0).try_dg().is_none());
     }
 
@@ -1967,26 +2373,32 @@ mod tests {
     }
 
     #[test]
-    #[should_panic(expected = "not defined for Channel")]
-    fn dg_panics_for_channel() {
+    #[should_panic(expected = "not defined for Gate")]
+    fn dg_panics_for_gate() {
         let _ = MZ(0).dg();
     }
 
     #[test]
-    fn channel_qubits() {
+    fn gate_qubits() {
         let op = MZ(3);
         assert_eq!(op.qubits(), vec![3]);
         assert_eq!(op.num_qubits(), 4);
     }
 
     #[test]
-    fn channel_tensor_qubits() {
+    fn gate_tensor_qubits() {
         let op = PZ(0) & MZ(2);
         let mut qs = op.qubits();
         qs.sort_unstable();
         assert_eq!(qs, vec![0, 2]);
     }
 
+    #[test]
+    fn gate_channel_tensor_promotes_to_channel() {
+        let op = MZ(0) & Depolarizing(0.01, 1);
+        assert!(op.is_channel());
+    }
+
     #[test]
     fn to_channel_level_promotes() {
         assert!(X(0).to_channel_level().is_channel());
@@ -1995,12 +2407,6 @@ mod tests {
         assert!(MZ(0).to_channel_level().is_channel());
     }
 
-    #[test]
-    fn level_ordering_with_channel() {
-        assert!(Level::Unitary < Level::Channel);
-        assert!(Level::Pauli < Level::Channel);
-    }
-
     // --- Noise channels ---
 
     #[test]
@@ -2091,12 +2497,26 @@ mod tests {
         assert!(op.is_channel());
     }
 
+    #[test]
+    fn non_clifford_unitary_channel_tensor_promotes_to_channel_tensor() {
+        let op = T(0) & Depolarizing(0.1, 1);
+        assert!(op.is_channel());
+        assert!(matches!(op, Op::Channel(ChannelExpr::Tensor(parts)) if parts.len() == 2));
+    }
+
     #[test]
     fn noise_compose_with_gate() {
         let op = H(0) * Dephasing(0.05, 0);
         assert!(op.is_channel());
     }
 
+    #[test]
+    fn non_clifford_unitary_channel_compose_promotes_to_channel_compose() {
+        let op = T(0) * Dephasing(0.05, 0);
+        assert!(op.is_channel());
+        assert!(matches!(op, Op::Channel(ChannelExpr::Compose(parts)) if parts.len() == 2));
+    }
+
     #[test]
     fn mixed_unitary_qubits() {
         let op = Depolarizing(0.1, 5);
@@ -2170,10 +2590,32 @@ mod tests {
     }
 
     #[test]
-    fn reset_is_channel() {
+    fn reset_is_gate() {
         let op = Reset(0);
-        assert!(op.is_channel());
+        assert!(op.is_gate());
         assert_eq!(op.qubits(), vec![0]);
+
+        assert!(matches!(
+            PX(1),
+            Op::Gate(GateExpr::Prep {
+                basis: Basis::X,
+                qubit: 1
+            })
+        ));
+        assert!(matches!(
+            PY(2),
+            Op::Gate(GateExpr::Prep {
+                basis: Basis::Y,
+                qubit: 2
+            })
+        ));
+        assert!(matches!(
+            PZ(3),
+            Op::Gate(GateExpr::Prep {
+                basis: Basis::Z,
+                qubit: 3
+            })
+        ));
     }
 
     #[test]
@@ -2195,7 +2637,6 @@ mod tests {
         let ops = vec![
             PhaseDamping(0.1, 0),
             Erasure(0.05, 0),
-            Reset(0),
             Leakage(0.01, 0),
             AmplitudeDamping(0.1, 0),
         ];
@@ -2333,25 +2774,25 @@ mod tests {
     #[test]
     #[should_panic(expected = "not defined for Channel")]
     fn i_times_channel_panics() {
-        let _ = i * MZ(0);
+        let _ = i * Depolarizing(0.01, 0);
     }
 
     #[test]
     #[should_panic(expected = "not defined for Channel")]
     fn neg_channel_panics() {
-        let _ = -MZ(0);
+        let _ = -Depolarizing(0.01, 0);
     }
 
     #[test]
     #[should_panic(expected = "not defined for Channel")]
     fn generic_phase_channel_panics() {
-        let _ = phase(Angle64::QUARTER_TURN) * MZ(0);
+        let _ = phase(Angle64::QUARTER_TURN) * Depolarizing(0.01, 0);
     }
 
     #[test]
     #[should_panic(expected = "negation is not defined for Channel")]
     fn minus_one_channel_panics() {
-        let _ = -1 * MZ(0);
+        let _ = -1 * Depolarizing(0.01, 0);
     }
 
     // --- Noise boundary values ---
diff --git a/crates/pecos-core/src/operator.rs b/crates/pecos-core/src/operator.rs
deleted file mode 100644
index aae35de9d..000000000
--- a/crates/pecos-core/src/operator.rs
+++ /dev/null
@@ -1,4037 +0,0 @@
-// Copyright 2024 The PECOS Developers
-//
-// Licensed under the Apache License, Version 2.0 (the "License"); you may not use this file except
-// in compliance with the License.You may obtain a copy of the License at
-//
-//     https://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software distributed under the License
-// is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express
-// or implied. See the License for the specific language governing permissions and limitations under
-// the License.
-
-//! Gate expression algebra for quantum circuits.
-//!
-//! This module provides a lazy expression tree for building and manipulating
-//! quantum gate sequences with algebraic simplification.
-//!
-//! # Representation Hierarchy
-//!
-//! 1. **Rotation gates**: `exp(-i θ/2 P)` where P is a Pauli - covers most gates
-//! 2. **Control gates**: CX, CZ, SWAP, etc. - stay as named gates
-//!
-//! # Operators
-//!
-//! - `&` - Tensor product (operators on different qubits)
-//! - `*` - Composition (matrix multiplication order: A * B means apply B then A)
-//! - `.dg()` - Adjoint (Hermitian conjugate)
-//!
-//! # Examples
-//!
-//! ```
-//! use pecos_core::operator::*;
-//! use pecos_core::Angle64;
-//!
-//! // Build a circuit: H on q0, then CX(0,1), then T on q1
-//! let circuit = T(1) * CX(0, 1) * H(0);
-//!
-//! // Check if it's Clifford
-//! assert!(!circuit.is_clifford());  // T is not Clifford
-//!
-//! // Clifford circuit
-//! let cliff = CX(0, 1) * H(0);
-//! assert!(cliff.is_clifford());
-//!
-//! // Tensor product
-//! let two_qubit = X(0) & Z(1);
-//!
-//! // Adjoint
-//! let inv = circuit.dg();
-//! ```
-
-use crate::gate_type::GateType;
-use crate::pauli::PauliOperator;
-use crate::phase::Phase;
-use crate::{Angle64, PauliString, QuarterPhase, QubitId};
-use smallvec::SmallVec;
-use std::ops::{BitAnd, Mul, Neg};
-
-// --- Phase macros for exact arithmetic ---
-
-/// Creates a `PhaseValue` from a pi-based expression for use with operators.
-///
-/// This is a convenience wrapper around `angle!` that returns a `PhaseValue`
-/// which can be directly multiplied with gate expressions.
-///
-/// # Examples
-///
-/// ```
-/// use pecos_core::{phase, Angle64};
-/// use pecos_core::operator::X;
-///
-/// // e^{iπ/4} * X - exact, no floating point
-/// let op = phase!(pi / 4) * X(0);
-///
-/// // e^{iπ/2} * X = i * X
-/// let op = phase!(pi / 2) * X(0);
-///
-/// // e^{i * 2π/3} * X
-/// let op = phase!(2 * pi / 3) * X(0);
-/// ```
-#[macro_export]
-macro_rules! phase {
-    ($($tokens:tt)*) => {
-        $crate::operator::PhaseValue($crate::angle!($($tokens)*))
-    };
-}
-
-/// Creates a `PhaseValue` from a turn-based fraction for use with operators.
-///
-/// This is a convenience wrapper around `turn!` that returns a `PhaseValue`
-/// which can be directly multiplied with gate expressions.
-///
-/// # Examples
-///
-/// ```
-/// use pecos_core::phase_turn;
-/// use pecos_core::operator::X;
-///
-/// // T gate phase: e^{i * 2π/8} = e^{iπ/4}
-/// let op = phase_turn!(1 / 8) * X(0);
-///
-/// // SZ gate phase: e^{i * 2π/4} = e^{iπ/2} = i
-/// let op = phase_turn!(1 / 4) * X(0);
-///
-/// // Third of a turn: e^{i * 2π/3}
-/// let op = phase_turn!(1 / 3) * X(0);
-/// ```
-#[macro_export]
-macro_rules! phase_turn {
-    ($($tokens:tt)*) => {
-        $crate::operator::PhaseValue($crate::turn!($($tokens)*))
-    };
-}
-
-/// Rotation gate types - gates parameterized by an angle.
-#[derive(Debug, Clone, Copy, PartialEq, Eq, Hash)]
-pub enum RotationType {
-    /// Rotation around X axis: exp(-i θ/2 X)
-    RX,
-    /// Rotation around Y axis: exp(-i θ/2 Y)
-    RY,
-    /// Rotation around Z axis: exp(-i θ/2 Z)
-    RZ,
-    /// Two-qubit XX rotation: exp(-i θ/2 X⊗X)
-    RXX,
-    /// Two-qubit YY rotation: exp(-i θ/2 Y⊗Y)
-    RYY,
-    /// Two-qubit ZZ rotation: exp(-i θ/2 Z⊗Z)
-    RZZ,
-}
-
-impl RotationType {
-    /// Returns the number of qubits this rotation acts on.
-    #[must_use]
-    pub fn num_qubits(&self) -> usize {
-        match self {
-            Self::RX | Self::RY | Self::RZ => 1,
-            Self::RXX | Self::RYY | Self::RZZ => 2,
-        }
-    }
-
-    /// Returns the corresponding `GateType` for this rotation.
-    #[must_use]
-    pub fn to_gate_type(&self) -> GateType {
-        match self {
-            Self::RX => GateType::RX,
-            Self::RY => GateType::RY,
-            Self::RZ => GateType::RZ,
-            Self::RXX => GateType::RXX,
-            Self::RYY => GateType::RYY,
-            Self::RZZ => GateType::RZZ,
-        }
-    }
-}
-
-// --- Commutativity ---
-
-/// Result of checking whether two operators commute.
-#[derive(Debug, Clone, Copy, PartialEq, Eq, Hash)]
-pub enum Commutativity {
-    /// Operators commute: AB = BA
-    Commutes,
-    /// Operators anti-commute: AB = -BA
-    AntiCommutes,
-    /// Commutativity cannot be determined (non-Pauli operators)
-    Unknown,
-}
-
-// --- Qubit target types for polymorphic gate constructors ---
-
-/// Wrapper for qubit targets that can be a single qubit or multiple qubits.
-///
-/// Enables pluralized gate functions to accept various qubit collections:
-/// ```
-/// use pecos_core::operator::*;
-/// use pecos_core::QubitId;
-///
-/// // Multiple qubits via Xs - equivalent to X(0) & X(2) & X(5)
-/// let x_multi = Xs([0, 2, 5]);
-///
-/// // Also works with QubitId arrays
-/// let x_multi = Xs([QubitId(0), QubitId(2)]);
-/// ```
-#[derive(Debug, Clone)]
-pub struct Qubits(SmallVec<[QubitId; 4]>);
-
-impl From<usize> for Qubits {
-    fn from(q: usize) -> Self {
-        Qubits(smallvec::smallvec![QubitId(q)])
-    }
-}
-
-impl From<QubitId> for Qubits {
-    fn from(q: QubitId) -> Self {
-        Qubits(smallvec::smallvec![q])
-    }
-}
-
-impl<const N: usize> From<[usize; N]> for Qubits {
-    fn from(qs: [usize; N]) -> Self {
-        Qubits(qs.into_iter().map(QubitId).collect())
-    }
-}
-
-impl<const N: usize> From<[QubitId; N]> for Qubits {
-    fn from(qs: [QubitId; N]) -> Self {
-        Qubits(qs.into_iter().collect())
-    }
-}
-
-impl From<&[usize]> for Qubits {
-    fn from(qs: &[usize]) -> Self {
-        Qubits(qs.iter().copied().map(QubitId).collect())
-    }
-}
-
-impl From<&[QubitId]> for Qubits {
-    fn from(qs: &[QubitId]) -> Self {
-        Qubits(qs.iter().copied().collect())
-    }
-}
-
-impl From<Vec<usize>> for Qubits {
-    fn from(qs: Vec<usize>) -> Self {
-        Qubits(qs.into_iter().map(QubitId).collect())
-    }
-}
-
-impl From<Vec<QubitId>> for Qubits {
-    fn from(qs: Vec<QubitId>) -> Self {
-        Qubits(qs.into_iter().collect())
-    }
-}
-
-impl From<std::ops::Range<usize>> for Qubits {
-    fn from(range: std::ops::Range<usize>) -> Self {
-        assert!(!range.is_empty(), "empty range not allowed for Qubits");
-        Qubits(range.map(QubitId).collect())
-    }
-}
-
-impl From<std::ops::RangeInclusive<usize>> for Qubits {
-    fn from(range: std::ops::RangeInclusive<usize>) -> Self {
-        assert!(!range.is_empty(), "empty range not allowed for Qubits");
-        Qubits(range.map(QubitId).collect())
-    }
-}
-
-impl Qubits {
-    /// Returns true if there are no qubits.
-    #[must_use]
-    pub fn is_empty(&self) -> bool {
-        self.0.is_empty()
-    }
-
-    /// Returns the number of qubits.
-    #[must_use]
-    pub fn len(&self) -> usize {
-        self.0.len()
-    }
-
-    /// Returns the qubits as a slice.
-    #[must_use]
-    pub fn as_slice(&self) -> &[QubitId] {
-        &self.0
-    }
-
-    /// Applies a gate function to each qubit and returns the result.
-    /// For a single qubit, returns the gate directly.
-    /// For multiple qubits, returns a Tensor of the gates.
-    #[must_use]
-    pub fn apply<F>(self, gate_fn: F) -> Operator
-    where
-        F: Fn(usize) -> Operator,
-    {
-        match self.0.len() {
-            0 => Operator::Pauli(PauliString::default()), // Identity
-            1 => gate_fn(self.0[0].0),
-            _ => Operator::Tensor(self.0.iter().map(|q| gate_fn(q.0)).collect()),
-        }
-    }
-}
-
-/// Wrapper for qubit pairs used by pluralized two-qubit gates.
-///
-/// ```
-/// use pecos_core::operator::*;
-/// use pecos_core::QubitId;
-///
-/// // Multiple CX gates via CXs
-/// let cx_multi = CXs([(0, 1), (2, 3)]);
-///
-/// // Also works with QubitId pairs
-/// let cx_multi = CXs([(QubitId(0), QubitId(1))]);
-/// ```
-#[derive(Debug, Clone)]
-pub struct QubitPairs(SmallVec<[(QubitId, QubitId); 2]>);
-
-impl From<(usize, usize)> for QubitPairs {
-    fn from(pair: (usize, usize)) -> Self {
-        QubitPairs(smallvec::smallvec![(QubitId(pair.0), QubitId(pair.1))])
-    }
-}
-
-impl From<(QubitId, QubitId)> for QubitPairs {
-    fn from(pair: (QubitId, QubitId)) -> Self {
-        QubitPairs(smallvec::smallvec![pair])
-    }
-}
-
-impl<const N: usize> From<[(usize, usize); N]> for QubitPairs {
-    fn from(pairs: [(usize, usize); N]) -> Self {
-        QubitPairs(
-            pairs
-                .into_iter()
-                .map(|(a, b)| (QubitId(a), QubitId(b)))
-                .collect(),
-        )
-    }
-}
-
-impl<const N: usize> From<[(QubitId, QubitId); N]> for QubitPairs {
-    fn from(pairs: [(QubitId, QubitId); N]) -> Self {
-        QubitPairs(pairs.into_iter().collect())
-    }
-}
-
-impl From<&[(usize, usize)]> for QubitPairs {
-    fn from(pairs: &[(usize, usize)]) -> Self {
-        QubitPairs(
-            pairs
-                .iter()
-                .map(|&(a, b)| (QubitId(a), QubitId(b)))
-                .collect(),
-        )
-    }
-}
-
-impl From<&[(QubitId, QubitId)]> for QubitPairs {
-    fn from(pairs: &[(QubitId, QubitId)]) -> Self {
-        QubitPairs(pairs.iter().copied().collect())
-    }
-}
-
-impl From<Vec<(usize, usize)>> for QubitPairs {
-    fn from(pairs: Vec<(usize, usize)>) -> Self {
-        QubitPairs(
-            pairs
-                .into_iter()
-                .map(|(a, b)| (QubitId(a), QubitId(b)))
-                .collect(),
-        )
-    }
-}
-
-impl From<Vec<(QubitId, QubitId)>> for QubitPairs {
-    fn from(pairs: Vec<(QubitId, QubitId)>) -> Self {
-        QubitPairs(pairs.into_iter().collect())
-    }
-}
-
-impl QubitPairs {
-    /// Returns true if there are no pairs.
-    #[must_use]
-    pub fn is_empty(&self) -> bool {
-        self.0.is_empty()
-    }
-
-    /// Returns the number of pairs.
-    #[must_use]
-    pub fn len(&self) -> usize {
-        self.0.len()
-    }
-
-    /// Applies a gate function to each pair and returns the result.
-    /// For a single pair, returns the gate directly.
-    /// For multiple pairs, returns a Tensor of the gates.
-    #[must_use]
-    pub fn apply<F>(self, gate_fn: F) -> Operator
-    where
-        F: Fn(usize, usize) -> Operator,
-    {
-        match self.0.len() {
-            0 => Operator::Pauli(PauliString::default()), // Identity
-            1 => gate_fn(self.0[0].0.0, self.0[0].1.0),
-            _ => Operator::Tensor(self.0.iter().map(|(q0, q1)| gate_fn(q0.0, q1.0)).collect()),
-        }
-    }
-}
-
-/// A gate/operator expression - lazy representation of quantum operators.
-///
-/// This is the unified type for all quantum operators including Pauli operators,
-/// Clifford gates, and general unitaries.
-#[derive(Debug, Clone, PartialEq)]
-pub enum Operator {
-    /// Pauli operator (single or multi-qubit)
-    /// Wraps `PauliString` for exact Pauli algebra
-    Pauli(PauliString),
-
-    /// Rotation gate with angle: exp(-i θ/2 P)
-    Rotation {
-        rotation_type: RotationType,
-        angle: Angle64,
-        qubits: SmallVec<[usize; 2]>,
-    },
-
-    /// Fixed gate (control gates, etc.) without angle parameter
-    Gate {
-        gate_type: GateType,
-        qubits: SmallVec<[usize; 3]>,
-    },
-
-    /// Tensor product of expressions (operators on different qubits)
-    Tensor(Vec<Operator>),
-
-    /// Sequential composition (matrix multiplication order)
-    /// Compose([A, B, C]) means apply A, then B, then C
-    Compose(Vec<Operator>),
-
-    /// Adjoint (Hermitian conjugate)
-    Adjoint(Box<Operator>),
-
-    /// Global phase: e^{i*phase} * inner
-    /// Phase is represented as Angle64 for exact arithmetic
-    Phase {
-        phase: Angle64,
-        inner: Box<Operator>,
-    },
-}
-
-impl Operator {
-    /// Creates a rotation gate expression.
-    #[must_use]
-    pub fn rotation(
-        rotation_type: RotationType,
-        angle: Angle64,
-        qubits: impl Into<SmallVec<[usize; 2]>>,
-    ) -> Self {
-        Self::Rotation {
-            rotation_type,
-            angle,
-            qubits: qubits.into(),
-        }
-    }
-
-    /// Creates a fixed gate expression.
-    #[must_use]
-    pub fn gate(gate_type: GateType, qubits: impl Into<SmallVec<[usize; 3]>>) -> Self {
-        Self::Gate {
-            gate_type,
-            qubits: qubits.into(),
-        }
-    }
-
-    /// Returns the adjoint (Hermitian conjugate) of this expression.
-    #[must_use]
-    pub fn dg(&self) -> Self {
-        match self {
-            // Pauli adjoint: Paulis are Hermitian, but phase conjugates
-            Self::Pauli(ps) => {
-                let conj_phase = ps.phase().conjugate();
-                Self::Pauli(PauliString::with_phase_and_paulis(
-                    conj_phase,
-                    ps.iter_pairs().collect(),
-                ))
-            }
-            // Rotation adjoint: negate the angle
-            Self::Rotation {
-                rotation_type,
-                angle,
-                qubits,
-            } => Self::Rotation {
-                rotation_type: *rotation_type,
-                angle: negate_angle(*angle),
-                qubits: qubits.clone(),
-            },
-            // Gate adjoint: wrap or simplify for self-adjoint gates
-            Self::Gate {
-                gate_type,
-                qubits: _,
-            } => {
-                if gate_type.is_self_adjoint() {
-                    self.clone()
-                } else {
-                    Self::Adjoint(Box::new(self.clone()))
-                }
-            }
-            // Tensor adjoint: adjoint of each part
-            Self::Tensor(parts) => Self::Tensor(parts.iter().map(Operator::dg).collect()),
-            // Compose adjoint: reverse order and adjoint each
-            Self::Compose(parts) => Self::Compose(parts.iter().rev().map(Operator::dg).collect()),
-            // Double adjoint: unwrap
-            Self::Adjoint(inner) => (**inner).clone(),
-            // Phase adjoint: conjugate phase (negate), adjoint inner
-            Self::Phase { phase, inner } => Self::Phase {
-                phase: negate_angle(*phase),
-                inner: Box::new(inner.dg()),
-            },
-        }
-    }
-
-    /// Applies a global phase to this expression: e^{i*phase} * self
-    #[must_use]
-    pub fn with_phase(self, phase: Angle64) -> Self {
-        if phase == Angle64::ZERO {
-            return self;
-        }
-
-        // For Pauli variants, try to absorb the phase into the PauliString
-        // if it's a multiple of π/2 (quarter turn)
-        if let Self::Pauli(ps) = self {
-            if let Some(quarter_phase) = angle_to_quarter_phase(phase) {
-                let new_phase = ps.phase().multiply(&quarter_phase);
-                return Self::Pauli(PauliString::with_phase_and_paulis(
-                    new_phase,
-                    ps.iter_pairs().collect(),
-                ));
-            }
-            // Not a quarter turn multiple, wrap in Phase
-            return Self::Phase {
-                phase,
-                inner: Box::new(Self::Pauli(ps)),
-            };
-        }
-
-        Self::Phase {
-            phase,
-            inner: Box::new(self),
-        }
-    }
-
-    /// Checks if this expression represents a Clifford operation.
-    ///
-    /// Clifford gates are those where all rotation angles are multiples of π/2.
-    #[must_use]
-    pub fn is_clifford(&self) -> bool {
-        match self {
-            // Paulis are always Clifford
-            Self::Pauli(_) => true,
-            Self::Rotation { angle, .. } => {
-                // Clifford if angle is multiple of π/2 (quarter turn)
-                is_multiple_of_quarter_turn(*angle)
-            }
-            Self::Gate { gate_type, .. } => gate_type.is_clifford(),
-            Self::Tensor(parts) | Self::Compose(parts) => parts.iter().all(Operator::is_clifford),
-            // Phase doesn't affect Clifford-ness (global phase)
-            Self::Adjoint(inner) | Self::Phase { inner, .. } => inner.is_clifford(),
-        }
-    }
-
-    /// Returns the qubits this expression acts on.
-    #[must_use]
-    pub fn qubits(&self) -> Vec<usize> {
-        let mut result = Vec::new();
-        self.collect_qubits(&mut result);
-        result.sort_unstable();
-        result.dedup();
-        result
-    }
-
-    fn collect_qubits(&self, result: &mut Vec<usize>) {
-        match self {
-            Self::Pauli(ps) => {
-                result.extend(ps.iter_pairs().map(|(_, q)| usize::from(q)));
-            }
-            Self::Rotation { qubits, .. } => result.extend(qubits.iter().copied()),
-            Self::Gate { qubits, .. } => result.extend(qubits.iter().copied()),
-            Self::Tensor(parts) | Self::Compose(parts) => {
-                for part in parts {
-                    part.collect_qubits(result);
-                }
-            }
-            Self::Adjoint(inner) | Self::Phase { inner, .. } => inner.collect_qubits(result),
-        }
-    }
-}
-
-// --- Negation operator: -op (phase by π) ---
-
-impl Neg for Operator {
-    type Output = Operator;
-
-    fn neg(self) -> Operator {
-        self.with_phase(Angle64::HALF_TURN)
-    }
-}
-
-impl Neg for &Operator {
-    type Output = Operator;
-
-    fn neg(self) -> Operator {
-        self.clone().with_phase(Angle64::HALF_TURN)
-    }
-}
-
-// --- Imaginary unit for phase multiplication ---
-
-/// Imaginary unit for phase multiplication: i * op
-#[derive(Debug, Clone, Copy, PartialEq, Eq)]
-pub struct ImaginaryUnit;
-
-/// The imaginary unit `i`.
-#[allow(non_upper_case_globals)]
-pub const i: ImaginaryUnit = ImaginaryUnit;
-
-impl Neg for ImaginaryUnit {
-    type Output = NegImaginaryUnit;
-
-    fn neg(self) -> NegImaginaryUnit {
-        NegImaginaryUnit
-    }
-}
-
-/// Negative imaginary unit (-i).
-#[derive(Debug, Clone, Copy, PartialEq, Eq)]
-pub struct NegImaginaryUnit;
-
-impl Mul<Operator> for ImaginaryUnit {
-    type Output = Operator;
-
-    fn mul(self, rhs: Operator) -> Operator {
-        rhs.with_phase(Angle64::QUARTER_TURN) // i = e^{iπ/2}
-    }
-}
-
-impl Mul<&Operator> for ImaginaryUnit {
-    type Output = Operator;
-
-    fn mul(self, rhs: &Operator) -> Operator {
-        rhs.clone().with_phase(Angle64::QUARTER_TURN)
-    }
-}
-
-impl Mul<Operator> for NegImaginaryUnit {
-    type Output = Operator;
-
-    #[allow(clippy::suspicious_arithmetic_impl)] // Adding angles for phase computation
-    fn mul(self, rhs: Operator) -> Operator {
-        rhs.with_phase(Angle64::QUARTER_TURN + Angle64::HALF_TURN) // -i = e^{i3π/2}
-    }
-}
-
-impl Mul<&Operator> for NegImaginaryUnit {
-    type Output = Operator;
-
-    #[allow(clippy::suspicious_arithmetic_impl)] // Adding angles for phase computation
-    fn mul(self, rhs: &Operator) -> Operator {
-        rhs.clone()
-            .with_phase(Angle64::QUARTER_TURN + Angle64::HALF_TURN)
-    }
-}
-
-// --- General phase value for arbitrary phase multiplication ---
-
-/// A phase value e^{i*angle} that can be multiplied with operators.
-///
-/// # Example
-/// ```
-/// use pecos_core::operator::{phase, X};
-/// use pecos_core::Angle64;
-///
-/// // Create a phase of e^{iπ/4}
-/// let eighth_turn = Angle64::HALF_TURN / 4;
-/// let op = phase(eighth_turn) * X(0);  // e^{iπ/4} * X
-/// ```
-#[derive(Debug, Clone, Copy, PartialEq)]
-pub struct PhaseValue(pub Angle64);
-
-/// Creates a phase value e^{i*angle} that can be multiplied with operators.
-///
-/// The phase represents the complex number e^{i*angle} = cos(angle) + i*sin(angle).
-///
-/// # Example
-/// ```
-/// use pecos_core::operator::{phase, X, Z};
-/// use pecos_core::Angle64;
-///
-/// // e^{iπ/4} * X
-/// let op = phase(Angle64::HALF_TURN / 4) * X(0);
-///
-/// // e^{iπ/2} * Z = i * Z
-/// let op = phase(Angle64::QUARTER_TURN) * Z(0);
-/// ```
-#[must_use]
-pub fn phase(angle: Angle64) -> PhaseValue {
-    PhaseValue(angle)
-}
-
-impl Neg for PhaseValue {
-    type Output = PhaseValue;
-
-    fn neg(self) -> PhaseValue {
-        // -e^{iθ} = e^{i(θ + π)}
-        PhaseValue(self.0 + Angle64::HALF_TURN)
-    }
-}
-
-impl Mul<PhaseValue> for ImaginaryUnit {
-    type Output = PhaseValue;
-
-    #[allow(clippy::suspicious_arithmetic_impl)] // Adding angles for phase computation
-    fn mul(self, rhs: PhaseValue) -> PhaseValue {
-        // i * e^{iθ} = e^{i(θ + π/2)}
-        PhaseValue(rhs.0 + Angle64::QUARTER_TURN)
-    }
-}
-
-impl Mul<PhaseValue> for NegImaginaryUnit {
-    type Output = PhaseValue;
-
-    #[allow(clippy::suspicious_arithmetic_impl)] // Adding angles for phase computation
-    fn mul(self, rhs: PhaseValue) -> PhaseValue {
-        // -i * e^{iθ} = e^{i(θ + 3π/2)}
-        PhaseValue(rhs.0 + Angle64::QUARTER_TURN + Angle64::HALF_TURN)
-    }
-}
-
-impl Mul<Operator> for PhaseValue {
-    type Output = Operator;
-
-    fn mul(self, rhs: Operator) -> Operator {
-        rhs.with_phase(self.0)
-    }
-}
-
-impl Mul<&Operator> for PhaseValue {
-    type Output = Operator;
-
-    fn mul(self, rhs: &Operator) -> Operator {
-        rhs.clone().with_phase(self.0)
-    }
-}
-
-impl Operator {
-    /// Attempts to convert a rotation to its named `GateType` equivalent.
-    #[must_use]
-    pub fn to_named_gate(&self) -> Option<GateType> {
-        match self {
-            Self::Pauli(ps) => {
-                // Single-qubit Paulis map to named gates
-                if ps.weight() == 1 && ps.phase() == QuarterPhase::PlusOne {
-                    let (pauli, _qubit) = ps.iter_pairs().next()?;
-                    match pauli {
-                        crate::Pauli::I => Some(GateType::I),
-                        crate::Pauli::X => Some(GateType::X),
-                        crate::Pauli::Y => Some(GateType::Y),
-                        crate::Pauli::Z => Some(GateType::Z),
-                    }
-                } else {
-                    None
-                }
-            }
-            Self::Rotation {
-                rotation_type,
-                angle,
-                ..
-            } => rotation_to_gate_type(*rotation_type, *angle),
-            Self::Gate { gate_type, .. } => Some(*gate_type),
-            _ => None,
-        }
-    }
-
-    /// Returns a reference to the inner `PauliString` if this is a `Pauli` variant.
-    #[must_use]
-    pub fn as_pauli_string(&self) -> Option<&PauliString> {
-        if let Self::Pauli(ps) = self {
-            Some(ps)
-        } else {
-            None
-        }
-    }
-
-    /// Consumes this `Operator` and returns the inner `PauliString` if this is a `Pauli` variant.
-    #[must_use]
-    pub fn into_pauli_string(self) -> Option<PauliString> {
-        if let Self::Pauli(ps) = self {
-            Some(ps)
-        } else {
-            None
-        }
-    }
-
-    /// Attempts to convert this operator to a `PauliString`.
-    ///
-    /// This handles more cases than `into_pauli_string()`:
-    /// - `Pauli(ps)` → returns `ps` directly
-    /// - `Tensor([Pauli(a), Pauli(b), ...])` → merges into a single `PauliString`
-    /// - `Phase { phase, inner: Pauli(ps) }` → applies phase to `ps`
-    /// - Named Pauli gates (`X`, `Y`, `Z`) → corresponding single-qubit `PauliString`
-    /// - Half-turn rotations (`RX(π)`, `RY(π)`, `RZ(π)`) → corresponding `PauliString`
-    ///
-    /// Returns `None` if the operator cannot be represented as a `PauliString`.
-    ///
-    /// # Example
-    ///
-    /// ```
-    /// use pecos_core::{Xs, Zs, PauliOperator};
-    ///
-    /// // Tensor of Paulis on disjoint qubits
-    /// let op = Xs(0..2) & Zs(2..4);
-    /// let ps = op.try_to_pauli_string().unwrap();
-    /// assert_eq!(ps.weight(), 4); // X on 0,1 and Z on 2,3
-    /// ```
-    #[must_use]
-    pub fn try_to_pauli_string(self) -> Option<PauliString> {
-        match self {
-            Self::Pauli(ps) => Some(ps),
-
-            Self::Tensor(parts) => {
-                // Try to convert all parts to PauliStrings and merge
-                let mut result = PauliString::new();
-                for part in parts {
-                    let ps = part.try_to_pauli_string()?;
-                    // Merge: combine the Pauli operators
-                    // For disjoint qubits, this is just concatenation
-                    // For overlapping qubits, we multiply the Paulis
-                    result = result * ps;
-                }
-                Some(result)
-            }
-
-            Self::Phase { phase, inner } => {
-                let mut ps = inner.try_to_pauli_string()?;
-                // Apply the global phase to the PauliString phase
-                // phase is Angle64, we need to convert to QuarterPhase if possible
-                // For now, only handle quarter-turn phases exactly
-                let quarter_phase = if phase == Angle64::ZERO {
-                    QuarterPhase::PlusOne
-                } else if phase == Angle64::QUARTER_TURN {
-                    QuarterPhase::PlusI
-                } else if phase == Angle64::HALF_TURN {
-                    QuarterPhase::MinusOne
-                } else if phase == Angle64::THREE_QUARTERS_TURN {
-                    QuarterPhase::MinusI
-                } else {
-                    // Non-quarter-turn phase, can't represent exactly
-                    return None;
-                };
-                let new_phase = ps.phase().multiply(&quarter_phase);
-                ps.set_phase(new_phase);
-                Some(ps)
-            }
-
-            Self::Gate { gate_type, qubits } => {
-                let qubit = qubits.first().copied()?;
-                match gate_type {
-                    GateType::X => Some(PauliString::x(qubit)),
-                    GateType::Y => Some(PauliString::y(qubit)),
-                    GateType::Z => Some(PauliString::z(qubit)),
-                    GateType::I => Some(PauliString::identity()),
-                    _ => None,
-                }
-            }
-
-            Self::Rotation {
-                rotation_type,
-                angle,
-                qubits,
-            } => {
-                // Only half-turn rotations are Pauli operators
-                let half = Angle64::HALF_TURN;
-                let neg_half = negate_angle(half);
-                if angle != half && angle != neg_half {
-                    return None;
-                }
-                let qubit = qubits.first().copied()?;
-                match rotation_type {
-                    RotationType::RX => Some(PauliString::x(qubit)),
-                    RotationType::RY => Some(PauliString::y(qubit)),
-                    RotationType::RZ => Some(PauliString::z(qubit)),
-                    _ => None,
-                }
-            }
-
-            Self::Adjoint(inner) => {
-                // Paulis are Hermitian (self-adjoint), but phase conjugates
-                let mut ps = inner.try_to_pauli_string()?;
-                let conj_phase = ps.phase().conjugate();
-                ps.set_phase(conj_phase);
-                Some(ps)
-            }
-
-            Self::Compose(_) => {
-                // Composition of Paulis requires multiplication
-                // This is more complex; skip for now
-                None
-            }
-        }
-    }
-
-    /// Checks if this operator is equivalent to a Pauli operator.
-    ///
-    /// Returns true for:
-    /// - `Pauli` variants (any `PauliString`)
-    /// - Half-turn rotations: `RX(π)`, `RY(π)`, `RZ(π)`
-    /// - Named Pauli gates: `X`, `Y`, `Z`
-    #[must_use]
-    pub fn is_pauli_equivalent(&self) -> bool {
-        match self {
-            Self::Pauli(_) => true,
-            Self::Rotation {
-                rotation_type,
-                angle,
-                ..
-            } => {
-                let half = Angle64::HALF_TURN;
-                let neg_half = negate_angle(half);
-                (*angle == half || *angle == neg_half)
-                    && matches!(
-                        rotation_type,
-                        RotationType::RX | RotationType::RY | RotationType::RZ
-                    )
-            }
-            Self::Gate { gate_type, .. } => {
-                matches!(gate_type, GateType::X | GateType::Y | GateType::Z)
-            }
-            _ => false,
-        }
-    }
-
-    /// Attempts to convert this operator to a `Pauli` variant.
-    ///
-    /// Converts:
-    /// - `Pauli` → returns as-is
-    /// - `RX(π)` → `X`
-    /// - `RY(π)` → `Y`
-    /// - `RZ(π)` → `Z`
-    /// - Named gates `X`, `Y`, `Z` → corresponding `Pauli` variant
-    ///
-    /// Returns `None` if the operator is not Pauli-equivalent.
-    #[must_use]
-    pub fn try_to_pauli(self) -> Option<Self> {
-        match self {
-            Self::Pauli(_) => Some(self),
-            Self::Rotation {
-                rotation_type,
-                angle,
-                qubits,
-            } => {
-                let half = Angle64::HALF_TURN;
-                let neg_half = negate_angle(half);
-                if angle != half && angle != neg_half {
-                    return None;
-                }
-                let qubit = qubits[0];
-                match rotation_type {
-                    RotationType::RX => Some(X(qubit)),
-                    RotationType::RY => Some(Y(qubit)),
-                    RotationType::RZ => Some(Z(qubit)),
-                    _ => None,
-                }
-            }
-            Self::Gate { gate_type, qubits } => {
-                let qubit = qubits[0];
-                match gate_type {
-                    GateType::X => Some(X(qubit)),
-                    GateType::Y => Some(Y(qubit)),
-                    GateType::Z => Some(Z(qubit)),
-                    _ => None,
-                }
-            }
-            _ => None,
-        }
-    }
-
-    /// Simplifies this gate expression by:
-    /// - Merging adjacent rotations of the same type on the same qubits
-    /// - Canceling inverse operations (rotation + its negation)
-    /// - Removing identity operations (zero-angle rotations)
-    /// - Flattening single-element containers
-    #[must_use]
-    #[allow(clippy::missing_panics_doc)] // Internal expects are guarded by length checks
-    pub fn simplify(&self) -> Self {
-        match self {
-            // Pauli and Gate are already in simplified form
-            Self::Pauli(_) | Self::Gate { .. } => self.clone(),
-
-            Self::Rotation { angle, .. } => {
-                // Remove identity rotations
-                if *angle == Angle64::ZERO {
-                    return self.clone(); // Keep as-is, will be filtered at Compose level
-                }
-                self.clone()
-            }
-
-            Self::Tensor(parts) => {
-                // Simplify each part but preserve identities (they define the Hilbert space dimension)
-                let simplified: Vec<_> = parts.iter().map(Operator::simplify).collect();
-
-                match simplified.len() {
-                    0 => Self::Pauli(PauliString::default()), // Empty tensor = identity
-                    1 => simplified.into_iter().next().expect("length is 1"),
-                    _ => Self::Tensor(simplified),
-                }
-            }
-
-            Self::Compose(parts) => {
-                // First simplify each part
-                let simplified: Vec<_> = parts.iter().map(Operator::simplify).collect();
-
-                // Flatten nested Compose nodes
-                let flattened = flatten_compose(simplified);
-
-                // Merge adjacent compatible rotations
-                let merged = merge_adjacent_rotations(flattened);
-
-                // Filter out identities
-                let filtered: Vec<_> = merged.into_iter().filter(|p| !p.is_identity()).collect();
-
-                match filtered.len() {
-                    0 => I(0), // Empty composition = identity
-                    1 => filtered.into_iter().next().expect("length is 1"),
-                    _ => Self::Compose(filtered),
-                }
-            }
-
-            Self::Adjoint(inner) => {
-                // Simplify inner first, then take adjoint
-                let simplified_inner = inner.simplify();
-                simplified_inner.dg()
-            }
-
-            Self::Phase { phase, inner } => {
-                // Simplify inner and preserve phase
-                let simplified_inner = inner.simplify();
-                if *phase == Angle64::ZERO || *phase == Angle64::FULL_TURN {
-                    simplified_inner
-                } else {
-                    Self::Phase {
-                        phase: *phase,
-                        inner: Box::new(simplified_inner),
-                    }
-                }
-            }
-        }
-    }
-
-    /// Conjugates this operator by another: `gate * self * gate.dg()` (i.e., UAU†).
-    ///
-    /// This is the stabilizer update convention: when gate U is applied to a state,
-    /// a stabilizer S transforms as S → U S U†.
-    ///
-    /// For Heisenberg picture evolution (U†AU), use [`conjdg`](Self::conjdg).
-    ///
-    /// # Example
-    ///
-    /// ```
-    /// use pecos_core::operator::{X, Z, H, T};
-    ///
-    /// // Stabilizer update: applying H to qubit 0
-    /// let stabilizer = X(0) & Z(1);
-    /// let updated = stabilizer.conj(&H(0));  // H * (X⊗Z) * H†
-    ///
-    /// // Works with any operators
-    /// let a = T(0);
-    /// let b = X(0);
-    /// let conjugated = b.conj(&a);  // T X T†
-    /// ```
-    #[must_use]
-    pub fn conj(&self, gate: &Operator) -> Self {
-        gate.clone() * self.clone() * gate.dg()
-    }
-
-    /// Conjugates this operator by the adjoint of another: `gate.dg() * self * gate` (i.e., U†AU).
-    ///
-    /// This is the Heisenberg picture convention: operators evolve as A → U†AU.
-    ///
-    /// For stabilizer updates (UAU†), use [`conj`](Self::conj).
-    ///
-    /// # Example
-    ///
-    /// ```
-    /// use pecos_core::operator::{X, H};
-    ///
-    /// // Heisenberg evolution: how X evolves under H
-    /// let evolved = X(0).conjdg(&H(0));  // H† X H
-    /// ```
-    #[must_use]
-    pub fn conjdg(&self, gate: &Operator) -> Self {
-        gate.dg() * self.clone() * gate.clone()
-    }
-
-    /// Returns the global phase of this operator.
-    ///
-    /// # Example
-    ///
-    /// ```
-    /// use pecos_core::operator::{X, Y};
-    /// use pecos_core::{GlobalPhase, QuarterPhase};
-    ///
-    /// let op = X(0);
-    /// assert_eq!(op.phase(), GlobalPhase::one());
-    ///
-    /// let op = -Y(0);
-    /// assert_eq!(op.phase(), GlobalPhase::minus_one());
-    /// ```
-    #[must_use]
-    pub fn phase(&self) -> crate::GlobalPhase {
-        use crate::GlobalPhase;
-
-        match self {
-            Self::Pauli(ps) => GlobalPhase::from(ps.phase()),
-            Self::Phase { phase, .. } => GlobalPhase::from(*phase),
-            _ => GlobalPhase::one(),
-        }
-    }
-
-    /// Returns the weight (number of qubits) this operator acts on.
-    ///
-    /// # Example
-    ///
-    /// ```
-    /// use pecos_core::operator::{X, Z, CX};
-    ///
-    /// assert_eq!(X(0).weight(), 1);
-    /// assert_eq!((X(0) & Z(2)).weight(), 2);
-    /// assert_eq!(CX(0, 1).weight(), 2);
-    /// ```
-    #[must_use]
-    pub fn weight(&self) -> usize {
-        self.qubits().len()
-    }
-
-    /// Checks if this is structurally the identity operator.
-    ///
-    /// # Example
-    ///
-    /// ```
-    /// use pecos_core::operator::I;
-    ///
-    /// assert!(I(0).is_identity());
-    /// ```
-    #[must_use]
-    pub fn is_identity(&self) -> bool {
-        match self {
-            Self::Pauli(ps) => ps.weight() == 0 && ps.phase() == crate::QuarterPhase::PlusOne,
-            Self::Gate { gate_type, .. } => *gate_type == GateType::I,
-            Self::Rotation { angle, .. } => *angle == Angle64::ZERO,
-            Self::Tensor(parts) | Self::Compose(parts) => parts.iter().all(Operator::is_identity),
-            Self::Adjoint(inner) => inner.is_identity(),
-            Self::Phase { phase, inner } => *phase == Angle64::ZERO && inner.is_identity(),
-        }
-    }
-
-    /// Checks if this operator is Hermitian (self-adjoint): A = A†.
-    ///
-    /// # Example
-    ///
-    /// ```
-    /// use pecos_core::operator::{X, Y, Z, H, T};
-    ///
-    /// // Paulis are Hermitian
-    /// assert!(X(0).is_hermitian());
-    /// assert!(Y(0).is_hermitian());
-    /// assert!(Z(0).is_hermitian());
-    ///
-    /// // H is Hermitian
-    /// assert!(H(0).is_hermitian());
-    ///
-    /// // T is not Hermitian (T† ≠ T)
-    /// assert!(!T(0).is_hermitian());
-    /// ```
-    #[must_use]
-    pub fn is_hermitian(&self) -> bool {
-        // A is Hermitian if A = A†
-        // For structural comparison, we check known Hermitian operators
-        match self {
-            Self::Pauli(_) => true, // All Paulis are Hermitian
-            Self::Gate { gate_type, .. } => matches!(
-                gate_type,
-                GateType::I
-                    | GateType::X
-                    | GateType::Y
-                    | GateType::Z
-                    | GateType::H
-                    | GateType::CX
-                    | GateType::CY
-                    | GateType::CZ
-                    | GateType::SWAP
-            ),
-            Self::Rotation { angle, .. } => {
-                // Rotations are Hermitian only at angle 0 or π
-                *angle == Angle64::ZERO || *angle == Angle64::HALF_TURN
-            }
-            Self::Tensor(parts) => parts.iter().all(Operator::is_hermitian),
-            // Composition of Hermitians isn't generally Hermitian; phase factors break Hermiticity
-            Self::Compose(_) | Self::Phase { .. } => false,
-            Self::Adjoint(inner) => inner.is_hermitian(), // (A†)† = A, so same as inner
-        }
-    }
-
-    /// Returns the operator raised to a power (repeated composition).
-    ///
-    /// # Example
-    ///
-    /// ```
-    /// use pecos_core::operator::{X, H};
-    ///
-    /// let x = X(0);
-    /// let x2 = x.pow(2);  // X * X = I
-    ///
-    /// let h = H(0);
-    /// let h3 = h.pow(3);  // H * H * H = H
-    /// ```
-    #[must_use]
-    pub fn pow(&self, n: u32) -> Self {
-        match n {
-            0 => Self::Gate {
-                gate_type: GateType::I,
-                qubits: self
-                    .qubits()
-                    .into_iter()
-                    .next()
-                    .map_or(smallvec::smallvec![0], |q| smallvec::smallvec![q]),
-            },
-            1 => self.clone(),
-            _ => {
-                let mut result = self.clone();
-                for _ in 1..n {
-                    result = result * self.clone();
-                }
-                result
-            }
-        }
-    }
-
-    /// Checks whether this operator commutes with another.
-    ///
-    /// For Pauli operators, returns `Commutes` or `AntiCommutes`.
-    /// For non-Pauli operators, returns `Unknown`.
-    ///
-    /// # Example
-    ///
-    /// ```
-    /// use pecos_core::operator::{X, Z, Commutativity};
-    ///
-    /// let a = X(0);
-    /// let b = Z(0);
-    /// assert_eq!(a.commutes(&b), Commutativity::AntiCommutes);
-    ///
-    /// let c = X(0) & Z(1);
-    /// let d = Z(0) & X(1);
-    /// assert_eq!(c.commutes(&d), Commutativity::Commutes);
-    /// ```
-    #[must_use]
-    pub fn commutes(&self, other: &Operator) -> Commutativity {
-        use crate::PauliOperator;
-
-        match (self, other) {
-            (Self::Pauli(a), Self::Pauli(b)) => {
-                if a.commutes_with(b) {
-                    Commutativity::Commutes
-                } else {
-                    Commutativity::AntiCommutes
-                }
-            }
-            _ => Commutativity::Unknown,
-        }
-    }
-
-    /// Returns whether this operator is unitary.
-    ///
-    /// All operators in this enum are unitary by construction.
-    ///
-    /// # Example
-    ///
-    /// ```
-    /// use pecos_core::operator::{X, H, RZ};
-    /// use pecos_core::Angle64;
-    ///
-    /// assert!(X(0).is_unitary());
-    /// assert!(H(0).is_unitary());
-    /// assert!(RZ(Angle64::QUARTER_TURN, 0).is_unitary());
-    /// ```
-    #[must_use]
-    pub fn is_unitary(&self) -> bool {
-        true // All Operator variants are unitary by construction
-    }
-
-    /// Decomposes this operator into a sequence of primitive gates.
-    ///
-    /// Returns a flat vector of `Gate` structs representing the operator
-    /// as a sequence of native gates.
-    ///
-    /// # Example
-    ///
-    /// ```
-    /// use pecos_core::operator::{H, CX};
-    ///
-    /// let circuit = CX(0, 1) * H(0);  // H then CX
-    /// let gates = circuit.decompose();
-    /// assert_eq!(gates.len(), 2);
-    /// ```
-    #[must_use]
-    pub fn decompose(&self) -> Vec<crate::Gate> {
-        use crate::{Gate, Pauli};
-
-        match self {
-            Self::Pauli(ps) => {
-                // Convert PauliString to individual gates
-                let mut gates = Vec::new();
-                for (pauli, qubit) in ps.iter_pairs() {
-                    let gate = match pauli {
-                        Pauli::I => continue, // Skip identity
-                        Pauli::X => Gate::simple(GateType::X, smallvec::smallvec![qubit]),
-                        Pauli::Y => Gate::simple(GateType::Y, smallvec::smallvec![qubit]),
-                        Pauli::Z => Gate::simple(GateType::Z, smallvec::smallvec![qubit]),
-                    };
-                    gates.push(gate);
-                }
-                // Handle global phase if not +1
-                // (Phase is tracked separately in PauliString but not representable in Gate)
-                gates
-            }
-
-            Self::Rotation {
-                rotation_type,
-                angle,
-                qubits,
-            } => {
-                let gate_type = match rotation_type {
-                    RotationType::RX => GateType::RX,
-                    RotationType::RY => GateType::RY,
-                    RotationType::RZ => GateType::RZ,
-                    RotationType::RXX => GateType::RXX,
-                    RotationType::RYY => GateType::RYY,
-                    RotationType::RZZ => GateType::RZZ,
-                };
-                let qubit_ids: crate::GateQubits =
-                    qubits.iter().map(|&q| crate::QubitId(q)).collect();
-                vec![Gate::with_angles(
-                    gate_type,
-                    smallvec::smallvec![*angle],
-                    qubit_ids,
-                )]
-            }
-
-            Self::Gate { gate_type, qubits } => {
-                let qubit_ids: crate::GateQubits =
-                    qubits.iter().map(|&q| crate::QubitId(q)).collect();
-                vec![Gate::simple(*gate_type, qubit_ids)]
-            }
-
-            Self::Tensor(parts) => {
-                // Decompose each part and concatenate
-                parts.iter().flat_map(Operator::decompose).collect()
-            }
-
-            Self::Compose(parts) => {
-                // Decompose each part in application order
-                parts.iter().flat_map(Operator::decompose).collect()
-            }
-
-            Self::Adjoint(inner) => {
-                // Decompose inner, reverse, and adjoint each gate
-                let mut gates = inner.decompose();
-                gates.reverse();
-                for gate in &mut gates {
-                    // Negate angles for rotation gates
-                    for angle in &mut gate.angles {
-                        *angle = Angle64::ZERO - *angle;
-                    }
-                    // Some gates need special handling
-                    gate.gate_type = match gate.gate_type {
-                        GateType::SX => GateType::SXdg,
-                        GateType::SXdg => GateType::SX,
-                        GateType::SY => GateType::SYdg,
-                        GateType::SYdg => GateType::SY,
-                        GateType::SZ => GateType::SZdg,
-                        GateType::SZdg => GateType::SZ,
-                        GateType::T => GateType::Tdg,
-                        GateType::Tdg => GateType::T,
-                        GateType::SZZ => GateType::SZZdg,
-                        GateType::SZZdg => GateType::SZZ,
-                        other => other, // Self-adjoint gates unchanged
-                    };
-                }
-                gates
-            }
-
-            Self::Phase { inner, .. } => {
-                // Global phase doesn't affect gate sequence
-                // (Phase information is lost in decomposition)
-                inner.decompose()
-            }
-        }
-    }
-
-    /// Converts this gate expression to a `CliffordRep` (generator propagation).
-    ///
-    /// Returns `None` if the expression contains non-Clifford operations.
-    ///
-    /// # Arguments
-    /// * `num_qubits` - The total number of qubits in the system
-    #[must_use]
-    pub fn to_clifford_rep(&self, num_qubits: usize) -> Option<crate::clifford_rep::CliffordRep> {
-        use crate::clifford_rep::CliffordRep;
-
-        if !self.is_clifford() {
-            return None;
-        }
-
-        match self {
-            Self::Pauli(ps) => {
-                // Convert PauliString to CliffordRep by composing single-qubit Paulis
-                let mut result = CliffordRep::identity(num_qubits);
-                for (pauli, qubit) in ps.iter_pairs() {
-                    let q = usize::from(qubit);
-                    let cliff = match pauli {
-                        crate::Pauli::I => continue, // Skip identity
-                        crate::Pauli::X => CliffordRep::x_on(q, num_qubits),
-                        crate::Pauli::Y => CliffordRep::y_on(q, num_qubits),
-                        crate::Pauli::Z => CliffordRep::z_on(q, num_qubits),
-                    };
-                    result = cliff.compose(&result);
-                }
-                Some(result)
-            }
-
-            Self::Rotation {
-                rotation_type,
-                angle,
-                qubits,
-            } => rotation_to_clifford_rep(*rotation_type, *angle, qubits, num_qubits),
-
-            Self::Gate { gate_type, qubits } => {
-                gate_type_to_clifford_rep(*gate_type, qubits, num_qubits)
-            }
-
-            Self::Tensor(parts) => {
-                // For tensor products, compose all parts (they act on different qubits)
-                let mut result = CliffordRep::identity(num_qubits);
-                for part in parts {
-                    if let Some(cliff) = part.to_clifford_rep(num_qubits) {
-                        result = result.compose(&cliff);
-                    } else {
-                        return None;
-                    }
-                }
-                Some(result)
-            }
-
-            Self::Compose(parts) => {
-                // For composition, compose in order (parts are in application order)
-                let mut result = CliffordRep::identity(num_qubits);
-                for part in parts {
-                    if let Some(cliff) = part.to_clifford_rep(num_qubits) {
-                        result = cliff.compose(&result);
-                    } else {
-                        return None;
-                    }
-                }
-                Some(result)
-            }
-
-            Self::Adjoint(inner) => {
-                // Get the inner CliffordRep and take its inverse
-                inner
-                    .to_clifford_rep(num_qubits)
-                    .map(|cliff| cliff.inverse())
-            }
-
-            Self::Phase { inner, .. } => {
-                // Global phase is ignored in CliffordRep (Heisenberg picture)
-                inner.to_clifford_rep(num_qubits)
-            }
-        }
-    }
-}
-
-/// Convert a rotation to `CliffordRep` if it's Clifford.
-fn rotation_to_clifford_rep(
-    rotation_type: RotationType,
-    angle: Angle64,
-    qubits: &SmallVec<[usize; 2]>,
-    num_qubits: usize,
-) -> Option<crate::clifford_rep::CliffordRep> {
-    use crate::clifford_rep::CliffordRep;
-
-    // Check for Clifford angles (multiples of π/2)
-    let quarter = Angle64::QUARTER_TURN;
-    let neg_quarter = negate_angle(quarter);
-    let half = Angle64::HALF_TURN;
-    let neg_half = negate_angle(half);
-    let three_quarter = quarter + half;
-    let _neg_three_quarter = negate_angle(three_quarter);
-
-    // Identity
-    if angle == Angle64::ZERO {
-        return Some(CliffordRep::identity(num_qubits));
-    }
-
-    match rotation_type {
-        RotationType::RZ => {
-            let qubit = qubits[0];
-            let mut result = CliffordRep::identity(num_qubits);
-
-            if angle == quarter {
-                // S = RZ(π/2)
-                result = apply_s(&result, qubit);
-            } else if angle == neg_quarter || angle == three_quarter {
-                // S† = RZ(-π/2) = RZ(3π/2)
-                result = apply_sdg(&result, qubit);
-            } else if angle == half || angle == neg_half {
-                // Z = RZ(π)
-                result = apply_z(&result, qubit);
-            } else {
-                return None; // Not a Clifford angle
-            }
-            Some(result)
-        }
-
-        RotationType::RX => {
-            let qubit = qubits[0];
-            let mut result = CliffordRep::identity(num_qubits);
-
-            if angle == quarter {
-                // SX = RX(π/2)
-                result = apply_sx(&result, qubit);
-            } else if angle == neg_quarter || angle == three_quarter {
-                // SX† = RX(-π/2)
-                result = apply_sxdg(&result, qubit);
-            } else if angle == half || angle == neg_half {
-                // X = RX(π)
-                result = apply_x(&result, qubit);
-            } else {
-                return None;
-            }
-            Some(result)
-        }
-
-        RotationType::RY => {
-            let qubit = qubits[0];
-            let mut result = CliffordRep::identity(num_qubits);
-
-            if angle == quarter {
-                // SY = RY(π/2)
-                result = apply_sy(&result, qubit);
-            } else if angle == neg_quarter || angle == three_quarter {
-                // SY† = RY(-π/2)
-                result = apply_sydg(&result, qubit);
-            } else if angle == half || angle == neg_half {
-                // Y = RY(π)
-                result = apply_y(&result, qubit);
-            } else {
-                return None;
-            }
-            Some(result)
-        }
-
-        RotationType::RZZ => {
-            let q0 = qubits[0];
-            let q1 = qubits[1];
-
-            if angle == quarter {
-                Some(CliffordRep::cz(q0, q1).compose(&CliffordRep::identity(num_qubits)))
-            } else if angle == neg_quarter || angle == three_quarter {
-                // SZZ† - CZ with phase adjustment
-                Some(CliffordRep::cz(q0, q1).compose(&CliffordRep::identity(num_qubits)))
-            } else {
-                None
-            }
-        }
-
-        _ => None, // RXX, RYY at non-zero angles are not standard Cliffords
-    }
-}
-
-/// Convert a `GateType` to `CliffordRep`.
-fn gate_type_to_clifford_rep(
-    gate_type: GateType,
-    qubits: &SmallVec<[usize; 3]>,
-    num_qubits: usize,
-) -> Option<crate::clifford_rep::CliffordRep> {
-    use crate::clifford_rep::CliffordRep;
-
-    match gate_type {
-        GateType::I => Some(CliffordRep::identity(num_qubits)),
-        GateType::X => {
-            let mut result = CliffordRep::identity(num_qubits);
-            result = apply_x(&result, qubits[0]);
-            Some(result)
-        }
-        GateType::Y => {
-            let mut result = CliffordRep::identity(num_qubits);
-            result = apply_y(&result, qubits[0]);
-            Some(result)
-        }
-        GateType::Z => {
-            let mut result = CliffordRep::identity(num_qubits);
-            result = apply_z(&result, qubits[0]);
-            Some(result)
-        }
-        GateType::H => {
-            let cliff = CliffordRep::h(qubits[0]);
-            // Extend to num_qubits
-            Some(extend_clifford(cliff, num_qubits))
-        }
-        GateType::SX => {
-            let mut result = CliffordRep::identity(num_qubits);
-            result = apply_sx(&result, qubits[0]);
-            Some(result)
-        }
-        GateType::SY => {
-            let mut result = CliffordRep::identity(num_qubits);
-            result = apply_sy(&result, qubits[0]);
-            Some(result)
-        }
-        GateType::SZ => {
-            let mut result = CliffordRep::identity(num_qubits);
-            result = apply_s(&result, qubits[0]);
-            Some(result)
-        }
-        GateType::SXdg => {
-            let mut result = CliffordRep::identity(num_qubits);
-            result = apply_sxdg(&result, qubits[0]);
-            Some(result)
-        }
-        GateType::SYdg => {
-            let mut result = CliffordRep::identity(num_qubits);
-            result = apply_sydg(&result, qubits[0]);
-            Some(result)
-        }
-        GateType::SZdg => {
-            let mut result = CliffordRep::identity(num_qubits);
-            result = apply_sdg(&result, qubits[0]);
-            Some(result)
-        }
-        GateType::CX => {
-            let cliff = CliffordRep::cx(qubits[0], qubits[1]);
-            Some(extend_clifford(cliff, num_qubits))
-        }
-        GateType::CY => {
-            let cliff = CliffordRep::cy(qubits[0], qubits[1]);
-            Some(extend_clifford(cliff, num_qubits))
-        }
-        GateType::CZ => {
-            let cliff = CliffordRep::cz(qubits[0], qubits[1]);
-            Some(extend_clifford(cliff, num_qubits))
-        }
-        GateType::SWAP => {
-            let cliff = CliffordRep::swap(qubits[0], qubits[1]);
-            Some(extend_clifford(cliff, num_qubits))
-        }
-        _ => None, // Non-Clifford or unsupported gate
-    }
-}
-
-/// Extend a `CliffordRep` to act on more qubits (identity on new qubits).
-fn extend_clifford(
-    cliff: crate::clifford_rep::CliffordRep,
-    target_qubits: usize,
-) -> crate::clifford_rep::CliffordRep {
-    use crate::clifford_rep::CliffordRep;
-
-    if cliff.num_qubits() >= target_qubits {
-        return cliff;
-    }
-
-    // Create a new CliffordRep with more qubits, copying the original images
-    // and using identity for the additional qubits
-    let mut result = CliffordRep::identity(target_qubits);
-
-    // Copy the generator images from the original
-    for q in 0..cliff.num_qubits() {
-        result.set_x_image(q, cliff.x_image(q).clone());
-        result.set_z_image(q, cliff.z_image(q).clone());
-    }
-    // Additional qubits remain as identity (already set by CliffordRep::identity)
-
-    result
-}
-
-// Helper functions to apply single-qubit Cliffords to a CliffordRep
-fn apply_x(
-    cliff: &crate::clifford_rep::CliffordRep,
-    qubit: usize,
-) -> crate::clifford_rep::CliffordRep {
-    let x_cliff = crate::clifford_rep::CliffordRep::x(qubit);
-    extend_clifford(x_cliff, cliff.num_qubits()).compose(cliff)
-}
-
-fn apply_y(
-    cliff: &crate::clifford_rep::CliffordRep,
-    qubit: usize,
-) -> crate::clifford_rep::CliffordRep {
-    let y_cliff = crate::clifford_rep::CliffordRep::y(qubit);
-    extend_clifford(y_cliff, cliff.num_qubits()).compose(cliff)
-}
-
-fn apply_z(
-    cliff: &crate::clifford_rep::CliffordRep,
-    qubit: usize,
-) -> crate::clifford_rep::CliffordRep {
-    let z_cliff = crate::clifford_rep::CliffordRep::z(qubit);
-    extend_clifford(z_cliff, cliff.num_qubits()).compose(cliff)
-}
-
-fn apply_s(
-    cliff: &crate::clifford_rep::CliffordRep,
-    qubit: usize,
-) -> crate::clifford_rep::CliffordRep {
-    let s_cliff = crate::clifford_rep::CliffordRep::s(qubit);
-    extend_clifford(s_cliff, cliff.num_qubits()).compose(cliff)
-}
-
-fn apply_sdg(
-    cliff: &crate::clifford_rep::CliffordRep,
-    qubit: usize,
-) -> crate::clifford_rep::CliffordRep {
-    let sdg_cliff = crate::clifford_rep::CliffordRep::sdg(qubit);
-    extend_clifford(sdg_cliff, cliff.num_qubits()).compose(cliff)
-}
-
-fn apply_sx(
-    cliff: &crate::clifford_rep::CliffordRep,
-    qubit: usize,
-) -> crate::clifford_rep::CliffordRep {
-    let sx_cliff = crate::clifford_rep::CliffordRep::sx(qubit);
-    extend_clifford(sx_cliff, cliff.num_qubits()).compose(cliff)
-}
-
-fn apply_sxdg(
-    cliff: &crate::clifford_rep::CliffordRep,
-    qubit: usize,
-) -> crate::clifford_rep::CliffordRep {
-    // SX† = SX^3 = SX * SX * SX
-    let sx_cliff = crate::clifford_rep::CliffordRep::sx(qubit);
-    let extended = extend_clifford(sx_cliff.clone(), cliff.num_qubits());
-    extended
-        .compose(&extended)
-        .compose(&extended)
-        .compose(cliff)
-}
-
-fn apply_sy(
-    cliff: &crate::clifford_rep::CliffordRep,
-    qubit: usize,
-) -> crate::clifford_rep::CliffordRep {
-    let sy_cliff = crate::clifford_rep::CliffordRep::sy(qubit);
-    extend_clifford(sy_cliff, cliff.num_qubits()).compose(cliff)
-}
-
-fn apply_sydg(
-    cliff: &crate::clifford_rep::CliffordRep,
-    qubit: usize,
-) -> crate::clifford_rep::CliffordRep {
-    // SY† = SY^3
-    let sy_cliff = crate::clifford_rep::CliffordRep::sy(qubit);
-    let extended = extend_clifford(sy_cliff.clone(), cliff.num_qubits());
-    extended
-        .compose(&extended)
-        .compose(&extended)
-        .compose(cliff)
-}
-
-/// Flatten nested Compose nodes into a single level.
-fn flatten_compose(parts: Vec<Operator>) -> Vec<Operator> {
-    let mut result = Vec::new();
-    for part in parts {
-        match part {
-            Operator::Compose(inner_parts) => {
-                result.extend(flatten_compose(inner_parts));
-            }
-            other => result.push(other),
-        }
-    }
-    result
-}
-
-/// Merge adjacent rotations of the same type on the same qubits.
-fn merge_adjacent_rotations(parts: Vec<Operator>) -> Vec<Operator> {
-    if parts.len() < 2 {
-        return parts;
-    }
-
-    let mut result = Vec::with_capacity(parts.len());
-    let mut idx = 0;
-
-    while idx < parts.len() {
-        let current = &parts[idx];
-
-        // Check if next element can be merged with current
-        if idx + 1 < parts.len()
-            && let Some(merged) = try_merge_rotations(current, &parts[idx + 1])
-        {
-            // Skip the merged element
-            if merged.is_identity() {
-                // Both cancelled out, skip both
-                idx += 2;
-                continue;
-            }
-            result.push(merged);
-            idx += 2;
-            continue;
-        }
-
-        result.push(parts[idx].clone());
-        idx += 1;
-    }
-
-    // Recurse if we made any merges (might enable more merges)
-    if result.len() < parts.len() {
-        merge_adjacent_rotations(result)
-    } else {
-        result
-    }
-}
-
-/// Try to merge two rotations if they are compatible.
-/// Returns None if they cannot be merged.
-fn try_merge_rotations(a: &Operator, b: &Operator) -> Option<Operator> {
-    match (a, b) {
-        (
-            Operator::Rotation {
-                rotation_type: rt_a,
-                angle: angle_a,
-                qubits: qubits_a,
-            },
-            Operator::Rotation {
-                rotation_type: rt_b,
-                angle: angle_b,
-                qubits: qubits_b,
-            },
-        ) => {
-            // Can only merge if same rotation type and same qubits
-            if rt_a == rt_b && qubits_a == qubits_b {
-                let combined_angle = *angle_a + *angle_b;
-                Some(Operator::Rotation {
-                    rotation_type: *rt_a,
-                    angle: combined_angle,
-                    qubits: qubits_a.clone(),
-                })
-            } else {
-                None
-            }
-        }
-        _ => None,
-    }
-}
-
-/// Convert a rotation (type + angle) to a named `GateType` if one exists.
-#[must_use]
-pub fn rotation_to_gate_type(rotation_type: RotationType, angle: Angle64) -> Option<GateType> {
-    // Check for standard angles
-    let quarter = Angle64::QUARTER_TURN;
-    let neg_quarter = negate_angle(quarter);
-    let half = Angle64::HALF_TURN;
-    let eighth = half / 4; // π/4
-    let neg_eighth = negate_angle(eighth);
-
-    match rotation_type {
-        RotationType::RZ => {
-            if angle == quarter {
-                Some(GateType::SZ)
-            } else if angle == neg_quarter {
-                Some(GateType::SZdg)
-            } else if angle == half {
-                Some(GateType::Z)
-            } else if angle == eighth {
-                Some(GateType::T)
-            } else if angle == neg_eighth {
-                Some(GateType::Tdg)
-            } else {
-                None
-            }
-        }
-        RotationType::RX => {
-            if angle == quarter {
-                Some(GateType::SX)
-            } else if angle == neg_quarter {
-                Some(GateType::SXdg)
-            } else if angle == half {
-                Some(GateType::X)
-            } else {
-                None
-            }
-        }
-        RotationType::RY => {
-            if angle == quarter {
-                Some(GateType::SY)
-            } else if angle == neg_quarter {
-                Some(GateType::SYdg)
-            } else if angle == half {
-                Some(GateType::Y)
-            } else {
-                None
-            }
-        }
-        RotationType::RZZ => {
-            if angle == quarter {
-                Some(GateType::SZZ)
-            } else if angle == neg_quarter {
-                Some(GateType::SZZdg)
-            } else {
-                None
-            }
-        }
-        _ => None,
-    }
-}
-
-// --- Gate type helpers ---
-
-trait GateTypeExt {
-    fn is_clifford(&self) -> bool;
-    fn is_self_adjoint(&self) -> bool;
-}
-
-impl GateTypeExt for GateType {
-    fn is_clifford(&self) -> bool {
-        use GateType::{CX, CY, CZ, H, I, SWAP, SX, SXdg, SY, SYdg, SZ, SZZ, SZZdg, SZdg, X, Y, Z};
-        matches!(
-            self,
-            I | X
-                | Y
-                | Z
-                | H
-                | SX
-                | SXdg
-                | SY
-                | SYdg
-                | SZ
-                | SZdg
-                | CX
-                | CY
-                | CZ
-                | SWAP
-                | SZZ
-                | SZZdg
-        )
-    }
-
-    fn is_self_adjoint(&self) -> bool {
-        use GateType::{CX, CY, CZ, H, I, SWAP, X, Y, Z};
-        matches!(self, I | X | Y | Z | H | CX | CY | CZ | SWAP)
-    }
-}
-
-// --- Angle64 helpers ---
-
-/// Check if an angle is a multiple of a quarter turn (π/2).
-///
-/// This is used to determine if a rotation is a Clifford gate.
-fn is_multiple_of_quarter_turn(angle: Angle64) -> bool {
-    let quarter_fraction = Angle64::QUARTER_TURN.fraction();
-    if quarter_fraction == 0 {
-        return true; // Edge case: if quarter is 0, everything is a multiple
-    }
-    angle.fraction().is_multiple_of(quarter_fraction)
-}
-
-/// Negate an angle (for adjoint operations).
-fn negate_angle(angle: Angle64) -> Angle64 {
-    Angle64::ZERO - angle
-}
-
-/// Convert an angle to a `QuarterPhase` if it's a multiple of π/2.
-///
-/// Returns None if the angle is not a multiple of π/2.
-fn angle_to_quarter_phase(angle: Angle64) -> Option<QuarterPhase> {
-    let quarter = Angle64::QUARTER_TURN;
-    let half = Angle64::HALF_TURN;
-    let three_quarters = quarter + half;
-
-    if angle == Angle64::ZERO {
-        Some(QuarterPhase::PlusOne)
-    } else if angle == quarter {
-        Some(QuarterPhase::PlusI)
-    } else if angle == half {
-        Some(QuarterPhase::MinusOne)
-    } else if angle == three_quarters {
-        Some(QuarterPhase::MinusI)
-    } else {
-        None
-    }
-}
-
-// --- Gate constructors - Single qubit rotations ---
-
-/// Rotation around X axis by the given angle.
-///
-/// For multiple qubits, use `RXs(angle, [0, 1, 2])`.
-#[must_use]
-#[allow(non_snake_case)]
-pub fn RX(angle: Angle64, qubit: impl Into<QubitId>) -> Operator {
-    Operator::rotation(RotationType::RX, angle, smallvec::smallvec![qubit.into().0])
-}
-
-/// RX rotations on multiple qubits.
-///
-/// `RXs(angle, [0, 1, 2])` is equivalent to `RX(angle, 0) & RX(angle, 1) & RX(angle, 2)`
-#[must_use]
-#[allow(non_snake_case)]
-pub fn RXs(angle: Angle64, qubits: impl Into<Qubits>) -> Operator {
-    qubits
-        .into()
-        .apply(|q| Operator::rotation(RotationType::RX, angle, smallvec::smallvec![q]))
-}
-
-/// Rotation around Y axis by the given angle.
-///
-/// For multiple qubits, use `RYs(angle, [0, 1, 2])`.
-#[must_use]
-#[allow(non_snake_case)]
-pub fn RY(angle: Angle64, qubit: impl Into<QubitId>) -> Operator {
-    Operator::rotation(RotationType::RY, angle, smallvec::smallvec![qubit.into().0])
-}
-
-/// RY rotations on multiple qubits.
-///
-/// `RYs(angle, [0, 1, 2])` is equivalent to `RY(angle, 0) & RY(angle, 1) & RY(angle, 2)`
-#[must_use]
-#[allow(non_snake_case)]
-pub fn RYs(angle: Angle64, qubits: impl Into<Qubits>) -> Operator {
-    qubits
-        .into()
-        .apply(|q| Operator::rotation(RotationType::RY, angle, smallvec::smallvec![q]))
-}
-
-/// Rotation around Z axis by the given angle.
-///
-/// For multiple qubits, use `RZs(angle, [0, 1, 2])`.
-#[must_use]
-#[allow(non_snake_case)]
-pub fn RZ(angle: Angle64, qubit: impl Into<QubitId>) -> Operator {
-    Operator::rotation(RotationType::RZ, angle, smallvec::smallvec![qubit.into().0])
-}
-
-/// RZ rotations on multiple qubits.
-///
-/// `RZs(angle, [0, 1, 2])` is equivalent to `RZ(angle, 0) & RZ(angle, 1) & RZ(angle, 2)`
-#[must_use]
-#[allow(non_snake_case)]
-pub fn RZs(angle: Angle64, qubits: impl Into<Qubits>) -> Operator {
-    qubits
-        .into()
-        .apply(|q| Operator::rotation(RotationType::RZ, angle, smallvec::smallvec![q]))
-}
-
-// --- Gate constructors - Two qubit rotations ---
-
-/// Two-qubit XX rotation by the given angle.
-///
-/// For multiple pairs, use `RXXs(angle, [(0, 1), (2, 3)])` or tensor.
-#[must_use]
-#[allow(non_snake_case)]
-pub fn RXX(angle: Angle64, q0: impl Into<QubitId>, q1: impl Into<QubitId>) -> Operator {
-    Operator::rotation(
-        RotationType::RXX,
-        angle,
-        smallvec::smallvec![q0.into().0, q1.into().0],
-    )
-}
-
-/// RXX rotations on multiple qubit pairs.
-///
-/// `RXXs(angle, [(0, 1), (2, 3)])` is equivalent to `RXX(angle, 0, 1) & RXX(angle, 2, 3)`
-#[must_use]
-#[allow(non_snake_case)]
-pub fn RXXs(angle: Angle64, pairs: impl Into<QubitPairs>) -> Operator {
-    pairs
-        .into()
-        .apply(|q0, q1| Operator::rotation(RotationType::RXX, angle, smallvec::smallvec![q0, q1]))
-}
-
-/// Two-qubit YY rotation by the given angle.
-///
-/// For multiple pairs, use `RYYs(angle, [(0, 1), (2, 3)])` or tensor.
-#[must_use]
-#[allow(non_snake_case)]
-pub fn RYY(angle: Angle64, q0: impl Into<QubitId>, q1: impl Into<QubitId>) -> Operator {
-    Operator::rotation(
-        RotationType::RYY,
-        angle,
-        smallvec::smallvec![q0.into().0, q1.into().0],
-    )
-}
-
-/// RYY rotations on multiple qubit pairs.
-///
-/// `RYYs(angle, [(0, 1), (2, 3)])` is equivalent to `RYY(angle, 0, 1) & RYY(angle, 2, 3)`
-#[must_use]
-#[allow(non_snake_case)]
-pub fn RYYs(angle: Angle64, pairs: impl Into<QubitPairs>) -> Operator {
-    pairs
-        .into()
-        .apply(|q0, q1| Operator::rotation(RotationType::RYY, angle, smallvec::smallvec![q0, q1]))
-}
-
-/// Two-qubit ZZ rotation by the given angle.
-///
-/// For multiple pairs, use `RZZs(angle, [(0, 1), (2, 3)])` or tensor.
-#[must_use]
-#[allow(non_snake_case)]
-pub fn RZZ(angle: Angle64, q0: impl Into<QubitId>, q1: impl Into<QubitId>) -> Operator {
-    Operator::rotation(
-        RotationType::RZZ,
-        angle,
-        smallvec::smallvec![q0.into().0, q1.into().0],
-    )
-}
-
-/// RZZ rotations on multiple qubit pairs.
-///
-/// `RZZs(angle, [(0, 1), (2, 3)])` is equivalent to `RZZ(angle, 0, 1) & RZZ(angle, 2, 3)`
-#[must_use]
-#[allow(non_snake_case)]
-pub fn RZZs(angle: Angle64, pairs: impl Into<QubitPairs>) -> Operator {
-    pairs
-        .into()
-        .apply(|q0, q1| Operator::rotation(RotationType::RZZ, angle, smallvec::smallvec![q0, q1]))
-}
-
-// --- Gate constructors - Named single-qubit Cliffords ---
-
-/// Identity gate on a single qubit.
-#[must_use]
-#[allow(non_snake_case)]
-pub fn I(qubit: impl Into<QubitId>) -> Operator {
-    RZ(Angle64::ZERO, qubit.into().0)
-}
-
-/// Identity gates on multiple qubits.
-#[must_use]
-#[allow(non_snake_case)]
-pub fn Is(qubits: impl Into<Qubits>) -> Operator {
-    qubits.into().apply(|q| RZ(Angle64::ZERO, q))
-}
-
-/// Pauli X operator on a single qubit.
-///
-/// For multiple qubits, use `Xs([0, 2, 5])` or tensor: `X(0) & X(2) & X(5)`
-#[must_use]
-#[allow(non_snake_case)]
-pub fn X(qubit: impl Into<QubitId>) -> Operator {
-    Operator::Pauli(PauliString::x(qubit.into().0))
-}
-
-/// Pauli X operators on multiple qubits.
-///
-/// `Xs([0, 2, 5])` is equivalent to `X(0) & X(2) & X(5)`
-#[must_use]
-#[allow(non_snake_case)]
-pub fn Xs(qubits: impl Into<Qubits>) -> Operator {
-    let qs = qubits.into();
-    if qs.0.is_empty() {
-        Operator::Pauli(PauliString::default())
-    } else {
-        let mut ps = PauliString::x(qs.0[0].0);
-        for q in &qs.0[1..] {
-            ps = ps & PauliString::x(q.0);
-        }
-        Operator::Pauli(ps)
-    }
-}
-
-/// Pauli Y operator on a single qubit.
-///
-/// For multiple qubits, use `Ys([0, 2, 5])` or tensor: `Y(0) & Y(2) & Y(5)`
-#[must_use]
-#[allow(non_snake_case)]
-pub fn Y(qubit: impl Into<QubitId>) -> Operator {
-    Operator::Pauli(PauliString::y(qubit.into().0))
-}
-
-/// Pauli Y operators on multiple qubits.
-///
-/// `Ys([0, 2, 5])` is equivalent to `Y(0) & Y(2) & Y(5)`
-#[must_use]
-#[allow(non_snake_case)]
-pub fn Ys(qubits: impl Into<Qubits>) -> Operator {
-    let qs = qubits.into();
-    if qs.0.is_empty() {
-        Operator::Pauli(PauliString::default())
-    } else {
-        let mut ps = PauliString::y(qs.0[0].0);
-        for q in &qs.0[1..] {
-            ps = ps & PauliString::y(q.0);
-        }
-        Operator::Pauli(ps)
-    }
-}
-
-/// Pauli Z operator on a single qubit.
-///
-/// For multiple qubits, use `Zs([0, 2, 5])` or tensor: `Z(0) & Z(2) & Z(5)`
-#[must_use]
-#[allow(non_snake_case)]
-pub fn Z(qubit: impl Into<QubitId>) -> Operator {
-    Operator::Pauli(PauliString::z(qubit.into().0))
-}
-
-/// Pauli Z operators on multiple qubits.
-///
-/// `Zs([0, 2, 5])` is equivalent to `Z(0) & Z(2) & Z(5)`
-#[must_use]
-#[allow(non_snake_case)]
-pub fn Zs(qubits: impl Into<Qubits>) -> Operator {
-    let qs = qubits.into();
-    if qs.0.is_empty() {
-        Operator::Pauli(PauliString::default())
-    } else {
-        let mut ps = PauliString::z(qs.0[0].0);
-        for q in &qs.0[1..] {
-            ps = ps & PauliString::z(q.0);
-        }
-        Operator::Pauli(ps)
-    }
-}
-
-/// SX gate (sqrt X): RX(π/2)
-#[must_use]
-#[allow(non_snake_case)]
-pub fn SX(qubit: impl Into<QubitId>) -> Operator {
-    RX(Angle64::QUARTER_TURN, qubit.into().0)
-}
-
-/// SX gates on multiple qubits.
-#[must_use]
-#[allow(non_snake_case)]
-pub fn SXs(qubits: impl Into<Qubits>) -> Operator {
-    qubits.into().apply(|q| RX(Angle64::QUARTER_TURN, q))
-}
-
-/// SY gate (sqrt Y): RY(π/2)
-#[must_use]
-#[allow(non_snake_case)]
-pub fn SY(qubit: impl Into<QubitId>) -> Operator {
-    RY(Angle64::QUARTER_TURN, qubit.into().0)
-}
-
-/// SY gates on multiple qubits.
-#[must_use]
-#[allow(non_snake_case)]
-pub fn SYs(qubits: impl Into<Qubits>) -> Operator {
-    qubits.into().apply(|q| RY(Angle64::QUARTER_TURN, q))
-}
-
-/// SZ gate (sqrt Z): RZ(π/2)
-#[must_use]
-#[allow(non_snake_case)]
-pub fn SZ(qubit: impl Into<QubitId>) -> Operator {
-    RZ(Angle64::QUARTER_TURN, qubit.into().0)
-}
-
-/// SZ gates on multiple qubits.
-#[must_use]
-#[allow(non_snake_case)]
-pub fn SZs(qubits: impl Into<Qubits>) -> Operator {
-    qubits.into().apply(|q| RZ(Angle64::QUARTER_TURN, q))
-}
-
-/// T gate: RZ(π/4)
-#[must_use]
-#[allow(non_snake_case)]
-pub fn T(qubit: impl Into<QubitId>) -> Operator {
-    RZ(Angle64::HALF_TURN / 4, qubit.into().0)
-}
-
-/// T gates on multiple qubits.
-#[must_use]
-#[allow(non_snake_case)]
-pub fn Ts(qubits: impl Into<Qubits>) -> Operator {
-    qubits.into().apply(|q| RZ(Angle64::HALF_TURN / 4, q))
-}
-
-/// Hadamard gate: RZ(π) * RY(π/2) (up to global phase)
-#[must_use]
-#[allow(non_snake_case)]
-pub fn H(qubit: impl Into<QubitId>) -> Operator {
-    let q = qubit.into().0;
-    Operator::Gate {
-        gate_type: GateType::H,
-        qubits: smallvec::smallvec![q],
-    }
-}
-
-/// Hadamard gates on multiple qubits.
-#[must_use]
-#[allow(non_snake_case)]
-pub fn Hs(qubits: impl Into<Qubits>) -> Operator {
-    qubits.into().apply(|q| {
-        Operator::Compose(vec![
-            RZ(Angle64::HALF_TURN, q),
-            RY(Angle64::QUARTER_TURN, q),
-        ])
-    })
-}
-
-// --- Gate constructors - Named two-qubit gates ---
-
-/// CNOT (CX) gate.
-///
-/// For multiple pairs, use `CXs([(0, 1), (2, 3)])` or tensor: `CX(0, 1) & CX(2, 3)`
-#[must_use]
-#[allow(non_snake_case)]
-pub fn CX(control: impl Into<QubitId>, target: impl Into<QubitId>) -> Operator {
-    Operator::gate(
-        GateType::CX,
-        smallvec::smallvec![control.into().0, target.into().0],
-    )
-}
-
-/// CX gates on multiple qubit pairs.
-///
-/// `CXs([(0, 1), (2, 3)])` is equivalent to `CX(0, 1) & CX(2, 3)`
-#[must_use]
-#[allow(non_snake_case)]
-pub fn CXs(pairs: impl Into<QubitPairs>) -> Operator {
-    pairs
-        .into()
-        .apply(|ctrl, tgt| Operator::gate(GateType::CX, smallvec::smallvec![ctrl, tgt]))
-}
-
-/// Controlled-Y gate.
-///
-/// For multiple pairs, use `CYs([(0, 1), (2, 3)])` or tensor: `CY(0, 1) & CY(2, 3)`
-#[must_use]
-#[allow(non_snake_case)]
-pub fn CY(control: impl Into<QubitId>, target: impl Into<QubitId>) -> Operator {
-    Operator::gate(
-        GateType::CY,
-        smallvec::smallvec![control.into().0, target.into().0],
-    )
-}
-
-/// CY gates on multiple qubit pairs.
-///
-/// `CYs([(0, 1), (2, 3)])` is equivalent to `CY(0, 1) & CY(2, 3)`
-#[must_use]
-#[allow(non_snake_case)]
-pub fn CYs(pairs: impl Into<QubitPairs>) -> Operator {
-    pairs
-        .into()
-        .apply(|ctrl, tgt| Operator::gate(GateType::CY, smallvec::smallvec![ctrl, tgt]))
-}
-
-/// Controlled-Z gate.
-///
-/// For multiple pairs, use `CZs([(0, 1), (2, 3)])` or tensor: `CZ(0, 1) & CZ(2, 3)`
-#[must_use]
-#[allow(non_snake_case)]
-pub fn CZ(q0: impl Into<QubitId>, q1: impl Into<QubitId>) -> Operator {
-    Operator::gate(GateType::CZ, smallvec::smallvec![q0.into().0, q1.into().0])
-}
-
-/// CZ gates on multiple qubit pairs.
-///
-/// `CZs([(0, 1), (2, 3)])` is equivalent to `CZ(0, 1) & CZ(2, 3)`
-#[must_use]
-#[allow(non_snake_case)]
-pub fn CZs(pairs: impl Into<QubitPairs>) -> Operator {
-    pairs
-        .into()
-        .apply(|q0, q1| Operator::gate(GateType::CZ, smallvec::smallvec![q0, q1]))
-}
-
-/// SWAP gate.
-///
-/// For multiple pairs, use `SWAPs([(0, 1), (2, 3)])` or tensor: `SWAP(0, 1) & SWAP(2, 3)`
-#[must_use]
-#[allow(non_snake_case)]
-pub fn SWAP(q0: impl Into<QubitId>, q1: impl Into<QubitId>) -> Operator {
-    Operator::gate(
-        GateType::SWAP,
-        smallvec::smallvec![q0.into().0, q1.into().0],
-    )
-}
-
-/// SWAP gates on multiple qubit pairs.
-///
-/// `SWAPs([(0, 1), (2, 3)])` is equivalent to `SWAP(0, 1) & SWAP(2, 3)`
-#[must_use]
-#[allow(non_snake_case)]
-pub fn SWAPs(pairs: impl Into<QubitPairs>) -> Operator {
-    pairs
-        .into()
-        .apply(|q0, q1| Operator::gate(GateType::SWAP, smallvec::smallvec![q0, q1]))
-}
-
-/// SZZ gate: RZZ(π/2)
-///
-/// For multiple pairs, use `SZZs([(0, 1), (2, 3)])` or tensor: `SZZ(0, 1) & SZZ(2, 3)`
-#[must_use]
-#[allow(non_snake_case)]
-pub fn SZZ(q0: impl Into<QubitId>, q1: impl Into<QubitId>) -> Operator {
-    Operator::rotation(
-        RotationType::RZZ,
-        Angle64::QUARTER_TURN,
-        smallvec::smallvec![q0.into().0, q1.into().0],
-    )
-}
-
-/// SZZ gates on multiple qubit pairs.
-///
-/// `SZZs([(0, 1), (2, 3)])` is equivalent to `SZZ(0, 1) & SZZ(2, 3)`
-#[must_use]
-#[allow(non_snake_case)]
-pub fn SZZs(pairs: impl Into<QubitPairs>) -> Operator {
-    pairs.into().apply(|q0, q1| {
-        Operator::rotation(
-            RotationType::RZZ,
-            Angle64::QUARTER_TURN,
-            smallvec::smallvec![q0, q1],
-        )
-    })
-}
-
-// --- Gate constructors - Three-qubit gates ---
-
-/// Toffoli (CCX) gate.
-#[must_use]
-#[allow(non_snake_case)]
-pub fn CCX(c0: impl Into<QubitId>, c1: impl Into<QubitId>, target: impl Into<QubitId>) -> Operator {
-    Operator::gate(
-        GateType::CCX,
-        smallvec::smallvec![c0.into().0, c1.into().0, target.into().0],
-    )
-}
-
-// --- Operator implementations ---
-
-// Tensor product: &
-impl BitAnd for Operator {
-    type Output = Operator;
-
-    fn bitand(self, rhs: Operator) -> Operator {
-        match (self, rhs) {
-            // Pauli & Pauli: use PauliString tensor product
-            (Operator::Pauli(a), Operator::Pauli(b)) => Operator::Pauli(a & b),
-            // Flatten nested tensors
-            (Operator::Tensor(mut parts), Operator::Tensor(rhs_parts)) => {
-                parts.extend(rhs_parts);
-                Operator::Tensor(parts)
-            }
-            (Operator::Tensor(mut parts), rhs) => {
-                parts.push(rhs);
-                Operator::Tensor(parts)
-            }
-            (lhs, Operator::Tensor(mut parts)) => {
-                parts.insert(0, lhs);
-                Operator::Tensor(parts)
-            }
-            (lhs, rhs) => Operator::Tensor(vec![lhs, rhs]),
-        }
-    }
-}
-
-// Composition: *
-impl Mul for Operator {
-    type Output = Operator;
-
-    fn mul(self, rhs: Operator) -> Operator {
-        // A * B means apply B first, then A (matrix multiplication order)
-        // So we store as [B, A] in the Compose vec (application order)
-        match (self, rhs) {
-            // Pauli * Pauli: use PauliString algebra
-            (Operator::Pauli(a), Operator::Pauli(b)) => Operator::Pauli(a * b),
-            // Flatten nested compositions
-            (Operator::Compose(lhs_parts), Operator::Compose(rhs_parts)) => {
-                // rhs applied first, then lhs
-                let mut result = rhs_parts;
-                result.extend(lhs_parts);
-                Operator::Compose(result)
-            }
-            (Operator::Compose(lhs_parts), rhs) => {
-                // rhs applied first
-                let mut result = vec![rhs];
-                result.extend(lhs_parts);
-                Operator::Compose(result)
-            }
-            (lhs, Operator::Compose(mut rhs_parts)) => {
-                // rhs_parts applied first, then lhs
-                rhs_parts.push(lhs);
-                Operator::Compose(rhs_parts)
-            }
-            (lhs, rhs) => {
-                // rhs applied first, then lhs
-                Operator::Compose(vec![rhs, lhs])
-            }
-        }
-    }
-}
-
-// --- Circuit diagram generation ---
-
-impl Operator {
-    /// Generates an ASCII circuit diagram for this expression.
-    #[must_use]
-    pub fn to_diagram(&self, num_qubits: usize) -> String {
-        let mut diagram = CircuitDiagram::new(num_qubits);
-        self.add_to_diagram(&mut diagram);
-        diagram.render()
-    }
-
-    fn add_to_diagram(&self, diagram: &mut CircuitDiagram) {
-        match self {
-            Self::Pauli(ps) => {
-                // Draw each Pauli on its qubit
-                for (pauli, qubit) in ps.iter_pairs() {
-                    let q = usize::from(qubit);
-                    let name = match pauli {
-                        crate::Pauli::I => continue,
-                        crate::Pauli::X => "X",
-                        crate::Pauli::Y => "Y",
-                        crate::Pauli::Z => "Z",
-                    };
-                    diagram.add_single_gate(q, name);
-                }
-            }
-            Self::Rotation {
-                rotation_type,
-                angle,
-                qubits,
-            } => {
-                let name = if let Some(gate_type) = rotation_to_gate_type(*rotation_type, *angle) {
-                    format!("{gate_type:?}")
-                } else {
-                    format!("{rotation_type:?}")
-                };
-
-                if qubits.len() == 1 {
-                    diagram.add_single_gate(qubits[0], &name);
-                } else if qubits.len() == 2 {
-                    diagram.add_two_qubit_gate(qubits[0], qubits[1], &name);
-                }
-            }
-            Self::Gate { gate_type, qubits } => match gate_type {
-                GateType::CX => {
-                    diagram.add_controlled_gate(qubits[0], qubits[1], "X");
-                }
-                GateType::CY => {
-                    diagram.add_controlled_gate(qubits[0], qubits[1], "Y");
-                }
-                GateType::CZ => {
-                    diagram.add_controlled_gate(qubits[0], qubits[1], "Z");
-                }
-                GateType::SWAP => {
-                    diagram.add_swap(qubits[0], qubits[1]);
-                }
-                GateType::CCX => {
-                    diagram.add_toffoli(qubits[0], qubits[1], qubits[2]);
-                }
-                _ => {
-                    if qubits.len() == 1 {
-                        diagram.add_single_gate(qubits[0], &format!("{gate_type:?}"));
-                    }
-                }
-            },
-            Self::Tensor(parts) => {
-                // Tensor products can be drawn simultaneously
-                for part in parts {
-                    part.add_to_diagram(diagram);
-                }
-            }
-            Self::Compose(parts) => {
-                // Sequential composition: draw in order
-                for part in parts {
-                    part.add_to_diagram(diagram);
-                    diagram.advance();
-                }
-            }
-            Self::Adjoint(inner) => {
-                // Mark as adjoint somehow?
-                inner.add_to_diagram(diagram);
-            }
-            Self::Phase { inner, .. } => {
-                // Global phase doesn't appear in circuit diagrams
-                inner.add_to_diagram(diagram);
-            }
-        }
-    }
-}
-
-struct CircuitDiagram {
-    num_qubits: usize,
-    columns: Vec<Vec<String>>,
-    current_col: usize,
-}
-
-impl CircuitDiagram {
-    fn new(num_qubits: usize) -> Self {
-        Self {
-            num_qubits,
-            columns: vec![vec![String::new(); num_qubits * 2 - 1]],
-            current_col: 0,
-        }
-    }
-
-    fn ensure_column(&mut self) {
-        if self.current_col >= self.columns.len() {
-            self.columns
-                .push(vec![String::new(); self.num_qubits * 2 - 1]);
-        }
-    }
-
-    fn advance(&mut self) {
-        self.current_col += 1;
-    }
-
-    fn add_single_gate(&mut self, qubit: usize, name: &str) {
-        self.ensure_column();
-        let row = qubit * 2;
-        if row < self.columns[self.current_col].len() {
-            self.columns[self.current_col][row] = format!("[{name}]");
-        }
-    }
-
-    fn add_controlled_gate(&mut self, control: usize, target: usize, target_name: &str) {
-        self.ensure_column();
-        let ctrl_row = control * 2;
-        let targ_row = target * 2;
-
-        if ctrl_row < self.columns[self.current_col].len() {
-            self.columns[self.current_col][ctrl_row] = "●".to_string();
-        }
-        if targ_row < self.columns[self.current_col].len() {
-            self.columns[self.current_col][targ_row] = format!("[{target_name}]");
-        }
-
-        // Draw vertical line
-        let (min_row, max_row) = if ctrl_row < targ_row {
-            (ctrl_row, targ_row)
-        } else {
-            (targ_row, ctrl_row)
-        };
-        for row in (min_row + 1)..max_row {
-            if row % 2 == 1 && self.columns[self.current_col][row].is_empty() {
-                self.columns[self.current_col][row] = "│".to_string();
-            }
-        }
-    }
-
-    fn add_swap(&mut self, q0: usize, q1: usize) {
-        self.ensure_column();
-        let row0 = q0 * 2;
-        let row1 = q1 * 2;
-
-        if row0 < self.columns[self.current_col].len() {
-            self.columns[self.current_col][row0] = "×".to_string();
-        }
-        if row1 < self.columns[self.current_col].len() {
-            self.columns[self.current_col][row1] = "×".to_string();
-        }
-
-        // Draw vertical line
-        let (min_row, max_row) = (row0.min(row1), row0.max(row1));
-        for row in (min_row + 1)..max_row {
-            if row % 2 == 1 && self.columns[self.current_col][row].is_empty() {
-                self.columns[self.current_col][row] = "│".to_string();
-            }
-        }
-    }
-
-    fn add_toffoli(&mut self, c0: usize, c1: usize, target: usize) {
-        self.ensure_column();
-        let c0_row = c0 * 2;
-        let c1_row = c1 * 2;
-        let targ_row = target * 2;
-
-        if c0_row < self.columns[self.current_col].len() {
-            self.columns[self.current_col][c0_row] = "●".to_string();
-        }
-        if c1_row < self.columns[self.current_col].len() {
-            self.columns[self.current_col][c1_row] = "●".to_string();
-        }
-        if targ_row < self.columns[self.current_col].len() {
-            self.columns[self.current_col][targ_row] = "[X]".to_string();
-        }
-
-        // Draw vertical lines
-        let min_row = c0_row.min(c1_row).min(targ_row);
-        let max_row = c0_row.max(c1_row).max(targ_row);
-        for row in (min_row + 1)..max_row {
-            if row % 2 == 1 && self.columns[self.current_col][row].is_empty() {
-                self.columns[self.current_col][row] = "│".to_string();
-            }
-        }
-    }
-
-    fn add_two_qubit_gate(&mut self, q0: usize, q1: usize, name: &str) {
-        self.ensure_column();
-        let row0 = q0 * 2;
-        let row1 = q1 * 2;
-
-        if row0 < self.columns[self.current_col].len() {
-            self.columns[self.current_col][row0] = format!("[{name}]");
-        }
-        if row1 < self.columns[self.current_col].len() {
-            self.columns[self.current_col][row1] = format!("[{name}]");
-        }
-
-        // Draw vertical line
-        let (min_row, max_row) = (row0.min(row1), row0.max(row1));
-        for row in (min_row + 1)..max_row {
-            if row % 2 == 1 && self.columns[self.current_col][row].is_empty() {
-                self.columns[self.current_col][row] = "│".to_string();
-            }
-        }
-    }
-
-    fn render(&self) -> String {
-        let lines: Vec<String> = (0..self.num_qubits).map(|q| format!("q{q}: ")).collect();
-
-        // Add spacing lines between qubits
-        let mut all_lines: Vec<String> = Vec::new();
-        for (idx, line) in lines.iter().enumerate() {
-            all_lines.push(line.clone());
-            if idx < self.num_qubits - 1 {
-                all_lines.push("    ".to_string()); // spacing line
-            }
-        }
-
-        // Process each column
-        for col in &self.columns {
-            // Find max width in this column
-            let max_width = col
-                .iter()
-                .map(|s| s.chars().count())
-                .max()
-                .unwrap_or(0)
-                .max(3);
-
-            for (row, cell) in col.iter().enumerate() {
-                if row < all_lines.len() {
-                    if cell.is_empty() {
-                        // Wire or empty
-                        if row % 2 == 0 {
-                            all_lines[row].push_str(&"─".repeat(max_width));
-                        } else {
-                            all_lines[row].push_str(&" ".repeat(max_width));
-                        }
-                    } else {
-                        // Center the cell content
-                        let padding = max_width.saturating_sub(cell.chars().count());
-                        let left_pad = padding / 2;
-                        let right_pad = padding - left_pad;
-
-                        if row % 2 == 0 {
-                            // Qubit line
-                            all_lines[row].push_str(&"─".repeat(left_pad));
-                            all_lines[row].push_str(cell);
-                            all_lines[row].push_str(&"─".repeat(right_pad));
-                        } else {
-                            // Spacing line
-                            all_lines[row].push_str(&" ".repeat(left_pad));
-                            all_lines[row].push_str(cell);
-                            all_lines[row].push_str(&" ".repeat(right_pad));
-                        }
-                    }
-                }
-            }
-        }
-
-        // Add trailing wire
-        for (idx, line) in all_lines.iter_mut().enumerate() {
-            if idx % 2 == 0 {
-                line.push('─');
-            }
-        }
-
-        all_lines.join("\n")
-    }
-}
-
-
-#[cfg(test)]
-mod tests {
-    use super::*;
-
-    #[test]
-    fn test_single_qubit_gates() {
-        let x = X(0);
-        let z = Z(1);
-        let h = H(0);
-
-        assert!(x.is_clifford());
-        assert!(z.is_clifford());
-        assert!(h.is_clifford());
-    }
-
-    #[test]
-    fn test_t_gate_not_clifford() {
-        let t = T(0);
-        assert!(!t.is_clifford());
-    }
-
-    #[test]
-    fn test_tensor_product() {
-        let op = X(0) & Z(1);
-        assert!(op.is_clifford());
-
-        // Pauli & Pauli now produces a single Pauli variant
-        if let Operator::Pauli(ps) = &op {
-            assert_eq!(ps.get(0), crate::Pauli::X);
-            assert_eq!(ps.get(1), crate::Pauli::Z);
-        } else {
-            panic!("Expected Pauli, got {op:?}");
-        }
-
-        // Mixed tensor (Pauli with non-Pauli) produces Tensor
-        let mixed = X(0) & H(1);
-        assert!(matches!(mixed, Operator::Tensor(_)));
-    }
-
-    #[test]
-    fn test_composition() {
-        let circuit = T(0) * H(0);
-        assert!(!circuit.is_clifford()); // T is not Clifford
-
-        let cliff_circuit = SZ(0) * H(0);
-        assert!(cliff_circuit.is_clifford());
-    }
-
-    #[test]
-    fn test_control_gates() {
-        let cx = CX(0, 1);
-        let cz = CZ(0, 1);
-
-        assert!(cx.is_clifford());
-        assert!(cz.is_clifford());
-    }
-
-    #[test]
-    fn test_adjoint() {
-        let t = T(0);
-        let t_dg = t.dg();
-
-        // T† should have negated angle
-        if let Operator::Rotation { angle, .. } = t_dg {
-            let t_angle = Angle64::HALF_TURN / 4;
-            let expected = negate_angle(t_angle);
-            assert_eq!(angle, expected);
-        } else {
-            panic!("Expected Rotation");
-        }
-    }
-
-    #[test]
-    fn test_double_adjoint() {
-        let h = H(0);
-        let h_dg_dg = h.dg().dg();
-
-        // H†† should equal H (structurally)
-        assert_eq!(h, h_dg_dg);
-    }
-
-    #[test]
-    fn test_qubits() {
-        let circuit = CX(0, 1) * H(0) * T(2);
-        let qubits = circuit.qubits();
-        assert_eq!(qubits, vec![0, 1, 2]);
-    }
-
-    #[test]
-    fn test_to_named_gate() {
-        let sz = SZ(0);
-        assert_eq!(sz.to_named_gate(), Some(GateType::SZ));
-
-        let t = T(0);
-        assert_eq!(t.to_named_gate(), Some(GateType::T));
-
-        let x = X(0);
-        assert_eq!(x.to_named_gate(), Some(GateType::X));
-    }
-
-    #[test]
-    fn test_diagram_single_qubit() {
-        let h = H(0);
-        let diagram = h.to_diagram(1);
-        assert!(diagram.contains("[H]"));
-    }
-
-    #[test]
-    fn test_diagram_cx() {
-        let cx = CX(0, 1);
-        let diagram = cx.to_diagram(2);
-        assert!(diagram.contains("●"));
-        assert!(diagram.contains("[X]"));
-    }
-
-    #[test]
-    fn test_diagram_complex() {
-        // Build a circuit: H(0), CX(0,1), T(1)
-        let circuit = T(1) * CX(0, 1) * H(0);
-        let diagram = circuit.to_diagram(2);
-        println!("Circuit diagram:\n{diagram}");
-
-        // Also test a 3-qubit circuit
-        let circuit3 = CCX(0, 1, 2) * H(0) * H(1);
-        let diagram3 = circuit3.to_diagram(3);
-        println!("\n3-qubit circuit:\n{diagram3}");
-    }
-
-    #[test]
-    fn test_composition_order() {
-        // A * B means apply B first, then A
-        // Test composition with rotations
-        let circuit = SZ(0) * SY(0) * SX(0); // Apply SX, then SY, then SZ
-
-        if let Operator::Compose(parts) = circuit {
-            assert_eq!(parts.len(), 3);
-            // All should be rotations
-            assert!(matches!(&parts[0], Operator::Rotation { .. }));
-            assert!(matches!(&parts[1], Operator::Rotation { .. }));
-            assert!(matches!(&parts[2], Operator::Rotation { .. }));
-        } else {
-            panic!("Expected Compose");
-        }
-    }
-
-// --- Simplify tests ---
-
-    #[test]
-    fn test_simplify_identity() {
-        let id = I(0);
-        assert!(id.is_identity());
-    }
-
-    #[test]
-    fn test_simplify_cancellation() {
-        // T * T† should simplify to identity
-        let t = T(0);
-        let t_dg = t.dg();
-        let circuit = t.clone() * t_dg;
-        let simplified = circuit.simplify();
-
-        // Should be identity (zero-angle rotation)
-        assert!(simplified.is_identity());
-    }
-
-    #[test]
-    fn test_simplify_merge_adjacent() {
-        // SZ * SZ = Z (RZ(π/2) + RZ(π/2) = RZ(π))
-        let circuit = SZ(0) * SZ(0);
-        let simplified = circuit.simplify();
-
-        // Should merge into a single rotation
-        if let Operator::Rotation {
-            angle,
-            rotation_type,
-            ..
-        } = simplified
-        {
-            assert_eq!(rotation_type, RotationType::RZ);
-            assert_eq!(angle, Angle64::HALF_TURN); // π
-        } else {
-            panic!("Expected single Rotation, got {simplified:?}");
-        }
-    }
-
-    #[test]
-    fn test_simplify_preserves_different_qubits() {
-        // RZ on different qubits shouldn't merge
-        let circuit = RZ(Angle64::QUARTER_TURN, 0) * RZ(Angle64::QUARTER_TURN, 1);
-        let simplified = circuit.simplify();
-
-        // Should remain a Compose with 2 parts
-        if let Operator::Compose(parts) = simplified {
-            assert_eq!(parts.len(), 2);
-        } else {
-            panic!("Expected Compose");
-        }
-    }
-
-    #[test]
-    fn test_simplify_preserves_different_rotation_types() {
-        // RX and RZ on same qubit shouldn't merge
-        let circuit = RX(Angle64::QUARTER_TURN, 0) * RZ(Angle64::QUARTER_TURN, 0);
-        let simplified = circuit.simplify();
-
-        // Should remain a Compose with 2 parts
-        if let Operator::Compose(parts) = simplified {
-            assert_eq!(parts.len(), 2);
-        } else {
-            panic!("Expected Compose");
-        }
-    }
-
-    #[test]
-    fn test_simplify_multiple_merges() {
-        // T * T * T * T = Z (4 * π/4 = π)
-        let circuit = T(0) * T(0) * T(0) * T(0);
-        let simplified = circuit.simplify();
-
-        if let Operator::Rotation { angle, .. } = simplified {
-            assert_eq!(angle, Angle64::HALF_TURN);
-        } else {
-            panic!("Expected single Rotation");
-        }
-    }
-
-    #[test]
-    fn test_simplify_tensor_preserves_identity() {
-        // X(0) & I(1) should preserve the identity to maintain Hilbert space dimension
-        let circuit = X(0) & I(1);
-        let simplified = circuit.simplify();
-
-        // Should still be a tensor with both parts (preserves 2-qubit space)
-        let qubits = simplified.qubits();
-        assert!(qubits.contains(&0));
-        assert!(qubits.contains(&1));
-    }
-
-    #[test]
-    fn test_simplify_compose_with_gate() {
-        // CX doesn't merge with rotations
-        let circuit = SZ(0) * CX(0, 1) * SZ(0);
-        let simplified = circuit.simplify();
-
-        // Should have 3 parts (S, CX, S)
-        if let Operator::Compose(parts) = simplified {
-            assert_eq!(parts.len(), 3);
-        } else {
-            panic!("Expected Compose");
-        }
-    }
-
-// --- CliffordRep conversion tests ---
-
-    #[test]
-    fn test_to_clifford_rep_non_clifford_returns_none() {
-        let t = T(0);
-        assert!(t.to_clifford_rep(1).is_none());
-    }
-
-    #[test]
-    fn test_to_clifford_rep_identity() {
-        let id = I(0);
-        let cliff = id.to_clifford_rep(1).unwrap();
-
-        // Identity should transform X -> X, Z -> Z
-        let x0 = PauliString::x(0);
-        let z0 = PauliString::z(0);
-
-        let tx = cliff.apply(&x0);
-        let tz = cliff.apply(&z0);
-
-        assert_eq!(tx.get(0), crate::Pauli::X);
-        assert_eq!(tz.get(0), crate::Pauli::Z);
-    }
-
-    #[test]
-    fn test_to_clifford_rep_x_gate() {
-        let x = X(0);
-        let cliff = x.to_clifford_rep(1).unwrap();
-
-        // X gate: X -> X, Z -> -Z
-        let z0 = PauliString::z(0);
-
-        let tz = cliff.apply(&z0);
-        assert_eq!(tz.get(0), crate::Pauli::Z);
-        assert_eq!(tz.phase(), crate::QuarterPhase::MinusOne);
-    }
-
-    #[test]
-    fn test_to_clifford_rep_s_gate() {
-        let s = SZ(0);
-        let cliff = s.to_clifford_rep(1).unwrap();
-
-        // SZ gate: X -> Y, Z -> Z
-        let x0 = PauliString::x(0);
-
-        let tx = cliff.apply(&x0);
-        assert_eq!(tx.get(0), crate::Pauli::Y);
-    }
-
-    #[test]
-    fn test_to_clifford_rep_cx_gate() {
-        let cx = CX(0, 1);
-        let cliff = cx.to_clifford_rep(2).unwrap();
-
-        // CX: X_control -> X_control * X_target
-        let x0 = PauliString::x(0);
-
-        let tx = cliff.apply(&x0);
-        // Should have X on both qubits
-        assert_eq!(tx.get(0), crate::Pauli::X);
-        assert_eq!(tx.get(1), crate::Pauli::X);
-    }
-
-    #[test]
-    fn test_to_clifford_rep_composition() {
-        // S * H should be convertible
-        let circuit = SZ(0) * H(0);
-        let cliff = circuit.to_clifford_rep(1);
-        assert!(cliff.is_some());
-    }
-
-// --- Phase tests ---
-
-    #[test]
-    fn test_phase_basic() {
-        // phase(π/4) * X should create a phased operator
-        // Since π/4 is not a quarter-turn multiple, it wraps in Phase
-        let eighth_turn = Angle64::HALF_TURN / 4;
-        let op = phase(eighth_turn) * X(0);
-
-        if let Operator::Phase { phase: p, inner } = op {
-            assert_eq!(p, eighth_turn);
-            // Inner should be Pauli(X)
-            assert!(matches!(*inner, Operator::Pauli(_)));
-        } else {
-            panic!("Expected Phase variant, got {op:?}");
-        }
-    }
-
-    #[test]
-    fn test_phase_negation() {
-        // -phase(θ) = phase(θ + π)
-        let quarter = Angle64::QUARTER_TURN;
-        let p = phase(quarter);
-        let neg_p = -p;
-
-        assert_eq!(neg_p.0, quarter + Angle64::HALF_TURN);
-    }
-
-    #[test]
-    fn test_phase_times_i() {
-        // i * phase(θ) = phase(θ + π/2)
-        let quarter = Angle64::QUARTER_TURN;
-        let p = phase(quarter);
-        let ip = i * p;
-
-        assert_eq!(ip.0, quarter + Angle64::QUARTER_TURN);
-    }
-
-    #[test]
-    fn test_phase_times_neg_i() {
-        // -i * phase(θ) = phase(θ + 3π/2)
-        let quarter = Angle64::QUARTER_TURN;
-        let p = phase(quarter);
-        let nip = -i * p;
-
-        assert_eq!(nip.0, quarter + Angle64::QUARTER_TURN + Angle64::HALF_TURN);
-    }
-
-    #[test]
-    fn test_phase_equivalence_with_i() {
-        // phase(π/2) * X should be equivalent to i * X
-        // Since π/2 is a quarter turn, the phase gets absorbed into the PauliString
-        let op1 = phase(Angle64::QUARTER_TURN) * X(0);
-        let op2 = i * X(0);
-
-        // Both should be Pauli with phase +i
-        if let (Operator::Pauli(ps1), Operator::Pauli(ps2)) = (&op1, &op2) {
-            assert_eq!(ps1.phase(), QuarterPhase::PlusI);
-            assert_eq!(ps2.phase(), QuarterPhase::PlusI);
-        } else {
-            panic!("Expected Pauli variants, got {op1:?} and {op2:?}");
-        }
-    }
-
-    #[test]
-    fn test_phase_zero_is_identity() {
-        // phase(0) * X should simplify to just X
-        let op = phase(Angle64::ZERO) * X(0);
-
-        // with_phase returns self when phase is zero
-        assert!(matches!(op, Operator::Pauli(_)));
-        if let Operator::Pauli(ps) = op {
-            assert_eq!(ps.phase(), QuarterPhase::PlusOne);
-        }
-    }
-
-// --- Macro tests ---
-
-    #[test]
-    fn test_angle_macro_pi() {
-        assert_eq!(crate::angle!(pi), Angle64::HALF_TURN);
-    }
-
-    #[test]
-    fn test_angle_macro_pi_over_2() {
-        assert_eq!(crate::angle!(pi / 2), Angle64::QUARTER_TURN);
-    }
-
-    #[test]
-    fn test_angle_macro_pi_over_4() {
-        // pi/4 = 1/8 turn
-        assert_eq!(crate::angle!(pi / 4), Angle64::from_turn_ratio(1, 8));
-    }
-
-    #[test]
-    fn test_angle_macro_2_pi_over_3() {
-        // 2*pi/3 = 2/6 = 1/3 turn
-        assert_eq!(crate::angle!(2 * pi / 3), Angle64::from_turn_ratio(1, 3));
-    }
-
-    #[test]
-    fn test_angle_macro_4_pi_over_3() {
-        // 4*pi/3 = 4/6 = 2/3 turn
-        assert_eq!(crate::angle!(4 * pi / 3), Angle64::from_turn_ratio(2, 3));
-    }
-
-    #[test]
-    fn test_angle_macro_negative() {
-        // -pi/2 should be the negative of pi/2
-        let neg = crate::angle!(-pi / 2);
-        let pos = crate::angle!(pi / 2);
-        assert_eq!(neg, Angle64::ZERO - pos);
-    }
-
-    #[test]
-    fn test_phase_macro_basic() {
-        // phase!(pi/4) should create a PhaseValue
-        let p = crate::phase!(pi / 4);
-        assert_eq!(p.0, Angle64::from_turn_ratio(1, 8));
-    }
-
-    #[test]
-    fn test_phase_macro_with_operator() {
-        // phase!(pi/2) * X should be same as i * X
-        // Since pi/2 is a quarter turn, the phase gets absorbed into PauliString
-        let op1 = crate::phase!(pi / 2) * X(0);
-        let op2 = i * X(0);
-
-        // Both should be Pauli with phase +i
-        if let (Operator::Pauli(ps1), Operator::Pauli(ps2)) = (&op1, &op2) {
-            assert_eq!(ps1.phase(), QuarterPhase::PlusI);
-            assert_eq!(ps2.phase(), QuarterPhase::PlusI);
-        } else {
-            panic!("Expected Pauli variants, got {op1:?} and {op2:?}");
-        }
-    }
-
-    #[test]
-    fn test_phase_macro_exact_cancellation() {
-        // 8 * (pi/4) should exactly equal 2*pi = 0
-        let eighth = crate::angle!(pi / 4);
-        let full = eighth + eighth + eighth + eighth + eighth + eighth + eighth + eighth;
-        assert_eq!(full, Angle64::ZERO);
-    }
-
-// --- Turn macro tests ---
-
-    #[test]
-    fn test_turn_macro_quarter() {
-        assert_eq!(crate::turn!(1 / 4), Angle64::QUARTER_TURN);
-    }
-
-    #[test]
-    fn test_turn_macro_half() {
-        assert_eq!(crate::turn!(1 / 2), Angle64::HALF_TURN);
-    }
-
-    #[test]
-    fn test_turn_macro_eighth() {
-        // 1/8 turn = T gate phase = pi/4 radians
-        assert_eq!(crate::turn!(1 / 8), crate::angle!(pi / 4));
-    }
-
-    #[test]
-    fn test_turn_macro_third() {
-        // 1/3 turn
-        assert_eq!(crate::turn!(1 / 3), Angle64::from_turn_ratio(1, 3));
-    }
-
-    #[test]
-    fn test_turn_macro_two_thirds() {
-        // 2/3 turn
-        assert_eq!(crate::turn!(2 / 3), Angle64::from_turn_ratio(2, 3));
-    }
-
-    #[test]
-    fn test_turn_vs_angle_equivalence() {
-        // turn!(1/4) should equal angle!(pi/2)
-        assert_eq!(crate::turn!(1 / 4), crate::angle!(pi / 2));
-
-        // turn!(1/8) should equal angle!(pi/4)
-        assert_eq!(crate::turn!(1 / 8), crate::angle!(pi / 4));
-
-        // turn!(1/2) should equal angle!(pi)
-        assert_eq!(crate::turn!(1 / 2), crate::angle!(pi));
-    }
-
-    #[test]
-    fn test_phase_turn_macro_basic() {
-        let p = crate::phase_turn!(1 / 8);
-        assert_eq!(p.0, Angle64::from_turn_ratio(1, 8));
-    }
-
-    #[test]
-    fn test_phase_turn_macro_with_operator() {
-        // phase_turn!(1/4) * X should be same as i * X (quarter turn = i)
-        // Since quarter turn is a quarter phase, it gets absorbed into the PauliString
-        let op1 = crate::phase_turn!(1 / 4) * X(0);
-        let op2 = i * X(0);
-
-        // Both should be Pauli with phase +i
-        if let (Operator::Pauli(ps1), Operator::Pauli(ps2)) = (&op1, &op2) {
-            assert_eq!(ps1.phase(), QuarterPhase::PlusI);
-            assert_eq!(ps2.phase(), QuarterPhase::PlusI);
-        } else {
-            panic!("Expected Pauli variants, got {op1:?} and {op2:?}");
-        }
-    }
-
-    #[test]
-    fn test_turn_exact_cancellation() {
-        // 8 * (1/8 turn) should exactly equal 1 full turn = 0
-        let eighth = crate::turn!(1 / 8);
-        let full = eighth + eighth + eighth + eighth + eighth + eighth + eighth + eighth;
-        assert_eq!(full, Angle64::ZERO);
-    }
-
-// --- Pauli equivalence tests ---
-
-    #[test]
-    fn test_is_pauli_equivalent_pauli() {
-        assert!(X(0).is_pauli_equivalent());
-        assert!(Y(1).is_pauli_equivalent());
-        assert!(Z(2).is_pauli_equivalent());
-        assert!((X(0) & Y(1)).is_pauli_equivalent());
-    }
-
-    #[test]
-    fn test_is_pauli_equivalent_rotation() {
-        // Half-turn rotations are Pauli-equivalent
-        assert!(RX(Angle64::HALF_TURN, 0).is_pauli_equivalent());
-        assert!(RY(Angle64::HALF_TURN, 0).is_pauli_equivalent());
-        assert!(RZ(Angle64::HALF_TURN, 0).is_pauli_equivalent());
-
-        // Quarter-turn rotations are not
-        assert!(!RX(Angle64::QUARTER_TURN, 0).is_pauli_equivalent());
-        assert!(!RZ(Angle64::QUARTER_TURN, 0).is_pauli_equivalent());
-    }
-
-    #[test]
-    #[allow(clippy::similar_names)]
-    fn test_try_to_pauli_rotation() {
-        // RX(π) = X
-        let rx_pi = RX(Angle64::HALF_TURN, 0);
-        let converted = rx_pi.try_to_pauli().expect("Should convert");
-        if let Operator::Pauli(ps) = converted {
-            assert_eq!(ps.get(0), crate::Pauli::X);
-        } else {
-            panic!("Expected Pauli variant");
-        }
-
-        // RY(π) = Y
-        let ry_pi = RY(Angle64::HALF_TURN, 1);
-        let converted = ry_pi.try_to_pauli().expect("Should convert");
-        if let Operator::Pauli(ps) = converted {
-            assert_eq!(ps.get(1), crate::Pauli::Y);
-        } else {
-            panic!("Expected Pauli variant");
-        }
-
-        // RZ(π) = Z
-        let rz_pi = RZ(Angle64::HALF_TURN, 2);
-        let converted = rz_pi.try_to_pauli().expect("Should convert");
-        if let Operator::Pauli(ps) = converted {
-            assert_eq!(ps.get(2), crate::Pauli::Z);
-        } else {
-            panic!("Expected Pauli variant");
-        }
-    }
-
-    #[test]
-    fn test_try_to_pauli_non_pauli() {
-        // Quarter-turn rotations should not convert
-        assert!(RX(Angle64::QUARTER_TURN, 0).try_to_pauli().is_none());
-        assert!(RZ(Angle64::QUARTER_TURN, 0).try_to_pauli().is_none());
-    }
-
-// --- Multi-qubit syntax tests ---
-
-    #[test]
-    fn test_x_multi_qubit() {
-        // Xs([0, 2, 5]) should be equivalent to X(0) & X(2) & X(5)
-        let multi = Xs([0, 2, 5]);
-        let tensor = X(0) & X(2) & X(5);
-
-        // Both should be Pauli variants with the same content
-        if let (Operator::Pauli(ps1), Operator::Pauli(ps2)) = (&multi, &tensor) {
-            assert_eq!(ps1.get(0), crate::Pauli::X);
-            assert_eq!(ps1.get(2), crate::Pauli::X);
-            assert_eq!(ps1.get(5), crate::Pauli::X);
-            assert_eq!(ps1, ps2);
-        } else {
-            panic!("Expected Pauli variants");
-        }
-    }
-
-    #[test]
-    fn test_t_multi_qubit() {
-        // Ts([0, 1, 2]) should be a tensor of T gates
-        let multi = Ts([0, 1, 2]);
-
-        if let Operator::Tensor(parts) = multi {
-            assert_eq!(parts.len(), 3);
-            // Each should be a rotation
-            assert!(matches!(&parts[0], Operator::Rotation { .. }));
-            assert!(matches!(&parts[1], Operator::Rotation { .. }));
-            assert!(matches!(&parts[2], Operator::Rotation { .. }));
-        } else {
-            panic!("Expected Tensor variant, got {multi:?}");
-        }
-    }
-
-    #[test]
-    fn test_h_multi_qubit() {
-        // Hs([0, 1]) should be a tensor of H gates
-        let multi = Hs([0, 1]);
-
-        if let Operator::Tensor(parts) = multi {
-            assert_eq!(parts.len(), 2);
-            // Each should be a Compose (H = RZ * RY)
-            assert!(matches!(&parts[0], Operator::Compose(_)));
-            assert!(matches!(&parts[1], Operator::Compose(_)));
-        } else {
-            panic!("Expected Tensor variant, got {multi:?}");
-        }
-    }
-
-    #[test]
-    fn test_single_qubit_still_works() {
-        // Single qubit syntax should still work
-        let x = X(0);
-        let t = T(1);
-        let h = H(2);
-
-        assert!(matches!(x, Operator::Pauli(_)));
-        assert!(matches!(t, Operator::Rotation { .. }));
-        assert!(matches!(
-            h,
-            Operator::Gate {
-                gate_type: GateType::H,
-                ..
-            }
-        ));
-    }
-
-    #[test]
-    fn test_range_syntax() {
-        // Range syntax: Xs(0..3) = X(0) & X(1) & X(2)
-        let multi_range = Xs(0..3);
-        let tensor = X(0) & X(1) & X(2);
-
-        if let (Operator::Pauli(ps1), Operator::Pauli(ps2)) = (&multi_range, &tensor) {
-            assert_eq!(ps1, ps2);
-        } else {
-            panic!("Expected Pauli variants");
-        }
-    }
-
-    #[test]
-    fn test_range_inclusive_syntax() {
-        // RangeInclusive syntax: Zs(1..=3) = Z(1) & Z(2) & Z(3)
-        let multi_range = Zs(1..=3);
-        let tensor = Z(1) & Z(2) & Z(3);
-
-        if let (Operator::Pauli(ps1), Operator::Pauli(ps2)) = (&multi_range, &tensor) {
-            assert_eq!(ps1, ps2);
-        } else {
-            panic!("Expected Pauli variants");
-        }
-    }
-
-    #[test]
-    fn test_identity_range_syntax() {
-        // Is(0..=2) should create identity operators on qubits 0, 1, 2
-        let identities = Is(0..=2);
-
-        if let Operator::Tensor(parts) = identities {
-            assert_eq!(parts.len(), 3);
-            for part in &parts {
-                assert!(part.is_identity());
-            }
-        } else {
-            panic!("Expected Tensor variant, got {identities:?}");
-        }
-    }
-
-    #[test]
-    #[should_panic(expected = "empty range not allowed")]
-    fn test_empty_range_panics() {
-        let _ = Xs(0..0);
-    }
-
-    #[test]
-    #[should_panic(expected = "empty range not allowed")]
-    #[allow(clippy::reversed_empty_ranges)] // Intentionally testing empty range
-    fn test_empty_range_inclusive_panics() {
-        // 1..=0 is empty
-        let _ = Zs(1..=0);
-    }
-
-    #[test]
-    fn test_single_element_range() {
-        // Xs(0..1) should be equivalent to X(0)
-        let from_range = Xs(0..1);
-        let direct = X(0);
-
-        if let (Operator::Pauli(ps1), Operator::Pauli(ps2)) = (&from_range, &direct) {
-            assert_eq!(ps1, ps2);
-        } else {
-            panic!("Expected Pauli variants");
-        }
-    }
-
-    #[test]
-    fn test_single_element_range_inclusive() {
-        // Ts(2..=2) should be equivalent to T(2)
-        let from_range = Ts(2..=2);
-        let direct = T(2);
-
-        // Both should be Rotation variants
-        if let (
-            Operator::Rotation {
-                angle: a1,
-                rotation_type: r1,
-                ..
-            },
-            Operator::Rotation {
-                angle: a2,
-                rotation_type: r2,
-                ..
-            },
-        ) = (&from_range, &direct)
-        {
-            assert_eq!(a1, a2);
-            assert_eq!(r1, r2);
-        } else {
-            panic!("Expected Rotation variants, got {from_range:?} and {direct:?}");
-        }
-    }
-
-// --- Conjugation tests ---
-    // Two conjugation conventions:
-    //   A.conj(U)   = U * A * U†  (stabilizer update: S →USU† when applying U)
-    //   A.conjdg(U) = U† * A * U  (Heisenberg picture: A → U†AU)
-
-    #[test]
-    fn test_conj_pauli_by_pauli() {
-        // X.conj(Z) = Z * X * Z† = Z * X * Z = -X (since Z is self-adjoint)
-        // ZX = -XZ, so ZXZ = -XZZ = -X
-        let x = X(0);
-        let z = Z(0);
-        let result = x.conj(&z);
-
-        // conj returns a Compose, simplify to get the Pauli
-        let simplified = result.simplify();
-        if let Operator::Pauli(ps) = simplified {
-            assert_eq!(ps.get(0), crate::Pauli::X);
-            assert_eq!(ps.phase(), QuarterPhase::MinusOne);
-        } else {
-            panic!("Expected Pauli variant, got {simplified:?}");
-        }
-    }
-
-    #[test]
-    fn test_conjdg_pauli_by_pauli() {
-        // X.conjdg(Z) = Z† * X * Z = Z * X * Z = -X (since Z is self-adjoint)
-        // Same result as conj for self-adjoint gates
-        let x = X(0);
-        let z = Z(0);
-        let result = x.conjdg(&z);
-
-        let simplified = result.simplify();
-        if let Operator::Pauli(ps) = simplified {
-            assert_eq!(ps.get(0), crate::Pauli::X);
-            assert_eq!(ps.phase(), QuarterPhase::MinusOne);
-        } else {
-            panic!("Expected Pauli variant, got {simplified:?}");
-        }
-    }
-
-    #[test]
-    fn test_conj_produces_compose() {
-        // A.conj(B) = B * A * B† produces a Compose
-        let x = X(0);
-        let h = H(0);
-        let result = x.conj(&h);
-
-        // Result is Compose(H, X, H†)
-        assert!(matches!(result, Operator::Compose(_)));
-    }
-
-    #[test]
-    fn test_conj_z_by_z() {
-        // Z.conj(Z) = Z * Z * Z† = Z * Z * Z = Z (since Z² = I, Z³ = Z)
-        let z = Z(0);
-        let result = z.conj(&z);
-
-        let simplified = result.simplify();
-        if let Operator::Pauli(ps) = simplified {
-            assert_eq!(ps.get(0), crate::Pauli::Z);
-            assert_eq!(ps.phase(), QuarterPhase::PlusOne);
-        } else {
-            panic!("Expected Pauli variant, got {simplified:?}");
-        }
-    }
-
-    #[test]
-    fn test_conj_structure_sz_gate() {
-        // X.conj(SZ) = SZ * X * SZ† should produce Compose with SZ first, X middle, SZ† last
-        let x = X(0);
-        let sz = SZ(0);
-        let result = x.conj(&sz);
-
-        // Verify structure: Compose([SZ, X, SZ†])
-        if let Operator::Compose(parts) = result {
-            assert_eq!(parts.len(), 3);
-            // First element is SZ (positive angle)
-            assert!(matches!(
-                &parts[0],
-                Operator::Rotation {
-                    rotation_type: RotationType::RZ,
-                    ..
-                }
-            ));
-            // Middle element is X
-            assert!(matches!(&parts[1], Operator::Pauli(_)));
-            // Last element is SZ† (negative angle)
-            assert!(matches!(
-                &parts[2],
-                Operator::Rotation {
-                    rotation_type: RotationType::RZ,
-                    ..
-                }
-            ));
-        } else {
-            panic!("Expected Compose variant, got {result:?}");
-        }
-    }
-
-    #[test]
-    fn test_conjdg_structure_sz_gate() {
-        // X.conjdg(SZ) = SZ† * X * SZ should produce Compose with SZ† first, X middle, SZ last
-        let x = X(0);
-        let sz = SZ(0);
-        let result = x.conjdg(&sz);
-
-        // Verify structure: Compose([SZ†, X, SZ])
-        if let Operator::Compose(parts) = result {
-            assert_eq!(parts.len(), 3);
-            // First element is SZ† (negative angle)
-            assert!(matches!(
-                &parts[0],
-                Operator::Rotation {
-                    rotation_type: RotationType::RZ,
-                    ..
-                }
-            ));
-            // Middle element is X
-            assert!(matches!(&parts[1], Operator::Pauli(_)));
-            // Last element is SZ (positive angle)
-            assert!(matches!(
-                &parts[2],
-                Operator::Rotation {
-                    rotation_type: RotationType::RZ,
-                    ..
-                }
-            ));
-        } else {
-            panic!("Expected Compose variant, got {result:?}");
-        }
-    }
-
-    #[test]
-    fn test_conj_conjdg_inverse_relationship() {
-        // For any operator A and gate U:
-        // A.conj(U).conjdg(U) should give back A (up to simplification)
-        // Because (UAU†).conjdg(U) = U†(UAU†)U = A
-        let x = X(0);
-        let sz = SZ(0);
-
-        let forward = x.clone().conj(&sz); // SZ X SZ†
-        let back = forward.conjdg(&sz); // SZ† (SZ X SZ†) SZ = X
-
-        let simplified = back.simplify();
-        if let Operator::Pauli(ps) = simplified {
-            assert_eq!(ps.get(0), crate::Pauli::X);
-            assert_eq!(ps.phase(), QuarterPhase::PlusOne);
-        } else {
-            panic!("Expected Pauli variant, got {simplified:?}");
-        }
-    }
-
-// --- Weight tests ---
-
-    #[test]
-    fn test_weight_single_pauli() {
-        assert_eq!(X(0).weight(), 1);
-        assert_eq!(Y(1).weight(), 1);
-        assert_eq!(Z(2).weight(), 1);
-    }
-
-    #[test]
-    fn test_weight_identity() {
-        // weight() returns number of qubits acted on
-        // I(0) = RZ(0, 0) acts on qubit 0
-        assert_eq!(I(0).weight(), 1);
-    }
-
-    #[test]
-    fn test_weight_tensor_product() {
-        let op = X(0) & Y(1) & Z(2);
-        assert_eq!(op.weight(), 3);
-    }
-
-    #[test]
-    fn test_weight_tensor_with_identity() {
-        // Id tensored still counts as acting on that qubit
-        let op = X(0) & I(1) & Z(2);
-        assert_eq!(op.weight(), 3);
-    }
-
-    #[test]
-    fn test_weight_rotation() {
-        // Rotations have weight equal to the number of qubits they act on
-        assert_eq!(RX(Angle64::QUARTER_TURN, 0).weight(), 1);
-        assert_eq!(RZZ(Angle64::QUARTER_TURN, 0, 1).weight(), 2);
-    }
-
-    #[test]
-    fn test_weight_gate() {
-        assert_eq!(H(0).weight(), 1);
-        assert_eq!(CX(0, 1).weight(), 2);
-        assert_eq!(CCX(0, 1, 2).weight(), 3);
-    }
-
-// --- is_hermitian tests ---
-
-    #[test]
-    fn test_is_hermitian_paulis() {
-        // All Paulis are Hermitian
-        assert!(X(0).is_hermitian());
-        assert!(Y(0).is_hermitian());
-        assert!(Z(0).is_hermitian());
-        assert!(I(0).is_hermitian());
-    }
-
-    #[test]
-    fn test_is_hermitian_pauli_tensor() {
-        // Tensor products of Paulis are Hermitian
-        let op = X(0) & Y(1) & Z(2);
-        assert!(op.is_hermitian());
-    }
-
-    #[test]
-    fn test_is_hermitian_hadamard() {
-        // H is Hermitian (H = H†)
-        assert!(H(0).is_hermitian());
-    }
-
-    #[test]
-    fn test_is_hermitian_rotation_not() {
-        // General rotations are not Hermitian (unless angle is 0 or π)
-        assert!(!RZ(Angle64::QUARTER_TURN, 0).is_hermitian());
-        assert!(!T(0).is_hermitian());
-        assert!(!SZ(0).is_hermitian());
-    }
-
-    #[test]
-    fn test_is_hermitian_rotation_half_turn() {
-        // Half-turn rotations are Hermitian (up to global phase)
-        // RX(π) = -iX, which is Hermitian
-        assert!(RX(Angle64::HALF_TURN, 0).is_hermitian());
-        assert!(RY(Angle64::HALF_TURN, 0).is_hermitian());
-        assert!(RZ(Angle64::HALF_TURN, 0).is_hermitian());
-    }
-
-// --- pow tests ---
-
-    #[test]
-    fn test_pow_zero() {
-        // X^0 = I
-        let x = X(0);
-        let result = x.pow(0);
-        assert!(result.is_identity());
-    }
-
-    #[test]
-    fn test_pow_one() {
-        // X^1 = X
-        let x = X(0);
-        let result = x.pow(1);
-        if let Operator::Pauli(ps) = result {
-            assert_eq!(ps.get(0), crate::Pauli::X);
-        } else {
-            panic!("Expected Pauli");
-        }
-    }
-
-    #[test]
-    fn test_pow_two_pauli() {
-        // X^2 = I after simplification
-        let x = X(0);
-        let result = x.pow(2).simplify();
-        assert!(result.is_identity());
-    }
-
-    #[test]
-    fn test_pow_creates_compose() {
-        // pow(n) creates a Compose of n copies without simplification
-        let t = T(0);
-        let result = t.pow(3);
-        assert!(matches!(result, Operator::Compose(_)));
-    }
-
-    #[test]
-    fn test_pow_rotation_simplify() {
-        // T^2 = S (RZ(π/4)^2 = RZ(π/2)) after simplification
-        let t = T(0);
-        let result = t.pow(2).simplify();
-
-        if let Operator::Rotation {
-            angle,
-            rotation_type,
-            ..
-        } = result
-        {
-            assert_eq!(rotation_type, RotationType::RZ);
-            assert_eq!(angle, Angle64::QUARTER_TURN);
-        } else {
-            panic!("Expected Rotation, got {result:?}");
-        }
-    }
-
-    #[test]
-    fn test_pow_four_t_simplify() {
-        // T^4 = Z (RZ(π/4)^4 = RZ(π)) after simplification
-        let t = T(0);
-        let result = t.pow(4).simplify();
-
-        if let Operator::Rotation { angle, .. } = result {
-            assert_eq!(angle, Angle64::HALF_TURN);
-        } else {
-            panic!("Expected Rotation, got {result:?}");
-        }
-    }
-
-    #[test]
-    fn test_pow_eight_t_simplify() {
-        // T^8 = I (RZ(π/4)^8 = RZ(2π) = I) after simplification
-        let t = T(0);
-        let result = t.pow(8).simplify();
-        assert!(result.is_identity());
-    }
-
-// --- commutes tests ---
-
-    #[test]
-    fn test_commutes_same_pauli() {
-        // X commutes with X
-        let x1 = X(0);
-        let x2 = X(0);
-        assert_eq!(x1.commutes(&x2), Commutativity::Commutes);
-    }
-
-    #[test]
-    fn test_commutes_different_paulis_same_qubit() {
-        // X and Z anticommute on same qubit
-        let x = X(0);
-        let z = Z(0);
-        assert_eq!(x.commutes(&z), Commutativity::AntiCommutes);
-
-        // X and Y anticommute
-        let y = Y(0);
-        assert_eq!(x.commutes(&y), Commutativity::AntiCommutes);
-
-        // Y and Z anticommute
-        assert_eq!(y.commutes(&z), Commutativity::AntiCommutes);
-    }
-
-    #[test]
-    fn test_commutes_different_qubits() {
-        // Operators on different qubits always commute
-        let x0 = X(0);
-        let z1 = Z(1);
-        assert_eq!(x0.commutes(&z1), Commutativity::Commutes);
-    }
-
-    #[test]
-    fn test_commutes_non_pauli_unknown() {
-        // Non-Pauli operators return Unknown
-        // I(0) is RZ(0, 0), not a Pauli variant
-        let id = I(0);
-        let x = X(0);
-        assert_eq!(id.commutes(&x), Commutativity::Unknown);
-
-        let h = H(0);
-        assert_eq!(h.commutes(&x), Commutativity::Unknown);
-    }
-
-    #[test]
-    fn test_commutes_pauli_strings() {
-        // XY and YX: overlap on both qubits, both anticommute -> commute
-        let xy = X(0) & Y(1);
-        let yx = Y(0) & X(1);
-        assert_eq!(xy.commutes(&yx), Commutativity::Commutes);
-
-        // XY and ZZ: both overlap, X-Z and Y-Z both anticommute -> commute
-        let zz = Z(0) & Z(1);
-        assert_eq!(xy.commutes(&zz), Commutativity::Commutes);
-
-        // XZ and Y: only qubit 0 overlaps, X-Y anticommute
-        let xz = X(0) & Z(1);
-        let y = Y(0);
-        assert_eq!(xz.commutes(&y), Commutativity::AntiCommutes);
-    }
-
-// --- decompose tests ---
-
-    #[test]
-    fn test_decompose_single_pauli() {
-        let x = X(0);
-        let gates = x.decompose();
-        assert_eq!(gates.len(), 1);
-        assert_eq!(gates[0].gate_type, GateType::X);
-    }
-
-    #[test]
-    fn test_decompose_pauli_tensor() {
-        let op = X(0) & Y(1) & Z(2);
-        let gates = op.decompose();
-        assert_eq!(gates.len(), 3);
-
-        let gate_types: Vec<_> = gates.iter().map(|g| g.gate_type).collect();
-        assert!(gate_types.contains(&GateType::X));
-        assert!(gate_types.contains(&GateType::Y));
-        assert!(gate_types.contains(&GateType::Z));
-    }
-
-    #[test]
-    fn test_decompose_identity() {
-        // I(0) = RZ(0, 0), so it decomposes to an RZ gate with angle 0
-        let id = I(0);
-        let gates = id.decompose();
-        assert_eq!(gates.len(), 1);
-        assert_eq!(gates[0].gate_type, GateType::RZ);
-        assert_eq!(gates[0].angles[0], Angle64::ZERO);
-    }
-
-    #[test]
-    fn test_decompose_pauli_identity_empty() {
-        // A true Pauli identity (from PauliString) decomposes to empty
-        let ps = PauliString::identity();
-        let op = Operator::Pauli(ps);
-        let gates = op.decompose();
-        assert!(gates.is_empty());
-    }
-
-    #[test]
-    fn test_decompose_rotation() {
-        let t = T(0);
-        let gates = t.decompose();
-        assert_eq!(gates.len(), 1);
-        assert_eq!(gates[0].gate_type, GateType::RZ);
-        assert_eq!(gates[0].angles.len(), 1);
-    }
-
-    #[test]
-    fn test_decompose_gate() {
-        let cx = CX(0, 1);
-        let gates = cx.decompose();
-        assert_eq!(gates.len(), 1);
-        assert_eq!(gates[0].gate_type, GateType::CX);
-    }
-
-    #[test]
-    fn test_decompose_composition() {
-        let circuit = SZ(0) * H(0) * X(0); // X, then H, then S
-        let gates = circuit.decompose();
-        assert_eq!(gates.len(), 3);
-    }
-
-    #[test]
-    fn test_decompose_adjoint() {
-        let t = T(0);
-        let t_dg = t.dg();
-        let gates = t_dg.decompose();
-
-        assert_eq!(gates.len(), 1);
-        assert_eq!(gates[0].gate_type, GateType::RZ);
-        // Angle should be negated
-        let expected_angle = Angle64::ZERO - (Angle64::HALF_TURN / 4);
-        assert_eq!(gates[0].angles[0], expected_angle);
-    }
-
-    #[test]
-    fn test_decompose_adjoint_named_gate() {
-        // S† should decompose to SZdg
-        let s = SZ(0);
-        let s_dg = s.dg();
-        let gates = s_dg.decompose();
-
-        // S is a rotation, S† negates the angle
-        assert_eq!(gates.len(), 1);
-        assert_eq!(gates[0].gate_type, GateType::RZ);
-    }
-
-// --- as_pauli_string / into_pauli_string tests ---
-
-    #[test]
-    fn test_as_pauli_string_pauli() {
-        let x = X(0);
-        let ps = x.as_pauli_string();
-        assert!(ps.is_some());
-        let ps = ps.unwrap();
-        assert_eq!(ps.get(0), crate::Pauli::X);
-    }
-
-    #[test]
-    fn test_as_pauli_string_non_pauli() {
-        let h = H(0);
-        assert!(h.as_pauli_string().is_none());
-
-        let t = T(0);
-        assert!(t.as_pauli_string().is_none());
-    }
-
-    #[test]
-    fn test_into_pauli_string_pauli() {
-        let xy = X(0) & Y(1);
-        let ps = xy.into_pauli_string();
-        assert!(ps.is_some());
-        let ps = ps.unwrap();
-        assert_eq!(ps.get(0), crate::Pauli::X);
-        assert_eq!(ps.get(1), crate::Pauli::Y);
-    }
-
-    #[test]
-    fn test_into_pauli_string_with_phase() {
-        let op = i * X(0);
-        let ps = op.into_pauli_string();
-        assert!(ps.is_some());
-        let ps = ps.unwrap();
-        assert_eq!(ps.get(0), crate::Pauli::X);
-        assert_eq!(ps.phase(), QuarterPhase::PlusI);
-    }
-}
diff --git a/crates/pecos-core/src/pauli.rs b/crates/pecos-core/src/pauli.rs
index e18f21402..87050ef04 100644
--- a/crates/pecos-core/src/pauli.rs
+++ b/crates/pecos-core/src/pauli.rs
@@ -13,9 +13,18 @@
 pub mod algebra;
 pub mod constructors;
 
+// Re-export constructors at the `pauli` level so `use pecos_core::pauli::*` works.
+pub use constructors::{I, X, Xs, Y, Ys, Z, Zs};
+
+// Re-export key types so `use pecos_core::pauli::*` gives the full Pauli toolkit.
+pub use pauli_string::PauliString;
+
 #[allow(clippy::module_name_repetitions)]
 pub mod pauli_bitmap;
 
+#[allow(clippy::module_name_repetitions)]
+pub mod pauli_bitmask;
+
 #[allow(clippy::module_name_repetitions)]
 pub mod pauli_sparse;
 
diff --git a/crates/pecos-core/src/pauli/algebra.rs b/crates/pecos-core/src/pauli/algebra.rs
index b859bf636..e038b56b7 100644
--- a/crates/pecos-core/src/pauli/algebra.rs
+++ b/crates/pecos-core/src/pauli/algebra.rs
@@ -45,6 +45,7 @@
 //! let ps = -PauliString::x(0);                            // -X
 //! ```
 
+use crate::qubit_support::overlapping_qubits;
 use crate::{Pauli, PauliString, Phase, QuarterPhase, QubitId};
 use std::ops::{BitAnd, Mul, Neg};
 
@@ -80,10 +81,16 @@ impl BitAnd for PauliString {
     type Output = PauliString;
 
     fn bitand(self, rhs: PauliString) -> PauliString {
+        let overlap = overlapping_qubits(self.qubits(), rhs.qubits());
+        assert!(
+            overlap.is_empty(),
+            "tensor product requires disjoint Pauli support; overlapping qubits: {overlap:?}"
+        );
+
         // Combine phases
         let new_phase = self.phase().multiply(&rhs.phase());
 
-        // Combine paulis (assuming no overlap - tensor product)
+        // Combine paulis.
         let mut paulis: Vec<(Pauli, QubitId)> = self.iter_pairs().collect();
         paulis.extend(rhs.iter_pairs());
 
@@ -289,6 +296,12 @@ mod tests {
         assert_eq!(ps.weight(), 2);
     }
 
+    #[test]
+    #[should_panic(expected = "tensor product requires disjoint Pauli support")]
+    fn test_tensor_product_rejects_overlapping_qubits() {
+        let _ = PauliString::x(0) & PauliString::z(0);
+    }
+
     #[test]
     fn test_triple_tensor() {
         let ps = PauliString::x(0) & PauliString::y(2) & PauliString::z(5);
diff --git a/crates/pecos-core/src/pauli/constructors.rs b/crates/pecos-core/src/pauli/constructors.rs
index fc67d9a76..507c509d9 100644
--- a/crates/pecos-core/src/pauli/constructors.rs
+++ b/crates/pecos-core/src/pauli/constructors.rs
@@ -18,7 +18,7 @@
 //! # Examples
 //!
 //! ```
-//! use pecos_core::pauli::constructors::*;
+//! use pecos_core::pauli::*;
 //! use pecos_core::PauliOperator;
 //!
 //! // Single-qubit Paulis
@@ -88,7 +88,7 @@ impl QubitArgs for std::ops::RangeInclusive<usize> {
 /// # Examples
 ///
 /// ```
-/// use pecos_core::pauli::constructors::X;
+/// use pecos_core::pauli::X;
 /// use pecos_core::{Pauli, PauliOperator};
 ///
 /// let p = X(0);
@@ -131,7 +131,7 @@ pub fn I() -> PauliString {
 /// # Examples
 ///
 /// ```
-/// use pecos_core::pauli::constructors::Xs;
+/// use pecos_core::pauli::Xs;
 /// use pecos_core::PauliOperator;
 ///
 /// let p = Xs([0, 1, 2]);
@@ -166,7 +166,7 @@ pub fn Ys(qubits: impl QubitArgs) -> PauliString {
 /// # Examples
 ///
 /// ```
-/// use pecos_core::pauli::constructors::Zs;
+/// use pecos_core::pauli::Zs;
 /// use pecos_core::PauliOperator;
 ///
 /// let stab = Zs([0, 1]);
diff --git a/crates/pecos-core/src/pauli/pauli_bitmask.rs b/crates/pecos-core/src/pauli/pauli_bitmask.rs
new file mode 100644
index 000000000..a7beef474
--- /dev/null
+++ b/crates/pecos-core/src/pauli/pauli_bitmask.rs
@@ -0,0 +1,1426 @@
+// Copyright 2026 The PECOS Developers
+//
+// Licensed under the Apache License, Version 2.0
+
+//! Compact Pauli operator using bitmasks with Clifford conjugation.
+//!
+//! Provides allocation-free Pauli arithmetic and Clifford conjugation
+//! for use in error propagation, fault analysis, and EEG algorithms.
+//!
+//! The default `PauliBitmask` uses `u128` (up to 128 qubits). For
+//! larger qubit counts, use `PauliBitmaskVec` which heap-allocates.
+
+use smallvec::SmallVec;
+use std::fmt;
+
+/// Trait for bitmask storage backends.
+///
+/// Enables `PauliBitmaskGeneric<B>` to work with different widths:
+/// `u64` (64 qubits), `u128` (128 qubits), or `Vec<u64>` (unlimited).
+pub trait BitmaskStorage: Clone + PartialEq + Eq + std::hash::Hash + Default + fmt::Debug {
+    fn zero() -> Self;
+    fn set_bit(&mut self, bit: usize);
+    fn clear_bit(&mut self, bit: usize);
+    fn get_bit(&self, bit: usize) -> bool;
+    fn xor_assign(&mut self, other: &Self);
+    fn xor_bit(&mut self, bit: usize);
+    fn and_count_ones_xor(&self, other_z: &Self, self_z: &Self, other_x: &Self) -> u32;
+    fn is_zero(&self) -> bool;
+    fn or_count_ones(&self, other: &Self) -> u32;
+    fn highest_set_bit(&self) -> Option<usize>;
+}
+
+impl BitmaskStorage for u128 {
+    fn zero() -> Self {
+        0
+    }
+    fn set_bit(&mut self, bit: usize) {
+        *self |= 1u128 << bit;
+    }
+    fn clear_bit(&mut self, bit: usize) {
+        *self &= !(1u128 << bit);
+    }
+    fn get_bit(&self, bit: usize) -> bool {
+        *self & (1u128 << bit) != 0
+    }
+    fn xor_assign(&mut self, other: &Self) {
+        *self ^= other;
+    }
+    fn xor_bit(&mut self, bit: usize) {
+        *self ^= 1u128 << bit;
+    }
+    fn and_count_ones_xor(&self, other_z: &Self, self_z: &Self, other_x: &Self) -> u32 {
+        ((*self & other_z) ^ (self_z & other_x)).count_ones()
+    }
+    fn is_zero(&self) -> bool {
+        *self == 0
+    }
+    fn or_count_ones(&self, other: &Self) -> u32 {
+        (*self | other).count_ones()
+    }
+    fn highest_set_bit(&self) -> Option<usize> {
+        if *self == 0 {
+            None
+        } else {
+            Some(127 - self.leading_zeros() as usize)
+        }
+    }
+}
+
+impl BitmaskStorage for Vec<u64> {
+    fn zero() -> Self {
+        Vec::new()
+    }
+    fn set_bit(&mut self, bit: usize) {
+        let word = bit / 64;
+        if word >= self.len() {
+            self.resize(word + 1, 0);
+        }
+        self[word] |= 1u64 << (bit % 64);
+    }
+    fn clear_bit(&mut self, bit: usize) {
+        let word = bit / 64;
+        if word < self.len() {
+            self[word] &= !(1u64 << (bit % 64));
+        }
+    }
+    fn get_bit(&self, bit: usize) -> bool {
+        let word = bit / 64;
+        word < self.len() && self[word] & (1u64 << (bit % 64)) != 0
+    }
+    fn xor_assign(&mut self, other: &Self) {
+        if self.len() < other.len() {
+            self.resize(other.len(), 0);
+        }
+        for (a, b) in self.iter_mut().zip(other.iter()) {
+            *a ^= b;
+        }
+    }
+    fn xor_bit(&mut self, bit: usize) {
+        let word = bit / 64;
+        if word >= self.len() {
+            self.resize(word + 1, 0);
+        }
+        self[word] ^= 1u64 << (bit % 64);
+    }
+    fn and_count_ones_xor(&self, other_z: &Self, self_z: &Self, other_x: &Self) -> u32 {
+        let max = self
+            .len()
+            .max(other_z.len())
+            .max(self_z.len())
+            .max(other_x.len());
+        let mut count = 0u32;
+        for i in 0..max {
+            let sx = self.get(i).copied().unwrap_or(0);
+            let oz = other_z.get(i).copied().unwrap_or(0);
+            let sz = self_z.get(i).copied().unwrap_or(0);
+            let ox = other_x.get(i).copied().unwrap_or(0);
+            count += ((sx & oz) ^ (sz & ox)).count_ones();
+        }
+        count
+    }
+    fn is_zero(&self) -> bool {
+        self.iter().all(|&w| w == 0)
+    }
+    fn or_count_ones(&self, other: &Self) -> u32 {
+        let max = self.len().max(other.len());
+        let mut count = 0u32;
+        for i in 0..max {
+            let a = self.get(i).copied().unwrap_or(0);
+            let b = other.get(i).copied().unwrap_or(0);
+            count += (a | b).count_ones();
+        }
+        count
+    }
+    fn highest_set_bit(&self) -> Option<usize> {
+        for (i, &w) in self.iter().enumerate().rev() {
+            if w != 0 {
+                return Some(i * 64 + 63 - w.leading_zeros() as usize);
+            }
+        }
+        None
+    }
+}
+
+/// `SmallVec<[u64; 8]>` backend: 512 bits inline (covers d≤9 surface codes),
+/// spills to heap for larger circuits. Zero allocation for typical QEC.
+impl BitmaskStorage for SmallVec<[u64; 8]> {
+    fn zero() -> Self {
+        SmallVec::new()
+    }
+    fn set_bit(&mut self, bit: usize) {
+        let word = bit / 64;
+        if word >= self.len() {
+            self.resize(word + 1, 0);
+        }
+        self[word] |= 1u64 << (bit % 64);
+    }
+    fn clear_bit(&mut self, bit: usize) {
+        let word = bit / 64;
+        if word < self.len() {
+            self[word] &= !(1u64 << (bit % 64));
+        }
+    }
+    fn get_bit(&self, bit: usize) -> bool {
+        let word = bit / 64;
+        word < self.len() && self[word] & (1u64 << (bit % 64)) != 0
+    }
+    fn xor_assign(&mut self, other: &Self) {
+        if self.len() < other.len() {
+            self.resize(other.len(), 0);
+        }
+        for (a, b) in self.iter_mut().zip(other.iter()) {
+            *a ^= b;
+        }
+    }
+    fn xor_bit(&mut self, bit: usize) {
+        let word = bit / 64;
+        if word >= self.len() {
+            self.resize(word + 1, 0);
+        }
+        self[word] ^= 1u64 << (bit % 64);
+    }
+    fn and_count_ones_xor(&self, other_z: &Self, self_z: &Self, other_x: &Self) -> u32 {
+        let max = self
+            .len()
+            .max(other_z.len())
+            .max(self_z.len())
+            .max(other_x.len());
+        let mut count = 0u32;
+        for i in 0..max {
+            let sx = self.get(i).copied().unwrap_or(0);
+            let oz = other_z.get(i).copied().unwrap_or(0);
+            let sz = self_z.get(i).copied().unwrap_or(0);
+            let ox = other_x.get(i).copied().unwrap_or(0);
+            count += ((sx & oz) ^ (sz & ox)).count_ones();
+        }
+        count
+    }
+    fn is_zero(&self) -> bool {
+        self.iter().all(|&w| w == 0)
+    }
+    fn or_count_ones(&self, other: &Self) -> u32 {
+        let max = self.len().max(other.len());
+        let mut count = 0u32;
+        for i in 0..max {
+            let a = self.get(i).copied().unwrap_or(0);
+            let b = other.get(i).copied().unwrap_or(0);
+            count += (a | b).count_ones();
+        }
+        count
+    }
+    fn highest_set_bit(&self) -> Option<usize> {
+        for (i, &w) in self.iter().enumerate().rev() {
+            if w != 0 {
+                return Some(i * 64 + 63 - w.leading_zeros() as usize);
+            }
+        }
+        None
+    }
+}
+
+/// N-qubit Pauli operator in symplectic binary representation.
+///
+/// Phase is NOT tracked internally — the caller tracks signs from
+/// multiplication and conjugation separately.
+///
+/// Type parameter `B` selects the bitmask backend:
+/// - `u128` (default): up to 128 qubits, stack-allocated, `Copy`
+/// - `Vec<u64>`: unlimited qubits, heap-allocated
+#[derive(Clone, Default)]
+pub struct PauliBitmaskGeneric<B: BitmaskStorage = u128> {
+    pub x_bits: B,
+    pub z_bits: B,
+}
+
+// --- PartialEq, Eq, Hash for u128 backend ---
+
+impl PartialEq for PauliBitmaskGeneric<u128> {
+    fn eq(&self, other: &Self) -> bool {
+        self.x_bits == other.x_bits && self.z_bits == other.z_bits
+    }
+}
+
+impl Eq for PauliBitmaskGeneric<u128> {}
+
+impl std::hash::Hash for PauliBitmaskGeneric<u128> {
+    fn hash<H: std::hash::Hasher>(&self, state: &mut H) {
+        self.x_bits.hash(state);
+        self.z_bits.hash(state);
+    }
+}
+
+// --- PartialEq, Eq, Hash for Vec<u64> backend ---
+// Trailing zero words are ignored so that Vecs of different lengths
+// representing the same logical value compare equal and hash identically.
+
+impl PartialEq for PauliBitmaskGeneric<Vec<u64>> {
+    fn eq(&self, other: &Self) -> bool {
+        vecs_eq_ignoring_trailing_zeros(&self.x_bits, &other.x_bits)
+            && vecs_eq_ignoring_trailing_zeros(&self.z_bits, &other.z_bits)
+    }
+}
+
+impl Eq for PauliBitmaskGeneric<Vec<u64>> {}
+
+impl std::hash::Hash for PauliBitmaskGeneric<Vec<u64>> {
+    fn hash<H: std::hash::Hasher>(&self, state: &mut H) {
+        hash_vec_ignoring_trailing_zeros(&self.x_bits, state);
+        hash_vec_ignoring_trailing_zeros(&self.z_bits, state);
+    }
+}
+
+fn vecs_eq_ignoring_trailing_zeros(a: &[u64], b: &[u64]) -> bool {
+    let max = a.len().max(b.len());
+    for i in 0..max {
+        let aw = a.get(i).copied().unwrap_or(0);
+        let bw = b.get(i).copied().unwrap_or(0);
+        if aw != bw {
+            return false;
+        }
+    }
+    true
+}
+
+fn hash_vec_ignoring_trailing_zeros<H: std::hash::Hasher>(v: &[u64], state: &mut H) {
+    use std::hash::Hash;
+    // Find the last non-zero word and hash only up to that point.
+    let effective_len = v.iter().rposition(|&w| w != 0).map_or(0, |i| i + 1);
+    effective_len.hash(state);
+    for &w in &v[..effective_len] {
+        w.hash(state);
+    }
+}
+
+/// Fixed-size Pauli bitmask for up to 128 qubits (stack-allocated, Copy).
+pub type PauliBitmask = PauliBitmaskGeneric<u128>;
+
+/// Dynamically-sized Pauli bitmask for unlimited qubits (heap-allocated).
+pub type PauliBitmaskVec = PauliBitmaskGeneric<Vec<u64>>;
+
+/// SmallVec-backed Pauli bitmask: 512 bits inline (d≤9 surface codes),
+/// spills to heap only for larger circuits. Best of both worlds.
+pub type PauliBitmaskSmall = PauliBitmaskGeneric<SmallVec<[u64; 8]>>;
+
+// --- PartialEq, Eq, Hash, Ord for SmallVec backend ---
+
+impl PartialEq for PauliBitmaskSmall {
+    fn eq(&self, other: &Self) -> bool {
+        vecs_eq_ignoring_trailing_zeros(&self.x_bits, &other.x_bits)
+            && vecs_eq_ignoring_trailing_zeros(&self.z_bits, &other.z_bits)
+    }
+}
+
+impl Eq for PauliBitmaskSmall {}
+
+impl std::hash::Hash for PauliBitmaskSmall {
+    fn hash<H: std::hash::Hasher>(&self, state: &mut H) {
+        hash_vec_ignoring_trailing_zeros(&self.x_bits, state);
+        hash_vec_ignoring_trailing_zeros(&self.z_bits, state);
+    }
+}
+
+impl PartialOrd for PauliBitmaskSmall {
+    fn partial_cmp(&self, other: &Self) -> Option<std::cmp::Ordering> {
+        Some(self.cmp(other))
+    }
+}
+
+impl Ord for PauliBitmaskSmall {
+    fn cmp(&self, other: &Self) -> std::cmp::Ordering {
+        let max_len = self
+            .x_bits
+            .len()
+            .max(other.x_bits.len())
+            .max(self.z_bits.len())
+            .max(other.z_bits.len());
+        for i in (0..max_len).rev() {
+            let sx = self.x_bits.get(i).copied().unwrap_or(0);
+            let ox = other.x_bits.get(i).copied().unwrap_or(0);
+            match sx.cmp(&ox) {
+                std::cmp::Ordering::Equal => {}
+                ord => return ord,
+            }
+        }
+        for i in (0..max_len).rev() {
+            let sz = self.z_bits.get(i).copied().unwrap_or(0);
+            let oz = other.z_bits.get(i).copied().unwrap_or(0);
+            match sz.cmp(&oz) {
+                std::cmp::Ordering::Equal => {}
+                ord => return ord,
+            }
+        }
+        std::cmp::Ordering::Equal
+    }
+}
+
+// Copy only for fixed-size backends
+impl Copy for PauliBitmask {}
+impl PartialOrd for PauliBitmask {
+    fn partial_cmp(&self, other: &Self) -> Option<std::cmp::Ordering> {
+        Some(self.cmp(other))
+    }
+}
+impl Ord for PauliBitmask {
+    fn cmp(&self, other: &Self) -> std::cmp::Ordering {
+        self.x_bits
+            .cmp(&other.x_bits)
+            .then(self.z_bits.cmp(&other.z_bits))
+    }
+}
+
+impl PartialOrd for PauliBitmaskVec {
+    fn partial_cmp(&self, other: &Self) -> Option<std::cmp::Ordering> {
+        Some(self.cmp(other))
+    }
+}
+impl Ord for PauliBitmaskVec {
+    fn cmp(&self, other: &Self) -> std::cmp::Ordering {
+        // Lexicographic comparison of the word vectors (most-significant word first)
+        let max_len = self
+            .x_bits
+            .len()
+            .max(other.x_bits.len())
+            .max(self.z_bits.len())
+            .max(other.z_bits.len());
+        for i in (0..max_len).rev() {
+            let sx = self.x_bits.get(i).copied().unwrap_or(0);
+            let ox = other.x_bits.get(i).copied().unwrap_or(0);
+            match sx.cmp(&ox) {
+                std::cmp::Ordering::Equal => {}
+                ord => return ord,
+            }
+        }
+        for i in (0..max_len).rev() {
+            let sz = self.z_bits.get(i).copied().unwrap_or(0);
+            let oz = other.z_bits.get(i).copied().unwrap_or(0);
+            match sz.cmp(&oz) {
+                std::cmp::Ordering::Equal => {}
+                ord => return ord,
+            }
+        }
+        std::cmp::Ordering::Equal
+    }
+}
+
+impl<B: BitmaskStorage> PauliBitmaskGeneric<B> {
+    /// Single-qubit X on qubit q.
+    #[must_use]
+    pub fn x(q: usize) -> Self {
+        let mut x = B::zero();
+        x.set_bit(q);
+        Self {
+            x_bits: x,
+            z_bits: B::zero(),
+        }
+    }
+
+    /// Single-qubit Z on qubit q.
+    #[must_use]
+    pub fn z(q: usize) -> Self {
+        let mut z = B::zero();
+        z.set_bit(q);
+        Self {
+            x_bits: B::zero(),
+            z_bits: z,
+        }
+    }
+
+    /// Single-qubit Y on qubit q.
+    #[must_use]
+    pub fn y(q: usize) -> Self {
+        let mut x = B::zero();
+        let mut z = B::zero();
+        x.set_bit(q);
+        z.set_bit(q);
+        Self {
+            x_bits: x,
+            z_bits: z,
+        }
+    }
+
+    /// Product of two Pauli labels (XOR of symplectic vectors, phase ignored).
+    #[must_use]
+    pub fn multiply(&self, other: &Self) -> Self {
+        let mut x = self.x_bits.clone();
+        x.xor_assign(&other.x_bits);
+        let mut z = self.z_bits.clone();
+        z.xor_assign(&other.z_bits);
+        Self {
+            x_bits: x,
+            z_bits: z,
+        }
+    }
+
+    /// Product of two Paulis with phase tracking.
+    ///
+    /// Returns `(product, phase_exponent)` where the full product is i^phase · product.
+    /// Phase exponent is in 0..4.
+    #[must_use]
+    pub fn multiply_with_phase(&self, other: &Self) -> (Self, u8) {
+        // Per-qubit phase from Pauli multiplication.
+        // Pauli types: I=0, X=1, Z=2, Y=3 (encoding: type = x + 2*z)
+        // Phase lookup: A*B = i^{phase[A][B]} * C
+        // I  X  Z  Y
+        // 0  0  0  0   (I * anything)
+        // 0  0  3  1   (X * I,X,Z,Y)
+        // 0  1  0  3   (Z * I,X,Z,Y)
+        // 0  3  1  0   (Y * I,X,Z,Y)
+        const PHASE_TABLE: [[u8; 4]; 4] = [
+            [0, 0, 0, 0], // I
+            [0, 0, 3, 1], // X
+            [0, 1, 0, 3], // Z
+            [0, 3, 1, 0], // Y
+        ];
+
+        let product = self.multiply(other);
+        let mut total_phase = 0u32;
+        let max_q = [
+            self.x_bits.highest_set_bit(),
+            other.x_bits.highest_set_bit(),
+            self.z_bits.highest_set_bit(),
+            other.z_bits.highest_set_bit(),
+        ]
+        .into_iter()
+        .flatten()
+        .max()
+        .map_or(0, |q| q + 1);
+
+        for q in 0..max_q {
+            let xa = usize::from(self.x_bits.get_bit(q));
+            let za = usize::from(self.z_bits.get_bit(q));
+            let xb = usize::from(other.x_bits.get_bit(q));
+            let zb = usize::from(other.z_bits.get_bit(q));
+            let type_a = xa + 2 * za; // I=0, X=1, Z=2, Y=3
+            let type_b = xb + 2 * zb;
+            total_phase += u32::from(PHASE_TABLE[type_a][type_b]);
+        }
+
+        (product, (total_phase % 4) as u8)
+    }
+
+    /// True if the two Paulis commute (symplectic inner product = 0 mod 2).
+    #[must_use]
+    pub fn commutes_with(&self, other: &Self) -> bool {
+        self.x_bits
+            .and_count_ones_xor(&other.z_bits, &self.z_bits, &other.x_bits)
+            .is_multiple_of(2)
+    }
+
+    #[must_use]
+    pub fn is_identity(&self) -> bool {
+        self.x_bits.is_zero() && self.z_bits.is_zero()
+    }
+
+    /// Number of non-identity single-qubit factors.
+    #[must_use]
+    pub fn weight(&self) -> u32 {
+        self.x_bits.or_count_ones(&self.z_bits)
+    }
+
+    #[must_use]
+    pub fn has_x(&self, q: usize) -> bool {
+        self.x_bits.get_bit(q)
+    }
+
+    #[must_use]
+    pub fn has_z(&self, q: usize) -> bool {
+        self.z_bits.get_bit(q)
+    }
+}
+
+impl PauliBitmask {
+    pub const IDENTITY: Self = Self {
+        x_bits: 0,
+        z_bits: 0,
+    };
+}
+
+impl<B: BitmaskStorage> PauliBitmaskGeneric<B> {
+    /// Identity Pauli (all qubits I).
+    #[must_use]
+    pub fn identity() -> Self {
+        Self {
+            x_bits: B::zero(),
+            z_bits: B::zero(),
+        }
+    }
+}
+
+/// Convert from u128 (fixed-size) to Vec<u64> (unlimited) backend.
+impl From<PauliBitmask> for PauliBitmaskVec {
+    fn from(p: PauliBitmask) -> Self {
+        let x_lo = u64::try_from(p.x_bits & u128::from(u64::MAX)).expect("masked low word fits");
+        let x_hi = u64::try_from(p.x_bits >> 64).expect("shifted high word fits");
+        let z_lo = u64::try_from(p.z_bits & u128::from(u64::MAX)).expect("masked low word fits");
+        let z_hi = u64::try_from(p.z_bits >> 64).expect("shifted high word fits");
+        Self {
+            x_bits: if x_hi != 0 {
+                vec![x_lo, x_hi]
+            } else if x_lo != 0 {
+                vec![x_lo]
+            } else {
+                vec![]
+            },
+            z_bits: if z_hi != 0 {
+                vec![z_lo, z_hi]
+            } else if z_lo != 0 {
+                vec![z_lo]
+            } else {
+                vec![]
+            },
+        }
+    }
+}
+
+impl From<PauliBitmask> for PauliBitmaskSmall {
+    fn from(p: PauliBitmask) -> Self {
+        let x_lo = u64::try_from(p.x_bits & u128::from(u64::MAX)).expect("masked low word fits");
+        let x_hi = u64::try_from(p.x_bits >> 64).expect("shifted high word fits");
+        let z_lo = u64::try_from(p.z_bits & u128::from(u64::MAX)).expect("masked low word fits");
+        let z_hi = u64::try_from(p.z_bits >> 64).expect("shifted high word fits");
+        let mut x = SmallVec::new();
+        if x_hi != 0 {
+            x.push(x_lo);
+            x.push(x_hi);
+        } else if x_lo != 0 {
+            x.push(x_lo);
+        }
+        let mut z = SmallVec::new();
+        if z_hi != 0 {
+            z.push(z_lo);
+            z.push(z_hi);
+        } else if z_lo != 0 {
+            z.push(z_lo);
+        }
+        Self {
+            x_bits: x,
+            z_bits: z,
+        }
+    }
+}
+
+impl<B: BitmaskStorage> fmt::Debug for PauliBitmaskGeneric<B> {
+    fn fmt(&self, f: &mut fmt::Formatter<'_>) -> fmt::Result {
+        if self.is_identity() {
+            return write!(f, "I");
+        }
+        let max_q = match self.x_bits.highest_set_bit() {
+            Some(a) => match self.z_bits.highest_set_bit() {
+                Some(b) => a.max(b) + 1,
+                None => a + 1,
+            },
+            None => match self.z_bits.highest_set_bit() {
+                Some(b) => b + 1,
+                None => return write!(f, "I"),
+            },
+        };
+        for q in 0..max_q {
+            match (self.has_x(q), self.has_z(q)) {
+                (false, false) => write!(f, "I")?,
+                (true, false) => write!(f, "X")?,
+                (false, true) => write!(f, "Z")?,
+                (true, true) => write!(f, "Y")?,
+            }
+        }
+        Ok(())
+    }
+}
+
+// ============================================================
+// Clifford conjugation: U†PU = sign * P'
+// ============================================================
+
+/// Result of Clifford conjugation U†PU.
+#[derive(Clone, Debug)]
+pub struct Conjugated<B: BitmaskStorage = u128> {
+    pub label: PauliBitmaskGeneric<B>,
+    /// True if the sign is negative (U†PU = -P').
+    pub sign_negative: bool,
+}
+
+impl Copy for Conjugated<u128> {}
+
+/// Hadamard on qubit q: X↔Z, Y→-Y.
+#[must_use]
+pub fn conjugate_h<B: BitmaskStorage>(p: &PauliBitmaskGeneric<B>, q: usize) -> Conjugated<B> {
+    let mut label = p.clone();
+    let sign_negative = conjugate_h_in_place(&mut label, q);
+    Conjugated {
+        label,
+        sign_negative,
+    }
+}
+
+/// In-place Hadamard conjugation on qubit q.
+///
+/// Returns `true` when the conjugation contributes a negative sign.
+#[must_use]
+pub fn conjugate_h_in_place<B: BitmaskStorage>(p: &mut PauliBitmaskGeneric<B>, q: usize) -> bool {
+    let has_x = p.x_bits.get_bit(q);
+    let has_z = p.z_bits.get_bit(q);
+    if has_x != has_z {
+        p.x_bits.xor_bit(q);
+        p.z_bits.xor_bit(q);
+    }
+    has_x && has_z
+}
+
+/// SZ gate on qubit q: X→Y, Y→-X, Z→Z.
+#[must_use]
+pub fn conjugate_sz<B: BitmaskStorage>(p: &PauliBitmaskGeneric<B>, q: usize) -> Conjugated<B> {
+    let mut label = p.clone();
+    let sign_negative = conjugate_sz_in_place(&mut label, q);
+    Conjugated {
+        label,
+        sign_negative,
+    }
+}
+
+/// In-place SZ conjugation on qubit q.
+///
+/// Returns `true` when the conjugation contributes a negative sign.
+#[must_use]
+pub fn conjugate_sz_in_place<B: BitmaskStorage>(p: &mut PauliBitmaskGeneric<B>, q: usize) -> bool {
+    if !p.x_bits.get_bit(q) {
+        return false;
+    }
+    let was_y = p.z_bits.get_bit(q);
+    p.z_bits.xor_bit(q);
+    was_y
+}
+
+/// `SZdg` gate on qubit q: X→-Y, Y→X, Z→Z.
+#[must_use]
+pub fn conjugate_szdg<B: BitmaskStorage>(p: &PauliBitmaskGeneric<B>, q: usize) -> Conjugated<B> {
+    let mut label = p.clone();
+    let sign_negative = conjugate_szdg_in_place(&mut label, q);
+    Conjugated {
+        label,
+        sign_negative,
+    }
+}
+
+/// In-place `SZdg` conjugation on qubit q.
+///
+/// Returns `true` when the conjugation contributes a negative sign.
+#[must_use]
+pub fn conjugate_szdg_in_place<B: BitmaskStorage>(
+    p: &mut PauliBitmaskGeneric<B>,
+    q: usize,
+) -> bool {
+    if !p.x_bits.get_bit(q) {
+        return false;
+    }
+    let was_y = p.z_bits.get_bit(q);
+    p.z_bits.xor_bit(q);
+    !was_y
+}
+
+/// CX (CNOT) with control c, target t: XI→XX, IZ→ZZ.
+///
+/// The sign comes from Pauli multiplication phases when the control's
+/// Pauli multiplies Z (from target Z spreading) and the target's Pauli
+/// multiplies X (from control X spreading):
+///   `phase_c` = phase(Pc · Z)  if target has Z, else 0
+///   `phase_t` = phase(X · Pt)  if control has X, else 0
+///   `sign_negative` = (`phase_c` + `phase_t`) % 4 == 2
+#[must_use]
+pub fn conjugate_cx<B: BitmaskStorage>(
+    p: &PauliBitmaskGeneric<B>,
+    c: usize,
+    t: usize,
+) -> Conjugated<B> {
+    let mut label = p.clone();
+    let sign_negative = conjugate_cx_in_place(&mut label, c, t);
+    Conjugated {
+        label,
+        sign_negative,
+    }
+}
+
+/// In-place CX conjugation with control c and target t.
+///
+/// Returns `true` when the conjugation contributes a negative sign.
+#[must_use]
+pub fn conjugate_cx_in_place<B: BitmaskStorage>(
+    p: &mut PauliBitmaskGeneric<B>,
+    c: usize,
+    t: usize,
+) -> bool {
+    const PHASE: [[u8; 4]; 4] = [
+        [0, 0, 0, 0], // I·{I,X,Z,Y}
+        [0, 0, 3, 1], // X·{I,X,Z,Y}
+        [0, 1, 0, 3], // Z·{I,X,Z,Y}
+        [0, 3, 1, 0], // Y·{I,X,Z,Y}
+    ];
+
+    let cx = p.x_bits.get_bit(c);
+    let cz = p.z_bits.get_bit(c);
+    let tx = p.x_bits.get_bit(t);
+    let tz = p.z_bits.get_bit(t);
+    if cx {
+        p.x_bits.xor_bit(t);
+    }
+    if tz {
+        p.z_bits.xor_bit(c);
+    }
+    // Pauli type encoding: I=0, X=1, Z=2, Y=3 (x + 2*z)
+    // Phase from Pauli multiplication table:
+    //   Pc·Z at control (if tz), X·Pt at target (if cx)
+    let pc = u8::from(cx) + 2 * u8::from(cz);
+    let pt = u8::from(tx) + 2 * u8::from(tz);
+    let phase_c = if tz { PHASE[pc as usize][2] } else { 0 };
+    let phase_t = if cx { PHASE[1][pt as usize] } else { 0 };
+    (phase_c + phase_t) % 4 == 2
+}
+
+/// CZ on qubits a, b: XI→XZ, IX→ZX, ZI→ZI, IZ→IZ.
+#[must_use]
+pub fn conjugate_cz<B: BitmaskStorage>(
+    p: &PauliBitmaskGeneric<B>,
+    a: usize,
+    b: usize,
+) -> Conjugated<B> {
+    let mut label = p.clone();
+    let sign_negative = conjugate_cz_in_place(&mut label, a, b);
+    Conjugated {
+        label,
+        sign_negative,
+    }
+}
+
+/// In-place CZ conjugation on qubits a and b.
+///
+/// Returns `true` when the conjugation contributes a negative sign.
+#[must_use]
+pub fn conjugate_cz_in_place<B: BitmaskStorage>(
+    p: &mut PauliBitmaskGeneric<B>,
+    a: usize,
+    b: usize,
+) -> bool {
+    let ax = p.x_bits.get_bit(a);
+    let az = p.z_bits.get_bit(a);
+    let bx = p.x_bits.get_bit(b);
+    let bz = p.z_bits.get_bit(b);
+    if bx {
+        p.z_bits.xor_bit(a);
+    }
+    if ax {
+        p.z_bits.xor_bit(b);
+    }
+    ax && bx && (az != bz)
+}
+
+/// Pauli X gate on qubit q: Z→-Z, Y→-Y.
+#[must_use]
+pub fn conjugate_x<B: BitmaskStorage>(p: &PauliBitmaskGeneric<B>, q: usize) -> Conjugated<B> {
+    let mut label = p.clone();
+    let sign_negative = conjugate_x_in_place(&mut label, q);
+    Conjugated {
+        label,
+        sign_negative,
+    }
+}
+
+/// In-place Pauli X conjugation on qubit q.
+///
+/// Returns `true` when the conjugation contributes a negative sign.
+#[must_use]
+pub fn conjugate_x_in_place<B: BitmaskStorage>(p: &mut PauliBitmaskGeneric<B>, q: usize) -> bool {
+    p.z_bits.get_bit(q)
+}
+
+/// Pauli Y gate on qubit q: X→-X, Z→-Z.
+#[must_use]
+pub fn conjugate_y<B: BitmaskStorage>(p: &PauliBitmaskGeneric<B>, q: usize) -> Conjugated<B> {
+    let mut label = p.clone();
+    let sign_negative = conjugate_y_in_place(&mut label, q);
+    Conjugated {
+        label,
+        sign_negative,
+    }
+}
+
+/// In-place Pauli Y conjugation on qubit q.
+///
+/// Returns `true` when the conjugation contributes a negative sign.
+#[must_use]
+pub fn conjugate_y_in_place<B: BitmaskStorage>(p: &mut PauliBitmaskGeneric<B>, q: usize) -> bool {
+    p.x_bits.get_bit(q) != p.z_bits.get_bit(q)
+}
+
+/// Pauli Z gate on qubit q: X→-X, Y→-Y.
+#[must_use]
+pub fn conjugate_z<B: BitmaskStorage>(p: &PauliBitmaskGeneric<B>, q: usize) -> Conjugated<B> {
+    let mut label = p.clone();
+    let sign_negative = conjugate_z_in_place(&mut label, q);
+    Conjugated {
+        label,
+        sign_negative,
+    }
+}
+
+/// In-place Pauli Z conjugation on qubit q.
+///
+/// Returns `true` when the conjugation contributes a negative sign.
+#[must_use]
+pub fn conjugate_z_in_place<B: BitmaskStorage>(p: &mut PauliBitmaskGeneric<B>, q: usize) -> bool {
+    p.x_bits.get_bit(q)
+}
+
+/// SWAP on qubits a, b: exchanges the Pauli at both sites.
+#[must_use]
+pub fn conjugate_swap<B: BitmaskStorage>(
+    p: &PauliBitmaskGeneric<B>,
+    a: usize,
+    b: usize,
+) -> Conjugated<B> {
+    let mut label = p.clone();
+    let sign_negative = conjugate_swap_in_place(&mut label, a, b);
+    Conjugated {
+        label,
+        sign_negative,
+    }
+}
+
+/// In-place SWAP conjugation on qubits a and b.
+///
+/// Returns `true` when the conjugation contributes a negative sign.
+#[must_use]
+pub fn conjugate_swap_in_place<B: BitmaskStorage>(
+    p: &mut PauliBitmaskGeneric<B>,
+    a: usize,
+    b: usize,
+) -> bool {
+    let ax = p.x_bits.get_bit(a);
+    let az = p.z_bits.get_bit(a);
+    let bx = p.x_bits.get_bit(b);
+    let bz = p.z_bits.get_bit(b);
+    // Clear both positions
+    p.x_bits.clear_bit(a);
+    p.x_bits.clear_bit(b);
+    if az {
+        p.z_bits.clear_bit(a);
+    }
+    if bz {
+        p.z_bits.clear_bit(b);
+    }
+    // Set swapped
+    if bx {
+        p.x_bits.set_bit(a);
+    }
+    if ax {
+        p.x_bits.set_bit(b);
+    }
+    if bz {
+        p.z_bits.set_bit(a);
+    }
+    if az {
+        p.z_bits.set_bit(b);
+    }
+    false
+}
+
+/// SX gate on qubit q: X→X, Z→-Y, Y→Z.
+#[must_use]
+pub fn conjugate_sx<B: BitmaskStorage>(p: &PauliBitmaskGeneric<B>, q: usize) -> Conjugated<B> {
+    let mut label = p.clone();
+    let sign_negative = conjugate_sx_in_place(&mut label, q);
+    Conjugated {
+        label,
+        sign_negative,
+    }
+}
+
+/// In-place SX conjugation on qubit q.
+///
+/// Returns `true` when the conjugation contributes a negative sign.
+#[must_use]
+pub fn conjugate_sx_in_place<B: BitmaskStorage>(p: &mut PauliBitmaskGeneric<B>, q: usize) -> bool {
+    let xq = p.x_bits.get_bit(q);
+    let zq = p.z_bits.get_bit(q);
+    if zq {
+        p.x_bits.xor_bit(q);
+    }
+    !xq && zq
+}
+
+/// `SXdg` gate on qubit q: X→X, Z→Y, Y→-Z.
+#[must_use]
+pub fn conjugate_sxdg<B: BitmaskStorage>(p: &PauliBitmaskGeneric<B>, q: usize) -> Conjugated<B> {
+    let mut label = p.clone();
+    let sign_negative = conjugate_sxdg_in_place(&mut label, q);
+    Conjugated {
+        label,
+        sign_negative,
+    }
+}
+
+/// In-place `SXdg` conjugation on qubit q.
+///
+/// Returns `true` when the conjugation contributes a negative sign.
+#[must_use]
+pub fn conjugate_sxdg_in_place<B: BitmaskStorage>(
+    p: &mut PauliBitmaskGeneric<B>,
+    q: usize,
+) -> bool {
+    let xq = p.x_bits.get_bit(q);
+    let zq = p.z_bits.get_bit(q);
+    if zq {
+        p.x_bits.xor_bit(q);
+    }
+    xq && zq
+}
+
+/// SY gate on qubit q: X→-Z, Y→Y, Z→X.
+#[must_use]
+pub fn conjugate_sy<B: BitmaskStorage>(p: &PauliBitmaskGeneric<B>, q: usize) -> Conjugated<B> {
+    let mut label = p.clone();
+    let sign_negative = conjugate_sy_in_place(&mut label, q);
+    Conjugated {
+        label,
+        sign_negative,
+    }
+}
+
+/// In-place SY conjugation on qubit q.
+///
+/// Returns `true` when the conjugation contributes a negative sign.
+#[must_use]
+pub fn conjugate_sy_in_place<B: BitmaskStorage>(p: &mut PauliBitmaskGeneric<B>, q: usize) -> bool {
+    let xq = p.x_bits.get_bit(q);
+    let zq = p.z_bits.get_bit(q);
+    if xq != zq {
+        p.x_bits.xor_bit(q);
+        p.z_bits.xor_bit(q);
+    }
+    xq && !zq
+}
+
+/// `SYdg` gate on qubit q: X→Z, Y→Y, Z→-X.
+#[must_use]
+pub fn conjugate_sydg<B: BitmaskStorage>(p: &PauliBitmaskGeneric<B>, q: usize) -> Conjugated<B> {
+    let mut label = p.clone();
+    let sign_negative = conjugate_sydg_in_place(&mut label, q);
+    Conjugated {
+        label,
+        sign_negative,
+    }
+}
+
+/// In-place `SYdg` conjugation on qubit q.
+///
+/// Returns `true` when the conjugation contributes a negative sign.
+#[must_use]
+pub fn conjugate_sydg_in_place<B: BitmaskStorage>(
+    p: &mut PauliBitmaskGeneric<B>,
+    q: usize,
+) -> bool {
+    let xq = p.x_bits.get_bit(q);
+    let zq = p.z_bits.get_bit(q);
+    if xq != zq {
+        p.x_bits.xor_bit(q);
+        p.z_bits.xor_bit(q);
+    }
+    !xq && zq
+}
+
+/// CY (controlled-Y) with control c, target t.
+///
+/// Decomposed as CY = (I⊗SZ) · CX · (I⊗SZdg), so conjugation is:
+/// 1. conjugate by `SZdg` on target
+/// 2. conjugate by CX
+/// 3. conjugate by SZ on target
+#[must_use]
+pub fn conjugate_cy<B: BitmaskStorage>(
+    p: &PauliBitmaskGeneric<B>,
+    c: usize,
+    t: usize,
+) -> Conjugated<B> {
+    let mut label = p.clone();
+    let sign_negative = conjugate_cy_in_place(&mut label, c, t);
+    Conjugated {
+        label,
+        sign_negative,
+    }
+}
+
+/// In-place CY conjugation with control c and target t.
+///
+/// Returns `true` when the conjugation contributes a negative sign.
+#[must_use]
+pub fn conjugate_cy_in_place<B: BitmaskStorage>(
+    p: &mut PauliBitmaskGeneric<B>,
+    c: usize,
+    t: usize,
+) -> bool {
+    conjugate_szdg_in_place(p, t) ^ conjugate_cx_in_place(p, c, t) ^ conjugate_sz_in_place(p, t)
+}
+
+#[cfg(test)]
+mod tests {
+    use super::*;
+
+    // --- PauliBitmask basics ---
+
+    #[test]
+    fn test_commutation() {
+        assert!(!PauliBitmask::x(0).commutes_with(&PauliBitmask::z(0)));
+        assert!(PauliBitmask::x(0).commutes_with(&PauliBitmask::x(1)));
+        assert!(!PauliBitmask::x(0).commutes_with(&PauliBitmask::y(0)));
+
+        let a = PauliBitmask {
+            x_bits: 1,
+            z_bits: 2,
+        };
+        let b = PauliBitmask {
+            x_bits: 2,
+            z_bits: 1,
+        };
+        assert!(a.commutes_with(&b));
+    }
+
+    #[test]
+    fn test_multiply() {
+        assert_eq!(
+            PauliBitmask::x(0).multiply(&PauliBitmask::z(0)),
+            PauliBitmask::y(0)
+        );
+    }
+
+    #[test]
+    fn test_h() {
+        let r = conjugate_h(&PauliBitmask::x(0), 0);
+        assert_eq!(r.label, PauliBitmask::z(0));
+        assert!(!r.sign_negative);
+
+        let r = conjugate_h(&PauliBitmask::z(0), 0);
+        assert_eq!(r.label, PauliBitmask::x(0));
+        assert!(!r.sign_negative);
+
+        let r = conjugate_h(&PauliBitmask::y(0), 0);
+        assert_eq!(r.label, PauliBitmask::y(0));
+        assert!(r.sign_negative);
+    }
+
+    #[test]
+    fn test_sz() {
+        let r = conjugate_sz(&PauliBitmask::x(0), 0);
+        assert_eq!(r.label, PauliBitmask::y(0));
+        assert!(!r.sign_negative);
+
+        let r = conjugate_sz(&PauliBitmask::y(0), 0);
+        assert_eq!(r.label, PauliBitmask::x(0));
+        assert!(r.sign_negative);
+
+        let r = conjugate_sz(&PauliBitmask::z(0), 0);
+        assert_eq!(r.label, PauliBitmask::z(0));
+        assert!(!r.sign_negative);
+    }
+
+    #[test]
+    fn test_szdg() {
+        let r = conjugate_szdg(&PauliBitmask::x(0), 0);
+        assert_eq!(r.label, PauliBitmask::y(0));
+        assert!(r.sign_negative);
+
+        let r = conjugate_szdg(&PauliBitmask::y(0), 0);
+        assert_eq!(r.label, PauliBitmask::x(0));
+        assert!(!r.sign_negative);
+    }
+
+    #[test]
+    fn test_cx() {
+        let r = conjugate_cx(&PauliBitmask::x(0), 0, 1);
+        assert_eq!(
+            r.label,
+            PauliBitmask {
+                x_bits: 0b11,
+                z_bits: 0
+            }
+        );
+        assert!(!r.sign_negative);
+
+        let r = conjugate_cx(&PauliBitmask::z(1), 0, 1);
+        assert_eq!(
+            r.label,
+            PauliBitmask {
+                x_bits: 0,
+                z_bits: 0b11
+            }
+        );
+        assert!(!r.sign_negative);
+
+        let r = conjugate_cx(&PauliBitmask::x(1), 0, 1);
+        assert_eq!(r.label, PauliBitmask::x(1));
+        assert!(!r.sign_negative);
+    }
+
+    #[test]
+    fn test_cz() {
+        let r = conjugate_cz(&PauliBitmask::x(0), 0, 1);
+        assert_eq!(
+            r.label,
+            PauliBitmask {
+                x_bits: 1,
+                z_bits: 2
+            }
+        );
+        assert!(!r.sign_negative);
+
+        let r = conjugate_cz(&PauliBitmask::z(0), 0, 1);
+        assert_eq!(r.label, PauliBitmask::z(0));
+        assert!(!r.sign_negative);
+    }
+
+    #[test]
+    fn test_swap() {
+        let r = conjugate_swap(&PauliBitmask::x(0), 0, 1);
+        assert_eq!(r.label, PauliBitmask::x(1));
+        assert!(!r.sign_negative);
+    }
+
+    #[test]
+    fn test_h_involution() {
+        for p in [PauliBitmask::x(0), PauliBitmask::z(0), PauliBitmask::y(0)] {
+            let r1 = conjugate_h(&p, 0);
+            let r2 = conjugate_h(&r1.label, 0);
+            assert_eq!(r2.label, p);
+            assert!(!(r1.sign_negative ^ r2.sign_negative));
+        }
+    }
+
+    #[test]
+    fn test_sz_fourth_power() {
+        let p = PauliBitmask::x(0);
+        let mut label = p;
+        let mut sign = false;
+        for _ in 0..4 {
+            let r = conjugate_sz(&label, 0);
+            label = r.label;
+            sign ^= r.sign_negative;
+        }
+        assert_eq!(label, p);
+        assert!(!sign);
+    }
+
+    #[test]
+    fn test_sx() {
+        // X→X (no sign)
+        let r = conjugate_sx(&PauliBitmask::x(0), 0);
+        assert_eq!(r.label, PauliBitmask::x(0));
+        assert!(!r.sign_negative);
+
+        // Z→-Y
+        let r = conjugate_sx(&PauliBitmask::z(0), 0);
+        assert_eq!(r.label, PauliBitmask::y(0));
+        assert!(r.sign_negative);
+
+        // Y→Z (no sign)
+        let r = conjugate_sx(&PauliBitmask::y(0), 0);
+        assert_eq!(r.label, PauliBitmask::z(0));
+        assert!(!r.sign_negative);
+    }
+
+    #[test]
+    fn test_sxdg() {
+        // X→X
+        let r = conjugate_sxdg(&PauliBitmask::x(0), 0);
+        assert_eq!(r.label, PauliBitmask::x(0));
+        assert!(!r.sign_negative);
+
+        // Z→Y
+        let r = conjugate_sxdg(&PauliBitmask::z(0), 0);
+        assert_eq!(r.label, PauliBitmask::y(0));
+        assert!(!r.sign_negative);
+
+        // Y→-Z
+        let r = conjugate_sxdg(&PauliBitmask::y(0), 0);
+        assert_eq!(r.label, PauliBitmask::z(0));
+        assert!(r.sign_negative);
+    }
+
+    #[test]
+    fn test_sy() {
+        // X→-Z
+        let r = conjugate_sy(&PauliBitmask::x(0), 0);
+        assert_eq!(r.label, PauliBitmask::z(0));
+        assert!(r.sign_negative);
+
+        // Z→X
+        let r = conjugate_sy(&PauliBitmask::z(0), 0);
+        assert_eq!(r.label, PauliBitmask::x(0));
+        assert!(!r.sign_negative);
+
+        // Y→Y
+        let r = conjugate_sy(&PauliBitmask::y(0), 0);
+        assert_eq!(r.label, PauliBitmask::y(0));
+        assert!(!r.sign_negative);
+    }
+
+    #[test]
+    fn test_sydg() {
+        // X→Z
+        let r = conjugate_sydg(&PauliBitmask::x(0), 0);
+        assert_eq!(r.label, PauliBitmask::z(0));
+        assert!(!r.sign_negative);
+
+        // Z→-X
+        let r = conjugate_sydg(&PauliBitmask::z(0), 0);
+        assert_eq!(r.label, PauliBitmask::x(0));
+        assert!(r.sign_negative);
+
+        // Y→Y
+        let r = conjugate_sydg(&PauliBitmask::y(0), 0);
+        assert_eq!(r.label, PauliBitmask::y(0));
+        assert!(!r.sign_negative);
+    }
+
+    #[test]
+    fn test_sx_fourth_power() {
+        let p = PauliBitmask::z(0);
+        let mut label = p;
+        let mut sign = false;
+        for _ in 0..4 {
+            let r = conjugate_sx(&label, 0);
+            label = r.label;
+            sign ^= r.sign_negative;
+        }
+        assert_eq!(label, p);
+        assert!(!sign);
+    }
+
+    #[test]
+    fn test_sy_fourth_power() {
+        let p = PauliBitmask::x(0);
+        let mut label = p;
+        let mut sign = false;
+        for _ in 0..4 {
+            let r = conjugate_sy(&label, 0);
+            label = r.label;
+            sign ^= r.sign_negative;
+        }
+        assert_eq!(label, p);
+        assert!(!sign);
+    }
+
+    #[test]
+    fn test_sx_sxdg_inverse() {
+        for p in [PauliBitmask::x(0), PauliBitmask::z(0), PauliBitmask::y(0)] {
+            let r1 = conjugate_sx(&p, 0);
+            let r2 = conjugate_sxdg(&r1.label, 0);
+            assert_eq!(r2.label, p);
+            assert!(!(r1.sign_negative ^ r2.sign_negative));
+        }
+    }
+
+    #[test]
+    fn test_sy_sydg_inverse() {
+        for p in [PauliBitmask::x(0), PauliBitmask::z(0), PauliBitmask::y(0)] {
+            let r1 = conjugate_sy(&p, 0);
+            let r2 = conjugate_sydg(&r1.label, 0);
+            assert_eq!(r2.label, p);
+            assert!(!(r1.sign_negative ^ r2.sign_negative));
+        }
+    }
+
+    #[test]
+    fn test_cy() {
+        // X_c → X_c Y_t
+        let r = conjugate_cy(&PauliBitmask::x(0), 0, 1);
+        assert_eq!(
+            r.label,
+            PauliBitmask {
+                x_bits: 0b11,
+                z_bits: 0b10
+            }
+        );
+        assert!(!r.sign_negative);
+
+        // Z_c → Z_c
+        let r = conjugate_cy(&PauliBitmask::z(0), 0, 1);
+        assert_eq!(r.label, PauliBitmask::z(0));
+        assert!(!r.sign_negative);
+
+        // X_t → Z_c X_t
+        let r = conjugate_cy(&PauliBitmask::x(1), 0, 1);
+        assert_eq!(
+            r.label,
+            PauliBitmask {
+                x_bits: 0b10,
+                z_bits: 0b01
+            }
+        );
+        assert!(!r.sign_negative);
+
+        // Z_t → Z_c Z_t
+        let r = conjugate_cy(&PauliBitmask::z(1), 0, 1);
+        assert_eq!(
+            r.label,
+            PauliBitmask {
+                x_bits: 0,
+                z_bits: 0b11
+            }
+        );
+        assert!(!r.sign_negative);
+    }
+
+    #[test]
+    fn test_multiply_with_phase() {
+        // X * Z = -iY (phase = 3, i.e., i^3 = -i)
+        let (prod, phase) = PauliBitmask::x(0).multiply_with_phase(&PauliBitmask::z(0));
+        assert_eq!(prod, PauliBitmask::y(0));
+        assert_eq!(phase, 3); // i^3 = -i
+
+        // Z * X = iY (phase = 1)
+        let (prod, phase) = PauliBitmask::z(0).multiply_with_phase(&PauliBitmask::x(0));
+        assert_eq!(prod, PauliBitmask::y(0));
+        assert_eq!(phase, 1); // i^1 = i
+
+        // X * X = I (phase = 0)
+        let (prod, phase) = PauliBitmask::x(0).multiply_with_phase(&PauliBitmask::x(0));
+        assert!(prod.is_identity());
+        assert_eq!(phase, 0);
+
+        // Y * Y = I (phase = 0)
+        let (prod, phase) = PauliBitmask::y(0).multiply_with_phase(&PauliBitmask::y(0));
+        assert!(prod.is_identity());
+        assert_eq!(phase, 0);
+
+        // Multi-qubit: (X⊗Z) * (Z⊗X) = (XZ)⊗(ZX) = (-iY)⊗(iY) = (-i·i)(Y⊗Y) = Y⊗Y
+        let a = PauliBitmask {
+            x_bits: 0b01,
+            z_bits: 0b10,
+        }; // XZ
+        let b = PauliBitmask {
+            x_bits: 0b10,
+            z_bits: 0b01,
+        }; // ZX
+        let (prod, phase) = a.multiply_with_phase(&b);
+        assert_eq!(
+            prod,
+            PauliBitmask {
+                x_bits: 0b11,
+                z_bits: 0b11
+            }
+        ); // YY
+        assert_eq!(phase, 0); // (-i)(i) = 1, phase = 3+1 = 4 mod 4 = 0
+    }
+
+    #[test]
+    fn test_cy_involution() {
+        // CY is hermitian (CY² = I), so double conjugation should be identity
+        for p in [
+            PauliBitmask::x(0),
+            PauliBitmask::z(0),
+            PauliBitmask::x(1),
+            PauliBitmask::z(1),
+        ] {
+            let r1 = conjugate_cy(&p, 0, 1);
+            let r2 = conjugate_cy(&r1.label, 0, 1);
+            assert_eq!(r2.label, p);
+            assert!(!(r1.sign_negative ^ r2.sign_negative));
+        }
+    }
+}
diff --git a/crates/pecos-core/src/qubit_support.rs b/crates/pecos-core/src/qubit_support.rs
new file mode 100644
index 000000000..38dc41ce0
--- /dev/null
+++ b/crates/pecos-core/src/qubit_support.rs
@@ -0,0 +1,82 @@
+// Copyright 2026 The PECOS Developers
+//
+// Licensed under the Apache License, Version 2.0 (the "License"); you may not use this file except
+// in compliance with the License. You may obtain a copy of the License at
+//
+//     https://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software distributed under the License
+// is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express
+// or implied. See the License for the specific language governing permissions and limitations under
+// the License.
+
+pub(crate) fn overlapping_qubits(
+    lhs: impl IntoIterator<Item = usize>,
+    rhs: impl IntoIterator<Item = usize>,
+) -> Vec<usize> {
+    let mut lhs_qubits: Vec<usize> = lhs.into_iter().collect();
+    lhs_qubits.sort_unstable();
+    lhs_qubits.dedup();
+
+    let mut rhs_qubits: Vec<usize> = rhs.into_iter().collect();
+    rhs_qubits.sort_unstable();
+    rhs_qubits.dedup();
+
+    let mut overlap = Vec::new();
+    let mut lhs_idx = 0;
+    let mut rhs_idx = 0;
+    while lhs_idx < lhs_qubits.len() && rhs_idx < rhs_qubits.len() {
+        match lhs_qubits[lhs_idx].cmp(&rhs_qubits[rhs_idx]) {
+            std::cmp::Ordering::Less => lhs_idx += 1,
+            std::cmp::Ordering::Greater => rhs_idx += 1,
+            std::cmp::Ordering::Equal => {
+                overlap.push(lhs_qubits[lhs_idx]);
+                lhs_idx += 1;
+                rhs_idx += 1;
+            }
+        }
+    }
+    overlap
+}
+
+pub(crate) fn duplicate_qubits(qubits: impl IntoIterator<Item = usize>) -> Vec<usize> {
+    let mut qubits: Vec<usize> = qubits.into_iter().collect();
+    qubits.sort_unstable();
+
+    let mut duplicates = Vec::new();
+    for window in qubits.windows(2) {
+        if window[0] == window[1] && duplicates.last() != Some(&window[0]) {
+            duplicates.push(window[0]);
+        }
+    }
+    duplicates
+}
+
+pub(crate) fn assert_distinct_qubits(context: &str, qubits: impl IntoIterator<Item = usize>) {
+    let duplicates = duplicate_qubits(qubits);
+    assert!(
+        duplicates.is_empty(),
+        "{context} requires distinct qubits; duplicated qubits: {duplicates:?}"
+    );
+}
+
+#[cfg(test)]
+mod tests {
+    use super::*;
+
+    #[test]
+    fn overlapping_qubits_returns_sorted_deduplicated_intersection() {
+        assert_eq!(overlapping_qubits([3, 1, 1, 2], [2, 2, 3, 4]), vec![2, 3]);
+    }
+
+    #[test]
+    fn duplicate_qubits_returns_sorted_deduplicated_repeats() {
+        assert_eq!(duplicate_qubits([5, 1, 5, 2, 2, 2]), vec![2, 5]);
+    }
+
+    #[test]
+    #[should_panic(expected = "CX requires distinct qubits; duplicated qubits: [0, 2]")]
+    fn assert_distinct_qubits_reports_context_and_duplicates() {
+        assert_distinct_qubits("CX", [2, 0, 1, 2, 0]);
+    }
+}
diff --git a/crates/pecos-core/src/unitary.rs b/crates/pecos-core/src/unitary.rs
new file mode 100644
index 000000000..cf37279e9
--- /dev/null
+++ b/crates/pecos-core/src/unitary.rs
@@ -0,0 +1,29 @@
+// Copyright 2026 The PECOS Developers
+//
+// Licensed under the Apache License, Version 2.0 (the "License"); you may not use this file except
+// in compliance with the License.You may obtain a copy of the License at
+//
+//     https://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software distributed under the License
+// is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express
+// or implied. See the License for the specific language governing permissions and limitations under
+// the License.
+
+//! Unitary gate algebra namespace.
+//!
+//! Re-exports the full unitary-level API so users can write:
+//!
+//! ```
+//! use pecos_core::unitary::*;
+//! use pecos_core::Angle64;
+//!
+//! let circuit = T(1) * CX(0, 1) * H(0);
+//! let layer = RZ(Angle64::HALF_TURN / 4, 0) & H(1);
+//! ```
+
+pub use crate::unitary_rep::{
+    CCX, CX, CXs, CY, CYs, CZ, CZs, Commutativity, H, Hs, I, Is, ParseUnitaryRepError, PhaseValue,
+    QubitPairs, Qubits, RX, RXX, RXXs, RXs, RY, RYY, RYYs, RYs, RZ, RZZ, RZZs, RZs, RotationType,
+    SWAP, SWAPs, SX, SXs, SY, SYs, SZ, SZs, T, Ts, Unitary, UnitaryRep, X, Xs, Y, Ys, Z, Zs, phase,
+};
diff --git a/crates/pecos-core/src/unitary_rep.rs b/crates/pecos-core/src/unitary_rep.rs
index 95eac8d96..04e4917e5 100644
--- a/crates/pecos-core/src/unitary_rep.rs
+++ b/crates/pecos-core/src/unitary_rep.rs
@@ -29,7 +29,7 @@
 //! # Examples
 //!
 //! ```
-//! use pecos_core::unitary_rep::*;
+//! use pecos_core::unitary::*;
 //! use pecos_core::Angle64;
 //!
 //! // Build a circuit: H on q0, then CX(0,1), then T on q1
@@ -52,6 +52,7 @@
 use crate::gate_type::GateType;
 use crate::pauli::PauliOperator;
 use crate::phase::Phase;
+use crate::qubit_support::{assert_distinct_qubits, duplicate_qubits, overlapping_qubits};
 use crate::{Angle64, Pauli, PauliString, QuarterPhase, QubitId};
 use smallvec::SmallVec;
 use std::ops::{BitAnd, Mul, Neg};
@@ -68,7 +69,7 @@ use std::str::FromStr;
 ///
 /// ```
 /// use pecos_core::{phase, Angle64};
-/// use pecos_core::unitary_rep::X;
+/// use pecos_core::unitary::X;
 ///
 /// // e^{iπ/4} * X - exact, no floating point
 /// let op = phase!(pi / 4) * X(0);
@@ -95,7 +96,7 @@ macro_rules! phase {
 ///
 /// ```
 /// use pecos_core::phase_turn;
-/// use pecos_core::unitary_rep::X;
+/// use pecos_core::unitary::X;
 ///
 /// // T gate phase: e^{i * 2π/8} = e^{iπ/4}
 /// let op = phase_turn!(1 / 8) * X(0);
@@ -386,7 +387,7 @@ pub enum Commutativity {
 ///
 /// Enables pluralized gate functions to accept various qubit collections:
 /// ```
-/// use pecos_core::unitary_rep::*;
+/// use pecos_core::unitary::*;
 /// use pecos_core::QubitId;
 ///
 /// // Multiple qubits via Xs - equivalent to X(0) & X(2) & X(5)
@@ -487,18 +488,18 @@ impl Qubits {
     where
         F: Fn(usize) -> UnitaryRep,
     {
-        match self.0.len() {
-            0 => UnitaryRep::Pauli(PauliString::default()), // Identity
-            1 => gate_fn(self.0[0].0),
-            _ => UnitaryRep::Tensor(self.0.iter().map(|q| gate_fn(q.0)).collect()),
-        }
+        self.0
+            .iter()
+            .map(|q| gate_fn(q.0))
+            .reduce(|lhs, rhs| lhs & rhs)
+            .unwrap_or_else(|| UnitaryRep::Pauli(PauliString::default()))
     }
 }
 
 /// Wrapper for qubit pairs used by pluralized two-qubit gates.
 ///
 /// ```
-/// use pecos_core::unitary_rep::*;
+/// use pecos_core::unitary::*;
 /// use pecos_core::QubitId;
 ///
 /// // Multiple CX gates via CXs
@@ -594,11 +595,11 @@ impl QubitPairs {
     where
         F: Fn(usize, usize) -> UnitaryRep,
     {
-        match self.0.len() {
-            0 => UnitaryRep::Pauli(PauliString::default()), // Identity
-            1 => gate_fn(self.0[0].0.0, self.0[0].1.0),
-            _ => UnitaryRep::Tensor(self.0.iter().map(|(q0, q1)| gate_fn(q0.0, q1.0)).collect()),
-        }
+        self.0
+            .iter()
+            .map(|(q0, q1)| gate_fn(q0.0, q1.0))
+            .reduce(|lhs, rhs| lhs & rhs)
+            .unwrap_or_else(|| UnitaryRep::Pauli(PauliString::default()))
     }
 }
 
@@ -756,6 +757,22 @@ fn parse_qubits(tokens: &[&str]) -> Result<Vec<usize>, ParseUnitaryRepError> {
         .collect()
 }
 
+fn require_distinct_parsed_qubits(
+    context: &str,
+    qubits: &[usize],
+) -> Result<(), ParseUnitaryRepError> {
+    let duplicates = duplicate_qubits(qubits.iter().copied());
+    if duplicates.is_empty() {
+        Ok(())
+    } else {
+        Err(ParseUnitaryRepError {
+            message: format!(
+                "{context} requires distinct qubits; duplicated qubits: {duplicates:?}"
+            ),
+        })
+    }
+}
+
 impl FromStr for UnitaryRep {
     type Err = ParseUnitaryRepError;
 
@@ -840,6 +857,9 @@ impl FromStr for UnitaryRep {
                         ),
                     });
                 }
+                if expected > 1 {
+                    require_distinct_parsed_qubits(rot_name, &qubits)?;
+                }
                 return Ok(UnitaryRep::rotation(
                     rot_type,
                     angle,
@@ -877,6 +897,9 @@ impl FromStr for UnitaryRep {
                         ),
                     });
                 }
+                if expected > 1 {
+                    require_distinct_parsed_qubits(gate_name, &qubits)?;
+                }
                 Ok(UnitaryRep::gate(gate_type, SmallVec::from_vec(qubits)))
             }
 
@@ -942,6 +965,7 @@ impl FromStr for UnitaryRep {
                         message: format!("{gate_name} requires 2 qubits, got {}", qubits.len()),
                     });
                 }
+                require_distinct_parsed_qubits(gate_name, &qubits)?;
                 Ok(UnitaryRep::gate(GateType::CX, SmallVec::from_vec(qubits)))
             }
             "CY" => {
@@ -951,6 +975,7 @@ impl FromStr for UnitaryRep {
                         message: format!("CY requires 2 qubits, got {}", qubits.len()),
                     });
                 }
+                require_distinct_parsed_qubits("CY", &qubits)?;
                 Ok(UnitaryRep::gate(GateType::CY, SmallVec::from_vec(qubits)))
             }
             "CZ" => {
@@ -960,6 +985,7 @@ impl FromStr for UnitaryRep {
                         message: format!("CZ requires 2 qubits, got {}", qubits.len()),
                     });
                 }
+                require_distinct_parsed_qubits("CZ", &qubits)?;
                 Ok(UnitaryRep::gate(GateType::CZ, SmallVec::from_vec(qubits)))
             }
             "SWAP" => {
@@ -969,6 +995,7 @@ impl FromStr for UnitaryRep {
                         message: format!("SWAP requires 2 qubits, got {}", qubits.len()),
                     });
                 }
+                require_distinct_parsed_qubits("SWAP", &qubits)?;
                 Ok(UnitaryRep::gate(GateType::SWAP, SmallVec::from_vec(qubits)))
             }
 
@@ -980,6 +1007,7 @@ impl FromStr for UnitaryRep {
                         message: format!("{gate_name} requires 3 qubits, got {}", qubits.len()),
                     });
                 }
+                require_distinct_parsed_qubits(gate_name, &qubits)?;
                 Ok(UnitaryRep::gate(GateType::CCX, SmallVec::from_vec(qubits)))
             }
 
@@ -994,25 +1022,61 @@ impl FromStr for UnitaryRep {
 
 impl UnitaryRep {
     /// Creates a rotation gate expression.
+    ///
+    /// # Panics
+    ///
+    /// Panics if `qubits` does not match the rotation arity, or if a
+    /// multi-qubit rotation repeats a qubit.
     #[must_use]
     pub fn rotation(
         rotation_type: RotationType,
         angle: Angle64,
         qubits: impl Into<SmallVec<[usize; 3]>>,
     ) -> Self {
+        let qubits = qubits.into();
+        let expected = rotation_type.num_qubits();
+        assert_eq!(
+            qubits.len(),
+            expected,
+            "{:?} requires {expected} qubit(s), got {}",
+            rotation_type.to_gate_type(),
+            qubits.len()
+        );
+        if expected > 1 {
+            assert_distinct_qubits(
+                &format!("{:?}", rotation_type.to_gate_type()),
+                qubits.iter().copied(),
+            );
+        }
         Self::Gate(
             Unitary::Rotation {
                 rotation_type,
                 angle,
             },
-            qubits.into(),
+            qubits,
         )
     }
 
     /// Creates a fixed gate expression.
+    ///
+    /// # Panics
+    ///
+    /// Panics if `qubits` does not match the gate arity, or if a
+    /// multi-qubit gate repeats a qubit.
     #[must_use]
     pub fn gate(gate_type: GateType, qubits: impl Into<SmallVec<[usize; 3]>>) -> Self {
-        Self::Gate(Unitary::Named(gate_type), qubits.into())
+        let qubits = qubits.into();
+        let expected = gate_type.quantum_arity();
+        assert_eq!(
+            qubits.len(),
+            expected,
+            "{gate_type:?} requires {expected} qubit(s), got {}",
+            qubits.len()
+        );
+        if expected > 1 {
+            assert_distinct_qubits(&format!("{gate_type:?}"), qubits.iter().copied());
+        }
+        Self::Gate(Unitary::Named(gate_type), qubits)
     }
 
     /// Returns the adjoint (Hermitian conjugate) of this expression.
@@ -1251,7 +1315,7 @@ impl Mul<&UnitaryRep> for NegImaginaryUnit {
 ///
 /// # Example
 /// ```
-/// use pecos_core::unitary_rep::{phase, X};
+/// use pecos_core::unitary::{phase, X};
 /// use pecos_core::Angle64;
 ///
 /// // Create a phase of e^{iπ/4}
@@ -1267,7 +1331,7 @@ pub struct PhaseValue(pub Angle64);
 ///
 /// # Example
 /// ```
-/// use pecos_core::unitary_rep::{phase, X, Z};
+/// use pecos_core::unitary::{phase, X, Z};
 /// use pecos_core::Angle64;
 ///
 /// // e^{iπ/4} * X
@@ -1384,7 +1448,7 @@ impl UnitaryRep {
     /// # Example
     ///
     /// ```
-    /// use pecos_core::unitary_rep::{Xs, Zs};
+    /// use pecos_core::unitary::{Xs, Zs};
     /// use pecos_core::PauliOperator;
     ///
     /// // Tensor of Paulis on disjoint qubits
@@ -1402,10 +1466,10 @@ impl UnitaryRep {
                 let mut result = PauliString::new();
                 for part in parts {
                     let ps = part.try_to_pauli_string()?;
-                    // Merge: combine the Pauli operators
-                    // For disjoint qubits, this is just concatenation
-                    // For overlapping qubits, we multiply the Paulis
-                    result = result * ps;
+                    if !overlapping_qubits(result.qubits(), ps.qubits()).is_empty() {
+                        return None;
+                    }
+                    result = result & ps;
                 }
                 Some(result)
             }
@@ -1450,6 +1514,10 @@ impl UnitaryRep {
                 },
                 qubits,
             ) => {
+                if angle == Angle64::ZERO {
+                    return Some(PauliString::identity());
+                }
+
                 // Only half-turn rotations are Pauli operators
                 let half = Angle64::HALF_TURN;
                 let neg_half = negate_angle(half);
@@ -1643,7 +1711,7 @@ impl UnitaryRep {
     /// # Example
     ///
     /// ```
-    /// use pecos_core::unitary_rep::{X, Z, H, T};
+    /// use pecos_core::unitary::{X, Z, H, T};
     ///
     /// // Stabilizer update: applying H to qubit 0
     /// let stabilizer = X(0) & Z(1);
@@ -1668,7 +1736,7 @@ impl UnitaryRep {
     /// # Example
     ///
     /// ```
-    /// use pecos_core::unitary_rep::{X, H};
+    /// use pecos_core::unitary::{X, H};
     ///
     /// // Heisenberg evolution: how X evolves under H
     /// let evolved = X(0).conjdg(&H(0));  // H† X H
@@ -1683,7 +1751,7 @@ impl UnitaryRep {
     /// # Example
     ///
     /// ```
-    /// use pecos_core::unitary_rep::{X, Y};
+    /// use pecos_core::unitary::{X, Y};
     /// use pecos_core::{GlobalPhase, QuarterPhase};
     ///
     /// let op = X(0);
@@ -1708,7 +1776,7 @@ impl UnitaryRep {
     /// # Example
     ///
     /// ```
-    /// use pecos_core::unitary_rep::{X, Z, CX};
+    /// use pecos_core::unitary::{X, Z, CX};
     ///
     /// assert_eq!(X(0).weight(), 1);
     /// assert_eq!((X(0) & Z(2)).weight(), 2);
@@ -1724,7 +1792,7 @@ impl UnitaryRep {
     /// # Example
     ///
     /// ```
-    /// use pecos_core::unitary_rep::I;
+    /// use pecos_core::unitary::I;
     ///
     /// assert!(I(0).is_identity());
     /// ```
@@ -1744,7 +1812,7 @@ impl UnitaryRep {
     /// # Example
     ///
     /// ```
-    /// use pecos_core::unitary_rep::{X, Y, Z, H, T};
+    /// use pecos_core::unitary::{X, Y, Z, H, T};
     ///
     /// // Paulis are Hermitian
     /// assert!(X(0).is_hermitian());
@@ -1806,7 +1874,7 @@ impl UnitaryRep {
     /// # Example
     ///
     /// ```
-    /// use pecos_core::unitary_rep::{X, H};
+    /// use pecos_core::unitary::{X, H};
     ///
     /// let x = X(0);
     /// let x2 = x.pow(2);  // X * X = I
@@ -1843,7 +1911,7 @@ impl UnitaryRep {
     /// # Example
     ///
     /// ```
-    /// use pecos_core::unitary_rep::{X, Z, Commutativity};
+    /// use pecos_core::unitary::{X, Z, Commutativity};
     ///
     /// let a = X(0);
     /// let b = Z(0);
@@ -1876,7 +1944,7 @@ impl UnitaryRep {
     /// # Example
     ///
     /// ```
-    /// use pecos_core::unitary_rep::{X, H, RZ};
+    /// use pecos_core::unitary::{X, H, RZ};
     /// use pecos_core::Angle64;
     ///
     /// assert!(X(0).is_unitary());
@@ -1896,7 +1964,7 @@ impl UnitaryRep {
     /// # Example
     ///
     /// ```
-    /// use pecos_core::unitary_rep::{H, CX};
+    /// use pecos_core::unitary::{H, CX};
     ///
     /// let circuit = CX(0, 1) * H(0);  // H then CX
     /// let gates = circuit.decompose();
@@ -2943,11 +3011,10 @@ pub fn RZs(angle: Angle64, qubits: impl Into<Qubits>) -> UnitaryRep {
 #[must_use]
 #[allow(non_snake_case)]
 pub fn RXX(angle: Angle64, q0: impl Into<QubitId>, q1: impl Into<QubitId>) -> UnitaryRep {
-    UnitaryRep::rotation(
-        RotationType::RXX,
-        angle,
-        smallvec::smallvec![q0.into().0, q1.into().0],
-    )
+    let q0 = q0.into();
+    let q1 = q1.into();
+    assert_distinct_qubits("RXX", [q0.0, q1.0]);
+    UnitaryRep::rotation(RotationType::RXX, angle, smallvec::smallvec![q0.0, q1.0])
 }
 
 /// RXX rotations on multiple qubit pairs.
@@ -2956,9 +3023,7 @@ pub fn RXX(angle: Angle64, q0: impl Into<QubitId>, q1: impl Into<QubitId>) -> Un
 #[must_use]
 #[allow(non_snake_case)]
 pub fn RXXs(angle: Angle64, pairs: impl Into<QubitPairs>) -> UnitaryRep {
-    pairs
-        .into()
-        .apply(|q0, q1| UnitaryRep::rotation(RotationType::RXX, angle, smallvec::smallvec![q0, q1]))
+    pairs.into().apply(|q0, q1| RXX(angle, q0, q1))
 }
 
 /// Two-qubit YY rotation by the given angle.
@@ -2967,11 +3032,10 @@ pub fn RXXs(angle: Angle64, pairs: impl Into<QubitPairs>) -> UnitaryRep {
 #[must_use]
 #[allow(non_snake_case)]
 pub fn RYY(angle: Angle64, q0: impl Into<QubitId>, q1: impl Into<QubitId>) -> UnitaryRep {
-    UnitaryRep::rotation(
-        RotationType::RYY,
-        angle,
-        smallvec::smallvec![q0.into().0, q1.into().0],
-    )
+    let q0 = q0.into();
+    let q1 = q1.into();
+    assert_distinct_qubits("RYY", [q0.0, q1.0]);
+    UnitaryRep::rotation(RotationType::RYY, angle, smallvec::smallvec![q0.0, q1.0])
 }
 
 /// RYY rotations on multiple qubit pairs.
@@ -2980,9 +3044,7 @@ pub fn RYY(angle: Angle64, q0: impl Into<QubitId>, q1: impl Into<QubitId>) -> Un
 #[must_use]
 #[allow(non_snake_case)]
 pub fn RYYs(angle: Angle64, pairs: impl Into<QubitPairs>) -> UnitaryRep {
-    pairs
-        .into()
-        .apply(|q0, q1| UnitaryRep::rotation(RotationType::RYY, angle, smallvec::smallvec![q0, q1]))
+    pairs.into().apply(|q0, q1| RYY(angle, q0, q1))
 }
 
 /// Two-qubit ZZ rotation by the given angle.
@@ -2991,11 +3053,10 @@ pub fn RYYs(angle: Angle64, pairs: impl Into<QubitPairs>) -> UnitaryRep {
 #[must_use]
 #[allow(non_snake_case)]
 pub fn RZZ(angle: Angle64, q0: impl Into<QubitId>, q1: impl Into<QubitId>) -> UnitaryRep {
-    UnitaryRep::rotation(
-        RotationType::RZZ,
-        angle,
-        smallvec::smallvec![q0.into().0, q1.into().0],
-    )
+    let q0 = q0.into();
+    let q1 = q1.into();
+    assert_distinct_qubits("RZZ", [q0.0, q1.0]);
+    UnitaryRep::rotation(RotationType::RZZ, angle, smallvec::smallvec![q0.0, q1.0])
 }
 
 /// RZZ rotations on multiple qubit pairs.
@@ -3004,9 +3065,7 @@ pub fn RZZ(angle: Angle64, q0: impl Into<QubitId>, q1: impl Into<QubitId>) -> Un
 #[must_use]
 #[allow(non_snake_case)]
 pub fn RZZs(angle: Angle64, pairs: impl Into<QubitPairs>) -> UnitaryRep {
-    pairs
-        .into()
-        .apply(|q0, q1| UnitaryRep::rotation(RotationType::RZZ, angle, smallvec::smallvec![q0, q1]))
+    pairs.into().apply(|q0, q1| RZZ(angle, q0, q1))
 }
 
 // --- Gate constructors - Named single-qubit Cliffords ---
@@ -3190,10 +3249,10 @@ pub fn Hs(qubits: impl Into<Qubits>) -> UnitaryRep {
 #[must_use]
 #[allow(non_snake_case)]
 pub fn CX(control: impl Into<QubitId>, target: impl Into<QubitId>) -> UnitaryRep {
-    UnitaryRep::gate(
-        GateType::CX,
-        smallvec::smallvec![control.into().0, target.into().0],
-    )
+    let control = control.into();
+    let target = target.into();
+    assert_distinct_qubits("CX", [control.0, target.0]);
+    UnitaryRep::gate(GateType::CX, smallvec::smallvec![control.0, target.0])
 }
 
 /// CX gates on multiple qubit pairs.
@@ -3202,9 +3261,7 @@ pub fn CX(control: impl Into<QubitId>, target: impl Into<QubitId>) -> UnitaryRep
 #[must_use]
 #[allow(non_snake_case)]
 pub fn CXs(pairs: impl Into<QubitPairs>) -> UnitaryRep {
-    pairs
-        .into()
-        .apply(|ctrl, tgt| UnitaryRep::gate(GateType::CX, smallvec::smallvec![ctrl, tgt]))
+    pairs.into().apply(CX)
 }
 
 /// Controlled-Y gate.
@@ -3213,10 +3270,10 @@ pub fn CXs(pairs: impl Into<QubitPairs>) -> UnitaryRep {
 #[must_use]
 #[allow(non_snake_case)]
 pub fn CY(control: impl Into<QubitId>, target: impl Into<QubitId>) -> UnitaryRep {
-    UnitaryRep::gate(
-        GateType::CY,
-        smallvec::smallvec![control.into().0, target.into().0],
-    )
+    let control = control.into();
+    let target = target.into();
+    assert_distinct_qubits("CY", [control.0, target.0]);
+    UnitaryRep::gate(GateType::CY, smallvec::smallvec![control.0, target.0])
 }
 
 /// CY gates on multiple qubit pairs.
@@ -3225,9 +3282,7 @@ pub fn CY(control: impl Into<QubitId>, target: impl Into<QubitId>) -> UnitaryRep
 #[must_use]
 #[allow(non_snake_case)]
 pub fn CYs(pairs: impl Into<QubitPairs>) -> UnitaryRep {
-    pairs
-        .into()
-        .apply(|ctrl, tgt| UnitaryRep::gate(GateType::CY, smallvec::smallvec![ctrl, tgt]))
+    pairs.into().apply(CY)
 }
 
 /// Controlled-Z gate.
@@ -3236,7 +3291,10 @@ pub fn CYs(pairs: impl Into<QubitPairs>) -> UnitaryRep {
 #[must_use]
 #[allow(non_snake_case)]
 pub fn CZ(q0: impl Into<QubitId>, q1: impl Into<QubitId>) -> UnitaryRep {
-    UnitaryRep::gate(GateType::CZ, smallvec::smallvec![q0.into().0, q1.into().0])
+    let q0 = q0.into();
+    let q1 = q1.into();
+    assert_distinct_qubits("CZ", [q0.0, q1.0]);
+    UnitaryRep::gate(GateType::CZ, smallvec::smallvec![q0.0, q1.0])
 }
 
 /// CZ gates on multiple qubit pairs.
@@ -3245,9 +3303,7 @@ pub fn CZ(q0: impl Into<QubitId>, q1: impl Into<QubitId>) -> UnitaryRep {
 #[must_use]
 #[allow(non_snake_case)]
 pub fn CZs(pairs: impl Into<QubitPairs>) -> UnitaryRep {
-    pairs
-        .into()
-        .apply(|q0, q1| UnitaryRep::gate(GateType::CZ, smallvec::smallvec![q0, q1]))
+    pairs.into().apply(CZ)
 }
 
 /// SWAP gate.
@@ -3256,10 +3312,10 @@ pub fn CZs(pairs: impl Into<QubitPairs>) -> UnitaryRep {
 #[must_use]
 #[allow(non_snake_case)]
 pub fn SWAP(q0: impl Into<QubitId>, q1: impl Into<QubitId>) -> UnitaryRep {
-    UnitaryRep::gate(
-        GateType::SWAP,
-        smallvec::smallvec![q0.into().0, q1.into().0],
-    )
+    let q0 = q0.into();
+    let q1 = q1.into();
+    assert_distinct_qubits("SWAP", [q0.0, q1.0]);
+    UnitaryRep::gate(GateType::SWAP, smallvec::smallvec![q0.0, q1.0])
 }
 
 /// SWAP gates on multiple qubit pairs.
@@ -3268,9 +3324,7 @@ pub fn SWAP(q0: impl Into<QubitId>, q1: impl Into<QubitId>) -> UnitaryRep {
 #[must_use]
 #[allow(non_snake_case)]
 pub fn SWAPs(pairs: impl Into<QubitPairs>) -> UnitaryRep {
-    pairs
-        .into()
-        .apply(|q0, q1| UnitaryRep::gate(GateType::SWAP, smallvec::smallvec![q0, q1]))
+    pairs.into().apply(SWAP)
 }
 
 /// SZZ gate: RZZ(π/2)
@@ -3279,10 +3333,13 @@ pub fn SWAPs(pairs: impl Into<QubitPairs>) -> UnitaryRep {
 #[must_use]
 #[allow(non_snake_case)]
 pub fn SZZ(q0: impl Into<QubitId>, q1: impl Into<QubitId>) -> UnitaryRep {
+    let q0 = q0.into();
+    let q1 = q1.into();
+    assert_distinct_qubits("SZZ", [q0.0, q1.0]);
     UnitaryRep::rotation(
         RotationType::RZZ,
         Angle64::QUARTER_TURN,
-        smallvec::smallvec![q0.into().0, q1.into().0],
+        smallvec::smallvec![q0.0, q1.0],
     )
 }
 
@@ -3292,13 +3349,7 @@ pub fn SZZ(q0: impl Into<QubitId>, q1: impl Into<QubitId>) -> UnitaryRep {
 #[must_use]
 #[allow(non_snake_case)]
 pub fn SZZs(pairs: impl Into<QubitPairs>) -> UnitaryRep {
-    pairs.into().apply(|q0, q1| {
-        UnitaryRep::rotation(
-            RotationType::RZZ,
-            Angle64::QUARTER_TURN,
-            smallvec::smallvec![q0, q1],
-        )
-    })
+    pairs.into().apply(SZZ)
 }
 
 // --- Gate constructors - Three-qubit gates ---
@@ -3311,19 +3362,25 @@ pub fn CCX(
     c1: impl Into<QubitId>,
     target: impl Into<QubitId>,
 ) -> UnitaryRep {
-    UnitaryRep::gate(
-        GateType::CCX,
-        smallvec::smallvec![c0.into().0, c1.into().0, target.into().0],
-    )
+    let c0 = c0.into();
+    let c1 = c1.into();
+    let target = target.into();
+    assert_distinct_qubits("CCX", [c0.0, c1.0, target.0]);
+    UnitaryRep::gate(GateType::CCX, smallvec::smallvec![c0.0, c1.0, target.0])
 }
 
 // --- UnitaryRep implementations ---
 
-// Tensor product: &
 impl BitAnd for UnitaryRep {
     type Output = UnitaryRep;
 
     fn bitand(self, rhs: UnitaryRep) -> UnitaryRep {
+        let overlap = overlapping_qubits(self.qubits(), rhs.qubits());
+        assert!(
+            overlap.is_empty(),
+            "tensor product requires disjoint unitary support; overlapping qubits: {overlap:?}"
+        );
+
         match (self, rhs) {
             // Pauli & Pauli: use PauliString tensor product
             (UnitaryRep::Pauli(a), UnitaryRep::Pauli(b)) => UnitaryRep::Pauli(a & b),
@@ -3653,6 +3710,12 @@ mod tests {
         assert!(matches!(mixed, UnitaryRep::Tensor(_)));
     }
 
+    #[test]
+    #[should_panic(expected = "tensor product requires disjoint unitary support")]
+    fn test_tensor_product_rejects_overlapping_qubits() {
+        let _ = X(0) & H(0);
+    }
+
     #[test]
     fn test_composition() {
         let circuit = T(0) * H(0);
@@ -3671,6 +3734,22 @@ mod tests {
         assert!(cz.is_clifford());
     }
 
+    #[test]
+    #[should_panic(expected = "CX requires 2 qubit(s), got 1")]
+    fn test_low_level_gate_constructor_rejects_wrong_arity() {
+        let _ = UnitaryRep::gate(GateType::CX, smallvec::smallvec![0]);
+    }
+
+    #[test]
+    #[should_panic(expected = "RXX requires 2 qubit(s), got 1")]
+    fn test_low_level_rotation_constructor_rejects_wrong_arity() {
+        let _ = UnitaryRep::rotation(
+            RotationType::RXX,
+            Angle64::QUARTER_TURN,
+            smallvec::smallvec![0],
+        );
+    }
+
     #[test]
     fn test_adjoint() {
         let t = T(0);
@@ -4218,6 +4297,28 @@ mod tests {
         }
     }
 
+    #[test]
+    fn test_try_to_pauli_string_zero_rotation_is_identity() {
+        for unitary in [
+            I(0),
+            RX(Angle64::ZERO, 0),
+            RY(Angle64::ZERO, 1),
+            RZ(Angle64::ZERO, 2),
+        ] {
+            let ps = unitary
+                .try_to_pauli_string()
+                .expect("zero rotation should convert to identity Pauli");
+            assert_eq!(ps.weight(), 0);
+        }
+    }
+
+    #[test]
+    fn test_try_to_pauli_string_rejects_overlapping_tensor_node() {
+        let invalid_tensor = UnitaryRep::Tensor(vec![X(0), Z(0)]);
+
+        assert!(invalid_tensor.try_to_pauli_string().is_none());
+    }
+
     #[test]
     fn test_try_to_pauli_non_pauli() {
         // Quarter-turn rotations should not convert
@@ -4354,6 +4455,100 @@ mod tests {
         let _ = Zs(1..=0);
     }
 
+    #[test]
+    #[should_panic(expected = "tensor product requires disjoint unitary support")]
+    fn test_plural_single_qubit_tensor_rejects_duplicate_qubits() {
+        let _ = Hs([0, 0]);
+    }
+
+    #[test]
+    #[should_panic(expected = "tensor product requires disjoint unitary support")]
+    fn test_plural_two_qubit_tensor_rejects_overlapping_pairs() {
+        let _ = CXs([(0, 1), (1, 2)]);
+    }
+
+    #[test]
+    #[should_panic(expected = "CX requires distinct qubits")]
+    fn test_two_qubit_gate_rejects_repeated_qubit() {
+        let _ = CX(0, 0);
+    }
+
+    #[test]
+    #[should_panic(expected = "RZZ requires distinct qubits")]
+    fn test_two_qubit_rotation_rejects_repeated_qubit() {
+        let _ = RZZ(Angle64::QUARTER_TURN, 1, 1);
+    }
+
+    #[test]
+    #[should_panic(expected = "CCX requires distinct qubits")]
+    fn test_three_qubit_gate_rejects_repeated_qubit() {
+        let _ = CCX(0, 1, 1);
+    }
+
+    #[test]
+    #[should_panic(expected = "CX requires distinct qubits")]
+    fn test_low_level_gate_constructor_rejects_repeated_qubit() {
+        let _ = UnitaryRep::gate(GateType::CX, smallvec::smallvec![0, 0]);
+    }
+
+    #[test]
+    #[should_panic(expected = "RXX requires distinct qubits")]
+    fn test_low_level_rotation_constructor_rejects_repeated_qubit() {
+        let _ = UnitaryRep::rotation(
+            RotationType::RXX,
+            Angle64::QUARTER_TURN,
+            smallvec::smallvec![2, 2],
+        );
+    }
+
+    #[test]
+    fn test_plural_helpers_match_chained_tensor_forms() {
+        assert_eq!(Xs([0, 2, 5]), X(0) & X(2) & X(5));
+        assert_eq!(Ys([0, 2, 5]), Y(0) & Y(2) & Y(5));
+        assert_eq!(Zs([0, 2, 5]), Z(0) & Z(2) & Z(5));
+        assert_eq!(Ts([0, 1, 2]), T(0) & T(1) & T(2));
+        assert_eq!(CXs([(0, 1), (2, 3)]), CX(0, 1) & CX(2, 3));
+        assert_eq!(CZs([(0, 1), (2, 3)]), CZ(0, 1) & CZ(2, 3));
+        assert_eq!(SWAPs([(0, 1), (2, 3)]), SWAP(0, 1) & SWAP(2, 3));
+        assert_eq!(SZZs([(0, 1), (2, 3)]), SZZ(0, 1) & SZZ(2, 3));
+        assert_eq!(
+            RZZs(Angle64::QUARTER_TURN, [(0, 1), (2, 3)]),
+            RZZ(Angle64::QUARTER_TURN, 0, 1) & RZZ(Angle64::QUARTER_TURN, 2, 3)
+        );
+    }
+
+    #[test]
+    fn test_plural_helpers_reject_duplicate_and_overlapping_supports() {
+        fn assert_tensor_overlap_panic(f: impl FnOnce() + std::panic::UnwindSafe) {
+            let err = std::panic::catch_unwind(f).expect_err("expected tensor overlap panic");
+            let message = err
+                .downcast_ref::<String>()
+                .map(String::as_str)
+                .or_else(|| err.downcast_ref::<&str>().copied())
+                .unwrap_or("<non-string panic>");
+            assert!(
+                message.contains("tensor product requires disjoint"),
+                "unexpected panic message: {message}"
+            );
+        }
+
+        assert_tensor_overlap_panic(|| {
+            let _ = Xs([0, 0]);
+        });
+        assert_tensor_overlap_panic(|| {
+            let _ = Ts([1, 1]);
+        });
+        assert_tensor_overlap_panic(|| {
+            let _ = SWAPs([(0, 1), (1, 2)]);
+        });
+        assert_tensor_overlap_panic(|| {
+            let _ = SZZs([(0, 2), (2, 3)]);
+        });
+        assert_tensor_overlap_panic(|| {
+            let _ = RZZs(Angle64::QUARTER_TURN, [(0, 2), (2, 3)]);
+        });
+    }
+
     #[test]
     fn test_single_element_range() {
         // Xs(0..1) should be equivalent to X(0)
@@ -5171,6 +5366,27 @@ mod tests {
         assert!("CCX 0 1".parse::<UnitaryRep>().is_err());
     }
 
+    #[test]
+    fn from_str_rejects_repeated_multi_qubit_gate_args() {
+        for (text, expected) in [
+            ("CX 0 0", "CX requires distinct qubits"),
+            ("CY 0 0", "CY requires distinct qubits"),
+            ("CH 0 0", "CH requires distinct qubits"),
+            ("SWAP 2 2", "SWAP requires distinct qubits"),
+            ("RXX(pi/2) 1 1", "RXX requires distinct qubits"),
+            ("RYY(pi/2) 1 1", "RYY requires distinct qubits"),
+            ("RZZ(pi/2) 1 1", "RZZ requires distinct qubits"),
+            ("CCX 0 1 0", "CCX requires distinct qubits"),
+            ("TOFFOLI 0 0 1", "TOFFOLI requires distinct qubits"),
+        ] {
+            let err = text.parse::<UnitaryRep>().unwrap_err();
+            assert!(
+                err.message.contains(expected),
+                "{text} produced unexpected error: {err}"
+            );
+        }
+    }
+
     #[test]
     fn from_str_case_insensitive() {
         assert!("h 0".parse::<UnitaryRep>().is_ok());
diff --git a/crates/pecos-cuquantum-sys/Cargo.toml b/crates/pecos-cuquantum-sys/Cargo.toml
index 4c22c8171..a1b3dc4cd 100644
--- a/crates/pecos-cuquantum-sys/Cargo.toml
+++ b/crates/pecos-cuquantum-sys/Cargo.toml
@@ -26,8 +26,6 @@ env_logger.workspace = true
 
 [features]
 default = []
-# Generate bindings at build time (requires cuQuantum headers)
-runtime-bindgen = []
 
 [package.metadata.docs.rs]
 # Don't try to build docs on docs.rs (no CUDA/cuQuantum available)
diff --git a/crates/pecos-cuquantum/src/lib.rs b/crates/pecos-cuquantum/src/lib.rs
index 2cf231b17..7d54f46e6 100644
--- a/crates/pecos-cuquantum/src/lib.rs
+++ b/crates/pecos-cuquantum/src/lib.rs
@@ -89,6 +89,43 @@ pub fn is_cuquantum_available() -> bool {
     pecos_cuquantum_sys::is_available()
 }
 
+/// Check if the cuStateVec backend can create a simulator on this machine.
+///
+/// This is stricter than [`is_cuquantum_available`]: it verifies not only that
+/// cuQuantum libraries can be loaded, but also that a CUDA device/runtime can
+/// initialize the cuStateVec handle and allocate a minimal state vector.
+#[must_use]
+pub fn is_custatevec_usable() -> bool {
+    CuStateVec::new(1).is_ok()
+}
+
+/// Check if the cuStabilizer backend can create a frame simulator.
+///
+/// This is stricter than [`is_cuquantum_available`] and catches environments
+/// where the libraries are present but the CUDA runtime cannot initialize.
+#[must_use]
+pub fn is_custabilizer_usable() -> bool {
+    CuFrameSimulator::new(1, 1, 1).is_ok()
+}
+
+/// Check if the cuTensorNet backend can create a handle.
+///
+/// This is stricter than [`is_cuquantum_available`] and catches environments
+/// where the libraries are present but the CUDA runtime cannot initialize.
+#[must_use]
+pub fn is_cutensornet_usable() -> bool {
+    CuTensorNet::new().is_ok()
+}
+
+/// Check if the cuDensityMat backend can create a simulator on this machine.
+///
+/// This is stricter than [`is_cuquantum_available`] and catches environments
+/// where the libraries are present but the CUDA runtime cannot initialize.
+#[must_use]
+pub fn is_cudensitymat_usable() -> bool {
+    CuDensityMat::new(1).is_ok()
+}
+
 #[cfg(test)]
 mod tests {
     use super::*;
diff --git a/crates/pecos-decoder-core/Cargo.toml b/crates/pecos-decoder-core/Cargo.toml
index e165df193..0b1031d92 100644
--- a/crates/pecos-decoder-core/Cargo.toml
+++ b/crates/pecos-decoder-core/Cargo.toml
@@ -15,6 +15,8 @@ description = "Core traits and utilities for PECOS decoders"
 ndarray.workspace = true
 thiserror.workspace = true
 anyhow.workspace = true
+pecos-random.workspace = true
+rayon.workspace = true
 
 [lints]
 workspace = true
diff --git a/crates/pecos-decoder-core/src/adaptive.rs b/crates/pecos-decoder-core/src/adaptive.rs
new file mode 100644
index 000000000..c05d5cc18
--- /dev/null
+++ b/crates/pecos-decoder-core/src/adaptive.rs
@@ -0,0 +1,185 @@
+// Copyright 2026 The PECOS Developers
+//
+// Licensed under the Apache License, Version 2.0 (the "License"); you may not use this file except
+// in compliance with the License. You may obtain a copy of the License at
+//
+//     https://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software distributed under the License
+// is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express
+// or implied. See the License for the specific language governing permissions and limitations under
+// the License.
+
+//! Adaptive decoder wrapper for time-varying noise.
+//!
+//! Wraps any `ObservableDecoder` with automatic rebuilding when the
+//! noise model changes. The decoder factory is called with a new DEM
+//! whenever `update_noise` is invoked.
+//!
+//! Use cases:
+//! - Neutral atoms: noise drifts on hour timescales (calibration drift)
+//! - Trapped ions: slow parameter drift between recalibrations
+//! - Any platform where the DEM becomes stale
+
+use crate::ObservableDecoder;
+use crate::errors::DecoderError;
+
+type DecoderFactory = dyn FnMut(&str) -> Result<Box<dyn ObservableDecoder>, DecoderError>;
+
+fn fraction(numerator: usize, denominator: usize) -> f64 {
+    let numerator = u32::try_from(numerator).expect("monitoring count fits in u32");
+    let denominator = u32::try_from(denominator).expect("monitoring window fits in u32");
+    f64::from(numerator) / f64::from(denominator)
+}
+
+/// Adaptive decoder that rebuilds when noise changes.
+///
+/// Holds a decoder factory and the current DEM. When `update_dem` is
+/// called with a new DEM string, the decoder is rebuilt transparently.
+pub struct AdaptiveDecoder {
+    decoder: Box<dyn ObservableDecoder>,
+    factory: Box<DecoderFactory>,
+    current_dem: String,
+    rebuild_count: usize,
+    /// Calibration monitoring: recent outcomes (true = logical error).
+    recent_outcomes: std::collections::VecDeque<bool>,
+    /// Size of the monitoring window.
+    monitoring_window: usize,
+    /// Error rate threshold above which recalibration is recommended.
+    recalibration_threshold: f64,
+}
+
+impl AdaptiveDecoder {
+    /// Create from a DEM string and factory.
+    ///
+    /// # Errors
+    ///
+    /// Returns `DecoderError` if the factory fails.
+    pub fn new<F>(dem: &str, mut factory: F) -> Result<Self, DecoderError>
+    where
+        F: FnMut(&str) -> Result<Box<dyn ObservableDecoder>, DecoderError> + 'static,
+    {
+        let decoder = factory(dem)?;
+        Ok(Self {
+            decoder,
+            factory: Box::new(factory),
+            current_dem: dem.to_string(),
+            rebuild_count: 0,
+            recent_outcomes: std::collections::VecDeque::new(),
+            monitoring_window: 1000,
+            recalibration_threshold: 0.1,
+        })
+    }
+
+    /// Update the DEM and rebuild the decoder.
+    ///
+    /// # Errors
+    ///
+    /// Returns `DecoderError` if the factory fails on the new DEM.
+    pub fn update_dem(&mut self, new_dem: &str) -> Result<(), DecoderError> {
+        self.decoder = (self.factory)(new_dem)?;
+        self.current_dem = new_dem.to_string();
+        self.rebuild_count += 1;
+        Ok(())
+    }
+
+    /// Number of times the decoder has been rebuilt.
+    #[must_use]
+    pub fn rebuild_count(&self) -> usize {
+        self.rebuild_count
+    }
+
+    /// The current DEM string.
+    #[must_use]
+    pub fn current_dem(&self) -> &str {
+        &self.current_dem
+    }
+
+    /// Report a logical outcome for calibration monitoring.
+    ///
+    /// `was_logical_error`: true if this QEC cycle resulted in a logical error.
+    /// The adaptive decoder tracks recent error rate and signals when
+    /// recalibration may be needed (noise model drift).
+    pub fn report_outcome(&mut self, was_logical_error: bool) {
+        self.recent_outcomes.push_back(was_logical_error);
+        if self.recent_outcomes.len() > self.monitoring_window {
+            self.recent_outcomes.pop_front();
+        }
+    }
+
+    /// Check if recalibration is recommended.
+    ///
+    /// Returns true if the recent error rate exceeds `recalibration_threshold`.
+    /// This suggests the noise model has drifted and the DEM should be regenerated.
+    #[must_use]
+    pub fn should_recalibrate(&self) -> bool {
+        if self.recent_outcomes.len() < self.monitoring_window / 2 {
+            return false; // Not enough data
+        }
+        let errors = self.recent_outcomes.iter().filter(|&&e| e).count();
+        let rate = fraction(errors, self.recent_outcomes.len());
+        rate > self.recalibration_threshold
+    }
+
+    /// Recent logical error rate from monitoring window.
+    #[must_use]
+    pub fn recent_error_rate(&self) -> f64 {
+        if self.recent_outcomes.is_empty() {
+            return 0.0;
+        }
+        let errors = self.recent_outcomes.iter().filter(|&&e| e).count();
+        fraction(errors, self.recent_outcomes.len())
+    }
+
+    /// Set the monitoring window size and recalibration threshold.
+    pub fn set_monitoring(&mut self, window: usize, threshold: f64) {
+        self.monitoring_window = window;
+        self.recalibration_threshold = threshold;
+    }
+}
+
+impl ObservableDecoder for AdaptiveDecoder {
+    fn decode_to_observables(&mut self, syndrome: &[u8]) -> Result<u64, DecoderError> {
+        self.decoder.decode_to_observables(syndrome)
+    }
+}
+
+#[cfg(test)]
+mod tests {
+    use super::*;
+
+    #[test]
+    fn test_adaptive_decode() {
+        let dec = AdaptiveDecoder::new("error(0.1) D0\n", |_dem| {
+            struct Zero;
+            impl ObservableDecoder for Zero {
+                fn decode_to_observables(&mut self, _: &[u8]) -> Result<u64, DecoderError> {
+                    Ok(0)
+                }
+            }
+            Ok(Box::new(Zero))
+        });
+        assert!(dec.is_ok());
+        let mut dec = dec.unwrap();
+        assert_eq!(dec.decode_to_observables(&[0]).unwrap(), 0);
+        assert_eq!(dec.rebuild_count(), 0);
+    }
+
+    #[test]
+    fn test_adaptive_update() {
+        let mut dec = AdaptiveDecoder::new("error(0.1) D0\n", |_dem| {
+            struct Zero;
+            impl ObservableDecoder for Zero {
+                fn decode_to_observables(&mut self, _: &[u8]) -> Result<u64, DecoderError> {
+                    Ok(0)
+                }
+            }
+            Ok(Box::new(Zero))
+        })
+        .unwrap();
+
+        dec.update_dem("error(0.2) D0\n").unwrap();
+        assert_eq!(dec.rebuild_count(), 1);
+        assert_eq!(dec.current_dem(), "error(0.2) D0\n");
+    }
+}
diff --git a/crates/pecos-decoder-core/src/bp_matching.rs b/crates/pecos-decoder-core/src/bp_matching.rs
new file mode 100644
index 000000000..7e8f6477f
--- /dev/null
+++ b/crates/pecos-decoder-core/src/bp_matching.rs
@@ -0,0 +1,127 @@
+// Copyright 2026 The PECOS Developers
+//
+// Licensed under the Apache License, Version 2.0 (the "License"); you may not use this file except
+// in compliance with the License. You may obtain a copy of the License at
+//
+//     https://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software distributed under the License
+// is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express
+// or implied. See the License for the specific language governing permissions and limitations under
+// the License.
+
+//! Belief-matching: BP soft info → reweighted matching decoder.
+//!
+//! Wraps any `MatchingDecoder` with BP-computed edge weights.
+//! The BP posteriors are computed by an external `BpWeightProvider`,
+//! then fed to the matching decoder via `decode_with_weights`.
+//!
+//! This achieves belief-matching (Higgott 2022) with any matching backend:
+//! - Fusion Blossom (MWPM, ~0.94% threshold)
+//! - UF (already in BP+UF, ~0.5% threshold)
+//! - `PyMatching` (if it had dynamic weights)
+
+use crate::correlated_decoder::MatchingDecoder;
+use crate::correlation_table::CorrelationTable;
+use crate::errors::DecoderError;
+
+/// Trait for providing BP-adjusted weights per syndrome.
+pub trait BpWeightProvider {
+    /// Compute BP-adjusted matching graph edge weights for a syndrome.
+    /// Returns one weight per matching graph edge.
+    fn compute_weights(&mut self, syndrome: &[u8]) -> Vec<f64>;
+
+    /// Number of matching graph edges.
+    fn num_edges(&self) -> usize;
+
+    /// Check if this syndrome is trivial (predecoder can handle it).
+    fn is_trivial(&self, syndrome: &[u8]) -> Option<u64>;
+}
+
+/// Belief-matching decoder: BP weights → matching decoder.
+///
+/// Optionally performs a second pass with correlation table adjustment
+/// (correlated belief-matching) for exploiting X-Z cross-lattice correlations.
+pub struct BpMatchingDecoder<M: MatchingDecoder, B: BpWeightProvider> {
+    matching: M,
+    bp: B,
+    /// Optional correlation table for two-pass correlated decoding.
+    correlation: Option<CorrelationTable>,
+    /// Reusable buffer for adjusted weights in the second pass.
+    adjusted_weights: Vec<f64>,
+}
+
+impl<M: MatchingDecoder, B: BpWeightProvider> BpMatchingDecoder<M, B> {
+    /// Create a single-pass belief-matching decoder.
+    pub fn new(matching: M, bp: B) -> Self {
+        let n = bp.num_edges();
+        Self {
+            matching,
+            bp,
+            correlation: None,
+            adjusted_weights: vec![0.0; n],
+        }
+    }
+
+    /// Create a two-pass correlated belief-matching decoder.
+    ///
+    /// First pass: BP weights → MWPM → matched edges.
+    /// Second pass: correlation table adjusts weights → MWPM again.
+    pub fn with_correlations(matching: M, bp: B, correlation: CorrelationTable) -> Self {
+        let n = bp.num_edges();
+        Self {
+            matching,
+            bp,
+            correlation: Some(correlation),
+            adjusted_weights: vec![0.0; n],
+        }
+    }
+}
+
+impl<M: MatchingDecoder, B: BpWeightProvider> crate::ObservableDecoder for BpMatchingDecoder<M, B> {
+    fn decode_to_observables(&mut self, syndrome: &[u8]) -> Result<u64, DecoderError> {
+        // Predecoder fast path: only for zero-defect syndromes.
+        // At d>=5, always use full MWPM (predecoder can be suboptimal).
+        // At d=3, BP + predecoder is actually better than MWPM for simple
+        // syndromes, but we can't easily detect d here. So we skip the
+        // predecoder and let MWPM handle everything for consistency.
+        let num_defects = syndrome.iter().filter(|&&v| v != 0).count();
+        if num_defects == 0 {
+            return Ok(0);
+        }
+
+        // Compute BP-adjusted weights.
+        let bp_weights = self.bp.compute_weights(syndrome);
+
+        if let Some(corr) = &self.correlation
+            && corr.has_correlations()
+        {
+            // Two-pass correlated belief-matching.
+
+            // First pass: decode with BP weights to get matched edges.
+            let (_, matched_edges) = self.matching.decode_with_weights(syndrome, &bp_weights)?;
+
+            // Apply correlation adjustments to BP weights.
+            self.adjusted_weights.copy_from_slice(&bp_weights);
+            for &edge_idx in &matched_edges {
+                if edge_idx < corr.implied_weights.len() {
+                    for iw in &corr.implied_weights[edge_idx] {
+                        if iw.conditional_weight < self.adjusted_weights[iw.target_edge_idx] {
+                            self.adjusted_weights[iw.target_edge_idx] = iw.conditional_weight;
+                        }
+                    }
+                }
+            }
+
+            // Second pass: decode with correlation-adjusted weights.
+            let (obs, _) = self
+                .matching
+                .decode_with_weights(syndrome, &self.adjusted_weights)?;
+            return Ok(obs);
+        }
+
+        // Single-pass belief-matching.
+        let (obs, _) = self.matching.decode_with_weights(syndrome, &bp_weights)?;
+        Ok(obs)
+    }
+}
diff --git a/crates/pecos-decoder-core/src/committed_osd.rs b/crates/pecos-decoder-core/src/committed_osd.rs
new file mode 100644
index 000000000..8157cd6a8
--- /dev/null
+++ b/crates/pecos-decoder-core/src/committed_osd.rs
@@ -0,0 +1,175 @@
+// Copyright 2026 The PECOS Developers
+//
+// Licensed under the Apache License, Version 2.0 (the "License"); you may not use this file except
+// in compliance with the License. You may obtain a copy of the License at
+//
+//     https://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software distributed under the License
+// is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express
+// or implied. See the License for the specific language governing permissions and limitations under
+// the License.
+
+//! OSD with software commitment for streaming decoding.
+//!
+//! Wraps an `ObservableSubgraphDecoder` with per-detector commitment
+//! tracking. Committed detectors are masked during future decodes,
+//! implementing the "software commitment" concept from Cain et al.
+//! (arXiv:2505.13587).
+//!
+//! This enables streaming: decode a region, commit it, decode the next
+//! region. Only uncommitted detectors participate in matching.
+
+use crate::ObservableDecoder;
+use crate::decode_budget::{DecodeStrategy, DetectorRegion};
+use crate::errors::DecoderError;
+use crate::observable_subgraph::ObservableSubgraphDecoder;
+
+/// Observable subgraph decoder with software commitment.
+///
+/// After decoding a region, call `commit_range()` to mark those
+/// detectors as finalized. Future decodes will mask committed
+/// detectors (treat as syndrome=0), preventing re-matching of
+/// already-corrected errors.
+///
+/// The total correction is `committed_obs ^ active_obs`: the XOR
+/// of committed corrections and the latest active decode.
+pub struct CommittedOsdDecoder {
+    /// The underlying OSD (unchanged).
+    inner: ObservableSubgraphDecoder,
+    /// Per-detector commitment state. True = committed.
+    committed: Vec<bool>,
+    /// Accumulated observable correction from committed regions.
+    committed_obs: u64,
+    /// Total number of detectors.
+    num_detectors: usize,
+    /// Reusable masked syndrome buffer.
+    masked_syndrome: Vec<u8>,
+}
+
+impl CommittedOsdDecoder {
+    /// Wrap an existing OSD with commitment tracking.
+    #[must_use]
+    pub fn new(inner: ObservableSubgraphDecoder, num_detectors: usize) -> Self {
+        Self {
+            inner,
+            committed: vec![false; num_detectors],
+            committed_obs: 0,
+            num_detectors,
+            masked_syndrome: vec![0u8; num_detectors],
+        }
+    }
+
+    /// Decode only uncommitted detectors.
+    ///
+    /// Committed detectors are masked to 0 before passing to the
+    /// inner OSD. Returns the correction for the active (uncommitted)
+    /// region.
+    pub fn decode_active(&mut self, syndrome: &[u8]) -> Result<u64, DecoderError> {
+        // Build masked syndrome: zero out committed detectors
+        let len = syndrome.len().min(self.num_detectors);
+        self.masked_syndrome[..len].copy_from_slice(&syndrome[..len]);
+        for i in 0..len {
+            if self.committed[i] {
+                self.masked_syndrome[i] = 0;
+            }
+        }
+        self.inner
+            .decode_to_observables(&self.masked_syndrome[..len])
+    }
+
+    /// Mark detectors in [start, end) as committed.
+    ///
+    /// Before committing, decodes the full syndrome to get the
+    /// correction that includes the about-to-be-committed region.
+    /// The committed correction is stored for accumulation.
+    pub fn commit_range(
+        &mut self,
+        syndrome: &[u8],
+        region: &DetectorRegion,
+    ) -> Result<u64, DecoderError> {
+        // Decode with current syndrome (including uncommitted detectors)
+        let obs = self.decode_active(syndrome)?;
+
+        // Mark detectors as committed
+        for i in region.start..region.end.min(self.num_detectors) {
+            self.committed[i] = true;
+        }
+
+        // Accumulate the correction
+        self.committed_obs ^= obs;
+        Ok(obs)
+    }
+
+    /// Total correction: committed + latest active.
+    ///
+    /// Call `decode_active` first to get the active correction,
+    /// then XOR with `committed_obs` for the full correction.
+    #[must_use]
+    pub fn committed_obs(&self) -> u64 {
+        self.committed_obs
+    }
+
+    /// Number of committed detectors.
+    #[must_use]
+    pub fn num_committed(&self) -> usize {
+        self.committed.iter().filter(|&&c| c).count()
+    }
+
+    /// Reset all commitment state for the next shot.
+    pub fn reset(&mut self) {
+        self.committed.fill(false);
+        self.committed_obs = 0;
+    }
+}
+
+impl ObservableDecoder for CommittedOsdDecoder {
+    fn decode_to_observables(&mut self, syndrome: &[u8]) -> Result<u64, DecoderError> {
+        // Full decode: committed XOR active
+        let active = self.decode_active(syndrome)?;
+        Ok(self.committed_obs ^ active)
+    }
+}
+
+impl DecodeStrategy for CommittedOsdDecoder {
+    fn decode(&mut self, syndrome: &[u8]) -> Result<u64, DecoderError> {
+        self.decode_active(syndrome)
+    }
+
+    fn commit(&mut self, region: &DetectorRegion) -> Result<u64, DecoderError> {
+        // Commit with zeros — the actual syndrome was already decoded
+        // via decode(). Just mark the region.
+        for i in region.start..region.end.min(self.num_detectors) {
+            self.committed[i] = true;
+        }
+        Ok(self.committed_obs)
+    }
+
+    fn committed_obs(&self) -> u64 {
+        self.committed_obs
+    }
+
+    fn reset(&mut self) {
+        CommittedOsdDecoder::reset(self);
+    }
+}
+
+#[cfg(test)]
+mod tests {
+    use super::*;
+
+    #[test]
+    fn test_detector_region() {
+        let r = DetectorRegion { start: 5, end: 15 };
+        assert_eq!(r.len(), 10);
+        assert!(r.contains(5));
+        assert!(!r.contains(15));
+    }
+
+    #[test]
+    fn test_decode_strategy_trait() {
+        // Verify the trait exists and has the right methods
+        // (compile-time check via trait bound)
+        fn _assert_strategy<T: DecodeStrategy>() {}
+    }
+}
diff --git a/crates/pecos-decoder-core/src/correlated_decoder.rs b/crates/pecos-decoder-core/src/correlated_decoder.rs
new file mode 100644
index 000000000..4c3f81e4c
--- /dev/null
+++ b/crates/pecos-decoder-core/src/correlated_decoder.rs
@@ -0,0 +1,243 @@
+// Copyright 2026 The PECOS Developers
+//
+// Licensed under the Apache License, Version 2.0 (the "License"); you may not use this file except
+// in compliance with the License. You may obtain a copy of the License at
+//
+//     https://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software distributed under the License
+// is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express
+// or implied. See the License for the specific language governing permissions and limitations under
+// the License.
+
+//! Two-pass correlated MWPM decoder (DGR-style).
+//!
+//! Wraps any `ObservableDecoder` that also supports a `decode_with_weights`
+//! interface. After a training phase to build correlation statistics, each
+//! shot is decoded twice:
+//!
+//! 1. First pass with alignment-corrected weights (from observed frequencies)
+//! 2. Second pass with correlation-adjusted weights (from first-pass matching)
+//!
+//! This improves accuracy by exploiting pairwise edge correlations that
+//! standard MWPM ignores.
+
+use crate::correlated_reweighting::EdgeCorrelationTracker;
+use crate::errors::DecoderError;
+
+/// Configuration for the correlated decoder.
+#[derive(Debug, Clone)]
+pub struct CorrelatedDecoderConfig {
+    /// Number of training shots before enabling correlation re-weighting.
+    /// During training, shots are decoded normally and matchings are recorded.
+    pub training_shots: usize,
+    /// Whether to use alignment re-weighting (update base weights from
+    /// observed edge frequencies).
+    pub use_alignment: bool,
+    /// Whether to use correlation re-weighting (per-shot two-pass decode).
+    pub use_correlation: bool,
+}
+
+impl Default for CorrelatedDecoderConfig {
+    fn default() -> Self {
+        Self {
+            training_shots: 1000,
+            use_alignment: true,
+            use_correlation: true,
+        }
+    }
+}
+
+/// Trait for decoders that can report which edges were matched.
+///
+/// This is needed for the correlation tracker to build statistics.
+/// The decoder must return both the observable mask and the matched edge
+/// indices from each decode.
+pub trait MatchingDecoder {
+    /// Decode a syndrome and return (`observable_mask`, `matched_edge_indices`).
+    fn decode_with_matching(&mut self, syndrome: &[u8]) -> Result<(u64, Vec<usize>), DecoderError>;
+
+    /// Decode with adjusted per-edge weights.
+    /// The weights slice has one entry per edge in the matching graph.
+    fn decode_with_weights(
+        &mut self,
+        syndrome: &[u8],
+        weights: &[f64],
+    ) -> Result<(u64, Vec<usize>), DecoderError>;
+
+    /// Number of edges in the matching graph.
+    fn num_edges(&self) -> usize;
+}
+
+/// Extension of `MatchingDecoder` that exposes per-edge metadata.
+///
+/// Used by overlapping/sandwich windowed decoders to classify matched edges
+/// as core or buffer based on endpoint locations and weight thresholds.
+pub trait EdgeTrackingDecoder: MatchingDecoder {
+    /// First endpoint node index of the given edge.
+    fn edge_node1(&self, edge_idx: usize) -> u32;
+
+    /// Second endpoint node index. Boundary nodes have index >= `num_detectors()`.
+    fn edge_node2(&self, edge_idx: usize) -> u32;
+
+    /// Log-likelihood weight of the given edge.
+    fn edge_weight(&self, edge_idx: usize) -> f64;
+
+    /// Observable bitmask for the given edge.
+    fn edge_obs_mask(&self, edge_idx: usize) -> u64;
+
+    /// Number of detector nodes (not counting boundary/virtual nodes).
+    fn num_detectors(&self) -> usize;
+}
+
+/// Two-pass correlated MWPM decoder.
+///
+/// Wraps a `MatchingDecoder` with DGR-style correlation tracking and
+/// re-weighting. Transparent to the `ObservableDecoder` interface --
+/// callers see the same API, just better accuracy.
+pub struct CorrelatedDecoder<D: MatchingDecoder> {
+    inner: D,
+    tracker: EdgeCorrelationTracker,
+    config: CorrelatedDecoderConfig,
+    shots_decoded: usize,
+    /// Base weights (from DEM, updated by alignment after training).
+    base_weights: Vec<f64>,
+    /// Buffer for matched-edge flags (avoids per-shot allocation).
+    matched_flags: Vec<bool>,
+}
+
+impl<D: MatchingDecoder> CorrelatedDecoder<D> {
+    /// Create a new correlated decoder wrapping an inner decoder.
+    pub fn new(inner: D, base_weights: Vec<f64>, config: CorrelatedDecoderConfig) -> Self {
+        let num_edges = inner.num_edges();
+        Self {
+            tracker: EdgeCorrelationTracker::new(num_edges),
+            matched_flags: vec![false; num_edges],
+            inner,
+            config,
+            shots_decoded: 0,
+            base_weights,
+        }
+    }
+
+    /// Whether the training phase is complete.
+    #[must_use]
+    pub fn is_trained(&self) -> bool {
+        self.shots_decoded >= self.config.training_shots
+    }
+
+    /// Number of training shots remaining.
+    #[must_use]
+    pub fn training_remaining(&self) -> usize {
+        self.config
+            .training_shots
+            .saturating_sub(self.shots_decoded)
+    }
+}
+
+impl<D: MatchingDecoder> crate::ObservableDecoder for CorrelatedDecoder<D> {
+    fn decode_to_observables(&mut self, syndrome: &[u8]) -> Result<u64, DecoderError> {
+        self.shots_decoded += 1;
+
+        // During training: decode normally, record matchings
+        if !self.is_trained() {
+            let (mask, matched_edges) = self.inner.decode_with_matching(syndrome)?;
+            self.tracker.record_matching(&matched_edges);
+
+            // After training is complete, update base weights from alignment
+            if self.is_trained() && self.config.use_alignment {
+                self.base_weights = self.tracker.aligned_weights();
+            }
+
+            return Ok(mask);
+        }
+
+        // After training: two-pass decode with correlation adjustment
+
+        // First pass: decode with (possibly alignment-corrected) base weights
+        let (first_mask, first_matching) = self
+            .inner
+            .decode_with_weights(syndrome, &self.base_weights)?;
+
+        // Record the matching for ongoing statistics
+        self.tracker.record_matching(&first_matching);
+
+        if !self.config.use_correlation {
+            return Ok(first_mask);
+        }
+
+        // Build matched-edge flags for correlation adjustment
+        self.matched_flags.fill(false);
+        for &e in &first_matching {
+            if e < self.matched_flags.len() {
+                self.matched_flags[e] = true;
+            }
+        }
+
+        // Compute correlation-adjusted weights
+        let adjusted_weights = self
+            .tracker
+            .correlation_adjusted_weights(&self.base_weights, &self.matched_flags);
+
+        // Second pass: re-decode with adjusted weights
+        let (second_mask, _) = self
+            .inner
+            .decode_with_weights(syndrome, &adjusted_weights)?;
+
+        Ok(second_mask)
+    }
+}
+
+#[cfg(test)]
+mod tests {
+    use super::*;
+    use crate::ObservableDecoder;
+
+    /// Simple mock decoder for testing.
+    struct MockDecoder {
+        num_edges: usize,
+    }
+
+    impl MatchingDecoder for MockDecoder {
+        fn decode_with_matching(
+            &mut self,
+            _syndrome: &[u8],
+        ) -> Result<(u64, Vec<usize>), DecoderError> {
+            Ok((0, vec![0, 2]))
+        }
+
+        fn decode_with_weights(
+            &mut self,
+            _syndrome: &[u8],
+            _weights: &[f64],
+        ) -> Result<(u64, Vec<usize>), DecoderError> {
+            Ok((0, vec![0, 2]))
+        }
+
+        fn num_edges(&self) -> usize {
+            self.num_edges
+        }
+    }
+
+    #[test]
+    fn test_training_phase() {
+        let mock = MockDecoder { num_edges: 5 };
+        let weights = vec![1.0; 5];
+        let config = CorrelatedDecoderConfig {
+            training_shots: 3,
+            ..Default::default()
+        };
+        let mut decoder = CorrelatedDecoder::new(mock, weights, config);
+
+        assert!(!decoder.is_trained());
+        assert_eq!(decoder.training_remaining(), 3);
+
+        // Decode 3 training shots
+        for _ in 0..3 {
+            let _ = decoder.decode_to_observables(&[0, 0, 0]);
+        }
+
+        assert!(decoder.is_trained());
+        assert_eq!(decoder.training_remaining(), 0);
+    }
+}
diff --git a/crates/pecos-decoder-core/src/correlated_reweighting.rs b/crates/pecos-decoder-core/src/correlated_reweighting.rs
new file mode 100644
index 000000000..edbc16633
--- /dev/null
+++ b/crates/pecos-decoder-core/src/correlated_reweighting.rs
@@ -0,0 +1,274 @@
+// Copyright 2026 The PECOS Developers
+//
+// Licensed under the Apache License, Version 2.0 (the "License"); you may not use this file except
+// in compliance with the License. You may obtain a copy of the License at
+//
+//     https://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software distributed under the License
+// is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express
+// or implied. See the License for the specific language governing permissions and limitations under
+// the License.
+
+//! Correlated edge re-weighting for MWPM decoders.
+//!
+//! Implements a simplified version of the DGR (Decoding Graph Re-weighting)
+//! scheme from arXiv:2311.16214. The key idea: after an initial MWPM decode,
+//! adjust edge weights based on pairwise correlations between edges, then
+//! re-decode with the adjusted weights.
+//!
+//! Two phases:
+//! 1. **Alignment**: track edge frequencies across shots, update weights to
+//!    match observed probabilities (corrects for DEM inaccuracies).
+//! 2. **Correlation**: for each shot, adjust weights based on which correlated
+//!    edges were/weren't in the initial matching, then re-decode.
+
+/// Tracks edge occurrence statistics for alignment and correlation re-weighting.
+pub struct EdgeCorrelationTracker {
+    /// Number of edges in the matching graph.
+    num_edges: usize,
+    /// Number of shots observed.
+    num_shots: usize,
+    /// Per-edge occurrence count (how many times edge appeared in a matching).
+    edge_counts: Vec<u64>,
+    /// Pairwise co-occurrence counts: `co_counts`[i * `num_edges` + j] = count of
+    /// edges i and j both appearing in the same matching.
+    /// Only stores upper triangle (i < j) to save memory.
+    co_counts: Vec<u64>,
+}
+
+impl EdgeCorrelationTracker {
+    /// Create a new tracker for the given number of edges.
+    #[must_use]
+    pub fn new(num_edges: usize) -> Self {
+        // For large graphs, the co-occurrence matrix is O(E^2).
+        // At d=5 with ~200 edges, this is ~40K entries (320KB) -- fine.
+        // At d=9 with ~2000 edges, this is ~4M entries (32MB) -- manageable.
+        let co_size = num_edges * (num_edges - 1) / 2;
+        Self {
+            num_edges,
+            num_shots: 0,
+            edge_counts: vec![0; num_edges],
+            co_counts: vec![0; co_size],
+        }
+    }
+
+    /// Index into the upper-triangle co-occurrence array.
+    fn co_index(&self, i: usize, j: usize) -> usize {
+        let (a, b) = if i < j { (i, j) } else { (j, i) };
+        a * self.num_edges - a * (a + 1) / 2 + b - a - 1
+    }
+
+    /// Record a matching result: which edges were selected.
+    pub fn record_matching(&mut self, matched_edges: &[usize]) {
+        self.num_shots += 1;
+
+        // Update single-edge counts
+        for &e in matched_edges {
+            if e < self.num_edges {
+                self.edge_counts[e] += 1;
+            }
+        }
+
+        // Update co-occurrence counts for all pairs in the matching
+        for (idx_a, &e_a) in matched_edges.iter().enumerate() {
+            for &e_b in &matched_edges[idx_a + 1..] {
+                if e_a < self.num_edges && e_b < self.num_edges && e_a != e_b {
+                    let co_idx = self.co_index(e_a, e_b);
+                    if co_idx < self.co_counts.len() {
+                        self.co_counts[co_idx] += 1;
+                    }
+                }
+            }
+        }
+    }
+
+    /// Get the empirical probability of edge e appearing in a matching.
+    #[must_use]
+    pub fn edge_probability(&self, e: usize) -> f64 {
+        if self.num_shots == 0 || e >= self.num_edges {
+            return 0.0;
+        }
+        self.edge_counts[e] as f64 / self.num_shots as f64
+    }
+
+    /// Get the empirical co-occurrence probability of edges i and j.
+    #[must_use]
+    pub fn co_occurrence_probability(&self, i: usize, j: usize) -> f64 {
+        if self.num_shots == 0 || i >= self.num_edges || j >= self.num_edges || i == j {
+            return 0.0;
+        }
+        let co_idx = self.co_index(i, j);
+        if co_idx >= self.co_counts.len() {
+            return 0.0;
+        }
+        self.co_counts[co_idx] as f64 / self.num_shots as f64
+    }
+
+    /// Number of shots recorded.
+    #[must_use]
+    pub fn num_shots(&self) -> usize {
+        self.num_shots
+    }
+
+    /// Compute alignment-reweighted edge weights.
+    ///
+    /// Replaces original DEM weights with weights derived from observed
+    /// edge frequencies: `w_e` = -`ln(p_e` / (1 - `p_e`)) where `p_e` is the
+    /// empirical edge probability.
+    #[must_use]
+    pub fn aligned_weights(&self) -> Vec<f64> {
+        (0..self.num_edges)
+            .map(|e| {
+                let p = self.edge_probability(e);
+                if p <= 0.0 || p >= 1.0 {
+                    // Edge never/always matched -- keep a default weight
+                    if p <= 0.0 { 20.0 } else { 0.0 }
+                } else {
+                    ((1.0 - p) / p).ln()
+                }
+            })
+            .collect()
+    }
+
+    /// Compute correlation-adjusted weights for a specific matching.
+    ///
+    /// Given an initial matching M, adjust each edge weight based on
+    /// correlations with matched/unmatched edges (DGR Equation 1):
+    ///
+    ///   `w̃_j` = `w_j` - Σ_{`e_i` ∈ M} `p(e_i,e_j)/p(e_i)` + Σ_{`e_i` ∉ M} `p(e_i,e_j)/p(e_i)`
+    ///
+    /// Intuition: if edge j is correlated with matched edges, decrease its
+    /// weight (make it more likely). If correlated with unmatched edges,
+    /// increase its weight (make it less likely).
+    /// Compute correlation-adjusted weights for a specific matching.
+    ///
+    /// Given an initial matching M, adjust each edge weight based on
+    /// correlations with matched/unmatched edges (DGR Equation 1):
+    ///
+    ///   `w̃_j` = `w_j` - Σ_{`e_i` ∈ M} `p(e_i,e_j)/p(e_i)` + Σ_{`e_i` ∉ M} `p(e_i,e_j)/p(e_i)`
+    ///
+    /// Only edges with significant correlation (conditional probability >
+    /// `min_conditional`) contribute to the sum. This avoids the bias from
+    /// summing over hundreds of near-zero terms.
+    #[must_use]
+    pub fn correlation_adjusted_weights(
+        &self,
+        base_weights: &[f64],
+        matched_edges: &[bool],
+    ) -> Vec<f64> {
+        self.correlation_adjusted_weights_filtered(base_weights, matched_edges, 0.05)
+    }
+
+    /// Correlation adjustment with configurable significance threshold.
+    ///
+    /// `min_conditional`: minimum p(i,j)/p(i) to include an edge pair.
+    /// Higher values mean fewer pairs contribute (sparser adjustment).
+    #[must_use]
+    pub fn correlation_adjusted_weights_filtered(
+        &self,
+        base_weights: &[f64],
+        matched_edges: &[bool],
+        min_conditional: f64,
+    ) -> Vec<f64> {
+        let mut adjusted = base_weights.to_vec();
+
+        for (j, adjusted_weight) in adjusted.iter_mut().enumerate().take(self.num_edges) {
+            let mut adjustment = 0.0;
+            for (i, matched) in matched_edges.iter().enumerate().take(self.num_edges) {
+                if i == j {
+                    continue;
+                }
+                let p_i = self.edge_probability(i);
+                if p_i <= 0.0 {
+                    continue;
+                }
+                let p_ij = self.co_occurrence_probability(i, j);
+                let conditional = p_ij / p_i;
+
+                // Only include significantly correlated pairs
+                if conditional < min_conditional {
+                    continue;
+                }
+
+                if *matched {
+                    // Correlated edge is matched -> decrease weight (more likely).
+                    // We only adjust for matched edges -- the unmatched term
+                    // creates a large positive bias that dominates when most
+                    // edges are unmatched.
+                    adjustment -= conditional;
+                }
+            }
+            *adjusted_weight += adjustment;
+            // Clamp to prevent negative weights
+            if *adjusted_weight < 0.0 {
+                *adjusted_weight = 0.0;
+            }
+        }
+
+        adjusted
+    }
+}
+
+#[cfg(test)]
+mod tests {
+    use super::*;
+
+    #[test]
+    fn test_tracker_basic() {
+        let mut tracker = EdgeCorrelationTracker::new(5);
+
+        // Record some matchings
+        tracker.record_matching(&[0, 2]);
+        tracker.record_matching(&[0, 3]);
+        tracker.record_matching(&[1, 2]);
+        tracker.record_matching(&[0, 2]);
+
+        assert_eq!(tracker.num_shots(), 4);
+        assert!((tracker.edge_probability(0) - 0.75).abs() < 1e-10);
+        assert!((tracker.edge_probability(1) - 0.25).abs() < 1e-10);
+        assert!((tracker.edge_probability(2) - 0.75).abs() < 1e-10);
+        assert!((tracker.edge_probability(4) - 0.0).abs() < 1e-10);
+
+        // Co-occurrence: edges 0 and 2 both appear in 2 matchings
+        assert!((tracker.co_occurrence_probability(0, 2) - 0.5).abs() < 1e-10);
+        // Edges 0 and 3 both appear in 1 matching
+        assert!((tracker.co_occurrence_probability(0, 3) - 0.25).abs() < 1e-10);
+    }
+
+    #[test]
+    fn test_aligned_weights() {
+        let mut tracker = EdgeCorrelationTracker::new(3);
+        for _ in 0..100 {
+            tracker.record_matching(&[0]);
+        }
+        for _ in 0..900 {
+            tracker.record_matching(&[]);
+        }
+        // Edge 0 appears in 10% of matchings -> p=0.1 -> w = ln(0.9/0.1) = ln(9) ≈ 2.197
+        let weights = tracker.aligned_weights();
+        assert!((weights[0] - 9.0_f64.ln()).abs() < 0.01);
+    }
+
+    #[test]
+    fn test_correlation_adjustment() {
+        let mut tracker = EdgeCorrelationTracker::new(3);
+        // Edges 0 and 1 are highly correlated (always appear together)
+        for _ in 0..100 {
+            tracker.record_matching(&[0, 1]);
+        }
+        for _ in 0..900 {
+            tracker.record_matching(&[]);
+        }
+
+        let base_weights = vec![2.0, 2.0, 2.0];
+        // If edge 0 is matched, edge 1's weight should decrease (correlated)
+        let matched = vec![true, false, false];
+        let adjusted = tracker.correlation_adjusted_weights(&base_weights, &matched);
+
+        // Edge 1 should have lower weight (more likely given edge 0 is matched)
+        assert!(adjusted[1] < base_weights[1]);
+        // Edge 2 should be unchanged (no correlation with edge 0)
+        assert!((adjusted[2] - base_weights[2]).abs() < 1e-10);
+    }
+}
diff --git a/crates/pecos-decoder-core/src/correlation_table.rs b/crates/pecos-decoder-core/src/correlation_table.rs
new file mode 100644
index 000000000..1e2345a5c
--- /dev/null
+++ b/crates/pecos-decoder-core/src/correlation_table.rs
@@ -0,0 +1,275 @@
+// Copyright 2026 The PECOS Developers
+//
+// Licensed under the Apache License, Version 2.0 (the "License"); you may not use this file except
+// in compliance with the License. You may obtain a copy of the License at
+//
+//     https://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software distributed under the License
+// is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express
+// or implied. See the License for the specific language governing permissions and limitations under
+// the License.
+
+//! Pre-computed correlation table from DEM decomposition.
+//!
+//! Extracts pairwise edge correlations from the `^` decomposition in a DEM
+//! and pre-computes conditional weights for two-pass correlated decoding.
+//!
+//! The algorithm (matching `PyMatching`'s implementation):
+//!
+//! 1. Parse decomposed error mechanisms (with `^` separators)
+//! 2. For each pair of components (A, B) in a decomposed mechanism with
+//!    probability p, accumulate joint probability: `p_joint = p_a*(1-p) + p*(1-p_a)`
+//! 3. Also accumulate marginal probability for each edge
+//! 4. Conditional probability: `P(B|A) = P_joint(A,B) / P_marginal(A)`
+//! 5. Conditional weight: `w_cond = ln((1-P(B|A)) / P(B|A))`
+//!
+//! The conditional weight is only applied during decoding if it's LOWER than
+//! the current weight (makes the correlated edge more likely).
+
+use crate::errors::DecoderError;
+use std::collections::BTreeMap;
+
+/// An implied weight change: if edge (node1, node2) was matched,
+/// change the weight of edge (`target_node1`, `target_node2`) to `conditional_weight`.
+#[derive(Debug, Clone)]
+pub struct ImpliedWeight {
+    /// Target edge (by index in the matching graph).
+    pub target_edge_idx: usize,
+    /// Conditional weight: the weight edge should have given the source was matched.
+    pub conditional_weight: f64,
+}
+
+/// Pre-computed correlation table from DEM decomposition.
+///
+/// For each edge in the matching graph, stores a list of implied weight
+/// changes that should be applied when that edge is matched in the first
+/// pass of a two-pass decode.
+#[derive(Debug, Clone)]
+pub struct CorrelationTable {
+    /// For each edge index, the list of implied weights for correlated edges.
+    pub implied_weights: Vec<Vec<ImpliedWeight>>,
+    /// Number of edges.
+    pub num_edges: usize,
+}
+
+/// Edge key for lookup: (`min_node`, `max_node`), where `max_node` = `u32::MAX` for boundary.
+type EdgeKey = (u32, u32);
+
+/// Independent probability combination (Bernoulli XOR):
+/// `p_combined = p_a * (1 - p_b) + p_b * (1 - p_a)`
+fn bernoulli_xor(p_a: f64, p_b: f64) -> f64 {
+    p_a * (1.0 - p_b) + p_b * (1.0 - p_a)
+}
+
+/// Convert probability to weight for correlations: `ln((1-p) / p)`
+/// Clamped to avoid infinite weights.
+fn prob_to_weight(p: f64) -> f64 {
+    let p_clamped = p.clamp(1e-15, 0.5);
+    ((1.0 - p_clamped) / p_clamped).ln()
+}
+
+impl CorrelationTable {
+    /// Build a correlation table from a DEM string.
+    ///
+    /// Parses the DEM, identifies decomposed error mechanisms (with `^`),
+    /// computes joint probabilities between component pairs, and derives
+    /// conditional weights.
+    ///
+    /// `edge_index_map` maps (node1, node2) pairs to edge indices in the
+    /// matching graph (after merging). This must match the decoder's edge
+    /// indexing.
+    ///
+    /// # Errors
+    ///
+    /// Returns `DecoderError` if the DEM is malformed.
+    pub fn from_dem_str(
+        dem: &str,
+        edge_index_map: &BTreeMap<EdgeKey, usize>,
+        num_edges: usize,
+    ) -> Result<Self, DecoderError> {
+        // Accumulate joint and marginal probabilities.
+        // joint_probs[(edge_A, edge_B)] = P(A and B both fire from shared mechanisms)
+        // marginal_probs[edge_A] = P(A fires from any mechanism)
+        let mut joint_probs: BTreeMap<(EdgeKey, EdgeKey), f64> = BTreeMap::new();
+
+        for line in dem.lines() {
+            let line = line.trim();
+            if !line.starts_with("error(") {
+                continue;
+            }
+
+            let close_paren = line.find(')').ok_or_else(|| {
+                DecoderError::InvalidConfiguration("Missing closing parenthesis".into())
+            })?;
+            let prob_str = &line[6..close_paren];
+            let probability: f64 = prob_str.parse().map_err(|_| {
+                DecoderError::InvalidConfiguration(format!("Invalid probability: {prob_str}"))
+            })?;
+
+            if probability <= 0.0 || probability > 0.5 {
+                continue;
+            }
+
+            let tokens_str = &line[close_paren + 1..];
+            let components: Vec<&str> = tokens_str.split('^').collect();
+
+            if components.len() < 2 {
+                // Non-decomposed mechanism: accumulate marginal only
+                let key = parse_component_edge_key(components[0]);
+                if let Some(key) = key {
+                    let marginal = joint_probs.entry((key, key)).or_insert(0.0);
+                    *marginal = bernoulli_xor(*marginal, probability);
+                }
+                continue;
+            }
+
+            // Decomposed mechanism: accumulate joint and marginal for all pairs
+            let mut component_keys: Vec<EdgeKey> = Vec::new();
+            for component in &components {
+                if let Some(key) = parse_component_edge_key(component) {
+                    component_keys.push(key);
+                }
+            }
+
+            // Joint probabilities for all pairs
+            for i in 0..component_keys.len() {
+                for j in (i + 1)..component_keys.len() {
+                    let k0 = component_keys[i];
+                    let k1 = component_keys[j];
+                    let p01 = joint_probs.entry((k0, k1)).or_insert(0.0);
+                    *p01 = bernoulli_xor(*p01, probability);
+                    let p10 = joint_probs.entry((k1, k0)).or_insert(0.0);
+                    *p10 = bernoulli_xor(*p10, probability);
+                }
+            }
+
+            // Marginal for each component
+            for &key in &component_keys {
+                let marginal = joint_probs.entry((key, key)).or_insert(0.0);
+                *marginal = bernoulli_xor(*marginal, probability);
+            }
+        }
+
+        // Build implied weight table
+        let mut implied_weights: Vec<Vec<ImpliedWeight>> = vec![Vec::new(); num_edges];
+
+        for (&(causal_key, affected_key), &joint_p) in &joint_probs {
+            if causal_key == affected_key {
+                continue; // Skip marginals
+            }
+
+            let marginal_p = joint_probs
+                .get(&(causal_key, causal_key))
+                .copied()
+                .unwrap_or(0.0);
+            if marginal_p <= 0.0 {
+                continue;
+            }
+
+            let conditional_p = (joint_p / marginal_p).min(0.5);
+            if conditional_p <= 0.0 {
+                continue;
+            }
+
+            let conditional_weight = prob_to_weight(conditional_p);
+
+            if let (Some(&causal_idx), Some(&affected_idx)) = (
+                edge_index_map.get(&causal_key),
+                edge_index_map.get(&affected_key),
+            ) {
+                implied_weights[causal_idx].push(ImpliedWeight {
+                    target_edge_idx: affected_idx,
+                    conditional_weight,
+                });
+            }
+        }
+
+        Ok(Self {
+            implied_weights,
+            num_edges,
+        })
+    }
+
+    /// Check if the table has any correlations.
+    #[must_use]
+    pub fn has_correlations(&self) -> bool {
+        self.implied_weights.iter().any(|v| !v.is_empty())
+    }
+
+    /// Number of correlated edge pairs.
+    #[must_use]
+    pub fn num_correlations(&self) -> usize {
+        self.implied_weights.iter().map(Vec::len).sum()
+    }
+}
+
+/// Parse detector indices from a DEM component string, return edge key.
+fn parse_component_edge_key(component: &str) -> Option<EdgeKey> {
+    let mut detectors: Vec<u32> = Vec::new();
+    for token in component.split_whitespace() {
+        if let Some(d_str) = token.strip_prefix('D')
+            && let Ok(d) = d_str.parse::<u32>()
+        {
+            detectors.push(d);
+        }
+    }
+    // Pure observables and hyperedges do not define graph edges.
+    match detectors.len() {
+        1 => Some((detectors[0], u32::MAX)), // Boundary edge
+        2 => {
+            let (a, b) = if detectors[0] <= detectors[1] {
+                (detectors[0], detectors[1])
+            } else {
+                (detectors[1], detectors[0])
+            };
+            Some((a, b))
+        }
+        _ => None,
+    }
+}
+
+#[cfg(test)]
+mod tests {
+    use super::*;
+
+    #[test]
+    fn test_bernoulli_xor() {
+        assert!((bernoulli_xor(0.1, 0.2) - 0.26).abs() < 1e-10);
+        assert!((bernoulli_xor(0.0, 0.5) - 0.5).abs() < 1e-10);
+        assert!((bernoulli_xor(0.5, 0.5) - 0.5).abs() < 1e-10);
+    }
+
+    #[test]
+    fn test_decomposed_dem() {
+        // DEM with one decomposed mechanism: D0 D1 ^ D2 D3
+        // When D0-D1 is matched, D2-D3 should get a lower weight
+        let dem = "error(0.01) D0 D1 ^ D2 D3\nerror(0.02) D0 D1\nerror(0.02) D2 D3";
+
+        let mut edge_map = BTreeMap::new();
+        edge_map.insert((0, 1), 0usize); // D0-D1 = edge 0
+        edge_map.insert((2, 3), 1usize); // D2-D3 = edge 1
+
+        let table = CorrelationTable::from_dem_str(dem, &edge_map, 2).unwrap();
+        assert!(table.has_correlations());
+
+        // Edge 0 should have an implied weight for edge 1
+        assert!(!table.implied_weights[0].is_empty());
+        let iw = &table.implied_weights[0][0];
+        assert_eq!(iw.target_edge_idx, 1);
+        // The conditional weight should be lower than the unconditional
+        let unconditional_weight = prob_to_weight(0.02 + 0.01); // approximate
+        assert!(iw.conditional_weight < unconditional_weight);
+    }
+
+    #[test]
+    fn test_no_decomposition() {
+        let dem = "error(0.01) D0 D1\nerror(0.02) D2 D3";
+        let mut edge_map = BTreeMap::new();
+        edge_map.insert((0, 1), 0usize);
+        edge_map.insert((2, 3), 1usize);
+
+        let table = CorrelationTable::from_dem_str(dem, &edge_map, 2).unwrap();
+        assert!(!table.has_correlations());
+    }
+}
diff --git a/crates/pecos-decoder-core/src/decode_budget.rs b/crates/pecos-decoder-core/src/decode_budget.rs
new file mode 100644
index 000000000..140b89582
--- /dev/null
+++ b/crates/pecos-decoder-core/src/decode_budget.rs
@@ -0,0 +1,245 @@
+// Copyright 2026 The PECOS Developers
+//
+// Licensed under the Apache License, Version 2.0 (the "License"); you may not use this file except
+// in compliance with the License. You may obtain a copy of the License at
+//
+//     https://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software distributed under the License
+// is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express
+// or implied. See the License for the specific language governing permissions and limitations under
+// the License.
+
+//! Decode budget and strategy framework for real-time QEC.
+//!
+//! Different hardware platforms have different time budgets for decoding:
+//! superconducting (~1μs), neutral atoms (~1ms), ion traps (~10ms).
+//! The framework selects the best decode strategy based on the budget.
+//!
+//! # Example
+//!
+//! ```
+//! use std::time::Duration;
+//!
+//! use pecos_decoder_core::decode_budget::{DecodeBudget, DetectorRegion};
+//!
+//! let distance = 7;
+//! let budget = DecodeBudget::from_reaction_time(Duration::from_millis(1), distance);
+//! assert!(budget.is_windowed());
+//! assert_eq!(budget.code_distance, distance);
+//!
+//! let first_round = DetectorRegion { start: 0, end: distance * distance };
+//! assert!(first_round.contains(0));
+//! assert!(!first_round.is_empty());
+//! ```
+
+use crate::errors::DecoderError;
+use std::time::Duration;
+
+/// Time and resource budget for decoding.
+///
+/// Two timing constraints govern QEC decoding:
+///
+/// - **Throughput**: decoder must keep up with syndrome generation to
+///   avoid backlog. Measured in time per syndrome round.
+/// - **Reaction time**: at feed-forward decision points (T gates, magic
+///   state injection), the decoder must produce a correction within a
+///   deadline. For Clifford-only circuits, this is unlimited (corrections
+///   are metadata applied at the end).
+///
+/// The budget also controls the accuracy/latency trade-off via window
+/// size and overlap parameters.
+#[derive(Debug, Clone)]
+pub struct DecodeBudget {
+    /// Maximum wall-clock time per decode at a decision point.
+    /// For Clifford circuits this is unlimited; for T gates it's
+    /// the time between last syndrome and correction application.
+    pub reaction_time: Duration,
+    /// Maximum detectors to include in a single decode call.
+    /// Controls memory usage and decode time.
+    pub max_window_detectors: usize,
+    /// Number of overlap rounds at window boundaries.
+    /// More overlap = better accuracy, more compute.
+    /// Set to 0 for non-overlapping (fastest, least accurate).
+    pub overlap_rounds: usize,
+    /// Code distance (used to scale window sizes).
+    pub code_distance: usize,
+}
+
+impl DecodeBudget {
+    /// Unlimited budget: full-circuit decode. Maximum accuracy.
+    ///
+    /// Use for Clifford-only circuits (no feed-forward decisions),
+    /// offline simulation, or any situation where the decoder can
+    /// take as long as needed.
+    #[must_use]
+    pub fn unlimited() -> Self {
+        Self {
+            reaction_time: Duration::from_hours(1),
+            max_window_detectors: usize::MAX,
+            overlap_rounds: usize::MAX,
+            code_distance: 0,
+        }
+    }
+
+    /// Create a budget from the reaction time at decision points.
+    ///
+    /// `reaction_time`: time available between last syndrome and when
+    /// the correction must be applied (e.g., at T gate injection).
+    ///
+    /// Window size and overlap are scaled based on available time:
+    /// - Very generous (>100ms): unlimited (full-circuit decode)
+    /// - Generous (1ms - 100ms): large windows, d overlap
+    /// - Medium (10μs - 1ms): d-round windows, d/2 overlap
+    /// - Tight (<10μs): minimal windows, no overlap
+    #[must_use]
+    pub fn from_reaction_time(reaction_time: Duration, distance: usize) -> Self {
+        let us = reaction_time.as_micros() as usize;
+
+        let (max_dets, overlap) = if us >= 100_000 {
+            (usize::MAX, usize::MAX)
+        } else if us >= 1_000 {
+            (distance * distance * 4 * distance, distance)
+        } else if us >= 10 {
+            (distance * distance * 2 * distance, distance / 2)
+        } else {
+            (distance * distance * 2, 0)
+        };
+
+        Self {
+            reaction_time,
+            max_window_detectors: max_dets,
+            overlap_rounds: overlap,
+            code_distance: distance,
+        }
+    }
+
+    /// Create a budget with explicit parameters.
+    #[must_use]
+    pub fn with_params(
+        reaction_time: Duration,
+        max_window_detectors: usize,
+        overlap_rounds: usize,
+        code_distance: usize,
+    ) -> Self {
+        Self {
+            reaction_time,
+            max_window_detectors,
+            overlap_rounds,
+            code_distance,
+        }
+    }
+
+    /// Whether the budget allows full-circuit decoding (unlimited window).
+    #[must_use]
+    pub fn is_unlimited(&self) -> bool {
+        self.max_window_detectors == usize::MAX && self.overlap_rounds == usize::MAX
+    }
+
+    /// Whether windowed decoding is needed (non-unlimited budget).
+    #[must_use]
+    pub fn is_windowed(&self) -> bool {
+        !self.is_unlimited()
+    }
+}
+
+/// A region of detectors in the circuit.
+///
+/// Represents a contiguous block of detectors by their global indices.
+/// Used by strategies to define decode/commit boundaries.
+#[derive(Debug, Clone)]
+pub struct DetectorRegion {
+    /// First global detector index in this region.
+    pub start: usize,
+    /// One past the last global detector index.
+    pub end: usize,
+}
+
+impl DetectorRegion {
+    /// Number of detectors in this region.
+    #[must_use]
+    pub fn len(&self) -> usize {
+        self.end.saturating_sub(self.start)
+    }
+
+    /// Whether the region is empty.
+    #[must_use]
+    pub fn is_empty(&self) -> bool {
+        self.start >= self.end
+    }
+
+    /// Whether a detector index is in this region.
+    #[must_use]
+    pub fn contains(&self, det: usize) -> bool {
+        det >= self.start && det < self.end
+    }
+}
+
+/// Strategy for decoding a logical circuit.
+///
+/// Strategies implement different decode/commit patterns depending
+/// on the time budget. All strategies produce the same type of output
+/// (observable correction mask) but with different accuracy/latency
+/// trade-offs.
+pub trait DecodeStrategy: Send + Sync {
+    /// Decode a syndrome and return the observable correction mask.
+    ///
+    /// The syndrome covers the full circuit. The strategy decides
+    /// which portion to decode based on its internal state and budget.
+    fn decode(&mut self, syndrome: &[u8]) -> Result<u64, DecoderError>;
+
+    /// Commit corrections for a detector region.
+    ///
+    /// After commitment, detectors in this region are excluded from
+    /// future decode calls. Their corrections are accumulated into
+    /// the committed observable mask.
+    fn commit(&mut self, region: &DetectorRegion) -> Result<u64, DecoderError>;
+
+    /// Total committed observable correction so far.
+    fn committed_obs(&self) -> u64;
+
+    /// Reset all state for the next shot.
+    fn reset(&mut self);
+}
+
+#[cfg(test)]
+mod tests {
+    use super::*;
+
+    #[test]
+    fn test_budget_unlimited() {
+        let b = DecodeBudget::unlimited();
+        assert!(b.is_unlimited());
+        assert!(!b.is_windowed());
+    }
+
+    #[test]
+    fn test_budget_from_reaction_time() {
+        // Very tight: no overlap
+        let b = DecodeBudget::from_reaction_time(Duration::from_micros(1), 7);
+        assert_eq!(b.overlap_rounds, 0);
+        assert!(b.is_windowed());
+
+        // Medium: d/2 overlap
+        let b = DecodeBudget::from_reaction_time(Duration::from_micros(100), 7);
+        assert_eq!(b.overlap_rounds, 3);
+
+        // Generous: d overlap
+        let b = DecodeBudget::from_reaction_time(Duration::from_millis(10), 7);
+        assert_eq!(b.overlap_rounds, 7);
+
+        // Very generous: unlimited
+        let b = DecodeBudget::from_reaction_time(Duration::from_millis(200), 7);
+        assert!(b.is_unlimited());
+    }
+
+    #[test]
+    fn test_detector_region() {
+        let r = DetectorRegion { start: 10, end: 20 };
+        assert_eq!(r.len(), 10);
+        assert!(r.contains(10));
+        assert!(r.contains(19));
+        assert!(!r.contains(20));
+        assert!(!r.contains(9));
+    }
+}
diff --git a/crates/pecos-decoder-core/src/dem.rs b/crates/pecos-decoder-core/src/dem.rs
index a04d96216..324a21e50 100644
--- a/crates/pecos-decoder-core/src/dem.rs
+++ b/crates/pecos-decoder-core/src/dem.rs
@@ -200,6 +200,571 @@ pub mod utils {
     }
 }
 
+/// Check matrix representation extracted from a Detector Error Model.
+///
+/// Converts a DEM string into the matrices needed by check-matrix-based
+/// decoders (BP+OSD, `UnionFind`, `RelayBP`, etc.):
+///
+/// - **`check_matrix`** `H[d][m]`: 1 if error mechanism `m` flips detector `d`
+/// - **`observable_matrix`** `L[o][m]`: 1 if mechanism `m` flips observable `o`
+/// - **`error_priors`** `p[m]`: probability of mechanism `m`
+///
+/// # Example
+///
+/// ```
+/// use pecos_decoder_core::dem::DemCheckMatrix;
+///
+/// let dem = "error(0.01) D0 D1 L0\nerror(0.02) D1 D2";
+/// let dcm = DemCheckMatrix::from_dem_str(dem).unwrap();
+/// assert_eq!(dcm.num_detectors, 3);
+/// assert_eq!(dcm.num_observables, 1);
+/// assert_eq!(dcm.num_mechanisms, 2);
+/// assert_eq!(dcm.error_priors, vec![0.01, 0.02]);
+/// ```
+#[derive(Debug, Clone)]
+pub struct DemCheckMatrix {
+    /// Check matrix: rows = detectors, columns = error mechanisms.
+    pub check_matrix: ndarray::Array2<u8>,
+    /// Observable matrix: rows = observables, columns = error mechanisms.
+    pub observable_matrix: ndarray::Array2<u8>,
+    /// Error probability per mechanism.
+    pub error_priors: Vec<f64>,
+    /// Number of detectors (rows of `check_matrix`).
+    pub num_detectors: usize,
+    /// Number of observables (rows of `observable_matrix`).
+    pub num_observables: usize,
+    /// Number of error mechanisms (columns of both matrices).
+    pub num_mechanisms: usize,
+}
+
+impl DemCheckMatrix {
+    /// Parse a DEM string into check matrix form.
+    ///
+    /// Each `error(p) D_i D_j ... L_k ...` line becomes one column in the
+    /// check matrix (for the D entries) and one column in the observable
+    /// matrix (for the L entries). Decomposed mechanisms (`D0 ^ D1`) are
+    /// combined by XOR.
+    ///
+    /// # Errors
+    ///
+    /// Returns [`DecoderError`] if the DEM string is malformed.
+    pub fn from_dem_str(dem: &str) -> Result<Self, DecoderError> {
+        // First pass: collect mechanisms and find dimensions.
+        let mut mechanisms: Vec<(f64, Vec<u32>, Vec<u32>)> = Vec::new();
+        let mut max_detector: Option<u32> = None;
+        let mut max_observable: Option<u32> = None;
+
+        for line in dem.lines() {
+            let line = line.trim();
+            if line.is_empty() || line.starts_with('#') {
+                continue;
+            }
+            if !line.starts_with("error(") {
+                // Skip non-error lines (detector, logical_observable, etc.)
+                continue;
+            }
+
+            // Parse "error(p) D0 D1 ... L0 ..." or "error(p) D0 ^ D1 ..."
+            let close_paren = line.find(')').ok_or_else(|| {
+                DecoderError::InvalidConfiguration(
+                    "Missing closing parenthesis in error line".into(),
+                )
+            })?;
+            let prob_str = &line[6..close_paren];
+            let probability: f64 = prob_str.parse().map_err(|_| {
+                DecoderError::InvalidConfiguration(format!("Invalid probability: {prob_str}"))
+            })?;
+
+            let tokens_str = &line[close_paren + 1..];
+
+            // Handle decomposed mechanisms (with ^) by XOR-ing components.
+            let mut det_set = std::collections::BTreeSet::new();
+            let mut obs_set = std::collections::BTreeSet::new();
+
+            for component in tokens_str.split('^') {
+                for token in component.split_whitespace() {
+                    if let Some(d_str) = token.strip_prefix('D') {
+                        let d: u32 = d_str.parse().map_err(|_| {
+                            DecoderError::InvalidConfiguration(format!("Invalid detector: {token}"))
+                        })?;
+                        // XOR: toggle membership
+                        if !det_set.remove(&d) {
+                            det_set.insert(d);
+                        }
+                        max_detector = Some(max_detector.map_or(d, |m| m.max(d)));
+                    } else if let Some(l_str) = token.strip_prefix('L') {
+                        let l: u32 = l_str.parse().map_err(|_| {
+                            DecoderError::InvalidConfiguration(format!(
+                                "Invalid observable: {token}"
+                            ))
+                        })?;
+                        if !obs_set.remove(&l) {
+                            obs_set.insert(l);
+                        }
+                        max_observable = Some(max_observable.map_or(l, |m| m.max(l)));
+                    }
+                }
+            }
+
+            let detectors: Vec<u32> = det_set.into_iter().collect();
+            let observables: Vec<u32> = obs_set.into_iter().collect();
+            mechanisms.push((probability, detectors, observables));
+        }
+
+        let num_detectors = max_detector.map_or(0, |m| m as usize + 1);
+        let num_observables = max_observable.map_or(0, |m| m as usize + 1);
+        let num_mechanisms = mechanisms.len();
+
+        // Build matrices.
+        let mut check_matrix = ndarray::Array2::<u8>::zeros((num_detectors, num_mechanisms));
+        let mut observable_matrix = ndarray::Array2::<u8>::zeros((num_observables, num_mechanisms));
+        let mut error_priors = Vec::with_capacity(num_mechanisms);
+
+        for (col, (prob, detectors, observables)) in mechanisms.iter().enumerate() {
+            error_priors.push(*prob);
+            for &d in detectors {
+                check_matrix[[d as usize, col]] = 1;
+            }
+            for &o in observables {
+                observable_matrix[[o as usize, col]] = 1;
+            }
+        }
+
+        Ok(Self {
+            check_matrix,
+            observable_matrix,
+            error_priors,
+            num_detectors,
+            num_observables,
+            num_mechanisms,
+        })
+    }
+
+    /// Compute the observable prediction from a correction vector.
+    ///
+    /// Given a binary correction vector (one entry per mechanism, from a
+    /// check-matrix decoder), returns the observable mask as
+    /// `observable_matrix @ correction (mod 2)`.
+    #[must_use]
+    pub fn observables_from_correction(&self, correction: &[u8]) -> Vec<u8> {
+        let mut obs = vec![0u8; self.num_observables];
+        for (o, row) in self.observable_matrix.rows().into_iter().enumerate() {
+            let mut sum = 0u8;
+            for (m, &val) in row.iter().enumerate() {
+                if val != 0 && m < correction.len() && correction[m] != 0 {
+                    sum ^= 1;
+                }
+            }
+            obs[o] = sum;
+        }
+        obs
+    }
+
+    /// Pack observable predictions into a bitmask (u64).
+    ///
+    /// Bit `i` is set if observable `i` is predicted to flip.
+    #[must_use]
+    pub fn observables_mask_from_correction(&self, correction: &[u8]) -> u64 {
+        let obs = self.observables_from_correction(correction);
+        let mut mask = 0u64;
+        for (i, &v) in obs.iter().enumerate() {
+            if v != 0 {
+                mask |= 1 << i;
+            }
+        }
+        mask
+    }
+}
+
+/// An edge in a matching graph extracted from a DEM.
+#[derive(Debug, Clone)]
+pub struct MatchingEdge {
+    /// First detector node (always present).
+    pub node1: u32,
+    /// Second detector node, or `None` for a boundary edge.
+    pub node2: Option<u32>,
+    /// Weight for MWPM: `ln((1-p) / p)`.
+    pub weight: f64,
+    /// Observable indices flipped by this error.
+    pub observables: Vec<u32>,
+    /// Original error probability.
+    pub probability: f64,
+    /// Fault mechanism ID (DEM line number). Components from the same
+    /// decomposed mechanism share the same `fault_id`.
+    pub fault_id: usize,
+}
+
+/// Matching graph representation extracted from a Detector Error Model.
+///
+/// Parses a DEM into edges suitable for MWPM decoders (`PyMatching`, Fusion
+/// Blossom). Each graphlike error mechanism (1-2 detectors) becomes one edge.
+/// Decomposed mechanisms (`D0 ^ D1`) are split into their components.
+/// Hyperedges (3+ detectors after resolution) are skipped with a warning.
+///
+/// # Example
+///
+/// ```
+/// use pecos_decoder_core::dem::DemMatchingGraph;
+///
+/// let dem = "error(0.01) D0 D1 L0\nerror(0.02) D1";
+/// let graph = DemMatchingGraph::from_dem_str(dem).unwrap();
+/// assert_eq!(graph.edges.len(), 2);
+/// assert_eq!(graph.num_detectors, 2);
+/// ```
+#[derive(Debug, Clone)]
+pub struct DemMatchingGraph {
+    /// Edges in the matching graph.
+    pub edges: Vec<MatchingEdge>,
+    /// Number of detectors (max detector ID + 1).
+    pub num_detectors: usize,
+    /// Number of observables (max observable ID + 1).
+    pub num_observables: usize,
+    /// Number of hyperedges skipped (3+ detectors).
+    pub skipped_hyperedges: usize,
+    /// Detector coordinates (from `detector(x,y,t) D_i` declarations).
+    /// Indexed by detector ID. Empty if no detector declarations in DEM.
+    pub detector_coords: Vec<Option<Vec<f64>>>,
+}
+
+impl DemMatchingGraph {
+    /// Parse a DEM string into a matching graph.
+    ///
+    /// # Errors
+    ///
+    /// Returns [`DecoderError`] if the DEM string is malformed.
+    pub fn from_dem_str(dem: &str) -> Result<Self, DecoderError> {
+        let mut edges = Vec::new();
+        let mut max_detector: Option<u32> = None;
+        let mut max_observable: Option<u32> = None;
+        let mut skipped = 0usize;
+        let mut fault_id = 0usize;
+
+        for line in dem.lines() {
+            let line = line.trim();
+            if line.is_empty() || line.starts_with('#') || !line.starts_with("error(") {
+                continue;
+            }
+
+            let close_paren = line.find(')').ok_or_else(|| {
+                DecoderError::InvalidConfiguration("Missing closing parenthesis".into())
+            })?;
+            let prob_str = &line[6..close_paren];
+            let probability: f64 = prob_str.parse().map_err(|_| {
+                DecoderError::InvalidConfiguration(format!("Invalid probability: {prob_str}"))
+            })?;
+
+            if probability <= 0.0 {
+                continue;
+            }
+
+            let weight = if probability < 1.0 {
+                ((1.0 - probability) / probability).ln()
+            } else {
+                0.0
+            };
+
+            let tokens_str = &line[close_paren + 1..];
+
+            // For decomposed mechanisms (with ^), each component is a separate edge.
+            // For non-decomposed mechanisms, there's one component.
+            let components: Vec<&str> = tokens_str.split('^').collect();
+
+            for component in &components {
+                let mut detectors = Vec::new();
+                let mut observables = Vec::new();
+
+                for token in component.split_whitespace() {
+                    if let Some(d_str) = token.strip_prefix('D') {
+                        let d: u32 = d_str.parse().map_err(|_| {
+                            DecoderError::InvalidConfiguration(format!("Invalid detector: {token}"))
+                        })?;
+                        detectors.push(d);
+                        max_detector = Some(max_detector.map_or(d, |m| m.max(d)));
+                    } else if let Some(l_str) = token.strip_prefix('L') {
+                        let l: u32 = l_str.parse().map_err(|_| {
+                            DecoderError::InvalidConfiguration(format!(
+                                "Invalid observable: {token}"
+                            ))
+                        })?;
+                        observables.push(l);
+                        max_observable = Some(max_observable.map_or(l, |m| m.max(l)));
+                    }
+                }
+
+                match detectors.len() {
+                    0 => {} // Pure observable error, skip
+                    1 => {
+                        edges.push(MatchingEdge {
+                            node1: detectors[0],
+                            node2: None, // boundary
+                            weight,
+                            observables,
+                            probability,
+                            fault_id,
+                        });
+                    }
+                    2 => {
+                        edges.push(MatchingEdge {
+                            node1: detectors[0],
+                            node2: Some(detectors[1]),
+                            weight,
+                            observables,
+                            probability,
+                            fault_id,
+                        });
+                    }
+                    _ => {
+                        skipped += 1;
+                    }
+                }
+            }
+            fault_id += 1;
+        }
+
+        let num_detectors = max_detector.map_or(0, |m| m as usize + 1);
+        let num_observables = max_observable.map_or(0, |m| m as usize + 1);
+
+        let edges = Self::merge_parallel_edges(edges);
+
+        // Parse detector coordinates
+        let coords = parse_detector_coords(dem);
+        let mut detector_coords = vec![None; num_detectors];
+        for dc in coords {
+            if (dc.id as usize) < num_detectors {
+                detector_coords[dc.id as usize] = Some(dc.coords);
+            }
+        }
+
+        Ok(Self {
+            edges,
+            num_detectors,
+            num_observables,
+            skipped_hyperedges: skipped,
+            detector_coords,
+        })
+    }
+
+    /// Merge edges with independent fault-ID-aware probability combination.
+    ///
+    /// Components from the same fault mechanism (same `fault_id`) that land on
+    /// the same edge pair are NOT merged -- they're part of one correlated event.
+    /// Components from different fault mechanisms (different `fault_id`) are
+    /// combined using: `p_combined = p_a*(1-p_b) + p_b*(1-p_a)`.
+    ///
+    /// This matches `PyMatching`'s "independent" merge strategy with fault ID tracking.
+    pub(crate) fn merge_parallel_edges(edges: Vec<MatchingEdge>) -> Vec<MatchingEdge> {
+        use std::collections::BTreeMap;
+
+        type EdgeKey = (u32, Option<u32>);
+
+        // First, deduplicate: for each (edge_key, fault_id), keep only one entry.
+        // Multiple components from the same fault_id on the same edge just confirm
+        // that the fault affects this edge -- don't double-count the probability.
+        let mut per_fault: BTreeMap<(EdgeKey, usize), MatchingEdge> = BTreeMap::new();
+
+        for edge in edges {
+            let key = match edge.node2 {
+                Some(n2) if edge.node1 > n2 => (n2, Some(edge.node1)),
+                _ => (edge.node1, edge.node2),
+            };
+            let fault_key = (key, edge.fault_id);
+            // First occurrence of this (edge, fault_id) wins
+            per_fault.entry(fault_key).or_insert(MatchingEdge {
+                node1: key.0,
+                node2: key.1,
+                ..edge
+            });
+        }
+
+        // Now merge across different fault_ids for the same edge pair
+        let mut merged: BTreeMap<EdgeKey, MatchingEdge> = BTreeMap::new();
+
+        for ((edge_key, _fault_id), edge) in per_fault {
+            if let Some(existing) = merged.get_mut(&edge_key) {
+                // Independent combination: p_ab = p_a*(1-p_b) + p_b*(1-p_a)
+                let p_a = existing.probability;
+                let p_b = edge.probability;
+                let p_combined = p_a * (1.0 - p_b) + p_b * (1.0 - p_a);
+                existing.probability = p_combined;
+                existing.weight = if p_combined > 0.0 && p_combined < 1.0 {
+                    ((1.0 - p_combined) / p_combined).ln()
+                } else if p_combined >= 1.0 {
+                    0.0
+                } else {
+                    1e6
+                };
+
+                // Keep the first edge's observables (matching PyMatching's
+                // INDEPENDENT strategy). If observables differ between parallel
+                // edges on the same node pair, the code has distance 2.
+            } else {
+                merged.insert(edge_key, edge);
+            }
+        }
+
+        merged.into_values().collect()
+    }
+}
+
+/// Generic wrapper that combines any [`Decoder`] with a [`DemCheckMatrix`]
+/// to implement [`ObservableDecoder`].
+///
+/// This is the proper way to use check-matrix decoders (BP+OSD, `UnionFind`,
+/// `RelayBP`, etc.) in a sample+decode loop. The wrapper:
+/// 1. Passes the syndrome to the inner decoder
+/// 2. Gets back a correction vector
+/// 3. Multiplies by the observable matrix to get the observable prediction
+///
+/// # Example
+///
+/// ```
+/// use ndarray::ArrayView1;
+///
+/// use pecos_decoder_core::{
+///     CheckMatrixObservableDecoder, Decoder, DecoderError, DecodingResultTrait, DemCheckMatrix,
+///     ObservableDecoder,
+/// };
+///
+/// struct CorrectionResult {
+///     correction: Vec<u8>,
+/// }
+///
+/// impl DecodingResultTrait for CorrectionResult {
+///     fn is_successful(&self) -> bool {
+///         true
+///     }
+///
+///     fn correction(&self) -> &[u8] {
+///         &self.correction
+///     }
+/// }
+///
+/// struct FirstMechanismDecoder {
+///     checks: usize,
+///     bits: usize,
+/// }
+///
+/// impl Decoder for FirstMechanismDecoder {
+///     type Result = CorrectionResult;
+///     type Error = DecoderError;
+///
+///     fn decode(&mut self, input: &ArrayView1<u8>) -> Result<Self::Result, Self::Error> {
+///         assert_eq!(input.len(), self.checks);
+///         let mut correction = vec![0; self.bits];
+///         correction[0] = 1;
+///         Ok(CorrectionResult { correction })
+///     }
+///
+///     fn check_count(&self) -> usize {
+///         self.checks
+///     }
+///
+///     fn bit_count(&self) -> usize {
+///         self.bits
+///     }
+/// }
+///
+/// let dem_str = "error(0.01) D0 L0\nerror(0.02) D0";
+/// let dcm = DemCheckMatrix::from_dem_str(dem_str).unwrap();
+/// let inner_decoder = FirstMechanismDecoder {
+///     checks: dcm.num_detectors,
+///     bits: dcm.num_mechanisms,
+/// };
+/// let mut decoder = CheckMatrixObservableDecoder::new(inner_decoder, dcm);
+///
+/// let mask = decoder.decode_to_observables(&[1]).unwrap();
+/// assert_eq!(mask, 0b1);
+/// ```
+pub struct CheckMatrixObservableDecoder<D> {
+    /// The inner check-matrix decoder.
+    pub decoder: D,
+    /// The DEM check matrix (holds observable matrix for prediction).
+    pub dem: DemCheckMatrix,
+    /// Reusable syndrome buffer (avoids per-shot ndarray allocation).
+    syndrome_arr: ndarray::Array1<u8>,
+}
+
+impl<D> CheckMatrixObservableDecoder<D> {
+    /// Create a new wrapper from a decoder and its DEM check matrix.
+    pub fn new(decoder: D, dem: DemCheckMatrix) -> Self {
+        let len = dem.num_detectors;
+        Self {
+            decoder,
+            dem,
+            syndrome_arr: ndarray::Array1::zeros(len),
+        }
+    }
+}
+
+impl<D> super::ObservableDecoder for CheckMatrixObservableDecoder<D>
+where
+    D: super::Decoder,
+{
+    fn decode_to_observables(&mut self, syndrome: &[u8]) -> Result<u64, DecoderError> {
+        use super::DecodingResultTrait;
+
+        // Copy syndrome into reusable buffer (no allocation after first call)
+        let len = syndrome.len();
+        if self.syndrome_arr.len() != len {
+            self.syndrome_arr = ndarray::Array1::zeros(len);
+        }
+        self.syndrome_arr
+            .as_slice_mut()
+            .unwrap()
+            .copy_from_slice(syndrome);
+        let result = self
+            .decoder
+            .decode(&self.syndrome_arr.view())
+            .map_err(|e| DecoderError::DecodingFailed(e.to_string()))?;
+
+        let correction = result.correction();
+        Ok(self.dem.observables_mask_from_correction(correction))
+    }
+}
+
+/// Detector coordinate parsed from a DEM `detector(x, y, t) D_i` line.
+#[derive(Debug, Clone)]
+pub struct DetectorCoord {
+    /// Detector ID.
+    pub id: u32,
+    /// Coordinates (typically x, y, t for surface codes).
+    pub coords: Vec<f64>,
+}
+
+/// Parse detector coordinates from a DEM string.
+///
+/// Returns a list of `DetectorCoord` for each `detector(...)` declaration.
+#[must_use]
+pub fn parse_detector_coords(dem: &str) -> Vec<DetectorCoord> {
+    let mut result = Vec::new();
+    for line in dem.lines() {
+        let line = line.trim();
+        if !line.starts_with("detector(") {
+            continue;
+        }
+        if let Some(close) = line.find(')') {
+            let coord_str = &line[9..close];
+            let coords: Vec<f64> = coord_str
+                .split(',')
+                .filter_map(|s| s.trim().parse().ok())
+                .collect();
+            // Find D_i after the closing paren
+            let rest = &line[close + 1..];
+            for token in rest.split_whitespace() {
+                if let Some(d_str) = token.strip_prefix('D')
+                    && let Ok(id) = d_str.parse::<u32>()
+                {
+                    result.push(DetectorCoord {
+                        id,
+                        coords: coords.clone(),
+                    });
+                }
+            }
+        }
+    }
+    result
+}
+
 /// Information about a detector error model
 #[derive(Debug, Clone, PartialEq)]
 pub struct DemInfo {
@@ -301,6 +866,63 @@ mod tests {
         assert_eq!(observables, 2); // L0 and L1
     }
 
+    #[test]
+    fn test_dem_check_matrix_basic() {
+        let dem = "error(0.01) D0 D1 L0\nerror(0.02) D1 D2\nerror(0.03) D0 D2 L0";
+        let dcm = DemCheckMatrix::from_dem_str(dem).unwrap();
+
+        assert_eq!(dcm.num_detectors, 3);
+        assert_eq!(dcm.num_observables, 1);
+        assert_eq!(dcm.num_mechanisms, 3);
+        assert_eq!(dcm.error_priors, vec![0.01, 0.02, 0.03]);
+
+        // Check matrix: mechanism 0 -> D0,D1; mechanism 1 -> D1,D2; mechanism 2 -> D0,D2
+        assert_eq!(dcm.check_matrix[[0, 0]], 1); // D0, mech 0
+        assert_eq!(dcm.check_matrix[[1, 0]], 1); // D1, mech 0
+        assert_eq!(dcm.check_matrix[[2, 0]], 0); // D2, mech 0
+        assert_eq!(dcm.check_matrix[[0, 1]], 0); // D0, mech 1
+        assert_eq!(dcm.check_matrix[[1, 1]], 1); // D1, mech 1
+        assert_eq!(dcm.check_matrix[[2, 1]], 1); // D2, mech 1
+
+        // Observable matrix: mechanism 0 -> L0; mechanism 1 -> none; mechanism 2 -> L0
+        assert_eq!(dcm.observable_matrix[[0, 0]], 1);
+        assert_eq!(dcm.observable_matrix[[0, 1]], 0);
+        assert_eq!(dcm.observable_matrix[[0, 2]], 1);
+    }
+
+    #[test]
+    fn test_dem_check_matrix_observables_from_correction() {
+        let dem = "error(0.01) D0 L0\nerror(0.01) D1 L1\nerror(0.01) D0 D1 L0 L1";
+        let dcm = DemCheckMatrix::from_dem_str(dem).unwrap();
+
+        // Correction activates mechanism 0 -> L0 flips
+        assert_eq!(dcm.observables_mask_from_correction(&[1, 0, 0]), 0b01);
+        // Correction activates mechanism 2 -> L0 and L1 flip
+        assert_eq!(dcm.observables_mask_from_correction(&[0, 0, 1]), 0b11);
+        // Correction activates mechanisms 0 and 2 -> L0 xor L0 = 0, L1 flips
+        assert_eq!(dcm.observables_mask_from_correction(&[1, 0, 1]), 0b10);
+    }
+
+    #[test]
+    fn test_dem_check_matrix_decomposed() {
+        // Decomposed mechanism: D0 ^ D1 means XOR
+        let dem = "error(0.01) D0 D1 ^ D1 D2";
+        let dcm = DemCheckMatrix::from_dem_str(dem).unwrap();
+
+        // D1 appears in both components -> XOR cancels it
+        assert_eq!(dcm.check_matrix[[0, 0]], 1); // D0
+        assert_eq!(dcm.check_matrix[[1, 0]], 0); // D1 cancels
+        assert_eq!(dcm.check_matrix[[2, 0]], 1); // D2
+    }
+
+    #[test]
+    fn test_dem_check_matrix_empty() {
+        let dem = "";
+        let dcm = DemCheckMatrix::from_dem_str(dem).unwrap();
+        assert_eq!(dcm.num_mechanisms, 0);
+        assert_eq!(dcm.num_detectors, 0);
+    }
+
     #[test]
     fn test_dem_config_builder() {
         let config = DemConfigBuilder::new()
diff --git a/crates/pecos-decoder-core/src/ensemble.rs b/crates/pecos-decoder-core/src/ensemble.rs
new file mode 100644
index 000000000..c969f22c3
--- /dev/null
+++ b/crates/pecos-decoder-core/src/ensemble.rs
@@ -0,0 +1,270 @@
+// Copyright 2026 The PECOS Developers
+//
+// Licensed under the Apache License, Version 2.0 (the "License"); you may not use this file except
+// in compliance with the License. You may obtain a copy of the License at
+//
+//     https://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software distributed under the License
+// is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express
+// or implied. See the License for the specific language governing permissions and limitations under
+// the License.
+
+//! Multi-decoder ensemble with per-observable majority vote.
+//!
+//! Runs multiple decoders on the same syndrome, then combines their
+//! predictions via (optionally weighted) majority vote on each
+//! observable bit independently.
+
+use crate::ObservableDecoder;
+use crate::errors::DecoderError;
+
+/// Voting strategy for combining decoder predictions.
+#[derive(Debug, Clone)]
+pub enum VotingStrategy {
+    /// Each decoder gets one vote. Ties go to 0 (no flip).
+    Majority,
+    /// Each decoder gets a weight. Higher weight = more influence.
+    /// Ties (equal total weight for 0 and 1) go to 0.
+    Weighted(Vec<f64>),
+}
+
+/// Multi-decoder ensemble that votes on observable predictions.
+///
+/// Each member decoder runs independently on the same syndrome,
+/// then the ensemble combines their observable masks via majority
+/// vote (per bit).
+pub struct EnsembleDecoder {
+    decoders: Vec<Box<dyn ObservableDecoder>>,
+    strategy: VotingStrategy,
+    /// Reusable buffer for collecting predictions.
+    predictions: Vec<u64>,
+}
+
+impl EnsembleDecoder {
+    /// Create an ensemble with uniform (majority) voting.
+    #[must_use]
+    pub fn new(decoders: Vec<Box<dyn ObservableDecoder>>) -> Self {
+        let n = decoders.len();
+        Self {
+            decoders,
+            strategy: VotingStrategy::Majority,
+            predictions: Vec::with_capacity(n),
+        }
+    }
+
+    /// Create an ensemble with weighted voting.
+    ///
+    /// # Panics
+    ///
+    /// Panics if `weights.len() != decoders.len()`.
+    #[must_use]
+    pub fn with_weights(decoders: Vec<Box<dyn ObservableDecoder>>, weights: Vec<f64>) -> Self {
+        assert_eq!(
+            decoders.len(),
+            weights.len(),
+            "number of weights must match number of decoders"
+        );
+        let n = decoders.len();
+        Self {
+            decoders,
+            strategy: VotingStrategy::Weighted(weights),
+            predictions: Vec::with_capacity(n),
+        }
+    }
+
+    /// Number of decoders in the ensemble.
+    #[must_use]
+    pub fn len(&self) -> usize {
+        self.decoders.len()
+    }
+
+    /// Whether the ensemble has no decoders.
+    #[must_use]
+    pub fn is_empty(&self) -> bool {
+        self.decoders.is_empty()
+    }
+}
+
+impl ObservableDecoder for EnsembleDecoder {
+    fn decode_to_observables(&mut self, syndrome: &[u8]) -> Result<u64, DecoderError> {
+        if self.decoders.is_empty() {
+            return Ok(0);
+        }
+
+        // Collect predictions from all decoders.
+        self.predictions.clear();
+        for decoder in &mut self.decoders {
+            self.predictions
+                .push(decoder.decode_to_observables(syndrome)?);
+        }
+
+        // Vote on each observable bit independently.
+        let mut result = 0u64;
+        for bit in 0..64 {
+            let mask = 1u64 << bit;
+
+            // Check if any decoder cares about this bit.
+            let any_set = self.predictions.iter().any(|&p| p & mask != 0);
+            if !any_set {
+                continue;
+            }
+
+            let vote_for_flip = match &self.strategy {
+                VotingStrategy::Majority => {
+                    let count = self.predictions.iter().filter(|&&p| p & mask != 0).count();
+                    // Strict majority: more than half must vote flip.
+                    count * 2 > self.decoders.len()
+                }
+                VotingStrategy::Weighted(weights) => {
+                    let mut weight_flip = 0.0;
+                    let mut weight_no_flip = 0.0;
+                    for (i, &pred) in self.predictions.iter().enumerate() {
+                        if pred & mask != 0 {
+                            weight_flip += weights[i];
+                        } else {
+                            weight_no_flip += weights[i];
+                        }
+                    }
+                    weight_flip > weight_no_flip
+                }
+            };
+
+            if vote_for_flip {
+                result |= mask;
+            }
+        }
+
+        Ok(result)
+    }
+}
+
+/// Thread-safe ensemble decoder that decodes K members in parallel using rayon.
+///
+/// Same majority-vote logic as `EnsembleDecoder` but runs all members
+/// concurrently. Requires inner decoders to be `Send`.
+pub struct ParallelEnsembleDecoder {
+    decoders: Vec<Box<dyn ObservableDecoder + Send>>,
+}
+
+impl ParallelEnsembleDecoder {
+    /// Create a parallel ensemble with majority voting.
+    #[must_use]
+    pub fn new(decoders: Vec<Box<dyn ObservableDecoder + Send>>) -> Self {
+        Self { decoders }
+    }
+
+    /// Number of decoders.
+    #[must_use]
+    pub fn len(&self) -> usize {
+        self.decoders.len()
+    }
+
+    /// Whether the ensemble is empty.
+    #[must_use]
+    pub fn is_empty(&self) -> bool {
+        self.decoders.is_empty()
+    }
+}
+
+impl ObservableDecoder for ParallelEnsembleDecoder {
+    fn decode_to_observables(&mut self, syndrome: &[u8]) -> Result<u64, DecoderError> {
+        use rayon::prelude::*;
+
+        if self.decoders.is_empty() {
+            return Ok(0);
+        }
+
+        // Decode all members in parallel.
+        let predictions: Result<Vec<u64>, DecoderError> = self
+            .decoders
+            .par_iter_mut()
+            .map(|decoder| decoder.decode_to_observables(syndrome))
+            .collect();
+        let predictions = predictions?;
+
+        // Majority vote.
+        let half = predictions.len() / 2;
+        let mut result = 0u64;
+        for bit in 0..64 {
+            let mask = 1u64 << bit;
+            let count = predictions.iter().filter(|&&p| p & mask != 0).count();
+            if count > half {
+                result |= mask;
+            }
+        }
+        Ok(result)
+    }
+}
+
+#[cfg(test)]
+mod tests {
+    use super::*;
+
+    /// Fake decoder that always returns a fixed observable mask.
+    struct FixedDecoder(u64);
+
+    impl ObservableDecoder for FixedDecoder {
+        fn decode_to_observables(&mut self, _syndrome: &[u8]) -> Result<u64, DecoderError> {
+            Ok(self.0)
+        }
+    }
+
+    #[test]
+    fn test_majority_unanimous() {
+        let decoders: Vec<Box<dyn ObservableDecoder>> = vec![
+            Box::new(FixedDecoder(0b101)),
+            Box::new(FixedDecoder(0b101)),
+            Box::new(FixedDecoder(0b101)),
+        ];
+        let mut ensemble = EnsembleDecoder::new(decoders);
+        assert_eq!(ensemble.decode_to_observables(&[]).unwrap(), 0b101);
+    }
+
+    #[test]
+    fn test_majority_split() {
+        let decoders: Vec<Box<dyn ObservableDecoder>> = vec![
+            Box::new(FixedDecoder(0b11)),
+            Box::new(FixedDecoder(0b01)),
+            Box::new(FixedDecoder(0b01)),
+        ];
+        let mut ensemble = EnsembleDecoder::new(decoders);
+        // Bit 0: 3/3 vote flip -> flip. Bit 1: 1/3 vote flip -> no flip.
+        assert_eq!(ensemble.decode_to_observables(&[]).unwrap(), 0b01);
+    }
+
+    #[test]
+    fn test_majority_tie_goes_to_zero() {
+        // With 2 decoders, need >50% for flip. 1/2 is not >50%.
+        let decoders: Vec<Box<dyn ObservableDecoder>> =
+            vec![Box::new(FixedDecoder(1)), Box::new(FixedDecoder(0))];
+        let mut ensemble = EnsembleDecoder::new(decoders);
+        assert_eq!(ensemble.decode_to_observables(&[]).unwrap(), 0);
+    }
+
+    #[test]
+    fn test_weighted_vote() {
+        let decoders: Vec<Box<dyn ObservableDecoder>> = vec![
+            Box::new(FixedDecoder(1)), // votes flip, weight 3.0
+            Box::new(FixedDecoder(0)), // votes no flip, weight 1.0
+            Box::new(FixedDecoder(0)), // votes no flip, weight 1.0
+        ];
+        let mut ensemble = EnsembleDecoder::with_weights(decoders, vec![3.0, 1.0, 1.0]);
+        // Weight for flip: 3.0, weight for no flip: 2.0. Flip wins.
+        assert_eq!(ensemble.decode_to_observables(&[]).unwrap(), 1);
+    }
+
+    #[test]
+    fn test_empty_ensemble() {
+        let mut ensemble = EnsembleDecoder::new(vec![]);
+        assert_eq!(ensemble.decode_to_observables(&[]).unwrap(), 0);
+        assert!(ensemble.is_empty());
+    }
+
+    #[test]
+    fn test_single_decoder() {
+        let decoders: Vec<Box<dyn ObservableDecoder>> = vec![Box::new(FixedDecoder(42))];
+        let mut ensemble = EnsembleDecoder::new(decoders);
+        assert_eq!(ensemble.decode_to_observables(&[]).unwrap(), 42);
+    }
+}
diff --git a/crates/pecos-decoder-core/src/erasure.rs b/crates/pecos-decoder-core/src/erasure.rs
new file mode 100644
index 000000000..0fb661a96
--- /dev/null
+++ b/crates/pecos-decoder-core/src/erasure.rs
@@ -0,0 +1,48 @@
+// Copyright 2026 The PECOS Developers
+//
+// Licensed under the Apache License, Version 2.0 (the "License"); you may not use this file except
+// in compliance with the License. You may obtain a copy of the License at
+//
+//     https://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software distributed under the License
+// is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express
+// or implied. See the License for the specific language governing permissions and limitations under
+// the License.
+
+//! Erasure-aware observable decoder for neutral atom QEC.
+//!
+//! Neutral atoms have a dominant erasure channel: atom loss is detectable
+//! via fluorescence, giving the decoder side-channel information about
+//! which qubits were lost. This raises the surface code threshold from
+//! ~1% to ~4%.
+//!
+//! The decoder receives:
+//! - A syndrome (detection events)
+//! - A list of erased qubit/edge indices (known error locations)
+//!
+//! Erased edges are set to zero weight (certain error) during matching,
+//! guiding the decoder to incorporate them into the correction.
+
+use crate::errors::DecoderError;
+
+/// Trait for decoders that can handle erasure information alongside the syndrome.
+///
+/// For neutral atoms, erasures come from atom loss detection. The decoder
+/// sets erased edge weights to zero (guaranteed error) and finds the
+/// minimum-weight correction incorporating the known erasures.
+pub trait ObservableErasureDecoder {
+    /// Decode a syndrome with erasure side-channel information.
+    ///
+    /// `erasure_edges`: indices of edges (error mechanisms) known to have
+    /// fired. These are set to zero weight during matching.
+    ///
+    /// # Errors
+    ///
+    /// Returns `DecoderError` if decoding fails.
+    fn decode_with_erasures(
+        &mut self,
+        syndrome: &[u8],
+        erasure_edges: &[usize],
+    ) -> Result<u64, DecoderError>;
+}
diff --git a/crates/pecos-decoder-core/src/ghost_protocol.rs b/crates/pecos-decoder-core/src/ghost_protocol.rs
new file mode 100644
index 000000000..44cba87cc
--- /dev/null
+++ b/crates/pecos-decoder-core/src/ghost_protocol.rs
@@ -0,0 +1,349 @@
+// Copyright 2026 The PECOS Developers
+//
+// Licensed under the Apache License, Version 2.0 (the "License"); you may not use this file except
+// in compliance with the License. You may obtain a copy of the License at
+//
+//     https://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software distributed under the License
+// is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express
+// or implied. See the License for the specific language governing permissions and limitations under
+// the License.
+
+//! Ghost protocol for modular per-qubit decoding across transversal gates.
+//!
+//! Based on Turner et al. (arXiv:2505.23567): decomposes order-3
+//! hyperedges from transversal CNOT into per-qubit ghost edges.
+//! Each qubit's decoder runs independently with sparse message passing,
+//! enabling scalable decoding of many logical qubits.
+//!
+//! # Algorithm
+//!
+//! 1. Decompose cross-qubit hyperedges into ghost edge + ghost singleton
+//! 2. Each qubit decoded independently with ghost edges in its graph
+//! 3. If matching includes a ghost edge: refine syndrome, message partner
+//! 4. Partner flips its ghost singleton defect, re-decodes
+//! 5. Iterate until convergence (no new ghost edges detected)
+//!
+//! # References
+//!
+//! - Turner et al. "Scalable decoding protocols for fast transversal
+//!   logic in the surface code" (arXiv:2505.23567, PRX Quantum 2026)
+//! - Cain et al. "Fast correlated decoding of transversal logical
+//!   algorithms" (arXiv:2505.13587)
+
+/// A ghost edge: fragment of a cross-qubit hyperedge.
+///
+/// When a measurement error before a transversal CNOT creates a
+/// 3-detector hyperedge spanning two qubits, it decomposes into:
+/// - `ghost_edge`: time-like edge within one qubit (connects two
+///   detectors on the same qubit across the gate boundary)
+/// - `ghost_singleton`: boundary edge on the partner qubit (flips
+///   one detector on the partner)
+#[derive(Debug, Clone)]
+pub struct GhostEdge {
+    /// Qubit (patch) that owns this ghost edge.
+    pub owner_qubit: usize,
+    /// Local detector index for the first endpoint.
+    pub det_a: u32,
+    /// Local detector index for the second endpoint.
+    pub det_b: u32,
+    /// Partner qubit that owns the ghost singleton.
+    pub partner_qubit: usize,
+    /// Local detector index of the ghost singleton on the partner.
+    pub partner_det: u32,
+    /// Edge weight (log-likelihood ratio).
+    pub weight: f64,
+}
+
+/// Ghost protocol state for iterative decoding.
+///
+/// Tracks ghost edges, messages between per-qubit decoders, and
+/// syndrome refinement state. Created once per circuit structure,
+/// reused across shots.
+pub struct GhostProtocolState {
+    /// Ghost edges grouped by owner qubit.
+    pub ghost_edges: Vec<Vec<GhostEdge>>,
+    /// Number of logical qubits (patches).
+    pub num_qubits: usize,
+    /// Maximum iterations before giving up.
+    pub max_iterations: usize,
+}
+
+impl GhostProtocolState {
+    /// Create ghost protocol state for a circuit.
+    ///
+    /// `ghost_edges`: all ghost edges, will be grouped by owner qubit.
+    /// `num_qubits`: number of logical qubits.
+    #[must_use]
+    pub fn new(ghost_edges: Vec<GhostEdge>, num_qubits: usize) -> Self {
+        let mut grouped = vec![Vec::new(); num_qubits];
+        for ge in ghost_edges {
+            if ge.owner_qubit < num_qubits {
+                grouped[ge.owner_qubit].push(ge);
+            }
+        }
+        Self {
+            ghost_edges: grouped,
+            num_qubits,
+            max_iterations: 10,
+        }
+    }
+
+    /// Number of ghost edges for a qubit.
+    #[must_use]
+    pub fn num_ghost_edges(&self, qubit: usize) -> usize {
+        self.ghost_edges.get(qubit).map_or(0, std::vec::Vec::len)
+    }
+
+    /// Total ghost edges across all qubits.
+    #[must_use]
+    pub fn total_ghost_edges(&self) -> usize {
+        self.ghost_edges.iter().map(std::vec::Vec::len).sum()
+    }
+}
+
+/// Message from one qubit's decoder to another.
+///
+/// When a ghost edge is detected in the matching, the owner sends
+/// this message to the partner: "flip your ghost singleton defect."
+#[derive(Debug, Clone)]
+pub struct GhostMessage {
+    /// Target qubit.
+    pub target_qubit: usize,
+    /// Detector to flip on the target.
+    pub flip_detector: u32,
+}
+
+/// Extract ghost edges from a DEM at transversal CNOT boundaries.
+///
+/// Identifies 3-detector mechanisms where:
+/// - 2 detectors are on one qubit (the ghost edge endpoints)
+/// - 1 detector is on another qubit (the ghost singleton)
+///
+/// The qubit assignment comes from the detector's spatial coordinates
+/// and the stabilizer coordinate map.
+///
+/// Returns the ghost edges for the ghost protocol.
+/// Extract ghost edges from a DEM by identifying 3-detector hyperedges
+/// and decomposing them by qubit ownership.
+///
+/// For each 3-detector mechanism where 2 detectors are on one qubit
+/// and 1 is on another:
+/// - `ghost_edge` = the 2-detector pair (within one qubit)
+/// - `ghost_singleton` = the lone detector (on the partner qubit)
+#[must_use]
+pub fn extract_ghost_edges_from_dem(
+    dem_str: &str,
+    stab_coords: &crate::observable_subgraph::StabCoords,
+) -> Vec<GhostEdge> {
+    use crate::observable_subgraph::classify_detector;
+    use std::collections::BTreeMap;
+
+    // Parse detector coordinates
+    let det_coords = crate::dem::parse_detector_coords(dem_str);
+    let mut coord_map: BTreeMap<usize, Vec<f64>> = BTreeMap::new();
+    for dc in &det_coords {
+        coord_map.insert(dc.id as usize, dc.coords.clone());
+    }
+
+    // Classify detectors by qubit
+    let mut det_qubit: BTreeMap<usize, usize> = BTreeMap::new();
+    for (&d, coords) in &coord_map {
+        if coords.len() >= 2
+            && let Some(group) = classify_detector(coords[0], coords[1], stab_coords)
+        {
+            det_qubit.insert(d, group.qubit_idx);
+        }
+    }
+
+    let mut ghost_edges = Vec::new();
+
+    for line in dem_str.lines() {
+        let line = line.trim();
+        if !line.starts_with("error(") {
+            continue;
+        }
+
+        let Some(close) = line.find(')') else {
+            continue;
+        };
+
+        let prob: f64 = match line[6..close].parse() {
+            Ok(p) => p,
+            Err(_) => continue,
+        };
+
+        let mut dets = Vec::new();
+        for token in line[close + 1..].split_whitespace() {
+            if let Some(d_str) = token.strip_prefix('D')
+                && let Ok(d) = d_str.parse::<usize>()
+            {
+                dets.push(d);
+            }
+        }
+
+        if dets.len() != 3 {
+            continue;
+        }
+
+        let qs: Vec<Option<usize>> = dets.iter().map(|d| det_qubit.get(d).copied()).collect();
+
+        if qs.iter().any(std::option::Option::is_none) {
+            continue;
+        }
+        let qs: Vec<usize> = qs.into_iter().flatten().collect();
+
+        let weight = if prob < 1.0 && prob > 0.0 {
+            ((1.0 - prob) / prob).ln()
+        } else {
+            0.0
+        };
+
+        // Decompose: 2 on one qubit (ghost edge), 1 on another (singleton)
+        let decompose =
+            |owner_q: usize, a: usize, b: usize, partner_q: usize, c: usize| GhostEdge {
+                owner_qubit: owner_q,
+                det_a: a as u32,
+                det_b: b as u32,
+                partner_qubit: partner_q,
+                partner_det: c as u32,
+                weight,
+            };
+
+        if qs[0] == qs[1] && qs[0] != qs[2] {
+            ghost_edges.push(decompose(qs[0], dets[0], dets[1], qs[2], dets[2]));
+        } else if qs[0] == qs[2] && qs[0] != qs[1] {
+            ghost_edges.push(decompose(qs[0], dets[0], dets[2], qs[1], dets[1]));
+        } else if qs[1] == qs[2] && qs[1] != qs[0] {
+            ghost_edges.push(decompose(qs[1], dets[1], dets[2], qs[0], dets[0]));
+        }
+    }
+
+    ghost_edges
+}
+
+#[cfg(test)]
+mod tests {
+    use super::*;
+
+    #[test]
+    fn test_ghost_protocol_state() {
+        let edges = vec![
+            GhostEdge {
+                owner_qubit: 0,
+                det_a: 5,
+                det_b: 10,
+                partner_qubit: 1,
+                partner_det: 7,
+                weight: 3.0,
+            },
+            GhostEdge {
+                owner_qubit: 1,
+                det_a: 3,
+                det_b: 8,
+                partner_qubit: 0,
+                partner_det: 12,
+                weight: 3.0,
+            },
+        ];
+
+        let state = GhostProtocolState::new(edges, 2);
+        assert_eq!(state.num_qubits, 2);
+        assert_eq!(state.num_ghost_edges(0), 1);
+        assert_eq!(state.num_ghost_edges(1), 1);
+        assert_eq!(state.total_ghost_edges(), 2);
+    }
+
+    #[test]
+    fn test_empty_ghost_protocol() {
+        let state = GhostProtocolState::new(Vec::new(), 4);
+        assert_eq!(state.total_ghost_edges(), 0);
+    }
+
+    #[test]
+    fn test_extract_ghost_edges_from_synthetic_dem() {
+        use crate::observable_subgraph::QubitStabCoords;
+
+        // Two qubits: qubit 0 has X-stab at (1,1) and Z-stab at (3,1),
+        // qubit 1 has X-stab at (7,1) and Z-stab at (9,1).
+        let stab_coords = vec![
+            QubitStabCoords {
+                x_positions: vec![(1.0, 1.0)],
+                z_positions: vec![(3.0, 1.0)],
+            },
+            QubitStabCoords {
+                x_positions: vec![(7.0, 1.0)],
+                z_positions: vec![(9.0, 1.0)],
+            },
+        ];
+
+        // DEM with:
+        // - D0 at (1,1,0) -> qubit 0 (X-stab)
+        // - D1 at (3,1,0) -> qubit 0 (Z-stab)
+        // - D2 at (7,1,0) -> qubit 1 (X-stab)
+        // - 3-body error: D0 D1 D2 (2 on qubit 0, 1 on qubit 1)
+        // - 2-body error: D0 D1 (same qubit, no ghost edge)
+        let dem = "\
+            detector(1, 1, 0) D0\n\
+            detector(3, 1, 0) D1\n\
+            detector(7, 1, 0) D2\n\
+            error(0.01) D0 D1 D2\n\
+            error(0.02) D0 D1\n";
+
+        let edges = extract_ghost_edges_from_dem(dem, &stab_coords);
+
+        // Should extract exactly 1 ghost edge from the 3-body mechanism
+        assert_eq!(edges.len(), 1);
+
+        let e = &edges[0];
+        assert_eq!(e.owner_qubit, 0); // D0 and D1 are on qubit 0
+        assert_eq!(e.det_a, 0);
+        assert_eq!(e.det_b, 1);
+        assert_eq!(e.partner_qubit, 1); // D2 is on qubit 1
+        assert_eq!(e.partner_det, 2);
+
+        // Weight should be ln((1 - 0.01) / 0.01) ≈ 4.595
+        assert!((e.weight - 4.595).abs() < 0.01);
+    }
+
+    #[test]
+    fn test_extract_no_ghost_edges_graphlike_dem() {
+        use crate::observable_subgraph::QubitStabCoords;
+
+        let stab_coords = vec![QubitStabCoords {
+            x_positions: vec![(1.0, 1.0)],
+            z_positions: vec![(3.0, 1.0)],
+        }];
+
+        // Only 2-body errors -> no ghost edges
+        let dem = "\
+            detector(1, 1, 0) D0\n\
+            detector(3, 1, 0) D1\n\
+            error(0.01) D0 D1\n\
+            error(0.005) D0\n";
+
+        let edges = extract_ghost_edges_from_dem(dem, &stab_coords);
+        assert_eq!(edges.len(), 0);
+    }
+
+    #[test]
+    fn test_extract_three_same_qubit_no_ghost() {
+        use crate::observable_subgraph::QubitStabCoords;
+
+        let stab_coords = vec![QubitStabCoords {
+            x_positions: vec![(1.0, 1.0), (1.0, 3.0)],
+            z_positions: vec![(3.0, 1.0)],
+        }];
+
+        // All 3 detectors on same qubit -> no decomposition
+        let dem = "\
+            detector(1, 1, 0) D0\n\
+            detector(1, 3, 0) D1\n\
+            detector(3, 1, 0) D2\n\
+            error(0.01) D0 D1 D2\n";
+
+        let edges = extract_ghost_edges_from_dem(dem, &stab_coords);
+        assert_eq!(edges.len(), 0);
+    }
+}
diff --git a/crates/pecos-decoder-core/src/k_mwpm.rs b/crates/pecos-decoder-core/src/k_mwpm.rs
new file mode 100644
index 000000000..7814059f7
--- /dev/null
+++ b/crates/pecos-decoder-core/src/k_mwpm.rs
@@ -0,0 +1,276 @@
+// Copyright 2026 The PECOS Developers
+//
+// Licensed under the Apache License, Version 2.0 (the "License"); you may not use this file except
+// in compliance with the License. You may obtain a copy of the License at
+//
+//     https://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software distributed under the License
+// is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express
+// or implied. See the License for the specific language governing permissions and limitations under
+// the License.
+
+//! K-MWPM decoder: enumerate K lowest-weight matchings, majority vote.
+//!
+//! Based on the Chegireddy-Hamacher algorithm adapted for QEC by
+//! Mao Lin (Phys. Rev. A 112, 042436, 2025; arXiv:2510.06531).
+//!
+//! Builds a "decoding tree" where each branch removes one matched edge
+//! from the parent and re-matches. The K lowest-weight matchings give
+//! K observable predictions; majority vote selects the final answer.
+//!
+//! Works with any `MatchingDecoder` backend (UF, Fusion Blossom).
+
+use crate::ObservableDecoder;
+use crate::correlated_decoder::EdgeTrackingDecoder;
+use crate::errors::DecoderError;
+use std::cmp::Reverse;
+use std::collections::BinaryHeap;
+
+/// Configuration for the K-MWPM decoder.
+#[derive(Debug, Clone, Copy)]
+pub struct KMwpmConfig {
+    /// Number of matchings to enumerate. Default 10.
+    pub k: usize,
+}
+
+impl Default for KMwpmConfig {
+    fn default() -> Self {
+        Self { k: 10 }
+    }
+}
+
+/// One node in the decoding tree.
+struct TreeNode {
+    /// Matched edge indices from the MWPM solve.
+    matched_edges: Vec<usize>,
+    /// Edges that were removed (set to infinity) for this branch.
+    removed_edges: Vec<usize>,
+    /// Syndrome modifications: detector indices to flip.
+    flipped_detectors: Vec<usize>,
+    /// Index in `matched_edges` up to which edges are "committed" (removed).
+    commit_idx: usize,
+}
+
+/// K-MWPM decoder wrapping any `EdgeTrackingDecoder`.
+pub struct KMwpmDecoder<D> {
+    decoder: D,
+    config: KMwpmConfig,
+    num_edges: usize,
+}
+
+impl<D: EdgeTrackingDecoder> KMwpmDecoder<D> {
+    /// Create from an existing decoder.
+    pub fn new(decoder: D, config: KMwpmConfig) -> Self {
+        let num_edges = decoder.num_edges();
+        Self {
+            decoder,
+            config,
+            num_edges,
+        }
+    }
+}
+
+impl<D: EdgeTrackingDecoder> ObservableDecoder for KMwpmDecoder<D> {
+    fn decode_to_observables(&mut self, syndrome: &[u8]) -> Result<u64, DecoderError> {
+        let k = self.config.k;
+
+        // First matching: standard MWPM.
+        let (obs1, edges1) = self.decoder.decode_with_matching(syndrome)?;
+
+        if edges1.is_empty() {
+            return Ok(obs1);
+        }
+
+        // Collect K matchings via decoding tree.
+        let mut predictions: Vec<u64> = vec![obs1];
+
+        // Priority queue of tree nodes to expand (by weight, lowest first).
+        let mut pq: BinaryHeap<(Reverse<u64>, usize)> = BinaryHeap::new();
+        let mut nodes: Vec<TreeNode> = Vec::new();
+
+        let root = TreeNode {
+            matched_edges: edges1,
+            removed_edges: Vec::new(),
+            flipped_detectors: Vec::new(),
+            commit_idx: 0,
+        };
+        nodes.push(root);
+        pq.push((Reverse(0), 0)); // Weight 0 for expansion priority (children will have real weights)
+
+        while predictions.len() < k {
+            let Some((_, node_idx)) = pq.pop() else {
+                break; // No more candidates
+            };
+
+            // Expand this node: for each matched edge from commit_idx onward,
+            // create a child that removes that edge and re-matches.
+            let (matched_edges, removed_edges, flipped_detectors, commit_idx) = {
+                let node = &nodes[node_idx];
+                (
+                    node.matched_edges.clone(),
+                    node.removed_edges.clone(),
+                    node.flipped_detectors.clone(),
+                    node.commit_idx,
+                )
+            };
+
+            for j in commit_idx..matched_edges.len() {
+                // Build modified weights: removed edges get infinite weight.
+                let mut weights = vec![0.0f64; self.num_edges];
+                // Start with original weights for all edges.
+                for (e, weight) in weights.iter_mut().enumerate().take(self.num_edges) {
+                    *weight = self.decoder.edge_weight(e);
+                }
+                // Remove previously removed edges.
+                for &re in &removed_edges {
+                    weights[re] = 1e10;
+                }
+                // Remove edges e_{commit_idx}..e_j (inclusive).
+                for &re in &matched_edges[commit_idx..=j] {
+                    weights[re] = 1e10;
+                }
+
+                // Build modified syndrome: flip endpoints of committed edges.
+                let mut syn_mod = syndrome.to_vec();
+                for &det in &flipped_detectors {
+                    if det < syn_mod.len() {
+                        syn_mod[det] ^= 1;
+                    }
+                }
+                // Also flip endpoints of edges commit_idx..j-1 (newly committed).
+                let num_det = self.decoder.num_detectors();
+                for &edge_idx in &matched_edges[commit_idx..j] {
+                    let n1 = self.decoder.edge_node1(edge_idx) as usize;
+                    let n2 = self.decoder.edge_node2(edge_idx) as usize;
+                    if n1 < syn_mod.len() && n1 < num_det {
+                        syn_mod[n1] ^= 1;
+                    }
+                    if n2 < syn_mod.len() && n2 < num_det {
+                        syn_mod[n2] ^= 1;
+                    }
+                }
+
+                // Re-match with modified weights and syndrome.
+                let result = self.decoder.decode_with_weights(&syn_mod, &weights);
+                if let Ok((child_obs, child_edges)) = result {
+                    // The full observable includes committed edges' observables.
+                    let mut full_obs = child_obs;
+                    for &edge_idx in &matched_edges[..j] {
+                        full_obs ^= self.decoder.edge_obs_mask(edge_idx);
+                    }
+
+                    // Build child's removed set and flipped set.
+                    let mut child_removed = removed_edges.clone();
+                    for &re in &matched_edges[commit_idx..=j] {
+                        child_removed.push(re);
+                    }
+                    let mut child_flipped = flipped_detectors.clone();
+                    for &edge_idx in &matched_edges[commit_idx..j] {
+                        let n1 = self.decoder.edge_node1(edge_idx) as usize;
+                        let n2 = self.decoder.edge_node2(edge_idx) as usize;
+                        if n1 < num_det {
+                            child_flipped.push(n1);
+                        }
+                        if n2 < num_det {
+                            child_flipped.push(n2);
+                        }
+                    }
+
+                    predictions.push(full_obs);
+
+                    let child_node = TreeNode {
+                        matched_edges: child_edges,
+                        removed_edges: child_removed,
+                        flipped_detectors: child_flipped,
+                        commit_idx: 0,
+                    };
+                    let child_idx = nodes.len();
+                    nodes.push(child_node);
+                    // Priority by expansion order (breadth-first).
+                    pq.push((Reverse(child_idx as u64), child_idx));
+                }
+
+                if predictions.len() >= k {
+                    break;
+                }
+            }
+        }
+
+        // Majority vote across K predictions.
+        let half = predictions.len() / 2;
+        let mut result = 0u64;
+        for bit in 0..64u32 {
+            let mask = 1u64 << bit;
+            let count = predictions.iter().filter(|&&p| p & mask != 0).count();
+            if count > half {
+                result |= mask;
+            }
+        }
+        Ok(result)
+    }
+}
+
+#[cfg(test)]
+mod tests {
+    use super::*;
+    use crate::errors::DecoderError;
+
+    /// Trivial decoder: always returns obs=0, no matched edges.
+    struct TrivialDecoder {
+        num_edges: usize,
+    }
+
+    impl crate::correlated_decoder::MatchingDecoder for TrivialDecoder {
+        fn decode_with_matching(
+            &mut self,
+            _syndrome: &[u8],
+        ) -> Result<(u64, Vec<usize>), DecoderError> {
+            Ok((0, Vec::new()))
+        }
+        fn decode_with_weights(
+            &mut self,
+            _syndrome: &[u8],
+            _weights: &[f64],
+        ) -> Result<(u64, Vec<usize>), DecoderError> {
+            Ok((0, Vec::new()))
+        }
+        fn num_edges(&self) -> usize {
+            self.num_edges
+        }
+    }
+
+    impl crate::correlated_decoder::EdgeTrackingDecoder for TrivialDecoder {
+        fn edge_node1(&self, _: usize) -> u32 {
+            0
+        }
+        fn edge_node2(&self, _: usize) -> u32 {
+            1
+        }
+        fn edge_weight(&self, _: usize) -> f64 {
+            1.0
+        }
+        fn edge_obs_mask(&self, _: usize) -> u64 {
+            0
+        }
+        fn num_detectors(&self) -> usize {
+            2
+        }
+    }
+
+    #[test]
+    fn test_k_mwpm_zero_syndrome() {
+        let decoder = TrivialDecoder { num_edges: 2 };
+        let mut k_dec = KMwpmDecoder::new(decoder, KMwpmConfig { k: 5 });
+        let obs = k_dec.decode_to_observables(&[0, 0]).unwrap();
+        assert_eq!(obs, 0);
+    }
+
+    #[test]
+    fn test_k_mwpm_k1() {
+        let decoder = TrivialDecoder { num_edges: 2 };
+        let mut k_dec = KMwpmDecoder::new(decoder, KMwpmConfig { k: 1 });
+        let obs = k_dec.decode_to_observables(&[0, 0]).unwrap();
+        assert_eq!(obs, 0);
+    }
+}
diff --git a/crates/pecos-decoder-core/src/lib.rs b/crates/pecos-decoder-core/src/lib.rs
index d7d47fe1b..6ac5e2bba 100644
--- a/crates/pecos-decoder-core/src/lib.rs
+++ b/crates/pecos-decoder-core/src/lib.rs
@@ -11,12 +11,44 @@
 //! - `matrix` - Common matrix types and check matrix traits
 //! - `dem` - Detector error model traits and utilities
 
+// Decoder prototypes expose public traits while the API is still stabilizing,
+// and their metrics/index conversions intentionally cross integer and floating
+// domains. Keep this list narrow: mechanical style lints are fixed in code.
+#![allow(
+    clippy::cast_possible_truncation,
+    clippy::cast_precision_loss,
+    clippy::missing_errors_doc,
+    clippy::missing_panics_doc,
+    clippy::needless_pass_by_value
+)]
+
+pub mod adaptive;
 pub mod advanced;
+pub mod bp_matching;
+pub mod committed_osd;
 pub mod config;
+pub mod correlated_decoder;
+pub mod correlated_reweighting;
+pub mod correlation_table;
+pub mod decode_budget;
 pub mod dem;
+pub mod ensemble;
+pub mod erasure;
 pub mod errors;
+pub mod ghost_protocol;
+pub mod k_mwpm;
+pub mod logical_algorithm;
 pub mod matrix;
+pub mod multi_decoder;
+pub mod observable_subgraph;
+pub mod pauli_frame;
+pub mod perturbed;
+pub mod preprocessor;
 pub mod results;
+pub mod streaming;
+pub mod telemetry;
+pub mod two_pass_decoder;
+pub mod windowed_osd;
 
 use ndarray::ArrayView1;
 
@@ -28,7 +60,10 @@ pub use advanced::{
 pub use config::{
     BatchConfig, ConfigBuilder, DecoderConfig, DecodingMethod, PerformanceConfig, SolverType,
 };
-pub use dem::{DemConfig, DemConfigBuilder, DemDecoder, DemInfo};
+pub use dem::{
+    CheckMatrixObservableDecoder, DemCheckMatrix, DemConfig, DemConfigBuilder, DemDecoder, DemInfo,
+    DemMatchingGraph, DetectorCoord, MatchingEdge, parse_detector_coords,
+};
 pub use errors::{ConfigError, DecoderError, ErrorConvert, GraphError, MatrixError};
 pub use matrix::{CheckMatrixConfig, CheckMatrixDecoder, SparseCheckMatrix};
 pub use results::{
@@ -123,6 +158,46 @@ pub trait BatchDecoder: Decoder {
     -> Result<Vec<Self::Result>, Self::Error>;
 }
 
+// ============================================================================
+// Observable Decoder Trait (for sample+decode loops)
+// ============================================================================
+
+/// Minimal trait for decoders used in threshold estimation loops.
+///
+/// Takes a detection event syndrome (dense `&[u8]`), returns the predicted
+/// observable flip mask. This is the only interface the sample+decode
+/// orchestrator needs -- it doesn't care about decoder internals, weights,
+/// convergence, or matched edges.
+pub trait ObservableDecoder {
+    /// Decode a dense syndrome and return predicted observable flips as a bitmask.
+    ///
+    /// Bit `i` of the returned value is 1 if observable `i` is predicted to flip.
+    ///
+    /// # Errors
+    ///
+    /// Returns [`DecoderError`] if decoding fails.
+    fn decode_to_observables(&mut self, syndrome: &[u8]) -> Result<u64, DecoderError>;
+
+    /// Batch decode: flat buffer of `num_shots × num_detectors` bytes.
+    /// Returns one `u64` observable mask per shot.
+    ///
+    /// Default: loops over shots calling `decode_to_observables`.
+    /// Override for decoders with native batch support (e.g. `PyMatching`).
+    fn decode_batch_to_observables(
+        &mut self,
+        shots: &[u8],
+        num_shots: usize,
+        num_detectors: usize,
+    ) -> Result<Vec<u64>, DecoderError> {
+        let mut results = Vec::with_capacity(num_shots);
+        for i in 0..num_shots {
+            let syn = &shots[i * num_detectors..(i + 1) * num_detectors];
+            results.push(self.decode_to_observables(syn)?);
+        }
+        Ok(results)
+    }
+}
+
 // ============================================================================
 // Re-exports
 // ============================================================================
diff --git a/crates/pecos-decoder-core/src/logical_algorithm.rs b/crates/pecos-decoder-core/src/logical_algorithm.rs
new file mode 100644
index 000000000..cb97a7113
--- /dev/null
+++ b/crates/pecos-decoder-core/src/logical_algorithm.rs
@@ -0,0 +1,1050 @@
+// Copyright 2026 The PECOS Developers
+//
+// Licensed under the Apache License, Version 2.0 (the "License"); you may not use this file except
+// in compliance with the License. You may obtain a copy of the License at
+//
+//     https://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software distributed under the License
+// is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express
+// or implied. See the License for the specific language governing permissions and limitations under
+// the License.
+
+//! Logical algorithm decoder for real-time QEC.
+//!
+//! Decodes logical algorithms (sequences of memory segments separated by
+//! transversal gates) using the full-circuit DEM for accuracy, with
+//! segment structure metadata for streaming and frame propagation.
+//!
+//! # Decoding Modes
+//!
+//! - **Full-circuit**: Uses the full DEM's OSD for maximum accuracy.
+//!   Equivalent to `ObservableSubgraphDecoder` on the full circuit.
+//! - **Per-segment** (future streaming): Each segment decoded independently
+//!   with buffer overlap at gate boundaries.
+
+use crate::ObservableDecoder;
+use crate::errors::DecoderError;
+
+/// One segment of a logical algorithm.
+pub struct SegmentDescriptor {
+    /// Number of detectors in this segment's DEM.
+    pub num_detectors: usize,
+    /// Number of observables in this segment's DEM.
+    pub num_observables: usize,
+}
+
+/// Gate at a segment boundary.
+#[derive(Debug, Clone)]
+pub enum BoundaryGate {
+    /// Transversal Hadamard: swaps X↔Z frame bits for a qubit.
+    Hadamard { x_obs_bit: u32, z_obs_bit: u32 },
+    /// Transversal CNOT: propagates X forward, Z backward.
+    Cnot {
+        ctrl_x_bit: u32,
+        ctrl_z_bit: u32,
+        tgt_x_bit: u32,
+        tgt_z_bit: u32,
+    },
+    /// Transversal S gate: X corrections induce Z corrections.
+    SGate { x_obs_bit: u32, z_obs_bit: u32 },
+    /// T-gate via magic state injection (decision point).
+    ///
+    /// At this boundary, the decoder MUST produce a correction before
+    /// the hardware can proceed. The corrected measurement outcome
+    /// determines whether an S correction is applied:
+    ///   corrected = `raw_measurement` XOR frame[`z_obs_bit`]
+    ///   if corrected == 1: apply S gate on the data qubit
+    ///
+    /// This is a feed-forward decision point with a reaction time
+    /// deadline. The decoder's frame must be ready.
+    TGateInjection {
+        /// Observable bit for the data qubit's Z correction.
+        z_obs_bit: u32,
+        /// Observable bit for the ancilla's Z measurement.
+        ancilla_z_bit: u32,
+    },
+}
+
+/// Marks whether a segment boundary is a decision point.
+///
+/// At decision points, the decoder must provide the Pauli frame
+/// within the reaction time budget. At non-decision boundaries
+/// (Clifford gates), the frame is metadata — no deadline.
+impl BoundaryGate {
+    /// Whether this gate is a feed-forward decision point.
+    #[must_use]
+    pub fn is_decision_point(&self) -> bool {
+        matches!(self, Self::TGateInjection { .. })
+    }
+}
+
+/// Full description of a logical algorithm for decoding.
+pub struct AlgorithmDescriptor {
+    /// Per-segment descriptors.
+    pub segments: Vec<SegmentDescriptor>,
+    /// Gates at segment boundaries. `boundary_gates[i]` between segment i and i+1.
+    pub boundary_gates: Vec<Vec<BoundaryGate>>,
+    /// Total number of observables.
+    pub num_observables: usize,
+}
+
+/// Decoder for logical quantum algorithms.
+///
+/// Wraps a full-circuit decoder (OSD) with segment metadata. The
+/// segment structure enables:
+/// - Tracking which gates occur at which point in the circuit
+/// - Pauli frame propagation for T-gate/measurement corrections
+/// - Future streaming mode with per-segment windowed decoding
+///
+/// In the current implementation, `decode_shot` delegates to the
+/// full-circuit OSD for maximum accuracy. The segment structure is
+/// metadata for frame tracking and streaming (step 5).
+pub struct LogicalAlgorithmDecoder {
+    /// Full-circuit decoder (OSD on the complete DEM).
+    full_decoder: Box<dyn ObservableDecoder + Send + Sync>,
+    /// Segment metadata for streaming/frame tracking.
+    segments: Vec<SegmentDescriptor>,
+    /// Gates at segment boundaries.
+    boundary_gates: Vec<Vec<BoundaryGate>>,
+    /// Total number of observables.
+    _num_observables: usize,
+}
+
+impl LogicalAlgorithmDecoder {
+    /// Build from a full-circuit decoder and algorithm descriptor.
+    ///
+    /// The `full_decoder` is typically an `ObservableSubgraphDecoder`
+    /// built from the full circuit DEM.
+    #[must_use]
+    pub fn new(
+        full_decoder: Box<dyn ObservableDecoder + Send + Sync>,
+        descriptor: AlgorithmDescriptor,
+    ) -> Self {
+        Self {
+            full_decoder,
+            segments: descriptor.segments,
+            boundary_gates: descriptor.boundary_gates,
+            _num_observables: descriptor.num_observables,
+        }
+    }
+
+    /// Decode one shot using the full-circuit decoder.
+    pub fn decode_shot(&mut self, syndrome: &[u8]) -> Result<u64, DecoderError> {
+        self.full_decoder.decode_to_observables(syndrome)
+    }
+
+    /// Number of segments.
+    #[must_use]
+    pub fn num_segments(&self) -> usize {
+        self.segments.len()
+    }
+
+    /// Total detectors across all segments.
+    #[must_use]
+    pub fn total_detectors(&self) -> usize {
+        self.segments.iter().map(|s| s.num_detectors).sum()
+    }
+
+    /// Apply boundary gate to a Pauli frame.
+    /// Used when consuming the frame at logical operations.
+    pub fn apply_boundary_gate(frame: &mut u64, gate: &BoundaryGate) {
+        match gate {
+            BoundaryGate::Hadamard {
+                x_obs_bit,
+                z_obs_bit,
+            } => {
+                let x_set = (*frame >> x_obs_bit) & 1;
+                let z_set = (*frame >> z_obs_bit) & 1;
+                *frame &= !(1u64 << x_obs_bit);
+                *frame &= !(1u64 << z_obs_bit);
+                *frame |= z_set << x_obs_bit;
+                *frame |= x_set << z_obs_bit;
+            }
+            BoundaryGate::Cnot {
+                ctrl_x_bit,
+                ctrl_z_bit,
+                tgt_x_bit,
+                tgt_z_bit,
+            } => {
+                if (*frame >> ctrl_x_bit) & 1 != 0 {
+                    *frame ^= 1u64 << tgt_x_bit;
+                }
+                if (*frame >> tgt_z_bit) & 1 != 0 {
+                    *frame ^= 1u64 << ctrl_z_bit;
+                }
+            }
+            BoundaryGate::SGate {
+                x_obs_bit,
+                z_obs_bit,
+            } => {
+                if (*frame >> x_obs_bit) & 1 != 0 {
+                    *frame ^= 1u64 << z_obs_bit;
+                }
+            }
+            BoundaryGate::TGateInjection {
+                z_obs_bit,
+                ancilla_z_bit,
+            } => {
+                // T-gate teleportation: CX(data, ancilla) + measure ancilla Z.
+                // The ancilla Z measurement outcome (corrected by frame)
+                // determines whether to apply S correction on data.
+                //
+                // Frame propagation: the ancilla's Z observable is folded
+                // into the data's Z observable. If the ancilla Z bit is
+                // set in the frame, flip the data's Z bit.
+                if (*frame >> ancilla_z_bit) & 1 != 0 {
+                    *frame ^= 1u64 << z_obs_bit;
+                }
+            }
+        }
+    }
+}
+
+impl ObservableDecoder for LogicalAlgorithmDecoder {
+    fn decode_to_observables(&mut self, syndrome: &[u8]) -> Result<u64, DecoderError> {
+        self.decode_shot(syndrome)
+    }
+}
+
+// ============================================================================
+// Streaming mode
+// ============================================================================
+
+/// Streaming wrapper for `LogicalAlgorithmDecoder`.
+///
+/// Buffers syndrome data round-by-round. The full-circuit OSD decodes
+/// the entire accumulated syndrome at `flush()` for maximum accuracy.
+///
+/// The segment structure tracks which rounds belong to which segment.
+/// At each segment boundary, the Pauli frame can be queried and
+/// propagated through the boundary gate.
+///
+/// # Usage
+///
+/// ```
+/// use pecos_decoder_core::{DecoderError, ObservableDecoder};
+/// use pecos_decoder_core::logical_algorithm::{
+///     AlgorithmDescriptor, LogicalAlgorithmDecoder, SegmentDescriptor, StreamingLogicalDecoder,
+/// };
+///
+/// struct AnyDetectionDecoder;
+///
+/// impl ObservableDecoder for AnyDetectionDecoder {
+///     fn decode_to_observables(&mut self, syndrome: &[u8]) -> Result<u64, DecoderError> {
+///         Ok(u64::from(syndrome.iter().any(|&bit| bit != 0)))
+///     }
+/// }
+///
+/// let descriptor = AlgorithmDescriptor {
+///     segments: vec![SegmentDescriptor {
+///         num_detectors: 2,
+///         num_observables: 1,
+///     }],
+///     boundary_gates: vec![],
+///     num_observables: 1,
+/// };
+/// let decoder = LogicalAlgorithmDecoder::new(Box::new(AnyDetectionDecoder), descriptor);
+/// let mut stream = StreamingLogicalDecoder::new(decoder);
+///
+/// // Feed syndrome round by round
+/// for sparse_round in [vec![(0, 1)], vec![(1, 0)]] {
+///     stream.feed_sparse(&sparse_round);
+/// }
+///
+/// // Decode at the end
+/// let obs = stream.flush().unwrap();
+/// assert_eq!(obs, 1);
+/// ```
+pub struct StreamingLogicalDecoder {
+    /// The underlying batch decoder (full-circuit OSD).
+    inner: LogicalAlgorithmDecoder,
+    /// Accumulated syndrome buffer (full circuit size).
+    syndrome: Vec<u8>,
+    /// Total detectors.
+    total_detectors: usize,
+    /// Rounds fed so far.
+    rounds_fed: usize,
+    /// Accumulated observable correction from last flush.
+    accumulated_obs: u64,
+}
+
+impl StreamingLogicalDecoder {
+    /// Create from a `LogicalAlgorithmDecoder`.
+    #[must_use]
+    pub fn new(decoder: LogicalAlgorithmDecoder) -> Self {
+        let total = decoder.total_detectors();
+        Self {
+            inner: decoder,
+            syndrome: vec![0u8; total],
+            total_detectors: total,
+            rounds_fed: 0,
+            accumulated_obs: 0,
+        }
+    }
+
+    /// Feed one detection event into the syndrome buffer.
+    #[inline]
+    pub fn feed_detection(&mut self, detector_idx: usize, value: u8) {
+        if detector_idx < self.total_detectors {
+            self.syndrome[detector_idx] = value;
+        }
+    }
+
+    /// Feed a dense syndrome slice (all detectors, in order).
+    pub fn feed_dense(&mut self, syndrome: &[u8]) {
+        let len = syndrome.len().min(self.total_detectors);
+        self.syndrome[..len].copy_from_slice(&syndrome[..len]);
+    }
+
+    /// Feed sparse detection events: (`detector_index`, value) pairs.
+    pub fn feed_sparse(&mut self, detectors: &[(u32, u8)]) {
+        for &(det, val) in detectors {
+            self.feed_detection(det as usize, val);
+        }
+        self.rounds_fed += 1;
+    }
+
+    /// Decode the accumulated syndrome using the full-circuit OSD.
+    ///
+    /// Returns the observable correction mask. This is the final
+    /// correction to apply to raw measurement outcomes.
+    pub fn flush(&mut self) -> Result<u64, DecoderError> {
+        let obs = self.inner.decode_shot(&self.syndrome)?;
+        self.accumulated_obs = obs;
+        Ok(obs)
+    }
+
+    /// Decode a full syndrome at once (convenience for batch mode).
+    pub fn decode_shot(&mut self, syndrome: &[u8]) -> Result<u64, DecoderError> {
+        self.feed_dense(syndrome);
+        self.flush()
+    }
+
+    /// Current accumulated observable correction.
+    #[must_use]
+    pub fn accumulated_obs(&self) -> u64 {
+        self.accumulated_obs
+    }
+
+    /// Number of segments in the algorithm.
+    #[must_use]
+    pub fn num_segments(&self) -> usize {
+        self.inner.num_segments()
+    }
+
+    /// Rounds fed so far.
+    #[must_use]
+    pub fn rounds_fed(&self) -> usize {
+        self.rounds_fed
+    }
+
+    /// Access the boundary gates for frame propagation.
+    #[must_use]
+    pub fn boundary_gates(&self) -> &[Vec<BoundaryGate>] {
+        &self.inner.boundary_gates
+    }
+
+    /// Apply boundary gate to a Pauli frame (delegates to inner).
+    pub fn apply_boundary_gate(frame: &mut u64, gate: &BoundaryGate) {
+        LogicalAlgorithmDecoder::apply_boundary_gate(frame, gate);
+    }
+
+    /// Reset for the next shot.
+    pub fn reset(&mut self) {
+        self.syndrome.fill(0);
+        self.rounds_fed = 0;
+        self.accumulated_obs = 0;
+    }
+}
+
+/// Simulate streaming decode on a batch of samples.
+///
+/// For each shot: feeds the dense syndrome, flushes, checks against expected.
+/// Returns the number of logical errors. This simulates what a real-time
+/// system would do — feed syndromes and flush at the end.
+pub fn streaming_decode_count(
+    decoder: &mut StreamingLogicalDecoder,
+    syndromes: &[Vec<u8>],
+    expected_masks: &[u64],
+) -> Result<usize, DecoderError> {
+    let mut errors = 0;
+    for (syn, &expected) in syndromes.iter().zip(expected_masks.iter()) {
+        decoder.reset();
+        let predicted = decoder.decode_shot(syn)?;
+        if predicted != expected {
+            errors += 1;
+        }
+    }
+    Ok(errors)
+}
+
+// ============================================================================
+// Budget-aware logical circuit decoder
+// ============================================================================
+
+use crate::decode_budget::{DecodeBudget, DecodeStrategy, DetectorRegion};
+
+/// Budget-aware decoder for logical quantum circuits.
+///
+/// Composes a `DecodeStrategy` (which handles the decode/commit pattern)
+/// with segment tracking and Pauli frame propagation. The strategy is
+/// selected based on the hardware's time budget.
+///
+/// # Decode Modes
+///
+/// - **Offline** (ion trap / simulation): `FullCircuitStrategy` — buffer
+///   everything, decode at end. Maximum accuracy.
+/// - **Streaming** (neutral atom): `CommittedOsdStrategy` — decode and
+///   commit at segment boundaries. Bounded memory.
+/// - **Real-time** (superconducting): windowed UF with ghost protocol
+///   (future).
+///
+/// All modes use the same segment + gate + frame infrastructure.
+pub struct LogicalCircuitDecoder {
+    /// The decode strategy (owns the inner decoder).
+    strategy: Box<dyn DecodeStrategy + Send + Sync>,
+    /// Segment metadata.
+    segments: Vec<SegmentDescriptor>,
+    /// Cumulative detector offsets per segment.
+    _segment_offsets: Vec<usize>,
+    /// Gates at segment boundaries.
+    boundary_gates: Vec<Vec<BoundaryGate>>,
+    /// Per-qubit Pauli frames.
+    frames: Vec<u64>,
+    /// Decode budget.
+    budget: DecodeBudget,
+    /// Syndrome buffer.
+    syndrome: Vec<u8>,
+    /// Total detectors.
+    total_detectors: usize,
+    /// Current segment being fed.
+    current_segment: usize,
+    /// Detectors fed into the current segment so far.
+    current_segment_fed: usize,
+}
+
+impl LogicalCircuitDecoder {
+    /// Build from an algorithm descriptor, decode strategy, and budget.
+    #[must_use]
+    pub fn new(
+        descriptor: AlgorithmDescriptor,
+        strategy: Box<dyn DecodeStrategy + Send + Sync>,
+        budget: DecodeBudget,
+        num_qubits: usize,
+    ) -> Self {
+        let mut segment_offsets = Vec::with_capacity(descriptor.segments.len());
+        let mut offset = 0;
+        for seg in &descriptor.segments {
+            segment_offsets.push(offset);
+            offset += seg.num_detectors;
+        }
+        let total_detectors = offset;
+
+        Self {
+            strategy,
+            segments: descriptor.segments,
+            _segment_offsets: segment_offsets,
+            boundary_gates: descriptor.boundary_gates,
+            frames: vec![0u64; num_qubits],
+            budget,
+            syndrome: vec![0u8; total_detectors],
+            total_detectors,
+            current_segment: 0,
+            current_segment_fed: 0,
+        }
+    }
+
+    /// Decode a full shot (batch mode).
+    ///
+    /// For offline/ion trap budgets: equivalent to full-circuit OSD.
+    /// For streaming budgets: decodes and commits each segment.
+    pub fn decode_shot(&mut self, full_syndrome: &[u8]) -> Result<u64, DecoderError> {
+        self.reset();
+        let len = full_syndrome.len().min(self.total_detectors);
+        self.syndrome[..len].copy_from_slice(&full_syndrome[..len]);
+
+        // Single decode of the full syndrome. The strategy handles
+        // commitment internally if it supports it.
+        self.strategy.decode(&self.syndrome)
+    }
+
+    /// Batch decode: count logical errors across a batch of shots.
+    pub fn decode_count(
+        &mut self,
+        syndromes: &[Vec<u8>],
+        expected_masks: &[u64],
+    ) -> Result<usize, DecoderError> {
+        let mut errors = 0;
+        for (syn, &expected) in syndromes.iter().zip(expected_masks.iter()) {
+            let predicted = self.decode_shot(syn)?;
+            if predicted != expected {
+                errors += 1;
+            }
+        }
+        Ok(errors)
+    }
+
+    /// Number of segments.
+    #[must_use]
+    pub fn num_segments(&self) -> usize {
+        self.segments.len()
+    }
+
+    /// Whether the algorithm has any feed-forward decision points.
+    ///
+    /// If false, the budget doesn't matter — all corrections are
+    /// metadata applied at the end (Clifford-only circuit).
+    /// If true, the reaction time budget is meaningful.
+    #[must_use]
+    pub fn has_decision_points(&self) -> bool {
+        self.boundary_gates
+            .iter()
+            .any(|gates| gates.iter().any(BoundaryGate::is_decision_point))
+    }
+
+    /// Number of decision points (T gates, magic state injections).
+    #[must_use]
+    pub fn num_decision_points(&self) -> usize {
+        self.boundary_gates
+            .iter()
+            .flat_map(|gates| gates.iter())
+            .filter(|g| g.is_decision_point())
+            .count()
+    }
+
+    /// Total detectors.
+    #[must_use]
+    pub fn total_detectors(&self) -> usize {
+        self.total_detectors
+    }
+
+    /// Current Pauli frames (per qubit).
+    #[must_use]
+    pub fn frames(&self) -> &[u64] {
+        &self.frames
+    }
+
+    /// The decode budget.
+    #[must_use]
+    pub fn budget(&self) -> &DecodeBudget {
+        &self.budget
+    }
+
+    /// Reset for next shot.
+    pub fn reset(&mut self) {
+        self.strategy.reset();
+        self.syndrome.fill(0);
+        self.frames.fill(0);
+        self.current_segment = 0;
+        self.current_segment_fed = 0;
+    }
+}
+
+impl ObservableDecoder for LogicalCircuitDecoder {
+    fn decode_to_observables(&mut self, syndrome: &[u8]) -> Result<u64, DecoderError> {
+        self.decode_shot(syndrome)
+    }
+}
+
+// ============================================================================
+// Strategy: Full Circuit (offline / ion trap)
+// ============================================================================
+
+/// Full-circuit decode strategy.
+///
+/// Buffers the entire syndrome, decodes at flush. Maximum accuracy.
+/// Used for offline analysis, ion trap systems, or any budget that
+/// allows full-circuit processing.
+pub struct FullCircuitStrategy {
+    inner: Box<dyn ObservableDecoder + Send + Sync>,
+}
+
+impl FullCircuitStrategy {
+    /// Wrap any `ObservableDecoder` (typically OSD).
+    #[must_use]
+    pub fn new(decoder: Box<dyn ObservableDecoder + Send + Sync>) -> Self {
+        Self { inner: decoder }
+    }
+}
+
+impl DecodeStrategy for FullCircuitStrategy {
+    fn decode(&mut self, syndrome: &[u8]) -> Result<u64, DecoderError> {
+        self.inner.decode_to_observables(syndrome)
+    }
+
+    fn commit(&mut self, _region: &DetectorRegion) -> Result<u64, DecoderError> {
+        // Full circuit doesn't commit incrementally
+        Ok(0)
+    }
+
+    fn committed_obs(&self) -> u64 {
+        0
+    }
+
+    fn reset(&mut self) {
+        // No state to reset for full-circuit strategy
+    }
+}
+
+// ============================================================================
+// Strategy: Windowed OSD (neutral atom / medium budget)
+// ============================================================================
+
+/// Windowed OSD strategy: per-observable subgraph windowed decoding.
+///
+/// Each observable's subgraph is graphlike (no hyperedges). A windowed
+/// decoder (sandwich or plain PM) runs inside each subgraph with bounded
+/// latency. The full matching graph is pre-built; only syndrome routing
+/// and per-window matching are per-shot work.
+///
+/// This achieves bounded-latency streaming with OSD-level accuracy.
+pub struct WindowedOsdStrategy {
+    /// Per-subgraph decoders (windowed or plain).
+    subgraph_decoders: Vec<Box<dyn ObservableDecoder + Send + Sync>>,
+    /// Per-subgraph detector maps: `subgraph_detector_maps`[i][local] = global.
+    detector_maps: Vec<Vec<usize>>,
+    /// Per-subgraph sub-syndrome buffers (reusable).
+    sub_syndromes: Vec<Vec<u8>>,
+    /// Number of observables.
+    _num_observables: usize,
+}
+
+impl WindowedOsdStrategy {
+    /// Build from pre-extracted subgraph DEMs and detector maps.
+    ///
+    /// `subgraph_dems`: per-observable DEM strings (graphlike).
+    /// `detector_maps`: per-observable local→global detector index maps.
+    /// `factory`: creates the inner decoder for each subgraph DEM.
+    pub fn new<F>(
+        subgraph_dems: Vec<String>,
+        detector_maps: Vec<Vec<usize>>,
+        mut factory: F,
+    ) -> Result<Self, DecoderError>
+    where
+        F: FnMut(&str) -> Result<Box<dyn ObservableDecoder + Send + Sync>, DecoderError>,
+    {
+        let num_observables = subgraph_dems.len();
+        let mut decoders = Vec::with_capacity(num_observables);
+        let mut sub_syndromes = Vec::with_capacity(num_observables);
+
+        for (i, dem_str) in subgraph_dems.iter().enumerate() {
+            let dec = factory(dem_str)?;
+            let n = detector_maps.get(i).map_or(0, std::vec::Vec::len);
+            sub_syndromes.push(vec![0u8; n]);
+            decoders.push(dec);
+        }
+
+        Ok(Self {
+            subgraph_decoders: decoders,
+            detector_maps,
+            sub_syndromes,
+            _num_observables: num_observables,
+        })
+    }
+}
+
+impl DecodeStrategy for WindowedOsdStrategy {
+    fn decode(&mut self, syndrome: &[u8]) -> Result<u64, DecoderError> {
+        let mut obs_mask = 0u64;
+
+        for (i, (dec, dmap)) in self
+            .subgraph_decoders
+            .iter_mut()
+            .zip(self.detector_maps.iter())
+            .enumerate()
+        {
+            let n = dmap.len();
+            if n == 0 {
+                continue;
+            }
+
+            // Route global syndrome to subgraph-local syndrome
+            let buf = &mut self.sub_syndromes[i];
+            for (local, &global) in dmap.iter().enumerate() {
+                buf[local] = if global < syndrome.len() {
+                    syndrome[global]
+                } else {
+                    0
+                };
+            }
+
+            // Decode this subgraph
+            let sub_obs = dec.decode_to_observables(&buf[..n])?;
+            if sub_obs & 1 != 0 {
+                obs_mask |= 1 << i;
+            }
+        }
+
+        Ok(obs_mask)
+    }
+
+    fn commit(&mut self, _region: &DetectorRegion) -> Result<u64, DecoderError> {
+        // Commitment is handled internally by the windowed inner decoders
+        Ok(0)
+    }
+
+    fn committed_obs(&self) -> u64 {
+        0
+    }
+
+    fn reset(&mut self) {
+        for buf in &mut self.sub_syndromes {
+            buf.fill(0);
+        }
+    }
+}
+
+#[cfg(test)]
+mod tests {
+    use super::*;
+
+    struct FixedDecoder(u64);
+    impl ObservableDecoder for FixedDecoder {
+        fn decode_to_observables(&mut self, _: &[u8]) -> Result<u64, DecoderError> {
+            Ok(self.0)
+        }
+    }
+
+    #[test]
+    fn test_single_segment() {
+        let desc = AlgorithmDescriptor {
+            segments: vec![SegmentDescriptor {
+                num_detectors: 4,
+                num_observables: 2,
+            }],
+            boundary_gates: vec![],
+            num_observables: 2,
+        };
+        let mut dec = LogicalAlgorithmDecoder::new(Box::new(FixedDecoder(0b01)), desc);
+        assert_eq!(dec.decode_shot(&[0, 1, 0, 1]).unwrap(), 0b01);
+    }
+
+    #[test]
+    fn test_hadamard_frame() {
+        let mut frame = 0b01u64; // X correction on bit 0
+        LogicalAlgorithmDecoder::apply_boundary_gate(
+            &mut frame,
+            &BoundaryGate::Hadamard {
+                x_obs_bit: 0,
+                z_obs_bit: 1,
+            },
+        );
+        assert_eq!(frame, 0b10); // X became Z
+    }
+
+    #[test]
+    fn test_cnot_frame() {
+        let mut frame = 0b0001u64; // X on control (bit 0)
+        LogicalAlgorithmDecoder::apply_boundary_gate(
+            &mut frame,
+            &BoundaryGate::Cnot {
+                ctrl_x_bit: 0,
+                ctrl_z_bit: 1,
+                tgt_x_bit: 2,
+                tgt_z_bit: 3,
+            },
+        );
+        assert_eq!(frame, 0b0101); // X propagated to target
+    }
+
+    #[test]
+    fn test_logical_circuit_decoder_unlimited() {
+        let desc = AlgorithmDescriptor {
+            segments: vec![
+                SegmentDescriptor {
+                    num_detectors: 4,
+                    num_observables: 2,
+                },
+                SegmentDescriptor {
+                    num_detectors: 4,
+                    num_observables: 2,
+                },
+            ],
+            boundary_gates: vec![vec![BoundaryGate::Hadamard {
+                x_obs_bit: 0,
+                z_obs_bit: 1,
+            }]],
+            num_observables: 2,
+        };
+
+        let strategy = FullCircuitStrategy::new(Box::new(FixedDecoder(0b01)));
+        let budget = DecodeBudget::unlimited();
+
+        let mut dec = LogicalCircuitDecoder::new(desc, Box::new(strategy), budget, 1);
+        let result = dec.decode_shot(&[0, 0, 0, 0, 0, 0, 0, 0]).unwrap();
+        assert_eq!(result, 0b01);
+    }
+
+    #[test]
+    fn test_cnot_frame_z_backward() {
+        // Z on target should propagate back to control
+        let mut frame = 0b1000u64; // Z on target (bit 3)
+        LogicalAlgorithmDecoder::apply_boundary_gate(
+            &mut frame,
+            &BoundaryGate::Cnot {
+                ctrl_x_bit: 0,
+                ctrl_z_bit: 1,
+                tgt_x_bit: 2,
+                tgt_z_bit: 3,
+            },
+        );
+        assert_eq!(frame, 0b1010); // Z propagated back to control Z (bit 1)
+    }
+
+    #[test]
+    fn test_cnot_frame_both_directions() {
+        // X on control + Z on target -> both propagate
+        let mut frame = 0b1001u64; // X on ctrl (bit 0), Z on tgt (bit 3)
+        LogicalAlgorithmDecoder::apply_boundary_gate(
+            &mut frame,
+            &BoundaryGate::Cnot {
+                ctrl_x_bit: 0,
+                ctrl_z_bit: 1,
+                tgt_x_bit: 2,
+                tgt_z_bit: 3,
+            },
+        );
+        // X ctrl -> X tgt (bit 2), Z tgt -> Z ctrl (bit 1)
+        assert_eq!(frame, 0b1111);
+    }
+
+    #[test]
+    fn test_sgate_frame_x_induces_z() {
+        // S gate: X correction induces Z correction (X -> XZ = Y)
+        let mut frame = 0b01u64; // X correction on bit 0
+        LogicalAlgorithmDecoder::apply_boundary_gate(
+            &mut frame,
+            &BoundaryGate::SGate {
+                x_obs_bit: 0,
+                z_obs_bit: 1,
+            },
+        );
+        assert_eq!(frame, 0b11); // X stays, Z also set
+    }
+
+    #[test]
+    fn test_sgate_frame_z_unchanged() {
+        // S gate: Z correction is unchanged (S commutes with Z)
+        let mut frame = 0b10u64; // Z correction on bit 1
+        LogicalAlgorithmDecoder::apply_boundary_gate(
+            &mut frame,
+            &BoundaryGate::SGate {
+                x_obs_bit: 0,
+                z_obs_bit: 1,
+            },
+        );
+        assert_eq!(frame, 0b10); // Z stays, no X induced
+    }
+
+    #[test]
+    fn test_sgate_frame_no_correction() {
+        let mut frame = 0u64;
+        LogicalAlgorithmDecoder::apply_boundary_gate(
+            &mut frame,
+            &BoundaryGate::SGate {
+                x_obs_bit: 0,
+                z_obs_bit: 1,
+            },
+        );
+        assert_eq!(frame, 0); // No correction, no change
+    }
+
+    #[test]
+    fn test_t_injection_frame_ancilla_z_folds() {
+        // T injection: ancilla Z bit folds into data Z bit
+        let mut frame = 0b1000u64; // ancilla Z set (bit 3)
+        LogicalAlgorithmDecoder::apply_boundary_gate(
+            &mut frame,
+            &BoundaryGate::TGateInjection {
+                z_obs_bit: 1,     // data Z
+                ancilla_z_bit: 3, // ancilla Z
+            },
+        );
+        assert_eq!(frame, 0b1010); // data Z (bit 1) flipped
+    }
+
+    #[test]
+    fn test_t_injection_frame_ancilla_z_cancels() {
+        // If data Z already set and ancilla Z set, they cancel (XOR)
+        let mut frame = 0b1010u64; // both data Z (bit 1) and ancilla Z (bit 3)
+        LogicalAlgorithmDecoder::apply_boundary_gate(
+            &mut frame,
+            &BoundaryGate::TGateInjection {
+                z_obs_bit: 1,
+                ancilla_z_bit: 3,
+            },
+        );
+        assert_eq!(frame, 0b1000); // data Z cancelled, ancilla unchanged
+    }
+
+    #[test]
+    fn test_t_injection_frame_no_ancilla_z() {
+        // No ancilla Z -> no change
+        let mut frame = 0b0010u64; // data Z set, ancilla Z not set
+        LogicalAlgorithmDecoder::apply_boundary_gate(
+            &mut frame,
+            &BoundaryGate::TGateInjection {
+                z_obs_bit: 1,
+                ancilla_z_bit: 3,
+            },
+        );
+        assert_eq!(frame, 0b0010); // unchanged
+    }
+
+    #[test]
+    fn test_hadamard_frame_swap_both() {
+        // Both X and Z set -> swap
+        let mut frame = 0b11u64;
+        LogicalAlgorithmDecoder::apply_boundary_gate(
+            &mut frame,
+            &BoundaryGate::Hadamard {
+                x_obs_bit: 0,
+                z_obs_bit: 1,
+            },
+        );
+        assert_eq!(frame, 0b11); // Swap of (1,1) is still (1,1)
+    }
+
+    #[test]
+    fn test_hadamard_frame_z_to_x() {
+        let mut frame = 0b10u64; // Z only
+        LogicalAlgorithmDecoder::apply_boundary_gate(
+            &mut frame,
+            &BoundaryGate::Hadamard {
+                x_obs_bit: 0,
+                z_obs_bit: 1,
+            },
+        );
+        assert_eq!(frame, 0b01); // Z became X
+    }
+
+    #[test]
+    fn test_is_decision_point() {
+        assert!(
+            BoundaryGate::TGateInjection {
+                z_obs_bit: 1,
+                ancilla_z_bit: 3,
+            }
+            .is_decision_point()
+        );
+
+        assert!(
+            !BoundaryGate::Hadamard {
+                x_obs_bit: 0,
+                z_obs_bit: 1,
+            }
+            .is_decision_point()
+        );
+
+        assert!(
+            !BoundaryGate::Cnot {
+                ctrl_x_bit: 0,
+                ctrl_z_bit: 1,
+                tgt_x_bit: 2,
+                tgt_z_bit: 3,
+            }
+            .is_decision_point()
+        );
+
+        assert!(
+            !BoundaryGate::SGate {
+                x_obs_bit: 0,
+                z_obs_bit: 1,
+            }
+            .is_decision_point()
+        );
+    }
+
+    #[test]
+    fn test_budget_windowed_vs_unlimited() {
+        use std::time::Duration;
+        let windowed = DecodeBudget::from_reaction_time(Duration::from_millis(1), 7);
+        assert!(windowed.is_windowed());
+
+        let unlimited = DecodeBudget::unlimited();
+        assert!(unlimited.is_unlimited());
+    }
+
+    #[test]
+    fn test_streaming_feed_dense_and_flush() {
+        let desc = AlgorithmDescriptor {
+            segments: vec![SegmentDescriptor {
+                num_detectors: 4,
+                num_observables: 2,
+            }],
+            boundary_gates: vec![],
+            num_observables: 2,
+        };
+        let inner = LogicalAlgorithmDecoder::new(Box::new(FixedDecoder(0b10)), desc);
+        let mut streaming = StreamingLogicalDecoder::new(inner);
+
+        // Feed full syndrome at once
+        let result = streaming.decode_shot(&[0, 1, 0, 1]).unwrap();
+        assert_eq!(result, 0b10);
+        assert_eq!(streaming.accumulated_obs(), 0b10);
+    }
+
+    #[test]
+    fn test_streaming_feed_sparse() {
+        let desc = AlgorithmDescriptor {
+            segments: vec![SegmentDescriptor {
+                num_detectors: 4,
+                num_observables: 2,
+            }],
+            boundary_gates: vec![],
+            num_observables: 2,
+        };
+        let inner = LogicalAlgorithmDecoder::new(Box::new(FixedDecoder(0b01)), desc);
+        let mut streaming = StreamingLogicalDecoder::new(inner);
+
+        // Feed individual detectors
+        streaming.feed_detection(1, 1);
+        streaming.feed_detection(3, 1);
+        let result = streaming.flush().unwrap();
+        assert_eq!(result, 0b01);
+    }
+
+    #[test]
+    fn test_streaming_reset() {
+        let desc = AlgorithmDescriptor {
+            segments: vec![SegmentDescriptor {
+                num_detectors: 4,
+                num_observables: 2,
+            }],
+            boundary_gates: vec![],
+            num_observables: 2,
+        };
+        let inner = LogicalAlgorithmDecoder::new(Box::new(FixedDecoder(0b11)), desc);
+        let mut streaming = StreamingLogicalDecoder::new(inner);
+
+        streaming.decode_shot(&[1, 0, 1, 0]).unwrap();
+        assert_eq!(streaming.accumulated_obs(), 0b11);
+
+        streaming.reset();
+        assert_eq!(streaming.accumulated_obs(), 0);
+    }
+
+    #[test]
+    fn test_streaming_decode_count() {
+        let desc = AlgorithmDescriptor {
+            segments: vec![SegmentDescriptor {
+                num_detectors: 2,
+                num_observables: 1,
+            }],
+            boundary_gates: vec![],
+            num_observables: 1,
+        };
+        let inner = LogicalAlgorithmDecoder::new(
+            Box::new(FixedDecoder(0b1)),
+            desc, // always predicts obs flip
+        );
+        let mut streaming = StreamingLogicalDecoder::new(inner);
+
+        let syndromes = vec![vec![0u8, 0], vec![1, 0], vec![0, 1]];
+        let expected = vec![0b1, 0b0, 0b1]; // matches on shot 0 and 2
+
+        let errors = streaming_decode_count(&mut streaming, &syndromes, &expected).unwrap();
+        assert_eq!(errors, 1); // only shot 1 is wrong (predicted 1, expected 0)
+    }
+}
diff --git a/crates/pecos-decoder-core/src/multi_decoder.rs b/crates/pecos-decoder-core/src/multi_decoder.rs
new file mode 100644
index 000000000..c88e291b6
--- /dev/null
+++ b/crates/pecos-decoder-core/src/multi_decoder.rs
@@ -0,0 +1,245 @@
+// Copyright 2026 The PECOS Developers
+//
+// Licensed under the Apache License, Version 2.0 (the "License"); you may not use this file except
+// in compliance with the License. You may obtain a copy of the License at
+//
+//     https://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software distributed under the License
+// is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express
+// or implied. See the License for the specific language governing permissions and limitations under
+// the License.
+
+//! Multi-logical-qubit decoder manager.
+//!
+//! Manages decoder instances for K logical qubits, each with its own
+//! Pauli frame. Routes syndromes to the right decoder and maintains
+//! per-qubit frames.
+
+use crate::ObservableDecoder;
+use crate::errors::DecoderError;
+
+/// Manages multiple logical qubit decoders with per-qubit Pauli frames.
+pub struct MultiDecoderManager {
+    /// (label, decoder) per logical qubit.
+    decoders: Vec<(String, Box<dyn ObservableDecoder>)>,
+    /// Per-qubit accumulated Pauli frame.
+    frames: Vec<u64>,
+    /// Per-qubit cycle count.
+    cycle_counts: Vec<usize>,
+}
+
+impl MultiDecoderManager {
+    /// Create with no decoders.
+    #[must_use]
+    pub fn new() -> Self {
+        Self {
+            decoders: Vec::new(),
+            frames: Vec::new(),
+            cycle_counts: Vec::new(),
+        }
+    }
+
+    /// Add a logical qubit decoder with a label.
+    pub fn add_qubit(&mut self, label: impl Into<String>, decoder: Box<dyn ObservableDecoder>) {
+        self.decoders.push((label.into(), decoder));
+        self.frames.push(0);
+        self.cycle_counts.push(0);
+    }
+
+    /// Number of logical qubits managed.
+    #[must_use]
+    pub fn num_qubits(&self) -> usize {
+        self.decoders.len()
+    }
+
+    /// Decode one QEC cycle for a specific logical qubit.
+    ///
+    /// # Errors
+    ///
+    /// Returns `DecoderError` if the decoder fails or the qubit index is out of bounds.
+    pub fn decode_cycle(&mut self, qubit_idx: usize, syndrome: &[u8]) -> Result<u64, DecoderError> {
+        if qubit_idx >= self.decoders.len() {
+            return Err(DecoderError::InvalidNodeIndex {
+                index: qubit_idx,
+                max: self.decoders.len(),
+            });
+        }
+        let obs = self.decoders[qubit_idx].1.decode_to_observables(syndrome)?;
+        self.frames[qubit_idx] ^= obs;
+        self.cycle_counts[qubit_idx] += 1;
+        Ok(obs)
+    }
+
+    /// Get the current Pauli frame for a logical qubit.
+    #[must_use]
+    pub fn frame(&self, qubit_idx: usize) -> u64 {
+        self.frames.get(qubit_idx).copied().unwrap_or(0)
+    }
+
+    /// Consume and reset the frame for a logical qubit.
+    pub fn consume_frame(&mut self, qubit_idx: usize) -> u64 {
+        if qubit_idx >= self.frames.len() {
+            return 0;
+        }
+        let f = self.frames[qubit_idx];
+        self.frames[qubit_idx] = 0;
+        self.cycle_counts[qubit_idx] = 0;
+        f
+    }
+
+    /// Label of a logical qubit.
+    #[must_use]
+    pub fn label(&self, qubit_idx: usize) -> Option<&str> {
+        self.decoders.get(qubit_idx).map(|(l, _)| l.as_str())
+    }
+
+    /// Apply a transversal CNOT between two logical qubits' Pauli frames.
+    ///
+    /// `x_obs_mask`: observable bits that are X-type (propagate control→target).
+    /// `z_obs_mask`: observable bits that are Z-type (propagate target→control).
+    ///
+    /// For a standard surface code with observable 0 = logical observable:
+    /// use `x_obs_mask = 1, z_obs_mask = 1` (single observable, both X and Z
+    /// corrections matter depending on the basis).
+    pub fn apply_transversal_cnot(
+        &mut self,
+        control_idx: usize,
+        target_idx: usize,
+        x_obs_mask: u64,
+        z_obs_mask: u64,
+    ) {
+        if control_idx >= self.frames.len() || target_idx >= self.frames.len() {
+            return;
+        }
+        let ctrl_frame = self.frames[control_idx];
+        let tgt_frame = self.frames[target_idx];
+
+        // X-type: control → target
+        self.frames[target_idx] ^= ctrl_frame & x_obs_mask;
+        // Z-type: target → control
+        self.frames[control_idx] ^= tgt_frame & z_obs_mask;
+    }
+
+    /// Apply a logical Hadamard to a qubit's Pauli frame.
+    ///
+    /// Swaps X-type and Z-type frame bits.
+    pub fn apply_hadamard(&mut self, qubit_idx: usize, x_obs_mask: u64, z_obs_mask: u64) {
+        if qubit_idx >= self.frames.len() {
+            return;
+        }
+        let f = self.frames[qubit_idx];
+        let x_bits = f & x_obs_mask;
+        let z_bits = f & z_obs_mask;
+        self.frames[qubit_idx] &= !(x_obs_mask | z_obs_mask);
+        self.frames[qubit_idx] |= if x_bits != 0 { z_obs_mask } else { 0 };
+        self.frames[qubit_idx] |= if z_bits != 0 { x_obs_mask } else { 0 };
+    }
+
+    /// Mutable access to the frame for a qubit (for custom gate propagation).
+    pub fn frame_mut(&mut self, qubit_idx: usize) -> Option<&mut u64> {
+        self.frames.get_mut(qubit_idx)
+    }
+
+    /// Replace the decoder for a qubit (e.g., after lattice surgery changes the DEM).
+    ///
+    /// # Errors
+    ///
+    /// Returns error if `qubit_idx` is out of bounds.
+    pub fn replace_decoder(
+        &mut self,
+        qubit_idx: usize,
+        decoder: Box<dyn ObservableDecoder>,
+    ) -> Result<(), crate::errors::DecoderError> {
+        if qubit_idx >= self.decoders.len() {
+            return Err(crate::errors::DecoderError::InvalidNodeIndex {
+                index: qubit_idx,
+                max: self.decoders.len(),
+            });
+        }
+        self.decoders[qubit_idx].1 = decoder;
+        Ok(())
+    }
+}
+
+impl Default for MultiDecoderManager {
+    fn default() -> Self {
+        Self::new()
+    }
+}
+
+#[cfg(test)]
+mod tests {
+    use super::*;
+
+    struct FixedDecoder(u64);
+    impl ObservableDecoder for FixedDecoder {
+        fn decode_to_observables(&mut self, _: &[u8]) -> Result<u64, DecoderError> {
+            Ok(self.0)
+        }
+    }
+
+    #[test]
+    fn test_multi_qubit() {
+        let mut mgr = MultiDecoderManager::new();
+        mgr.add_qubit("q0", Box::new(FixedDecoder(0b01)));
+        mgr.add_qubit("q1", Box::new(FixedDecoder(0b10)));
+
+        assert_eq!(mgr.num_qubits(), 2);
+        assert_eq!(mgr.label(0), Some("q0"));
+
+        mgr.decode_cycle(0, &[]).unwrap();
+        mgr.decode_cycle(1, &[]).unwrap();
+
+        assert_eq!(mgr.frame(0), 0b01);
+        assert_eq!(mgr.frame(1), 0b10);
+    }
+
+    #[test]
+    fn test_consume_frame() {
+        let mut mgr = MultiDecoderManager::new();
+        mgr.add_qubit("q0", Box::new(FixedDecoder(1)));
+        mgr.decode_cycle(0, &[]).unwrap();
+        assert_eq!(mgr.consume_frame(0), 1);
+        assert_eq!(mgr.frame(0), 0);
+    }
+
+    #[test]
+    fn test_transversal_cnot() {
+        let mut mgr = MultiDecoderManager::new();
+        mgr.add_qubit("ctrl", Box::new(FixedDecoder(0)));
+        mgr.add_qubit("tgt", Box::new(FixedDecoder(0)));
+
+        // Set X correction on control (bit 0).
+        *mgr.frame_mut(0).unwrap() = 0b01;
+
+        // Transversal CNOT: X propagates ctrl→tgt.
+        mgr.apply_transversal_cnot(0, 1, 0b01, 0b10);
+        assert_eq!(mgr.frame(0), 0b01);
+        assert_eq!(mgr.frame(1), 0b01); // X propagated
+    }
+
+    #[test]
+    fn test_hadamard() {
+        let mut mgr = MultiDecoderManager::new();
+        mgr.add_qubit("q0", Box::new(FixedDecoder(0)));
+        *mgr.frame_mut(0).unwrap() = 0b01; // X correction
+
+        mgr.apply_hadamard(0, 0b01, 0b10);
+        assert_eq!(mgr.frame(0), 0b10); // became Z correction
+    }
+
+    #[test]
+    fn test_replace_decoder() {
+        let mut mgr = MultiDecoderManager::new();
+        mgr.add_qubit("q0", Box::new(FixedDecoder(0b01)));
+        mgr.decode_cycle(0, &[]).unwrap();
+        assert_eq!(mgr.frame(0), 0b01);
+
+        // Replace decoder (e.g., after lattice surgery changes the DEM).
+        mgr.replace_decoder(0, Box::new(FixedDecoder(0b10)))
+            .unwrap();
+        mgr.decode_cycle(0, &[]).unwrap();
+        assert_eq!(mgr.frame(0), 0b11); // 01 ^ 10 = 11
+    }
+}
diff --git a/crates/pecos-decoder-core/src/observable_subgraph.rs b/crates/pecos-decoder-core/src/observable_subgraph.rs
new file mode 100644
index 000000000..31ce1480a
--- /dev/null
+++ b/crates/pecos-decoder-core/src/observable_subgraph.rs
@@ -0,0 +1,949 @@
+// Copyright 2026 The PECOS Developers
+//
+// Licensed under the Apache License, Version 2.0 (the "License"); you may not use this file except
+// in compliance with the License. You may obtain a copy of the License at
+//
+//     https://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software distributed under the License
+// is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express
+// or implied. See the License for the specific language governing permissions and limitations under
+// the License.
+
+//! Per-observable subgraph decoder for transversal gates.
+//!
+//! Based on the insight (proved independently by Serra-Peralta et al.
+//! arXiv:2505.13599 and Cain et al. arXiv:2505.13587) that per-observable
+//! subgraphs of a transversal-gate DEM are always graphlike — even when
+//! the full DEM contains weight-3+ hyperedges.
+//!
+//! # Algorithm
+//!
+//! 1. Classify each detector by (`logical_qubit`, `stabilizer_type`) using
+//!    spatial coordinates
+//! 2. For each observable, find its boundary edges (1-detector mechanisms)
+//!    to identify which (qubit, `stab_type`) groups form its observing region
+//! 3. Extract a sub-DEM restricted to those detectors
+//! 4. Run any MWPM-compatible decoder on each subgraph independently
+//! 5. Combine per-observable corrections
+//!
+//! # Observing Region
+//!
+//! The observing region for observable k is NOT a transitive closure over
+//! shared detectors. It is determined by the *physical structure*:
+//! - Find boundary edges (1-detector + observable) for observable k
+//! - Each boundary edge's detector belongs to a (qubit, `stab_type`) group
+//! - ALL detectors in those groups form the observing region
+//! - This preserves the graphlike property of each subgraph
+
+use std::collections::{BTreeMap, BTreeSet};
+
+use crate::ObservableDecoder;
+use crate::dem::{DemMatchingGraph, MatchingEdge};
+use crate::errors::DecoderError;
+
+/// Sparse representation of a parsed DEM, avoiding the dense matrix
+/// allocation of [`DemCheckMatrix`]. Also collects detector coordinates
+/// in a single pass to avoid re-scanning the DEM string.
+struct SparseDem {
+    /// Per-mechanism: (probability, `detector_ids`, `observable_ids`).
+    mechanisms: Vec<(f64, Vec<u32>, Vec<u32>)>,
+    /// Detector id → coordinates (spatial + time).
+    detector_coords: BTreeMap<usize, Vec<f64>>,
+    num_detectors: usize,
+    num_observables: usize,
+}
+
+/// Parse ASCII digits into u32. Faster than `str::parse` for the common case.
+#[inline]
+fn parse_u32_fast(s: &[u8]) -> Option<u32> {
+    if s.is_empty() {
+        return None;
+    }
+    let mut n: u32 = 0;
+    for &b in s {
+        if !b.is_ascii_digit() {
+            return None;
+        }
+        n = n.wrapping_mul(10).wrapping_add(u32::from(b - b'0'));
+    }
+    Some(n)
+}
+
+impl SparseDem {
+    fn from_dem_str(dem: &str) -> Result<Self, DecoderError> {
+        // Estimate capacity: ~1 mechanism per 55 bytes of DEM string.
+        let est_mechs = dem.len() / 55;
+        let mut mechanisms = Vec::with_capacity(est_mechs);
+        let mut detector_coords = BTreeMap::new();
+        let mut max_detector: u32 = 0;
+        let mut max_observable: u32 = 0;
+        let mut has_any_detector = false;
+
+        let bytes = dem.as_bytes();
+        let mut pos = 0;
+        let len = bytes.len();
+
+        while pos < len {
+            // Skip to start of line content (skip whitespace/newlines)
+            while pos < len
+                && (bytes[pos] == b' '
+                    || bytes[pos] == b'\n'
+                    || bytes[pos] == b'\r'
+                    || bytes[pos] == b'\t')
+            {
+                pos += 1;
+            }
+            if pos >= len {
+                break;
+            }
+
+            if bytes[pos] == b'e' && pos + 6 < len && &bytes[pos..pos + 6] == b"error(" {
+                // Parse error line at byte level.
+                pos += 6;
+                // Find closing paren — probability string
+                let prob_start = pos;
+                while pos < len && bytes[pos] != b')' {
+                    pos += 1;
+                }
+                if pos >= len {
+                    return Err(DecoderError::InvalidConfiguration(
+                        "Missing ) in error line".into(),
+                    ));
+                }
+                let prob: f64 = std::str::from_utf8(&bytes[prob_start..pos])
+                    .unwrap_or("0")
+                    .parse()
+                    .map_err(|_| DecoderError::InvalidConfiguration("Bad probability".into()))?;
+                pos += 1; // skip ')'
+
+                // Scan for ^ to decide fast vs slow path
+                let line_start = pos;
+                while pos < len && bytes[pos] != b'\n' {
+                    pos += 1;
+                }
+                let line_end = pos;
+                let line_bytes = &bytes[line_start..line_end];
+
+                if line_bytes.contains(&b'^') {
+                    // Slow path: XOR decomposition
+                    let line_str = std::str::from_utf8(line_bytes).unwrap_or("");
+                    let mut det_set = BTreeSet::new();
+                    let mut obs_set = BTreeSet::new();
+                    for component in line_str.split('^') {
+                        for token in component.split_whitespace() {
+                            if let Some(d_str) = token.strip_prefix('D') {
+                                if let Some(d) = parse_u32_fast(d_str.as_bytes()) {
+                                    if !det_set.remove(&d) {
+                                        det_set.insert(d);
+                                    }
+                                    if d > max_detector {
+                                        max_detector = d;
+                                        has_any_detector = true;
+                                    }
+                                }
+                            } else if let Some(l_str) = token.strip_prefix('L')
+                                && let Some(l) = parse_u32_fast(l_str.as_bytes())
+                            {
+                                if !obs_set.remove(&l) {
+                                    obs_set.insert(l);
+                                }
+                                if l > max_observable {
+                                    max_observable = l;
+                                }
+                            }
+                        }
+                    }
+                    mechanisms.push((
+                        prob,
+                        det_set.into_iter().collect(),
+                        obs_set.into_iter().collect(),
+                    ));
+                } else {
+                    // Fast path: no XOR. Parse tokens directly into Vecs.
+                    let mut dets = Vec::with_capacity(3);
+                    let mut obs = Vec::with_capacity(1);
+                    let mut i = 0;
+                    while i < line_bytes.len() {
+                        // Skip whitespace
+                        while i < line_bytes.len() && line_bytes[i] == b' ' {
+                            i += 1;
+                        }
+                        if i >= line_bytes.len() {
+                            break;
+                        }
+
+                        if line_bytes[i] == b'D' {
+                            i += 1;
+                            let start = i;
+                            while i < line_bytes.len()
+                                && line_bytes[i] >= b'0'
+                                && line_bytes[i] <= b'9'
+                            {
+                                i += 1;
+                            }
+                            if let Some(d) = parse_u32_fast(&line_bytes[start..i]) {
+                                dets.push(d);
+                                if d > max_detector {
+                                    max_detector = d;
+                                    has_any_detector = true;
+                                }
+                            }
+                        } else if line_bytes[i] == b'L' {
+                            i += 1;
+                            let start = i;
+                            while i < line_bytes.len()
+                                && line_bytes[i] >= b'0'
+                                && line_bytes[i] <= b'9'
+                            {
+                                i += 1;
+                            }
+                            if let Some(l) = parse_u32_fast(&line_bytes[start..i]) {
+                                obs.push(l);
+                                if l > max_observable {
+                                    max_observable = l;
+                                }
+                            }
+                        } else {
+                            // Skip unknown token
+                            while i < line_bytes.len() && line_bytes[i] != b' ' {
+                                i += 1;
+                            }
+                        }
+                    }
+                    mechanisms.push((prob, dets, obs));
+                }
+            } else if bytes[pos] == b'd' && pos + 9 < len && &bytes[pos..pos + 9] == b"detector(" {
+                // Parse detector coordinate declaration.
+                pos += 9;
+                let coord_start = pos;
+                while pos < len && bytes[pos] != b')' {
+                    pos += 1;
+                }
+                if pos < len {
+                    let coord_str = std::str::from_utf8(&bytes[coord_start..pos]).unwrap_or("");
+                    let coords: Vec<f64> = coord_str
+                        .split(',')
+                        .filter_map(|s| s.trim().parse().ok())
+                        .collect();
+                    pos += 1; // skip ')'
+                    // Find detector ID: "D123"
+                    while pos < len && bytes[pos] == b' ' {
+                        pos += 1;
+                    }
+                    if pos < len && bytes[pos] == b'D' {
+                        pos += 1;
+                        let start = pos;
+                        while pos < len && bytes[pos] >= b'0' && bytes[pos] <= b'9' {
+                            pos += 1;
+                        }
+                        if let Some(d) = parse_u32_fast(&bytes[start..pos]) {
+                            detector_coords.insert(d as usize, coords);
+                            if d > max_detector {
+                                max_detector = d;
+                                has_any_detector = true;
+                            }
+                        }
+                    }
+                }
+                // Skip rest of line
+                while pos < len && bytes[pos] != b'\n' {
+                    pos += 1;
+                }
+            } else {
+                // Skip unknown line
+                while pos < len && bytes[pos] != b'\n' {
+                    pos += 1;
+                }
+            }
+        }
+
+        let has_any_obs = max_observable > 0 || mechanisms.iter().any(|(_, _, o)| !o.is_empty());
+        Ok(Self {
+            mechanisms,
+            detector_coords,
+            num_detectors: if has_any_detector {
+                max_detector as usize + 1
+            } else {
+                0
+            },
+            num_observables: if has_any_obs {
+                max_observable as usize + 1
+            } else {
+                0
+            },
+        })
+    }
+}
+
+// ============================================================================
+// Stabilizer coordinate mapping
+// ============================================================================
+
+/// Identifies a group of detectors by logical qubit and stabilizer type.
+#[derive(Debug, Clone, Copy, PartialEq, Eq, PartialOrd, Ord, Hash)]
+pub struct DetectorGroup {
+    pub qubit_idx: usize,
+    pub stab_type: StabType,
+}
+
+/// Stabilizer type (X or Z).
+#[derive(Debug, Clone, Copy, PartialEq, Eq, PartialOrd, Ord, Hash)]
+pub enum StabType {
+    X,
+    Z,
+}
+
+/// Stabilizer coordinate map for one logical qubit.
+///
+/// Maps stabilizer spatial positions to their type (X or Z).
+/// Used to classify detectors by their coordinates.
+#[derive(Debug, Clone)]
+pub struct QubitStabCoords {
+    /// X-stabilizer ancilla positions.
+    pub x_positions: Vec<(f64, f64)>,
+    /// Z-stabilizer ancilla positions.
+    pub z_positions: Vec<(f64, f64)>,
+}
+
+/// Stabilizer coordinates for all logical qubits.
+///
+/// Entry `i` describes the stabilizers of logical qubit `i`.
+pub type StabCoords = Vec<QubitStabCoords>;
+
+/// Classify a detector's spatial coordinates into a `DetectorGroup`.
+///
+/// Finds the nearest stabilizer position across all qubits and returns
+/// the matching (`qubit_idx`, `stab_type`). Uses exact floating-point
+/// comparison with a small tolerance for rounding.
+#[must_use]
+pub fn classify_detector(x: f64, y: f64, stab_coords: &StabCoords) -> Option<DetectorGroup> {
+    let eps = 0.01;
+    for (qubit_idx, qsc) in stab_coords.iter().enumerate() {
+        for &(sx, sy) in &qsc.x_positions {
+            if (x - sx).abs() < eps && (y - sy).abs() < eps {
+                return Some(DetectorGroup {
+                    qubit_idx,
+                    stab_type: StabType::X,
+                });
+            }
+        }
+        for &(sx, sy) in &qsc.z_positions {
+            if (x - sx).abs() < eps && (y - sy).abs() < eps {
+                return Some(DetectorGroup {
+                    qubit_idx,
+                    stab_type: StabType::Z,
+                });
+            }
+        }
+    }
+    None
+}
+
+// ============================================================================
+// Subgraph partitioning
+// ============================================================================
+
+/// A sub-DEM for one observable's observing region.
+#[derive(Debug, Clone)]
+pub struct ObservableSubgraph {
+    /// Which observable this subgraph decodes.
+    pub observable_idx: usize,
+    /// Maps subgraph detector index → full DEM detector index.
+    pub detector_map: Vec<usize>,
+    /// Maps full DEM detector index → subgraph detector index (None if outside).
+    pub inverse_map: Vec<Option<usize>>,
+    /// The matching graph for this subgraph.
+    pub graph: DemMatchingGraph,
+}
+
+/// Partition a DEM into per-observable subgraphs using stabilizer coordinates.
+///
+/// This is the correct algorithm: uses the physical structure (which detectors
+/// belong to which stabilizer type on which qubit) to determine observing
+/// regions, rather than a topological transitive closure.
+///
+/// # Arguments
+///
+/// * `dem_str` — DEM string in Stim format. Must include `detector(...) D_i`
+///   declarations with spatial coordinates.
+/// * `stab_coords` — Per-qubit stabilizer coordinate map. Entry `i` gives
+///   the X and Z ancilla positions for logical qubit `i`.
+///
+/// # Errors
+///
+/// Returns error if the DEM is malformed or detector coordinates don't
+/// match any stabilizer position.
+///
+/// Extra time padding around each boundary edge.
+/// `None` = exact boundary edge times only (default, matches lomatching).
+/// `Some(r)` = include detectors at times `t ± r` around each boundary
+/// edge time `t`, for additional matching context.
+pub type MaxTimeRadius = Option<i64>;
+
+pub fn partition_dem_by_observable(
+    dem_str: &str,
+    stab_coords: &StabCoords,
+) -> Result<Vec<ObservableSubgraph>, DecoderError> {
+    partition_dem_by_observable_windowed(dem_str, stab_coords, None)
+}
+
+pub fn partition_dem_by_observable_windowed(
+    dem_str: &str,
+    stab_coords: &StabCoords,
+    max_time_radius: MaxTimeRadius,
+) -> Result<Vec<ObservableSubgraph>, DecoderError> {
+    // Single-pass sparse DEM parsing: mechanisms + detector coordinates.
+    let sdem = SparseDem::from_dem_str(dem_str)?;
+    let coord_map = &sdem.detector_coords;
+
+    // Classify each detector into a (qubit, stab_type) group.
+    let mut det_group: Vec<Option<DetectorGroup>> = vec![None; sdem.num_detectors];
+    let mut group_detectors: BTreeMap<DetectorGroup, BTreeSet<usize>> = BTreeMap::new();
+
+    for (d, group_slot) in det_group.iter_mut().enumerate().take(sdem.num_detectors) {
+        if let Some(coords) = coord_map.get(&d)
+            && coords.len() >= 2
+        {
+            let (x, y) = (coords[0], coords[1]);
+            if let Some(group) = classify_detector(x, y, stab_coords) {
+                *group_slot = Some(group);
+                group_detectors.entry(group).or_default().insert(d);
+            }
+        }
+    }
+
+    // For each observable, find its observing region.
+    let mut subgraphs = Vec::with_capacity(sdem.num_observables);
+
+    for obs_idx in 0..sdem.num_observables {
+        // Step 1: Find boundary edges — 1-detector mechanisms that flip
+        // this observable. Collect (group, time) from each boundary detector.
+        let mut group_times: BTreeMap<DetectorGroup, BTreeSet<i64>> = BTreeMap::new();
+
+        for (_, dets, obs) in &sdem.mechanisms {
+            if !obs.contains(&(obs_idx as u32)) {
+                continue;
+            }
+            if dets.len() == 1 {
+                let d = dets[0] as usize;
+                if let Some(group) = det_group[d] {
+                    let time = coord_map
+                        .get(&d)
+                        .and_then(|c| c.last().copied())
+                        .map_or(0, |t| t as i64);
+                    group_times.entry(group).or_default().insert(time);
+                }
+            }
+        }
+
+        // Step 2: For each (group, time) boundary edge, include ALL
+        // detectors of that group at that time. This matches lomatching's
+        // per-time-step approach: detectors are included only at times
+        // where boundary edges exist, not across the full time range.
+        // With max_time_radius, extend each boundary time by ±radius.
+        let mut region_detectors = BTreeSet::new();
+        for (group, times) in &group_times {
+            if let Some(dets) = group_detectors.get(group) {
+                for &d in dets {
+                    let det_time = coord_map
+                        .get(&d)
+                        .and_then(|c| c.last().copied())
+                        .map_or(0, |t| t as i64);
+                    let in_region = if let Some(radius) = max_time_radius {
+                        times.iter().any(|&t| (det_time - t).abs() <= radius)
+                    } else {
+                        times.contains(&det_time)
+                    };
+                    if in_region {
+                        region_detectors.insert(d);
+                    }
+                }
+            }
+        }
+
+        if region_detectors.is_empty() {
+            subgraphs.push(ObservableSubgraph {
+                observable_idx: obs_idx,
+                detector_map: Vec::new(),
+                inverse_map: vec![None; sdem.num_detectors],
+                graph: DemMatchingGraph {
+                    edges: Vec::new(),
+                    num_detectors: 0,
+                    num_observables: 1,
+                    skipped_hyperedges: 0,
+                    detector_coords: Vec::new(),
+                },
+            });
+            continue;
+        }
+
+        // Step 3: Build detector mapping.
+        let detector_map: Vec<usize> = region_detectors.into_iter().collect();
+        let mut inverse_map = vec![None; sdem.num_detectors];
+        for (sub_idx, &full_idx) in detector_map.iter().enumerate() {
+            inverse_map[full_idx] = Some(sub_idx);
+        }
+
+        // Step 4: Extract edges for this subgraph.
+        let mut edges = Vec::new();
+        let mut skipped = 0;
+
+        for (m, (p, dets, obs)) in sdem.mechanisms.iter().enumerate() {
+            if *p <= 0.0 {
+                continue;
+            }
+
+            // Map mechanism detectors to subgraph indices.
+            let sub_dets: Vec<u32> = dets
+                .iter()
+                .filter_map(|&d| inverse_map[d as usize].map(|s| s as u32))
+                .collect();
+
+            if sub_dets.is_empty() {
+                continue;
+            }
+
+            let weight = if *p < 1.0 { ((1.0 - p) / p).ln() } else { 0.0 };
+            let flips_obs = obs.contains(&(obs_idx as u32));
+            let observables = if flips_obs { vec![0u32] } else { vec![] };
+
+            match sub_dets.len() {
+                1 => edges.push(MatchingEdge {
+                    node1: sub_dets[0],
+                    node2: None,
+                    weight,
+                    observables,
+                    probability: *p,
+                    fault_id: m,
+                }),
+                2 => edges.push(MatchingEdge {
+                    node1: sub_dets[0],
+                    node2: Some(sub_dets[1]),
+                    weight,
+                    observables,
+                    probability: *p,
+                    fault_id: m,
+                }),
+                _ => skipped += 1,
+            }
+        }
+
+        let num_sub = detector_map.len();
+        let edges = DemMatchingGraph::merge_parallel_edges(edges);
+
+        subgraphs.push(ObservableSubgraph {
+            observable_idx: obs_idx,
+            detector_map,
+            inverse_map,
+            graph: DemMatchingGraph {
+                edges,
+                num_detectors: num_sub,
+                num_observables: 1,
+                skipped_hyperedges: skipped,
+                detector_coords: Vec::new(),
+            },
+        });
+    }
+
+    Ok(subgraphs)
+}
+
+// ============================================================================
+// Decoder
+// ============================================================================
+
+/// Per-observable subgraph decoder.
+///
+/// Wraps a factory function that creates per-subgraph inner decoders.
+/// Any `ObservableDecoder` works as the inner decoder (UF, Fusion Blossom,
+/// perturbed ensemble, etc.).
+pub struct ObservableSubgraphDecoder {
+    subgraphs: Vec<ObservableSubgraph>,
+    decoders: Vec<Box<dyn ObservableDecoder + Send + Sync>>,
+    num_observables: usize,
+    sub_syndromes: Vec<Vec<u8>>,
+}
+
+impl ObservableSubgraphDecoder {
+    /// Build from a DEM string, stabilizer coordinates, and inner decoder factory.
+    ///
+    /// # Errors
+    ///
+    /// Returns error if the DEM is malformed or the factory fails.
+    pub fn from_dem<F>(
+        dem: &str,
+        stab_coords: &StabCoords,
+        factory: F,
+    ) -> Result<Self, DecoderError>
+    where
+        F: FnMut(
+            &DemMatchingGraph,
+        ) -> Result<Box<dyn ObservableDecoder + Send + Sync>, DecoderError>,
+    {
+        Self::from_dem_windowed(dem, stab_coords, None, factory)
+    }
+
+    pub fn from_dem_windowed<F>(
+        dem: &str,
+        stab_coords: &StabCoords,
+        max_time_radius: MaxTimeRadius,
+        mut factory: F,
+    ) -> Result<Self, DecoderError>
+    where
+        F: FnMut(
+            &DemMatchingGraph,
+        ) -> Result<Box<dyn ObservableDecoder + Send + Sync>, DecoderError>,
+    {
+        let subgraphs = partition_dem_by_observable_windowed(dem, stab_coords, max_time_radius)?;
+        let num_observables = subgraphs.len();
+
+        let mut decoders = Vec::with_capacity(subgraphs.len());
+        let mut sub_syndromes = Vec::with_capacity(subgraphs.len());
+        for sg in &subgraphs {
+            decoders.push(factory(&sg.graph)?);
+            sub_syndromes.push(vec![0u8; sg.detector_map.len()]);
+        }
+
+        Ok(Self {
+            subgraphs,
+            decoders,
+            num_observables,
+            sub_syndromes,
+        })
+    }
+
+    /// Number of observables.
+    #[must_use]
+    pub fn num_observables(&self) -> usize {
+        self.num_observables
+    }
+
+    /// Access a subgraph.
+    #[must_use]
+    pub fn subgraph(&self, obs_idx: usize) -> Option<&ObservableSubgraph> {
+        self.subgraphs.get(obs_idx)
+    }
+
+    /// Batch decode multiple syndromes, returning error count.
+    ///
+    /// For each subgraph, extracts all sub-syndromes into a flat buffer
+    /// and calls `decode_batch_to_observables` once — avoiding per-shot
+    /// reset overhead in decoders like `PyMatching`.
+    pub fn decode_count_batched(
+        &mut self,
+        syndromes: &[Vec<u8>],
+        expected_masks: &[u64],
+    ) -> Result<usize, DecoderError> {
+        let num_shots = syndromes.len();
+        if num_shots == 0 {
+            return Ok(0);
+        }
+
+        // Per-shot observable predictions, accumulated across subgraphs.
+        let mut shot_obs: Vec<u64> = vec![0u64; num_shots];
+
+        for (i, (sg, dec)) in self
+            .subgraphs
+            .iter()
+            .zip(self.decoders.iter_mut())
+            .enumerate()
+        {
+            let n = sg.detector_map.len();
+            if n == 0 {
+                continue;
+            }
+
+            // Build flat sub-syndrome buffer: num_shots × n bytes.
+            let mut flat = vec![0u8; num_shots * n];
+            for (shot_idx, syn) in syndromes.iter().enumerate() {
+                let row = &mut flat[shot_idx * n..(shot_idx + 1) * n];
+                for (sub_idx, &full_idx) in sg.detector_map.iter().enumerate() {
+                    row[sub_idx] = if full_idx < syn.len() {
+                        syn[full_idx]
+                    } else {
+                        0
+                    };
+                }
+            }
+
+            // Batch decode this subgraph.
+            let sub_masks = dec.decode_batch_to_observables(&flat, num_shots, n)?;
+
+            for (shot_idx, &sub_obs) in sub_masks.iter().enumerate() {
+                if sub_obs & 1 != 0 {
+                    shot_obs[shot_idx] |= 1 << i;
+                }
+            }
+        }
+
+        // Count errors.
+        let errors = shot_obs
+            .iter()
+            .zip(expected_masks.iter())
+            .filter(|(predicted, expected)| predicted != expected)
+            .count();
+
+        Ok(errors)
+    }
+}
+
+impl ObservableDecoder for ObservableSubgraphDecoder {
+    fn decode_to_observables(&mut self, syndrome: &[u8]) -> Result<u64, DecoderError> {
+        let mut obs_mask = 0u64;
+
+        for (i, (sg, dec)) in self
+            .subgraphs
+            .iter()
+            .zip(self.decoders.iter_mut())
+            .enumerate()
+        {
+            let n = sg.detector_map.len();
+            if n == 0 {
+                continue;
+            }
+
+            let buf = &mut self.sub_syndromes[i];
+            for (sub_idx, &full_idx) in sg.detector_map.iter().enumerate() {
+                buf[sub_idx] = if full_idx < syndrome.len() {
+                    syndrome[full_idx]
+                } else {
+                    0
+                };
+            }
+
+            let sub_obs = dec.decode_to_observables(&buf[..n])?;
+
+            if sub_obs & 1 != 0 {
+                obs_mask |= 1 << i;
+            }
+        }
+
+        Ok(obs_mask)
+    }
+}
+
+/// Parallel per-observable subgraph decoder using rayon.
+pub struct ParallelObservableSubgraphDecoder {
+    subgraphs: Vec<ObservableSubgraph>,
+    decoders: Vec<std::sync::Mutex<Box<dyn ObservableDecoder + Send>>>,
+}
+
+impl ParallelObservableSubgraphDecoder {
+    /// Build from a DEM string, stabilizer coordinates, and inner decoder factory.
+    ///
+    /// # Errors
+    ///
+    /// Returns error if the DEM is malformed or the factory fails.
+    pub fn from_dem<F>(
+        dem: &str,
+        stab_coords: &StabCoords,
+        mut factory: F,
+    ) -> Result<Self, DecoderError>
+    where
+        F: FnMut(&DemMatchingGraph) -> Result<Box<dyn ObservableDecoder + Send>, DecoderError>,
+    {
+        let subgraphs = partition_dem_by_observable(dem, stab_coords)?;
+
+        let mut decoders = Vec::with_capacity(subgraphs.len());
+        for sg in &subgraphs {
+            decoders.push(std::sync::Mutex::new(factory(&sg.graph)?));
+        }
+
+        Ok(Self {
+            subgraphs,
+            decoders,
+        })
+    }
+
+    /// Decode using parallel subgraph decoding.
+    ///
+    /// # Errors
+    ///
+    /// Returns error if any subgraph decoder fails.
+    pub fn decode_parallel(&self, syndrome: &[u8]) -> Result<u64, DecoderError> {
+        use rayon::prelude::*;
+
+        let results: Vec<Result<bool, DecoderError>> = self
+            .subgraphs
+            .par_iter()
+            .zip(self.decoders.par_iter())
+            .map(|(sg, dec_mutex)| {
+                let n = sg.detector_map.len();
+                if n == 0 {
+                    return Ok(false);
+                }
+
+                let mut sub_syn = vec![0u8; n];
+                for (sub_idx, &full_idx) in sg.detector_map.iter().enumerate() {
+                    sub_syn[sub_idx] = if full_idx < syndrome.len() {
+                        syndrome[full_idx]
+                    } else {
+                        0
+                    };
+                }
+
+                let mut dec = dec_mutex.lock().unwrap();
+                let sub_obs = dec.decode_to_observables(&sub_syn)?;
+                Ok(sub_obs & 1 != 0)
+            })
+            .collect();
+
+        let mut obs_mask = 0u64;
+        for (i, result) in results.into_iter().enumerate() {
+            if result? {
+                obs_mask |= 1 << i;
+            }
+        }
+        Ok(obs_mask)
+    }
+}
+
+// ============================================================================
+// Tests
+// ============================================================================
+
+#[cfg(test)]
+mod tests {
+    use super::*;
+
+    struct NullDecoder;
+    impl ObservableDecoder for NullDecoder {
+        fn decode_to_observables(&mut self, _: &[u8]) -> Result<u64, DecoderError> {
+            Ok(0)
+        }
+    }
+
+    struct FixedDecoder(u64);
+    impl ObservableDecoder for FixedDecoder {
+        fn decode_to_observables(&mut self, syndrome: &[u8]) -> Result<u64, DecoderError> {
+            if syndrome.iter().any(|&v| v != 0) {
+                Ok(self.0)
+            } else {
+                Ok(0)
+            }
+        }
+    }
+
+    fn simple_stab_coords() -> StabCoords {
+        // Two qubits with non-overlapping X/Z positions.
+        vec![
+            QubitStabCoords {
+                x_positions: vec![(1.0, 0.0)],
+                z_positions: vec![(0.0, 1.0)],
+            },
+            QubitStabCoords {
+                x_positions: vec![(3.0, 0.0)],
+                z_positions: vec![(2.0, 1.0)],
+            },
+        ]
+    }
+
+    #[test]
+    fn test_classify_detector() {
+        let sc = simple_stab_coords();
+        assert_eq!(
+            classify_detector(1.0, 0.0, &sc),
+            Some(DetectorGroup {
+                qubit_idx: 0,
+                stab_type: StabType::X
+            }),
+        );
+        assert_eq!(
+            classify_detector(0.0, 1.0, &sc),
+            Some(DetectorGroup {
+                qubit_idx: 0,
+                stab_type: StabType::Z
+            }),
+        );
+        assert_eq!(
+            classify_detector(3.0, 0.0, &sc),
+            Some(DetectorGroup {
+                qubit_idx: 1,
+                stab_type: StabType::X
+            }),
+        );
+        assert_eq!(classify_detector(99.0, 99.0, &sc), None);
+    }
+
+    #[test]
+    fn test_partition_simple() {
+        // Two detectors with coords, one observable.
+        let dem = concat!(
+            "detector(1, 0, 0) D0\n",
+            "detector(0, 1, 0) D1\n",
+            "error(0.01) D0 D1 L0\n",
+            "error(0.01) D0 L0\n", // boundary edge → D0 is (qubit 0, X)
+        );
+        let sc = simple_stab_coords();
+        let sgs = partition_dem_by_observable(dem, &sc).unwrap();
+        assert_eq!(sgs.len(), 1);
+        // Boundary edge D0 L0 → D0 is qubit 0 X-type.
+        // Observing region = all qubit-0 X-type detectors = {D0}.
+        // But D0-D1 is also an observable mechanism, and D1 is qubit 0 Z-type.
+        // Since D1 is NOT in the same group as D0, it's excluded from the
+        // observing region. The edge D0-D1 projects to D0-boundary within
+        // the subgraph.
+        assert_eq!(sgs[0].detector_map, vec![0]);
+    }
+
+    #[test]
+    fn test_partition_two_qubits() {
+        let dem = concat!(
+            "detector(1, 0, 0) D0\n",
+            "detector(0, 1, 0) D1\n",
+            "detector(3, 0, 0) D2\n",
+            "detector(2, 1, 0) D3\n",
+            "error(0.01) D0 L0\n", // boundary: D0 = qubit 0 X
+            "error(0.01) D0 D1\n", // D0-D1 edge
+            "error(0.01) D2 L1\n", // boundary: D2 = qubit 1 X
+            "error(0.01) D2 D3\n", // D2-D3 edge
+        );
+        let sc = simple_stab_coords();
+        let sgs = partition_dem_by_observable(dem, &sc).unwrap();
+        assert_eq!(sgs.len(), 2);
+        assert_eq!(sgs[0].detector_map, vec![0]); // qubit 0 X-type only
+        assert_eq!(sgs[1].detector_map, vec![2]); // qubit 1 X-type only
+    }
+
+    #[test]
+    fn test_decoder_routing() {
+        let dem = concat!(
+            "detector(1, 0, 0) D0\n",
+            "detector(3, 0, 0) D1\n",
+            "error(0.01) D0 L0\n",
+            "error(0.01) D1 L1\n",
+        );
+        let sc = simple_stab_coords();
+        let mut dec = ObservableSubgraphDecoder::from_dem(dem, &sc, |_| {
+            Ok(Box::new(FixedDecoder(1)) as Box<dyn ObservableDecoder + Send + Sync>)
+        })
+        .unwrap();
+
+        // Defect in obs 0's region only
+        let obs = dec.decode_to_observables(&[1, 0]).unwrap();
+        assert_eq!(obs, 0b01);
+
+        // Defect in obs 1's region only
+        let obs = dec.decode_to_observables(&[0, 1]).unwrap();
+        assert_eq!(obs, 0b10);
+    }
+
+    #[test]
+    fn test_parallel_decoder() {
+        let dem = concat!(
+            "detector(1, 0, 0) D0\n",
+            "detector(3, 0, 0) D1\n",
+            "error(0.01) D0 L0\n",
+            "error(0.01) D1 L1\n",
+        );
+        let sc = simple_stab_coords();
+        let dec = ParallelObservableSubgraphDecoder::from_dem(dem, &sc, |_| {
+            Ok(Box::new(NullDecoder) as Box<dyn ObservableDecoder + Send>)
+        })
+        .unwrap();
+
+        let obs = dec.decode_parallel(&[0, 0]).unwrap();
+        assert_eq!(obs, 0);
+    }
+}
diff --git a/crates/pecos-decoder-core/src/pauli_frame.rs b/crates/pecos-decoder-core/src/pauli_frame.rs
new file mode 100644
index 000000000..c5182c999
--- /dev/null
+++ b/crates/pecos-decoder-core/src/pauli_frame.rs
@@ -0,0 +1,259 @@
+// Copyright 2026 The PECOS Developers
+//
+// Licensed under the Apache License, Version 2.0 (the "License"); you may not use this file except
+// in compliance with the License. You may obtain a copy of the License at
+//
+//     https://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software distributed under the License
+// is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express
+// or implied. See the License for the specific language governing permissions and limitations under
+// the License.
+
+//! Pauli frame accumulator for real-time QEC.
+//!
+//! In a real QEC system, the decoder runs once per QEC cycle, producing
+//! an observable mask. These masks accumulate into a Pauli frame that
+//! tracks the net logical correction. The frame is consumed only when
+//! a logical operation requires it (T-gate injection, logical measurement).
+//!
+//! # Example
+//!
+//! ```
+//! use pecos_decoder_core::{DecoderError, ObservableDecoder};
+//! use pecos_decoder_core::pauli_frame::PauliFrameAccumulator;
+//!
+//! struct FixedDecoder(u64);
+//!
+//! impl ObservableDecoder for FixedDecoder {
+//!     fn decode_to_observables(&mut self, _syndrome: &[u8]) -> Result<u64, DecoderError> {
+//!         Ok(self.0)
+//!     }
+//! }
+//!
+//! let mut frame = PauliFrameAccumulator::new(Box::new(FixedDecoder(0b01)));
+//!
+//! // QEC cycles
+//! for syndrome in [&[1, 0][..], &[0, 1][..]] {
+//!     frame.decode_cycle(syndrome).unwrap();
+//! }
+//! assert_eq!(frame.current_frame(), 0b00);
+//!
+//! // At logical measurement: consume frame
+//! let correction = frame.consume_frame();
+//! let raw_measurement = 1;
+//! let logical_result = raw_measurement ^ (correction & 1);
+//! assert_eq!(logical_result, 1);
+//! ```
+
+use crate::ObservableDecoder;
+use crate::errors::DecoderError;
+
+/// Accumulates Pauli frame corrections across QEC cycles.
+///
+/// Wraps any `ObservableDecoder` and XORs each cycle's observable mask
+/// into a running frame. The frame represents the net logical correction
+/// needed at the current point in the computation.
+pub struct PauliFrameAccumulator {
+    decoder: Box<dyn ObservableDecoder>,
+    frame: u64,
+    cycle_count: usize,
+}
+
+impl PauliFrameAccumulator {
+    /// Create from any observable decoder.
+    #[must_use]
+    pub fn new(decoder: Box<dyn ObservableDecoder>) -> Self {
+        Self {
+            decoder,
+            frame: 0,
+            cycle_count: 0,
+        }
+    }
+
+    /// Decode one QEC cycle's syndrome and accumulate into the frame.
+    ///
+    /// # Errors
+    ///
+    /// Returns `DecoderError` if the inner decoder fails.
+    pub fn decode_cycle(&mut self, syndrome: &[u8]) -> Result<u64, DecoderError> {
+        let obs = self.decoder.decode_to_observables(syndrome)?;
+        self.frame ^= obs;
+        self.cycle_count += 1;
+        Ok(obs)
+    }
+
+    /// Current accumulated Pauli frame (does not reset).
+    #[must_use]
+    pub fn current_frame(&self) -> u64 {
+        self.frame
+    }
+
+    /// Consume the frame: returns the accumulated mask and resets to zero.
+    ///
+    /// Call this at logical operations (T-gate, measurement) to get the
+    /// correction and start fresh for the next logical cycle.
+    pub fn consume_frame(&mut self) -> u64 {
+        let f = self.frame;
+        self.frame = 0;
+        self.cycle_count = 0;
+        f
+    }
+
+    /// Number of QEC cycles since last reset/consume.
+    #[must_use]
+    pub fn cycle_count(&self) -> usize {
+        self.cycle_count
+    }
+
+    /// Manually flip a frame bit (e.g., for deterministic corrections).
+    pub fn flip_bit(&mut self, bit: u32) {
+        self.frame ^= 1u64 << bit;
+    }
+
+    /// Direct access to the frame bits.
+    #[must_use]
+    pub fn frame_mut(&mut self) -> &mut u64 {
+        &mut self.frame
+    }
+
+    /// Access the inner decoder.
+    pub fn decoder_mut(&mut self) -> &mut dyn ObservableDecoder {
+        &mut *self.decoder
+    }
+}
+
+/// Propagate Pauli frames through a transversal CNOT.
+///
+/// When a logical CNOT is applied from control to target:
+/// - X errors propagate: control → target (`X_c` → `X_c` ⊗ `X_t`)
+/// - Z errors propagate: target → control (`Z_t` → `Z_c` ⊗ `Z_t`)
+///
+/// For observable masks (bit k = observable k):
+/// - X-type observables on control propagate to target
+/// - Z-type observables on target propagate to control
+///
+/// `x_obs_mask`: which observable bits are X-type (propagate forward)
+/// `z_obs_mask`: which observable bits are Z-type (propagate backward)
+pub fn propagate_cnot_frames(
+    control: &mut PauliFrameAccumulator,
+    target: &mut PauliFrameAccumulator,
+    x_obs_mask: u64,
+    z_obs_mask: u64,
+) {
+    let ctrl_frame = control.current_frame();
+    let tgt_frame = target.current_frame();
+
+    // X-type bits on control propagate to target: target ^= control & x_mask
+    *target.frame_mut() ^= ctrl_frame & x_obs_mask;
+
+    // Z-type bits on target propagate to control: control ^= target & z_mask
+    *control.frame_mut() ^= tgt_frame & z_obs_mask;
+}
+
+/// Propagate Pauli frame through a logical S gate (phase gate).
+///
+/// S gate: X → Y = iXZ, Z → Z. For the frame:
+/// - Z-type bits are unchanged
+/// - X-type bits that are set also flip the corresponding Z-type bit
+pub fn propagate_s_gate_frame(frame: &mut PauliFrameAccumulator, x_obs_mask: u64, z_obs_mask: u64) {
+    let f = frame.current_frame();
+    // X-type corrections also induce Z-type corrections after S gate
+    *frame.frame_mut() ^= (f & x_obs_mask) & z_obs_mask;
+}
+
+/// Propagate Pauli frame through a logical Hadamard.
+///
+/// H gate: X ↔ Z. Swaps X-type and Z-type frame bits.
+pub fn propagate_h_gate_frame(frame: &mut PauliFrameAccumulator, x_obs_mask: u64, z_obs_mask: u64) {
+    let f = frame.current_frame();
+    let x_bits = f & x_obs_mask;
+    let z_bits = f & z_obs_mask;
+    // Clear both, then swap
+    *frame.frame_mut() &= !(x_obs_mask | z_obs_mask);
+    // X bits go to Z positions, Z bits go to X positions
+    // (This assumes x_obs_mask and z_obs_mask don't overlap and have
+    // matching bit positions. For a single logical qubit with obs 0 = X
+    // and obs 1 = Z: x_mask=0b01, z_mask=0b10, swap bits 0 and 1.)
+    *frame.frame_mut() |= if x_bits != 0 { z_obs_mask } else { 0 };
+    *frame.frame_mut() |= if z_bits != 0 { x_obs_mask } else { 0 };
+}
+
+#[cfg(test)]
+mod tests {
+    use super::*;
+
+    struct FixedDecoder(u64);
+    impl ObservableDecoder for FixedDecoder {
+        fn decode_to_observables(&mut self, _: &[u8]) -> Result<u64, DecoderError> {
+            Ok(self.0)
+        }
+    }
+
+    #[test]
+    fn test_accumulate_xor() {
+        let mut frame = PauliFrameAccumulator::new(Box::new(FixedDecoder(0b01)));
+        frame.decode_cycle(&[]).unwrap();
+        assert_eq!(frame.current_frame(), 0b01);
+        frame.decode_cycle(&[]).unwrap();
+        assert_eq!(frame.current_frame(), 0b00); // XOR cancels
+        frame.decode_cycle(&[]).unwrap();
+        assert_eq!(frame.current_frame(), 0b01);
+        assert_eq!(frame.cycle_count(), 3);
+    }
+
+    #[test]
+    fn test_consume_resets() {
+        let mut frame = PauliFrameAccumulator::new(Box::new(FixedDecoder(0b11)));
+        frame.decode_cycle(&[]).unwrap();
+        assert_eq!(frame.consume_frame(), 0b11);
+        assert_eq!(frame.current_frame(), 0);
+        assert_eq!(frame.cycle_count(), 0);
+    }
+
+    #[test]
+    fn test_flip_bit() {
+        let mut frame = PauliFrameAccumulator::new(Box::new(FixedDecoder(0)));
+        frame.flip_bit(2);
+        assert_eq!(frame.current_frame(), 0b100);
+        frame.flip_bit(2);
+        assert_eq!(frame.current_frame(), 0);
+    }
+
+    #[test]
+    fn test_cnot_frame_propagation() {
+        // Two logical qubits with obs bit 0 = X-type, bit 1 = Z-type.
+        let mut ctrl = PauliFrameAccumulator::new(Box::new(FixedDecoder(0)));
+        let mut tgt = PauliFrameAccumulator::new(Box::new(FixedDecoder(0)));
+
+        // Control has X correction (bit 0).
+        ctrl.flip_bit(0);
+        assert_eq!(ctrl.current_frame(), 0b01);
+        assert_eq!(tgt.current_frame(), 0b00);
+
+        // CNOT: X on control propagates to target.
+        propagate_cnot_frames(&mut ctrl, &mut tgt, 0b01, 0b10);
+        assert_eq!(ctrl.current_frame(), 0b01); // unchanged
+        assert_eq!(tgt.current_frame(), 0b01); // X propagated
+
+        // Now target has Z correction (bit 1).
+        tgt.flip_bit(1);
+        assert_eq!(tgt.current_frame(), 0b11);
+
+        // CNOT: Z on target propagates to control.
+        propagate_cnot_frames(&mut ctrl, &mut tgt, 0b01, 0b10);
+        assert_eq!(ctrl.current_frame(), 0b11); // Z propagated back
+    }
+
+    #[test]
+    fn test_hadamard_frame() {
+        let mut frame = PauliFrameAccumulator::new(Box::new(FixedDecoder(0)));
+        // Set X correction (bit 0).
+        frame.flip_bit(0);
+        assert_eq!(frame.current_frame(), 0b01);
+
+        // Hadamard: X ↔ Z (swap bits 0 and 1).
+        propagate_h_gate_frame(&mut frame, 0b01, 0b10);
+        assert_eq!(frame.current_frame(), 0b10); // X became Z
+    }
+}
diff --git a/crates/pecos-decoder-core/src/perturbed.rs b/crates/pecos-decoder-core/src/perturbed.rs
new file mode 100644
index 000000000..a2fb1e81e
--- /dev/null
+++ b/crates/pecos-decoder-core/src/perturbed.rs
@@ -0,0 +1,213 @@
+// Copyright 2026 The PECOS Developers
+//
+// Licensed under the Apache License, Version 2.0 (the "License"); you may not use this file except
+// in compliance with the License. You may obtain a copy of the License at
+//
+//     https://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software distributed under the License
+// is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express
+// or implied. See the License for the specific language governing permissions and limitations under
+// the License.
+
+//! Perturbed-weight ensemble decoder.
+//!
+//! Builds K decoders from K perturbed copies of a DEM, then majority-votes
+//! on each observable bit per shot. The weight perturbation creates diversity
+//! in matching decisions, and the ensemble smooths out individual mistakes.
+//!
+//! At d=5 with K=15 sigma=0.7 `PyMatching` inner, this gives ~5% fewer errors
+//! than a single correlated `PyMatching` — a practical accuracy improvement
+//! over the state of the art.
+
+use crate::ObservableDecoder;
+use crate::ensemble::EnsembleDecoder;
+use crate::errors::DecoderError;
+
+/// Configuration for the perturbed-weight ensemble.
+#[derive(Debug, Clone)]
+pub struct PerturbedConfig {
+    /// Number of ensemble members (including the unperturbed anchor).
+    pub k: usize,
+    /// Standard deviation of the log-normal weight perturbation.
+    /// Each error(p) becomes error(p * exp(N(0, sigma^2))).
+    pub sigma: f64,
+    /// RNG seed for reproducibility.
+    pub seed: u64,
+}
+
+impl Default for PerturbedConfig {
+    fn default() -> Self {
+        Self {
+            k: 15,
+            sigma: 0.7,
+            seed: 42,
+        }
+    }
+}
+
+/// Perturb error probabilities in a DEM string by multiplicative log-normal noise.
+pub fn perturb_dem(dem: &str, sigma: f64, rng: &mut dyn FnMut() -> f64) -> String {
+    use std::fmt::Write;
+    let mut out = String::with_capacity(dem.len());
+    for line in dem.lines() {
+        let trimmed = line.trim();
+        if let Some(rest) = trimmed.strip_prefix("error(")
+            && let Some(close) = rest.find(')')
+            && let Ok(p) = rest[..close].parse::<f64>()
+        {
+            let u1 = rng().max(1e-10);
+            let u2 = rng();
+            let z = (-2.0_f64 * u1.ln()).sqrt() * (2.0_f64 * std::f64::consts::PI * u2).cos();
+            let factor = (sigma * z).exp();
+            let p_new = (p * factor).clamp(1e-15, 0.499);
+            let _ = write!(out, "error({p_new})");
+            out.push_str(&rest[close..]);
+            out.push('\n');
+            continue;
+        }
+        out.push_str(trimmed);
+        out.push('\n');
+    }
+    out
+}
+
+/// Build a perturbed-weight ensemble from a DEM and a decoder factory.
+///
+/// Creates K decoders: one unperturbed anchor + (K-1) perturbed copies.
+/// Returns an `EnsembleDecoder` with majority voting.
+///
+/// The factory is called once per member with a (possibly perturbed) DEM string.
+///
+/// # Errors
+///
+/// Returns `DecoderError` if the factory fails on the unperturbed DEM.
+pub fn build_perturbed_ensemble<F>(
+    dem: &str,
+    config: &PerturbedConfig,
+    mut factory: F,
+) -> Result<EnsembleDecoder, DecoderError>
+where
+    F: FnMut(&str) -> Result<Box<dyn ObservableDecoder>, DecoderError>,
+{
+    let mut members: Vec<Box<dyn ObservableDecoder>> = Vec::with_capacity(config.k);
+
+    // Unperturbed anchor
+    members.push(factory(dem)?);
+
+    // Use PecosRng for high-quality perturbation randomness.
+    let mut rng = pecos_random::PecosRng::seed_from_u64(config.seed);
+    let mut next_f64 = move || -> f64 { rng.next_f64() };
+
+    for _ in 1..config.k {
+        let perturbed = perturb_dem(dem, config.sigma, &mut next_f64);
+        if let Ok(dec) = factory(&perturbed) {
+            members.push(dec);
+        }
+    }
+
+    Ok(EnsembleDecoder::new(members))
+}
+
+/// Build a parallel perturbed-weight ensemble (rayon-accelerated).
+///
+/// Same as `build_perturbed_ensemble` but returns a `ParallelEnsembleDecoder`
+/// that decodes all K members concurrently. Factory must produce `Send` decoders.
+///
+/// # Errors
+///
+/// Returns `DecoderError` if the factory fails on the unperturbed DEM.
+pub fn build_parallel_perturbed_ensemble<F>(
+    dem: &str,
+    config: &PerturbedConfig,
+    mut factory: F,
+) -> Result<crate::ensemble::ParallelEnsembleDecoder, DecoderError>
+where
+    F: FnMut(&str) -> Result<Box<dyn ObservableDecoder + Send>, DecoderError>,
+{
+    let mut members: Vec<Box<dyn ObservableDecoder + Send>> = Vec::with_capacity(config.k);
+    members.push(factory(dem)?);
+
+    let mut rng = pecos_random::PecosRng::seed_from_u64(config.seed);
+    let mut next_f64 = move || -> f64 { rng.next_f64() };
+
+    for _ in 1..config.k {
+        let perturbed = perturb_dem(dem, config.sigma, &mut next_f64);
+        if let Ok(dec) = factory(&perturbed) {
+            members.push(dec);
+        }
+    }
+
+    Ok(crate::ensemble::ParallelEnsembleDecoder::new(members))
+}
+
+#[cfg(test)]
+mod tests {
+    use super::*;
+
+    const SIMPLE_DEM: &str = "error(0.1) D0 D1 L0\nerror(0.05) D1\n";
+
+    #[test]
+    fn test_perturb_dem_preserves_structure() {
+        let mut i = 0u64;
+        let mut rng = || -> f64 {
+            i += 1;
+            // Deterministic: 0.5, 0.6, 0.7, ...
+            0.5 + (i as f64) * 0.01
+        };
+        let perturbed = perturb_dem(SIMPLE_DEM, 0.5, &mut rng);
+        // Should still have error() lines.
+        assert!(perturbed.contains("error("));
+        // Should have D0, D1, L0.
+        assert!(perturbed.contains("D0"));
+        assert!(perturbed.contains("D1"));
+        assert!(perturbed.contains("L0"));
+        // Probabilities should be different from original.
+        assert!(!perturbed.contains("error(0.1)"));
+    }
+
+    #[test]
+    fn test_perturb_dem_clamps_probability() {
+        // With sigma=10, some probabilities could go very high or low.
+        let mut i = 0u64;
+        let mut rng = || -> f64 {
+            i += 1;
+            0.999 // Will push exp(10 * z) very high
+        };
+        let perturbed = perturb_dem(SIMPLE_DEM, 10.0, &mut rng);
+        // Should still parse (probabilities clamped to 0.499 max).
+        for line in perturbed.lines() {
+            let trimmed = line.trim();
+            if let Some(rest) = trimmed.strip_prefix("error(")
+                && let Some(close) = rest.find(')')
+            {
+                let p: f64 = rest[..close].parse().unwrap();
+                assert!(p > 0.0 && p < 0.5, "p={p} out of bounds");
+            }
+        }
+    }
+
+    #[test]
+    fn test_build_perturbed_ensemble_k1() {
+        let config = PerturbedConfig {
+            k: 1,
+            sigma: 0.5,
+            seed: 42,
+        };
+        let ensemble = build_perturbed_ensemble(SIMPLE_DEM, &config, |_dem| {
+            // Trivial decoder that always returns 0.
+            struct Zero;
+            impl crate::ObservableDecoder for Zero {
+                fn decode_to_observables(
+                    &mut self,
+                    _: &[u8],
+                ) -> Result<u64, crate::errors::DecoderError> {
+                    Ok(0)
+                }
+            }
+            Ok(Box::new(Zero))
+        });
+        assert!(ensemble.is_ok());
+        assert_eq!(ensemble.unwrap().len(), 1);
+    }
+}
diff --git a/crates/pecos-decoder-core/src/preprocessor.rs b/crates/pecos-decoder-core/src/preprocessor.rs
new file mode 100644
index 000000000..19505fcc9
--- /dev/null
+++ b/crates/pecos-decoder-core/src/preprocessor.rs
@@ -0,0 +1,199 @@
+// Copyright 2026 The PECOS Developers
+//
+// Licensed under the Apache License, Version 2.0 (the "License"); you may not use this file except
+// in compliance with the License. You may obtain a copy of the License at
+//
+//     https://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software distributed under the License
+// is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express
+// or implied. See the License for the specific language governing permissions and limitations under
+// the License.
+
+//! Syndrome preprocessor for real-system QEC decoding.
+//!
+//! Sits between the hardware readout and the decoder. Responsibilities:
+//! - Convert leakage flags (from PECOS's `MeasureLeaked` simulation or
+//!   neutral atom loss detection) into erasure edge indices for the decoder
+//! - Detect syndrome anomalies (excessive weight, all-ones, etc.)
+//! - Validate syndrome dimensions
+//!
+//! # Leakage-to-Erasure Pipeline
+//!
+//! Neutral atoms: atom loss is detected per-qubit. Each lost qubit
+//! affects specific error mechanisms (edges in the matching graph).
+//! The preprocessor maps qubit loss → affected DEM edges → erasure
+//! indices for `ObservableErasureDecoder`.
+//!
+//! The mapping is built at construction from the DEM's detector
+//! coordinates or a user-provided qubit-to-edge mapping.
+
+/// Anomaly detected in a syndrome.
+#[derive(Debug, Clone)]
+pub enum SyndromeAnomaly {
+    /// More defects than expected (possible burst error or readout failure).
+    ExcessiveWeight { weight: usize, threshold: usize },
+    /// All detectors fired (likely readout failure, not a real syndrome).
+    AllOnes,
+    /// Wrong syndrome length.
+    WrongLength { expected: usize, actual: usize },
+}
+
+/// Preprocessed syndrome ready for the decoder.
+#[derive(Debug, Clone)]
+pub struct ProcessedSyndrome {
+    /// The syndrome (possibly with leakage-affected bits cleared/modified).
+    pub syndrome: Vec<u8>,
+    /// DEM edge indices known to be erased (from leakage detection).
+    pub erasure_edges: Vec<usize>,
+    /// Anomaly if detected, None if syndrome looks normal.
+    pub anomaly: Option<SyndromeAnomaly>,
+}
+
+/// Syndrome preprocessor.
+pub struct SyndromePreprocessor {
+    num_detectors: usize,
+    /// Maximum expected syndrome weight before flagging anomaly.
+    /// Set to 0 to disable (default).
+    weight_threshold: usize,
+    /// Qubit index → list of DEM edge indices affected by that qubit's loss.
+    /// Built from the DEM structure at construction time.
+    qubit_to_erasure_edges: Vec<Vec<usize>>,
+}
+
+impl SyndromePreprocessor {
+    /// Create with basic syndrome validation.
+    #[must_use]
+    pub fn new(num_detectors: usize) -> Self {
+        Self {
+            num_detectors,
+            weight_threshold: 0,
+            qubit_to_erasure_edges: Vec::new(),
+        }
+    }
+
+    /// Set the maximum expected syndrome weight for anomaly detection.
+    pub fn set_weight_threshold(&mut self, threshold: usize) {
+        self.weight_threshold = threshold;
+    }
+
+    /// Set the qubit-to-erasure-edge mapping for leakage conversion.
+    ///
+    /// `mapping[qubit_idx]` = list of DEM edge indices affected by that qubit.
+    /// Built from the DEM: for each edge, find which data qubits it involves.
+    pub fn set_erasure_mapping(&mut self, mapping: Vec<Vec<usize>>) {
+        self.qubit_to_erasure_edges = mapping;
+    }
+
+    /// Preprocess a raw syndrome with optional leakage flags.
+    ///
+    /// `leakage_flags`: one byte per qubit, nonzero = qubit leaked/lost.
+    /// Converts leaked qubits to erasure edge indices via the mapping.
+    #[must_use]
+    pub fn preprocess(
+        &self,
+        raw_syndrome: &[u8],
+        leakage_flags: Option<&[u8]>,
+    ) -> ProcessedSyndrome {
+        let mut anomaly = None;
+
+        // Validate length.
+        if raw_syndrome.len() != self.num_detectors {
+            return ProcessedSyndrome {
+                syndrome: raw_syndrome.to_vec(),
+                erasure_edges: Vec::new(),
+                anomaly: Some(SyndromeAnomaly::WrongLength {
+                    expected: self.num_detectors,
+                    actual: raw_syndrome.len(),
+                }),
+            };
+        }
+
+        // Check weight.
+        let weight = raw_syndrome.iter().filter(|&&v| v != 0).count();
+        if weight == self.num_detectors && self.num_detectors > 0 {
+            anomaly = Some(SyndromeAnomaly::AllOnes);
+        } else if self.weight_threshold > 0 && weight > self.weight_threshold {
+            anomaly = Some(SyndromeAnomaly::ExcessiveWeight {
+                weight,
+                threshold: self.weight_threshold,
+            });
+        }
+
+        // Convert leakage flags to erasure edges.
+        let mut erasure_edges = Vec::new();
+        if let Some(flags) = leakage_flags {
+            for (qubit, &leaked) in flags.iter().enumerate() {
+                if leaked != 0 && qubit < self.qubit_to_erasure_edges.len() {
+                    erasure_edges.extend_from_slice(&self.qubit_to_erasure_edges[qubit]);
+                }
+            }
+            erasure_edges.sort_unstable();
+            erasure_edges.dedup();
+        }
+
+        ProcessedSyndrome {
+            syndrome: raw_syndrome.to_vec(),
+            erasure_edges,
+            anomaly,
+        }
+    }
+}
+
+#[cfg(test)]
+mod tests {
+    use super::*;
+
+    #[test]
+    fn test_basic_preprocessing() {
+        let pp = SyndromePreprocessor::new(4);
+        let result = pp.preprocess(&[0, 1, 0, 1], None);
+        assert!(result.anomaly.is_none());
+        assert!(result.erasure_edges.is_empty());
+    }
+
+    #[test]
+    fn test_wrong_length() {
+        let pp = SyndromePreprocessor::new(4);
+        let result = pp.preprocess(&[0, 1], None);
+        assert!(matches!(
+            result.anomaly,
+            Some(SyndromeAnomaly::WrongLength { .. })
+        ));
+    }
+
+    #[test]
+    fn test_excessive_weight() {
+        let mut pp = SyndromePreprocessor::new(4);
+        pp.set_weight_threshold(2);
+        let result = pp.preprocess(&[1, 1, 1, 0], None);
+        assert!(matches!(
+            result.anomaly,
+            Some(SyndromeAnomaly::ExcessiveWeight { weight: 3, .. })
+        ));
+    }
+
+    #[test]
+    fn test_all_ones() {
+        let pp = SyndromePreprocessor::new(3);
+        let result = pp.preprocess(&[1, 1, 1], None);
+        assert!(matches!(result.anomaly, Some(SyndromeAnomaly::AllOnes)));
+    }
+
+    #[test]
+    fn test_leakage_to_erasure() {
+        let mut pp = SyndromePreprocessor::new(4);
+        // Qubit 0 affects edges [0, 2], qubit 1 affects edge [1]
+        pp.set_erasure_mapping(vec![vec![0, 2], vec![1]]);
+        let result = pp.preprocess(&[0, 1, 0, 0], Some(&[1, 0])); // qubit 0 leaked
+        assert_eq!(result.erasure_edges, vec![0, 2]);
+    }
+
+    #[test]
+    fn test_multiple_leakage() {
+        let mut pp = SyndromePreprocessor::new(4);
+        pp.set_erasure_mapping(vec![vec![0, 2], vec![1, 2]]); // edge 2 shared
+        let result = pp.preprocess(&[0, 0, 0, 0], Some(&[1, 1])); // both leaked
+        assert_eq!(result.erasure_edges, vec![0, 1, 2]); // deduped
+    }
+}
diff --git a/crates/pecos-decoder-core/src/results.rs b/crates/pecos-decoder-core/src/results.rs
index ac0f85a4e..96528cbfc 100644
--- a/crates/pecos-decoder-core/src/results.rs
+++ b/crates/pecos-decoder-core/src/results.rs
@@ -61,6 +61,14 @@ pub trait DecodingResultTrait {
     /// Whether the decoding was successful
     fn is_successful(&self) -> bool;
 
+    /// Get the raw correction/decoding vector (one entry per error mechanism).
+    ///
+    /// For check-matrix decoders this is the estimated error pattern.
+    /// For MWPM decoders this may be the observable prediction directly.
+    fn correction(&self) -> &[u8] {
+        &[]
+    }
+
     /// Get the cost of the decoding (if available)
     fn cost(&self) -> Option<f64> {
         None
diff --git a/crates/pecos-decoder-core/src/streaming.rs b/crates/pecos-decoder-core/src/streaming.rs
new file mode 100644
index 000000000..3ab3757a3
--- /dev/null
+++ b/crates/pecos-decoder-core/src/streaming.rs
@@ -0,0 +1,54 @@
+// Copyright 2026 The PECOS Developers
+//
+// Licensed under the Apache License, Version 2.0 (the "License"); you may not use this file except
+// in compliance with the License. You may obtain a copy of the License at
+//
+//     https://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software distributed under the License
+// is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express
+// or implied. See the License for the specific language governing permissions and limitations under
+// the License.
+
+//! Streaming decoder trait for real-time QEC.
+//!
+//! Accepts syndrome data incrementally (round by round) and emits
+//! partial observable corrections as windows complete.
+
+use crate::errors::DecoderError;
+
+/// Streaming decoder that accepts syndrome data incrementally.
+///
+/// For real-time decoding where syndrome arrives round-by-round.
+/// The decoder manages windows internally and emits committed
+/// corrections as each window's core region becomes decodable.
+pub trait StreamingDecoder {
+    /// Feed one round of detection events.
+    ///
+    /// `round` is the time coordinate (0-indexed).
+    /// `detectors` contains `(detector_index, value)` pairs for this round.
+    ///
+    /// Returns any newly committed observable corrections as a bitmask.
+    /// Returns 0 if no window completed this round.
+    ///
+    /// # Errors
+    ///
+    /// Returns `DecoderError` if window decoding fails.
+    fn feed_round(&mut self, round: usize, detectors: &[(u32, u8)]) -> Result<u64, DecoderError>;
+
+    /// Signal that no more rounds will arrive.
+    ///
+    /// Forces decode of any remaining buffered windows and returns
+    /// the final observable correction for uncommitted windows.
+    ///
+    /// # Errors
+    ///
+    /// Returns `DecoderError` if window decoding fails.
+    fn flush(&mut self) -> Result<u64, DecoderError>;
+
+    /// Total observable mask accumulated so far (XOR of all committed corrections).
+    fn accumulated_obs(&self) -> u64;
+
+    /// Reset for the next shot (clear syndrome buffer and accumulated state).
+    fn reset(&mut self);
+}
diff --git a/crates/pecos-decoder-core/src/telemetry.rs b/crates/pecos-decoder-core/src/telemetry.rs
new file mode 100644
index 000000000..395fc6940
--- /dev/null
+++ b/crates/pecos-decoder-core/src/telemetry.rs
@@ -0,0 +1,200 @@
+// Copyright 2026 The PECOS Developers
+//
+// Licensed under the Apache License, Version 2.0 (the "License"); you may not use this file except
+// in compliance with the License. You may obtain a copy of the License at
+//
+//     https://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software distributed under the License
+// is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express
+// or implied. See the License for the specific language governing permissions and limitations under
+// the License.
+
+//! Decoder telemetry wrapper for real-time monitoring.
+//!
+//! Wraps any `ObservableDecoder` with transparent per-decode latency
+//! measurement and statistics tracking. Useful for monitoring decoder
+//! health in a real QEC system.
+
+use crate::ObservableDecoder;
+use crate::errors::DecoderError;
+use std::collections::VecDeque;
+use std::time::Instant;
+
+/// Live decoder statistics.
+#[derive(Debug, Clone)]
+pub struct DecoderTelemetry {
+    /// Total decodes performed.
+    pub decode_count: u64,
+    /// Total decode time in nanoseconds.
+    pub total_decode_ns: u64,
+    /// Sum of syndrome weights (number of defects per decode).
+    pub syndrome_weight_sum: u64,
+    /// Number of decodes that produced nonzero observable.
+    pub nonzero_observable_count: u64,
+    /// Maximum single-decode latency in nanoseconds.
+    pub max_decode_ns: u64,
+    /// Recent decode latencies for rolling statistics.
+    pub recent_latencies_ns: VecDeque<u64>,
+    /// Maximum size of the rolling window.
+    window_size: usize,
+}
+
+impl DecoderTelemetry {
+    fn new(window_size: usize) -> Self {
+        Self {
+            decode_count: 0,
+            total_decode_ns: 0,
+            syndrome_weight_sum: 0,
+            nonzero_observable_count: 0,
+            max_decode_ns: 0,
+            recent_latencies_ns: VecDeque::with_capacity(window_size),
+            window_size,
+        }
+    }
+
+    fn record(&mut self, latency_ns: u64, syndrome_weight: u64, obs_nonzero: bool) {
+        self.decode_count += 1;
+        self.total_decode_ns += latency_ns;
+        self.syndrome_weight_sum += syndrome_weight;
+        if obs_nonzero {
+            self.nonzero_observable_count += 1;
+        }
+        if latency_ns > self.max_decode_ns {
+            self.max_decode_ns = latency_ns;
+        }
+        if self.recent_latencies_ns.len() >= self.window_size {
+            self.recent_latencies_ns.pop_front();
+        }
+        self.recent_latencies_ns.push_back(latency_ns);
+    }
+
+    /// Average decode latency in nanoseconds.
+    #[must_use]
+    pub fn avg_decode_ns(&self) -> f64 {
+        if self.decode_count == 0 {
+            0.0
+        } else {
+            self.total_decode_ns as f64 / self.decode_count as f64
+        }
+    }
+
+    /// Average syndrome weight (defects per decode).
+    #[must_use]
+    pub fn avg_syndrome_weight(&self) -> f64 {
+        if self.decode_count == 0 {
+            0.0
+        } else {
+            self.syndrome_weight_sum as f64 / self.decode_count as f64
+        }
+    }
+
+    /// Fraction of decodes that produced a nonzero observable (logical correction).
+    #[must_use]
+    pub fn correction_rate(&self) -> f64 {
+        if self.decode_count == 0 {
+            0.0
+        } else {
+            self.nonzero_observable_count as f64 / self.decode_count as f64
+        }
+    }
+
+    /// P99 latency from recent window in nanoseconds.
+    #[must_use]
+    pub fn p99_latency_ns(&self) -> u64 {
+        if self.recent_latencies_ns.is_empty() {
+            return 0;
+        }
+        let mut sorted: Vec<u64> = self.recent_latencies_ns.iter().copied().collect();
+        sorted.sort_unstable();
+        let idx = (sorted.len() * 99 / 100).min(sorted.len() - 1);
+        sorted[idx]
+    }
+}
+
+/// Telemetry-instrumented decoder.
+///
+/// Wraps any `ObservableDecoder` with transparent latency and statistics
+/// tracking. The inner decoder's behavior is unchanged.
+pub struct TelemetryDecoder {
+    inner: Box<dyn ObservableDecoder>,
+    /// Live telemetry data. Read via `telemetry()`.
+    stats: DecoderTelemetry,
+}
+
+impl TelemetryDecoder {
+    /// Create with a rolling window of `window_size` recent latencies.
+    #[must_use]
+    pub fn new(inner: Box<dyn ObservableDecoder>, window_size: usize) -> Self {
+        Self {
+            inner,
+            stats: DecoderTelemetry::new(window_size),
+        }
+    }
+
+    /// Access the telemetry data.
+    #[must_use]
+    pub fn telemetry(&self) -> &DecoderTelemetry {
+        &self.stats
+    }
+
+    /// Reset all statistics.
+    pub fn reset_telemetry(&mut self) {
+        self.stats = DecoderTelemetry::new(self.stats.window_size);
+    }
+}
+
+impl ObservableDecoder for TelemetryDecoder {
+    fn decode_to_observables(&mut self, syndrome: &[u8]) -> Result<u64, DecoderError> {
+        let syndrome_weight = syndrome.iter().filter(|&&v| v != 0).count() as u64;
+        let start = Instant::now();
+        let obs = self.inner.decode_to_observables(syndrome)?;
+        let elapsed_ns = start.elapsed().as_nanos() as u64;
+        self.stats.record(elapsed_ns, syndrome_weight, obs != 0);
+        Ok(obs)
+    }
+}
+
+#[cfg(test)]
+mod tests {
+    use super::*;
+
+    struct FixedDecoder(u64);
+    impl ObservableDecoder for FixedDecoder {
+        fn decode_to_observables(&mut self, _: &[u8]) -> Result<u64, DecoderError> {
+            Ok(self.0)
+        }
+    }
+
+    #[test]
+    fn test_telemetry_counts() {
+        let mut dec = TelemetryDecoder::new(Box::new(FixedDecoder(1)), 100);
+        dec.decode_to_observables(&[0, 1, 0]).unwrap();
+        dec.decode_to_observables(&[0, 0, 0]).unwrap();
+
+        let t = dec.telemetry();
+        assert_eq!(t.decode_count, 2);
+        assert_eq!(t.nonzero_observable_count, 2); // FixedDecoder always returns 1
+        assert_eq!(t.syndrome_weight_sum, 1); // only first syndrome has weight 1
+    }
+
+    #[test]
+    fn test_telemetry_latency() {
+        let mut dec = TelemetryDecoder::new(Box::new(FixedDecoder(0)), 10);
+        for _ in 0..5 {
+            dec.decode_to_observables(&[]).unwrap();
+        }
+        let t = dec.telemetry();
+        assert_eq!(t.decode_count, 5);
+        assert!(t.avg_decode_ns() >= 0.0);
+        assert!(t.p99_latency_ns() > 0);
+    }
+
+    #[test]
+    fn test_reset() {
+        let mut dec = TelemetryDecoder::new(Box::new(FixedDecoder(0)), 10);
+        dec.decode_to_observables(&[]).unwrap();
+        dec.reset_telemetry();
+        assert_eq!(dec.telemetry().decode_count, 0);
+    }
+}
diff --git a/crates/pecos-decoder-core/src/two_pass_decoder.rs b/crates/pecos-decoder-core/src/two_pass_decoder.rs
new file mode 100644
index 000000000..8c7298855
--- /dev/null
+++ b/crates/pecos-decoder-core/src/two_pass_decoder.rs
@@ -0,0 +1,175 @@
+// Copyright 2026 The PECOS Developers
+//
+// Licensed under the Apache License, Version 2.0 (the "License"); you may not use this file except
+// in compliance with the License. You may obtain a copy of the License at
+//
+//     https://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software distributed under the License
+// is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express
+// or implied. See the License for the specific language governing permissions and limitations under
+// the License.
+
+//! Two-pass correlated decoder using pre-computed correlation table.
+//!
+//! Wraps any `MatchingDecoder` with a two-pass decode:
+//! 1. First pass: standard decode to identify matched edges
+//! 2. Apply conditional weight adjustments from `CorrelationTable`
+//! 3. Second pass: re-decode with adjusted weights
+//!
+//! This is the decoder-agnostic equivalent of `PyMatching`'s correlated matching.
+
+use crate::correlated_decoder::MatchingDecoder;
+use crate::correlation_table::CorrelationTable;
+use crate::errors::DecoderError;
+
+/// Two-pass correlated decoder.
+///
+/// Uses a pre-computed `CorrelationTable` (from DEM decomposition) to
+/// adjust edge weights between the first and second decode passes.
+/// Works with any decoder implementing `MatchingDecoder`.
+pub struct TwoPassDecoder<D: MatchingDecoder> {
+    inner: D,
+    correlation_table: CorrelationTable,
+    base_weights: Vec<f64>,
+    /// Reusable buffer for adjusted weights (avoids per-shot allocation).
+    adjusted_weights: Vec<f64>,
+}
+
+impl<D: MatchingDecoder> TwoPassDecoder<D> {
+    /// Create a new two-pass decoder.
+    ///
+    /// `base_weights` should have one entry per edge in the matching graph,
+    /// in the same order as the decoder's edge indices.
+    pub fn new(inner: D, base_weights: Vec<f64>, correlation_table: CorrelationTable) -> Self {
+        let n = base_weights.len();
+        Self {
+            inner,
+            correlation_table,
+            adjusted_weights: vec![0.0; n],
+            base_weights,
+        }
+    }
+
+    /// Whether the correlation table has any correlations to exploit.
+    #[must_use]
+    pub fn has_correlations(&self) -> bool {
+        self.correlation_table.has_correlations()
+    }
+}
+
+impl<D: MatchingDecoder> crate::ObservableDecoder for TwoPassDecoder<D> {
+    fn decode_to_observables(&mut self, syndrome: &[u8]) -> Result<u64, DecoderError> {
+        if !self.correlation_table.has_correlations() {
+            // No correlations: single-pass decode (no overhead)
+            let (mask, _) = self.inner.decode_with_matching(syndrome)?;
+            return Ok(mask);
+        }
+
+        // First pass: decode to get matched edges
+        let (_, matched_edges) = self.inner.decode_with_matching(syndrome)?;
+
+        // Apply correlation adjustments: for each matched edge, look up
+        // its implied weights and lower correlated edges' weights.
+        self.adjusted_weights.copy_from_slice(&self.base_weights);
+        for &edge_idx in &matched_edges {
+            if edge_idx < self.correlation_table.implied_weights.len() {
+                for iw in &self.correlation_table.implied_weights[edge_idx] {
+                    // Only lower the weight (make the correlated edge more likely)
+                    if iw.conditional_weight < self.adjusted_weights[iw.target_edge_idx] {
+                        self.adjusted_weights[iw.target_edge_idx] = iw.conditional_weight;
+                    }
+                }
+            }
+        }
+
+        // Second pass: decode with adjusted weights
+        let (mask, _) = self
+            .inner
+            .decode_with_weights(syndrome, &self.adjusted_weights)?;
+        Ok(mask)
+    }
+}
+
+#[cfg(test)]
+mod tests {
+    use super::*;
+    use crate::ObservableDecoder;
+    use crate::correlation_table::ImpliedWeight;
+
+    struct MockDecoder {
+        num_edges: usize,
+        calls: std::cell::RefCell<usize>,
+    }
+
+    impl MatchingDecoder for MockDecoder {
+        fn decode_with_matching(
+            &mut self,
+            _syndrome: &[u8],
+        ) -> Result<(u64, Vec<usize>), DecoderError> {
+            *self.calls.borrow_mut() += 1;
+            Ok((0, vec![0])) // Always match edge 0
+        }
+
+        fn decode_with_weights(
+            &mut self,
+            _syndrome: &[u8],
+            _weights: &[f64],
+        ) -> Result<(u64, Vec<usize>), DecoderError> {
+            *self.calls.borrow_mut() += 1;
+            Ok((1, vec![0, 1])) // Different result with adjusted weights
+        }
+
+        fn num_edges(&self) -> usize {
+            self.num_edges
+        }
+    }
+
+    #[test]
+    fn test_two_pass_with_correlations() {
+        let mock = MockDecoder {
+            num_edges: 3,
+            calls: std::cell::RefCell::new(0),
+        };
+        let weights = vec![5.0, 5.0, 5.0];
+        let table = CorrelationTable {
+            implied_weights: vec![
+                vec![ImpliedWeight {
+                    target_edge_idx: 1,
+                    conditional_weight: 2.0,
+                }],
+                vec![],
+                vec![],
+            ],
+            num_edges: 3,
+        };
+
+        let mut decoder = TwoPassDecoder::new(mock, weights, table);
+        let mask = decoder.decode_to_observables(&[1, 0, 0]).unwrap();
+
+        // Second pass should be called (returns mask=1)
+        assert_eq!(mask, 1);
+        // Two calls: first pass + second pass
+        assert_eq!(*decoder.inner.calls.borrow(), 2);
+    }
+
+    #[test]
+    fn test_two_pass_no_correlations() {
+        let mock = MockDecoder {
+            num_edges: 3,
+            calls: std::cell::RefCell::new(0),
+        };
+        let weights = vec![5.0, 5.0, 5.0];
+        let table = CorrelationTable {
+            implied_weights: vec![vec![], vec![], vec![]],
+            num_edges: 3,
+        };
+
+        let mut decoder = TwoPassDecoder::new(mock, weights, table);
+        let mask = decoder.decode_to_observables(&[1, 0, 0]).unwrap();
+
+        // No correlations: single pass only (returns mask=0)
+        assert_eq!(mask, 0);
+        assert_eq!(*decoder.inner.calls.borrow(), 1);
+    }
+}
diff --git a/crates/pecos-decoder-core/src/windowed_osd.rs b/crates/pecos-decoder-core/src/windowed_osd.rs
new file mode 100644
index 000000000..00e575ffe
--- /dev/null
+++ b/crates/pecos-decoder-core/src/windowed_osd.rs
@@ -0,0 +1,294 @@
+// Copyright 2026 The PECOS Developers
+//
+// Licensed under the Apache License, Version 2.0 (the "License"); you may not use this file except
+// in compliance with the License. You may obtain a copy of the License at
+//
+//     https://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software distributed under the License
+// is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express
+// or implied. See the License for the specific language governing permissions and limitations under
+// the License.
+
+//! Windowed observable subgraph decoder.
+//!
+//! Splits a DEM into time windows, runs per-observable subgraph decoding
+//! within each window. This prevents the observing region from spanning
+//! the full circuit at deep depths, maintaining decoding accuracy.
+//!
+//! Window types:
+//! - **Non-overlapping**: each detector belongs to exactly one window
+//! - **Overlapping**: buffer zones extend beyond the core for matching context
+//!
+//! The observable correction from each window is XOR'd together.
+
+use std::collections::BTreeMap;
+
+use crate::ObservableDecoder;
+use crate::dem::{DemCheckMatrix, DemMatchingGraph, MatchingEdge, parse_detector_coords};
+use crate::errors::DecoderError;
+use crate::observable_subgraph::{ObservableSubgraphDecoder, StabCoords};
+
+/// Configuration for windowed OSD.
+#[derive(Debug, Clone)]
+pub struct WindowedOsdConfig {
+    /// Core window size in time steps.
+    pub step: usize,
+    /// Buffer size on each side (0 = non-overlapping).
+    pub buffer: usize,
+}
+
+impl Default for WindowedOsdConfig {
+    fn default() -> Self {
+        Self { step: 8, buffer: 4 }
+    }
+}
+
+/// A single time window with its own OSD.
+pub struct OsdWindow {
+    decoder: ObservableSubgraphDecoder,
+    /// Maps local detector index → global detector index.
+    local_to_global: Vec<usize>,
+    num_local: usize,
+    /// Which local detectors are in the core (vs buffer).
+    _is_core: Vec<bool>,
+}
+
+/// Windowed observable subgraph decoder.
+///
+/// Splits the DEM into time windows, each decoded with its own OSD.
+/// The observing region within each window is naturally bounded,
+/// preventing the scaling degradation seen at deep circuits.
+pub struct WindowedOsdDecoder {
+    pub windows: Vec<OsdWindow>,
+    _num_detectors: usize,
+    /// Reusable window syndrome buffer
+    window_syn: Vec<u8>,
+}
+
+impl WindowedOsdDecoder {
+    /// Build from a DEM string with time-based windowing.
+    ///
+    /// # Errors
+    ///
+    /// Returns error if the DEM is malformed.
+    pub fn from_dem<F>(
+        dem: &str,
+        stab_coords: &StabCoords,
+        config: &WindowedOsdConfig,
+        mut inner_factory: F,
+    ) -> Result<Self, DecoderError>
+    where
+        F: FnMut(
+            &DemMatchingGraph,
+        ) -> Result<Box<dyn ObservableDecoder + Send + Sync>, DecoderError>,
+    {
+        // Parse detector coordinates to get time values
+        let coords = parse_detector_coords(dem);
+        let mut det_time: BTreeMap<usize, f64> = BTreeMap::new();
+        for dc in &coords {
+            if let Some(t) = dc.coords.last() {
+                det_time.insert(dc.id as usize, *t);
+            }
+        }
+
+        let dcm = DemCheckMatrix::from_dem_str(dem)
+            .map_err(|e| DecoderError::InvalidGraph(e.to_string()))?;
+        let num_detectors = dcm.num_detectors;
+
+        // Find time range
+        let min_t = det_time.values().copied().fold(f64::INFINITY, f64::min);
+        let max_t = det_time.values().copied().fold(f64::NEG_INFINITY, f64::max);
+
+        if max_t <= min_t {
+            // Single time step or empty — just use full OSD
+            let full_osd =
+                ObservableSubgraphDecoder::from_dem(dem, stab_coords, &mut inner_factory)?;
+            return Ok(Self {
+                windows: vec![OsdWindow {
+                    decoder: full_osd,
+                    local_to_global: (0..num_detectors).collect(),
+                    num_local: num_detectors,
+                    _is_core: vec![true; num_detectors],
+                }],
+                _num_detectors: num_detectors,
+                window_syn: vec![0u8; num_detectors],
+            });
+        }
+
+        let step = config.step as f64;
+        let buffer = config.buffer as f64;
+        let mut windows = Vec::new();
+        let mut t_start = min_t;
+        let mut max_local = 0;
+
+        while t_start <= max_t {
+            let core_end = (t_start + step).min(max_t + 1.0);
+            let win_start = (t_start - buffer).max(min_t);
+            let win_end = (core_end + buffer).min(max_t + 1.0);
+
+            // Detectors in this window
+            let mut local_to_global = Vec::new();
+            let mut is_core = Vec::new();
+
+            for d in 0..num_detectors {
+                if let Some(&t) = det_time.get(&d)
+                    && t >= win_start
+                    && t < win_end
+                {
+                    local_to_global.push(d);
+                    is_core.push(t >= t_start && t < core_end);
+                }
+            }
+
+            if local_to_global.is_empty() {
+                t_start += step;
+                continue;
+            }
+
+            let num_local = local_to_global.len();
+            if num_local > max_local {
+                max_local = num_local;
+            }
+
+            // Build sub-DEM for this window
+            let mut inverse = vec![None; num_detectors];
+            for (local, &global) in local_to_global.iter().enumerate() {
+                inverse[global] = Some(local);
+            }
+
+            let mut edges = Vec::new();
+            let mut skipped = 0;
+
+            for m in 0..dcm.num_mechanisms {
+                let p = dcm.error_priors[m];
+                if p <= 0.0 {
+                    continue;
+                }
+
+                let sub_dets: Vec<u32> = (0..dcm.num_detectors)
+                    .filter(|&d| dcm.check_matrix[[d, m]] != 0)
+                    .filter_map(|d| inverse[d].map(|s| s as u32))
+                    .collect();
+
+                if sub_dets.is_empty() {
+                    continue;
+                }
+
+                let weight = if p < 1.0 { ((1.0 - p) / p).ln() } else { 0.0 };
+
+                // Observable: include if ANY observable is flipped
+                let mut observables = Vec::new();
+                for o in 0..dcm.num_observables {
+                    if dcm.observable_matrix[[o, m]] != 0 {
+                        observables.push(o as u32);
+                    }
+                }
+
+                match sub_dets.len() {
+                    1 => edges.push(MatchingEdge {
+                        node1: sub_dets[0],
+                        node2: None,
+                        weight,
+                        observables,
+                        probability: p,
+                        fault_id: m,
+                    }),
+                    2 => edges.push(MatchingEdge {
+                        node1: sub_dets[0],
+                        node2: Some(sub_dets[1]),
+                        weight,
+                        observables,
+                        probability: p,
+                        fault_id: m,
+                    }),
+                    _ => skipped += 1,
+                }
+            }
+
+            let edges = DemMatchingGraph::merge_parallel_edges(edges);
+            let sub_graph = DemMatchingGraph {
+                edges,
+                num_detectors: num_local,
+                num_observables: dcm.num_observables,
+                skipped_hyperedges: skipped,
+                detector_coords: Vec::new(),
+            };
+
+            // Build sub-DEM string with detector coordinate declarations.
+            // The OSD needs these to classify detectors by (qubit, stab_type).
+            let mut sub_dem_lines = Vec::new();
+            for (local_id, &global_id) in local_to_global.iter().enumerate() {
+                // Find this detector's coordinates from the parsed coords
+                if let Some(dc) = coords.iter().find(|dc| dc.id as usize == global_id) {
+                    let coord_str: Vec<String> = dc.coords.iter().map(|c| format!("{c}")).collect();
+                    sub_dem_lines.push(format!("detector({}) D{local_id}", coord_str.join(", ")));
+                }
+            }
+            sub_dem_lines.push(graph_to_dem_string(&sub_graph));
+            let sub_dem = sub_dem_lines.join("\n");
+
+            // Build OSD for this window using the sub-DEM
+            let window_osd =
+                ObservableSubgraphDecoder::from_dem(&sub_dem, stab_coords, &mut inner_factory)?;
+
+            windows.push(OsdWindow {
+                decoder: window_osd,
+                local_to_global,
+                num_local,
+                _is_core: is_core,
+            });
+
+            t_start += step;
+        }
+
+        Ok(Self {
+            windows,
+            _num_detectors: num_detectors,
+            window_syn: vec![0u8; max_local],
+        })
+    }
+}
+
+impl ObservableDecoder for WindowedOsdDecoder {
+    fn decode_to_observables(&mut self, syndrome: &[u8]) -> Result<u64, DecoderError> {
+        let mut obs_mask = 0u64;
+
+        for window in &mut self.windows {
+            // Extract window syndrome
+            let n = window.num_local;
+            for (local, &global) in window.local_to_global.iter().enumerate() {
+                self.window_syn[local] = if global < syndrome.len() {
+                    syndrome[global]
+                } else {
+                    0
+                };
+            }
+
+            // Decode this window
+            let window_obs = window
+                .decoder
+                .decode_to_observables(&self.window_syn[..n])?;
+            obs_mask ^= window_obs;
+        }
+
+        Ok(obs_mask)
+    }
+}
+
+fn graph_to_dem_string(graph: &DemMatchingGraph) -> String {
+    let mut lines = Vec::new();
+    for edge in &graph.edges {
+        let p = edge.probability;
+        let mut targets = Vec::new();
+        targets.push(format!("D{}", edge.node1));
+        if let Some(n2) = edge.node2 {
+            targets.push(format!("D{n2}"));
+        }
+        for &obs in &edge.observables {
+            targets.push(format!("L{obs}"));
+        }
+        lines.push(format!("error({p}) {}", targets.join(" ")));
+    }
+    lines.join("\n")
+}
diff --git a/crates/pecos-decoder-core/tests/ensemble_integration.rs b/crates/pecos-decoder-core/tests/ensemble_integration.rs
new file mode 100644
index 000000000..38073875c
--- /dev/null
+++ b/crates/pecos-decoder-core/tests/ensemble_integration.rs
@@ -0,0 +1,128 @@
+// Copyright 2026 The PECOS Developers
+//
+// Licensed under the Apache License, Version 2.0 (the "License"); you may not use this file except
+// in compliance with the License. You may obtain a copy of the License at
+//
+//     https://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software distributed under the License
+// is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express
+// or implied. See the License for the specific language governing permissions and limitations under
+// the License.
+
+//! Integration tests for the ensemble decoder.
+
+use pecos_decoder_core::ObservableDecoder;
+use pecos_decoder_core::ensemble::EnsembleDecoder;
+use pecos_decoder_core::errors::DecoderError;
+
+/// A decoder that returns a configurable mask based on syndrome content.
+struct ConfigurableDecoder {
+    /// Observable mask to return when syndrome has any defects.
+    defect_mask: u64,
+}
+
+impl ObservableDecoder for ConfigurableDecoder {
+    fn decode_to_observables(&mut self, syndrome: &[u8]) -> Result<u64, DecoderError> {
+        let has_defects = syndrome.iter().any(|&v| v != 0);
+        if has_defects {
+            Ok(self.defect_mask)
+        } else {
+            Ok(0)
+        }
+    }
+}
+
+/// A decoder that always fails.
+struct FailingDecoder;
+
+impl ObservableDecoder for FailingDecoder {
+    fn decode_to_observables(&mut self, _syndrome: &[u8]) -> Result<u64, DecoderError> {
+        Err(DecoderError::DecodingFailed("always fails".into()))
+    }
+}
+
+#[test]
+fn test_ensemble_with_three_agreeing_decoders() {
+    let decoders: Vec<Box<dyn ObservableDecoder>> = vec![
+        Box::new(ConfigurableDecoder { defect_mask: 0b11 }),
+        Box::new(ConfigurableDecoder { defect_mask: 0b11 }),
+        Box::new(ConfigurableDecoder { defect_mask: 0b11 }),
+    ];
+    let mut ens = EnsembleDecoder::new(decoders);
+    assert_eq!(ens.decode_to_observables(&[1]).unwrap(), 0b11);
+    assert_eq!(ens.decode_to_observables(&[0]).unwrap(), 0);
+}
+
+#[test]
+fn test_ensemble_majority_per_bit() {
+    // Decoder 1: flips obs 0 and 1
+    // Decoder 2: flips obs 0 only
+    // Decoder 3: flips obs 0 only
+    // Majority: obs 0 = 3/3 flip, obs 1 = 1/3 flip
+    let decoders: Vec<Box<dyn ObservableDecoder>> = vec![
+        Box::new(ConfigurableDecoder { defect_mask: 0b11 }),
+        Box::new(ConfigurableDecoder { defect_mask: 0b01 }),
+        Box::new(ConfigurableDecoder { defect_mask: 0b01 }),
+    ];
+    let mut ens = EnsembleDecoder::new(decoders);
+    assert_eq!(ens.decode_to_observables(&[1]).unwrap(), 0b01);
+}
+
+#[test]
+fn test_ensemble_weighted_overrides_majority() {
+    // 1 decoder votes flip (weight 10), 2 decoders vote no flip (weight 1 each)
+    let decoders: Vec<Box<dyn ObservableDecoder>> = vec![
+        Box::new(ConfigurableDecoder { defect_mask: 1 }),
+        Box::new(ConfigurableDecoder { defect_mask: 0 }),
+        Box::new(ConfigurableDecoder { defect_mask: 0 }),
+    ];
+    let mut ens = EnsembleDecoder::with_weights(decoders, vec![10.0, 1.0, 1.0]);
+    // Weight for flip: 10, weight for no flip: 2. Flip wins despite 1/3 majority.
+    assert_eq!(ens.decode_to_observables(&[1]).unwrap(), 1);
+}
+
+#[test]
+fn test_ensemble_propagates_errors() {
+    let decoders: Vec<Box<dyn ObservableDecoder>> = vec![
+        Box::new(ConfigurableDecoder { defect_mask: 1 }),
+        Box::new(FailingDecoder),
+    ];
+    let mut ens = EnsembleDecoder::new(decoders);
+    let result = ens.decode_to_observables(&[1]);
+    assert!(result.is_err(), "Should propagate decoder error");
+}
+
+#[test]
+fn test_ensemble_repeated_shots_consistent() {
+    let decoders: Vec<Box<dyn ObservableDecoder>> = vec![
+        Box::new(ConfigurableDecoder { defect_mask: 1 }),
+        Box::new(ConfigurableDecoder { defect_mask: 1 }),
+        Box::new(ConfigurableDecoder { defect_mask: 0 }),
+    ];
+    let mut ens = EnsembleDecoder::new(decoders);
+
+    // Run the same syndrome 100 times -- must be deterministic.
+    for _ in 0..100 {
+        assert_eq!(ens.decode_to_observables(&[1]).unwrap(), 1);
+        assert_eq!(ens.decode_to_observables(&[0]).unwrap(), 0);
+    }
+}
+
+#[test]
+fn test_ensemble_five_decoders_complex_vote() {
+    // 5 decoders, 3 bits:
+    // D0: 0b111, D1: 0b101, D2: 0b100, D3: 0b110, D4: 0b010
+    // Bit 0: D0,D1 flip (2/5 < majority) -> 0
+    // Bit 1: D0,D3,D4 flip (3/5 majority) -> 1
+    // Bit 2: D0,D1,D2,D3 flip (4/5 majority) -> 1
+    let decoders: Vec<Box<dyn ObservableDecoder>> = vec![
+        Box::new(ConfigurableDecoder { defect_mask: 0b111 }),
+        Box::new(ConfigurableDecoder { defect_mask: 0b101 }),
+        Box::new(ConfigurableDecoder { defect_mask: 0b100 }),
+        Box::new(ConfigurableDecoder { defect_mask: 0b110 }),
+        Box::new(ConfigurableDecoder { defect_mask: 0b010 }),
+    ];
+    let mut ens = EnsembleDecoder::new(decoders);
+    assert_eq!(ens.decode_to_observables(&[1]).unwrap(), 0b110);
+}
diff --git a/crates/pecos-decoders/Cargo.toml b/crates/pecos-decoders/Cargo.toml
index 5d0731e45..4e219d9dd 100644
--- a/crates/pecos-decoders/Cargo.toml
+++ b/crates/pecos-decoders/Cargo.toml
@@ -15,20 +15,24 @@ description = "Unified decoder meta-crate for PECOS"
 pecos-decoder-core.workspace = true
 pecos-ldpc-decoders = { workspace = true, optional = true }
 pecos-fusion-blossom = { workspace = true, optional = true }
+pecos-mwpf = { workspace = true, optional = true }
 pecos-pymatching = { workspace = true, optional = true }
 pecos-tesseract = { workspace = true, optional = true }
 pecos-chromobius = { workspace = true, optional = true }
 pecos-relay-bp = { workspace = true, optional = true }
+pecos-uf-decoder = { workspace = true, optional = true }
 
 [features]
 default = []
 ldpc = ["dep:pecos-ldpc-decoders"]
 fusion-blossom = ["dep:pecos-fusion-blossom"]
+mwpf = ["dep:pecos-mwpf"]
 pymatching = ["dep:pecos-pymatching"]
 tesseract = ["dep:pecos-tesseract"]
 chromobius = ["dep:pecos-chromobius"]
 relay-bp = ["dep:pecos-relay-bp"]
-all = ["ldpc", "fusion-blossom", "pymatching", "tesseract", "chromobius", "relay-bp"]
+uf = ["dep:pecos-uf-decoder"]
+all = ["ldpc", "fusion-blossom", "mwpf", "pymatching", "tesseract", "chromobius", "relay-bp", "uf"]
 
 [lints]
 workspace = true
diff --git a/crates/pecos-decoders/src/lib.rs b/crates/pecos-decoders/src/lib.rs
index 53b687f4b..5c9906a45 100644
--- a/crates/pecos-decoders/src/lib.rs
+++ b/crates/pecos-decoders/src/lib.rs
@@ -11,11 +11,20 @@
 //! - `tesseract` - Tesseract search-based decoder (C++ FFI)
 //! - `chromobius` - Chromobius color code decoder (C++ FFI)
 //! - `relay-bp` - Relay BP decoder for qLDPC codes (pure Rust)
+//! - `uf` - Syndrome-graph Union-Find decoder (pure Rust)
 //! - `all` - Enable all decoders
 
 // Re-export core traits
 pub use pecos_decoder_core::{
-    BatchDecoder, CssDecoder, Decoder, DecoderError, DecodingResultTrait, SoftDecoder,
+    BatchDecoder, CssDecoder, Decoder, DecoderError, DecodingResultTrait, ObservableDecoder,
+    SoftDecoder,
+};
+
+// Re-export observable subgraph decoder (for transversal gates)
+pub use pecos_decoder_core::observable_subgraph::{
+    DetectorGroup, ObservableSubgraph, ObservableSubgraphDecoder,
+    ParallelObservableSubgraphDecoder, QubitStabCoords, StabCoords, StabType,
+    partition_dem_by_observable,
 };
 
 // Re-export LDPC decoders when feature is enabled
@@ -51,13 +60,19 @@ pub use pecos_ldpc_decoders::{
     UnionFindDecoder,
 };
 
+// Re-export MWPF decoder when feature is enabled
+#[cfg(feature = "mwpf")]
+pub use pecos_mwpf::{MwpfConfig, MwpfDecoder, MwpfDecodingResult, MwpfError, MwpfSolverType};
+
 // Re-export Fusion Blossom decoder when feature is enabled
 #[cfg(feature = "fusion-blossom")]
 pub use pecos_fusion_blossom::{
     DecodingOptions as FusionBlossomDecodingOptions, DecodingResult as FusionBlossomDecodingResult,
     FusionBlossomBuilder, FusionBlossomConfig, FusionBlossomDecoder, FusionBlossomError,
-    PerfectMatchingInfo, SolverType, StandardCode, SyndromeData,
+    ParsedCorrelatedDem, PerfectMatchingInfo, SolverType, StandardCode, SyndromeData,
 };
+#[cfg(feature = "fusion-blossom")]
+pub use pecos_fusion_blossom::{PartitionConfig, VertexRange};
 
 // Re-export PyMatching decoder when feature is enabled
 #[cfg(feature = "pymatching")]
@@ -82,6 +97,15 @@ pub use pecos_chromobius::{
     DecodingResult as ChromobiusDecodingResult,
 };
 
+// Re-export UF decoder when feature is enabled
+#[cfg(feature = "uf")]
+pub use pecos_uf_decoder::{
+    AStarConfig, AStarDecoder, BeamSearchConfig, BeamSearchWindowedDecoder,
+    BpSchedule as UfBpSchedule, BpUfConfig, BpUfDecoder, CssUfDecoder, OverlappingWindowedDecoder,
+    QubitEdgeMapping, SandwichWindowedDecoder, StreamingWindowedDecoder, UfDecoder,
+    UfDecoderConfig, WindowedConfig, WindowedDecoder,
+};
+
 // Re-export Relay BP decoder when feature is enabled
 #[cfg(feature = "relay-bp")]
 pub use pecos_relay_bp::{
diff --git a/crates/pecos-engines/src/byte_message/builder.rs b/crates/pecos-engines/src/byte_message/builder.rs
index d641511f1..309f275d8 100644
--- a/crates/pecos-engines/src/byte_message/builder.rs
+++ b/crates/pecos-engines/src/byte_message/builder.rs
@@ -155,6 +155,10 @@ impl ByteMessageBuilder {
     where
         I: IntoIterator<Item = usize>,
     {
+        assert!(
+            gate_type != GateType::Channel,
+            "Channel gates carry typed payloads and cannot be encoded in ByteMessage gate commands"
+        );
         let payload_size = size_of::<GateHeader>()
             + num_qubits * size_of::<u32>()
             + (angles.len() + params.len()) * size_of::<f64>();
@@ -326,6 +330,12 @@ impl ByteMessageBuilder {
     /// This function will panic if the number of qubits in the gate exceeds 255,
     /// as the protocol uses a u8 to represent the qubit count.
     pub fn add_gate_command(&mut self, gate: &Gate) -> &mut Self {
+        gate.validate()
+            .unwrap_or_else(|err| panic!("Invalid gate command: {err}"));
+        assert!(
+            !gate.is_channel(),
+            "Channel gates carry typed payloads and cannot be encoded in ByteMessage gate commands"
+        );
         self.add_gate_parts_from_usizes(
             gate.gate_type,
             gate.qubits.len(),
@@ -969,6 +979,28 @@ mod tests {
         assert!(!message.is_empty().unwrap());
     }
 
+    #[test]
+    #[should_panic(
+        expected = "Channel gates carry typed payloads and cannot be encoded in ByteMessage gate commands"
+    )]
+    fn test_add_gate_command_rejects_channel_gate() {
+        let mut builder = ByteMessageBuilder::new();
+        let _ = builder.for_quantum_operations();
+
+        let gate = Gate::channel(pecos_core::channel::Depolarizing(0.01, 0));
+        builder.add_gate_command(&gate);
+    }
+
+    #[test]
+    #[should_panic(expected = "Invalid gate command")]
+    fn test_add_gate_command_rejects_invalid_gate_payload() {
+        let mut builder = ByteMessageBuilder::new();
+        let _ = builder.for_quantum_operations();
+
+        let gate = Gate::cx(&[(0, 0)]);
+        builder.add_gate_command(&gate);
+    }
+
     #[test]
     fn test_builder_basic() {
         // Create a builder
diff --git a/crates/pecos-engines/src/byte_message/message.rs b/crates/pecos-engines/src/byte_message/message.rs
index 35a9c7163..82b82c566 100644
--- a/crates/pecos-engines/src/byte_message/message.rs
+++ b/crates/pecos-engines/src/byte_message/message.rs
@@ -288,15 +288,7 @@ impl ByteMessage {
                 }
             }
 
-            match Self::parse_gate_command(payload) {
-                Ok(cmd) => Some(cmd),
-                Err(e) => {
-                    if trace_enabled {
-                        trace!("Error parsing gate: {e}");
-                    }
-                    None
-                }
-            }
+            Some(Self::parse_gate_command(payload)?)
         } else {
             None
         };
@@ -722,6 +714,12 @@ impl ByteMessage {
         let num_qubits = header.num_qubits as usize;
         let has_params = header.has_params != 0;
         let gate_type = GateType::from(header.gate_type);
+        if gate_type == GateType::Channel {
+            return Err(PecosError::Input(
+                "Channel gates carry typed payloads and cannot be encoded in ByteMessage gate commands"
+                    .to_string(),
+            ));
+        }
 
         if trace_enabled {
             trace!(
@@ -767,7 +765,13 @@ impl ByteMessage {
             );
         }
 
-        Ok(Gate::new(gate_type, angles, params, qubits))
+        let gate = Gate::new(gate_type, angles, params, qubits);
+        gate.validate().map_err(|err| {
+            PecosError::Input(format!(
+                "Invalid gate command payload for {gate_type:?}: {err}"
+            ))
+        })?;
+        Ok(gate)
     }
 
     // The parse_simple_measurement method has been removed as part of simplifying the protocol.
@@ -801,6 +805,67 @@ mod tests {
         );
     }
 
+    #[test]
+    fn test_raw_channel_gate_message_is_rejected() {
+        use crate::byte_message::protocol::{GateHeader, MessageFlags, MessageType};
+
+        let header = GateHeader {
+            gate_type: GateType::Channel as u8,
+            num_qubits: 1,
+            has_params: 0,
+            reserved: 0,
+        };
+        let mut payload = Vec::new();
+        payload.extend_from_slice(bytemuck::bytes_of(&header));
+        payload.extend_from_slice(&0u32.to_le_bytes());
+
+        let mut builder = ByteMessage::quantum_operations_builder();
+        builder.add_message(MessageType::Gate, &payload, MessageFlags::NONE);
+        let message = builder.build();
+
+        let err = message
+            .quantum_ops()
+            .expect_err("ByteMessage cannot carry typed channel payloads");
+
+        assert!(
+            err.to_string()
+                .contains("Channel gates carry typed payloads")
+        );
+    }
+
+    #[test]
+    fn test_raw_invalid_gate_payload_is_rejected_after_parse() {
+        use crate::byte_message::protocol::{GateHeader, MessageFlags, MessageType};
+
+        let header = GateHeader {
+            gate_type: GateType::CX as u8,
+            num_qubits: 2,
+            has_params: 0,
+            reserved: 0,
+        };
+        let mut payload = Vec::new();
+        payload.extend_from_slice(bytemuck::bytes_of(&header));
+        payload.extend_from_slice(&0u32.to_le_bytes());
+        payload.extend_from_slice(&0u32.to_le_bytes());
+
+        let mut builder = ByteMessage::quantum_operations_builder();
+        builder.add_message(MessageType::Gate, &payload, MessageFlags::NONE);
+        let message = builder.build();
+
+        let err = message
+            .quantum_ops()
+            .expect_err("raw CX payload cannot use the same qubit twice");
+
+        assert!(
+            err.to_string().contains("Invalid gate command payload"),
+            "unexpected error: {err}"
+        );
+        assert!(
+            err.to_string().contains("requires distinct qubits"),
+            "unexpected error: {err}"
+        );
+    }
+
     #[test]
     fn test_message_type() {
         // Create an empty message
diff --git a/crates/pecos-engines/src/noise/biased_depolarizing.rs b/crates/pecos-engines/src/noise/biased_depolarizing.rs
index 47d992f12..2bd3cce99 100644
--- a/crates/pecos-engines/src/noise/biased_depolarizing.rs
+++ b/crates/pecos-engines/src/noise/biased_depolarizing.rs
@@ -73,6 +73,13 @@ pub struct BiasedDepolarizingNoiseModel {
 impl ProbabilityValidator for BiasedDepolarizingNoiseModel {}
 
 impl BiasedDepolarizingNoiseModel {
+    fn channel_gate_error() -> PecosError {
+        PecosError::Input(
+            "ByteMessage noise models cannot process GateType::Channel; channel operations carry typed payloads and must use a channel-aware circuit path"
+                .to_string(),
+        )
+    }
+
     /// Create a new general noise model with the given probabilities
     #[must_use]
     pub fn new(p_prep: f64, p_meas_0: f64, p_meas_1: f64, p1: f64, p2: f64) -> Self {
@@ -217,12 +224,16 @@ impl BiasedDepolarizingNoiseModel {
                     trace!("Applying preparation with possible fault");
                     self.apply_prep_faults(&mut builder, gate);
                 }
+                GateType::Channel => {
+                    unreachable!("channel gates are rejected before noise is applied")
+                }
                 GateType::I
                 | GateType::Idle
                 | GateType::MeasCrosstalkLocalPayload
                 | GateType::MeasCrosstalkGlobalPayload
                 | GateType::QFree
-                | GateType::Custom => {}
+                | GateType::Custom
+                | GateType::TrackedPauliMeta => {}
             }
         }
 
@@ -440,6 +451,9 @@ impl ControlEngine for BiasedDepolarizingNoiseModel {
 
         // Parse the input as quantum operations
         let gates: Vec<crate::Gate> = input.quantum_ops()?;
+        if gates.iter().any(Gate::is_channel) {
+            return Err(Self::channel_gate_error());
+        }
 
         // Apply noise to the gates
         let noisy_gates = self.apply_noise_to_gates(&gates);
diff --git a/crates/pecos-engines/src/noise/depolarizing.rs b/crates/pecos-engines/src/noise/depolarizing.rs
index 9ffd2e171..6f6d3c198 100644
--- a/crates/pecos-engines/src/noise/depolarizing.rs
+++ b/crates/pecos-engines/src/noise/depolarizing.rs
@@ -81,6 +81,13 @@ pub struct DepolarizingNoiseModel {
 impl ProbabilityValidator for DepolarizingNoiseModel {}
 
 impl DepolarizingNoiseModel {
+    fn channel_gate_error() -> PecosError {
+        PecosError::Input(
+            "ByteMessage noise models cannot process GateType::Channel; channel operations carry typed payloads and must use a channel-aware circuit path"
+                .to_string(),
+        )
+    }
+
     /// Compute a probability threshold from a f64 probability
     #[inline]
     fn compute_threshold(p: f64) -> u64 {
@@ -231,12 +238,14 @@ impl DepolarizingNoiseModel {
                 trace!("Applying preparation with possible fault");
                 Self::apply_prep_faults(rng, p_prep_threshold, builder, gate);
             }
+            GateType::Channel => unreachable!("channel gates are rejected before noise is applied"),
             GateType::I
             | GateType::Idle
             | GateType::MeasCrosstalkLocalPayload
             | GateType::MeasCrosstalkGlobalPayload
             | GateType::QFree
-            | GateType::Custom => {
+            | GateType::Custom
+            | GateType::TrackedPauliMeta => {
                 // Just pass through with no added noise.
             }
         }
@@ -563,6 +572,15 @@ impl ControlEngine for DepolarizingNoiseModel {
         // For quantum operations, apply gate noise
         trace!("DepolarizingNoise::start - applying noise to quantum operations");
 
+        self.scratch_gates.clear();
+        input
+            .quantum_ops_into(&mut self.scratch_gates)
+            .map_err(|e| PecosError::Input(format!("Failed to parse quantum operations: {e}")))?;
+
+        if self.scratch_gates.iter().any(Gate::is_channel) {
+            return Err(Self::channel_gate_error());
+        }
+
         if self.p_prep_threshold == 0
             && self.p_meas_threshold == 0
             && self.p1_threshold == 0
@@ -571,11 +589,6 @@ impl ControlEngine for DepolarizingNoiseModel {
             return Ok(EngineStage::NeedsProcessing(input));
         }
 
-        self.scratch_gates.clear();
-        input
-            .quantum_ops_into(&mut self.scratch_gates)
-            .map_err(|e| PecosError::Input(format!("Failed to parse quantum operations: {e}")))?;
-
         self.scratch_builder.reset();
         let _ = self.scratch_builder.for_quantum_operations();
 
diff --git a/crates/pecos-engines/src/noise/general.rs b/crates/pecos-engines/src/noise/general.rs
index 28bf37574..d64b4dde2 100644
--- a/crates/pecos-engines/src/noise/general.rs
+++ b/crates/pecos-engines/src/noise/general.rs
@@ -447,6 +447,11 @@ impl RngManageable for GeneralNoiseModel {
 impl ProbabilityValidator for GeneralNoiseModel {}
 
 impl GeneralNoiseModel {
+    fn channel_gate_error() -> String {
+        "ByteMessage noise models cannot process GateType::Channel; channel operations carry typed payloads and must use a channel-aware circuit path"
+            .to_string()
+    }
+
     /// Create a new noise model with the specified error parameters
     ///
     /// Creates a `GeneralNoiseModel` with the specified error probabilities while using default values
@@ -517,6 +522,9 @@ impl GeneralNoiseModel {
         let gates = input
             .quantum_ops()
             .expect("Failed to parse input as quantum operations");
+        if gates.iter().any(Gate::is_channel) {
+            return Err(Self::channel_gate_error());
+        }
 
         for gate in gates {
             // Track which qubits are being measured for leakage handling
@@ -1559,6 +1567,8 @@ mod tests {
                 angles: vec![].into(),
                 qubits: vec![QubitId(qubit)].into(),
                 params: vec![].into(),
+                meas_ids: vec![].into(),
+                channel: None,
             });
         }
         let measurement_request = request_builder.build();
@@ -1640,6 +1650,8 @@ mod tests {
             angles: vec![].into(),
             qubits: vec![QubitId(0)].into(),
             params: vec![].into(),
+            meas_ids: vec![].into(),
+            channel: None,
         };
 
         // Create a builder and apply noise
@@ -1829,6 +1841,8 @@ mod tests {
             angles: vec![].into(),
             qubits: vec![QubitId(0)].into(),
             params: vec![].into(),
+            meas_ids: vec![].into(),
+            channel: None,
         };
         noise.apply_prep_faults(&prep_gate, &mut builder);
 
@@ -2746,6 +2760,8 @@ mod tests {
             angles: vec![].into(),
             qubits: vec![QubitId(0)].into(),
             params: vec![1.0].into(), // 1 second duration
+            meas_ids: vec![].into(),
+            channel: None,
         };
 
         // Apply idle faults - should use coherent dephasing (RZ gates)
@@ -2769,6 +2785,8 @@ mod tests {
             angles: vec![].into(),
             qubits: vec![QubitId(0), QubitId(1), QubitId(2)].into(), // 3 qubits
             params: vec![1.0].into(),                                // 1 second duration
+            meas_ids: vec![].into(),
+            channel: None,
         };
 
         model.apply_idle_faults(
@@ -2905,6 +2923,8 @@ mod tests {
             angles: vec![Angle64::from_radians(0.1)].into(),
             qubits: vec![QubitId(0)].into(),
             params: vec![].into(),
+            meas_ids: vec![].into(),
+            channel: None,
         };
 
         // Create an X gate (not noiseless - should have noise applied)
@@ -2913,6 +2933,8 @@ mod tests {
             angles: vec![].into(),
             qubits: vec![QubitId(0)].into(),
             params: vec![].into(),
+            meas_ids: vec![].into(),
+            channel: None,
         };
 
         // Make sure RZ is recognized as noiseless
diff --git a/crates/pecos-engines/src/quantum.rs b/crates/pecos-engines/src/quantum.rs
index 7f10035d3..9039080cb 100644
--- a/crates/pecos-engines/src/quantum.rs
+++ b/crates/pecos-engines/src/quantum.rs
@@ -4,6 +4,7 @@ use crate::byte_message::GateType;
 use dyn_clone::DynClone;
 use log::debug;
 use pecos_core::Angle64;
+use pecos_core::ChannelExpr;
 use pecos_core::QubitId;
 use pecos_core::RngManageable;
 use pecos_core::errors::PecosError;
@@ -54,6 +55,26 @@ fn flat_to_pairs(qubits: &[QubitId]) -> Vec<(QubitId, QubitId)> {
     pairs
 }
 
+trait ChannelDispatch {
+    fn apply_channel_expr(&mut self, channel: &ChannelExpr) -> Result<(), PecosError>;
+}
+
+impl ChannelDispatch for StabVec {
+    fn apply_channel_expr(&mut self, _channel: &ChannelExpr) -> Result<(), PecosError> {
+        Err(quantum_error(
+            "Channel gate requires a channel-aware simulator path",
+        ))
+    }
+}
+
+impl ChannelDispatch for DensityMatrix {
+    fn apply_channel_expr(&mut self, channel: &ChannelExpr) -> Result<(), PecosError> {
+        DensityMatrix::apply_channel_expr(self, channel)
+            .map(|_| ())
+            .map_err(|err| quantum_error(format!("invalid channel gate: {err}")))
+    }
+}
+
 /// Process a `ByteMessage` against any Clifford-capable simulator.
 ///
 /// Shared gate dispatch for `SparseStabEngine`, `StabilizerEngine`, etc.
@@ -169,9 +190,9 @@ fn process_clifford_message<S: CliffordGateable + CliffordRotation + QuantumSimu
                     cmd_idx += 1;
                     mz_qubits.extend_from_slice(&batch[cmd_idx].qubits);
                 }
-                let meas_results = sim.mz(&mz_qubits);
-                for meas_result in meas_results {
-                    measurements.push(usize::from(meas_result.outcome));
+                let meas_ids = sim.mz(&mz_qubits);
+                for meas_id in meas_ids {
+                    measurements.push(usize::from(meas_id.outcome));
                 }
             }
 
@@ -274,7 +295,9 @@ fn process_clifford_message<S: CliffordGateable + CliffordRotation + QuantumSimu
 /// Shared gate dispatch for `StabVecEngine`, `DensityMatrixEngine`, etc.
 /// Supports all Clifford gates, arbitrary rotations, composite gates (CH, CCX, CRZ),
 /// preparations, and measurements with MZ batching.
-fn process_general_message<S: CliffordGateable + ArbitraryRotationGateable + QuantumSimulator>(
+fn process_general_message<
+    S: CliffordGateable + ArbitraryRotationGateable + QuantumSimulator + ChannelDispatch,
+>(
     sim: &mut S,
     message: &ByteMessage,
 ) -> Result<ByteMessage, PecosError> {
@@ -519,15 +542,15 @@ fn process_general_message<S: CliffordGateable + ArbitraryRotationGateable + Qua
                     cmd_idx += 1;
                     mz_qubits.extend_from_slice(&batch[cmd_idx].qubits);
                 }
-                let meas_results = sim.mz(&mz_qubits);
-                for meas_result in meas_results {
-                    measurements.push(usize::from(meas_result.outcome));
+                let meas_ids = sim.mz(&mz_qubits);
+                for meas_id in meas_ids {
+                    measurements.push(usize::from(meas_id.outcome));
                 }
             }
             GateType::MeasureFree => {
-                let meas_results = sim.mz(&cmd.qubits);
-                for meas_result in meas_results {
-                    measurements.push(usize::from(meas_result.outcome));
+                let meas_ids = sim.mz(&cmd.qubits);
+                for meas_id in meas_ids {
+                    measurements.push(usize::from(meas_id.outcome));
                 }
             }
 
@@ -535,6 +558,12 @@ fn process_general_message<S: CliffordGateable + ArbitraryRotationGateable + Qua
             GateType::PZ | GateType::QAlloc => {
                 sim.pz(&cmd.qubits);
             }
+            GateType::Channel => {
+                let channel = cmd
+                    .channel_expr()
+                    .ok_or_else(|| quantum_error("Channel gate is missing its channel payload"))?;
+                sim.apply_channel_expr(channel)?;
+            }
 
             // No-ops
             GateType::I
@@ -542,7 +571,8 @@ fn process_general_message<S: CliffordGateable + ArbitraryRotationGateable + Qua
             | GateType::MeasCrosstalkLocalPayload
             | GateType::MeasCrosstalkGlobalPayload
             | GateType::QFree
-            | GateType::Custom => {}
+            | GateType::Custom
+            | GateType::TrackedPauliMeta => {}
         }
         cmd_idx += 1;
     }
@@ -1084,21 +1114,27 @@ where
                         "Processing batched measurement on {} qubits",
                         mz_qubits.len()
                     );
-                    let meas_results = self.simulator.mz(&mz_qubits);
-                    for meas_result in meas_results {
-                        measurements.push(usize::from(meas_result.outcome));
+                    let meas_ids = self.simulator.mz(&mz_qubits);
+                    for meas_id in meas_ids {
+                        measurements.push(usize::from(meas_id.outcome));
                     }
                 }
                 GateType::PZ => {
                     debug!("Processing Prep gate on qubits {:?}", cmd.qubits);
                     self.simulator.pz(&cmd.qubits);
                 }
+                GateType::Channel => {
+                    return Err(quantum_error(
+                        "Channel gate requires a channel-aware simulator path",
+                    ));
+                }
                 GateType::I
                 | GateType::Idle
                 | GateType::MeasCrosstalkLocalPayload
                 | GateType::MeasCrosstalkGlobalPayload
                 | GateType::QFree
-                | GateType::Custom => {
+                | GateType::Custom
+                | GateType::TrackedPauliMeta => {
                     // Just let the system naturally evolve for the specified duration
                     // No active operation needed in the simulator
                     // QFree is a no-op for state vector simulation (qubit tracking is handled elsewhere)
@@ -1142,9 +1178,9 @@ where
                 GateType::MeasureFree => {
                     // Measure and deallocate - measure first, then the qubit is implicitly freed
                     debug!("Processing MeasureFree gate on qubits {:?}", cmd.qubits);
-                    let meas_results = self.simulator.mz(&cmd.qubits);
-                    for meas_result in meas_results {
-                        measurements.push(usize::from(meas_result.outcome));
+                    let meas_ids = self.simulator.mz(&cmd.qubits);
+                    for meas_id in meas_ids {
+                        measurements.push(usize::from(meas_id.outcome));
                     }
                 }
                 GateType::U => {
@@ -1629,9 +1665,9 @@ impl Engine for CoinTossEngine {
                 GateType::MZ | GateType::MeasureLeaked | GateType::MeasureFree => {
                     for q in &cmd.qubits {
                         debug!("CoinToss: Processing measurement on qubit {q:?}");
-                        let meas_results = self.simulator.mz(&[*q]);
-                        for meas_result in &meas_results {
-                            let outcome = u32::from(meas_result.outcome);
+                        let meas_ids = self.simulator.mz(&[*q]);
+                        for meas_id in &meas_ids {
+                            let outcome = u32::from(meas_id.outcome);
                             measurements.push(outcome);
                         }
                     }
diff --git a/crates/pecos-foreign/src/conformance.rs b/crates/pecos-foreign/src/conformance.rs
index 103d80e45..e2387f279 100644
--- a/crates/pecos-foreign/src/conformance.rs
+++ b/crates/pecos-foreign/src/conformance.rs
@@ -15,9 +15,14 @@
 //!
 //! # Usage from Rust
 //!
-//! ```rust,ignore
-//! let results = run_conformance_tests(&mut foreign_sim);
-//! assert!(results.all_passed());
+//! ```rust,no_run
+//! use pecos_foreign::ForeignSimulator;
+//! use pecos_foreign::conformance::run_conformance_tests;
+//!
+//! fn check_foreign_simulator(mut foreign_sim: ForeignSimulator) {
+//!     let results = run_conformance_tests(&mut foreign_sim);
+//!     assert!(results.all_passed());
+//! }
 //! ```
 
 use crate::simulator::{ForeignSimulator, ForeignSimulatorVTable};
diff --git a/crates/pecos-foreign/src/gate_support.rs b/crates/pecos-foreign/src/gate_support.rs
index 31e232b3a..c42416c6b 100644
--- a/crates/pecos-foreign/src/gate_support.rs
+++ b/crates/pecos-foreign/src/gate_support.rs
@@ -11,9 +11,14 @@
 //!
 //! # Example
 //!
-//! ```rust,ignore
-//! let sim = ForeignSimulator::new(handle, vtable);
-//! let runner = configure_runner_for_foreign(&sim);
+//! ```rust,no_run
+//! use pecos_foreign::ForeignSimulator;
+//! use pecos_foreign::gate_support::configure_runner_for_foreign;
+//!
+//! fn configure_foreign_runner(sim: &ForeignSimulator) {
+//!     let runner = configure_runner_for_foreign(sim);
+//!     let _ = runner;
+//! }
 //! // runner will decompose unsupported gates into {SZ, H, CX, MZ, RX?, RZ?, RZZ?}
 //! ```
 
diff --git a/crates/pecos-fusion-blossom/Cargo.toml b/crates/pecos-fusion-blossom/Cargo.toml
index 3c4d73b99..9ebfc8370 100644
--- a/crates/pecos-fusion-blossom/Cargo.toml
+++ b/crates/pecos-fusion-blossom/Cargo.toml
@@ -16,6 +16,7 @@ pecos-decoder-core.workspace = true
 ndarray.workspace = true
 thiserror.workspace = true
 fusion-blossom.workspace = true
+serde_json.workspace = true
 
 [lib]
 name = "pecos_fusion_blossom"
diff --git a/crates/pecos-fusion-blossom/examples/fusion_blossom_usage.rs b/crates/pecos-fusion-blossom/examples/fusion_blossom_usage.rs
index 1c049ce75..ec3fe5128 100644
--- a/crates/pecos-fusion-blossom/examples/fusion_blossom_usage.rs
+++ b/crates/pecos-fusion-blossom/examples/fusion_blossom_usage.rs
@@ -85,7 +85,7 @@ fn main() -> Result<(), Box<dyn std::error::Error>> {
         let result = decoder.decode(&syndrome.view())?;
         println!("Decoded observables: {:?}", result.observable);
         println!("Total weight: {:.2}", result.weight);
-        println!("Observable errors detected: ");
+        println!("Logical observable errors detected: ");
         for (i, &obs) in result.observable.iter().enumerate() {
             if obs != 0 {
                 println!("  - Observable {i} flipped");
diff --git a/crates/pecos-fusion-blossom/src/core_traits.rs b/crates/pecos-fusion-blossom/src/core_traits.rs
index cded1dada..ee44d32b4 100644
--- a/crates/pecos-fusion-blossom/src/core_traits.rs
+++ b/crates/pecos-fusion-blossom/src/core_traits.rs
@@ -33,6 +33,165 @@ impl Decoder for FusionBlossomDecoder {
     }
 }
 
+/// Implement `ObservableDecoder` for `FusionBlossomDecoder`.
+///
+/// Uses the fast decode path with pre-computed observable bitmasks.
+impl pecos_decoder_core::ObservableDecoder for FusionBlossomDecoder {
+    fn decode_to_observables(
+        &mut self,
+        syndrome: &[u8],
+    ) -> Result<u64, pecos_decoder_core::DecoderError> {
+        self.decode_to_obs_mask(syndrome)
+            .map_err(|e| pecos_decoder_core::DecoderError::DecodingFailed(e.to_string()))
+    }
+}
+
+/// Implement `ObservableErasureDecoder` for `FusionBlossomDecoder`.
+///
+/// Neutral atom erasure support: erased edges are marked in the syndrome data,
+/// causing the solver to treat them as known errors (zero weight).
+impl pecos_decoder_core::erasure::ObservableErasureDecoder for FusionBlossomDecoder {
+    fn decode_with_erasures(
+        &mut self,
+        syndrome: &[u8],
+        erasure_edges: &[usize],
+    ) -> Result<u64, pecos_decoder_core::DecoderError> {
+        if erasure_edges.is_empty() {
+            return self
+                .decode_to_obs_mask(syndrome)
+                .map_err(|e| pecos_decoder_core::DecoderError::DecodingFailed(e.to_string()));
+        }
+
+        let defects: Vec<usize> = syndrome
+            .iter()
+            .enumerate()
+            .filter_map(|(i, &v)| if v != 0 { Some(i) } else { None })
+            .collect();
+
+        if defects.is_empty() && erasure_edges.is_empty() {
+            return Ok(0);
+        }
+
+        let syndrome_data = SyndromeData::with_erasures(defects, erasure_edges.to_vec());
+
+        let result = self
+            .decode_with_options(syndrome_data, DecodingOptions::default())
+            .map_err(|e| pecos_decoder_core::DecoderError::DecodingFailed(e.to_string()))?;
+
+        let edge_indices: Vec<usize> = result.matched_edges.clone();
+        Ok(self.obs_mask_from_edges(&edge_indices))
+    }
+}
+
+/// Implement `MatchingDecoder` for `FusionBlossomDecoder`.
+///
+/// Enables the two-pass correlated DGR decode by exposing which edges
+/// were matched and accepting per-shot dynamic weight adjustments.
+impl pecos_decoder_core::correlated_decoder::MatchingDecoder for FusionBlossomDecoder {
+    fn decode_with_matching(
+        &mut self,
+        syndrome: &[u8],
+    ) -> Result<(u64, Vec<usize>), pecos_decoder_core::DecoderError> {
+        // Extract defects
+        let defects: Vec<usize> = syndrome
+            .iter()
+            .enumerate()
+            .filter_map(|(i, &v)| if v != 0 { Some(i) } else { None })
+            .collect();
+
+        if defects.is_empty() {
+            return Ok((0, Vec::new()));
+        }
+
+        let syndrome_data = SyndromeData::from_defects(defects);
+        let result = self
+            .decode_with_options(syndrome_data, DecodingOptions::default())
+            .map_err(|e| pecos_decoder_core::DecoderError::DecodingFailed(e.to_string()))?;
+
+        let edge_indices: Vec<usize> = result.matched_edges.clone();
+        let mask = self.obs_mask_from_edges(&edge_indices);
+
+        Ok((mask, edge_indices))
+    }
+
+    fn decode_with_weights(
+        &mut self,
+        syndrome: &[u8],
+        weights: &[f64],
+    ) -> Result<(u64, Vec<usize>), pecos_decoder_core::DecoderError> {
+        let defects: Vec<usize> = syndrome
+            .iter()
+            .enumerate()
+            .filter_map(|(i, &v)| if v != 0 { Some(i) } else { None })
+            .collect();
+
+        if defects.is_empty() {
+            return Ok((0, Vec::new()));
+        }
+
+        // Convert f64 weights to Fusion Blossom's integer dynamic weights.
+        // FB uses integer weights with 1000x scaling, must be even.
+        // Only include edges whose weight differs from the original to avoid
+        // disrupting the solver with redundant overrides.
+        #[allow(clippy::cast_possible_truncation)]
+        let dynamic_weights: Vec<(usize, i32)> = weights
+            .iter()
+            .enumerate()
+            .filter_map(|(i, &w)| {
+                // Clamp to positive (FB doesn't handle negative weights)
+                let clamped = w.max(0.01);
+                let int_w = ((clamped * 1000.0) as i32 / 2) * 2;
+                // Only include if it's a real weight (not a huge default)
+                if int_w > 0 && int_w < 40_000 {
+                    Some((i, int_w))
+                } else {
+                    None
+                }
+            })
+            .collect();
+
+        let mut syndrome_data = SyndromeData::from_defects(defects);
+        if !dynamic_weights.is_empty() {
+            syndrome_data.dynamic_weights = Some(dynamic_weights);
+        }
+
+        let result = self
+            .decode_with_options(syndrome_data, DecodingOptions::default())
+            .map_err(|e| pecos_decoder_core::DecoderError::DecodingFailed(e.to_string()))?;
+
+        let edge_indices: Vec<usize> = result.matched_edges.clone();
+        let mask = self.obs_mask_from_edges(&edge_indices);
+
+        Ok((mask, edge_indices))
+    }
+
+    fn num_edges(&self) -> usize {
+        self.num_edges()
+    }
+}
+
+impl pecos_decoder_core::correlated_decoder::EdgeTrackingDecoder for FusionBlossomDecoder {
+    fn edge_node1(&self, edge_idx: usize) -> u32 {
+        self.edge_endpoints(edge_idx).map_or(0, |(n1, _, _)| n1)
+    }
+
+    fn edge_node2(&self, edge_idx: usize) -> u32 {
+        self.edge_endpoints(edge_idx).map_or(0, |(_, n2, _)| n2)
+    }
+
+    fn edge_weight(&self, edge_idx: usize) -> f64 {
+        self.edge_endpoints(edge_idx).map_or(0.0, |(_, _, w)| w)
+    }
+
+    fn edge_obs_mask(&self, edge_idx: usize) -> u64 {
+        self.edge_obs_mask(edge_idx)
+    }
+
+    fn num_detectors(&self) -> usize {
+        self.num_nodes()
+    }
+}
+
 /// Implement `DecodingResultTrait` for `FusionBlossom`'s `DecodingResult`
 impl DecodingResultTrait for DecodingResult {
     fn is_successful(&self) -> bool {
@@ -40,6 +199,10 @@ impl DecodingResultTrait for DecodingResult {
         true
     }
 
+    fn correction(&self) -> &[u8] {
+        &self.observable
+    }
+
     fn cost(&self) -> Option<f64> {
         Some(self.weight)
     }
diff --git a/crates/pecos-fusion-blossom/src/decoder.rs b/crates/pecos-fusion-blossom/src/decoder.rs
index abe3bc0c7..ad05cd961 100644
--- a/crates/pecos-fusion-blossom/src/decoder.rs
+++ b/crates/pecos-fusion-blossom/src/decoder.rs
@@ -6,13 +6,19 @@ use fusion_blossom::{
         CircuitLevelPlanarCode, CodeCapacityPlanarCode, CodeCapacityRotatedCode, ExampleCode,
         PhenomenologicalPlanarCode, PhenomenologicalRotatedCode,
     },
-    mwpm_solver::{LegacySolverSerial, PrimalDualSolver, SolverSerial},
-    util::{EdgeIndex, SolverInitializer, SyndromePattern, VertexIndex, Weight},
+    mwpm_solver::{LegacySolverSerial, SolverDualParallel, SolverSerial},
+    util::{EdgeIndex, PartitionConfig, SolverInitializer, SyndromePattern, VertexIndex, Weight},
 };
 use ndarray::{Array2, ArrayView1};
-use std::collections::HashMap;
+use std::collections::{BTreeMap, HashMap};
 use std::fmt;
 
+struct ParsedEdgeInfo {
+    obs: Vec<usize>,
+    prob: f64,
+    best_prob: f64,
+}
+
 /// Solver type selection
 #[derive(Debug, Clone, Copy, PartialEq, Eq, Default)]
 pub enum SolverType {
@@ -21,6 +27,8 @@ pub enum SolverType {
     /// Serial solver (improved performance)
     #[default]
     Serial,
+    /// Parallel solver (intra-shot parallelism via partitioning)
+    Parallel,
 }
 
 /// Configuration for Fusion Blossom decoder
@@ -179,6 +187,18 @@ pub enum StandardCode {
 enum Solver {
     Legacy(LegacySolverSerial),
     Serial(SolverSerial),
+    Parallel(SolverDualParallel),
+}
+
+/// Pre-parsed correlated DEM for fast repeated FB construction.
+#[derive(Clone)]
+pub struct ParsedCorrelatedDem {
+    /// Number of detector nodes.
+    pub num_detectors: usize,
+    /// Number of observables.
+    pub num_observables: usize,
+    /// Per mechanism: (`detector_indices`, `observable_indices`, `original_weight`).
+    pub mechanisms: Vec<(Vec<usize>, Vec<usize>, f64)>,
 }
 
 /// Fusion Blossom decoder
@@ -186,6 +206,8 @@ pub struct FusionBlossomDecoder {
     config: FusionBlossomConfig,
     /// Map from edge index to observable mask
     edge_observables: HashMap<EdgeIndex, Vec<usize>>,
+    /// Pre-computed observable bitmask per edge (for fast decode path)
+    edge_obs_masks: Vec<u64>,
     /// Number of nodes (detectors)
     num_nodes: usize,
     /// Virtual boundary node (if used)
@@ -193,11 +215,17 @@ pub struct FusionBlossomDecoder {
     /// Edges to be added to the initializer
     weighted_edges: Vec<(VertexIndex, VertexIndex, Weight)>,
     /// Virtual vertices
-    virtual_vertices: Vec<VertexIndex>,
+    pub virtual_vertices: Vec<VertexIndex>,
     /// Cached solver instance for reuse
     solver: Option<Solver>,
     /// Cached initializer
     initializer: Option<SolverInitializer>,
+    /// Partition config for parallel solver (None for serial)
+    partition_config: Option<PartitionConfig>,
+    /// Reusable buffer for padded syndrome (avoids per-shot allocation)
+    _syndrome_buf: Vec<u8>,
+    /// Reusable buffer for defect vertices
+    defect_buf: Vec<VertexIndex>,
 }
 
 impl FusionBlossomDecoder {
@@ -235,15 +263,295 @@ impl FusionBlossomDecoder {
         Ok(Self {
             config,
             edge_observables: HashMap::new(),
+            edge_obs_masks: Vec::new(),
+            partition_config: None,
             num_nodes,
             boundary_node: None,
             weighted_edges: Vec::new(),
             virtual_vertices: Vec::new(),
             solver: None,
             initializer: None,
+            _syndrome_buf: vec![0u8; num_nodes + 1], // +1 for possible boundary node
+            defect_buf: Vec::new(),
+        })
+    }
+
+    /// Create decoder from a `DemMatchingGraph`.
+    ///
+    /// # Errors
+    ///
+    /// Returns error if the graph is empty or construction fails.
+    pub fn from_matching_graph(graph: &pecos_decoder_core::dem::DemMatchingGraph) -> Result<Self> {
+        let config = FusionBlossomConfig {
+            num_nodes: Some(graph.num_detectors),
+            num_observables: graph.num_observables,
+            ..Default::default()
+        };
+        let mut decoder = Self::new(config)?;
+        for edge in &graph.edges {
+            let obs: Vec<usize> = edge.observables.iter().map(|&o| o as usize).collect();
+            match edge.node2 {
+                Some(n2) => {
+                    decoder.add_edge(edge.node1 as usize, n2 as usize, &obs, Some(edge.weight))?;
+                }
+                None => {
+                    decoder.add_boundary_edge(edge.node1 as usize, &obs, Some(edge.weight))?;
+                }
+            }
+        }
+        decoder.build_obs_masks();
+        Ok(decoder)
+    }
+
+    /// Create decoder from a DEM string.
+    ///
+    /// # Errors
+    ///
+    /// Returns error if the DEM is malformed.
+    pub fn from_dem(dem: &str) -> Result<Self> {
+        let graph = pecos_decoder_core::dem::DemMatchingGraph::from_dem_str(dem)
+            .map_err(|e| FusionBlossomError::Configuration(e.to_string()))?;
+        Self::from_matching_graph(&graph)
+    }
+
+    /// Parse a DEM string into a reusable structure for correlated FB construction.
+    ///
+    /// # Errors
+    ///
+    /// Returns error if the DEM is malformed.
+    pub fn parse_correlated_dem(dem: &str) -> Result<ParsedCorrelatedDem> {
+        use pecos_decoder_core::dem::DemCheckMatrix;
+
+        let dcm = DemCheckMatrix::from_dem_str(dem)
+            .map_err(|e| FusionBlossomError::Configuration(e.to_string()))?;
+
+        let mut mechanisms = Vec::new();
+        for m in 0..dcm.num_mechanisms {
+            let p = dcm.error_priors[m];
+            if p <= 0.0 {
+                continue;
+            }
+
+            let detectors: Vec<usize> = (0..dcm.num_detectors)
+                .filter(|&d| dcm.check_matrix[[d, m]] != 0)
+                .collect();
+
+            let obs: Vec<usize> = (0..dcm.num_observables)
+                .filter(|&o| dcm.observable_matrix[[o, m]] != 0)
+                .collect();
+
+            let weight = if p < 1.0 { ((1.0 - p) / p).ln() } else { 0.0 };
+
+            // Only graphlike (1-2 detector) mechanisms.
+            if detectors.len() <= 2 {
+                mechanisms.push((detectors, obs, weight));
+            }
+        }
+
+        Ok(ParsedCorrelatedDem {
+            num_detectors: dcm.num_detectors,
+            num_observables: dcm.num_observables,
+            mechanisms,
         })
     }
 
+    /// Build a correlated FB decoder from pre-parsed data with optional weight perturbation.
+    ///
+    /// `weight_factors[i]` multiplies the i-th mechanism's weight. Pass `None` for no perturbation.
+    /// Duplicate edges (same endpoints) are merged by keeping the lowest weight
+    /// (highest probability) mechanism's observable — matching PM's INDEPENDENT strategy.
+    ///
+    /// # Errors
+    ///
+    /// Returns error if construction fails.
+    pub fn from_parsed_correlated(
+        parsed: &ParsedCorrelatedDem,
+        weight_factors: Option<&[f64]>,
+    ) -> Result<Self> {
+        let config = FusionBlossomConfig {
+            num_nodes: Some(parsed.num_detectors),
+            num_observables: parsed.num_observables,
+            ..Default::default()
+        };
+        let mut decoder = Self::new(config)?;
+
+        // Deduplicate edges: merge by independent-union probability,
+        // first-observable-wins (stable under perturbation).
+        // Key: (min_node, max_node, is_boundary). Value: (obs, prob, best_prob).
+        let mut edge_map: BTreeMap<(usize, usize, bool), ParsedEdgeInfo> = BTreeMap::new();
+
+        for (i, (detectors, obs, base_weight)) in parsed.mechanisms.iter().enumerate() {
+            let weight = if let Some(factors) = weight_factors {
+                if i < factors.len() {
+                    (base_weight * factors[i]).max(0.01)
+                } else {
+                    *base_weight
+                }
+            } else {
+                *base_weight
+            };
+            // Convert weight to probability for merging.
+            let prob = 1.0 / (1.0 + weight.exp());
+
+            let key = match detectors.len() {
+                1 => (detectors[0], usize::MAX, true),
+                2 => {
+                    let (a, b) = if detectors[0] < detectors[1] {
+                        (detectors[0], detectors[1])
+                    } else {
+                        (detectors[1], detectors[0])
+                    };
+                    (a, b, false)
+                }
+                _ => continue,
+            };
+
+            let entry = edge_map.entry(key).or_insert_with(|| ParsedEdgeInfo {
+                obs: obs.clone(),
+                prob,
+                best_prob: prob,
+            });
+            // Independent union: P(A or B) = P(A) + P(B) - P(A)*P(B)
+            entry.prob = entry.prob + prob - entry.prob * prob;
+            if prob > entry.best_prob {
+                entry.obs.clone_from(obs);
+                entry.best_prob = prob;
+            }
+        }
+
+        for ((n1, n2, is_boundary), info) in &edge_map {
+            // Convert combined probability back to weight.
+            let p = info.prob.clamp(1e-15, 1.0 - 1e-15);
+            let weight = ((1.0 - p) / p).ln();
+            if *is_boundary {
+                decoder.add_boundary_edge(*n1, &info.obs, Some(weight))?;
+            } else {
+                decoder.add_edge(*n1, *n2, &info.obs, Some(weight))?;
+            }
+        }
+
+        decoder.build_obs_masks();
+        Ok(decoder)
+    }
+
+    /// Create decoder from a pre-parsed `DemCheckMatrix` preserving all mechanisms.
+    ///
+    /// Like `from_dem_correlated` but skips DEM string parsing.
+    /// Optionally applies multiplicative weight perturbation via `weight_factors`.
+    ///
+    /// # Errors
+    ///
+    /// Returns error if construction fails.
+    pub fn from_check_matrix_correlated(
+        dcm: &pecos_decoder_core::dem::DemCheckMatrix,
+        weight_factors: Option<&[f64]>,
+    ) -> Result<Self> {
+        // Use Legacy solver which tolerates duplicate edges (no assertion).
+        let config = FusionBlossomConfig {
+            num_nodes: Some(dcm.num_detectors),
+            num_observables: dcm.num_observables,
+            solver_type: SolverType::Legacy,
+            ..Default::default()
+        };
+        let mut decoder = Self::new(config)?;
+
+        for m in 0..dcm.num_mechanisms {
+            let p = dcm.error_priors[m];
+            if p <= 0.0 {
+                continue;
+            }
+
+            let detectors: Vec<usize> = (0..dcm.num_detectors)
+                .filter(|&d| dcm.check_matrix[[d, m]] != 0)
+                .collect();
+
+            let obs: Vec<usize> = (0..dcm.num_observables)
+                .filter(|&o| dcm.observable_matrix[[o, m]] != 0)
+                .collect();
+
+            let mut weight = if p < 1.0 { ((1.0 - p) / p).ln() } else { 0.0 };
+
+            if let Some(factors) = weight_factors
+                && m < factors.len()
+            {
+                weight *= factors[m];
+                weight = weight.max(0.01);
+            }
+
+            match detectors.len() {
+                1 => {
+                    decoder.add_boundary_edge(detectors[0], &obs, Some(weight))?;
+                }
+                2 => {
+                    decoder.add_edge(detectors[0], detectors[1], &obs, Some(weight))?;
+                }
+                _ => {}
+            }
+        }
+
+        decoder.build_obs_masks();
+        Ok(decoder)
+    }
+
+    /// Create decoder from a DEM string preserving all mechanisms.
+    ///
+    /// Unlike `from_dem` which uses `DemMatchingGraph` (merges duplicate edges),
+    /// this uses `DemCheckMatrix` to keep every mechanism as a separate edge.
+    /// This preserves X-Z correlations from Y errors, similar to `PyMatching`'s
+    /// `enable_correlations` mode.
+    ///
+    /// Only 2-detector mechanisms are included (3+ detector hyperedges are
+    /// skipped since FB is a matching decoder).
+    ///
+    /// # Errors
+    ///
+    /// Returns error if the DEM is malformed.
+    pub fn from_dem_correlated(dem: &str) -> Result<Self> {
+        use pecos_decoder_core::dem::DemCheckMatrix;
+
+        let dcm = DemCheckMatrix::from_dem_str(dem)
+            .map_err(|e| FusionBlossomError::Configuration(e.to_string()))?;
+
+        let config = FusionBlossomConfig {
+            num_nodes: Some(dcm.num_detectors),
+            num_observables: dcm.num_observables,
+            ..Default::default()
+        };
+        let mut decoder = Self::new(config)?;
+
+        for m in 0..dcm.num_mechanisms {
+            let p = dcm.error_priors[m];
+            if p <= 0.0 {
+                continue;
+            }
+
+            let detectors: Vec<usize> = (0..dcm.num_detectors)
+                .filter(|&d| dcm.check_matrix[[d, m]] != 0)
+                .collect();
+
+            // Only handle 2-detector (graphlike) mechanisms.
+            // 1-detector = boundary, 3+ = hyperedge (skip).
+            let obs: Vec<usize> = (0..dcm.num_observables)
+                .filter(|&o| dcm.observable_matrix[[o, m]] != 0)
+                .collect();
+
+            let weight = if p < 1.0 { ((1.0 - p) / p).ln() } else { 0.0 };
+
+            match detectors.len() {
+                1 => {
+                    decoder.add_boundary_edge(detectors[0], &obs, Some(weight))?;
+                }
+                2 => {
+                    decoder.add_edge(detectors[0], detectors[1], &obs, Some(weight))?;
+                }
+                _ => {} // Skip hyperedges
+            }
+        }
+
+        decoder.build_obs_masks();
+        Ok(decoder)
+    }
+
     /// Create decoder from a standard QEC code
     ///
     /// # Errors
@@ -331,12 +639,16 @@ impl FusionBlossomDecoder {
                 ..config
             },
             edge_observables,
+            edge_obs_masks: Vec::new(),
             num_nodes,
             boundary_node: None,
             weighted_edges: initializer.weighted_edges.clone(),
             virtual_vertices: initializer.virtual_vertices.clone(),
             solver: None,
             initializer: Some(initializer),
+            partition_config: None,
+            _syndrome_buf: vec![0u8; num_nodes + 1],
+            defect_buf: Vec::new(),
         };
 
         // Identify boundary nodes from virtual vertices
@@ -508,9 +820,21 @@ impl FusionBlossomDecoder {
         Ok(decoder)
     }
 
-    /// Clear the solver state for reuse
+    /// Set partition config for parallel solving.
+    ///
+    /// The partition config defines how the matching graph is split across
+    /// threads for intra-shot parallelism.
+    pub fn set_partition_config(&mut self, config: PartitionConfig) {
+        self.partition_config = Some(config);
+        self.config.solver_type = SolverType::Parallel;
+        self.solver = None; // force solver recreation
+    }
+
+    /// Clear the solver state for reuse between decodes.
+    ///
+    /// The Serial solver is cleared inline after each solve. This method
+    /// exists for external callers and the Legacy solver fallback.
     pub fn clear(&mut self) {
-        // For Fusion Blossom, we need to recreate the solver to clear state
         self.solver = None;
     }
 
@@ -544,6 +868,18 @@ impl FusionBlossomDecoder {
             let solver = match self.config.solver_type {
                 SolverType::Legacy => Solver::Legacy(LegacySolverSerial::new(&initializer)),
                 SolverType::Serial => Solver::Serial(SolverSerial::new(&initializer)),
+                SolverType::Parallel => {
+                    let partition_info = self
+                        .partition_config
+                        .as_ref()
+                        .expect("partition_config must be set for Parallel solver")
+                        .info();
+                    Solver::Parallel(SolverDualParallel::new(
+                        &initializer,
+                        &partition_info,
+                        serde_json::json!({}),
+                    ))
+                }
             };
 
             self.solver = Some(solver);
@@ -561,7 +897,7 @@ impl FusionBlossomDecoder {
     pub fn decode_with_options(
         &mut self,
         syndrome_data: SyndromeData,
-        options: DecodingOptions,
+        _options: DecodingOptions,
     ) -> Result<DecodingResult> {
         // Convert defects to VertexIndex
         let defect_vertices: Vec<VertexIndex> = syndrome_data
@@ -602,34 +938,27 @@ impl FusionBlossomDecoder {
                 SyndromePattern::new_vertices(defect_vertices)
             };
 
-        // Get or create solver
+        // Get or create solver, solve, extract results, then clear for next use.
         let solver = self.get_or_create_solver();
 
-        // Solve and get perfect matching if requested
         let (matched_edges, perfect_matching_info) = match solver {
             Solver::Legacy(s) => {
                 let edges = s.solve_subgraph(&syndrome_pattern);
-                let pm_info = if options.include_perfect_matching {
-                    // Legacy solver doesn't have easy access to perfect matching
-                    None
-                } else {
-                    None
-                };
-                (edges, pm_info)
+                (edges, None)
             }
             Solver::Serial(s) => {
+                use fusion_blossom::mwpm_solver::PrimalDualSolver;
                 s.solve(&syndrome_pattern);
                 let edges = s.subgraph();
-
-                let pm_info = if options.include_perfect_matching {
-                    // For Serial solver, we can't easily get perfect matching details
-                    // without accessing internal structures
-                    None
-                } else {
-                    None
-                };
-
-                (edges, pm_info)
+                s.clear();
+                (edges, None)
+            }
+            Solver::Parallel(s) => {
+                use fusion_blossom::mwpm_solver::PrimalDualSolver;
+                s.solve(&syndrome_pattern);
+                let edges = s.subgraph();
+                s.clear();
+                (edges, None)
             }
         };
 
@@ -712,7 +1041,13 @@ impl FusionBlossomDecoder {
         self.initializer = None;
     }
 
-    /// Get number of nodes
+    /// Get the boundary node index, if one exists.
+    #[must_use]
+    pub fn boundary_node(&self) -> Option<VertexIndex> {
+        self.boundary_node
+    }
+
+    /// Get number of nodes.
     #[must_use]
     pub fn num_nodes(&self) -> usize {
         self.num_nodes
@@ -723,4 +1058,103 @@ impl FusionBlossomDecoder {
     pub fn num_edges(&self) -> usize {
         self.weighted_edges.len()
     }
+
+    /// Get node endpoints and weight of an edge by index.
+    #[must_use]
+    pub fn edge_endpoints(&self, edge_idx: usize) -> Option<(u32, u32, f64)> {
+        self.weighted_edges
+            .get(edge_idx)
+            .map(|&(n1, n2, w)| (n1 as u32, n2 as u32, (w as f64) / 1000.0))
+    }
+
+    /// Get per-edge observable bitmask.
+    #[must_use]
+    pub fn edge_obs_mask(&self, edge_idx: usize) -> u64 {
+        self.edge_obs_masks.get(edge_idx).copied().unwrap_or(0)
+    }
+
+    /// Compute observable mask from a set of matched edge indices.
+    /// Uses pre-computed bitmasks (builds them on first call).
+    pub fn obs_mask_from_edges(&mut self, matched_edges: &[usize]) -> u64 {
+        if self.edge_obs_masks.is_empty() && !self.edge_observables.is_empty() {
+            self.build_obs_masks();
+        }
+        let mut mask = 0u64;
+        for &edge_idx in matched_edges {
+            if let Some(&m) = self.edge_obs_masks.get(edge_idx) {
+                mask ^= m;
+            }
+        }
+        mask
+    }
+
+    /// Build pre-computed observable bitmasks for fast decode path.
+    /// Call once after all edges are added.
+    pub fn build_obs_masks(&mut self) {
+        let n = self.weighted_edges.len();
+        self.edge_obs_masks = vec![0u64; n];
+        for (&edge_idx, obs_indices) in &self.edge_observables {
+            if edge_idx < n {
+                let mut mask = 0u64;
+                for &obs_idx in obs_indices {
+                    mask |= 1 << obs_idx;
+                }
+                self.edge_obs_masks[edge_idx] = mask;
+            }
+        }
+    }
+
+    /// Fast decode: syndrome bytes -> observable bitmask.
+    /// Uses reusable buffers and pre-computed observable masks.
+    /// Handles padding for boundary node internally.
+    ///
+    /// # Errors
+    ///
+    /// Returns a `FusionBlossomError` if the solver cannot decode the supplied
+    /// syndrome.
+    pub fn decode_to_obs_mask(&mut self, syndrome: &[u8]) -> Result<u64> {
+        // Build obs masks on first call
+        if self.edge_obs_masks.is_empty() && !self.edge_observables.is_empty() {
+            self.build_obs_masks();
+        }
+
+        // Fill defect buffer from syndrome (pad to num_nodes for boundary)
+        self.defect_buf.clear();
+        for (i, &v) in syndrome.iter().enumerate() {
+            if v != 0 {
+                self.defect_buf.push(i as VertexIndex);
+            }
+        }
+        // No defects in padding region (boundary node always 0)
+
+        if self.defect_buf.is_empty() {
+            return Ok(0);
+        }
+
+        let syndrome_pattern = SyndromePattern::new_vertices(self.defect_buf.clone());
+        let solver = self.get_or_create_solver();
+
+        let matched_edges = match solver {
+            Solver::Legacy(s) => s.solve_subgraph(&syndrome_pattern),
+            Solver::Serial(s) => {
+                use fusion_blossom::mwpm_solver::PrimalDualSolver;
+                s.solve(&syndrome_pattern);
+                let edges = s.subgraph();
+                s.clear();
+                edges
+            }
+            Solver::Parallel(s) => {
+                use fusion_blossom::mwpm_solver::PrimalDualSolver;
+                s.solve(&syndrome_pattern);
+                let edges = s.subgraph();
+                s.clear();
+                edges
+            }
+        };
+
+        // Compute observable mask using pre-computed bitmasks
+        let edge_indices: Vec<usize> = matched_edges.clone();
+        let mask = self.obs_mask_from_edges(&edge_indices);
+        Ok(mask)
+    }
 }
diff --git a/crates/pecos-fusion-blossom/src/lib.rs b/crates/pecos-fusion-blossom/src/lib.rs
index b4f09f3da..bbc122a18 100644
--- a/crates/pecos-fusion-blossom/src/lib.rs
+++ b/crates/pecos-fusion-blossom/src/lib.rs
@@ -19,6 +19,9 @@ pub mod errors;
 pub use builder::FusionBlossomBuilder;
 pub use decoder::{
     DecodingOptions, DecodingResult, FusionBlossomConfig, FusionBlossomDecoder,
-    PerfectMatchingInfo, SolverType, StandardCode, SyndromeData,
+    ParsedCorrelatedDem, PerfectMatchingInfo, SolverType, StandardCode, SyndromeData,
 };
 pub use errors::FusionBlossomError;
+
+// Re-export partition types from fusion-blossom for parallel solver
+pub use fusion_blossom::util::{PartitionConfig, VertexRange};
diff --git a/crates/pecos-gpu-sims/examples/benchmark_influence_sampler.rs b/crates/pecos-gpu-sims/examples/benchmark_influence_sampler.rs
index ae000b21e..dbd23c3e8 100644
--- a/crates/pecos-gpu-sims/examples/benchmark_influence_sampler.rs
+++ b/crates/pecos-gpu-sims/examples/benchmark_influence_sampler.rs
@@ -42,15 +42,15 @@ fn create_test_influence_map(num_locations: usize, num_detectors: usize) -> GpuI
     GpuInfluenceMapData {
         num_locations: num_locations as u32,
         num_detectors: num_detectors as u32,
-        num_logicals: 2,
+        num_dem_outputs: 2,
         detector_offsets_x,
         detector_data_x,
         detector_offsets_y,
         detector_data_y,
         detector_offsets_z,
         detector_data_z,
-        // Logicals: location 0 X -> log 0, location 1 X -> log 1
-        logical_offsets_x: {
+        // DEM outputs: location 0 X -> L0, location 1 X -> L1
+        dem_output_offsets_x: {
             let mut v = vec![0u32; num_locations + 1];
             if num_locations > 0 {
                 v[1] = 1;
@@ -63,27 +63,27 @@ fn create_test_influence_map(num_locations: usize, num_detectors: usize) -> GpuI
             }
             v
         },
-        logical_data_x: vec![0, 1],
-        logical_offsets_y: vec![0; num_locations + 1],
-        logical_data_y: vec![],
-        logical_offsets_z: vec![0; num_locations + 1],
-        logical_data_z: vec![],
+        dem_output_data_x: vec![0, 1],
+        dem_output_offsets_y: vec![0; num_locations + 1],
+        dem_output_data_y: vec![],
+        dem_output_offsets_z: vec![0; num_locations + 1],
+        dem_output_data_z: vec![],
     }
 }
 
-/// Simple CPU sampler for comparison (mirrors the pecos-qec `NoisySampler` logic)
+/// Simple CPU sampler for comparison (mirrors the pecos-qec `DemSampler` logic)
 struct CpuSampler {
     num_locations: usize,
     num_detectors: usize,
-    num_logicals: usize,
+    num_dem_outputs: usize,
     detector_offsets_x: Vec<u32>,
     detector_data_x: Vec<u32>,
     detector_offsets_y: Vec<u32>,
     detector_data_y: Vec<u32>,
     detector_offsets_z: Vec<u32>,
     detector_data_z: Vec<u32>,
-    logical_offsets_x: Vec<u32>,
-    logical_data_x: Vec<u32>,
+    dem_output_offsets_x: Vec<u32>,
+    dem_output_data_x: Vec<u32>,
     rng_state: u64,
 }
 
@@ -92,15 +92,15 @@ impl CpuSampler {
         Self {
             num_locations: map.num_locations as usize,
             num_detectors: map.num_detectors as usize,
-            num_logicals: map.num_logicals as usize,
+            num_dem_outputs: map.num_dem_outputs as usize,
             detector_offsets_x: map.detector_offsets_x.clone(),
             detector_data_x: map.detector_data_x.clone(),
             detector_offsets_y: map.detector_offsets_y.clone(),
             detector_data_y: map.detector_data_y.clone(),
             detector_offsets_z: map.detector_offsets_z.clone(),
             detector_data_z: map.detector_data_z.clone(),
-            logical_offsets_x: map.logical_offsets_x.clone(),
-            logical_data_x: map.logical_data_x.clone(),
+            dem_output_offsets_x: map.dem_output_offsets_x.clone(),
+            dem_output_data_x: map.dem_output_data_x.clone(),
             rng_state: seed,
         }
     }
@@ -120,11 +120,11 @@ impl CpuSampler {
         #[allow(clippy::cast_sign_loss, clippy::cast_possible_truncation)]
         // probability in [0,1] maps to [0, u32::MAX]
         let threshold = (p_error * f64::from(u32::MAX)) as u32;
-        let mut logical_errors = 0;
+        let mut logical_error_count = 0;
 
         for _ in 0..num_shots {
             let mut detector_flips = vec![0u8; self.num_detectors.max(1)];
-            let mut logical_flips = vec![0u8; self.num_logicals.max(1)];
+            let mut dem_output_flips = vec![0u8; self.num_dem_outputs.max(1)];
 
             for loc in 0..self.num_locations {
                 let rand = self.next_u32();
@@ -135,7 +135,7 @@ impl CpuSampler {
                 // Sample Pauli type
                 let pauli = self.next_u32() % 3;
 
-                // Get affected detectors and logicals
+                // Get affected detectors and DEM outputs
                 let (det_start, det_end, det_data) = match pauli {
                     0 => (
                         self.detector_offsets_x[loc] as usize,
@@ -161,25 +161,25 @@ impl CpuSampler {
                     }
                 }
 
-                // Only X affects logicals in our test map
+                // Only X affects DEM outputs in our test map
                 if pauli == 0 {
-                    let log_start = self.logical_offsets_x[loc] as usize;
-                    let log_end = self.logical_offsets_x[loc + 1] as usize;
-                    for i in log_start..log_end {
-                        let log_idx = self.logical_data_x[i] as usize;
-                        if log_idx < logical_flips.len() {
-                            logical_flips[log_idx] ^= 1;
+                    let dem_output_start = self.dem_output_offsets_x[loc] as usize;
+                    let dem_output_end = self.dem_output_offsets_x[loc + 1] as usize;
+                    for i in dem_output_start..dem_output_end {
+                        let dem_output_idx = self.dem_output_data_x[i] as usize;
+                        if dem_output_idx < dem_output_flips.len() {
+                            dem_output_flips[dem_output_idx] ^= 1;
                         }
                     }
                 }
             }
 
-            if logical_flips.contains(&1) {
-                logical_errors += 1;
+            if dem_output_flips.contains(&1) {
+                logical_error_count += 1;
             }
         }
 
-        logical_errors
+        logical_error_count
     }
 }
 
@@ -195,8 +195,8 @@ fn benchmark_gpu(
     let result = sampler.sample_uniform(num_shots, p_error);
     let elapsed = start.elapsed();
 
-    let logical_errors = result.count_logical_errors();
-    (elapsed, logical_errors)
+    let logical_error_count = result.count_logical_errors();
+    (elapsed, logical_error_count)
 }
 
 fn benchmark_cpu(
@@ -208,10 +208,10 @@ fn benchmark_cpu(
     let mut sampler = CpuSampler::new(map, seed);
 
     let start = Instant::now();
-    let logical_errors = sampler.sample(num_shots, p_error);
+    let logical_error_count = sampler.sample(num_shots, p_error);
     let elapsed = start.elapsed();
 
-    (elapsed, logical_errors)
+    (elapsed, logical_error_count)
 }
 
 fn main() {
diff --git a/crates/pecos-gpu-sims/examples/cpu_vs_gpu_comparison.rs b/crates/pecos-gpu-sims/examples/cpu_vs_gpu_comparison.rs
index 1bdd2b61c..8bf404caa 100644
--- a/crates/pecos-gpu-sims/examples/cpu_vs_gpu_comparison.rs
+++ b/crates/pecos-gpu-sims/examples/cpu_vs_gpu_comparison.rs
@@ -4,7 +4,7 @@
 
 use pecos_gpu_sims::{GpuInfluenceMapData, GpuInfluenceSampler};
 use pecos_qec::fault_tolerance::InfluenceBuilder;
-use pecos_qec::fault_tolerance::noisy_sampler::{NoisySampler, UniformNoiseModel};
+use pecos_qec::fault_tolerance::dem_builder::DemSampler;
 use pecos_quantum::DagCircuit;
 use std::time::Instant;
 
@@ -91,8 +91,8 @@ fn main() {
         let num_data = distance * distance;
 
         // Build influence map
-        let logical_qubits: Vec<usize> = (0..num_data).collect();
-        let builder = InfluenceBuilder::new(&circuit).with_logical_z(logical_qubits);
+        let tracked_pauli_qubits: Vec<usize> = (0..num_data).collect();
+        let builder = InfluenceBuilder::new(&circuit).with_z(&tracked_pauli_qubits);
         let influence_map = builder.build();
 
         let num_locations = influence_map.locations.len();
@@ -101,32 +101,46 @@ fn main() {
         let (
             num_loc,
             num_det,
-            num_log,
+            num_dem_outputs,
             det_off_x,
             det_data_x,
             det_off_y,
             det_data_y,
             det_off_z,
             det_data_z,
-            log_off_x,
-            log_data_x,
-            log_off_y,
-            log_data_y,
-            log_off_z,
-            log_data_z,
+            dem_output_offsets_x,
+            dem_output_data_x,
+            dem_output_offsets_y,
+            dem_output_data_y,
+            dem_output_offsets_z,
+            dem_output_data_z,
         ) = influence_map.export_csr();
 
         let gpu_map = GpuInfluenceMapData::from_csr(
-            num_loc, num_det, num_log, det_off_x, det_data_x, det_off_y, det_data_y, det_off_z,
-            det_data_z, log_off_x, log_data_x, log_off_y, log_data_y, log_off_z, log_data_z,
+            num_loc,
+            num_det,
+            num_dem_outputs,
+            det_off_x,
+            det_data_x,
+            det_off_y,
+            det_data_y,
+            det_off_z,
+            det_data_z,
+            dem_output_offsets_x,
+            dem_output_data_x,
+            dem_output_offsets_y,
+            dem_output_data_y,
+            dem_output_offsets_z,
+            dem_output_data_z,
         );
 
         // CPU benchmark
-        let noise = UniformNoiseModel::depolarizing(p_error);
-        let mut cpu_sampler = NoisySampler::new(&influence_map, noise, seed);
+        let num_loc = influence_map.locations.len();
+        let probs = vec![p_error; num_loc];
+        let cpu_sampler = DemSampler::from_influence_map(&influence_map, &probs);
 
         let cpu_start = Instant::now();
-        let _ = cpu_sampler.sample(num_shots as usize);
+        let _ = cpu_sampler.sample_statistics(num_shots as usize, seed);
         let cpu_time = cpu_start.elapsed();
 
         // GPU benchmark (with warmup)
@@ -165,38 +179,51 @@ fn main() {
         let circuit = build_surface_code_grid(distance, num_rounds);
         let num_data = distance * distance;
 
-        let logical_qubits: Vec<usize> = (0..num_data).collect();
-        let builder = InfluenceBuilder::new(&circuit).with_logical_z(logical_qubits);
+        let tracked_pauli_qubits: Vec<usize> = (0..num_data).collect();
+        let builder = InfluenceBuilder::new(&circuit).with_z(&tracked_pauli_qubits);
         let influence_map = builder.build();
 
         let (
             num_loc,
             num_det,
-            num_log,
+            num_dem_outputs,
             det_off_x,
             det_data_x,
             det_off_y,
             det_data_y,
             det_off_z,
             det_data_z,
-            log_off_x,
-            log_data_x,
-            log_off_y,
-            log_data_y,
-            log_off_z,
-            log_data_z,
+            dem_output_offsets_x,
+            dem_output_data_x,
+            dem_output_offsets_y,
+            dem_output_data_y,
+            dem_output_offsets_z,
+            dem_output_data_z,
         ) = influence_map.export_csr();
 
         let gpu_map = GpuInfluenceMapData::from_csr(
-            num_loc, num_det, num_log, det_off_x, det_data_x, det_off_y, det_data_y, det_off_z,
-            det_data_z, log_off_x, log_data_x, log_off_y, log_data_y, log_off_z, log_data_z,
+            num_loc,
+            num_det,
+            num_dem_outputs,
+            det_off_x,
+            det_data_x,
+            det_off_y,
+            det_data_y,
+            det_off_z,
+            det_data_z,
+            dem_output_offsets_x,
+            dem_output_data_x,
+            dem_output_offsets_y,
+            dem_output_data_y,
+            dem_output_offsets_z,
+            dem_output_data_z,
         );
 
         // CPU
-        let noise = UniformNoiseModel::depolarizing(p_error);
-        let mut cpu_sampler = NoisySampler::new(&influence_map, noise, seed);
+        let probs2 = vec![p_error; influence_map.locations.len()];
+        let cpu_sampler = DemSampler::from_influence_map(&influence_map, &probs2);
         let cpu_start = Instant::now();
-        let _ = cpu_sampler.sample(num_shots as usize);
+        let _ = cpu_sampler.sample_statistics(num_shots as usize, seed);
         let cpu_time = cpu_start.elapsed();
 
         // GPU
diff --git a/crates/pecos-gpu-sims/examples/full_pipeline_example.rs b/crates/pecos-gpu-sims/examples/full_pipeline_example.rs
index 519d00e99..f882e1094 100644
--- a/crates/pecos-gpu-sims/examples/full_pipeline_example.rs
+++ b/crates/pecos-gpu-sims/examples/full_pipeline_example.rs
@@ -83,8 +83,8 @@ fn main() {
     let circuit = build_repetition_code_circuit(2);
     println!("   Circuit built: {} gates", circuit.gate_count());
 
-    // Build influence map with logical Z (sensitive to X errors)
-    let builder = InfluenceBuilder::new(&circuit).with_logical_z(vec![0, 1, 2]);
+    // Build influence map with a tracked Z Pauli (sensitive to X errors)
+    let builder = InfluenceBuilder::new(&circuit).with_z(&[0, 1, 2]);
 
     let influence_map = builder.build();
     println!("   Locations: {}", influence_map.locations.len());
@@ -95,41 +95,41 @@ fn main() {
     let (
         num_locations,
         num_detectors,
-        num_logicals,
+        num_dem_outputs,
         det_off_x,
         det_data_x,
         det_off_y,
         det_data_y,
         det_off_z,
         det_data_z,
-        log_off_x,
-        log_data_x,
-        log_off_y,
-        log_data_y,
-        log_off_z,
-        log_data_z,
+        dem_output_offsets_x,
+        dem_output_data_x,
+        dem_output_offsets_y,
+        dem_output_data_y,
+        dem_output_offsets_z,
+        dem_output_data_z,
     ) = influence_map.export_csr();
 
     println!(
-        "   Exported CSR: {num_locations} locations, {num_detectors} detectors, {num_logicals} logicals"
+        "   Exported CSR: {num_locations} locations, {num_detectors} detectors, {num_dem_outputs} DEM outputs"
     );
 
     let gpu_map = GpuInfluenceMapData::from_csr(
         num_locations,
         num_detectors,
-        num_logicals,
+        num_dem_outputs,
         det_off_x,
         det_data_x,
         det_off_y,
         det_data_y,
         det_off_z,
         det_data_z,
-        log_off_x,
-        log_data_x,
-        log_off_y,
-        log_data_y,
-        log_off_z,
-        log_data_z,
+        dem_output_offsets_x,
+        dem_output_data_x,
+        dem_output_offsets_y,
+        dem_output_data_y,
+        dem_output_offsets_z,
+        dem_output_data_z,
     );
 
     // Sample with GPU
@@ -139,15 +139,15 @@ fn main() {
     let p_error = 0.001; // 0.1% error rate
 
     let result = sampler.sample_uniform(num_shots, p_error);
-    let logical_errors = result.count_logical_errors();
+    let logical_error_count = result.count_logical_errors();
     #[allow(clippy::cast_precision_loss)] // rate calculation
-    let error_rate = logical_errors as f64 / f64::from(num_shots);
+    let logical_error_rate = logical_error_count as f64 / f64::from(num_shots);
 
     println!(
         "   GPU Sampling: {} shots, p={}, logical error rate: {:.4}%",
         num_shots,
         p_error,
-        error_rate * 100.0
+        logical_error_rate * 100.0
     );
 
     // =========================================================================
@@ -158,8 +158,8 @@ fn main() {
     let circuit = build_surface_code_plaquette(3);
     println!("   Circuit built: {} gates", circuit.gate_count());
 
-    // Build influence map with logical X (sensitive to Z errors on this plaquette)
-    let builder = InfluenceBuilder::new(&circuit).with_logical_x(vec![0, 1, 2, 3]);
+    // Build influence map with a tracked X Pauli (sensitive to Z errors on this plaquette)
+    let builder = InfluenceBuilder::new(&circuit).with_x(&[0, 1, 2, 3]);
 
     let influence_map = builder.build();
     println!("   Locations: {}", influence_map.locations.len());
@@ -169,51 +169,51 @@ fn main() {
     let (
         num_locations,
         num_detectors,
-        num_logicals,
+        num_dem_outputs,
         det_off_x,
         det_data_x,
         det_off_y,
         det_data_y,
         det_off_z,
         det_data_z,
-        log_off_x,
-        log_data_x,
-        log_off_y,
-        log_data_y,
-        log_off_z,
-        log_data_z,
+        dem_output_offsets_x,
+        dem_output_data_x,
+        dem_output_offsets_y,
+        dem_output_data_y,
+        dem_output_offsets_z,
+        dem_output_data_z,
     ) = influence_map.export_csr();
 
     let gpu_map = GpuInfluenceMapData::from_csr(
         num_locations,
         num_detectors,
-        num_logicals,
+        num_dem_outputs,
         det_off_x,
         det_data_x,
         det_off_y,
         det_data_y,
         det_off_z,
         det_data_z,
-        log_off_x,
-        log_data_x,
-        log_off_y,
-        log_data_y,
-        log_off_z,
-        log_data_z,
+        dem_output_offsets_x,
+        dem_output_data_x,
+        dem_output_offsets_y,
+        dem_output_data_y,
+        dem_output_offsets_z,
+        dem_output_data_z,
     );
 
     let mut sampler = GpuInfluenceSampler::new(&gpu_map, 42).expect("Failed to create GPU sampler");
 
     let result = sampler.sample_uniform(num_shots, p_error);
-    let logical_errors = result.count_logical_errors();
+    let logical_error_count = result.count_logical_errors();
     #[allow(clippy::cast_precision_loss)] // rate calculation
-    let error_rate = logical_errors as f64 / f64::from(num_shots);
+    let logical_error_rate = logical_error_count as f64 / f64::from(num_shots);
 
     println!(
         "   GPU Sampling: {} shots, p={}, logical error rate: {:.4}%",
         num_shots,
         p_error,
-        error_rate * 100.0
+        logical_error_rate * 100.0
     );
 
     // =========================================================================
@@ -223,43 +223,43 @@ fn main() {
 
     for num_rounds in [1, 2, 4, 8] {
         let circuit = build_repetition_code_circuit(num_rounds);
-        let builder = InfluenceBuilder::new(&circuit).with_logical_z(vec![0, 1, 2]);
+        let builder = InfluenceBuilder::new(&circuit).with_z(&[0, 1, 2]);
         let influence_map = builder.build();
 
         let (
             num_locations,
             num_detectors,
-            num_logicals,
+            num_dem_outputs,
             det_off_x,
             det_data_x,
             det_off_y,
             det_data_y,
             det_off_z,
             det_data_z,
-            log_off_x,
-            log_data_x,
-            log_off_y,
-            log_data_y,
-            log_off_z,
-            log_data_z,
+            dem_output_offsets_x,
+            dem_output_data_x,
+            dem_output_offsets_y,
+            dem_output_data_y,
+            dem_output_offsets_z,
+            dem_output_data_z,
         ) = influence_map.export_csr();
 
         let gpu_map = GpuInfluenceMapData::from_csr(
             num_locations,
             num_detectors,
-            num_logicals,
+            num_dem_outputs,
             det_off_x,
             det_data_x,
             det_off_y,
             det_data_y,
             det_off_z,
             det_data_z,
-            log_off_x,
-            log_data_x,
-            log_off_y,
-            log_data_y,
-            log_off_z,
-            log_data_z,
+            dem_output_offsets_x,
+            dem_output_data_x,
+            dem_output_offsets_y,
+            dem_output_data_y,
+            dem_output_offsets_z,
+            dem_output_data_z,
         );
 
         let mut sampler =
@@ -269,14 +269,14 @@ fn main() {
         let result = sampler.sample_uniform(100_000, 0.001);
         let elapsed = start.elapsed();
 
-        let logical_errors = result.count_logical_errors();
+        let logical_error_count = result.count_logical_errors();
 
         println!(
-            "   {} rounds: {} locations, {} detectors, {} logical errors, {:.2}ms",
+            "   {} rounds: {} locations, {} detectors, {} logical error shots, {:.2}ms",
             num_rounds,
             num_locations,
             num_detectors,
-            logical_errors,
+            logical_error_count,
             elapsed.as_secs_f64() * 1000.0
         );
     }
diff --git a/crates/pecos-gpu-sims/examples/pipeline_benchmark.rs b/crates/pecos-gpu-sims/examples/pipeline_benchmark.rs
index 387ba372f..3b28b931a 100644
--- a/crates/pecos-gpu-sims/examples/pipeline_benchmark.rs
+++ b/crates/pecos-gpu-sims/examples/pipeline_benchmark.rs
@@ -9,7 +9,7 @@
 
 use pecos_gpu_sims::{GpuInfluenceMapData, GpuInfluenceSampler};
 use pecos_qec::fault_tolerance::InfluenceBuilder;
-use pecos_qec::fault_tolerance::noisy_sampler::{NoisySampler, UniformNoiseModel};
+use pecos_qec::fault_tolerance::dem_builder::DemSampler;
 use pecos_quantum::DagCircuit;
 use std::time::{Duration, Instant};
 
@@ -127,8 +127,8 @@ struct BenchmarkResult {
     build_time: Duration,
     cpu_time: Duration,
     gpu_time: Duration,
-    _cpu_logical_errors: usize,
-    _gpu_logical_errors: usize,
+    _cpu_logical_error_count: usize,
+    _gpu_logical_error_count: usize,
 }
 
 impl BenchmarkResult {
@@ -150,14 +150,14 @@ impl BenchmarkResult {
 fn benchmark_circuit(
     name: &str,
     circuit: &DagCircuit,
-    logical_qubits: Vec<usize>,
+    tracked_pauli_qubits: &[usize],
     num_shots: u32,
     p_error: f64,
     seed: u64,
 ) -> BenchmarkResult {
     // Build influence map (common to both pipelines)
     let build_start = Instant::now();
-    let builder = InfluenceBuilder::new(circuit).with_logical_z(logical_qubits);
+    let builder = InfluenceBuilder::new(circuit).with_z(tracked_pauli_qubits);
     let influence_map = builder.build();
     let build_time = build_start.elapsed();
 
@@ -165,37 +165,50 @@ fn benchmark_circuit(
     let num_detectors = influence_map.detectors.len();
 
     // CPU sampling
-    let noise = UniformNoiseModel::depolarizing(p_error);
-    let mut cpu_sampler = NoisySampler::new(&influence_map, noise, seed);
+    let probs = vec![p_error; num_locations];
+    let cpu_sampler = DemSampler::from_influence_map(&influence_map, &probs);
 
     let cpu_start = Instant::now();
-    let cpu_results = cpu_sampler.sample(num_shots as usize);
+    let cpu_stats = cpu_sampler.sample_statistics(num_shots as usize, seed);
     let cpu_time = cpu_start.elapsed();
 
-    let cpu_logical_errors = cpu_results.iter().filter(|r| r.has_logical_error()).count();
+    let cpu_logical_error_count = cpu_stats.logical_error_count;
 
     // GPU sampling
     let (
         num_loc,
         num_det,
-        num_log,
+        num_dem_outputs,
         det_off_x,
         det_data_x,
         det_off_y,
         det_data_y,
         det_off_z,
         det_data_z,
-        log_off_x,
-        log_data_x,
-        log_off_y,
-        log_data_y,
-        log_off_z,
-        log_data_z,
+        dem_output_offsets_x,
+        dem_output_data_x,
+        dem_output_offsets_y,
+        dem_output_data_y,
+        dem_output_offsets_z,
+        dem_output_data_z,
     ) = influence_map.export_csr();
 
     let gpu_map = GpuInfluenceMapData::from_csr(
-        num_loc, num_det, num_log, det_off_x, det_data_x, det_off_y, det_data_y, det_off_z,
-        det_data_z, log_off_x, log_data_x, log_off_y, log_data_y, log_off_z, log_data_z,
+        num_loc,
+        num_det,
+        num_dem_outputs,
+        det_off_x,
+        det_data_x,
+        det_off_y,
+        det_data_y,
+        det_off_z,
+        det_data_z,
+        dem_output_offsets_x,
+        dem_output_data_x,
+        dem_output_offsets_y,
+        dem_output_data_y,
+        dem_output_offsets_z,
+        dem_output_data_z,
     );
 
     let mut gpu_sampler =
@@ -208,7 +221,7 @@ fn benchmark_circuit(
     let gpu_result = gpu_sampler.sample_uniform(num_shots, p_error);
     let gpu_time = gpu_start.elapsed();
 
-    let gpu_logical_errors = gpu_result.count_logical_errors();
+    let gpu_logical_error_count = gpu_result.count_logical_errors();
 
     BenchmarkResult {
         name: name.to_string(),
@@ -218,8 +231,8 @@ fn benchmark_circuit(
         build_time,
         cpu_time,
         gpu_time,
-        _cpu_logical_errors: cpu_logical_errors,
-        _gpu_logical_errors: gpu_logical_errors,
+        _cpu_logical_error_count: cpu_logical_error_count,
+        _gpu_logical_error_count: gpu_logical_error_count,
     }
 }
 
@@ -283,10 +296,17 @@ fn main() {
 
     for (num_data, num_rounds) in [(3, 2), (5, 3), (7, 4), (9, 5), (11, 6), (15, 8)] {
         let circuit = build_repetition_code(num_data, num_rounds);
-        let logical_qubits: Vec<usize> = (0..num_data).collect();
+        let tracked_pauli_qubits: Vec<usize> = (0..num_data).collect();
         let name = format!("rep_d{num_data}r{num_rounds}");
 
-        let result = benchmark_circuit(&name, &circuit, logical_qubits, num_shots, p_error, seed);
+        let result = benchmark_circuit(
+            &name,
+            &circuit,
+            &tracked_pauli_qubits,
+            num_shots,
+            p_error,
+            seed,
+        );
         results.push(result);
     }
 
@@ -298,7 +318,7 @@ fn main() {
     println!("\nTest 2: Fixed Circuit (rep_d7r4) - Varying Shots\n");
 
     let circuit = build_repetition_code(7, 4);
-    let logical_qubits: Vec<usize> = (0..7).collect();
+    let tracked_pauli_qubits: Vec<usize> = (0..7).collect();
 
     let mut shot_results = Vec::new();
 
@@ -307,7 +327,7 @@ fn main() {
         let result = benchmark_circuit(
             &name,
             &circuit,
-            logical_qubits.clone(),
+            &tracked_pauli_qubits,
             num_shots,
             p_error,
             seed,
@@ -328,10 +348,17 @@ fn main() {
     for (distance, rounds) in [(3, 2), (4, 2), (5, 3), (6, 3), (7, 4)] {
         let circuit = build_surface_code_grid(distance, rounds);
         let num_data = distance * distance;
-        let logical_qubits: Vec<usize> = (0..num_data).collect();
+        let tracked_pauli_qubits: Vec<usize> = (0..num_data).collect();
         let name = format!("surf_d{distance}r{rounds}");
 
-        let result = benchmark_circuit(&name, &circuit, logical_qubits, num_shots, p_error, seed);
+        let result = benchmark_circuit(
+            &name,
+            &circuit,
+            &tracked_pauli_qubits,
+            num_shots,
+            p_error,
+            seed,
+        );
         surface_results.push(result);
     }
 
diff --git a/crates/pecos-gpu-sims/examples/profile_samplers.rs b/crates/pecos-gpu-sims/examples/profile_samplers.rs
index 54d979fc0..cefa9cd37 100644
--- a/crates/pecos-gpu-sims/examples/profile_samplers.rs
+++ b/crates/pecos-gpu-sims/examples/profile_samplers.rs
@@ -5,9 +5,7 @@
 use bytemuck::{Pod, Zeroable};
 use pecos_gpu_sims::GpuInfluenceMapData;
 use pecos_qec::fault_tolerance::InfluenceBuilder;
-use pecos_qec::fault_tolerance::noisy_sampler::{
-    FastNoisySampler, NoisySampler, UniformNoiseModel,
-};
+use pecos_qec::fault_tolerance::dem_builder::DemSampler;
 use pecos_quantum::DagCircuit;
 use pecos_random::PecosRng;
 use std::time::Instant;
@@ -74,19 +72,18 @@ fn build_surface_code_grid(distance: usize, num_rounds: usize) -> DagCircuit {
     dag
 }
 
-/// Profile the CPU sampler with detailed timing
+/// Profile the CPU `DemSampler` with detailed timing
 fn profile_cpu_sampler(
     influence_map: &pecos_qec::fault_tolerance::DagFaultInfluenceMap,
     p_error: f64,
     seed: u64,
     num_shots: usize,
 ) -> CpuProfile {
-    let noise = UniformNoiseModel::depolarizing(p_error);
-    let mut sampler = NoisySampler::new(influence_map, noise, seed);
+    let probs = vec![p_error; influence_map.locations.len()];
+    let sampler = DemSampler::from_influence_map(influence_map, &probs);
 
-    // Time the actual sampling
     let start = Instant::now();
-    let _results = sampler.sample(num_shots);
+    let _stats = sampler.sample_statistics(num_shots, seed);
     let total_time = start.elapsed();
 
     CpuProfile {
@@ -103,27 +100,6 @@ struct CpuProfile {
     locations: usize,
 }
 
-/// Profile the optimized `FastNoisySampler`
-fn profile_fast_cpu_sampler(
-    influence_map: &pecos_qec::fault_tolerance::DagFaultInfluenceMap,
-    p_error: f64,
-    seed: u64,
-    num_shots: usize,
-) -> CpuProfile {
-    let mut sampler = FastNoisySampler::new(influence_map, p_error, seed);
-
-    // Time the actual sampling
-    let start = Instant::now();
-    let _results = sampler.sample(num_shots);
-    let total_time = start.elapsed();
-
-    CpuProfile {
-        total_ms: total_time.as_secs_f64() * 1000.0,
-        shots: num_shots,
-        locations: influence_map.locations.len(),
-    }
-}
-
 /// Parameters for the sampling shader
 #[repr(C)]
 #[derive(Copy, Clone, Debug, Pod, Zeroable)]
@@ -131,10 +107,10 @@ struct SamplerParams {
     num_locations: u32,
     num_shots: u32,
     num_detectors: u32,
-    num_logicals: u32,
+    num_dem_outputs: u32,
     p_error_threshold: u32,
     detector_words: u32,
-    logical_words: u32,
+    dem_output_words: u32,
     _padding: u32,
 }
 
@@ -188,12 +164,12 @@ fn profile_gpu_sampler(
     let detector_data_y_buffer = create_buffer(&gpu_map.detector_data_y, "DetDataY");
     let detector_offsets_z_buffer = create_buffer(&gpu_map.detector_offsets_z, "DetOffZ");
     let detector_data_z_buffer = create_buffer(&gpu_map.detector_data_z, "DetDataZ");
-    let logical_offsets_x_buffer = create_buffer(&gpu_map.logical_offsets_x, "LogOffX");
-    let logical_data_x_buffer = create_buffer(&gpu_map.logical_data_x, "LogDataX");
-    let logical_offsets_y_buffer = create_buffer(&gpu_map.logical_offsets_y, "LogOffY");
-    let logical_data_y_buffer = create_buffer(&gpu_map.logical_data_y, "LogDataY");
-    let logical_offsets_z_buffer = create_buffer(&gpu_map.logical_offsets_z, "LogOffZ");
-    let logical_data_z_buffer = create_buffer(&gpu_map.logical_data_z, "LogDataZ");
+    let dem_output_offsets_x_buffer = create_buffer(&gpu_map.dem_output_offsets_x, "DemOutOffX");
+    let dem_output_data_x_buffer = create_buffer(&gpu_map.dem_output_data_x, "DemOutDataX");
+    let dem_output_offsets_y_buffer = create_buffer(&gpu_map.dem_output_offsets_y, "DemOutOffY");
+    let dem_output_data_y_buffer = create_buffer(&gpu_map.dem_output_data_y, "DemOutDataY");
+    let dem_output_offsets_z_buffer = create_buffer(&gpu_map.dem_output_offsets_z, "DemOutOffZ");
+    let dem_output_data_z_buffer = create_buffer(&gpu_map.dem_output_data_z, "DemOutDataZ");
     let upload_map_time = upload_map_start.elapsed();
 
     // Phase 3: Create shader and pipeline (done once)
@@ -245,7 +221,7 @@ fn profile_gpu_sampler(
     // Phase 4: Create params buffer
     let params_start = Instant::now();
     let detector_words = gpu_map.num_detectors.div_ceil(32).max(1);
-    let logical_words = gpu_map.num_logicals.div_ceil(32).max(1);
+    let dem_output_words = gpu_map.num_dem_outputs.div_ceil(32).max(1);
     #[allow(clippy::cast_sign_loss, clippy::cast_possible_truncation)]
     // probability in [0,1] maps to [0, u32::MAX]
     let p_threshold = (p_error * f64::from(u32::MAX)) as u32;
@@ -253,10 +229,10 @@ fn profile_gpu_sampler(
         num_locations: gpu_map.num_locations,
         num_shots,
         num_detectors: gpu_map.num_detectors,
-        num_logicals: gpu_map.num_logicals,
+        num_dem_outputs: gpu_map.num_dem_outputs,
         p_error_threshold: p_threshold,
         detector_words,
-        logical_words,
+        dem_output_words,
         _padding: 0,
     };
     let params_buffer = device.create_buffer_init(&wgpu::util::BufferInitDescriptor {
@@ -282,7 +258,7 @@ fn profile_gpu_sampler(
     // Phase 6: Create output buffers
     let output_start = Instant::now();
     let detector_output_size = (num_shots as usize * detector_words as usize * 4) as u64;
-    let logical_output_size = (num_shots as usize * logical_words as usize * 4) as u64;
+    let dem_output_size = (num_shots as usize * dem_output_words as usize * 4) as u64;
 
     let detector_output_buffer = device.create_buffer(&wgpu::BufferDescriptor {
         label: Some("Detector Output"),
@@ -291,9 +267,9 @@ fn profile_gpu_sampler(
         mapped_at_creation: false,
     });
 
-    let logical_output_buffer = device.create_buffer(&wgpu::BufferDescriptor {
-        label: Some("Logical Output"),
-        size: logical_output_size.max(4),
+    let dem_output_buffer = device.create_buffer(&wgpu::BufferDescriptor {
+        label: Some("DEM Output"),
+        size: dem_output_size.max(4),
         usage: wgpu::BufferUsages::STORAGE | wgpu::BufferUsages::COPY_SRC,
         mapped_at_creation: false,
     });
@@ -335,27 +311,27 @@ fn profile_gpu_sampler(
             },
             wgpu::BindGroupEntry {
                 binding: 7,
-                resource: logical_offsets_x_buffer.as_entire_binding(),
+                resource: dem_output_offsets_x_buffer.as_entire_binding(),
             },
             wgpu::BindGroupEntry {
                 binding: 8,
-                resource: logical_data_x_buffer.as_entire_binding(),
+                resource: dem_output_data_x_buffer.as_entire_binding(),
             },
             wgpu::BindGroupEntry {
                 binding: 9,
-                resource: logical_offsets_y_buffer.as_entire_binding(),
+                resource: dem_output_offsets_y_buffer.as_entire_binding(),
             },
             wgpu::BindGroupEntry {
                 binding: 10,
-                resource: logical_data_y_buffer.as_entire_binding(),
+                resource: dem_output_data_y_buffer.as_entire_binding(),
             },
             wgpu::BindGroupEntry {
                 binding: 11,
-                resource: logical_offsets_z_buffer.as_entire_binding(),
+                resource: dem_output_offsets_z_buffer.as_entire_binding(),
             },
             wgpu::BindGroupEntry {
                 binding: 12,
-                resource: logical_data_z_buffer.as_entire_binding(),
+                resource: dem_output_data_z_buffer.as_entire_binding(),
             },
             wgpu::BindGroupEntry {
                 binding: 13,
@@ -367,7 +343,7 @@ fn profile_gpu_sampler(
             },
             wgpu::BindGroupEntry {
                 binding: 15,
-                resource: logical_output_buffer.as_entire_binding(),
+                resource: dem_output_buffer.as_entire_binding(),
             },
         ],
     });
@@ -404,9 +380,9 @@ fn profile_gpu_sampler(
         usage: wgpu::BufferUsages::COPY_DST | wgpu::BufferUsages::MAP_READ,
         mapped_at_creation: false,
     });
-    let logical_staging = device.create_buffer(&wgpu::BufferDescriptor {
-        label: Some("Logical Staging"),
-        size: logical_output_size.max(4),
+    let dem_output_staging = device.create_buffer(&wgpu::BufferDescriptor {
+        label: Some("DEM Output Staging"),
+        size: dem_output_size.max(4),
         usage: wgpu::BufferUsages::COPY_DST | wgpu::BufferUsages::MAP_READ,
         mapped_at_creation: false,
     });
@@ -420,11 +396,11 @@ fn profile_gpu_sampler(
         detector_output_size.max(4),
     );
     encoder.copy_buffer_to_buffer(
-        &logical_output_buffer,
+        &dem_output_buffer,
         0,
-        &logical_staging,
+        &dem_output_staging,
         0,
-        logical_output_size.max(4),
+        dem_output_size.max(4),
     );
     queue.submit(std::iter::once(encoder.finish()));
 
@@ -435,9 +411,9 @@ fn profile_gpu_sampler(
         tx1.send(result).unwrap();
     });
 
-    let log_slice = logical_staging.slice(..);
+    let dem_output_slice = dem_output_staging.slice(..);
     let (tx2, rx2) = std::sync::mpsc::channel();
-    log_slice.map_async(wgpu::MapMode::Read, move |result| {
+    dem_output_slice.map_async(wgpu::MapMode::Read, move |result| {
         tx2.send(result).unwrap();
     });
 
@@ -450,9 +426,9 @@ fn profile_gpu_sampler(
     let _det_results: Vec<u32> = bytemuck::cast_slice(&det_data).to_vec();
     drop(det_data);
 
-    let log_data = log_slice.get_mapped_range();
-    let _log_results: Vec<u32> = bytemuck::cast_slice(&log_data).to_vec();
-    drop(log_data);
+    let dem_output_data = dem_output_slice.get_mapped_range();
+    let _dem_output_results: Vec<u32> = bytemuck::cast_slice(&dem_output_data).to_vec();
+    drop(dem_output_data);
 
     let read_time = read_start.elapsed();
 
@@ -471,7 +447,7 @@ fn profile_gpu_sampler(
         #[allow(clippy::cast_possible_truncation)] // 64-bit target
         detector_output_bytes: detector_output_size as usize,
         #[allow(clippy::cast_possible_truncation)] // 64-bit target
-        logical_output_bytes: logical_output_size as usize,
+        dem_output_bytes: dem_output_size as usize,
     }
 }
 
@@ -489,7 +465,7 @@ struct GpuProfile {
     #[allow(dead_code)]
     shots: usize,
     detector_output_bytes: usize,
-    logical_output_bytes: usize,
+    dem_output_bytes: usize,
 }
 
 impl GpuProfile {
@@ -536,8 +512,8 @@ fn main() {
         let num_data = distance * distance;
 
         // Build influence map
-        let logical_qubits: Vec<usize> = (0..num_data).collect();
-        let builder = InfluenceBuilder::new(&circuit).with_logical_z(logical_qubits);
+        let tracked_pauli_qubits: Vec<usize> = (0..num_data).collect();
+        let builder = InfluenceBuilder::new(&circuit).with_z(&tracked_pauli_qubits);
         let influence_map = builder.build();
         let num_locations = influence_map.locations.len();
 
@@ -545,24 +521,37 @@ fn main() {
         let (
             num_loc,
             num_det,
-            num_log,
+            num_dem_outputs,
             det_off_x,
             det_data_x,
             det_off_y,
             det_data_y,
             det_off_z,
             det_data_z,
-            log_off_x,
-            log_data_x,
-            log_off_y,
-            log_data_y,
-            log_off_z,
-            log_data_z,
+            dem_output_offsets_x,
+            dem_output_data_x,
+            dem_output_offsets_y,
+            dem_output_data_y,
+            dem_output_offsets_z,
+            dem_output_data_z,
         ) = influence_map.export_csr();
 
         let gpu_map = GpuInfluenceMapData::from_csr(
-            num_loc, num_det, num_log, det_off_x, det_data_x, det_off_y, det_data_y, det_off_z,
-            det_data_z, log_off_x, log_data_x, log_off_y, log_data_y, log_off_z, log_data_z,
+            num_loc,
+            num_det,
+            num_dem_outputs,
+            det_off_x,
+            det_data_x,
+            det_off_y,
+            det_data_y,
+            det_off_z,
+            det_data_z,
+            dem_output_offsets_x,
+            dem_output_data_x,
+            dem_output_offsets_y,
+            dem_output_data_y,
+            dem_output_offsets_z,
+            dem_output_data_z,
         );
 
         println!(
@@ -570,9 +559,9 @@ fn main() {
         );
         println!("{:-<70}", "");
 
-        // CPU profile (original)
+        // CPU profile (DemSampler)
         let cpu = profile_cpu_sampler(&influence_map, p_error, seed, num_shots as usize);
-        println!("\nCPU Pipeline (Original NoisySampler):");
+        println!("\nCPU Pipeline (DemSampler):");
         println!("  Total time:            {:>10.2} ms", cpu.total_ms);
         println!(
             "  Per-shot:              {:>10.2} us",
@@ -583,21 +572,6 @@ fn main() {
             cpu.shots as f64 / cpu.total_ms / 1000.0
         );
 
-        // CPU profile (fast/optimized)
-        let cpu_fast = profile_fast_cpu_sampler(&influence_map, p_error, seed, num_shots as usize);
-        println!("\nCPU Pipeline (FastNoisySampler - PecosRng + Sparse):");
-        println!("  Total time:            {:>10.2} ms", cpu_fast.total_ms);
-        println!(
-            "  Per-shot:              {:>10.2} us",
-            cpu_fast.total_ms * 1000.0 / cpu_fast.shots as f64
-        );
-        println!(
-            "  Throughput:            {:>10.3} M shots/sec",
-            cpu_fast.shots as f64 / cpu_fast.total_ms / 1000.0
-        );
-        let cpu_speedup = cpu.total_ms / cpu_fast.total_ms;
-        println!("  Speedup vs original:   {cpu_speedup:>10.2}x");
-
         // GPU profile
         let gpu = profile_gpu_sampler(&gpu_map, p_error, seed, num_shots);
         println!("\nGPU Pipeline:");
@@ -617,22 +591,17 @@ fn main() {
         println!("    Subtotal (per-call): {:>10.2} ms", gpu.per_sample_ms());
         println!("  Total:                 {:>10.2} ms", gpu.total_ms());
         println!(
-            "  Output size:           {:>10.2} KB (det) + {:.2} KB (log)",
+            "  Output size:           {:>10.2} KB (det) + {:.2} KB (DEM out)",
             gpu.detector_output_bytes as f64 / 1024.0,
-            gpu.logical_output_bytes as f64 / 1024.0
+            gpu.dem_output_bytes as f64 / 1024.0
         );
 
         println!("\nComparison:");
-        println!("  CPU (original):        {:>10.2} ms", cpu.total_ms);
-        println!("  CPU (fast):            {:>10.2} ms", cpu_fast.total_ms);
+        println!("  CPU (DemSampler):      {:>10.2} ms", cpu.total_ms);
         println!("  GPU total (with init): {:>10.2} ms", gpu.total_ms());
         println!("  GPU per-call only:     {:>10.2} ms", gpu.per_sample_ms());
-        let speedup_fast_vs_orig = cpu.total_ms / cpu_fast.total_ms;
-        let speedup_gpu_vs_orig = cpu.total_ms / gpu.per_sample_ms();
-        let speedup_gpu_vs_fast = cpu_fast.total_ms / gpu.per_sample_ms();
-        println!("  Fast CPU vs Original:  {speedup_fast_vs_orig:>10.1}x");
-        println!("  GPU vs Original CPU:   {speedup_gpu_vs_orig:>10.1}x");
-        println!("  GPU vs Fast CPU:       {speedup_gpu_vs_fast:>10.1}x");
+        let speedup_gpu_vs_cpu = cpu.total_ms / gpu.per_sample_ms();
+        println!("  GPU vs CPU:            {speedup_gpu_vs_cpu:>10.1}x");
 
         println!("\n");
     }
diff --git a/crates/pecos-gpu-sims/src/gpu_influence_sampler.rs b/crates/pecos-gpu-sims/src/gpu_influence_sampler.rs
index b550c22ad..b3d1024ba 100644
--- a/crates/pecos-gpu-sims/src/gpu_influence_sampler.rs
+++ b/crates/pecos-gpu-sims/src/gpu_influence_sampler.rs
@@ -11,14 +11,14 @@ use wgpu::util::DeviceExt;
 /// Influence map data for GPU sampling.
 ///
 /// Contains CSR (Compressed Sparse Row) arrays mapping fault locations
-/// to their detector and logical influences for X, Y, and Z Pauli faults.
+/// to their detector and DEM-output influences for X, Y, and Z Pauli faults.
 pub struct GpuInfluenceMapData {
     /// Number of fault locations.
     pub num_locations: u32,
     /// Number of detectors.
     pub num_detectors: u32,
-    /// Number of logicals.
-    pub num_logicals: u32,
+    /// Number of DEM `L<n>` outputs.
+    pub num_dem_outputs: u32,
 
     // CSR arrays for detector influences
     /// Offsets for X detector influences: `offsets_x`[loc] to `offsets_x`[loc+1]
@@ -34,19 +34,19 @@ pub struct GpuInfluenceMapData {
     /// Detector indices for Z faults.
     pub detector_data_z: Vec<u32>,
 
-    // CSR arrays for logical influences
-    /// Offsets for X logical influences.
-    pub logical_offsets_x: Vec<u32>,
-    /// Logical indices for X faults.
-    pub logical_data_x: Vec<u32>,
-    /// Offsets for Y logical influences.
-    pub logical_offsets_y: Vec<u32>,
-    /// Logical indices for Y faults.
-    pub logical_data_y: Vec<u32>,
-    /// Offsets for Z logical influences.
-    pub logical_offsets_z: Vec<u32>,
-    /// Logical indices for Z faults.
-    pub logical_data_z: Vec<u32>,
+    // CSR arrays for DEM-output influences
+    /// Offsets for X DEM-output influences.
+    pub dem_output_offsets_x: Vec<u32>,
+    /// DEM-output indices for X faults.
+    pub dem_output_data_x: Vec<u32>,
+    /// Offsets for Y DEM-output influences.
+    pub dem_output_offsets_y: Vec<u32>,
+    /// DEM-output indices for Y faults.
+    pub dem_output_data_y: Vec<u32>,
+    /// Offsets for Z DEM-output influences.
+    pub dem_output_offsets_z: Vec<u32>,
+    /// DEM-output indices for Z faults.
+    pub dem_output_data_z: Vec<u32>,
 }
 
 impl GpuInfluenceMapData {
@@ -56,19 +56,19 @@ impl GpuInfluenceMapData {
         Self {
             num_locations: 0,
             num_detectors: 0,
-            num_logicals: 0,
+            num_dem_outputs: 0,
             detector_offsets_x: vec![0],
             detector_data_x: vec![],
             detector_offsets_y: vec![0],
             detector_data_y: vec![],
             detector_offsets_z: vec![0],
             detector_data_z: vec![],
-            logical_offsets_x: vec![0],
-            logical_data_x: vec![],
-            logical_offsets_y: vec![0],
-            logical_data_y: vec![],
-            logical_offsets_z: vec![0],
-            logical_data_z: vec![],
+            dem_output_offsets_x: vec![0],
+            dem_output_data_x: vec![],
+            dem_output_offsets_y: vec![0],
+            dem_output_data_y: vec![],
+            dem_output_offsets_z: vec![0],
+            dem_output_data_z: vec![],
         }
     }
 
@@ -78,36 +78,36 @@ impl GpuInfluenceMapData {
     pub fn from_csr(
         num_locations: u32,
         num_detectors: u32,
-        num_logicals: u32,
+        num_dem_outputs: u32,
         detector_offsets_x: Vec<u32>,
         detector_data_x: Vec<u32>,
         detector_offsets_y: Vec<u32>,
         detector_data_y: Vec<u32>,
         detector_offsets_z: Vec<u32>,
         detector_data_z: Vec<u32>,
-        logical_offsets_x: Vec<u32>,
-        logical_data_x: Vec<u32>,
-        logical_offsets_y: Vec<u32>,
-        logical_data_y: Vec<u32>,
-        logical_offsets_z: Vec<u32>,
-        logical_data_z: Vec<u32>,
+        dem_output_offsets_x: Vec<u32>,
+        dem_output_data_x: Vec<u32>,
+        dem_output_offsets_y: Vec<u32>,
+        dem_output_data_y: Vec<u32>,
+        dem_output_offsets_z: Vec<u32>,
+        dem_output_data_z: Vec<u32>,
     ) -> Self {
         Self {
             num_locations,
             num_detectors,
-            num_logicals,
+            num_dem_outputs,
             detector_offsets_x,
             detector_data_x,
             detector_offsets_y,
             detector_data_y,
             detector_offsets_z,
             detector_data_z,
-            logical_offsets_x,
-            logical_data_x,
-            logical_offsets_y,
-            logical_data_y,
-            logical_offsets_z,
-            logical_data_z,
+            dem_output_offsets_x,
+            dem_output_data_x,
+            dem_output_offsets_y,
+            dem_output_data_y,
+            dem_output_offsets_z,
+            dem_output_data_z,
         }
     }
 }
@@ -119,10 +119,10 @@ struct SamplerParams {
     num_locations: u32,
     num_shots: u32,
     num_detectors: u32,
-    num_logicals: u32,
+    num_dem_outputs: u32,
     p_error_threshold: u32,
     detector_words: u32,
-    logical_words: u32,
+    dem_output_words: u32,
     _padding: u32,
 }
 
@@ -133,7 +133,7 @@ struct SamplerParams {
 pub struct GpuInfluenceSampler {
     num_locations: u32,
     num_detectors: u32,
-    num_logicals: u32,
+    num_dem_outputs: u32,
 
     device: wgpu::Device,
     queue: wgpu::Queue,
@@ -147,12 +147,12 @@ pub struct GpuInfluenceSampler {
     detector_data_y_buffer: wgpu::Buffer,
     detector_offsets_z_buffer: wgpu::Buffer,
     detector_data_z_buffer: wgpu::Buffer,
-    logical_offsets_x_buffer: wgpu::Buffer,
-    logical_data_x_buffer: wgpu::Buffer,
-    logical_offsets_y_buffer: wgpu::Buffer,
-    logical_data_y_buffer: wgpu::Buffer,
-    logical_offsets_z_buffer: wgpu::Buffer,
-    logical_data_z_buffer: wgpu::Buffer,
+    dem_output_offsets_x_buffer: wgpu::Buffer,
+    dem_output_data_x_buffer: wgpu::Buffer,
+    dem_output_offsets_y_buffer: wgpu::Buffer,
+    dem_output_data_y_buffer: wgpu::Buffer,
+    dem_output_offsets_z_buffer: wgpu::Buffer,
+    dem_output_data_z_buffer: wgpu::Buffer,
 
     bind_group_layout: wgpu::BindGroupLayout,
     pipeline: wgpu::ComputePipeline,
@@ -199,22 +199,22 @@ impl GpuInfluenceSampler {
         let detector_data_y_buffer = create_buffer(&map.detector_data_y, "DetDataY");
         let detector_offsets_z_buffer = create_buffer(&map.detector_offsets_z, "DetOffZ");
         let detector_data_z_buffer = create_buffer(&map.detector_data_z, "DetDataZ");
-        let logical_offsets_x_buffer = create_buffer(&map.logical_offsets_x, "LogOffX");
-        let logical_data_x_buffer = create_buffer(&map.logical_data_x, "LogDataX");
-        let logical_offsets_y_buffer = create_buffer(&map.logical_offsets_y, "LogOffY");
-        let logical_data_y_buffer = create_buffer(&map.logical_data_y, "LogDataY");
-        let logical_offsets_z_buffer = create_buffer(&map.logical_offsets_z, "LogOffZ");
-        let logical_data_z_buffer = create_buffer(&map.logical_data_z, "LogDataZ");
+        let dem_output_offsets_x_buffer = create_buffer(&map.dem_output_offsets_x, "DemOutOffX");
+        let dem_output_data_x_buffer = create_buffer(&map.dem_output_data_x, "DemOutDataX");
+        let dem_output_offsets_y_buffer = create_buffer(&map.dem_output_offsets_y, "DemOutOffY");
+        let dem_output_data_y_buffer = create_buffer(&map.dem_output_data_y, "DemOutDataY");
+        let dem_output_offsets_z_buffer = create_buffer(&map.dem_output_offsets_z, "DemOutOffZ");
+        let dem_output_data_z_buffer = create_buffer(&map.dem_output_data_z, "DemOutDataZ");
 
         // Create params buffer
         let params = SamplerParams {
             num_locations: map.num_locations,
             num_shots: 0,
             num_detectors: map.num_detectors,
-            num_logicals: map.num_logicals,
+            num_dem_outputs: map.num_dem_outputs,
             p_error_threshold: 0,
             detector_words: 0,
-            logical_words: 0,
+            dem_output_words: 0,
             _padding: 0,
         };
         let params_buffer = device.create_buffer_init(&wgpu::util::BufferInitDescriptor {
@@ -419,7 +419,7 @@ impl GpuInfluenceSampler {
         Ok(Self {
             num_locations: map.num_locations,
             num_detectors: map.num_detectors,
-            num_logicals: map.num_logicals,
+            num_dem_outputs: map.num_dem_outputs,
             device,
             queue,
             params_buffer,
@@ -429,12 +429,12 @@ impl GpuInfluenceSampler {
             detector_data_y_buffer,
             detector_offsets_z_buffer,
             detector_data_z_buffer,
-            logical_offsets_x_buffer,
-            logical_data_x_buffer,
-            logical_offsets_y_buffer,
-            logical_data_y_buffer,
-            logical_offsets_z_buffer,
-            logical_data_z_buffer,
+            dem_output_offsets_x_buffer,
+            dem_output_data_x_buffer,
+            dem_output_offsets_y_buffer,
+            dem_output_data_y_buffer,
+            dem_output_offsets_z_buffer,
+            dem_output_data_z_buffer,
             bind_group_layout,
             pipeline,
             rng: PecosRng::seed_from_u64(seed),
@@ -444,7 +444,7 @@ impl GpuInfluenceSampler {
     /// Sample with uniform depolarizing noise.
     pub fn sample_uniform(&mut self, num_shots: u32, p_error: f64) -> GpuSamplingResult {
         let detector_words = self.num_detectors.div_ceil(32).max(1);
-        let logical_words = self.num_logicals.div_ceil(32).max(1);
+        let dem_output_words = self.num_dem_outputs.div_ceil(32).max(1);
 
         // Update params
         #[allow(clippy::cast_sign_loss, clippy::cast_possible_truncation)]
@@ -454,10 +454,10 @@ impl GpuInfluenceSampler {
             num_locations: self.num_locations,
             num_shots,
             num_detectors: self.num_detectors,
-            num_logicals: self.num_logicals,
+            num_dem_outputs: self.num_dem_outputs,
             p_error_threshold: p_threshold,
             detector_words,
-            logical_words,
+            dem_output_words,
             _padding: 0,
         };
         self.queue
@@ -476,7 +476,7 @@ impl GpuInfluenceSampler {
 
         // Create output buffers - layout: [shot * words + word_idx]
         let detector_output_size = (num_shots as usize * detector_words as usize * 4) as u64;
-        let logical_output_size = (num_shots as usize * logical_words as usize * 4) as u64;
+        let dem_output_size = (num_shots as usize * dem_output_words as usize * 4) as u64;
 
         let detector_output_buffer = self.device.create_buffer(&wgpu::BufferDescriptor {
             label: Some("Detector Output"),
@@ -485,9 +485,9 @@ impl GpuInfluenceSampler {
             mapped_at_creation: false,
         });
 
-        let logical_output_buffer = self.device.create_buffer(&wgpu::BufferDescriptor {
-            label: Some("Logical Output"),
-            size: logical_output_size.max(4),
+        let dem_output_buffer = self.device.create_buffer(&wgpu::BufferDescriptor {
+            label: Some("DEM Output"),
+            size: dem_output_size.max(4),
             usage: wgpu::BufferUsages::STORAGE | wgpu::BufferUsages::COPY_SRC,
             mapped_at_creation: false,
         });
@@ -527,27 +527,27 @@ impl GpuInfluenceSampler {
                 },
                 wgpu::BindGroupEntry {
                     binding: 7,
-                    resource: self.logical_offsets_x_buffer.as_entire_binding(),
+                    resource: self.dem_output_offsets_x_buffer.as_entire_binding(),
                 },
                 wgpu::BindGroupEntry {
                     binding: 8,
-                    resource: self.logical_data_x_buffer.as_entire_binding(),
+                    resource: self.dem_output_data_x_buffer.as_entire_binding(),
                 },
                 wgpu::BindGroupEntry {
                     binding: 9,
-                    resource: self.logical_offsets_y_buffer.as_entire_binding(),
+                    resource: self.dem_output_offsets_y_buffer.as_entire_binding(),
                 },
                 wgpu::BindGroupEntry {
                     binding: 10,
-                    resource: self.logical_data_y_buffer.as_entire_binding(),
+                    resource: self.dem_output_data_y_buffer.as_entire_binding(),
                 },
                 wgpu::BindGroupEntry {
                     binding: 11,
-                    resource: self.logical_offsets_z_buffer.as_entire_binding(),
+                    resource: self.dem_output_offsets_z_buffer.as_entire_binding(),
                 },
                 wgpu::BindGroupEntry {
                     binding: 12,
-                    resource: self.logical_data_z_buffer.as_entire_binding(),
+                    resource: self.dem_output_data_z_buffer.as_entire_binding(),
                 },
                 wgpu::BindGroupEntry {
                     binding: 13,
@@ -559,7 +559,7 @@ impl GpuInfluenceSampler {
                 },
                 wgpu::BindGroupEntry {
                     binding: 15,
-                    resource: logical_output_buffer.as_entire_binding(),
+                    resource: dem_output_buffer.as_entire_binding(),
                 },
             ],
         });
@@ -591,20 +591,20 @@ impl GpuInfluenceSampler {
             num_shots as usize,
             detector_words as usize,
         );
-        let logical_flips = self.read_output(
-            &logical_output_buffer,
+        let dem_output_flips = self.read_output(
+            &dem_output_buffer,
             num_shots as usize,
-            logical_words as usize,
+            dem_output_words as usize,
         );
 
         GpuSamplingResult {
             num_shots: num_shots as usize,
             detector_flips,
-            logical_flips,
+            dem_output_flips,
             num_detectors: self.num_detectors as usize,
-            num_logicals: self.num_logicals as usize,
+            num_dem_outputs: self.num_dem_outputs as usize,
             detector_words: detector_words as usize,
-            logical_words: logical_words as usize,
+            dem_output_words: dem_output_words as usize,
         }
     }
 
@@ -652,42 +652,61 @@ pub struct GpuSamplingResult {
     pub num_shots: usize,
     /// Flat array: [shot * `detector_words` + word]
     pub detector_flips: Vec<u32>,
-    /// Flat array: [shot * `logical_words` + word]
-    pub logical_flips: Vec<u32>,
+    /// Flat array: [shot * `dem_output_words` + word]
+    pub dem_output_flips: Vec<u32>,
     pub num_detectors: usize,
-    pub num_logicals: usize,
+    pub num_dem_outputs: usize,
     pub detector_words: usize,
-    pub logical_words: usize,
+    pub dem_output_words: usize,
 }
 
 impl GpuSamplingResult {
+    fn logical_word_mask(&self, word_idx: usize) -> u32 {
+        if self.num_dem_outputs == 0 || word_idx >= self.dem_output_words {
+            return 0;
+        }
+        let remaining = self.num_dem_outputs.saturating_sub(word_idx * 32);
+        if remaining >= 32 {
+            u32::MAX
+        } else if remaining == 0 {
+            0
+        } else {
+            (1u32 << remaining) - 1
+        }
+    }
+
     /// Count shots with any logical error.
     #[must_use]
     pub fn count_logical_errors(&self) -> usize {
-        if self.num_logicals == 0 {
+        if self.num_dem_outputs == 0 {
             return 0;
         }
 
         let mut count = 0;
         for shot in 0..self.num_shots {
-            let base = shot * self.logical_words;
-            let has_error = (0..self.logical_words)
-                .any(|w| self.logical_flips.get(base + w).copied().unwrap_or(0) != 0);
-            if has_error {
+            let base = shot * self.dem_output_words;
+            let has_flip = (0..self.dem_output_words).any(|w| {
+                let word = self.dem_output_flips.get(base + w).copied().unwrap_or(0);
+                (word & self.logical_word_mask(w)) != 0
+            });
+            if has_flip {
                 count += 1;
             }
         }
         count
     }
 
-    /// Check if a specific shot has a logical error.
+    /// Check if a specific shot has any logical error.
     #[must_use]
     pub fn has_logical_error(&self, shot: usize) -> bool {
-        if shot >= self.num_shots || self.num_logicals == 0 {
+        if shot >= self.num_shots || self.num_dem_outputs == 0 {
             return false;
         }
-        let base = shot * self.logical_words;
-        (0..self.logical_words).any(|w| self.logical_flips.get(base + w).copied().unwrap_or(0) != 0)
+        let base = shot * self.dem_output_words;
+        (0..self.dem_output_words).any(|w| {
+            let word = self.dem_output_flips.get(base + w).copied().unwrap_or(0);
+            (word & self.logical_word_mask(w)) != 0
+        })
     }
 
     /// Get detector flip bits for a specific shot.
diff --git a/crates/pecos-gpu-sims/src/gpu_noisy_sampler.rs b/crates/pecos-gpu-sims/src/gpu_noisy_sampler.rs
index 7e7703f1d..fd6d752d8 100644
--- a/crates/pecos-gpu-sims/src/gpu_noisy_sampler.rs
+++ b/crates/pecos-gpu-sims/src/gpu_noisy_sampler.rs
@@ -326,9 +326,9 @@ impl NoiseSampler for BiasedDepolarizingNoiseSampler {
     }
 }
 
-/// Operations that can be added to a circuit.
+/// Ideal gates that can be added to a noisy sampler circuit.
 #[derive(Debug, Clone)]
-pub enum CircuitOp {
+pub enum Gate {
     // Single-qubit gates
     H(usize),
     S(usize),
@@ -344,29 +344,39 @@ pub enum CircuitOp {
 
     // Measurements
     Mz(usize),
+}
 
-    // Noise injection points
-    Noise1Q(usize),
-    Noise2Q(usize, usize),
+/// Explicit noise injection point in a noisy sampler circuit.
+#[derive(Debug, Clone)]
+pub enum NoiseInjection {
+    OneQ(usize),
+    TwoQ(usize, usize),
+}
+
+/// A circuit step for the noisy sampler.
+#[derive(Debug, Clone)]
+pub enum NoisyCircuitStep {
+    Gate(Gate),
+    Noise(NoiseInjection),
 }
 
 /// Builder for constructing circuits with noise injection points.
 #[derive(Default)]
 pub struct CircuitBuilder {
-    ops: Vec<CircuitOp>,
+    steps: Vec<NoisyCircuitStep>,
 }
 
 impl CircuitBuilder {
     /// Create a new empty circuit builder.
     #[must_use]
     pub fn new() -> Self {
-        Self { ops: Vec::new() }
+        Self { steps: Vec::new() }
     }
 
     /// Hadamard gate.
     pub fn h(&mut self, qubits: &[usize]) -> &mut Self {
         for &q in qubits {
-            self.ops.push(CircuitOp::H(q));
+            self.steps.push(NoisyCircuitStep::Gate(Gate::H(q)));
         }
         self
     }
@@ -374,7 +384,7 @@ impl CircuitBuilder {
     /// S gate (sqrt Z).
     pub fn s(&mut self, qubits: &[usize]) -> &mut Self {
         for &q in qubits {
-            self.ops.push(CircuitOp::S(q));
+            self.steps.push(NoisyCircuitStep::Gate(Gate::S(q)));
         }
         self
     }
@@ -382,7 +392,7 @@ impl CircuitBuilder {
     /// S-dagger gate.
     pub fn sdg(&mut self, qubits: &[usize]) -> &mut Self {
         for &q in qubits {
-            self.ops.push(CircuitOp::Sdg(q));
+            self.steps.push(NoisyCircuitStep::Gate(Gate::Sdg(q)));
         }
         self
     }
@@ -390,7 +400,7 @@ impl CircuitBuilder {
     /// Pauli X gate.
     pub fn x(&mut self, qubits: &[usize]) -> &mut Self {
         for &q in qubits {
-            self.ops.push(CircuitOp::X(q));
+            self.steps.push(NoisyCircuitStep::Gate(Gate::X(q)));
         }
         self
     }
@@ -398,7 +408,7 @@ impl CircuitBuilder {
     /// Pauli Y gate.
     pub fn y(&mut self, qubits: &[usize]) -> &mut Self {
         for &q in qubits {
-            self.ops.push(CircuitOp::Y(q));
+            self.steps.push(NoisyCircuitStep::Gate(Gate::Y(q)));
         }
         self
     }
@@ -406,7 +416,7 @@ impl CircuitBuilder {
     /// Pauli Z gate.
     pub fn z(&mut self, qubits: &[usize]) -> &mut Self {
         for &q in qubits {
-            self.ops.push(CircuitOp::Z(q));
+            self.steps.push(NoisyCircuitStep::Gate(Gate::Z(q)));
         }
         self
     }
@@ -414,7 +424,8 @@ impl CircuitBuilder {
     /// CNOT gate.
     pub fn cx(&mut self, pairs: &[(usize, usize)]) -> &mut Self {
         for &(control, target) in pairs {
-            self.ops.push(CircuitOp::Cx(control, target));
+            self.steps
+                .push(NoisyCircuitStep::Gate(Gate::Cx(control, target)));
         }
         self
     }
@@ -422,7 +433,7 @@ impl CircuitBuilder {
     /// CZ gate.
     pub fn cz(&mut self, pairs: &[(usize, usize)]) -> &mut Self {
         for &(a, b) in pairs {
-            self.ops.push(CircuitOp::Cz(a, b));
+            self.steps.push(NoisyCircuitStep::Gate(Gate::Cz(a, b)));
         }
         self
     }
@@ -430,7 +441,7 @@ impl CircuitBuilder {
     /// SWAP gate.
     pub fn swap(&mut self, pairs: &[(usize, usize)]) -> &mut Self {
         for &(a, b) in pairs {
-            self.ops.push(CircuitOp::Swap(a, b));
+            self.steps.push(NoisyCircuitStep::Gate(Gate::Swap(a, b)));
         }
         self
     }
@@ -438,7 +449,7 @@ impl CircuitBuilder {
     /// Measure qubit(s) in Z basis.
     pub fn mz(&mut self, qubits: &[usize]) -> &mut Self {
         for &q in qubits {
-            self.ops.push(CircuitOp::Mz(q));
+            self.steps.push(NoisyCircuitStep::Gate(Gate::Mz(q)));
         }
         self
     }
@@ -446,7 +457,8 @@ impl CircuitBuilder {
     /// Mark a noise injection point for single-qubit noise.
     pub fn noise_1q(&mut self, qubits: &[usize]) -> &mut Self {
         for &q in qubits {
-            self.ops.push(CircuitOp::Noise1Q(q));
+            self.steps
+                .push(NoisyCircuitStep::Noise(NoiseInjection::OneQ(q)));
         }
         self
     }
@@ -454,20 +466,21 @@ impl CircuitBuilder {
     /// Mark a noise injection point for two-qubit noise.
     pub fn noise_2q(&mut self, pairs: &[(usize, usize)]) -> &mut Self {
         for &(a, b) in pairs {
-            self.ops.push(CircuitOp::Noise2Q(a, b));
+            self.steps
+                .push(NoisyCircuitStep::Noise(NoiseInjection::TwoQ(a, b)));
         }
         self
     }
 
-    /// Get the operations in this circuit.
+    /// Get the steps in this noisy sampler circuit.
     #[must_use]
-    pub fn ops(&self) -> &[CircuitOp] {
-        &self.ops
+    pub fn steps(&self) -> &[NoisyCircuitStep] {
+        &self.steps
     }
 
     /// Clear the circuit for reuse.
     pub fn clear(&mut self) {
-        self.ops.clear();
+        self.steps.clear();
     }
 }
 
@@ -522,7 +535,7 @@ impl<N: NoiseSampler> GpuNoisySampler<N> {
         // Build the circuit once
         let mut builder = CircuitBuilder::new();
         circuit_fn(&mut builder);
-        let ops = builder.ops().to_vec();
+        let steps = builder.steps().to_vec();
 
         let mut results = Vec::with_capacity(shots);
 
@@ -542,36 +555,36 @@ impl<N: NoiseSampler> GpuNoisySampler<N> {
             let mut outcomes = Vec::new();
 
             // Execute the circuit with noise injection
-            for op in &ops {
-                match op {
-                    CircuitOp::H(q) => {
+            for step in &steps {
+                match step {
+                    NoisyCircuitStep::Gate(Gate::H(q)) => {
                         sim.h(&[QubitId(*q)]);
                     }
-                    CircuitOp::S(q) => {
+                    NoisyCircuitStep::Gate(Gate::S(q)) => {
                         sim.sz(&[QubitId(*q)]);
                     }
-                    CircuitOp::Sdg(q) => {
+                    NoisyCircuitStep::Gate(Gate::Sdg(q)) => {
                         sim.szdg(&[QubitId(*q)]);
                     }
-                    CircuitOp::X(q) => {
+                    NoisyCircuitStep::Gate(Gate::X(q)) => {
                         sim.x(&[QubitId(*q)]);
                     }
-                    CircuitOp::Y(q) => {
+                    NoisyCircuitStep::Gate(Gate::Y(q)) => {
                         sim.y(&[QubitId(*q)]);
                     }
-                    CircuitOp::Z(q) => {
+                    NoisyCircuitStep::Gate(Gate::Z(q)) => {
                         sim.z(&[QubitId(*q)]);
                     }
-                    CircuitOp::Cx(ctrl, tgt) => {
+                    NoisyCircuitStep::Gate(Gate::Cx(ctrl, tgt)) => {
                         sim.cx(&[(QubitId(*ctrl), QubitId(*tgt))]);
                     }
-                    CircuitOp::Cz(a, b) => {
+                    NoisyCircuitStep::Gate(Gate::Cz(a, b)) => {
                         sim.cz(&[(QubitId(*a), QubitId(*b))]);
                     }
-                    CircuitOp::Swap(a, b) => {
+                    NoisyCircuitStep::Gate(Gate::Swap(a, b)) => {
                         sim.swap(&[(QubitId(*a), QubitId(*b))]);
                     }
-                    CircuitOp::Mz(q) => {
+                    NoisyCircuitStep::Gate(Gate::Mz(q)) => {
                         let results = sim.mz(&[QubitId(*q)]);
                         let mut outcome = results[0].outcome;
 
@@ -585,7 +598,7 @@ impl<N: NoiseSampler> GpuNoisySampler<N> {
 
                         outcomes.push(outcome);
                     }
-                    CircuitOp::Noise1Q(q) => {
+                    NoisyCircuitStep::Noise(NoiseInjection::OneQ(q)) => {
                         // Sample and apply single-qubit noise
                         match self.noise_sampler.sample_1q(*q) {
                             Pauli::I => {}
@@ -600,7 +613,7 @@ impl<N: NoiseSampler> GpuNoisySampler<N> {
                             }
                         }
                     }
-                    CircuitOp::Noise2Q(a, b) => {
+                    NoisyCircuitStep::Noise(NoiseInjection::TwoQ(a, b)) => {
                         // Sample and apply two-qubit noise
                         let (pa, pb) = self.noise_sampler.sample_2q(*a, *b);
                         match pa {
@@ -688,13 +701,31 @@ mod tests {
             .noise_2q(&[(0, 1)])
             .mz(&[0, 1]);
 
-        assert_eq!(builder.ops().len(), 6);
-        assert!(matches!(builder.ops()[0], CircuitOp::H(0)));
-        assert!(matches!(builder.ops()[1], CircuitOp::Noise1Q(0)));
-        assert!(matches!(builder.ops()[2], CircuitOp::Cx(0, 1)));
-        assert!(matches!(builder.ops()[3], CircuitOp::Noise2Q(0, 1)));
-        assert!(matches!(builder.ops()[4], CircuitOp::Mz(0)));
-        assert!(matches!(builder.ops()[5], CircuitOp::Mz(1)));
+        assert_eq!(builder.steps().len(), 6);
+        assert!(matches!(
+            builder.steps()[0],
+            NoisyCircuitStep::Gate(Gate::H(0))
+        ));
+        assert!(matches!(
+            builder.steps()[1],
+            NoisyCircuitStep::Noise(NoiseInjection::OneQ(0))
+        ));
+        assert!(matches!(
+            builder.steps()[2],
+            NoisyCircuitStep::Gate(Gate::Cx(0, 1))
+        ));
+        assert!(matches!(
+            builder.steps()[3],
+            NoisyCircuitStep::Noise(NoiseInjection::TwoQ(0, 1))
+        ));
+        assert!(matches!(
+            builder.steps()[4],
+            NoisyCircuitStep::Gate(Gate::Mz(0))
+        ));
+        assert!(matches!(
+            builder.steps()[5],
+            NoisyCircuitStep::Gate(Gate::Mz(1))
+        ));
     }
 
     #[test]
@@ -715,23 +746,59 @@ mod tests {
             .noise_2q(&[(0, 1)])
             .mz(&[0]);
 
-        assert_eq!(builder.ops().len(), 12);
-        assert!(matches!(builder.ops()[0], CircuitOp::H(0)));
-        assert!(matches!(builder.ops()[1], CircuitOp::S(0)));
-        assert!(matches!(builder.ops()[2], CircuitOp::Sdg(0)));
-        assert!(matches!(builder.ops()[3], CircuitOp::X(0)));
-        assert!(matches!(builder.ops()[4], CircuitOp::Y(0)));
-        assert!(matches!(builder.ops()[5], CircuitOp::Z(0)));
-        assert!(matches!(builder.ops()[6], CircuitOp::Cx(0, 1)));
-        assert!(matches!(builder.ops()[7], CircuitOp::Cz(0, 1)));
-        assert!(matches!(builder.ops()[8], CircuitOp::Swap(0, 1)));
-        assert!(matches!(builder.ops()[9], CircuitOp::Noise1Q(0)));
-        assert!(matches!(builder.ops()[10], CircuitOp::Noise2Q(0, 1)));
-        assert!(matches!(builder.ops()[11], CircuitOp::Mz(0)));
+        assert_eq!(builder.steps().len(), 12);
+        assert!(matches!(
+            builder.steps()[0],
+            NoisyCircuitStep::Gate(Gate::H(0))
+        ));
+        assert!(matches!(
+            builder.steps()[1],
+            NoisyCircuitStep::Gate(Gate::S(0))
+        ));
+        assert!(matches!(
+            builder.steps()[2],
+            NoisyCircuitStep::Gate(Gate::Sdg(0))
+        ));
+        assert!(matches!(
+            builder.steps()[3],
+            NoisyCircuitStep::Gate(Gate::X(0))
+        ));
+        assert!(matches!(
+            builder.steps()[4],
+            NoisyCircuitStep::Gate(Gate::Y(0))
+        ));
+        assert!(matches!(
+            builder.steps()[5],
+            NoisyCircuitStep::Gate(Gate::Z(0))
+        ));
+        assert!(matches!(
+            builder.steps()[6],
+            NoisyCircuitStep::Gate(Gate::Cx(0, 1))
+        ));
+        assert!(matches!(
+            builder.steps()[7],
+            NoisyCircuitStep::Gate(Gate::Cz(0, 1))
+        ));
+        assert!(matches!(
+            builder.steps()[8],
+            NoisyCircuitStep::Gate(Gate::Swap(0, 1))
+        ));
+        assert!(matches!(
+            builder.steps()[9],
+            NoisyCircuitStep::Noise(NoiseInjection::OneQ(0))
+        ));
+        assert!(matches!(
+            builder.steps()[10],
+            NoisyCircuitStep::Noise(NoiseInjection::TwoQ(0, 1))
+        ));
+        assert!(matches!(
+            builder.steps()[11],
+            NoisyCircuitStep::Gate(Gate::Mz(0))
+        ));
 
         // Test clear
         builder.clear();
-        assert_eq!(builder.ops().len(), 0);
+        assert_eq!(builder.steps().len(), 0);
     }
 
     #[test]
diff --git a/crates/pecos-gpu-sims/src/gpu_pauli_prop.rs b/crates/pecos-gpu-sims/src/gpu_pauli_prop.rs
index 067fb8b26..d353873b9 100644
--- a/crates/pecos-gpu-sims/src/gpu_pauli_prop.rs
+++ b/crates/pecos-gpu-sims/src/gpu_pauli_prop.rs
@@ -651,15 +651,15 @@ impl GpuPauliProp {
 
     /// Check if a Pauli string anticommutes with the accumulated faults.
     ///
-    /// This is used to check for logical errors: if the fault anticommutes
-    /// with a logical operator, it's a logical error.
+    /// This is used to check whether faults flip a tracked Pauli string:
+    /// an odd number of anticommutations means the tracked Pauli flips.
     ///
     /// # Arguments
     /// * `x_qubits` - Qubits with X in the Pauli string
     /// * `z_qubits` - Qubits with Z in the Pauli string
     ///
     /// # Returns
-    /// A vector of bools, one per shot, true if anticommutes (logical error).
+    /// A vector of bools, one per shot, true if the tracked Pauli string flips.
     pub fn check_anticommutation(&mut self, x_qubits: &[usize], z_qubits: &[usize]) -> Vec<bool> {
         self.sync();
 
@@ -674,7 +674,7 @@ impl GpuPauliProp {
 
             let mut anticom_count = 0u32;
 
-            // X in logical anticommutes with Z faults
+            // X in the tracked Pauli anticommutes with Z faults.
             for &q in x_qubits {
                 let base = q * self.shot_words as usize;
                 if (z_faults[base + word_idx] >> bit_idx) & 1 != 0 {
@@ -682,7 +682,7 @@ impl GpuPauliProp {
                 }
             }
 
-            // Z in logical anticommutes with X faults
+            // Z in the tracked Pauli anticommutes with X faults.
             for &q in z_qubits {
                 let base = q * self.shot_words as usize;
                 if (x_faults[base + word_idx] >> bit_idx) & 1 != 0 {
@@ -885,11 +885,11 @@ mod tests {
         prop.inject_x_fault(0);
         prop.flush();
 
-        // Check against Z logical on qubit 0 (should anticommute)
+        // Check against tracked Z on qubit 0 (should anticommute)
         let results = prop.check_anticommutation(&[], &[0]);
         assert!(results.iter().all(|&b| b)); // All shots: anticommutes
 
-        // Check against X logical on qubit 0 (should commute)
+        // Check against tracked X on qubit 0 (should commute)
         let results = prop.check_anticommutation(&[0], &[]);
         assert!(results.iter().all(|&b| !b)); // All shots: commutes
     }
diff --git a/crates/pecos-gpu-sims/src/gpu_stab_multi.rs b/crates/pecos-gpu-sims/src/gpu_stab_multi.rs
index 283ebf8ea..0c734a965 100644
--- a/crates/pecos-gpu-sims/src/gpu_stab_multi.rs
+++ b/crates/pecos-gpu-sims/src/gpu_stab_multi.rs
@@ -48,7 +48,7 @@ pub struct GpuStabMulti<R: Rng + SeedableRng = PecosRng> {
     #[allow(dead_code)]
     meas_data_buffer: wgpu::Buffer,
     meas_random_buffer: wgpu::Buffer,
-    meas_results_buffer: wgpu::Buffer,
+    meas_ids_buffer: wgpu::Buffer,
     meas_staging_buffer: wgpu::Buffer,
     meas_bind_group: wgpu::BindGroup,
     meas_find_pipeline: wgpu::ComputePipeline,
@@ -228,7 +228,7 @@ impl<R: Rng + SeedableRng + Debug> GpuStabMulti<R> {
             mapped_at_creation: false,
         });
 
-        let meas_results_buffer = device.create_buffer(&wgpu::BufferDescriptor {
+        let meas_ids_buffer = device.create_buffer(&wgpu::BufferDescriptor {
             label: Some("Multi Measurement Results Buffer"),
             size: u64::from(shots_per_batch) * 4,
             usage: wgpu::BufferUsages::STORAGE
@@ -506,7 +506,7 @@ impl<R: Rng + SeedableRng + Debug> GpuStabMulti<R> {
                 },
                 wgpu::BindGroupEntry {
                     binding: 3,
-                    resource: meas_results_buffer.as_entire_binding(),
+                    resource: meas_ids_buffer.as_entire_binding(),
                 },
             ],
         });
@@ -602,7 +602,7 @@ impl<R: Rng + SeedableRng + Debug> GpuStabMulti<R> {
             // GPU-side measurement
             meas_data_buffer,
             meas_random_buffer,
-            meas_results_buffer,
+            meas_ids_buffer,
             meas_staging_buffer,
             meas_bind_group,
             meas_find_pipeline,
@@ -1427,7 +1427,7 @@ impl<R: Rng + SeedableRng + Debug> GpuStabMulti<R> {
 
             // Copy this measurement's results to staging buffer
             encoder.copy_buffer_to_buffer(
-                &self.meas_results_buffer,
+                &self.meas_ids_buffer,
                 0,
                 &self.meas_staging_buffer,
                 0,
@@ -1576,7 +1576,7 @@ impl<R: Rng + SeedableRng + Debug> GpuStabMulti<R> {
             }
 
             encoder.copy_buffer_to_buffer(
-                &self.meas_results_buffer,
+                &self.meas_ids_buffer,
                 0,
                 &self.meas_staging_buffer,
                 0,
diff --git a/crates/pecos-gpu-sims/src/influence_sampler_shader.wgsl b/crates/pecos-gpu-sims/src/influence_sampler_shader.wgsl
index 7a290b759..1dbbc788d 100644
--- a/crates/pecos-gpu-sims/src/influence_sampler_shader.wgsl
+++ b/crates/pecos-gpu-sims/src/influence_sampler_shader.wgsl
@@ -16,10 +16,10 @@ struct Params {
     num_locations: u32,
     num_shots: u32,
     num_detectors: u32,
-    num_logicals: u32,
+    num_dem_outputs: u32,
     p_error_threshold: u32,  // Fixed-point threshold (p * 0xFFFFFFFF)
     detector_words: u32,     // ceil(num_detectors / 32)
-    logical_words: u32,      // ceil(num_logicals / 32)
+    dem_output_words: u32,   // ceil(num_dem_outputs / 32)
     _padding: u32,
 }
 
@@ -33,22 +33,22 @@ struct Params {
 @group(0) @binding(5) var<storage, read> det_offsets_z: array<u32>;
 @group(0) @binding(6) var<storage, read> det_data_z: array<u32>;
 
-// Logical influence CSR arrays
-@group(0) @binding(7) var<storage, read> log_offsets_x: array<u32>;
-@group(0) @binding(8) var<storage, read> log_data_x: array<u32>;
-@group(0) @binding(9) var<storage, read> log_offsets_y: array<u32>;
-@group(0) @binding(10) var<storage, read> log_data_y: array<u32>;
-@group(0) @binding(11) var<storage, read> log_offsets_z: array<u32>;
-@group(0) @binding(12) var<storage, read> log_data_z: array<u32>;
+// DEM-output influence CSR arrays
+@group(0) @binding(7) var<storage, read> dem_output_offsets_x: array<u32>;
+@group(0) @binding(8) var<storage, read> dem_output_data_x: array<u32>;
+@group(0) @binding(9) var<storage, read> dem_output_offsets_y: array<u32>;
+@group(0) @binding(10) var<storage, read> dem_output_data_y: array<u32>;
+@group(0) @binding(11) var<storage, read> dem_output_offsets_z: array<u32>;
+@group(0) @binding(12) var<storage, read> dem_output_data_z: array<u32>;
 
 // Random seeds (one per shot)
 @group(0) @binding(13) var<storage, read> random_seeds: array<u32>;
 
-// Output: detector and logical flips
+// Output: detector and DEM-output flips
 // Layout: [shot * words + word_idx] - each shot has its own contiguous region
 // NO atomics needed since each shot is processed by exactly one thread
 @group(0) @binding(14) var<storage, read_write> detector_flips: array<u32>;
-@group(0) @binding(15) var<storage, read_write> logical_flips: array<u32>;
+@group(0) @binding(15) var<storage, read_write> dem_output_flips: array<u32>;
 
 // PCG-style hash function for deterministic randomness
 fn hash(seed: u32, loc: u32, extra: u32) -> u32 {
@@ -71,12 +71,12 @@ fn xor_detector(shot_base: u32, det_idx: u32, detector_words: u32) {
     }
 }
 
-fn xor_logical(shot_base: u32, log_idx: u32, logical_words: u32) {
-    let word = log_idx / 32u;
-    let bit = log_idx % 32u;
-    if (word < logical_words) {
+fn xor_dem_output(shot_base: u32, dem_output_idx: u32, dem_output_words: u32) {
+    let word = dem_output_idx / 32u;
+    let bit = dem_output_idx % 32u;
+    if (word < dem_output_words) {
         let idx = shot_base + word;
-        logical_flips[idx] = logical_flips[idx] ^ (1u << bit);
+        dem_output_flips[idx] = dem_output_flips[idx] ^ (1u << bit);
     }
 }
 
@@ -90,14 +90,14 @@ fn main(@builtin(global_invocation_id) global_id: vec3<u32>) {
 
     let seed = random_seeds[shot];
     let det_base = shot * params.detector_words;
-    let log_base = shot * params.logical_words;
+    let dem_output_base = shot * params.dem_output_words;
 
     // Initialize this shot's output to zero
     for (var w = 0u; w < params.detector_words; w = w + 1u) {
         detector_flips[det_base + w] = 0u;
     }
-    for (var w = 0u; w < params.logical_words; w = w + 1u) {
-        logical_flips[log_base + w] = 0u;
+    for (var w = 0u; w < params.dem_output_words; w = w + 1u) {
+        dem_output_flips[dem_output_base + w] = 0u;
     }
 
     // Process ALL locations for this shot
@@ -113,7 +113,7 @@ fn main(@builtin(global_invocation_id) global_id: vec3<u32>) {
         let rand_pauli = hash(seed, loc, 1u);
         let pauli = rand_pauli % 3u;
 
-        // Process detector and logical influences based on Pauli type
+        // Process detector and DEM-output influences based on Pauli type
         if (pauli == 0u) {
             // X fault - process detector influences
             let det_start = det_offsets_x[loc];
@@ -122,11 +122,11 @@ fn main(@builtin(global_invocation_id) global_id: vec3<u32>) {
                 xor_detector(det_base, det_data_x[i], params.detector_words);
             }
 
-            // X fault - process logical influences
-            let log_start = log_offsets_x[loc];
-            let log_end = log_offsets_x[loc + 1u];
-            for (var i = log_start; i < log_end; i = i + 1u) {
-                xor_logical(log_base, log_data_x[i], params.logical_words);
+            // X fault - process DEM-output influences
+            let dem_output_start = dem_output_offsets_x[loc];
+            let dem_output_end = dem_output_offsets_x[loc + 1u];
+            for (var i = dem_output_start; i < dem_output_end; i = i + 1u) {
+                xor_dem_output(dem_output_base, dem_output_data_x[i], params.dem_output_words);
             }
         } else if (pauli == 1u) {
             // Y fault - process detector influences
@@ -136,11 +136,11 @@ fn main(@builtin(global_invocation_id) global_id: vec3<u32>) {
                 xor_detector(det_base, det_data_y[i], params.detector_words);
             }
 
-            // Y fault - process logical influences
-            let log_start = log_offsets_y[loc];
-            let log_end = log_offsets_y[loc + 1u];
-            for (var i = log_start; i < log_end; i = i + 1u) {
-                xor_logical(log_base, log_data_y[i], params.logical_words);
+            // Y fault - process DEM-output influences
+            let dem_output_start = dem_output_offsets_y[loc];
+            let dem_output_end = dem_output_offsets_y[loc + 1u];
+            for (var i = dem_output_start; i < dem_output_end; i = i + 1u) {
+                xor_dem_output(dem_output_base, dem_output_data_y[i], params.dem_output_words);
             }
         } else {
             // Z fault - process detector influences
@@ -150,11 +150,11 @@ fn main(@builtin(global_invocation_id) global_id: vec3<u32>) {
                 xor_detector(det_base, det_data_z[i], params.detector_words);
             }
 
-            // Z fault - process logical influences
-            let log_start = log_offsets_z[loc];
-            let log_end = log_offsets_z[loc + 1u];
-            for (var i = log_start; i < log_end; i = i + 1u) {
-                xor_logical(log_base, log_data_z[i], params.logical_words);
+            // Z fault - process DEM-output influences
+            let dem_output_start = dem_output_offsets_z[loc];
+            let dem_output_end = dem_output_offsets_z[loc + 1u];
+            for (var i = dem_output_start; i < dem_output_end; i = i + 1u) {
+                xor_dem_output(dem_output_base, dem_output_data_z[i], params.dem_output_words);
             }
         }
     }
diff --git a/crates/pecos-gpu-sims/src/lib.rs b/crates/pecos-gpu-sims/src/lib.rs
index b734d4cb3..126ac27bf 100644
--- a/crates/pecos-gpu-sims/src/lib.rs
+++ b/crates/pecos-gpu-sims/src/lib.rs
@@ -48,6 +48,7 @@ mod gpu_sampler;
 mod gpu_stab;
 mod gpu_stab_multi;
 pub mod prelude;
+pub mod state_access;
 
 #[cfg(test)]
 mod gpu_sampler_validation;
@@ -68,13 +69,14 @@ pub use gpu64::GpuStateVec64;
 pub type GpuStateVec = GpuStateVec64;
 pub use gpu_influence_sampler::{GpuInfluenceMapData, GpuInfluenceSampler, GpuSamplingResult};
 pub use gpu_noisy_sampler::{
-    BiasedDepolarizingNoiseSampler, CircuitBuilder, CircuitOp, DepolarizingNoiseSampler,
-    GpuNoisySampler, NoiseSampler, Pauli, ShotResult,
+    BiasedDepolarizingNoiseSampler, CircuitBuilder, DepolarizingNoiseSampler, Gate,
+    GpuNoisySampler, NoiseInjection, NoiseSampler, NoisyCircuitStep, Pauli, ShotResult,
 };
 pub use gpu_pauli_prop::GpuPauliProp;
 pub use gpu_sampler::{GpuMeasurementSampler, GpuSampleResult};
 pub use gpu_stab::GpuStab;
 pub use gpu_stab_multi::GpuStabMulti;
+pub use state_access::{GpuDensityMatrixHostAccess, GpuStateVectorHostAccess};
 
 /// Default GPU stabilizer simulator using `PecosRng`
 pub type DefaultGpuStab = GpuStab<pecos_random::PecosRng>;
diff --git a/crates/pecos-gpu-sims/src/state_access.rs b/crates/pecos-gpu-sims/src/state_access.rs
new file mode 100644
index 000000000..95dd7f032
--- /dev/null
+++ b/crates/pecos-gpu-sims/src/state_access.rs
@@ -0,0 +1,177 @@
+// Copyright 2026 The PECOS Developers
+//
+// Licensed under the Apache License, Version 2.0 (the "License"); you may not use this file except
+// in compliance with the License. You may obtain a copy of the License at
+//
+//     https://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software distributed under the License
+// is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express
+// or implied. See the License for the specific language governing permissions and limitations under
+// the License.
+
+//! Explicit host-snapshot state access for GPU-backed simulators.
+//!
+//! The generic `pecos_simulators::StateVectorAccess` and
+//! `DensityMatrixAccess` traits look like ordinary passive inspection. For GPU
+//! simulators, inspection requires synchronization and device-to-host copy. The
+//! traits in this module make that transfer explicit in the method names while
+//! returning the same little-endian data shapes as the CPU state-access traits.
+
+use num_complex::Complex64;
+use pecos_simulators::{QuantumSimulator, StateAccessError};
+
+use crate::{GpuDensityMatrix, GpuStateVec32, GpuStateVec64, GpuStateVecBackend};
+
+/// Explicit host readback for GPU state-vector simulators.
+pub trait GpuStateVectorHostAccess {
+    /// Returns the number of qubits represented by the device state.
+    fn num_qubits(&self) -> usize;
+
+    /// Synchronizes pending GPU work and returns a host-owned state vector.
+    ///
+    /// The vector is in little-endian computational-basis order. Calling this
+    /// method performs a device-to-host transfer.
+    ///
+    /// # Errors
+    ///
+    /// Returns an error if the Hilbert-space dimension overflows.
+    fn state_vector_host_snapshot(&mut self) -> Result<Vec<Complex64>, StateAccessError>;
+
+    /// Synchronizes pending GPU work and returns one host-copied amplitude.
+    ///
+    /// # Errors
+    ///
+    /// Returns an error if `basis_state` is outside the Hilbert space.
+    fn amplitude_host_snapshot(
+        &mut self,
+        basis_state: usize,
+    ) -> Result<Complex64, StateAccessError> {
+        validate_basis_index(self.num_qubits(), basis_state)?;
+        Ok(self.state_vector_host_snapshot()?[basis_state])
+    }
+}
+
+/// Explicit host readback for GPU density-matrix simulators.
+pub trait GpuDensityMatrixHostAccess {
+    /// Returns the number of physical qubits represented by the density matrix.
+    fn num_qubits(&self) -> usize;
+
+    /// Synchronizes pending GPU work and returns a host-owned density matrix.
+    ///
+    /// The matrix is in little-endian computational-basis order. Calling this
+    /// method performs a device-to-host transfer and, for the current
+    /// Choi-state implementation, reconstructs the density matrix on the host.
+    ///
+    /// # Errors
+    ///
+    /// Returns an error if the Hilbert-space dimension overflows.
+    fn density_matrix_host_snapshot(&mut self) -> Result<Vec<Vec<Complex64>>, StateAccessError>;
+
+    /// Synchronizes pending GPU work and returns one host-copied density-matrix
+    /// element.
+    ///
+    /// # Errors
+    ///
+    /// Returns an error if either basis index is outside the Hilbert space.
+    fn density_matrix_element_host_snapshot(
+        &mut self,
+        row: usize,
+        col: usize,
+    ) -> Result<Complex64, StateAccessError> {
+        validate_basis_index(self.num_qubits(), row)?;
+        validate_basis_index(self.num_qubits(), col)?;
+        Ok(self.density_matrix_host_snapshot()?[row][col])
+    }
+}
+
+impl GpuStateVectorHostAccess for GpuStateVec32 {
+    fn num_qubits(&self) -> usize {
+        QuantumSimulator::num_qubits(self)
+    }
+
+    fn state_vector_host_snapshot(&mut self) -> Result<Vec<Complex64>, StateAccessError> {
+        hilbert_dim(GpuStateVectorHostAccess::num_qubits(self))?;
+        Ok(self
+            .state()
+            .into_iter()
+            .map(|[re, im]| Complex64::new(f64::from(re), f64::from(im)))
+            .collect())
+    }
+}
+
+impl GpuStateVectorHostAccess for GpuStateVec64 {
+    fn num_qubits(&self) -> usize {
+        QuantumSimulator::num_qubits(self)
+    }
+
+    fn state_vector_host_snapshot(&mut self) -> Result<Vec<Complex64>, StateAccessError> {
+        hilbert_dim(GpuStateVectorHostAccess::num_qubits(self))?;
+        Ok(self
+            .state()
+            .into_iter()
+            .map(|[re, im]| Complex64::new(re, im))
+            .collect())
+    }
+}
+
+impl<SV: GpuStateVecBackend> GpuDensityMatrixHostAccess for GpuDensityMatrix<SV> {
+    fn num_qubits(&self) -> usize {
+        self.num_qubits()
+    }
+
+    fn density_matrix_host_snapshot(&mut self) -> Result<Vec<Vec<Complex64>>, StateAccessError> {
+        hilbert_dim(self.num_qubits())?;
+        Ok(self.get_density_matrix())
+    }
+}
+
+fn validate_basis_index(num_qubits: usize, index: usize) -> Result<(), StateAccessError> {
+    let dim = hilbert_dim(num_qubits)?;
+    if index >= dim {
+        return Err(StateAccessError::BasisIndexOutOfRange {
+            num_qubits,
+            dim,
+            index,
+        });
+    }
+    Ok(())
+}
+
+fn hilbert_dim(num_qubits: usize) -> Result<usize, StateAccessError> {
+    2usize
+        .checked_pow(
+            num_qubits
+                .try_into()
+                .map_err(|_| StateAccessError::DimensionOverflow { num_qubits })?,
+        )
+        .ok_or(StateAccessError::DimensionOverflow { num_qubits })
+}
+
+#[cfg(test)]
+mod tests {
+    use super::*;
+
+    #[test]
+    fn validates_basis_indices_against_hilbert_dimension() {
+        assert_eq!(validate_basis_index(3, 7), Ok(()));
+        assert_eq!(
+            validate_basis_index(3, 8),
+            Err(StateAccessError::BasisIndexOutOfRange {
+                num_qubits: 3,
+                dim: 8,
+                index: 8,
+            })
+        );
+    }
+
+    #[test]
+    fn reports_dimension_overflow() {
+        assert_eq!(hilbert_dim(0), Ok(1));
+        assert_eq!(hilbert_dim(3), Ok(8));
+        assert!(matches!(
+            hilbert_dim(usize::BITS as usize),
+            Err(StateAccessError::DimensionOverflow { .. })
+        ));
+    }
+}
diff --git a/crates/pecos-gpu-sims/tests/influence_sampler_audit.rs b/crates/pecos-gpu-sims/tests/influence_sampler_audit.rs
index 530d5b58d..0db043ac9 100644
--- a/crates/pecos-gpu-sims/tests/influence_sampler_audit.rs
+++ b/crates/pecos-gpu-sims/tests/influence_sampler_audit.rs
@@ -9,59 +9,72 @@
 //!
 //! Semantics: for each shot, each location has probability `p_error` of a
 //! fault. If a fault fires, a random Pauli (X/Y/Z, uniformly) is applied.
-//! Each fault toggles a CSR-encoded set of detectors and logicals.
+//! Each fault toggles a CSR-encoded set of detectors and DEM outputs.
 //!
 //! We don't have a CPU reference implementation to cross-check against.
 //! Instead, we use tight edge-case tests + distributional sanity checks.
 
-use pecos_gpu_sims::{GpuInfluenceMapData, GpuInfluenceSampler};
+use pecos_gpu_sims::{GpuInfluenceMapData, GpuInfluenceSampler, GpuSamplingResult};
 
 /// Build an influence map with `n_loc` locations, `n_det` detectors, and
-/// `n_log` logicals, where:
+/// `n_dem_outputs` DEM outputs, where:
 ///   - X fault at location `k` toggles detector `k % n_det`
-///   - Z fault at location `k` toggles logical `k % n_log`
+///   - Z fault at location `k` toggles DEM output `k % n_dem_outputs`
 ///   - Y fault at location `k` toggles both
 ///
 /// Written as three separate CSR tables (X, Y, Z each have a row per location).
 #[allow(clippy::cast_possible_truncation)] // CSR row offsets, n_loc bounded by test inputs (<= u32::MAX trivially)
-fn simple_diagonal_map(n_loc: u32, n_det: u32, n_log: u32) -> GpuInfluenceMapData {
+fn simple_diagonal_map(n_loc: u32, n_det: u32, n_dem_outputs: u32) -> GpuInfluenceMapData {
     let mut det_off_x = vec![0u32; (n_loc + 1) as usize];
     let mut det_dat_x = Vec::<u32>::new();
     let mut det_off_y = vec![0u32; (n_loc + 1) as usize];
     let mut det_dat_y = Vec::<u32>::new();
     let mut det_off_z = vec![0u32; (n_loc + 1) as usize];
     let det_dat_z = Vec::<u32>::new();
-    let mut log_off_x = vec![0u32; (n_loc + 1) as usize];
-    let log_dat_x = Vec::<u32>::new();
-    let mut log_off_y = vec![0u32; (n_loc + 1) as usize];
-    let mut log_dat_y = Vec::<u32>::new();
-    let mut log_off_z = vec![0u32; (n_loc + 1) as usize];
-    let mut log_dat_z = Vec::<u32>::new();
+    let mut dem_output_offsets_x = vec![0u32; (n_loc + 1) as usize];
+    let dem_output_dat_x = Vec::<u32>::new();
+    let mut dem_output_offsets_y = vec![0u32; (n_loc + 1) as usize];
+    let mut dem_output_dat_y = Vec::<u32>::new();
+    let mut dem_output_offsets_z = vec![0u32; (n_loc + 1) as usize];
+    let mut dem_output_dat_z = Vec::<u32>::new();
 
     for k in 0..n_loc {
         // X at k -> detector (k % n_det)
         det_dat_x.push(k % n_det);
         det_off_x[(k + 1) as usize] = det_dat_x.len() as u32;
 
-        // Z at k -> logical (k % n_log)
-        log_dat_z.push(k % n_log);
-        log_off_z[(k + 1) as usize] = log_dat_z.len() as u32;
+        // Z at k -> DEM output (k % n_dem_outputs)
+        dem_output_dat_z.push(k % n_dem_outputs);
+        dem_output_offsets_z[(k + 1) as usize] = dem_output_dat_z.len() as u32;
 
         // Y at k -> both
         det_dat_y.push(k % n_det);
         det_off_y[(k + 1) as usize] = det_dat_y.len() as u32;
-        log_dat_y.push(k % n_log);
-        log_off_y[(k + 1) as usize] = log_dat_y.len() as u32;
+        dem_output_dat_y.push(k % n_dem_outputs);
+        dem_output_offsets_y[(k + 1) as usize] = dem_output_dat_y.len() as u32;
 
-        // X touches no logicals (empty row)
-        log_off_x[(k + 1) as usize] = log_dat_x.len() as u32;
+        // X touches no DEM outputs (empty row)
+        dem_output_offsets_x[(k + 1) as usize] = dem_output_dat_x.len() as u32;
         // Z touches no detectors (empty row)
         det_off_z[(k + 1) as usize] = det_dat_z.len() as u32;
     }
 
     GpuInfluenceMapData::from_csr(
-        n_loc, n_det, n_log, det_off_x, det_dat_x, det_off_y, det_dat_y, det_off_z, det_dat_z,
-        log_off_x, log_dat_x, log_off_y, log_dat_y, log_off_z, log_dat_z,
+        n_loc,
+        n_det,
+        n_dem_outputs,
+        det_off_x,
+        det_dat_x,
+        det_off_y,
+        det_dat_y,
+        det_off_z,
+        det_dat_z,
+        dem_output_offsets_x,
+        dem_output_dat_x,
+        dem_output_offsets_y,
+        dem_output_dat_y,
+        dem_output_offsets_z,
+        dem_output_dat_z,
     )
 }
 
@@ -69,6 +82,40 @@ fn no_flips(flips: &[u32]) -> bool {
     flips.iter().all(|&w| w == 0)
 }
 
+#[test]
+fn logical_error_helpers_ignore_padding_bits() {
+    let result = GpuSamplingResult {
+        num_shots: 3,
+        detector_flips: vec![0; 3],
+        dem_output_flips: vec![
+            0b10,    // shot 0: valid output 1 flips
+            1 << 31, // shot 1: padding bit only, should be ignored
+            0,       // shot 2: no logical output
+        ],
+        num_detectors: 0,
+        num_dem_outputs: 2,
+        detector_words: 1,
+        dem_output_words: 1,
+    };
+
+    assert_eq!(result.count_logical_errors(), 1);
+    assert!(result.has_logical_error(0));
+    assert!(!result.has_logical_error(1));
+    assert!(!result.has_logical_error(2));
+
+    let tracked_only_result = GpuSamplingResult {
+        num_shots: 1,
+        detector_flips: vec![0],
+        dem_output_flips: vec![u32::MAX],
+        num_detectors: 0,
+        num_dem_outputs: 0,
+        detector_words: 1,
+        dem_output_words: 1,
+    };
+    assert_eq!(tracked_only_result.count_logical_errors(), 0);
+    assert!(!tracked_only_result.has_logical_error(0));
+}
+
 #[test]
 fn zero_prob_no_flips() {
     let map = simple_diagonal_map(32, 8, 4);
@@ -109,12 +156,12 @@ fn empty_map_no_flips() {
 #[test]
 fn full_prob_saturates_parity() {
     // At p=1 every location fires every shot. For a map where every
-    // location touches at most one detector and one logical, every shot is
+    // location touches at most one detector and one DEM output, every shot is
     // an independent draw of X/Y/Z per location. The parity of the total
     // toggle count per detector is a deterministic function of the
     // per-location Pauli choices, but statistically the number of shots
     // that flip detector 0 should be non-zero.
-    let map = simple_diagonal_map(16, 1, 1); // all locations -> detector 0, logical 0
+    let map = simple_diagonal_map(16, 1, 1); // all locations -> detector 0, DEM output 0
     let Ok(mut sampler) = GpuInfluenceSampler::new(&map, 7) else {
         return;
     };
@@ -168,7 +215,7 @@ fn determinism_with_same_seed() {
         assert_eq!(
             ra.has_logical_error(shot),
             rb.has_logical_error(shot),
-            "shot {shot} logical mismatch"
+            "shot {shot} DEM-output mismatch"
         );
         assert_eq!(
             ra.detector_flips_for_shot(shot),
@@ -180,7 +227,7 @@ fn determinism_with_same_seed() {
 
 #[test]
 fn scaling_with_p_error() {
-    // Logical error rate should monotonically increase with p.
+    // logical error rate should monotonically increase with p.
     let map = simple_diagonal_map(32, 8, 4);
     let Ok(mut sampler) = GpuInfluenceSampler::new(&map, 42) else {
         return;
diff --git a/crates/pecos-hugr/src/engine/control_flow/cfg.rs b/crates/pecos-hugr/src/engine/control_flow/cfg.rs
index b05553754..b0930ee2c 100644
--- a/crates/pecos-hugr/src/engine/control_flow/cfg.rs
+++ b/crates/pecos-hugr/src/engine/control_flow/cfg.rs
@@ -320,10 +320,10 @@ impl HugrEngine {
 
             // Check the current block
             if let Some(block_info) = cfg_info.blocks.get(&active_cfg.current_block) {
-                // Check if this block has tracked ops that drive completion
-                // Quantum, calls, conditionals, bool, extension, and tailloops are tracked
-                // Classical_ops are not tracked (they complete when their inputs are ready)
-                let has_tracked_ops = !block_info.quantum_ops.is_empty()
+                // Check if this block has operations that drive completion.
+                // Quantum, calls, conditionals, bool, extension, and tailloops
+                // complete explicitly. Classical_ops complete when their inputs are ready.
+                let has_completion_driving_ops = !block_info.quantum_ops.is_empty()
                     || !block_info.call_nodes.is_empty()
                     || !block_info.conditional_nodes.is_empty()
                     || !block_info.bool_ops.is_empty()
@@ -331,7 +331,7 @@ impl HugrEngine {
                     || !block_info.tailloop_nodes.is_empty();
 
                 // Check if the processed node is in this block
-                let is_in_block = if has_tracked_ops {
+                let is_in_block = if has_completion_driving_ops {
                     block_info.quantum_ops.contains(&processed_node)
                         || block_info.call_nodes.contains(&processed_node)
                         || block_info.conditional_nodes.contains(&processed_node)
@@ -345,8 +345,8 @@ impl HugrEngine {
 
                 if is_in_block {
                     // Check completion based on block type
-                    let block_complete = if has_tracked_ops {
-                        // Block with tracked ops: wait for all tracked op types
+                    let block_complete = if has_completion_driving_ops {
+                        // Block with completion-driving ops: wait for all such op types.
                         let all_quantum_done = block_info
                             .quantum_ops
                             .iter()
diff --git a/crates/pecos-ldpc-decoders/pecos.toml b/crates/pecos-ldpc-decoders/pecos.toml
index 9a2b4b7a7..55fab446c 100644
--- a/crates/pecos-ldpc-decoders/pecos.toml
+++ b/crates/pecos-ldpc-decoders/pecos.toml
@@ -10,13 +10,13 @@ sha256 = "6478edfe2f3305127cffe8caf73ea0176c53769f4bf1585be237eb30798c3b8e"
 description = "C++ Boost libraries"
 
 [dependencies.ldpc]
-version = "31cf9f33872f32579af1efbe1e84552d42b03ea8"
-url = "https://github.com/quantumgizmos/ldpc/archive/31cf9f33872f32579af1efbe1e84552d42b03ea8.tar.gz"
-sha256 = "43ea9bfe543233c5f65e2dfb7966229df803040b4b26e25e99c3068eb23a797a"
+version = "d3429964cd4ffe1abfc041c6ec8b8425cb174f40"
+url = "https://github.com/quantumgizmos/ldpc/archive/d3429964cd4ffe1abfc041c6ec8b8425cb174f40.tar.gz"
+sha256 = "76af0f01446ee7cbed33a47d6b597c10d8d12b2f10d508911b3d0763844d467e"
 description = "LDPC decoders"
 
 [dependencies.stim]
-version = "bd60b73525fd5a9b30839020eb7554ad369e4337"
-url = "https://github.com/quantumlib/Stim/archive/bd60b73525fd5a9b30839020eb7554ad369e4337.tar.gz"
-sha256 = "2a4be24295ce3018d79e08369b31e401a2d33cd8b3a75675d57dac3afd9de37d"
+version = "213275795e49027772bea7c610b6aac3a80583e1"
+url = "https://github.com/quantumlib/Stim/archive/213275795e49027772bea7c610b6aac3a80583e1.tar.gz"
+sha256 = "b63c4ae94494a8819d440757776cf80a829ec1e30454fa7c9b0f670e981938ab"
 description = "Stabilizer simulator for QEC"
diff --git a/crates/pecos-ldpc-decoders/src/bridge.cpp b/crates/pecos-ldpc-decoders/src/bridge.cpp
index 362249f23..473b7bd7b 100644
--- a/crates/pecos-ldpc-decoders/src/bridge.cpp
+++ b/crates/pecos-ldpc-decoders/src/bridge.cpp
@@ -102,7 +102,7 @@ std::unique_ptr<BpOsdDecoder> create_bp_osd_decoder(
         omp_thread_count,
         serial_schedule_vec,
         random_schedule_seed,
-        true,  // random_schedule_at_every_iteration
+        serial_schedule_vec.empty(),  // random_serial_schedule: use random if no fixed schedule
         static_cast<bp::BpInputType>(input_vector_type)
     );
 
@@ -254,7 +254,7 @@ std::unique_ptr<BpLsdDecoder> create_bp_lsd_decoder(
         omp_thread_count,
         serial_schedule_vec,
         random_schedule_seed,
-        true,  // random_schedule_at_every_iteration
+        serial_schedule_vec.empty(),  // random_serial_schedule: use random if no fixed schedule
         static_cast<bp::BpInputType>(input_vector_type)
     );
 
diff --git a/crates/pecos-ldpc-decoders/src/core_traits_simple.rs b/crates/pecos-ldpc-decoders/src/core_traits_simple.rs
index c786919c2..7201162c1 100644
--- a/crates/pecos-ldpc-decoders/src/core_traits_simple.rs
+++ b/crates/pecos-ldpc-decoders/src/core_traits_simple.rs
@@ -5,7 +5,7 @@
 //! parameters required by LDPC decoders.
 
 use crate::decoders::{
-    BeliefFindDecoder, BpLsdDecoder, BpOsdDecoder, FlipDecoder, SoftInfoBpDecoder,
+    BeliefFindDecoder, BpLsdDecoder, BpOsdDecoder, FlipDecoder, SoftInfoBpDecoder, UnionFindDecoder,
 };
 use crate::{DecodingResult, LdpcError};
 use ndarray::ArrayView1;
@@ -37,6 +37,10 @@ impl DecodingResultTrait for DecodingResult {
         self.converged
     }
 
+    fn correction(&self) -> &[u8] {
+        self.decoding.as_slice().unwrap_or(&[])
+    }
+
     fn iterations(&self) -> Option<usize> {
         Some(self.iterations)
     }
@@ -88,6 +92,24 @@ impl Decoder for BpLsdDecoder {
     }
 }
 
+/// Implement Decoder trait for `UnionFindDecoder`
+impl Decoder for UnionFindDecoder {
+    type Result = DecodingResult;
+    type Error = LdpcError;
+
+    fn decode(&mut self, input: &ArrayView1<u8>) -> Result<Self::Result, Self::Error> {
+        self.decode(input, &[], 0)
+    }
+
+    fn check_count(&self) -> usize {
+        self.check_count()
+    }
+
+    fn bit_count(&self) -> usize {
+        self.bit_count()
+    }
+}
+
 /// Implement Decoder trait for `FlipDecoder`
 impl Decoder for FlipDecoder {
     type Result = DecodingResult;
diff --git a/crates/pecos-mwpf/Cargo.toml b/crates/pecos-mwpf/Cargo.toml
new file mode 100644
index 000000000..64e6302e7
--- /dev/null
+++ b/crates/pecos-mwpf/Cargo.toml
@@ -0,0 +1,25 @@
+[package]
+name = "pecos-mwpf"
+version.workspace = true
+edition.workspace = true
+readme = "README.md"
+authors.workspace = true
+homepage.workspace = true
+repository.workspace = true
+license.workspace = true
+keywords.workspace = true
+categories.workspace = true
+description = "MWPF hypergraph decoder for PECOS"
+
+[dependencies]
+pecos-decoder-core.workspace = true
+ndarray.workspace = true
+thiserror.workspace = true
+mwpf.workspace = true
+serde_json.workspace = true
+
+[lib]
+name = "pecos_mwpf"
+
+[lints]
+workspace = true
diff --git a/crates/pecos-mwpf/README.md b/crates/pecos-mwpf/README.md
new file mode 100644
index 000000000..9772ce17f
--- /dev/null
+++ b/crates/pecos-mwpf/README.md
@@ -0,0 +1,16 @@
+# pecos-mwpf
+
+PECOS wrapper for the [MWPF (Minimum-Weight Parity Factor)](https://github.com/yuewuo/mwpf) hypergraph decoder by Yue Wu (Yale).
+
+Unlike MWPM decoders (PyMatching, Fusion Blossom), MWPF handles hyperedges natively. This means it can decode Y errors, depolarizing noise, color codes, and small QLDPC codes with higher accuracy than graph-based decoders that must decompose hyperedges.
+
+The tradeoff is a heavier worst-case latency tail. MWPF is best suited for offline benchmarks, correlated-noise studies, and accuracy-first decoding.
+
+## Key configuration
+
+- `cluster_node_limit` (default 50): Controls accuracy vs speed. Lower values are faster.
+- `timeout`: Optional solver timeout in seconds.
+
+## License
+
+MWPF is MIT-licensed. This wrapper is Apache-2.0-licensed as part of PECOS.
diff --git a/crates/pecos-mwpf/src/core_traits.rs b/crates/pecos-mwpf/src/core_traits.rs
new file mode 100644
index 000000000..fe7922ccb
--- /dev/null
+++ b/crates/pecos-mwpf/src/core_traits.rs
@@ -0,0 +1,31 @@
+// Copyright 2026 The PECOS Developers
+//
+// Licensed under the Apache License, Version 2.0 (the "License"); you may not use this file except
+// in compliance with the License. You may obtain a copy of the License at
+//
+//     https://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software distributed under the License
+// is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express
+// or implied. See the License for the specific language governing permissions and limitations under
+// the License.
+
+//! Implementation of core decoder traits for MWPF
+
+use crate::decoder::MwpfDecoder;
+
+/// Implement `ObservableDecoder` for `MwpfDecoder`.
+///
+/// This is the primary trait used by the fast decode path
+/// (`SampleBatch.decode_count`, `sample_decode_count`, etc.).
+impl pecos_decoder_core::ObservableDecoder for MwpfDecoder {
+    fn decode_to_observables(
+        &mut self,
+        syndrome: &[u8],
+    ) -> std::result::Result<u64, pecos_decoder_core::DecoderError> {
+        let result = self
+            .decode_syndrome(syndrome)
+            .map_err(|e| pecos_decoder_core::DecoderError::DecodingFailed(e.to_string()))?;
+        Ok(result.observable_mask)
+    }
+}
diff --git a/crates/pecos-mwpf/src/decoder.rs b/crates/pecos-mwpf/src/decoder.rs
new file mode 100644
index 000000000..244fa6edf
--- /dev/null
+++ b/crates/pecos-mwpf/src/decoder.rs
@@ -0,0 +1,337 @@
+// Copyright 2026 The PECOS Developers
+//
+// Licensed under the Apache License, Version 2.0 (the "License"); you may not use this file except
+// in compliance with the License. You may obtain a copy of the License at
+//
+//     https://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software distributed under the License
+// is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express
+// or implied. See the License for the specific language governing permissions and limitations under
+// the License.
+
+//! MWPF hypergraph decoder implementation
+//!
+//! Wraps the Minimum-Weight Parity Factor solver by Yue Wu (Yale).
+//! Unlike MWPM decoders, MWPF handles hyperedges natively -- it does not
+//! need graphlike decomposition, so it can decode Y errors, depolarizing
+//! noise, color codes, and small QLDPC codes with higher accuracy.
+
+use crate::errors::{MwpfError, Result};
+use mwpf::mwpf_solver::{
+    SolverBPWrapper, SolverBase, SolverSerialJointSingleHair, SolverSerialSingleHair,
+    SolverSerialUnionFind, SolverTrait,
+};
+use mwpf::util::{HyperEdge, SolverInitializer, SyndromePattern};
+use pecos_decoder_core::dem::DemCheckMatrix;
+use std::collections::BTreeMap;
+use std::sync::Arc;
+
+/// Which MWPF solver variant to use.
+#[derive(Debug, Clone, Copy, Default)]
+pub enum MwpfSolverType {
+    /// Union-find only -- fastest, lowest accuracy.
+    UnionFind,
+    /// Single hair plugin pass -- moderate speed and accuracy.
+    SingleHair,
+    /// BP preprocessing + `JointSingleHair`. BP guides the solver to
+    /// converge faster while maintaining accuracy.
+    BpHybrid,
+    /// Joint single hair with repeated optimization -- best accuracy, slowest.
+    #[default]
+    JointSingleHair,
+}
+
+/// Configuration for the MWPF decoder.
+///
+/// MWPF has three knobs at the solver level:
+/// - `cluster_node_limit`: controls optimization depth (accuracy vs speed)
+/// - `timeout`: wall-clock cap, falls back to union-find on expiry
+/// - `only_solve_primal_once`: skip intermediate primal solutions
+#[derive(Debug, Clone, Copy)]
+pub struct MwpfConfig {
+    /// Which solver variant to use. Default: `JointSingleHair` (best accuracy).
+    pub solver_type: MwpfSolverType,
+
+    /// Maximum number of nodes per cluster during optimization.
+    /// Lower values are faster but less accurate.
+    /// Default: 50 (paper's sweet spot for d=7 circuit-level).
+    pub cluster_node_limit: usize,
+
+    /// Timeout in seconds for the solver. When exceeded, the solver stops
+    /// optimizing and returns the best solution found so far (union-find
+    /// baseline). `None` means no timeout.
+    ///
+    /// Setting this is the main way to tame the p99 latency tail.
+    pub timeout: Option<f64>,
+
+    /// If true, solve the primal only once at the end instead of after each
+    /// plugin iteration. Can be faster at the cost of missing local optima.
+    pub only_solve_primal_once: bool,
+}
+
+impl Default for MwpfConfig {
+    fn default() -> Self {
+        Self {
+            solver_type: MwpfSolverType::default(),
+            cluster_node_limit: 50,
+            timeout: None,
+            only_solve_primal_once: false,
+        }
+    }
+}
+
+impl MwpfConfig {
+    /// Build the `serde_json` config object for the MWPF solver.
+    fn to_solver_config(self) -> serde_json::Value {
+        let mut map = serde_json::Map::new();
+        map.insert(
+            "cluster_node_limit".to_string(),
+            serde_json::Number::from(self.cluster_node_limit).into(),
+        );
+        if let Some(t) = self.timeout
+            && let Some(n) = serde_json::Number::from_f64(t)
+        {
+            map.insert("timeout".to_string(), serde_json::Value::Number(n));
+        }
+        if self.only_solve_primal_once {
+            map.insert("only_solve_primal_once".to_string(), true.into());
+        }
+        serde_json::Value::Object(map)
+    }
+}
+
+/// Decoding result from the MWPF decoder.
+#[derive(Debug, Clone)]
+pub struct MwpfDecodingResult {
+    /// Observable prediction as a bitmask (bit i set = observable i flipped).
+    pub observable_mask: u64,
+    /// Edge indices in the solution subgraph.
+    pub subgraph: Vec<usize>,
+}
+
+/// Internal solver enum holding any MWPF solver variant.
+#[allow(clippy::large_enum_variant)] // Solver structs are owned to avoid extra solver indirection.
+enum Solver {
+    UnionFind(SolverSerialUnionFind),
+    SingleHair(SolverSerialSingleHair),
+    JointSingleHair(SolverSerialJointSingleHair),
+    BpHybrid(SolverBPWrapper),
+}
+
+struct EdgeInfo {
+    prob: f64,
+    obs_mask: u64,
+    best_prob: f64,
+}
+
+impl Solver {
+    fn solve(&mut self, syndrome: SyndromePattern) {
+        match self {
+            Self::UnionFind(s) => s.solve(syndrome),
+            Self::SingleHair(s) => s.solve(syndrome),
+            Self::JointSingleHair(s) => s.solve(syndrome),
+            Self::BpHybrid(s) => s.solve(syndrome),
+        }
+    }
+
+    fn subgraph(&mut self) -> mwpf::util::OutputSubgraph {
+        match self {
+            Self::UnionFind(s) => s.subgraph(),
+            Self::SingleHair(s) => s.subgraph(),
+            Self::JointSingleHair(s) => s.subgraph(),
+            Self::BpHybrid(s) => s.subgraph(),
+        }
+    }
+
+    fn clear(&mut self) {
+        match self {
+            Self::UnionFind(s) => s.clear(),
+            Self::SingleHair(s) => s.clear(),
+            Self::JointSingleHair(s) => s.clear(),
+            Self::BpHybrid(s) => s.clear(),
+        }
+    }
+}
+
+/// MWPF hypergraph decoder.
+///
+/// Constructed from a full (non-decomposed) DEM string. Each error mechanism
+/// in the DEM becomes one hyperedge in the solver, preserving correlations
+/// that MWPM decoders must decompose away.
+pub struct MwpfDecoder {
+    /// The MWPF solver instance.
+    solver: Solver,
+    /// Per-edge observable bitmask (indexed by deduped edge index).
+    edge_obs: Vec<u64>,
+    /// Number of detectors.
+    num_detectors: usize,
+    /// Reusable buffer for defect vertices (avoids per-shot allocation).
+    defect_buf: Vec<usize>,
+}
+
+impl MwpfDecoder {
+    /// Create a decoder from a DEM string and configuration.
+    ///
+    /// The DEM should be full (non-decomposed) to preserve hyperedges.
+    ///
+    /// # Errors
+    ///
+    /// Returns `MwpfError` if the DEM is malformed or the solver cannot be
+    /// constructed.
+    pub fn from_dem(dem_str: &str, config: MwpfConfig) -> Result<Self> {
+        let dem = DemCheckMatrix::from_dem_str(dem_str)
+            .map_err(|e| MwpfError::InvalidDem(e.to_string()))?;
+
+        // Build hyperedges from the check matrix. Each mechanism (column) becomes
+        // one HyperEdge with all its incident detectors.
+        // Merge duplicate vertex sets and build per-edge observable masks.
+        // Decomposed DEMs can have multiple mechanisms with the same detector set.
+        // Merge by combining probabilities (independent union) and tracking the
+        // observable from the highest-probability mechanism (first-observable-wins).
+        let mut edge_map: BTreeMap<Vec<usize>, EdgeInfo> = BTreeMap::new();
+        for m in 0..dem.num_mechanisms {
+            let p = dem.error_priors[m];
+            if p <= 0.0 {
+                continue;
+            }
+
+            let vertices: Vec<usize> = (0..dem.num_detectors)
+                .filter(|&d| dem.check_matrix[[d, m]] != 0)
+                .collect();
+
+            if vertices.is_empty() {
+                continue;
+            }
+
+            // Compute this mechanism's observable mask.
+            let mut obs: u64 = 0;
+            for o in 0..dem.num_observables {
+                if dem.observable_matrix[[o, m]] != 0 {
+                    obs |= 1 << o;
+                }
+            }
+
+            let entry = edge_map.entry(vertices).or_insert(EdgeInfo {
+                prob: 0.0,
+                obs_mask: obs,
+                best_prob: p,
+            });
+            let old_p = entry.prob;
+            entry.prob = old_p + p - old_p * p;
+            if p > entry.best_prob {
+                entry.obs_mask = obs;
+                entry.best_prob = p;
+            }
+        }
+
+        let mut hyperedges = Vec::with_capacity(edge_map.len());
+        let mut edge_obs = Vec::with_capacity(edge_map.len());
+        for (vertices, info) in edge_map {
+            let weight = if info.prob < 1.0 {
+                ((1.0 - info.prob) / info.prob).ln()
+            } else {
+                0.0
+            };
+            hyperedges.push(HyperEdge::new(vertices, weight.into()));
+            edge_obs.push(info.obs_mask);
+        }
+
+        let initializer = Arc::new(SolverInitializer::new(dem.num_detectors, hyperedges));
+        let solver_config = config.to_solver_config();
+        let solver = match config.solver_type {
+            MwpfSolverType::UnionFind => {
+                Solver::UnionFind(SolverSerialUnionFind::new(&initializer, solver_config))
+            }
+            MwpfSolverType::SingleHair => {
+                Solver::SingleHair(SolverSerialSingleHair::new(&initializer, solver_config))
+            }
+            MwpfSolverType::JointSingleHair => Solver::JointSingleHair(
+                SolverSerialJointSingleHair::new(&initializer, solver_config),
+            ),
+            MwpfSolverType::BpHybrid => {
+                let base = SolverBase {
+                    inner: mwpf::mwpf_solver::SolverEnum::SolverSerialJointSingleHair(
+                        SolverSerialJointSingleHair::new(&initializer, solver_config),
+                    ),
+                };
+                // BP with 50 iterations and 0.5 application ratio (paper defaults).
+                Solver::BpHybrid(SolverBPWrapper::new(base, 50, 0.5))
+            }
+        };
+
+        Ok(Self {
+            solver,
+            edge_obs,
+            num_detectors: dem.num_detectors,
+            defect_buf: Vec::new(),
+        })
+    }
+
+    /// Decode a syndrome and return the observable mask.
+    ///
+    /// The syndrome is a byte slice of length `num_detectors`, where
+    /// non-zero entries indicate triggered detectors.
+    ///
+    /// # Errors
+    ///
+    /// Returns `MwpfError::DecodingFailed` if decoding fails.
+    pub fn decode_syndrome(&mut self, syndrome: &[u8]) -> Result<MwpfDecodingResult> {
+        // Reuse defect buffer across shots
+        self.defect_buf.clear();
+        for (i, &v) in syndrome.iter().enumerate() {
+            if v != 0 {
+                self.defect_buf.push(i);
+            }
+        }
+
+        if self.defect_buf.is_empty() {
+            return Ok(MwpfDecodingResult {
+                observable_mask: 0,
+                subgraph: Vec::new(),
+            });
+        }
+
+        self.solver
+            .solve(SyndromePattern::new_vertices(self.defect_buf.clone()));
+        let output = self.solver.subgraph();
+        self.solver.clear();
+
+        // Compute observable mask from the correction subgraph.
+        let mut observable_mask = 0u64;
+        for &edge_idx in &output.subgraph {
+            if edge_idx < self.edge_obs.len() {
+                observable_mask ^= self.edge_obs[edge_idx];
+            }
+        }
+
+        Ok(MwpfDecodingResult {
+            observable_mask,
+            subgraph: output.subgraph,
+        })
+    }
+
+    /// Number of detectors in the model.
+    #[must_use]
+    pub fn num_detectors(&self) -> usize {
+        self.num_detectors
+    }
+
+    /// Number of edges in the model (after deduplication).
+    #[must_use]
+    pub fn num_edges(&self) -> usize {
+        self.edge_obs.len()
+    }
+
+    /// Number of observables in the model.
+    #[must_use]
+    pub fn num_observables(&self) -> usize {
+        let mut max_bit = 0usize;
+        for &obs in &self.edge_obs {
+            if obs != 0 {
+                max_bit = max_bit.max(64 - obs.leading_zeros() as usize);
+            }
+        }
+        max_bit
+    }
+}
diff --git a/crates/pecos-mwpf/src/errors.rs b/crates/pecos-mwpf/src/errors.rs
new file mode 100644
index 000000000..dd95cfd6b
--- /dev/null
+++ b/crates/pecos-mwpf/src/errors.rs
@@ -0,0 +1,46 @@
+// Copyright 2026 The PECOS Developers
+//
+// Licensed under the Apache License, Version 2.0 (the "License"); you may not use this file except
+// in compliance with the License. You may obtain a copy of the License at
+//
+//     https://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software distributed under the License
+// is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express
+// or implied. See the License for the specific language governing permissions and limitations under
+// the License.
+
+//! Error types for the MWPF decoder
+
+use thiserror::Error;
+
+/// Error type for MWPF operations
+#[derive(Error, Debug)]
+pub enum MwpfError {
+    /// Configuration error
+    #[error("Configuration error: {0}")]
+    Configuration(String),
+
+    /// Decoding failed
+    #[error("Decoding failed: {0}")]
+    DecodingFailed(String),
+
+    /// Invalid DEM format
+    #[error("Invalid DEM: {0}")]
+    InvalidDem(String),
+}
+
+/// Result type for MWPF operations
+pub type Result<T> = std::result::Result<T, MwpfError>;
+
+/// Convert `MwpfError` to `DecoderError`
+impl From<MwpfError> for pecos_decoder_core::DecoderError {
+    fn from(e: MwpfError) -> Self {
+        match e {
+            MwpfError::Configuration(msg) | MwpfError::InvalidDem(msg) => {
+                pecos_decoder_core::DecoderError::InvalidConfiguration(msg)
+            }
+            MwpfError::DecodingFailed(msg) => pecos_decoder_core::DecoderError::DecodingFailed(msg),
+        }
+    }
+}
diff --git a/crates/pecos-mwpf/src/lib.rs b/crates/pecos-mwpf/src/lib.rs
new file mode 100644
index 000000000..81f301876
--- /dev/null
+++ b/crates/pecos-mwpf/src/lib.rs
@@ -0,0 +1,36 @@
+// Copyright 2026 The PECOS Developers
+//
+// Licensed under the Apache License, Version 2.0 (the "License"); you may not use this file except
+// in compliance with the License. You may obtain a copy of the License at
+//
+//     https://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software distributed under the License
+// is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express
+// or implied. See the License for the specific language governing permissions and limitations under
+// the License.
+
+//! MWPF hypergraph decoder module
+//!
+//! This module provides Rust bindings for the Minimum-Weight Parity Factor
+//! decoder for quantum error correction. Unlike MWPM decoders, MWPF handles
+//! hyperedges natively -- it can decode Y errors, depolarizing noise, color
+//! codes, and small QLDPC codes with higher accuracy than graphlike decoders.
+//!
+//! Tradeoff: MWPF has a heavier worst-case latency tail than MWPM. Good for
+//! offline benchmarks, correlated-noise studies, and accuracy-first decoding.
+
+// Allow casts between float/int for weight conversions
+#![allow(
+    clippy::cast_possible_truncation,
+    clippy::cast_precision_loss,
+    clippy::cast_sign_loss
+)]
+
+pub mod core_traits;
+pub mod decoder;
+pub mod errors;
+
+// Re-export main types
+pub use decoder::{MwpfConfig, MwpfDecoder, MwpfDecodingResult, MwpfSolverType};
+pub use errors::MwpfError;
diff --git a/crates/pecos-mwpf/tests/basic.rs b/crates/pecos-mwpf/tests/basic.rs
new file mode 100644
index 000000000..6f3172cb8
--- /dev/null
+++ b/crates/pecos-mwpf/tests/basic.rs
@@ -0,0 +1,112 @@
+// Copyright 2026 The PECOS Developers
+//
+// Licensed under the Apache License, Version 2.0 (the "License"); you may not use this file except
+// in compliance with the License. You may obtain a copy of the License at
+//
+//     https://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software distributed under the License
+// is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express
+// or implied. See the License for the specific language governing permissions and limitations under
+// the License.
+
+use pecos_decoder_core::ObservableDecoder;
+use pecos_mwpf::{MwpfConfig, MwpfDecoder};
+
+/// Simple repetition-code-like DEM: two detectors, two error mechanisms.
+const SIMPLE_DEM: &str = "\
+error(0.1) D0 D1 L0
+error(0.1) D1
+";
+
+/// A d=3 surface-code-like DEM with a hyperedge (3 detectors).
+const HYPEREDGE_DEM: &str = "\
+error(0.01) D0 D1 L0
+error(0.01) D1 D2
+error(0.01) D0 D1 D2 L0
+error(0.01) D2
+";
+
+#[test]
+fn construct_from_simple_dem() {
+    let decoder = MwpfDecoder::from_dem(SIMPLE_DEM, MwpfConfig::default());
+    assert!(decoder.is_ok());
+    let decoder = decoder.unwrap();
+    assert_eq!(decoder.num_detectors(), 2);
+    assert_eq!(decoder.num_observables(), 1);
+}
+
+#[test]
+fn construct_from_hyperedge_dem() {
+    let decoder = MwpfDecoder::from_dem(HYPEREDGE_DEM, MwpfConfig::default());
+    assert!(decoder.is_ok());
+    let decoder = decoder.unwrap();
+    assert_eq!(decoder.num_detectors(), 3);
+    assert_eq!(decoder.num_observables(), 1);
+}
+
+#[test]
+fn decode_no_errors() {
+    let mut decoder = MwpfDecoder::from_dem(SIMPLE_DEM, MwpfConfig::default()).unwrap();
+    // No detectors triggered -> no observable flips.
+    let syndrome = vec![0u8; 2];
+    let result = decoder.decode_syndrome(&syndrome).unwrap();
+    assert_eq!(result.observable_mask, 0);
+}
+
+#[test]
+fn decode_single_error() {
+    let mut decoder = MwpfDecoder::from_dem(SIMPLE_DEM, MwpfConfig::default()).unwrap();
+    // Both D0 and D1 triggered -> mechanism 0 (D0 D1 L0), observable L0 flips.
+    let syndrome = vec![1u8, 1];
+    let result = decoder.decode_syndrome(&syndrome).unwrap();
+    assert_eq!(result.observable_mask, 1);
+}
+
+#[test]
+fn decode_boundary_error() {
+    let mut decoder = MwpfDecoder::from_dem(SIMPLE_DEM, MwpfConfig::default()).unwrap();
+    // Only D1 triggered -> mechanism 1 (D1, boundary), no observable flip.
+    let syndrome = vec![0u8, 1];
+    let result = decoder.decode_syndrome(&syndrome).unwrap();
+    assert_eq!(result.observable_mask, 0);
+}
+
+#[test]
+fn observable_decoder_trait() {
+    let mut decoder = MwpfDecoder::from_dem(SIMPLE_DEM, MwpfConfig::default()).unwrap();
+    let mask = decoder.decode_to_observables(&[1, 1]).unwrap();
+    assert_eq!(mask, 1);
+}
+
+#[test]
+fn decode_multiple_shots() {
+    // Verify solver reuse works (clear() between shots).
+    let mut decoder = MwpfDecoder::from_dem(SIMPLE_DEM, MwpfConfig::default()).unwrap();
+    for _ in 0..10 {
+        let _ = decoder.decode_syndrome(&[1, 1]).unwrap();
+        let _ = decoder.decode_syndrome(&[0, 1]).unwrap();
+        let _ = decoder.decode_syndrome(&[0, 0]).unwrap();
+    }
+}
+
+#[test]
+fn custom_config() {
+    let config = MwpfConfig {
+        cluster_node_limit: 10,
+        timeout: Some(5.0),
+        ..MwpfConfig::default()
+    };
+    let mut decoder = MwpfDecoder::from_dem(SIMPLE_DEM, config).unwrap();
+    let result = decoder.decode_syndrome(&[1, 1]).unwrap();
+    assert_eq!(result.observable_mask, 1);
+}
+
+#[test]
+fn hyperedge_decode() {
+    let mut decoder = MwpfDecoder::from_dem(HYPEREDGE_DEM, MwpfConfig::default()).unwrap();
+    // All three detectors triggered: the hyperedge mechanism (D0 D1 D2 L0)
+    // is the minimum weight explanation.
+    let result = decoder.decode_syndrome(&[1, 1, 1]).unwrap();
+    assert_eq!(result.observable_mask, 1);
+}
diff --git a/crates/pecos-num/src/array.rs b/crates/pecos-num/src/array.rs
index 31f7430e6..acd6615e1 100644
--- a/crates/pecos-num/src/array.rs
+++ b/crates/pecos-num/src/array.rs
@@ -358,6 +358,46 @@ pub fn linspace(start: f64, stop: f64, num: usize, endpoint: bool) -> Array1<f64
     result
 }
 
+/// Generate geometrically spaced values between `start` and `stop`.
+///
+/// This is a Rust implementation of `numpy.geomspace()`. Values are evenly
+/// spaced on a log scale between `start` and `stop`. Both `start` and `stop`
+/// must be positive.
+///
+/// # Arguments
+///
+/// * `start` - Start value (must be positive)
+/// * `stop` - End value (must be positive)
+/// * `num` - Number of values to generate
+/// * `endpoint` - Whether to include the stop value
+///
+/// # Examples
+///
+/// ```
+/// use pecos_num::array::geomspace;
+///
+/// let values = geomspace(1e-4, 1e-2, 5, true);
+/// assert_eq!(values.len(), 5);
+/// assert!((values[0] - 1e-4).abs() < 1e-10);
+/// assert!((values[4] - 1e-2).abs() < 1e-10);
+/// ```
+///
+/// # Panics
+///
+/// Panics if `start` or `stop` is not positive.
+pub fn geomspace(start: f64, stop: f64, num: usize, endpoint: bool) -> Array1<f64> {
+    assert!(
+        start > 0.0,
+        "geomspace: start must be positive, got {start}"
+    );
+    assert!(stop > 0.0, "geomspace: stop must be positive, got {stop}");
+
+    let log_start = start.ln();
+    let log_stop = stop.ln();
+    let log_values = linspace(log_start, log_stop, num, endpoint);
+    log_values.mapv(f64::exp)
+}
+
 // Note: sum() for slices removed - use values.iter().sum() directly (idiomatic Rust)
 // sum_axis() below is kept for multi-dimensional operations
 
diff --git a/crates/pecos-num/src/lib.rs b/crates/pecos-num/src/lib.rs
index 180c78c92..e95d1dbd3 100644
--- a/crates/pecos-num/src/lib.rs
+++ b/crates/pecos-num/src/lib.rs
@@ -46,6 +46,7 @@ pub mod polynomial;
 pub mod prelude;
 pub mod random;
 pub mod stats;
+pub mod z2_linalg;
 
 pub use compare::{allclose, relative_eq};
 pub use curve_fit::{CurveFitError, CurveFitOptions, CurveFitResult, curve_fit};
diff --git a/crates/pecos-num/src/prelude.rs b/crates/pecos-num/src/prelude.rs
index 5ea6129d5..b8e0044bb 100644
--- a/crates/pecos-num/src/prelude.rs
+++ b/crates/pecos-num/src/prelude.rs
@@ -99,8 +99,8 @@ pub use num_complex::{Complex, Complex32, Complex64};
 // Re-export array operations
 // Note: sum() for slices removed - use .iter().sum() directly (idiomatic Rust)
 pub use crate::array::{
-    arange, broadcast_shapes, broadcast_to, delete, diag, diag_matrix, linspace, ones, sum_axis,
-    zeros,
+    arange, broadcast_shapes, broadcast_to, delete, diag, diag_matrix, geomspace, linspace, ones,
+    sum_axis, zeros,
 };
 
 // Re-export graph types and algorithms
diff --git a/crates/pecos-num/src/z2_linalg.rs b/crates/pecos-num/src/z2_linalg.rs
new file mode 100644
index 000000000..7c91088f4
--- /dev/null
+++ b/crates/pecos-num/src/z2_linalg.rs
@@ -0,0 +1,264 @@
+// Copyright 2026 The PECOS Developers
+//
+// Licensed under the Apache License, Version 2.0 (the "License"); you may not use this file except
+// in compliance with the License. You may obtain a copy of the License at
+//
+//     https://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software distributed under the License
+// is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express
+// or implied. See the License for the specific language governing permissions and limitations under
+// the License.
+
+//! Sparse linear algebra over `Z_2` (GF(2)).
+//!
+//! Operations on binary vectors and matrices represented as sorted index
+//! sets. This is the natural representation for QEC detector definitions
+//! where each detector is an XOR (sum mod 2) of a small number of
+//! measurements.
+//!
+//! # Representation
+//!
+//! A `Z_2` vector is a sorted `Vec<usize>` of indices where the vector has
+//! value 1. Addition (XOR) is computed as sorted-merge symmetric difference.
+//! A `Z_2` matrix is a `Vec<Vec<usize>>` of row vectors.
+//!
+//! # Example
+//!
+//! ```
+//! use pecos_num::z2_linalg::{z2_rank, z2_xor};
+//!
+//! // Three detectors: D0=[0], D1=[1], D2=[0,1]
+//! // D2 = D0 + D1 → rank should be 2
+//! let rows = vec![vec![0], vec![1], vec![0, 1]];
+//! assert_eq!(z2_rank(&rows), 2);
+//!
+//! // XOR of two sparse vectors
+//! assert_eq!(z2_xor(&[1, 3, 5], &[2, 3, 4]), vec![1, 2, 4, 5]);
+//! ```
+
+use std::collections::BTreeMap;
+
+/// Compute the rank of a binary matrix over `Z_2`.
+///
+/// Each row is a sorted list of column indices where the row has value 1.
+/// Uses sparse Gaussian elimination with leftmost-column pivoting.
+///
+/// Complexity: O(n * k * log(n)) where n is the number of rows and k is
+/// the average number of nonzeros per row. For QEC detectors with k ≈ 2,
+/// this is effectively O(n * log(n)).
+///
+/// # Arguments
+///
+/// * `rows` - Binary matrix as a slice of sorted index vectors.
+///
+/// # Example
+///
+/// ```
+/// use pecos_num::z2_linalg::z2_rank;
+///
+/// // Two independent rows
+/// assert_eq!(z2_rank(&[vec![0], vec![1]]), 2);
+///
+/// // Three rows, one dependent (D2 = D0 + D1)
+/// assert_eq!(z2_rank(&[vec![0, 1], vec![1, 2], vec![0, 2]]), 2);
+/// ```
+#[must_use]
+pub fn z2_rank(rows: &[Vec<usize>]) -> usize {
+    let mut work: Vec<Vec<usize>> = rows.to_vec();
+    let mut pivot_rows: BTreeMap<usize, usize> = BTreeMap::new();
+    let mut rank = 0;
+
+    for i in 0..work.len() {
+        // Reduce row i by XOR-ing with existing pivot rows
+        loop {
+            if work[i].is_empty() {
+                break;
+            }
+            let min_col = work[i][0];
+            if let Some(&pr) = pivot_rows.get(&min_col) {
+                let pivot = work[pr].clone();
+                work[i] = z2_xor(&work[i], &pivot);
+            } else {
+                break;
+            }
+        }
+
+        if !work[i].is_empty() {
+            let min_col = work[i][0];
+            pivot_rows.insert(min_col, i);
+            rank += 1;
+        }
+    }
+
+    rank
+}
+
+/// Compute the rank of detector definitions given as record offsets.
+///
+/// Each record is a list of measurement indices (possibly negative for
+/// Stim-style offsets from the end). Negative offsets are resolved against
+/// `num_measurements`.
+///
+/// # Arguments
+///
+/// * `records` - Detector definitions as record offset lists.
+/// * `num_measurements` - Total number of measurements (for resolving
+///   negative offsets).
+#[must_use]
+pub fn z2_rank_from_records(records: &[Vec<i32>], num_measurements: usize) -> usize {
+    let rows: Vec<Vec<usize>> = records
+        .iter()
+        .map(|record| {
+            let mut indices: Vec<usize> = record
+                .iter()
+                .filter_map(|&offset| {
+                    let abs = if offset < 0 {
+                        num_measurements.checked_sub(offset.unsigned_abs() as usize)?
+                    } else {
+                        offset.unsigned_abs() as usize
+                    };
+                    (abs < num_measurements).then_some(abs)
+                })
+                .collect();
+            indices.sort_unstable();
+            indices.dedup();
+            indices
+        })
+        .collect();
+
+    z2_rank(&rows)
+}
+
+/// XOR (symmetric difference) of two sorted `Z_2` vectors.
+///
+/// Both inputs must be sorted and deduplicated. The result is also sorted
+/// and deduplicated.
+///
+/// # Example
+///
+/// ```
+/// use pecos_num::z2_linalg::z2_xor;
+///
+/// assert_eq!(z2_xor(&[1, 3, 5], &[2, 3, 4]), vec![1, 2, 4, 5]);
+/// assert_eq!(z2_xor(&[0, 1], &[0, 1]), Vec::<usize>::new());
+/// assert_eq!(z2_xor(&[], &[1, 2, 3]), vec![1, 2, 3]);
+/// ```
+#[must_use]
+pub fn z2_xor(a: &[usize], b: &[usize]) -> Vec<usize> {
+    let mut result = Vec::with_capacity(a.len() + b.len());
+    let (mut i, mut j) = (0, 0);
+
+    while i < a.len() && j < b.len() {
+        match a[i].cmp(&b[j]) {
+            std::cmp::Ordering::Less => {
+                result.push(a[i]);
+                i += 1;
+            }
+            std::cmp::Ordering::Greater => {
+                result.push(b[j]);
+                j += 1;
+            }
+            std::cmp::Ordering::Equal => {
+                i += 1;
+                j += 1;
+            }
+        }
+    }
+
+    result.extend_from_slice(&a[i..]);
+    result.extend_from_slice(&b[j..]);
+    result
+}
+
+/// Check if a set of `Z_2` row vectors are linearly independent.
+///
+/// # Example
+///
+/// ```
+/// use pecos_num::z2_linalg::z2_are_independent;
+///
+/// assert!(z2_are_independent(&[vec![0], vec![1]]));
+/// assert!(!z2_are_independent(&[vec![0], vec![1], vec![0, 1]]));
+/// ```
+#[must_use]
+pub fn z2_are_independent(rows: &[Vec<usize>]) -> bool {
+    z2_rank(rows) == rows.len()
+}
+
+#[cfg(test)]
+mod tests {
+    use super::*;
+
+    #[test]
+    fn rank_empty() {
+        assert_eq!(z2_rank(&[]), 0);
+    }
+
+    #[test]
+    fn rank_single() {
+        assert_eq!(z2_rank(&[vec![0]]), 1);
+    }
+
+    #[test]
+    fn rank_independent() {
+        assert_eq!(z2_rank(&[vec![0], vec![1], vec![2]]), 3);
+    }
+
+    #[test]
+    fn rank_dependent() {
+        assert_eq!(z2_rank(&[vec![0], vec![1], vec![0, 1]]), 2);
+    }
+
+    #[test]
+    fn rank_all_identical() {
+        assert_eq!(z2_rank(&[vec![0, 1], vec![0, 1], vec![0, 1]]), 1);
+    }
+
+    #[test]
+    fn rank_chain_dependent() {
+        // D0=[0,1], D1=[1,2], D2=[0,2] → D2 = D0 + D1 → rank 2
+        assert_eq!(z2_rank(&[vec![0, 1], vec![1, 2], vec![0, 2]]), 2);
+    }
+
+    #[test]
+    fn rank_large_sparse() {
+        let rows: Vec<Vec<usize>> = (0..1000).map(|i| vec![i]).collect();
+        assert_eq!(z2_rank(&rows), 1000);
+    }
+
+    #[test]
+    fn rank_from_records_negative_offsets() {
+        let records = vec![vec![-1i32], vec![-2]];
+        assert_eq!(z2_rank_from_records(&records, 10), 2);
+    }
+
+    #[test]
+    fn rank_from_records_dependent() {
+        let records = vec![vec![0i32], vec![1], vec![0, 1]];
+        assert_eq!(z2_rank_from_records(&records, 10), 2);
+    }
+
+    #[test]
+    fn xor_basic() {
+        assert_eq!(z2_xor(&[1, 3, 5], &[2, 3, 4]), vec![1, 2, 4, 5]);
+    }
+
+    #[test]
+    fn xor_cancel() {
+        assert_eq!(z2_xor(&[1, 2], &[1, 2]), Vec::<usize>::new());
+    }
+
+    #[test]
+    fn xor_empty() {
+        assert_eq!(z2_xor(&[], &[1, 2]), vec![1, 2]);
+        assert_eq!(z2_xor(&[1, 2], &[]), vec![1, 2]);
+    }
+
+    #[test]
+    fn independence_check() {
+        assert!(z2_are_independent(&[vec![0], vec![1]]));
+        assert!(!z2_are_independent(&[vec![0], vec![1], vec![0, 1]]));
+        assert!(z2_are_independent(&[]));
+    }
+}
diff --git a/crates/pecos-phir-json/src/v0_1/ast.rs b/crates/pecos-phir-json/src/v0_1/ast.rs
index 4f565dfc9..2a81b0aff 100644
--- a/crates/pecos-phir-json/src/v0_1/ast.rs
+++ b/crates/pecos-phir-json/src/v0_1/ast.rs
@@ -1,4 +1,4 @@
-use serde::{Deserialize, Deserializer};
+use serde::Deserialize;
 use std::collections::BTreeMap;
 use std::f64::consts::PI;
 
@@ -12,9 +12,13 @@ pub struct PHIRProgram {
     pub ops: Vec<Operation>,
 }
 
-/// Represents an operation in the PHIR program
-#[derive(Debug, Deserialize, Clone)]
-#[serde(untagged)]
+/// Represents an operation in the PHIR program.
+///
+/// Deserialized via a manual `Deserialize` impl that inspects which discriminating
+/// key is present (`qop`, `cop`, `block`, `mop`, `meta`, `data`, `//`).
+/// This avoids `#[serde(untagged)]` whose `ContentDeserializer` can silently fail
+/// with certain nested types (serde issue 1183).
+#[derive(Debug, Clone)]
 pub enum Operation {
     /// Variable definition for quantum or classical variables
     VariableDefinition {
@@ -22,63 +26,45 @@ pub enum Operation {
         data_type: String,
         variable: String,
         /// Size in bits. Optional -- if omitted, inferred from `data_type`.
-        #[serde(default)]
         size: Option<usize>,
     },
     /// Quantum operation (gates, measurements)
     QuantumOp {
         qop: String,
-        #[serde(default)]
-        #[serde(deserialize_with = "deserialize_angles_to_radians")]
-        angles: Option<Vec<f64>>, // Now just Vec<f64> in radians, no unit string
+        /// Angles in radians (converted from the JSON `[[values...], "unit"]` format)
+        angles: Option<Vec<f64>>,
         args: Vec<QubitArg>,
-        #[serde(default)]
         returns: Vec<(String, usize)>,
-        #[serde(default)]
         metadata: Option<BTreeMap<String, serde_json::Value>>,
     },
     /// Classical operation (e.g., Result for exporting values)
     ClassicalOp {
         cop: String,
-        #[serde(default)]
         args: Vec<ArgItem>,
-        #[serde(default)]
         returns: Vec<ArgItem>,
-        #[serde(default)]
         metadata: Option<BTreeMap<String, serde_json::Value>>,
-        #[serde(default, skip_serializing_if = "Option::is_none")]
-        function: Option<String>, // For ffcall
+        function: Option<String>,
     },
     /// Block operation (e.g., sequence, qparallel, if)
     Block {
         block: String,
-        #[serde(default)]
         ops: Vec<Operation>,
-        #[serde(default)]
         condition: Option<Expression>,
-        #[serde(default)]
         true_branch: Option<Vec<Operation>>,
-        #[serde(default)]
         false_branch: Option<Vec<Operation>>,
-        #[serde(default)]
         metadata: Option<BTreeMap<String, serde_json::Value>>,
     },
     /// Machine operation (e.g., Idle, Transport)
     MachineOp {
         mop: String,
-        #[serde(default)]
         args: Option<Vec<QubitArg>>,
-        #[serde(default)]
         duration: Option<(f64, String)>,
-        #[serde(default)]
         metadata: Option<BTreeMap<String, serde_json::Value>>,
     },
     /// Meta instruction (e.g., barrier)
     MetaInstruction {
         meta: String,
-        #[serde(default)]
         args: Vec<(String, usize)>,
-        #[serde(default)]
         metadata: Option<BTreeMap<String, serde_json::Value>>,
     },
     /// Data export (`cvar_export`) -- specifies which variables to export
@@ -87,10 +73,249 @@ pub enum Operation {
         variables: Vec<String>,
     },
     /// Comment
-    Comment {
-        #[serde(rename = "//")]
-        comment: String,
-    },
+    Comment { comment: String },
+}
+
+// ---------------------------------------------------------------------------
+// Manual Deserialize for Operation -- key-based dispatch on serde_json::Value
+// ---------------------------------------------------------------------------
+
+/// Convert raw JSON angles `[[values...], "unit"]` to radians.
+fn convert_angles(raw: &serde_json::Value) -> Result<Option<Vec<f64>>, String> {
+    if raw.is_null() {
+        return Ok(None);
+    }
+    let arr = raw.as_array().ok_or("angles: expected array")?;
+    if arr.len() != 2 {
+        return Err(format!(
+            "angles: expected [values, unit], got {} elements",
+            arr.len()
+        ));
+    }
+    let values = arr[0]
+        .as_array()
+        .ok_or("angles: first element must be an array of numbers")?
+        .iter()
+        .map(|v| {
+            v.as_f64()
+                .ok_or_else(|| format!("angles: expected number, got {v}"))
+        })
+        .collect::<Result<Vec<f64>, _>>()?;
+    let unit = arr[1]
+        .as_str()
+        .ok_or("angles: second element must be a string")?;
+    match unit {
+        "rad" => Ok(Some(values)),
+        "deg" => Ok(Some(values.into_iter().map(|v| v * PI / 180.0).collect())),
+        "pi" => Ok(Some(values.into_iter().map(|v| v * PI).collect())),
+        _ => Err(format!("Unsupported angle unit: {unit}")),
+    }
+}
+
+/// Helper: extract optional metadata from a JSON object.
+fn extract_metadata(
+    obj: &serde_json::Map<String, serde_json::Value>,
+) -> Option<BTreeMap<String, serde_json::Value>> {
+    obj.get("metadata").and_then(|v| {
+        if v.is_null() {
+            None
+        } else {
+            serde_json::from_value(v.clone()).ok()
+        }
+    })
+}
+
+impl<'de> Deserialize<'de> for Operation {
+    fn deserialize<D>(deserializer: D) -> Result<Self, D::Error>
+    where
+        D: serde::Deserializer<'de>,
+    {
+        use serde::de::Error;
+
+        let val = serde_json::Value::deserialize(deserializer)?;
+        let obj = val
+            .as_object()
+            .ok_or_else(|| D::Error::custom("operation must be a JSON object"))?;
+
+        // Dispatch on the discriminating key
+        if let Some(qop_val) = obj.get("qop") {
+            // QuantumOp
+            let qop = qop_val
+                .as_str()
+                .ok_or_else(|| D::Error::custom("qop must be a string"))?
+                .to_string();
+            let angles = obj
+                .get("angles")
+                .map_or(Ok(None), convert_angles)
+                .map_err(D::Error::custom)?;
+            let args: Vec<QubitArg> = obj
+                .get("args")
+                .map_or(Ok(vec![]), |v| serde_json::from_value(v.clone()))
+                .map_err(|e| D::Error::custom(format!("args: {e}")))?;
+            let returns: Vec<(String, usize)> = obj
+                .get("returns")
+                .map_or(Ok(vec![]), |v| serde_json::from_value(v.clone()))
+                .map_err(|e| D::Error::custom(format!("returns: {e}")))?;
+            let metadata = extract_metadata(obj);
+            Ok(Operation::QuantumOp {
+                qop,
+                angles,
+                args,
+                returns,
+                metadata,
+            })
+        } else if let Some(cop_val) = obj.get("cop") {
+            // ClassicalOp
+            let cop = cop_val
+                .as_str()
+                .ok_or_else(|| D::Error::custom("cop must be a string"))?
+                .to_string();
+            let args: Vec<ArgItem> = obj
+                .get("args")
+                .map_or(Ok(vec![]), |v| serde_json::from_value(v.clone()))
+                .map_err(|e| D::Error::custom(format!("args: {e}")))?;
+            let returns: Vec<ArgItem> = obj
+                .get("returns")
+                .map_or(Ok(vec![]), |v| serde_json::from_value(v.clone()))
+                .map_err(|e| D::Error::custom(format!("returns: {e}")))?;
+            let metadata = extract_metadata(obj);
+            let function: Option<String> = obj
+                .get("function")
+                .and_then(|v| v.as_str().map(String::from));
+            Ok(Operation::ClassicalOp {
+                cop,
+                args,
+                returns,
+                metadata,
+                function,
+            })
+        } else if let Some(block_val) = obj.get("block") {
+            // Block
+            let block = block_val
+                .as_str()
+                .ok_or_else(|| D::Error::custom("block must be a string"))?
+                .to_string();
+            let ops: Vec<Operation> = obj
+                .get("ops")
+                .map_or(Ok(vec![]), |v| serde_json::from_value(v.clone()))
+                .map_err(|e| D::Error::custom(format!("ops: {e}")))?;
+            let condition: Option<Expression> = obj
+                .get("condition")
+                .filter(|v| !v.is_null())
+                .map(|v| serde_json::from_value(v.clone()))
+                .transpose()
+                .map_err(|e| D::Error::custom(format!("condition: {e}")))?;
+            let true_branch: Option<Vec<Operation>> = obj
+                .get("true_branch")
+                .filter(|v| !v.is_null())
+                .map(|v| serde_json::from_value(v.clone()))
+                .transpose()
+                .map_err(|e| D::Error::custom(format!("true_branch: {e}")))?;
+            let false_branch: Option<Vec<Operation>> = obj
+                .get("false_branch")
+                .filter(|v| !v.is_null())
+                .map(|v| serde_json::from_value(v.clone()))
+                .transpose()
+                .map_err(|e| D::Error::custom(format!("false_branch: {e}")))?;
+            let metadata = extract_metadata(obj);
+            Ok(Operation::Block {
+                block,
+                ops,
+                condition,
+                true_branch,
+                false_branch,
+                metadata,
+            })
+        } else if let Some(mop_val) = obj.get("mop") {
+            // MachineOp
+            let mop = mop_val
+                .as_str()
+                .ok_or_else(|| D::Error::custom("mop must be a string"))?
+                .to_string();
+            let args: Option<Vec<QubitArg>> = obj.get("args").and_then(|v| {
+                if v.is_null() {
+                    None
+                } else {
+                    serde_json::from_value(v.clone()).ok()
+                }
+            });
+            let duration: Option<(f64, String)> = obj.get("duration").and_then(|v| {
+                if v.is_null() {
+                    None
+                } else {
+                    serde_json::from_value(v.clone()).ok()
+                }
+            });
+            let metadata = extract_metadata(obj);
+            Ok(Operation::MachineOp {
+                mop,
+                args,
+                duration,
+                metadata,
+            })
+        } else if let Some(meta_val) = obj.get("meta") {
+            // MetaInstruction
+            let meta = meta_val
+                .as_str()
+                .ok_or_else(|| D::Error::custom("meta must be a string"))?
+                .to_string();
+            let args: Vec<(String, usize)> = obj
+                .get("args")
+                .map_or(Ok(vec![]), |v| serde_json::from_value(v.clone()))
+                .map_err(|e| D::Error::custom(format!("args: {e}")))?;
+            let metadata = extract_metadata(obj);
+            Ok(Operation::MetaInstruction {
+                meta,
+                args,
+                metadata,
+            })
+        } else if let Some(comment_val) = obj.get("//") {
+            // Comment
+            let comment = comment_val
+                .as_str()
+                .ok_or_else(|| D::Error::custom("comment must be a string"))?
+                .to_string();
+            Ok(Operation::Comment { comment })
+        } else if let Some(data_val) = obj.get("data") {
+            let data = data_val
+                .as_str()
+                .ok_or_else(|| D::Error::custom("data must be a string"))?
+                .to_string();
+            if obj.contains_key("variables") {
+                // DataExport
+                let variables: Vec<String> = serde_json::from_value(obj["variables"].clone())
+                    .map_err(|e| D::Error::custom(format!("variables: {e}")))?;
+                Ok(Operation::DataExport { data, variables })
+            } else {
+                // VariableDefinition
+                let data_type: String = obj
+                    .get("data_type")
+                    .and_then(|v| v.as_str())
+                    .ok_or_else(|| D::Error::custom("missing data_type"))?
+                    .to_string();
+                let variable: String = obj
+                    .get("variable")
+                    .and_then(|v| v.as_str())
+                    .ok_or_else(|| D::Error::custom("missing variable"))?
+                    .to_string();
+                let size: Option<usize> = obj
+                    .get("size")
+                    .and_then(serde_json::Value::as_u64)
+                    .and_then(|n| usize::try_from(n).ok());
+                Ok(Operation::VariableDefinition {
+                    data,
+                    data_type,
+                    variable,
+                    size,
+                })
+            }
+        } else {
+            Err(D::Error::custom(format!(
+                "unknown operation: no recognized key (qop, cop, block, mop, meta, //, data) found in {:?}",
+                obj.keys().collect::<Vec<_>>()
+            )))
+        }
+    }
 }
 
 /// Represents an argument to a quantum operation
@@ -148,25 +373,133 @@ pub fn infer_size(data_type: &str, explicit_size: Option<usize>) -> usize {
     digits.parse().unwrap_or(0)
 }
 
-/// Custom deserializer to convert angles to radians
-fn deserialize_angles_to_radians<'de, D>(deserializer: D) -> Result<Option<Vec<f64>>, D::Error>
-where
-    D: Deserializer<'de>,
-{
-    // First, deserialize as Option<(Vec<f64>, String)>
-    Option::<(Vec<f64>, String)>::deserialize(deserializer)?.map_or(Ok(None), |(values, unit)| {
-        // Convert to radians based on unit
-        let converted_values = match unit.as_str() {
-            "rad" => values, // Already in radians
-            "deg" => values.into_iter().map(|v| v * PI / 180.0).collect(),
-            "pi" => values.into_iter().map(|v| v * PI).collect(),
-            _ => {
-                return Err(serde::de::Error::custom(format!(
-                    "Unsupported angle unit: {unit}"
-                )));
+#[cfg(test)]
+mod tests {
+    use super::*;
+
+    #[test]
+    fn test_parse_qparallel_with_angles() {
+        let json = r#"{
+            "format": "PHIR/JSON",
+            "version": "0.1.0",
+            "metadata": {},
+            "ops": [
+                {"data": "qvar_define", "data_type": "qubits", "variable": "q", "size": 2},
+                {"data": "cvar_define", "data_type": "u32", "variable": "m", "size": 2},
+                {"qop": "RZ", "angles": [[1.0], "pi"], "args": [["q", 0], ["q", 1]]},
+                {"block": "qparallel", "ops": [
+                    {"qop": "R1XY", "angles": [[0.5, 0.5], "pi"], "args": [["q", 0]]},
+                    {"qop": "R1XY", "angles": [[1.5, 0.5], "pi"], "args": [["q", 1]]}
+                ]},
+                {"qop": "RZZ", "angles": [[0.5], "pi"], "args": [[["q", 0], ["q", 1]]]},
+                {"qop": "Measure", "args": [["q", 0], ["q", 1]], "returns": [["m", 0], ["m", 1]]}
+            ]
+        }"#;
+        let program: PHIRProgram = serde_json::from_str(json).expect("should parse");
+        assert_eq!(program.ops.len(), 6);
+
+        // Verify angles were converted to radians (pi units)
+        if let Operation::QuantumOp { angles, .. } = &program.ops[2] {
+            let a = angles.as_ref().unwrap();
+            assert!((a[0] - PI).abs() < 1e-10, "RZ angle should be pi");
+        } else {
+            panic!("Expected QuantumOp");
+        }
+
+        // Verify inner ops of qparallel block
+        if let Operation::Block { ops, .. } = &program.ops[3] {
+            assert_eq!(ops.len(), 2);
+            if let Operation::QuantumOp { qop, angles, .. } = &ops[0] {
+                assert_eq!(qop, "R1XY");
+                let a = angles.as_ref().unwrap();
+                assert_eq!(a.len(), 2);
+                assert!((a[0] - 0.5 * PI).abs() < 1e-10);
+                assert!((a[1] - 0.5 * PI).abs() < 1e-10);
+            } else {
+                panic!("Expected QuantumOp inside block");
             }
-        };
+        } else {
+            panic!("Expected Block");
+        }
+    }
 
-        Ok(Some(converted_values))
-    })
+    #[test]
+    fn test_parse_bell_qparallel_compact() {
+        // Simulate what Python json.dumps produces (compact, single-line)
+        let json = r#"{"format": "PHIR/JSON", "version": "0.1.0", "metadata": {"source": "pytket-phir v0.2.0", "strict_parallelism": "true"}, "ops": [{"data": "qvar_define", "data_type": "qubits", "variable": "q", "size": 2}, {"data": "cvar_define", "data_type": "u32", "variable": "m", "size": 2}, {"qop": "RZ", "angles": [[1.0], "pi"], "args": [["q", 0], ["q", 1]]}, {"block": "qparallel", "ops": [{"qop": "R1XY", "angles": [[0.5, 0.5], "pi"], "args": [["q", 0]]}, {"qop": "R1XY", "angles": [[1.5, 0.5], "pi"], "args": [["q", 1]]}]}, {"qop": "RZ", "angles": [[1.0], "pi"], "args": [["q", 0]]}, {"qop": "RZZ", "angles": [[0.5], "pi"], "args": [[["q", 0], ["q", 1]]]}, {"block": "qparallel", "ops": [{"qop": "RZ", "angles": [[1.5], "pi"], "args": [["q", 0]]}, {"qop": "RZ", "angles": [[0.5], "pi"], "args": [["q", 1]]}]}, {"qop": "R1XY", "angles": [[1.5, 0.5], "pi"], "args": [["q", 1]]}, {"qop": "Measure", "args": [["q", 0], ["q", 1]], "returns": [["m", 0], ["m", 1]]}]}"#;
+        let program: PHIRProgram = serde_json::from_str(json).expect("should parse");
+        assert_eq!(program.ops.len(), 9);
+    }
+
+    #[test]
+    fn test_angle_units() {
+        // Test all three angle unit types
+        let json = r#"{
+            "format": "PHIR/JSON", "version": "0.1.0", "metadata": {},
+            "ops": [
+                {"data": "qvar_define", "data_type": "qubits", "variable": "q", "size": 1},
+                {"qop": "RZ", "angles": [[1.5707963267948966], "rad"], "args": [["q", 0]]},
+                {"qop": "RZ", "angles": [[90.0], "deg"], "args": [["q", 0]]},
+                {"qop": "RZ", "angles": [[0.5], "pi"], "args": [["q", 0]]}
+            ]
+        }"#;
+        let program: PHIRProgram = serde_json::from_str(json).expect("should parse");
+
+        // All three should produce the same angle (pi/2)
+        for i in 1..=3 {
+            if let Operation::QuantumOp { angles, .. } = &program.ops[i] {
+                let a = angles.as_ref().unwrap();
+                assert!(
+                    (a[0] - std::f64::consts::FRAC_PI_2).abs() < 1e-10,
+                    "op {i}: expected pi/2, got {}",
+                    a[0]
+                );
+            }
+        }
+    }
+
+    #[test]
+    fn test_no_angles() {
+        let json = r#"{
+            "format": "PHIR/JSON", "version": "0.1.0", "metadata": {},
+            "ops": [
+                {"data": "qvar_define", "data_type": "qubits", "variable": "q", "size": 1},
+                {"qop": "H", "args": [["q", 0]]},
+                {"qop": "Measure", "args": [["q", 0]], "returns": [["m", 0]]}
+            ]
+        }"#;
+        let program: PHIRProgram = serde_json::from_str(json).expect("should parse");
+        if let Operation::QuantumOp { angles, .. } = &program.ops[1] {
+            assert!(angles.is_none());
+        }
+    }
+
+    #[test]
+    fn test_comment() {
+        let json = r#"{
+            "format": "PHIR/JSON", "version": "0.1.0", "metadata": {},
+            "ops": [{"//": "this is a comment"}]
+        }"#;
+        let program: PHIRProgram = serde_json::from_str(json).expect("should parse");
+        if let Operation::Comment { comment } = &program.ops[0] {
+            assert_eq!(comment, "this is a comment");
+        } else {
+            panic!("Expected Comment");
+        }
+    }
+
+    #[test]
+    fn test_data_export() {
+        let json = r#"{
+            "format": "PHIR/JSON", "version": "0.1.0", "metadata": {},
+            "ops": [{"data": "cvar_export", "variables": ["m", "n"]}]
+        }"#;
+        let program: PHIRProgram = serde_json::from_str(json).expect("should parse");
+        if let Operation::DataExport { data, variables } = &program.ops[0] {
+            assert_eq!(data, "cvar_export");
+            assert_eq!(variables, &["m", "n"]);
+        } else {
+            panic!("Expected DataExport");
+        }
+    }
 }
diff --git a/crates/pecos-phir/src/hugr_parser.rs b/crates/pecos-phir/src/hugr_parser.rs
index eb91fb6ce..f4521fba9 100644
--- a/crates/pecos-phir/src/hugr_parser.rs
+++ b/crates/pecos-phir/src/hugr_parser.rs
@@ -517,16 +517,16 @@ impl HugrToPhirConverter {
         }
 
         // Step 1: Emit all Measure instructions
-        let mut meas_results: Vec<(SSAValue, usize)> = Vec::with_capacity(measurements.len());
+        let mut meas_ids: Vec<(SSAValue, usize)> = Vec::with_capacity(measurements.len());
         for &(qubit_ssa, bit_idx) in measurements {
-            let meas_result = self.fresh_ssa();
+            let meas_id = self.fresh_ssa();
             block.add_instruction(Instruction::new(
                 Operation::Quantum(QuantumOp::Measure),
                 vec![qubit_ssa],
-                vec![meas_result],
+                vec![meas_id],
                 vec![Type::Bit],
             ));
-            meas_results.push((meas_result, bit_idx));
+            meas_ids.push((meas_id, bit_idx));
         }
 
         // Step 2: Combine bits into a single integer and emit Result
@@ -541,7 +541,7 @@ impl HugrToPhirConverter {
 
         let mut accum = zero_ssa;
 
-        for &(meas_ssa, bit_idx) in &meas_results {
+        for &(meas_ssa, bit_idx) in &meas_ids {
             // Bitcast measurement bit to i64
             let cast_ssa = self.fresh_ssa();
             block.add_instruction(Instruction::new(
diff --git a/crates/pecos-pymatching/Cargo.toml b/crates/pecos-pymatching/Cargo.toml
index 8d88bc287..bbabfe235 100644
--- a/crates/pecos-pymatching/Cargo.toml
+++ b/crates/pecos-pymatching/Cargo.toml
@@ -10,6 +10,7 @@ license.workspace = true
 keywords.workspace = true
 categories.workspace = true
 description = "PyMatching MWPM decoder for PECOS"
+links = "pymatching-pecos"
 
 [dependencies]
 pecos-decoder-core.workspace = true
diff --git a/crates/pecos-pymatching/build_pymatching.rs b/crates/pecos-pymatching/build_pymatching.rs
index 7dc42c4e2..640da3024 100644
--- a/crates/pecos-pymatching/build_pymatching.rs
+++ b/crates/pecos-pymatching/build_pymatching.rs
@@ -60,6 +60,16 @@ pub fn build() -> Result<()> {
     let pymatching_dir = ensure_dep_ready("pymatching", &manifest)?;
     let stim_dir = ensure_dep_ready("stim", &manifest)?;
 
+    // Export paths so downstream crates (e.g., pecos-chromobius) can include
+    // PyMatching/Stim headers and link against our compiled objects without
+    // compiling their own copy.
+    let pymatching_src = pymatching_dir.join("src");
+    let stim_src = stim_dir.join("src");
+    println!("cargo:pymatching_include={}", pymatching_src.display());
+    println!("cargo:stim_include={}", stim_src.display());
+    println!("cargo:stim_dir={}", stim_dir.display());
+    println!("cargo:lib_dir={}", out_dir.display());
+
     // Build using cxx
     build_cxx_bridge(&pymatching_dir, &stim_dir)?;
 
@@ -180,7 +190,6 @@ fn collect_pymatching_sources(pymatching_src_dir: &Path) -> Result<Vec<PathBuf>>
     sources.extend([
         driver_dir.join("user_graph.cc"),
         driver_dir.join("mwpm_decoding.cc"),
-        driver_dir.join("io.cc"),
     ]);
 
     // Matcher files
diff --git a/crates/pecos-pymatching/include/pymatching_bridge.h b/crates/pecos-pymatching/include/pymatching_bridge.h
index a72d10602..a76c20163 100644
--- a/crates/pecos-pymatching/include/pymatching_bridge.h
+++ b/crates/pecos-pymatching/include/pymatching_bridge.h
@@ -20,7 +20,8 @@ class PyMatchingGraph {
     // Constructors
     PyMatchingGraph(size_t num_nodes);
     PyMatchingGraph(size_t num_nodes, size_t num_observables);
-    static std::unique_ptr<PyMatchingGraph> from_dem(const std::string& dem_string);
+    static std::unique_ptr<PyMatchingGraph> from_dem(
+        const std::string& dem_string, bool enable_correlations = false);
     ~PyMatchingGraph();
 
     // Edge management
@@ -104,6 +105,8 @@ std::unique_ptr<PyMatchingGraph> create_pymatching_graph_with_observables(
     size_t num_nodes, size_t num_observables);
 std::unique_ptr<PyMatchingGraph> create_pymatching_graph_from_dem(
     const rust::Str dem_string);
+std::unique_ptr<PyMatchingGraph> create_pymatching_graph_from_dem_with_correlations(
+    const rust::Str dem_string, bool enable_correlations);
 
 void add_edge(
     PyMatchingGraph& graph,
diff --git a/crates/pecos-pymatching/pecos.toml b/crates/pecos-pymatching/pecos.toml
index 16daa358c..635349187 100644
--- a/crates/pecos-pymatching/pecos.toml
+++ b/crates/pecos-pymatching/pecos.toml
@@ -4,13 +4,13 @@
 version = 1
 
 [dependencies.pymatching]
-version = "2b72b2c558eec678656da20ab6c358aa123fb664"
-url = "https://github.com/oscarhiggott/PyMatching/archive/2b72b2c558eec678656da20ab6c358aa123fb664.tar.gz"
-sha256 = "1470520b66ad7899f85020664aeeadfc6e2967f0b5e19ad205829968b845cd70"
+version = "c60642af5a5b342d633e2e2b818b9fdb9696e828"
+url = "https://github.com/oscarhiggott/PyMatching/archive/c60642af5a5b342d633e2e2b818b9fdb9696e828.tar.gz"
+sha256 = "c9e775619a791a3a0a58073447fd3f2c61a9804ecaa716fd753ef8f0a81783de"
 description = "MWPM decoder"
 
 [dependencies.stim]
-version = "bd60b73525fd5a9b30839020eb7554ad369e4337"
-url = "https://github.com/quantumlib/Stim/archive/bd60b73525fd5a9b30839020eb7554ad369e4337.tar.gz"
-sha256 = "2a4be24295ce3018d79e08369b31e401a2d33cd8b3a75675d57dac3afd9de37d"
+version = "213275795e49027772bea7c610b6aac3a80583e1"
+url = "https://github.com/quantumlib/Stim/archive/213275795e49027772bea7c610b6aac3a80583e1.tar.gz"
+sha256 = "b63c4ae94494a8819d440757776cf80a829ec1e30454fa7c9b0f670e981938ab"
 description = "Stabilizer simulator for QEC"
diff --git a/crates/pecos-pymatching/src/bridge.cpp b/crates/pecos-pymatching/src/bridge.cpp
index 30ddc3e42..7bbef999d 100644
--- a/crates/pecos-pymatching/src/bridge.cpp
+++ b/crates/pecos-pymatching/src/bridge.cpp
@@ -15,7 +15,6 @@
 // PyMatching includes
 #include "pymatching/sparse_blossom/driver/user_graph.h"
 #include "pymatching/sparse_blossom/driver/mwpm_decoding.h"
-#include "pymatching/sparse_blossom/driver/io.h"
 #include "pymatching/sparse_blossom/search/search_graph.h"
 #include "pymatching/rand/rand_gen.h"
 
@@ -32,6 +31,7 @@ class PyMatchingGraph::Impl {
     std::unique_ptr<pm::Mwpm> mwpm_;
     pm::SearchFlooder* search_flooder_ = nullptr;
     double normalising_constant_ = 1.0;
+    bool enable_correlations_ = false;
 
     // Constructor
     Impl(size_t num_nodes, size_t num_observables) {
@@ -39,7 +39,7 @@ class PyMatchingGraph::Impl {
     }
 
     // Initialize MWPM decoder when needed
-    void ensure_mwpm(bool include_search_graph = false) {
+    void ensure_mwpm(bool include_search_graph) {
         if (!mwpm_ || (include_search_graph && !search_flooder_)) {
             normalising_constant_ = user_graph_->get_edge_weight_normalising_constant(pm::NUM_DISTINCT_WEIGHTS);
             if (normalising_constant_ == 0) {
@@ -73,12 +73,14 @@ PyMatchingGraph::PyMatchingGraph(size_t num_nodes, size_t num_observables)
 
 PyMatchingGraph::~PyMatchingGraph() = default;
 
-std::unique_ptr<PyMatchingGraph> PyMatchingGraph::from_dem(const std::string& dem_string) {
+std::unique_ptr<PyMatchingGraph> PyMatchingGraph::from_dem(
+    const std::string& dem_string, bool enable_correlations) {
     try {
         auto dem = stim::DetectorErrorModel(dem_string.c_str());
 
         // Create user graph from DEM
-        auto user_graph = pm::detector_error_model_to_user_graph(dem);
+        auto user_graph = pm::detector_error_model_to_user_graph(
+            dem, enable_correlations, pm::NUM_DISTINCT_WEIGHTS);
 
         // Create PyMatchingGraph and move the user graph
         auto graph = std::make_unique<PyMatchingGraph>(
@@ -88,6 +90,7 @@ std::unique_ptr<PyMatchingGraph> PyMatchingGraph::from_dem(const std::string& de
 
         // Replace the default user graph with the one from DEM
         graph->pimpl_->user_graph_ = std::make_unique<pm::UserGraph>(std::move(user_graph));
+        graph->pimpl_->enable_correlations_ = enable_correlations;
 
         return graph;
     } catch (const std::exception& e) {
@@ -305,7 +308,7 @@ bool PyMatchingGraph::is_boundary_node(size_t node) const {
 ExtendedMatchingResult PyMatchingGraph::decode_detection_events_64(
     const rust::Slice<const uint8_t> detection_events) {
 
-    pimpl_->ensure_mwpm();
+    pimpl_->ensure_mwpm(pimpl_->enable_correlations_);
 
     // Convert detection events to vector of indices
     std::vector<uint64_t> detections;
@@ -316,7 +319,8 @@ ExtendedMatchingResult PyMatchingGraph::decode_detection_events_64(
     }
 
     try {
-        auto result = pm::decode_detection_events_for_up_to_64_observables(*pimpl_->mwpm_, detections);
+        auto result = pm::decode_detection_events_for_up_to_64_observables(
+            *pimpl_->mwpm_, detections, pimpl_->enable_correlations_);
         pimpl_->reset_mwpm();
 
         ExtendedMatchingResult ext_result;
@@ -338,7 +342,7 @@ ExtendedMatchingResult PyMatchingGraph::decode_detection_events_64(
 ExtendedMatchingResult PyMatchingGraph::decode_detection_events_extended(
     const rust::Slice<const uint8_t> detection_events) {
 
-    pimpl_->ensure_mwpm();
+    pimpl_->ensure_mwpm(pimpl_->enable_correlations_);
 
     // Convert detection events
     std::vector<uint64_t> detections;
@@ -353,7 +357,8 @@ ExtendedMatchingResult PyMatchingGraph::decode_detection_events_extended(
         std::vector<uint8_t> obs_vec(num_obs, 0);
         pm::total_weight_int weight = 0;
 
-        pm::decode_detection_events(*pimpl_->mwpm_, detections, obs_vec.data(), weight);
+        pm::decode_detection_events(
+            *pimpl_->mwpm_, detections, obs_vec.data(), weight, pimpl_->enable_correlations_);
         pimpl_->reset_mwpm();
 
         ExtendedMatchingResult result;
@@ -373,7 +378,7 @@ ExtendedMatchingResult PyMatchingGraph::decode_detection_events_extended(
 rust::Vec<MatchedPair> PyMatchingGraph::decode_to_matched_pairs(
     const rust::Slice<const uint8_t> detection_events) {
 
-    pimpl_->ensure_mwpm();
+    pimpl_->ensure_mwpm(pimpl_->enable_correlations_);
 
     // Convert detection events
     std::vector<uint64_t> detections;
@@ -408,7 +413,7 @@ rust::Vec<MatchedPair> PyMatchingGraph::decode_to_matched_pairs(
 rust::Vec<MatchedPair> PyMatchingGraph::decode_to_edges(
     const rust::Slice<const uint8_t> detection_events) {
 
-    pimpl_->ensure_mwpm();
+    pimpl_->ensure_mwpm(pimpl_->enable_correlations_);
 
     // Convert detection events
     std::vector<uint64_t> detections;
@@ -450,7 +455,7 @@ BatchDecodingResult PyMatchingGraph::decode_batch(
     bool bit_packed_shots,
     bool bit_packed_predictions) {
 
-    pimpl_->ensure_mwpm();
+    pimpl_->ensure_mwpm(pimpl_->enable_correlations_);
 
     BatchDecodingResult result;
     result.predictions = rust::Vec<uint8_t>();
@@ -493,7 +498,8 @@ BatchDecodingResult PyMatchingGraph::decode_batch(
 
             // Decode
             if (num_obs <= 64) {
-                auto res = pm::decode_detection_events_for_up_to_64_observables(*pimpl_->mwpm_, detections);
+                auto res = pm::decode_detection_events_for_up_to_64_observables(
+                    *pimpl_->mwpm_, detections, pimpl_->enable_correlations_);
 
                 if (bit_packed_predictions) {
                     // Pack obs_mask into bytes
@@ -518,7 +524,8 @@ BatchDecodingResult PyMatchingGraph::decode_batch(
                 std::vector<uint8_t> obs_vec(num_obs, 0);
                 pm::total_weight_int weight = 0;
 
-                pm::decode_detection_events(*pimpl_->mwpm_, detections, obs_vec.data(), weight);
+                pm::decode_detection_events(
+                    *pimpl_->mwpm_, detections, obs_vec.data(), weight, pimpl_->enable_correlations_);
 
                 if (bit_packed_predictions) {
                     // Pack observables into bytes
@@ -678,7 +685,12 @@ std::unique_ptr<PyMatchingGraph> create_pymatching_graph_with_observables(
 }
 
 std::unique_ptr<PyMatchingGraph> create_pymatching_graph_from_dem(const rust::Str dem_string) {
-    return PyMatchingGraph::from_dem(std::string(dem_string));
+    return PyMatchingGraph::from_dem(std::string(dem_string), false);
+}
+
+std::unique_ptr<PyMatchingGraph> create_pymatching_graph_from_dem_with_correlations(
+    const rust::Str dem_string, bool enable_correlations) {
+    return PyMatchingGraph::from_dem(std::string(dem_string), enable_correlations);
 }
 
 void add_edge(
diff --git a/crates/pecos-pymatching/src/bridge.rs b/crates/pecos-pymatching/src/bridge.rs
index f267743da..b2becdc86 100644
--- a/crates/pecos-pymatching/src/bridge.rs
+++ b/crates/pecos-pymatching/src/bridge.rs
@@ -73,6 +73,19 @@ pub(crate) mod ffi {
         fn create_pymatching_graph_from_dem(dem_string: &str)
         -> Result<UniquePtr<PyMatchingGraph>>;
 
+        /// Create a `PyMatching` graph from a DEM string with correlation support.
+        ///
+        /// When `enable_correlations` is true, the decoder tracks edge correlations
+        /// during graph construction and uses them during decoding.
+        ///
+        /// # Errors
+        ///
+        /// Returns a CXX exception if the DEM string is malformed.
+        fn create_pymatching_graph_from_dem_with_correlations(
+            dem_string: &str,
+            enable_correlations: bool,
+        ) -> Result<UniquePtr<PyMatchingGraph>>;
+
         // ===== Edge Management =====
 
         /// Add an edge between two nodes.
diff --git a/crates/pecos-pymatching/src/core_traits.rs b/crates/pecos-pymatching/src/core_traits.rs
index 708aa4042..8a96c2b16 100644
--- a/crates/pecos-pymatching/src/core_traits.rs
+++ b/crates/pecos-pymatching/src/core_traits.rs
@@ -7,8 +7,8 @@ use crate::decoder::{CheckMatrix, CheckMatrixConfig, DecodingResult, PyMatchingD
 use crate::errors::PyMatchingError;
 use ndarray::{ArrayView1, ArrayView2};
 use pecos_decoder_core::{
-    BatchDecoder, CheckMatrixDecoder, Decoder, DecodingStats, DemDecoder, DetailedDecoder,
-    MatchedEdge, MatchedPair as CoreMatchedPair,
+    BatchDecoder, CheckMatrixDecoder, Decoder, DecoderError, DecodingStats, DemDecoder,
+    DetailedDecoder, MatchedEdge, MatchedPair as CoreMatchedPair, ObservableDecoder,
 };
 
 /// Implement the core Decoder trait for `PyMatchingDecoder`
@@ -184,6 +184,52 @@ impl DetailedDecoder for PyMatchingDecoder {
     }
 }
 
+/// Implement `ObservableDecoder` for `PyMatchingDecoder`.
+///
+/// Converts the observable vector to a bitmask for the sample+decode loop.
+impl ObservableDecoder for PyMatchingDecoder {
+    fn decode_to_observables(&mut self, syndrome: &[u8]) -> Result<u64, DecoderError> {
+        let result = self
+            .decode(syndrome)
+            .map_err(|e| DecoderError::DecodingFailed(e.to_string()))?;
+        let mut mask = 0u64;
+        for (i, &v) in result.observable.iter().enumerate() {
+            if v != 0 {
+                mask |= 1 << i;
+            }
+        }
+        Ok(mask)
+    }
+
+    fn decode_batch_to_observables(
+        &mut self,
+        shots: &[u8],
+        num_shots: usize,
+        num_detectors: usize,
+    ) -> Result<Vec<u64>, DecoderError> {
+        use crate::decoder::BatchConfig;
+        let config = BatchConfig {
+            bit_packed_input: false,
+            bit_packed_output: true,
+            return_weights: false,
+        };
+        let result = self
+            .decode_batch_with_config(shots, num_shots, num_detectors, config)
+            .map_err(|e| DecoderError::DecodingFailed(e.to_string()))?;
+
+        // Convert per-shot bit-packed predictions to u64 masks.
+        let mut masks = Vec::with_capacity(num_shots);
+        for pred in &result.predictions {
+            let mut mask = 0u64;
+            for (byte_idx, &byte) in pred.iter().enumerate() {
+                mask |= u64::from(byte) << (byte_idx * 8);
+            }
+            masks.push(mask);
+        }
+        Ok(masks)
+    }
+}
+
 #[cfg(test)]
 mod tests {
     use super::*;
diff --git a/crates/pecos-pymatching/src/decoder.rs b/crates/pecos-pymatching/src/decoder.rs
index 55feb0e3b..f63a67d6d 100644
--- a/crates/pecos-pymatching/src/decoder.rs
+++ b/crates/pecos-pymatching/src/decoder.rs
@@ -535,6 +535,31 @@ impl PyMatchingDecoder {
         Ok(Self { graph, config })
     }
 
+    /// Create a decoder from a DEM string with correlation support
+    ///
+    /// When `enable_correlations` is true, the decoder tracks edge correlations
+    /// during graph construction and uses them during decoding.
+    ///
+    /// # Errors
+    /// Returns an error if the DEM string is invalid or cannot be parsed.
+    pub fn from_dem_with_correlations(dem_string: &str, enable_correlations: bool) -> Result<Self> {
+        let graph = ffi::create_pymatching_graph_from_dem_with_correlations(
+            dem_string,
+            enable_correlations,
+        )?;
+
+        let num_nodes = ffi::pymatching_get_num_nodes(&graph);
+        let num_observables = ffi::pymatching_get_num_observables(&graph);
+
+        let config = PyMatchingConfig {
+            num_neighbours: None,
+            num_nodes: Some(num_nodes),
+            num_observables,
+        };
+
+        Ok(Self { graph, config })
+    }
+
     /// Create a decoder from a check matrix
     ///
     /// The check matrix should be in sparse format where:
diff --git a/crates/pecos-qasm/src/engine.rs b/crates/pecos-qasm/src/engine.rs
index a4413d397..f795d1b41 100644
--- a/crates/pecos-qasm/src/engine.rs
+++ b/crates/pecos-qasm/src/engine.rs
@@ -623,7 +623,8 @@ impl QASMEngine {
             | GateType::MeasCrosstalkLocalPayload
             | GateType::MeasCrosstalkGlobalPayload
             | GateType::QFree
-            | GateType::Custom => Ok(()), // No-op gates (QFree is just a marker, Custom is a placeholder)
+            | GateType::Custom
+            | GateType::TrackedPauliMeta => Ok(()), // No-op gates
             GateType::X
             | GateType::Z
             | GateType::Y
@@ -650,7 +651,7 @@ impl QASMEngine {
             | GateType::SYY
             | GateType::SYYdg => self.process_two_qubit_gate(gate.gate_type, &qubits),
             // Gates not yet supported in QASM engine
-            GateType::SWAP | GateType::CCX | GateType::CRZ | GateType::CH => {
+            GateType::SWAP | GateType::CCX | GateType::CRZ | GateType::CH | GateType::Channel => {
                 Err(PecosError::Processing(format!(
                     "Gate type {:?} is not yet supported in the QASM engine",
                     gate.gate_type
diff --git a/crates/pecos-qasm/src/qasm_to_phir.rs b/crates/pecos-qasm/src/qasm_to_phir.rs
index ed55a47a4..576e0404a 100644
--- a/crates/pecos-qasm/src/qasm_to_phir.rs
+++ b/crates/pecos-qasm/src/qasm_to_phir.rs
@@ -228,14 +228,14 @@ impl Converter {
             Vec::with_capacity(measurements.len());
 
         for (qubit_ssa, reg_name, bit_idx) in measurements {
-            let meas_result = self.new_ssa();
+            let meas_id = self.new_ssa();
             block.add_instruction(Instruction::new(
                 Operation::Quantum(QuantumOp::Measure),
                 vec![*qubit_ssa],
-                vec![meas_result],
+                vec![meas_id],
                 vec![Type::Bit],
             ));
-            measure_results.push((meas_result, reg_name.clone(), *bit_idx));
+            measure_results.push((meas_id, reg_name.clone(), *bit_idx));
         }
 
         // Step 2: Group by register and combine bits
diff --git a/crates/pecos-qec/Cargo.toml b/crates/pecos-qec/Cargo.toml
index f2acb8fee..30a043360 100644
--- a/crates/pecos-qec/Cargo.toml
+++ b/crates/pecos-qec/Cargo.toml
@@ -15,15 +15,21 @@ readme = "README.md"
 ndarray.workspace = true
 pecos-core.workspace = true
 pecos-decoder-core.workspace = true
+pecos-num.workspace = true
 pecos-quantum.workspace = true
 pecos-simulators.workspace = true
 pecos-random.workspace = true
 rand.workspace = true
 rand_core.workspace = true
 rayon.workspace = true
+serde_json.workspace = true
 smallvec.workspace = true
 thiserror.workspace = true
 wide.workspace = true
 
+[[example]]
+name = "surface_d3_fault_catalog_lookup"
+path = "../../examples/surface/d3_fault_catalog_lookup.rs"
+
 [lints]
 workspace = true
diff --git a/crates/pecos-qec/examples/influence_builder_example.rs b/crates/pecos-qec/examples/influence_builder_example.rs
index 363b06fe5..0266c42d5 100644
--- a/crates/pecos-qec/examples/influence_builder_example.rs
+++ b/crates/pecos-qec/examples/influence_builder_example.rs
@@ -3,14 +3,12 @@
 //! Pipeline steps:
 //! 1. Build a syndrome extraction circuit using `DagCircuit`
 //! 2. Use `InfluenceBuilder` to extract detectors and build influence map
-//! 3. Use `NoisySampler` for CPU-based noisy sampling
+//! 3. Use `DemSampler` for fast CPU-based noisy sampling
 //!
 //! Run with: cargo run --example `influence_builder_example` --release -p pecos-qec
 
 use pecos_qec::fault_tolerance::InfluenceBuilder;
-use pecos_qec::fault_tolerance::noisy_sampler::{
-    NoisySampler, SamplingStatistics, UniformNoiseModel,
-};
+use pecos_qec::fault_tolerance::dem_builder::DemSampler;
 use pecos_quantum::DagCircuit;
 
 /// Build a simple repetition code syndrome extraction circuit.
@@ -42,7 +40,7 @@ fn build_repetition_code_circuit(num_rounds: usize) -> DagCircuit {
 }
 
 fn main() {
-    println!("CPU Pipeline Example: Circuit -> Influence Map -> CPU Sampling\n");
+    println!("CPU Pipeline Example: Circuit -> Influence Map -> DemSampler\n");
     println!("{:=<70}", "");
 
     // =========================================================================
@@ -57,7 +55,7 @@ fn main() {
     // =========================================================================
     // Build influence map with InfluenceBuilder
     // =========================================================================
-    let builder = InfluenceBuilder::new(&circuit).with_logical_z(vec![0, 1, 2]); // Z logical on all data qubits
+    let builder = InfluenceBuilder::new(&circuit).with_z(&[0, 1, 2]); // Z logical on all data qubits
 
     let influence_map = builder.build();
 
@@ -78,28 +76,24 @@ fn main() {
     }
 
     // =========================================================================
-    // Sample with CPU NoisySampler
+    // Sample with DemSampler
     // =========================================================================
     let p_error = 0.001; // 0.1% error rate per location
-    let noise_model = UniformNoiseModel::depolarizing(p_error);
     let seed = 42u64;
+    let num_locations = influence_map.locations.len();
+    let per_location_probs = vec![p_error; num_locations];
 
-    let mut sampler = NoisySampler::new(&influence_map, noise_model, seed);
+    let sampler = DemSampler::from_influence_map(&influence_map, &per_location_probs);
 
-    println!("\n3. Sampling with CPU NoisySampler:");
+    println!("\n3. Sampling with DemSampler:");
     println!("   Error rate: {p_error}");
+    println!("   Mechanisms: {}", sampler.num_mechanisms());
 
     let num_shots = 100_000;
     let start = std::time::Instant::now();
-    let results = sampler.sample(num_shots);
+    let stats = sampler.sample_statistics(num_shots, seed);
     let elapsed = start.elapsed();
 
-    // Collect statistics
-    let mut stats = SamplingStatistics::new();
-    for result in &results {
-        stats.record(result);
-    }
-
     println!("   Shots: {num_shots}");
     println!("   Time: {:.2}ms", elapsed.as_secs_f64() * 1000.0);
     #[allow(clippy::cast_precision_loss)]
@@ -116,7 +110,6 @@ fn main() {
         "   Undetectable error rate: {:.6}%",
         stats.undetectable_rate() * 100.0
     );
-    println!("   Avg faults per shot: {:.2}", stats.average_faults());
 
     // =========================================================================
     // Compare with different error rates
@@ -129,14 +122,9 @@ fn main() {
     println!("   {:->8} {:->15} {:->15}", "", "", "");
 
     for p in [0.0001, 0.0005, 0.001, 0.002, 0.005] {
-        let noise = UniformNoiseModel::depolarizing(p);
-        let mut sampler = NoisySampler::new(&influence_map, noise, seed);
-        let results = sampler.sample(50_000);
-
-        let mut stats = SamplingStatistics::new();
-        for result in &results {
-            stats.record(result);
-        }
+        let probs = vec![p; num_locations];
+        let sampler = DemSampler::from_influence_map(&influence_map, &probs);
+        let stats = sampler.sample_statistics(50_000, seed);
 
         println!(
             "   {:>8.4} {:>14.4}% {:>14.4}%",
diff --git a/crates/pecos-qec/src/dem_stab.rs b/crates/pecos-qec/src/dem_stab.rs
new file mode 100644
index 000000000..2b3532961
--- /dev/null
+++ b/crates/pecos-qec/src/dem_stab.rs
@@ -0,0 +1,267 @@
+// Copyright 2026 The PECOS Developers
+//
+// Licensed under the Apache License, Version 2.0 (the "License"); you may not use this file except
+// in compliance with the License. You may obtain a copy of the License at
+//
+//     https://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software distributed under the License
+// is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express
+// or implied. See the License for the specific language governing permissions and limitations under
+// the License.
+
+//! `DemStabSim` -- Clifford + depolarizing-family noise simulator backed by DEM sampling.
+//!
+//! Wraps the existing DAG -> fault-influence -> DEM-sampler pipeline as a single
+//! simulator type that consumes a static [`DagCircuit`] plus detector / observable
+//! definitions plus a [`NoiseConfig`] and produces shot batches of detector and
+//! observable flips.
+//!
+//! # Scope
+//!
+//! Clifford circuits only, no classical feed-forward. For adaptive circuits use
+//! `sparse_stab` + `pecos-neo` instead. For non-Clifford circuits use `CliffordRz`,
+//! `STN`, or `MAST`.
+//!
+//! # Example
+//!
+//! ```
+//! use pecos_qec::dem_stab::DemStabSim;
+//! use pecos_qec::fault_tolerance::dem_builder::{DemOutput, DetectorDef, NoiseConfig};
+//! use pecos_quantum::DagCircuit;
+//! use rand::SeedableRng;
+//! use rand::rngs::SmallRng;
+//!
+//! let mut dag = DagCircuit::new();
+//! dag.pz(&[2]);
+//! dag.cx(&[(0, 2)]);
+//! dag.cx(&[(1, 2)]);
+//! dag.mz(&[2]);
+//!
+//! let sim = DemStabSim::builder()
+//!     .circuit(dag)
+//!     .noise(NoiseConfig::uniform(0.01))
+//!     .detectors(vec![DetectorDef::new(0).with_records([-1])])
+//!     .build()
+//!     .unwrap();
+//!
+//! let mut rng = SmallRng::seed_from_u64(42);
+//! let batch = sim.sample_batch(100, &mut rng);
+//! assert_eq!(batch.detector_flips.len(), 100);
+//! ```
+
+use crate::fault_tolerance::dem_builder::{
+    DemOutput, DemSampler, DemSamplerBuilder, DetectorDef, DetectorErrorModel,
+    DetectorValidationError, NoiseConfig, PerGateTypeNoise,
+};
+use crate::fault_tolerance::propagator::DagFaultAnalyzer;
+use pecos_quantum::DagCircuit;
+use rand_core::Rng;
+use thiserror::Error;
+
+/// Errors that can occur when building a [`DemStabSim`].
+#[derive(Debug, Error)]
+pub enum DemStabError {
+    /// Builder called without a circuit.
+    #[error("DemStabSim requires a circuit; call .circuit(dag) before .build()")]
+    MissingCircuit,
+    /// Detector definitions are invalid for the circuit.
+    #[error(transparent)]
+    DetectorValidation(#[from] DetectorValidationError),
+}
+
+/// Shot-batch output from [`DemStabSim::sample_batch`].
+///
+/// `detector_flips[i]` is the bit-vector of detector outcomes for shot `i` (length
+/// equals the number of registered detectors). `observable_flips[i]` is the
+/// corresponding observable outcomes.
+#[derive(Debug, Clone)]
+pub struct DemStabShotBatch {
+    /// Per-shot detector flip vectors. Outer length = `num_shots`, inner length = `num_detectors`.
+    pub detector_flips: Vec<Vec<bool>>,
+    /// Per-shot observable flip vectors. Outer length = `num_shots`, inner length = `num_observables`.
+    pub observable_flips: Vec<Vec<bool>>,
+}
+
+/// Clifford + depolarizing-family noise simulator backed by DEM sampling.
+///
+/// Built once via [`DemStabSim::builder`], sampled many times via [`Self::sample_batch`].
+/// The underlying [`DemSampler`] is constructed eagerly at build time; subsequent
+/// shots reuse the cached mechanism table.
+#[derive(Debug, Clone)]
+pub struct DemStabSim {
+    sampler: DemSampler,
+    /// Detector definitions preserved from the builder, used to produce
+    /// a text-serializable [`DetectorErrorModel`] with full metadata.
+    detectors: Vec<DetectorDef>,
+    observables: Vec<DemOutput>,
+}
+
+impl DemStabSim {
+    /// Start building a [`DemStabSim`].
+    #[must_use]
+    pub fn builder() -> DemStabSimBuilder {
+        DemStabSimBuilder::default()
+    }
+
+    /// Number of registered detectors.
+    #[must_use]
+    pub fn num_detectors(&self) -> usize {
+        self.sampler.num_detectors()
+    }
+
+    /// Number of registered observables.
+    #[must_use]
+    pub fn num_observables(&self) -> usize {
+        self.sampler.num_observables()
+    }
+
+    /// Number of error mechanisms in the compiled DEM.
+    #[must_use]
+    pub fn num_mechanisms(&self) -> usize {
+        self.sampler.num_mechanisms()
+    }
+
+    /// Access the underlying [`DemSampler`] for advanced use (e.g. statistics-only APIs).
+    #[must_use]
+    pub fn sampler(&self) -> &DemSampler {
+        &self.sampler
+    }
+
+    /// Produce a [`DetectorErrorModel`] reflecting the compiled mechanism
+    /// set and the detector / observable definitions the builder was
+    /// given. Use [`DetectorErrorModel::to_string`] for Stim-compatible
+    /// text output.
+    ///
+    /// Note: the probabilities are recovered from the sampler's stored
+    /// `u64` thresholds, which round-trips to ~machine precision.
+    #[must_use]
+    pub fn detector_error_model(&self) -> DetectorErrorModel {
+        let mut dem = self.sampler.to_detector_error_model();
+        for det in &self.detectors {
+            dem.add_detector(det.clone());
+        }
+        for obs in &self.observables {
+            dem.add_observable(obs.clone());
+        }
+        dem
+    }
+
+    /// Sample `num_shots` independent shots from the compiled DEM.
+    #[must_use]
+    pub fn sample_batch<R: Rng>(&self, num_shots: usize, rng: &mut R) -> DemStabShotBatch {
+        let (detector_flips, observable_flips) = self.sampler.sample_batch(num_shots, rng);
+        DemStabShotBatch {
+            detector_flips,
+            observable_flips,
+        }
+    }
+}
+
+/// Builder for [`DemStabSim`].
+#[derive(Debug, Default)]
+pub struct DemStabSimBuilder {
+    circuit: Option<DagCircuit>,
+    noise: NoiseConfig,
+    per_gate_noise: Option<PerGateTypeNoise>,
+    detectors: Vec<DetectorDef>,
+    observables: Vec<DemOutput>,
+    measurement_order: Option<Vec<usize>>,
+}
+
+impl DemStabSimBuilder {
+    /// Set the circuit. Required.
+    #[must_use]
+    pub fn circuit(mut self, dag: DagCircuit) -> Self {
+        self.circuit = Some(dag);
+        self
+    }
+
+    /// Set the uniform-depolarizing noise configuration. When both this
+    /// and [`Self::per_gate_noise`] are set, the per-gate spec takes
+    /// precedence.
+    #[must_use]
+    pub fn noise(mut self, config: NoiseConfig) -> Self {
+        self.noise = config;
+        self
+    }
+
+    /// Set a per-gate-type per-Pauli noise specification. Overrides
+    /// [`Self::noise`] scalars for any gate type present in the spec.
+    /// Intended consumer for `pecos-lindblad::PauliLindbladModel`
+    /// adapter output.
+    #[must_use]
+    pub fn per_gate_noise(mut self, cfg: PerGateTypeNoise) -> Self {
+        self.per_gate_noise = Some(cfg);
+        self
+    }
+
+    /// Register detectors by [`DetectorDef`].
+    #[must_use]
+    pub fn detectors(mut self, detectors: Vec<DetectorDef>) -> Self {
+        self.detectors = detectors;
+        self
+    }
+
+    /// Register measurement-record observables.
+    #[must_use]
+    pub fn observables(mut self, observables: Vec<DemOutput>) -> Self {
+        self.observables = observables;
+        self
+    }
+
+    /// Set the measurement order mapping from a `TickCircuit` (advanced).
+    #[must_use]
+    pub fn measurement_order(mut self, order: Vec<usize>) -> Self {
+        self.measurement_order = Some(order);
+        self
+    }
+
+    /// Build the [`DemStabSim`], consuming the builder.
+    ///
+    /// # Errors
+    ///
+    /// Returns [`DemStabError::MissingCircuit`] if no circuit was set.
+    pub fn build(self) -> Result<DemStabSim, DemStabError> {
+        let dag = self.circuit.ok_or(DemStabError::MissingCircuit)?;
+
+        let analyzer = DagFaultAnalyzer::new(&dag);
+        let influence_map = analyzer.build_influence_map();
+
+        let detector_records: Vec<Vec<i32>> =
+            self.detectors.iter().map(|d| d.records.to_vec()).collect();
+        let observable_records: Vec<Vec<i32>> = self
+            .observables
+            .iter()
+            .map(|o| o.records.to_vec())
+            .collect();
+
+        let mut builder = DemSamplerBuilder::new(&influence_map);
+        builder = if let Some(cfg) = self.per_gate_noise {
+            builder.with_per_gate_noise(cfg)
+        } else {
+            builder.with_noise(
+                self.noise.p1,
+                self.noise.p2,
+                self.noise.p_meas,
+                self.noise.p_prep,
+            )
+        };
+        builder = builder
+            .with_detector_records(detector_records)
+            .with_observable_records(observable_records);
+
+        if let Some(order) = self.measurement_order {
+            builder = builder.with_measurement_order(order);
+        }
+
+        let detectors = self.detectors.clone();
+        let observables = self.observables.clone();
+
+        Ok(DemStabSim {
+            sampler: builder.build()?,
+            detectors,
+            observables,
+        })
+    }
+}
diff --git a/crates/pecos-qec/src/fault_tolerance.rs b/crates/pecos-qec/src/fault_tolerance.rs
index b73107f66..8aa05b7a7 100644
--- a/crates/pecos-qec/src/fault_tolerance.rs
+++ b/crates/pecos-qec/src/fault_tolerance.rs
@@ -18,14 +18,17 @@
 //! For a full guide, see `docs/user-guide/fault-tolerance.md`.
 
 pub mod circuit_runner;
+pub mod correlation;
 pub mod decoder_integration;
 pub mod dem_builder;
+pub mod fault_sampler;
 pub mod gadget_checker;
 pub mod influence_builder;
-pub mod noisy_sampler;
+pub mod lookup_decoder;
 pub mod pauli_prop_checker;
 pub mod propagator;
 pub mod stabilizer_flip_checker;
+pub mod targeted_lookup_decoder;
 
 use pecos_core::QubitId;
 use pecos_core::gate_type::GateType;
@@ -53,11 +56,12 @@ pub use pauli_prop_checker::{
     has_syndrome, propagate_fault, propagate_faults,
 };
 pub use propagator::{
-    DagFaultAnalyzer, DagFaultInfluenceMap, DagPropagator, DagSpacetimeLocation, DetectorId,
-    Direction, FaultInfluence, FaultInfluenceMap, InfluenceBasedChecker, LogicalId, MeasurementId,
-    TickFaultAnalyzer, apply_gate, propagate_backward_from_node, propagate_backward_from_tick,
-    propagate_fault_backward, propagate_observable_backward, propagate_sparse_dag,
-    propagate_through_circuit, propagate_through_dag, propagate_tick_range,
+    DagFaultAnalyzer, DagFaultInfluenceMap, DagPropagator, DagSpacetimeLocation, DemOutputKind,
+    DemOutputMetadata, DetectorId, Direction, FaultInfluence, FaultInfluenceMap,
+    InfluenceBasedChecker, MeasurementId, TickFaultAnalyzer, TrackedPauliId, apply_gate,
+    propagate_backward_from_node, propagate_backward_from_tick, propagate_fault_backward,
+    propagate_observable_backward, propagate_sparse_dag, propagate_through_circuit,
+    propagate_through_dag, propagate_tick_range,
 };
 pub use stabilizer_flip_checker::{
     ErrorClass, StabilizerFlipAnalysis, StabilizerFlipChecker, StabilizerFlips,
diff --git a/crates/pecos-qec/src/fault_tolerance/circuit_runner.rs b/crates/pecos-qec/src/fault_tolerance/circuit_runner.rs
index d4b5c2cd6..1f16ca073 100644
--- a/crates/pecos-qec/src/fault_tolerance/circuit_runner.rs
+++ b/crates/pecos-qec/src/fault_tolerance/circuit_runner.rs
@@ -60,7 +60,7 @@ pub fn extract_spacetime_locations(
 
     // Iterate through all ticks
     for (tick_idx, tick) in circuit.iter_ticks() {
-        for (gate_idx, gate) in tick.gates().iter().enumerate() {
+        for gate in tick.iter_gate_batches() {
             let qubits: Vec<QubitId> = gate.qubits.iter().copied().collect();
             let is_measurement = matches!(gate.gate_type, GateType::MZ | GateType::MeasureFree);
 
@@ -69,7 +69,7 @@ pub fn extract_spacetime_locations(
                 qubits,
                 is_measurement, // Measurements get "before" errors
                 gate.gate_type,
-                gate_idx,
+                gate.batch_index(),
             ));
         }
     }
@@ -105,10 +105,10 @@ fn apply_fault<S: CliffordGateable>(sim: &mut S, fault: &PauliFault) {
 /// simulator-level batch optimizations (gate fusion, SIMD batching, etc.).
 fn apply_tick_gates<S: CliffordGateable>(sim: &mut S, tick: &pecos_quantum::Tick) {
     // For ticks with few gates, skip consolidation overhead
-    let gate_count = tick.gates().len();
+    let gate_count = tick.len();
     if gate_count <= 2 {
-        for gate in tick.gates() {
-            apply_gate(sim, gate);
+        for gate in tick.iter_gate_batches() {
+            apply_gate(sim, gate.as_gate());
         }
         return;
     }
@@ -139,7 +139,7 @@ fn apply_tick_gates<S: CliffordGateable>(sim: &mut S, tick: &pecos_quantum::Tick
     let mut mz_qubits: Vec<QubitId> = Vec::new();
     let mut pz_qubits: Vec<QubitId> = Vec::new();
 
-    for gate in tick.gates() {
+    for gate in tick.iter_gate_batches() {
         match gate.gate_type {
             GateType::H => h_qubits.extend(gate.qubits.iter()),
             GateType::X => x_qubits.extend(gate.qubits.iter()),
@@ -208,7 +208,7 @@ fn apply_tick_gates<S: CliffordGateable>(sim: &mut S, tick: &pecos_quantum::Tick
             GateType::I => {}
             _ => {
                 // Fallback: apply individually for unsupported gate types
-                apply_gate(sim, gate);
+                apply_gate(sim, gate.as_gate());
             }
         }
     }
@@ -1315,7 +1315,8 @@ mod tests {
         let mut circuit = TickCircuit::new();
         circuit.tick().pz(&[0, 1, 2]); // All prepared
         circuit.tick().h(&[0]);
-        circuit.tick().cx(&[(0, 1), (0, 2)]);
+        circuit.tick().cx(&[(0, 1)]);
+        circuit.tick().cx(&[(0, 2)]);
         // No measurement - outputs go to next stage
 
         let checker = FaultChecker::new(&circuit);
@@ -1527,9 +1528,13 @@ mod tests {
         circuit.tick().h(&[0, 1, 3]);
 
         // Entangle to create logical |0>
-        circuit.tick().cx(&[(0, 2), (1, 2)]);
-        circuit.tick().cx(&[(0, 4), (1, 5), (3, 5)]);
-        circuit.tick().cx(&[(0, 6), (1, 6), (3, 6)]);
+        circuit.tick().cx(&[(0, 2)]);
+        circuit.tick().cx(&[(1, 2)]);
+        circuit.tick().cx(&[(0, 4), (1, 5)]);
+        circuit.tick().cx(&[(3, 5)]);
+        circuit.tick().cx(&[(0, 6)]);
+        circuit.tick().cx(&[(1, 6)]);
+        circuit.tick().cx(&[(3, 6)]);
         circuit.tick().cx(&[(3, 4)]);
 
         circuit
diff --git a/crates/pecos-qec/src/fault_tolerance/correlation.rs b/crates/pecos-qec/src/fault_tolerance/correlation.rs
new file mode 100644
index 000000000..7c4430b3e
--- /dev/null
+++ b/crates/pecos-qec/src/fault_tolerance/correlation.rs
@@ -0,0 +1,617 @@
+// Copyright 2026 The PECOS Developers
+//
+// Licensed under the Apache License, Version 2.0 (the "License"); you may not use this file except
+// in compliance with the License. You may obtain a copy of the License at
+//
+//     https://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software distributed under the License
+// is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express
+// or implied. See the License for the specific language governing permissions and limitations under
+// the License.
+
+//! Detector correlation analysis for DEM validation.
+//!
+//! Computes k-body detector firing rates from sampled syndromes and
+//! compares them between simulation and DEM outputs. This captures
+//! both marginal detection rates and the correlated error structure
+//! that determines decoding quality.
+//!
+//! # Flip frequency matrix
+//!
+//! The pairwise flip frequency matrix `M` for `n` detectors:
+//! - `M[i][i]` = P(detector i fires)   (marginal rate)
+//! - `M[i][j]` = 0.5 * P(i AND j fire) (half joint rate, i != j)
+//!
+//! # Higher-order correlations
+//!
+//! K-body rates map each k-subset of detectors to its joint firing
+//! probability. For order 1 these are marginals; for order 2, pairwise;
+//! for order 3, triple correlations that test whether the DEM's
+//! independent error decomposition is adequate.
+
+use std::collections::{BTreeMap, BTreeSet};
+
+type CorrelationEntry<'a> = (&'a Vec<u32>, f64, f64);
+
+fn count_as_f64<T>(items: &[T]) -> f64 {
+    items.iter().fold(0.0, |count, _| count + 1.0)
+}
+
+/// Flat `n x n` detector flip frequency matrix.
+///
+/// Stored row-major. Use `index(i, j, n) = i * n + j`.
+#[must_use]
+pub fn flip_matrix_from_fired(fired_per_shot: &[Vec<u32>], num_detectors: usize) -> Vec<f64> {
+    let n = num_detectors;
+    let shots = fired_per_shot.len();
+    if shots == 0 {
+        return vec![0.0; n * n];
+    }
+
+    let inv = 1.0 / count_as_f64(fired_per_shot);
+    let half_inv = 0.5 * inv;
+    let mut m = vec![0.0; n * n];
+
+    for fired in fired_per_shot {
+        for (ai, &a) in fired.iter().enumerate() {
+            let a = a as usize;
+            if a >= n {
+                continue;
+            }
+            m[a * n + a] += inv;
+            for &b in &fired[ai + 1..] {
+                let b = b as usize;
+                if b >= n {
+                    continue;
+                }
+                m[a * n + b] += half_inv;
+                m[b * n + a] += half_inv;
+            }
+        }
+    }
+
+    m
+}
+
+/// Per-round flip frequency matrices.
+///
+/// Returns one flat `k x k` matrix per round, where `k = dets_per_round`.
+#[must_use]
+pub fn flip_matrices_by_round(
+    fired_per_shot: &[Vec<u32>],
+    num_detectors: usize,
+    dets_per_round: usize,
+) -> Vec<Vec<f64>> {
+    let k = dets_per_round;
+    let num_rounds = num_detectors.div_ceil(k);
+    let shots = fired_per_shot.len();
+    if shots == 0 {
+        return vec![vec![0.0; k * k]; num_rounds];
+    }
+
+    let inv = 1.0 / count_as_f64(fired_per_shot);
+    let half_inv = 0.5 * inv;
+    let mut matrices = vec![vec![0.0; k * k]; num_rounds];
+
+    for fired in fired_per_shot {
+        // Bin by round
+        let mut round_local: Vec<Vec<u32>> = vec![Vec::new(); num_rounds];
+        for &d in fired {
+            let r = d as usize / k;
+            let local = d as usize % k;
+            if r >= num_rounds {
+                continue;
+            }
+            if let Ok(local) = u32::try_from(local) {
+                round_local[r].push(local);
+            }
+        }
+
+        for (r, local_ids) in round_local.iter().enumerate() {
+            let mat = &mut matrices[r];
+            for (ai, &a) in local_ids.iter().enumerate() {
+                let a = a as usize;
+                mat[a * k + a] += inv;
+                for &b in &local_ids[ai + 1..] {
+                    let b = b as usize;
+                    mat[a * k + b] += half_inv;
+                    mat[b * k + a] += half_inv;
+                }
+            }
+        }
+    }
+
+    matrices
+}
+
+/// K-body detector firing rates up to `max_order`.
+///
+/// Returns a map from sorted detector index tuples to joint firing
+/// probability. Keys are ordered ascending.
+#[must_use]
+pub fn k_body_rates(
+    fired_per_shot: &[Vec<u32>],
+    num_detectors: usize,
+    max_order: usize,
+) -> BTreeMap<Vec<u32>, f64> {
+    let shots = fired_per_shot.len();
+    if shots == 0 {
+        return BTreeMap::new();
+    }
+
+    let inv = 1.0 / count_as_f64(fired_per_shot);
+    let mut rates: BTreeMap<Vec<u32>, f64> = BTreeMap::new();
+
+    for fired in fired_per_shot {
+        let valid_fired: Vec<u32> = fired
+            .iter()
+            .copied()
+            .filter(|&d| (d as usize) < num_detectors)
+            .collect();
+        let n = valid_fired.len().min(max_order);
+        for order in 1..=n {
+            for_each_combination(&valid_fired, order, |combo| {
+                *rates.entry(combo.to_vec()).or_insert(0.0) += inv;
+            });
+        }
+    }
+
+    rates
+}
+
+/// Per-round k-body rates. Detector indices in the returned maps are
+/// round-local (0..dets_per_round-1).
+#[must_use]
+pub fn k_body_rates_by_round(
+    fired_per_shot: &[Vec<u32>],
+    num_detectors: usize,
+    dets_per_round: usize,
+    max_order: usize,
+) -> Vec<BTreeMap<Vec<u32>, f64>> {
+    let k = dets_per_round;
+    let num_rounds = num_detectors.div_ceil(k);
+    let shots = fired_per_shot.len();
+    if shots == 0 {
+        return vec![BTreeMap::new(); num_rounds];
+    }
+
+    let inv = 1.0 / count_as_f64(fired_per_shot);
+    let mut round_rates: Vec<BTreeMap<Vec<u32>, f64>> = vec![BTreeMap::new(); num_rounds];
+
+    for fired in fired_per_shot {
+        let mut round_local: Vec<Vec<u32>> = vec![Vec::new(); num_rounds];
+        for &d in fired {
+            let r = d as usize / k;
+            let local = d as usize % k;
+            if r >= num_rounds {
+                continue;
+            }
+            if let Ok(local) = u32::try_from(local) {
+                round_local[r].push(local);
+            }
+        }
+
+        for (r, local_ids) in round_local.iter().enumerate() {
+            let n = local_ids.len().min(max_order);
+            let rr = &mut round_rates[r];
+            for order in 1..=n {
+                for_each_combination(local_ids, order, |combo| {
+                    *rr.entry(combo.to_vec()).or_insert(0.0) += inv;
+                });
+            }
+        }
+    }
+
+    round_rates
+}
+
+/// Compare k-body rates between two sets, grouped by order.
+///
+/// Returns a map from order to `(max_rel_error, rms_rel_error, worst_event)`.
+#[must_use]
+pub fn compare_k_body(
+    sim: &BTreeMap<Vec<u32>, f64>,
+    dem: &BTreeMap<Vec<u32>, f64>,
+    min_rate: f64,
+) -> BTreeMap<usize, (f64, f64, Vec<u32>)> {
+    let all_keys: BTreeSet<&Vec<u32>> = sim.keys().chain(dem.keys()).collect();
+
+    let mut by_order: BTreeMap<usize, Vec<CorrelationEntry<'_>>> = BTreeMap::new();
+    for &key in &all_keys {
+        let s = sim.get(key).copied().unwrap_or(0.0);
+        let d = dem.get(key).copied().unwrap_or(0.0);
+        by_order.entry(key.len()).or_default().push((key, s, d));
+    }
+
+    let mut result = BTreeMap::new();
+    for (order, entries) in &by_order {
+        let mut max_err = 0.0_f64;
+        let mut worst: Vec<u32> = Vec::new();
+        let mut sum_sq = 0.0;
+        let mut count = 0.0;
+
+        for &(key, s, d) in entries {
+            if s > min_rate {
+                let rel = (d / s - 1.0).abs();
+                if rel > max_err {
+                    max_err = rel;
+                    worst.clone_from(key);
+                }
+                sum_sq += rel * rel;
+                count += 1.0;
+            }
+        }
+
+        let rms = if count > 0.0 {
+            (sum_sq / count).sqrt()
+        } else {
+            0.0
+        };
+        result.insert(*order, (max_err, rms, worst));
+    }
+
+    result
+}
+
+/// Compare two flat flip matrices. Returns `(max_rel_err, frob_rel_err, worst_i, worst_j)`.
+#[must_use]
+pub fn compare_flip_matrices(
+    sim: &[f64],
+    dem: &[f64],
+    n: usize,
+    min_rate: f64,
+) -> (f64, f64, usize, usize) {
+    let mut max_err = 0.0_f64;
+    let mut worst_i = 0;
+    let mut worst_j = 0;
+    let mut sum_sq_diff = 0.0;
+    let mut sum_sq_sim = 0.0;
+
+    for i in 0..n {
+        for j in 0..n {
+            let idx = i * n + j;
+            let s = sim[idx];
+            let d = dem[idx];
+            let diff = d - s;
+            sum_sq_diff += diff * diff;
+            sum_sq_sim += s * s;
+            if s > min_rate {
+                let rel = diff.abs() / s;
+                if rel > max_err {
+                    max_err = rel;
+                    worst_i = i;
+                    worst_j = j;
+                }
+            }
+        }
+    }
+
+    let frob = sum_sq_diff.sqrt() / sum_sq_sim.sqrt().max(1e-30);
+    (max_err, frob, worst_i, worst_j)
+}
+
+// ---------------------------------------------------------------------------
+// Hybrid DEM: fit mechanism probabilities to target marginals
+// ---------------------------------------------------------------------------
+
+/// A DEM mechanism: probability + detector/DEM-output sets.
+#[derive(Debug, Clone)]
+pub struct DemMechanism {
+    pub probability: f64,
+    pub detectors: Vec<u32>,
+    pub observables: Vec<u32>,
+}
+
+/// Fit DEM mechanism probabilities to match target detector marginals.
+///
+/// Given a set of mechanisms (each with a detector set and initial
+/// probability) and target per-detector marginal rates, adjusts the
+/// mechanism probabilities so the DEM's independent-error marginals
+/// match the targets as closely as possible.
+///
+/// Uses iterative proportional fitting on the exact DEM marginal equation:
+///
+/// ```text
+/// p_d = 1/2 - 1/2 * prod_{m: d in S_m} (1 - 2*q_m)
+/// ```
+///
+/// Each iteration computes current marginals, then scales each mechanism
+/// by the geometric mean of (target/current) ratios for the detectors
+/// it affects. Mechanisms with no detector overlap are untouched.
+///
+/// Returns the fitted mechanisms and per-detector residual errors.
+#[must_use]
+pub fn fit_dem_to_marginals(
+    mechanisms: &[DemMechanism],
+    target_marginals: &[f64],
+    max_iterations: usize,
+    tolerance: f64,
+) -> (Vec<DemMechanism>, Vec<f64>) {
+    let num_dets = target_marginals.len();
+    let n_mech = mechanisms.len();
+
+    // Build sparse incidence: for each detector, which mechanisms touch it
+    let mut det_to_mechs: Vec<Vec<usize>> = vec![Vec::new(); num_dets];
+    for (m, mech) in mechanisms.iter().enumerate() {
+        for &d in &mech.detectors {
+            if (d as usize) < num_dets {
+                det_to_mechs[d as usize].push(m);
+            }
+        }
+    }
+
+    let mut q: Vec<f64> = mechanisms.iter().map(|m| m.probability).collect();
+
+    for _iter in 0..max_iterations {
+        // Compute current marginals from mechanism probabilities
+        let mut current = vec![0.0_f64; num_dets];
+        for d in 0..num_dets {
+            let mut prod = 1.0;
+            for &m in &det_to_mechs[d] {
+                prod *= 1.0 - 2.0 * q[m];
+            }
+            current[d] = (1.0 - prod) / 2.0;
+        }
+
+        // Compute per-detector ratios
+        let mut ratios = vec![1.0_f64; num_dets];
+        for d in 0..num_dets {
+            if current[d] > 1e-20 {
+                ratios[d] = target_marginals[d] / current[d];
+            } else if target_marginals[d] > 1e-20 {
+                ratios[d] = 10.0; // large but bounded nudge
+            }
+        }
+
+        // Scale each mechanism by geometric mean of its detector ratios
+        let mut max_change = 0.0_f64;
+        for m in 0..n_mech {
+            let dets = &mechanisms[m].detectors;
+            if dets.is_empty() {
+                continue;
+            }
+            let mut log_ratio = 0.0;
+            let mut count = 0;
+            for &d in dets {
+                if (d as usize) < num_dets {
+                    log_ratio += ratios[d as usize].max(1e-10).ln();
+                    count += 1;
+                }
+            }
+            if count == 0 {
+                continue;
+            }
+            let scale = (log_ratio / f64::from(count)).exp();
+            let new_q = (q[m] * scale).clamp(0.0, 0.499);
+            max_change = max_change.max((new_q - q[m]).abs());
+            q[m] = new_q;
+        }
+
+        if max_change < tolerance {
+            break;
+        }
+    }
+
+    // Compute final residuals
+    let mut residuals = vec![0.0; num_dets];
+    for d in 0..num_dets {
+        let mut prod = 1.0;
+        for &m in &det_to_mechs[d] {
+            prod *= 1.0 - 2.0 * q[m];
+        }
+        let fitted = (1.0 - prod) / 2.0;
+        residuals[d] = (fitted - target_marginals[d]).abs();
+    }
+
+    let fitted: Vec<DemMechanism> = mechanisms
+        .iter()
+        .zip(q.iter())
+        .map(|(mech, &prob)| DemMechanism {
+            probability: prob,
+            detectors: mech.detectors.clone(),
+            observables: mech.observables.clone(),
+        })
+        .collect();
+
+    (fitted, residuals)
+}
+
+/// Format fitted mechanisms as a standard DEM string.
+#[must_use]
+pub fn mechanisms_to_dem_string(mechanisms: &[DemMechanism]) -> String {
+    let mut lines = Vec::new();
+    for mech in mechanisms {
+        if mech.probability > 1e-15 {
+            let mut tokens = Vec::new();
+            for &d in &mech.detectors {
+                tokens.push(format!("D{d}"));
+            }
+            for &o in &mech.observables {
+                tokens.push(format!("L{o}"));
+            }
+            if !tokens.is_empty() {
+                lines.push(format!(
+                    "error({:.10e}) {}",
+                    mech.probability,
+                    tokens.join(" ")
+                ));
+            }
+        }
+    }
+    lines.join("\n")
+}
+
+// --- Internal helpers ---
+
+/// Iterate over all k-combinations of `items`, calling `f` with each sorted combination.
+fn for_each_combination(items: &[u32], k: usize, mut f: impl FnMut(&[u32])) {
+    if k == 0 || items.len() < k {
+        return;
+    }
+    let mut combo = vec![0u32; k];
+    combination_recurse(items, k, 0, 0, &mut combo, &mut f);
+}
+
+fn combination_recurse(
+    items: &[u32],
+    k: usize,
+    start: usize,
+    depth: usize,
+    combo: &mut [u32],
+    f: &mut impl FnMut(&[u32]),
+) {
+    if depth == k {
+        f(&combo[..k]);
+        return;
+    }
+    let remaining = k - depth;
+    if start + remaining > items.len() {
+        return;
+    }
+    for i in start..=items.len() - remaining {
+        combo[depth] = items[i];
+        combination_recurse(items, k, i + 1, depth + 1, combo, f);
+    }
+}
+
+#[cfg(test)]
+mod tests {
+    use super::*;
+
+    #[test]
+    fn test_flip_matrix_single_detector() {
+        // 100 shots, detector 0 fires 30 times
+        let fired: Vec<Vec<u32>> = (0..100)
+            .map(|i| if i < 30 { vec![0] } else { vec![] })
+            .collect();
+        let m = flip_matrix_from_fired(&fired, 2);
+        assert!((m[0] - 0.3).abs() < 1e-10); // M[0,0] = 0.3
+        assert!(m[1].abs() < 1e-10); // M[0,1] = 0
+        assert!(m[3].abs() < 1e-10); // M[1,1] = 0
+    }
+
+    #[test]
+    fn test_flip_matrix_correlated_pair() {
+        // 100 shots, detectors 0 and 1 always fire together
+        let fired: Vec<Vec<u32>> = (0..100)
+            .map(|i| if i < 20 { vec![0, 1] } else { vec![] })
+            .collect();
+        let m = flip_matrix_from_fired(&fired, 2);
+        assert!((m[0] - 0.2).abs() < 1e-10); // M[0,0]
+        assert!((m[3] - 0.2).abs() < 1e-10); // M[1,1]
+        assert!((m[1] - 0.1).abs() < 1e-10); // M[0,1] = 0.5 * 0.2
+        assert!((m[2] - 0.1).abs() < 1e-10); // M[1,0] = 0.5 * 0.2
+    }
+
+    #[test]
+    fn test_k_body_rates_basic() {
+        let fired = vec![vec![0, 1, 2], vec![0, 1], vec![0], vec![]];
+        let rates = k_body_rates(&fired, 3, 3);
+        assert!((rates[&vec![0]] - 0.75).abs() < 1e-10);
+        assert!((rates[&vec![1]] - 0.5).abs() < 1e-10);
+        assert!((rates[&vec![0, 1]] - 0.5).abs() < 1e-10);
+        assert!((rates[&vec![0, 1, 2]] - 0.25).abs() < 1e-10);
+    }
+
+    #[test]
+    fn test_compare_k_body_basic() {
+        let mut sim = BTreeMap::new();
+        sim.insert(vec![0], 0.1);
+        sim.insert(vec![1], 0.2);
+        sim.insert(vec![0, 1], 0.01);
+
+        let mut dem = BTreeMap::new();
+        dem.insert(vec![0], 0.1);
+        dem.insert(vec![1], 0.2);
+        dem.insert(vec![0, 1], 0.012);
+
+        let result = compare_k_body(&sim, &dem, 0.005);
+        // 1-body: exact match
+        assert!(result[&1].0 < 1e-10);
+        // 2-body: 20% relative error on (0,1)
+        assert!((result[&2].0 - 0.2).abs() < 1e-10);
+    }
+
+    #[test]
+    fn test_by_round_splits_correctly() {
+        // 4 detectors, 2 per round -> 2 rounds
+        let fired = vec![vec![0, 2], vec![1, 3]];
+        let mats = flip_matrices_by_round(&fired, 4, 2);
+        assert_eq!(mats.len(), 2);
+        // Round 0: det 0 in shot 0, det 1 in shot 1
+        assert!((mats[0][0] - 0.5).abs() < 1e-10); // M[0,0]
+        assert!((mats[0][3] - 0.5).abs() < 1e-10); // M[1,1]
+        // Round 1: det 0(=global 2) in shot 0, det 1(=global 3) in shot 1
+        assert!((mats[1][0] - 0.5).abs() < 1e-10);
+        assert!((mats[1][3] - 0.5).abs() < 1e-10);
+    }
+
+    #[test]
+    fn test_fit_dem_to_marginals_exact() {
+        // Two mechanisms: M0 flips {D0}, M1 flips {D0, D1}
+        // Target: P(D0) = 0.15, P(D1) = 0.05
+        let mechs = vec![
+            DemMechanism {
+                probability: 0.1,
+                detectors: vec![0],
+                observables: vec![],
+            },
+            DemMechanism {
+                probability: 0.05,
+                detectors: vec![0, 1],
+                observables: vec![],
+            },
+        ];
+        let target = vec![0.15, 0.05];
+        let (fitted, residuals) = fit_dem_to_marginals(&mechs, &target, 100, 1e-12);
+
+        // M1 flips only D1, so q1 must satisfy (1-2*q1)/2 ≈ 0.05 → q1 ≈ 0.05
+        // Then q0 must satisfy 1/2(1-(1-2*q0)(1-2*q1)) = 0.15
+        assert!(residuals[0] < 1e-6, "D0 residual: {}", residuals[0]);
+        assert!(residuals[1] < 1e-6, "D1 residual: {}", residuals[1]);
+        assert!(fitted[1].probability > 0.04 && fitted[1].probability < 0.06);
+    }
+
+    #[test]
+    fn test_fit_dem_preserves_structure() {
+        let mechs = vec![
+            DemMechanism {
+                probability: 0.01,
+                detectors: vec![0],
+                observables: vec![0],
+            },
+            DemMechanism {
+                probability: 0.02,
+                detectors: vec![1],
+                observables: vec![],
+            },
+        ];
+        let target = vec![0.05, 0.08];
+        let (fitted, _) = fit_dem_to_marginals(&mechs, &target, 100, 1e-12);
+
+        // Structure preserved
+        assert_eq!(fitted[0].detectors, vec![0]);
+        assert_eq!(fitted[0].observables, vec![0]);
+        assert_eq!(fitted[1].detectors, vec![1]);
+    }
+
+    #[test]
+    fn test_mechanisms_to_dem_string() {
+        let mechs = vec![
+            DemMechanism {
+                probability: 0.01,
+                detectors: vec![0, 1],
+                observables: vec![],
+            },
+            DemMechanism {
+                probability: 0.001,
+                detectors: vec![2],
+                observables: vec![0],
+            },
+        ];
+        let s = mechanisms_to_dem_string(&mechs);
+        assert!(s.contains("D0 D1"));
+        assert!(s.contains("D2 L0"));
+    }
+}
diff --git a/crates/pecos-qec/src/fault_tolerance/dem_builder.rs b/crates/pecos-qec/src/fault_tolerance/dem_builder.rs
index 50b81940f..59d79fd0a 100644
--- a/crates/pecos-qec/src/fault_tolerance/dem_builder.rs
+++ b/crates/pecos-qec/src/fault_tolerance/dem_builder.rs
@@ -12,14 +12,13 @@
 
 //! Detector Error Model (DEM) generation from fault influence maps.
 //!
-//! This module provides Rust-native DEM generation that produces output
-//! compatible with Stim's format. It uses the per-qubit fault model for
-//! accurate depolarizing noise analysis.
+//! This module provides Rust-native DEM generation in standard DEM text format.
+//! It uses the per-qubit fault model for accurate depolarizing noise analysis.
 //!
 //! # Architecture
 //!
 //! The DEM builder takes a [`DagFaultInfluenceMap`] (which maps fault locations
-//! to their effects on measurements) and detector/observable metadata to produce
+//! to their effects on measurements) and detector/DEM-output metadata to produce
 //! a complete DEM.
 //!
 //! # Example
@@ -39,7 +38,7 @@
 //!     .with_observables_json("[]")?
 //!     .build();
 //!
-//! // Output in Stim format (non-decomposed).
+//! // Output in standard DEM format (non-decomposed).
 //! let _ = dem.to_string();
 //! # Ok(())
 //! # }
@@ -47,7 +46,7 @@
 //!
 //! # Error Decomposition
 //!
-//! When using `to_stim_format_decomposed()`, hyperedge errors (affecting 3+
+//! When using decomposed DEM output, hyperedge errors (affecting 3+
 //! detectors) are decomposed into combinations of graphlike errors (affecting
 //! 1-2 detectors). This is necessary for MWPM decoders which only work on
 //! graphs, not hypergraphs.
@@ -64,7 +63,7 @@
 //!   Pauli combinations (IX, IY, IZ, XI, ..., ZZ) are considered.
 //!
 //! - **XOR effect combining**: Correlated errors are properly combined
-//!   by XOR-ing detector/observable effects.
+//!   by XOR-ing detector/DEM-output effects.
 //!
 //! - **Independent probability combination**: When the same fault mechanism
 //!   is triggered by multiple error sources, probabilities are combined
@@ -72,50 +71,35 @@
 //!
 //! # Measurement Noise Model (MNM)
 //!
-//! In addition to the DEM, this module provides a Measurement Noise Model (MNM)
-//! for fast approximate sampling. Unlike the DEM which maps to detectors, the
-//! MNM maps directly to raw measurement effects.
-//!
-//! ```
-//! use pecos_qec::fault_tolerance::dem_builder::MemBuilder;
-//! use pecos_qec::fault_tolerance::propagator::DagFaultInfluenceMap;
-//! use rand::SeedableRng;
-//! use rand::rngs::StdRng;
-//!
-//! // Normally `influence_map` comes from `DagFaultAnalyzer::build_influence_map()`;
-//! // here we use an empty map to keep the doctest self-contained.
-//! let influence_map = DagFaultInfluenceMap::with_capacity(0);
-//!
-//! let mnm = MemBuilder::new(&influence_map)
-//!     .with_noise(0.01, 0.01, 0.01, 0.01)
-//!     .build();
-//!
-//! let mut rng = StdRng::seed_from_u64(0);
-//! let _outcomes = mnm.sample(&mut rng);
-//! ```
-//!
-//! The MNM aggregates fault locations by their measurement effects (which
-//! measurements flip together), enabling faster sampling with fewer random
-//! draws compared to per-fault-location sampling.
+//! The [`DemSampler`] provides both raw measurement and detector-event
+//! output from a single mechanism engine. It replaces the former `MemBuilder`
+//! (measurement-level) and `DemSamplerBuilder` (detector-level) paths with a
+//! unified interface that validates detector definitions at build time.
 
 mod builder;
 mod dem_sampler;
 mod equivalence;
 mod mem_builder;
+pub(crate) mod sampler;
 mod types;
 
 pub use builder::{DemBuilder, DemBuilderError};
-pub use dem_sampler::{DemSampler, DemSamplerBuilder, SamplingStatistics};
+pub use dem_sampler::{SamplingEngine, SamplingStatistics};
 pub use equivalence::{
     ComparisonDetails, ComparisonMethod, DemParseError, EffectKey, EquivalenceResult,
     MechanismComponent, ParsedDem, ParsedMechanism, ProbabilityMismatch, compare_dems_exact,
     compare_dems_statistical, verify_dem_equivalence,
 };
 pub use mem_builder::MemBuilder;
+pub use sampler::{
+    DemSampler, DemSamplerBuilder, DetectorValidationError, DualSampleResult, OutputMode,
+    SamplerLabels,
+};
 pub use types::{
     ContributionEffectSummary, ContributionRenderRecord, ContributionRenderStrategy,
-    ContributionRenderSummary, DecomposedFault, DetectorDef, DetectorErrorModel,
-    DirectSourceFamily, FaultContribution, FaultMechanism, FaultSourceType, LogicalObservable,
-    MeasurementMechanism, MeasurementNoiseModel, NoiseConfig, TwoDetectorDirectRenderPolicy,
-    combine_probabilities, record_offset_to_absolute_index,
+    ContributionRenderSummary, DecomposedFault, DemOutput, DetectorDef, DetectorErrorModel,
+    DirectSourceFamily, FaultContribution, FaultMechanism, FaultSourceType, MeasurementMechanism,
+    MeasurementNoiseModel, NoiseConfig, PAULI_1Q_ORDER, PAULI_2Q_ORDER, PauliProbs, PauliWeights,
+    PecosDemMetadataError, PerGateTypeNoise, TwoDetectorDirectRenderPolicy, combine_probabilities,
+    record_offset_to_absolute_index,
 };
diff --git a/crates/pecos-qec/src/fault_tolerance/dem_builder/builder.rs b/crates/pecos-qec/src/fault_tolerance/dem_builder/builder.rs
index 0a4db2452..ae792f1b1 100644
--- a/crates/pecos-qec/src/fault_tolerance/dem_builder/builder.rs
+++ b/crates/pecos-qec/src/fault_tolerance/dem_builder/builder.rs
@@ -13,12 +13,13 @@
 //! DEM (Detector Error Model) builder implementation.
 //!
 //! This module provides the main builder for constructing DEMs from fault
-//! influence maps and detector/observable metadata.
+//! influence maps and detector/DEM-output metadata.
 
 use super::types::{
-    DetectorDef, DetectorErrorModel, DirectSourceComponents, FaultMechanism, LogicalObservable,
-    NoiseConfig, SourceMetadata, record_offset_to_absolute_index,
+    DemOutput, DetectorDef, DetectorErrorModel, DirectSourceComponents, FaultMechanism,
+    NoiseConfig, PerGateTypeNoise, SourceMetadata, record_offset_to_absolute_index,
 };
+use crate::fault_tolerance::propagator::dag::DagSpacetimeLocation;
 use crate::fault_tolerance::propagator::{DagFaultInfluenceMap, Pauli};
 use pecos_core::gate_type::GateType;
 use smallvec::SmallVec;
@@ -49,39 +50,56 @@ struct ParsedObservable {
 
 /// Builder for Detector Error Models (DEMs).
 ///
-/// Constructs a DEM from a fault influence map and detector/observable metadata.
-/// Uses the per-qubit fault model for accurate depolarizing noise analysis.
+/// # Simple API (recommended)
 ///
-/// # Example
+/// For most use cases, use the one-liner:
 ///
 /// ```
 /// use pecos_qec::fault_tolerance::dem_builder::DemBuilder;
-/// use pecos_qec::fault_tolerance::propagator::DagFaultInfluenceMap;
+/// use pecos_quantum::DagCircuit;
 ///
-/// # fn main() -> Result<(), Box<dyn std::error::Error>> {
-/// let influence_map = DagFaultInfluenceMap::with_capacity(0);
-/// let detectors_json = "[]";
-/// let observables_json = "[]";
+/// // Build DEM from circuit + noise (reads detectors from circuit metadata)
+/// let dag = DagCircuit::new();
+/// let dem = DemBuilder::from_circuit(&dag, 0.001, 0.01, 0.001, 0.001);
+/// assert_eq!(dem.num_detectors(), 0);
+/// ```
+///
+/// Also works with `TickCircuit`:
+///
+/// ```
+/// use pecos_qec::fault_tolerance::dem_builder::DemBuilder;
+/// use pecos_quantum::TickCircuit;
+///
+/// let tc = TickCircuit::new();
+/// let dem = DemBuilder::from_tick_circuit(&tc, 0.001, 0.01, 0.001, 0.001);
+/// assert_eq!(dem.num_detectors(), 0);
+/// ```
+///
+/// # Advanced API
 ///
+/// For custom influence maps, non-standard noise, or manual detector
+/// definitions, use the step-by-step builder:
+///
+/// ```no_run
+/// # use pecos_qec::fault_tolerance::dem_builder::DemBuilder;
+/// # use pecos_qec::fault_tolerance::propagator::DagFaultInfluenceMap;
+/// # let influence_map = DagFaultInfluenceMap::with_capacity(0);
 /// let dem = DemBuilder::new(&influence_map)
 ///     .with_noise(0.01, 0.01, 0.01, 0.01)
-///     .with_detectors_json(detectors_json)?
-///     .with_observables_json(observables_json)?
+///     .with_detectors_json("[]").unwrap()
 ///     .build();
-///
-/// // Non-decomposed output (matches Stim's decompose_errors=False)
-/// let _ = dem.to_string();
-///
-/// // Decomposed output (matches Stim's decompose_errors=True)
-/// let _ = dem.to_string_decomposed();
-/// # Ok(())
-/// # }
 /// ```
 pub struct DemBuilder<'a> {
     /// Reference to the fault influence map.
     influence_map: &'a DagFaultInfluenceMap,
-    /// Noise configuration.
+    /// Uniform-depolarizing noise configuration. When `per_gate` is also
+    /// set, its per-qubit / per-Pauli overrides take precedence; this
+    /// `NoiseConfig` still seeds measurement/prep scalars.
     noise: NoiseConfig,
+    /// Optional per-gate-type per-Pauli noise spec. Mirrors the
+    /// `DemSamplerBuilder` path so DEM text export reflects the same
+    /// asymmetric noise structure that the sampler does.
+    per_gate: Option<PerGateTypeNoise>,
     /// Parsed detector definitions.
     detectors: Vec<ParsedDetector>,
     /// Parsed observable definitions.
@@ -94,12 +112,56 @@ pub struct DemBuilder<'a> {
 }
 
 impl<'a> DemBuilder<'a> {
+    /// Build a `DetectorErrorModel` directly from a circuit and noise.
+    ///
+    /// One-liner for the common case. Reads detector/DEM output definitions
+    /// from circuit metadata (`"detectors"`, `"observables"` attributes).
+    ///
+    /// ```
+    /// use pecos_qec::fault_tolerance::dem_builder::DemBuilder;
+    /// use pecos_quantum::DagCircuit;
+    ///
+    /// let dag = DagCircuit::new();
+    /// let dem = DemBuilder::from_circuit(&dag, 0.001, 0.01, 0.001, 0.001);
+    /// assert_eq!(dem.num_detectors(), 0);
+    /// ```
+    /// Build a `DetectorErrorModel` directly from a `DagCircuit` and noise.
+    ///
+    /// One-liner for the common case. Reads detector/DEM output definitions
+    /// from circuit metadata.
+    #[must_use]
+    pub fn from_circuit(
+        circuit: &pecos_quantum::DagCircuit,
+        p1: f64,
+        p2: f64,
+        p_meas: f64,
+        p_prep: f64,
+    ) -> DetectorErrorModel {
+        build_dem_from_circuit(circuit, p1, p2, p_meas, p_prep)
+    }
+
+    /// Build a `DetectorErrorModel` from a `TickCircuit` and noise.
+    ///
+    /// Converts to `DagCircuit` internally.
+    #[must_use]
+    pub fn from_tick_circuit(
+        circuit: &pecos_quantum::TickCircuit,
+        p1: f64,
+        p2: f64,
+        p_meas: f64,
+        p_prep: f64,
+    ) -> DetectorErrorModel {
+        let dag = pecos_quantum::DagCircuit::from(circuit);
+        build_dem_from_circuit(&dag, p1, p2, p_meas, p_prep)
+    }
+
     /// Creates a new DEM builder from a fault influence map.
     #[must_use]
     pub fn new(influence_map: &'a DagFaultInfluenceMap) -> Self {
         Self {
             influence_map,
             noise: NoiseConfig::default(),
+            per_gate: None,
             detectors: Vec::new(),
             observables: Vec::new(),
             num_measurements: influence_map.measurements.len(),
@@ -107,13 +169,140 @@ impl<'a> DemBuilder<'a> {
         }
     }
 
-    /// Sets the noise configuration.
+    /// Sets the noise configuration from individual parameters.
+    #[must_use]
+    pub fn with_noise(mut self, p1: f64, p2: f64, p_meas: f64, p_prep: f64) -> Self {
+        self.noise = NoiseConfig::new(p1, p2, p_meas, p_prep);
+        self
+    }
+
+    /// Sets the full noise configuration (supports custom weights, T1/T2, idle).
+    #[must_use]
+    pub fn with_noise_config(mut self, noise: NoiseConfig) -> Self {
+        self.noise = noise;
+        self
+    }
+
+    /// Attach per-gate-type per-Pauli noise. When present, overrides
+    /// [`Self::with_noise`] scalars for gate types in the spec's maps.
+    /// Mirrors
+    /// [`crate::fault_tolerance::dem_builder::DemSamplerBuilder::with_per_gate_noise`]
+    /// so the DEM text output reflects the same noise structure.
     #[must_use]
-    pub fn with_noise(mut self, p1: f64, p2: f64, p_meas: f64, p_init: f64) -> Self {
-        self.noise = NoiseConfig::new(p1, p2, p_meas, p_init);
+    pub fn with_per_gate_noise(mut self, cfg: PerGateTypeNoise) -> Self {
+        self.noise.p_meas = cfg.p_meas;
+        self.noise.p_prep = cfg.p_init;
+        self.per_gate = Some(cfg);
         self
     }
 
+    /// Resolve preparation X-error rate at a specific location.
+    fn init_rate_for_loc(&self, loc: &DagSpacetimeLocation) -> f64 {
+        if let Some(pg) = &self.per_gate
+            && let Some(q) = loc.qubits.first()
+        {
+            return pg.init_rate_on(*q);
+        }
+        self.noise.p_prep
+    }
+
+    /// Resolve measurement X-flip rate at a specific location.
+    fn measurement_rate_for_loc(&self, loc: &DagSpacetimeLocation) -> f64 {
+        if let Some(pg) = &self.per_gate
+            && let Some(q) = loc.qubits.first()
+        {
+            return pg.measurement_rate_on(*q);
+        }
+        self.noise.p_meas
+    }
+
+    /// Resolve `[rate_X, rate_Y, rate_Z]` for a 1Q gate location.
+    fn rates_1q_for_loc(&self, loc: &DagSpacetimeLocation) -> [f64; 3] {
+        if let Some(pg) = &self.per_gate {
+            if let Some(q) = loc.qubits.first() {
+                return [
+                    pg.rate_1q_on(loc.gate_type, *q, 0),
+                    pg.rate_1q_on(loc.gate_type, *q, 1),
+                    pg.rate_1q_on(loc.gate_type, *q, 2),
+                ];
+            }
+            return [
+                pg.rate_1q(loc.gate_type, 0),
+                pg.rate_1q(loc.gate_type, 1),
+                pg.rate_1q(loc.gate_type, 2),
+            ];
+        }
+        if let Some(weights) = &self.noise.p1_weights {
+            use pecos_core::pauli::{X, Y, Z};
+            return [
+                self.noise.p1 * weights.weight_for(&X(0)),
+                self.noise.p1 * weights.weight_for(&Y(0)),
+                self.noise.p1 * weights.weight_for(&Z(0)),
+            ];
+        }
+        let per = per_channel_probability(self.noise.p1, 3);
+        [per, per, per]
+    }
+
+    /// Resolve `[rate_X, rate_Y, rate_Z]` for an explicit idle location.
+    fn idle_rates_for_loc(&self, loc: &DagSpacetimeLocation) -> [f64; 3] {
+        if let Some(pg) = &self.per_gate {
+            let explicit_rates = loc
+                .qubits
+                .first()
+                .and_then(|q| pg.explicit_1q_rates_on(GateType::Idle, *q))
+                .or_else(|| pg.explicit_1q_rates(GateType::Idle));
+            if let Some(rates) = explicit_rates {
+                return rates;
+            }
+            if pg.base.uses_dedicated_idle_noise() {
+                #[allow(clippy::cast_precision_loss)]
+                let duration = loc.idle_duration.max(1) as f64;
+                let probs = pg.base.idle_pauli_probs(duration);
+                return [probs.px, probs.py, probs.pz];
+            }
+            return [0.0; 3];
+        }
+
+        if self.noise.uses_dedicated_idle_noise() {
+            #[allow(clippy::cast_precision_loss)]
+            let duration = loc.idle_duration.max(1) as f64;
+            let probs = self.noise.idle_pauli_probs(duration);
+            return [probs.px, probs.py, probs.pz];
+        }
+        [0.0; 3]
+    }
+
+    /// Resolve the 15-entry 2Q per-Pauli-pair rate array for a gate
+    /// spanning two fault locations.
+    fn rates_2q_for_locs(
+        &self,
+        loc1: &DagSpacetimeLocation,
+        loc2: &DagSpacetimeLocation,
+    ) -> [f64; 15] {
+        if let Some(pg) = &self.per_gate {
+            let gate = loc1.gate_type;
+            let mut qubits = loc1
+                .qubits
+                .iter()
+                .copied()
+                .chain(loc2.qubits.iter().copied());
+            if let (Some(qc), Some(qt)) = (qubits.next(), qubits.next()) {
+                return std::array::from_fn(|i| pg.rate_2q_on(gate, qc, qt, i));
+            }
+            return std::array::from_fn(|i| pg.rate_2q(gate, i));
+        }
+        if let Some(weights) = &self.noise.p2_weights {
+            return std::array::from_fn(|idx| {
+                let flat = idx + 1;
+                let p1 = flat / 4;
+                let p2 = flat % 4;
+                self.noise.p2 * weights.weight_for(&pauli_pair_for_weight(p1, p2))
+            });
+        }
+        [per_channel_probability(self.noise.p2, 15); 15]
+    }
+
     /// Sets the number of measurements (used for record offset calculation).
     #[must_use]
     pub fn with_num_measurements(mut self, num: usize) -> Self {
@@ -129,6 +318,13 @@ impl<'a> DemBuilder<'a> {
     /// indices (which may use a different order based on DAG topology).
     ///
     /// # Arguments
+    /// Set the measurement order for legacy circuits without `MeasId` on gates.
+    ///
+    /// **Not needed for circuits built with `TickCircuit.mz()`** — the `MeasId`
+    /// values on gates ensure correct ordering automatically.
+    ///
+    /// Only use this for circuits where MZ gates lack `meas_ids` (e.g.,
+    /// circuits imported from external formats without measurement IDs).
     ///
     /// * `order` - List of qubit indices in measurement execution order.
     ///   `order[i]` is the qubit measured at `TickCircuit` measurement index `i`.
@@ -160,15 +356,10 @@ impl<'a> DemBuilder<'a> {
 
     /// Parses and sets observable definitions from JSON.
     ///
-    /// Each object accepts either `"id"` or `"observable_id"` as the identifier key.
+    /// Tracked Paulis are carried by the influence map; this helper is only
+    /// for observable metadata.
     ///
-    /// Expected format:
-    /// ```json
-    /// [
-    ///   {"id": 0, "records": [-1, -3, -5]},
-    ///   {"observable_id": 1, "records": [-2]}
-    /// ]
-    /// ```
+    /// Each object accepts either `"id"` or `"observable_id"` as the identifier key.
     ///
     /// # Errors
     ///
@@ -178,6 +369,21 @@ impl<'a> DemBuilder<'a> {
         Ok(self)
     }
 
+    /// Sets observable definitions from measurement-record offsets.
+    #[must_use]
+    pub fn with_observable_records(mut self, records: Vec<Vec<i32>>) -> Self {
+        self.observables = records
+            .into_iter()
+            .enumerate()
+            .map(|(id, records)| ParsedObservable {
+                #[allow(clippy::cast_possible_truncation)] // observable count fits in u32
+                id: id as u32,
+                records,
+            })
+            .collect();
+        self
+    }
+
     /// Builds the Detector Error Model with source tracking.
     ///
     /// This performs fault propagation analysis and tracks error sources (X/Z vs Y)
@@ -186,6 +392,9 @@ impl<'a> DemBuilder<'a> {
     /// Use `dem.to_string()` or `dem.to_string_decomposed()` for output.
     #[must_use]
     pub fn build(&self) -> DetectorErrorModel {
+        let num_influence_dem_outputs = self
+            .num_influence_dem_outputs()
+            .max(self.influence_map.dem_output_metadata.len());
         let mut dem =
             DetectorErrorModel::with_capacity(self.detectors.len(), self.observables.len());
 
@@ -199,13 +408,42 @@ impl<'a> DemBuilder<'a> {
             dem.add_detector(def);
         }
 
-        // Add observable definitions
+        // Add non-detector outputs carried directly by the influence map.
+        // Metadata-bearing outputs use separate compact ID spaces for standard
+        // observables and PECOS tracked Paulis.
+        if self.influence_map.dem_output_metadata.is_empty() {
+            for dem_output_idx in 0..num_influence_dem_outputs {
+                #[allow(clippy::cast_possible_truncation)] // DEM output count fits in u32
+                dem.add_observable(DemOutput::new(dem_output_idx as u32));
+            }
+        } else {
+            for (internal_idx, metadata) in
+                self.influence_map.dem_output_metadata.iter().enumerate()
+            {
+                #[allow(clippy::cast_possible_truncation)] // DEM output count fits in u32
+                let internal_id = internal_idx as u32;
+                if let Some(dem_output_id) = self
+                    .influence_map
+                    .tracked_pauli_id_for_internal_dem_output(internal_id)
+                {
+                    dem.add_tracked_pauli(DemOutput::from_metadata(dem_output_id, metadata));
+                } else if let Some(dem_output_id) = self
+                    .influence_map
+                    .observable_id_for_internal_dem_output(internal_id)
+                {
+                    dem.add_observable(DemOutput::from_metadata(dem_output_id, metadata));
+                }
+            }
+        }
+
+        // Add observable definitions in the standard `L<n>` namespace.
+        // Observable IDs are not shifted by tracked Paulis.
         for obs in &self.observables {
-            let def = LogicalObservable::new(obs.id).with_records(obs.records.iter().copied());
+            let def = DemOutput::new(obs.id).with_records(obs.records.iter().copied());
             dem.add_observable(def);
         }
 
-        // Build measurement -> detector/observable mappings
+        // Build measurement -> detector/DEM-output mappings
         let (meas_to_detectors, meas_to_observables) = self.build_measurement_mappings();
 
         // Process all fault locations with source tracking
@@ -218,6 +456,13 @@ impl<'a> DemBuilder<'a> {
         dem
     }
 
+    fn num_influence_dem_outputs(&self) -> usize {
+        self.influence_map
+            .influences
+            .max_dem_output_index()
+            .map_or(0, |idx| idx + 1)
+    }
+
     /// Processes fault locations with source tracking.
     ///
     /// This version uses `add_direct_contribution` and `add_y_decomposed_contribution`
@@ -235,7 +480,9 @@ impl<'a> DemBuilder<'a> {
 
         for (loc_idx, loc) in locations.iter().enumerate() {
             match loc.gate_type {
-                GateType::PZ | GateType::QAlloc if self.noise.p_init > 0.0 && !loc.before => {
+                GateType::PZ | GateType::QAlloc
+                    if !loc.before && self.init_rate_for_loc(loc) > 0.0 =>
+                {
                     self.process_prep_fault_source_tracked(
                         loc_idx,
                         dem,
@@ -243,7 +490,9 @@ impl<'a> DemBuilder<'a> {
                         meas_to_observables,
                     );
                 }
-                GateType::MZ | GateType::MeasureFree if self.noise.p_meas > 0.0 && loc.before => {
+                GateType::MZ | GateType::MeasureFree
+                    if loc.before && self.measurement_rate_for_loc(loc) > 0.0 =>
+                {
                     self.process_meas_fault_source_tracked(
                         loc_idx,
                         dem,
@@ -254,6 +503,12 @@ impl<'a> DemBuilder<'a> {
                 GateType::CX
                 | GateType::CZ
                 | GateType::CY
+                | GateType::SZZ
+                | GateType::SZZdg
+                | GateType::SXX
+                | GateType::SXXdg
+                | GateType::SYY
+                | GateType::SYYdg
                 | GateType::SWAP
                 | GateType::RXX
                 | GateType::RYY
@@ -263,6 +518,8 @@ impl<'a> DemBuilder<'a> {
                     cx_groups.entry(loc.node).or_default().push(loc_idx);
                 }
                 GateType::H
+                | GateType::F
+                | GateType::Fdg
                 | GateType::SZ
                 | GateType::SZdg
                 | GateType::SX
@@ -279,26 +536,49 @@ impl<'a> DemBuilder<'a> {
                 | GateType::RZ
                 | GateType::U
                 | GateType::R1XY
-                    if self.noise.p1 > 0.0 && !loc.before =>
+                    if !loc.before =>
                 {
-                    self.process_single_qubit_fault_source_tracked(
-                        loc_idx,
-                        dem,
-                        meas_to_detectors,
-                        meas_to_observables,
-                    );
+                    let rates = self.rates_1q_for_loc(loc);
+                    if rates.iter().any(|r| *r > 0.0) {
+                        self.process_single_qubit_fault_source_tracked(
+                            loc_idx,
+                            rates,
+                            dem,
+                            meas_to_detectors,
+                            meas_to_observables,
+                        );
+                    }
+                }
+                GateType::Idle if !loc.before => {
+                    let rates = self.idle_rates_for_loc(loc);
+                    if rates.iter().any(|r| *r > 0.0) {
+                        self.process_single_qubit_fault_source_tracked(
+                            loc_idx,
+                            rates,
+                            dem,
+                            meas_to_detectors,
+                            meas_to_observables,
+                        );
+                    }
                 }
                 _ => {}
             }
         }
 
-        // Process two-qubit gates
-        if self.noise.p2 > 0.0 {
-            for (_, loc_indices) in cx_groups {
-                if loc_indices.len() == 2 {
+        // Process two-qubit gates.
+        for (_, loc_indices) in cx_groups {
+            for pair in loc_indices.chunks(2) {
+                if pair.len() != 2 {
+                    continue;
+                }
+                let loc1 = &locations[pair[0]];
+                let loc2 = &locations[pair[1]];
+                let rates = self.rates_2q_for_locs(loc1, loc2);
+                if rates.iter().any(|r| *r > 0.0) {
                     self.process_two_qubit_fault_source_tracked(
-                        loc_indices[0],
-                        loc_indices[1],
+                        pair[0],
+                        pair[1],
+                        rates,
                         dem,
                         meas_to_detectors,
                         meas_to_observables,
@@ -316,19 +596,16 @@ impl<'a> DemBuilder<'a> {
         meas_to_detectors: &BTreeMap<usize, Vec<u32>>,
         meas_to_observables: &BTreeMap<usize, Vec<u32>>,
     ) {
+        let loc = &self.influence_map.locations[loc_idx];
+        let p = self.init_rate_for_loc(loc);
         // For Z-basis prep, X error matters - this is a direct source
         let mechanism =
             self.compute_mechanism(loc_idx, Pauli::X, meas_to_detectors, meas_to_observables);
         if !mechanism.is_empty() {
             dem.add_direct_contribution_with_source(
                 mechanism,
-                self.noise.p_init,
-                SourceMetadata::new(
-                    &[loc_idx],
-                    &[Pauli::X],
-                    &[self.influence_map.locations[loc_idx].gate_type],
-                    &[self.influence_map.locations[loc_idx].before],
-                ),
+                p,
+                SourceMetadata::new(&[loc_idx], &[Pauli::X], &[loc.gate_type], &[loc.before]),
             );
         }
     }
@@ -341,32 +618,31 @@ impl<'a> DemBuilder<'a> {
         meas_to_detectors: &BTreeMap<usize, Vec<u32>>,
         meas_to_observables: &BTreeMap<usize, Vec<u32>>,
     ) {
+        let loc = &self.influence_map.locations[loc_idx];
+        let p = self.measurement_rate_for_loc(loc);
         // Measurement error is a bit flip (X error) - this is a direct source
         let mechanism =
             self.compute_mechanism(loc_idx, Pauli::X, meas_to_detectors, meas_to_observables);
         if !mechanism.is_empty() {
             dem.add_direct_contribution_with_source(
                 mechanism,
-                self.noise.p_meas,
-                SourceMetadata::new(
-                    &[loc_idx],
-                    &[Pauli::X],
-                    &[self.influence_map.locations[loc_idx].gate_type],
-                    &[self.influence_map.locations[loc_idx].before],
-                ),
+                p,
+                SourceMetadata::new(&[loc_idx], &[Pauli::X], &[loc.gate_type], &[loc.before]),
             );
         }
     }
 
     /// Processes a single-qubit gate fault with source tracking.
+    /// `rates` is `[rate_X, rate_Y, rate_Z]` -- zero entries are skipped.
     fn process_single_qubit_fault_source_tracked(
         &self,
         loc_idx: usize,
+        rates: [f64; 3],
         dem: &mut DetectorErrorModel,
         meas_to_detectors: &BTreeMap<usize, Vec<u32>>,
         meas_to_observables: &BTreeMap<usize, Vec<u32>>,
     ) {
-        let prob = per_channel_probability(self.noise.p1, 3);
+        let [rate_x, rate_y, rate_z] = rates;
 
         let x_effect =
             self.compute_mechanism(loc_idx, Pauli::X, meas_to_detectors, meas_to_observables);
@@ -374,10 +650,10 @@ impl<'a> DemBuilder<'a> {
             self.compute_mechanism(loc_idx, Pauli::Z, meas_to_detectors, meas_to_observables);
 
         // X error: direct source
-        if !x_effect.is_empty() {
+        if rate_x > 0.0 && !x_effect.is_empty() {
             dem.add_direct_contribution_with_source(
                 x_effect.clone(),
-                prob,
+                rate_x,
                 SourceMetadata::new(
                     &[loc_idx],
                     &[Pauli::X],
@@ -388,10 +664,10 @@ impl<'a> DemBuilder<'a> {
         }
 
         // Z error: direct source
-        if !z_effect.is_empty() {
+        if rate_z > 0.0 && !z_effect.is_empty() {
             dem.add_direct_contribution_with_source(
                 z_effect.clone(),
-                prob,
+                rate_z,
                 SourceMetadata::new(
                     &[loc_idx],
                     &[Pauli::Z],
@@ -402,19 +678,13 @@ impl<'a> DemBuilder<'a> {
         }
 
         // Y error: Y = XZ, so effect is XOR of X and Z effects
-        // Handle all cases:
-        // 1. Both non-empty and different: decomposable Y = X ^ Z
-        // 2. X non-empty, Z empty: Y has same effect as X (direct)
-        // 3. X empty, Z non-empty: Y has same effect as Z (direct)
-        // 4. Both non-empty and equal: Y effect is empty (X XOR X = nothing)
         let y_effect = x_effect.xor(&z_effect);
-        if !y_effect.is_empty() {
+        if rate_y > 0.0 && !y_effect.is_empty() {
             if !x_effect.is_empty() && !z_effect.is_empty() {
-                // Both non-empty, so Y is decomposable as X ^ Z
                 dem.add_y_decomposed_contribution_with_source(
                     &x_effect,
                     &z_effect,
-                    prob,
+                    rate_y,
                     SourceMetadata::new(
                         &[loc_idx],
                         &[Pauli::Y],
@@ -426,7 +696,7 @@ impl<'a> DemBuilder<'a> {
                 // One is empty, so Y has same effect as the non-empty one (direct source)
                 dem.add_direct_contribution_with_source(
                     y_effect,
-                    prob,
+                    rate_y,
                     SourceMetadata::new(
                         &[loc_idx],
                         &[Pauli::Y],
@@ -439,15 +709,17 @@ impl<'a> DemBuilder<'a> {
     }
 
     /// Processes a two-qubit gate fault with source tracking and intra-channel decomposition.
+    /// `rates` is the 15-entry array in `PAULI_2Q_ORDER` order -- zero entries
+    /// are skipped.
     fn process_two_qubit_fault_source_tracked(
         &self,
         loc1: usize,
         loc2: usize,
+        rates: [f64; 15],
         dem: &mut DetectorErrorModel,
         meas_to_detectors: &BTreeMap<usize, Vec<u32>>,
         meas_to_observables: &BTreeMap<usize, Vec<u32>>,
     ) {
-        let prob = per_channel_probability(self.noise.p2, 15);
         let loc1_meta = &self.influence_map.locations[loc1];
         let loc2_meta = &self.influence_map.locations[loc2];
 
@@ -489,16 +761,23 @@ impl<'a> DemBuilder<'a> {
                     continue;
                 }
 
+                // Per-pair rate: index = 4*p1 + p2 - 1 (skipping II at idx 0).
+                let flat = 4 * (p1 as usize) + (p2 as usize);
+                let prob = rates[flat - 1];
+                if prob == 0.0 {
+                    continue;
+                }
+
                 // Get component effects (P1I and IP2)
                 let e1 = &effects[p1 as usize][0]; // P1 on qubit 1, I on qubit 2
                 let e2 = &effects[0][p2 as usize]; // I on qubit 1, P2 on qubit 2
 
                 // Check if this is a "graphlike decomposable" source:
-                // - Combined effect has exactly 2 detectors and no logicals
+                // - Combined effect has exactly 2 detectors and no dem_outputs
                 // - Both component effects are non-empty
                 // - Both component effects are graphlike (≤2 detectors)
                 let graphlike_decomposable = effect.num_detectors() == 2
-                    && effect.logicals.is_empty()
+                    && effect.dem_outputs.is_empty()
                     && !e1.is_empty()
                     && !e2.is_empty()
                     && e1.num_detectors() <= 2
@@ -547,7 +826,7 @@ impl<'a> DemBuilder<'a> {
         }
     }
 
-    /// Builds mappings from measurement indices to detector/observable IDs.
+    /// Builds mappings from measurement indices to detector/DEM-output IDs.
     ///
     /// When `measurement_order` is provided, this properly maps between
     /// `TickCircuit` measurement indices (used in record offsets) and influence
@@ -559,6 +838,7 @@ impl<'a> DemBuilder<'a> {
     fn build_measurement_mappings(&self) -> (BTreeMap<usize, Vec<u32>>, BTreeMap<usize, Vec<u32>>) {
         let mut meas_to_detectors: BTreeMap<usize, Vec<u32>> = BTreeMap::new();
         let mut meas_to_observables: BTreeMap<usize, Vec<u32>> = BTreeMap::new();
+        let influence_observable_ids = self.influence_map.observable_ids();
 
         // Build a mapping from (qubit, occurrence_index) to influence_map_index
         // This handles multi-round circuits where the same qubit is measured multiple times
@@ -622,6 +902,9 @@ impl<'a> DemBuilder<'a> {
         }
 
         for obs in &self.observables {
+            if influence_observable_ids.contains(&obs.id) {
+                continue;
+            }
             for &rec in &obs.records {
                 if let Some(tc_meas_idx) =
                     record_offset_to_absolute_index(self.num_measurements, rec)
@@ -646,7 +929,7 @@ impl<'a> DemBuilder<'a> {
         meas_to_detectors: &BTreeMap<usize, Vec<u32>>,
         meas_to_observables: &BTreeMap<usize, Vec<u32>>,
     ) -> FaultMechanism {
-        // Get the Rust detector indices that this fault flips
+        // Get the measurement indices that this fault flips
         let rust_dets = self
             .influence_map
             .get_detector_indices(loc_idx, pauli.as_u8());
@@ -654,6 +937,20 @@ impl<'a> DemBuilder<'a> {
         // Convert to pre-defined detector IDs using XOR
         let mut triggered_dets: SmallVec<[u32; 4]> = SmallVec::new();
         let mut triggered_obs: SmallVec<[u32; 2]> = SmallVec::new();
+        let mut triggered_tracked_paulis: SmallVec<[u32; 2]> = SmallVec::new();
+
+        for dem_output_idx in self
+            .influence_map
+            .get_observable_indices(loc_idx, pauli.as_u8())
+        {
+            xor_toggle_2(&mut triggered_obs, dem_output_idx);
+        }
+        for tracked_pauli_idx in self
+            .influence_map
+            .get_tracked_pauli_indices(loc_idx, pauli.as_u8())
+        {
+            xor_toggle_2(&mut triggered_tracked_paulis, tracked_pauli_idx);
+        }
 
         for &rust_det in rust_dets {
             let meas_idx = rust_det as usize;
@@ -676,8 +973,13 @@ impl<'a> DemBuilder<'a> {
         // Sort for canonical form
         triggered_dets.sort_unstable();
         triggered_obs.sort_unstable();
+        triggered_tracked_paulis.sort_unstable();
 
-        FaultMechanism::from_sorted(triggered_dets, triggered_obs)
+        FaultMechanism::from_sorted_with_tracked_paulis(
+            triggered_dets,
+            triggered_obs,
+            triggered_tracked_paulis,
+        )
     }
 }
 
@@ -699,6 +1001,26 @@ fn xor_toggle_2(vec: &mut SmallVec<[u32; 2]>, value: u32) {
     }
 }
 
+fn pauli_pair_for_weight(p1: usize, p2: usize) -> pecos_core::PauliString {
+    let mut paulis = Vec::new();
+    let pauli_from_index = |idx| match idx {
+        0 => pecos_core::Pauli::I,
+        1 => pecos_core::Pauli::X,
+        2 => pecos_core::Pauli::Y,
+        3 => pecos_core::Pauli::Z,
+        _ => unreachable!("Pauli index must be 0-3"),
+    };
+    let pa1 = pauli_from_index(p1);
+    let pa2 = pauli_from_index(p2);
+    if pa1 != pecos_core::Pauli::I {
+        paulis.push((pa1, pecos_core::QubitId::from(0usize)));
+    }
+    if pa2 != pecos_core::Pauli::I {
+        paulis.push((pa2, pecos_core::QubitId::from(1usize)));
+    }
+    pecos_core::PauliString::with_phase_and_paulis(pecos_core::QuarterPhase::PlusOne, paulis)
+}
+
 /// Computes the per-error probability for independent error channels.
 ///
 /// For a depolarizing channel with total error probability `p` split among `n`
@@ -949,6 +1271,120 @@ fn extract_records(json: &str) -> Vec<i32> {
     Vec::new()
 }
 
+// ============================================================================
+// Convenience: build DEM from circuit (free function to handle lifetimes)
+// ============================================================================
+
+/// Build a `DetectorErrorModel` from a `DagCircuit` and noise parameters.
+///
+/// Reads detector/DEM output definitions from circuit metadata attributes.
+fn build_dem_from_circuit(
+    circuit: &pecos_quantum::DagCircuit,
+    p1: f64,
+    p2: f64,
+    p_meas: f64,
+    p_prep: f64,
+) -> DetectorErrorModel {
+    use crate::fault_tolerance::influence_builder::InfluenceBuilder;
+    use crate::fault_tolerance::propagator::DagFaultAnalyzer;
+    use pecos_num::graph::Attribute;
+
+    let mut influence_map = DagFaultAnalyzer::new(circuit).build_influence_map();
+    let annotated_observable_records = observable_records_from_annotations(circuit, &influence_map);
+    let annotation_map = InfluenceBuilder::new(circuit)
+        .with_circuit_annotations(circuit)
+        .build();
+    influence_map.merge_dem_outputs_from(&annotation_map);
+
+    // Extract metadata before building (to avoid borrow issues)
+    let det_json = circuit.get_attr("detectors").and_then(|a| {
+        if let Attribute::String(s) = a {
+            Some(s.clone())
+        } else {
+            None
+        }
+    });
+    let obs_json = circuit.get_attr("observables").and_then(|a| {
+        if let Attribute::String(s) = a {
+            Some(s.clone())
+        } else {
+            None
+        }
+    });
+    let num_meas = circuit.get_attr("num_measurements").and_then(|a| {
+        if let Attribute::String(s) = a {
+            s.parse::<usize>().ok()
+        } else {
+            None
+        }
+    });
+
+    let builder = DemBuilder::new(&influence_map).with_noise(p1, p2, p_meas, p_prep);
+
+    let builder = if let Some(ref dj) = det_json {
+        builder
+            .with_detectors_json(dj)
+            .unwrap_or_else(|_| DemBuilder::new(&influence_map).with_noise(p1, p2, p_meas, p_prep))
+    } else {
+        builder
+    };
+
+    let builder = if let Some(ref oj) = obs_json {
+        builder
+            .with_observables_json(oj)
+            .unwrap_or_else(|_| DemBuilder::new(&influence_map).with_noise(p1, p2, p_meas, p_prep))
+    } else if !annotated_observable_records.is_empty() {
+        builder.with_observable_records(annotated_observable_records)
+    } else {
+        builder
+    };
+
+    let builder = if let Some(n) = num_meas {
+        builder.with_num_measurements(n)
+    } else {
+        builder
+    };
+
+    builder.build()
+}
+
+fn observable_records_from_annotations(
+    circuit: &pecos_quantum::DagCircuit,
+    influence_map: &DagFaultInfluenceMap,
+) -> Vec<Vec<i32>> {
+    use pecos_quantum::AnnotationKind;
+
+    let num_measurements = influence_map.measurements.len();
+    if num_measurements == 0 {
+        return Vec::new();
+    }
+
+    let mut node_to_meas_idx: BTreeMap<usize, usize> = BTreeMap::new();
+    for (meas_idx, &(node, _qubit, _basis)) in influence_map.measurements.iter().enumerate() {
+        node_to_meas_idx.entry(node).or_insert(meas_idx);
+    }
+
+    circuit
+        .observables()
+        .map(|ann| {
+            if let AnnotationKind::Observable { measurement_nodes } = &ann.kind {
+                measurement_nodes
+                    .iter()
+                    .filter_map(|node| node_to_meas_idx.get(node).copied())
+                    .map(|meas_idx| {
+                        #[allow(clippy::cast_possible_wrap, clippy::cast_possible_truncation)]
+                        {
+                            meas_idx as i32 - num_measurements as i32
+                        }
+                    })
+                    .collect()
+            } else {
+                Vec::new()
+            }
+        })
+        .collect()
+}
+
 // ============================================================================
 // Error Type
 // ============================================================================
@@ -974,6 +1410,497 @@ impl std::error::Error for DemBuilderError {}
 mod tests {
     use super::*;
 
+    #[test]
+    fn test_from_circuit_tracks_tracked_pauli() {
+        use pecos_core::pauli::X;
+        use pecos_quantum::DagCircuit;
+
+        let mut circuit = DagCircuit::new();
+        circuit.pz(&[0]);
+        circuit.h(&[0]);
+        circuit.tracked_pauli_labeled("x_check", X(0));
+
+        let dem = DemBuilder::from_circuit(&circuit, 0.03, 0.0, 0.0, 0.0);
+
+        assert_eq!(dem.num_dem_outputs(), 0);
+        assert_eq!(dem.num_tracked_paulis(), 1);
+        assert_eq!(dem.num_observables(), 0);
+        assert_eq!(
+            dem.tracked_paulis()[0].kind,
+            Some(crate::fault_tolerance::DemOutputKind::TrackedPauli)
+        );
+        assert_eq!(dem.tracked_paulis()[0].label.as_deref(), Some("x_check"));
+        assert_eq!(
+            dem.tracked_paulis()[0]
+                .pauli
+                .as_ref()
+                .unwrap()
+                .to_sparse_str(),
+            "+X0"
+        );
+        assert!(!dem.to_string().contains("logical_observable"));
+        assert!(!dem.to_string().contains("TP0"));
+        let pecos_text = dem.to_pecos_string();
+        assert!(pecos_text.contains("TP0"));
+        assert!(pecos_text.contains("pecos_tracked_pauli"));
+    }
+
+    #[test]
+    fn test_tracked_pauli_and_observable_use_distinct_tracked_paulis() {
+        use pecos_core::pauli::Z;
+        use pecos_quantum::{Attribute, DagCircuit};
+
+        let mut circuit = DagCircuit::new();
+        circuit.pz(&[0]);
+        circuit.tracked_pauli_labeled("z_check", Z(0));
+        circuit.mz(&[0]);
+        circuit.set_attr("num_measurements", Attribute::String("1".to_string()));
+        circuit.set_attr(
+            "observables",
+            Attribute::String(r#"[{"id":0,"records":[-1]}]"#.to_string()),
+        );
+
+        let dem = DemBuilder::from_circuit(&circuit, 0.0, 0.0, 0.02, 0.03);
+
+        assert_eq!(dem.num_dem_outputs(), 1);
+        assert_eq!(dem.num_tracked_paulis(), 1);
+        assert_eq!(dem.num_observables(), 1);
+        assert_eq!(
+            dem.dem_outputs()[0].kind,
+            Some(crate::fault_tolerance::DemOutputKind::Observable)
+        );
+        assert_eq!(dem.tracked_paulis()[0].label.as_deref(), Some("z_check"));
+        let dem_str = dem.to_string();
+        assert!(dem_str.contains("logical_observable L0"));
+        assert!(!dem_str.contains("logical_observable L1"));
+        assert!(!dem_str.contains("TP0"));
+        let pecos_text = dem.to_pecos_string();
+        assert!(pecos_text.contains("TP0"));
+        assert!(pecos_text.contains("pecos_tracked_pauli"));
+        let summaries = dem.contribution_effect_summaries();
+        assert!(
+            summaries
+                .iter()
+                .any(|summary| summary.effect.dem_outputs.as_slice() == [0]),
+            "observable should remain L0"
+        );
+        assert!(
+            summaries
+                .iter()
+                .any(|summary| summary.effect.tracked_paulis.as_slice() == [0]),
+            "tracked Pauli should remain TP0"
+        );
+    }
+
+    #[test]
+    fn test_tick_dag_tick_dem_keeps_detector_observable_and_tracked_pauli_distinct() {
+        use pecos_core::pauli::X;
+        use pecos_quantum::{DagCircuit, TickCircuit};
+
+        let mut circuit = TickCircuit::new();
+        circuit.tick().pz(&[0, 1]);
+        circuit.tick().h(&[0]);
+        circuit.tracked_pauli_labeled("tracked_x0", X(0));
+        circuit.tick().mz(&[0, 1]);
+        circuit.set_meta(
+            "num_measurements",
+            pecos_quantum::Attribute::String(circuit.num_measurements().to_string()),
+        );
+        circuit
+            .add_detector_metadata(&[-2], None, Some("D0"), Some(0))
+            .unwrap();
+        circuit
+            .add_observable_metadata(&[-1], Some(0), Some("L0"))
+            .unwrap();
+        let round_tripped = TickCircuit::from(&DagCircuit::from(&circuit));
+        let dem = DemBuilder::from_tick_circuit(&round_tripped, 0.03, 0.0, 0.02, 0.0);
+
+        assert_eq!(dem.num_detectors(), 1);
+        assert_eq!(dem.num_observables(), 1);
+        assert_eq!(dem.num_dem_outputs(), 1);
+        assert_eq!(dem.dem_outputs()[0].id, 0);
+        assert_eq!(dem.num_tracked_paulis(), 1);
+        assert_eq!(dem.tracked_paulis()[0].id, 0);
+        assert_eq!(dem.tracked_paulis()[0].label.as_deref(), Some("tracked_x0"));
+        assert_eq!(
+            dem.tracked_paulis()[0]
+                .pauli
+                .as_ref()
+                .unwrap()
+                .to_sparse_str(),
+            "+X0"
+        );
+
+        let standard_text = dem.to_string();
+        assert!(standard_text.contains("logical_observable L0"));
+        assert!(!standard_text.contains("logical_observable L1"));
+        assert!(!standard_text.contains("pecos_tracked_pauli"));
+
+        let pecos_text = dem.to_pecos_string();
+        assert!(pecos_text.contains("pecos_observable"));
+        assert!(pecos_text.contains("pecos_tracked_pauli"));
+
+        let summaries = dem.contribution_effect_summaries();
+        assert!(
+            summaries
+                .iter()
+                .any(|summary| summary.effect.detectors.as_slice() == [0]),
+            "detector effects should survive Tick -> DAG -> Tick"
+        );
+        assert!(
+            summaries
+                .iter()
+                .any(|summary| summary.effect.dem_outputs.as_slice() == [0]),
+            "observable effects should remain in L0"
+        );
+    }
+
+    #[test]
+    fn test_circuit_observable_annotation_is_not_double_counted() {
+        use pecos_quantum::DagCircuit;
+
+        let mut circuit = DagCircuit::new();
+        circuit.pz(&[0]);
+        let meas = circuit.mz(&[0]);
+        circuit.observable_labeled("obs0", &[meas[0]]);
+
+        let dem = DemBuilder::from_circuit(&circuit, 0.0, 0.0, 1.0, 0.0);
+
+        assert_eq!(dem.num_dem_outputs(), 1);
+        assert_eq!(dem.num_observables(), 1);
+        assert_eq!(dem.dem_outputs().len(), 1);
+        assert_eq!(dem.dem_outputs()[0].id, 0);
+        assert_eq!(dem.dem_outputs()[0].records.as_slice(), &[-1]);
+        assert_eq!(dem.dem_outputs()[0].label.as_deref(), Some("obs0"));
+
+        let logical_observable_lines = dem
+            .to_string()
+            .lines()
+            .filter(|line| *line == "logical_observable L0")
+            .count();
+        assert_eq!(logical_observable_lines, 1);
+
+        let summaries = dem.contribution_effect_summaries();
+        assert!(
+            summaries
+                .iter()
+                .any(|summary| summary.effect.dem_outputs.as_slice() == [0]),
+            "measurement fault should flip observable L0 once, not cancel"
+        );
+    }
+
+    #[test]
+    fn test_from_tick_circuit_tracks_face_gate_fault_sources() {
+        use pecos_core::QubitId;
+        use pecos_quantum::{Attribute, TickCircuit};
+
+        for gate_type in [GateType::F, GateType::Fdg] {
+            let mut circuit = TickCircuit::new();
+            circuit.tick().pz(&[QubitId(0)]);
+            match gate_type {
+                GateType::F => {
+                    circuit.tick().f(&[QubitId(0)]);
+                }
+                GateType::Fdg => {
+                    circuit.tick().fdg(&[QubitId(0)]);
+                }
+                _ => unreachable!(),
+            }
+            circuit.tick().mz(&[QubitId(0)]);
+            circuit.set_meta("num_measurements", Attribute::String("1".to_string()));
+            circuit.set_meta(
+                "detectors",
+                Attribute::String(r#"[{"id":0,"records":[-1]}]"#.to_string()),
+            );
+            circuit.set_meta("observables", Attribute::String("[]".to_string()));
+
+            let dem = DemBuilder::from_tick_circuit(&circuit, 0.03, 0.0, 0.0, 0.0);
+            let contributions = dem.contributions_for_effect(&[0], &[]);
+
+            assert!(
+                contributions
+                    .iter()
+                    .any(|contribution| contribution.source_gate_types.contains(&gate_type)),
+                "DEM should include a tracked {gate_type:?} fault source"
+            );
+        }
+    }
+
+    #[test]
+    fn test_fault_catalog_and_dem_cover_standard_clifford_gate_sources() {
+        use crate::fault_tolerance::fault_sampler::{
+            FaultCatalog, StochasticNoiseParams, build_fault_catalog,
+        };
+        use pecos_core::QubitId;
+        use pecos_quantum::{Attribute, TickCircuit};
+        use std::collections::BTreeMap;
+
+        fn set_meta(circuit: &mut TickCircuit, num_measurements: usize, detectors: &str) {
+            circuit.set_meta(
+                "num_measurements",
+                Attribute::String(num_measurements.to_string()),
+            );
+            circuit.set_meta("detectors", Attribute::String(detectors.to_string()));
+            circuit.set_meta("observables", Attribute::String("[]".to_string()));
+        }
+
+        fn add_1q_gate(circuit: &mut TickCircuit, gate_type: GateType) {
+            match gate_type {
+                GateType::X => {
+                    circuit.tick().x(&[QubitId(0)]);
+                }
+                GateType::Y => {
+                    circuit.tick().y(&[QubitId(0)]);
+                }
+                GateType::Z => {
+                    circuit.tick().z(&[QubitId(0)]);
+                }
+                GateType::H => {
+                    circuit.tick().h(&[QubitId(0)]);
+                }
+                GateType::F => {
+                    circuit.tick().f(&[QubitId(0)]);
+                }
+                GateType::Fdg => {
+                    circuit.tick().fdg(&[QubitId(0)]);
+                }
+                GateType::SX => {
+                    circuit.tick().sx(&[QubitId(0)]);
+                }
+                GateType::SXdg => {
+                    circuit.tick().sxdg(&[QubitId(0)]);
+                }
+                GateType::SY => {
+                    circuit.tick().sy(&[QubitId(0)]);
+                }
+                GateType::SYdg => {
+                    circuit.tick().sydg(&[QubitId(0)]);
+                }
+                GateType::SZ => {
+                    circuit.tick().sz(&[QubitId(0)]);
+                }
+                GateType::SZdg => {
+                    circuit.tick().szdg(&[QubitId(0)]);
+                }
+                _ => panic!("not a 1q standard Clifford gate: {gate_type:?}"),
+            }
+        }
+
+        fn add_2q_gate(circuit: &mut TickCircuit, gate_type: GateType) {
+            let pair = &[(QubitId(0), QubitId(1))];
+            match gate_type {
+                GateType::CX => {
+                    circuit.tick().cx(pair);
+                }
+                GateType::CY => {
+                    circuit.tick().cy(pair);
+                }
+                GateType::CZ => {
+                    circuit.tick().cz(pair);
+                }
+                GateType::SXX => {
+                    circuit.tick().sxx(pair);
+                }
+                GateType::SXXdg => {
+                    circuit.tick().sxxdg(pair);
+                }
+                GateType::SYY => {
+                    circuit.tick().syy(pair);
+                }
+                GateType::SYYdg => {
+                    circuit.tick().syydg(pair);
+                }
+                GateType::SZZ => {
+                    circuit.tick().szz(pair);
+                }
+                GateType::SZZdg => {
+                    circuit.tick().szzdg(pair);
+                }
+                GateType::SWAP => {
+                    circuit.tick().swap(pair);
+                }
+                _ => panic!("not a 2q standard Clifford gate: {gate_type:?}"),
+            }
+        }
+
+        fn dem_has_source(dem: &DetectorErrorModel, gate_type: GateType) -> bool {
+            dem.contribution_render_records()
+                .iter()
+                .any(|record| record.contribution.source_gate_types.contains(&gate_type))
+        }
+
+        fn catalog_dem_channel_effect_probabilities(
+            catalog: &FaultCatalog,
+        ) -> BTreeMap<(Vec<u32>, Vec<u32>), f64> {
+            let mut by_effect = BTreeMap::new();
+            for location in &catalog.locations {
+                if location.num_alternatives == 0 {
+                    continue;
+                }
+                let num_alternatives = f64::from(
+                    u32::try_from(location.num_alternatives)
+                        .expect("fault alternative count fits in u32"),
+                );
+                let per_channel_probability =
+                    1.0 - location.no_fault_probability.powf(1.0 / num_alternatives);
+                for fault in &location.faults {
+                    if fault.affected_detectors.is_empty() && fault.affected_observables.is_empty()
+                    {
+                        continue;
+                    }
+                    let detectors: Vec<u32> = fault
+                        .affected_detectors
+                        .iter()
+                        .map(|&det| u32::try_from(det).unwrap())
+                        .collect();
+                    let observables: Vec<u32> = fault
+                        .affected_observables
+                        .iter()
+                        .map(|&obs| u32::try_from(obs).unwrap())
+                        .collect();
+                    *by_effect.entry((detectors, observables)).or_insert(0.0) +=
+                        per_channel_probability;
+                }
+            }
+            by_effect
+        }
+
+        fn dem_effect_probabilities(
+            dem: &DetectorErrorModel,
+        ) -> BTreeMap<(Vec<u32>, Vec<u32>), f64> {
+            dem.contribution_effect_summaries()
+                .into_iter()
+                .filter(|summary| {
+                    !summary.effect.detectors.is_empty() || !summary.effect.dem_outputs.is_empty()
+                })
+                .map(|summary| {
+                    (
+                        (
+                            summary.effect.detectors.into_iter().collect(),
+                            summary.effect.dem_outputs.into_iter().collect(),
+                        ),
+                        summary.total_probability,
+                    )
+                })
+                .collect()
+        }
+
+        fn assert_catalog_dem_probabilities_match(
+            catalog: &FaultCatalog,
+            dem: &DetectorErrorModel,
+            gate_type: GateType,
+        ) {
+            let catalog_probs = catalog_dem_channel_effect_probabilities(catalog);
+            let dem_probs = dem_effect_probabilities(dem);
+            assert_eq!(
+                catalog_probs.keys().collect::<Vec<_>>(),
+                dem_probs.keys().collect::<Vec<_>>(),
+                "{gate_type:?} should produce the same non-empty effects in the fault catalog and DEM"
+            );
+            for (effect, catalog_probability) in catalog_probs {
+                let dem_probability = dem_probs[&effect];
+                assert!(
+                    (catalog_probability - dem_probability).abs() < 1e-12,
+                    "{gate_type:?} effect {effect:?}: catalog probability {catalog_probability} != DEM probability {dem_probability}"
+                );
+            }
+        }
+
+        for gate_type in [
+            GateType::X,
+            GateType::Y,
+            GateType::Z,
+            GateType::H,
+            GateType::F,
+            GateType::Fdg,
+            GateType::SX,
+            GateType::SXdg,
+            GateType::SY,
+            GateType::SYdg,
+            GateType::SZ,
+            GateType::SZdg,
+        ] {
+            let mut circuit = TickCircuit::new();
+            circuit.tick().pz(&[QubitId(0)]);
+            add_1q_gate(&mut circuit, gate_type);
+            circuit.tick().mz(&[QubitId(0)]);
+            set_meta(&mut circuit, 1, r#"[{"id":0,"records":[-1]}]"#);
+
+            let catalog = build_fault_catalog(
+                &circuit,
+                &StochasticNoiseParams {
+                    p1: 0.03,
+                    p2: 0.0,
+                    p_meas: 0.0,
+                    p_prep: 0.0,
+                },
+            )
+            .unwrap();
+            let locations: Vec<_> = catalog
+                .locations
+                .iter()
+                .filter(|location| location.gate_type == gate_type)
+                .collect();
+            assert_eq!(locations.len(), 1, "{gate_type:?}");
+            assert_eq!(locations[0].faults.len(), 3, "{gate_type:?}");
+
+            let dem = DemBuilder::from_tick_circuit(&circuit, 0.03, 0.0, 0.0, 0.0);
+            assert!(
+                dem_has_source(&dem, gate_type),
+                "DEM should track a source contribution for {gate_type:?}"
+            );
+            assert_catalog_dem_probabilities_match(&catalog, &dem, gate_type);
+        }
+
+        for gate_type in [
+            GateType::CX,
+            GateType::CY,
+            GateType::CZ,
+            GateType::SXX,
+            GateType::SXXdg,
+            GateType::SYY,
+            GateType::SYYdg,
+            GateType::SZZ,
+            GateType::SZZdg,
+            GateType::SWAP,
+        ] {
+            let mut circuit = TickCircuit::new();
+            circuit.tick().pz(&[QubitId(0), QubitId(1)]);
+            add_2q_gate(&mut circuit, gate_type);
+            circuit.tick().mz(&[QubitId(0), QubitId(1)]);
+            set_meta(
+                &mut circuit,
+                2,
+                r#"[{"id":0,"records":[-2]},{"id":1,"records":[-1]}]"#,
+            );
+
+            let catalog = build_fault_catalog(
+                &circuit,
+                &StochasticNoiseParams {
+                    p1: 0.0,
+                    p2: 0.15,
+                    p_meas: 0.0,
+                    p_prep: 0.0,
+                },
+            )
+            .unwrap();
+            let locations: Vec<_> = catalog
+                .locations
+                .iter()
+                .filter(|location| location.gate_type == gate_type)
+                .collect();
+            assert_eq!(locations.len(), 1, "{gate_type:?}");
+            assert_eq!(locations[0].faults.len(), 15, "{gate_type:?}");
+
+            let dem = DemBuilder::from_tick_circuit(&circuit, 0.0, 0.15, 0.0, 0.0);
+            assert!(
+                dem_has_source(&dem, gate_type),
+                "DEM should track a source contribution for {gate_type:?}"
+            );
+            assert_catalog_dem_probabilities_match(&catalog, &dem, gate_type);
+        }
+    }
+
     #[test]
     fn test_parse_detectors_json() {
         let json = r#"[
@@ -1002,6 +1929,20 @@ mod tests {
         assert_eq!(observables[0].records, vec![-1, -3, -5]);
     }
 
+    #[test]
+    fn test_dem_builder_accepts_observables_json_alias() {
+        let influence_map = DagFaultInfluenceMap::with_capacity(0);
+        let dem = DemBuilder::new(&influence_map)
+            .with_observables_json(r#"[{"id": 0, "records": [-1, -3]}]"#)
+            .unwrap()
+            .build();
+
+        assert_eq!(dem.num_dem_outputs(), 1);
+        assert_eq!(dem.num_observables(), 1);
+        assert_eq!(dem.num_tracked_paulis(), 0);
+        assert_eq!(dem.dem_outputs()[0].records.as_slice(), &[-1, -3]);
+    }
+
     #[test]
     fn test_parse_empty_json() {
         assert!(parse_detectors_json("").unwrap().is_empty());
diff --git a/crates/pecos-qec/src/fault_tolerance/dem_builder/dem_sampler.rs b/crates/pecos-qec/src/fault_tolerance/dem_builder/dem_sampler.rs
index 2aa147dcf..7ba0febe2 100644
--- a/crates/pecos-qec/src/fault_tolerance/dem_builder/dem_sampler.rs
+++ b/crates/pecos-qec/src/fault_tolerance/dem_builder/dem_sampler.rs
@@ -10,10 +10,18 @@
 // or implied. See the License for the specific language governing permissions and limitations under
 // the License.
 
+//! Internal sampling engine for threshold estimation.
+//!
+//! This is the core CSR/geometric-skip engine used by [`super::DemSampler`].
+//! External consumers should use `DemSampler` and `DemSamplerBuilder` from
+//! the parent module.
+#![allow(dead_code)] // Many methods are public for internal use but not called externally yet
+
 //! Fast DEM-style sampler for threshold estimation.
 //!
 //! This module provides a sampler that aggregates fault effects directly into
-//! detector/observable signatures, matching Stim's DEM sampler semantics.
+//! detector/standard observable `L<n>` signatures, matching DEM sampling
+//! semantics.
 //!
 //! # Data-Oriented Design
 //!
@@ -21,7 +29,7 @@
 //! cache-efficient sampling:
 //!
 //! - **Probabilities**: Stored in a contiguous array for sequential access
-//! - **Detector/Observable indices**: CSR layout (offsets + flat data) for variable-length lists
+//! - **Detector/observable indices**: CSR layout (offsets + flat data) for variable-length lists
 //! - **Bit-packed outcomes**: Uses `u64` words for compact detector/observable state
 //!
 //! # Example
@@ -30,8 +38,7 @@
 //! use pecos_qec::fault_tolerance::DagFaultAnalyzer;
 //! use pecos_qec::fault_tolerance::dem_builder::DemSamplerBuilder;
 //! use pecos_quantum::DagCircuit;
-//! use rand::SeedableRng;
-//! use rand::rngs::SmallRng;
+//! use pecos_random::PecosRng;
 //!
 //! let mut dag = DagCircuit::new();
 //! dag.pz(&[2]);
@@ -41,19 +48,18 @@
 //!
 //! let analyzer = DagFaultAnalyzer::new(&dag);
 //! let influence_map = analyzer.build_influence_map();
-//! let detectors_json = r#"[{"id": 0, "records": [-1]}]"#;
-//! let observables_json = "[]";
 //!
-//! // Build from circuit with detector definitions
+//! // Build sampler with detector definitions
 //! let sampler = DemSamplerBuilder::new(&influence_map)
 //!     .with_noise(0.01, 0.01, 0.01, 0.01)
-//!     .with_detectors_json(detectors_json).unwrap()
-//!     .with_observables_json(observables_json).unwrap()
-//!     .build();
+//!     .with_detectors_json(r#"[{"id": 0, "records": [-1]}]"#).unwrap()
+//!     .with_observables_json("[]").unwrap()
+//!     .build()
+//!     .unwrap();
 //!
 //! // Fast batch sampling for threshold estimation
-//! let mut rng = SmallRng::seed_from_u64(42);
-//! let (det_events, obs_flips) = sampler.sample_batch(100, &mut rng);
+//! let mut rng = PecosRng::seed_from_u64(42);
+//! let (det_events, dem_output_flips) = sampler.sample_batch(100, &mut rng);
 //! ```
 
 use crate::fault_tolerance::propagator::{DagFaultInfluenceMap, Pauli};
@@ -62,44 +68,44 @@ use pecos_random::{PecosRng, RngProbabilityExt};
 use rand_core::Rng;
 use rayon::prelude::*;
 use smallvec::SmallVec;
-use std::collections::BTreeMap;
+use std::collections::{BTreeMap, BTreeSet};
 use wide::u64x4;
 
-use super::types::combine_probabilities;
+use super::types::{NoiseConfig, PerGateTypeNoise, combine_probabilities};
 
 // ============================================================================
 // DEM Mechanism (used during building)
 // ============================================================================
 
-/// A single fault mechanism with its detector/observable effects.
+/// A single fault mechanism with its detector and standard observable `L<n>` effects.
 /// Used during building, then converted to `SoA` layout.
 #[derive(Debug, Clone, PartialEq, Eq, PartialOrd, Ord, Hash)]
 struct DemMechanism {
     /// Sorted detector indices that flip when this mechanism fires.
     detectors: SmallVec<[u32; 4]>,
-    /// Sorted observable indices that flip when this mechanism fires.
-    observables: SmallVec<[u32; 2]>,
+    /// Sorted standard observable `L<n>` indices that flip when this mechanism fires.
+    dem_outputs: SmallVec<[u32; 2]>,
 }
 
 impl DemMechanism {
-    fn new(mut detectors: SmallVec<[u32; 4]>, mut observables: SmallVec<[u32; 2]>) -> Self {
+    fn new(mut detectors: SmallVec<[u32; 4]>, mut dem_outputs: SmallVec<[u32; 2]>) -> Self {
         detectors.sort_unstable();
-        observables.sort_unstable();
+        dem_outputs.sort_unstable();
         Self {
             detectors,
-            observables,
+            dem_outputs,
         }
     }
 
     fn empty() -> Self {
         Self {
             detectors: SmallVec::new(),
-            observables: SmallVec::new(),
+            dem_outputs: SmallVec::new(),
         }
     }
 
     fn is_empty(&self) -> bool {
-        self.detectors.is_empty() && self.observables.is_empty()
+        self.detectors.is_empty() && self.dem_outputs.is_empty()
     }
 }
 
@@ -169,13 +175,13 @@ impl PackedBits {
 /// Fast DEM-style sampler for threshold estimation.
 ///
 /// Uses Structure of Arrays (`SoA`) layout with CSR-style indexing for
-/// cache-efficient sampling. Detector and observable outcomes are bit-packed
+/// cache-efficient sampling. Detector and `L<n>` target outcomes are bit-packed
 /// for compact storage and fast XOR operations.
 ///
 /// # Data-Oriented Design
 ///
 /// - **Precomputed thresholds**: Probabilities converted to u64 thresholds at build time
-/// - **CSR layout**: Detector/observable indices in flat arrays with offsets
+/// - **CSR layout**: Detector/`L<n>` target indices in flat arrays with offsets
 /// - **Bit-packed outcomes**: Uses u64 words for compact XOR operations
 /// - **Batch RNG**: Can use bulk random number generation for cache efficiency
 ///
@@ -185,15 +191,15 @@ impl PackedBits {
 /// thresholds:          [t0, t1, t2, ...]           (precomputed u64, sequential read)
 /// detector_offsets:    [0, 2, 3, 5, ...]           (CSR row pointers)
 /// detector_data:       [d0, d1, d2, d3, d4, ...]   (flat detector indices)
-/// observable_offsets:  [0, 0, 1, 1, ...]           (CSR row pointers)
-/// observable_data:     [o0, ...]                   (flat observable indices)
+/// dem_output_offsets:  [0, 0, 1, 1, ...]           (CSR row pointers)
+/// dem_output_data:     [t0, ...]                   (flat `L<n>` target indices)
 /// ```
 ///
 /// For mechanism i:
 /// - Detector indices: `detector_data[detector_offsets[i]..detector_offsets[i+1]]`
-/// - Observable indices: `observable_data[observable_offsets[i]..observable_offsets[i+1]]`
+/// - `L<n>` target indices: `dem_output_data[dem_output_offsets[i]..dem_output_offsets[i+1]]`
 #[derive(Debug, Clone)]
-pub struct DemSampler {
+pub struct SamplingEngine {
     // SoA layout for cache efficiency
     /// Precomputed u64 thresholds (faster than f64 comparison).
     thresholds: Vec<u64>,
@@ -207,18 +213,29 @@ pub struct DemSampler {
     /// Flat array of detector indices.
     detector_data: Vec<u32>,
 
-    /// CSR-style offsets into `observable_data`. Length = `num_mechanisms` + 1.
-    observable_offsets: Vec<u32>,
-    /// Flat array of observable indices.
-    observable_data: Vec<u32>,
+    /// CSR-style offsets into `dem_output_data`. Length = `num_mechanisms` + 1.
+    /// These are standard observable `L<n>` DEM outputs.
+    dem_output_offsets: Vec<u32>,
+    /// Flat array of `L<n>` target indices.
+    dem_output_data: Vec<u32>,
 
     /// Number of detectors.
     num_detectors: usize,
-    /// Number of observables.
-    num_observables: usize,
+    /// Number of DEM `L<n>` outputs.
+    num_dem_outputs: usize,
+}
+
+const U32_BASE_AS_F64: f64 = 4_294_967_296.0;
+const U64_MAX_AS_F64: f64 = 18_446_744_073_709_551_615.0;
+
+fn threshold_to_probability(threshold: u64) -> f64 {
+    let hi = u32::try_from(threshold >> 32).expect("upper threshold word fits in u32");
+    let lo =
+        u32::try_from(threshold & u64::from(u32::MAX)).expect("lower threshold word fits in u32");
+    (f64::from(hi) * U32_BASE_AS_F64 + f64::from(lo)) / U64_MAX_AS_F64
 }
 
-impl DemSampler {
+impl SamplingEngine {
     /// Number of mechanisms in the sampler.
     #[must_use]
     pub fn num_mechanisms(&self) -> usize {
@@ -231,25 +248,64 @@ impl DemSampler {
         self.num_detectors
     }
 
-    /// Number of observables.
+    /// Number of observables represented by `L<n>` columns.
+    ///
+    /// When no PECOS tracked-Pauli metadata is present, every `L<n>` output
+    /// is treated as an observable.
     #[must_use]
     pub fn num_observables(&self) -> usize {
-        self.num_observables
+        self.num_dem_outputs
     }
 
-    /// Create a [`DemSampler`] from raw mechanism data.
+    /// Number of DEM `L<n>` outputs.
+    #[must_use]
+    pub fn num_dem_outputs(&self) -> usize {
+        self.num_dem_outputs
+    }
+
+    /// Reconstruct a [`DetectorErrorModel`] from the aggregated `SoA`
+    /// mechanism state for text output (e.g. Stim-format via
+    /// [`DetectorErrorModel::to_string`]).
+    ///
+    /// Each stored mechanism becomes a `direct` contribution with its
+    /// approximate probability (recovered from the `u64` threshold).
+    /// Detector / observable declarations are NOT emitted -- those
+    /// require the original `DetectorDef` / observable metadata
+    /// definitions held by higher-level wrappers such as
+    /// [`crate::dem_stab::DemStabSim`]. Callers who need full metadata
+    /// should populate those on the returned DEM.
+    #[must_use]
+    pub fn to_detector_error_model(&self) -> super::types::DetectorErrorModel {
+        use super::types::{DetectorErrorModel, FaultMechanism};
+        let mut dem = DetectorErrorModel::with_capacity(self.num_detectors, self.num_dem_outputs);
+        for i in 0..self.thresholds.len() {
+            let prob = threshold_to_probability(self.thresholds[i]);
+            let det_start = self.detector_offsets[i] as usize;
+            let det_end = self.detector_offsets[i + 1] as usize;
+            let obs_start = self.dem_output_offsets[i] as usize;
+            let obs_end = self.dem_output_offsets[i + 1] as usize;
+            let mechanism = FaultMechanism::from_unsorted(
+                self.detector_data[det_start..det_end].iter().copied(),
+                self.dem_output_data[obs_start..obs_end].iter().copied(),
+            );
+            dem.add_direct_contribution(mechanism, prob);
+        }
+        dem
+    }
+
+    /// Create a [`SamplingEngine`] from raw mechanism data.
     ///
     /// This constructor is used when building from a parsed DEM string rather than
     /// from a circuit analysis. Each mechanism is specified by its probability and
-    /// the detector/observable indices it affects.
+    /// the detector/`L<n>` target indices it affects.
     ///
     /// # Arguments
     ///
-    /// * `mechanisms` - Iterator of (probability, `detector_indices`, `observable_indices`)
+    /// * `mechanisms` - Iterator of (probability, `detector_indices`, `dem_output_indices`)
     /// * `num_detectors` - Total number of detectors
-    /// * `num_observables` - Total number of observables
+    /// * `num_dem_outputs` - Total number of standard observable `L<n>` outputs
     #[must_use]
-    pub fn from_mechanisms<I>(mechanisms: I, num_detectors: usize, num_observables: usize) -> Self
+    pub fn from_mechanisms<I>(mechanisms: I, num_detectors: usize, num_dem_outputs: usize) -> Self
     where
         I: IntoIterator<Item = (f64, Vec<u32>, Vec<u32>)>,
     {
@@ -260,16 +316,16 @@ impl DemSampler {
         let mut inv_log_1_minus_p = Vec::with_capacity(num_mechanisms);
         let mut detector_offsets = Vec::with_capacity(num_mechanisms + 1);
         let mut detector_data = Vec::new();
-        let mut observable_offsets = Vec::with_capacity(num_mechanisms + 1);
-        let mut observable_data = Vec::new();
+        let mut dem_output_offsets = Vec::with_capacity(num_mechanisms + 1);
+        let mut dem_output_data = Vec::new();
 
         detector_offsets.push(0);
-        observable_offsets.push(0);
+        dem_output_offsets.push(0);
 
-        for (prob, mut detectors, mut observables) in mechanisms {
+        for (prob, mut detectors, mut dem_outputs) in mechanisms {
             // Sort for canonical representation
             detectors.sort_unstable();
-            observables.sort_unstable();
+            dem_outputs.sort_unstable();
 
             // Precompute u64 threshold: p * u64::MAX
             #[allow(
@@ -293,9 +349,9 @@ impl DemSampler {
             #[allow(clippy::cast_possible_truncation)] // detector data length fits in u32
             detector_offsets.push(detector_data.len() as u32);
 
-            observable_data.extend_from_slice(&observables);
-            #[allow(clippy::cast_possible_truncation)] // observable data length fits in u32
-            observable_offsets.push(observable_data.len() as u32);
+            dem_output_data.extend_from_slice(&dem_outputs);
+            #[allow(clippy::cast_possible_truncation)] // `L<n>` target data length fits in u32
+            dem_output_offsets.push(dem_output_data.len() as u32);
         }
 
         Self {
@@ -303,20 +359,153 @@ impl DemSampler {
             inv_log_1_minus_p,
             detector_offsets,
             detector_data,
-            observable_offsets,
-            observable_data,
+            dem_output_offsets,
+            dem_output_data,
             num_detectors,
-            num_observables,
+            num_dem_outputs,
+        }
+    }
+
+    /// Create a [`SamplingEngine`] directly from a [`DagFaultInfluenceMap`] and
+    /// per-location error probabilities.
+    ///
+    /// Each fault location is treated as depolarizing: probability `p` at
+    /// location `i` means X, Y, and Z faults each occur with probability
+    /// `p/3`. Mechanisms with identical detector/`L<n>` target effects are
+    /// aggregated automatically.
+    ///
+    /// This constructor works with the influence map's raw measurement and
+    /// DEM-output indices — no explicit detector or observable metadata
+    /// definitions are needed.
+    ///
+    /// # Arguments
+    ///
+    /// * `influence_map` - Precomputed fault influence map.
+    /// * `per_location_probs` - Error probability for each per-qubit fault location
+    ///   (length must equal `influence_map.locations.len()`).
+    ///
+    /// Uses the per-gate noise model: each gate faults with probability p,
+    /// and each non-identity Pauli is equally likely (p/3 for 1-qubit,
+    /// p/15 for 2-qubit). For idle gates with T1/T2 noise, the Pauli
+    /// distribution is biased (more Z than X/Y).
+    #[must_use]
+    pub fn from_influence_map(
+        influence_map: &DagFaultInfluenceMap,
+        per_location_probs: &[f64],
+        noise: &super::NoiseConfig,
+    ) -> Self {
+        use pecos_core::gate_type::GateType;
+
+        let mut aggregated: BTreeMap<DemMechanism, f64> = BTreeMap::new();
+
+        let gate_locs = influence_map.gate_fault_locations();
+
+        for loc in &gate_locs {
+            let p = super::sampler::gate_location_prob_from_locations(
+                loc,
+                per_location_probs,
+                &influence_map.locations,
+            );
+            if p <= 0.0 {
+                continue;
+            }
+
+            let events = loc.all_events();
+            if events.is_empty() {
+                continue;
+            }
+
+            // For idle gates with T1/T2 noise, use per-Pauli probabilities.
+            // For all other gates, divide equally among events.
+            let is_idle = loc.gate_type == GateType::Idle;
+            let idle_pauli_probs = if is_idle {
+                let duration = influence_map
+                    .locations
+                    .iter()
+                    .find(|l| l.node == loc.node && l.before == loc.before)
+                    .map_or(1, |l| l.idle_duration.max(1));
+                // Duration values are small integers; precision loss is not a concern.
+                #[allow(clippy::cast_precision_loss)]
+                Some(noise.idle_pauli_probs(duration as f64))
+            } else {
+                None
+            };
+
+            // Get per-event probabilities based on gate type and noise config
+            let n_qubits = loc.num_qubits();
+            let custom_weights = if idle_pauli_probs.is_some() {
+                None
+            } else if n_qubits == 1 {
+                noise.p1_weights.as_ref()
+            } else {
+                noise.p2_weights.as_ref()
+            };
+
+            let event_weights: Vec<f64> = if let Some(pp) = &idle_pauli_probs {
+                // T1/T2 idle: absolute per-Pauli probabilities
+                events
+                    .iter()
+                    .map(|event| {
+                        let pauli = event
+                            .pauli
+                            .paulis()
+                            .first()
+                            .map_or(pecos_core::Pauli::I, |&(pa, _)| pa);
+                        match pauli {
+                            pecos_core::Pauli::X => pp.px,
+                            pecos_core::Pauli::Y => pp.py,
+                            pecos_core::Pauli::Z => pp.pz,
+                            pecos_core::Pauli::I => 0.0,
+                        }
+                    })
+                    .collect()
+            } else if let Some(weights) = custom_weights {
+                // Custom per-Pauli weights: p * weight_for(pauli)
+                events
+                    .iter()
+                    .map(|event| p * weights.weight_for(&event.pauli))
+                    .collect()
+            } else {
+                // Default uniform: p / num_events
+                // Event count is a small integer; precision loss is not a concern.
+                #[allow(clippy::cast_precision_loss)]
+                let per_event = p / events.len() as f64;
+                vec![per_event; events.len()]
+            };
+
+            for (event, &event_prob) in events.iter().zip(&event_weights) {
+                let det_indices: SmallVec<[u32; 4]> = event.detectors.iter().copied().collect();
+                let dem_output_indices: SmallVec<[u32; 2]> = event
+                    .dem_outputs
+                    .iter()
+                    .filter_map(|&idx| influence_map.observable_id_for_internal_dem_output(idx))
+                    .collect();
+
+                let mech = DemMechanism::new(det_indices, dem_output_indices);
+                if !mech.is_empty() {
+                    let entry = aggregated.entry(mech).or_insert(0.0);
+                    *entry = combine_probabilities(*entry, event_prob);
+                }
+            }
         }
+
+        let num_detectors = influence_map.detectors.len();
+        let num_dem_outputs = influence_map.num_dem_outputs();
+
+        let mechanisms = aggregated
+            .into_iter()
+            .map(|(mech, prob)| (prob, mech.detectors.to_vec(), mech.dem_outputs.to_vec()));
+
+        Self::from_mechanisms(mechanisms, num_detectors, num_dem_outputs)
     }
 
     /// Sample a single shot.
     ///
-    /// Returns (`detection_events`, `observable_flips`) as boolean vectors.
+    /// Returns (`detection_events`, `dem_output_flips`) as boolean vectors.
     #[must_use]
     pub fn sample<R: Rng>(&self, rng: &mut R) -> (Vec<bool>, Vec<bool>) {
         let mut det_bits = PackedBits::new(self.num_detectors);
-        let mut obs_bits = PackedBits::new(self.num_observables);
+        let mut obs_bits = PackedBits::new(self.num_dem_outputs);
 
         self.sample_into_packed(&mut det_bits, &mut obs_bits, rng);
 
@@ -341,16 +530,16 @@ impl DemSampler {
         for i in 0..num_mechanisms {
             // Fast integer comparison with precomputed threshold
             if rng.check_probability(self.thresholds[i]) {
-                // Mechanism fired - XOR in detector/observable effects
+                // Mechanism fired - XOR in detector/`L<n>` target effects
                 let det_start = self.detector_offsets[i] as usize;
                 let det_end = self.detector_offsets[i + 1] as usize;
                 for &d in &self.detector_data[det_start..det_end] {
                     det_bits.flip(d as usize);
                 }
 
-                let obs_start = self.observable_offsets[i] as usize;
-                let obs_end = self.observable_offsets[i + 1] as usize;
-                for &o in &self.observable_data[obs_start..obs_end] {
+                let obs_start = self.dem_output_offsets[i] as usize;
+                let obs_end = self.dem_output_offsets[i + 1] as usize;
+                for &o in &self.dem_output_data[obs_start..obs_end] {
                     obs_bits.flip(o as usize);
                 }
             }
@@ -359,24 +548,66 @@ impl DemSampler {
 
     /// Sample multiple shots.
     ///
-    /// Returns (`all_detection_events`, `all_observable_flips`).
+    /// Uses geometric skip sampling internally — O(fired mechanisms) per
+    /// shot instead of O(all mechanisms). Automatically converts from
+    /// columnar bit-packed format to row-major `Vec<bool>`.
+    ///
+    /// Returns (`all_detection_events`, `all_dem_output_flips`).
     #[must_use]
     pub fn sample_batch<R: Rng>(
         &self,
         num_shots: usize,
         rng: &mut R,
     ) -> (Vec<Vec<bool>>, Vec<Vec<bool>>) {
-        let mut all_det_events = Vec::with_capacity(num_shots);
-        let mut all_obs_flips = Vec::with_capacity(num_shots);
+        if num_shots == 0 {
+            return (vec![], vec![]);
+        }
 
-        // Pre-allocate work arrays
-        let mut det_bits = PackedBits::new(self.num_detectors);
-        let mut obs_bits = PackedBits::new(self.num_observables);
+        // Sample using geometric skip (fast at low error rates).
+        let (det_columns, obs_columns) = self.sample_batch_columnar_geometric(num_shots, rng);
 
-        for _ in 0..num_shots {
-            self.sample_into_packed(&mut det_bits, &mut obs_bits, rng);
-            all_det_events.push(det_bits.to_vec());
-            all_obs_flips.push(obs_bits.to_vec());
+        // Convert columnar bit-packed → row-major Vec<bool>.
+        let mut all_det_events: Vec<Vec<bool>> = (0..num_shots)
+            .map(|_| vec![false; self.num_detectors])
+            .collect();
+        let mut all_obs_flips: Vec<Vec<bool>> = (0..num_shots)
+            .map(|_| vec![false; self.num_dem_outputs])
+            .collect();
+
+        for (det_idx, col) in det_columns.iter().enumerate() {
+            for (word_idx, &word) in col.iter().enumerate() {
+                if word == 0 {
+                    continue;
+                }
+                let base_shot = word_idx * BITS_PER_WORD;
+                let mut w = word;
+                while w != 0 {
+                    let bit = w.trailing_zeros() as usize;
+                    let shot = base_shot + bit;
+                    if shot < num_shots {
+                        all_det_events[shot][det_idx] = true;
+                    }
+                    w &= w - 1;
+                }
+            }
+        }
+
+        for (obs_idx, col) in obs_columns.iter().enumerate() {
+            for (word_idx, &word) in col.iter().enumerate() {
+                if word == 0 {
+                    continue;
+                }
+                let base_shot = word_idx * BITS_PER_WORD;
+                let mut w = word;
+                while w != 0 {
+                    let bit = w.trailing_zeros() as usize;
+                    let shot = base_shot + bit;
+                    if shot < num_shots {
+                        all_obs_flips[shot][obs_idx] = true;
+                    }
+                    w &= w - 1;
+                }
+            }
         }
 
         (all_det_events, all_obs_flips)
@@ -411,6 +642,31 @@ impl DemSampler {
         self.sample_statistics_auto_internal(&mut rng, num_shots)
     }
 
+    /// Compute statistics where only the specified DEM outputs count as observables.
+    ///
+    /// The sampler still reports per-DEM-output flip counts for every `L<n>`
+    /// output. `logical_error_count` and `undetectable_count` are computed
+    /// from the selected observable outputs only, so unmeasured tracked
+    /// Paulis do not affect decoder-style observable statistics.
+    #[must_use]
+    pub fn sample_statistics_for_observable_indices(
+        &self,
+        num_shots: usize,
+        seed: u64,
+        observable_indices: &[usize],
+    ) -> SamplingStatistics {
+        if self.all_dem_outputs_selected(observable_indices) {
+            return self.sample_statistics(num_shots, seed);
+        }
+
+        let mut rng = PecosRng::seed_from_u64(seed);
+        self.sample_statistics_with_rng_for_observable_indices(
+            num_shots,
+            &mut rng,
+            observable_indices,
+        )
+    }
+
     /// Compute statistics with a user-provided RNG.
     ///
     /// Use this when you need control over the random number generator,
@@ -429,6 +685,43 @@ impl DemSampler {
         self.sample_statistics_auto_internal(rng, num_shots)
     }
 
+    /// Compute statistics with a user-provided RNG and explicit observable DEM-output indices.
+    #[must_use]
+    pub fn sample_statistics_with_rng_for_observable_indices<R: Rng>(
+        &self,
+        num_shots: usize,
+        rng: &mut R,
+        observable_indices: &[usize],
+    ) -> SamplingStatistics {
+        if self.all_dem_outputs_selected(observable_indices) {
+            return self.sample_statistics_with_rng(num_shots, rng);
+        }
+        if num_shots == 0 || self.thresholds.is_empty() {
+            return SamplingStatistics::with_channels(
+                num_shots,
+                self.num_detectors,
+                self.num_dem_outputs,
+            );
+        }
+
+        let (det_columns, dem_output_columns) =
+            self.sample_batch_columnar_geometric(num_shots, rng);
+        Self::compute_statistics_from_columns_for_observables(
+            &det_columns,
+            &dem_output_columns,
+            num_shots,
+            observable_indices,
+        )
+    }
+
+    fn all_dem_outputs_selected(&self, observable_indices: &[usize]) -> bool {
+        observable_indices.len() == self.num_dem_outputs
+            && observable_indices
+                .iter()
+                .copied()
+                .eq(0..self.num_dem_outputs)
+    }
+
     /// Internal: sample statistics using the most efficient method.
     ///
     /// Uses chunked processing for large working sets (>6 MB) to improve cache
@@ -445,7 +738,7 @@ impl DemSampler {
     /// Optimized statistics sampling using flat array layout.
     ///
     /// This method provides faster sampling than nested Vec<Vec<u64>> by:
-    /// - Using a flat contiguous array for detector/observable columns
+    /// - Using a flat contiguous array for detector/`L<n>` target columns
     /// - Better cache locality due to predictable memory access patterns
     ///
     /// This method is semantically equivalent to the columnar methods.
@@ -461,9 +754,9 @@ impl DemSampler {
         // XOR semantics required for correct detector behavior
         let mut det_data: Vec<u64> = vec![0u64; self.num_detectors * num_words];
 
-        // Flat array for observable columns (XOR semantics)
+        // Flat array for `L<n>` target columns (XOR semantics)
         // Layout: obs_data[obs_idx * num_words + word_idx]
-        let mut obs_data: Vec<u64> = vec![0u64; self.num_observables * num_words];
+        let mut obs_data: Vec<u64> = vec![0u64; self.num_dem_outputs * num_words];
 
         for mech_idx in 0..num_mechanisms {
             let threshold = self.thresholds[mech_idx];
@@ -473,8 +766,8 @@ impl DemSampler {
 
             let det_start = self.detector_offsets[mech_idx] as usize;
             let det_end = self.detector_offsets[mech_idx + 1] as usize;
-            let obs_start = self.observable_offsets[mech_idx] as usize;
-            let obs_end = self.observable_offsets[mech_idx + 1] as usize;
+            let obs_start = self.dem_output_offsets[mech_idx] as usize;
+            let obs_end = self.dem_output_offsets[mech_idx + 1] as usize;
 
             // Skip if mechanism affects nothing
             if det_start == det_end && obs_start == obs_end {
@@ -507,7 +800,7 @@ impl DemSampler {
                 }
 
                 // XOR each affected observable
-                for &o in &self.observable_data[obs_start..obs_end] {
+                for &o in &self.dem_output_data[obs_start..obs_end] {
                     let idx = o as usize * num_words + word_idx;
                     obs_data[idx] ^= mask;
                 }
@@ -525,20 +818,62 @@ impl DemSampler {
             }
         }
 
-        // Compute logical error mask by ORing all observable columns
-        let mut logical_words = vec![0u64; num_words];
-        for obs_idx in 0..self.num_observables {
+        // Compute logical-error mask by ORing all selected standard observable columns.
+        let mut observable_words = vec![0u64; num_words];
+        for obs_idx in 0..self.num_dem_outputs {
             let base = obs_idx * num_words;
             for word_idx in 0..num_words {
-                logical_words[word_idx] |= obs_data[base + word_idx];
+                observable_words[word_idx] |= obs_data[base + word_idx];
             }
         }
 
         // Count statistics
-        let mut stats = SamplingStatistics::new(num_shots);
+        let mut stats =
+            SamplingStatistics::with_channels(num_shots, self.num_detectors, self.num_dem_outputs);
+
+        // Per-channel counts (cheap -- data is already in cache from the OR passes above)
+        for det_idx in 0..self.num_detectors {
+            let base = det_idx * num_words;
+            let mut count = 0usize;
+            for word_idx in 0..num_words {
+                let valid_bits = if word_idx == num_words - 1 {
+                    let remaining = num_shots % BITS_PER_WORD;
+                    if remaining == 0 {
+                        !0u64
+                    } else {
+                        (1u64 << remaining) - 1
+                    }
+                } else {
+                    !0u64
+                };
+                count += (det_data[base + word_idx] & valid_bits).count_ones() as usize;
+            }
+            stats.per_detector[det_idx] = count;
+        }
+
+        for obs_idx in 0..self.num_dem_outputs {
+            let base = obs_idx * num_words;
+            let mut count = 0usize;
+            for word_idx in 0..num_words {
+                let valid_bits = if word_idx == num_words - 1 {
+                    let remaining = num_shots % BITS_PER_WORD;
+                    if remaining == 0 {
+                        !0u64
+                    } else {
+                        (1u64 << remaining) - 1
+                    }
+                } else {
+                    !0u64
+                };
+                count += (obs_data[base + word_idx] & valid_bits).count_ones() as usize;
+            }
+            stats.per_dem_output[obs_idx] = count;
+        }
+
+        // Aggregate counts
         for word_idx in 0..num_words {
             let syndrome = syndrome_words[word_idx];
-            let logical = logical_words[word_idx];
+            let observable = observable_words[word_idx];
 
             let valid_bits = if word_idx == num_words - 1 {
                 let remaining = num_shots % BITS_PER_WORD;
@@ -552,11 +887,12 @@ impl DemSampler {
             };
 
             let syndrome_masked = syndrome & valid_bits;
-            let logical_masked = logical & valid_bits;
+            let observable_masked = observable & valid_bits;
 
             stats.syndrome_count += syndrome_masked.count_ones() as usize;
-            stats.logical_error_count += logical_masked.count_ones() as usize;
-            stats.undetectable_count += (logical_masked & !syndrome_masked).count_ones() as usize;
+            stats.logical_error_count += observable_masked.count_ones() as usize;
+            stats.undetectable_count +=
+                (observable_masked & !syndrome_masked).count_ones() as usize;
         }
 
         stats
@@ -568,9 +904,9 @@ impl DemSampler {
     /// within the target cache size (L3). Returns `None` if the buffer is already
     /// small enough that chunking wouldn't help.
     fn optimal_chunk_size(&self, num_shots: usize) -> Option<usize> {
-        // Calculate full buffer size: (num_detectors + num_observables) * num_words * 8 bytes
+        // Calculate full buffer size: (num_detectors + num_dem_outputs) * num_words * 8 bytes
         let num_words = num_shots.div_ceil(BITS_PER_WORD);
-        let full_buffer_bytes = (self.num_detectors + self.num_observables) * num_words * 8;
+        let full_buffer_bytes = (self.num_detectors + self.num_dem_outputs) * num_words * 8;
 
         // Only chunk if buffer exceeds target cache size
         if full_buffer_bytes <= TARGET_CHUNK_BUFFER_BYTES {
@@ -578,9 +914,9 @@ impl DemSampler {
         }
 
         // Calculate chunk size that fits in cache
-        // Buffer = (num_detectors + num_observables) * (chunk_shots / 64) * 8
-        // chunk_shots = TARGET * 64 / ((num_detectors + num_observables) * 8)
-        let total_columns = self.num_detectors + self.num_observables;
+        // Buffer = (num_detectors + num_dem_outputs) * (chunk_shots / 64) * 8
+        // chunk_shots = TARGET * 64 / ((num_detectors + num_dem_outputs) * 8)
+        let total_columns = self.num_detectors + self.num_dem_outputs;
         if total_columns == 0 {
             return None;
         }
@@ -616,7 +952,8 @@ impl DemSampler {
             return self.sample_statistics_direct(num_shots, rng);
         };
 
-        let mut total_stats = SamplingStatistics::new(num_shots);
+        let mut total_stats =
+            SamplingStatistics::with_channels(num_shots, self.num_detectors, self.num_dem_outputs);
         let mut shot_offset = 0;
 
         while shot_offset < num_shots {
@@ -626,6 +963,20 @@ impl DemSampler {
             total_stats.syndrome_count += chunk_stats.syndrome_count;
             total_stats.logical_error_count += chunk_stats.logical_error_count;
             total_stats.undetectable_count += chunk_stats.undetectable_count;
+            for (total, chunk) in total_stats
+                .per_detector
+                .iter_mut()
+                .zip(&chunk_stats.per_detector)
+            {
+                *total += chunk;
+            }
+            for (total, chunk) in total_stats
+                .per_dem_output
+                .iter_mut()
+                .zip(&chunk_stats.per_dem_output)
+            {
+                *total += chunk;
+            }
 
             shot_offset += chunk_shots;
         }
@@ -641,26 +992,39 @@ impl DemSampler {
         num_shots: usize,
         rng: &mut R,
     ) -> SamplingStatistics {
-        let mut stats = SamplingStatistics::new(num_shots);
+        let mut stats =
+            SamplingStatistics::with_channels(num_shots, self.num_detectors, self.num_dem_outputs);
 
         let mut det_bits = PackedBits::new(self.num_detectors);
-        let mut obs_bits = PackedBits::new(self.num_observables);
+        let mut obs_bits = PackedBits::new(self.num_dem_outputs);
 
         for _ in 0..num_shots {
             self.sample_into_packed(&mut det_bits, &mut obs_bits, rng);
 
             let has_syndrome = det_bits.any();
-            let has_logical_error = obs_bits.any();
+            let has_observable_error = obs_bits.any();
 
-            if has_logical_error {
+            if has_observable_error {
                 stats.logical_error_count += 1;
             }
             if has_syndrome {
                 stats.syndrome_count += 1;
             }
-            if has_logical_error && !has_syndrome {
+            if has_observable_error && !has_syndrome {
                 stats.undetectable_count += 1;
             }
+
+            // Per-channel counts
+            for (i, count) in stats.per_detector.iter_mut().enumerate() {
+                if det_bits.get(i) {
+                    *count += 1;
+                }
+            }
+            for (i, count) in stats.per_dem_output.iter_mut().enumerate() {
+                if obs_bits.get(i) {
+                    *count += 1;
+                }
+            }
         }
 
         stats
@@ -675,7 +1039,7 @@ impl DemSampler {
     /// This method processes all shots for each mechanism at once, enabling:
     /// - Bulk random number generation (64 shots per u64)
     /// - Better cache locality for threshold comparisons
-    /// - Vectorized XOR operations on detector/observable columns
+    /// - Vectorized XOR operations on detector/`L<n>` target columns
     ///
     /// Returns columnar bit-packed results: (detector_columns, observable_columns)
     /// where each column is a Vec<u64> with bit i of word w = shot w*64 + i.
@@ -689,17 +1053,17 @@ impl DemSampler {
         if num_shots == 0 {
             return (
                 vec![vec![]; self.num_detectors],
-                vec![vec![]; self.num_observables],
+                vec![vec![]; self.num_dem_outputs],
             );
         }
 
         let num_words = num_shots.div_ceil(BITS_PER_WORD);
 
-        // Initialize detector and observable columns (all zeros)
+        // Initialize detector and `L<n>` target columns (all zeros)
         let mut det_columns: Vec<Vec<u64>> = (0..self.num_detectors)
             .map(|_| vec![0u64; num_words])
             .collect();
-        let mut obs_columns: Vec<Vec<u64>> = (0..self.num_observables)
+        let mut obs_columns: Vec<Vec<u64>> = (0..self.num_dem_outputs)
             .map(|_| vec![0u64; num_words])
             .collect();
 
@@ -716,9 +1080,7 @@ impl DemSampler {
             }
 
             // Generate bulk random numbers for this mechanism
-            for word in &mut random_words {
-                *word = rng.next_u64();
-            }
+            rng.fill_u64(&mut random_words);
 
             // For each word, check threshold and apply effects
             for word_idx in 0..num_words {
@@ -737,10 +1099,10 @@ impl DemSampler {
                     det_columns[d as usize][word_idx] ^= !0u64;
                 }
 
-                // XOR effects into observable columns
-                let obs_start = self.observable_offsets[mech_idx] as usize;
-                let obs_end = self.observable_offsets[mech_idx + 1] as usize;
-                for &o in &self.observable_data[obs_start..obs_end] {
+                // XOR effects into `L<n>` target columns
+                let obs_start = self.dem_output_offsets[mech_idx] as usize;
+                let obs_end = self.dem_output_offsets[mech_idx + 1] as usize;
+                for &o in &self.dem_output_data[obs_start..obs_end] {
                     obs_columns[o as usize][word_idx] ^= !0u64;
                 }
             }
@@ -763,17 +1125,17 @@ impl DemSampler {
         if num_shots == 0 {
             return (
                 vec![vec![]; self.num_detectors],
-                vec![vec![]; self.num_observables],
+                vec![vec![]; self.num_dem_outputs],
             );
         }
 
         let num_words = num_shots.div_ceil(BITS_PER_WORD);
 
-        // Initialize detector and observable columns (all zeros)
+        // Initialize detector and `L<n>` target columns (all zeros)
         let mut det_columns: Vec<Vec<u64>> = (0..self.num_detectors)
             .map(|_| vec![0u64; num_words])
             .collect();
-        let mut obs_columns: Vec<Vec<u64>> = (0..self.num_observables)
+        let mut obs_columns: Vec<Vec<u64>> = (0..self.num_dem_outputs)
             .map(|_| vec![0u64; num_words])
             .collect();
 
@@ -786,11 +1148,11 @@ impl DemSampler {
                 continue;
             }
 
-            // Get detector/observable indices for this mechanism
+            // Get detector/`L<n>` target indices for this mechanism
             let det_start = self.detector_offsets[mech_idx] as usize;
             let det_end = self.detector_offsets[mech_idx + 1] as usize;
-            let obs_start = self.observable_offsets[mech_idx] as usize;
-            let obs_end = self.observable_offsets[mech_idx + 1] as usize;
+            let obs_start = self.dem_output_offsets[mech_idx] as usize;
+            let obs_end = self.dem_output_offsets[mech_idx + 1] as usize;
 
             // For each word (64 shots), generate random bits and check threshold
             for word_idx in 0..num_words {
@@ -824,8 +1186,8 @@ impl DemSampler {
                     det_columns[d as usize][word_idx] ^= fired_mask;
                 }
 
-                // XOR the fired mask into affected observable columns
-                for &o in &self.observable_data[obs_start..obs_end] {
+                // XOR the fired mask into affected `L<n>` target columns
+                for &o in &self.dem_output_data[obs_start..obs_end] {
                     obs_columns[o as usize][word_idx] ^= fired_mask;
                 }
             }
@@ -858,18 +1220,18 @@ impl DemSampler {
             }
         }
 
-        // OR all observable columns to get logical error mask
-        let mut logical_words = vec![0u64; num_words];
+        // OR all standard observable columns to get a logical-error mask.
+        let mut observable_words = vec![0u64; num_words];
         for col in &obs_columns {
             for (i, &word) in col.iter().enumerate() {
-                logical_words[i] |= word;
+                observable_words[i] |= word;
             }
         }
 
-        // Count shots with syndrome, logical error, undetectable
+        // Count shots with syndrome, logical error, undetectable error
         for word_idx in 0..num_words {
             let syndrome = syndrome_words[word_idx];
-            let logical = logical_words[word_idx];
+            let observable = observable_words[word_idx];
 
             // Mask out unused bits in the last word
             let valid_bits = if word_idx == num_words - 1 {
@@ -884,11 +1246,12 @@ impl DemSampler {
             };
 
             let syndrome_masked = syndrome & valid_bits;
-            let logical_masked = logical & valid_bits;
+            let observable_masked = observable & valid_bits;
 
             stats.syndrome_count += syndrome_masked.count_ones() as usize;
-            stats.logical_error_count += logical_masked.count_ones() as usize;
-            stats.undetectable_count += (logical_masked & !syndrome_masked).count_ones() as usize;
+            stats.logical_error_count += observable_masked.count_ones() as usize;
+            stats.undetectable_count +=
+                (observable_masked & !syndrome_masked).count_ones() as usize;
         }
 
         stats
@@ -911,18 +1274,18 @@ impl DemSampler {
         if num_shots == 0 {
             return (
                 vec![vec![]; self.num_detectors],
-                vec![vec![]; self.num_observables],
+                vec![vec![]; self.num_dem_outputs],
             );
         }
 
         let num_words = num_shots.div_ceil(BITS_PER_WORD);
         let num_simd_words = num_words.div_ceil(4);
 
-        // Initialize detector and observable columns as SIMD vectors
+        // Initialize detector and `L<n>` target columns as SIMD vectors
         let mut det_columns: Vec<Vec<u64x4>> = (0..self.num_detectors)
             .map(|_| vec![u64x4::ZERO; num_simd_words])
             .collect();
-        let mut obs_columns: Vec<Vec<u64x4>> = (0..self.num_observables)
+        let mut obs_columns: Vec<Vec<u64x4>> = (0..self.num_dem_outputs)
             .map(|_| vec![u64x4::ZERO; num_simd_words])
             .collect();
 
@@ -937,11 +1300,11 @@ impl DemSampler {
                 continue;
             }
 
-            // Get detector/observable indices for this mechanism
+            // Get detector/`L<n>` target indices for this mechanism
             let det_start = self.detector_offsets[mech_idx] as usize;
             let det_end = self.detector_offsets[mech_idx + 1] as usize;
-            let obs_start = self.observable_offsets[mech_idx] as usize;
-            let obs_end = self.observable_offsets[mech_idx + 1] as usize;
+            let obs_start = self.dem_output_offsets[mech_idx] as usize;
+            let obs_end = self.dem_output_offsets[mech_idx + 1] as usize;
 
             // Generate all random numbers for this mechanism at once
             // Use fill_u64 from RngProbabilityExt for potentially optimized bulk generation
@@ -995,8 +1358,8 @@ impl DemSampler {
                     det_columns[d as usize][simd_idx] ^= fired_vec;
                 }
 
-                // XOR into affected observable columns
-                for &o in &self.observable_data[obs_start..obs_end] {
+                // XOR into affected `L<n>` target columns
+                for &o in &self.dem_output_data[obs_start..obs_end] {
                     obs_columns[o as usize][simd_idx] ^= fired_vec;
                 }
             }
@@ -1060,17 +1423,17 @@ impl DemSampler {
         if num_shots == 0 {
             return (
                 vec![vec![]; self.num_detectors],
-                vec![vec![]; self.num_observables],
+                vec![vec![]; self.num_dem_outputs],
             );
         }
 
         let num_words = num_shots.div_ceil(BITS_PER_WORD);
 
-        // Initialize detector and observable columns
+        // Initialize detector and `L<n>` target columns
         let mut det_columns: Vec<Vec<u64>> = (0..self.num_detectors)
             .map(|_| vec![0u64; num_words])
             .collect();
-        let mut obs_columns: Vec<Vec<u64>> = (0..self.num_observables)
+        let mut obs_columns: Vec<Vec<u64>> = (0..self.num_dem_outputs)
             .map(|_| vec![0u64; num_words])
             .collect();
 
@@ -1082,11 +1445,11 @@ impl DemSampler {
                 continue;
             }
 
-            // Get detector/observable indices
+            // Get detector/`L<n>` target indices
             let det_start = self.detector_offsets[mech_idx] as usize;
             let det_end = self.detector_offsets[mech_idx + 1] as usize;
-            let obs_start = self.observable_offsets[mech_idx] as usize;
-            let obs_end = self.observable_offsets[mech_idx + 1] as usize;
+            let obs_start = self.dem_output_offsets[mech_idx] as usize;
+            let obs_end = self.dem_output_offsets[mech_idx + 1] as usize;
 
             // Use precomputed 1/ln(1-p) for geometric sampling
             let inv_log = self.inv_log_1_minus_p[mech_idx];
@@ -1115,7 +1478,7 @@ impl DemSampler {
                     det_columns[d as usize][word_idx] ^= mask;
                 }
 
-                for &o in &self.observable_data[obs_start..obs_end] {
+                for &o in &self.dem_output_data[obs_start..obs_end] {
                     obs_columns[o as usize][word_idx] ^= mask;
                 }
 
@@ -1158,23 +1521,25 @@ impl DemSampler {
     ///
     /// Used to decide between geometric (low p) and SIMD (high p) sampling.
     #[must_use]
-    #[allow(clippy::cast_precision_loss)]
     pub fn average_error_probability(&self) -> f64 {
         if self.thresholds.is_empty() {
             return 0.0;
         }
-        let sum: u128 = self.thresholds.iter().map(|&t| u128::from(t)).sum();
-        let avg_threshold = (sum / self.thresholds.len() as u128) as f64;
-        avg_threshold / u64::MAX as f64
+        let mut sum = 0.0;
+        let mut count = 0.0;
+        for &threshold in &self.thresholds {
+            sum += threshold_to_probability(threshold);
+            count += 1.0;
+        }
+        sum / count
     }
 
     /// Maximum error probability across all mechanisms.
     #[must_use]
-    #[allow(clippy::cast_precision_loss)]
     pub fn max_error_probability(&self) -> f64 {
         self.thresholds
             .iter()
-            .map(|&t| t as f64 / u64::MAX as f64)
+            .map(|&t| threshold_to_probability(t))
             .fold(0.0, f64::max)
     }
 
@@ -1221,11 +1586,18 @@ impl DemSampler {
             .collect();
 
         // Sum up partial statistics
-        let mut total = SamplingStatistics::new(num_shots);
+        let mut total =
+            SamplingStatistics::with_channels(num_shots, self.num_detectors, self.num_dem_outputs);
         for stats in partial_stats {
             total.syndrome_count += stats.syndrome_count;
             total.logical_error_count += stats.logical_error_count;
             total.undetectable_count += stats.undetectable_count;
+            for (t, s) in total.per_detector.iter_mut().zip(&stats.per_detector) {
+                *t += s;
+            }
+            for (t, s) in total.per_dem_output.iter_mut().zip(&stats.per_dem_output) {
+                *t += s;
+            }
         }
 
         total
@@ -1249,30 +1621,75 @@ impl DemSampler {
         det_columns: &[Vec<u64>],
         obs_columns: &[Vec<u64>],
         num_shots: usize,
+    ) -> SamplingStatistics {
+        let observable_indices: Vec<usize> = (0..obs_columns.len()).collect();
+        Self::compute_statistics_from_columns_for_observables(
+            det_columns,
+            obs_columns,
+            num_shots,
+            &observable_indices,
+        )
+    }
+
+    fn compute_statistics_from_columns_for_observables(
+        det_columns: &[Vec<u64>],
+        obs_columns: &[Vec<u64>],
+        num_shots: usize,
+        observable_indices: &[usize],
     ) -> SamplingStatistics {
         let num_words = num_shots.div_ceil(BITS_PER_WORD);
-        let mut stats = SamplingStatistics::new(num_shots);
+        let mut stats =
+            SamplingStatistics::with_channels(num_shots, det_columns.len(), obs_columns.len());
 
-        // OR all detector columns to get syndrome mask
+        // Per-channel and aggregate syndrome
         let mut syndrome_words = vec![0u64; num_words];
-        for col in det_columns {
+        for (det_idx, col) in det_columns.iter().enumerate() {
+            let mut count = 0usize;
             for (i, &word) in col.iter().enumerate() {
                 syndrome_words[i] |= word;
+                let valid = if i == num_words - 1 {
+                    let r = num_shots % BITS_PER_WORD;
+                    if r == 0 { !0u64 } else { (1u64 << r) - 1 }
+                } else {
+                    !0u64
+                };
+                count += (word & valid).count_ones() as usize;
             }
+            stats.per_detector[det_idx] = count;
         }
 
-        // OR all observable columns to get logical error mask
-        let mut logical_words = vec![0u64; num_words];
-        for col in obs_columns {
+        // Per-channel DEM-output counts.
+        let mut dem_output_words = vec![vec![0u64; num_words]; obs_columns.len()];
+        for (obs_idx, col) in obs_columns.iter().enumerate() {
+            let mut count = 0usize;
             for (i, &word) in col.iter().enumerate() {
-                logical_words[i] |= word;
+                dem_output_words[obs_idx][i] = word;
+                let valid = if i == num_words - 1 {
+                    let r = num_shots % BITS_PER_WORD;
+                    if r == 0 { !0u64 } else { (1u64 << r) - 1 }
+                } else {
+                    !0u64
+                };
+                count += (word & valid).count_ones() as usize;
+            }
+            stats.per_dem_output[obs_idx] = count;
+        }
+
+        // Aggregate logical-error mask from observables only. Tracked Paulis
+        // remain in per_dem_output but do not define decoder failures.
+        let mut observable_words = vec![0u64; num_words];
+        for &obs_idx in observable_indices {
+            if let Some(col) = dem_output_words.get(obs_idx) {
+                for (i, &word) in col.iter().enumerate() {
+                    observable_words[i] |= word;
+                }
             }
         }
 
-        // Count shots with syndrome, logical error, undetectable
+        // Aggregate counts
         for word_idx in 0..num_words {
             let syndrome = syndrome_words[word_idx];
-            let logical = logical_words[word_idx];
+            let observable = observable_words[word_idx];
 
             let valid_bits = if word_idx == num_words - 1 {
                 let remaining = num_shots % BITS_PER_WORD;
@@ -1286,11 +1703,12 @@ impl DemSampler {
             };
 
             let syndrome_masked = syndrome & valid_bits;
-            let logical_masked = logical & valid_bits;
+            let observable_masked = observable & valid_bits;
 
             stats.syndrome_count += syndrome_masked.count_ones() as usize;
-            stats.logical_error_count += logical_masked.count_ones() as usize;
-            stats.undetectable_count += (logical_masked & !syndrome_masked).count_ones() as usize;
+            stats.logical_error_count += observable_masked.count_ones() as usize;
+            stats.undetectable_count +=
+                (observable_masked & !syndrome_masked).count_ones() as usize;
         }
 
         stats
@@ -1302,12 +1720,16 @@ impl DemSampler {
 pub struct SamplingStatistics {
     /// Total number of shots.
     pub total_shots: usize,
-    /// Shots with at least one logical error.
+    /// Shots with at least one selected observable flip.
     pub logical_error_count: usize,
     /// Shots with at least one detector firing.
     pub syndrome_count: usize,
-    /// Shots with logical error but no syndrome (undetectable errors).
+    /// Shots with an observable flip but no syndrome.
     pub undetectable_count: usize,
+    /// Per-detector firing counts (shots where this detector fired).
+    pub per_detector: Vec<usize>,
+    /// Per-`L<n>` DEM-output flip counts (shots where this `L<n>` output flipped).
+    pub per_dem_output: Vec<usize>,
 }
 
 impl SamplingStatistics {
@@ -1317,52 +1739,119 @@ impl SamplingStatistics {
             logical_error_count: 0,
             syndrome_count: 0,
             undetectable_count: 0,
+            per_detector: Vec::new(),
+            per_dem_output: Vec::new(),
+        }
+    }
+
+    fn with_channels(total_shots: usize, num_detectors: usize, num_dem_outputs: usize) -> Self {
+        Self {
+            total_shots,
+            logical_error_count: 0,
+            syndrome_count: 0,
+            undetectable_count: 0,
+            per_detector: vec![0; num_detectors],
+            per_dem_output: vec![0; num_dem_outputs],
         }
     }
 
     /// Logical error rate.
     #[must_use]
-    #[allow(clippy::cast_precision_loss)] // rate calculation
+    #[allow(clippy::cast_precision_loss)]
     pub fn logical_error_rate(&self) -> f64 {
         self.logical_error_count as f64 / self.total_shots as f64
     }
 
     /// Syndrome rate (fraction of shots with non-trivial syndrome).
     #[must_use]
-    #[allow(clippy::cast_precision_loss)] // rate calculation
+    #[allow(clippy::cast_precision_loss)]
     pub fn syndrome_rate(&self) -> f64 {
         self.syndrome_count as f64 / self.total_shots as f64
     }
 
     /// Undetectable error rate.
     #[must_use]
-    #[allow(clippy::cast_precision_loss)] // rate calculation
+    #[allow(clippy::cast_precision_loss)]
     pub fn undetectable_rate(&self) -> f64 {
         self.undetectable_count as f64 / self.total_shots as f64
     }
+
+    /// Per-detector firing rates.
+    #[must_use]
+    #[allow(clippy::cast_precision_loss)]
+    pub fn detector_rates(&self) -> Vec<f64> {
+        let n = self.total_shots as f64;
+        self.per_detector.iter().map(|&c| c as f64 / n).collect()
+    }
+
+    /// Per-`L<n>` DEM-output flip rates.
+    #[must_use]
+    #[allow(clippy::cast_precision_loss)]
+    pub fn dem_output_rates(&self) -> Vec<f64> {
+        let n = self.total_shots as f64;
+        self.per_dem_output.iter().map(|&c| c as f64 / n).collect()
+    }
+
+    /// Per-`L<n>` DEM-output flip counts.
+    #[must_use]
+    pub fn dem_output_counts(&self) -> &[usize] {
+        &self.per_dem_output
+    }
+
+    /// Per-observable flip counts selected from standard `L<n>` observable columns.
+    #[must_use]
+    pub fn observable_counts(&self, observable_indices: &[usize]) -> Vec<usize> {
+        observable_indices
+            .iter()
+            .filter_map(|&idx| self.per_dem_output.get(idx).copied())
+            .collect()
+    }
+
+    /// Per-observable flip rates selected from standard `L<n>` observable columns.
+    #[must_use]
+    #[allow(clippy::cast_precision_loss)]
+    pub fn logical_rates(&self, observable_indices: &[usize]) -> Vec<f64> {
+        let n = self.total_shots as f64;
+        self.observable_counts(observable_indices)
+            .into_iter()
+            .map(|c| c as f64 / n)
+            .collect()
+    }
 }
 
 // ============================================================================
 // DEM Sampler Builder
 // ============================================================================
 
-/// Builder for [`DemSampler`].
+/// Builder for [`SamplingEngine`].
 ///
-/// Constructs a [`DemSampler`] from a fault influence map, noise parameters,
-/// and explicit detector/observable definitions.
-pub struct DemSamplerBuilder<'a> {
+/// Constructs a [`SamplingEngine`] from a fault influence map, noise parameters,
+/// and explicit detector/standard observable `L<n>` definitions.
+pub(crate) struct SamplingEngineBuilder<'a> {
+    /// Optional per-gate-type noise specification. If set, overrides the
+    /// uniform scalar `p1, p2` for any gate type present in its maps.
+    /// Measurement / prep errors come from the scalar `p_meas` / `p_prep`
+    /// or the per-qubit overrides in the per-gate spec.
+    per_gate: Option<PerGateTypeNoise>,
     influence_map: &'a DagFaultInfluenceMap,
     p1: f64,
     p2: f64,
     p_meas: f64,
-    p_init: f64,
+    p_prep: f64,
+    idle_noise: Option<NoiseConfig>,
     detector_records: Vec<Vec<i32>>,
     observable_records: Vec<Vec<i32>>,
     measurement_order: Option<Vec<usize>>,
     num_tc_measurements: Option<usize>,
 }
 
-impl<'a> DemSamplerBuilder<'a> {
+struct FaultMechanismContext<'a> {
+    im_to_tc: Option<&'a [usize]>,
+    influence_observable_ids: &'a BTreeSet<u32>,
+    num_tc_measurements: usize,
+}
+
+impl<'a> SamplingEngineBuilder<'a> {
     /// Create a new builder from an influence map.
     #[must_use]
     pub fn new(influence_map: &'a DagFaultInfluenceMap) -> Self {
@@ -1371,7 +1860,9 @@ impl<'a> DemSamplerBuilder<'a> {
             p1: 0.01,
             p2: 0.01,
             p_meas: 0.01,
-            p_init: 0.01,
+            p_prep: 0.01,
+            idle_noise: None,
+            per_gate: None,
             detector_records: Vec::new(),
             observable_records: Vec::new(),
             measurement_order: None,
@@ -1379,13 +1870,42 @@ impl<'a> DemSamplerBuilder<'a> {
         }
     }
 
-    /// Set noise parameters.
+    /// Set uniform-depolarizing noise parameters.
     #[must_use]
-    pub fn with_noise(mut self, p1: f64, p2: f64, p_meas: f64, p_init: f64) -> Self {
+    pub fn with_noise(mut self, p1: f64, p2: f64, p_meas: f64, p_prep: f64) -> Self {
         self.p1 = p1;
         self.p2 = p2;
         self.p_meas = p_meas;
-        self.p_init = p_init;
+        self.p_prep = p_prep;
+        self
+    }
+
+    /// Set idle gate noise rate.
+    #[must_use]
+    pub fn with_idle_noise(mut self, p_idle: f64) -> Self {
+        self.idle_noise = Some(NoiseConfig::new(0.0, 0.0, 0.0, 0.0).set_idle(p_idle));
+        self
+    }
+
+    /// Set the full idle-noise model for idle gates.
+    #[must_use]
+    pub fn with_idle_noise_config(mut self, noise: NoiseConfig) -> Self {
+        self.idle_noise = Some(noise);
+        self
+    }
+
+    /// Set per-gate-type per-Pauli noise specification. When provided,
+    /// overrides the uniform `p1, p2` for any gate type present in the
+    /// spec's maps. Measurement / prep fault rates come from
+    /// `p_meas, p_init` on the [`PerGateTypeNoise`] struct.
+    ///
+    /// Intended consumer: `pecos-lindblad::PauliLindbladModel` via
+    /// per-gate-type adapter helpers.
+    #[must_use]
+    pub fn with_per_gate_noise(mut self, cfg: PerGateTypeNoise) -> Self {
+        self.p_meas = cfg.p_meas;
+        self.p_prep = cfg.p_init;
+        self.per_gate = Some(cfg);
         self
     }
 
@@ -1418,7 +1938,7 @@ impl<'a> DemSamplerBuilder<'a> {
         self
     }
 
-    /// Set observable records directly.
+    /// Set observable definitions directly.
     #[must_use]
     pub fn with_observable_records(mut self, records: Vec<Vec<i32>>) -> Self {
         self.observable_records = records;
@@ -1436,16 +1956,23 @@ impl<'a> DemSamplerBuilder<'a> {
         self
     }
 
-    /// Build the [`DemSampler`].
+    /// Build the [`SamplingEngine`].
     #[must_use]
-    pub fn build(self) -> DemSampler {
+    pub fn build(self) -> SamplingEngine {
         let num_detectors = self.detector_records.len();
-        let num_observables = self.observable_records.len();
+        let influence_observable_ids = self.influence_map.observable_ids();
+        let num_influence_observables = self.influence_map.num_observables();
+        let num_dem_outputs = num_influence_observables.max(self.observable_records.len());
         let num_im_measurements = self.influence_map.measurements.len();
         let num_tc_measurements = self.num_tc_measurements.unwrap_or(num_im_measurements);
 
         // Build IM -> TC index mapping
         let im_to_tc = self.build_im_to_tc_mapping();
+        let mechanism_context = FaultMechanismContext {
+            im_to_tc: im_to_tc.as_deref(),
+            influence_observable_ids: &influence_observable_ids,
+            num_tc_measurements,
+        };
 
         // Aggregation map: mechanism -> probability
         let mut aggregated: BTreeMap<DemMechanism, f64> = BTreeMap::new();
@@ -1458,31 +1985,43 @@ impl<'a> DemSamplerBuilder<'a> {
             match loc.gate_type {
                 GateType::PZ | GateType::QAlloc
                     // Prep errors: only "after" locations (X error for Z-basis prep)
-                    if self.p_init > 0.0 && !loc.before => {
+                    if !loc.before =>
+                {
+                    let p = self.init_rate_for_location(loc);
+                    if p > 0.0 {
                         self.process_single_pauli_fault(
                             loc_idx,
                             Pauli::X,
-                            self.p_init,
-                            im_to_tc.as_deref(),
-                            num_tc_measurements,
+                            p,
+                            &mechanism_context,
                             &mut aggregated,
                         );
                     }
+                }
                 GateType::MZ | GateType::MeasureFree
                     // Measurement errors: only "before" locations (X error = bit flip)
-                    if self.p_meas > 0.0 && loc.before => {
+                    if loc.before =>
+                {
+                    let p = self.measurement_rate_for_location(loc);
+                    if p > 0.0 {
                         self.process_single_pauli_fault(
                             loc_idx,
                             Pauli::X,
-                            self.p_meas,
-                            im_to_tc.as_deref(),
-                            num_tc_measurements,
+                            p,
+                            &mechanism_context,
                             &mut aggregated,
                         );
                     }
+                }
                 GateType::CX
                 | GateType::CZ
                 | GateType::CY
+                | GateType::SZZ
+                | GateType::SZZdg
+                | GateType::SXX
+                | GateType::SXXdg
+                | GateType::SYY
+                | GateType::SYYdg
                 | GateType::SWAP
                 | GateType::RXX
                 | GateType::RYY
@@ -1492,6 +2031,8 @@ impl<'a> DemSamplerBuilder<'a> {
                         cx_groups.entry(loc.node).or_default().push(loc_idx);
                     }
                 GateType::H
+                | GateType::F
+                | GateType::Fdg
                 | GateType::SZ
                 | GateType::SZdg
                 | GateType::SX
@@ -1509,30 +2050,68 @@ impl<'a> DemSamplerBuilder<'a> {
                 | GateType::U
                 | GateType::R1XY
                     // Single-qubit gate errors: only "after" locations, depolarizing
-                    if self.p1 > 0.0 && !loc.before => {
-                        self.process_depolarizing_fault(
+                    if !loc.before =>
+                {
+                    let rates = self.rates_1q(loc.gate_type, &loc.qubits);
+                    if rates.iter().any(|r| *r > 0.0) {
+                        self.process_depolarizing_fault_rates(
                             loc_idx,
-                            self.p1,
-                            im_to_tc.as_deref(),
-                            num_tc_measurements,
+                            rates,
+                            &mechanism_context,
                             &mut aggregated,
                         );
                     }
+                }
+                GateType::Idle
+                    // Idle gate errors: only "after" locations. Idle is
+                    // noiseless unless idle noise or per-gate Idle rates are
+                    // explicitly configured.
+                    if !loc.before =>
+                {
+                    let rates = self.idle_rates(loc);
+                    if rates.iter().any(|r| *r > 0.0) {
+                        self.process_depolarizing_fault_rates(
+                            loc_idx,
+                            rates,
+                            &mechanism_context,
+                            &mut aggregated,
+                        );
+                    }
+                }
                 _ => {}
             }
         }
 
         // Process two-qubit gates as pairs
-        if self.p2 > 0.0 {
+        let has_any_2q_noise = self.per_gate.is_some() || self.p2 > 0.0;
+        if has_any_2q_noise {
             for loc_indices in cx_groups.values() {
-                if loc_indices.len() == 2 {
-                    self.process_two_qubit_fault(
-                        loc_indices[0],
-                        loc_indices[1],
-                        im_to_tc.as_deref(),
-                        num_tc_measurements,
-                        &mut aggregated,
-                    );
+                for pair in loc_indices.chunks(2) {
+                    if pair.len() != 2 {
+                        continue;
+                    }
+                    // For 2Q gates, each fault location covers exactly one
+                    // qubit; combine the two locations' qubits into an
+                    // ordered (control, target) pair.
+                    let loc0 = &self.influence_map.locations[pair[0]];
+                    let loc1 = &self.influence_map.locations[pair[1]];
+                    let gate_type = loc0.gate_type;
+                    let pair_qubits: Vec<_> = loc0
+                        .qubits
+                        .iter()
+                        .chain(loc1.qubits.iter())
+                        .copied()
+                        .collect();
+                    let rates = self.rates_2q(gate_type, &pair_qubits);
+                    if rates.iter().any(|r| *r > 0.0) {
+                        self.process_two_qubit_fault_rates(
+                            pair[0],
+                            pair[1],
+                            rates,
+                            &mechanism_context,
+                            &mut aggregated,
+                        );
+                    }
                 }
             }
         }
@@ -1542,11 +2121,11 @@ impl<'a> DemSamplerBuilder<'a> {
         let mut thresholds = Vec::with_capacity(num_mechanisms);
         let mut detector_offsets = Vec::with_capacity(num_mechanisms + 1);
         let mut detector_data = Vec::new();
-        let mut observable_offsets = Vec::with_capacity(num_mechanisms + 1);
-        let mut observable_data = Vec::new();
+        let mut dem_output_offsets = Vec::with_capacity(num_mechanisms + 1);
+        let mut dem_output_data = Vec::new();
 
         detector_offsets.push(0);
-        observable_offsets.push(0);
+        dem_output_offsets.push(0);
 
         let mut inv_log_1_minus_p = Vec::with_capacity(num_mechanisms);
 
@@ -1575,20 +2154,20 @@ impl<'a> DemSamplerBuilder<'a> {
             #[allow(clippy::cast_possible_truncation)] // detector data length fits in u32
             detector_offsets.push(detector_data.len() as u32);
 
-            observable_data.extend_from_slice(&mech.observables);
-            #[allow(clippy::cast_possible_truncation)] // observable data length fits in u32
-            observable_offsets.push(observable_data.len() as u32);
+            dem_output_data.extend_from_slice(&mech.dem_outputs);
+            #[allow(clippy::cast_possible_truncation)] // `L<n>` target data length fits in u32
+            dem_output_offsets.push(dem_output_data.len() as u32);
         }
 
-        DemSampler {
+        SamplingEngine {
             thresholds,
             inv_log_1_minus_p,
             detector_offsets,
             detector_data,
-            observable_offsets,
-            observable_data,
+            dem_output_offsets,
+            dem_output_data,
             num_detectors,
-            num_observables,
+            num_dem_outputs,
         }
     }
 
@@ -1631,29 +2210,142 @@ impl<'a> DemSamplerBuilder<'a> {
         loc_idx: usize,
         pauli: Pauli,
         prob: f64,
-        im_to_tc: Option<&[usize]>,
-        num_tc_measurements: usize,
+        context: &FaultMechanismContext<'_>,
         aggregated: &mut BTreeMap<DemMechanism, f64>,
     ) {
-        let mechanism = self.compute_mechanism(loc_idx, pauli, im_to_tc, num_tc_measurements);
+        let mechanism = self.compute_mechanism(
+            loc_idx,
+            pauli,
+            context.im_to_tc,
+            context.influence_observable_ids,
+            context.num_tc_measurements,
+        );
         if !mechanism.is_empty() {
             let entry = aggregated.entry(mechanism).or_insert(0.0);
             *entry = combine_probabilities(*entry, prob);
         }
     }
 
-    /// Process a depolarizing fault (X, Y, Z each with prob/3).
-    fn process_depolarizing_fault(
+    /// Resolve the X-error rate for a prep location. Uses `per_gate`'s
+    /// per-qubit `init_rates` if set, otherwise the scalar `self.p_prep`.
+    fn init_rate_for_location(
+        &self,
+        loc: &super::super::propagator::dag::DagSpacetimeLocation,
+    ) -> f64 {
+        if let Some(pg) = &self.per_gate
+            && let Some(q) = loc.qubits.first()
+        {
+            return pg.init_rate_on(*q);
+        }
+        self.p_prep
+    }
+
+    /// Resolve the X-flip rate for a measurement location. Uses
+    /// `per_gate`'s per-qubit `measurement_rates` if set, otherwise the
+    /// scalar `self.p_meas`.
+    fn measurement_rate_for_location(
+        &self,
+        loc: &super::super::propagator::dag::DagSpacetimeLocation,
+    ) -> f64 {
+        if let Some(pg) = &self.per_gate
+            && let Some(q) = loc.qubits.first()
+        {
+            return pg.measurement_rate_on(*q);
+        }
+        self.p_meas
+    }
+
+    /// Resolve per-Pauli rates for a 1Q gate on a specific qubit. Uses
+    /// `per_gate`'s per-qubit map if set, falling back to per-gate-type,
+    /// then uniform `p1 / 3`.
+    fn rates_1q(&self, gate: GateType, qubits: &[pecos_core::QubitId]) -> [f64; 3] {
+        if let Some(pg) = &self.per_gate {
+            if let Some(q) = qubits.first() {
+                [
+                    pg.rate_1q_on(gate, *q, 0),
+                    pg.rate_1q_on(gate, *q, 1),
+                    pg.rate_1q_on(gate, *q, 2),
+                ]
+            } else {
+                [
+                    pg.rate_1q(gate, 0),
+                    pg.rate_1q(gate, 1),
+                    pg.rate_1q(gate, 2),
+                ]
+            }
+        } else {
+            [self.p1 / 3.0; 3]
+        }
+    }
+
+    /// Resolve per-Pauli rates for an explicit idle location.
+    fn idle_rates(
+        &self,
+        loc: &crate::fault_tolerance::propagator::dag::DagSpacetimeLocation,
+    ) -> [f64; 3] {
+        if let Some(pg) = &self.per_gate {
+            let explicit_rates = loc
+                .qubits
+                .first()
+                .and_then(|q| pg.explicit_1q_rates_on(GateType::Idle, *q))
+                .or_else(|| pg.explicit_1q_rates(GateType::Idle));
+            if let Some(rates) = explicit_rates {
+                return rates;
+            }
+            if pg.base.uses_dedicated_idle_noise() {
+                #[allow(clippy::cast_precision_loss)]
+                let duration = loc.idle_duration.max(1) as f64;
+                let probs = pg.base.idle_pauli_probs(duration);
+                return [probs.px, probs.py, probs.pz];
+            }
+            return [0.0; 3];
+        }
+
+        if let Some(noise) = &self.idle_noise
+            && noise.uses_dedicated_idle_noise()
+        {
+            #[allow(clippy::cast_precision_loss)]
+            let duration = loc.idle_duration.max(1) as f64;
+            let probs = noise.idle_pauli_probs(duration);
+            return [probs.px, probs.py, probs.pz];
+        }
+        [0.0; 3]
+    }
+
+    /// Resolve per-Pauli-pair rates for a 2Q gate (15 non-II pairs) on a
+    /// specific ordered qubit pair.
+    fn rates_2q(&self, gate: GateType, qubits: &[pecos_core::QubitId]) -> [f64; 15] {
+        if let Some(pg) = &self.per_gate {
+            if qubits.len() >= 2 {
+                let (qc, qt) = (qubits[0], qubits[1]);
+                std::array::from_fn(|i| pg.rate_2q_on(gate, qc, qt, i))
+            } else {
+                std::array::from_fn(|i| pg.rate_2q(gate, i))
+            }
+        } else {
+            [self.p2 / 15.0; 15]
+        }
+    }
+
+    /// Process a 1Q depolarizing-family fault with explicit per-Pauli rates.
+    fn process_depolarizing_fault_rates(
         &self,
         loc_idx: usize,
-        prob: f64,
-        im_to_tc: Option<&[usize]>,
-        num_tc_measurements: usize,
+        rates: [f64; 3],
+        context: &FaultMechanismContext<'_>,
         aggregated: &mut BTreeMap<DemMechanism, f64>,
     ) {
-        let per_pauli_prob = prob / 3.0;
-        for pauli in [Pauli::X, Pauli::Y, Pauli::Z] {
-            let mechanism = self.compute_mechanism(loc_idx, pauli, im_to_tc, num_tc_measurements);
+        for (pauli, &per_pauli_prob) in [Pauli::X, Pauli::Y, Pauli::Z].iter().zip(rates.iter()) {
+            if per_pauli_prob == 0.0 {
+                continue;
+            }
+            let mechanism = self.compute_mechanism(
+                loc_idx,
+                *pauli,
+                context.im_to_tc,
+                context.influence_observable_ids,
+                context.num_tc_measurements,
+            );
             if !mechanism.is_empty() {
                 let entry = aggregated.entry(mechanism).or_insert(0.0);
                 *entry = combine_probabilities(*entry, per_pauli_prob);
@@ -1661,53 +2353,63 @@ impl<'a> DemSamplerBuilder<'a> {
         }
     }
 
-    /// Process a two-qubit gate fault (15 non-identity Pauli combinations with p2/15 each).
-    fn process_two_qubit_fault(
+    /// Process a two-qubit gate fault with explicit per-Pauli-pair rates.
+    /// `rates[i]` corresponds to [`PAULI_2Q_ORDER[i]`] ordering.
+    fn process_two_qubit_fault_rates(
         &self,
         loc1: usize,
         loc2: usize,
-        im_to_tc: Option<&[usize]>,
-        num_tc_measurements: usize,
+        rates: [f64; 15],
+        context: &FaultMechanismContext<'_>,
         aggregated: &mut BTreeMap<DemMechanism, f64>,
     ) {
-        let prob = self.p2 / 15.0;
         let paulis = [Pauli::I, Pauli::X, Pauli::Y, Pauli::Z];
 
-        // Cache single-qubit mechanisms for each Pauli on each location
         let mut effects1: [Option<DemMechanism>; 4] = [None, None, None, None];
         let mut effects2: [Option<DemMechanism>; 4] = [None, None, None, None];
 
         for &p in &[Pauli::X, Pauli::Y, Pauli::Z] {
-            effects1[p as usize] =
-                Some(self.compute_mechanism(loc1, p, im_to_tc, num_tc_measurements));
-            effects2[p as usize] =
-                Some(self.compute_mechanism(loc2, p, im_to_tc, num_tc_measurements));
+            effects1[p as usize] = Some(self.compute_mechanism(
+                loc1,
+                p,
+                context.im_to_tc,
+                context.influence_observable_ids,
+                context.num_tc_measurements,
+            ));
+            effects2[p as usize] = Some(self.compute_mechanism(
+                loc2,
+                p,
+                context.im_to_tc,
+                context.influence_observable_ids,
+                context.num_tc_measurements,
+            ));
         }
 
-        // Process all 15 non-trivial Pauli combinations
+        // Iterate (p1, p2) with global index = 4*p1 + p2 (skipping II at idx 0).
         for &p1 in &paulis {
             for &p2 in &paulis {
                 if p1 == Pauli::I && p2 == Pauli::I {
-                    continue; // Skip II
+                    continue;
+                }
+                let flat = 4 * (p1 as usize) + (p2 as usize);
+                let prob = rates[flat - 1];
+                if prob == 0.0 {
+                    continue;
                 }
-
                 let mechanism = if p1 == Pauli::I {
-                    // IX, IY, IZ - only second qubit
                     effects2[p2 as usize]
                         .clone()
                         .unwrap_or_else(DemMechanism::empty)
                 } else if p2 == Pauli::I {
-                    // XI, YI, ZI - only first qubit
                     effects1[p1 as usize]
                         .clone()
                         .unwrap_or_else(DemMechanism::empty)
                 } else {
-                    // Correlated: XOR the detector/observable effects
+                    // Correlated: XOR the detector/standard observable effects
                     let e1 = effects1[p1 as usize].as_ref();
                     let e2 = effects2[p2 as usize].as_ref();
                     xor_mechanisms(e1, e2)
                 };
-
                 if !mechanism.is_empty() {
                     let entry = aggregated.entry(mechanism).or_insert(0.0);
                     *entry = combine_probabilities(*entry, prob);
@@ -1716,12 +2418,13 @@ impl<'a> DemSamplerBuilder<'a> {
         }
     }
 
-    /// Compute the mechanism (detector/observable effects) for a fault.
+    /// Compute the mechanism (detector/standard observable effects) for a fault.
     fn compute_mechanism(
         &self,
         loc_idx: usize,
         pauli: Pauli,
         im_to_tc: Option<&[usize]>,
+        influence_observable_ids: &BTreeSet<u32>,
         num_tc_measurements: usize,
     ) -> DemMechanism {
         // Get measurement indices that flip (in IM order)
@@ -1729,6 +2432,14 @@ impl<'a> DemSamplerBuilder<'a> {
             .influence_map
             .get_detector_indices(loc_idx, pauli as u8);
 
+        let mut dem_outputs: SmallVec<[u32; 2]> = SmallVec::new();
+        for dem_output_idx in self
+            .influence_map
+            .get_observable_indices(loc_idx, pauli as u8)
+        {
+            xor_toggle_u32(&mut dem_outputs, dem_output_idx);
+        }
+
         // Convert to TC order measurement outcomes
         let mut tc_outcomes = vec![false; num_tc_measurements];
         for &im_idx in im_meas_flips {
@@ -1776,48 +2487,59 @@ impl<'a> DemSamplerBuilder<'a> {
             })
             .collect();
 
-        // Apply observable definitions (XOR of measurement outcomes)
-        let observables: SmallVec<[u32; 2]> = self
-            .observable_records
-            .iter()
-            .enumerate()
-            .filter_map(|(obs_id, records)| {
-                let mut xor_result = false;
-                for &offset in records {
-                    #[allow(clippy::cast_possible_wrap, clippy::cast_possible_truncation)] // measurement count fits in i32
-                    #[allow(clippy::cast_sign_loss)]
-                    // negative offset + total count, or non-negative offset
-                    let abs_idx = if offset < 0 {
-                        (num_tc_measurements as i32 + offset) as usize
-                    } else {
-                        offset as usize
-                    };
-                    if abs_idx < num_tc_measurements && tc_outcomes[abs_idx] {
-                        xor_result = !xor_result;
-                    }
-                }
-                if xor_result {
-                    #[allow(clippy::cast_possible_truncation)] // observable ID fits in u32
-                    Some(obs_id as u32)
+        // Apply standard observable `L<n>` definitions (XOR of measurement outcomes)
+        for (obs_id, records) in self.observable_records.iter().enumerate() {
+            #[allow(clippy::cast_possible_truncation)] // observable ID fits in u32
+            let obs_id_u32 = obs_id as u32;
+            if influence_observable_ids.contains(&obs_id_u32) {
+                continue;
+            }
+            let mut xor_result = false;
+            for &offset in records {
+                #[allow(clippy::cast_possible_wrap, clippy::cast_possible_truncation)] // measurement count fits in i32
+                #[allow(clippy::cast_sign_loss)]
+                // negative offset + total count, or non-negative offset
+                let abs_idx = if offset < 0 {
+                    (num_tc_measurements as i32 + offset) as usize
                 } else {
-                    None
+                    offset as usize
+                };
+                if abs_idx < num_tc_measurements && tc_outcomes[abs_idx] {
+                    xor_result = !xor_result;
                 }
-            })
-            .collect();
+            }
+            if xor_result {
+                #[allow(clippy::cast_possible_truncation)] // `L<n>` target ID fits in u32
+                xor_toggle_u32(&mut dem_outputs, obs_id_u32);
+            }
+        }
+        dem_outputs.sort_unstable();
+
+        DemMechanism::new(detectors, dem_outputs)
+    }
+}
 
-        DemMechanism::new(detectors, observables)
+/// Toggles an element in a parity vector.
+fn xor_toggle_u32<const N: usize>(values: &mut SmallVec<[u32; N]>, value: u32)
+where
+    [u32; N]: smallvec::Array<Item = u32>,
+{
+    if let Some(pos) = values.iter().position(|&v| v == value) {
+        values.remove(pos);
+    } else {
+        values.push(value);
     }
 }
 
-/// XORs two [`DemMechanism`]s (symmetric difference of detectors and observables).
+/// XORs two [`DemMechanism`]s (symmetric difference of detectors and standard observables).
 fn xor_mechanisms(a: Option<&DemMechanism>, b: Option<&DemMechanism>) -> DemMechanism {
     match (a, b) {
         (Some(m1), Some(m2)) => {
             let detectors = xor_u32_vecs::<4>(&m1.detectors, &m2.detectors);
-            let observables = xor_u32_vecs::<2>(&m1.observables, &m2.observables);
+            let dem_outputs = xor_u32_vecs::<2>(&m1.dem_outputs, &m2.dem_outputs);
             DemMechanism {
                 detectors,
-                observables,
+                dem_outputs,
             }
         }
         (Some(m), None) | (None, Some(m)) => m.clone(),
@@ -1857,7 +2579,7 @@ where
     result
 }
 
-/// Parse detector or observable records from JSON.
+/// Parse detector or observable definitions from JSON.
 ///
 /// Uses a simple custom parser to avoid `serde_json` dependency.
 /// Expected format: `[{"id": 0, "records": [-1, -5]}, ...]`
@@ -1975,8 +2697,8 @@ mod tests {
 
         // Detectors: {0,1,2} XOR {1,2,3} = {0,3}
         assert_eq!(result.detectors.as_slice(), &[0, 3]);
-        // Observables: {0} XOR {0,1} = {1}
-        assert_eq!(result.observables.as_slice(), &[1]);
+        // DEM outputs: {0} XOR {0,1} = {1}
+        assert_eq!(result.dem_outputs.as_slice(), &[1]);
     }
 
     #[test]
@@ -2030,11 +2752,13 @@ mod tests {
         let influence_map = analyzer.build_influence_map();
 
         // Zero noise should produce no errors
-        let sampler = DemSamplerBuilder::new(&influence_map)
+        let sampler = SamplingEngineBuilder::new(&influence_map)
             .with_noise(0.0, 0.0, 0.0, 0.0)
             .build();
 
         assert_eq!(sampler.num_mechanisms(), 0);
+        assert_eq!(sampler.num_dem_outputs(), 0);
+        assert_eq!(sampler.num_observables(), 0);
 
         let stats = sampler.sample_statistics(100, 42);
         assert_eq!(stats.logical_error_count, 0);
@@ -2060,7 +2784,7 @@ mod tests {
         let detectors_json = r#"[{"id": 0, "records": [-1]}]"#;
         let observables_json = r"[]";
 
-        let sampler = DemSamplerBuilder::new(&influence_map)
+        let sampler = SamplingEngineBuilder::new(&influence_map)
             .with_noise(0.1, 0.1, 0.1, 0.1)
             .with_detectors_json(detectors_json)
             .unwrap()
@@ -2077,6 +2801,36 @@ mod tests {
         assert!(stats.syndrome_count > 0);
     }
 
+    #[test]
+    fn test_sampling_engine_builder_accepts_observable_record_inputs() {
+        use crate::fault_tolerance::propagator::DagFaultAnalyzer;
+        use pecos_quantum::DagCircuit;
+
+        let mut dag = DagCircuit::new();
+        dag.pz(&[0]);
+        dag.h(&[0]);
+        dag.mz(&[0]);
+
+        let analyzer = DagFaultAnalyzer::new(&dag);
+        let influence_map = analyzer.build_influence_map();
+
+        let json_sampler = SamplingEngineBuilder::new(&influence_map)
+            .with_detectors_json(r#"[{"id": 0, "records": [-1]}]"#)
+            .unwrap()
+            .with_observables_json(r#"[{"id": 0, "records": [-1]}]"#)
+            .unwrap()
+            .build();
+        assert_eq!(json_sampler.num_detectors(), 1);
+        assert_eq!(json_sampler.num_dem_outputs(), 1);
+
+        let record_sampler = SamplingEngineBuilder::new(&influence_map)
+            .with_detector_records(vec![vec![-1]])
+            .with_observable_records(vec![vec![-1]])
+            .build();
+        assert_eq!(record_sampler.num_detectors(), 1);
+        assert_eq!(record_sampler.num_dem_outputs(), 1);
+    }
+
     #[test]
     fn test_columnar_sampling_statistics() {
         use crate::fault_tolerance::propagator::DagFaultAnalyzer;
@@ -2096,7 +2850,7 @@ mod tests {
         let analyzer = DagFaultAnalyzer::new(&dag);
         let influence_map = analyzer.build_influence_map();
 
-        let sampler = DemSamplerBuilder::new(&influence_map)
+        let sampler = SamplingEngineBuilder::new(&influence_map)
             .with_noise(0.01, 0.01, 0.01, 0.01)
             .with_detector_records(vec![vec![-1], vec![-2]])
             .with_observable_records(vec![])
@@ -2140,7 +2894,7 @@ mod tests {
         let analyzer = DagFaultAnalyzer::new(&dag);
         let influence_map = analyzer.build_influence_map();
 
-        let sampler = DemSamplerBuilder::new(&influence_map)
+        let sampler = SamplingEngineBuilder::new(&influence_map)
             .with_noise(0.5, 0.0, 0.0, 0.0) // High noise rate for testing
             .with_detector_records(vec![vec![-1]])
             .with_observable_records(vec![])
@@ -2176,7 +2930,7 @@ mod tests {
         let analyzer = DagFaultAnalyzer::new(&dag);
         let influence_map = analyzer.build_influence_map();
 
-        let sampler = DemSamplerBuilder::new(&influence_map)
+        let sampler = SamplingEngineBuilder::new(&influence_map)
             .with_noise(0.01, 0.01, 0.01, 0.01)
             .with_detector_records(vec![vec![-1], vec![-2]])
             .with_observable_records(vec![])
@@ -2217,7 +2971,7 @@ mod tests {
         let influence_map = analyzer.build_influence_map();
 
         // Use low noise to exercise geometric sampling effectively
-        let sampler = DemSamplerBuilder::new(&influence_map)
+        let sampler = SamplingEngineBuilder::new(&influence_map)
             .with_noise(0.001, 0.001, 0.001, 0.001)
             .with_detector_records(vec![vec![-1], vec![-2]])
             .with_observable_records(vec![])
@@ -2261,7 +3015,7 @@ mod tests {
         let influence_map = analyzer.build_influence_map();
 
         // Low error rate - should use geometric
-        let sampler = DemSamplerBuilder::new(&influence_map)
+        let sampler = SamplingEngineBuilder::new(&influence_map)
             .with_noise(0.001, 0.001, 0.001, 0.001)
             .with_detector_records(vec![vec![-1]])
             .with_observable_records(vec![])
@@ -2291,7 +3045,7 @@ mod tests {
         let influence_map = analyzer.build_influence_map();
 
         // High error rate - should use SIMD
-        let sampler = DemSamplerBuilder::new(&influence_map)
+        let sampler = SamplingEngineBuilder::new(&influence_map)
             .with_noise(0.1, 0.1, 0.1, 0.1)
             .with_detector_records(vec![vec![-1]])
             .with_observable_records(vec![])
@@ -2323,7 +3077,7 @@ mod tests {
         let analyzer = DagFaultAnalyzer::new(&dag);
         let influence_map = analyzer.build_influence_map();
 
-        let sampler = DemSamplerBuilder::new(&influence_map)
+        let sampler = SamplingEngineBuilder::new(&influence_map)
             .with_noise(0.001, 0.001, 0.001, 0.001)
             .with_detector_records(vec![vec![-1], vec![-2]])
             .with_observable_records(vec![])
@@ -2358,7 +3112,7 @@ mod tests {
 
     #[test]
     fn test_from_mechanisms_empty() {
-        let sampler = DemSampler::from_mechanisms(std::iter::empty(), 0, 0);
+        let sampler = SamplingEngine::from_mechanisms(std::iter::empty(), 0, 0);
         assert_eq!(sampler.num_mechanisms(), 0);
         assert_eq!(sampler.num_detectors(), 0);
         assert_eq!(sampler.num_observables(), 0);
@@ -2372,7 +3126,7 @@ mod tests {
     fn test_from_mechanisms_single_detector() {
         // Single mechanism that flips D0 with p=0.5
         let mechanisms = vec![(0.5, vec![0u32], vec![])];
-        let sampler = DemSampler::from_mechanisms(mechanisms, 1, 0);
+        let sampler = SamplingEngine::from_mechanisms(mechanisms, 1, 0);
 
         assert_eq!(sampler.num_mechanisms(), 1);
         assert_eq!(sampler.num_detectors(), 1);
@@ -2390,7 +3144,7 @@ mod tests {
     fn test_from_mechanisms_multiple_detectors() {
         // Two mechanisms: D0 with p=0.1, D1 with p=0.2
         let mechanisms = vec![(0.1, vec![0u32], vec![]), (0.2, vec![1u32], vec![])];
-        let sampler = DemSampler::from_mechanisms(mechanisms, 2, 0);
+        let sampler = SamplingEngine::from_mechanisms(mechanisms, 2, 0);
 
         assert_eq!(sampler.num_mechanisms(), 2);
         assert_eq!(sampler.num_detectors(), 2);
@@ -2408,7 +3162,7 @@ mod tests {
     fn test_from_mechanisms_correlated_detectors() {
         // Single mechanism that flips both D0 and D1 together with p=0.3
         let mechanisms = vec![(0.3, vec![0u32, 1u32], vec![])];
-        let sampler = DemSampler::from_mechanisms(mechanisms, 2, 0);
+        let sampler = SamplingEngine::from_mechanisms(mechanisms, 2, 0);
 
         assert_eq!(sampler.num_mechanisms(), 1);
         assert_eq!(sampler.num_detectors(), 2);
@@ -2427,7 +3181,7 @@ mod tests {
         // Two mechanisms that both flip D0 with the same probability
         // When both fire, they XOR and cancel
         let mechanisms = vec![(0.5, vec![0u32], vec![]), (0.5, vec![0u32], vec![])];
-        let sampler = DemSampler::from_mechanisms(mechanisms, 1, 0);
+        let sampler = SamplingEngine::from_mechanisms(mechanisms, 1, 0);
 
         // With two independent p=0.5 mechanisms that both flip D0:
         // P(D0 fires) = P(exactly one fires) = 2 * 0.5 * 0.5 = 0.5
@@ -2440,15 +3194,21 @@ mod tests {
     }
 
     #[test]
-    fn test_from_mechanisms_with_observables() {
+    fn test_from_mechanisms_with_tracked_paulis() {
         // Mechanism that flips D0 and L0
         let mechanisms = vec![(0.1, vec![0u32], vec![0u32])];
-        let sampler = DemSampler::from_mechanisms(mechanisms, 1, 1);
+        let sampler = SamplingEngine::from_mechanisms(mechanisms, 1, 1);
 
-        assert_eq!(sampler.num_observables(), 1);
+        assert_eq!(sampler.num_dem_outputs(), 1);
 
         // Logical error rate should be approximately 0.1
         let stats = sampler.sample_statistics(10000, 42);
+        assert_eq!(stats.dem_output_counts(), stats.per_dem_output.as_slice());
+        assert_eq!(
+            stats.observable_counts(&[0]).as_slice(),
+            stats.per_dem_output.as_slice()
+        );
+        assert_eq!(stats.logical_rates(&[0]), stats.dem_output_rates());
         let logical_rate = stats.logical_error_rate();
         assert!(
             (logical_rate - 0.1).abs() < 0.03,
@@ -2456,11 +3216,30 @@ mod tests {
         );
     }
 
+    #[test]
+    fn test_selected_observable_statistics_ignore_unselected_tracked_outputs() {
+        // L0 is the measured observable column; L1 represents a tracked
+        // operator column. The mechanism flips only L1, so observable-only
+        // logical statistics for L0 must stay zero while per-output counts
+        // still report the tracked-column flips.
+        let mechanisms = vec![(1.0, vec![], vec![1u32])];
+        let sampler = SamplingEngine::from_mechanisms(mechanisms, 0, 2);
+
+        let stats = sampler.sample_statistics_for_observable_indices(32, 42, &[0]);
+
+        assert_eq!(stats.total_shots, 32);
+        assert_eq!(stats.per_dem_output, vec![0, 32]);
+        assert_eq!(stats.logical_error_count, 0);
+        assert_eq!(stats.undetectable_count, 0);
+        assert_eq!(stats.observable_counts(&[0]), vec![0]);
+        assert_eq!(stats.observable_counts(&[1]), vec![32]);
+    }
+
     #[test]
     fn test_from_mechanisms_very_low_error_rate() {
         // Test geometric sampling efficiency with low error rate
         let mechanisms = vec![(0.0001, vec![0u32], vec![])];
-        let sampler = DemSampler::from_mechanisms(mechanisms, 1, 0);
+        let sampler = SamplingEngine::from_mechanisms(mechanisms, 1, 0);
 
         // Should still work correctly
         let stats = sampler.sample_statistics(100_000, 42);
@@ -2475,11 +3254,12 @@ mod tests {
     fn test_from_mechanisms_sorting() {
         // Verify that detector indices are sorted regardless of input order
         let mechanisms = vec![(0.1, vec![2u32, 0u32, 1u32], vec![1u32, 0u32])];
-        let sampler = DemSampler::from_mechanisms(mechanisms, 3, 2);
+        let sampler = SamplingEngine::from_mechanisms(mechanisms, 3, 2);
 
         // Verify internal storage is sorted (by checking that sampling works)
         assert_eq!(sampler.num_detectors(), 3);
         assert_eq!(sampler.num_observables(), 2);
+        assert_eq!(sampler.num_dem_outputs(), 2);
 
         let stats = sampler.sample_statistics(1000, 42);
         // Just verify it runs without panicking
diff --git a/crates/pecos-qec/src/fault_tolerance/dem_builder/equivalence.rs b/crates/pecos-qec/src/fault_tolerance/dem_builder/equivalence.rs
index 0cc578a27..d18e60b01 100644
--- a/crates/pecos-qec/src/fault_tolerance/dem_builder/equivalence.rs
+++ b/crates/pecos-qec/src/fault_tolerance/dem_builder/equivalence.rs
@@ -18,7 +18,7 @@
 //! # Key Concepts
 //!
 //! - Two DEMs are equivalent if they produce the same probability distribution
-//!   over (`detector_events`, `observable_flips`) patterns.
+//!   over (`detector_events`, `dem_output_flips`) patterns.
 //! - Decomposed DEMs (using ^) create independent error channels that are `XORed`.
 //! - Different decomposition strategies can produce equivalent sampling results.
 //! - For non-decomposed DEMs, mechanisms must match exactly.
@@ -58,7 +58,7 @@ use std::collections::{BTreeMap, BTreeSet};
 use std::fmt;
 use std::str::FromStr;
 
-use super::types::combine_probabilities;
+use super::types::{DemOutput, combine_probabilities, parse_pecos_dem_metadata_line};
 
 // ============================================================================
 // Parsed DEM Types
@@ -86,6 +86,7 @@ impl ParsedMechanism {
             components: vec![MechanismComponent {
                 detectors,
                 observables,
+                tracked_paulis: Vec::new(),
             }],
         }
     }
@@ -98,9 +99,10 @@ impl ParsedMechanism {
 
     /// Returns the combined effect of this mechanism (XOR of all components).
     #[must_use]
-    pub fn combined_effect(&self) -> (Vec<u32>, Vec<u32>) {
+    pub fn combined_effect(&self) -> (Vec<u32>, Vec<u32>, Vec<u32>) {
         let mut all_dets: BTreeSet<u32> = BTreeSet::new();
         let mut all_obs: BTreeSet<u32> = BTreeSet::new();
+        let mut all_tracked_paulis: BTreeSet<u32> = BTreeSet::new();
 
         for comp in &self.components {
             for &d in &comp.detectors {
@@ -117,23 +119,55 @@ impl ParsedMechanism {
                     all_obs.insert(o);
                 }
             }
+            for &op in &comp.tracked_paulis {
+                if all_tracked_paulis.contains(&op) {
+                    all_tracked_paulis.remove(&op);
+                } else {
+                    all_tracked_paulis.insert(op);
+                }
+            }
         }
 
         // BTreeSet is already sorted, so just collect
         let dets: Vec<u32> = all_dets.into_iter().collect();
         let obs: Vec<u32> = all_obs.into_iter().collect();
-        (dets, obs)
+        let tracked_paulis: Vec<u32> = all_tracked_paulis.into_iter().collect();
+        (dets, obs, tracked_paulis)
     }
 
     /// Creates an effect key for this mechanism (for aggregation).
     #[must_use]
     pub fn effect_key(&self) -> EffectKey {
-        let (dets, obs) = self.combined_effect();
+        let (dets, obs, tracked_paulis) = self.combined_effect();
         EffectKey {
             detectors: dets,
             observables: obs,
+            tracked_paulis,
         }
     }
+
+    /// Format the target string for this mechanism (e.g., "D0 D3 L0" or "D0 ^ D1 D3").
+    #[must_use]
+    pub fn format_targets(&self) -> String {
+        let parts: Vec<String> = self
+            .components
+            .iter()
+            .map(|comp| {
+                let mut tokens = Vec::new();
+                for &d in &comp.detectors {
+                    tokens.push(format!("D{d}"));
+                }
+                for &o in &comp.observables {
+                    tokens.push(format!("L{o}"));
+                }
+                for &op in &comp.tracked_paulis {
+                    tokens.push(format!("TP{op}"));
+                }
+                tokens.join(" ")
+            })
+            .collect();
+        parts.join(" ^ ")
+    }
 }
 
 /// A single component of a mechanism (the part between ^ separators).
@@ -143,6 +177,8 @@ pub struct MechanismComponent {
     pub detectors: Vec<u32>,
     /// Observable IDs in this component.
     pub observables: Vec<u32>,
+    /// PECOS tracked-Pauli IDs in this component.
+    pub tracked_paulis: Vec<u32>,
 }
 
 /// Key for aggregating mechanisms by their effect.
@@ -152,6 +188,8 @@ pub struct EffectKey {
     pub detectors: Vec<u32>,
     /// Sorted observable IDs.
     pub observables: Vec<u32>,
+    /// Sorted tracked-Pauli IDs.
+    pub tracked_paulis: Vec<u32>,
 }
 
 impl EffectKey {
@@ -163,6 +201,7 @@ impl EffectKey {
         Self {
             detectors,
             observables,
+            tracked_paulis: Vec::new(),
         }
     }
 }
@@ -176,6 +215,9 @@ impl fmt::Display for EffectKey {
         for &o in &self.observables {
             parts.push(format!("L{o}"));
         }
+        for &op in &self.tracked_paulis {
+            parts.push(format!("TP{op}"));
+        }
         if parts.is_empty() {
             write!(f, "(empty)")
         } else {
@@ -195,8 +237,12 @@ pub struct ParsedDem {
     pub mechanisms: Vec<ParsedMechanism>,
     /// Number of detectors (max ID + 1).
     pub num_detectors: u32,
-    /// Number of observables (max ID + 1).
-    pub num_observables: u32,
+    /// Total number of outputs in the DEM `L<n>` namespace.
+    pub num_dem_outputs: u32,
+    /// PECOS metadata for `L<n>` observables, indexed by `L<n>`.
+    pub dem_outputs: Vec<Option<DemOutput>>,
+    /// PECOS metadata for tracked Paulis in their own ID space.
+    pub tracked_paulis: Vec<Option<DemOutput>>,
 }
 
 impl ParsedDem {
@@ -206,13 +252,15 @@ impl ParsedDem {
         Self {
             mechanisms: Vec::new(),
             num_detectors: 0,
-            num_observables: 0,
+            num_dem_outputs: 0,
+            dem_outputs: Vec::new(),
+            tracked_paulis: Vec::new(),
         }
     }
 
     /// Parses a DEM from a string.
     ///
-    /// Supports both Stim and PECOS DEM formats.
+    /// Supports both standard and PECOS DEM formats.
     ///
     /// # Errors
     ///
@@ -221,6 +269,32 @@ impl ParsedDem {
         dem_str.parse()
     }
 
+    /// Total number of outputs in the DEM `L<n>` namespace.
+    #[must_use]
+    pub fn num_dem_outputs(&self) -> u32 {
+        self.num_dem_outputs
+    }
+
+    /// Number of observables.
+    #[must_use]
+    pub fn num_observables(&self) -> u32 {
+        self.num_dem_outputs
+    }
+
+    /// Number of tracked Paulis.
+    #[must_use]
+    pub fn num_tracked_paulis(&self) -> u32 {
+        u32::try_from(self.tracked_paulis.len()).unwrap_or(u32::MAX)
+    }
+
+    fn record_metadata(ops: &mut Vec<Option<DemOutput>>, op: DemOutput) {
+        let idx = op.id as usize;
+        if ops.len() <= idx {
+            ops.resize(idx + 1, None);
+        }
+        ops[idx] = Some(op);
+    }
+
     /// Parses a single error line.
     fn parse_error_line(line: &str) -> Result<ParsedMechanism, DemParseError> {
         // Extract probability: error(0.01) ...
@@ -265,6 +339,7 @@ impl ParsedDem {
     fn parse_component(s: &str) -> Result<MechanismComponent, DemParseError> {
         let mut detectors = Vec::new();
         let mut observables = Vec::new();
+        let mut tracked_paulis = Vec::new();
 
         for token in s.split_whitespace() {
             if let Some(id_str) = token.strip_prefix('D') {
@@ -277,16 +352,24 @@ impl ParsedDem {
                     .parse()
                     .map_err(|_| DemParseError::InvalidObservableId(token.to_string()))?;
                 observables.push(id);
+            } else if let Some(id_str) = token.strip_prefix("TP") {
+                let id: u32 = id_str
+                    .parse()
+                    .map_err(|_| DemParseError::InvalidTrackedPauliId(token.to_string()))?;
+                tracked_paulis.push(id);
+            } else {
+                return Err(DemParseError::InvalidTarget(token.to_string()));
             }
-            // Skip unknown tokens
         }
 
         detectors.sort_unstable();
         observables.sort_unstable();
+        tracked_paulis.sort_unstable();
 
         Ok(MechanismComponent {
             detectors,
             observables,
+            tracked_paulis,
         })
     }
 
@@ -322,7 +405,9 @@ impl ParsedDem {
             if mech.is_decomposed() {
                 // For decomposed mechanisms, each component fires independently
                 for comp in &mech.components {
-                    let key = EffectKey::new(comp.detectors.clone(), comp.observables.clone());
+                    let mut key = EffectKey::new(comp.detectors.clone(), comp.observables.clone());
+                    key.tracked_paulis.clone_from(&comp.tracked_paulis);
+                    key.tracked_paulis.sort_unstable();
                     aggregated
                         .entry(key)
                         .and_modify(|p| *p = combine_probabilities(*p, mech.probability))
@@ -343,17 +428,17 @@ impl ParsedDem {
 
     /// Samples from this DEM.
     ///
-    /// Returns (`detector_events`, `observable_flips`).
+    /// Returns (`detector_events`, `dem_output_flips`).
     ///
     /// # Semantics
     ///
-    /// In Stim's DEM format, `error(p) A ^ B` means that when the error fires
+    /// In DEM syntax, `error(p) A ^ B` means that when the error fires
     /// (with probability p), ALL components (A and B) flip together. The `^`
     /// separator is used for error tracking/decomposition but doesn't create
     /// independent firing - all components fire together as a single error.
     pub fn sample<R: Rng>(&self, rng: &mut R) -> (Vec<bool>, Vec<bool>) {
         let mut det_events = vec![false; self.num_detectors as usize];
-        let mut obs_flips = vec![false; self.num_observables as usize];
+        let mut obs_flips = vec![false; self.num_dem_outputs as usize];
 
         for mech in &self.mechanisms {
             // Single random check for the entire mechanism
@@ -379,7 +464,7 @@ impl ParsedDem {
 
     /// Samples multiple shots from this DEM.
     ///
-    /// Returns (`detector_events_per_shot`, `observable_flips_per_shot`).
+    /// Returns (`detector_events_per_shot`, `dem_output_flips_per_shot`).
     pub fn sample_batch<R: Rng>(
         &self,
         num_shots: usize,
@@ -408,25 +493,130 @@ impl ParsedDem {
     ///
     /// # Note on decomposed errors
     ///
-    /// In Stim's DEM format, `error(p) D0 ^ D1` means that when the error fires
+    /// In DEM syntax, `error(p) D0 ^ D1` means that when the error fires
     /// (with probability p), BOTH D0 and D1 flip together. The `^` separator is
     /// used for error tracking/decomposition but doesn't affect sampling - all
     /// components fire together.
     #[must_use]
-    pub fn to_dem_sampler(&self) -> super::dem_sampler::DemSampler {
-        // Convert mechanisms to the format expected by DemSampler::from_mechanisms
+    pub fn to_dem_sampler(&self) -> super::sampler::DemSampler {
+        // Convert mechanisms to the format expected by SamplingEngine::from_mechanisms
         // Use combined_effect() to get the union of all detectors/observables
         // since all components fire together when the error occurs
         let mechanisms = self.mechanisms.iter().map(|mech| {
-            let (dets, obs) = mech.combined_effect();
+            let (dets, obs, _tracked_paulis) = mech.combined_effect();
             (mech.probability, dets, obs)
         });
 
-        super::dem_sampler::DemSampler::from_mechanisms(
+        let engine = super::dem_sampler::SamplingEngine::from_mechanisms(
             mechanisms,
             self.num_detectors as usize,
-            self.num_observables as usize,
-        )
+            self.num_dem_outputs as usize,
+        );
+        let dem_outputs = self
+            .dem_outputs
+            .iter()
+            .enumerate()
+            .map(|(id, output)| {
+                output.clone().or_else(|| {
+                    #[allow(clippy::cast_possible_truncation)]
+                    // parsed DEM output count fits in u32
+                    {
+                        Some(
+                            DemOutput::new(id as u32)
+                                .with_kind(crate::fault_tolerance::DemOutputKind::Observable),
+                        )
+                    }
+                })
+            })
+            .collect();
+        let tracked_paulis = self
+            .tracked_paulis
+            .iter()
+            .enumerate()
+            .map(|(id, output)| {
+                output.clone().or_else(|| {
+                    #[allow(clippy::cast_possible_truncation)]
+                    // parsed tracked-Pauli count fits in u32
+                    {
+                        Some(
+                            DemOutput::new(id as u32)
+                                .with_kind(crate::fault_tolerance::DemOutputKind::TrackedPauli),
+                        )
+                    }
+                })
+            })
+            .collect();
+
+        super::sampler::DemSampler::from_engine(engine)
+            .with_dem_output_metadata(dem_outputs, tracked_paulis)
+    }
+
+    /// Convert to a decomposed (graphlike) DEM string.
+    ///
+    /// Mechanisms with <= 2 detectors pass through unchanged. Already-decomposed
+    /// mechanisms (with `^` notation) pass through unchanged.
+    ///
+    /// Hyperedges (3+ detectors, not already decomposed) cannot be decomposed
+    /// without Pauli provenance and will cause an error. Use
+    /// `coherent_dem_decomposed()` or `noise_characterization()` for proper
+    /// X/Z-aware decomposition.
+    ///
+    /// # Errors
+    ///
+    /// Returns an error if any mechanism has 3+ detectors without decomposition.
+    pub fn to_string_decomposed(&self) -> Result<String, String> {
+        let mut lines = Vec::new();
+
+        // Accumulate by target string to merge identical decomposed entries
+        let mut by_targets: BTreeMap<String, f64> = BTreeMap::new();
+
+        for mech in &self.mechanisms {
+            if mech.probability <= 0.0 {
+                continue;
+            }
+
+            if mech.is_decomposed() {
+                // Already decomposed — pass through
+                let targets = mech.format_targets();
+                by_targets
+                    .entry(targets)
+                    .and_modify(|p| *p = combine_probabilities(*p, mech.probability))
+                    .or_insert(mech.probability);
+                continue;
+            }
+
+            // Single component
+            let comp = &mech.components[0];
+
+            if comp.detectors.len() <= 2 {
+                // Graphlike — pass through
+                let targets = mech.format_targets();
+                by_targets
+                    .entry(targets)
+                    .and_modify(|p| *p = combine_probabilities(*p, mech.probability))
+                    .or_insert(mech.probability);
+            } else {
+                // Hyperedge (3+ detectors) cannot be decomposed without Pauli
+                // provenance (X/Z component info). Use `coherent_dem_decomposed()`
+                // or `noise_characterization()` which track X/Z components from
+                // the backward mechanism extraction.
+                return Err(format!(
+                    "Cannot decompose hyperedge with {} detectors ({:?}) without \
+                     Pauli provenance. Use coherent_dem_decomposed() or \
+                     noise_characterization() for proper X/Z decomposition.",
+                    comp.detectors.len(),
+                    comp.detectors,
+                ));
+            }
+        }
+
+        for (targets, prob) in &by_targets {
+            if *prob > 0.0 {
+                lines.push(format!("error({prob}) {targets}"));
+            }
+        }
+
+        Ok(lines.join("\n"))
     }
 }
 
@@ -443,6 +633,9 @@ impl FromStr for ParsedDem {
         let mut mechanisms = Vec::new();
         let mut max_det: i32 = -1;
         let mut max_obs: i32 = -1;
+        let mut max_tracked_pauli: i32 = -1;
+        let mut dem_outputs: Vec<Option<DemOutput>> = Vec::new();
+        let mut tracked_paulis: Vec<Option<DemOutput>> = Vec::new();
 
         for line in dem_str.lines() {
             let line = line.trim();
@@ -470,6 +663,12 @@ impl FromStr for ParsedDem {
                             max_obs = max_obs.max(o as i32);
                         }
                     }
+                    for &op in &comp.tracked_paulis {
+                        #[allow(clippy::cast_possible_wrap)] // tracked-Pauli ID fits in i32
+                        {
+                            max_tracked_pauli = max_tracked_pauli.max(op as i32);
+                        }
+                    }
                 }
 
                 mechanisms.push(mech);
@@ -491,6 +690,51 @@ impl FromStr for ParsedDem {
                 {
                     max_obs = max_obs.max(id as i32);
                 }
+                Self::record_metadata(
+                    &mut dem_outputs,
+                    DemOutput::new(id).with_kind(crate::fault_tolerance::DemOutputKind::Observable),
+                );
+            }
+            // Parse PECOS DEM-superset metadata declarations.
+            else if line.starts_with("pecos_observable")
+                || line.starts_with("pecos_tracked_pauli")
+            {
+                let op = parse_pecos_dem_metadata_line(line)
+                    .map_err(|err| DemParseError::InvalidPecosMetadata(err.to_string()))?;
+                if op.is_tracked_pauli() {
+                    #[allow(clippy::cast_possible_wrap)] // tracked-Pauli ID fits in i32
+                    {
+                        max_tracked_pauli = max_tracked_pauli.max(op.id as i32);
+                    }
+                    Self::record_metadata(&mut tracked_paulis, op);
+                } else {
+                    #[allow(clippy::cast_possible_wrap)] // observable ID fits in i32
+                    {
+                        max_obs = max_obs.max(op.id as i32);
+                    }
+                    Self::record_metadata(&mut dem_outputs, op);
+                }
+            }
+            // PECOS extensions are explicit; ordinary DEM lines remain valid,
+            // but unknown PECOS extension statements should not be silently
+            // accepted as historical aliases.
+            else if line.starts_with("pecos_") {
+                return Err(DemParseError::InvalidPecosMetadata(format!(
+                    "unsupported PECOS DEM extension line: {line}"
+                )));
+            }
+        }
+
+        if max_obs >= 0 {
+            #[allow(clippy::cast_sign_loss)] // guarded by >= 0 check
+            {
+                dem_outputs.resize(max_obs as usize + 1, None);
+            }
+        }
+        if max_tracked_pauli >= 0 {
+            #[allow(clippy::cast_sign_loss)] // guarded by >= 0 check
+            {
+                tracked_paulis.resize(max_tracked_pauli as usize + 1, None);
             }
         }
 
@@ -504,7 +748,7 @@ impl FromStr for ParsedDem {
             } else {
                 0
             },
-            num_observables: if max_obs >= 0 {
+            num_dem_outputs: if max_obs >= 0 {
                 #[allow(clippy::cast_sign_loss)] // guarded by >= 0 check
                 {
                     max_obs as u32 + 1
@@ -512,6 +756,8 @@ impl FromStr for ParsedDem {
             } else {
                 0
             },
+            dem_outputs,
+            tracked_paulis,
         })
     }
 }
@@ -531,6 +777,12 @@ pub enum DemParseError {
     InvalidDetectorId(String),
     /// Invalid observable ID.
     InvalidObservableId(String),
+    /// Invalid tracked-Pauli ID.
+    InvalidTrackedPauliId(String),
+    /// Invalid target token in an error line.
+    InvalidTarget(String),
+    /// Invalid PECOS DEM-superset metadata.
+    InvalidPecosMetadata(String),
 }
 
 impl std::fmt::Display for DemParseError {
@@ -540,6 +792,9 @@ impl std::fmt::Display for DemParseError {
             Self::InvalidProbability(s) => write!(f, "Invalid probability: {s}"),
             Self::InvalidDetectorId(s) => write!(f, "Invalid detector ID: {s}"),
             Self::InvalidObservableId(s) => write!(f, "Invalid observable ID: {s}"),
+            Self::InvalidTrackedPauliId(s) => write!(f, "Invalid tracked Pauli ID: {s}"),
+            Self::InvalidTarget(s) => write!(f, "Invalid DEM error target: {s}"),
+            Self::InvalidPecosMetadata(s) => write!(f, "Invalid PECOS DEM metadata: {s}"),
         }
     }
 }
@@ -713,7 +968,7 @@ pub fn compare_dems_statistical(
 
     // Compute detector firing rates (marginals)
     let num_det = dem1.num_detectors.max(dem2.num_detectors) as usize;
-    let num_obs = dem1.num_observables.max(dem2.num_observables) as usize;
+    let num_obs = dem1.num_dem_outputs.max(dem2.num_dem_outputs) as usize;
 
     let mut det_rates1 = vec![0.0; num_det];
     let mut det_rates2 = vec![0.0; num_det];
@@ -1002,6 +1257,140 @@ mod tests {
         assert_eq!(dem.mechanisms[0].components[0].observables, vec![0]);
     }
 
+    #[test]
+    fn test_parse_accepts_pecos_dem_superset_metadata() {
+        let dem_str = r#"
+            error(0.02) D0 TP0
+            pecos_tracked_pauli {"id":0,"kind":"tracked_pauli","label":"track","pauli":"+X0 Z2","records":[]}
+        "#;
+        let dem = ParsedDem::from_str(dem_str).unwrap();
+
+        assert_eq!(dem.mechanisms.len(), 1);
+        assert_eq!(dem.num_detectors, 1);
+        assert_eq!(dem.num_dem_outputs(), 0);
+        assert_eq!(dem.num_observables(), 0);
+        assert_eq!(dem.num_tracked_paulis(), 1);
+        assert_eq!(dem.mechanisms[0].components[0].tracked_paulis, vec![0]);
+        assert_eq!(dem.mechanisms[0].format_targets(), "D0 TP0");
+        assert_eq!(dem.mechanisms[0].effect_key().to_string(), "D0 TP0");
+        let op = dem.tracked_paulis[0].as_ref().unwrap();
+        assert_eq!(op.label.as_deref(), Some("track"));
+        assert_eq!(
+            op.kind,
+            Some(crate::fault_tolerance::DemOutputKind::TrackedPauli)
+        );
+        assert_eq!(op.pauli.as_ref().unwrap().to_sparse_str(), "+X0 Z2");
+    }
+
+    #[test]
+    fn test_parse_rejects_malformed_pecos_dem_superset_metadata() {
+        let err = ParsedDem::from_str("pecos_tracked_pauli not-json").unwrap_err();
+        assert!(matches!(err, DemParseError::InvalidPecosMetadata(_)));
+    }
+
+    #[test]
+    fn test_parse_accepts_tracked_pauli_targets_without_metadata() {
+        let dem = ParsedDem::from_str("error(0.125) D1 L0 TP2").unwrap();
+
+        assert_eq!(dem.num_detectors, 2);
+        assert_eq!(dem.num_dem_outputs(), 1);
+        assert_eq!(dem.num_tracked_paulis(), 3);
+        assert_eq!(dem.mechanisms[0].components[0].detectors, vec![1]);
+        assert_eq!(dem.mechanisms[0].components[0].observables, vec![0]);
+        assert_eq!(dem.mechanisms[0].components[0].tracked_paulis, vec![2]);
+        assert_eq!(dem.mechanisms[0].effect_key().to_string(), "D1 L0 TP2");
+    }
+
+    #[test]
+    fn test_decomposed_tracked_pauli_targets_xor_by_parity() {
+        let cancels = ParsedDem::from_str("error(0.5) TP0 ^ TP0").unwrap();
+        let (dets, obs, tracked_paulis) = cancels.mechanisms[0].combined_effect();
+        assert!(dets.is_empty());
+        assert!(obs.is_empty());
+        assert!(tracked_paulis.is_empty());
+        assert_eq!(cancels.mechanisms[0].effect_key().to_string(), "(empty)");
+
+        let leaves_detector = ParsedDem::from_str("error(0.5) D0 TP0 ^ TP0").unwrap();
+        let (dets, obs, tracked_paulis) = leaves_detector.mechanisms[0].combined_effect();
+        assert_eq!(dets, vec![0]);
+        assert!(obs.is_empty());
+        assert!(tracked_paulis.is_empty());
+        assert_eq!(leaves_detector.mechanisms[0].effect_key().to_string(), "D0");
+    }
+
+    #[test]
+    fn test_duplicate_tracked_pauli_targets_cancel_by_parity() {
+        let dem = ParsedDem::from_str("error(0.1) TP0 TP0").unwrap();
+        assert_eq!(dem.mechanisms[0].components[0].tracked_paulis, vec![0, 0]);
+
+        let (dets, obs, tracked_paulis) = dem.mechanisms[0].combined_effect();
+        assert!(dets.is_empty());
+        assert!(obs.is_empty());
+        assert!(tracked_paulis.is_empty());
+        assert_eq!(dem.mechanisms[0].effect_key().to_string(), "(empty)");
+    }
+
+    #[test]
+    fn test_parse_rejects_unknown_error_targets() {
+        let err = ParsedDem::from_str("error(0.125) D1 T0").unwrap_err();
+        assert!(matches!(err, DemParseError::InvalidTarget(_)));
+        assert!(err.to_string().contains("Invalid DEM error target: T0"));
+    }
+
+    #[test]
+    fn test_parse_rejects_malformed_tracked_pauli_targets() {
+        for target in ["TP", "TPx", "TP-1"] {
+            let err = ParsedDem::from_str(&format!("error(0.125) {target}")).unwrap_err();
+            assert!(
+                matches!(err, DemParseError::InvalidTrackedPauliId(_)),
+                "{target} should be rejected as a malformed tracked-Pauli target"
+            );
+        }
+    }
+
+    #[test]
+    fn test_parsed_dem_sampler_projects_tracked_pauli_effects_but_keeps_metadata() {
+        let dem = ParsedDem::from_str("error(1.0) TP0").unwrap();
+        let sampler = dem.to_dem_sampler();
+        let mut rng = PecosRng::seed_from_u64(123);
+
+        assert_eq!(dem.num_tracked_paulis(), 1);
+        assert_eq!(sampler.num_detectors(), 0);
+        assert_eq!(sampler.num_dem_outputs(), 0);
+        assert_eq!(sampler.num_tracked_paulis(), 1);
+        let (detectors, dem_outputs) = sampler.sample(&mut rng);
+        assert!(detectors.is_empty());
+        assert!(dem_outputs.is_empty());
+        let err = sampler.sample_tracked_pauli_flips(&mut rng).unwrap_err();
+        assert_eq!(err.backend(), "DemSampler");
+        assert_eq!(err.num_tracked_paulis(), 1);
+    }
+
+    #[test]
+    fn test_parsed_dem_samplers_project_different_tracked_paulis_the_same() {
+        let dem1 = ParsedDem::from_str("error(1.0) D0 TP0").unwrap();
+        let dem2 = ParsedDem::from_str("error(1.0) D0 TP1").unwrap();
+        let sampler1 = dem1.to_dem_sampler();
+        let sampler2 = dem2.to_dem_sampler();
+        let mut rng1 = PecosRng::seed_from_u64(11);
+        let mut rng2 = PecosRng::seed_from_u64(11);
+
+        assert_eq!(sampler1.num_detectors(), 1);
+        assert_eq!(sampler2.num_detectors(), 1);
+        assert_eq!(sampler1.num_dem_outputs(), 0);
+        assert_eq!(sampler2.num_dem_outputs(), 0);
+        assert_eq!(sampler1.num_tracked_paulis(), 1);
+        assert_eq!(sampler2.num_tracked_paulis(), 2);
+        assert_eq!(sampler1.sample(&mut rng1), sampler2.sample(&mut rng2));
+    }
+
+    #[test]
+    fn test_parse_rejects_unknown_pecos_dem_extension() {
+        let err = ParsedDem::from_str("pecos_old_extension {}").unwrap_err();
+        assert!(matches!(err, DemParseError::InvalidPecosMetadata(_)));
+        assert!(err.to_string().contains("unsupported PECOS DEM extension"));
+    }
+
     #[test]
     fn test_aggregate() {
         let dem_str = r"
@@ -1050,6 +1439,41 @@ error(0.02) D1 D2
         assert!(!result.details.only_in_dem2.is_empty());
     }
 
+    #[test]
+    fn test_compare_exact_distinguishes_tracked_pauli_targets() {
+        let dem1 = ParsedDem::from_str("error(0.01) D0 TP0").unwrap();
+        let dem2 = ParsedDem::from_str("error(0.01) D0 TP1").unwrap();
+
+        let result = compare_dems_exact(&dem1, &dem2, 1e-6);
+        assert!(!result.equivalent);
+        assert_eq!(
+            result
+                .details
+                .only_in_dem1
+                .iter()
+                .map(ToString::to_string)
+                .collect::<Vec<_>>(),
+            ["D0 TP0"]
+        );
+        assert_eq!(
+            result
+                .details
+                .only_in_dem2
+                .iter()
+                .map(ToString::to_string)
+                .collect::<Vec<_>>(),
+            ["D0 TP1"]
+        );
+
+        let decomposed1 = ParsedDem::from_str("error(0.01) D0 TP0 ^ D1").unwrap();
+        let decomposed2 = ParsedDem::from_str("error(0.01) D0 TP1 ^ D1").unwrap();
+        let result = compare_dems_exact(&decomposed1, &decomposed2, 1e-6);
+        assert!(
+            !result.equivalent,
+            "exact PECOS DEM comparison must include tracked targets on decomposed components"
+        );
+    }
+
     #[test]
     fn test_statistical_comparison() {
         let dem_str = "error(0.5) D0";
@@ -1062,7 +1486,7 @@ error(0.02) D1 D2
 
     #[test]
     fn test_decomposed_equivalent_to_simple() {
-        // In Stim's DEM format, these should be equivalent for sampling:
+        // In DEM syntax, these should be equivalent for sampling:
         // - error(0.1) D0 D1: D0 and D1 flip together with p=0.1
         // - error(0.1) D0 ^ D1: D0 and D1 flip together with p=0.1 (^ is for decomposition tracking)
         let dem1 = ParsedDem::from_str("error(0.1) D0 D1").unwrap();
@@ -1093,9 +1517,10 @@ error(0.02) D1 D2
         let dem = ParsedDem::from_str("error(0.5) D0 ^ D0").unwrap();
 
         // The combined effect should be empty
-        let (dets, obs) = dem.mechanisms[0].combined_effect();
+        let (dets, obs, tracked_paulis) = dem.mechanisms[0].combined_effect();
         assert!(dets.is_empty());
         assert!(obs.is_empty());
+        assert!(tracked_paulis.is_empty());
 
         // Sample and verify D0 never fires
         let mut rng = PecosRng::seed_from_u64(42);
diff --git a/crates/pecos-qec/src/fault_tolerance/dem_builder/mem_builder.rs b/crates/pecos-qec/src/fault_tolerance/dem_builder/mem_builder.rs
index 201bab51b..85176ec4c 100644
--- a/crates/pecos-qec/src/fault_tolerance/dem_builder/mem_builder.rs
+++ b/crates/pecos-qec/src/fault_tolerance/dem_builder/mem_builder.rs
@@ -12,36 +12,10 @@
 
 //! Measurement Noise Model (MNM) builder implementation.
 //!
-//! This module builds a MNM from a fault influence map. Unlike the DEM builder
-//! which maps to detector effects, the MNM maps directly to measurement effects
-//! for fast approximate sampling.
-//!
-//! # Usage
-//!
-//! ```
-//! use pecos_qec::fault_tolerance::DagFaultAnalyzer;
-//! use pecos_qec::fault_tolerance::dem_builder::MemBuilder;
-//! use pecos_quantum::DagCircuit;
-//! use rand::SeedableRng;
-//! use rand::rngs::SmallRng;
-//!
-//! let mut dag = DagCircuit::new();
-//! dag.pz(&[2]);
-//! dag.cx(&[(0, 2)]);
-//! dag.cx(&[(1, 2)]);
-//! dag.mz(&[2]);
-//!
-//! let analyzer = DagFaultAnalyzer::new(&dag);
-//! let influence_map = analyzer.build_influence_map();
-//!
-//! let mnm = MemBuilder::new(&influence_map)
-//!     .with_noise(0.01, 0.01, 0.01, 0.01)
-//!     .build();
-//!
-//! // Sample measurement outcomes
-//! let mut rng = SmallRng::seed_from_u64(42);
-//! let outcomes = mnm.sample(&mut rng);
-//! ```
+//! This module builds a measurement-level noise model from a fault influence
+//! map. Unlike a DEM, which maps faults to detector and observable effects,
+//! the MNM maps faults directly to raw measurement flips for fast approximate
+//! sampling.
 
 use super::types::{MeasurementMechanism, MeasurementNoiseModel, NoiseConfig};
 use crate::fault_tolerance::propagator::{DagFaultInfluenceMap, Pauli};
@@ -49,28 +23,12 @@ use pecos_core::gate_type::GateType;
 use smallvec::SmallVec;
 
 /// Builder for Measurement Noise Models (MNMs).
-///
-/// Constructs a MNM from a fault influence map. The MNM aggregates fault locations
-/// by their measurement effects (which measurements flip), enabling fast approximate
-/// sampling.
-///
-/// # Comparison with DEM
-///
-/// | Aspect | DEM | MNM |
-/// |--------|-----|-----|
-/// | Maps to | Detectors | Measurements |
-/// | Use case | Decoding | Sampling |
-/// | Aggregates by | Detector signature | Measurement signature |
-/// | Output | Stim-compatible DEM | Raw measurement outcomes |
 pub struct MemBuilder<'a> {
     /// Reference to the fault influence map.
     influence_map: &'a DagFaultInfluenceMap,
     /// Noise configuration.
     noise: NoiseConfig,
-    /// Measurement order from the original circuit (e.g., `TickCircuit`).
-    /// This is a list of qubits in the order they were measured.
-    /// `measurement_order[tc_idx] = qubit` means the tc_idx-th measurement
-    /// in the `TickCircuit` was on this qubit.
+    /// Optional measurement order from the original circuit.
     measurement_order: Option<Vec<usize>>,
 }
 
@@ -85,114 +43,69 @@ impl<'a> MemBuilder<'a> {
         }
     }
 
-    /// Sets the noise configuration.
+    /// Sets the scalar noise configuration.
     #[must_use]
-    pub fn with_noise(mut self, p1: f64, p2: f64, p_meas: f64, p_init: f64) -> Self {
-        self.noise = NoiseConfig::new(p1, p2, p_meas, p_init);
+    pub fn with_noise(mut self, p1: f64, p2: f64, p_meas: f64, p_prep: f64) -> Self {
+        self.noise = NoiseConfig::new(p1, p2, p_meas, p_prep);
         self
     }
 
-    /// Sets the measurement order from the original circuit (e.g., `TickCircuit`).
-    ///
-    /// This is needed when detector definitions use `TickCircuit` measurement indices
-    /// but the influence map uses a different ordering based on DAG topology.
-    ///
-    /// # Arguments
-    ///
-    /// * `order` - List of qubit indices in measurement execution order.
-    ///   `order[tc_idx] = qubit` means the tc_idx-th measurement in the `TickCircuit`
-    ///   was on this qubit.
+    /// Sets the full noise configuration.
     #[must_use]
-    pub fn with_measurement_order(mut self, order: Vec<usize>) -> Self {
-        self.measurement_order = Some(order);
+    pub fn with_noise_config(mut self, noise: NoiseConfig) -> Self {
+        self.noise = noise;
         self
     }
 
-    /// Computes the mapping from influence map measurement indices to `TickCircuit` indices.
-    ///
-    /// Returns a vector where `result[im_idx] = tc_idx`, mapping each influence map
-    /// measurement to its corresponding `TickCircuit` measurement.
-    fn compute_im_to_tc_mapping(&self, tc_order: &[usize]) -> Vec<usize> {
-        let im_measurements = &self.influence_map.measurements;
-        let num_measurements = im_measurements.len();
-
-        // Build map: qubit -> list of TC indices where that qubit is measured
-        let mut tc_indices_by_qubit: std::collections::BTreeMap<usize, Vec<usize>> =
-            std::collections::BTreeMap::new();
-        for (tc_idx, &qubit) in tc_order.iter().enumerate() {
-            tc_indices_by_qubit.entry(qubit).or_default().push(tc_idx);
-        }
-
-        // Build map: qubit -> list of IM indices where that qubit is measured
-        let mut im_indices_by_qubit: std::collections::BTreeMap<usize, Vec<usize>> =
-            std::collections::BTreeMap::new();
-        for (im_idx, &(_node, qubit, _basis)) in im_measurements.iter().enumerate() {
-            im_indices_by_qubit.entry(qubit).or_default().push(im_idx);
-        }
-
-        // Build the mapping: for each qubit, match IM indices to TC indices in order
-        let mut im_to_tc = vec![0; num_measurements];
-        for (qubit, im_indices) in &im_indices_by_qubit {
-            if let Some(tc_indices) = tc_indices_by_qubit.get(qubit) {
-                // Match in order - the i-th IM measurement of this qubit maps to
-                // the i-th TC measurement of this qubit
-                for (i, &im_idx) in im_indices.iter().enumerate() {
-                    if i < tc_indices.len() {
-                        im_to_tc[im_idx] = tc_indices[i];
-                    }
-                }
-            }
-        }
-
-        im_to_tc
+    /// Sets the measurement order from the original circuit.
+    #[must_use]
+    pub fn with_measurement_order(mut self, order: Vec<usize>) -> Self {
+        self.measurement_order = Some(order);
+        self
     }
 
     /// Builds the Measurement Noise Model.
-    ///
-    /// This aggregates all fault locations by their measurement effects.
-    /// Locations that produce the same measurement signature have their
-    /// probabilities combined using the independent error formula.
     #[must_use]
     pub fn build(&self) -> MeasurementNoiseModel {
         let num_measurements = self.influence_map.measurements.len();
         let mut mem = MeasurementNoiseModel::new(num_measurements);
 
-        // Compute im_to_tc mapping if measurement order is provided
         if let Some(ref tc_order) = self.measurement_order {
-            let im_to_tc = self.compute_im_to_tc_mapping(tc_order);
-            mem.set_measurement_order(im_to_tc);
+            mem.set_measurement_order(self.compute_im_to_tc_mapping(tc_order));
         }
 
         let locations = &self.influence_map.locations;
-
-        // Group CX locations by node for two-qubit gate processing
-        let mut cx_groups: std::collections::BTreeMap<usize, Vec<usize>> =
+        let mut two_qubit_groups: std::collections::BTreeMap<usize, Vec<usize>> =
             std::collections::BTreeMap::new();
 
         for (loc_idx, loc) in locations.iter().enumerate() {
             match loc.gate_type {
-                GateType::PZ | GateType::QAlloc
-                    // Prep errors: only "after" locations
-                    if self.noise.p_init > 0.0 && !loc.before => {
-                        self.process_prep_fault(loc_idx, &mut mem);
-                    }
-                GateType::MZ | GateType::MeasureFree
-                    // Measurement errors: only "before" locations
-                    if self.noise.p_meas > 0.0 && loc.before => {
-                        self.process_meas_fault(loc_idx, &mut mem);
-                    }
+                GateType::PZ | GateType::QAlloc if self.noise.p_prep > 0.0 && !loc.before => {
+                    self.process_single_pauli_fault(loc_idx, Pauli::X, self.noise.p_prep, &mut mem);
+                }
+                GateType::MZ | GateType::MeasureFree if self.noise.p_meas > 0.0 && loc.before => {
+                    self.process_single_pauli_fault(loc_idx, Pauli::X, self.noise.p_meas, &mut mem);
+                }
                 GateType::CX
                 | GateType::CZ
                 | GateType::CY
+                | GateType::SZZ
+                | GateType::SZZdg
+                | GateType::SXX
+                | GateType::SXXdg
+                | GateType::SYY
+                | GateType::SYYdg
                 | GateType::SWAP
                 | GateType::RXX
                 | GateType::RYY
                 | GateType::RZZ
-                    // Two-qubit gate errors: only "after" locations
-                    if !loc.before => {
-                        cx_groups.entry(loc.node).or_default().push(loc_idx);
-                    }
+                    if !loc.before =>
+                {
+                    two_qubit_groups.entry(loc.node).or_default().push(loc_idx);
+                }
                 GateType::H
+                | GateType::F
+                | GateType::Fdg
                 | GateType::SZ
                 | GateType::SZdg
                 | GateType::SX
@@ -209,19 +122,38 @@ impl<'a> MemBuilder<'a> {
                 | GateType::RZ
                 | GateType::U
                 | GateType::R1XY
-                    // Single-qubit gate errors: only "after" locations
-                    if self.noise.p1 > 0.0 && !loc.before => {
+                    if self.noise.p1 > 0.0 && !loc.before =>
+                {
+                    self.process_single_qubit_fault(loc_idx, &mut mem);
+                }
+                GateType::Idle if !loc.before => {
+                    if self.noise.uses_dedicated_idle_noise() {
+                        #[allow(clippy::cast_precision_loss)]
+                        let duration = loc.idle_duration.max(1) as f64;
+                        let probs = self.noise.idle_pauli_probs(duration);
+                        if probs.px > 0.0 {
+                            self.process_single_pauli_fault(loc_idx, Pauli::X, probs.px, &mut mem);
+                        }
+                        if probs.py > 0.0 {
+                            self.process_single_pauli_fault(loc_idx, Pauli::Y, probs.py, &mut mem);
+                        }
+                        if probs.pz > 0.0 {
+                            self.process_single_pauli_fault(loc_idx, Pauli::Z, probs.pz, &mut mem);
+                        }
+                    } else if self.noise.p1 > 0.0 {
                         self.process_single_qubit_fault(loc_idx, &mut mem);
                     }
+                }
                 _ => {}
             }
         }
 
-        // Process two-qubit gates
         if self.noise.p2 > 0.0 {
-            for (_, loc_indices) in cx_groups {
-                if loc_indices.len() == 2 {
-                    self.process_two_qubit_fault(loc_indices[0], loc_indices[1], &mut mem);
+            for loc_indices in two_qubit_groups.values() {
+                for pair in loc_indices.chunks(2) {
+                    if pair.len() == 2 {
+                        self.process_two_qubit_fault(pair[0], pair[1], &mut mem);
+                    }
                 }
             }
         }
@@ -229,45 +161,57 @@ impl<'a> MemBuilder<'a> {
         mem
     }
 
-    /// Processes a prep/initialization fault location.
-    fn process_prep_fault(&self, loc_idx: usize, mem: &mut MeasurementNoiseModel) {
-        // For Z-basis prep, X error matters
-        let mechanism = self.compute_mechanism(loc_idx, Pauli::X);
-        if !mechanism.is_empty() {
-            mem.add_mechanism(mechanism, self.noise.p_init);
+    fn compute_im_to_tc_mapping(&self, tc_order: &[usize]) -> Vec<usize> {
+        let im_measurements = &self.influence_map.measurements;
+        let mut tc_indices_by_qubit: std::collections::BTreeMap<usize, Vec<usize>> =
+            std::collections::BTreeMap::new();
+        for (tc_idx, &qubit) in tc_order.iter().enumerate() {
+            tc_indices_by_qubit.entry(qubit).or_default().push(tc_idx);
         }
+
+        let mut im_indices_by_qubit: std::collections::BTreeMap<usize, Vec<usize>> =
+            std::collections::BTreeMap::new();
+        for (im_idx, &(_node, qubit, _basis)) in im_measurements.iter().enumerate() {
+            im_indices_by_qubit.entry(qubit).or_default().push(im_idx);
+        }
+
+        let mut im_to_tc = vec![0; im_measurements.len()];
+        for (qubit, im_indices) in &im_indices_by_qubit {
+            if let Some(tc_indices) = tc_indices_by_qubit.get(qubit) {
+                for (i, &im_idx) in im_indices.iter().enumerate() {
+                    if let Some(&tc_idx) = tc_indices.get(i) {
+                        im_to_tc[im_idx] = tc_idx;
+                    }
+                }
+            }
+        }
+        im_to_tc
     }
 
-    /// Processes a measurement fault location.
-    fn process_meas_fault(&self, loc_idx: usize, mem: &mut MeasurementNoiseModel) {
-        // Measurement error is a bit flip (X error)
-        let mechanism = self.compute_mechanism(loc_idx, Pauli::X);
+    fn process_single_pauli_fault(
+        &self,
+        loc_idx: usize,
+        pauli: Pauli,
+        prob: f64,
+        mem: &mut MeasurementNoiseModel,
+    ) {
+        let mechanism = self.compute_mechanism(loc_idx, pauli);
         if !mechanism.is_empty() {
-            mem.add_mechanism(mechanism, self.noise.p_meas);
+            mem.add_mechanism(mechanism, prob);
         }
     }
 
-    /// Processes a single-qubit gate fault location.
     fn process_single_qubit_fault(&self, loc_idx: usize, mem: &mut MeasurementNoiseModel) {
-        // Depolarizing: each of X, Y, Z with probability p1/3
         let prob = self.noise.p1 / 3.0;
-
         for pauli in [Pauli::X, Pauli::Y, Pauli::Z] {
-            let mechanism = self.compute_mechanism(loc_idx, pauli);
-            if !mechanism.is_empty() {
-                mem.add_mechanism(mechanism, prob);
-            }
+            self.process_single_pauli_fault(loc_idx, pauli, prob, mem);
         }
     }
 
-    /// Processes a two-qubit gate fault (CX or CZ).
     fn process_two_qubit_fault(&self, loc1: usize, loc2: usize, mem: &mut MeasurementNoiseModel) {
-        // Two-qubit depolarizing: 15 non-identity Pauli combinations with p2/15 each
         let prob = self.noise.p2 / 15.0;
-
         let paulis = [Pauli::I, Pauli::X, Pauli::Y, Pauli::Z];
 
-        // Cache single-qubit effects for each Pauli on each qubit
         let mut effects1: [Option<MeasurementMechanism>; 4] = [None, None, None, None];
         let mut effects2: [Option<MeasurementMechanism>; 4] = [None, None, None, None];
 
@@ -276,24 +220,21 @@ impl<'a> MemBuilder<'a> {
             effects2[p.as_u8() as usize] = Some(self.compute_mechanism(loc2, p));
         }
 
-        // Process all 15 non-trivial Pauli combinations
         for &p1 in &paulis {
             for &p2 in &paulis {
                 if p1 == Pauli::I && p2 == Pauli::I {
-                    continue; // Skip II
+                    continue;
                 }
 
                 let mechanism = if p1 == Pauli::I {
-                    // IX, IY, IZ
                     effects2[p2.as_u8() as usize].clone().unwrap_or_default()
                 } else if p2 == Pauli::I {
-                    // XI, YI, ZI
                     effects1[p1.as_u8() as usize].clone().unwrap_or_default()
                 } else {
-                    // Correlated: XOR the measurement effects
-                    let e1 = effects1[p1.as_u8() as usize].as_ref();
-                    let e2 = effects2[p2.as_u8() as usize].as_ref();
-                    xor_measurement_mechanisms(e1, e2)
+                    xor_measurement_mechanisms(
+                        effects1[p1.as_u8() as usize].as_ref(),
+                        effects2[p2.as_u8() as usize].as_ref(),
+                    )
                 };
 
                 if !mechanism.is_empty() {
@@ -303,9 +244,7 @@ impl<'a> MemBuilder<'a> {
         }
     }
 
-    /// Computes the measurement mechanism for a fault at the given location and Pauli type.
     fn compute_mechanism(&self, loc_idx: usize, pauli: Pauli) -> MeasurementMechanism {
-        // Get the measurement indices that this fault flips
         let measurements = self
             .influence_map
             .get_detector_indices(loc_idx, pauli.as_u8());
@@ -317,7 +256,6 @@ impl<'a> MemBuilder<'a> {
     }
 }
 
-/// XORs two measurement mechanisms (symmetric difference).
 fn xor_measurement_mechanisms(
     a: Option<&MeasurementMechanism>,
     b: Option<&MeasurementMechanism>,
@@ -339,7 +277,6 @@ fn xor_measurement_mechanisms(
                         j += 1;
                     }
                     std::cmp::Ordering::Equal => {
-                        // Same element in both - XOR cancels
                         i += 1;
                         j += 1;
                     }
@@ -348,124 +285,9 @@ fn xor_measurement_mechanisms(
 
             result.extend_from_slice(&m1.measurements[i..]);
             result.extend_from_slice(&m2.measurements[j..]);
-
             MeasurementMechanism::from_sorted(result)
         }
         (Some(m), None) | (None, Some(m)) => m.clone(),
         (None, None) => MeasurementMechanism::new(),
     }
 }
-
-#[cfg(test)]
-mod tests {
-    use super::*;
-    use crate::fault_tolerance::propagator::DagFaultAnalyzer;
-    use pecos_quantum::DagCircuit;
-
-    #[test]
-    fn test_mem_builder_simple() {
-        // Simple circuit: prep, cx, measure
-        let mut dag = DagCircuit::new();
-        dag.pz(&[2]); // Prep ancilla
-        dag.cx(&[(0, 2)]); // CNOT data -> ancilla
-        dag.cx(&[(1, 2)]); // CNOT data -> ancilla
-        dag.mz(&[2]); // Measure ancilla
-
-        let analyzer = DagFaultAnalyzer::new(&dag);
-        let influence_map = analyzer.build_influence_map();
-
-        let mem = MemBuilder::new(&influence_map)
-            .with_noise(0.01, 0.01, 0.01, 0.01)
-            .build();
-
-        // Should have some mechanisms
-        assert!(mem.num_mechanisms() > 0);
-        assert_eq!(mem.num_measurements, 1);
-    }
-
-    #[test]
-    fn test_mem_builder_aggregation() {
-        // Circuit where multiple locations produce the same measurement effect
-        let mut dag = DagCircuit::new();
-        dag.pz(&[2]);
-        dag.cx(&[(0, 2)]);
-        dag.cx(&[(1, 2)]);
-        dag.mz(&[2]);
-
-        let analyzer = DagFaultAnalyzer::new(&dag);
-        let influence_map = analyzer.build_influence_map();
-
-        let mem = MemBuilder::new(&influence_map)
-            .with_noise(0.01, 0.01, 0.01, 0.01)
-            .build();
-
-        // Count how many mechanisms flip measurement 0
-        let single_meas_mechanisms: Vec<_> = mem
-            .iter()
-            .filter(|(m, _)| m.measurements.as_slice() == [0])
-            .collect();
-
-        // Should have aggregated multiple sources into one mechanism
-        // (prep X error + measurement X error both flip measurement 0)
-        assert!(
-            single_meas_mechanisms.len() == 1,
-            "Expected aggregation of mechanisms with same effect"
-        );
-
-        // Combined probability should be > individual probability
-        let combined_prob = single_meas_mechanisms[0].1;
-        assert!(
-            *combined_prob > 0.01,
-            "Combined probability should be greater than single source"
-        );
-    }
-
-    #[test]
-    fn test_mem_sampling() {
-        use rand::SeedableRng;
-        use rand::rngs::SmallRng;
-
-        let mut dag = DagCircuit::new();
-        dag.pz(&[2]);
-        dag.cx(&[(0, 2)]);
-        dag.mz(&[2]);
-
-        let analyzer = DagFaultAnalyzer::new(&dag);
-        let influence_map = analyzer.build_influence_map();
-
-        let mem = MemBuilder::new(&influence_map)
-            .with_noise(0.1, 0.1, 0.1, 0.1) // High error rate for testing
-            .build();
-
-        let mut rng = SmallRng::seed_from_u64(42);
-
-        // Sample many shots and count flips
-        let num_shots = 10000;
-        let mut flip_count = 0;
-
-        for _ in 0..num_shots {
-            let outcomes = mem.sample(&mut rng);
-            if outcomes.first().copied().unwrap_or(false) {
-                flip_count += 1;
-            }
-        }
-
-        // Should have some flips (not 0) and some non-flips (not all)
-        assert!(flip_count > 0, "Should have some measurement flips");
-        assert!(
-            flip_count < num_shots,
-            "Should not have all measurements flipped"
-        );
-    }
-
-    #[test]
-    fn test_xor_measurement_mechanisms() {
-        let m1 = MeasurementMechanism::from_unsorted([0, 1, 2]);
-        let m2 = MeasurementMechanism::from_unsorted([1, 2, 3]);
-
-        let result = xor_measurement_mechanisms(Some(&m1), Some(&m2));
-
-        // {0, 1, 2} XOR {1, 2, 3} = {0, 3}
-        assert_eq!(result.measurements.as_slice(), &[0, 3]);
-    }
-}
diff --git a/crates/pecos-qec/src/fault_tolerance/dem_builder/sampler.rs b/crates/pecos-qec/src/fault_tolerance/dem_builder/sampler.rs
new file mode 100644
index 000000000..d564fbf49
--- /dev/null
+++ b/crates/pecos-qec/src/fault_tolerance/dem_builder/sampler.rs
@@ -0,0 +1,2137 @@
+// Copyright 2026 The PECOS Developers
+//
+// Licensed under the Apache License, Version 2.0 (the "License"); you may not use this file except
+// in compliance with the License. You may obtain a copy of the License at
+//
+//     https://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software distributed under the License
+// is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express
+// or implied. See the License for the specific language governing permissions and limitations under
+// the License.
+
+//! Unified sampler for noisy QEC measurement outcomes.
+//!
+//! This sampler unifies the DEM (detector-level) and MNM (measurement-level)
+//! sampling paths into a single type. Internally it uses [`DemSampler`]'s
+//! efficient geometric-skip engine for fault mechanism sampling, then applies
+//! an optional detector basis change and non-deterministic coin flips depending
+//! on the requested output mode.
+//!
+//! # Coordinate systems
+//!
+//! Deterministic measurements form a basis in `Z_2`. User-defined detectors are
+//! linear combinations (XOR chains) of these measurements — a change of basis.
+//! The sampler always builds its mechanism table in raw measurement coordinates,
+//! then applies the basis change at build time if detector definitions are
+//! provided.
+//!
+//! # Construction modes
+//!
+//! - **Raw measurements**: each deterministic measurement is its own "detector."
+//!   Output includes coin flips for non-deterministic measurements.
+//! - **Auto-detected detectors**: uses the influence builder's detector
+//!   definitions (round-to-round XOR of stabilizer measurements).
+//! - **User-defined detectors**: arbitrary XOR combinations of measurements,
+//!   validated at build time.
+
+use super::dem_sampler::SamplingEngine;
+use super::types::{DemOutput, NoiseConfig, PerGateTypeNoise};
+use crate::fault_tolerance::propagator::{DagFaultInfluenceMap, DemOutputKind};
+use pecos_core::prelude::GateType;
+use pecos_num::z2_linalg::z2_rank_from_records;
+use pecos_random::RngProbabilityExt;
+use rand_core::Rng;
+
+/// Errors from detector definition validation.
+#[derive(Debug, Clone)]
+pub enum DetectorValidationError {
+    /// A detector definition references a non-deterministic measurement.
+    NonDeterministicReference {
+        detector_id: usize,
+        measurement_idx: usize,
+    },
+    /// Detector definitions are not linearly independent over `Z_2`.
+    LinearlyDependent { rank: usize, num_detectors: usize },
+    /// Circuit contains gates not supported by the symbolic determinism analysis.
+    /// Raw measurement mode requires all gates to be in the supported Clifford
+    /// subset (`H`, `X`, `Y`, `Z`, `SZ`, `SZdg`, `CX`, `CZ`, `SWAP`, `MZ`, `PZ`, `I`).
+    UnsupportedGateForDeterminismAnalysis { gate_type: String },
+}
+
+impl std::fmt::Display for DetectorValidationError {
+    fn fmt(&self, f: &mut std::fmt::Formatter<'_>) -> std::fmt::Result {
+        match self {
+            Self::NonDeterministicReference {
+                detector_id,
+                measurement_idx,
+            } => {
+                write!(
+                    f,
+                    "Detector {detector_id} references non-deterministic measurement {measurement_idx}. \
+                     Detectors should only XOR deterministic measurements."
+                )
+            }
+            Self::LinearlyDependent {
+                rank,
+                num_detectors,
+            } => {
+                write!(
+                    f,
+                    "Detector definitions are not linearly independent: \
+                     rank {rank} < {num_detectors} detectors. \
+                     Some detectors are redundant (XOR of other detectors)."
+                )
+            }
+            Self::UnsupportedGateForDeterminismAnalysis { gate_type } => {
+                write!(
+                    f,
+                    "Circuit contains gate type '{gate_type}' which is not supported by \
+                     raw measurement determinism analysis. Supported Clifford gates: \
+                     H, X, Y, Z, SZ, SZdg, CX, CZ, SWAP, MZ, PZ/QAlloc, I/Idle."
+                )
+            }
+        }
+    }
+}
+
+impl std::error::Error for DetectorValidationError {}
+
+/// Error returned when a sampler backend is asked to directly evaluate tracked
+/// Paulis it only preserves as metadata.
+#[derive(Debug, Clone, PartialEq, Eq)]
+pub struct TrackedPauliSamplingError {
+    backend: &'static str,
+    num_tracked_paulis: usize,
+}
+
+impl TrackedPauliSamplingError {
+    fn new(backend: &'static str, num_tracked_paulis: usize) -> Self {
+        Self {
+            backend,
+            num_tracked_paulis,
+        }
+    }
+
+    /// Backend that rejected direct tracked-Pauli sampling.
+    #[must_use]
+    pub fn backend(&self) -> &'static str {
+        self.backend
+    }
+
+    /// Number of tracked Paulis carried as metadata by that backend.
+    #[must_use]
+    pub fn num_tracked_paulis(&self) -> usize {
+        self.num_tracked_paulis
+    }
+}
+
+impl std::fmt::Display for TrackedPauliSamplingError {
+    fn fmt(&self, f: &mut std::fmt::Formatter<'_>) -> std::fmt::Result {
+        write!(
+            f,
+            "{} cannot directly sample tracked Pauli flips for {} tracked Pauli(s). \
+             This backend samples decoder-facing detectors and observables only; tracked \
+             Paulis are preserved as PECOS metadata and fault effects.",
+            self.backend, self.num_tracked_paulis
+        )
+    }
+}
+
+impl std::error::Error for TrackedPauliSamplingError {}
+
+/// Output mode for the unified sampler.
+#[derive(Debug, Clone, Copy, PartialEq, Eq)]
+pub enum OutputMode {
+    /// Output raw measurement values (deterministic flips + non-det coin flips).
+    RawMeasurements,
+    /// Output detector events (XOR of measurement groups) + observable flips.
+    DetectorEvents,
+}
+
+/// Unified sampler that handles both measurement-level and detector-level output.
+///
+/// Uses [`DemSampler`]'s geometric-skip engine internally. The mechanism table
+/// is always in the output coordinate system (raw measurements or user detectors),
+/// determined at build time.
+/// Result of dual-mode sampling: both raw measurements and detector events.
+#[derive(Debug, Clone)]
+pub struct DualSampleResult {
+    /// Raw measurement values (deterministic flips + non-det coin flips).
+    pub raw_measurements: Vec<bool>,
+    /// Detector events (XOR of measurement groups).
+    pub detector_events: Vec<bool>,
+    /// Standard DEM `L<n>` observable output flips.
+    pub dem_output_flips: Vec<bool>,
+}
+
+/// Labels for sampler output channels.
+#[derive(Debug, Clone, Default)]
+pub struct SamplerLabels {
+    /// Labels for output channels (raw measurements or detectors, depending on mode).
+    pub outputs: Vec<Option<String>>,
+    /// Labels for standard DEM `L<n>` observable outputs.
+    /// Indices match `per_dem_output` in `SamplingStatistics`.
+    pub dem_output_labels: Vec<Option<String>>,
+    /// Full PECOS metadata for standard DEM `L<n>` observables.
+    pub dem_outputs: Vec<Option<DemOutput>>,
+    /// Labels for PECOS tracked Paulis.
+    pub tracked_pauli_labels: Vec<Option<String>>,
+    /// Full PECOS metadata for tracked Paulis in their own ID space.
+    pub tracked_paulis: Vec<Option<DemOutput>>,
+    /// Labels for dual-output detector channels.
+    pub dual_detectors: Vec<Option<String>>,
+}
+
+fn dem_outputs_by_id(targets: &[DemOutput], num_dem_outputs: usize) -> Vec<Option<DemOutput>> {
+    let mut by_id = vec![None; num_dem_outputs];
+    for target in targets {
+        let idx = target.id as usize;
+        if idx < by_id.len() {
+            by_id[idx] = Some(target.clone());
+        }
+    }
+    by_id
+}
+
+fn labels_from_dem_outputs(targets: &[Option<DemOutput>]) -> Vec<Option<String>> {
+    targets
+        .iter()
+        .map(|target| target.as_ref().and_then(|target| target.label.clone()))
+        .collect()
+}
+
+fn dem_outputs_from_influence_map(
+    influence_map: &DagFaultInfluenceMap,
+    num_dem_outputs: usize,
+) -> Vec<Option<DemOutput>> {
+    let mut targets = vec![None; num_dem_outputs];
+    for (internal_id, metadata) in influence_map.dem_output_metadata.iter().enumerate() {
+        if metadata.kind == DemOutputKind::Observable {
+            #[allow(clippy::cast_possible_truncation)] // DEM output count fits in u32
+            if let Some(dem_output_id) =
+                influence_map.observable_id_for_internal_dem_output(internal_id as u32)
+            {
+                let idx = dem_output_id as usize;
+                if idx < targets.len() {
+                    targets[idx] = Some(DemOutput::from_metadata(dem_output_id, metadata));
+                }
+            }
+        }
+    }
+    targets
+}
+
+fn tracked_paulis_from_influence_map(
+    influence_map: &DagFaultInfluenceMap,
+) -> Vec<Option<DemOutput>> {
+    let mut tracked_paulis = Vec::new();
+    for metadata in &influence_map.dem_output_metadata {
+        if metadata.kind == DemOutputKind::TrackedPauli {
+            #[allow(clippy::cast_possible_truncation)] // tracked-Pauli count fits in u32
+            let id = tracked_paulis.len() as u32;
+            tracked_paulis.push(Some(DemOutput::from_metadata(id, metadata)));
+        }
+    }
+    tracked_paulis
+}
+
+fn dem_outputs_from_records(
+    influence_map: &DagFaultInfluenceMap,
+    observable_records: &[Vec<i32>],
+    num_dem_outputs: usize,
+) -> Vec<Option<DemOutput>> {
+    let mut targets = dem_outputs_from_influence_map(influence_map, num_dem_outputs);
+
+    for (record_id, records) in observable_records.iter().enumerate() {
+        let dem_output_id = record_id;
+        if dem_output_id < targets.len() {
+            if let Some(target) = &mut targets[dem_output_id] {
+                if target.records.is_empty() {
+                    target.records = DemOutput::new(target.id)
+                        .with_records(records.iter().copied())
+                        .records;
+                }
+                target.kind.get_or_insert(DemOutputKind::Observable);
+            } else {
+                #[allow(clippy::cast_possible_truncation)] // DEM output count fits in u32
+                {
+                    targets[dem_output_id] = Some(
+                        DemOutput::new(dem_output_id as u32).with_records(records.iter().copied()),
+                    );
+                }
+            }
+        }
+    }
+
+    targets
+}
+
+fn merge_dem_output_metadata(
+    mut labels: SamplerLabels,
+    targets: Vec<Option<DemOutput>>,
+    tracked_paulis: Vec<Option<DemOutput>>,
+) -> SamplerLabels {
+    if labels.dem_outputs.len() < targets.len() {
+        labels.dem_outputs.resize(targets.len(), None);
+    }
+    for (idx, target) in targets.into_iter().enumerate() {
+        if labels.dem_outputs[idx].is_none() {
+            labels.dem_outputs[idx] = target;
+        }
+    }
+
+    let target_labels = labels_from_dem_outputs(&labels.dem_outputs);
+    if labels.dem_output_labels.len() < target_labels.len() {
+        labels.dem_output_labels.resize(target_labels.len(), None);
+    }
+    for (idx, label) in target_labels.into_iter().enumerate() {
+        if labels.dem_output_labels[idx].is_none() {
+            labels.dem_output_labels[idx] = label;
+        }
+    }
+
+    if labels.tracked_paulis.len() < tracked_paulis.len() {
+        labels.tracked_paulis.resize(tracked_paulis.len(), None);
+    }
+    for (idx, tracked_pauli) in tracked_paulis.into_iter().enumerate() {
+        if labels.tracked_paulis[idx].is_none() {
+            labels.tracked_paulis[idx] = tracked_pauli;
+        }
+    }
+
+    let tracked_pauli_labels = labels_from_dem_outputs(&labels.tracked_paulis);
+    if labels.tracked_pauli_labels.len() < tracked_pauli_labels.len() {
+        labels
+            .tracked_pauli_labels
+            .resize(tracked_pauli_labels.len(), None);
+    }
+    for (idx, label) in tracked_pauli_labels.into_iter().enumerate() {
+        if labels.tracked_pauli_labels[idx].is_none() {
+            labels.tracked_pauli_labels[idx] = label;
+        }
+    }
+
+    labels
+}
+
+#[derive(Debug, Clone)]
+pub struct DemSampler {
+    /// The efficient sampling engine (mechanism table in raw measurement coords).
+    inner: SamplingEngine,
+
+    /// Which output indices are non-deterministic (true = coin flip, not from mechanisms).
+    /// Length = `num_outputs` (full measurement space in raw mode).
+    non_det_mask: Vec<bool>,
+
+    /// Deterministic measurement dependencies for raw mode.
+    /// `measurement_deps[i] = Some((deps, flip))` means measurement i is determined by
+    /// XOR(measurements[j] for j in deps) XOR flip. None = non-det (coin flip) or fault-only.
+    /// Used to propagate non-det coin flips through the dependency chain.
+    measurement_deps: Vec<Option<(Vec<usize>, bool)>>,
+
+    /// Detector definitions for dual-output mode.
+    /// Each entry is a list of absolute measurement indices to XOR.
+    detector_records_abs: Vec<Vec<usize>>,
+
+    /// Output mode this sampler was built for.
+    mode: OutputMode,
+
+    /// Total number of output channels (measurements or detectors).
+    num_outputs: usize,
+
+    /// Total number of outputs in the DEM `L<n>` namespace.
+    num_dem_outputs: usize,
+
+    /// Optional labels for output channels.
+    labels: SamplerLabels,
+
+    /// Remap table for raw mode: engine index → absolute measurement index.
+    /// When set, the engine operates in compressed coordinates (only fault-reachable
+    /// measurements) and the output is expanded to the full measurement space.
+    /// None when engine coordinates == output coordinates (no expansion needed).
+    raw_remap: Option<Vec<usize>>,
+}
+
+impl DemSampler {
+    /// Build a `DemSampler` directly from an annotated circuit and noise config.
+    ///
+    /// This is the simplest way to go from circuit to sampler. It:
+    /// 1. Builds a raw-measurement influence map via `DagFaultAnalyzer`
+    /// 2. Extracts detector, observable, and Pauli check annotations from the circuit
+    /// 3. Applies the noise configuration
+    /// 4. Returns a ready-to-sample `DemSampler`
+    ///
+    /// For circuits with Pauli check annotations, this also builds
+    /// the influence map with those checks via `InfluenceBuilder`.
+    ///
+    /// # Errors
+    ///
+    /// Returns [`DetectorValidationError`] if any detector references a
+    /// non-deterministic measurement or the detectors are linearly dependent.
+    ///
+    /// # Example
+    ///
+    /// ```
+    /// use rand::SeedableRng;
+    /// use rand::rngs::StdRng;
+    ///
+    /// use pecos_qec::fault_tolerance::dem_builder::{DemSampler, NoiseConfig};
+    /// use pecos_quantum::DagCircuit;
+    ///
+    /// let dag = DagCircuit::new();
+    /// let noise = NoiseConfig::uniform(0.01);
+    /// let sampler = DemSampler::from_circuit(&dag, &noise).unwrap();
+    ///
+    /// let mut rng = StdRng::seed_from_u64(123);
+    /// let (det, obs) = sampler.sample(&mut rng);
+    /// assert!(det.is_empty());
+    /// assert!(obs.is_empty());
+    /// ```
+    /// Build a sampler from a `TickCircuit` and noise parameters.
+    ///
+    /// Converts to `DagCircuit` internally. Returns detector-mode sampler.
+    pub fn from_tick_circuit(
+        circuit: &pecos_quantum::TickCircuit,
+        noise: &super::types::NoiseConfig,
+    ) -> Result<Self, DetectorValidationError> {
+        let dag = pecos_quantum::DagCircuit::from(circuit);
+        Self::from_circuit(&dag, noise)
+    }
+
+    /// Build a sampler from a `DagCircuit` and noise parameters.
+    ///
+    /// # Errors
+    ///
+    /// Returns [`DetectorValidationError`] when detector metadata is invalid
+    /// for the circuit's measurement record.
+    pub fn from_circuit(
+        circuit: &pecos_quantum::DagCircuit,
+        noise: &super::types::NoiseConfig,
+    ) -> Result<Self, DetectorValidationError> {
+        // Build the DetectorErrorModel via DemBuilder (single code path for
+        // DEM computation), then convert to sampler.
+        use super::builder::DemBuilder;
+        use crate::fault_tolerance::influence_builder::InfluenceBuilder;
+        use crate::fault_tolerance::propagator::DagFaultAnalyzer;
+
+        let mut influence_map = DagFaultAnalyzer::new(circuit).build_influence_map();
+        let annotation_map = InfluenceBuilder::new(circuit)
+            .with_circuit_annotations(circuit)
+            .build();
+        influence_map.merge_dem_outputs_from(&annotation_map);
+
+        // Extract metadata before building (avoids ownership issues with builder methods)
+        let det_json = {
+            use pecos_num::graph::Attribute;
+            circuit.get_attr("detectors").and_then(|a| {
+                if let Attribute::String(s) = a {
+                    Some(s.clone())
+                } else {
+                    None
+                }
+            })
+        };
+        let observables_json = {
+            use pecos_num::graph::Attribute;
+            circuit.get_attr("observables").and_then(|a| {
+                if let Attribute::String(s) = a {
+                    Some(s.clone())
+                } else {
+                    None
+                }
+            })
+        };
+        let num_meas = {
+            use pecos_num::graph::Attribute;
+            circuit.get_attr("num_measurements").and_then(|a| {
+                if let Attribute::String(s) = a {
+                    s.parse::<usize>().ok()
+                } else {
+                    None
+                }
+            })
+        };
+
+        // Build DemBuilder, applying detector/DEM-output JSON if available.
+        // with_detectors_json/with_observables_json consume self, so we
+        // chain them carefully.
+        let builder = DemBuilder::new(&influence_map).with_noise_config(noise.clone());
+
+        let builder = if let Some(ref dj) = det_json {
+            builder.with_detectors_json(dj).unwrap_or_else(|_| {
+                DemBuilder::new(&influence_map).with_noise_config(noise.clone())
+            })
+        } else {
+            builder
+        };
+
+        let builder = if let Some(ref oj) = observables_json {
+            builder.with_observables_json(oj).unwrap_or_else(|_| {
+                DemBuilder::new(&influence_map).with_noise_config(noise.clone())
+            })
+        } else {
+            builder
+        };
+
+        let builder = if let Some(n) = num_meas {
+            builder.with_num_measurements(n)
+        } else {
+            builder
+        };
+
+        let dem = builder.build();
+        Ok(Self::from_detector_error_model(&dem))
+    }
+
+    /// Wrap a raw [`SamplingEngine`] as a detector-mode `DemSampler`.
+    ///
+    /// Used when the engine was constructed externally (e.g., from
+    /// [`ParsedDem::to_dem_sampler`]).
+    #[must_use]
+    /// Create a `DemSampler` from a pre-built `SamplingEngine`.
+    pub fn from_engine(engine: SamplingEngine) -> Self {
+        let num_outputs = engine.num_detectors();
+        let num_dem_outputs = engine.num_dem_outputs();
+        Self {
+            inner: engine,
+            non_det_mask: Vec::new(),
+            detector_records_abs: Vec::new(),
+            mode: OutputMode::DetectorEvents,
+            num_outputs,
+            num_dem_outputs,
+            labels: SamplerLabels::default(),
+            raw_remap: None,
+            measurement_deps: Vec::new(),
+        }
+    }
+
+    /// Build a detector-event sampler from a [`DetectorErrorModel`], preserving
+    /// PECOS metadata for observables and tracked Paulis.
+    #[must_use]
+    pub fn from_detector_error_model(dem: &super::types::DetectorErrorModel) -> Self {
+        let (mechanisms, _coords) = dem.to_mechanisms();
+        let engine =
+            SamplingEngine::from_mechanisms(mechanisms, dem.num_detectors(), dem.num_dem_outputs());
+        let mut sampler = Self::from_engine(engine);
+        sampler.labels.dem_outputs = dem_outputs_by_id(dem.dem_outputs(), dem.num_dem_outputs());
+        sampler.labels.dem_output_labels = labels_from_dem_outputs(&sampler.labels.dem_outputs);
+        sampler.labels.tracked_paulis =
+            dem_outputs_by_id(dem.tracked_paulis(), dem.num_tracked_paulis());
+        sampler.labels.tracked_pauli_labels =
+            labels_from_dem_outputs(&sampler.labels.tracked_paulis);
+        sampler
+    }
+
+    /// Attach observable and tracked-Pauli metadata to an existing sampler.
+    ///
+    /// This is useful for parser paths where the sampling engine projects to
+    /// detector/observable columns but the original PECOS DEM still declared
+    /// tracked Paulis in a separate ID space.
+    #[must_use]
+    pub fn with_dem_output_metadata(
+        mut self,
+        dem_outputs: Vec<Option<DemOutput>>,
+        tracked_paulis: Vec<Option<DemOutput>>,
+    ) -> Self {
+        self.labels.dem_outputs = dem_outputs;
+        self.labels.dem_output_labels = labels_from_dem_outputs(&self.labels.dem_outputs);
+        self.labels.tracked_paulis = tracked_paulis;
+        self.labels.tracked_pauli_labels = labels_from_dem_outputs(&self.labels.tracked_paulis);
+        self
+    }
+
+    /// Reconstruct a detector error model from the compiled mechanism table.
+    ///
+    /// The returned model contains mechanism probabilities and effects. Higher
+    /// level wrappers that own detector / observable definitions should add
+    /// those declarations to preserve metadata in serialized text.
+    #[must_use]
+    pub fn to_detector_error_model(&self) -> super::types::DetectorErrorModel {
+        self.inner.to_detector_error_model()
+    }
+
+    /// Create a `DemSampler` directly from an influence map with per-location
+    /// probabilities (raw measurement mode).
+    #[must_use]
+    pub fn from_influence_map(
+        influence_map: &DagFaultInfluenceMap,
+        per_location_probs: &[f64],
+    ) -> Self {
+        let default_noise = super::NoiseConfig::default();
+        let inner =
+            SamplingEngine::from_influence_map(influence_map, per_location_probs, &default_noise);
+        let num_outputs = inner.num_detectors();
+        let num_dem_outputs = inner.num_dem_outputs();
+        let mut labels = SamplerLabels::default();
+        labels.dem_outputs = dem_outputs_from_influence_map(influence_map, num_dem_outputs);
+        labels.dem_output_labels = labels_from_dem_outputs(&labels.dem_outputs);
+        labels.tracked_paulis = tracked_paulis_from_influence_map(influence_map);
+        labels.tracked_pauli_labels = labels_from_dem_outputs(&labels.tracked_paulis);
+        Self {
+            inner,
+            non_det_mask: Vec::new(),
+            detector_records_abs: Vec::new(),
+            mode: OutputMode::RawMeasurements,
+            num_outputs,
+            num_dem_outputs,
+            labels,
+            raw_remap: None,
+            measurement_deps: Vec::new(),
+        }
+    }
+
+    /// Number of output channels (measurements in raw mode, detectors in detector mode).
+    #[must_use]
+    pub fn num_outputs(&self) -> usize {
+        self.num_outputs
+    }
+
+    /// Number of detectors (alias for [`num_outputs`] in detector mode).
+    #[must_use]
+    pub fn num_detectors(&self) -> usize {
+        self.num_outputs
+    }
+
+    /// Number of observables.
+    #[must_use]
+    pub fn num_observables(&self) -> usize {
+        self.num_dem_outputs
+    }
+
+    /// Number of DEM `L<n>` output channels.
+    #[must_use]
+    pub fn num_dem_outputs(&self) -> usize {
+        self.num_dem_outputs
+    }
+
+    /// Number of tracked Paulis.
+    #[must_use]
+    pub fn num_tracked_paulis(&self) -> usize {
+        self.labels.tracked_paulis.len()
+    }
+
+    /// Standard observable `L<n>` IDs selected from this sampler.
+    #[must_use]
+    pub fn observable_ids(&self) -> Vec<usize> {
+        (0..self.num_dem_outputs).collect()
+    }
+
+    /// PECOS tracked-Pauli IDs selected from this sampler.
+    ///
+    /// Decoder-facing DEM samplers do not directly evaluate tracked Paulis:
+    /// tracked Paulis are preserved in metadata and in PECOS DEM fault
+    /// effects, but the sampled bit columns are detectors plus standard
+    /// observable `L<n>` outputs only.
+    ///
+    /// # Errors
+    ///
+    /// Returns [`TrackedPauliSamplingError`] when tracked Paulis are
+    /// present and the caller is asking for a direct sampled tracked-Pauli
+    /// output space.
+    pub fn tracked_pauli_ids(&self) -> Result<Vec<usize>, TrackedPauliSamplingError> {
+        self.ensure_tracked_pauli_sampling_supported()?;
+        Ok(Vec::new())
+    }
+
+    /// Sample direct tracked-Pauli flips.
+    ///
+    /// This returns an empty vector when the sampler carries no tracked
+    /// Paulis. If tracked Paulis are present, this backend fails
+    /// explicitly instead of returning silently empty data.
+    ///
+    /// # Errors
+    ///
+    /// Returns [`TrackedPauliSamplingError`] when tracked Paulis are
+    /// present because [`DemSampler`] samples detector and observable columns,
+    /// not tracked-Pauli columns.
+    pub fn sample_tracked_pauli_flips<R: Rng>(
+        &self,
+        _rng: &mut R,
+    ) -> Result<Vec<bool>, TrackedPauliSamplingError> {
+        self.ensure_tracked_pauli_sampling_supported()?;
+        Ok(Vec::new())
+    }
+
+    /// Sample direct tracked-Pauli flips for multiple shots.
+    ///
+    /// # Errors
+    ///
+    /// Returns [`TrackedPauliSamplingError`] when tracked Paulis are
+    /// present for the same reason as [`Self::sample_tracked_pauli_flips`].
+    pub fn sample_tracked_pauli_batch<R: Rng>(
+        &self,
+        num_shots: usize,
+        _rng: &mut R,
+    ) -> Result<Vec<Vec<bool>>, TrackedPauliSamplingError> {
+        self.ensure_tracked_pauli_sampling_supported()?;
+        Ok(vec![Vec::new(); num_shots])
+    }
+
+    fn ensure_tracked_pauli_sampling_supported(&self) -> Result<(), TrackedPauliSamplingError> {
+        let num_tracked_paulis = self.num_tracked_paulis();
+        if num_tracked_paulis == 0 {
+            Ok(())
+        } else {
+            Err(TrackedPauliSamplingError::new(
+                "DemSampler",
+                num_tracked_paulis,
+            ))
+        }
+    }
+
+    /// Bit mask selecting observable outputs.
+    ///
+    /// Existing decoder APIs use `u64` observable masks, so outputs with index
+    /// \>= 64 are not representable here and are ignored consistently with the
+    /// existing mask-based paths.
+    #[must_use]
+    pub fn observable_dem_output_mask(&self) -> u64 {
+        self.observable_ids()
+            .into_iter()
+            .filter(|&idx| idx < u64::BITS as usize)
+            .fold(0u64, |acc, idx| acc | (1u64 << idx))
+    }
+
+    /// Converts a sampled DEM-output flip vector into an observable-only mask.
+    #[must_use]
+    pub fn observable_mask_from_dem_output_flips(&self, flips: &[bool]) -> u64 {
+        let observable_mask = self.observable_dem_output_mask();
+        flips
+            .iter()
+            .enumerate()
+            .filter(|(idx, flipped)| {
+                **flipped && *idx < u64::BITS as usize && (observable_mask & (1u64 << *idx)) != 0
+            })
+            .fold(0u64, |acc, (idx, _)| acc | (1u64 << idx))
+    }
+
+    /// Number of mechanisms in the sampler.
+    #[must_use]
+    pub fn num_mechanisms(&self) -> usize {
+        self.inner.num_mechanisms()
+    }
+
+    /// Average mechanism firing probability.
+    #[must_use]
+    pub fn average_error_probability(&self) -> f64 {
+        self.inner.average_error_probability()
+    }
+
+    /// Maximum mechanism firing probability.
+    #[must_use]
+    pub fn max_error_probability(&self) -> f64 {
+        self.inner.max_error_probability()
+    }
+
+    /// Get the labels for this sampler's output channels.
+    #[must_use]
+    pub fn labels(&self) -> &SamplerLabels {
+        &self.labels
+    }
+
+    /// Output mode this sampler was built for.
+    #[must_use]
+    pub fn mode(&self) -> OutputMode {
+        self.mode
+    }
+
+    /// Finalize raw measurement outputs: expand coordinates, apply non-det coin
+    /// flips, and propagate deterministic dependencies.
+    ///
+    /// This is the single post-processing path for all raw-mode sampling methods.
+    fn finalize_raw_output<R: Rng>(&self, engine_outputs: Vec<bool>, rng: &mut R) -> Vec<bool> {
+        // Step 1: Expand engine output to full measurement space if remapping
+        let mut outputs = if let Some(ref remap) = self.raw_remap {
+            let mut full = vec![false; self.num_outputs];
+            for (engine_idx, &abs_idx) in remap.iter().enumerate() {
+                if engine_idx < engine_outputs.len() && abs_idx < full.len() {
+                    full[abs_idx] = engine_outputs[engine_idx];
+                }
+            }
+            full
+        } else {
+            engine_outputs
+        };
+
+        // Step 2: Add coin flips for non-deterministic measurements
+        for (i, &is_non_det) in self.non_det_mask.iter().enumerate() {
+            if is_non_det && i < outputs.len() {
+                outputs[i] ^= rng.coin_flip();
+            }
+        }
+
+        // Step 3: Propagate deterministic measurement dependencies.
+        // For m_i with deps {j, k, ...}: m_i XOR= XOR(m_j, m_k, ...) XOR flip
+        // Dependencies are always to earlier measurements (processed in order).
+        for i in 0..outputs.len().min(self.measurement_deps.len()) {
+            if let Some((ref deps, flip)) = self.measurement_deps[i] {
+                let dep_xor = deps
+                    .iter()
+                    .filter(|&&j| j < outputs.len())
+                    .fold(flip, |acc, &j| acc ^ outputs[j]);
+                outputs[i] ^= dep_xor;
+            }
+        }
+
+        outputs
+    }
+
+    /// Sample a single shot.
+    ///
+    /// Returns `(outputs, dem_output_flips)` where outputs are either raw
+    /// measurement values or detector events depending on the mode.
+    #[must_use]
+    pub fn sample<R: Rng>(&self, rng: &mut R) -> (Vec<bool>, Vec<bool>) {
+        let (engine_outputs, dem_outputs) = self.inner.sample(rng);
+
+        let outputs = if self.mode == OutputMode::RawMeasurements {
+            self.finalize_raw_output(engine_outputs, rng)
+        } else {
+            engine_outputs
+        };
+
+        (outputs, dem_outputs)
+    }
+
+    /// Sample multiple shots.
+    #[must_use]
+    pub fn sample_batch<R: Rng>(
+        &self,
+        num_shots: usize,
+        rng: &mut R,
+    ) -> (Vec<Vec<bool>>, Vec<Vec<bool>>) {
+        let (engine_batches, all_dem_outputs) = self.inner.sample_batch(num_shots, rng);
+
+        let all_outputs: Vec<Vec<bool>> = if self.mode == OutputMode::RawMeasurements {
+            engine_batches
+                .into_iter()
+                .map(|engine_out| self.finalize_raw_output(engine_out, rng))
+                .collect()
+        } else {
+            engine_batches
+        };
+
+        (all_outputs, all_dem_outputs)
+    }
+
+    /// Batch sample using geometric skip — O(fired) instead of O(all mechanisms).
+    ///
+    /// Returns columnar bit-packed data:
+    /// - detector columns: `[num_detectors][ceil(num_shots/64)]` u64 words
+    /// - `L<n>` target columns: `[num_dem_outputs][ceil(num_shots/64)]` u64 words
+    ///
+    /// Much faster than `sample_batch` at low error rates where few mechanisms fire.
+    /// Only available in detector-event mode (not raw measurement mode).
+    ///
+    /// # Panics
+    ///
+    /// Panics if the sampler is in raw measurement mode.
+    #[must_use]
+    pub fn sample_batch_geometric<R: Rng>(
+        &self,
+        num_shots: usize,
+        rng: &mut R,
+    ) -> (Vec<Vec<u64>>, Vec<Vec<u64>>) {
+        assert!(
+            self.mode != OutputMode::RawMeasurements,
+            "sample_batch_geometric() does not support raw measurement mode \
+             (requires non-det coin flips + dependency propagation per shot). \
+             Use sample_batch() instead."
+        );
+        self.inner.sample_batch_columnar_geometric(num_shots, rng)
+    }
+
+    /// Sample a single shot and return both raw measurements and detector events.
+    ///
+    /// This uses a single RNG sequence to produce both outputs consistently.
+    /// Requires the sampler to have been built in raw measurement mode with
+    /// detector definitions stored via the builder.
+    ///
+    /// Returns `None` if no detector definitions are available.
+    #[must_use]
+    pub fn sample_dual<R: Rng>(&self, rng: &mut R) -> Option<DualSampleResult> {
+        if self.detector_records_abs.is_empty() {
+            return None;
+        }
+
+        // Sample mechanism flips in raw measurement coordinates
+        let (raw_flips, dem_output_flips) = self.inner.sample(rng);
+
+        // Finalize raw measurements (expand, coin flips, dependency propagation)
+        let raw_measurements = self.finalize_raw_output(raw_flips, rng);
+
+        // Compute detector events from FINALIZED raw measurements
+        // (includes non-det coin flips and dependency propagation)
+        let detector_events: Vec<bool> = self
+            .detector_records_abs
+            .iter()
+            .map(|record| {
+                record.iter().fold(false, |acc, &idx| {
+                    acc ^ raw_measurements.get(idx).copied().unwrap_or(false)
+                })
+            })
+            .collect();
+
+        Some(DualSampleResult {
+            raw_measurements,
+            detector_events,
+            dem_output_flips,
+        })
+    }
+
+    /// Compute statistics with a user-provided RNG.
+    #[must_use]
+    pub fn sample_statistics_with_rng<R: Rng>(
+        &self,
+        num_shots: usize,
+        rng: &mut R,
+    ) -> super::dem_sampler::SamplingStatistics {
+        let observable_indices = self.observable_ids();
+        self.inner
+            .sample_statistics_with_rng_for_observable_indices(num_shots, rng, &observable_indices)
+    }
+
+    /// Compute statistics without storing individual shots.
+    ///
+    /// Delegates to [`DemSampler::sample_statistics`] which auto-selects
+    /// the fastest algorithm. Non-deterministic coin flips do NOT affect
+    /// statistics since they are independent of faults and cancel in
+    /// expectation for any well-formed detector.
+    #[must_use]
+    pub fn sample_statistics(
+        &self,
+        num_shots: usize,
+        seed: u64,
+    ) -> super::dem_sampler::SamplingStatistics {
+        let observable_indices = self.observable_ids();
+        self.inner
+            .sample_statistics_for_observable_indices(num_shots, seed, &observable_indices)
+    }
+}
+
+// ============================================================================
+// Builder
+// ============================================================================
+
+/// Builder for [`DemSampler`].
+///
+/// Constructs a sampler from a fault influence map and noise parameters.
+/// The output mode (raw measurements vs detector events) is determined by
+/// how the builder is configured.
+pub struct DemSamplerBuilder<'a> {
+    influence_map: &'a DagFaultInfluenceMap,
+    noise: NoiseConfig,
+    per_gate: Option<PerGateTypeNoise>,
+    output_mode: OutputMode,
+    detector_records: Option<Vec<Vec<i32>>>,
+    observable_records: Option<Vec<Vec<i32>>>,
+    measurement_order: Option<Vec<usize>>,
+    detector_records_abs: Option<Vec<Vec<usize>>>,
+    labels: SamplerLabels,
+}
+
+impl<'a> DemSamplerBuilder<'a> {
+    /// Create a new builder. Default mode is raw measurements.
+    #[must_use]
+    pub fn new(influence_map: &'a DagFaultInfluenceMap) -> Self {
+        Self {
+            influence_map,
+            noise: NoiseConfig::default(),
+            per_gate: None,
+            output_mode: OutputMode::RawMeasurements,
+            detector_records: None,
+            observable_records: None,
+            measurement_order: None,
+            detector_records_abs: None,
+            labels: SamplerLabels::default(),
+        }
+    }
+
+    /// Set noise parameters.
+    #[must_use]
+    pub fn with_noise(mut self, p1: f64, p2: f64, p_meas: f64, p_prep: f64) -> Self {
+        self.noise = NoiseConfig::new(p1, p2, p_meas, p_prep);
+        self
+    }
+
+    /// Set noise from a `NoiseConfig` (includes `p_idle` if set).
+    #[must_use]
+    pub fn with_noise_config(mut self, config: NoiseConfig) -> Self {
+        self.noise = config;
+        self
+    }
+
+    /// Set per-gate-type and optional per-qubit Pauli rates.
+    #[must_use]
+    pub fn with_per_gate_noise(mut self, config: PerGateTypeNoise) -> Self {
+        self.noise = config.base.clone();
+        self.per_gate = Some(config);
+        self
+    }
+
+    /// Set uniform noise (same probability for all gate types, including idle).
+    #[must_use]
+    pub fn with_uniform_noise(self, p: f64) -> Self {
+        let mut s = self.with_noise(p, p, p, p);
+        s.noise.p_idle = p;
+        s
+    }
+
+    /// Set idle gate noise rate.
+    #[must_use]
+    pub fn with_idle_noise(mut self, p_idle: f64) -> Self {
+        self.noise.p_idle = p_idle;
+        self
+    }
+
+    /// Request raw measurement output (default).
+    ///
+    /// Each deterministic measurement is its own output channel. Non-deterministic
+    /// measurements get independent coin flips.
+    #[must_use]
+    pub fn raw_measurements(mut self) -> Self {
+        self.output_mode = OutputMode::RawMeasurements;
+        self.detector_records = None;
+        self.observable_records = None;
+        self
+    }
+
+    /// Request detector-event output with the given detector/DEM output definitions.
+    ///
+    /// Detector records use DEM-style negative offsets: `[-1]` means "the last
+    /// measurement", `[-3, -1]` means "XOR of the last and third-to-last."
+    #[must_use]
+    pub fn with_detectors(
+        mut self,
+        detector_records: Vec<Vec<i32>>,
+        observable_records: Vec<Vec<i32>>,
+    ) -> Self {
+        self.output_mode = OutputMode::DetectorEvents;
+        self.detector_records = Some(detector_records);
+        self.observable_records = Some(observable_records);
+        self
+    }
+
+    /// Set detector records directly (without observables).
+    #[must_use]
+    pub fn with_detector_records(mut self, records: Vec<Vec<i32>>) -> Self {
+        self.output_mode = OutputMode::DetectorEvents;
+        self.detector_records = Some(records);
+        if self.observable_records.is_none() {
+            self.observable_records = Some(Vec::new());
+        }
+        self
+    }
+
+    /// Set observable definitions directly.
+    #[must_use]
+    pub fn with_observable_records(mut self, records: Vec<Vec<i32>>) -> Self {
+        self.observable_records = Some(records);
+        self
+    }
+
+    /// Set detector definitions from JSON.
+    ///
+    /// Format: `[{"id": 0, "records": [-1, -5]}, ...]`
+    ///
+    /// # Errors
+    /// Returns an error if the JSON is malformed.
+    pub fn with_detectors_json(self, json: &str) -> Result<Self, String> {
+        let records = parse_records_json(json);
+        Ok(self.with_detector_records(records))
+    }
+
+    /// Set observable definitions from JSON.
+    ///
+    /// Format: `[{"id": 0, "records": [-1, -3, -5]}, ...]`
+    ///
+    /// # Errors
+    /// Returns an error if the JSON is malformed.
+    pub fn with_observables_json(self, json: &str) -> Result<Self, String> {
+        let records = parse_records_json(json);
+        Ok(self.with_observable_records(records))
+    }
+
+    /// Enable dual output (raw measurements + detector events from same sample).
+    ///
+    /// When building in raw measurement mode, stores the detector definitions
+    /// so that [`DemSampler::sample_dual`] can compute both outputs.
+    /// The records use absolute measurement indices (not negative offsets).
+    #[must_use]
+    pub fn with_dual_output(mut self, detector_records_abs: Vec<Vec<usize>>) -> Self {
+        self.detector_records_abs = Some(detector_records_abs);
+        self
+    }
+
+    /// Extract detector, observable, and tracked-Pauli definitions from a [`DagCircuit`]'s
+    /// in-circuit annotations.
+    ///
+    /// Extract annotations from a [`DagCircuit`] and configure the sampler.
+    ///
+    /// Detector annotations are mapped to auto-detected detector indices.
+    /// Observables are converted to measurement-record outputs. Tracked
+    /// Paulis remain unmeasured Pauli annotations and are carried
+    /// through PECOS metadata only.
+    #[must_use]
+    pub fn with_circuit_annotations(mut self, circuit: &pecos_quantum::DagCircuit) -> Self {
+        use pecos_quantum::AnnotationKind;
+
+        let mut node_to_meas_idx: std::collections::BTreeMap<usize, usize> =
+            std::collections::BTreeMap::new();
+        for (meas_idx, &(node, _qubit, _basis)) in
+            self.influence_map.measurements.iter().enumerate()
+        {
+            node_to_meas_idx.entry(node).or_insert(meas_idx);
+        }
+
+        let detectors: Vec<&pecos_quantum::PauliAnnotation> = circuit.detectors().collect();
+        let observables: Vec<&pecos_quantum::PauliAnnotation> = circuit.observables().collect();
+
+        // Map user-defined detector annotations to auto-detected detector indices
+        if !detectors.is_empty() {
+            // For each IM measurement index, find which auto-detector contains it
+            let mut meas_idx_to_auto_det: Vec<Option<usize>> =
+                vec![None; self.influence_map.measurements.len()];
+            for (det_idx, det) in self.influence_map.detectors.iter().enumerate() {
+                for meas_id in &det.measurements {
+                    for (im_idx, &(_node, qubit, basis)) in
+                        self.influence_map.measurements.iter().enumerate()
+                    {
+                        if qubit == meas_id.qubit
+                            && basis == meas_id.basis
+                            && meas_idx_to_auto_det[im_idx].is_none()
+                        {
+                            meas_idx_to_auto_det[im_idx] = Some(det_idx);
+                            break;
+                        }
+                    }
+                }
+            }
+
+            // Map each user detector: measurement_nodes → IM meas index → auto-detector index
+            let det_records_abs: Vec<Vec<usize>> = detectors
+                .iter()
+                .map(|ann| {
+                    if let AnnotationKind::Detector {
+                        measurement_nodes, ..
+                    } = &ann.kind
+                    {
+                        measurement_nodes
+                            .iter()
+                            .filter_map(|&node| {
+                                let im_idx = node_to_meas_idx.get(&node)?;
+                                meas_idx_to_auto_det[*im_idx]
+                            })
+                            .collect()
+                    } else {
+                        Vec::new()
+                    }
+                })
+                .collect();
+
+            self.labels.dual_detectors = detectors.iter().map(|a| a.label.clone()).collect();
+            self.detector_records_abs = Some(det_records_abs);
+        }
+
+        if !observables.is_empty() && self.observable_records.is_none() {
+            let records = if let Ok(num_measurements) =
+                i32::try_from(self.influence_map.measurements.len())
+            {
+                observables
+                    .iter()
+                    .map(|ann| {
+                        if let AnnotationKind::Observable { measurement_nodes } = &ann.kind {
+                            measurement_nodes
+                                .iter()
+                                .filter_map(|node| node_to_meas_idx.get(node).copied())
+                                .filter_map(|meas_idx| {
+                                    i32::try_from(meas_idx)
+                                        .ok()
+                                        .map(|meas_idx| meas_idx - num_measurements)
+                                })
+                                .collect()
+                        } else {
+                            Vec::new()
+                        }
+                    })
+                    .collect()
+            } else {
+                vec![Vec::new(); observables.len()]
+            };
+            self.observable_records = Some(records);
+        }
+
+        let observable_labels: Vec<Option<String>> =
+            observables.iter().map(|a| a.label.clone()).collect();
+        if !observable_labels.is_empty() {
+            self.labels.dem_output_labels = observable_labels;
+        }
+
+        let tracked_pauli_labels: Vec<Option<String>> = circuit
+            .annotations()
+            .iter()
+            .filter(|a| matches!(a.kind, AnnotationKind::TrackedPauli))
+            .map(|a| a.label.clone())
+            .collect();
+        if !tracked_pauli_labels.is_empty() {
+            self.labels.tracked_pauli_labels = tracked_pauli_labels;
+        }
+
+        self
+    }
+
+    /// Set the measurement order for legacy circuits without `MeasId` on gates.
+    ///
+    /// **Not needed for circuits built with `TickCircuit.mz()`** — the `MeasId`
+    /// values on gates ensure correct ordering automatically.
+    #[must_use]
+    pub fn with_measurement_order(mut self, order: Vec<usize>) -> Self {
+        self.measurement_order = Some(order);
+        self
+    }
+
+    /// Build the sampler.
+    ///
+    /// # Errors
+    ///
+    /// Returns an error if detector definitions reference non-deterministic
+    /// measurements or are not linearly independent over `Z_2`.
+    pub fn build(self) -> Result<DemSampler, DetectorValidationError> {
+        match self.output_mode {
+            OutputMode::RawMeasurements => Ok(self.build_raw()),
+            OutputMode::DetectorEvents => self.build_detector(),
+        }
+    }
+
+    /// Build in raw measurement mode.
+    ///
+    /// Mechanism table is in measurement coordinates. Non-deterministic
+    /// measurements are identified and marked for coin-flip output.
+    fn build_raw(self) -> DemSampler {
+        let num_measurements = self.influence_map.measurements.len();
+
+        // Build per-location probabilities from gate-type noise
+        let per_location_probs = self.compute_per_location_probs();
+
+        // Build mechanism table in raw measurement coordinates
+        let inner = SamplingEngine::from_influence_map(
+            self.influence_map,
+            &per_location_probs,
+            &self.noise,
+        );
+
+        // Identify non-deterministic measurements.
+        // A measurement is deterministic if the influence builder found it
+        // as part of a detector definition. If it's NOT in any detector,
+        // it might be non-deterministic (first-round stabilizer, data readout).
+        //
+        // Conservative approach: mark a measurement as non-deterministic if
+        // it doesn't appear in any detector definition. This isn't perfect
+        // (some deterministic measurements might not be in detectors) but
+        // is safe — extra coin flips on deterministic measurements that
+        // happen to not be in detectors just add noise.
+        let mut in_detector = vec![false; num_measurements];
+        for det in &self.influence_map.detectors {
+            for m in &det.measurements {
+                // Find measurement index by matching qubit + tick
+                for (idx, &(_node, qubit, _basis)) in
+                    self.influence_map.measurements.iter().enumerate()
+                {
+                    if qubit == m.qubit {
+                        in_detector[idx] = true;
+                    }
+                }
+            }
+        }
+        let non_det_mask: Vec<bool> = in_detector.iter().map(|&in_det| !in_det).collect();
+
+        let num_dem_outputs = inner.num_dem_outputs();
+        let dem_outputs = dem_outputs_from_influence_map(self.influence_map, num_dem_outputs);
+        let tracked_paulis = tracked_paulis_from_influence_map(self.influence_map);
+
+        DemSampler {
+            inner,
+            non_det_mask,
+            detector_records_abs: self.detector_records_abs.unwrap_or_default(),
+            mode: OutputMode::RawMeasurements,
+            num_outputs: num_measurements,
+            num_dem_outputs,
+            labels: merge_dem_output_metadata(self.labels, dem_outputs, tracked_paulis),
+            raw_remap: None,
+            measurement_deps: Vec::new(), // No expansion needed (engine covers all measurements)
+        }
+    }
+
+    /// Build in detector-event mode.
+    ///
+    /// Validates detector definitions, then uses `DemSamplerBuilder` to build
+    /// the mechanism table in detector coordinates.
+    fn build_detector(self) -> Result<DemSampler, DetectorValidationError> {
+        use super::dem_sampler::SamplingEngineBuilder;
+
+        let num_measurements = self.influence_map.measurements.len();
+
+        // Validate: check which measurements are deterministic (before partial move)
+        let deterministic = self.compute_deterministic_mask();
+
+        let detector_records = self.detector_records.unwrap_or_default();
+        let observable_records = self.observable_records.unwrap_or_default();
+        let num_detectors = detector_records.len();
+
+        // Check that all detector records reference deterministic measurements
+        for (det_id, records) in detector_records.iter().enumerate() {
+            for &offset in records {
+                // Resolve offset to an absolute index: negative offsets count
+                // backward from the end of the measurement list.
+                #[allow(clippy::cast_sign_loss)] // offset is non-negative in else branch
+                let abs_idx = if offset < 0 {
+                    let neg = offset.unsigned_abs() as usize;
+                    if neg > num_measurements {
+                        continue;
+                    }
+                    num_measurements - neg
+                } else {
+                    offset as usize
+                };
+
+                if abs_idx < num_measurements && !deterministic[abs_idx] {
+                    return Err(DetectorValidationError::NonDeterministicReference {
+                        detector_id: det_id,
+                        measurement_idx: abs_idx,
+                    });
+                }
+            }
+        }
+
+        // Check linear independence via Gaussian elimination over Z_2
+        if num_detectors > 0 {
+            let rank = z2_rank_from_records(&detector_records, num_measurements);
+            if rank < num_detectors {
+                return Err(DetectorValidationError::LinearlyDependent {
+                    rank,
+                    num_detectors,
+                });
+            }
+        }
+
+        let mut builder = SamplingEngineBuilder::new(self.influence_map)
+            .with_noise(
+                self.noise.p1,
+                self.noise.p2,
+                self.noise.p_meas,
+                self.noise.p_prep,
+            )
+            .with_detector_records(detector_records)
+            .with_observable_records(observable_records.clone());
+
+        if let Some(per_gate) = self.per_gate {
+            builder = builder.with_per_gate_noise(per_gate);
+        } else if self.noise.uses_dedicated_idle_noise() {
+            builder = builder.with_idle_noise_config(self.noise.clone());
+        }
+
+        if let Some(order) = self.measurement_order {
+            builder = builder.with_measurement_order(order);
+        }
+
+        let inner = builder.build();
+        let num_dem_outputs = inner.num_dem_outputs();
+        let dem_outputs =
+            dem_outputs_from_records(self.influence_map, &observable_records, num_dem_outputs);
+        let tracked_paulis = tracked_paulis_from_influence_map(self.influence_map);
+
+        Ok(DemSampler {
+            inner,
+            non_det_mask: Vec::new(),
+            detector_records_abs: Vec::new(),
+            mode: OutputMode::DetectorEvents,
+            num_outputs: num_detectors,
+            num_dem_outputs,
+            labels: merge_dem_output_metadata(self.labels, dem_outputs, tracked_paulis),
+            raw_remap: None,
+            measurement_deps: Vec::new(),
+        })
+    }
+
+    /// Compute which measurements are deterministic.
+    ///
+    /// A measurement is considered deterministic if it appears in at least
+    /// one detector definition in the influence map.
+    fn compute_deterministic_mask(&self) -> Vec<bool> {
+        let num_measurements = self.influence_map.measurements.len();
+        let mut deterministic = vec![false; num_measurements];
+
+        for det in &self.influence_map.detectors {
+            for m in &det.measurements {
+                for (idx, &(_node, qubit, _basis)) in
+                    self.influence_map.measurements.iter().enumerate()
+                {
+                    if qubit == m.qubit {
+                        deterministic[idx] = true;
+                    }
+                }
+            }
+        }
+
+        deterministic
+    }
+
+    /// Compute per-location error probabilities from gate-type noise config.
+    ///
+    /// Returns the total error probability per location. For T1/T2 idle noise,
+    /// this is the sum of the biased Pauli probabilities.
+    fn compute_per_location_probs(&self) -> Vec<f64> {
+        compute_location_probs_from_noise(&self.influence_map.locations, &self.noise)
+    }
+}
+
+/// Compute per-location total error probabilities from noise config.
+///
+/// For T1/T2 idle noise, returns the sum of biased Pauli probabilities.
+/// For all other gates, returns the gate-type probability.
+pub(crate) fn compute_location_probs_from_noise(
+    locations: &[super::super::propagator::dag::DagSpacetimeLocation],
+    noise: &NoiseConfig,
+) -> Vec<f64> {
+    locations
+        .iter()
+        .map(|loc| {
+            #[allow(clippy::match_same_arms)]
+            match loc.gate_type {
+                GateType::PZ | GateType::QAlloc => noise.p_prep,
+                GateType::MZ | GateType::MeasureFree => noise.p_meas,
+                GateType::CX
+                | GateType::CZ
+                | GateType::CY
+                | GateType::SZZ
+                | GateType::SZZdg
+                | GateType::SXX
+                | GateType::SXXdg
+                | GateType::SYY
+                | GateType::SYYdg
+                | GateType::SWAP
+                | GateType::RXX
+                | GateType::RYY
+                | GateType::RZZ => noise.p2,
+                GateType::Idle => {
+                    if noise.uses_dedicated_idle_noise() {
+                        // Duration values are small integers; precision loss is not a concern.
+                        #[allow(clippy::cast_precision_loss)]
+                        let duration = loc.idle_duration.max(1) as f64;
+                        noise.idle_pauli_probs(duration).total()
+                    } else {
+                        0.0
+                    }
+                }
+                _ => noise.p1,
+            }
+        })
+        .collect()
+}
+
+/// Get the per-qubit error probability for a gate fault location.
+pub(crate) fn gate_location_prob_from_locations(
+    loc: &super::super::propagator::dag::GateFaultLocation<'_>,
+    loc_probs: &[f64],
+    all_locations: &[super::super::propagator::dag::DagSpacetimeLocation],
+) -> f64 {
+    for (i, l) in all_locations.iter().enumerate() {
+        if l.node == loc.node && l.before == loc.before {
+            return loc_probs[i];
+        }
+    }
+    0.0
+}
+
+/// Parse detector or observable definitions from JSON.
+///
+/// Run noiseless symbolic simulation on a `TickCircuit` to identify non-deterministic measurements.
+///
+/// Returns a Vec<bool> where true = non-deterministic (needs coin flip).
+/// Uses `SymbolicSparseStab` which tracks measurement determinism symbolically.
+/// Run noiseless symbolic simulation to identify non-deterministic measurements
+/// and their dependency structure.
+///
+/// Returns:
+/// - `Vec<bool>`: non-det mask (true = needs coin flip)
+/// - `Vec<Option<(Vec<usize>, bool)>>`: per-measurement dependencies
+///   (Some((deps, flip)) for deterministic measurements, None for non-det)
+///
+/// Only supports the Clifford gate subset. Returns error for unsupported gates.
+fn parse_records_json(json: &str) -> Vec<Vec<i32>> {
+    let json = json.trim();
+    if json.is_empty() || json == "[]" {
+        return Vec::new();
+    }
+
+    let mut results = Vec::new();
+    let mut depth = 0;
+    let mut start = None;
+
+    for (i, c) in json.char_indices() {
+        match c {
+            '{' => {
+                if depth == 1 {
+                    start = Some(i);
+                }
+                depth += 1;
+            }
+            '}' => {
+                depth -= 1;
+                if depth == 1 {
+                    if let Some(s) = start {
+                        let obj_str = &json[s..i + c.len_utf8()];
+                        results.push(extract_records_array(obj_str));
+                    }
+                    start = None;
+                }
+            }
+            '[' if depth == 0 => depth = 1,
+            ']' if depth == 1 => depth = 0,
+            _ => {}
+        }
+    }
+
+    results
+}
+
+/// Extract measurement record indices from a JSON object string.
+///
+/// Prefers `"meas_ids"` (absolute `MeasId` IDs) when available.
+/// Also accepts `"records"` for DEM-style negative offsets.
+fn extract_records_array(json: &str) -> Vec<i32> {
+    // Prefer meas_ids (absolute, stable IDs from MeasId)
+    if let Some(pos) = json.find("\"meas_ids\"") {
+        let rest = &json[pos..];
+        if let (Some(arr_start), Some(arr_end)) = (rest.find('['), rest.find(']'))
+            && arr_start < arr_end
+        {
+            let arr_str = &rest[arr_start + 1..arr_end];
+            let ids: Vec<i32> = arr_str
+                .split(',')
+                .filter_map(|s| s.trim().parse::<i32>().ok())
+                .collect();
+            if !ids.is_empty() {
+                // Convert absolute MeasId IDs to negative offsets:
+                // not needed — the DemBuilder resolves negative offsets against
+                // num_measurements. With absolute IDs, we store them as positive
+                // values and handle them in the DemBuilder's build_measurement_mappings.
+                //
+                // For now, keep the negative-offset convention internally but
+                // convert: absolute ID i becomes offset -(num_measurements - i).
+                // We don't know num_measurements here, so return the absolute IDs
+                // as positive i32. The DemBuilder recognizes positive values as
+                // absolute MeasId indices.
+                return ids;
+            }
+        }
+    }
+
+    // Fallback: "records" with negative offsets
+    if let Some(pos) = json.find("\"records\"") {
+        let rest = &json[pos..];
+        if let (Some(arr_start), Some(arr_end)) = (rest.find('['), rest.find(']'))
+            && arr_start < arr_end
+        {
+            let arr_str = &rest[arr_start + 1..arr_end];
+            return arr_str
+                .split(',')
+                .filter_map(|s| s.trim().parse::<i32>().ok())
+                .collect();
+        }
+    }
+    Vec::new()
+}
+
+#[cfg(test)]
+mod tests {
+    use super::*;
+    use crate::fault_tolerance::InfluenceBuilder;
+    use pecos_quantum::DagCircuit;
+    use pecos_random::PecosRng;
+
+    fn repetition_code(rounds: usize) -> DagCircuit {
+        let mut dag = DagCircuit::new();
+        for _ in 0..rounds {
+            dag.pz(&[3]);
+            dag.pz(&[4]);
+            dag.cx(&[(0, 3)]);
+            dag.cx(&[(1, 3)]);
+            dag.cx(&[(1, 4)]);
+            dag.cx(&[(2, 4)]);
+            dag.mz(&[3]);
+            dag.mz(&[4]);
+        }
+        dag
+    }
+
+    #[test]
+    fn raw_mode_output_length_matches_measurements() {
+        let circuit = repetition_code(2);
+        let im = InfluenceBuilder::new(&circuit).with_z(&[0, 1, 2]).build();
+
+        let sampler = DemSamplerBuilder::new(&im)
+            .with_uniform_noise(0.01)
+            .raw_measurements()
+            .build()
+            .unwrap();
+
+        let mut rng = PecosRng::seed_from_u64(42);
+        let (outputs, _obs) = sampler.sample(&mut rng);
+
+        assert_eq!(outputs.len(), im.measurements.len());
+        assert_eq!(sampler.mode(), OutputMode::RawMeasurements);
+    }
+
+    #[test]
+    fn zero_noise_raw_mode_deterministic_measurements_are_zero() {
+        let circuit = repetition_code(3);
+        let im = InfluenceBuilder::new(&circuit).with_z(&[0, 1, 2]).build();
+
+        let sampler = DemSamplerBuilder::new(&im)
+            .with_uniform_noise(0.0)
+            .raw_measurements()
+            .build()
+            .unwrap();
+
+        // With zero noise, deterministic measurement flips should all be false.
+        // Non-deterministic ones get coin flips so we can't assert on those.
+        // But the mechanism-driven part should be all-zero.
+        let stats = sampler.sample_statistics(1000, 42);
+        assert_eq!(stats.syndrome_count, 0);
+        assert_eq!(stats.logical_error_count, 0);
+    }
+
+    #[test]
+    fn raw_mode_matches_dem_sampler_from_influence_map() {
+        let circuit = repetition_code(3);
+        let im = InfluenceBuilder::new(&circuit).with_z(&[0, 1, 2]).build();
+
+        let p = 0.01;
+        let num_shots = 20_000;
+
+        // DemSampler raw mode
+        let sampler = DemSamplerBuilder::new(&im)
+            .with_uniform_noise(p)
+            .raw_measurements()
+            .build()
+            .unwrap();
+
+        let unified_stats = sampler.sample_statistics(num_shots, 42);
+
+        // DemSampler::from_influence_map (same mechanism construction)
+        let probs = vec![p; im.locations.len()];
+        let dem = DemSampler::from_influence_map(&im, &probs);
+        let dem_stats = dem.sample_statistics(num_shots, 42);
+
+        // Same seed, same mechanism construction → identical results
+        assert_eq!(unified_stats.syndrome_count, dem_stats.syndrome_count);
+        assert_eq!(
+            unified_stats.logical_error_count,
+            dem_stats.logical_error_count
+        );
+    }
+
+    #[test]
+    fn detector_mode_output_length_matches_definitions() {
+        let circuit = repetition_code(3);
+        let im = InfluenceBuilder::new(&circuit).build();
+
+        // Define 2 simple detectors (last two measurements)
+        let detector_records = vec![vec![-1i32], vec![-2]];
+        let observable_records = vec![vec![-1i32]]; // 1 observable
+
+        let sampler = DemSamplerBuilder::new(&im)
+            .with_noise(0.001, 0.01, 0.005, 0.001)
+            .with_detectors(detector_records, observable_records)
+            .build()
+            .unwrap();
+
+        let mut rng = PecosRng::seed_from_u64(42);
+        let (det_events, obs_flips) = sampler.sample(&mut rng);
+
+        assert_eq!(det_events.len(), 2);
+        assert_eq!(obs_flips.len(), 1);
+        assert_eq!(sampler.mode(), OutputMode::DetectorEvents);
+    }
+
+    #[test]
+    fn detector_mode_accepts_observable_aliases() {
+        let circuit = repetition_code(3);
+        let im = InfluenceBuilder::new(&circuit).build();
+
+        let records_sampler = DemSamplerBuilder::new(&im)
+            .with_detector_records(vec![vec![-1]])
+            .with_observable_records(vec![vec![-1]])
+            .build()
+            .unwrap();
+
+        assert_eq!(records_sampler.num_detectors(), 1);
+        assert_eq!(records_sampler.num_dem_outputs(), 1);
+        assert_eq!(records_sampler.num_observables(), 1);
+        assert_eq!(records_sampler.num_tracked_paulis(), 0);
+        assert_eq!(records_sampler.mode(), OutputMode::DetectorEvents);
+
+        let json_sampler = DemSamplerBuilder::new(&im)
+            .with_detectors_json(r#"[{"id":0,"records":[-1]}]"#)
+            .unwrap()
+            .with_observables_json(r#"[{"id":0,"records":[-1]}]"#)
+            .unwrap()
+            .build()
+            .unwrap();
+
+        assert_eq!(json_sampler.num_detectors(), 1);
+        assert_eq!(json_sampler.num_dem_outputs(), 1);
+        assert_eq!(json_sampler.num_observables(), 1);
+        assert_eq!(json_sampler.num_tracked_paulis(), 0);
+        assert_eq!(json_sampler.mode(), OutputMode::DetectorEvents);
+    }
+
+    #[test]
+    fn from_circuit_preserves_tracked_paulis() {
+        use crate::fault_tolerance::dem_builder::NoiseConfig;
+        use pecos_core::pauli::X;
+
+        let mut circuit = DagCircuit::new();
+        circuit.pz(&[0]);
+        circuit.h(&[0]);
+        circuit.tracked_pauli_labeled("x_check", X(0));
+
+        let noise = NoiseConfig::new(0.03, 0.0, 0.0, 0.0);
+        let sampler = DemSampler::from_circuit(&circuit, &noise).unwrap();
+
+        assert_eq!(sampler.num_tracked_paulis(), 1);
+        assert_eq!(sampler.num_observables(), 0);
+        assert_eq!(
+            sampler.labels().tracked_pauli_labels[0].as_deref(),
+            Some("x_check")
+        );
+        let op = sampler.labels().tracked_paulis[0].as_ref().unwrap();
+        assert_eq!(op.label.as_deref(), Some("x_check"));
+        assert_eq!(
+            op.kind,
+            Some(crate::fault_tolerance::DemOutputKind::TrackedPauli)
+        );
+        assert_eq!(op.pauli.as_ref().unwrap().to_sparse_str(), "+X0");
+    }
+
+    #[test]
+    fn detector_mode_keeps_observables_unshifted_with_tracked_paulis() {
+        use pecos_core::pauli::X;
+
+        let mut circuit = DagCircuit::new();
+        circuit.pz(&[0]);
+        circuit.h(&[0]);
+        circuit.tracked_pauli_labeled("x_check", X(0));
+        circuit.mz(&[0]);
+
+        let im = InfluenceBuilder::new(&circuit)
+            .with_circuit_annotations(&circuit)
+            .build();
+
+        let sampler = DemSamplerBuilder::new(&im)
+            .with_noise(0.03, 0.0, 0.02, 0.0)
+            .with_detectors(Vec::new(), vec![vec![-1]])
+            .build()
+            .unwrap();
+
+        assert_eq!(sampler.num_dem_outputs(), 1);
+        assert_eq!(sampler.num_observables(), 1);
+        assert_eq!(sampler.num_tracked_paulis(), 1);
+        assert_eq!(sampler.labels().dem_outputs.len(), 1);
+        assert_eq!(
+            sampler.labels().dem_outputs[0].as_ref().unwrap().kind,
+            Some(crate::fault_tolerance::DemOutputKind::Observable)
+        );
+        assert_eq!(
+            sampler.labels().tracked_paulis[0].as_ref().unwrap().kind,
+            Some(crate::fault_tolerance::DemOutputKind::TrackedPauli)
+        );
+    }
+
+    #[test]
+    fn detector_mode_does_not_double_apply_annotation_observable_records() {
+        let mut circuit = DagCircuit::new();
+        circuit.pz(&[0]);
+        let meas = circuit.mz(&[0]);
+        circuit.observable_labeled("obs0", &[meas[0]]);
+
+        let im = InfluenceBuilder::new(&circuit)
+            .with_circuit_annotations(&circuit)
+            .build();
+
+        let sampler = DemSamplerBuilder::new(&im)
+            .with_noise(0.0, 0.0, 1.0, 0.0)
+            .with_detectors(Vec::new(), vec![vec![-1]])
+            .build()
+            .unwrap();
+
+        assert_eq!(sampler.num_dem_outputs(), 1);
+        assert_eq!(sampler.num_observables(), 1);
+        assert_eq!(sampler.num_tracked_paulis(), 0);
+        assert_eq!(
+            sampler.labels().dem_outputs[0]
+                .as_ref()
+                .unwrap()
+                .label
+                .as_deref(),
+            Some("obs0")
+        );
+        assert_eq!(
+            sampler.labels().dem_outputs[0]
+                .as_ref()
+                .unwrap()
+                .records
+                .as_slice(),
+            &[-1]
+        );
+
+        let mut rng = PecosRng::seed_from_u64(42);
+        let (_detectors, observables) = sampler.sample(&mut rng);
+        assert_eq!(observables, vec![true]);
+    }
+
+    #[test]
+    fn from_detector_error_model_preserves_observable_and_tracked_pauli_split() {
+        use super::super::builder::DemBuilder;
+        use pecos_core::pauli::X;
+        use pecos_quantum::Attribute;
+
+        let mut circuit = DagCircuit::new();
+        circuit.pz(&[0]);
+        circuit.h(&[0]);
+        circuit.tracked_pauli_labeled("x_check", X(0));
+        circuit.mz(&[0]);
+        circuit.set_attr("num_measurements", Attribute::String("1".to_string()));
+        circuit.set_attr(
+            "observables",
+            Attribute::String(r#"[{"id":0,"records":[-1]}]"#.to_string()),
+        );
+
+        let dem = DemBuilder::from_circuit(&circuit, 0.03, 0.0, 0.02, 0.0);
+
+        let sampler = DemSampler::from_detector_error_model(&dem);
+
+        assert_eq!(sampler.num_dem_outputs(), 1);
+        assert_eq!(sampler.num_observables(), 1);
+        assert_eq!(sampler.num_tracked_paulis(), 1);
+        assert_eq!(
+            sampler.labels().dem_outputs[0].as_ref().unwrap().kind,
+            Some(crate::fault_tolerance::DemOutputKind::Observable)
+        );
+        assert_eq!(
+            sampler.labels().tracked_paulis[0].as_ref().unwrap().kind,
+            Some(crate::fault_tolerance::DemOutputKind::TrackedPauli)
+        );
+    }
+
+    #[test]
+    fn sampler_paths_preserve_output_split_for_noiseless_and_forced_faults() {
+        use super::super::builder::DemBuilder;
+        use super::super::types::NoiseConfig;
+        use pecos_core::pauli::X;
+        use pecos_quantum::Attribute;
+
+        fn assert_metadata(sampler: &DemSampler) {
+            assert_eq!(sampler.num_detectors(), 1);
+            assert_eq!(sampler.num_dem_outputs(), 1);
+            assert_eq!(sampler.num_observables(), 1);
+            assert_eq!(sampler.num_tracked_paulis(), 1);
+            assert_eq!(sampler.observable_ids(), vec![0]);
+            let err = sampler.tracked_pauli_ids().unwrap_err();
+            assert_eq!(err.backend(), "DemSampler");
+            assert_eq!(err.num_tracked_paulis(), 1);
+            assert!(
+                err.to_string()
+                    .contains("cannot directly sample tracked Pauli flips")
+            );
+            assert_eq!(
+                sampler.labels().dem_outputs[0]
+                    .as_ref()
+                    .unwrap()
+                    .label
+                    .as_deref(),
+                Some("obs0")
+            );
+            assert_eq!(
+                sampler.labels().tracked_paulis[0]
+                    .as_ref()
+                    .unwrap()
+                    .label
+                    .as_deref(),
+                Some("tracked_x0")
+            );
+        }
+
+        fn sample_once(sampler: &DemSampler) -> (Vec<bool>, Vec<bool>) {
+            let mut rng = PecosRng::seed_from_u64(123);
+            sampler.sample(&mut rng)
+        }
+
+        let mut circuit = DagCircuit::new();
+        circuit.pz(&[0]);
+        let meas = circuit.mz(&[0]);
+        circuit.detector_labeled("det0", &[meas[0]]);
+        circuit.observable_labeled("obs0", &[meas[0]]);
+        circuit.tracked_pauli_labeled("tracked_x0", X(0));
+        circuit.set_attr("num_measurements", Attribute::String("1".to_string()));
+        circuit.set_attr(
+            "detectors",
+            Attribute::String(r#"[{"id":0,"records":[-1],"label":"det0"}]"#.to_string()),
+        );
+        circuit.set_attr(
+            "observables",
+            Attribute::String(r#"[{"id":0,"records":[-1],"label":"obs0"}]"#.to_string()),
+        );
+
+        let noiseless = DemSampler::from_circuit(&circuit, &NoiseConfig::default()).unwrap();
+        assert_metadata(&noiseless);
+        assert_eq!(sample_once(&noiseless), (vec![false], vec![false]));
+
+        let forced_noise = NoiseConfig::new(0.0, 0.0, 1.0, 0.0);
+        let from_circuit = DemSampler::from_circuit(&circuit, &forced_noise).unwrap();
+        assert_metadata(&from_circuit);
+        assert_eq!(sample_once(&from_circuit), (vec![true], vec![true]));
+
+        let dem = DemBuilder::from_circuit(&circuit, 0.0, 0.0, 1.0, 0.0);
+        let from_dem = DemSampler::from_detector_error_model(&dem);
+        assert_metadata(&from_dem);
+        assert_eq!(sample_once(&from_dem), (vec![true], vec![true]));
+
+        let influence_map = InfluenceBuilder::new(&circuit)
+            .with_circuit_annotations(&circuit)
+            .build();
+        let from_builder = DemSamplerBuilder::new(&influence_map)
+            .with_noise(0.0, 0.0, 1.0, 0.0)
+            .with_detector_records(vec![vec![-1]])
+            .with_observable_records(vec![vec![-1]])
+            .build()
+            .unwrap();
+        assert_metadata(&from_builder);
+        assert_eq!(sample_once(&from_builder), (vec![true], vec![true]));
+    }
+
+    #[test]
+    fn sampler_xors_detectors_and_observables_while_tracked_paulis_stay_metadata() {
+        use super::super::types::{DetectorDef, DetectorErrorModel, FaultMechanism};
+        use pecos_core::pauli::Z;
+
+        let mut dem = DetectorErrorModel::new();
+        dem.add_detector(DetectorDef::new(0));
+        dem.add_observable(DemOutput::new(0).with_records([-1]).with_label("L0"));
+        dem.add_tracked_pauli(DemOutput::new(0).with_pauli(Z(3)).with_label("tracked_z3"));
+        dem.add_direct_contribution(FaultMechanism::from_unsorted([0], [0]), 1.0);
+        dem.add_direct_contribution(FaultMechanism::from_unsorted([0], []), 1.0);
+
+        let sampler = DemSampler::from_detector_error_model(&dem);
+        let mut rng = PecosRng::seed_from_u64(99);
+
+        assert_eq!(sampler.num_detectors(), 1);
+        assert_eq!(sampler.num_observables(), 1);
+        assert_eq!(sampler.num_tracked_paulis(), 1);
+        assert_eq!(
+            sampler.labels().tracked_paulis[0]
+                .as_ref()
+                .unwrap()
+                .label
+                .as_deref(),
+            Some("tracked_z3")
+        );
+        assert_eq!(sampler.sample(&mut rng), (vec![false], vec![true]));
+    }
+
+    #[test]
+    fn raw_mode_without_dem_outputs_reports_zero_dem_outputs() {
+        let mut circuit = DagCircuit::new();
+        circuit.pz(&[0]);
+        circuit.h(&[0]);
+        circuit.mz(&[0]);
+        let im = InfluenceBuilder::new(&circuit).build();
+
+        let sampler = DemSamplerBuilder::new(&im)
+            .with_uniform_noise(0.01)
+            .raw_measurements()
+            .build()
+            .unwrap();
+
+        assert_eq!(sampler.num_dem_outputs(), 0);
+        assert_eq!(sampler.num_observables(), 0);
+        assert_eq!(sampler.num_tracked_paulis(), 0);
+    }
+
+    #[test]
+    fn observable_mask_ignores_tracked_pauli_outputs() {
+        use super::super::builder::DemBuilder;
+        use pecos_core::pauli::X;
+        use pecos_quantum::Attribute;
+
+        let mut circuit = DagCircuit::new();
+        circuit.pz(&[0]);
+        circuit.h(&[0]);
+        circuit.tracked_pauli_labeled("x_check", X(0));
+        circuit.mz(&[0]);
+        circuit.set_attr("num_measurements", Attribute::String("1".to_string()));
+        circuit.set_attr(
+            "observables",
+            Attribute::String(r#"[{"id":0,"records":[-1]}]"#.to_string()),
+        );
+
+        let dem = DemBuilder::from_circuit(&circuit, 0.03, 0.0, 0.02, 0.0);
+        let sampler = DemSampler::from_detector_error_model(&dem);
+
+        assert_eq!(sampler.observable_ids(), vec![0]);
+        assert_eq!(
+            sampler
+                .tracked_pauli_ids()
+                .unwrap_err()
+                .num_tracked_paulis(),
+            1
+        );
+        assert_eq!(sampler.observable_dem_output_mask(), 1);
+        assert_eq!(sampler.observable_mask_from_dem_output_flips(&[false]), 0);
+        assert_eq!(sampler.observable_mask_from_dem_output_flips(&[true]), 1);
+    }
+
+    #[test]
+    fn tracked_pauli_direct_sampling_fails_explicitly_when_unsupported() {
+        use super::super::types::{DetectorErrorModel, FaultMechanism};
+        use pecos_core::pauli::X;
+
+        let mut dem = DetectorErrorModel::new();
+        dem.add_tracked_pauli(DemOutput::new(0).with_pauli(X(0)).with_label("tracked_x0"));
+        dem.add_direct_contribution(
+            FaultMechanism::from_unsorted_with_tracked_paulis([], [], [0]),
+            0.25,
+        );
+
+        let sampler = DemSampler::from_detector_error_model(&dem);
+        let mut rng = PecosRng::seed_from_u64(17);
+
+        let err = sampler
+            .sample_tracked_pauli_flips(&mut rng)
+            .expect_err("DemSampler should reject direct tracked-Pauli sampling");
+        assert_eq!(err.backend(), "DemSampler");
+        assert_eq!(err.num_tracked_paulis(), 1);
+        assert!(
+            err.to_string()
+                .contains("samples decoder-facing detectors and observables only")
+        );
+
+        let err = sampler
+            .sample_tracked_pauli_batch(4, &mut rng)
+            .expect_err("DemSampler should reject direct tracked-Pauli batch sampling");
+        assert_eq!(err.num_tracked_paulis(), 1);
+
+        let empty = DemSampler::from_detector_error_model(&DetectorErrorModel::new());
+        assert_eq!(
+            empty.sample_tracked_pauli_flips(&mut rng).unwrap(),
+            Vec::<bool>::new()
+        );
+        assert_eq!(
+            empty.sample_tracked_pauli_batch(3, &mut rng).unwrap(),
+            vec![Vec::<bool>::new(), Vec::new(), Vec::new()]
+        );
+    }
+
+    #[test]
+    fn high_noise_produces_nonzero_rates_both_modes() {
+        let circuit = repetition_code(2);
+        let im = InfluenceBuilder::new(&circuit).with_z(&[0, 1, 2]).build();
+
+        let p = 0.1;
+        let num_shots = 5_000;
+
+        // Raw mode
+        let raw_sampler = DemSamplerBuilder::new(&im)
+            .with_uniform_noise(p)
+            .raw_measurements()
+            .build()
+            .unwrap();
+        let raw_stats = raw_sampler.sample_statistics(num_shots, 42);
+        assert!(
+            raw_stats.syndrome_rate() > 0.05,
+            "Raw mode should detect syndromes at p=0.1"
+        );
+
+        // Detector mode with simple detectors
+        let detector_records = vec![vec![-1i32], vec![-2]];
+        let observable_records: Vec<Vec<i32>> = vec![];
+        let det_sampler = DemSamplerBuilder::new(&im)
+            .with_uniform_noise(p)
+            .with_detectors(detector_records, observable_records)
+            .build()
+            .unwrap();
+        let det_stats = det_sampler.sample_statistics(num_shots, 42);
+        assert!(
+            det_stats.syndrome_rate() > 0.05,
+            "Detector mode should detect syndromes at p=0.1"
+        );
+    }
+
+    #[test]
+    fn dual_output_returns_none_without_definitions() {
+        let circuit = repetition_code(2);
+        let im = InfluenceBuilder::new(&circuit).with_z(&[0, 1, 2]).build();
+
+        let sampler = DemSamplerBuilder::new(&im)
+            .with_uniform_noise(0.01)
+            .raw_measurements()
+            .build()
+            .unwrap();
+
+        let mut rng = PecosRng::seed_from_u64(42);
+        assert!(sampler.sample_dual(&mut rng).is_none());
+    }
+
+    #[test]
+    fn dual_output_produces_both_views() {
+        let circuit = repetition_code(3);
+        let im = InfluenceBuilder::new(&circuit).with_z(&[0, 1, 2]).build();
+
+        // Define detectors: first and second measurements
+        let det_defs = vec![vec![0usize], vec![1]];
+
+        let sampler = DemSamplerBuilder::new(&im)
+            .with_uniform_noise(0.05)
+            .raw_measurements()
+            .with_dual_output(det_defs)
+            .build()
+            .unwrap();
+
+        let mut rng = PecosRng::seed_from_u64(42);
+        let result = sampler.sample_dual(&mut rng).unwrap();
+
+        // Raw measurements should have length = num measurements
+        assert_eq!(result.raw_measurements.len(), im.measurements.len());
+        // Detector events should have length = 2 (our 2 detector defs)
+        assert_eq!(result.detector_events.len(), 2);
+    }
+
+    #[test]
+    fn dual_output_detector_events_consistent_with_raw() {
+        let circuit = repetition_code(3);
+        let im = InfluenceBuilder::new(&circuit).with_z(&[0, 1, 2]).build();
+
+        // Detector = XOR of measurements 0 and 1
+        let det_defs = vec![vec![0usize, 1]];
+
+        let sampler = DemSamplerBuilder::new(&im)
+            .with_uniform_noise(0.1)
+            .raw_measurements()
+            .with_dual_output(det_defs)
+            .build()
+            .unwrap();
+
+        // Run many shots and verify detector = raw[0] XOR raw[1]
+        let mut rng = PecosRng::seed_from_u64(42);
+        for _ in 0..100 {
+            let result = sampler.sample_dual(&mut rng).unwrap();
+            let expected_det = result.raw_measurements[0] ^ result.raw_measurements[1];
+            assert_eq!(
+                result.detector_events[0], expected_det,
+                "Detector event should equal XOR of raw measurements 0 and 1"
+            );
+        }
+    }
+}
diff --git a/crates/pecos-qec/src/fault_tolerance/dem_builder/types.rs b/crates/pecos-qec/src/fault_tolerance/dem_builder/types.rs
index a7d466064..3deda7745 100644
--- a/crates/pecos-qec/src/fault_tolerance/dem_builder/types.rs
+++ b/crates/pecos-qec/src/fault_tolerance/dem_builder/types.rs
@@ -13,20 +13,36 @@
 //! Types for Detector Error Model (DEM) generation.
 //!
 //! This module provides data structures for representing fault mechanisms,
-//! detectors, and logical observables in DEM format.
+//! detectors, observables, and PECOS tracked Paulis.
+//!
+//! # Terminology
+//!
+//! - **Detectors** are syndrome bits defined by measurement-record parity.
+//! - **Observables** are values observed through measurements. In a DEM they are
+//!   defined by measurement records and rendered as standard `L<n>` observable
+//!   outputs.
+//! - **Tracked Paulis** are not measured values and are not applied to the
+//!   simulated computation. They are Pauli operators annotated at a circuit point
+//!   (for example a logical operator, stabilizer, or other Pauli of interest);
+//!   PECOS reports whether each fault event anticommutes with, and therefore
+//!   would flip, that operator under propagation.
+//!
+//! PECOS keeps the standard `L<n>` namespace reserved for measurement-record
+//! observables only. Tracked Paulis are PECOS metadata with their own
+//! ID space, so decoders can ignore them while PECOS tools can still inspect
+//! them.
 //!
 //! # Output Formats
 //!
 //! The DEM supports two output formats:
 //!
-//! - [`DetectorErrorModel::to_string()`] - Non-decomposed format matching Stim's
-//!   `decompose_errors=False` output. Each mechanism is output once with its
-//!   combined probability.
+//! - [`DetectorErrorModel::to_string()`] - Non-decomposed format. Each
+//!   mechanism is output once with its combined probability.
 //!
-//! - [`DetectorErrorModel::to_string_decomposed()`] - Decomposed format matching
-//!   Stim's `decompose_errors=True` output. Hyperedge errors (3+ detectors) are
-//!   decomposed into graphlike components, and 2-detector mechanisms may have
-//!   multiple representations for decoder compatibility.
+//! - [`DetectorErrorModel::to_string_decomposed()`] - Decomposed format.
+//!   Hyperedge errors (3+ detectors) are decomposed into graphlike components,
+//!   and 2-detector mechanisms may have multiple representations for decoder
+//!   compatibility.
 //!
 //! Decomposed errors use the `^` separator to indicate XOR composition:
 //!
@@ -37,6 +53,7 @@
 //! This indicates an error decomposed into two parts whose XOR equals the
 //! original mechanism.
 
+use pecos_core::PauliString;
 use pecos_core::gate_type::GateType;
 use rand::RngExt;
 use smallvec::SmallVec;
@@ -45,7 +62,7 @@ use std::collections::{BTreeMap, BTreeSet};
 use std::fmt;
 use std::hash::{Hash, Hasher};
 
-use crate::fault_tolerance::propagator::Pauli;
+use crate::fault_tolerance::propagator::{DemOutputKind, DemOutputMetadata, Pauli};
 
 // ============================================================================
 // Error Source Tracking
@@ -78,12 +95,12 @@ pub enum FaultSourceType {
     YDecomposed {
         /// Detector effect of the X component (sorted detector IDs).
         x_detectors: SmallVec<[u32; 4]>,
-        /// Logical effect of the X component (sorted logical IDs).
-        x_logicals: SmallVec<[u32; 2]>,
+        /// DEM-output effect of the X component (sorted `L<n>` IDs).
+        x_dem_outputs: SmallVec<[u32; 2]>,
         /// Detector effect of the Z component (sorted detector IDs).
         z_detectors: SmallVec<[u32; 4]>,
-        /// Logical effect of the Z component (sorted logical IDs).
-        z_logicals: SmallVec<[u32; 2]>,
+        /// DEM-output effect of the Z component (sorted `L<n>` IDs).
+        z_dem_outputs: SmallVec<[u32; 2]>,
     },
 }
 
@@ -121,7 +138,7 @@ pub enum DirectSourceFamily {
 /// determining how they are output (direct vs decomposed forms).
 #[derive(Debug, Clone)]
 pub struct FaultContribution {
-    /// The detector/logical effect of this error.
+    /// The detector/DEM-output effect of this error.
     pub effect: FaultMechanism,
 
     /// Probability of this error.
@@ -319,9 +336,9 @@ impl FaultContribution {
             probability,
             source_type: FaultSourceType::YDecomposed {
                 x_detectors: x_effect.detectors.clone(),
-                x_logicals: x_effect.logicals.clone(),
+                x_dem_outputs: x_effect.dem_outputs.clone(),
                 z_detectors: z_effect.detectors.clone(),
-                z_logicals: z_effect.logicals.clone(),
+                z_dem_outputs: z_effect.dem_outputs.clone(),
             },
             location_indices: SmallVec::new(),
             paulis: SmallVec::new(),
@@ -349,9 +366,9 @@ impl FaultContribution {
             probability,
             source_type: FaultSourceType::YDecomposed {
                 x_detectors: x_effect.detectors.clone(),
-                x_logicals: x_effect.logicals.clone(),
+                x_dem_outputs: x_effect.dem_outputs.clone(),
                 z_detectors: z_effect.detectors.clone(),
-                z_logicals: z_effect.logicals.clone(),
+                z_dem_outputs: z_effect.dem_outputs.clone(),
             },
             location_indices: source.location_indices.iter().copied().collect(),
             paulis: source.paulis.iter().copied().collect(),
@@ -377,12 +394,12 @@ impl FaultContribution {
         match &self.source_type {
             FaultSourceType::YDecomposed {
                 x_detectors,
-                x_logicals,
+                x_dem_outputs,
                 z_detectors,
-                z_logicals,
+                z_dem_outputs,
             } => {
-                let x = FaultMechanism::from_sorted(x_detectors.clone(), x_logicals.clone());
-                let z = FaultMechanism::from_sorted(z_detectors.clone(), z_logicals.clone());
+                let x = FaultMechanism::from_sorted(x_detectors.clone(), x_dem_outputs.clone());
+                let z = FaultMechanism::from_sorted(z_detectors.clone(), z_dem_outputs.clone());
                 Some((x, z))
             }
             FaultSourceType::Direct | FaultSourceType::DirectOneSidedComponent => None,
@@ -399,7 +416,7 @@ impl FaultContribution {
 /// Aggregated source-tracked information for one unique effect.
 #[derive(Debug, Clone)]
 pub struct ContributionEffectSummary {
-    /// The detector/logical effect being summarized.
+    /// The detector/DEM-output effect being summarized.
     pub effect: FaultMechanism,
     /// Total number of contributing sources for this effect.
     pub num_contributions: usize,
@@ -415,7 +432,7 @@ pub struct ContributionEffectSummary {
     pub y_decomposed_probability: f64,
     /// Number of builder-marked graphlike-decomposable two-qubit sources for this effect.
     ///
-    /// This is only non-zero for 2-detector, 0-logical effects. It reflects the
+    /// This is only non-zero for 2-detector, 0-DEM-output effects. It reflects the
     /// dormant representation-diversity bookkeeping recorded by the DEM builder.
     pub graphlike_decomposable_count: u32,
 }
@@ -423,7 +440,7 @@ pub struct ContributionEffectSummary {
 /// Structured summary of how tracked contributions render before final regrouping.
 #[derive(Debug, Clone)]
 pub struct ContributionRenderSummary {
-    /// Original full detector/logical effect before rendering.
+    /// Original full detector/DEM-output effect before rendering.
     pub effect: FaultMechanism,
     /// Rendered targets string that this contribution group maps to.
     pub rendered_targets: String,
@@ -471,7 +488,7 @@ pub enum ContributionRenderStrategy {
     SourceComponents,
     /// Used recorded direct-source component targets instead of the direct edge.
     RecordedComponents,
-    /// Kept a 2-detector, 0-logical effect graphlike as-is.
+    /// Kept a 2-detector, 0-DEM-output effect graphlike as-is.
     TwoDetectorDirect,
     /// Decomposed a hyperedge using graphlike effect decomposition.
     HyperedgeGraphlike,
@@ -493,18 +510,25 @@ pub enum TwoDetectorDirectRenderPolicy {
 // Error Mechanism
 // ============================================================================
 
-/// An fault mechanism: a set of detectors and logical observables that flip together.
+/// A fault mechanism: a set of detectors and `L<n>` targets that flip together.
 ///
 /// When an error occurs, it flips a specific set of detectors and may flip
-/// logical observables. Mechanisms with the same effect are aggregated together.
+/// `L<n>` targets. Mechanisms with the same effect are aggregated together.
 ///
-/// The detectors and logicals are stored in sorted order for canonical representation.
+/// Detector and `L<n>` target indices are stored in sorted order for canonical representation.
 #[derive(Clone, Default)]
 pub struct FaultMechanism {
     /// Detector indices that flip together (sorted).
     pub detectors: SmallVec<[u32; 4]>,
-    /// Logical observable indices that flip together (sorted).
-    pub logicals: SmallVec<[u32; 2]>,
+    /// DEM `L<n>` target indices that flip together (sorted).
+    ///
+    /// New code should treat these as standard observable `L<n>` output channels.
+    pub dem_outputs: SmallVec<[u32; 2]>,
+    /// PECOS tracked-Pauli indices that flip together (sorted).
+    ///
+    /// These are rendered as `TP<n>` only in PECOS DEM text. Standard DEM text
+    /// and decoder-facing mechanism tables intentionally ignore them.
+    pub tracked_paulis: SmallVec<[u32; 2]>,
 }
 
 impl FaultMechanism {
@@ -514,36 +538,64 @@ impl FaultMechanism {
         Self::default()
     }
 
-    /// Creates a mechanism from unsorted detector and logical indices.
+    /// Creates a mechanism from unsorted detector and DEM-output indices.
     #[must_use]
     pub fn from_unsorted(
         detectors: impl IntoIterator<Item = u32>,
-        logicals: impl IntoIterator<Item = u32>,
+        dem_outputs: impl IntoIterator<Item = u32>,
+    ) -> Self {
+        Self::from_unsorted_with_tracked_paulis(detectors, dem_outputs, std::iter::empty())
+    }
+
+    /// Creates a mechanism from unsorted detector, DEM-output, and tracked-Pauli indices.
+    #[must_use]
+    pub fn from_unsorted_with_tracked_paulis(
+        detectors: impl IntoIterator<Item = u32>,
+        dem_outputs: impl IntoIterator<Item = u32>,
+        tracked_paulis: impl IntoIterator<Item = u32>,
     ) -> Self {
         let mut dets: SmallVec<[u32; 4]> = detectors.into_iter().collect();
-        let mut logs: SmallVec<[u32; 2]> = logicals.into_iter().collect();
+        let mut dem_outputs: SmallVec<[u32; 2]> = dem_outputs.into_iter().collect();
+        let mut tracked_paulis: SmallVec<[u32; 2]> = tracked_paulis.into_iter().collect();
         dets.sort_unstable();
-        logs.sort_unstable();
+        dem_outputs.sort_unstable();
+        tracked_paulis.sort_unstable();
         Self {
             detectors: dets,
-            logicals: logs,
+            dem_outputs,
+            tracked_paulis,
         }
     }
 
-    /// Creates a mechanism from pre-sorted detector and logical indices.
+    /// Creates a mechanism from pre-sorted detector and DEM-output indices.
+    #[must_use]
+    pub fn from_sorted(detectors: SmallVec<[u32; 4]>, dem_outputs: SmallVec<[u32; 2]>) -> Self {
+        Self::from_sorted_with_tracked_paulis(detectors, dem_outputs, SmallVec::new())
+    }
+
+    /// Creates a mechanism from pre-sorted detector, DEM-output, and tracked-Pauli indices.
     #[must_use]
-    pub fn from_sorted(detectors: SmallVec<[u32; 4]>, logicals: SmallVec<[u32; 2]>) -> Self {
+    pub fn from_sorted_with_tracked_paulis(
+        detectors: SmallVec<[u32; 4]>,
+        dem_outputs: SmallVec<[u32; 2]>,
+        tracked_paulis: SmallVec<[u32; 2]>,
+    ) -> Self {
         debug_assert!(
             detectors.windows(2).all(|w| w[0] <= w[1]),
             "detectors must be sorted"
         );
         debug_assert!(
-            logicals.windows(2).all(|w| w[0] <= w[1]),
-            "logicals must be sorted"
+            dem_outputs.windows(2).all(|w| w[0] <= w[1]),
+            "dem_outputs must be sorted"
+        );
+        debug_assert!(
+            tracked_paulis.windows(2).all(|w| w[0] <= w[1]),
+            "tracked_paulis must be sorted"
         );
         Self {
             detectors,
-            logicals,
+            dem_outputs,
+            tracked_paulis,
         }
     }
 
@@ -551,7 +603,27 @@ impl FaultMechanism {
     #[inline]
     #[must_use]
     pub fn is_empty(&self) -> bool {
-        self.detectors.is_empty() && self.logicals.is_empty()
+        self.detectors.is_empty() && self.dem_outputs.is_empty() && self.tracked_paulis.is_empty()
+    }
+
+    /// Returns true if this mechanism has no decoder-facing effect.
+    ///
+    /// This ignores PECOS tracked-Pauli effects, matching standard DEM and
+    /// decoder-facing sampler behavior.
+    #[inline]
+    #[must_use]
+    pub fn is_standard_empty(&self) -> bool {
+        self.detectors.is_empty() && self.dem_outputs.is_empty()
+    }
+
+    /// Returns the decoder-facing projection of this mechanism.
+    #[must_use]
+    pub fn standard_effect(&self) -> Self {
+        Self {
+            detectors: self.detectors.clone(),
+            dem_outputs: self.dem_outputs.clone(),
+            tracked_paulis: SmallVec::new(),
+        }
     }
 
     /// Returns the number of detectors in this mechanism.
@@ -561,11 +633,18 @@ impl FaultMechanism {
         self.detectors.len()
     }
 
-    /// Returns the number of logicals in this mechanism.
+    /// Returns the number of outputs in the DEM `L<n>` namespace.
+    #[inline]
+    #[must_use]
+    pub fn num_dem_outputs(&self) -> usize {
+        self.dem_outputs.len()
+    }
+
+    /// Returns the number of tracked Pauli outputs in this mechanism.
     #[inline]
     #[must_use]
-    pub fn num_logicals(&self) -> usize {
-        self.logicals.len()
+    pub fn num_tracked_paulis(&self) -> usize {
+        self.tracked_paulis.len()
     }
 
     /// XOR this mechanism with another, returning the combined effect.
@@ -575,15 +654,16 @@ impl FaultMechanism {
     pub fn xor(&self, other: &Self) -> Self {
         Self {
             detectors: symmetric_difference_4(&self.detectors, &other.detectors),
-            logicals: symmetric_difference_2(&self.logicals, &other.logicals),
+            dem_outputs: symmetric_difference_2(&self.dem_outputs, &other.dem_outputs),
+            tracked_paulis: symmetric_difference_2(&self.tracked_paulis, &other.tracked_paulis),
         }
     }
 
     /// Returns true if this mechanism is graphlike.
     ///
     /// A graphlike mechanism has at most 2 detectors.
-    /// Logical observables do not affect graph-likeness; MWPM decoders attach
-    /// them as frame-change masks on graph edges.
+    /// DEM outputs do not affect graph-likeness; MWPM decoders attach them as
+    /// frame-change masks on graph edges.
     #[inline]
     #[must_use]
     pub fn is_graphlike(&self) -> bool {
@@ -661,7 +741,9 @@ fn symmetric_difference_2(a: &SmallVec<[u32; 2]>, b: &SmallVec<[u32; 2]>) -> Sma
 
 impl PartialEq for FaultMechanism {
     fn eq(&self, other: &Self) -> bool {
-        self.detectors == other.detectors && self.logicals == other.logicals
+        self.detectors == other.detectors
+            && self.dem_outputs == other.dem_outputs
+            && self.tracked_paulis == other.tracked_paulis
     }
 }
 
@@ -670,7 +752,8 @@ impl Eq for FaultMechanism {}
 impl Hash for FaultMechanism {
     fn hash<H: Hasher>(&self, state: &mut H) {
         self.detectors.hash(state);
-        self.logicals.hash(state);
+        self.dem_outputs.hash(state);
+        self.tracked_paulis.hash(state);
     }
 }
 
@@ -684,7 +767,8 @@ impl Ord for FaultMechanism {
     fn cmp(&self, other: &Self) -> Ordering {
         self.detectors
             .cmp(&other.detectors)
-            .then_with(|| self.logicals.cmp(&other.logicals))
+            .then_with(|| self.dem_outputs.cmp(&other.dem_outputs))
+            .then_with(|| self.tracked_paulis.cmp(&other.tracked_paulis))
     }
 }
 
@@ -692,9 +776,10 @@ impl fmt::Debug for FaultMechanism {
     fn fmt(&self, f: &mut fmt::Formatter<'_>) -> fmt::Result {
         write!(
             f,
-            "FaultMechanism(dets={:?}, logs={:?})",
+            "FaultMechanism(dets={:?}, dem_outputs={:?}, tracked_paulis={:?})",
             self.detectors.as_slice(),
-            self.logicals.as_slice()
+            self.dem_outputs.as_slice(),
+            self.tracked_paulis.as_slice()
         )
     }
 }
@@ -754,16 +839,17 @@ impl DecomposedFault {
     pub fn to_stim_targets(&self) -> String {
         self.components
             .iter()
-            .map(|comp| {
-                let mut targets = Vec::new();
-                for &det in &comp.detectors {
-                    targets.push(format!("D{det}"));
-                }
-                for &log in &comp.logicals {
-                    targets.push(format!("L{log}"));
-                }
-                targets.join(" ")
-            })
+            .map(format_mechanism_targets)
+            .collect::<Vec<_>>()
+            .join(" ^ ")
+    }
+
+    /// Formats this error for PECOS DEM output, including tracked Pauli `TP<n>` targets.
+    #[must_use]
+    pub fn to_pecos_targets(&self) -> String {
+        self.components
+            .iter()
+            .map(format_pecos_mechanism_targets)
             .collect::<Vec<_>>()
             .join(" ^ ")
     }
@@ -792,19 +878,18 @@ impl DecomposedFault {
 /// # Algorithm
 ///
 /// Uses a detector-driven recursive search over graphlike components whose
-/// detector sets are subsets of the hyperedge. This is closer to Stim's
-/// decomposition strategy than the older fixed-width 2-part/3-part search,
-/// and it allows decompositions into 4+ graphlike pieces when needed.
+/// detector sets are subsets of the hyperedge. This is more general than the
+/// older fixed-width 2-part/3-part search, and it allows decompositions into 4+
+/// graphlike pieces when needed.
 ///
 /// Decompositions are filtered to only include components whose detectors are
-/// subsets of the original hyperedge's detectors, matching Stim's behavior of
-/// not introducing extra detector symptoms.
+/// subsets of the original hyperedge's detectors, so decomposition does not
+/// introduce extra detector symptoms.
 ///
 /// # Selection
 ///
 /// The search returns the first valid decomposition found using a deterministic
-/// ordering that prefers detector pairs before singlets, similar to Stim's
-/// decompose pass over known graphlike symptoms.
+/// ordering that prefers detector pairs before singlets.
 #[cfg(test)]
 fn find_hyperedge_decomposition(
     hyperedge: &FaultMechanism,
@@ -965,7 +1050,7 @@ fn find_singleton_decomposition(
 /// before this was lifted out.
 struct SingletonDecompositionIndex {
     /// `candidates_by_detector[det]` lists every singleton mechanism whose sole
-    /// detector is `det`, sorted by `(logicals.len, logicals, detectors)` so the
+    /// detector is `det`, sorted by `(dem_outputs.len, dem_outputs, detectors)` so the
     /// decomposition search prefers simpler candidates deterministically.
     candidates_by_detector: Vec<Vec<FaultMechanism>>,
 }
@@ -997,10 +1082,10 @@ impl SingletonDecompositionIndex {
         }
         for candidates in &mut candidates_by_detector {
             candidates.sort_by(|a, b| {
-                a.logicals
+                a.dem_outputs
                     .len()
-                    .cmp(&b.logicals.len())
-                    .then_with(|| a.logicals.cmp(&b.logicals))
+                    .cmp(&b.dem_outputs.len())
+                    .then_with(|| a.dem_outputs.cmp(&b.dem_outputs))
                     .then_with(|| a.detectors.cmp(&b.detectors))
             });
         }
@@ -1063,9 +1148,9 @@ fn shares_element(a: &FaultMechanism, b: &FaultMechanism) -> bool {
             return true;
         }
     }
-    // Check logicals
-    for l in &a.logicals {
-        if b.logicals.contains(l) {
+    // Check dem_outputs
+    for l in &a.dem_outputs {
+        if b.dem_outputs.contains(l) {
             return true;
         }
     }
@@ -1079,7 +1164,7 @@ fn convert_location_indices(location_indices: &[usize]) -> SmallVec<[u32; 2]> {
         .collect()
 }
 
-/// Converts a measurement record offset (Stim-style) to an absolute measurement index.
+/// Converts a DEM measurement-record offset to an absolute measurement index.
 ///
 /// Negative offsets count backward from the end of the measurement record
 /// (`-1` is the last measurement). Positive offsets are treated as absolute
@@ -1149,54 +1234,363 @@ impl DetectorDef {
 }
 
 // ============================================================================
-// Logical Observable
+// DEM Outputs
 // ============================================================================
 
-/// A logical observable definition.
+/// Metadata for a non-detector output definition.
 ///
-/// Logical observables track the parity of certain measurement outcomes
-/// to detect logical errors.
+/// Observables are rendered as standard `L<n>` targets. Tracked Paulis
+/// use the same metadata shape but live in a separate PECOS-only ID space and
+/// are never rendered as `L<n>` because they are unmeasured Pauli-operator
+/// annotations, not measurement-record observables.
 #[derive(Debug, Clone)]
-pub struct LogicalObservable {
-    /// Unique observable ID.
+pub struct DemOutput {
+    /// Unique ID within this output's ID space.
     pub id: u32,
-    /// Measurement record offsets (negative indices from end of record).
+    /// Measurement record offsets (negative indices from end of record), when
+    /// this output is tied to measurement records.
     pub records: SmallVec<[i32; 4]>,
+    /// PECOS DEM output kind, when known.
+    pub kind: Option<DemOutputKind>,
+    /// Pauli string whose flip is tracked, when this came from a Pauli
+    /// annotation or logical operator builder.
+    pub pauli: Option<PauliString>,
+    /// Optional user label.
+    pub label: Option<String>,
 }
 
-impl LogicalObservable {
-    /// Creates a new logical observable.
+impl DemOutput {
+    /// Creates a new unclassified DEM output.
     #[must_use]
     pub fn new(id: u32) -> Self {
         Self {
             id,
             records: SmallVec::new(),
+            kind: None,
+            pauli: None,
+            label: None,
+        }
+    }
+
+    /// Creates a DEM output from PECOS propagation metadata.
+    #[must_use]
+    pub fn from_metadata(id: u32, metadata: &DemOutputMetadata) -> Self {
+        Self {
+            id,
+            records: SmallVec::new(),
+            kind: Some(metadata.kind),
+            pauli: Some(metadata.pauli.clone()),
+            label: metadata.label.clone(),
         }
     }
 
     /// Sets the measurement records.
     #[must_use]
     pub fn with_records(mut self, records: impl IntoIterator<Item = i32>) -> Self {
-        self.records = records.into_iter().collect();
+        self.records.clear();
+        for record in records {
+            toggle_dem_output_record(&mut self.records, record);
+        }
+        self.kind.get_or_insert(DemOutputKind::Observable);
+        self
+    }
+
+    /// Sets the DEM output kind.
+    #[must_use]
+    pub fn with_kind(mut self, kind: DemOutputKind) -> Self {
+        self.kind = Some(kind);
+        self
+    }
+
+    /// Sets the tracked Pauli string.
+    #[must_use]
+    pub fn with_pauli(mut self, mut pauli: PauliString) -> Self {
+        // A DEM output flip is an anticommutation property; global phase
+        // has no meaning for DEM/sampler output.
+        pauli.set_phase(pecos_core::QuarterPhase::PlusOne);
+        self.pauli = Some(pauli);
+        self
+    }
+
+    /// Sets a user-facing label.
+    #[must_use]
+    pub fn with_label(mut self, label: impl Into<String>) -> Self {
+        self.label = Some(label.into());
         self
     }
+
+    /// Returns true when this DEM output is an observable.
+    #[must_use]
+    pub fn is_observable(&self) -> bool {
+        match self.kind {
+            Some(DemOutputKind::Observable) => true,
+            Some(DemOutputKind::TrackedPauli) => false,
+            None => !self.records.is_empty(),
+        }
+    }
+
+    /// Returns true when this DEM output is a tracked Pauli.
+    #[must_use]
+    pub fn is_tracked_pauli(&self) -> bool {
+        match self.kind {
+            Some(DemOutputKind::TrackedPauli) => true,
+            Some(DemOutputKind::Observable) => false,
+            None => self.pauli.is_some() && self.records.is_empty(),
+        }
+    }
+}
+
+fn merge_record_parity(existing: &mut SmallVec<[i32; 4]>, incoming: SmallVec<[i32; 4]>) {
+    for record in incoming {
+        toggle_dem_output_record(existing, record);
+    }
+}
+
+fn toggle_dem_output_record(records: &mut SmallVec<[i32; 4]>, record: i32) {
+    if let Some(pos) = records
+        .iter()
+        .position(|&existing_record| existing_record == record)
+    {
+        records.remove(pos);
+    } else {
+        records.push(record);
+    }
+}
+
+/// Error returned when parsing or applying PECOS DEM metadata JSON.
+#[derive(Debug, Clone, PartialEq, Eq)]
+pub struct PecosDemMetadataError {
+    message: String,
+}
+
+impl PecosDemMetadataError {
+    fn new(message: impl Into<String>) -> Self {
+        Self {
+            message: message.into(),
+        }
+    }
+
+    /// Human-readable parse/apply error.
+    #[must_use]
+    pub fn message(&self) -> &str {
+        &self.message
+    }
+}
+
+impl fmt::Display for PecosDemMetadataError {
+    fn fmt(&self, f: &mut fmt::Formatter<'_>) -> fmt::Result {
+        write!(f, "{}", self.message)
+    }
 }
 
+impl std::error::Error for PecosDemMetadataError {}
+
 // ============================================================================
 // Noise Configuration
 // ============================================================================
 
-/// Noise model configuration for DEM generation.
-#[derive(Debug, Clone, Copy)]
+/// Per-Pauli fault probability weights.
+///
+/// Maps `PauliString` to relative probability. Entries must sum to ~1.0.
+/// Used to customize the fault distribution for single-qubit or two-qubit gates.
+///
+/// # Examples
+///
+/// ```
+/// use pecos_core::pauli::{X, Y, Z};
+/// use pecos_qec::fault_tolerance::dem_builder::PauliWeights;
+///
+/// // Single-qubit: biased toward dephasing
+/// let w = PauliWeights::from([(Z(0), 0.8), (X(0), 0.1), (Y(0), 0.1)]);
+/// assert_eq!(w.entries().len(), 3);
+///
+/// // Two-qubit: uniform (convenience)
+/// let w = PauliWeights::uniform_2q();
+/// assert_eq!(w.entries().len(), 15);
+/// ```
+#[derive(Debug, Clone)]
+pub struct PauliWeights {
+    /// (`PauliString`, weight) pairs. Weights must sum to ~1.0.
+    entries: Vec<(pecos_core::PauliString, f64)>,
+}
+
+impl PauliWeights {
+    /// Create from an iterator of `(PauliString, weight)` pairs.
+    ///
+    /// Validates that weights sum to approximately 1.0 (within 1e-6).
+    ///
+    /// # Panics
+    ///
+    /// Panics if weights don't sum to ~1.0 or if any weight is negative.
+    pub fn new(entries: impl IntoIterator<Item = (pecos_core::PauliString, f64)>) -> Self {
+        let entries: Vec<_> = entries.into_iter().collect();
+        let sum: f64 = entries.iter().map(|(_, w)| w).sum();
+        assert!(
+            (sum - 1.0).abs() < 1e-6,
+            "PauliWeights must sum to 1.0, got {sum}"
+        );
+        for (ps, w) in &entries {
+            assert!(*w >= 0.0, "Weight for {ps} must be non-negative, got {w}");
+        }
+        Self { entries }
+    }
+
+    /// Uniform weights for single-qubit gates: X, Y, Z each with 1/3.
+    #[must_use]
+    pub fn uniform_1q() -> Self {
+        use pecos_core::pauli::{X, Y, Z};
+        Self {
+            entries: vec![(X(0), 1.0 / 3.0), (Y(0), 1.0 / 3.0), (Z(0), 1.0 / 3.0)],
+        }
+    }
+
+    /// Uniform weights for two-qubit gates: all 15 non-identity Paulis at 1/15.
+    #[must_use]
+    pub fn uniform_2q() -> Self {
+        use pecos_core::pauli::{X, Y, Z};
+        let w = 1.0 / 15.0;
+        Self {
+            entries: vec![
+                (X(1), w),
+                (Y(1), w),
+                (Z(1), w),
+                (X(0), w),
+                (X(0) & X(1), w),
+                (X(0) & Y(1), w),
+                (X(0) & Z(1), w),
+                (Y(0), w),
+                (Y(0) & X(1), w),
+                (Y(0) & Y(1), w),
+                (Y(0) & Z(1), w),
+                (Z(0), w),
+                (Z(0) & X(1), w),
+                (Z(0) & Y(1), w),
+                (Z(0) & Z(1), w),
+            ],
+        }
+    }
+
+    /// Look up the weight for a specific `PauliString`.
+    ///
+    /// Matches by Pauli type pattern only, ignoring qubit IDs.
+    /// E.g., `X(3) & Z(7)` matches a weight entry `X(0) & Z(1)` because
+    /// both have the pattern [X, Z] (sorted by qubit position).
+    #[must_use]
+    pub fn weight_for(&self, pauli: &pecos_core::PauliString) -> f64 {
+        let query_pattern = pauli_pattern(pauli);
+        self.entries
+            .iter()
+            .find(|(ps, _)| pauli_pattern(ps) == query_pattern)
+            .map_or(0.0, |(_, w)| *w)
+    }
+
+    /// Get all entries as `(PauliString, weight)` pairs.
+    #[must_use]
+    pub fn entries(&self) -> &[(pecos_core::PauliString, f64)] {
+        &self.entries
+    }
+}
+
+impl<const N: usize> From<[(pecos_core::PauliString, f64); N]> for PauliWeights {
+    fn from(entries: [(pecos_core::PauliString, f64); N]) -> Self {
+        Self::new(entries)
+    }
+}
+
+/// Noise model configuration for circuit-level fault analysis.
+#[derive(Debug, Clone)]
 pub struct NoiseConfig {
-    /// Single-qubit depolarizing error rate.
+    /// Single-qubit gate error rate.
     pub p1: f64,
-    /// Two-qubit depolarizing error rate.
+    /// Two-qubit gate error rate.
     pub p2: f64,
     /// Measurement error rate.
     pub p_meas: f64,
     /// Initialization (prep) error rate.
-    pub p_init: f64,
+    pub p_prep: f64,
+    /// Idle gate error rate per time unit.
+    ///
+    /// The actual error probability for an idle gate is `p_idle * duration`
+    /// (clamped to [0, 1]), where `duration` is the gate's `TimeUnits` value.
+    /// Default is 0.0 (no idle noise).
+    pub p_idle: f64,
+    /// Optional T1 relaxation time (in the same time units as idle duration).
+    ///
+    /// When set (along with T2), idle noise uses the Pauli-twirled
+    /// amplitude damping + dephasing model instead of uniform depolarizing.
+    /// This gives biased noise: P(Z) > P(X) = P(Y).
+    pub t1: Option<f64>,
+    /// Optional T2 dephasing time (must satisfy T2 <= 2*T1).
+    pub t2: Option<f64>,
+    /// Optional per-Pauli weights for single-qubit gates.
+    ///
+    /// Maps each Pauli fault to its relative probability. Must sum to ~1.0.
+    /// Default (None) = uniform depolarizing.
+    pub p1_weights: Option<PauliWeights>,
+    /// Optional per-Pauli weights for two-qubit gates.
+    ///
+    /// Maps each two-qubit Pauli fault to its relative probability. Must sum to ~1.0.
+    /// Default (None) = uniform depolarizing.
+    pub p2_weights: Option<PauliWeights>,
+    /// Coherent idle RZ rotation angle per time unit.
+    ///
+    /// When set (> 0), idle gates contribute a coherent Z rotation in addition
+    /// to any stochastic idle noise. Idle fault locations with the same
+    /// detector set have their angles accumulated coherently (angles add),
+    /// giving probability `sin²(total_angle/2)` instead of independent combination.
+    ///
+    /// This is the EEG H-type noise model for idle gates. Default is 0.0.
+    pub idle_rz: f64,
+}
+
+/// Per-Pauli error probabilities for a single qubit.
+#[derive(Debug, Clone, Copy)]
+pub struct PauliProbs {
+    /// Probability of X error.
+    pub px: f64,
+    /// Probability of Y error.
+    pub py: f64,
+    /// Probability of Z error.
+    pub pz: f64,
+}
+
+impl PauliProbs {
+    /// Total error probability (px + py + pz).
+    #[must_use]
+    pub fn total(&self) -> f64 {
+        self.px + self.py + self.pz
+    }
+
+    /// Uniform depolarizing: each Pauli with probability p/3.
+    #[must_use]
+    pub fn depolarizing(p: f64) -> Self {
+        Self {
+            px: p / 3.0,
+            py: p / 3.0,
+            pz: p / 3.0,
+        }
+    }
+
+    /// Pauli-twirled T1/T2 noise for idle duration t.
+    ///
+    /// Approximates the combined amplitude damping (T1) and pure
+    /// dephasing (T2) channel as a Pauli channel via Pauli twirling:
+    ///
+    ///   P(X) = P(Y) = (1 - e^{-t/T1}) / 4
+    ///   P(Z) = (1 - e^{-t/T2}) / 2 - (1 - e^{-t/T1}) / 4
+    ///
+    /// Requires T2 <= 2*T1 (physical constraint).
+    #[must_use]
+    pub fn from_t1_t2(t: f64, t1: f64, t2: f64) -> Self {
+        let gamma = 1.0 - (-t / t1).exp(); // amplitude damping parameter
+        let lambda_t2 = 1.0 - (-t / t2).exp(); // total dephasing parameter
+
+        let px = gamma / 4.0;
+        let py = gamma / 4.0;
+        let pz = (lambda_t2 / 2.0 - gamma / 4.0).max(0.0);
+
+        Self { px, py, pz }
+    }
 }
 
 impl Default for NoiseConfig {
@@ -1205,127 +1599,1295 @@ impl Default for NoiseConfig {
             p1: 0.01,
             p2: 0.01,
             p_meas: 0.01,
-            p_init: 0.01,
+            p_prep: 0.01,
+            p_idle: 0.0,
+            t1: None,
+            t2: None,
+            p1_weights: None,
+            p2_weights: None,
+            idle_rz: 0.0,
         }
     }
 }
 
 impl NoiseConfig {
-    /// Creates a new noise configuration.
+    /// Creates a new noise configuration (idle defaults to `None`).
+    #[must_use]
+    pub fn new(p1: f64, p2: f64, p_meas: f64, p_prep: f64) -> Self {
+        Self {
+            p1,
+            p2,
+            p_meas,
+            p_prep,
+            p_idle: 0.0,
+            t1: None,
+            t2: None,
+            p1_weights: None,
+            p2_weights: None,
+            idle_rz: 0.0,
+        }
+    }
+
+    /// Creates a new noise configuration with uniform depolarizing idle noise.
     #[must_use]
-    pub fn new(p1: f64, p2: f64, p_meas: f64, p_init: f64) -> Self {
+    pub fn with_idle(p1: f64, p2: f64, p_meas: f64, p_prep: f64, p_idle: f64) -> Self {
         Self {
             p1,
             p2,
             p_meas,
-            p_init,
+            p_prep,
+            p_idle,
+            t1: None,
+            t2: None,
+            p1_weights: None,
+            p2_weights: None,
+            idle_rz: 0.0,
         }
     }
 
-    /// Creates a uniform noise configuration.
+    /// Creates a uniform noise configuration (including depolarizing idle).
     #[must_use]
     pub fn uniform(p: f64) -> Self {
         Self {
             p1: p,
             p2: p,
             p_meas: p,
-            p_init: p,
+            p_prep: p,
+            p_idle: p,
+            t1: None,
+            t2: None,
+            p1_weights: None,
+            p2_weights: None,
+            idle_rz: 0.0,
         }
     }
-}
-
-// ============================================================================
-// Detector Error Model
-// ============================================================================
-
-/// A complete Detector Error Model (DEM).
-///
-/// This represents the noise model of a quantum circuit. It maps mechanisms
-/// (detector/logical effects) to their probabilities.
-///
-/// # Aggregation Modes
-///
-/// The DEM supports two modes controlled by `aggregate`:
-///
-/// - **Aggregated mode** (`aggregate = true`): Mechanisms with the same effect
-///   are combined into a single entry using the independent error formula.
-///   This is more compact but loses information about noise sources.
-///
-/// - **Non-aggregated mode** (`aggregate = false`, default): Each noise source
-///   is kept as a separate entry. This preserves correlation information and
-///   allows advanced decoders to understand the noise structure.
-///
-/// # Decomposed Entries
-///
-/// In addition to direct mechanisms, the DEM can store "decomposed" entries
-/// that represent Y faults as X^Z. These are stored separately because:
-///
-/// 1. They help MWPM decoders understand correlation structure
-/// 2. They preserve information about fault sources
-///
-/// When a Y fault has X-effect {`D_x`} and Z-effect {`D_z`} where both are non-empty
-/// and different, it can be represented as `{D_x} ^ {D_z}` instead of XOR-ing
-/// into a single mechanism.
-#[derive(Debug, Clone)]
-pub struct DetectorErrorModel {
-    /// Detector definitions.
-    pub detectors: Vec<DetectorDef>,
-    /// Logical observable definitions.
-    pub observables: Vec<LogicalObservable>,
-    /// Error contributions with source tracking.
-    /// Each contribution tracks whether it came from a direct (X, Z) or decomposable (Y) source.
-    contributions: Vec<FaultContribution>,
-    /// Count of graphlike decomposable sources per 2-detector mechanism.
-    /// Key is (d0, d1) with d0 < d1. A source is "graphlike decomposable" if both
-    /// component effects are non-empty and graphlike (≤2 detectors).
-    /// Used to determine output format: ≥2 → 3 forms, 1 → 2 forms, 0 → 1 form.
-    graphlike_decomposable_counts: BTreeMap<(u32, u32), u32>,
-}
 
-impl DetectorErrorModel {
-    /// Creates a new empty DEM.
+    /// Sets the idle noise rate on an existing config (uniform depolarizing).
     #[must_use]
-    pub fn new() -> Self {
-        Self {
-            detectors: Vec::new(),
-            observables: Vec::new(),
-            contributions: Vec::new(),
-            graphlike_decomposable_counts: BTreeMap::new(),
-        }
+    pub fn set_idle(mut self, p_idle: f64) -> Self {
+        self.p_idle = p_idle;
+        self
     }
 
-    /// Creates a DEM with pre-allocated capacity.
+    /// Sets T1/T2 relaxation times for idle noise.
+    ///
+    /// When set, idle gates use the Pauli-twirled T1/T2 model instead of
+    /// uniform depolarizing. This produces biased noise where Z errors
+    /// (dephasing) are more likely than X/Y errors (relaxation).
+    ///
+    /// T1 and T2 are in the same time units as idle gate durations.
+    /// Must satisfy T2 <= 2*T1 (physical constraint).
+    ///
+    /// # Panics
+    ///
+    /// Panics if `t2 > 2 * t1`, which violates the physical constraint
+    /// that the dephasing time cannot exceed twice the relaxation time.
     #[must_use]
-    pub fn with_capacity(num_detectors: usize, num_observables: usize) -> Self {
-        Self {
-            detectors: Vec::with_capacity(num_detectors),
-            observables: Vec::with_capacity(num_observables),
-            contributions: Vec::new(),
-            graphlike_decomposable_counts: BTreeMap::new(),
-        }
+    pub fn set_t1_t2(mut self, t1: f64, t2: f64) -> Self {
+        assert!(
+            t2 <= 2.0 * t1,
+            "T2 ({t2}) must be <= 2*T1 ({}) (physical constraint)",
+            2.0 * t1
+        );
+        self.t1 = Some(t1);
+        self.t2 = Some(t2);
+        self
     }
 
-    /// Returns the number of detectors.
-    #[inline]
+    /// Sets custom per-Pauli weights for single-qubit gates.
+    ///
+    /// ```
+    /// use pecos_core::pauli::{X, Y, Z};
+    /// use pecos_qec::fault_tolerance::dem_builder::{NoiseConfig, PauliWeights};
+    ///
+    /// let noise = NoiseConfig::uniform(0.001).set_p1_weights(PauliWeights::from([
+    ///     (X(0), 0.1), (Y(0), 0.1), (Z(0), 0.8),
+    /// ]));
+    /// assert_eq!(noise.p1_weights.as_ref().unwrap().weight_for(&Z(7)), 0.8);
+    /// ```
     #[must_use]
-    pub fn num_detectors(&self) -> usize {
-        self.detectors.len()
+    pub fn set_p1_weights(mut self, weights: PauliWeights) -> Self {
+        self.p1_weights = Some(weights);
+        self
     }
 
-    /// Returns the number of observables.
-    #[inline]
+    /// Sets custom per-Pauli weights for two-qubit gates.
     #[must_use]
-    pub fn num_observables(&self) -> usize {
-        self.observables.len()
+    pub fn set_p2_weights(mut self, weights: PauliWeights) -> Self {
+        self.p2_weights = Some(weights);
+        self
     }
 
-    /// Returns the number of tracked contributions.
-    #[inline]
-    #[must_use]
+    /// Sets idle noise from a coherent RZ rotation angle per time unit.
+    ///
+    /// Converts `idle_rz` (the angle theta of an RZ(theta) rotation applied
+    /// per idle time unit) to an equivalent stochastic Z-biased noise:
+    ///
+    ///   P(Z) = sin^2(theta/2)   per idle time unit
+    ///   P(X) = P(Y) = 0
+    ///
+    /// This is the exact Pauli twirling of a pure dephasing channel and
+    /// gives the non-EEG DEM builder correct idle noise behavior including
+    /// proper correlations through the fault influence map.
+    #[must_use]
+    pub fn set_idle_rz(mut self, idle_rz: f64) -> Self {
+        self.idle_rz = idle_rz;
+        let pz = (idle_rz / 2.0).sin().powi(2);
+        // Use T1/T2 model: T1=infinity (no amplitude damping), T2 chosen to match pz.
+        // From the T1/T2 model: pz = (1 - exp(-t/T2))/2 for T1=inf, t=1.
+        // Solve: T2 = -1/ln(1 - 2*pz)
+        // This provides a stochastic representation for non-coherent code paths.
+        if pz > 0.0 && pz < 0.5 {
+            let t2 = -1.0 / (1.0 - 2.0 * pz).ln();
+            let t1 = 1e15; // effectively infinity
+            self.t1 = Some(t1);
+            self.t2 = Some(t2);
+        }
+        self.p_idle = 0.0;
+        self
+    }
+
+    /// Compute per-Pauli idle noise probabilities for a given duration.
+    ///
+    /// If T1/T2 are set, uses the Pauli-twirled model (biased noise).
+    /// Otherwise, uses uniform depolarizing with `p_idle * duration`.
+    #[must_use]
+    pub fn idle_pauli_probs(&self, duration: f64) -> PauliProbs {
+        if let (Some(t1), Some(t2)) = (self.t1, self.t2) {
+            PauliProbs::from_t1_t2(duration, t1, t2)
+        } else {
+            PauliProbs::depolarizing((self.p_idle * duration).min(1.0))
+        }
+    }
+
+    /// Returns true when idle locations use the dedicated idle-noise model.
+    ///
+    /// Otherwise `Idle` is a no-op for noise.
+    #[must_use]
+    pub fn uses_dedicated_idle_noise(&self) -> bool {
+        self.p_idle > 0.0 || matches!((self.t1, self.t2), (Some(_), Some(_)))
+    }
+}
+
+/// Extract the Pauli type pattern from a `PauliString`, ignoring qubit IDs.
+///
+/// Returns the sequence of Pauli types sorted by qubit position.
+/// E.g., X(3) & Z(7) -> [X, Z], same as X(0) & Z(1) -> [X, Z].
+fn pauli_pattern(ps: &pecos_core::PauliString) -> Vec<pecos_core::Pauli> {
+    ps.paulis().iter().map(|&(p, _)| p).collect()
+}
+
+fn pecos_metadata_dem_output_value(target: &DemOutput) -> serde_json::Value {
+    serde_json::json!({
+        "id": target.id,
+        "kind": target.kind.map_or("dem_output", DemOutputKind::as_str),
+        "label": target.label,
+        "pauli": target.pauli.as_ref().map(PauliString::to_sparse_str),
+        "records": target.records.iter().copied().collect::<Vec<_>>(),
+    })
+}
+
+#[derive(Debug, Clone, Default)]
+struct ParsedPecosDemMetadata {
+    observables: Vec<DemOutput>,
+    tracked_paulis: Vec<DemOutput>,
+}
+
+pub(crate) fn parse_pecos_dem_metadata_line(
+    line: &str,
+) -> Result<DemOutput, PecosDemMetadataError> {
+    let line = line.trim();
+    let (prefix, payload, forced_kind) =
+        if let Some(payload) = line.strip_prefix("pecos_tracked_pauli") {
+            (
+                "pecos_tracked_pauli",
+                payload.trim(),
+                Some(DemOutputKind::TrackedPauli),
+            )
+        } else if let Some(payload) = line.strip_prefix("pecos_observable") {
+            (
+                "pecos_observable",
+                payload.trim(),
+                Some(DemOutputKind::Observable),
+            )
+        } else {
+            return Err(PecosDemMetadataError::new(
+                "missing PECOS DEM metadata prefix",
+            ));
+        };
+    if payload.is_empty() {
+        return Err(PecosDemMetadataError::new(format!(
+            "{prefix} is missing its JSON payload"
+        )));
+    }
+
+    let value: serde_json::Value = serde_json::from_str(payload).map_err(|err| {
+        PecosDemMetadataError::new(format!("invalid {prefix} JSON payload: {err}"))
+    })?;
+    let mut output = parse_pecos_metadata_dem_output(0, &value)?;
+    if let Some(kind) = forced_kind {
+        output.kind = Some(kind);
+    }
+    if output.is_tracked_pauli() && !output.records.is_empty() {
+        return Err(PecosDemMetadataError::new(
+            "tracked Pauli metadata cannot have measurement records",
+        ));
+    }
+    Ok(output)
+}
+
+fn parse_pecos_metadata_json(json: &str) -> Result<ParsedPecosDemMetadata, PecosDemMetadataError> {
+    let root: serde_json::Value = serde_json::from_str(json).map_err(|err| {
+        PecosDemMetadataError::new(format!("invalid PECOS DEM metadata JSON: {err}"))
+    })?;
+
+    let format = root
+        .get("format")
+        .and_then(serde_json::Value::as_str)
+        .ok_or_else(|| PecosDemMetadataError::new("missing metadata format"))?;
+    if format != "pecos.dem.metadata" {
+        return Err(PecosDemMetadataError::new(format!(
+            "unsupported metadata format: {format}"
+        )));
+    }
+
+    let version = root
+        .get("version")
+        .and_then(serde_json::Value::as_u64)
+        .ok_or_else(|| PecosDemMetadataError::new("missing metadata version"))?;
+    if version != 1 {
+        return Err(PecosDemMetadataError::new(format!(
+            "unsupported PECOS DEM metadata version: {version}"
+        )));
+    }
+
+    for old_name in ["tracked_ops", "tracked_operators", "pauli_operators"] {
+        if root.get(old_name).is_some() {
+            return Err(PecosDemMetadataError::new(format!(
+                "unsupported legacy metadata field: {old_name}; use tracked_paulis"
+            )));
+        }
+    }
+
+    let parse_array =
+        |name: &str, kind: DemOutputKind| -> Result<Vec<DemOutput>, PecosDemMetadataError> {
+            let Some(values) = root.get(name) else {
+                return Ok(Vec::new());
+            };
+            let values = values.as_array().ok_or_else(|| {
+                PecosDemMetadataError::new(format!("{name} metadata is not an array"))
+            })?;
+            values
+                .iter()
+                .enumerate()
+                .map(|(idx, value)| {
+                    let mut output = parse_pecos_metadata_dem_output(idx, value)?;
+                    output.kind = Some(kind);
+                    if kind == DemOutputKind::TrackedPauli && !output.records.is_empty() {
+                        return Err(PecosDemMetadataError::new(format!(
+                            "tracked Pauli metadata {idx} cannot have measurement records"
+                        )));
+                    }
+                    Ok(output)
+                })
+                .collect()
+        };
+
+    let parsed = ParsedPecosDemMetadata {
+        observables: parse_array("observables", DemOutputKind::Observable)?,
+        tracked_paulis: parse_array("tracked_paulis", DemOutputKind::TrackedPauli)?,
+    };
+
+    if root.get("observables").is_none() && root.get("tracked_paulis").is_none() {
+        return Err(PecosDemMetadataError::new(
+            "missing observables or tracked_paulis metadata arrays",
+        ));
+    }
+
+    Ok(parsed)
+}
+
+fn parse_pecos_metadata_dem_output(
+    idx: usize,
+    target: &serde_json::Value,
+) -> Result<DemOutput, PecosDemMetadataError> {
+    let object = target
+        .as_object()
+        .ok_or_else(|| PecosDemMetadataError::new(format!("DEM output {idx} is not an object")))?;
+
+    let id = object
+        .get("id")
+        .and_then(serde_json::Value::as_u64)
+        .ok_or_else(|| PecosDemMetadataError::new(format!("DEM output {idx} is missing id")))?;
+    let id = u32::try_from(id).map_err(|_| {
+        PecosDemMetadataError::new(format!("DEM output {idx} id does not fit in u32"))
+    })?;
+
+    let mut dem_output = DemOutput::new(id);
+    let mut explicit_kind = None;
+
+    if let Some(kind_value) = object.get("kind") {
+        let kind = kind_value.as_str().ok_or_else(|| {
+            PecosDemMetadataError::new(format!("DEM output {idx} kind is not a string"))
+        })?;
+        if kind != "dem_output" {
+            let parsed_kind = DemOutputKind::from_metadata_str(kind).ok_or_else(|| {
+                PecosDemMetadataError::new(format!("DEM output {idx} has unknown kind: {kind}"))
+            })?;
+            explicit_kind = Some(parsed_kind);
+            dem_output = dem_output.with_kind(parsed_kind);
+        }
+    }
+
+    if let Some(label_value) = object.get("label")
+        && !label_value.is_null()
+    {
+        let label = label_value.as_str().ok_or_else(|| {
+            PecosDemMetadataError::new(format!("DEM output {idx} label is not a string or null"))
+        })?;
+        dem_output = dem_output.with_label(label);
+    }
+
+    if let Some(pauli_value) = object.get("pauli")
+        && !pauli_value.is_null()
+    {
+        let pauli = pauli_value.as_str().ok_or_else(|| {
+            PecosDemMetadataError::new(format!("DEM output {idx} pauli is not a string or null"))
+        })?;
+        let pauli = pauli.parse::<PauliString>().map_err(|err| {
+            PecosDemMetadataError::new(format!("DEM output {idx} has invalid PauliString: {err}"))
+        })?;
+        dem_output = dem_output.with_pauli(pauli);
+    }
+
+    let records = if let Some(records_value) = object.get("records") {
+        if records_value.is_null() {
+            Vec::new()
+        } else {
+            let records = records_value.as_array().ok_or_else(|| {
+                PecosDemMetadataError::new(format!(
+                    "DEM output {idx} records is not an array or null"
+                ))
+            })?;
+            records
+                .iter()
+                .enumerate()
+                .map(|(record_idx, record)| {
+                    let record = record.as_i64().ok_or_else(|| {
+                        PecosDemMetadataError::new(format!(
+                            "DEM output {idx} record {record_idx} is not an integer"
+                        ))
+                    })?;
+                    i32::try_from(record).map_err(|_| {
+                        PecosDemMetadataError::new(format!(
+                            "DEM output {idx} record {record_idx} does not fit in i32"
+                        ))
+                    })
+                })
+                .collect::<Result<Vec<_>, _>>()?
+        }
+    } else {
+        Vec::new()
+    };
+
+    if explicit_kind == Some(DemOutputKind::TrackedPauli) && !records.is_empty() {
+        return Err(PecosDemMetadataError::new(format!(
+            "tracked Pauli DEM output {idx} cannot have measurement records"
+        )));
+    }
+
+    if !records.is_empty() || explicit_kind == Some(DemOutputKind::Observable) {
+        dem_output = dem_output.with_records(records);
+    }
+
+    Ok(dem_output)
+}
+
+// ============================================================================
+// Per-gate-type noise configuration
+// ============================================================================
+
+use pecos_core::QubitId;
+use std::collections::HashMap;
+
+/// Ordered indices for the 3 non-identity 1Q Paulis: `[X, Y, Z]`.
+pub const PAULI_1Q_ORDER: [&str; 3] = ["X", "Y", "Z"];
+
+/// Ordered indices for the 15 non-identity 2Q Pauli pairs. Row/col order:
+/// `I=0, X=1, Y=2, Z=3`; pair `p1 ⊗ p2` index is `4*p1 + p2 - 1` (skip II).
+/// Concretely: `["IX", "IY", "IZ", "XI", "XX", "XY", "XZ", "YI", "YX",
+/// "YY", "YZ", "ZI", "ZX", "ZY", "ZZ"]`.
+pub const PAULI_2Q_ORDER: [&str; 15] = [
+    "IX", "IY", "IZ", "XI", "XX", "XY", "XZ", "YI", "YX", "YY", "YZ", "ZI", "ZX", "ZY", "ZZ",
+];
+
+/// Per-gate-type, optionally per-qubit noise specification. Replaces the
+/// uniform scalar `NoiseConfig` with per-`GateType` per-Pauli rates, with
+/// an optional per-qubit override layer for devices where `T_1`/`T_2`
+/// varies qubit-to-qubit.
+///
+/// # Layered lookup
+///
+/// Rate resolution uses the most specific configured entry:
+///
+/// ```text
+/// 1. rates_1q_per_qubit[(gate, qubit)]         // most specific
+/// 2. rates_1q[gate]                            // per-gate-type default
+/// 3. base.p1 / 3.0                             // base noise model
+/// ```
+///
+/// (And analogously for 2Q with `(gate, (q_control, q_target))`.)
+///
+/// This lets users specify "H on qubit 0 has these rates (high `T_1`), H on
+/// qubit 1 has these (low `T_1`), every other H uses the per-gate default".
+///
+/// # Integration with `pecos-lindblad`
+///
+/// The intended workflow is:
+///   1. Synthesize a `PauliLindbladModel` for each gate type *and* per
+///      qubit if needed via `pecos_lindblad::synthesize_superop(...)`.
+///   2. Convert to `[f64; 3]` / `[f64; 15]` arrays.
+///   3. Register with [`Self::with_1q_rates_for_qubit`] /
+///      [`Self::with_2q_rates_for_qubits`] for heterogeneous devices, or
+///      [`Self::with_1q_rates`] / [`Self::with_2q_rates`] for homogeneous
+///      models.
+#[derive(Debug, Clone, Default)]
+pub struct PerGateTypeNoise {
+    pub rates_1q: HashMap<GateType, [f64; 3]>,
+    pub rates_2q: HashMap<GateType, [f64; 15]>,
+    pub rates_1q_per_qubit: HashMap<(GateType, QubitId), [f64; 3]>,
+    pub rates_2q_per_qubits: HashMap<(GateType, QubitId, QubitId), [f64; 15]>,
+    /// Per-qubit readout (MZ) X-flip probabilities. Qubits not in this map use
+    /// [`Self::p_meas`].
+    pub measurement_rates: HashMap<QubitId, f64>,
+    /// Per-qubit preparation (PZ) X-error probabilities. Qubits not in this map
+    /// use [`Self::p_init`].
+    pub init_rates: HashMap<QubitId, f64>,
+    pub p_meas: f64,
+    pub p_init: f64,
+    pub base: NoiseConfig,
+}
+
+impl PerGateTypeNoise {
+    /// Construct with empty gate maps; unspecified gates use `base`.
+    #[must_use]
+    pub fn from_base_noise(base: NoiseConfig) -> Self {
+        Self {
+            rates_1q: HashMap::new(),
+            rates_2q: HashMap::new(),
+            rates_1q_per_qubit: HashMap::new(),
+            rates_2q_per_qubits: HashMap::new(),
+            measurement_rates: HashMap::new(),
+            init_rates: HashMap::new(),
+            p_meas: base.p_meas,
+            p_init: base.p_prep,
+            base,
+        }
+    }
+
+    /// Attach measurement X-flip probability for a specific qubit.
+    /// Overrides [`Self::p_meas`] when set. Use for devices with
+    /// heterogeneous readout fidelity.
+    #[must_use]
+    pub fn with_measurement_rate(mut self, q: QubitId, p: f64) -> Self {
+        self.measurement_rates.insert(q, p);
+        self
+    }
+
+    /// Attach preparation X-error probability for a specific qubit.
+    /// Overrides [`Self::p_init`] when set.
+    #[must_use]
+    pub fn with_init_rate(mut self, q: QubitId, p: f64) -> Self {
+        self.init_rates.insert(q, p);
+        self
+    }
+
+    /// Lookup measurement X-flip rate for a qubit. Unspecified qubits use
+    /// [`Self::p_meas`], which is seeded from the base `NoiseConfig::p_meas`.
+    #[must_use]
+    pub fn measurement_rate_on(&self, q: QubitId) -> f64 {
+        *self.measurement_rates.get(&q).unwrap_or(&self.p_meas)
+    }
+
+    /// Lookup preparation X-error rate for a qubit. Unspecified qubits use
+    /// [`Self::p_init`].
+    #[must_use]
+    pub fn init_rate_on(&self, q: QubitId) -> f64 {
+        *self.init_rates.get(&q).unwrap_or(&self.p_init)
+    }
+
+    /// Attach rates for a 1Q gate type applied to any qubit.
+    #[must_use]
+    pub fn with_1q_rates(mut self, g: GateType, rates: [f64; 3]) -> Self {
+        self.rates_1q.insert(g, rates);
+        self
+    }
+
+    /// Attach rates for a 2Q gate type applied to any qubit pair.
+    #[must_use]
+    pub fn with_2q_rates(mut self, g: GateType, rates: [f64; 15]) -> Self {
+        self.rates_2q.insert(g, rates);
+        self
+    }
+
+    /// Attach rates for a 1Q gate on a specific qubit. Takes precedence
+    /// over [`Self::with_1q_rates`] for that `(gate, qubit)` combination.
+    #[must_use]
+    pub fn with_1q_rates_for_qubit(mut self, g: GateType, q: QubitId, rates: [f64; 3]) -> Self {
+        self.rates_1q_per_qubit.insert((g, q), rates);
+        self
+    }
+
+    /// Return explicitly attached 1Q Pauli rates for a gate type.
+    #[must_use]
+    pub fn explicit_1q_rates(&self, gate: GateType) -> Option<[f64; 3]> {
+        self.rates_1q.get(&gate).copied()
+    }
+
+    /// Return explicitly attached 1Q Pauli rates for a gate on a specific qubit.
+    ///
+    /// Per-qubit rates take precedence over gate-type rates. Unlike
+    /// [`Self::rate_1q_on`], this does not fall back to the base noise model.
+    #[must_use]
+    pub fn explicit_1q_rates_on(&self, gate: GateType, qubit: QubitId) -> Option<[f64; 3]> {
+        self.rates_1q_per_qubit
+            .get(&(gate, qubit))
+            .copied()
+            .or_else(|| self.explicit_1q_rates(gate))
+    }
+
+    /// Attach rates for a 2Q gate on a specific ordered qubit pair.
+    /// Takes precedence over [`Self::with_2q_rates`] for that
+    /// `(gate, q_control, q_target)` combination.
+    #[must_use]
+    pub fn with_2q_rates_for_qubits(
+        mut self,
+        g: GateType,
+        q_control: QubitId,
+        q_target: QubitId,
+        rates: [f64; 15],
+    ) -> Self {
+        self.rates_2q_per_qubits
+            .insert((g, q_control, q_target), rates);
+        self
+    }
+
+    /// Lookup 1Q Pauli rate for a gate. Returns `base.p1 / 3.0` if the
+    /// gate type is not in the map. `pauli_idx` is 0=X, 1=Y, 2=Z.
+    ///
+    /// `Idle` is a no-op by default. It receives noise only from explicitly
+    /// attached idle rates or from the base idle-noise model.
+    #[must_use]
+    pub fn rate_1q(&self, gate: GateType, pauli_idx: usize) -> f64 {
+        if let Some(rates) = self.rates_1q.get(&gate) {
+            return rates[pauli_idx];
+        }
+        if gate == GateType::Idle {
+            if self.base.uses_dedicated_idle_noise() {
+                let probs = self.base.idle_pauli_probs(1.0);
+                return match pauli_idx {
+                    0 => probs.px,
+                    1 => probs.py,
+                    2 => probs.pz,
+                    _ => 0.0,
+                };
+            }
+            return 0.0;
+        }
+        self.base.p1 / 3.0
+    }
+
+    /// Lookup 1Q Pauli rate for a gate on a specific qubit. Tries the
+    /// per-qubit map first, then the per-gate-type map, then `base.p1 / 3.0`.
+    /// `pauli_idx` is 0=X, 1=Y, 2=Z.
+    #[must_use]
+    pub fn rate_1q_on(&self, gate: GateType, qubit: QubitId, pauli_idx: usize) -> f64 {
+        if let Some(rates) = self.rates_1q_per_qubit.get(&(gate, qubit)) {
+            return rates[pauli_idx];
+        }
+        self.rate_1q(gate, pauli_idx)
+    }
+
+    /// Lookup 2Q Pauli pair rate for a gate. Returns `base.p2 / 15.0`
+    /// if the gate type is not in the map. `pair_idx` follows [`PAULI_2Q_ORDER`].
+    #[must_use]
+    pub fn rate_2q(&self, gate: GateType, pair_idx: usize) -> f64 {
+        self.rates_2q
+            .get(&gate)
+            .map_or(self.base.p2 / 15.0, |r| r[pair_idx])
+    }
+
+    /// Lookup 2Q Pauli pair rate for a gate on a specific ordered
+    /// qubit pair. Tries `(gate, q_control, q_target)` in the per-qubits
+    /// map first, then the per-gate-type map, then `base.p2 / 15.0`.
+    #[must_use]
+    pub fn rate_2q_on(
+        &self,
+        gate: GateType,
+        q_control: QubitId,
+        q_target: QubitId,
+        pair_idx: usize,
+    ) -> f64 {
+        if let Some(rates) = self.rates_2q_per_qubits.get(&(gate, q_control, q_target)) {
+            return rates[pair_idx];
+        }
+        self.rate_2q(gate, pair_idx)
+    }
+}
+
+// ============================================================================
+// Measurement Noise Model (MNM)
+// ============================================================================
+
+/// A measurement fault mechanism: a set of measurements that flip together.
+///
+/// Unlike [`FaultMechanism`], this operates directly on raw measurement
+/// indices. This is useful for sampling measurement outcomes without needing
+/// detector definitions.
+#[derive(Clone, Default)]
+pub struct MeasurementMechanism {
+    /// Measurement indices that flip together, sorted canonically.
+    pub measurements: SmallVec<[u32; 4]>,
+}
+
+impl MeasurementMechanism {
+    /// Creates a new empty measurement mechanism.
+    #[must_use]
+    pub fn new() -> Self {
+        Self::default()
+    }
+
+    /// Creates a mechanism from unsorted measurement indices.
+    #[must_use]
+    pub fn from_unsorted(measurements: impl IntoIterator<Item = u32>) -> Self {
+        let mut measurements: SmallVec<[u32; 4]> = measurements.into_iter().collect();
+        measurements.sort_unstable();
+        Self { measurements }
+    }
+
+    /// Creates a mechanism from pre-sorted measurement indices.
+    #[must_use]
+    pub fn from_sorted(measurements: SmallVec<[u32; 4]>) -> Self {
+        debug_assert!(
+            measurements.windows(2).all(|w| w[0] <= w[1]),
+            "measurements must be sorted"
+        );
+        Self { measurements }
+    }
+
+    /// Returns true if this mechanism has no effect.
+    #[inline]
+    #[must_use]
+    pub fn is_empty(&self) -> bool {
+        self.measurements.is_empty()
+    }
+
+    /// Returns the number of measurements in this mechanism.
+    #[inline]
+    #[must_use]
+    pub fn len(&self) -> usize {
+        self.measurements.len()
+    }
+}
+
+impl PartialEq for MeasurementMechanism {
+    fn eq(&self, other: &Self) -> bool {
+        self.measurements == other.measurements
+    }
+}
+
+impl Eq for MeasurementMechanism {}
+
+impl Hash for MeasurementMechanism {
+    fn hash<H: Hasher>(&self, state: &mut H) {
+        self.measurements.hash(state);
+    }
+}
+
+impl PartialOrd for MeasurementMechanism {
+    fn partial_cmp(&self, other: &Self) -> Option<Ordering> {
+        Some(self.cmp(other))
+    }
+}
+
+impl Ord for MeasurementMechanism {
+    fn cmp(&self, other: &Self) -> Ordering {
+        self.measurements.cmp(&other.measurements)
+    }
+}
+
+impl fmt::Debug for MeasurementMechanism {
+    fn fmt(&self, f: &mut fmt::Formatter<'_>) -> fmt::Result {
+        write!(
+            f,
+            "MeasurementMechanism({:?})",
+            self.measurements.as_slice()
+        )
+    }
+}
+
+/// A measurement noise model for fast approximate raw-measurement sampling.
+#[derive(Debug, Clone, Default)]
+pub struct MeasurementNoiseModel {
+    /// Fault mechanisms mapped to their probabilities.
+    pub mechanisms: BTreeMap<MeasurementMechanism, f64>,
+    /// Total number of measurements in the circuit.
+    pub num_measurements: usize,
+    /// Optional mapping from influence-map index to original circuit order.
+    pub im_to_tc_order: Option<Vec<usize>>,
+}
+
+impl MeasurementNoiseModel {
+    /// Creates a new empty measurement noise model.
+    #[must_use]
+    pub fn new(num_measurements: usize) -> Self {
+        Self {
+            mechanisms: BTreeMap::new(),
+            num_measurements,
+            im_to_tc_order: None,
+        }
+    }
+
+    /// Sets the measurement order mapping from influence-map order to circuit order.
+    #[must_use]
+    pub fn with_measurement_order(mut self, im_to_tc: Vec<usize>) -> Self {
+        self.im_to_tc_order = Some(im_to_tc);
+        self
+    }
+
+    /// Sets the measurement order mapping in place.
+    pub fn set_measurement_order(&mut self, im_to_tc: Vec<usize>) {
+        self.im_to_tc_order = Some(im_to_tc);
+    }
+
+    /// Returns the number of distinct mechanisms.
+    #[inline]
+    #[must_use]
+    pub fn num_mechanisms(&self) -> usize {
+        self.mechanisms.len()
+    }
+
+    /// Adds a mechanism with probability, combining with any existing identical mechanism.
+    pub fn add_mechanism(&mut self, mechanism: MeasurementMechanism, probability: f64) {
+        if mechanism.is_empty() || probability <= 0.0 {
+            return;
+        }
+
+        self.mechanisms
+            .entry(mechanism)
+            .and_modify(|p| *p = combine_probabilities(*p, probability))
+            .or_insert(probability);
+    }
+
+    /// Samples measurement outcomes into a pre-sized buffer.
+    pub fn sample_into<R: rand::Rng>(&self, outcomes: &mut [bool], rng: &mut R) {
+        outcomes.fill(false);
+
+        for (mechanism, &prob) in &self.mechanisms {
+            if rng.random_bool(prob.clamp(0.0, 1.0)) {
+                for &meas_idx in &mechanism.measurements {
+                    if (meas_idx as usize) < outcomes.len() {
+                        outcomes[meas_idx as usize] ^= true;
+                    }
+                }
+            }
+        }
+    }
+
+    /// Samples and returns measurement outcomes.
+    #[must_use]
+    pub fn sample<R: rand::Rng>(&self, rng: &mut R) -> Vec<bool> {
+        let mut outcomes = vec![false; self.num_measurements];
+        self.sample_into(&mut outcomes, rng);
+        outcomes
+    }
+
+    /// Iterates over all mechanisms and their probabilities.
+    pub fn iter(&self) -> impl Iterator<Item = (&MeasurementMechanism, &f64)> {
+        self.mechanisms.iter()
+    }
+
+    /// Computes detector events from raw measurement outcomes and detector records.
+    #[must_use]
+    pub fn compute_detection_events(
+        &self,
+        outcomes: &[bool],
+        detector_records: &[Vec<i32>],
+    ) -> Vec<bool> {
+        let tc_outcomes: Vec<bool> = if let Some(ref im_to_tc) = self.im_to_tc_order {
+            let mut reordered = vec![false; outcomes.len()];
+            for (im_idx, &tc_idx) in im_to_tc.iter().enumerate() {
+                if im_idx < outcomes.len() && tc_idx < reordered.len() {
+                    reordered[tc_idx] = outcomes[im_idx];
+                }
+            }
+            reordered
+        } else {
+            outcomes.to_vec()
+        };
+
+        Self::to_detection_events_internal(&tc_outcomes, detector_records)
+    }
+
+    fn to_detection_events_internal(outcomes: &[bool], detector_records: &[Vec<i32>]) -> Vec<bool> {
+        let num_measurements = outcomes.len();
+        detector_records
+            .iter()
+            .map(|records| {
+                records.iter().fold(false, |fired, &offset| {
+                    if let Some(abs_idx) = record_offset_to_absolute_index(num_measurements, offset)
+                        && abs_idx < num_measurements
+                        && outcomes[abs_idx]
+                    {
+                        return !fired;
+                    }
+                    fired
+                })
+            })
+            .collect()
+    }
+
+    /// Static detector-event conversion without reordering.
+    #[must_use]
+    pub fn to_detection_events(outcomes: &[bool], detector_records: &[Vec<i32>]) -> Vec<bool> {
+        Self::to_detection_events_internal(outcomes, detector_records)
+    }
+
+    /// Samples and converts to detection events in one step.
+    pub fn sample_with_detectors<R: rand::Rng>(
+        &self,
+        detector_records: &[Vec<i32>],
+        rng: &mut R,
+    ) -> (Vec<bool>, Vec<bool>) {
+        let outcomes = self.sample(rng);
+        let detection_events = self.compute_detection_events(&outcomes, detector_records);
+        (outcomes, detection_events)
+    }
+
+    /// Computes observable flips from measurement outcomes.
+    #[must_use]
+    pub fn compute_observable_flips(
+        &self,
+        outcomes: &[bool],
+        observable_records: &[Vec<i32>],
+    ) -> Vec<bool> {
+        self.compute_detection_events(outcomes, observable_records)
+    }
+
+    /// Samples detector events and observable flips in one step.
+    pub fn sample_for_decoding<R: rand::Rng>(
+        &self,
+        detector_records: &[Vec<i32>],
+        observable_records: &[Vec<i32>],
+        rng: &mut R,
+    ) -> (Vec<bool>, Vec<bool>) {
+        let outcomes = self.sample(rng);
+        let detection_events = self.compute_detection_events(&outcomes, detector_records);
+        let observable_flips = self.compute_detection_events(&outcomes, observable_records);
+        (detection_events, observable_flips)
+    }
+
+    /// Batch samples detector events and observable flips.
+    pub fn sample_batch_for_decoding<R: rand::Rng>(
+        &self,
+        num_shots: usize,
+        detector_records: &[Vec<i32>],
+        observable_records: &[Vec<i32>],
+        rng: &mut R,
+    ) -> (Vec<Vec<bool>>, Vec<Vec<bool>>) {
+        let mut all_detection_events = Vec::with_capacity(num_shots);
+        let mut all_observable_flips = Vec::with_capacity(num_shots);
+
+        for _ in 0..num_shots {
+            let (det_events, obs_flips) =
+                self.sample_for_decoding(detector_records, observable_records, rng);
+            all_detection_events.push(det_events);
+            all_observable_flips.push(obs_flips);
+        }
+
+        (all_detection_events, all_observable_flips)
+    }
+}
+
+// ============================================================================
+// Detector Error Model
+// ============================================================================
+
+/// A complete Detector Error Model (DEM).
+///
+/// This represents the noise model of a quantum circuit. It maps mechanisms
+/// (detector/DEM-output effects) to their probabilities.
+///
+/// # Aggregation Modes
+///
+/// The DEM supports two modes controlled by `aggregate`:
+///
+/// - **Aggregated mode** (`aggregate = true`): Mechanisms with the same effect
+///   are combined into a single entry using the independent error formula.
+///   This is more compact but loses information about noise sources.
+///
+/// - **Non-aggregated mode** (`aggregate = false`, default): Each noise source
+///   is kept as a separate entry. This preserves correlation information and
+///   allows advanced decoders to understand the noise structure.
+///
+/// # Decomposed Entries
+///
+/// In addition to direct mechanisms, the DEM can store "decomposed" entries
+/// that represent Y faults as X^Z. These are stored separately because:
+///
+/// 1. They help MWPM decoders understand correlation structure
+/// 2. They preserve information about fault sources
+///
+/// When a Y fault has X-effect {`D_x`} and Z-effect {`D_z`} where both are non-empty
+/// and different, it can be represented as `{D_x} ^ {D_z}` instead of XOR-ing
+/// into a single mechanism.
+#[derive(Debug, Clone)]
+pub struct DetectorErrorModel {
+    /// Detector definitions.
+    pub detectors: Vec<DetectorDef>,
+    /// Measurement-record observables rendered as standard `L<n>` outputs.
+    pub observables: Vec<DemOutput>,
+    /// PECOS tracked Paulis.
+    ///
+    /// These have their own ID space and are emitted only as PECOS metadata.
+    pub tracked_paulis: Vec<DemOutput>,
+    /// Error contributions with source tracking.
+    /// Each contribution tracks whether it came from a direct (X, Z) or decomposable (Y) source.
+    contributions: Vec<FaultContribution>,
+    /// Count of graphlike decomposable sources per 2-detector mechanism.
+    /// Key is (d0, d1) with d0 < d1. A source is "graphlike decomposable" if both
+    /// component effects are non-empty and graphlike (≤2 detectors).
+    /// Used to determine output format: ≥2 → 3 forms, 1 → 2 forms, 0 → 1 form.
+    graphlike_decomposable_counts: BTreeMap<(u32, u32), u32>,
+}
+
+/// Structured DEM mechanism tuple: `(probability, detector_ids, observable_ids)`.
+pub type MechanismTuple = (f64, Vec<u32>, Vec<u32>);
+
+/// Detector-coordinate tuple: `(detector_id, coordinates)`.
+pub type DetectorCoordinateTuple = (u32, Vec<f64>);
+
+impl DetectorErrorModel {
+    /// Creates a new empty DEM.
+    #[must_use]
+    pub fn new() -> Self {
+        Self {
+            detectors: Vec::new(),
+            observables: Vec::new(),
+            tracked_paulis: Vec::new(),
+            contributions: Vec::new(),
+            graphlike_decomposable_counts: BTreeMap::new(),
+        }
+    }
+
+    /// Creates a DEM with pre-allocated capacity.
+    #[must_use]
+    pub fn with_capacity(num_detectors: usize, num_observables: usize) -> Self {
+        Self {
+            detectors: Vec::with_capacity(num_detectors),
+            observables: Vec::with_capacity(num_observables),
+            tracked_paulis: Vec::new(),
+            contributions: Vec::new(),
+            graphlike_decomposable_counts: BTreeMap::new(),
+        }
+    }
+
+    /// Returns the number of detectors.
+    #[inline]
+    #[must_use]
+    pub fn num_detectors(&self) -> usize {
+        self.detectors.len()
+    }
+
+    /// Returns the number of observables.
+    #[inline]
+    #[must_use]
+    pub fn num_observables(&self) -> usize {
+        self.observables
+            .iter()
+            .map(|op| op.id as usize + 1)
+            .max()
+            .unwrap_or(0)
+    }
+
+    /// Returns the number of standard DEM `L<n>` observable outputs.
+    ///
+    /// This is a DEM-output alias for [`Self::num_observables`]. It does
+    /// not include PECOS tracked Paulis.
+    #[inline]
+    #[must_use]
+    pub fn num_dem_outputs(&self) -> usize {
+        self.num_observables()
+    }
+
+    /// Returns the number of tracked Paulis.
+    #[inline]
+    #[must_use]
+    pub fn num_tracked_paulis(&self) -> usize {
+        self.tracked_paulis
+            .iter()
+            .map(|op| op.id as usize + 1)
+            .max()
+            .unwrap_or(0)
+    }
+
+    /// Returns standard DEM output definitions (`L<n>` observables).
+    ///
+    /// This DEM-output accessor does not include PECOS tracked Paulis;
+    /// use [`Self::tracked_paulis`] for those.
+    #[inline]
+    #[must_use]
+    pub fn dem_outputs(&self) -> &[DemOutput] {
+        &self.observables
+    }
+
+    /// Returns mutable standard DEM output definitions (`L<n>` observables).
+    ///
+    /// This DEM-output accessor does not include PECOS tracked Paulis.
+    #[inline]
+    #[must_use]
+    pub fn dem_outputs_mut(&mut self) -> &mut [DemOutput] {
+        &mut self.observables
+    }
+
+    /// Iterates over observables.
+    pub fn observables(&self) -> impl Iterator<Item = &DemOutput> {
+        self.observables.iter()
+    }
+
+    /// Returns all tracked Pauli definitions.
+    #[inline]
+    #[must_use]
+    pub fn tracked_paulis(&self) -> &[DemOutput] {
+        &self.tracked_paulis
+    }
+
+    /// Iterates over tracked Paulis.
+    pub fn iter_tracked_paulis(&self) -> impl Iterator<Item = &DemOutput> {
+        self.tracked_paulis.iter()
+    }
+
+    /// Returns the number of tracked contributions.
+    #[inline]
+    #[must_use]
     pub fn num_contributions(&self) -> usize {
         self.contributions.len()
     }
 
+    /// Exports PECOS-only metadata that is not representable in standard DEM syntax.
+    ///
+    /// The standard DEM string remains decoder-compatible and uses ordinary
+    /// `logical_observable L<n>` declarations. This JSON form preserves the
+    /// richer PECOS DEM-output information, including tracked Paulis.
+    ///
+    /// # Panics
+    ///
+    /// Panics only if serializing a JSON value constructed in this method fails.
+    #[must_use]
+    pub fn to_pecos_metadata_json(&self) -> String {
+        let observables: Vec<serde_json::Value> = self
+            .observables
+            .iter()
+            .map(pecos_metadata_dem_output_value)
+            .collect();
+        let tracked_paulis: Vec<serde_json::Value> = self
+            .tracked_paulis
+            .iter()
+            .map(pecos_metadata_dem_output_value)
+            .collect();
+
+        serde_json::to_string_pretty(&serde_json::json!({
+            "format": "pecos.dem.metadata",
+            "version": 1,
+            "observables": observables,
+            "tracked_paulis": tracked_paulis,
+        }))
+        .expect("serializing PECOS DEM metadata should not fail")
+    }
+
+    /// Applies PECOS DEM metadata JSON to this model.
+    ///
+    /// This is the inverse of [`Self::to_pecos_metadata_json`] for DEM output
+    /// definitions. It updates existing outputs by `id` and adds any that
+    /// are present in the metadata but missing from the DEM.
+    ///
+    /// # Errors
+    ///
+    /// Returns an error if the JSON is malformed, uses an unsupported metadata
+    /// version, has an unknown op kind, or contains invalid Pauli/record
+    /// fields.
+    pub fn apply_pecos_metadata_json(&mut self, json: &str) -> Result<(), PecosDemMetadataError> {
+        let metadata = parse_pecos_metadata_json(json)?;
+        for observable in metadata.observables {
+            self.apply_observable_metadata(observable);
+        }
+        for tracked_pauli in metadata.tracked_paulis {
+            self.apply_tracked_pauli_metadata(tracked_pauli);
+        }
+        Ok(())
+    }
+
+    /// Returns a copy of this model with PECOS DEM metadata JSON applied.
+    ///
+    /// # Errors
+    ///
+    /// See [`Self::apply_pecos_metadata_json`].
+    pub fn with_pecos_metadata_json(mut self, json: &str) -> Result<Self, PecosDemMetadataError> {
+        self.apply_pecos_metadata_json(json)?;
+        Ok(self)
+    }
+
+    /// Converts the DEM to PECOS DEM text.
+    ///
+    /// This format is a strict superset of standard DEM text. It uses `D<n>`
+    /// detector targets and `L<n>` measurement-defined observable targets as
+    /// usual, and adds PECOS-only `TP<n>` tracked-Pauli targets for tracked
+    /// operator flips. Metadata follows as `pecos_observable {json}` and
+    /// `pecos_tracked_pauli {json}` statements.
+    ///
+    /// # Panics
+    ///
+    /// Panics only if serializing JSON values constructed in this method fails.
+    #[must_use]
+    pub fn to_pecos_string(&self) -> String {
+        let mut lines = Vec::new();
+
+        for det in &self.detectors {
+            if let Some([x, y, z]) = det.coords {
+                lines.push(format!("detector({x}, {y}, {z}) D{}", det.id));
+            } else {
+                lines.push(format!("detector D{}", det.id));
+            }
+        }
+
+        for obs in &self.observables {
+            lines.push(format!("logical_observable L{}", obs.id));
+        }
+
+        let mut by_effect: BTreeMap<FaultMechanism, f64> = BTreeMap::new();
+        for contrib in &self.contributions {
+            by_effect
+                .entry(contrib.effect.clone())
+                .and_modify(|p| *p = combine_independent_probs(*p, contrib.probability))
+                .or_insert(contrib.probability);
+        }
+
+        for (effect, total_prob) in by_effect {
+            if effect.is_empty() || total_prob <= 0.0 {
+                continue;
+            }
+
+            let targets = format_pecos_mechanism_targets(&effect);
+            if !targets.is_empty() {
+                lines.push(format!(
+                    "error({}) {}",
+                    format_probability(total_prob),
+                    targets
+                ));
+            }
+        }
+
+        let metadata_lines = self.pecos_metadata_lines();
+
+        if metadata_lines.is_empty() {
+            return lines.join("\n");
+        }
+        lines.extend(metadata_lines);
+        lines.join("\n")
+    }
+
+    fn pecos_metadata_lines(&self) -> Vec<String> {
+        let observable_lines = self.observables.iter().map(|observable| {
+            let value = pecos_metadata_dem_output_value(observable);
+            let payload = serde_json::to_string(&value)
+                .expect("serializing PECOS observable metadata should not fail");
+            format!("pecos_observable {payload}")
+        });
+        let tracked_pauli_lines = self.tracked_paulis.iter().map(|tracked_pauli| {
+            let value = pecos_metadata_dem_output_value(tracked_pauli);
+            let payload = serde_json::to_string(&value)
+                .expect("serializing PECOS tracked-Pauli metadata should not fail");
+            format!("pecos_tracked_pauli {payload}")
+        });
+        observable_lines.chain(tracked_pauli_lines).collect()
+    }
+
+    /// Applies PECOS metadata embedded in extended DEM text.
+    ///
+    /// Standard DEM lines are ignored by this method. PECOS extension lines
+    /// are parsed and merged into the observable/tracked-Pauli definitions.
+    ///
+    /// # Errors
+    ///
+    /// Returns an error if a PECOS metadata line is malformed.
+    pub fn apply_pecos_dem_metadata(
+        &mut self,
+        dem_text: &str,
+    ) -> Result<(), PecosDemMetadataError> {
+        for line in dem_text.lines() {
+            let line = line.trim();
+            if line.is_empty() || line.starts_with('#') {
+                continue;
+            }
+            if line.starts_with("pecos_observable") || line.starts_with("pecos_tracked_pauli") {
+                self.apply_dem_output_metadata(parse_pecos_dem_metadata_line(line)?);
+            } else if line.starts_with("pecos_") {
+                return Err(PecosDemMetadataError::new(format!(
+                    "unsupported PECOS DEM extension line: {line}"
+                )));
+            }
+        }
+        Ok(())
+    }
+
+    /// Returns a copy of this model with PECOS metadata from extended DEM text
+    /// applied.
+    ///
+    /// # Errors
+    ///
+    /// See [`Self::apply_pecos_dem_metadata`].
+    pub fn with_pecos_dem_metadata(
+        mut self,
+        dem_text: &str,
+    ) -> Result<Self, PecosDemMetadataError> {
+        self.apply_pecos_dem_metadata(dem_text)?;
+        Ok(self)
+    }
+
+    fn apply_dem_output_metadata(&mut self, target: DemOutput) {
+        if target.is_tracked_pauli() {
+            self.apply_tracked_pauli_metadata(target);
+        } else {
+            self.apply_observable_metadata(target);
+        }
+    }
+
+    fn apply_observable_metadata(&mut self, mut target: DemOutput) {
+        target.kind.get_or_insert(DemOutputKind::Observable);
+        if let Some(existing) = self
+            .observables
+            .iter_mut()
+            .find(|existing| existing.id == target.id)
+        {
+            *existing = target;
+        } else {
+            self.add_observable(target);
+        }
+    }
+
+    fn apply_tracked_pauli_metadata(&mut self, mut target: DemOutput) {
+        target.kind = Some(DemOutputKind::TrackedPauli);
+        if let Some(existing) = self
+            .tracked_paulis
+            .iter_mut()
+            .find(|existing| existing.id == target.id)
+        {
+            *existing = target;
+        } else {
+            self.add_tracked_pauli(target);
+        }
+    }
+
     /// Returns debug info about contributions for a specific mechanism.
     ///
     /// Format: One line per contribution showing source type and probability.
@@ -1335,7 +2897,7 @@ impl DetectorErrorModel {
         let mut lines = Vec::new();
 
         for contrib in &self.contributions {
-            if contrib.effect.detectors == target_dets && contrib.effect.logicals.is_empty() {
+            if contrib.effect.detectors == target_dets && contrib.effect.dem_outputs.is_empty() {
                 let source_type = match &contrib.source_type {
                     FaultSourceType::Direct => "Direct".to_string(),
                     FaultSourceType::DirectOneSidedComponent => {
@@ -1343,27 +2905,29 @@ impl DetectorErrorModel {
                     }
                     FaultSourceType::YDecomposed {
                         x_detectors,
-                        x_logicals,
+                        x_dem_outputs,
                         z_detectors,
-                        z_logicals,
+                        z_dem_outputs,
                     } => {
                         let x_dets: Vec<_> = x_detectors.iter().map(|d| format!("D{d}")).collect();
                         let z_dets: Vec<_> = z_detectors.iter().map(|d| format!("D{d}")).collect();
-                        let x_logs: Vec<_> = x_logicals.iter().map(|l| format!("L{l}")).collect();
-                        let z_logs: Vec<_> = z_logicals.iter().map(|l| format!("L{l}")).collect();
+                        let x_outputs: Vec<_> =
+                            x_dem_outputs.iter().map(|l| format!("L{l}")).collect();
+                        let z_outputs: Vec<_> =
+                            z_dem_outputs.iter().map(|l| format!("L{l}")).collect();
                         format!(
                             "YDecomposed(X=[{}{}], Z=[{}{}])",
                             x_dets.join(" "),
-                            if x_logs.is_empty() {
+                            if x_outputs.is_empty() {
                                 String::new()
                             } else {
-                                format!(" {}", x_logs.join(" "))
+                                format!(" {}", x_outputs.join(" "))
                             },
                             z_dets.join(" "),
-                            if z_logs.is_empty() {
+                            if z_outputs.is_empty() {
                                 String::new()
                             } else {
-                                format!(" {}", z_logs.join(" "))
+                                format!(" {}", z_outputs.join(" "))
                             }
                         )
                     }
@@ -1387,15 +2951,15 @@ impl DetectorErrorModel {
         }
     }
 
-    /// Returns all contributions matching a full detector/logical effect.
+    /// Returns all contributions matching a full detector/DEM-output effect.
     #[must_use]
     pub fn contributions_for_effect(
         &self,
         detectors: &[u32],
-        logicals: &[u32],
+        dem_outputs: &[u32],
     ) -> Vec<FaultContribution> {
         let target =
-            FaultMechanism::from_unsorted(detectors.iter().copied(), logicals.iter().copied());
+            FaultMechanism::from_unsorted(detectors.iter().copied(), dem_outputs.iter().copied());
         self.contributions
             .iter()
             .filter(|contrib| contrib.effect == target)
@@ -1419,7 +2983,7 @@ impl DetectorErrorModel {
                 .collect();
             let log_str: Vec<_> = contrib
                 .effect
-                .logicals
+                .dem_outputs
                 .iter()
                 .map(|l| format!("L{l}"))
                 .collect();
@@ -1491,7 +3055,7 @@ impl DetectorErrorModel {
         }
 
         for summary in by_effect.values_mut() {
-            if summary.effect.logicals.is_empty() && summary.effect.detectors.len() == 2 {
+            if summary.effect.dem_outputs.is_empty() && summary.effect.detectors.len() == 2 {
                 summary.graphlike_decomposable_count = self.graphlike_decomposable_count(
                     summary.effect.detectors[0],
                     summary.effect.detectors[1],
@@ -1746,8 +3310,8 @@ impl DetectorErrorModel {
         }
 
         // Y-containing channels are always classified as YDecomposed for source
-        // tracking purposes. This matches Stim's behavior where Y channels
-        // contribute to decomposed output forms regardless of component structure.
+        // tracking purposes so they can contribute to decomposed output forms
+        // regardless of component structure.
         //
         // The combined effect is X XOR Z. When one is empty, the combined effect
         // is just the non-empty one.
@@ -1823,11 +3387,51 @@ impl DetectorErrorModel {
     ///
     /// This should be called from the builder when processing 2-qubit gate channels
     /// where both component effects are graphlike.
+    /// Returns grouped mechanisms as (probability, `detector_ids`, `observable_ids`) tuples.
+    ///
+    /// Combines contributions with the same effect using the XOR probability formula.
+    /// Also returns detector coordinate map. This is the structured equivalent of
+    /// `to_string()` — same data, no string intermediary.
+    #[must_use]
+    pub fn to_mechanisms(&self) -> (Vec<MechanismTuple>, Vec<DetectorCoordinateTuple>) {
+        // Group contributions by effect
+        let mut by_effect: BTreeMap<FaultMechanism, f64> = BTreeMap::new();
+        for contrib in &self.contributions {
+            by_effect
+                .entry(contrib.effect.standard_effect())
+                .and_modify(|p| *p = combine_independent_probs(*p, contrib.probability))
+                .or_insert(contrib.probability);
+        }
+
+        let mechanisms: Vec<(f64, Vec<u32>, Vec<u32>)> = by_effect
+            .into_iter()
+            .filter(|(effect, prob)| !effect.is_standard_empty() && *prob > 0.0)
+            .map(|(effect, prob)| (prob, effect.detectors.to_vec(), effect.dem_outputs.to_vec()))
+            .collect();
+
+        let coords: Vec<(u32, Vec<f64>)> = self
+            .detectors
+            .iter()
+            .filter_map(|det| det.coords.map(|[x, y, z]| (det.id, vec![x, y, z])))
+            .collect();
+
+        (mechanisms, coords)
+    }
+
     pub fn mark_graphlike_decomposable(&mut self, d0: u32, d1: u32) {
         let key = if d0 < d1 { (d0, d1) } else { (d1, d0) };
         *self.graphlike_decomposable_counts.entry(key).or_insert(0) += 1;
     }
 
+    /// Merge contributions and graphlike counts from another DEM.
+    /// Used for parallelized DEM construction.
+    pub fn merge_contributions_from(&mut self, other: Self) {
+        self.contributions.extend(other.contributions);
+        for (key, count) in other.graphlike_decomposable_counts {
+            *self.graphlike_decomposable_counts.entry(key).or_insert(0) += count;
+        }
+    }
+
     /// Returns the number of graphlike decomposable sources for a 2-detector mechanism.
     #[must_use]
     pub fn graphlike_decomposable_count(&self, d0: u32, d1: u32) -> u32 {
@@ -1843,16 +3447,71 @@ impl DetectorErrorModel {
         self.detectors.push(detector);
     }
 
-    /// Adds a logical observable definition.
-    pub fn add_observable(&mut self, observable: LogicalObservable) {
+    /// Adds a non-detector DEM output definition.
+    ///
+    /// Observables are stored in the standard `L<n>` namespace. Tracked
+    /// Paulis are stored in PECOS metadata with a separate ID space.
+    pub fn add_dem_output(&mut self, output: DemOutput) {
+        if output.is_tracked_pauli() {
+            self.add_tracked_pauli(output);
+        } else {
+            self.add_observable(output);
+        }
+    }
+
+    /// Adds a standard DEM observable (`L<n>`) definition.
+    pub fn add_observable(&mut self, mut observable: DemOutput) {
+        observable.kind = Some(DemOutputKind::Observable);
+        if let Some(existing) = self
+            .observables
+            .iter_mut()
+            .find(|existing| existing.id == observable.id)
+        {
+            Self::merge_observable_definition(existing, observable);
+            return;
+        }
         self.observables.push(observable);
     }
 
+    fn merge_observable_definition(existing: &mut DemOutput, incoming: DemOutput) {
+        existing.kind = Some(DemOutputKind::Observable);
+        merge_record_parity(&mut existing.records, incoming.records);
+
+        if let Some(incoming_pauli) = incoming.pauli {
+            if let Some(existing_pauli) = &existing.pauli {
+                debug_assert_eq!(
+                    existing_pauli, &incoming_pauli,
+                    "conflicting Pauli metadata for observable L{}",
+                    existing.id
+                );
+            } else {
+                existing.pauli = Some(incoming_pauli);
+            }
+        }
+
+        if let Some(incoming_label) = incoming.label {
+            if let Some(existing_label) = &existing.label {
+                debug_assert_eq!(
+                    existing_label, &incoming_label,
+                    "conflicting labels for observable L{}",
+                    existing.id
+                );
+            } else {
+                existing.label = Some(incoming_label);
+            }
+        }
+    }
+
+    /// Adds a PECOS tracked Pauli definition.
+    pub fn add_tracked_pauli(&mut self, mut tracked_pauli: DemOutput) {
+        tracked_pauli.kind = Some(DemOutputKind::TrackedPauli);
+        self.tracked_paulis.push(tracked_pauli);
+    }
+
     /// Converts the DEM to a string in standard DEM format.
     ///
     /// Each fault mechanism is output with its total probability, with no
-    /// splitting into decomposed forms. This matches Stim's
-    /// `detector_error_model(decompose_errors=False)` output.
+    /// splitting into decomposed forms.
     ///
     /// Requires source tracking to be enabled and contributions to be populated.
     /// Use `build_with_source_tracking()` to create a DEM with contributions.
@@ -1870,7 +3529,7 @@ impl DetectorErrorModel {
             }
         }
 
-        // Add logical observable annotations
+        // Add standard observable annotations
         for obs in &self.observables {
             lines.push(format!("logical_observable L{}", obs.id));
         }
@@ -1880,14 +3539,14 @@ impl DetectorErrorModel {
         let mut by_effect: BTreeMap<FaultMechanism, f64> = BTreeMap::new();
         for contrib in &self.contributions {
             by_effect
-                .entry(contrib.effect.clone())
+                .entry(contrib.effect.standard_effect())
                 .and_modify(|p| *p = combine_independent_probs(*p, contrib.probability))
                 .or_insert(contrib.probability);
         }
 
         // Output each mechanism with its total probability
         for (effect, total_prob) in by_effect {
-            if effect.is_empty() || total_prob <= 0.0 {
+            if effect.is_standard_empty() || total_prob <= 0.0 {
                 continue;
             }
 
@@ -1986,7 +3645,7 @@ impl DetectorErrorModel {
         if let Some(cached) = cache.get(&key) {
             let strategy = if contrib.decomposition_components().is_some() {
                 ContributionRenderStrategy::SourceComponents
-            } else if contrib.effect.num_detectors() == 2 && contrib.effect.logicals.is_empty() {
+            } else if contrib.effect.num_detectors() == 2 && contrib.effect.dem_outputs.is_empty() {
                 let direct_targets =
                     Self::two_detector_direct_targets(&contrib.effect, singleton_set);
                 if matches!(
@@ -2007,7 +3666,7 @@ impl DetectorErrorModel {
             return (cached.clone(), strategy, recorded_component_targets);
         }
 
-        let effect = &contrib.effect;
+        let effect = contrib.effect.standard_effect();
         let (targets, strategy) = if let Some((x_effect, z_effect)) =
             contrib.decomposition_components()
         {
@@ -2032,8 +3691,8 @@ impl DetectorErrorModel {
                     targets
                 };
                 (targets, ContributionRenderStrategy::SourceComponents)
-            } else if effect.num_detectors() == 2 && effect.logicals.is_empty() {
-                let direct_targets = Self::two_detector_direct_targets(effect, singleton_set);
+            } else if effect.num_detectors() == 2 && effect.dem_outputs.is_empty() {
+                let direct_targets = Self::two_detector_direct_targets(&effect, singleton_set);
                 if matches!(
                     two_detector_direct_policy,
                     TwoDetectorDirectRenderPolicy::PreferRecordedComponents
@@ -2063,7 +3722,7 @@ impl DetectorErrorModel {
                     )
                 }
             } else if effect.is_hyperedge() {
-                if let Some(decomp) = graphlike_index.find_hyperedge_decomposition(effect) {
+                if let Some(decomp) = graphlike_index.find_hyperedge_decomposition(&effect) {
                     (
                         Self::maybe_maximally_decompose_parts(decomp, singleton_set)
                             .iter()
@@ -2074,7 +3733,7 @@ impl DetectorErrorModel {
                     )
                 } else {
                     (
-                        format_mechanism_targets(effect),
+                        format_mechanism_targets(&effect),
                         ContributionRenderStrategy::EffectDirect,
                     )
                 }
@@ -2088,8 +3747,8 @@ impl DetectorErrorModel {
                     ContributionRenderStrategy::EffectDirect,
                 )
             }
-        } else if effect.num_detectors() == 2 && effect.logicals.is_empty() {
-            let direct_targets = Self::two_detector_direct_targets(effect, singleton_set);
+        } else if effect.num_detectors() == 2 && effect.dem_outputs.is_empty() {
+            let direct_targets = Self::two_detector_direct_targets(&effect, singleton_set);
             if matches!(
                 two_detector_direct_policy,
                 TwoDetectorDirectRenderPolicy::PreferRecordedComponents
@@ -2119,7 +3778,7 @@ impl DetectorErrorModel {
                 )
             }
         } else if effect.is_hyperedge() {
-            if let Some(decomp) = graphlike_index.find_hyperedge_decomposition(effect) {
+            if let Some(decomp) = graphlike_index.find_hyperedge_decomposition(&effect) {
                 (
                     Self::maybe_maximally_decompose_parts(decomp, singleton_set)
                         .iter()
@@ -2130,7 +3789,7 @@ impl DetectorErrorModel {
                 )
             } else {
                 (
-                    format_mechanism_targets(effect),
+                    format_mechanism_targets(&effect),
                     ContributionRenderStrategy::EffectDirect,
                 )
             }
@@ -2166,9 +3825,8 @@ impl DetectorErrorModel {
         .0
     }
 
-    /// Converts the DEM to Stim format using source tracking (decomposed format).
+    /// Converts the DEM to decomposed text using source tracking.
     ///
-    /// This matches Stim's `detector_error_model(decompose_errors=True)` output.
     /// Fault mechanisms are split into direct and decomposed forms based on
     /// their source types (X/Z vs Y errors).
     ///
@@ -2188,7 +3846,7 @@ impl DetectorErrorModel {
     ///
     /// Hyperedges (3+ detectors) are decomposed into graphlike forms when
     /// possible. Mechanisms with up to 2 detectors are already graphlike even
-    /// when they carry multiple logical observables.
+    /// when they carry multiple DEM outputs.
     #[must_use]
     fn to_string_decomposed_inner(
         &self,
@@ -2206,7 +3864,7 @@ impl DetectorErrorModel {
             }
         }
 
-        // Add logical observable annotations
+        // Add standard observable annotations
         for obs in &self.observables {
             lines.push(format!("logical_observable L{}", obs.id));
         }
@@ -2229,8 +3887,8 @@ impl DetectorErrorModel {
         };
 
         // Process each tracked contribution individually, then regroup identical
-        // decomposed outputs. This is closer to Stim's decomposition pass, which
-        // rewrites each error class before merging identical rewritten targets.
+        // decomposed outputs. Rewriting each error class before merging keeps
+        // source-aware decompositions stable.
         for contrib in &self.contributions {
             if contrib.effect.is_empty() || contrib.probability <= 0.0 {
                 continue;
@@ -2305,8 +3963,9 @@ impl DetectorErrorModel {
     fn collect_graphlike_mechanisms(&self) -> BTreeSet<FaultMechanism> {
         let mut graphlike = BTreeSet::new();
         for contrib in &self.contributions {
-            if contrib.effect.is_graphlike() {
-                graphlike.insert(contrib.effect.clone());
+            let standard = contrib.effect.standard_effect();
+            if !standard.is_standard_empty() && standard.is_graphlike() {
+                graphlike.insert(standard);
             }
         }
         graphlike
@@ -2317,541 +3976,1014 @@ impl Default for DetectorErrorModel {
     fn default() -> Self {
         Self::new()
     }
-}
+}
+
+// ============================================================================
+// Probability Combination
+// ============================================================================
+
+/// Combines two independent error probabilities.
+///
+/// For independent errors with probabilities p1 and p2, the probability
+/// that exactly one error occurs is: p1*(1-p2) + p2*(1-p1).
+///
+/// This is the correct formula for combining probabilities when the same
+/// fault mechanism can be triggered by multiple independent error sources.
+#[inline]
+#[must_use]
+pub fn combine_probabilities(p1: f64, p2: f64) -> f64 {
+    p1 * (1.0 - p2) + p2 * (1.0 - p1)
+}
+
+/// Formats an fault mechanism's targets as a string (e.g., "D0 D1 L0").
+fn format_mechanism_targets(mechanism: &FaultMechanism) -> String {
+    let mut targets = Vec::new();
+    for &det in &mechanism.detectors {
+        targets.push(format!("D{det}"));
+    }
+    for &dem_output in &mechanism.dem_outputs {
+        targets.push(format!("L{dem_output}"));
+    }
+    targets.join(" ")
+}
+
+/// Formats a PECOS DEM mechanism's targets, including tracked Pauli `TP<n>` outputs.
+fn format_pecos_mechanism_targets(mechanism: &FaultMechanism) -> String {
+    let mut targets = Vec::new();
+    for &det in &mechanism.detectors {
+        targets.push(format!("D{det}"));
+    }
+    for &dem_output in &mechanism.dem_outputs {
+        targets.push(format!("L{dem_output}"));
+    }
+    for &tracked_pauli in &mechanism.tracked_paulis {
+        targets.push(format!("TP{tracked_pauli}"));
+    }
+    targets.join(" ")
+}
+
+/// Combines two independent error probabilities.
+///
+/// For two independent errors with probabilities p1 and p2, the combined
+/// probability of having an odd number of errors (i.e., the XOR of the effects) is:
+/// `p_combined` = p1*(1-p2) + p2*(1-p1)
+fn combine_independent_probs(p1: f64, p2: f64) -> f64 {
+    // For DEM probability aggregation, we use XOR combination because
+    // errors toggle detector bits - if two errors both flip the same detector,
+    // they cancel out (XOR behavior). We want P(odd number of errors).
+    // XOR formula: P(A XOR B) = P(A)*(1-P(B)) + P(B)*(1-P(A)) = p1 + p2 - 2*p1*p2
+    p1 * (1.0 - p2) + p2 * (1.0 - p1)
+}
+
+/// Formats a probability value similar to Python's %g format.
+/// Uses scientific notation for very small/large values, otherwise decimal.
+fn format_probability(p: f64) -> String {
+    if p == 0.0 {
+        return "0".to_string();
+    }
+
+    let abs_p = p.abs();
+
+    // Use scientific notation for very small or very large values
+    if (1e-4..1e6).contains(&abs_p) {
+        // Regular decimal notation
+        let formatted = format!("{p:.6}");
+        trim_trailing_zeros(&formatted)
+    } else {
+        // Format with up to 6 significant figures in scientific notation
+        let formatted = format!("{p:.6e}");
+        // Trim trailing zeros after decimal point
+        trim_trailing_zeros(&formatted)
+    }
+}
+
+/// Trims trailing zeros from a number string.
+fn trim_trailing_zeros(s: &str) -> String {
+    if let Some(e_pos) = s.find('e') {
+        // Scientific notation: trim zeros before 'e'
+        let (mantissa, exponent) = s.split_at(e_pos);
+        let trimmed = mantissa.trim_end_matches('0').trim_end_matches('.');
+        format!("{trimmed}{exponent}")
+    } else if s.contains('.') {
+        // Decimal notation: trim trailing zeros
+        s.trim_end_matches('0').trim_end_matches('.').to_string()
+    } else {
+        s.to_string()
+    }
+}
+
+#[cfg(test)]
+mod tests {
+    use super::*;
+
+    #[test]
+    fn test_error_mechanism_xor() {
+        let m1 = FaultMechanism::from_unsorted([0, 1, 2], [0]);
+        let m2 = FaultMechanism::from_unsorted([1, 2, 3], [0, 1]);
+
+        let result = m1.xor(&m2);
+
+        // Detectors: {0, 1, 2} XOR {1, 2, 3} = {0, 3}
+        assert_eq!(result.detectors.as_slice(), &[0, 3]);
+        // DEM outputs: {0} XOR {0, 1} = {1}
+        assert_eq!(result.dem_outputs.as_slice(), &[1]);
+    }
+
+    #[test]
+    fn test_error_mechanism_equality() {
+        let m1 = FaultMechanism::from_unsorted([2, 0, 1], [1, 0]);
+        let m2 = FaultMechanism::from_unsorted([0, 1, 2], [0, 1]);
+
+        assert_eq!(m1, m2);
+        assert_eq!(m1.detectors.as_slice(), &[0, 1, 2]);
+        assert_eq!(m1.dem_outputs.as_slice(), &[0, 1]);
+    }
+
+    #[test]
+    fn test_error_mechanism_equality_and_hash_include_tracked_paulis() {
+        let standard = FaultMechanism::from_unsorted([0], []);
+        let with_tracked = FaultMechanism::from_unsorted_with_tracked_paulis([0], [], [0]);
+
+        assert_ne!(standard, with_tracked);
+        assert_eq!(standard.standard_effect(), with_tracked.standard_effect());
+
+        let mut set = std::collections::HashSet::new();
+        set.insert(standard);
+        set.insert(with_tracked);
+        assert_eq!(
+            set.len(),
+            2,
+            "internal mechanism identity must keep tracked Paulis distinct"
+        );
+    }
+
+    #[test]
+    fn test_pecos_target_format_canonicalizes_tracked_paulis() {
+        let mechanism = FaultMechanism::from_unsorted_with_tracked_paulis([], [], [2, 0]);
+        assert_eq!(
+            DecomposedFault::single(mechanism).to_pecos_targets(),
+            "TP0 TP2"
+        );
+    }
+
+    #[test]
+    fn test_combine_probabilities() {
+        // Same probability twice
+        let p = combine_probabilities(0.01, 0.01);
+        // Expected: 0.01 * 0.99 + 0.01 * 0.99 = 0.0198
+        assert!((p - 0.0198).abs() < 1e-10);
+
+        // One zero probability
+        assert!((combine_probabilities(0.0, 0.5) - 0.5).abs() < 1e-10);
+        assert!((combine_probabilities(0.5, 0.0) - 0.5).abs() < 1e-10);
+
+        // Both zero
+        assert!((combine_probabilities(0.0, 0.0)).abs() < 1e-10);
+    }
 
-// ============================================================================
-// Measurement Noise Model (MNM)
-// ============================================================================
+    #[test]
+    fn test_pecos_metadata_json_preserves_tracked_paulis() {
+        use pecos_core::pauli::{X, Z};
 
-/// A measurement fault mechanism: a set of measurements that flip together.
-///
-/// Unlike [`FaultMechanism`] which operates on detectors, this operates directly
-/// on raw measurement indices. This is useful for sampling measurement outcomes
-/// without needing detector definitions.
-///
-/// Measurements are stored in sorted order for canonical representation.
-#[derive(Clone, Default)]
-pub struct MeasurementMechanism {
-    /// Measurement indices that flip together (sorted).
-    pub measurements: SmallVec<[u32; 4]>,
-}
+        let mut dem = DetectorErrorModel::new();
+        dem.add_dem_output(
+            DemOutput::new(0)
+                .with_kind(DemOutputKind::TrackedPauli)
+                .with_pauli(X(0) & Z(2))
+                .with_label("track_check"),
+        );
+        dem.add_dem_output(DemOutput::new(1).with_records([-1, -3]));
 
-impl MeasurementMechanism {
-    /// Creates a new empty measurement mechanism.
-    #[must_use]
-    pub fn new() -> Self {
-        Self::default()
-    }
+        let metadata: serde_json::Value =
+            serde_json::from_str(&dem.to_pecos_metadata_json()).unwrap();
+        let observables = metadata["observables"].as_array().unwrap();
+        let tracked_paulis = metadata["tracked_paulis"].as_array().unwrap();
 
-    /// Creates a mechanism from unsorted measurement indices.
-    #[must_use]
-    pub fn from_unsorted(measurements: impl IntoIterator<Item = u32>) -> Self {
-        let mut meas: SmallVec<[u32; 4]> = measurements.into_iter().collect();
-        meas.sort_unstable();
-        Self { measurements: meas }
+        assert_eq!(metadata["format"], "pecos.dem.metadata");
+        assert_eq!(metadata["version"], 1);
+        assert_eq!(tracked_paulis[0]["id"], 0);
+        assert_eq!(tracked_paulis[0]["kind"], "tracked_pauli");
+        assert_eq!(tracked_paulis[0]["label"], "track_check");
+        assert_eq!(tracked_paulis[0]["pauli"], "+X0 Z2");
+        assert_eq!(observables[0]["id"], 1);
+        assert_eq!(observables[0]["kind"], "observable");
+        assert_eq!(observables[0]["records"], serde_json::json!([-1, -3]));
     }
 
-    /// Creates a mechanism from pre-sorted measurement indices.
-    #[must_use]
-    pub fn from_sorted(measurements: SmallVec<[u32; 4]>) -> Self {
-        debug_assert!(
-            measurements.windows(2).all(|w| w[0] <= w[1]),
-            "measurements must be sorted"
+    #[test]
+    fn test_dem_counts_keep_detectors_observables_and_tracked_paulis_distinct() {
+        use pecos_core::pauli::X;
+
+        let mut dem = DetectorErrorModel::new();
+        dem.add_detector(DetectorDef::new(0).with_records([-1]));
+        dem.add_dem_output(DemOutput::new(0).with_records([-1, -3]));
+        dem.add_dem_output(
+            DemOutput::new(0)
+                .with_kind(DemOutputKind::TrackedPauli)
+                .with_pauli(X(0)),
         );
-        Self { measurements }
-    }
 
-    /// Returns true if this mechanism has no effect (empty).
-    #[inline]
-    #[must_use]
-    pub fn is_empty(&self) -> bool {
-        self.measurements.is_empty()
+        assert_eq!(dem.num_detectors(), 1);
+        assert_eq!(dem.num_dem_outputs(), 1);
+        assert_eq!(dem.num_observables(), 1);
+        assert_eq!(dem.num_tracked_paulis(), 1);
+        assert_eq!(dem.observables().map(|op| op.id).collect::<Vec<_>>(), [0]);
+        assert_eq!(
+            dem.tracked_paulis()
+                .iter()
+                .map(|op| op.id)
+                .collect::<Vec<_>>(),
+            [0]
+        );
     }
 
-    /// Returns the number of measurements in this mechanism.
-    #[inline]
-    #[must_use]
-    pub fn len(&self) -> usize {
-        self.measurements.len()
-    }
-}
+    #[test]
+    fn test_duplicate_observable_definitions_merge_records_by_parity() {
+        use pecos_core::pauli::X;
 
-impl PartialEq for MeasurementMechanism {
-    fn eq(&self, other: &Self) -> bool {
-        self.measurements == other.measurements
+        let mut dem = DetectorErrorModel::new();
+        dem.add_observable(
+            DemOutput::new(0)
+                .with_records([-1, -2])
+                .with_pauli(X(0))
+                .with_label("logical_z"),
+        );
+        dem.add_observable(
+            DemOutput::new(0)
+                .with_records([-2, -3])
+                .with_pauli(X(0))
+                .with_label("logical_z"),
+        );
+
+        assert_eq!(dem.num_observables(), 1);
+        let observable = &dem.dem_outputs()[0];
+        assert_eq!(observable.records.as_slice(), &[-1, -3]);
+        assert_eq!(observable.pauli.as_ref().unwrap().to_sparse_str(), "+X0");
+        assert_eq!(observable.label.as_deref(), Some("logical_z"));
     }
-}
 
-impl Eq for MeasurementMechanism {}
+    #[test]
+    fn test_observable_records_are_stored_by_xor_parity() {
+        let mut dem = DetectorErrorModel::new();
+        dem.add_observable(DemOutput::new(0).with_records([-1, -2, -1, -3]));
 
-impl Hash for MeasurementMechanism {
-    fn hash<H: Hasher>(&self, state: &mut H) {
-        self.measurements.hash(state);
+        assert_eq!(dem.dem_outputs()[0].records.as_slice(), &[-2, -3]);
     }
-}
 
-impl PartialOrd for MeasurementMechanism {
-    fn partial_cmp(&self, other: &Self) -> Option<Ordering> {
-        Some(self.cmp(other))
+    #[test]
+    #[cfg(debug_assertions)]
+    #[should_panic(expected = "conflicting labels for observable L0")]
+    fn test_duplicate_observable_definitions_reject_conflicting_labels() {
+        let mut dem = DetectorErrorModel::new();
+        dem.add_observable(DemOutput::new(0).with_label("first"));
+        dem.add_observable(DemOutput::new(0).with_label("second"));
     }
-}
 
-impl Ord for MeasurementMechanism {
-    fn cmp(&self, other: &Self) -> Ordering {
-        self.measurements.cmp(&other.measurements)
-    }
-}
+    #[test]
+    #[cfg(debug_assertions)]
+    #[should_panic(expected = "conflicting Pauli metadata for observable L0")]
+    fn test_duplicate_observable_definitions_reject_conflicting_paulis() {
+        use pecos_core::pauli::{X, Z};
 
-impl fmt::Debug for MeasurementMechanism {
-    fn fmt(&self, f: &mut fmt::Formatter<'_>) -> fmt::Result {
-        write!(
-            f,
-            "MeasurementMechanism({:?})",
-            self.measurements.as_slice()
-        )
+        let mut dem = DetectorErrorModel::new();
+        dem.add_observable(DemOutput::new(0).with_pauli(X(0)));
+        dem.add_observable(DemOutput::new(0).with_pauli(Z(0)));
     }
-}
 
-/// A Measurement Noise Model (MNM) for fast approximate sampling.
-///
-/// Unlike a DEM which maps fault mechanisms to detector effects, the MNM maps
-/// directly to measurement effects. This allows sampling raw measurement outcomes
-/// without needing detector definitions.
-///
-/// # Sampling Modes
-///
-/// - **Per-fault-location** (accurate): Sample each (location, Pauli) independently
-/// - **Per-mechanism** (fast, approximate): Sample each unique measurement effect once
-///
-/// The MNM enables the fast per-mechanism mode while still producing raw measurement
-/// outcomes that can be converted to detection events using any detector definition.
-///
-/// # Example
-///
-/// Build an MNM from a fault influence map and sample measurement outcomes.
-/// In practice you will use [`MemBuilder`] to populate mechanisms; here we
-/// use an empty MNM to keep the doctest self-contained.
-///
-/// ```
-/// use pecos_qec::fault_tolerance::dem_builder::MeasurementNoiseModel;
-/// use rand::SeedableRng;
-/// use rand::rngs::StdRng;
-///
-/// let num_measurements = 4;
-/// let mnm = MeasurementNoiseModel::new(num_measurements);
-///
-/// let mut outcomes = vec![false; num_measurements];
-/// let mut rng = StdRng::seed_from_u64(0);
-/// mnm.sample_into(&mut outcomes, &mut rng);
-/// ```
-#[derive(Debug, Clone, Default)]
-pub struct MeasurementNoiseModel {
-    /// Fault mechanisms mapped to their probabilities.
-    /// Uses `BTreeMap` for deterministic iteration order.
-    pub mechanisms: BTreeMap<MeasurementMechanism, f64>,
-    /// Total number of measurements in the circuit.
-    pub num_measurements: usize,
-    /// Optional mapping from influence map index to `TickCircuit` index.
-    /// If set, outcomes are reordered before detection event conversion.
-    /// `im_to_tc`[`im_idx`] = `tc_idx`
-    pub im_to_tc_order: Option<Vec<usize>>,
-}
+    #[test]
+    fn test_dem_output_kind_predicates_are_mutually_exclusive() {
+        use pecos_core::pauli::X;
 
-impl MeasurementNoiseModel {
-    /// Creates a new empty MNM.
-    #[must_use]
-    pub fn new(num_measurements: usize) -> Self {
-        Self {
-            mechanisms: BTreeMap::new(),
-            num_measurements,
-            im_to_tc_order: None,
-        }
+        let observable = DemOutput::new(0)
+            .with_kind(DemOutputKind::Observable)
+            .with_pauli(X(0));
+        assert!(observable.is_observable());
+        assert!(!observable.is_tracked_pauli());
+
+        let tracked = DemOutput::new(0)
+            .with_kind(DemOutputKind::TrackedPauli)
+            .with_records([-1]);
+        assert!(!tracked.is_observable());
+        assert!(tracked.is_tracked_pauli());
+
+        let inferred_observable = DemOutput::new(1).with_records([-1]);
+        assert!(inferred_observable.is_observable());
+        assert!(!inferred_observable.is_tracked_pauli());
+
+        let inferred_tracked = DemOutput::new(1).with_pauli(X(1));
+        assert!(!inferred_tracked.is_observable());
+        assert!(inferred_tracked.is_tracked_pauli());
     }
 
-    /// Sets the measurement order mapping from influence map to `TickCircuit` order.
-    ///
-    /// This is needed when detector definitions use `TickCircuit` measurement indices
-    /// but the influence map uses a different ordering.
-    ///
-    /// # Arguments
-    ///
-    /// * `im_to_tc` - Mapping where `im_to_tc[im_idx] = tc_idx`
-    #[must_use]
-    pub fn with_measurement_order(mut self, im_to_tc: Vec<usize>) -> Self {
-        self.im_to_tc_order = Some(im_to_tc);
-        self
+    #[test]
+    fn test_generic_dem_output_metadata_uses_consistent_kind_name() {
+        let mut dem = DetectorErrorModel::new();
+        dem.add_dem_output(DemOutput::new(0));
+
+        let metadata: serde_json::Value =
+            serde_json::from_str(&dem.to_pecos_metadata_json()).unwrap();
+        let ops = metadata["observables"].as_array().unwrap();
+
+        assert_eq!(ops[0]["kind"], "observable");
+
+        let recovered = DetectorErrorModel::new()
+            .with_pecos_metadata_json(&dem.to_pecos_metadata_json())
+            .unwrap();
+        assert_eq!(recovered.num_dem_outputs(), 1);
+        assert_eq!(recovered.num_tracked_paulis(), 0);
+        assert_eq!(recovered.dem_outputs()[0].id, 0);
+        assert_eq!(
+            recovered.dem_outputs()[0].kind,
+            Some(DemOutputKind::Observable)
+        );
     }
 
-    /// Sets the measurement order mapping (mutable version).
-    pub fn set_measurement_order(&mut self, im_to_tc: Vec<usize>) {
-        self.im_to_tc_order = Some(im_to_tc);
+    #[test]
+    fn test_pecos_metadata_json_round_trips_tracked_pauli_metadata() {
+        use pecos_core::pauli::{X, Z};
+
+        let mut dem = DetectorErrorModel::new();
+        dem.add_dem_output(DemOutput::new(0));
+        dem.add_dem_output(DemOutput::new(1));
+
+        let mut source = DetectorErrorModel::new();
+        source.add_dem_output(
+            DemOutput::new(0)
+                .with_kind(DemOutputKind::TrackedPauli)
+                .with_pauli(X(0) & Z(2))
+                .with_label("track_check"),
+        );
+        source.add_dem_output(DemOutput::new(1).with_records([-1, -3]));
+
+        dem.apply_pecos_metadata_json(&source.to_pecos_metadata_json())
+            .unwrap();
+
+        assert_eq!(
+            dem.tracked_paulis()[0].kind,
+            Some(DemOutputKind::TrackedPauli)
+        );
+        assert_eq!(
+            dem.tracked_paulis()[0].label.as_deref(),
+            Some("track_check")
+        );
+        assert_eq!(
+            dem.tracked_paulis()[0]
+                .pauli
+                .as_ref()
+                .unwrap()
+                .to_sparse_str(),
+            "+X0 Z2"
+        );
+        assert_eq!(dem.dem_outputs()[1].kind, Some(DemOutputKind::Observable));
+        assert_eq!(dem.dem_outputs()[1].records.as_slice(), &[-1, -3]);
     }
 
-    /// Returns the number of distinct mechanisms.
-    #[inline]
-    #[must_use]
-    pub fn num_mechanisms(&self) -> usize {
-        self.mechanisms.len()
+    #[test]
+    fn test_pecos_metadata_json_parser_requires_output_arrays() {
+        let old_metadata_json = r#"{
+            "format": "pecos.dem.metadata",
+            "version": 1,
+            "old_outputs": [
+                {
+                    "id": 4,
+                    "kind": "old_kind",
+                    "label": "old_name",
+                    "pauli": null,
+                    "records": []
+                }
+            ]
+        }"#;
+
+        let err = DetectorErrorModel::new()
+            .with_pecos_metadata_json(old_metadata_json)
+            .unwrap_err();
+        assert!(
+            err.message()
+                .contains("missing observables or tracked_paulis metadata arrays")
+        );
     }
 
-    /// Adds an fault mechanism with the given probability.
-    ///
-    /// If the mechanism already exists, probabilities are combined
-    /// using the independent error formula: p1*(1-p2) + p2*(1-p1).
-    pub fn add_mechanism(&mut self, mechanism: MeasurementMechanism, probability: f64) {
-        if mechanism.is_empty() || probability <= 0.0 {
-            return;
-        }
+    #[test]
+    fn test_pecos_metadata_json_parser_rejects_legacy_tracked_fields() {
+        let json = r#"{
+            "format": "pecos.dem.metadata",
+            "version": 1,
+            "observables": [],
+            "tracked_paulis": [],
+            "tracked_ops": [
+                {
+                    "id": 0,
+                    "kind": "tracked_op",
+                    "label": "old_name",
+                    "pauli": "+X0",
+                    "records": []
+                }
+            ]
+        }"#;
 
-        self.mechanisms
-            .entry(mechanism)
-            .and_modify(|p| *p = combine_probabilities(*p, probability))
-            .or_insert(probability);
+        let err = DetectorErrorModel::new()
+            .with_pecos_metadata_json(json)
+            .unwrap_err();
+        assert!(
+            err.message()
+                .contains("unsupported legacy metadata field: tracked_ops; use tracked_paulis")
+        );
     }
 
-    /// Samples measurement outcomes into the provided buffer.
-    ///
-    /// Each mechanism is sampled once according to its probability.
-    /// When a mechanism fires, its measurements are XOR'd into the outcomes.
-    ///
-    /// # Arguments
-    ///
-    /// * `outcomes` - Buffer to store measurement outcomes (must be pre-sized)
-    /// * `rng` - Random number generator
-    pub fn sample_into<R: rand::Rng>(&self, outcomes: &mut [bool], rng: &mut R) {
-        // Clear outcomes
-        outcomes.fill(false);
+    #[test]
+    fn test_pecos_metadata_json_parser_rejects_old_generic_kind_names() {
+        let json = r#"{
+            "format": "pecos.dem.metadata",
+            "version": 1,
+            "tracked_paulis": [
+                {
+                    "id": 4,
+                    "kind": "old_kind",
+                    "label": "old_name",
+                    "pauli": null,
+                    "records": []
+                }
+            ]
+        }"#;
 
-        for (mechanism, &prob) in &self.mechanisms {
-            if rng.random::<f64>() < prob {
-                for &meas_idx in &mechanism.measurements {
-                    if (meas_idx as usize) < outcomes.len() {
-                        outcomes[meas_idx as usize] ^= true;
-                    }
+        let err = DetectorErrorModel::new()
+            .with_pecos_metadata_json(json)
+            .unwrap_err();
+        assert!(
+            err.message()
+                .contains("DEM output 0 has unknown kind: old_kind")
+        );
+
+        let alias_json = r#"{
+            "format": "pecos.dem.metadata",
+            "version": 1,
+            "tracked_paulis": [
+                {
+                    "id": 4,
+                    "kind": "pauli_operator",
+                    "label": "old_alias",
+                    "pauli": "+X0",
+                    "records": []
                 }
-            }
-        }
+            ]
+        }"#;
+        let err = DetectorErrorModel::new()
+            .with_pecos_metadata_json(alias_json)
+            .unwrap_err();
+        assert!(
+            err.message()
+                .contains("DEM output 0 has unknown kind: pauli_operator")
+        );
     }
 
-    /// Samples and returns measurement outcomes as a vector.
-    #[must_use]
-    pub fn sample<R: rand::Rng>(&self, rng: &mut R) -> Vec<bool> {
-        let mut outcomes = vec![false; self.num_measurements];
-        self.sample_into(&mut outcomes, rng);
-        outcomes
+    #[test]
+    fn test_pecos_metadata_json_rejects_records_on_tracked_pauli() {
+        let json = r#"{
+            "format": "pecos.dem.metadata",
+            "version": 1,
+            "tracked_paulis": [
+                {
+                    "id": 0,
+                    "kind": "tracked_pauli",
+                    "pauli": "X0",
+                    "records": [-1]
+                }
+            ]
+        }"#;
+
+        let err = DetectorErrorModel::new()
+            .with_pecos_metadata_json(json)
+            .unwrap_err();
+        assert!(
+            err.message()
+                .contains("tracked Pauli DEM output 0 cannot have measurement records")
+        );
     }
 
-    /// Iterates over all mechanisms and their probabilities.
-    pub fn iter(&self) -> impl Iterator<Item = (&MeasurementMechanism, &f64)> {
-        self.mechanisms.iter()
+    #[test]
+    fn test_pecos_dem_text_is_stim_superset_with_dem_output_metadata() {
+        use pecos_core::pauli::{X, Z};
+
+        let mut dem = DetectorErrorModel::new();
+        dem.add_detector(DetectorDef::new(0));
+        dem.add_dem_output(
+            DemOutput::new(0)
+                .with_kind(DemOutputKind::TrackedPauli)
+                .with_pauli(X(0) & Z(2))
+                .with_label("track_check"),
+        );
+        dem.add_direct_contribution(
+            FaultMechanism::from_unsorted_with_tracked_paulis([0], [], [0]),
+            0.01,
+        );
+
+        let stim_text = dem.to_string();
+        assert!(!stim_text.contains("logical_observable L0"));
+        assert!(stim_text.contains("error(0.01) D0"));
+        assert!(!stim_text.contains("TP0"));
+        assert!(!stim_text.contains("pecos_"));
+
+        let pecos_text = dem.to_pecos_string();
+        assert!(pecos_text.contains("error(0.01) D0 TP0"));
+        assert!(pecos_text.contains("pecos_tracked_pauli"));
+        assert!(pecos_text.contains(r#""kind":"tracked_pauli""#));
+        assert!(pecos_text.contains(r#""pauli":"+X0 Z2""#));
+
+        let recovered = DetectorErrorModel::new()
+            .with_pecos_dem_metadata(&pecos_text)
+            .unwrap();
+        assert_eq!(recovered.num_dem_outputs(), 0);
+        assert_eq!(recovered.num_tracked_paulis(), 1);
+        assert_eq!(
+            recovered.tracked_paulis()[0].kind,
+            Some(DemOutputKind::TrackedPauli)
+        );
+        assert_eq!(
+            recovered.tracked_paulis()[0]
+                .pauli
+                .as_ref()
+                .unwrap()
+                .to_sparse_str(),
+            "+X0 Z2"
+        );
+        assert_eq!(
+            recovered.tracked_paulis()[0].label.as_deref(),
+            Some("track_check")
+        );
     }
 
-    /// Converts measurement outcomes to detection events.
-    ///
-    /// Given raw measurement outcomes and detector definitions (as measurement indices),
-    /// computes which detectors fire by XOR'ing the specified measurements for each detector.
-    ///
-    /// If `im_to_tc_order` is set, outcomes are first reordered from influence map
-    /// order to `TickCircuit` order before applying detector records.
-    ///
-    /// # Arguments
-    ///
-    /// * `outcomes` - Raw measurement outcomes in influence map order (from `sample()`)
-    /// * `detector_records` - For each detector, the list of measurement indices to XOR.
-    ///   Indices can be negative (offset from end) or positive (absolute).
-    ///   These indices refer to `TickCircuit` measurement order.
-    ///
-    /// # Returns
-    ///
-    /// Vector of detection events (true = detector fired)
-    #[must_use]
-    pub fn compute_detection_events(
-        &self,
-        outcomes: &[bool],
-        detector_records: &[Vec<i32>],
-    ) -> Vec<bool> {
-        // Reorder outcomes from IM order to TC order if mapping is set
-        let tc_outcomes: Vec<bool> = if let Some(ref im_to_tc) = self.im_to_tc_order {
-            let mut reordered = vec![false; outcomes.len()];
-            for (im_idx, &tc_idx) in im_to_tc.iter().enumerate() {
-                if im_idx < outcomes.len() && tc_idx < reordered.len() {
-                    reordered[tc_idx] = outcomes[im_idx];
-                }
-            }
-            reordered
-        } else {
-            outcomes.to_vec()
-        };
+    #[test]
+    fn test_pecos_dem_text_round_trips_observables_and_tracked_paulis() {
+        use pecos_core::pauli::Z;
 
-        Self::to_detection_events_internal(&tc_outcomes, detector_records)
+        let mut dem = DetectorErrorModel::new();
+        dem.add_detector(DetectorDef::new(0));
+        dem.add_dem_output(DemOutput::new(0).with_records([-1]));
+        dem.add_dem_output(DemOutput::new(1).with_records([-2]));
+        dem.add_dem_output(
+            DemOutput::new(0)
+                .with_kind(DemOutputKind::TrackedPauli)
+                .with_pauli(Z(3))
+                .with_label("tracked_z3"),
+        );
+        dem.add_direct_contribution(
+            FaultMechanism::from_unsorted_with_tracked_paulis([0], [0], [0]),
+            0.01,
+        );
+        dem.add_direct_contribution(FaultMechanism::from_unsorted([], [1]), 0.02);
+
+        let stim_text = dem.to_string();
+        assert!(stim_text.contains("logical_observable L0"));
+        assert!(stim_text.contains("logical_observable L1"));
+        assert!(!stim_text.contains("logical_observable L2"));
+        assert!(!stim_text.contains("TP0"));
+        assert!(!stim_text.contains("pecos_tracked_pauli"));
+
+        let pecos_text = dem.to_pecos_string();
+        assert!(pecos_text.contains("error(0.01) D0 L0 TP0"));
+        assert!(pecos_text.contains("pecos_observable"));
+        assert!(pecos_text.contains("pecos_tracked_pauli"));
+
+        let recovered = DetectorErrorModel::new()
+            .with_pecos_dem_metadata(&pecos_text)
+            .unwrap();
+        assert_eq!(recovered.num_observables(), 2);
+        assert_eq!(recovered.num_dem_outputs(), 2);
+        assert_eq!(recovered.num_tracked_paulis(), 1);
+        assert_eq!(
+            recovered
+                .dem_outputs()
+                .iter()
+                .map(|op| op.id)
+                .collect::<Vec<_>>(),
+            [0, 1]
+        );
+        assert_eq!(
+            recovered
+                .tracked_paulis()
+                .iter()
+                .map(|op| op.id)
+                .collect::<Vec<_>>(),
+            [0]
+        );
+        assert_eq!(
+            recovered.tracked_paulis()[0]
+                .pauli
+                .as_ref()
+                .unwrap()
+                .to_sparse_str(),
+            "+Z3"
+        );
+        assert_eq!(
+            recovered.tracked_paulis()[0].label.as_deref(),
+            Some("tracked_z3")
+        );
     }
 
-    /// Internal static helper for detection event conversion.
-    fn to_detection_events_internal(outcomes: &[bool], detector_records: &[Vec<i32>]) -> Vec<bool> {
-        let num_measurements = outcomes.len();
-        let mut detection_events = Vec::with_capacity(detector_records.len());
-
-        for records in detector_records {
-            let mut fired = false;
-            for &offset in records {
-                if let Some(abs_idx) = record_offset_to_absolute_index(num_measurements, offset)
-                    && abs_idx < num_measurements
-                    && outcomes[abs_idx]
-                {
-                    fired = !fired; // XOR
-                }
-            }
-            detection_events.push(fired);
-        }
+    #[test]
+    fn test_pecos_dem_text_parses_error_targets_and_metadata() {
+        use crate::fault_tolerance::dem_builder::ParsedDem;
+        use pecos_core::pauli::{X, Z};
 
-        detection_events
-    }
+        let mut dem = DetectorErrorModel::new();
+        dem.add_detector(DetectorDef::new(0).with_coords([1.0, 2.0, 3.0]));
+        dem.add_observable(DemOutput::new(0).with_records([-1]).with_label("L0"));
+        dem.add_tracked_pauli(
+            DemOutput::new(0)
+                .with_pauli(X(0) & Z(2))
+                .with_label("tracked_x0_z2"),
+        );
+        dem.add_direct_contribution(
+            FaultMechanism::from_unsorted_with_tracked_paulis([0], [0], [0]),
+            0.25,
+        );
 
-    /// Static version without reordering (for backwards compatibility).
-    #[must_use]
-    pub fn to_detection_events(outcomes: &[bool], detector_records: &[Vec<i32>]) -> Vec<bool> {
-        Self::to_detection_events_internal(outcomes, detector_records)
+        let pecos_text = dem.to_pecos_string();
+        let parsed: ParsedDem = pecos_text.parse().unwrap();
+
+        assert_eq!(parsed.num_detectors, 1);
+        assert_eq!(parsed.num_dem_outputs(), 1);
+        assert_eq!(parsed.num_tracked_paulis(), 1);
+        assert_eq!(parsed.mechanisms.len(), 1);
+        assert_eq!(parsed.mechanisms[0].format_targets(), "D0 L0 TP0");
+        assert_eq!(parsed.mechanisms[0].components[0].detectors, vec![0]);
+        assert_eq!(parsed.mechanisms[0].components[0].observables, vec![0]);
+        assert_eq!(parsed.mechanisms[0].components[0].tracked_paulis, vec![0]);
+        assert_eq!(
+            parsed.dem_outputs[0].as_ref().unwrap().label.as_deref(),
+            Some("L0")
+        );
+        assert_eq!(
+            parsed.tracked_paulis[0]
+                .as_ref()
+                .unwrap()
+                .pauli
+                .as_ref()
+                .unwrap()
+                .to_sparse_str(),
+            "+X0 Z2"
+        );
     }
 
-    /// Samples and converts to detection events in one step.
-    ///
-    /// # Arguments
-    ///
-    /// * `detector_records` - For each detector, the measurement indices to XOR
-    /// * `rng` - Random number generator
-    ///
-    /// # Returns
-    ///
-    /// Tuple of (`measurement_outcomes_in_im_order`, `detection_events`)
-    pub fn sample_with_detectors<R: rand::Rng>(
-        &self,
-        detector_records: &[Vec<i32>],
-        rng: &mut R,
-    ) -> (Vec<bool>, Vec<bool>) {
-        let outcomes = self.sample(rng);
-        let detection_events = self.compute_detection_events(&outcomes, detector_records);
-        (outcomes, detection_events)
-    }
+    #[test]
+    fn test_tracked_only_contribution_is_pecos_only_and_decoder_invisible() {
+        use pecos_core::pauli::X;
 
-    /// Computes observable flips from measurement outcomes.
-    ///
-    /// This works identically to `compute_detection_events` - `XORing` measurement
-    /// outcomes at the specified record positions. The difference is semantic:
-    /// - Detection events indicate which detectors fired (syndrome)
-    /// - Observable flips indicate which logical observables were flipped
-    ///
-    /// # Arguments
-    ///
-    /// * `outcomes` - Raw measurement outcomes in influence map order (from `sample()`)
-    /// * `observable_records` - For each observable, the list of measurement indices to XOR.
-    ///   Indices can be negative (offset from end) or positive (absolute).
-    ///   These indices refer to `TickCircuit` measurement order.
-    ///
-    /// # Returns
-    ///
-    /// Vector of observable flips (true = observable was flipped by errors)
-    #[must_use]
-    pub fn compute_observable_flips(
-        &self,
-        outcomes: &[bool],
-        observable_records: &[Vec<i32>],
-    ) -> Vec<bool> {
-        // Same logic as detection events - just different semantic meaning
-        self.compute_detection_events(outcomes, observable_records)
-    }
+        let mut dem = DetectorErrorModel::new();
+        dem.add_tracked_pauli(DemOutput::new(0).with_pauli(X(0)).with_label("tracked_x0"));
+        dem.add_direct_contribution(
+            FaultMechanism::from_unsorted_with_tracked_paulis([], [], [0]),
+            0.25,
+        );
 
-    /// Samples with full threshold estimation output.
-    ///
-    /// Returns detection events AND observable flips in one step, matching
-    /// Stim's DEM sampler output format.
-    ///
-    /// # Arguments
-    ///
-    /// * `detector_records` - For each detector, the measurement indices to XOR
-    /// * `observable_records` - For each observable, the measurement indices to XOR
-    /// * `rng` - Random number generator
-    ///
-    /// # Returns
-    ///
-    /// Tuple of (`detection_events`, `observable_flips`)
-    pub fn sample_for_decoding<R: rand::Rng>(
-        &self,
-        detector_records: &[Vec<i32>],
-        observable_records: &[Vec<i32>],
-        rng: &mut R,
-    ) -> (Vec<bool>, Vec<bool>) {
-        let outcomes = self.sample(rng);
-        let detection_events = self.compute_detection_events(&outcomes, detector_records);
-        let observable_flips = self.compute_detection_events(&outcomes, observable_records);
-        (detection_events, observable_flips)
+        let standard_text = dem.to_string();
+        assert!(!standard_text.contains("error("));
+        assert!(!standard_text.contains("TP0"));
+        assert!(!standard_text.contains("pecos_tracked_pauli"));
+
+        let pecos_text = dem.to_pecos_string();
+        assert!(pecos_text.contains("error(0.25) TP0"));
+        assert!(pecos_text.contains("pecos_tracked_pauli"));
+
+        let (mechanisms, coords) = dem.to_mechanisms();
+        assert!(mechanisms.is_empty());
+        assert!(coords.is_empty());
     }
 
-    /// Batch sampling for threshold estimation.
-    ///
-    /// Efficiently samples multiple shots and returns detection events and observable
-    /// flips for each shot.
-    ///
-    /// # Arguments
-    ///
-    /// * `num_shots` - Number of shots to sample
-    /// * `detector_records` - For each detector, the measurement indices to XOR
-    /// * `observable_records` - For each observable, the measurement indices to XOR
-    /// * `rng` - Random number generator
-    ///
-    /// # Returns
-    ///
-    /// Tuple of (`detection_events_per_shot`, `observable_flips_per_shot`)
-    pub fn sample_batch_for_decoding<R: rand::Rng>(
-        &self,
-        num_shots: usize,
-        detector_records: &[Vec<i32>],
-        observable_records: &[Vec<i32>],
-        rng: &mut R,
-    ) -> (Vec<Vec<bool>>, Vec<Vec<bool>>) {
-        let mut all_detection_events = Vec::with_capacity(num_shots);
-        let mut all_observable_flips = Vec::with_capacity(num_shots);
+    #[test]
+    fn test_standard_projection_merges_effects_that_differ_only_by_tracked_paulis() {
+        use pecos_core::pauli::{X, Z};
 
-        for _ in 0..num_shots {
-            let (det_events, obs_flips) =
-                self.sample_for_decoding(detector_records, observable_records, rng);
-            all_detection_events.push(det_events);
-            all_observable_flips.push(obs_flips);
-        }
+        let mut dem = DetectorErrorModel::new();
+        dem.add_detector(DetectorDef::new(0));
+        dem.add_tracked_pauli(DemOutput::new(0).with_pauli(X(0)).with_label("tracked_x0"));
+        dem.add_tracked_pauli(DemOutput::new(1).with_pauli(Z(0)).with_label("tracked_z0"));
+        dem.add_direct_contribution(
+            FaultMechanism::from_unsorted_with_tracked_paulis([0], [], [0]),
+            0.1,
+        );
+        dem.add_direct_contribution(
+            FaultMechanism::from_unsorted_with_tracked_paulis([0], [], [1]),
+            0.2,
+        );
 
-        (all_detection_events, all_observable_flips)
+        let standard_text = dem.to_string();
+        let error_lines = standard_text
+            .lines()
+            .filter(|line| line.starts_with("error("))
+            .collect::<Vec<_>>();
+        assert_eq!(error_lines, ["error(0.26) D0"]);
+        assert!(!standard_text.contains("TP0"));
+        assert!(!standard_text.contains("TP1"));
+
+        let (mechanisms, _coords) = dem.to_mechanisms();
+        assert_eq!(mechanisms.len(), 1);
+        assert!((mechanisms[0].0 - 0.26).abs() < 1e-12);
+        assert_eq!(mechanisms[0].1, vec![0]);
+        assert!(mechanisms[0].2.is_empty());
     }
-}
 
-// ============================================================================
-// Probability Combination
-// ============================================================================
+    #[test]
+    fn test_pecos_dem_preserves_effects_that_differ_by_tracked_paulis() {
+        use pecos_core::pauli::{X, Z};
 
-/// Combines two independent error probabilities.
-///
-/// For independent errors with probabilities p1 and p2, the probability
-/// that exactly one error occurs is: p1*(1-p2) + p2*(1-p1).
-///
-/// This is the correct formula for combining probabilities when the same
-/// fault mechanism can be triggered by multiple independent error sources.
-#[inline]
-#[must_use]
-pub fn combine_probabilities(p1: f64, p2: f64) -> f64 {
-    p1 * (1.0 - p2) + p2 * (1.0 - p1)
-}
+        let mut dem = DetectorErrorModel::new();
+        dem.add_detector(DetectorDef::new(0));
+        dem.add_tracked_pauli(DemOutput::new(0).with_pauli(X(0)).with_label("tracked_x0"));
+        dem.add_tracked_pauli(DemOutput::new(1).with_pauli(Z(0)).with_label("tracked_z0"));
+        dem.add_direct_contribution(
+            FaultMechanism::from_unsorted_with_tracked_paulis([0], [], [0]),
+            0.1,
+        );
+        dem.add_direct_contribution(
+            FaultMechanism::from_unsorted_with_tracked_paulis([0], [], [1]),
+            0.2,
+        );
 
-/// Formats an fault mechanism's targets as a string (e.g., "D0 D1 L0").
-fn format_mechanism_targets(mechanism: &FaultMechanism) -> String {
-    let mut targets = Vec::new();
-    for &det in &mechanism.detectors {
-        targets.push(format!("D{det}"));
-    }
-    for &log in &mechanism.logicals {
-        targets.push(format!("L{log}"));
+        let pecos_text = dem.to_pecos_string();
+        let error_lines = pecos_text
+            .lines()
+            .filter(|line| line.starts_with("error("))
+            .collect::<Vec<_>>();
+        assert_eq!(error_lines, ["error(0.1) D0 TP0", "error(0.2) D0 TP1"]);
+        assert!(pecos_text.contains(r#""label":"tracked_x0""#));
+        assert!(pecos_text.contains(r#""label":"tracked_z0""#));
     }
-    targets.join(" ")
-}
 
-/// Combines two independent error probabilities.
-///
-/// For two independent errors with probabilities p1 and p2, the combined
-/// probability of having an odd number of errors (i.e., the XOR of the effects) is:
-/// `p_combined` = p1*(1-p2) + p2*(1-p1)
-fn combine_independent_probs(p1: f64, p2: f64) -> f64 {
-    // For DEM probability aggregation, we use XOR combination because
-    // errors toggle detector bits - if two errors both flip the same detector,
-    // they cancel out (XOR behavior). We want P(odd number of errors).
-    // XOR formula: P(A XOR B) = P(A)*(1-P(B)) + P(B)*(1-P(A)) = p1 + p2 - 2*p1*p2
-    p1 * (1.0 - p2) + p2 * (1.0 - p1)
-}
+    #[test]
+    fn test_standard_dem_serialization_never_shifts_observable_ids_for_tracked_paulis() {
+        use pecos_core::pauli::{X, Z};
 
-/// Formats a probability value similar to Python's %g format.
-/// Uses scientific notation for very small/large values, otherwise decimal.
-fn format_probability(p: f64) -> String {
-    if p == 0.0 {
-        return "0".to_string();
+        let mut dem = DetectorErrorModel::new();
+        dem.add_detector(DetectorDef::new(0));
+        dem.add_observable(DemOutput::new(0).with_records([-1]).with_label("L0"));
+        dem.add_observable(DemOutput::new(2).with_records([-2]).with_label("L2"));
+        dem.add_tracked_pauli(
+            DemOutput::new(0)
+                .with_kind(DemOutputKind::TrackedPauli)
+                .with_pauli(X(0))
+                .with_label("tracked_x0"),
+        );
+        dem.add_tracked_pauli(
+            DemOutput::new(1)
+                .with_kind(DemOutputKind::TrackedPauli)
+                .with_pauli(Z(3))
+                .with_label("tracked_z3"),
+        );
+        dem.add_direct_contribution(
+            FaultMechanism::from_unsorted_with_tracked_paulis([0], [0, 2], [1]),
+            0.01,
+        );
+
+        assert_eq!(dem.num_observables(), 3);
+        assert_eq!(dem.num_dem_outputs(), 3);
+        assert_eq!(dem.num_tracked_paulis(), 2);
+
+        let standard_text = dem.to_string();
+        assert!(standard_text.contains("logical_observable L0"));
+        assert!(!standard_text.contains("logical_observable L1"));
+        assert!(standard_text.contains("logical_observable L2"));
+        assert!(!standard_text.contains("logical_observable L3"));
+        assert!(standard_text.contains("error(0.01) D0 L0 L2"));
+        assert!(!standard_text.contains("TP1"));
+        assert!(!standard_text.contains("pecos_observable"));
+        assert!(!standard_text.contains("pecos_tracked_pauli"));
+
+        let pecos_text = dem.to_pecos_string();
+        assert!(pecos_text.contains("error(0.01) D0 L0 L2 TP1"));
+        assert!(pecos_text.contains(r#""kind":"observable""#));
+        assert!(pecos_text.contains(r#""kind":"tracked_pauli""#));
+        assert!(pecos_text.contains(r#""id":0"#));
+        assert!(pecos_text.contains(r#""id":2"#));
+        assert!(pecos_text.contains(r#""pauli":"+X0""#));
+        assert!(pecos_text.contains(r#""pauli":"+Z3""#));
+
+        let recovered = DetectorErrorModel::new()
+            .with_pecos_dem_metadata(&pecos_text)
+            .unwrap();
+        assert_eq!(recovered.num_dem_outputs(), 3);
+        assert_eq!(recovered.num_tracked_paulis(), 2);
+        assert_eq!(
+            recovered
+                .dem_outputs()
+                .iter()
+                .map(|op| op.id)
+                .collect::<Vec<_>>(),
+            [0, 2]
+        );
+        assert_eq!(
+            recovered
+                .tracked_paulis()
+                .iter()
+                .map(|op| op.id)
+                .collect::<Vec<_>>(),
+            [0, 1]
+        );
     }
 
-    let abs_p = p.abs();
+    #[test]
+    fn test_pecos_dem_text_metadata_round_trip_keeps_observable_and_tracked_id_spaces() {
+        use pecos_core::pauli::{X, Y, Z};
 
-    // Use scientific notation for very small or very large values
-    if (1e-4..1e6).contains(&abs_p) {
-        // Regular decimal notation
-        let formatted = format!("{p:.6}");
-        trim_trailing_zeros(&formatted)
-    } else {
-        // Format with up to 6 significant figures in scientific notation
-        let formatted = format!("{p:.6e}");
-        // Trim trailing zeros after decimal point
-        trim_trailing_zeros(&formatted)
-    }
-}
+        let mut dem = DetectorErrorModel::new();
+        dem.add_detector(DetectorDef::new(0));
+        dem.add_detector(DetectorDef::new(1));
+        dem.add_observable(DemOutput::new(0).with_records([-1]).with_label("L0"));
+        dem.add_observable(
+            DemOutput::new(3)
+                .with_records([-2, -1])
+                .with_label("logical_aux"),
+        );
+        dem.add_tracked_pauli(
+            DemOutput::new(0)
+                .with_pauli(X(0) & Z(2))
+                .with_label("tracked_x0_z2"),
+        );
+        dem.add_tracked_pauli(DemOutput::new(2).with_pauli(Y(5)).with_label("tracked_y5"));
+        dem.add_direct_contribution(
+            FaultMechanism::from_unsorted_with_tracked_paulis([0, 1], [3], [2]),
+            0.125,
+        );
 
-/// Trims trailing zeros from a number string.
-fn trim_trailing_zeros(s: &str) -> String {
-    if let Some(e_pos) = s.find('e') {
-        // Scientific notation: trim zeros before 'e'
-        let (mantissa, exponent) = s.split_at(e_pos);
-        let trimmed = mantissa.trim_end_matches('0').trim_end_matches('.');
-        format!("{trimmed}{exponent}")
-    } else if s.contains('.') {
-        // Decimal notation: trim trailing zeros
-        s.trim_end_matches('0').trim_end_matches('.').to_string()
-    } else {
-        s.to_string()
-    }
-}
+        let standard_text = dem.to_string();
+        assert!(standard_text.contains("logical_observable L0"));
+        assert!(!standard_text.contains("logical_observable L1"));
+        assert!(!standard_text.contains("logical_observable L2"));
+        assert!(standard_text.contains("logical_observable L3"));
+        assert!(standard_text.contains("error(0.125) D0 D1 L3"));
+        assert!(!standard_text.contains("TP2"));
+        assert!(!standard_text.contains("pecos_tracked_pauli"));
+
+        let pecos_text = format!(
+            "# ordinary comments and standard DEM lines are allowed\n{}\n",
+            dem.to_pecos_string()
+        );
+        let recovered = DetectorErrorModel::new()
+            .with_pecos_dem_metadata(&pecos_text)
+            .unwrap();
+        assert_eq!(recovered.num_observables(), 4);
+        assert_eq!(recovered.num_dem_outputs(), 4);
+        assert_eq!(recovered.num_tracked_paulis(), 3);
+        assert_eq!(
+            recovered
+                .dem_outputs()
+                .iter()
+                .map(|op| (op.id, op.label.as_deref()))
+                .collect::<Vec<_>>(),
+            [(0, Some("L0")), (3, Some("logical_aux"))]
+        );
+        assert_eq!(
+            recovered
+                .tracked_paulis()
+                .iter()
+                .map(|op| (op.id, op.label.as_deref()))
+                .collect::<Vec<_>>(),
+            [(0, Some("tracked_x0_z2")), (2, Some("tracked_y5"))]
+        );
+        assert_eq!(
+            recovered.tracked_paulis()[0]
+                .pauli
+                .as_ref()
+                .unwrap()
+                .to_sparse_str(),
+            "+X0 Z2"
+        );
+        assert_eq!(
+            recovered.tracked_paulis()[1]
+                .pauli
+                .as_ref()
+                .unwrap()
+                .to_sparse_str(),
+            "+Y5"
+        );
 
-#[cfg(test)]
-mod tests {
-    use super::*;
+        let reserialized = recovered.to_pecos_string();
+        assert!(reserialized.contains("logical_observable L0"));
+        assert!(!reserialized.contains("logical_observable L1"));
+        assert!(!reserialized.contains("logical_observable L2"));
+        assert!(reserialized.contains("logical_observable L3"));
+        assert!(reserialized.contains(r#""kind":"observable""#));
+        assert!(reserialized.contains(r#""kind":"tracked_pauli""#));
+        assert!(reserialized.contains(r#""pauli":"+X0 Z2""#));
+        assert!(reserialized.contains(r#""pauli":"+Y5""#));
+        assert!(
+            !reserialized.contains("TP2"),
+            "metadata-only recovery should not invent mechanism effects"
+        );
+    }
 
     #[test]
-    fn test_error_mechanism_xor() {
-        let m1 = FaultMechanism::from_unsorted([0, 1, 2], [0]);
-        let m2 = FaultMechanism::from_unsorted([1, 2, 3], [0, 1]);
+    fn test_pecos_dem_text_and_metadata_json_preserve_same_output_metadata() {
+        use crate::fault_tolerance::dem_builder::ParsedDem;
+        use pecos_core::pauli::{X, Y, Z};
 
-        let result = m1.xor(&m2);
+        let mut dem = DetectorErrorModel::new();
+        dem.add_detector(DetectorDef::new(0).with_records([-1]));
+        dem.add_observable(DemOutput::new(0).with_records([-1]).with_label("L0"));
+        dem.add_observable(DemOutput::new(3).with_records([-2]).with_label("L3"));
+        dem.add_tracked_pauli(
+            DemOutput::new(0)
+                .with_pauli(X(0) & Z(2))
+                .with_label("tracked_x0_z2"),
+        );
+        dem.add_tracked_pauli(DemOutput::new(3).with_pauli(Y(5)).with_label("tracked_y5"));
+        dem.add_direct_contribution(
+            FaultMechanism::from_unsorted_with_tracked_paulis([0], [3], [3]),
+            0.125,
+        );
 
-        // Detectors: {0, 1, 2} XOR {1, 2, 3} = {0, 3}
-        assert_eq!(result.detectors.as_slice(), &[0, 3]);
-        // Logicals: {0} XOR {0, 1} = {1}
-        assert_eq!(result.logicals.as_slice(), &[1]);
+        let json_recovered = DetectorErrorModel::new()
+            .with_pecos_metadata_json(&dem.to_pecos_metadata_json())
+            .unwrap();
+        let text_recovered = DetectorErrorModel::new()
+            .with_pecos_dem_metadata(&dem.to_pecos_string())
+            .unwrap();
+
+        let source_json: serde_json::Value =
+            serde_json::from_str(&dem.to_pecos_metadata_json()).unwrap();
+        let from_json: serde_json::Value =
+            serde_json::from_str(&json_recovered.to_pecos_metadata_json()).unwrap();
+        let from_text: serde_json::Value =
+            serde_json::from_str(&text_recovered.to_pecos_metadata_json()).unwrap();
+
+        assert_eq!(from_json, source_json);
+        assert_eq!(from_text, source_json);
+
+        let parsed: ParsedDem = dem.to_pecos_string().parse().unwrap();
+        assert_eq!(parsed.num_dem_outputs(), 4);
+        assert_eq!(parsed.num_tracked_paulis(), 4);
+        assert_eq!(parsed.mechanisms[0].format_targets(), "D0 L3 TP3");
+        assert_eq!(parsed.mechanisms[0].components[0].observables, vec![3]);
+        assert_eq!(parsed.mechanisms[0].components[0].tracked_paulis, vec![3]);
+        assert_eq!(
+            parsed.dem_outputs[0].as_ref().unwrap().label.as_deref(),
+            Some("L0")
+        );
+        assert_eq!(
+            parsed.dem_outputs[3].as_ref().unwrap().label.as_deref(),
+            Some("L3")
+        );
+        assert_eq!(
+            parsed.tracked_paulis[0]
+                .as_ref()
+                .unwrap()
+                .pauli
+                .as_ref()
+                .unwrap()
+                .to_sparse_str(),
+            "+X0 Z2"
+        );
+        assert_eq!(
+            parsed.tracked_paulis[3].as_ref().unwrap().label.as_deref(),
+            Some("tracked_y5")
+        );
     }
 
     #[test]
-    fn test_error_mechanism_equality() {
-        let m1 = FaultMechanism::from_unsorted([2, 0, 1], [1, 0]);
-        let m2 = FaultMechanism::from_unsorted([0, 1, 2], [0, 1]);
-
-        assert_eq!(m1, m2);
-        assert_eq!(m1.detectors.as_slice(), &[0, 1, 2]);
-        assert_eq!(m1.logicals.as_slice(), &[0, 1]);
+    fn test_pecos_dem_metadata_parser_rejects_malformed_extension_line() {
+        let err = DetectorErrorModel::new()
+            .with_pecos_dem_metadata("error(0.01) D0\npecos_tracked_pauli not-json")
+            .unwrap_err();
+        assert!(
+            err.message()
+                .contains("invalid pecos_tracked_pauli JSON payload")
+        );
     }
 
     #[test]
-    fn test_combine_probabilities() {
-        // Same probability twice
-        let p = combine_probabilities(0.01, 0.01);
-        // Expected: 0.01 * 0.99 + 0.01 * 0.99 = 0.0198
-        assert!((p - 0.0198).abs() < 1e-10);
+    fn test_pecos_dem_metadata_parser_rejects_unknown_pecos_extension_line() {
+        let err = DetectorErrorModel::new()
+            .with_pecos_dem_metadata(r#"pecos_old_extension {"id":1}"#)
+            .unwrap_err();
 
-        // One zero probability
-        assert!((combine_probabilities(0.0, 0.5) - 0.5).abs() < 1e-10);
-        assert!((combine_probabilities(0.5, 0.0) - 0.5).abs() < 1e-10);
+        assert!(
+            err.message()
+                .contains("unsupported PECOS DEM extension line")
+        );
+    }
 
-        // Both zero
-        assert!((combine_probabilities(0.0, 0.0)).abs() < 1e-10);
+    #[test]
+    fn test_pecos_dem_metadata_parser_rejects_legacy_tracked_extension_line() {
+        let err = DetectorErrorModel::new()
+            .with_pecos_dem_metadata(r#"pecos_tracked_op {"id":0,"pauli":"+X0"}"#)
+            .unwrap_err();
+
+        assert!(
+            err.message()
+                .contains("unsupported PECOS DEM extension line: pecos_tracked_op")
+        );
     }
 
     #[test]
     fn test_decomposed_error_single() {
-        let mechanism = FaultMechanism::from_unsorted([0, 1], [0]);
+        let mechanism = FaultMechanism::from_unsorted_with_tracked_paulis([0, 1], [0], [2]);
         let decomposed = DecomposedFault::single(mechanism.clone());
 
         assert_eq!(decomposed.components.len(), 1);
         assert!(decomposed.is_graphlike());
         assert_eq!(decomposed.full_effect(), mechanism);
         assert_eq!(decomposed.to_stim_targets(), "D0 D1 L0");
+        assert_eq!(decomposed.to_pecos_targets(), "D0 D1 L0 TP2");
     }
 
     #[test]
@@ -2877,7 +5009,7 @@ mod tests {
 
         dem.add_detector(DetectorDef::new(0).with_coords([0.0, 0.0, 0.0]));
         dem.add_detector(DetectorDef::new(1).with_coords([1.0, 0.0, 0.0]));
-        dem.add_observable(LogicalObservable::new(0));
+        dem.add_dem_output(DemOutput::new(0));
 
         dem.add_direct_contribution(FaultMechanism::from_unsorted([0, 1], []), 0.01);
         dem.add_direct_contribution(FaultMechanism::from_unsorted([0], [0]), 0.02);
@@ -2928,7 +5060,8 @@ mod tests {
         let pair_summary = summaries
             .iter()
             .find(|summary| {
-                summary.effect.detectors.as_slice() == [0, 1] && summary.effect.logicals.is_empty()
+                summary.effect.detectors.as_slice() == [0, 1]
+                    && summary.effect.dem_outputs.is_empty()
             })
             .expect("pair summary missing");
         assert_eq!(pair_summary.graphlike_decomposable_count, 2);
@@ -2936,7 +5069,7 @@ mod tests {
         let singleton_summary = summaries
             .iter()
             .find(|summary| {
-                summary.effect.detectors.as_slice() == [0] && summary.effect.logicals.is_empty()
+                summary.effect.detectors.as_slice() == [0] && summary.effect.dem_outputs.is_empty()
             })
             .expect("singleton summary missing");
         assert_eq!(singleton_summary.graphlike_decomposable_count, 0);
@@ -2948,7 +5081,7 @@ mod tests {
 
         dem.add_detector(DetectorDef::new(0).with_coords([0.0, 0.0, 0.0]));
         dem.add_detector(DetectorDef::new(1).with_coords([1.0, 0.0, 0.0]));
-        dem.add_observable(LogicalObservable::new(0));
+        dem.add_dem_output(DemOutput::new(0));
 
         // Add contributions directly using the source tracking API
         dem.add_direct_contribution(FaultMechanism::from_unsorted([0, 1], []), 0.01);
@@ -2964,12 +5097,12 @@ mod tests {
     }
 
     #[test]
-    fn test_dem_to_string_decomposed_keeps_two_detector_one_logical_direct() {
+    fn test_dem_to_string_decomposed_keeps_two_detector_one_dem_output_direct() {
         let mut dem = DetectorErrorModel::new();
 
         dem.add_detector(DetectorDef::new(0).with_coords([0.0, 0.0, 0.0]));
         dem.add_detector(DetectorDef::new(1).with_coords([1.0, 0.0, 0.0]));
-        dem.add_observable(LogicalObservable::new(0));
+        dem.add_dem_output(DemOutput::new(0));
 
         dem.add_direct_contribution(FaultMechanism::from_unsorted([0, 1], [0]), 0.01);
         dem.add_direct_contribution(FaultMechanism::from_unsorted([0], std::iter::empty()), 0.02);
@@ -2987,7 +5120,7 @@ mod tests {
 
         dem.add_detector(DetectorDef::new(0).with_coords([0.0, 0.0, 0.0]));
         dem.add_detector(DetectorDef::new(1).with_coords([1.0, 0.0, 0.0]));
-        dem.add_observable(LogicalObservable::new(0));
+        dem.add_dem_output(DemOutput::new(0));
 
         let x = FaultMechanism::from_unsorted([0], std::iter::empty());
         let z = FaultMechanism::from_unsorted([1], [0]);
@@ -3000,7 +5133,7 @@ mod tests {
     }
 
     #[test]
-    fn test_error_mechanism_with_two_detectors_and_multiple_logicals_is_graphlike() {
+    fn test_error_mechanism_with_two_detectors_and_multiple_dem_outputs_is_graphlike() {
         let effect = FaultMechanism::from_unsorted([0, 1], [0, 1]);
 
         assert!(effect.is_graphlike());
diff --git a/crates/pecos-qec/src/fault_tolerance/fault_sampler.rs b/crates/pecos-qec/src/fault_tolerance/fault_sampler.rs
new file mode 100644
index 000000000..a369a1683
--- /dev/null
+++ b/crates/pecos-qec/src/fault_tolerance/fault_sampler.rs
@@ -0,0 +1,4587 @@
+// Copyright 2026 The PECOS Developers
+//
+// Licensed under the Apache License, Version 2.0 (the "License"); you may not use this file except
+// in compliance with the License. You may obtain a copy of the License at
+//
+//     https://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software distributed under the License
+// is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express
+// or implied. See the License for the specific language governing permissions and limitations under
+// the License.
+
+//! Stochastic raw-measurement sampling via fault table overlay.
+//!
+//! # Architecture
+//!
+//! Raw measurement output = ideal measurement values XOR sampled physical faults.
+//!
+//! These are computed independently:
+//! - **Ideal values** from [`MeasurementSampler`](pecos_simulators::measurement_sampler::MeasurementSampler),
+//!   which respects the Copy/Computed dependency graph from symbolic simulation.
+//!   Non-deterministic measurements share latent random variables through the
+//!   stabilizer eigenvalue structure.
+//! - **Physical faults** from a fault table where each entry has a probability
+//!   and a set of affected measurements. Faults are sampled independently per
+//!   shot (Bernoulli) and XOR'd onto the ideal values.
+//!
+//! This separation is critical: the dependency graph captures *ideal* measurement
+//! correlations (same stabilizer across resets), while fault events represent
+//! *physical* noise processes (gate errors, measurement flips, prep errors).
+//! Mixing them — e.g., flattening fault deps through Copy chains — incorrectly
+//! cancels faults that affect only one measurement in a correlated pair.
+
+use pecos_core::gate_type::GateType;
+use pecos_core::pauli::pauli_string::PauliString;
+use pecos_core::{Pauli, QubitId};
+use pecos_quantum::{AnnotationKind, TickCircuit};
+use pecos_random::{PecosRng, RngExt};
+use pecos_simulators::measurement_sampler::{MeasurementKind, SampleResult};
+use pecos_simulators::symbolic_sparse_stab::MeasurementHistory;
+use pecos_simulators::{BitmaskPauliProp, CliffordGateable};
+use std::collections::{BTreeSet, HashMap};
+use std::fmt;
+
+/// Error returned when `build_fault_table` encounters an unsupported gate.
+#[derive(Clone, Debug)]
+pub struct UnsupportedGateError {
+    pub gate_type: GateType,
+    pub tick: usize,
+    pub gate_in_tick: usize,
+    pub qubits: Vec<usize>,
+}
+
+impl fmt::Display for UnsupportedGateError {
+    fn fmt(&self, f: &mut fmt::Formatter<'_>) -> fmt::Result {
+        write!(
+            f,
+            "Unsupported gate {:?} at tick {} gate {} on qubits {:?}. \
+             Supported: H, X, Y, Z, SZ, SZdg, SX, SXdg, SY, SYdg, F, Fdg, \
+             CX, CY, CZ, SXX, SXXdg, SYY, SYYdg, SZZ, SZZdg, SWAP, \
+             MZ/MeasureFree/MeasureLeaked, PZ, QAlloc, QFree, I, Idle, \
+             plus metadata (MeasCrosstalk*, TrackedPauliMeta).",
+            self.gate_type, self.tick, self.gate_in_tick, self.qubits
+        )
+    }
+}
+
+impl std::error::Error for UnsupportedGateError {}
+
+/// Standard single-qubit Clifford gates supported by `CliffordGateable`.
+pub const STANDARD_1Q_CLIFFORD_GATES: &[GateType] = &[
+    GateType::X,
+    GateType::Y,
+    GateType::Z,
+    GateType::H,
+    GateType::SZ,
+    GateType::SZdg,
+    GateType::SX,
+    GateType::SXdg,
+    GateType::SY,
+    GateType::SYdg,
+    GateType::F,
+    GateType::Fdg,
+];
+
+/// Standard two-qubit Clifford gates supported by `CliffordGateable`.
+pub const STANDARD_2Q_CLIFFORD_GATES: &[GateType] = &[
+    GateType::CX,
+    GateType::CY,
+    GateType::CZ,
+    GateType::SXX,
+    GateType::SXXdg,
+    GateType::SYY,
+    GateType::SYYdg,
+    GateType::SZZ,
+    GateType::SZZdg,
+    GateType::SWAP,
+];
+
+#[inline]
+fn is_standard_1q_clifford_gate(gate_type: GateType) -> bool {
+    STANDARD_1Q_CLIFFORD_GATES.contains(&gate_type)
+}
+
+#[inline]
+fn is_standard_2q_clifford_gate(gate_type: GateType) -> bool {
+    STANDARD_2Q_CLIFFORD_GATES.contains(&gate_type)
+}
+
+#[inline]
+fn is_supported_measurement_gate(gate_type: GateType) -> bool {
+    matches!(
+        gate_type,
+        GateType::MZ | GateType::MeasureFree | GateType::MeasureLeaked
+    )
+}
+
+#[inline]
+fn is_supported_prep_gate(gate_type: GateType) -> bool {
+    matches!(gate_type, GateType::PZ | GateType::QAlloc)
+}
+
+#[inline]
+fn is_supported_noop_or_metadata_gate(gate_type: GateType) -> bool {
+    matches!(
+        gate_type,
+        GateType::QFree
+            | GateType::I
+            | GateType::Idle
+            | GateType::MeasCrosstalkGlobalPayload
+            | GateType::MeasCrosstalkLocalPayload
+            | GateType::TrackedPauliMeta
+    )
+}
+
+/// A fault mechanism: fires with probability `p`, then uniformly selects one
+/// of its alternatives to determine which measurements are flipped.
+///
+/// For a depolarizing channel with k non-identity Paulis and total error
+/// probability p: the mechanism fires with probability p, then each of the
+/// k alternatives is chosen with probability 1/k. This matches the stabilizer
+/// sim's "exactly one Pauli error per gate event" semantics.
+#[derive(Clone, Debug, PartialEq)]
+pub struct FaultMechanism {
+    /// Total probability that this mechanism fires (one Bernoulli per shot).
+    pub probability: f64,
+    /// Each alternative is a set of measurements that get flipped if that
+    /// alternative is selected. Empty alternatives (no measurements flipped)
+    /// are preserved — they represent Pauli errors that commute with all
+    /// subsequent measurements (e.g., Z after MZ). Keeping them maintains
+    /// the correct 1/k uniform denominator for the depolarizing channel.
+    pub alternatives: Vec<Vec<usize>>,
+}
+
+/// Noise parameters for depolarizing fault injection.
+#[derive(Clone, Debug)]
+pub struct StochasticNoiseParams {
+    pub p1: f64,
+    pub p2: f64,
+    pub p_meas: f64,
+    pub p_prep: f64,
+}
+
+/// A gate in the flattened gate list (one entry per qubit-pair or single qubit).
+#[derive(Clone, Debug)]
+pub(crate) struct GateLoc {
+    pub(crate) tick: usize,
+    pub(crate) gate_index: usize,
+    pub(crate) gate_type: GateType,
+    pub(crate) qubits: Vec<usize>,
+}
+
+/// Single-qubit Pauli type for fault injection.
+#[derive(Clone, Copy, Debug, PartialEq, Eq, Hash)]
+pub(crate) enum PauliType {
+    X,
+    Y,
+    Z,
+}
+
+/// Build a fault table from a `TickCircuit` and noise parameters.
+///
+/// Each entry describes one possible fault mechanism: its probability and
+/// which measurements it would flip if it occurs. The table is used for
+/// independent per-shot Bernoulli sampling.
+///
+/// Gate ordering follows the `TickCircuit` tick-by-tick structure, which must
+/// match the measurement numbering used by detector/DEM-output record indices.
+///
+/// # Supported gates
+///
+/// **Fault injection** (noise applied after these gates):
+/// - Single-qubit Clifford: `H`, `X`, `Y`, `Z`, `SZ`, `SZdg`, `SX`, `SXdg`,
+///   `SY`, `SYdg`, `F`, `Fdg` → `p=p1`, 3 alternatives
+/// - Two-qubit Clifford: `CX`, `CY`, `CZ`, `SXX`, `SXXdg`, `SYY`, `SYYdg`,
+///   `SZZ`, `SZZdg`, `SWAP` → `p=p2`, 15 alternatives
+/// - State preparation: `PZ`, `QAlloc` → mechanism with `p=p_prep`, 1 alternative (`X`)
+/// - Measurement: `MZ`, `MeasureFree`, `MeasureLeaked` → mechanism with
+///   `p=p_meas`, 1 alternative (flip)
+///
+/// Each mechanism fires at most once per shot (Bernoulli with total probability p).
+/// When it fires, exactly one alternative is chosen uniformly at random. This
+/// matches the depolarizing channel semantics: "with probability p, apply one
+/// of the k non-identity Paulis, each equally likely."
+///
+/// **Propagation** (gates that transform a propagating Pauli):
+/// - All single-qubit Cliffords: Clifford conjugation via direct Pauli-basis updates
+/// - All two-qubit Cliffords: Clifford conjugation via direct Pauli-basis updates
+/// - `PZ`, `QAlloc`: absorbs all Pauli components on the reset qubit
+/// - `MZ`: records `X`-component flip, then absorbs all components (state collapse)
+///
+/// **No-op** (pass through without noise or transformation):
+/// - `I`, `Idle`, `QFree`, `MeasCrosstalkGlobalPayload`,
+///   `MeasCrosstalkLocalPayload`, `TrackedPauliMeta`
+///
+/// Any gate not in the above lists returns [`UnsupportedGateError`].
+///
+/// # Errors
+///
+/// Returns [`UnsupportedGateError`] when the circuit contains a gate outside
+/// the supported Clifford/prep/measurement/metadata set.
+pub fn build_fault_table(
+    tc: &TickCircuit,
+    noise: &StochasticNoiseParams,
+) -> Result<Vec<FaultMechanism>, UnsupportedGateError> {
+    let mut catalog = FaultCatalog::from_circuit(tc)?;
+    catalog.with_noise(noise);
+    Ok(catalog.to_mechanisms())
+}
+
+/// Validate that all gates in the `TickCircuit` are supported (before flattening).
+fn validate_tick_circuit(tc: &TickCircuit) -> Result<(), UnsupportedGateError> {
+    for (tick_idx, tick) in tc.iter_ticks() {
+        for gate in tick.iter_gate_batches() {
+            if is_standard_1q_clifford_gate(gate.gate_type)
+                || is_standard_2q_clifford_gate(gate.gate_type)
+                || is_supported_measurement_gate(gate.gate_type)
+                || is_supported_prep_gate(gate.gate_type)
+                || is_supported_noop_or_metadata_gate(gate.gate_type)
+            {
+                continue;
+            }
+            return Err(UnsupportedGateError {
+                gate_type: gate.gate_type,
+                tick: tick_idx,
+                gate_in_tick: gate.batch_index(),
+                qubits: gate.qubits.iter().map(pecos_core::QubitId::index).collect(),
+            });
+        }
+    }
+    Ok(())
+}
+
+/// Flatten a `TickCircuit` into individual gate applications with measurement
+/// position tracking.
+///
+/// Stored batches are expanded through `TickCircuit`'s `GateInstanceRef`
+/// iterator so the qubit/measurement-id slicing semantics are shared with
+/// other consumers. Each measurement and each multi-qubit pair gets its own
+/// position for fault injection. Returns the gate list and a map from gate-list
+/// index to measurement index.
+pub(crate) fn flatten_tick_circuit(tc: &TickCircuit) -> (Vec<GateLoc>, HashMap<usize, usize>) {
+    let mut gates = Vec::new();
+    let mut meas_positions = HashMap::new();
+    let mut meas_count = 0usize;
+
+    for (tick_idx, tick) in tc.iter_ticks() {
+        for gate in tick.iter_gate_instances() {
+            let qs: Vec<usize> = gate
+                .qubits()
+                .iter()
+                .map(pecos_core::QubitId::index)
+                .collect();
+            if is_supported_measurement_gate(gate.gate_type()) {
+                meas_positions.insert(gates.len(), meas_count);
+                meas_count += 1;
+            }
+            gates.push(GateLoc {
+                tick: tick_idx,
+                gate_index: gate.batch_index(),
+                gate_type: gate.gate_type(),
+                qubits: qs,
+            });
+        }
+    }
+
+    (gates, meas_positions)
+}
+
+/// Propagate a single-qubit Pauli fault forward through the gate list.
+///
+/// Returns the set of measurement indices whose outcomes would be flipped
+/// by this Pauli error at this position.
+#[cfg(test)]
+pub(crate) fn propagate_single(
+    pauli: PauliType,
+    qubit: usize,
+    start: usize,
+    gates: &[GateLoc],
+    meas_positions: &HashMap<usize, usize>,
+) -> BTreeSet<usize> {
+    let mut prop = BitmaskPauliProp::new();
+    match pauli {
+        PauliType::X => prop.track_x(&[qubit]),
+        PauliType::Y => prop.track_y(&[qubit]),
+        PauliType::Z => prop.track_z(&[qubit]),
+    }
+
+    propagate_forward(&mut prop, start, gates, meas_positions)
+}
+
+fn propagate_single_effect(
+    pauli: PauliType,
+    qubit: usize,
+    start: usize,
+    gates: &[GateLoc],
+    meas_positions: &HashMap<usize, usize>,
+    tracked_paulis: &[PauliString],
+) -> PropagatedFaultEffect {
+    let mut prop = BitmaskPauliProp::new();
+    match pauli {
+        PauliType::X => prop.track_x(&[qubit]),
+        PauliType::Y => prop.track_y(&[qubit]),
+        PauliType::Z => prop.track_z(&[qubit]),
+    }
+
+    let affected_measurements = propagate_forward(&mut prop, start, gates, meas_positions);
+    let affected_tracked_paulis = tracked_paulis_flipped_by(&prop, tracked_paulis);
+    PropagatedFaultEffect {
+        affected_measurements,
+        affected_tracked_paulis,
+    }
+}
+
+#[cfg(test)]
+fn propagate_pair_effect(
+    faults: [(PauliType, usize); 2],
+    start: usize,
+    gates: &[GateLoc],
+    meas_positions: &HashMap<usize, usize>,
+    tracked_paulis: &[PauliString],
+) -> PropagatedFaultEffect {
+    let mut prop = BitmaskPauliProp::new();
+    for (pauli, qubit) in faults {
+        match pauli {
+            PauliType::X => prop.track_x(&[qubit]),
+            PauliType::Y => prop.track_y(&[qubit]),
+            PauliType::Z => prop.track_z(&[qubit]),
+        }
+    }
+
+    let affected_measurements = propagate_forward(&mut prop, start, gates, meas_positions);
+    let affected_tracked_paulis = tracked_paulis_flipped_by(&prop, tracked_paulis);
+    PropagatedFaultEffect {
+        affected_measurements,
+        affected_tracked_paulis,
+    }
+}
+
+#[derive(Clone, Debug, PartialEq, Eq)]
+struct PropagatedFaultEffect {
+    affected_measurements: BTreeSet<usize>,
+    affected_tracked_paulis: Vec<usize>,
+}
+
+#[derive(Default)]
+struct PropagatedEffectCache {
+    singles: HashMap<(usize, PauliType, usize), PropagatedFaultEffect>,
+}
+
+impl PropagatedEffectCache {
+    #[cfg(test)]
+    fn len(&self) -> usize {
+        self.singles.len()
+    }
+
+    fn single(
+        &mut self,
+        pauli: PauliType,
+        qubit: usize,
+        start: usize,
+        gates: &[GateLoc],
+        meas_positions: &HashMap<usize, usize>,
+        tracked_paulis: &[PauliString],
+    ) -> PropagatedFaultEffect {
+        self.singles
+            .entry((start, pauli, qubit))
+            .or_insert_with(|| {
+                propagate_single_effect(pauli, qubit, start, gates, meas_positions, tracked_paulis)
+            })
+            .clone()
+    }
+}
+
+fn xor_fault_effects(
+    left: &PropagatedFaultEffect,
+    right: &PropagatedFaultEffect,
+) -> PropagatedFaultEffect {
+    let mut affected_measurements = left.affected_measurements.clone();
+    for &measurement in &right.affected_measurements {
+        if !affected_measurements.remove(&measurement) {
+            affected_measurements.insert(measurement);
+        }
+    }
+
+    PropagatedFaultEffect {
+        affected_measurements,
+        affected_tracked_paulis: xor_sorted_unique_indices(
+            &left.affected_tracked_paulis,
+            &right.affected_tracked_paulis,
+        ),
+    }
+}
+
+fn xor_sorted_unique_indices(left: &[usize], right: &[usize]) -> Vec<usize> {
+    let mut out = Vec::with_capacity(left.len() + right.len());
+    let mut i = 0usize;
+    let mut j = 0usize;
+    while i < left.len() && j < right.len() {
+        match left[i].cmp(&right[j]) {
+            std::cmp::Ordering::Less => {
+                out.push(left[i]);
+                i += 1;
+            }
+            std::cmp::Ordering::Greater => {
+                out.push(right[j]);
+                j += 1;
+            }
+            std::cmp::Ordering::Equal => {
+                i += 1;
+                j += 1;
+            }
+        }
+    }
+    out.extend_from_slice(&left[i..]);
+    out.extend_from_slice(&right[j..]);
+    out
+}
+
+/// Core forward propagation: evolve a Pauli through gates, collecting affected measurements.
+fn propagate_forward(
+    prop: &mut BitmaskPauliProp,
+    start: usize,
+    gates: &[GateLoc],
+    meas_positions: &HashMap<usize, usize>,
+) -> BTreeSet<usize> {
+    let mut affected = BTreeSet::new();
+
+    for (loc_idx, loc) in gates.iter().enumerate().skip(start) {
+        match loc.gate_type {
+            GateType::H if !loc.qubits.is_empty() => {
+                prop.h(&[QubitId(loc.qubits[0])]);
+            }
+            GateType::SZ if !loc.qubits.is_empty() => {
+                prop.sz(&[QubitId(loc.qubits[0])]);
+            }
+            GateType::SZdg if !loc.qubits.is_empty() => {
+                let q = QubitId(loc.qubits[0]);
+                prop.szdg(&[q]);
+            }
+            GateType::SX if !loc.qubits.is_empty() => {
+                prop.sx(&[QubitId(loc.qubits[0])]);
+            }
+            GateType::SXdg if !loc.qubits.is_empty() => {
+                prop.sxdg(&[QubitId(loc.qubits[0])]);
+            }
+            GateType::SY if !loc.qubits.is_empty() => {
+                prop.sy(&[QubitId(loc.qubits[0])]);
+            }
+            GateType::SYdg if !loc.qubits.is_empty() => {
+                prop.sydg(&[QubitId(loc.qubits[0])]);
+            }
+            GateType::F if !loc.qubits.is_empty() => {
+                prop.f(&[QubitId(loc.qubits[0])]);
+            }
+            GateType::Fdg if !loc.qubits.is_empty() => {
+                prop.fdg(&[QubitId(loc.qubits[0])]);
+            }
+            GateType::CX if loc.qubits.len() >= 2 => {
+                prop.cx(&[(QubitId(loc.qubits[0]), QubitId(loc.qubits[1]))]);
+            }
+            GateType::CY if loc.qubits.len() >= 2 => {
+                let (q1, q2) = (QubitId(loc.qubits[0]), QubitId(loc.qubits[1]));
+                prop.cy(&[(q1, q2)]);
+            }
+            GateType::CZ if loc.qubits.len() >= 2 => {
+                let (q1, q2) = (QubitId(loc.qubits[0]), QubitId(loc.qubits[1]));
+                prop.cz(&[(q1, q2)]);
+            }
+            GateType::SXX if loc.qubits.len() >= 2 => {
+                let pair = [(QubitId(loc.qubits[0]), QubitId(loc.qubits[1]))];
+                prop.sxx(&pair);
+            }
+            GateType::SXXdg if loc.qubits.len() >= 2 => {
+                let pair = [(QubitId(loc.qubits[0]), QubitId(loc.qubits[1]))];
+                prop.sxxdg(&pair);
+            }
+            GateType::SYY if loc.qubits.len() >= 2 => {
+                let pair = [(QubitId(loc.qubits[0]), QubitId(loc.qubits[1]))];
+                prop.syy(&pair);
+            }
+            GateType::SYYdg if loc.qubits.len() >= 2 => {
+                let pair = [(QubitId(loc.qubits[0]), QubitId(loc.qubits[1]))];
+                prop.syydg(&pair);
+            }
+            GateType::SZZ if loc.qubits.len() >= 2 => {
+                let pair = [(QubitId(loc.qubits[0]), QubitId(loc.qubits[1]))];
+                prop.szz(&pair);
+            }
+            GateType::SZZdg if loc.qubits.len() >= 2 => {
+                let pair = [(QubitId(loc.qubits[0]), QubitId(loc.qubits[1]))];
+                prop.szzdg(&pair);
+            }
+            GateType::SWAP if loc.qubits.len() >= 2 => {
+                let pair = [(QubitId(loc.qubits[0]), QubitId(loc.qubits[1]))];
+                prop.swap(&pair);
+            }
+            // PZ/QAlloc absorbs propagating errors on the reset qubit
+            GateType::PZ | GateType::QAlloc if !loc.qubits.is_empty() => {
+                prop.clear_qubit(loc.qubits[0]);
+            }
+            // MZ: X component flips the measurement, then qubit state collapses
+            GateType::MZ | GateType::MeasureFree | GateType::MeasureLeaked
+                if !loc.qubits.is_empty() =>
+            {
+                let q = loc.qubits[0];
+                if prop.contains_x(q)
+                    && let Some(&meas_idx) = meas_positions.get(&loc_idx)
+                {
+                    affected.insert(meas_idx);
+                }
+                prop.clear_qubit(q);
+            }
+            _ => {}
+        }
+
+        if prop.is_identity() {
+            break;
+        }
+    }
+
+    affected
+}
+
+// ============================================================================
+// Fault Catalog: per-location, per-alternative lookup table
+// ============================================================================
+
+/// The kind of physical fault mechanism.
+#[derive(Clone, Debug, PartialEq, Eq)]
+pub enum FaultKind {
+    /// A Pauli error injected after a gate.
+    Pauli,
+    /// A measurement outcome flip.
+    MeasurementFlip,
+    /// A preparation error (X on |0⟩).
+    PrepFlip,
+}
+
+/// Which noise channel produced this fault location.
+#[derive(Clone, Copy, Debug, PartialEq, Eq)]
+pub enum FaultChannel {
+    /// Single-qubit depolarizing (`p1`).
+    P1,
+    /// Two-qubit depolarizing (`p2`).
+    P2,
+    /// Measurement flip (`p_meas`).
+    PMeas,
+    /// State preparation flip (`p_prep`).
+    PPrep,
+}
+
+/// One alternative within a physical fault location.
+#[derive(Clone, Debug)]
+pub struct FaultAlternative {
+    /// Kind of fault.
+    pub kind: FaultKind,
+    /// The Pauli error for this alternative (None for measurement/prep faults).
+    pub pauli: Option<PauliString>,
+    /// Raw measurement indices flipped by this fault.
+    pub affected_measurements: Vec<usize>,
+    /// Detector indices flipped (computed from measurement effects + detector records).
+    pub affected_detectors: Vec<usize>,
+    /// Observable indices flipped.
+    pub affected_observables: Vec<usize>,
+    /// Tracked-Pauli indices flipped.
+    pub affected_tracked_paulis: Vec<usize>,
+    /// Probability of this alternative conditioned on the mechanism firing (`1/k`).
+    pub conditional_probability: f64,
+    /// Marginal probability of this specific alternative at this location: `p_i / k_i`.
+    ///
+    /// This is NOT "probability of this fault and no others." A full-circuit
+    /// configuration probability requires multiplying by `(1 - p_j)` for all
+    /// other locations `j`.
+    pub absolute_probability: f64,
+}
+
+/// A physical fault location in the circuit.
+#[derive(Clone, Debug)]
+pub struct FaultLocation {
+    /// Tick index in the `TickCircuit`.
+    pub tick: usize,
+    /// Gate index within the tick.
+    pub gate_index: usize,
+    /// Gate type at this location.
+    pub gate_type: GateType,
+    /// Qubits involved.
+    pub qubits: Vec<usize>,
+    /// Which noise channel this location belongs to.
+    pub channel: FaultChannel,
+    /// Total probability that this mechanism fires: `p_i`.
+    pub channel_probability: f64,
+    /// Probability that no fault occurs at this location: `1 - p_i`.
+    pub no_fault_probability: f64,
+    /// Number of fault alternatives at this location: `k_i`.
+    pub num_alternatives: usize,
+    /// All fault alternatives at this location.
+    pub faults: Vec<FaultAlternative>,
+}
+
+/// Complete fault catalog for a circuit + noise model.
+///
+/// Each location is an independent physical fault mechanism.
+/// Each alternative within a location is one possible Pauli error
+/// (for depolarizing) or outcome flip (for measurement/prep).
+///
+/// Probability model (independent mechanisms):
+///
+/// For location `i` with `k_i` alternatives:
+/// - `channel_probability` = `p_i` (total probability mechanism fires)
+/// - `no_fault_probability` = `1 - p_i`
+/// - `conditional_probability` = `1/k_i` (uniform alternative choice)
+/// - `absolute_probability` = `p_i / k_i` (marginal alternative probability)
+///
+/// Full-circuit configuration probability for "alternative j at location i,
+/// no fault at all other locations":
+/// ```text
+/// P = (p_i / k_i) * product_{m != i} (1 - p_m)
+/// ```
+#[derive(Clone, Debug)]
+pub struct FaultCatalog {
+    pub locations: Vec<FaultLocation>,
+}
+
+/// One yielded configuration from `fault_configurations(k)`.
+#[derive(Clone, Debug)]
+pub struct FaultConfiguration {
+    /// Indices into `catalog.locations` for the k selected locations.
+    pub location_indices: Vec<usize>,
+    /// Alternative index chosen within each selected location.
+    pub alternative_indices: Vec<usize>,
+    /// Combined measurement indices (XOR parity across selected alternatives).
+    pub affected_measurements: Vec<usize>,
+    /// Combined detector indices (XOR parity).
+    pub affected_detectors: Vec<usize>,
+    /// Combined observable indices (XOR parity).
+    pub affected_observables: Vec<usize>,
+    /// Combined tracked-Pauli indices (XOR parity).
+    pub affected_tracked_paulis: Vec<usize>,
+    /// Product of selected alternatives' `absolute_probability`.
+    pub selected_probability: f64,
+    /// `selected_probability * product(unselected no_fault_probability)`.
+    pub configuration_probability: f64,
+}
+
+impl FaultCatalog {
+    /// Build a structural fault catalog from a circuit.
+    ///
+    /// The returned catalog includes all structurally supported noisy locations,
+    /// independent of any concrete noise point. All channel and alternative
+    /// probabilities are initialized to zero except `no_fault_probability`, which
+    /// is initialized to one.
+    ///
+    /// # Errors
+    ///
+    /// Returns [`UnsupportedGateError`] when the circuit contains a gate outside
+    /// the supported Clifford/prep/measurement/metadata set.
+    pub fn from_circuit(tc: &TickCircuit) -> Result<Self, UnsupportedGateError> {
+        build_structural_fault_catalog(tc)
+    }
+
+    /// Recompute noise-dependent probability fields for this catalog.
+    ///
+    /// This updates only `channel_probability`, `no_fault_probability`, and
+    /// `absolute_probability`. Structural fields such as `num_alternatives`,
+    /// `conditional_probability`, Pauli labels, and effect lists are unchanged.
+    ///
+    /// # Panics
+    ///
+    /// Panics if a malformed catalog contains more than `u32::MAX` alternatives
+    /// at one location. Catalogs produced by [`FaultCatalog::from_circuit`] have
+    /// at most 15 alternatives per location.
+    pub fn with_noise(&mut self, noise: &StochasticNoiseParams) -> &mut Self {
+        for loc in &mut self.locations {
+            let p = match loc.channel {
+                FaultChannel::P1 => noise.p1,
+                FaultChannel::P2 => noise.p2,
+                FaultChannel::PMeas => noise.p_meas,
+                FaultChannel::PPrep => noise.p_prep,
+            };
+            let k = loc.num_alternatives;
+            debug_assert!(k > 0, "fault location has no alternatives");
+            debug_assert_eq!(k, loc.faults.len(), "num_alternatives out of sync");
+            let k_f64 = f64::from(u32::try_from(k).expect("fault alternative count exceeds u32"));
+
+            loc.channel_probability = p;
+            loc.no_fault_probability = 1.0 - p;
+            for alt in &mut loc.faults {
+                alt.absolute_probability = p / k_f64;
+            }
+        }
+        self
+    }
+
+    /// Clone this catalog and apply a concrete noise point to the clone.
+    #[must_use]
+    pub fn parameterized(&self, noise: &StochasticNoiseParams) -> Self {
+        let mut copy = self.clone();
+        copy.with_noise(noise);
+        copy
+    }
+
+    /// Convert this catalog into raw-measurement sampling mechanisms.
+    ///
+    /// This is a materialization step for raw measurement sampling only. It
+    /// drops zero-probability locations and locations where every alternative has
+    /// empty `affected_measurements`, while preserving empty alternatives inside
+    /// any kept mechanism to maintain the correct uniform denominator.
+    #[must_use]
+    pub fn to_mechanisms(&self) -> Vec<FaultMechanism> {
+        self.locations
+            .iter()
+            .filter(|loc| loc.channel_probability > 0.0)
+            .filter(|loc| {
+                loc.faults
+                    .iter()
+                    .any(|alt| !alt.affected_measurements.is_empty())
+            })
+            .map(|loc| FaultMechanism {
+                probability: loc.channel_probability,
+                alternatives: loc
+                    .faults
+                    .iter()
+                    .map(|alt| alt.affected_measurements.clone())
+                    .collect(),
+            })
+            .collect()
+    }
+
+    /// Lazily iterate all k-fault configurations.
+    ///
+    /// Each yielded `FaultConfiguration` represents exactly k distinct locations
+    /// firing, with one alternative chosen per location. Effects are combined by
+    /// XOR parity. Probabilities follow the independent-mechanism model.
+    ///
+    /// Zero-probability alternatives are skipped. A structural location with
+    /// `channel_probability == 0` remains in [`FaultCatalog::locations`] but is
+    /// not yielded as a selected fault configuration.
+    ///
+    /// For k=0: yields one no-fault event.
+    #[must_use]
+    pub fn fault_configurations(&self, k: usize) -> FaultConfigurationIter<'_> {
+        FaultConfigurationIter::new(self, k)
+    }
+}
+
+/// Internal cursor for k-fault configuration iteration.
+///
+/// Holds the combination/alternative state machine. Shared by both
+/// `FaultConfigurationIter` (borrowed) and `OwnedFaultConfigIter` (owned).
+/// Combinations range over nonzero-probability fault alternatives only; the
+/// full structural catalog remains available through `FaultCatalog::locations`.
+struct FaultConfigCursor {
+    k: usize,
+    location_indices: Vec<usize>,
+    alternative_indices: Vec<Vec<usize>>,
+    combo: Vec<usize>,
+    alt_indices: Vec<usize>,
+    alt_counts: Vec<usize>,
+    started: bool,
+    done: bool,
+}
+
+impl FaultConfigCursor {
+    fn new(catalog: &FaultCatalog, k: usize) -> Self {
+        let mut location_indices = Vec::new();
+        let mut alternative_indices = Vec::new();
+        for (loc_idx, loc) in catalog.locations.iter().enumerate() {
+            let alts: Vec<usize> = loc
+                .faults
+                .iter()
+                .enumerate()
+                .filter_map(|(alt_idx, alt)| (alt.absolute_probability > 0.0).then_some(alt_idx))
+                .collect();
+            if !alts.is_empty() {
+                location_indices.push(loc_idx);
+                alternative_indices.push(alts);
+            }
+        }
+
+        let num_active_locations = location_indices.len();
+        if k == 0 || k > num_active_locations {
+            return Self {
+                k,
+                location_indices,
+                alternative_indices,
+                combo: Vec::new(),
+                alt_indices: Vec::new(),
+                alt_counts: Vec::new(),
+                started: false,
+                done: k > num_active_locations && k > 0,
+            };
+        }
+        let combo: Vec<usize> = (0..k).collect();
+        let alt_counts: Vec<usize> = combo
+            .iter()
+            .map(|&i| alternative_indices[i].len())
+            .collect();
+        let alt_indices = vec![0usize; k];
+        Self {
+            k,
+            location_indices,
+            alternative_indices,
+            combo,
+            alt_indices,
+            alt_counts,
+            started: false,
+            done: false,
+        }
+    }
+
+    /// Advance to the next state. Returns true if a new valid state exists.
+    fn advance(&mut self) -> bool {
+        // Try advancing alternatives (mixed-radix counter)
+        for i in (0..self.k).rev() {
+            self.alt_indices[i] += 1;
+            if self.alt_indices[i] < self.alt_counts[i] {
+                return true;
+            }
+            self.alt_indices[i] = 0;
+        }
+        // Try advancing combination
+        let mut i = self.k;
+        while i > 0 {
+            i -= 1;
+            self.combo[i] += 1;
+            if self.combo[i] <= self.location_indices.len() - self.k + i {
+                for j in (i + 1)..self.k {
+                    self.combo[j] = self.combo[j - 1] + 1;
+                }
+                for j in 0..self.k {
+                    self.alt_counts[j] = self.alternative_indices[self.combo[j]].len();
+                    self.alt_indices[j] = 0;
+                }
+                return true;
+            }
+        }
+        false
+    }
+
+    /// Build a `FaultConfiguration` from the current cursor state + catalog data.
+    fn build(&self, catalog: &FaultCatalog) -> FaultConfiguration {
+        if self.k == 0 {
+            let no_fault_prob: f64 = catalog
+                .locations
+                .iter()
+                .map(|l| l.no_fault_probability)
+                .product();
+            return FaultConfiguration {
+                location_indices: Vec::new(),
+                alternative_indices: Vec::new(),
+                affected_measurements: Vec::new(),
+                affected_detectors: Vec::new(),
+                affected_observables: Vec::new(),
+                affected_tracked_paulis: Vec::new(),
+                selected_probability: 1.0,
+                configuration_probability: no_fault_prob,
+            };
+        }
+
+        let mut meas_set = std::collections::BTreeSet::new();
+        let mut det_set = std::collections::BTreeSet::new();
+        let mut obs_set = std::collections::BTreeSet::new();
+        let mut tracked_pauli_set = std::collections::BTreeSet::new();
+        let mut selected_prob = 1.0;
+
+        for i in 0..self.k {
+            let location_index = self.location_indices[self.combo[i]];
+            let alternative_index = self.alternative_indices[self.combo[i]][self.alt_indices[i]];
+            let loc = &catalog.locations[location_index];
+            let alt = &loc.faults[alternative_index];
+            selected_prob *= alt.absolute_probability;
+            for &m in &alt.affected_measurements {
+                if !meas_set.remove(&m) {
+                    meas_set.insert(m);
+                }
+            }
+            for &d in &alt.affected_detectors {
+                if !det_set.remove(&d) {
+                    det_set.insert(d);
+                }
+            }
+            for &o in &alt.affected_observables {
+                if !obs_set.remove(&o) {
+                    obs_set.insert(o);
+                }
+            }
+            for &op in &alt.affected_tracked_paulis {
+                if !tracked_pauli_set.remove(&op) {
+                    tracked_pauli_set.insert(op);
+                }
+            }
+        }
+
+        let selected_set: std::collections::BTreeSet<usize> = self
+            .combo
+            .iter()
+            .map(|&i| self.location_indices[i])
+            .collect();
+        let unselected_no_fault: f64 = catalog
+            .locations
+            .iter()
+            .enumerate()
+            .filter(|(i, _)| !selected_set.contains(i))
+            .map(|(_, loc)| loc.no_fault_probability)
+            .product();
+
+        FaultConfiguration {
+            location_indices: self
+                .combo
+                .iter()
+                .map(|&i| self.location_indices[i])
+                .collect(),
+            alternative_indices: self
+                .combo
+                .iter()
+                .zip(self.alt_indices.iter())
+                .map(|(&loc_pos, &alt_pos)| self.alternative_indices[loc_pos][alt_pos])
+                .collect(),
+            affected_measurements: meas_set.into_iter().collect(),
+            affected_detectors: det_set.into_iter().collect(),
+            affected_observables: obs_set.into_iter().collect(),
+            affected_tracked_paulis: tracked_pauli_set.into_iter().collect(),
+            selected_probability: selected_prob,
+            configuration_probability: selected_prob * unselected_no_fault,
+        }
+    }
+
+    /// Drive the iterator: yield next configuration or None.
+    fn next_config(&mut self, catalog: &FaultCatalog) -> Option<FaultConfiguration> {
+        if self.done {
+            return None;
+        }
+        if self.k == 0 {
+            self.done = true;
+            return Some(self.build(catalog));
+        }
+        if !self.started {
+            self.started = true;
+            return Some(self.build(catalog));
+        }
+        if self.advance() {
+            Some(self.build(catalog))
+        } else {
+            self.done = true;
+            None
+        }
+    }
+}
+
+/// Lazy iterator over k-fault configurations (borrows catalog).
+pub struct FaultConfigurationIter<'a> {
+    catalog: &'a FaultCatalog,
+    cursor: FaultConfigCursor,
+}
+
+impl<'a> FaultConfigurationIter<'a> {
+    fn new(catalog: &'a FaultCatalog, k: usize) -> Self {
+        let cursor = FaultConfigCursor::new(catalog, k);
+        Self { catalog, cursor }
+    }
+}
+
+impl Iterator for FaultConfigurationIter<'_> {
+    type Item = FaultConfiguration;
+    fn next(&mut self) -> Option<Self::Item> {
+        self.cursor.next_config(self.catalog)
+    }
+}
+
+/// Owned k-fault configuration iterator (no lifetime borrows).
+/// Suitable for FFI / `PyO3` where lifetimes are not expressible.
+pub struct OwnedFaultConfigIter {
+    catalog: FaultCatalog,
+    cursor: FaultConfigCursor,
+}
+
+impl OwnedFaultConfigIter {
+    /// Create from an owned catalog clone.
+    #[must_use]
+    pub fn new(catalog: FaultCatalog, k: usize) -> Self {
+        let cursor = FaultConfigCursor::new(&catalog, k);
+        Self { catalog, cursor }
+    }
+}
+
+impl Iterator for OwnedFaultConfigIter {
+    type Item = FaultConfiguration;
+    fn next(&mut self) -> Option<Self::Item> {
+        self.cursor.next_config(&self.catalog)
+    }
+}
+
+/// Build a fault catalog from a `TickCircuit` and noise parameters.
+///
+/// Returns per-location, per-alternative fault data including Pauli labels,
+/// affected detectors, observables, tracked Paulis, and probability fields.
+///
+/// Reads detector/observable metadata and tracked-Pauli annotations
+/// from the circuit when present.
+///
+/// # Errors
+///
+/// Returns [`UnsupportedGateError`] when the circuit contains a gate outside
+/// the supported Clifford/prep/measurement/metadata set.
+pub fn build_fault_catalog(
+    tc: &TickCircuit,
+    noise: &StochasticNoiseParams,
+) -> Result<FaultCatalog, UnsupportedGateError> {
+    let mut catalog = FaultCatalog::from_circuit(tc)?;
+    catalog.with_noise(noise);
+    Ok(catalog)
+}
+
+fn build_structural_fault_catalog(tc: &TickCircuit) -> Result<FaultCatalog, UnsupportedGateError> {
+    validate_tick_circuit(tc)?;
+    let (gates, meas_positions) = flatten_tick_circuit(tc);
+
+    // Parse detector/DEM-output records for measurement→detector/op mapping
+    let det_records = parse_detector_records(tc);
+    let obs_records = parse_observable_records(tc);
+    let tracked_pauli_annotations = parse_tracked_pauli_annotations(tc);
+    let num_meas = tc
+        .get_meta("num_measurements")
+        .and_then(|a| {
+            if let pecos_quantum::Attribute::String(s) = a {
+                s.parse::<usize>().ok()
+            } else {
+                None
+            }
+        })
+        .unwrap_or(meas_positions.len());
+    let record_effect_index = RecordEffectIndex::new(&det_records, &obs_records, num_meas);
+
+    let mut locations = Vec::new();
+
+    let pauli_types = [PauliType::X, PauliType::Y, PauliType::Z];
+    let mut effect_cache = PropagatedEffectCache::default();
+
+    for (loc_idx, loc) in gates.iter().enumerate() {
+        let tick_idx = loc.tick;
+        let gate_idx = loc.gate_index;
+        let gate_type = loc.gate_type;
+        let qubits = &loc.qubits;
+
+        match gate_type {
+            gate_type if is_standard_1q_clifford_gate(gate_type) && !loc.qubits.is_empty() => {
+                let q = loc.qubits[0];
+                let num_alts = 3;
+                let conditional_probability = 1.0 / 3.0;
+                let mut faults = Vec::with_capacity(num_alts);
+                for &pt in &pauli_types {
+                    let effect = effect_cache.single(
+                        pt,
+                        q,
+                        loc_idx + 1,
+                        &gates,
+                        &meas_positions,
+                        &tracked_pauli_annotations,
+                    );
+                    let pauli = pauli_type_to_string(pt, q);
+                    let (affected, dets, obs, tracked) =
+                        catalog_effect_parts(effect, &record_effect_index);
+                    faults.push(FaultAlternative {
+                        kind: FaultKind::Pauli,
+                        pauli: Some(pauli),
+                        affected_measurements: affected,
+                        affected_detectors: dets,
+                        affected_observables: obs,
+                        affected_tracked_paulis: tracked,
+                        conditional_probability,
+                        absolute_probability: 0.0,
+                    });
+                }
+                let num_alts = faults.len();
+                locations.push(FaultLocation {
+                    tick: tick_idx,
+                    gate_index: gate_idx,
+                    gate_type,
+                    qubits: qubits.clone(),
+                    channel: FaultChannel::P1,
+                    channel_probability: 0.0,
+                    no_fault_probability: 1.0,
+                    num_alternatives: num_alts,
+                    faults,
+                });
+            }
+
+            gate_type if is_standard_2q_clifford_gate(gate_type) && loc.qubits.len() >= 2 => {
+                let (q1, q2) = (loc.qubits[0], loc.qubits[1]);
+                let num_alts = 15;
+                let conditional_probability = 1.0 / 15.0;
+                let mut faults = Vec::with_capacity(num_alts);
+
+                // 9 two-qubit pairs
+                for &p1 in &pauli_types {
+                    for &p2 in &pauli_types {
+                        let left = effect_cache.single(
+                            p1,
+                            q1,
+                            loc_idx + 1,
+                            &gates,
+                            &meas_positions,
+                            &tracked_pauli_annotations,
+                        );
+                        let right = effect_cache.single(
+                            p2,
+                            q2,
+                            loc_idx + 1,
+                            &gates,
+                            &meas_positions,
+                            &tracked_pauli_annotations,
+                        );
+                        let effect = xor_fault_effects(&left, &right);
+                        let pauli = pauli_pair_to_string(p1, q1, p2, q2);
+                        let (affected, dets, obs, tracked) =
+                            catalog_effect_parts(effect, &record_effect_index);
+                        faults.push(FaultAlternative {
+                            kind: FaultKind::Pauli,
+                            pauli: Some(pauli),
+                            affected_measurements: affected,
+                            affected_detectors: dets,
+                            affected_observables: obs,
+                            affected_tracked_paulis: tracked,
+                            conditional_probability,
+                            absolute_probability: 0.0,
+                        });
+                    }
+                }
+                // 6 single-qubit (PI and IP)
+                for &p in &pauli_types {
+                    let effect = effect_cache.single(
+                        p,
+                        q1,
+                        loc_idx + 1,
+                        &gates,
+                        &meas_positions,
+                        &tracked_pauli_annotations,
+                    );
+                    let pauli = pauli_type_to_string(p, q1);
+                    let (affected, dets, obs, tracked) =
+                        catalog_effect_parts(effect, &record_effect_index);
+                    faults.push(FaultAlternative {
+                        kind: FaultKind::Pauli,
+                        pauli: Some(pauli),
+                        affected_measurements: affected,
+                        affected_detectors: dets,
+                        affected_observables: obs,
+                        affected_tracked_paulis: tracked,
+                        conditional_probability,
+                        absolute_probability: 0.0,
+                    });
+
+                    let effect = effect_cache.single(
+                        p,
+                        q2,
+                        loc_idx + 1,
+                        &gates,
+                        &meas_positions,
+                        &tracked_pauli_annotations,
+                    );
+                    let pauli = pauli_type_to_string(p, q2);
+                    let (affected, dets, obs, tracked) =
+                        catalog_effect_parts(effect, &record_effect_index);
+                    faults.push(FaultAlternative {
+                        kind: FaultKind::Pauli,
+                        pauli: Some(pauli),
+                        affected_measurements: affected,
+                        affected_detectors: dets,
+                        affected_observables: obs,
+                        affected_tracked_paulis: tracked,
+                        conditional_probability,
+                        absolute_probability: 0.0,
+                    });
+                }
+                let n_alts = faults.len();
+                locations.push(FaultLocation {
+                    tick: tick_idx,
+                    gate_index: gate_idx,
+                    gate_type,
+                    qubits: qubits.clone(),
+                    channel: FaultChannel::P2,
+                    channel_probability: 0.0,
+                    no_fault_probability: 1.0,
+                    num_alternatives: n_alts,
+                    faults,
+                });
+            }
+
+            GateType::PZ | GateType::QAlloc if !loc.qubits.is_empty() => {
+                let q = loc.qubits[0];
+                let effect = effect_cache.single(
+                    PauliType::X,
+                    q,
+                    loc_idx + 1,
+                    &gates,
+                    &meas_positions,
+                    &tracked_pauli_annotations,
+                );
+                let (affected, dets, obs, tracked) =
+                    catalog_effect_parts(effect, &record_effect_index);
+                locations.push(FaultLocation {
+                    tick: tick_idx,
+                    gate_index: gate_idx,
+                    gate_type,
+                    qubits: qubits.clone(),
+                    channel: FaultChannel::PPrep,
+                    channel_probability: 0.0,
+                    no_fault_probability: 1.0,
+                    num_alternatives: 1,
+                    faults: vec![FaultAlternative {
+                        kind: FaultKind::PrepFlip,
+                        pauli: None,
+                        affected_measurements: affected,
+                        affected_detectors: dets,
+                        affected_observables: obs,
+                        affected_tracked_paulis: tracked,
+                        conditional_probability: 1.0,
+                        absolute_probability: 0.0,
+                    }],
+                });
+            }
+
+            GateType::MZ | GateType::MeasureFree | GateType::MeasureLeaked => {
+                if let Some(&meas_idx) = meas_positions.get(&loc_idx) {
+                    let affected = vec![meas_idx];
+                    let dets = record_effect_index.detectors_for_measurements(&affected);
+                    let obs = record_effect_index.observables_for_measurements(&affected);
+                    locations.push(FaultLocation {
+                        tick: tick_idx,
+                        gate_index: gate_idx,
+                        gate_type,
+                        qubits: qubits.clone(),
+                        channel: FaultChannel::PMeas,
+                        channel_probability: 0.0,
+                        no_fault_probability: 1.0,
+                        num_alternatives: 1,
+                        faults: vec![FaultAlternative {
+                            kind: FaultKind::MeasurementFlip,
+                            pauli: None,
+                            affected_measurements: affected,
+                            affected_detectors: dets,
+                            affected_observables: obs,
+                            affected_tracked_paulis: Vec::new(),
+                            conditional_probability: 1.0,
+                            absolute_probability: 0.0,
+                        }],
+                    });
+                }
+            }
+
+            _ => {}
+        }
+    }
+
+    Ok(FaultCatalog { locations })
+}
+
+// ---- Helpers for fault catalog ----
+
+fn pauli_type_to_pauli(pt: PauliType) -> Pauli {
+    match pt {
+        PauliType::X => Pauli::X,
+        PauliType::Y => Pauli::Y,
+        PauliType::Z => Pauli::Z,
+    }
+}
+
+fn pauli_type_to_string(pt: PauliType, qubit: usize) -> PauliString {
+    PauliString::with_phase_and_paulis(
+        pecos_core::QuarterPhase::PlusOne,
+        vec![(pauli_type_to_pauli(pt), QubitId(qubit))],
+    )
+}
+
+fn pauli_pair_to_string(p1: PauliType, q1: usize, p2: PauliType, q2: usize) -> PauliString {
+    PauliString::with_phase_and_paulis(
+        pecos_core::QuarterPhase::PlusOne,
+        vec![
+            (pauli_type_to_pauli(p1), QubitId(q1)),
+            (pauli_type_to_pauli(p2), QubitId(q2)),
+        ],
+    )
+}
+
+fn parse_records_from_meta(tc: &TickCircuit, key: &str) -> Vec<Vec<i32>> {
+    let Some(pecos_quantum::Attribute::String(json)) = tc.get_meta(key) else {
+        return Vec::new();
+    };
+    parse_records_array_list(json)
+}
+
+fn parse_detector_records(tc: &TickCircuit) -> Vec<Vec<i32>> {
+    parse_records_from_meta(tc, "detectors")
+}
+
+fn parse_observable_records(tc: &TickCircuit) -> Vec<Vec<i32>> {
+    parse_records_from_meta(tc, "observables")
+}
+
+fn parse_tracked_pauli_annotations(tc: &TickCircuit) -> Vec<PauliString> {
+    tc.annotations()
+        .iter()
+        .filter(|ann| matches!(ann.kind, AnnotationKind::TrackedPauli))
+        .map(|ann| {
+            let mut pauli = ann.pauli.clone();
+            pauli.set_phase(pecos_core::QuarterPhase::PlusOne);
+            pauli
+        })
+        .collect()
+}
+
+fn tracked_paulis_flipped_by(
+    prop: &BitmaskPauliProp,
+    tracked_paulis: &[PauliString],
+) -> Vec<usize> {
+    tracked_paulis
+        .iter()
+        .enumerate()
+        .filter_map(|(idx, tracked_pauli)| {
+            let mut parity = false;
+            for &(pauli, qubit) in tracked_pauli.paulis() {
+                let q = qubit.index();
+                match pauli {
+                    Pauli::X => parity ^= prop.contains_z(q),
+                    Pauli::Y => parity ^= prop.contains_x(q) ^ prop.contains_z(q),
+                    Pauli::Z => parity ^= prop.contains_x(q),
+                    Pauli::I => {}
+                }
+            }
+            parity.then_some(idx)
+        })
+        .collect()
+}
+
+/// Simple parser for `[{"records": [...]}, ...]` JSON without `serde_json`.
+fn parse_records_array_list(json: &str) -> Vec<Vec<i32>> {
+    let json = json.trim();
+    if json.is_empty() || json == "[]" {
+        return Vec::new();
+    }
+    let mut results = Vec::new();
+    // Find each "records": [...] within the JSON
+    let mut search_from = 0;
+    while let Some(pos) = json[search_from..].find("\"records\"") {
+        let pos = search_from + pos;
+        let rest = &json[pos..];
+        if let Some(arr_start) = rest.find('[') {
+            if let Some(arr_end) = rest[arr_start..].find(']') {
+                let arr_str = &rest[arr_start + 1..arr_start + arr_end];
+                let nums: Vec<i32> = arr_str
+                    .split(',')
+                    .filter_map(|s| s.trim().parse().ok())
+                    .collect();
+                results.push(nums);
+                search_from = pos + arr_start + arr_end + 1;
+            } else {
+                break;
+            }
+        } else {
+            break;
+        }
+    }
+    results
+}
+
+fn record_absolute_index(num_meas: usize, rec: i32) -> Option<usize> {
+    let base = i64::try_from(num_meas).ok()?;
+    let abs_idx = base.checked_add(i64::from(rec))?;
+    usize::try_from(abs_idx).ok()
+}
+
+struct RecordEffectIndex {
+    detectors_by_measurement: Vec<Vec<usize>>,
+    observables_by_measurement: Vec<Vec<usize>>,
+}
+
+impl RecordEffectIndex {
+    fn new(det_records: &[Vec<i32>], obs_records: &[Vec<i32>], num_meas: usize) -> Self {
+        Self {
+            detectors_by_measurement: records_by_measurement(det_records, num_meas),
+            observables_by_measurement: records_by_measurement(obs_records, num_meas),
+        }
+    }
+
+    /// Map measurement effects to detector effects via record XOR.
+    fn detectors_for_measurements(&self, affected_meas: &[usize]) -> Vec<usize> {
+        measurements_to_record_effects(affected_meas, &self.detectors_by_measurement)
+    }
+
+    /// Map measurement effects to observable effects via record XOR.
+    fn observables_for_measurements(&self, affected_meas: &[usize]) -> Vec<usize> {
+        measurements_to_record_effects(affected_meas, &self.observables_by_measurement)
+    }
+}
+
+fn catalog_effect_parts(
+    effect: PropagatedFaultEffect,
+    record_effect_index: &RecordEffectIndex,
+) -> (Vec<usize>, Vec<usize>, Vec<usize>, Vec<usize>) {
+    let affected: Vec<usize> = effect.affected_measurements.into_iter().collect();
+    let dets = record_effect_index.detectors_for_measurements(&affected);
+    let obs = record_effect_index.observables_for_measurements(&affected);
+    (affected, dets, obs, effect.affected_tracked_paulis)
+}
+
+fn records_by_measurement(records_by_output: &[Vec<i32>], num_meas: usize) -> Vec<Vec<usize>> {
+    let mut by_measurement = vec![Vec::new(); num_meas];
+    for (output_idx, records) in records_by_output.iter().enumerate() {
+        for &rec in records {
+            if let Some(meas_idx) = record_absolute_index(num_meas, rec)
+                && meas_idx < num_meas
+            {
+                by_measurement[meas_idx].push(output_idx);
+            }
+        }
+    }
+    by_measurement
+}
+
+fn measurements_to_record_effects(
+    affected_meas: &[usize],
+    outputs_by_measurement: &[Vec<usize>],
+) -> Vec<usize> {
+    let mut fired = Vec::new();
+    for &meas_idx in affected_meas {
+        if let Some(outputs) = outputs_by_measurement.get(meas_idx) {
+            for &output_idx in outputs {
+                toggle_sorted(&mut fired, output_idx);
+            }
+        }
+    }
+    fired
+}
+
+fn toggle_sorted(values: &mut Vec<usize>, value: usize) {
+    match values.binary_search(&value) {
+        Ok(pos) => {
+            values.remove(pos);
+        }
+        Err(pos) => {
+            values.insert(pos, value);
+        }
+    }
+}
+
+// ============================================================================
+// Shared symbolic simulation helper
+// ============================================================================
+
+/// Run `SymbolicSparseStab` through a `TickCircuit` with proper PZ (reset)
+/// semantics, returning the `MeasurementHistory` with correct cross-reset
+/// correlations.
+///
+/// Iterates tick-by-tick to match the `TickCircuit`'s measurement numbering
+/// (which detector/DEM-output record indices reference).
+///
+/// Errors on unsupported gates with tick/gate/qubit context (same gate set
+/// as [`build_fault_table`]).
+///
+/// # Errors
+///
+/// Returns [`UnsupportedGateError`] when the circuit contains a gate outside
+/// the supported Clifford/prep/measurement/metadata set.
+pub fn symbolic_measurement_history(
+    tc: &TickCircuit,
+) -> Result<MeasurementHistory, UnsupportedGateError> {
+    use pecos_simulators::SymbolicSparseStab;
+
+    let num_qubits = tc
+        .iter_gate_batches()
+        .flat_map(|g| g.as_gate().qubits.iter())
+        .map(|q| q.index() + 1)
+        .max()
+        .unwrap_or(0);
+
+    let mut sim = SymbolicSparseStab::new(num_qubits);
+
+    for (tick_idx, tick) in tc.iter_ticks() {
+        for gate in tick.iter_gate_batches() {
+            let gate_idx = gate.batch_index();
+            let qs: Vec<usize> = gate.qubits.iter().map(pecos_core::QubitId::index).collect();
+
+            match gate.gate_type {
+                GateType::PZ | GateType::QAlloc => {
+                    for &q in &qs {
+                        sim.pz(q);
+                    }
+                }
+                GateType::H => {
+                    sim.h(&qs);
+                }
+                GateType::X => {
+                    sim.x(&qs);
+                }
+                GateType::Y => {
+                    sim.y(&qs);
+                }
+                GateType::Z => {
+                    sim.z(&qs);
+                }
+                GateType::SZ => {
+                    sim.sz(&qs);
+                }
+                GateType::SZdg => {
+                    sim.szdg(&qs);
+                }
+                GateType::SX => {
+                    sim.sx(&qs);
+                }
+                GateType::SXdg => {
+                    sim.sxdg(&qs);
+                }
+                GateType::SY => {
+                    sim.sy(&qs);
+                }
+                GateType::SYdg => {
+                    sim.sydg(&qs);
+                }
+                GateType::F => {
+                    sim.sx(&qs);
+                    sim.sz(&qs);
+                }
+                GateType::Fdg => {
+                    sim.szdg(&qs);
+                    sim.sxdg(&qs);
+                }
+                GateType::CX => {
+                    let pairs = symbolic_pairs(&qs);
+                    sim.cx(&pairs);
+                }
+                GateType::CY => {
+                    sim.cy(&symbolic_pairs(&qs));
+                }
+                GateType::CZ => {
+                    sim.cz(&symbolic_pairs(&qs));
+                }
+                GateType::SXX => {
+                    sim.sxx(&symbolic_pairs(&qs));
+                }
+                GateType::SXXdg => {
+                    sim.sxxdg(&symbolic_pairs(&qs));
+                }
+                GateType::SYY => {
+                    sim.syy(&symbolic_pairs(&qs));
+                }
+                GateType::SYYdg => {
+                    sim.syydg(&symbolic_pairs(&qs));
+                }
+                GateType::SZZ => {
+                    sim.szz(&symbolic_pairs(&qs));
+                }
+                GateType::SZZdg => {
+                    sim.szzdg(&symbolic_pairs(&qs));
+                }
+                GateType::SWAP => {
+                    sim.swap(&symbolic_pairs(&qs));
+                }
+                GateType::MZ | GateType::MeasureFree | GateType::MeasureLeaked => {
+                    sim.mz(&qs);
+                }
+                GateType::I
+                | GateType::Idle
+                | GateType::QFree
+                | GateType::MeasCrosstalkGlobalPayload
+                | GateType::MeasCrosstalkLocalPayload
+                | GateType::TrackedPauliMeta => {}
+                other => {
+                    return Err(UnsupportedGateError {
+                        gate_type: other,
+                        tick: tick_idx,
+                        gate_in_tick: gate_idx,
+                        qubits: qs,
+                    });
+                }
+            }
+        }
+    }
+
+    Ok(sim.measurement_history().clone())
+}
+
+fn symbolic_pairs(qs: &[usize]) -> Vec<(usize, usize)> {
+    qs.chunks(2)
+        .filter(|c| c.len() == 2)
+        .map(|c| (c[0], c[1]))
+        .collect()
+}
+
+// ============================================================================
+// Raw Measurement Plan: geometric/O(fired) columnar sampling
+// ============================================================================
+
+/// Zero out bits beyond `shots` in the final word of each column.
+fn mask_partial_final_word(columns: &mut [Vec<u64>], shots: usize) {
+    let remainder = shots % 64;
+    if remainder == 0 {
+        return;
+    }
+    let mask = (1u64 << remainder) - 1;
+    for col in columns.iter_mut() {
+        if let Some(last) = col.last_mut() {
+            *last &= mask;
+        }
+    }
+}
+
+/// Columnar raw-measurement result with r-source access.
+///
+/// The measurement columns are the final output (base XOR faults).
+/// The `r_columns` field holds the latent random source columns that feed
+/// into the ideal measurement dependency graph.
+pub struct RawSampleResult {
+    /// Final measurement columns: `columns[meas_idx][word_idx]`, bit i = shot word*64+i.
+    /// Bits beyond `shots` in the final word are always zero.
+    pub columns: Vec<Vec<u64>>,
+    /// Latent r-source columns (one per Random measurement kind).
+    /// Bits beyond `shots` in the final word are always zero.
+    pub r_columns: Vec<Vec<u64>>,
+    /// Measurement index that introduced each r-source.
+    /// `r_source_measurements[k]` is the measurement index for `r_columns[k]`.
+    pub r_source_measurements: Vec<usize>,
+    pub shots: usize,
+}
+
+/// A compiled plan for sampling raw measurements from a stochastic circuit.
+///
+/// Combines:
+/// - **r-sources** (p=0.5): non-deterministic measurement variables from the
+///   ideal dependency graph. These fan out through Copy/Computed relationships.
+/// - **Physical mechanisms**: depolarizing gate faults, prep faults,
+///   measurement flips. These do NOT fan out through ideal dependencies.
+///
+/// Physical mechanisms are sampled using geometric skip (O(fired events) per
+/// mechanism), matching the DEM sampler's performance characteristics.
+pub struct RawMeasurementPlan {
+    pub num_measurements: usize,
+    kinds: Vec<MeasurementKind>,
+    pub mechanisms: Vec<FaultMechanism>,
+    /// Precomputed 1/ln(1-p) for geometric skip sampling, one per mechanism.
+    inv_log_1_minus_p: Vec<f64>,
+}
+
+impl RawMeasurementPlan {
+    /// Build a plan from a measurement history and fault mechanisms.
+    #[must_use]
+    pub fn new(history: &MeasurementHistory, mechanisms: Vec<FaultMechanism>) -> Self {
+        let kinds = MeasurementKind::from_history(history);
+        let inv_log_1_minus_p = mechanisms
+            .iter()
+            .map(|m| {
+                let log_1_minus_p = (1.0 - m.probability).ln();
+                if log_1_minus_p.abs() < f64::EPSILON {
+                    0.0
+                } else {
+                    1.0 / log_1_minus_p
+                }
+            })
+            .collect();
+        Self {
+            num_measurements: kinds.len(),
+            kinds,
+            mechanisms,
+            inv_log_1_minus_p,
+        }
+    }
+
+    /// Sample raw measurements using geometric skip for physical faults.
+    ///
+    /// Returns a `SampleResult` for compatibility with existing code.
+    /// For r-event access, use [`sample_raw`].
+    #[must_use]
+    pub fn sample(&self, shots: usize, seed: u64) -> SampleResult {
+        let raw = self.sample_raw(shots, seed);
+        SampleResult::new(raw.columns, shots)
+    }
+
+    /// Sample raw measurements with r-source column access.
+    ///
+    /// Physical mechanisms use geometric skip: O(p * shots) RNG calls per
+    /// mechanism, not O(shots). For typical QEC noise (p ~ 0.005, 20k shots),
+    /// this is ~100 firings per mechanism vs 20000 iterations.
+    #[must_use]
+    pub fn sample_raw(&self, shots: usize, seed: u64) -> RawSampleResult {
+        if shots == 0 {
+            let r_source_measurements = self.r_source_indices();
+            return RawSampleResult {
+                columns: vec![Vec::new(); self.num_measurements],
+                r_columns: vec![Vec::new(); r_source_measurements.len()],
+                r_source_measurements,
+                shots: 0,
+            };
+        }
+
+        let num_words = shots.div_ceil(64);
+
+        // 1. Sample base values (r-sources + constants) and capture r columns
+        let mut rng_base = PecosRng::seed_from_u64(seed);
+        let (mut columns, mut r_columns) = self.sample_base(num_words, &mut rng_base);
+
+        // 2. Overlay physical faults using geometric skip
+        if !self.mechanisms.is_empty() {
+            let mut rng_fault = PecosRng::seed_from_u64(seed.wrapping_add(1));
+            self.overlay_faults_geometric(shots, &mut columns, &mut rng_fault);
+        }
+
+        // 3. Mask partial final word so bits beyond `shots` are always zero
+        mask_partial_final_word(&mut columns, shots);
+        mask_partial_final_word(&mut r_columns, shots);
+
+        RawSampleResult {
+            columns,
+            r_columns,
+            r_source_measurements: self.r_source_indices(),
+            shots,
+        }
+    }
+
+    /// Returns the measurement indices that correspond to r-sources (Random kinds).
+    fn r_source_indices(&self) -> Vec<usize> {
+        self.kinds
+            .iter()
+            .enumerate()
+            .filter_map(|(i, k)| {
+                if matches!(k, MeasurementKind::Random) {
+                    Some(i)
+                } else {
+                    None
+                }
+            })
+            .collect()
+    }
+
+    /// Sample base measurement values from r-sources and constants.
+    /// Returns (`measurement_columns`, `r_source_columns`).
+    fn sample_base(&self, num_words: usize, rng: &mut PecosRng) -> (Vec<Vec<u64>>, Vec<Vec<u64>>) {
+        let mut columns: Vec<Vec<u64>> = Vec::with_capacity(self.num_measurements);
+        let mut r_columns: Vec<Vec<u64>> = Vec::new();
+
+        for kind in &self.kinds {
+            match kind {
+                MeasurementKind::Fixed(value) => {
+                    let fill = if *value { !0u64 } else { 0u64 };
+                    columns.push(vec![fill; num_words]);
+                }
+                MeasurementKind::Random => {
+                    let mut col = vec![0u64; num_words];
+                    for word in &mut col {
+                        *word = rng.next_u64();
+                    }
+                    r_columns.push(col.clone());
+                    columns.push(col);
+                }
+                MeasurementKind::Copy(src) => {
+                    columns.push(columns[*src].clone());
+                }
+                MeasurementKind::CopyFlipped(src) => {
+                    let flipped: Vec<u64> = columns[*src].iter().map(|w| !w).collect();
+                    columns.push(flipped);
+                }
+                MeasurementKind::Computed { deps, flip } => {
+                    let init = if *flip { !0u64 } else { 0u64 };
+                    let mut col = vec![init; num_words];
+                    for &dep in deps {
+                        for (w, &d) in col.iter_mut().zip(columns[dep].iter()) {
+                            *w ^= d;
+                        }
+                    }
+                    columns.push(col);
+                }
+            }
+        }
+
+        (columns, r_columns)
+    }
+
+    /// Overlay physical faults using geometric skip sampling.
+    ///
+    /// For each mechanism with probability p:
+    /// - Precomputed `inv_log = 1/ln(1-p)`
+    /// - Sample `skip = floor(ln(U) * inv_log)` to jump to next fired shot
+    /// - At fired shot: choose uniform alternative, XOR affected measurements
+    ///
+    /// Complexity: O(p * shots) per mechanism (geometric = O(fired events)).
+    fn overlay_faults_geometric(&self, shots: usize, columns: &mut [Vec<u64>], rng: &mut PecosRng) {
+        let num_words = columns.first().map_or(0, Vec::len);
+        for (mech_idx, mechanism) in self.mechanisms.iter().enumerate() {
+            let inv_log = self.inv_log_1_minus_p[mech_idx];
+            let p = mechanism.probability;
+            let num_alts = mechanism.alternatives.len();
+            if num_alts == 0 {
+                continue;
+            }
+
+            // p=1: every shot fires (handle before inv_log check since inv_log=0 for p=1)
+            if p >= 1.0 {
+                if num_alts == 1 {
+                    let word_masks = full_shot_word_masks(shots, num_words);
+                    apply_word_masks(columns, &mechanism.alternatives[0], &word_masks);
+                } else {
+                    let mut alt_word_masks = vec![vec![0u64; num_words]; num_alts];
+                    for shot in 0..shots {
+                        let word_idx = shot / 64;
+                        let bit_idx = shot % 64;
+                        let alt_idx = rng.random_range(0..num_alts);
+                        alt_word_masks[alt_idx][word_idx] ^= 1u64 << bit_idx;
+                    }
+                    apply_alternative_word_masks(columns, mechanism, &alt_word_masks);
+                }
+                continue;
+            }
+
+            // Skip p=0 mechanisms (inv_log=0 means p≈0 or exactly 0)
+            if p == 0.0 || inv_log == 0.0 {
+                continue;
+            }
+
+            // Geometric skip sampling: O(fired events)
+            let mut shot: usize = 0;
+            let mut alt_word_masks: Option<Vec<Vec<u64>>> = None;
+            while shot < shots {
+                // Sample skip distance
+                #[allow(clippy::cast_precision_loss)]
+                let u = (rng.next_u64() as f64) / (u64::MAX as f64);
+                let u = if u == 0.0 { f64::MIN_POSITIVE } else { u };
+                #[allow(clippy::cast_possible_truncation, clippy::cast_sign_loss)]
+                let skip = (u.ln() * inv_log).floor() as usize;
+
+                shot += skip;
+                if shot >= shots {
+                    break;
+                }
+
+                // This shot fires — choose alternative and XOR
+                let word_idx = shot / 64;
+                let bit_idx = shot % 64;
+                let mask = 1u64 << bit_idx;
+
+                let alt_idx = if num_alts == 1 {
+                    0
+                } else {
+                    rng.random_range(0..num_alts)
+                };
+                alt_word_masks.get_or_insert_with(|| vec![vec![0u64; num_words]; num_alts])
+                    [alt_idx][word_idx] ^= mask;
+
+                shot += 1;
+            }
+            if let Some(alt_word_masks) = alt_word_masks {
+                apply_alternative_word_masks(columns, mechanism, &alt_word_masks);
+            }
+        }
+    }
+}
+
+fn full_shot_word_masks(shots: usize, num_words: usize) -> Vec<u64> {
+    let mut masks = vec![!0u64; num_words];
+    mask_partial_final_word(std::slice::from_mut(&mut masks), shots);
+    masks
+}
+
+fn apply_alternative_word_masks(
+    columns: &mut [Vec<u64>],
+    mechanism: &FaultMechanism,
+    alt_word_masks: &[Vec<u64>],
+) {
+    for (measurements, word_masks) in mechanism.alternatives.iter().zip(alt_word_masks) {
+        apply_word_masks(columns, measurements, word_masks);
+    }
+}
+
+fn apply_word_masks(columns: &mut [Vec<u64>], measurements: &[usize], word_masks: &[u64]) {
+    if word_masks.iter().all(|&mask| mask == 0) {
+        return;
+    }
+    for &meas_idx in measurements {
+        if let Some(column) = columns.get_mut(meas_idx) {
+            for (word, &mask) in column.iter_mut().zip(word_masks) {
+                *word ^= mask;
+            }
+        }
+    }
+}
+
+#[cfg(test)]
+mod tests {
+    use super::*;
+
+    fn assert_close(actual: f64, expected: f64) {
+        assert!(
+            (actual - expected).abs() < 1e-12,
+            "expected {expected}, got {actual}"
+        );
+    }
+
+    #[test]
+    fn test_record_effect_index_maps_measurement_effects_by_xor() {
+        let det_records = vec![vec![-1], vec![-2, -1], vec![-1, -1], vec![-4], vec![1]];
+        let obs_records = vec![vec![-2], vec![-1, -2]];
+        let index = RecordEffectIndex::new(&det_records, &obs_records, 3);
+
+        assert_eq!(index.detectors_for_measurements(&[2]), vec![0, 1]);
+        assert_eq!(index.detectors_for_measurements(&[1, 2]), vec![0]);
+        assert_eq!(index.observables_for_measurements(&[1]), vec![0, 1]);
+        assert_eq!(index.observables_for_measurements(&[1, 2]), vec![0]);
+    }
+
+    /// Build a minimal `TickCircuit`: PZ(0) H(0) CX(0,1) H(0) MZ(0) PZ(0) H(0) CX(0,1) H(0) MZ(0)
+    fn two_round_x_check() -> TickCircuit {
+        let mut tc = TickCircuit::new();
+        // Round 1
+        tc.tick().h(&[QubitId(0)]);
+        tc.tick().cx(&[(QubitId(0), QubitId(1))]);
+        tc.tick().h(&[QubitId(0)]);
+        tc.tick().mz(&[QubitId(0)]);
+        tc.tick().pz(&[QubitId(0)]);
+        // Round 2
+        tc.tick().h(&[QubitId(0)]);
+        tc.tick().cx(&[(QubitId(0), QubitId(1))]);
+        tc.tick().h(&[QubitId(0)]);
+        tc.tick().mz(&[QubitId(0)]);
+        tc
+    }
+
+    #[test]
+    fn test_meas_fault_affects_single_measurement() {
+        let tc = two_round_x_check();
+        let noise = StochasticNoiseParams {
+            p1: 0.0,
+            p2: 0.0,
+            p_meas: 0.01,
+            p_prep: 0.0,
+        };
+        let mechanisms = build_fault_table(&tc, &noise).unwrap();
+
+        // Should have exactly 2 measurement mechanisms (one per MZ),
+        // each with 1 alternative that flips that measurement.
+        assert_eq!(mechanisms.len(), 2);
+        assert_eq!(mechanisms[0].alternatives, vec![vec![0]]);
+        assert_eq!(mechanisms[1].alternatives, vec![vec![1]]);
+        assert!((mechanisms[0].probability - 0.01).abs() < 1e-10);
+    }
+
+    #[test]
+    fn test_prep_fault_reaches_next_measurement_only() {
+        let tc = two_round_x_check();
+        let noise = StochasticNoiseParams {
+            p1: 0.0,
+            p2: 0.0,
+            p_meas: 0.0,
+            p_prep: 0.01,
+        };
+        let mechanisms = build_fault_table(&tc, &noise).unwrap();
+
+        // PZ(0) before round 2: single alternative affecting only m1
+        let round2_prep = mechanisms.iter().find(|m| m.alternatives == vec![vec![1]]);
+        assert!(
+            round2_prep.is_some(),
+            "PZ before round 2 should produce mechanism affecting m1"
+        );
+    }
+
+    #[test]
+    fn test_prep_fault_does_not_cross_pz() {
+        let tc = two_round_x_check();
+        let noise = StochasticNoiseParams {
+            p1: 0.0,
+            p2: 0.0,
+            p_meas: 0.0,
+            p_prep: 0.01,
+        };
+        let mechanisms = build_fault_table(&tc, &noise).unwrap();
+
+        // No alternative should affect BOTH m0 and m1 (PZ between rounds absorbs)
+        for m in &mechanisms {
+            for alt in &m.alternatives {
+                assert!(
+                    !(alt.contains(&0) && alt.contains(&1)),
+                    "Fault alternative crosses PZ boundary: {alt:?}"
+                );
+            }
+        }
+    }
+
+    #[test]
+    fn test_flatten_tick_circuit_preserves_source_metadata() {
+        let mut tc = TickCircuit::new();
+        tc.tick().h(&[QubitId(0), QubitId(1)]);
+        tc.tick()
+            .cx(&[(QubitId(0), QubitId(1)), (QubitId(2), QubitId(3))]);
+        tc.tick().mz(&[QubitId(0), QubitId(1)]);
+
+        let (gates, meas_positions) = flatten_tick_circuit(&tc);
+
+        assert_eq!(gates.len(), 6);
+        assert_eq!(meas_positions.get(&4), Some(&0));
+        assert_eq!(meas_positions.get(&5), Some(&1));
+
+        assert_eq!(gates[0].tick, 0);
+        assert_eq!(gates[0].gate_index, 0);
+        assert_eq!(gates[0].gate_type, GateType::H);
+        assert_eq!(gates[0].qubits, vec![0]);
+
+        assert_eq!(gates[1].tick, 0);
+        assert_eq!(gates[1].gate_index, 0);
+        assert_eq!(gates[1].gate_type, GateType::H);
+        assert_eq!(gates[1].qubits, vec![1]);
+
+        assert_eq!(gates[2].tick, 1);
+        assert_eq!(gates[2].gate_index, 0);
+        assert_eq!(gates[2].gate_type, GateType::CX);
+        assert_eq!(gates[2].qubits, vec![0, 1]);
+
+        assert_eq!(gates[3].tick, 1);
+        assert_eq!(gates[3].gate_index, 0);
+        assert_eq!(gates[3].gate_type, GateType::CX);
+        assert_eq!(gates[3].qubits, vec![2, 3]);
+
+        assert_eq!(gates[4].tick, 2);
+        assert_eq!(gates[4].gate_index, 0);
+        assert_eq!(gates[4].gate_type, GateType::MZ);
+        assert_eq!(gates[4].qubits, vec![0]);
+
+        assert_eq!(gates[5].tick, 2);
+        assert_eq!(gates[5].gate_index, 0);
+        assert_eq!(gates[5].gate_type, GateType::MZ);
+        assert_eq!(gates[5].qubits, vec![1]);
+    }
+
+    #[test]
+    fn test_flatten_tick_circuit_skips_zero_gate_metadata_batches() {
+        let mut tc = TickCircuit::new();
+        tc.tick().h(&[QubitId(0)]);
+        tc.insert_tick(1);
+        tc.get_tick_mut(1)
+            .unwrap()
+            .add_gate(pecos_core::Gate::simple(
+                GateType::TrackedPauliMeta,
+                vec![QubitId(1), QubitId(2)],
+            ));
+        tc.tick().mz(&[QubitId(0)]);
+
+        let (gates, meas_positions) = flatten_tick_circuit(&tc);
+
+        assert_eq!(gates.len(), 2);
+        assert_eq!(gates[0].gate_type, GateType::H);
+        assert_eq!(gates[1].gate_type, GateType::MZ);
+        assert_eq!(meas_positions.get(&1), Some(&0));
+    }
+
+    // ---- Direct propagation tests using propagate_single ----
+
+    #[test]
+    fn test_propagate_x_before_cx_reaches_target_mz() {
+        // Circuit: CX(0,1) MZ(1)
+        // X on q0 before CX: CX maps XI → XX → MZ(q1) sees X → flips
+        let mut tc = TickCircuit::new();
+        tc.tick().cx(&[(QubitId(0), QubitId(1))]);
+        tc.tick().mz(&[QubitId(1)]);
+
+        let (gates, meas_pos) = flatten_tick_circuit(&tc);
+        let affected = propagate_single(PauliType::X, 0, 0, &gates, &meas_pos);
+        assert_eq!(
+            affected,
+            BTreeSet::from([0]),
+            "X on q0 before CX(0,1) MZ(1) should flip m0"
+        );
+    }
+
+    #[test]
+    fn test_propagate_z_before_cx_stays_on_control() {
+        // Circuit: CX(0,1) MZ(1)
+        // Z on q0 before CX: CX maps ZI → ZI → MZ(q1) sees I → no flip
+        let mut tc = TickCircuit::new();
+        tc.tick().cx(&[(QubitId(0), QubitId(1))]);
+        tc.tick().mz(&[QubitId(1)]);
+
+        let (gates, meas_pos) = flatten_tick_circuit(&tc);
+        let affected = propagate_single(PauliType::Z, 0, 0, &gates, &meas_pos);
+        assert!(
+            affected.is_empty(),
+            "Z on q0 before CX(0,1) should not reach MZ(q1)"
+        );
+    }
+
+    #[test]
+    fn test_propagate_x_on_target_unchanged_by_cx() {
+        // Circuit: CX(0,1) MZ(1)
+        // X on q1 before CX: CX maps IX → IX → MZ(q1) sees X → flips
+        let mut tc = TickCircuit::new();
+        tc.tick().cx(&[(QubitId(0), QubitId(1))]);
+        tc.tick().mz(&[QubitId(1)]);
+
+        let (gates, meas_pos) = flatten_tick_circuit(&tc);
+        let affected = propagate_single(PauliType::X, 1, 0, &gates, &meas_pos);
+        assert_eq!(affected, BTreeSet::from([0]));
+    }
+
+    #[test]
+    fn test_propagate_z_on_target_spreads_to_control_via_cx() {
+        // Circuit: CX(0,1) MZ(0) MZ(1)
+        // Z on q1 before CX: CX maps IZ → ZZ → MZ(q0) sees Z (no flip), MZ(q1) sees Z (no flip)
+        let mut tc = TickCircuit::new();
+        tc.tick().cx(&[(QubitId(0), QubitId(1))]);
+        tc.tick().mz(&[QubitId(0)]);
+        tc.tick().mz(&[QubitId(1)]);
+
+        let (gates, meas_pos) = flatten_tick_circuit(&tc);
+        let affected = propagate_single(PauliType::Z, 1, 0, &gates, &meas_pos);
+        assert!(
+            affected.is_empty(),
+            "Z errors don't flip Z-basis measurements"
+        );
+    }
+
+    #[test]
+    fn test_propagate_x_through_h_becomes_z() {
+        // Circuit: H(0) MZ(0)
+        // X on q0 at position 0: H maps X→Z → MZ sees Z → no flip
+        let mut tc = TickCircuit::new();
+        tc.tick().h(&[QubitId(0)]);
+        tc.tick().mz(&[QubitId(0)]);
+
+        let (gates, meas_pos) = flatten_tick_circuit(&tc);
+        let affected = propagate_single(PauliType::X, 0, 0, &gates, &meas_pos);
+        assert!(
+            affected.is_empty(),
+            "X through H becomes Z, should not flip MZ"
+        );
+    }
+
+    #[test]
+    fn test_propagate_z_through_h_becomes_x() {
+        // Circuit: H(0) MZ(0)
+        // Z on q0 at position 0: H maps Z→X → MZ sees X → flips
+        let mut tc = TickCircuit::new();
+        tc.tick().h(&[QubitId(0)]);
+        tc.tick().mz(&[QubitId(0)]);
+
+        let (gates, meas_pos) = flatten_tick_circuit(&tc);
+        let affected = propagate_single(PauliType::Z, 0, 0, &gates, &meas_pos);
+        assert_eq!(
+            affected,
+            BTreeSet::from([0]),
+            "Z through H becomes X, should flip MZ"
+        );
+    }
+
+    #[test]
+    fn test_propagate_x_absorbed_by_pz() {
+        // Circuit: PZ(0) MZ(0)
+        // X on q0 at position 0: PZ absorbs it → MZ sees I → no flip
+        let mut tc = TickCircuit::new();
+        tc.tick().pz(&[QubitId(0)]);
+        tc.tick().mz(&[QubitId(0)]);
+
+        let (gates, meas_pos) = flatten_tick_circuit(&tc);
+        let affected = propagate_single(PauliType::X, 0, 0, &gates, &meas_pos);
+        assert!(affected.is_empty(), "X should be absorbed by PZ");
+    }
+
+    #[test]
+    fn test_pz_absorbs_all_pauli_components_before_reset() {
+        // Circuit: PZ(0) H(0) MZ(0)
+        // Any fault before the reset is absorbed. Faults after the reset still
+        // propagate through the H according to normal Clifford conjugation.
+        let mut tc = TickCircuit::new();
+        tc.tick().pz(&[QubitId(0)]);
+        tc.tick().h(&[QubitId(0)]);
+        tc.tick().mz(&[QubitId(0)]);
+
+        let (gates, meas_pos) = flatten_tick_circuit(&tc);
+        for pauli in [PauliType::X, PauliType::Y, PauliType::Z] {
+            let affected = propagate_single(pauli, 0, 0, &gates, &meas_pos);
+            assert!(
+                affected.is_empty(),
+                "{pauli:?} before PZ should be absorbed by the reset"
+            );
+        }
+
+        assert!(
+            propagate_single(PauliType::X, 0, 1, &gates, &meas_pos).is_empty(),
+            "X after PZ becomes Z through H and should not flip MZ"
+        );
+        assert_eq!(
+            propagate_single(PauliType::Y, 0, 1, &gates, &meas_pos),
+            BTreeSet::from([0]),
+            "Y after PZ keeps an X component through H and should flip MZ"
+        );
+        assert_eq!(
+            propagate_single(PauliType::Z, 0, 1, &gates, &meas_pos),
+            BTreeSet::from([0]),
+            "Z after PZ becomes X through H and should flip MZ"
+        );
+    }
+
+    #[test]
+    fn test_propagate_x_absorbed_by_mz() {
+        // Circuit: MZ(0) MZ(0) — X on q0 should flip first MZ only
+        // (MZ collapses qubit, absorbing the error)
+        let mut tc = TickCircuit::new();
+        tc.tick().mz(&[QubitId(0)]);
+        tc.tick().mz(&[QubitId(0)]);
+
+        let (gates, meas_pos) = flatten_tick_circuit(&tc);
+        let affected = propagate_single(PauliType::X, 0, 0, &gates, &meas_pos);
+        assert_eq!(
+            affected,
+            BTreeSet::from([0]),
+            "X should flip first MZ only, not second"
+        );
+    }
+
+    #[test]
+    fn test_xor_combined_single_effects_match_pair_propagation() {
+        let mut tc = TickCircuit::new();
+        tc.tick().h(&[QubitId(0)]);
+        tc.tick().cx(&[(QubitId(0), QubitId(1))]);
+        tc.tick().h(&[QubitId(1)]);
+        tc.tick().mz(&[QubitId(0), QubitId(1)]);
+        tc.tracked_pauli_labeled("tracked_z0", PauliString::z(0));
+        tc.tracked_pauli_labeled("tracked_z1", PauliString::z(1));
+
+        let (gates, meas_pos) = flatten_tick_circuit(&tc);
+        let tracked_paulis = parse_tracked_pauli_annotations(&tc);
+        let start = 1;
+        let left =
+            propagate_single_effect(PauliType::X, 0, start, &gates, &meas_pos, &tracked_paulis);
+        let right =
+            propagate_single_effect(PauliType::Z, 1, start, &gates, &meas_pos, &tracked_paulis);
+        let combined = xor_fault_effects(&left, &right);
+        let direct = propagate_pair_effect(
+            [(PauliType::X, 0), (PauliType::Z, 1)],
+            start,
+            &gates,
+            &meas_pos,
+            &tracked_paulis,
+        );
+
+        assert_eq!(combined, direct);
+    }
+
+    #[test]
+    fn test_propagated_effect_cache_matches_fresh_propagation() {
+        let mut tc = TickCircuit::new();
+        tc.tick().h(&[QubitId(0)]);
+        tc.tick().mz(&[QubitId(0)]);
+        tc.tracked_pauli_labeled("tracked_x0", PauliString::x(0));
+
+        let (gates, meas_pos) = flatten_tick_circuit(&tc);
+        let tracked_paulis = parse_tracked_pauli_annotations(&tc);
+        let fresh = propagate_single_effect(PauliType::Z, 0, 0, &gates, &meas_pos, &tracked_paulis);
+
+        let mut cache = PropagatedEffectCache::default();
+        let first = cache.single(PauliType::Z, 0, 0, &gates, &meas_pos, &tracked_paulis);
+        assert_eq!(first, fresh);
+        assert_eq!(cache.len(), 1);
+
+        let mut mutated_clone = first.clone();
+        mutated_clone.affected_measurements.clear();
+        mutated_clone.affected_tracked_paulis.clear();
+
+        let second = cache.single(PauliType::Z, 0, 0, &gates, &meas_pos, &tracked_paulis);
+        assert_eq!(second, fresh);
+        assert_ne!(second, mutated_clone);
+        assert_eq!(
+            cache.len(),
+            1,
+            "repeating the same propagation key should reuse the cached entry"
+        );
+
+        let other = cache.single(PauliType::X, 0, 0, &gates, &meas_pos, &tracked_paulis);
+        let other_fresh =
+            propagate_single_effect(PauliType::X, 0, 0, &gates, &meas_pos, &tracked_paulis);
+        assert_eq!(other, other_fresh);
+        assert_eq!(cache.len(), 2);
+    }
+
+    #[test]
+    fn test_propagate_x_check_round_reaches_ancilla_only() {
+        // X-check pattern: H(0) CX(0,1) CX(0,2) H(0) MZ(0)
+        // X on q1 (data) at start: CX maps IX→IX on q1 (target stays).
+        // After H-CX-CX-H, X on q1 doesn't propagate to ancilla.
+        let mut tc = TickCircuit::new();
+        tc.tick().h(&[QubitId(0)]);
+        tc.tick().cx(&[(QubitId(0), QubitId(1))]);
+        tc.tick().cx(&[(QubitId(0), QubitId(2))]);
+        tc.tick().h(&[QubitId(0)]);
+        tc.tick().mz(&[QubitId(0)]);
+
+        let (gates, meas_pos) = flatten_tick_circuit(&tc);
+
+        // X on data q1: CX(ctrl=0, tgt=1) doesn't spread X from target to control.
+        // So X stays on q1, never reaches MZ(q0).
+        let affected = propagate_single(PauliType::X, 1, 0, &gates, &meas_pos);
+        assert!(
+            affected.is_empty(),
+            "X on data qubit should not reach ancilla MZ in X-check"
+        );
+
+        // Z on data q1: CX maps IZ → ZZ (spreads to control q0).
+        // Then H(q0) maps Z→X on ancilla. MZ(q0) sees X → flips.
+        let affected = propagate_single(PauliType::Z, 1, 0, &gates, &meas_pos);
+        assert_eq!(
+            affected,
+            BTreeSet::from([0]),
+            "Z on data should reach ancilla MZ in X-check"
+        );
+    }
+
+    #[test]
+    fn test_empty_alternative_preserved_for_correct_denominator() {
+        // H(0); MZ(0): p1 faults are injected AFTER H, directly before MZ.
+        // The 3 alternatives (X, Y, Z injected between H and MZ):
+        //   X: has X component → flips MZ
+        //   Y: has X component → flips MZ
+        //   Z: commutes with MZ → no flip (empty alternative)
+        // All 3 must be present so each is chosen with probability 1/3.
+        let mut tc = TickCircuit::new();
+        tc.tick().h(&[QubitId(0)]);
+        tc.tick().mz(&[QubitId(0)]);
+
+        let noise = StochasticNoiseParams {
+            p1: 0.01,
+            p2: 0.0,
+            p_meas: 0.0,
+            p_prep: 0.0,
+        };
+        let mechanisms = build_fault_table(&tc, &noise).unwrap();
+
+        assert_eq!(mechanisms.len(), 1, "one mechanism for the H gate");
+        let m = &mechanisms[0];
+        assert_eq!(
+            m.alternatives.len(),
+            3,
+            "all 3 Pauli alternatives must be present"
+        );
+        // Exactly one alternative should be empty (Z between H and MZ commutes)
+        let empty_count = m.alternatives.iter().filter(|a| a.is_empty()).count();
+        assert_eq!(
+            empty_count, 1,
+            "Z injected after H commutes with MZ — should be empty no-op alternative"
+        );
+    }
+
+    #[test]
+    fn test_zero_noise_produces_no_faults() {
+        let tc = two_round_x_check();
+        let noise = StochasticNoiseParams {
+            p1: 0.0,
+            p2: 0.0,
+            p_meas: 0.0,
+            p_prep: 0.0,
+        };
+        let faults = build_fault_table(&tc, &noise).unwrap();
+        assert!(faults.is_empty());
+    }
+
+    #[test]
+    fn test_unsupported_gate_rejected_even_with_zero_noise() {
+        let mut tc = TickCircuit::new();
+        tc.tick().h(&[QubitId(0)]);
+        tc.tick().t(&[QubitId(0)]);
+        tc.tick().mz(&[QubitId(0)]);
+
+        // Zero noise — validation runs on raw TickCircuit before anything else
+        let noise = StochasticNoiseParams {
+            p1: 0.0,
+            p2: 0.0,
+            p_meas: 0.0,
+            p_prep: 0.0,
+        };
+        let result = build_fault_table(&tc, &noise);
+        assert!(result.is_err(), "T should be rejected");
+        let err = result.unwrap_err();
+        assert_eq!(err.gate_type, GateType::T);
+        assert_eq!(err.tick, 1, "T is in tick 1");
+        assert_eq!(err.gate_in_tick, 0, "T is gate 0 within that tick");
+        assert_eq!(err.qubits, vec![0], "full original qubit list");
+    }
+
+    // ---- symbolic_measurement_history tests ----
+
+    #[test]
+    fn test_symbolic_history_rejects_unsupported_gate() {
+        let mut tc = TickCircuit::new();
+        tc.tick().h(&[QubitId(0)]);
+        tc.tick().t(&[QubitId(0)]);
+        tc.tick().mz(&[QubitId(0)]);
+
+        let result = symbolic_measurement_history(&tc);
+        assert!(result.is_err(), "T should be rejected");
+        let err = result.unwrap_err();
+        assert_eq!(err.gate_type, GateType::T);
+        assert_eq!(err.tick, 1);
+        assert_eq!(err.qubits, vec![0]);
+    }
+
+    #[test]
+    fn test_symbolic_history_cy_circuit_succeeds() {
+        // CY(0,1) MZ(1): should not error; CY is a valid Clifford gate
+        let mut tc = TickCircuit::new();
+        tc.tick().h(&[QubitId(0)]);
+        let pairs = [(QubitId(0), QubitId(1))];
+        tc.tick().cy(&pairs);
+        tc.tick().mz(&[QubitId(0)]);
+        tc.tick().mz(&[QubitId(1)]);
+
+        let history = symbolic_measurement_history(&tc);
+        assert!(history.is_ok(), "CY should be supported");
+        assert_eq!(history.unwrap().len(), 2);
+    }
+
+    #[test]
+    fn test_symbolic_history_bell_produces_correct_kinds() {
+        let mut tc = TickCircuit::new();
+        tc.tick().h(&[QubitId(0)]);
+        tc.tick().cx(&[(QubitId(0), QubitId(1))]);
+        tc.tick().mz(&[QubitId(0)]);
+        tc.tick().mz(&[QubitId(1)]);
+
+        let history = symbolic_measurement_history(&tc).unwrap();
+        let kinds = MeasurementKind::from_history(&history);
+        assert_eq!(kinds.len(), 2);
+        assert!(matches!(kinds[0], MeasurementKind::Random));
+        assert!(matches!(kinds[1], MeasurementKind::Copy(0)));
+    }
+
+    #[test]
+    fn test_symbolic_history_reset_breaks_copy_chain_between_rounds() {
+        let mut tc = TickCircuit::new();
+        tc.tick().h(&[QubitId(0)]);
+        tc.tick().cx(&[(QubitId(0), QubitId(1))]);
+        tc.tick().mz(&[QubitId(0)]);
+        tc.tick().mz(&[QubitId(1)]);
+        tc.tick().pz(&[QubitId(0)]);
+        tc.tick().pz(&[QubitId(1)]);
+        tc.tick().h(&[QubitId(0)]);
+        tc.tick().cx(&[(QubitId(0), QubitId(1))]);
+        tc.tick().mz(&[QubitId(0)]);
+        tc.tick().mz(&[QubitId(1)]);
+
+        let history = symbolic_measurement_history(&tc).unwrap();
+        let kinds = MeasurementKind::from_history(&history);
+        assert_eq!(kinds.len(), 4);
+        assert!(matches!(kinds[0], MeasurementKind::Random));
+        assert!(matches!(kinds[1], MeasurementKind::Copy(0)));
+        assert!(
+            matches!(kinds[2], MeasurementKind::Random),
+            "measurement after reset should introduce a fresh random source"
+        );
+        assert!(
+            !matches!(kinds[2], MeasurementKind::Copy(0)),
+            "reset must break the copy chain from the first round"
+        );
+        assert!(matches!(kinds[3], MeasurementKind::Copy(2)));
+    }
+
+    // ---- FaultCatalog tests ----
+
+    #[test]
+    fn test_catalog_single_qubit_depolarizing() {
+        // H(0) MZ(0): p1 fault after H has 3 alternatives
+        let mut tc = TickCircuit::new();
+        tc.tick().h(&[QubitId(0)]);
+        tc.tick().mz(&[QubitId(0)]);
+        tc.set_meta(
+            "num_measurements",
+            pecos_quantum::Attribute::String("1".to_string()),
+        );
+        tc.set_meta(
+            "detectors",
+            pecos_quantum::Attribute::String("[]".to_string()),
+        );
+        tc.set_meta(
+            "observables",
+            pecos_quantum::Attribute::String("[]".to_string()),
+        );
+
+        let noise = StochasticNoiseParams {
+            p1: 0.03,
+            p2: 0.0,
+            p_meas: 0.0,
+            p_prep: 0.0,
+        };
+        let catalog = build_fault_catalog(&tc, &noise).unwrap();
+
+        // Should have exactly 1 location (H gate) with 3 alternatives
+        let h_locs: Vec<_> = catalog
+            .locations
+            .iter()
+            .filter(|l| l.gate_type == GateType::H)
+            .collect();
+        assert_eq!(h_locs.len(), 1);
+        let loc = &h_locs[0];
+        assert_eq!(loc.faults.len(), 3);
+        assert_eq!(loc.channel, FaultChannel::P1);
+        assert!((loc.channel_probability - 0.03).abs() < 1e-10);
+        assert!((loc.no_fault_probability - 0.97).abs() < 1e-10);
+        assert_eq!(loc.num_alternatives, 3);
+
+        for fault in &loc.faults {
+            assert_eq!(fault.kind, FaultKind::Pauli);
+            assert!(fault.pauli.is_some());
+            assert!((fault.conditional_probability - 1.0 / 3.0).abs() < 1e-10);
+            assert!((fault.absolute_probability - 0.01).abs() < 1e-10);
+        }
+    }
+
+    #[test]
+    fn test_catalog_two_qubit_depolarizing() {
+        // CX(0,1) MZ(0) MZ(1): p2 fault has 15 alternatives
+        let mut tc = TickCircuit::new();
+        tc.tick().cx(&[(QubitId(0), QubitId(1))]);
+        tc.tick().mz(&[QubitId(0)]);
+        tc.tick().mz(&[QubitId(1)]);
+        tc.set_meta(
+            "num_measurements",
+            pecos_quantum::Attribute::String("2".to_string()),
+        );
+        tc.set_meta(
+            "detectors",
+            pecos_quantum::Attribute::String("[]".to_string()),
+        );
+        tc.set_meta(
+            "observables",
+            pecos_quantum::Attribute::String("[]".to_string()),
+        );
+
+        let noise = StochasticNoiseParams {
+            p1: 0.0,
+            p2: 0.15,
+            p_meas: 0.0,
+            p_prep: 0.0,
+        };
+        let catalog = build_fault_catalog(&tc, &noise).unwrap();
+
+        let cx_locs: Vec<_> = catalog
+            .locations
+            .iter()
+            .filter(|l| l.gate_type == GateType::CX)
+            .collect();
+        assert_eq!(cx_locs.len(), 1);
+        let loc = &cx_locs[0];
+        assert_eq!(loc.faults.len(), 15);
+        assert_eq!(loc.num_alternatives, 15);
+
+        for fault in &loc.faults {
+            assert_eq!(fault.kind, FaultKind::Pauli);
+            assert!(fault.pauli.is_some());
+            assert!((fault.conditional_probability - 1.0 / 15.0).abs() < 1e-10);
+            assert!((fault.absolute_probability - 0.01).abs() < 1e-10);
+        }
+
+        // Verify 9 two-qubit PauliStrings and 6 single-qubit PauliStrings
+        let two_term: usize = loc
+            .faults
+            .iter()
+            .filter(|f| f.pauli.as_ref().unwrap().iter_pairs().count() == 2)
+            .count();
+        let one_term: usize = loc
+            .faults
+            .iter()
+            .filter(|f| f.pauli.as_ref().unwrap().iter_pairs().count() == 1)
+            .count();
+        assert_eq!(two_term, 9, "Should have 9 two-qubit Pauli alternatives");
+        assert_eq!(one_term, 6, "Should have 6 single-qubit Pauli alternatives");
+    }
+
+    #[test]
+    fn test_catalog_supports_all_traced_qis_clifford_gates() {
+        let mut tc = TickCircuit::new();
+        tc.tick().szdg(&[QubitId(0)]);
+        tc.tick().sx(&[QubitId(0)]);
+        tc.tick().sxdg(&[QubitId(1)]);
+        tc.tick().sy(&[QubitId(0)]);
+        tc.tick().sydg(&[QubitId(1)]);
+        tc.tick().f(&[QubitId(0)]);
+        tc.tick().fdg(&[QubitId(1)]);
+        tc.tick().cy(&[(QubitId(0), QubitId(1))]);
+        tc.tick().cz(&[(QubitId(0), QubitId(1))]);
+        tc.tick().sxx(&[(QubitId(0), QubitId(1))]);
+        tc.tick().sxxdg(&[(QubitId(0), QubitId(1))]);
+        tc.tick().syy(&[(QubitId(0), QubitId(1))]);
+        tc.tick().syydg(&[(QubitId(0), QubitId(1))]);
+        tc.tick().szz(&[(QubitId(0), QubitId(1))]);
+        tc.tick().szzdg(&[(QubitId(0), QubitId(1))]);
+        tc.tick().swap(&[(QubitId(0), QubitId(1))]);
+        tc.tick().mz(&[QubitId(0), QubitId(1)]);
+        tc.set_meta(
+            "num_measurements",
+            pecos_quantum::Attribute::String("2".to_string()),
+        );
+        tc.set_meta(
+            "detectors",
+            pecos_quantum::Attribute::String("[]".to_string()),
+        );
+        tc.set_meta(
+            "observables",
+            pecos_quantum::Attribute::String("[]".to_string()),
+        );
+
+        let noise = StochasticNoiseParams {
+            p1: 0.03,
+            p2: 0.15,
+            p_meas: 0.0,
+            p_prep: 0.0,
+        };
+        let catalog = build_fault_catalog(&tc, &noise).unwrap();
+
+        for (gate_type, expected_alternatives) in [
+            (GateType::SZdg, 3),
+            (GateType::SX, 3),
+            (GateType::SXdg, 3),
+            (GateType::SY, 3),
+            (GateType::SYdg, 3),
+            (GateType::F, 3),
+            (GateType::Fdg, 3),
+            (GateType::CY, 15),
+            (GateType::CZ, 15),
+            (GateType::SXX, 15),
+            (GateType::SXXdg, 15),
+            (GateType::SYY, 15),
+            (GateType::SYYdg, 15),
+            (GateType::SZZ, 15),
+            (GateType::SZZdg, 15),
+            (GateType::SWAP, 15),
+        ] {
+            let locations: Vec<_> = catalog
+                .locations
+                .iter()
+                .filter(|loc| loc.gate_type == gate_type)
+                .collect();
+            assert_eq!(locations.len(), 1, "{gate_type:?}");
+            assert_eq!(
+                locations[0].faults.len(),
+                expected_alternatives,
+                "{gate_type:?}"
+            );
+        }
+    }
+
+    #[test]
+    fn test_catalog_fault_effects_through_new_clifford_gates() {
+        fn fault_for_pauli<'a>(
+            loc: &'a FaultLocation,
+            pauli: &PauliString,
+        ) -> &'a FaultAlternative {
+            loc.faults
+                .iter()
+                .find(|fault| fault.pauli.as_ref() == Some(pauli))
+                .expect("missing expected Pauli fault")
+        }
+
+        let mut single = TickCircuit::new();
+        single.tick().h(&[QubitId(0)]);
+        single.tick().sy(&[QubitId(0)]);
+        single.tick().mz(&[QubitId(0)]);
+        single.set_meta(
+            "num_measurements",
+            pecos_quantum::Attribute::String("1".to_string()),
+        );
+        single.set_meta(
+            "detectors",
+            pecos_quantum::Attribute::String("[]".to_string()),
+        );
+        single.set_meta(
+            "observables",
+            pecos_quantum::Attribute::String("[]".to_string()),
+        );
+
+        let single_catalog = build_fault_catalog(
+            &single,
+            &StochasticNoiseParams {
+                p1: 0.03,
+                p2: 0.0,
+                p_meas: 0.0,
+                p_prep: 0.0,
+            },
+        )
+        .unwrap();
+        let h_loc = single_catalog
+            .locations
+            .iter()
+            .find(|loc| loc.gate_type == GateType::H)
+            .unwrap();
+        assert_eq!(
+            fault_for_pauli(h_loc, &pauli_type_to_string(PauliType::X, 0)).affected_measurements,
+            Vec::<usize>::new(),
+            "SY maps X to Z, so it should not flip MZ"
+        );
+        assert_eq!(
+            fault_for_pauli(h_loc, &pauli_type_to_string(PauliType::Y, 0)).affected_measurements,
+            vec![0],
+            "SY maps Y to Y, so it should flip MZ"
+        );
+        assert_eq!(
+            fault_for_pauli(h_loc, &pauli_type_to_string(PauliType::Z, 0)).affected_measurements,
+            vec![0],
+            "SY maps Z to X, so it should flip MZ"
+        );
+
+        let mut face = TickCircuit::new();
+        face.tick().h(&[QubitId(0)]);
+        face.tick().f(&[QubitId(0)]);
+        face.tick().mz(&[QubitId(0)]);
+        face.set_meta(
+            "num_measurements",
+            pecos_quantum::Attribute::String("1".to_string()),
+        );
+        face.set_meta(
+            "detectors",
+            pecos_quantum::Attribute::String("[]".to_string()),
+        );
+        face.set_meta(
+            "observables",
+            pecos_quantum::Attribute::String("[]".to_string()),
+        );
+
+        let face_catalog = build_fault_catalog(
+            &face,
+            &StochasticNoiseParams {
+                p1: 0.03,
+                p2: 0.0,
+                p_meas: 0.0,
+                p_prep: 0.0,
+            },
+        )
+        .unwrap();
+        let h_loc = face_catalog
+            .locations
+            .iter()
+            .find(|loc| loc.gate_type == GateType::H)
+            .unwrap();
+        assert_eq!(
+            fault_for_pauli(h_loc, &pauli_type_to_string(PauliType::X, 0)).affected_measurements,
+            vec![0],
+            "F maps X to Y, so it should flip MZ"
+        );
+        assert_eq!(
+            fault_for_pauli(h_loc, &pauli_type_to_string(PauliType::Y, 0)).affected_measurements,
+            Vec::<usize>::new(),
+            "F maps Y to Z, so it should not flip MZ"
+        );
+        assert_eq!(
+            fault_for_pauli(h_loc, &pauli_type_to_string(PauliType::Z, 0)).affected_measurements,
+            vec![0],
+            "F maps Z to X, so it should flip MZ"
+        );
+
+        let mut face_dagger = TickCircuit::new();
+        face_dagger.tick().h(&[QubitId(0)]);
+        face_dagger.tick().fdg(&[QubitId(0)]);
+        face_dagger.tick().mz(&[QubitId(0)]);
+        face_dagger.set_meta(
+            "num_measurements",
+            pecos_quantum::Attribute::String("1".to_string()),
+        );
+        face_dagger.set_meta(
+            "detectors",
+            pecos_quantum::Attribute::String("[]".to_string()),
+        );
+        face_dagger.set_meta(
+            "observables",
+            pecos_quantum::Attribute::String("[]".to_string()),
+        );
+
+        let face_dagger_catalog = build_fault_catalog(
+            &face_dagger,
+            &StochasticNoiseParams {
+                p1: 0.03,
+                p2: 0.0,
+                p_meas: 0.0,
+                p_prep: 0.0,
+            },
+        )
+        .unwrap();
+        let h_loc = face_dagger_catalog
+            .locations
+            .iter()
+            .find(|loc| loc.gate_type == GateType::H)
+            .unwrap();
+        assert_eq!(
+            fault_for_pauli(h_loc, &pauli_type_to_string(PauliType::X, 0)).affected_measurements,
+            Vec::<usize>::new(),
+            "Fdg maps X to Z, so it should not flip MZ"
+        );
+        assert_eq!(
+            fault_for_pauli(h_loc, &pauli_type_to_string(PauliType::Y, 0)).affected_measurements,
+            vec![0],
+            "Fdg maps Y to X, so it should flip MZ"
+        );
+        assert_eq!(
+            fault_for_pauli(h_loc, &pauli_type_to_string(PauliType::Z, 0)).affected_measurements,
+            vec![0],
+            "Fdg maps Z to Y, so it should flip MZ"
+        );
+
+        let mut two_qubit = TickCircuit::new();
+        two_qubit.tick().cx(&[(QubitId(0), QubitId(1))]);
+        two_qubit.tick().sxx(&[(QubitId(0), QubitId(1))]);
+        two_qubit.tick().mz(&[QubitId(0), QubitId(1)]);
+        two_qubit.set_meta(
+            "num_measurements",
+            pecos_quantum::Attribute::String("2".to_string()),
+        );
+        two_qubit.set_meta(
+            "detectors",
+            pecos_quantum::Attribute::String("[]".to_string()),
+        );
+        two_qubit.set_meta(
+            "observables",
+            pecos_quantum::Attribute::String("[]".to_string()),
+        );
+
+        let two_catalog = build_fault_catalog(
+            &two_qubit,
+            &StochasticNoiseParams {
+                p1: 0.0,
+                p2: 0.15,
+                p_meas: 0.0,
+                p_prep: 0.0,
+            },
+        )
+        .unwrap();
+        let cx_loc = two_catalog
+            .locations
+            .iter()
+            .find(|loc| loc.gate_type == GateType::CX)
+            .unwrap();
+        assert_eq!(
+            fault_for_pauli(cx_loc, &pauli_type_to_string(PauliType::X, 0)).affected_measurements,
+            vec![0],
+            "SXX leaves XI as XI"
+        );
+        assert_eq!(
+            fault_for_pauli(cx_loc, &pauli_type_to_string(PauliType::X, 1)).affected_measurements,
+            vec![1],
+            "SXX leaves IX as IX"
+        );
+        assert_eq!(
+            fault_for_pauli(cx_loc, &pauli_type_to_string(PauliType::Z, 0)).affected_measurements,
+            vec![0, 1],
+            "SXX maps ZI to YX"
+        );
+        assert_eq!(
+            fault_for_pauli(cx_loc, &pauli_type_to_string(PauliType::Z, 1)).affected_measurements,
+            vec![0, 1],
+            "SXX maps IZ to XY"
+        );
+    }
+
+    #[test]
+    fn test_catalog_keeps_observables_and_tracked_paulis_distinct() {
+        let mut tc = TickCircuit::new();
+        tc.tick().h(&[QubitId(0)]);
+        tc.tracked_pauli_labeled("tracked_z0", PauliString::z(0));
+        tc.set_meta(
+            "detectors",
+            pecos_quantum::Attribute::String("[]".to_string()),
+        );
+        tc.set_meta(
+            "observables",
+            pecos_quantum::Attribute::String("[]".to_string()),
+        );
+
+        let catalog = build_fault_catalog(
+            &tc,
+            &StochasticNoiseParams {
+                p1: 0.03,
+                p2: 0.0,
+                p_meas: 0.0,
+                p_prep: 0.0,
+            },
+        )
+        .unwrap();
+
+        let h_loc = catalog
+            .locations
+            .iter()
+            .find(|loc| loc.gate_type == GateType::H)
+            .unwrap();
+        let x_fault = h_loc
+            .faults
+            .iter()
+            .find(|fault| fault.pauli.as_ref() == Some(&PauliString::x(0)))
+            .unwrap();
+        let y_fault = h_loc
+            .faults
+            .iter()
+            .find(|fault| fault.pauli.as_ref() == Some(&PauliString::y(0)))
+            .unwrap();
+        let z_fault = h_loc
+            .faults
+            .iter()
+            .find(|fault| fault.pauli.as_ref() == Some(&PauliString::z(0)))
+            .unwrap();
+
+        assert_eq!(x_fault.affected_observables, Vec::<usize>::new());
+        assert_eq!(x_fault.affected_tracked_paulis, vec![0]);
+        assert_eq!(y_fault.affected_tracked_paulis, vec![0]);
+        assert_eq!(z_fault.affected_tracked_paulis, Vec::<usize>::new());
+
+        let configs: Vec<_> = catalog.fault_configurations(1).collect();
+        assert!(
+            configs
+                .iter()
+                .any(|config| config.affected_tracked_paulis.as_slice() == [0]
+                    && config.affected_observables.is_empty())
+        );
+    }
+
+    #[test]
+    fn test_catalog_after_tick_dag_round_trip_keeps_outputs_and_tracked_paulis_separate() {
+        let mut tc = TickCircuit::new();
+        tc.tick().h(&[QubitId(0), QubitId(1)]);
+        tc.tick().mz(&[QubitId(0)]);
+        tc.set_meta(
+            "num_measurements",
+            pecos_quantum::Attribute::String(tc.num_measurements().to_string()),
+        );
+        tc.add_detector_metadata(&[-1], None, Some("D0"), Some(0))
+            .unwrap();
+        tc.add_observable_metadata(&[-1], Some(0), Some("L0"))
+            .unwrap();
+        tc.tracked_pauli_labeled("tracked_z1", PauliString::z(1));
+
+        let round_tripped = TickCircuit::from(&pecos_quantum::DagCircuit::from(&tc));
+        assert_eq!(round_tripped.annotations().len(), 1);
+        assert!(matches!(
+            round_tripped.annotations()[0].kind,
+            AnnotationKind::TrackedPauli
+        ));
+
+        let catalog = build_fault_catalog(
+            &round_tripped,
+            &StochasticNoiseParams {
+                p1: 0.03,
+                p2: 0.0,
+                p_meas: 0.01,
+                p_prep: 0.0,
+            },
+        )
+        .unwrap();
+
+        let h_loc = catalog
+            .locations
+            .iter()
+            .find(|loc| loc.gate_type == GateType::H && loc.qubits.as_slice() == [0])
+            .unwrap();
+        let x_fault = h_loc
+            .faults
+            .iter()
+            .find(|fault| fault.pauli.as_ref() == Some(&PauliString::x(0)))
+            .unwrap();
+        assert_eq!(x_fault.affected_measurements, vec![0]);
+        assert_eq!(x_fault.affected_detectors, vec![0]);
+        assert_eq!(x_fault.affected_observables, vec![0]);
+        assert!(x_fault.affected_tracked_paulis.is_empty());
+
+        let tracked_h_loc = catalog
+            .locations
+            .iter()
+            .find(|loc| loc.gate_type == GateType::H && loc.qubits.as_slice() == [1])
+            .unwrap();
+        let tracked_x_fault = tracked_h_loc
+            .faults
+            .iter()
+            .find(|fault| fault.pauli.as_ref() == Some(&PauliString::x(1)))
+            .unwrap();
+        assert!(tracked_x_fault.affected_measurements.is_empty());
+        assert!(tracked_x_fault.affected_detectors.is_empty());
+        assert!(tracked_x_fault.affected_observables.is_empty());
+        assert_eq!(tracked_x_fault.affected_tracked_paulis, vec![0]);
+
+        let meas_fault = catalog
+            .locations
+            .iter()
+            .find(|loc| loc.channel == FaultChannel::PMeas)
+            .and_then(|loc| loc.faults.first())
+            .unwrap();
+        assert_eq!(meas_fault.affected_measurements, vec![0]);
+        assert_eq!(meas_fault.affected_detectors, vec![0]);
+        assert_eq!(meas_fault.affected_observables, vec![0]);
+        assert!(meas_fault.affected_tracked_paulis.is_empty());
+
+        assert!(catalog.to_mechanisms().iter().any(|mechanism| {
+            mechanism
+                .alternatives
+                .iter()
+                .any(|alternative| alternative.as_slice() == [0])
+        }));
+    }
+
+    #[test]
+    fn test_catalog_two_qubit_propagation_keeps_output_kinds_distinct() {
+        fn assert_case(gate_type: GateType, tracked_pauli: PauliString) {
+            let mut tc = TickCircuit::new();
+            tc.tick().h(&[QubitId(0)]);
+            match gate_type {
+                GateType::CX => {
+                    tc.tick().cx(&[(QubitId(0), QubitId(1))]);
+                    tc.tick().mz(&[QubitId(0)]);
+                }
+                GateType::CZ => {
+                    tc.tick().cz(&[(QubitId(0), QubitId(1))]);
+                    tc.tick().mz(&[QubitId(0)]);
+                }
+                GateType::SWAP => {
+                    tc.tick().swap(&[(QubitId(0), QubitId(1))]);
+                    tc.tick().cx(&[(QubitId(1), QubitId(2))]);
+                    tc.tick().mz(&[QubitId(2)]);
+                }
+                other => panic!("unexpected gate type {other:?}"),
+            }
+            tc.set_meta(
+                "num_measurements",
+                pecos_quantum::Attribute::String(tc.num_measurements().to_string()),
+            );
+            tc.add_detector_metadata(&[-1], None, Some("D0"), Some(0))
+                .unwrap();
+            tc.add_observable_metadata(&[-1], Some(0), Some("L0"))
+                .unwrap();
+            tc.tracked_pauli_labeled("tracked", tracked_pauli);
+
+            let catalog = build_fault_catalog(
+                &tc,
+                &StochasticNoiseParams {
+                    p1: 0.03,
+                    p2: 0.0,
+                    p_meas: 0.0,
+                    p_prep: 0.0,
+                },
+            )
+            .unwrap();
+
+            let h_loc = catalog
+                .locations
+                .iter()
+                .find(|loc| loc.gate_type == GateType::H && loc.qubits.as_slice() == [0])
+                .unwrap();
+            let x_fault = h_loc
+                .faults
+                .iter()
+                .find(|fault| fault.pauli.as_ref() == Some(&PauliString::x(0)))
+                .unwrap();
+
+            assert_eq!(x_fault.affected_measurements, vec![0], "{gate_type:?}");
+            assert_eq!(x_fault.affected_detectors, vec![0], "{gate_type:?}");
+            assert_eq!(x_fault.affected_observables, vec![0], "{gate_type:?}");
+            assert_eq!(x_fault.affected_tracked_paulis, vec![0], "{gate_type:?}");
+        }
+
+        // X0 before CX becomes X0 X1.
+        assert_case(GateType::CX, PauliString::z(1));
+        // X0 before CZ becomes X0 Z1.
+        assert_case(GateType::CZ, PauliString::x(1));
+        // X0 before SWAP becomes X1, then the extra CX maps it to X1 X2.
+        assert_case(GateType::SWAP, PauliString::z(1));
+    }
+
+    #[test]
+    fn test_catalog_all_two_qubit_cliffords_propagate_x_fault_measurement_support() {
+        fn apply_gate(tc: &mut TickCircuit, gate_type: GateType) {
+            match gate_type {
+                GateType::CX => {
+                    tc.tick().cx(&[(QubitId(0), QubitId(1))]);
+                }
+                GateType::CY => {
+                    tc.tick().cy(&[(QubitId(0), QubitId(1))]);
+                }
+                GateType::CZ => {
+                    tc.tick().cz(&[(QubitId(0), QubitId(1))]);
+                }
+                GateType::SXX => {
+                    tc.tick().sxx(&[(QubitId(0), QubitId(1))]);
+                }
+                GateType::SXXdg => {
+                    tc.tick().sxxdg(&[(QubitId(0), QubitId(1))]);
+                }
+                GateType::SYY => {
+                    tc.tick().syy(&[(QubitId(0), QubitId(1))]);
+                }
+                GateType::SYYdg => {
+                    tc.tick().syydg(&[(QubitId(0), QubitId(1))]);
+                }
+                GateType::SZZ => {
+                    tc.tick().szz(&[(QubitId(0), QubitId(1))]);
+                }
+                GateType::SZZdg => {
+                    tc.tick().szzdg(&[(QubitId(0), QubitId(1))]);
+                }
+                GateType::SWAP => {
+                    tc.tick().swap(&[(QubitId(0), QubitId(1))]);
+                }
+                other => panic!("unexpected gate type {other:?}"),
+            }
+        }
+
+        for (gate_type, expected_measurements) in [
+            (GateType::CX, &[0usize, 1][..]),
+            (GateType::CY, &[0usize, 1][..]),
+            (GateType::CZ, &[0usize][..]),
+            (GateType::SXX, &[0usize][..]),
+            (GateType::SXXdg, &[0usize][..]),
+            (GateType::SYY, &[1usize][..]),
+            (GateType::SYYdg, &[1usize][..]),
+            (GateType::SZZ, &[0usize][..]),
+            (GateType::SZZdg, &[0usize][..]),
+            (GateType::SWAP, &[1usize][..]),
+        ] {
+            let mut tc = TickCircuit::new();
+            tc.tick().h(&[QubitId(0)]);
+            apply_gate(&mut tc, gate_type);
+            tc.tick().mz(&[QubitId(0), QubitId(1)]);
+
+            let catalog = build_fault_catalog(
+                &tc,
+                &StochasticNoiseParams {
+                    p1: 0.03,
+                    p2: 0.0,
+                    p_meas: 0.0,
+                    p_prep: 0.0,
+                },
+            )
+            .unwrap();
+
+            let h_loc = catalog
+                .locations
+                .iter()
+                .find(|loc| loc.gate_type == GateType::H && loc.qubits.as_slice() == [0])
+                .unwrap();
+            let x_fault = h_loc
+                .faults
+                .iter()
+                .find(|fault| fault.pauli.as_ref() == Some(&PauliString::x(0)))
+                .unwrap();
+
+            assert_eq!(
+                x_fault.affected_measurements.as_slice(),
+                expected_measurements,
+                "{gate_type:?}"
+            );
+        }
+    }
+
+    #[test]
+    fn test_catalog_standard_cliffords_match_forward_pauli_oracle_for_all_alternatives() {
+        fn apply_single_gate(tc: &mut TickCircuit, gate_type: GateType) {
+            match gate_type {
+                GateType::X => {
+                    tc.tick().x(&[QubitId(0)]);
+                }
+                GateType::Y => {
+                    tc.tick().y(&[QubitId(0)]);
+                }
+                GateType::Z => {
+                    tc.tick().z(&[QubitId(0)]);
+                }
+                GateType::H => {
+                    tc.tick().h(&[QubitId(0)]);
+                }
+                GateType::SZ => {
+                    tc.tick().sz(&[QubitId(0)]);
+                }
+                GateType::SZdg => {
+                    tc.tick().szdg(&[QubitId(0)]);
+                }
+                GateType::SX => {
+                    tc.tick().sx(&[QubitId(0)]);
+                }
+                GateType::SXdg => {
+                    tc.tick().sxdg(&[QubitId(0)]);
+                }
+                GateType::SY => {
+                    tc.tick().sy(&[QubitId(0)]);
+                }
+                GateType::SYdg => {
+                    tc.tick().sydg(&[QubitId(0)]);
+                }
+                GateType::F => {
+                    tc.tick().f(&[QubitId(0)]);
+                }
+                GateType::Fdg => {
+                    tc.tick().fdg(&[QubitId(0)]);
+                }
+                other => panic!("unexpected single-qubit gate {other:?}"),
+            }
+        }
+
+        fn apply_pair_gate(tc: &mut TickCircuit, gate_type: GateType) {
+            match gate_type {
+                GateType::CX => {
+                    tc.tick().cx(&[(QubitId(0), QubitId(1))]);
+                }
+                GateType::CY => {
+                    tc.tick().cy(&[(QubitId(0), QubitId(1))]);
+                }
+                GateType::CZ => {
+                    tc.tick().cz(&[(QubitId(0), QubitId(1))]);
+                }
+                GateType::SXX => {
+                    tc.tick().sxx(&[(QubitId(0), QubitId(1))]);
+                }
+                GateType::SXXdg => {
+                    tc.tick().sxxdg(&[(QubitId(0), QubitId(1))]);
+                }
+                GateType::SYY => {
+                    tc.tick().syy(&[(QubitId(0), QubitId(1))]);
+                }
+                GateType::SYYdg => {
+                    tc.tick().syydg(&[(QubitId(0), QubitId(1))]);
+                }
+                GateType::SZZ => {
+                    tc.tick().szz(&[(QubitId(0), QubitId(1))]);
+                }
+                GateType::SZZdg => {
+                    tc.tick().szzdg(&[(QubitId(0), QubitId(1))]);
+                }
+                GateType::SWAP => {
+                    tc.tick().swap(&[(QubitId(0), QubitId(1))]);
+                }
+                other => panic!("unexpected two-qubit gate {other:?}"),
+            }
+        }
+
+        fn pauli_type(pauli: Pauli) -> PauliType {
+            match pauli {
+                Pauli::X => PauliType::X,
+                Pauli::Y => PauliType::Y,
+                Pauli::Z => PauliType::Z,
+                Pauli::I => panic!("identity is not a fault alternative"),
+            }
+        }
+
+        fn expected_effect(
+            pauli: &PauliString,
+            start: usize,
+            gates: &[GateLoc],
+            meas_positions: &HashMap<usize, usize>,
+            tracked_paulis: &[PauliString],
+        ) -> PropagatedFaultEffect {
+            let terms: Vec<_> = pauli
+                .iter_pairs()
+                .map(|(p, q)| (pauli_type(p), q.index()))
+                .collect();
+            match terms.as_slice() {
+                [(p, q)] => {
+                    propagate_single_effect(*p, *q, start, gates, meas_positions, tracked_paulis)
+                }
+                [(p0, q0), (p1, q1)] => propagate_pair_effect(
+                    [(*p0, *q0), (*p1, *q1)],
+                    start,
+                    gates,
+                    meas_positions,
+                    tracked_paulis,
+                ),
+                other => panic!("expected one- or two-qubit Pauli alternative, got {other:?}"),
+            }
+        }
+
+        for gate_type in STANDARD_1Q_CLIFFORD_GATES {
+            let mut tc = TickCircuit::new();
+            tc.tick().h(&[QubitId(0)]);
+            apply_single_gate(&mut tc, *gate_type);
+            tc.tick().cx(&[(QubitId(0), QubitId(1))]);
+            tc.tick().mz(&[QubitId(0)]);
+            tc.set_meta(
+                "num_measurements",
+                pecos_quantum::Attribute::String(tc.num_measurements().to_string()),
+            );
+            tc.add_detector_metadata(&[-1], None, Some("D0"), Some(0))
+                .unwrap();
+            tc.add_observable_metadata(&[-1], Some(0), Some("L0"))
+                .unwrap();
+            tc.tracked_pauli_labeled("tracked_x1", PauliString::x(1));
+            tc.tracked_pauli_labeled("tracked_y1", PauliString::y(1));
+            tc.tracked_pauli_labeled("tracked_z1", PauliString::z(1));
+
+            let (gates, meas_positions) = flatten_tick_circuit(&tc);
+            let tracked_paulis = parse_tracked_pauli_annotations(&tc);
+            let catalog = build_fault_catalog(
+                &tc,
+                &StochasticNoiseParams {
+                    p1: 0.03,
+                    p2: 0.0,
+                    p_meas: 0.0,
+                    p_prep: 0.0,
+                },
+            )
+            .unwrap();
+            let source_loc_idx = gates
+                .iter()
+                .position(|loc| loc.gate_type == GateType::H && loc.qubits.as_slice() == [0])
+                .unwrap();
+            let source_loc = catalog
+                .locations
+                .iter()
+                .find(|loc| {
+                    loc.tick == gates[source_loc_idx].tick
+                        && loc.gate_index == gates[source_loc_idx].gate_index
+                })
+                .unwrap();
+
+            for fault in &source_loc.faults {
+                let pauli = fault.pauli.as_ref().unwrap();
+                let effect = expected_effect(
+                    pauli,
+                    source_loc_idx + 1,
+                    &gates,
+                    &meas_positions,
+                    &tracked_paulis,
+                );
+                let measurements: Vec<_> = effect.affected_measurements.iter().copied().collect();
+                assert_eq!(
+                    fault.affected_measurements, measurements,
+                    "{gate_type:?} {pauli:?}"
+                );
+                assert_eq!(
+                    fault.affected_detectors, measurements,
+                    "{gate_type:?} {pauli:?}"
+                );
+                assert_eq!(
+                    fault.affected_observables, measurements,
+                    "{gate_type:?} {pauli:?}"
+                );
+                assert_eq!(
+                    fault.affected_tracked_paulis, effect.affected_tracked_paulis,
+                    "{gate_type:?} {pauli:?}"
+                );
+            }
+        }
+
+        for gate_type in STANDARD_2Q_CLIFFORD_GATES {
+            let mut tc = TickCircuit::new();
+            tc.tick().cx(&[(QubitId(0), QubitId(1))]);
+            apply_pair_gate(&mut tc, *gate_type);
+            tc.tick()
+                .cx(&[(QubitId(0), QubitId(2)), (QubitId(1), QubitId(3))]);
+            tc.tick().mz(&[QubitId(0), QubitId(1)]);
+            tc.set_meta(
+                "num_measurements",
+                pecos_quantum::Attribute::String(tc.num_measurements().to_string()),
+            );
+            tc.add_detector_metadata(&[-2], None, Some("D0"), Some(0))
+                .unwrap();
+            tc.add_detector_metadata(&[-1], None, Some("D1"), Some(1))
+                .unwrap();
+            tc.add_observable_metadata(&[-2], Some(0), Some("L0"))
+                .unwrap();
+            tc.add_observable_metadata(&[-1], Some(1), Some("L1"))
+                .unwrap();
+            tc.tracked_pauli_labeled("tracked_x2", PauliString::x(2));
+            tc.tracked_pauli_labeled("tracked_y2", PauliString::y(2));
+            tc.tracked_pauli_labeled("tracked_z2", PauliString::z(2));
+            tc.tracked_pauli_labeled("tracked_x3", PauliString::x(3));
+            tc.tracked_pauli_labeled("tracked_y3", PauliString::y(3));
+            tc.tracked_pauli_labeled("tracked_z3", PauliString::z(3));
+
+            let (gates, meas_positions) = flatten_tick_circuit(&tc);
+            let tracked_paulis = parse_tracked_pauli_annotations(&tc);
+            let catalog = build_fault_catalog(
+                &tc,
+                &StochasticNoiseParams {
+                    p1: 0.0,
+                    p2: 0.03,
+                    p_meas: 0.0,
+                    p_prep: 0.0,
+                },
+            )
+            .unwrap();
+            let source_loc_idx = gates
+                .iter()
+                .position(|loc| loc.gate_type == GateType::CX && loc.qubits.as_slice() == [0, 1])
+                .unwrap();
+            let source_loc = catalog
+                .locations
+                .iter()
+                .find(|loc| {
+                    loc.tick == gates[source_loc_idx].tick
+                        && loc.gate_index == gates[source_loc_idx].gate_index
+                })
+                .unwrap();
+
+            for fault in &source_loc.faults {
+                let pauli = fault.pauli.as_ref().unwrap();
+                let effect = expected_effect(
+                    pauli,
+                    source_loc_idx + 1,
+                    &gates,
+                    &meas_positions,
+                    &tracked_paulis,
+                );
+                let measurements: Vec<_> = effect.affected_measurements.iter().copied().collect();
+                assert_eq!(
+                    fault.affected_measurements, measurements,
+                    "{gate_type:?} {pauli:?}"
+                );
+                assert_eq!(
+                    fault.affected_detectors, measurements,
+                    "{gate_type:?} {pauli:?}"
+                );
+                assert_eq!(
+                    fault.affected_observables, measurements,
+                    "{gate_type:?} {pauli:?}"
+                );
+                assert_eq!(
+                    fault.affected_tracked_paulis, effect.affected_tracked_paulis,
+                    "{gate_type:?} {pauli:?}"
+                );
+            }
+        }
+    }
+
+    #[test]
+    fn test_fault_configurations_xor_detectors_observables_and_tracked_paulis_separately() {
+        let mut tc = TickCircuit::new();
+        tc.tick().h(&[QubitId(0), QubitId(1)]);
+        tc.tick().cx(&[(QubitId(0), QubitId(2))]);
+        tc.tick().mz(&[QubitId(0), QubitId(1)]);
+        tc.set_meta(
+            "num_measurements",
+            pecos_quantum::Attribute::String(tc.num_measurements().to_string()),
+        );
+        tc.add_detector_metadata(&[-2, -1], None, Some("D0"), Some(0))
+            .unwrap();
+        tc.add_observable_metadata(&[-2], Some(0), Some("L0"))
+            .unwrap();
+        tc.tracked_pauli_labeled("tracked_z2", PauliString::z(2));
+
+        let catalog = build_fault_catalog(
+            &tc,
+            &StochasticNoiseParams {
+                p1: 1.0,
+                p2: 0.0,
+                p_meas: 0.0,
+                p_prep: 0.0,
+            },
+        )
+        .unwrap();
+        let h0 = catalog
+            .locations
+            .iter()
+            .position(|loc| loc.gate_type == GateType::H && loc.qubits.as_slice() == [0])
+            .unwrap();
+        let h1 = catalog
+            .locations
+            .iter()
+            .position(|loc| loc.gate_type == GateType::H && loc.qubits.as_slice() == [1])
+            .unwrap();
+        let x0 = catalog.locations[h0]
+            .faults
+            .iter()
+            .position(|fault| fault.pauli.as_ref() == Some(&PauliString::x(0)))
+            .unwrap();
+        let x1 = catalog.locations[h1]
+            .faults
+            .iter()
+            .position(|fault| fault.pauli.as_ref() == Some(&PauliString::x(1)))
+            .unwrap();
+
+        let config = catalog
+            .fault_configurations(2)
+            .find(|config| {
+                config.location_indices == [h0, h1] && config.alternative_indices == [x0, x1]
+            })
+            .unwrap();
+
+        assert_eq!(catalog.locations[h0].faults[x0].affected_detectors, [0]);
+        assert_eq!(catalog.locations[h0].faults[x0].affected_observables, [0]);
+        assert_eq!(
+            catalog.locations[h0].faults[x0].affected_tracked_paulis,
+            [0]
+        );
+        assert_eq!(catalog.locations[h1].faults[x1].affected_detectors, [0]);
+        assert!(
+            catalog.locations[h1].faults[x1]
+                .affected_observables
+                .is_empty()
+        );
+        assert!(
+            catalog.locations[h1].faults[x1]
+                .affected_tracked_paulis
+                .is_empty()
+        );
+
+        assert_eq!(config.affected_measurements, [0, 1]);
+        assert!(config.affected_detectors.is_empty());
+        assert_eq!(config.affected_observables, [0]);
+        assert_eq!(config.affected_tracked_paulis, [0]);
+    }
+
+    #[test]
+    fn test_tracked_pauli_phase_is_ignored_for_flip_tracking() {
+        let mut tc = TickCircuit::new();
+        tc.tick().h(&[QubitId(0)]);
+        tc.tracked_pauli_labeled("plus_z0", PauliString::z(0));
+        tc.tracked_pauli_labeled(
+            "minus_z0",
+            PauliString::with_phase_and_paulis(
+                pecos_core::QuarterPhase::MinusOne,
+                vec![(Pauli::Z, QubitId(0))],
+            ),
+        );
+
+        let tracked_paulis = parse_tracked_pauli_annotations(&tc);
+        assert_eq!(tracked_paulis.len(), 2);
+        assert!(
+            tracked_paulis
+                .iter()
+                .all(|op| op.phase() == pecos_core::QuarterPhase::PlusOne)
+        );
+        assert_eq!(tracked_paulis[0], tracked_paulis[1]);
+
+        let catalog = build_fault_catalog(
+            &tc,
+            &StochasticNoiseParams {
+                p1: 0.03,
+                p2: 0.0,
+                p_meas: 0.0,
+                p_prep: 0.0,
+            },
+        )
+        .unwrap();
+
+        let h_loc = catalog
+            .locations
+            .iter()
+            .find(|loc| loc.gate_type == GateType::H)
+            .unwrap();
+        let x_fault = h_loc
+            .faults
+            .iter()
+            .find(|fault| fault.pauli.as_ref() == Some(&PauliString::x(0)))
+            .unwrap();
+        let z_fault = h_loc
+            .faults
+            .iter()
+            .find(|fault| fault.pauli.as_ref() == Some(&PauliString::z(0)))
+            .unwrap();
+
+        assert_eq!(x_fault.affected_tracked_paulis, vec![0, 1]);
+        assert_eq!(z_fault.affected_tracked_paulis, Vec::<usize>::new());
+    }
+
+    #[test]
+    fn test_structural_catalog_includes_zero_probability_locations() {
+        let mut tc = TickCircuit::new();
+        tc.tick().h(&[QubitId(0)]);
+        tc.tick().mz(&[QubitId(0)]);
+        tc.set_meta(
+            "num_measurements",
+            pecos_quantum::Attribute::String("1".to_string()),
+        );
+        tc.set_meta(
+            "detectors",
+            pecos_quantum::Attribute::String("[]".to_string()),
+        );
+        tc.set_meta(
+            "observables",
+            pecos_quantum::Attribute::String("[]".to_string()),
+        );
+
+        let catalog = FaultCatalog::from_circuit(&tc).unwrap();
+        assert_eq!(catalog.locations.len(), 2);
+        assert!(
+            catalog
+                .locations
+                .iter()
+                .all(|loc| loc.channel_probability.abs() < 1e-12)
+        );
+        assert!(
+            catalog
+                .locations
+                .iter()
+                .all(|loc| (loc.no_fault_probability - 1.0).abs() < 1e-12)
+        );
+        assert!(
+            catalog
+                .locations
+                .iter()
+                .flat_map(|loc| &loc.faults)
+                .all(|fault| fault.absolute_probability.abs() < 1e-12)
+        );
+        assert!(
+            catalog
+                .locations
+                .iter()
+                .any(|loc| loc.channel == FaultChannel::P1)
+        );
+        assert!(
+            catalog
+                .locations
+                .iter()
+                .any(|loc| loc.channel == FaultChannel::PMeas)
+        );
+    }
+
+    #[test]
+    fn test_parameterized_matches_direct_for_fully_nonzero_noise() {
+        let mut tc = TickCircuit::new();
+        tc.tick().pz(&[QubitId(0)]);
+        tc.tick().h(&[QubitId(0)]);
+        tc.tick().mz(&[QubitId(0)]);
+        tc.set_meta(
+            "num_measurements",
+            pecos_quantum::Attribute::String("1".to_string()),
+        );
+        tc.set_meta(
+            "detectors",
+            pecos_quantum::Attribute::String(r#"[{"records":[-1]}]"#.to_string()),
+        );
+        tc.set_meta(
+            "observables",
+            pecos_quantum::Attribute::String(r#"[{"records":[-1]}]"#.to_string()),
+        );
+
+        let noise = StochasticNoiseParams {
+            p1: 0.03,
+            p2: 0.02,
+            p_meas: 0.01,
+            p_prep: 0.004,
+        };
+        let direct = build_fault_catalog(&tc, &noise).unwrap();
+        let mut split = FaultCatalog::from_circuit(&tc).unwrap();
+        split.with_noise(&noise);
+
+        assert_eq!(direct.locations.len(), split.locations.len());
+        for (a, b) in direct.locations.iter().zip(&split.locations) {
+            assert_eq!(a.tick, b.tick);
+            assert_eq!(a.gate_index, b.gate_index);
+            assert_eq!(a.gate_type, b.gate_type);
+            assert_eq!(a.qubits, b.qubits);
+            assert_eq!(a.channel, b.channel);
+            assert_close(a.channel_probability, b.channel_probability);
+            assert_close(a.no_fault_probability, b.no_fault_probability);
+            assert_eq!(a.num_alternatives, b.num_alternatives);
+            assert_eq!(a.faults.len(), b.faults.len());
+            for (af, bf) in a.faults.iter().zip(&b.faults) {
+                assert_eq!(af.kind, bf.kind);
+                assert_eq!(af.pauli, bf.pauli);
+                assert_eq!(af.affected_measurements, bf.affected_measurements);
+                assert_eq!(af.affected_detectors, bf.affected_detectors);
+                assert_eq!(af.affected_observables, bf.affected_observables);
+                assert_eq!(af.affected_tracked_paulis, bf.affected_tracked_paulis);
+                assert_close(af.conditional_probability, bf.conditional_probability);
+                assert_close(af.absolute_probability, bf.absolute_probability);
+            }
+        }
+    }
+
+    #[test]
+    fn test_with_noise_overwrites_previous_probabilities() {
+        let mut tc = TickCircuit::new();
+        tc.tick().h(&[QubitId(0)]);
+        tc.tick().mz(&[QubitId(0)]);
+        tc.set_meta(
+            "num_measurements",
+            pecos_quantum::Attribute::String("1".to_string()),
+        );
+
+        let mut catalog = FaultCatalog::from_circuit(&tc).unwrap();
+        catalog.with_noise(&StochasticNoiseParams {
+            p1: 0.03,
+            p2: 0.0,
+            p_meas: 0.01,
+            p_prep: 0.0,
+        });
+        catalog.with_noise(&StochasticNoiseParams {
+            p1: 0.09,
+            p2: 0.0,
+            p_meas: 0.02,
+            p_prep: 0.0,
+        });
+
+        let h_loc = catalog
+            .locations
+            .iter()
+            .find(|loc| loc.channel == FaultChannel::P1)
+            .unwrap();
+        assert_close(h_loc.channel_probability, 0.09);
+        assert_close(h_loc.no_fault_probability, 0.91);
+        assert!(
+            h_loc
+                .faults
+                .iter()
+                .all(|fault| (fault.absolute_probability - 0.03).abs() < 1e-12)
+        );
+
+        let meas_loc = catalog
+            .locations
+            .iter()
+            .find(|loc| loc.channel == FaultChannel::PMeas)
+            .unwrap();
+        assert_close(meas_loc.channel_probability, 0.02);
+        assert_close(meas_loc.faults[0].absolute_probability, 0.02);
+    }
+
+    #[test]
+    fn test_sparse_channel_keeps_structure_but_filters_raw_mechanisms() {
+        let mut tc = TickCircuit::new();
+        tc.tick().h(&[QubitId(0)]);
+        tc.tick().mz(&[QubitId(0)]);
+        tc.set_meta(
+            "num_measurements",
+            pecos_quantum::Attribute::String("1".to_string()),
+        );
+
+        let noise = StochasticNoiseParams {
+            p1: 0.0,
+            p2: 0.0,
+            p_meas: 0.02,
+            p_prep: 0.0,
+        };
+        let catalog = build_fault_catalog(&tc, &noise).unwrap();
+        assert_eq!(catalog.locations.len(), 2);
+        assert!(
+            catalog
+                .locations
+                .iter()
+                .any(|loc| loc.channel == FaultChannel::P1 && loc.channel_probability.abs() < 1e-12)
+        );
+
+        let mechanisms = catalog.to_mechanisms();
+        assert_eq!(mechanisms.len(), 1);
+        assert_close(mechanisms[0].probability, 0.02);
+        assert_eq!(mechanisms[0].alternatives, vec![vec![0]]);
+        assert_eq!(mechanisms, build_fault_table(&tc, &noise).unwrap());
+    }
+
+    #[test]
+    fn test_fault_configurations_skip_zero_probability_fault_events() {
+        let mut tc = TickCircuit::new();
+        tc.tick().h(&[QubitId(0)]);
+        tc.tick().mz(&[QubitId(0)]);
+        tc.set_meta(
+            "num_measurements",
+            pecos_quantum::Attribute::String("1".to_string()),
+        );
+
+        let catalog = FaultCatalog::from_circuit(&tc).unwrap();
+        assert_eq!(catalog.fault_configurations(0).count(), 1);
+        assert_eq!(
+            catalog.fault_configurations(1).count(),
+            0,
+            "unparameterized structural catalogs should not yield zero-probability selected faults"
+        );
+
+        let mut parameterized = catalog.clone();
+        parameterized.with_noise(&StochasticNoiseParams {
+            p1: 0.0,
+            p2: 0.0,
+            p_meas: 0.02,
+            p_prep: 0.0,
+        });
+        assert_eq!(
+            parameterized.fault_configurations(1).count(),
+            1,
+            "only the nonzero measurement fault location should be yielded"
+        );
+        assert_eq!(
+            parameterized
+                .fault_configurations(1)
+                .next()
+                .unwrap()
+                .location_indices,
+            vec![1]
+        );
+    }
+
+    #[test]
+    fn test_tracked_only_effect_stays_in_catalog_but_not_raw_mechanisms() {
+        let mut tc = TickCircuit::new();
+        tc.tick().h(&[QubitId(0)]);
+        tc.tracked_pauli_labeled("tracked_z0", PauliString::z(0));
+
+        let mut catalog = FaultCatalog::from_circuit(&tc).unwrap();
+        catalog.with_noise(&StochasticNoiseParams {
+            p1: 0.03,
+            p2: 0.0,
+            p_meas: 0.0,
+            p_prep: 0.0,
+        });
+
+        let h_loc = catalog
+            .locations
+            .iter()
+            .find(|loc| loc.channel == FaultChannel::P1)
+            .unwrap();
+        assert!(h_loc.faults.iter().any(|fault| {
+            fault.affected_measurements.is_empty() && !fault.affected_tracked_paulis.is_empty()
+        }));
+        assert!(catalog.to_mechanisms().is_empty());
+    }
+
+    #[test]
+    fn test_to_mechanisms_matches_old_build_fault_table() {
+        // The key invariant: catalog.to_mechanisms() must produce the same
+        // mechanisms as the old build_fault_table path for nonzero noise.
+        let mut tc = TickCircuit::new();
+        tc.tick().pz(&[QubitId(0), QubitId(1)]);
+        tc.tick().h(&[QubitId(0)]);
+        tc.tick().cx(&[(QubitId(0), QubitId(1))]);
+        tc.tick().mz(&[QubitId(0), QubitId(1)]);
+        tc.set_meta(
+            "num_measurements",
+            pecos_quantum::Attribute::String("2".to_string()),
+        );
+        tc.set_meta(
+            "detectors",
+            pecos_quantum::Attribute::String("[]".to_string()),
+        );
+        tc.set_meta(
+            "observables",
+            pecos_quantum::Attribute::String("[]".to_string()),
+        );
+
+        let noise = StochasticNoiseParams {
+            p1: 0.01,
+            p2: 0.05,
+            p_meas: 0.02,
+            p_prep: 0.01,
+        };
+
+        // Old path (now a wrapper, but the output must match):
+        let old_mechanisms = build_fault_table(&tc, &noise).unwrap();
+
+        // New path:
+        let mut catalog = FaultCatalog::from_circuit(&tc).unwrap();
+        catalog.with_noise(&noise);
+        let new_mechanisms = catalog.to_mechanisms();
+
+        assert_eq!(
+            old_mechanisms.len(),
+            new_mechanisms.len(),
+            "mechanism count must match"
+        );
+        for (old, new) in old_mechanisms.iter().zip(&new_mechanisms) {
+            assert_close(old.probability, new.probability);
+            assert_eq!(
+                old.alternatives.len(),
+                new.alternatives.len(),
+                "alternative count must match"
+            );
+            for (old_alt, new_alt) in old.alternatives.iter().zip(&new.alternatives) {
+                assert_eq!(old_alt, new_alt, "measurement effects must match");
+            }
+        }
+    }
+
+    #[test]
+    fn test_catalog_meas_prep_probabilities() {
+        // PZ(0) MZ(0): prep X fault goes directly to MZ (flips it)
+        let mut tc = TickCircuit::new();
+        tc.tick().pz(&[QubitId(0)]);
+        tc.tick().mz(&[QubitId(0)]);
+        tc.set_meta(
+            "num_measurements",
+            pecos_quantum::Attribute::String("1".to_string()),
+        );
+        tc.set_meta(
+            "detectors",
+            pecos_quantum::Attribute::String("[]".to_string()),
+        );
+        tc.set_meta(
+            "observables",
+            pecos_quantum::Attribute::String("[]".to_string()),
+        );
+
+        let noise = StochasticNoiseParams {
+            p1: 0.0,
+            p2: 0.0,
+            p_meas: 0.007,
+            p_prep: 0.003,
+        };
+        let catalog = build_fault_catalog(&tc, &noise).unwrap();
+
+        let prep = catalog
+            .locations
+            .iter()
+            .find(|l| l.faults.iter().any(|f| f.kind == FaultKind::PrepFlip));
+        assert!(prep.is_some(), "Should have a prep fault location");
+        let prep = prep.unwrap();
+        assert!((prep.channel_probability - 0.003).abs() < 1e-10);
+        assert!(prep.faults[0].pauli.is_none());
+
+        let meas = catalog.locations.iter().find(|l| {
+            l.faults
+                .iter()
+                .any(|f| f.kind == FaultKind::MeasurementFlip)
+        });
+        assert!(meas.is_some(), "Should have a measurement fault location");
+        let meas = meas.unwrap();
+        assert!((meas.channel_probability - 0.007).abs() < 1e-10);
+        assert!(meas.faults[0].pauli.is_none());
+    }
+
+    #[test]
+    fn test_catalog_separate_locations_same_detector_effect() {
+        // Two H gates on same qubit → two separate locations
+        let mut tc = TickCircuit::new();
+        tc.tick().h(&[QubitId(0)]);
+        tc.tick().h(&[QubitId(0)]);
+        tc.tick().mz(&[QubitId(0)]);
+        tc.set_meta(
+            "num_measurements",
+            pecos_quantum::Attribute::String("1".to_string()),
+        );
+        tc.set_meta(
+            "detectors",
+            pecos_quantum::Attribute::String(r#"[{"records": [-1]}]"#.to_string()),
+        );
+        tc.set_meta(
+            "observables",
+            pecos_quantum::Attribute::String("[]".to_string()),
+        );
+
+        let noise = StochasticNoiseParams {
+            p1: 0.01,
+            p2: 0.0,
+            p_meas: 0.0,
+            p_prep: 0.0,
+        };
+        let catalog = build_fault_catalog(&tc, &noise).unwrap();
+
+        // Both H gates → separate locations even if they have the same detector effect
+        let h_locs: Vec<_> = catalog
+            .locations
+            .iter()
+            .filter(|l| l.gate_type == GateType::H)
+            .collect();
+        assert_eq!(
+            h_locs.len(),
+            2,
+            "Two H gates should produce two separate locations"
+        );
+    }
+
+    #[test]
+    fn test_catalog_full_configuration_probability() {
+        // H(0) MZ(0) with p1=0.03, p_meas=0.01.
+        // Two locations: H (3 alts) and MZ (1 alt).
+        // Pick alt 0 at H, no fault at MZ:
+        //   P = (0.03/3) * (1 - 0.01) = 0.01 * 0.99 = 0.0099
+        let mut tc = TickCircuit::new();
+        tc.tick().h(&[QubitId(0)]);
+        tc.tick().mz(&[QubitId(0)]);
+        tc.set_meta(
+            "num_measurements",
+            pecos_quantum::Attribute::String("1".to_string()),
+        );
+        tc.set_meta(
+            "detectors",
+            pecos_quantum::Attribute::String("[]".to_string()),
+        );
+        tc.set_meta(
+            "observables",
+            pecos_quantum::Attribute::String("[]".to_string()),
+        );
+
+        let noise = StochasticNoiseParams {
+            p1: 0.03,
+            p2: 0.0,
+            p_meas: 0.01,
+            p_prep: 0.0,
+        };
+        let catalog = build_fault_catalog(&tc, &noise).unwrap();
+        assert_eq!(catalog.locations.len(), 2); // H + MZ
+
+        let h_loc = &catalog.locations[0]; // H
+        let mz_loc = &catalog.locations[1]; // MZ
+
+        // Pick first H alternative, no fault at MZ
+        let alt_prob = h_loc.faults[0].absolute_probability; // 0.03/3 = 0.01
+        let no_mz_prob = mz_loc.no_fault_probability; // 1 - 0.01 = 0.99
+        let config_prob = alt_prob * no_mz_prob;
+
+        assert!((config_prob - 0.0099).abs() < 1e-10);
+    }
+
+    // ---- fault_configurations iterator tests ----
+
+    #[test]
+    fn test_configurations_k0_one_no_fault_event() {
+        let mut tc = TickCircuit::new();
+        tc.tick().h(&[QubitId(0)]);
+        tc.tick().mz(&[QubitId(0)]);
+        tc.set_meta(
+            "num_measurements",
+            pecos_quantum::Attribute::String("1".into()),
+        );
+        tc.set_meta("detectors", pecos_quantum::Attribute::String("[]".into()));
+        tc.set_meta("observables", pecos_quantum::Attribute::String("[]".into()));
+
+        let noise = StochasticNoiseParams {
+            p1: 0.03,
+            p2: 0.0,
+            p_meas: 0.01,
+            p_prep: 0.0,
+        };
+        let catalog = build_fault_catalog(&tc, &noise).unwrap();
+
+        let configs: Vec<_> = catalog.fault_configurations(0).collect();
+        assert_eq!(configs.len(), 1);
+        let c = &configs[0];
+        assert!(c.location_indices.is_empty());
+        assert!(c.alternative_indices.is_empty());
+        assert!(c.affected_measurements.is_empty());
+        assert!(c.affected_detectors.is_empty());
+        assert_close(c.selected_probability, 1.0);
+        // config_prob = product of all no_fault_probability
+        let expected: f64 = catalog
+            .locations
+            .iter()
+            .map(|l| l.no_fault_probability)
+            .product();
+        assert!((c.configuration_probability - expected).abs() < 1e-12);
+    }
+
+    #[test]
+    fn test_configurations_k1_matches_single_fault() {
+        let mut tc = TickCircuit::new();
+        tc.tick().h(&[QubitId(0)]);
+        tc.tick().mz(&[QubitId(0)]);
+        tc.set_meta(
+            "num_measurements",
+            pecos_quantum::Attribute::String("1".into()),
+        );
+        tc.set_meta("detectors", pecos_quantum::Attribute::String("[]".into()));
+        tc.set_meta("observables", pecos_quantum::Attribute::String("[]".into()));
+
+        let noise = StochasticNoiseParams {
+            p1: 0.03,
+            p2: 0.0,
+            p_meas: 0.01,
+            p_prep: 0.0,
+        };
+        let catalog = build_fault_catalog(&tc, &noise).unwrap();
+
+        let configs: Vec<_> = catalog.fault_configurations(1).collect();
+        // Total k=1 configs = sum of num_alternatives across all locations
+        let expected_count: usize = catalog.locations.iter().map(|l| l.num_alternatives).sum();
+        assert_eq!(configs.len(), expected_count);
+
+        // First config should match first location, first alternative
+        let c = &configs[0];
+        assert_eq!(c.location_indices, vec![0]);
+        assert_eq!(c.alternative_indices, vec![0]);
+        let alt = &catalog.locations[0].faults[0];
+        assert_eq!(c.affected_measurements, alt.affected_measurements);
+        assert!((c.selected_probability - alt.absolute_probability).abs() < 1e-12);
+    }
+
+    #[test]
+    fn test_configurations_skip_zero_probability_structural_locations() {
+        let mut tc = TickCircuit::new();
+        tc.tick().h(&[QubitId(0)]);
+        tc.tick().mz(&[QubitId(0)]);
+        tc.set_meta(
+            "num_measurements",
+            pecos_quantum::Attribute::String("1".into()),
+        );
+        tc.set_meta("detectors", pecos_quantum::Attribute::String("[]".into()));
+        tc.set_meta("observables", pecos_quantum::Attribute::String("[]".into()));
+
+        let noise = StochasticNoiseParams {
+            p1: 0.03,
+            p2: 0.0,
+            p_meas: 0.0,
+            p_prep: 0.0,
+        };
+        let catalog = build_fault_catalog(&tc, &noise).unwrap();
+        assert_eq!(catalog.locations.len(), 2);
+
+        let h_idx = catalog
+            .locations
+            .iter()
+            .position(|loc| loc.gate_type == GateType::H)
+            .unwrap();
+        let mz_idx = catalog
+            .locations
+            .iter()
+            .position(|loc| loc.gate_type == GateType::MZ)
+            .unwrap();
+        assert_close(catalog.locations[mz_idx].channel_probability, 0.0);
+
+        let configs: Vec<_> = catalog.fault_configurations(1).collect();
+        assert_eq!(configs.len(), 3);
+        assert!(configs.iter().all(|c| c.location_indices == vec![h_idx]));
+        assert!(configs.iter().all(|c| c.selected_probability > 0.0));
+        assert!(
+            configs
+                .iter()
+                .all(|c| !c.location_indices.contains(&mz_idx))
+        );
+        assert_eq!(catalog.fault_configurations(2).count(), 0);
+    }
+
+    #[test]
+    fn test_configurations_all_zero_noise_only_yields_k0() {
+        let mut tc = TickCircuit::new();
+        tc.tick().h(&[QubitId(0)]);
+        tc.tick().mz(&[QubitId(0)]);
+        tc.set_meta(
+            "num_measurements",
+            pecos_quantum::Attribute::String("1".into()),
+        );
+        tc.set_meta("detectors", pecos_quantum::Attribute::String("[]".into()));
+        tc.set_meta("observables", pecos_quantum::Attribute::String("[]".into()));
+
+        let catalog = build_fault_catalog(
+            &tc,
+            &StochasticNoiseParams {
+                p1: 0.0,
+                p2: 0.0,
+                p_meas: 0.0,
+                p_prep: 0.0,
+            },
+        )
+        .unwrap();
+
+        let k0: Vec<_> = catalog.fault_configurations(0).collect();
+        assert_eq!(k0.len(), 1);
+        assert_close(k0[0].configuration_probability, 1.0);
+        assert_eq!(catalog.fault_configurations(1).count(), 0);
+        assert_eq!(catalog.fault_configurations(2).count(), 0);
+    }
+
+    #[test]
+    fn test_configurations_include_nonzero_silent_faults() {
+        let mut tc = TickCircuit::new();
+        tc.tick().h(&[QubitId(0)]);
+        tc.set_meta(
+            "num_measurements",
+            pecos_quantum::Attribute::String("0".into()),
+        );
+        tc.set_meta("detectors", pecos_quantum::Attribute::String("[]".into()));
+        tc.set_meta("observables", pecos_quantum::Attribute::String("[]".into()));
+
+        let catalog = build_fault_catalog(
+            &tc,
+            &StochasticNoiseParams {
+                p1: 0.03,
+                p2: 0.0,
+                p_meas: 0.0,
+                p_prep: 0.0,
+            },
+        )
+        .unwrap();
+
+        let configs: Vec<_> = catalog.fault_configurations(1).collect();
+        assert_eq!(configs.len(), 3);
+        assert!(configs.iter().all(|c| c.affected_measurements.is_empty()));
+        assert!(configs.iter().all(|c| c.affected_detectors.is_empty()));
+        assert!(configs.iter().all(|c| c.affected_observables.is_empty()));
+        assert!(configs.iter().all(|c| c.selected_probability > 0.0));
+    }
+
+    #[test]
+    fn test_configurations_with_noise_zeroes_previous_channel() {
+        let mut tc = TickCircuit::new();
+        tc.tick().h(&[QubitId(0)]);
+        tc.tick().mz(&[QubitId(0)]);
+        tc.set_meta(
+            "num_measurements",
+            pecos_quantum::Attribute::String("1".into()),
+        );
+        tc.set_meta("detectors", pecos_quantum::Attribute::String("[]".into()));
+        tc.set_meta("observables", pecos_quantum::Attribute::String("[]".into()));
+
+        let mut catalog = FaultCatalog::from_circuit(&tc).unwrap();
+        catalog.with_noise(&StochasticNoiseParams {
+            p1: 0.03,
+            p2: 0.0,
+            p_meas: 0.01,
+            p_prep: 0.0,
+        });
+        catalog.with_noise(&StochasticNoiseParams {
+            p1: 0.0,
+            p2: 0.0,
+            p_meas: 0.02,
+            p_prep: 0.0,
+        });
+
+        let mz_idx = catalog
+            .locations
+            .iter()
+            .position(|loc| loc.gate_type == GateType::MZ)
+            .unwrap();
+        let configs: Vec<_> = catalog.fault_configurations(1).collect();
+        assert_eq!(configs.len(), 1);
+        assert_eq!(configs[0].location_indices, vec![mz_idx]);
+        assert_close(configs[0].selected_probability, 0.02);
+    }
+
+    #[test]
+    fn test_configurations_k2_xor_cancels_duplicate_effects() {
+        // Two H gates both flipping measurement 0 → XOR cancels
+        let mut tc = TickCircuit::new();
+        tc.tick().h(&[QubitId(0)]);
+        tc.tick().h(&[QubitId(0)]);
+        tc.tick().mz(&[QubitId(0)]);
+        tc.set_meta(
+            "num_measurements",
+            pecos_quantum::Attribute::String("1".into()),
+        );
+        tc.set_meta(
+            "detectors",
+            pecos_quantum::Attribute::String(r#"[{"records":[-1]}]"#.into()),
+        );
+        tc.set_meta("observables", pecos_quantum::Attribute::String("[]".into()));
+
+        let noise = StochasticNoiseParams {
+            p1: 0.03,
+            p2: 0.0,
+            p_meas: 0.0,
+            p_prep: 0.0,
+        };
+        let catalog = build_fault_catalog(&tc, &noise).unwrap();
+        assert_eq!(catalog.locations.len(), 3); // two H locations + structural MZ location
+
+        // Find a k=2 config where both locations fire with Z alternative (flips MZ)
+        // Z after first H → X at second H → X at MZ → flips meas 0
+        // Z after second H → Z at MZ → doesn't flip
+        // So to get XOR cancel: need two alternatives that BOTH flip meas 0
+        let configs: Vec<_> = catalog.fault_configurations(2).collect();
+        // Check that some configs have empty affected_measurements (XOR cancel)
+        let cancelled: Vec<_> = configs
+            .iter()
+            .filter(|c| c.affected_measurements.is_empty())
+            .collect();
+        assert!(!cancelled.is_empty(), "Some k=2 configs should XOR-cancel");
+    }
+
+    #[test]
+    fn test_configurations_k2_probability_hand_calc() {
+        let mut tc = TickCircuit::new();
+        tc.tick().h(&[QubitId(0)]);
+        tc.tick().mz(&[QubitId(0)]);
+        tc.set_meta(
+            "num_measurements",
+            pecos_quantum::Attribute::String("1".into()),
+        );
+        tc.set_meta("detectors", pecos_quantum::Attribute::String("[]".into()));
+        tc.set_meta("observables", pecos_quantum::Attribute::String("[]".into()));
+
+        let noise = StochasticNoiseParams {
+            p1: 0.03,
+            p2: 0.0,
+            p_meas: 0.01,
+            p_prep: 0.0,
+        };
+        let catalog = build_fault_catalog(&tc, &noise).unwrap();
+        // 2 locations: H (3 alts, p=0.03) and MZ (1 alt, p=0.01)
+
+        let configs: Vec<_> = catalog.fault_configurations(2).collect();
+        // k=2 means both locations fire
+        // selected_probability = (0.03/3) * (0.01/1) = 0.01 * 0.01 = 0.0001
+        // configuration_probability = selected * (no unselected) = 0.0001
+        assert_eq!(configs.len(), 3); // 3 alternatives at H × 1 at MZ
+        for c in &configs {
+            assert!((c.selected_probability - 0.0001).abs() < 1e-12);
+            assert!((c.configuration_probability - 0.0001).abs() < 1e-12);
+        }
+    }
+
+    #[test]
+    fn test_configurations_all_fault_weights_sum_to_one() {
+        let mut tc = TickCircuit::new();
+        tc.tick().pz(&[QubitId(0)]);
+        tc.tick().h(&[QubitId(0)]);
+        tc.tick().cx(&[(QubitId(0), QubitId(1))]);
+        tc.tick().mz(&[QubitId(0)]);
+        tc.tick().mz(&[QubitId(1)]);
+        tc.set_meta(
+            "num_measurements",
+            pecos_quantum::Attribute::String("2".into()),
+        );
+        tc.set_meta("detectors", pecos_quantum::Attribute::String("[]".into()));
+        tc.set_meta("observables", pecos_quantum::Attribute::String("[]".into()));
+
+        let noise = StochasticNoiseParams {
+            p1: 0.01,
+            p2: 0.05,
+            p_meas: 0.02,
+            p_prep: 0.01,
+        };
+        let catalog = build_fault_catalog(&tc, &noise).unwrap();
+
+        let total: f64 = (0..=catalog.locations.len())
+            .flat_map(|k| catalog.fault_configurations(k))
+            .map(|c| c.configuration_probability)
+            .sum();
+
+        assert!(
+            (total - 1.0).abs() < 1e-12,
+            "all truncated-by-k configurations across k=0..N should sum to 1, got {total}"
+        );
+    }
+
+    #[test]
+    fn test_configurations_iterator_is_lazy() {
+        let mut tc = TickCircuit::new();
+        tc.tick().h(&[QubitId(0)]);
+        tc.tick().mz(&[QubitId(0)]);
+        tc.set_meta(
+            "num_measurements",
+            pecos_quantum::Attribute::String("1".into()),
+        );
+        tc.set_meta("detectors", pecos_quantum::Attribute::String("[]".into()));
+        tc.set_meta("observables", pecos_quantum::Attribute::String("[]".into()));
+
+        let noise = StochasticNoiseParams {
+            p1: 0.03,
+            p2: 0.0,
+            p_meas: 0.01,
+            p_prep: 0.0,
+        };
+        let catalog = build_fault_catalog(&tc, &noise).unwrap();
+
+        // Take only first 2 items from k=1 iterator (doesn't allocate all)
+        let first_two: Vec<_> = catalog.fault_configurations(1).take(2).collect();
+        assert_eq!(first_two.len(), 2);
+    }
+
+    // ---- RawMeasurementPlan tests ----
+
+    #[test]
+    fn test_plan_bell_r_source_shared_by_copy() {
+        // Bell: H(0) CX(0,1) MZ(0) MZ(1)
+        // m0 = Random, m1 = Copy(m0). Both share the same r-source.
+        // With zero noise, m0 == m1 for all shots.
+        use pecos_simulators::SymbolicSparseStab;
+
+        let mut sim = SymbolicSparseStab::new(2);
+        sim.h(&[0]).cx(&[(0, 1)]);
+        sim.mz(&[0]);
+        sim.mz(&[1]);
+
+        let plan = RawMeasurementPlan::new(sim.measurement_history(), vec![]);
+        let result = plan.sample(1000, 42);
+
+        for shot in 0..1000 {
+            let m0 = result.get(shot, 0).0;
+            let m1 = result.get(shot, 1).0;
+            assert_eq!(m0, m1, "Bell pair: m0 must equal m1 (shot {shot})");
+        }
+    }
+
+    #[test]
+    fn test_plan_physical_fault_does_not_inherit_copy() {
+        // Bell: m0 = Random, m1 = Copy(m0).
+        // Add a physical fault that flips ONLY m0 with p=1.
+        // Result: m0 is flipped, m1 is NOT — the fault does not propagate
+        // through the ideal Copy dependency.
+        use pecos_simulators::SymbolicSparseStab;
+
+        let mut sim = SymbolicSparseStab::new(2);
+        sim.h(&[0]).cx(&[(0, 1)]);
+        sim.mz(&[0]);
+        sim.mz(&[1]);
+
+        // Fault that always fires, flipping only m0
+        let mechanisms = vec![FaultMechanism {
+            probability: 1.0,
+            alternatives: vec![vec![0]],
+        }];
+        let plan = RawMeasurementPlan::new(sim.measurement_history(), mechanisms);
+        let result = plan.sample(1000, 42);
+
+        for shot in 0..1000 {
+            let m0 = result.get(shot, 0).0;
+            let m1 = result.get(shot, 1).0;
+            // m0 = base XOR 1 (always flipped), m1 = base (not flipped)
+            // Since base m0 == base m1, after flip: m0 != m1
+            assert_ne!(m0, m1, "Fault on m0 must not inherit to m1 (shot {shot})");
+        }
+    }
+
+    #[test]
+    fn test_plan_grouped_alternatives_preserve_empty() {
+        // Deterministic base (m0 = Fixed(false) = always 0) with a p=1 mechanism
+        // having 3 alternatives: [flip m0, flip m0, no-op].
+        // Each shot fires and picks one uniformly → 2/3 get flipped.
+        use pecos_simulators::SymbolicSparseStab;
+
+        let mut sim = SymbolicSparseStab::new(1);
+        sim.mz(&[0]); // m0 = Fixed(false)
+
+        let mechanisms = vec![FaultMechanism {
+            probability: 1.0,
+            alternatives: vec![vec![0], vec![0], vec![]],
+        }];
+        let plan = RawMeasurementPlan::new(sim.measurement_history(), mechanisms);
+        let result = plan.sample(9000, 42);
+
+        // base=0, fault flips with prob 2/3 → mean should be ~2/3.
+        let ones: usize = (0..9000).filter(|&s| result.get(s, 0).0).count();
+        let mean = f64::from(u32::try_from(ones).expect("sample count fits in u32")) / 9000.0;
+        assert!(
+            (mean - 2.0 / 3.0).abs() < 0.03,
+            "Expected ~2/3 flip rate from grouped alternatives, got {mean:.4}"
+        );
+    }
+
+    #[test]
+    fn test_plan_geometric_sampling_firing_rates() {
+        use pecos_simulators::SymbolicSparseStab;
+
+        let mut sim = SymbolicSparseStab::new(1);
+        sim.mz(&[0]); // deterministic base measurement: m0 = 0
+
+        let shots = 200_000usize;
+        for (p, low, high) in [
+            (0.001, 120, 280),
+            (0.05, 9400, 10600),
+            (0.5, 99_000, 101_000),
+        ] {
+            let mechanisms = vec![FaultMechanism {
+                probability: p,
+                alternatives: vec![vec![0]],
+            }];
+            let plan = RawMeasurementPlan::new(sim.measurement_history(), mechanisms);
+            let result = plan.sample(shots, 42);
+
+            let firing_count = (0..shots).filter(|&shot| result.get(shot, 0).0).count();
+            assert!(
+                (low..=high).contains(&firing_count),
+                "p={p} firing count {firing_count} outside expected range [{low}, {high}]"
+            );
+        }
+    }
+
+    #[test]
+    fn test_sample_raw_word_boundaries_are_masked() {
+        use pecos_simulators::SymbolicSparseStab;
+
+        let mut sim = SymbolicSparseStab::new(1);
+        sim.mz(&[0]); // deterministic base measurement: m0 = 0
+
+        let mechanisms = vec![FaultMechanism {
+            probability: 1.0,
+            alternatives: vec![vec![0]],
+        }];
+        let plan = RawMeasurementPlan::new(sim.measurement_history(), mechanisms);
+
+        for shots in [63usize, 64, 65, 128, 129] {
+            let raw = plan.sample_raw(shots, 42);
+            let expected_words = shots.div_ceil(64);
+            assert_eq!(raw.columns[0].len(), expected_words);
+            for shot in 0..shots {
+                let word_idx = shot / 64;
+                let bit_idx = shot % 64;
+                assert_ne!(
+                    raw.columns[0][word_idx] & (1u64 << bit_idx),
+                    0,
+                    "shot {shot} should be flipped for p=1"
+                );
+            }
+
+            let remainder = shots % 64;
+            if remainder != 0 {
+                let tail_mask = !((1u64 << remainder) - 1);
+                assert_eq!(
+                    raw.columns[0].last().copied().unwrap() & tail_mask,
+                    0,
+                    "bits beyond {shots} shots should be masked off"
+                );
+            }
+        }
+    }
+
+    #[test]
+    fn test_sample_raw_masks_final_word_no_mechanisms() {
+        // 100 shots (not a multiple of 64): final word should have bits 100..128 = 0
+        use pecos_simulators::SymbolicSparseStab;
+
+        let mut sim = SymbolicSparseStab::new(1);
+        sim.h(&[0]);
+        sim.mz(&[0]); // Random
+
+        let plan = RawMeasurementPlan::new(sim.measurement_history(), vec![]);
+        let raw = plan.sample_raw(100, 42);
+
+        // 100 shots → 2 words. Last word should have bits 36..63 = 0 (100 - 64 = 36 valid bits)
+        assert_eq!(raw.columns[0].len(), 2);
+        let last_word = raw.columns[0][1];
+        let valid_bits = 100 - 64;
+        let tail_mask = !((1u64 << valid_bits) - 1);
+        assert_eq!(
+            last_word & tail_mask,
+            0,
+            "Bits beyond shots should be zero in measurement columns"
+        );
+    }
+
+    #[test]
+    fn test_sample_raw_r_columns_masked() {
+        use pecos_simulators::SymbolicSparseStab;
+
+        let mut sim = SymbolicSparseStab::new(1);
+        sim.h(&[0]);
+        sim.mz(&[0]); // Random
+
+        let plan = RawMeasurementPlan::new(sim.measurement_history(), vec![]);
+        let raw = plan.sample_raw(100, 42);
+
+        assert_eq!(raw.r_columns.len(), 1);
+        assert_eq!(raw.r_columns[0].len(), 2);
+        let last_word = raw.r_columns[0][1];
+        let valid_bits = 100 - 64;
+        let tail_mask = !((1u64 << valid_bits) - 1);
+        assert_eq!(
+            last_word & tail_mask,
+            0,
+            "Bits beyond shots should be zero in r_columns"
+        );
+    }
+
+    #[test]
+    fn test_sample_raw_bell_r_source_mapping() {
+        // Bell: H(0) CX(0,1) MZ(0) MZ(1)
+        // m0=Random, m1=Copy(m0) → exactly one r-source at measurement 0
+        use pecos_simulators::SymbolicSparseStab;
+
+        let mut sim = SymbolicSparseStab::new(2);
+        sim.h(&[0]).cx(&[(0, 1)]);
+        sim.mz(&[0]);
+        sim.mz(&[1]);
+
+        let plan = RawMeasurementPlan::new(sim.measurement_history(), vec![]);
+        let raw = plan.sample_raw(64, 42);
+
+        assert_eq!(raw.r_columns.len(), 1, "Bell pair has one r-source");
+        assert_eq!(
+            raw.r_source_measurements,
+            vec![0],
+            "r-source introduced at measurement 0"
+        );
+        // The r column should equal the m0 column (since m0 = Random = r0 directly)
+        assert_eq!(raw.r_columns[0], raw.columns[0]);
+        // And m1 = Copy(m0), so columns[1] == columns[0]
+        assert_eq!(raw.columns[0], raw.columns[1]);
+    }
+
+    #[test]
+    fn test_sample_raw_zero_shots_invariant() {
+        // Bell circuit with zero shots: r_columns length must match r_source_measurements
+        use pecos_simulators::SymbolicSparseStab;
+
+        let mut sim = SymbolicSparseStab::new(2);
+        sim.h(&[0]).cx(&[(0, 1)]);
+        sim.mz(&[0]);
+        sim.mz(&[1]);
+
+        let plan = RawMeasurementPlan::new(sim.measurement_history(), vec![]);
+        let raw = plan.sample_raw(0, 42);
+
+        assert_eq!(raw.columns.len(), 2);
+        assert!(raw.columns[0].is_empty());
+        assert!(raw.columns[1].is_empty());
+        assert_eq!(raw.r_source_measurements, vec![0]);
+        assert_eq!(raw.r_columns.len(), 1);
+        assert!(raw.r_columns[0].is_empty());
+        assert_eq!(raw.shots, 0);
+    }
+}
diff --git a/crates/pecos-qec/src/fault_tolerance/gadget_checker.rs b/crates/pecos-qec/src/fault_tolerance/gadget_checker.rs
index 69f598fe6..794cf541a 100644
--- a/crates/pecos-qec/src/fault_tolerance/gadget_checker.rs
+++ b/crates/pecos-qec/src/fault_tolerance/gadget_checker.rs
@@ -963,13 +963,31 @@ impl<'a> GadgetChecker<'a> {
     /// Propagate a `PauliProp` through the circuit without additional faults.
     fn propagate_through_circuit(&self, mut prop: PauliProp) -> PauliProp {
         for tick in self.circuit.ticks() {
-            for gate in tick.gates() {
+            for gate in tick.iter_gate_batches() {
                 let qubits: Vec<QubitId> = gate.qubits.to_vec();
 
                 match gate.gate_type {
                     pecos_core::gate_type::GateType::H => {
                         prop.h(&qubits);
                     }
+                    pecos_core::gate_type::GateType::F => {
+                        prop.f(&qubits);
+                    }
+                    pecos_core::gate_type::GateType::Fdg => {
+                        prop.fdg(&qubits);
+                    }
+                    pecos_core::gate_type::GateType::SX => {
+                        prop.sx(&qubits);
+                    }
+                    pecos_core::gate_type::GateType::SXdg => {
+                        prop.sxdg(&qubits);
+                    }
+                    pecos_core::gate_type::GateType::SY => {
+                        prop.sy(&qubits);
+                    }
+                    pecos_core::gate_type::GateType::SYdg => {
+                        prop.sydg(&qubits);
+                    }
                     pecos_core::gate_type::GateType::SZ => {
                         prop.sz(&qubits);
                     }
@@ -979,9 +997,33 @@ impl<'a> GadgetChecker<'a> {
                     pecos_core::gate_type::GateType::CX if qubits.len() >= 2 => {
                         prop.cx(&[(qubits[0], qubits[1])]);
                     }
+                    pecos_core::gate_type::GateType::CY if qubits.len() >= 2 => {
+                        prop.cy(&[(qubits[0], qubits[1])]);
+                    }
                     pecos_core::gate_type::GateType::CZ if qubits.len() >= 2 => {
                         prop.cz(&[(qubits[0], qubits[1])]);
                     }
+                    pecos_core::gate_type::GateType::SXX if qubits.len() >= 2 => {
+                        prop.sxx(&[(qubits[0], qubits[1])]);
+                    }
+                    pecos_core::gate_type::GateType::SXXdg if qubits.len() >= 2 => {
+                        prop.sxxdg(&[(qubits[0], qubits[1])]);
+                    }
+                    pecos_core::gate_type::GateType::SYY if qubits.len() >= 2 => {
+                        prop.syy(&[(qubits[0], qubits[1])]);
+                    }
+                    pecos_core::gate_type::GateType::SYYdg if qubits.len() >= 2 => {
+                        prop.syydg(&[(qubits[0], qubits[1])]);
+                    }
+                    pecos_core::gate_type::GateType::SZZ if qubits.len() >= 2 => {
+                        prop.szz(&[(qubits[0], qubits[1])]);
+                    }
+                    pecos_core::gate_type::GateType::SZZdg if qubits.len() >= 2 => {
+                        prop.szzdg(&[(qubits[0], qubits[1])]);
+                    }
+                    pecos_core::gate_type::GateType::SWAP if qubits.len() >= 2 => {
+                        prop.swap(&[(qubits[0], qubits[1])]);
+                    }
                     pecos_core::gate_type::GateType::X => {
                         prop.x(&qubits);
                     }
@@ -1677,7 +1719,7 @@ impl<'a> GadgetChecker<'a> {
         }
 
         // Propagate through circuit up to max_tick, injecting faults as we go
-        for (tick_idx, tick) in self.circuit.ticks().iter().enumerate() {
+        for (tick_idx, tick) in self.circuit.iter_ticks() {
             if tick_idx > max_tick {
                 break;
             }
@@ -1699,12 +1741,30 @@ impl<'a> GadgetChecker<'a> {
             }
 
             // Apply gates
-            for gate in tick.gates() {
+            for gate in tick.iter_gate_batches() {
                 let qubits: Vec<QubitId> = gate.qubits.to_vec();
                 match gate.gate_type {
                     pecos_core::gate_type::GateType::H => {
                         prop.h(&qubits);
                     }
+                    pecos_core::gate_type::GateType::F => {
+                        prop.f(&qubits);
+                    }
+                    pecos_core::gate_type::GateType::Fdg => {
+                        prop.fdg(&qubits);
+                    }
+                    pecos_core::gate_type::GateType::SX => {
+                        prop.sx(&qubits);
+                    }
+                    pecos_core::gate_type::GateType::SXdg => {
+                        prop.sxdg(&qubits);
+                    }
+                    pecos_core::gate_type::GateType::SY => {
+                        prop.sy(&qubits);
+                    }
+                    pecos_core::gate_type::GateType::SYdg => {
+                        prop.sydg(&qubits);
+                    }
                     pecos_core::gate_type::GateType::SZ => {
                         prop.sz(&qubits);
                     }
@@ -1714,9 +1774,33 @@ impl<'a> GadgetChecker<'a> {
                     pecos_core::gate_type::GateType::CX if qubits.len() >= 2 => {
                         prop.cx(&[(qubits[0], qubits[1])]);
                     }
+                    pecos_core::gate_type::GateType::CY if qubits.len() >= 2 => {
+                        prop.cy(&[(qubits[0], qubits[1])]);
+                    }
                     pecos_core::gate_type::GateType::CZ if qubits.len() >= 2 => {
                         prop.cz(&[(qubits[0], qubits[1])]);
                     }
+                    pecos_core::gate_type::GateType::SXX if qubits.len() >= 2 => {
+                        prop.sxx(&[(qubits[0], qubits[1])]);
+                    }
+                    pecos_core::gate_type::GateType::SXXdg if qubits.len() >= 2 => {
+                        prop.sxxdg(&[(qubits[0], qubits[1])]);
+                    }
+                    pecos_core::gate_type::GateType::SYY if qubits.len() >= 2 => {
+                        prop.syy(&[(qubits[0], qubits[1])]);
+                    }
+                    pecos_core::gate_type::GateType::SYYdg if qubits.len() >= 2 => {
+                        prop.syydg(&[(qubits[0], qubits[1])]);
+                    }
+                    pecos_core::gate_type::GateType::SZZ if qubits.len() >= 2 => {
+                        prop.szz(&[(qubits[0], qubits[1])]);
+                    }
+                    pecos_core::gate_type::GateType::SZZdg if qubits.len() >= 2 => {
+                        prop.szzdg(&[(qubits[0], qubits[1])]);
+                    }
+                    pecos_core::gate_type::GateType::SWAP if qubits.len() >= 2 => {
+                        prop.swap(&[(qubits[0], qubits[1])]);
+                    }
                     pecos_core::gate_type::GateType::X => {
                         prop.x(&qubits);
                     }
@@ -1942,7 +2026,8 @@ mod tests {
         let mut circuit = TickCircuit::new();
         circuit.tick().pz(&[0, 1, 2]); // Initialize all data qubits
         circuit.tick().h(&[0]); // Some operations
-        circuit.tick().cx(&[(0, 1), (0, 2)]);
+        circuit.tick().cx(&[(0, 1)]);
+        circuit.tick().cx(&[(0, 2)]);
         // Data qubits are OUTPUT (not measured)
         circuit
     }
@@ -2347,7 +2432,8 @@ mod tests {
         let mut circuit = TickCircuit::new();
         circuit.tick().pz(&[0, 1, 2]); // All qubits prepared
         circuit.tick().h(&[0]);
-        circuit.tick().cx(&[(0, 1), (0, 2)]);
+        circuit.tick().cx(&[(0, 1)]);
+        circuit.tick().cx(&[(0, 2)]);
         // No measurement - outputs go to next stage
 
         let checker = GadgetChecker::from_circuit(&circuit);
diff --git a/crates/pecos-qec/src/fault_tolerance/influence_builder.rs b/crates/pecos-qec/src/fault_tolerance/influence_builder.rs
index 4774ef4b0..aa77d8e71 100644
--- a/crates/pecos-qec/src/fault_tolerance/influence_builder.rs
+++ b/crates/pecos-qec/src/fault_tolerance/influence_builder.rs
@@ -10,7 +10,7 @@
 //!
 //! ```
 //! use pecos_qec::fault_tolerance::InfluenceBuilder;
-//! use pecos_qec::fault_tolerance::noisy_sampler::{NoisySampler, UniformNoiseModel};
+//! use pecos_qec::fault_tolerance::dem_builder::DemSampler;
 //! use pecos_quantum::DagCircuit;
 //!
 //! // Build a syndrome extraction circuit
@@ -24,13 +24,13 @@
 //! let builder = InfluenceBuilder::new(&dag);
 //! let influence_map = builder.build();
 //!
-//! // Use with CPU sampler
-//! let noise = UniformNoiseModel::depolarizing(0.001);
-//! let mut sampler = NoisySampler::new(&influence_map, noise, 42);
-//! let results = sampler.sample(100);
+//! // Build a fast DemSampler from the influence map
+//! let num_locations = influence_map.locations.len();
+//! let sampler = DemSampler::from_influence_map(&influence_map, &vec![0.001; num_locations]);
+//! let stats = sampler.sample_statistics(100, 42);
 //! ```
 
-use super::propagator::dag::{DagFaultInfluenceMap, DagSpacetimeLocation};
+use super::propagator::dag::{DagFaultInfluenceMap, DagSpacetimeLocation, DemOutputMetadata};
 use super::propagator::types::{DetectorId, MeasurementId};
 use super::propagator::{DagFaultAnalyzer, DagPropagator, Direction, Pauli, apply_gate};
 use pecos_core::QubitId;
@@ -38,15 +38,61 @@ use pecos_simulators::{PauliProp, SymbolicSparseStab};
 use smallvec::SmallVec;
 use std::collections::BinaryHeap;
 
+struct ObservablePropagationWork<'a> {
+    recorder: &'a mut CompoundRecorder,
+    visited: &'a mut [bool],
+    active_qubits: &'a mut [bool],
+    heap: &'a mut BinaryHeap<(usize, usize)>,
+}
+
 /// Builder for fault influence maps with proper detector definitions.
 ///
 /// This integrates forward symbolic simulation with backward propagation
 /// to create complete influence maps suitable for noisy sampling.
+/// Re-export `PauliString` as the type used for Pauli operator tracking.
+///
+/// All circuit annotations (detectors, observables, tracked Paulis) are Pauli
+/// strings tracked for flipping via backward propagation. The difference
+/// is role and readout:
+///
+/// | Kind | Meaning | Readout | API |
+/// |------|---------|---------|-----|
+/// | Detector | Syndrome parity from measurements | measurement XOR = 0 | `dag.detector(&[...])` |
+/// | Observable | Standard `L<n>` output from measurements | measurement XOR | `dag.observable(&[...])` |
+/// | Tracked Pauli | User Pauli string annotated at a circuit point | fault anticommutes with tracked Pauli | `dag.tracked_pauli(&[...])` |
+///
+/// Observables and tracked Paulis both use backward Pauli propagation, but
+/// they are not the same concept. Observables are values observed through
+/// measurements, are defined by measurement records, and are decoder-visible
+/// `L<n>` outputs. Tracked Paulis are not measured and are not applied to the
+/// computation; they ask whether a fault would flip the annotated Pauli placed as
+/// an annotation in the circuit, such as a logical operator, stabilizer, or
+/// other Pauli of interest. They live in a separate PECOS-only namespace.
+pub use pecos_core::PauliString;
+
+struct NonDetectorOutputTarget {
+    metadata: DemOutputMetadata,
+    terms: Vec<PauliPropagationTerm>,
+}
+
+struct PauliPropagationTerm {
+    pauli: PauliString,
+    start_node: Option<usize>,
+}
+
 pub struct InfluenceBuilder<'a> {
     dag: &'a pecos_quantum::DagCircuit,
-    /// Logical operators to track (qubit indices with X or Z component)
-    logical_x_qubits: Vec<usize>,
-    logical_z_qubits: Vec<usize>,
+    /// Non-detector parity outputs to track for flipping.
+    ///
+    /// This internal list contains both standard observables and PECOS tracked
+    /// operators. The metadata kind is the authority for which public namespace
+    /// each entry belongs to; callers should not infer that from the raw index.
+    ///
+    /// Each entry has one metadata item and one or more propagation terms.
+    /// Multiple terms accumulate into the same output index, which is needed
+    /// for measurement-record observables whose measurements occur at different
+    /// circuit positions.
+    non_detector_outputs: Vec<NonDetectorOutputTarget>,
 }
 
 impl<'a> InfluenceBuilder<'a> {
@@ -55,26 +101,133 @@ impl<'a> InfluenceBuilder<'a> {
     pub fn new(dag: &'a pecos_quantum::DagCircuit) -> Self {
         Self {
             dag,
-            logical_x_qubits: Vec::new(),
-            logical_z_qubits: Vec::new(),
+            non_detector_outputs: Vec::new(),
         }
     }
 
-    /// Add a logical X operator to track.
+    /// Add a tracked X Pauli (X on all specified qubits).
+    #[must_use]
+    pub fn with_x(mut self, qubits: &[usize]) -> Self {
+        self.push_single_term_output(
+            DemOutputMetadata::tracked_pauli(PauliString::xs(qubits)),
+            None,
+        );
+        self
+    }
+
+    /// Add a tracked Z Pauli (Z on all specified qubits).
+    #[must_use]
+    pub fn with_z(mut self, qubits: &[usize]) -> Self {
+        self.push_single_term_output(
+            DemOutputMetadata::tracked_pauli(PauliString::zs(qubits)),
+            None,
+        );
+        self
+    }
+
+    /// Add a tracked Y Pauli (Y on all specified qubits).
+    #[must_use]
+    pub fn with_y(mut self, qubits: &[usize]) -> Self {
+        self.push_single_term_output(
+            DemOutputMetadata::tracked_pauli(PauliString::ys(qubits)),
+            None,
+        );
+        self
+    }
+
+    /// Add a Pauli check: track whether this Pauli string flips due to faults.
+    ///
+    /// Unlike observables (`dag.observable()`), a Pauli check
+    /// uses backward propagation to detect flips WITHOUT requiring a measurement.
+    ///
+    /// # Example
     ///
-    /// The logical X is defined as X on all specified qubits.
+    /// ```
+    /// // Check if Y = X_0 * Z_1 * Z_2 flips
+    /// use pecos_core::{Pauli, PauliString};
+    /// use pecos_qec::fault_tolerance::InfluenceBuilder;
+    /// use pecos_quantum::DagCircuit;
+    ///
+    /// let dag = DagCircuit::new();
+    /// let builder = InfluenceBuilder::new(&dag).with_tracked_pauli(
+    ///     PauliString::from_paulis(&[Pauli::X, Pauli::Z, Pauli::Z]),
+    /// );
+    /// let _map = builder.build();
+    /// ```
     #[must_use]
-    pub fn with_logical_x(mut self, qubits: Vec<usize>) -> Self {
-        self.logical_x_qubits = qubits;
+    pub fn with_tracked_pauli(mut self, pauli: PauliString) -> Self {
+        self.push_single_term_output(DemOutputMetadata::tracked_pauli(pauli), None);
         self
     }
 
-    /// Add a logical Z operator to track.
+    fn push_single_term_output(&mut self, metadata: DemOutputMetadata, start_node: Option<usize>) {
+        self.non_detector_outputs.push(NonDetectorOutputTarget {
+            terms: vec![PauliPropagationTerm {
+                pauli: metadata.pauli.clone(),
+                start_node,
+            }],
+            metadata,
+        });
+    }
+
+    /// Extract observable and tracked-Pauli annotations from the circuit.
+    ///
+    /// Observable annotations define logical observables via measurement records.
+    /// For backward propagation, each referenced measurement contributes its
+    /// own Z-type propagation term starting at that measurement node. The terms
+    /// accumulate into the same observable `L<n>` output.
     ///
-    /// The logical Z is defined as Z on all specified qubits.
+    /// Tracked-Pauli annotations have a corresponding `TrackedPauliMeta` node
+    /// that marks their time position.
+    ///
+    /// Detector annotations are NOT handled here -- they are processed
+    /// by `DemSamplerBuilder::with_circuit_annotations` which maps them
+    /// to auto-detected detectors.
     #[must_use]
-    pub fn with_logical_z(mut self, qubits: Vec<usize>) -> Self {
-        self.logical_z_qubits = qubits;
+    pub fn with_circuit_annotations(mut self, circuit: &pecos_quantum::DagCircuit) -> Self {
+        // Find TrackedPauliMeta nodes in topological order.
+        // The nth meta-gate corresponds to the nth tracked-Pauli annotation.
+        let meta_nodes: Vec<usize> = circuit
+            .topological_order()
+            .into_iter()
+            .filter(|&node| circuit.gate(node).is_some_and(|g| g.gate_type.is_meta()))
+            .collect();
+
+        let mut operator_idx = 0;
+        for ann in circuit.annotations() {
+            match &ann.kind {
+                pecos_quantum::AnnotationKind::Observable { measurement_nodes } => {
+                    let mut terms = Vec::new();
+                    for &meas_node in measurement_nodes {
+                        if let Some(gate) = circuit.gate(meas_node) {
+                            let qubits: Vec<usize> =
+                                gate.qubits.iter().map(pecos_core::QubitId::index).collect();
+                            terms.push(PauliPropagationTerm {
+                                pauli: PauliString::zs(&qubits),
+                                start_node: Some(meas_node),
+                            });
+                        }
+                    }
+                    self.non_detector_outputs.push(NonDetectorOutputTarget {
+                        metadata: DemOutputMetadata::observable(ann.pauli.clone())
+                            .with_optional_label(ann.label.clone()),
+                        terms,
+                    });
+                }
+                pecos_quantum::AnnotationKind::TrackedPauli => {
+                    let meta_node = meta_nodes.get(operator_idx).copied();
+                    operator_idx += 1;
+                    self.push_single_term_output(
+                        DemOutputMetadata::tracked_pauli(ann.pauli.clone())
+                            .with_optional_label(ann.label.clone()),
+                        meta_node,
+                    );
+                }
+                pecos_quantum::AnnotationKind::Detector { .. } => {
+                    // Detectors handled separately by DemSamplerBuilder
+                }
+            }
+        }
         self
     }
 
@@ -83,7 +236,7 @@ impl<'a> InfluenceBuilder<'a> {
     /// This performs:
     /// 1. Forward symbolic simulation to get measurement correlations
     /// 2. Detector extraction from deterministic measurements
-    /// 3. Backward propagation from detectors and logicals
+    /// 3. Backward propagation from detectors and DEM outputs
     #[must_use]
     pub fn build(&self) -> DagFaultInfluenceMap {
         // Step 1: Run forward symbolic simulation
@@ -98,10 +251,10 @@ impl<'a> InfluenceBuilder<'a> {
 
     /// Run symbolic simulation to get measurement correlations.
     fn run_symbolic_simulation(&self) -> MeasurementInfo {
+        let topo_order = self.dag.topological_order();
+
         // Determine number of qubits from the circuit
-        let max_qubit = self
-            .dag
-            .topological_order()
+        let max_qubit = topo_order
             .iter()
             .filter_map(|&node| self.dag.gate(node))
             .flat_map(|op| op.qubits.iter())
@@ -113,11 +266,12 @@ impl<'a> InfluenceBuilder<'a> {
         let mut sim = SymbolicSparseStab::new(num_qubits);
 
         // Track node -> measurement index mapping
-        let mut node_to_meas_idx: Vec<Option<usize>> = vec![None; self.dag.gate_count() + 1];
+        let node_count = topo_order.iter().copied().max().map_or(0, |node| node + 1);
+        let mut node_to_meas_idx: Vec<Option<usize>> = vec![None; node_count];
         let mut meas_idx = 0;
 
         // Execute circuit symbolically
-        for &node in &self.dag.topological_order() {
+        for &node in &topo_order {
             if let Some(op) = self.dag.gate(node) {
                 let qubits: Vec<usize> = op.qubits.iter().map(pecos_core::QubitId::index).collect();
 
@@ -125,14 +279,31 @@ impl<'a> InfluenceBuilder<'a> {
                     pecos_quantum::GateType::H => {
                         sim.h(&[qubits[0]]);
                     }
+                    pecos_quantum::GateType::F => {
+                        sim.sx(&[qubits[0]]);
+                        sim.sz(&[qubits[0]]);
+                    }
+                    pecos_quantum::GateType::Fdg => {
+                        sim.szdg(&[qubits[0]]);
+                        sim.sxdg(&[qubits[0]]);
+                    }
+                    pecos_quantum::GateType::SX => {
+                        sim.sx(&[qubits[0]]);
+                    }
+                    pecos_quantum::GateType::SXdg => {
+                        sim.sxdg(&[qubits[0]]);
+                    }
+                    pecos_quantum::GateType::SY => {
+                        sim.sy(&[qubits[0]]);
+                    }
+                    pecos_quantum::GateType::SYdg => {
+                        sim.sydg(&[qubits[0]]);
+                    }
                     pecos_quantum::GateType::SZ => {
                         sim.sz(&[qubits[0]]);
                     }
                     pecos_quantum::GateType::SZdg => {
-                        // SZdg = SZ^3 = SZ * SZ * SZ
-                        sim.sz(&[qubits[0]]);
-                        sim.sz(&[qubits[0]]);
-                        sim.sz(&[qubits[0]]);
+                        sim.szdg(&[qubits[0]]);
                     }
                     pecos_quantum::GateType::X => {
                         sim.x(&[qubits[0]]);
@@ -146,11 +317,32 @@ impl<'a> InfluenceBuilder<'a> {
                     pecos_quantum::GateType::CX => {
                         sim.cx(&[(qubits[0], qubits[1])]);
                     }
+                    pecos_quantum::GateType::CY => {
+                        sim.cy(&[(qubits[0], qubits[1])]);
+                    }
                     pecos_quantum::GateType::CZ => {
-                        // CZ = H(target) CX H(target)
-                        sim.h(&[qubits[1]]);
-                        sim.cx(&[(qubits[0], qubits[1])]);
-                        sim.h(&[qubits[1]]);
+                        sim.cz(&[(qubits[0], qubits[1])]);
+                    }
+                    pecos_quantum::GateType::SXX => {
+                        sim.sxx(&[(qubits[0], qubits[1])]);
+                    }
+                    pecos_quantum::GateType::SXXdg => {
+                        sim.sxxdg(&[(qubits[0], qubits[1])]);
+                    }
+                    pecos_quantum::GateType::SYY => {
+                        sim.syy(&[(qubits[0], qubits[1])]);
+                    }
+                    pecos_quantum::GateType::SYYdg => {
+                        sim.syydg(&[(qubits[0], qubits[1])]);
+                    }
+                    pecos_quantum::GateType::SZZ => {
+                        sim.szz(&[(qubits[0], qubits[1])]);
+                    }
+                    pecos_quantum::GateType::SZZdg => {
+                        sim.szzdg(&[(qubits[0], qubits[1])]);
+                    }
+                    pecos_quantum::GateType::SWAP => {
+                        sim.swap(&[(qubits[0], qubits[1])]);
                     }
                     pecos_quantum::GateType::MZ | pecos_quantum::GateType::MeasureFree => {
                         sim.mz(&[qubits[0]]);
@@ -222,8 +414,9 @@ impl<'a> InfluenceBuilder<'a> {
         map.locations = Self::extract_locations(propagator);
 
         // Build measurement node lookup
-        let measurements = Self::extract_measurements(propagator);
+        let (measurements, meas_ids) = Self::extract_measurements(propagator);
         map.measurements.clone_from(&measurements);
+        map.meas_ids = meas_ids;
 
         // Create DetectorId entries for each detector
         for detector in detectors {
@@ -256,31 +449,30 @@ impl<'a> InfluenceBuilder<'a> {
             });
         }
 
-        // Add logical operators as additional "detectors" for tracking
-        let num_detectors = detectors.len();
-        let mut num_logicals = 0;
-
-        // Track logical X (sensitive to Z errors)
-        if !self.logical_x_qubits.is_empty() {
-            num_logicals += 1;
-        }
-        // Track logical Z (sensitive to X errors)
-        if !self.logical_z_qubits.is_empty() {
-            num_logicals += 1;
-        }
-
         // Build the influence structure using backward propagation
-        let mut recorder = CompoundRecorder::new(map.locations.len(), num_detectors, num_logicals);
+        let mut recorder = CompoundRecorder::new(map.locations.len());
 
         // Propagate from each detector
         Self::propagate_detectors(propagator, info, detectors, &mut recorder);
 
-        // Propagate from logicals
-        self.propagate_logicals(propagator, &mut recorder);
+        // Propagate from non-detector DEM outputs.
+        self.propagate_non_detector_outputs(propagator, &mut recorder);
 
         // Convert to SoA format
         map.influences = recorder.into_soa();
 
+        // Store DEM-output labels
+        map.dem_output_labels = self
+            .non_detector_outputs
+            .iter()
+            .map(|output| output.metadata.label.clone())
+            .collect();
+        map.dem_output_metadata = self
+            .non_detector_outputs
+            .iter()
+            .map(|output| output.metadata.clone())
+            .collect();
+
         map
     }
 
@@ -290,43 +482,32 @@ impl<'a> InfluenceBuilder<'a> {
 
         for &node in propagator.topo_order() {
             if let Some(gate) = propagator.gate(node) {
+                // Meta-gates are not physical -- they don't generate faults
+                if gate.gate_type.is_meta() {
+                    continue;
+                }
+
                 let qubits: Vec<QubitId> = gate.qubits.to_vec();
 
                 let is_measurement = matches!(
                     gate.gate_type,
                     pecos_quantum::GateType::MZ | pecos_quantum::GateType::MeasureFree
                 );
-                let is_prep = matches!(
-                    gate.gate_type,
-                    pecos_quantum::GateType::PZ | pecos_quantum::GateType::QAlloc
-                );
 
-                if is_measurement {
+                // Standard circuit noise model: one fault location per gate.
+                //   Measurement: before. All others: after.
+                let before = is_measurement;
+                for &q in &qubits {
+                    // idle_duration() returns a non-negative integer stored as f64;
+                    // truncation and sign loss are not a concern.
+                    #[allow(clippy::cast_possible_truncation, clippy::cast_sign_loss)]
+                    let idle_duration = gate.idle_duration() as u64;
                     locations.push(DagSpacetimeLocation {
                         node,
-                        qubits: qubits.clone(),
-                        before: true,
-                        gate_type: gate.gate_type,
-                    });
-                } else if is_prep {
-                    locations.push(DagSpacetimeLocation {
-                        node,
-                        qubits: qubits.clone(),
-                        before: false,
-                        gate_type: gate.gate_type,
-                    });
-                } else {
-                    locations.push(DagSpacetimeLocation {
-                        node,
-                        qubits: qubits.clone(),
-                        before: true,
-                        gate_type: gate.gate_type,
-                    });
-                    locations.push(DagSpacetimeLocation {
-                        node,
-                        qubits,
-                        before: false,
+                        qubits: vec![q],
+                        before,
                         gate_type: gate.gate_type,
+                        idle_duration,
                     });
                 }
             }
@@ -336,8 +517,10 @@ impl<'a> InfluenceBuilder<'a> {
     }
 
     /// Extract measurements from the propagator.
-    fn extract_measurements(propagator: &DagPropagator<'_>) -> Vec<(usize, usize, u8)> {
-        let mut measurements = Vec::new();
+    fn extract_measurements(
+        propagator: &DagPropagator<'_>,
+    ) -> (Vec<(usize, usize, u8)>, Vec<pecos_core::MeasId>) {
+        let mut entries: Vec<(usize, usize, usize, u8, Option<pecos_core::MeasId>)> = Vec::new();
 
         for &node in propagator.topo_order() {
             if let Some(gate) = propagator.gate(node) {
@@ -346,13 +529,39 @@ impl<'a> InfluenceBuilder<'a> {
                     _ => continue,
                 };
 
-                for qubit in &gate.qubits {
-                    measurements.push((node, qubit.index(), basis));
+                if gate.meas_ids.is_empty() {
+                    let topo_pos = propagator.topo_position(node);
+                    for qubit in &gate.qubits {
+                        entries.push((topo_pos, node, qubit.index(), basis, None));
+                    }
+                } else {
+                    for (i, qubit) in gate.qubits.iter().enumerate() {
+                        let mr = gate.meas_ids.get(i).copied();
+                        let sort_key = mr.map_or(usize::MAX, pecos_core::MeasId::index);
+                        entries.push((sort_key, node, qubit.index(), basis, mr));
+                    }
                 }
             }
         }
 
-        measurements
+        entries.sort_by_key(|&(sort_key, _, qubit, _, _)| (sort_key, qubit));
+
+        let has_meas_ids = entries.iter().any(|(_, _, _, _, mr)| mr.is_some());
+        let meas_ids = if has_meas_ids {
+            entries
+                .iter()
+                .map(|(_, _, _, _, mr)| mr.unwrap_or(pecos_core::MeasId(usize::MAX)))
+                .collect()
+        } else {
+            Vec::new()
+        };
+
+        let measurements = entries
+            .into_iter()
+            .map(|(_, node, qubit, basis, _)| (node, qubit, basis))
+            .collect();
+
+        (measurements, meas_ids)
     }
 
     /// Propagate backward from all detectors.
@@ -368,6 +577,12 @@ impl<'a> InfluenceBuilder<'a> {
         let mut visited = vec![false; max_node + 1];
         let mut active_qubits = vec![false; max_qubit + 1];
         let mut heap = BinaryHeap::new();
+        let mut work = ObservablePropagationWork {
+            recorder,
+            visited: &mut visited,
+            active_qubits: &mut active_qubits,
+            heap: &mut heap,
+        };
 
         for (det_idx, detector) in detectors.iter().enumerate() {
             // Build combined Pauli from all measurements in the detector
@@ -394,93 +609,100 @@ impl<'a> InfluenceBuilder<'a> {
                 &combined_prop,
                 det_idx,
                 true, // is_detector
-                recorder,
-                &mut visited,
-                &mut active_qubits,
-                &mut heap,
+                &mut work,
+                None, // detectors: walk from circuit end
             );
         }
     }
 
-    /// Propagate backward from logical operators.
-    fn propagate_logicals(&self, propagator: &DagPropagator<'_>, recorder: &mut CompoundRecorder) {
+    /// Propagate backward from non-detector DEM outputs.
+    ///
+    /// If a propagation term has a corresponding DAG node, propagation starts
+    /// from that node's topological position. Otherwise (e.g. operators added
+    /// via `with_z`/`with_x` without a circuit annotation), propagation walks
+    /// from the circuit end.
+    fn propagate_non_detector_outputs(
+        &self,
+        propagator: &DagPropagator<'_>,
+        recorder: &mut CompoundRecorder,
+    ) {
         let max_node = propagator.max_node();
         let max_qubit = propagator.max_qubit();
 
         let mut visited = vec![false; max_node + 1];
         let mut active_qubits = vec![false; max_qubit + 1];
         let mut heap = BinaryHeap::new();
-        let mut logical_idx = 0;
-
-        // Logical X (product of X on specified qubits) - sensitive to Z errors
-        if !self.logical_x_qubits.is_empty() {
-            let mut prop = PauliProp::new();
-            for &q in &self.logical_x_qubits {
-                prop.track_x(&[q]);
-            }
-
-            Self::propagate_observable(
-                propagator,
-                &prop,
-                logical_idx,
-                false, // is_detector (this is a logical)
-                recorder,
-                &mut visited,
-                &mut active_qubits,
-                &mut heap,
-            );
-            logical_idx += 1;
-        }
+        let mut work = ObservablePropagationWork {
+            recorder,
+            visited: &mut visited,
+            active_qubits: &mut active_qubits,
+            heap: &mut heap,
+        };
+
+        for (dem_output_idx, output) in self.non_detector_outputs.iter().enumerate() {
+            for term in &output.terms {
+                let mut prop = PauliProp::new();
+
+                for &(pauli, qubit) in term.pauli.paulis() {
+                    use pecos_core::Pauli;
+                    let q = qubit.index();
+                    match pauli {
+                        Pauli::X => prop.track_x(&[q]),
+                        Pauli::Y => prop.track_y(&[q]),
+                        Pauli::Z => prop.track_z(&[q]),
+                        Pauli::I => {}
+                    }
+                }
 
-        // Logical Z (product of Z on specified qubits) - sensitive to X errors
-        if !self.logical_z_qubits.is_empty() {
-            let mut prop = PauliProp::new();
-            for &q in &self.logical_z_qubits {
-                prop.track_z(&[q]);
+                // Resolve the term's node to its topological position.
+                // None means no positional bound (walk from circuit end).
+                let start_pos = term.start_node.map(|node| propagator.topo_position(node));
+
+                Self::propagate_observable(
+                    propagator,
+                    &prop,
+                    dem_output_idx,
+                    false, // is_detector = false (this is a DEM output)
+                    &mut work,
+                    start_pos,
+                );
             }
-
-            Self::propagate_observable(
-                propagator,
-                &prop,
-                logical_idx,
-                false, // is_detector (this is a logical)
-                recorder,
-                &mut visited,
-                &mut active_qubits,
-                &mut heap,
-            );
         }
     }
 
     /// Propagate a single observable backward and record influences.
-    #[allow(clippy::too_many_arguments)]
+    ///
+    /// When `start_topo_pos` is `Some(pos)`, only gates at or before that
+    /// topological position are considered. This makes Pauli operator
+    /// annotations positional: only faults before the meta-gate affect it.
     fn propagate_observable(
         propagator: &DagPropagator<'_>,
         initial_prop: &PauliProp,
         target_idx: usize,
         is_detector: bool,
-        recorder: &mut CompoundRecorder,
-        visited: &mut [bool],
-        active_qubits: &mut [bool],
-        heap: &mut BinaryHeap<(usize, usize)>,
+        work: &mut ObservablePropagationWork<'_>,
+        start_topo_pos: Option<usize>,
     ) {
         // Clear work arrays
-        visited.fill(false);
-        active_qubits.fill(false);
-        heap.clear();
+        work.visited.fill(false);
+        work.active_qubits.fill(false);
+        work.heap.clear();
 
         let mut prop = initial_prop.clone();
 
         // Initialize active qubits from the observable
-        for (q, is_active) in active_qubits.iter_mut().enumerate() {
+        for (q, is_active) in work.active_qubits.iter_mut().enumerate() {
             if prop.contains_x(q) || prop.contains_z(q) {
                 *is_active = true;
 
-                // Add all gates on this qubit to the heap
+                // Add gates on this qubit to the heap, bounded by start position
                 for (topo_pos, node) in propagator.qubit_gates_backward(q) {
-                    if !visited[node] {
-                        visited[node] = true;
-                        heap.push((topo_pos, node));
+                    if start_topo_pos.is_some_and(|max| topo_pos > max) {
+                        continue;
+                    }
+                    if !work.visited[node] {
+                        work.visited[node] = true;
+                        work.heap.push((topo_pos, node));
                     }
                 }
             }
@@ -490,44 +712,80 @@ impl<'a> InfluenceBuilder<'a> {
         let loc_map = Self::build_location_map(propagator);
 
         // Process gates in reverse topological order
-        while let Some((_, node)) = heap.pop() {
+        while let Some((_, node)) = work.heap.pop() {
             if let Some(gate) = propagator.gate(node) {
-                // Record influences at before=false location
-                if let Some(&loc_idx) = loc_map.get(&(node, false)) {
-                    Self::record_influence(&prop, loc_idx, target_idx, is_detector, recorder);
+                // Record per-qubit influences at before=false location
+                if let Some(qubit_locs) = loc_map.get(&(node, false)) {
+                    Self::record_influence(
+                        &prop,
+                        qubit_locs,
+                        target_idx,
+                        is_detector,
+                        &mut *work.recorder,
+                    );
                 }
 
                 // Track which qubits were active before the gate
                 let mut was_active = [false; 8];
                 for (j, q) in gate.qubits.iter().enumerate() {
-                    if j < was_active.len() && q.index() < active_qubits.len() {
-                        was_active[j] = active_qubits[q.index()];
+                    if j < was_active.len() && q.index() < work.active_qubits.len() {
+                        was_active[j] = work.active_qubits[q.index()];
+                    }
+                }
+
+                // Prep gates (PZ/QAlloc) reset the qubit -- kill the Pauli
+                // and mark the qubit inactive. Faults before the prep
+                // cannot propagate past it.
+                let is_prep = matches!(
+                    gate.gate_type,
+                    pecos_quantum::GateType::PZ | pecos_quantum::GateType::QAlloc
+                );
+                if is_prep {
+                    for q in &gate.qubits {
+                        let qi = q.index();
+                        // Toggle off X and Z components (XOR to zero)
+                        if prop.contains_x(qi) {
+                            prop.track_x(&[qi]);
+                        }
+                        if prop.contains_z(qi) {
+                            prop.track_z(&[qi]);
+                        }
+                        if qi < work.active_qubits.len() {
+                            work.active_qubits[qi] = false;
+                        }
                     }
+                    continue; // don't propagate further on these qubits
                 }
 
                 // Apply gate backward
                 apply_gate(&mut prop, gate, Direction::Backward);
 
-                // Record influences at before=true location
-                if let Some(&loc_idx) = loc_map.get(&(node, true)) {
-                    Self::record_influence(&prop, loc_idx, target_idx, is_detector, recorder);
+                // Record per-qubit influences at before=true location
+                if let Some(qubit_locs) = loc_map.get(&(node, true)) {
+                    Self::record_influence(
+                        &prop,
+                        qubit_locs,
+                        target_idx,
+                        is_detector,
+                        &mut *work.recorder,
+                    );
                 }
 
                 // Check if Pauli spread to new qubits
                 let node_topo_pos = propagator.topo_position(node);
                 for (j, q) in gate.qubits.iter().enumerate() {
                     let idx = q.index();
-                    if idx < active_qubits.len() {
+                    if idx < work.active_qubits.len() {
                         let now_active = prop.contains_x(idx) || prop.contains_z(idx);
                         let was = j < was_active.len() && was_active[j];
 
                         if now_active && !was {
                             // Pauli spread to this qubit - add its gates
-                            active_qubits[idx] = true;
+                            work.active_qubits[idx] = true;
                             for (topo_pos, pred_node) in propagator.qubit_gates_backward(idx) {
-                                if topo_pos < node_topo_pos && !visited[pred_node] {
-                                    visited[pred_node] = true;
-                                    heap.push((topo_pos, pred_node));
+                                if topo_pos < node_topo_pos && !work.visited[pred_node] {
+                                    work.visited[pred_node] = true;
+                                    work.heap.push((topo_pos, pred_node));
                                 }
                             }
                         }
@@ -537,34 +795,30 @@ impl<'a> InfluenceBuilder<'a> {
         }
     }
 
-    /// Build a map from (node, before) to location index.
+    /// Build a map from (node, before) to per-qubit location indices.
     fn build_location_map(
         propagator: &DagPropagator<'_>,
-    ) -> std::collections::HashMap<(usize, bool), usize> {
-        let mut map = std::collections::HashMap::new();
+    ) -> std::collections::HashMap<(usize, bool), Vec<(usize, usize)>> {
+        // (node, before) -> [(qubit_index, loc_idx), ...]
+        let mut map: std::collections::HashMap<(usize, bool), Vec<(usize, usize)>> =
+            std::collections::HashMap::new();
         let mut loc_idx = 0;
 
         for &node in propagator.topo_order() {
             if let Some(gate) = propagator.gate(node) {
+                if gate.gate_type.is_meta() {
+                    continue;
+                }
+
                 let is_measurement = matches!(
                     gate.gate_type,
                     pecos_quantum::GateType::MZ | pecos_quantum::GateType::MeasureFree
                 );
-                let is_prep = matches!(
-                    gate.gate_type,
-                    pecos_quantum::GateType::PZ | pecos_quantum::GateType::QAlloc
-                );
 
-                if is_measurement {
-                    map.insert((node, true), loc_idx);
-                    loc_idx += 1;
-                } else if is_prep {
-                    map.insert((node, false), loc_idx);
-                    loc_idx += 1;
-                } else {
-                    map.insert((node, true), loc_idx);
-                    loc_idx += 1;
-                    map.insert((node, false), loc_idx);
+                let before = is_measurement;
+                for q in &gate.qubits {
+                    let qi = q.index();
+                    map.entry((node, before)).or_default().push((qi, loc_idx));
                     loc_idx += 1;
                 }
             }
@@ -573,50 +827,41 @@ impl<'a> InfluenceBuilder<'a> {
         map
     }
 
-    /// Record influence of a fault at a location on a target (detector or logical).
+    /// Record per-qubit influence of a fault at a gate location.
     fn record_influence(
         prop: &PauliProp,
-        loc_idx: usize,
+        qubit_locs: &[(usize, usize)], // [(qubit, loc_idx), ...]
         target_idx: usize,
         is_detector: bool,
         recorder: &mut CompoundRecorder,
     ) {
-        // Check each Pauli type
-        for pauli in [Pauli::X, Pauli::Y, Pauli::Z] {
-            if Self::fault_anticommutes(prop, pauli) {
-                if is_detector {
-                    #[allow(clippy::cast_possible_truncation)] // index fits in u32
-                    recorder.record_detector(loc_idx, pauli, target_idx as u32);
-                } else {
-                    #[allow(clippy::cast_possible_truncation)] // index fits in u32
-                    recorder.record_logical(loc_idx, pauli, target_idx as u32);
+        for &(qubit, loc_idx) in qubit_locs {
+            for pauli in [Pauli::X, Pauli::Y, Pauli::Z] {
+                if Self::fault_anticommutes_qubit(prop, qubit, pauli) {
+                    if is_detector {
+                        #[allow(clippy::cast_possible_truncation)]
+                        recorder.record_detector(loc_idx, pauli, target_idx as u32);
+                    } else {
+                        #[allow(clippy::cast_possible_truncation)]
+                        recorder.record_dem_output(loc_idx, pauli, target_idx as u32);
+                    }
                 }
             }
         }
     }
 
-    /// Check if a fault Pauli anticommutes with the propagated observable.
-    fn fault_anticommutes(prop: &PauliProp, fault: Pauli) -> bool {
-        let mut anticom_count = 0;
+    /// Check if a single-qubit fault Pauli anticommutes with the propagated
+    /// observable on a specific qubit.
+    fn fault_anticommutes_qubit(prop: &PauliProp, qubit: usize, fault: Pauli) -> bool {
+        let has_x = prop.contains_x(qubit);
+        let has_z = prop.contains_z(qubit);
 
         match fault {
-            Pauli::I => return false,
-            Pauli::X => {
-                // X fault anticommutes with Z component
-                anticom_count += prop.get_z_qubits().len();
-            }
-            Pauli::Z => {
-                // Z fault anticommutes with X component
-                anticom_count += prop.get_x_qubits().len();
-            }
-            Pauli::Y => {
-                // Y fault anticommutes with both X and Z
-                anticom_count += prop.get_x_qubits().len();
-                anticom_count += prop.get_z_qubits().len();
-            }
+            Pauli::I => false,
+            Pauli::X => has_z,         // X anticommutes with Z
+            Pauli::Z => has_x,         // Z anticommutes with X
+            Pauli::Y => has_x ^ has_z, // Y anticommutes with X or Z but not both
         }
-
-        anticom_count % 2 == 1
     }
 }
 
@@ -640,34 +885,28 @@ struct DetectorDef {
 /// Recorder for compound detector propagation.
 struct CompoundRecorder {
     num_locations: usize,
-    #[allow(dead_code)]
-    num_detectors: usize,
-    #[allow(dead_code)]
-    num_logicals: usize,
 
     // Buckets for detector influences [loc_idx][pauli] -> Vec<detector_idx>
     detector_x: Vec<Vec<u32>>,
     detector_y: Vec<Vec<u32>>,
     detector_z: Vec<Vec<u32>>,
 
-    // Buckets for logical influences
-    logical_x: Vec<Vec<u32>>,
-    logical_y: Vec<Vec<u32>>,
-    logical_z: Vec<Vec<u32>>,
+    // Buckets for DEM-output influences.
+    dem_output_x: Vec<Vec<u32>>,
+    dem_output_y: Vec<Vec<u32>>,
+    dem_output_z: Vec<Vec<u32>>,
 }
 
 impl CompoundRecorder {
-    fn new(num_locations: usize, num_detectors: usize, num_logicals: usize) -> Self {
+    fn new(num_locations: usize) -> Self {
         Self {
             num_locations,
-            num_detectors,
-            num_logicals,
             detector_x: vec![Vec::new(); num_locations],
             detector_y: vec![Vec::new(); num_locations],
             detector_z: vec![Vec::new(); num_locations],
-            logical_x: vec![Vec::new(); num_locations],
-            logical_y: vec![Vec::new(); num_locations],
-            logical_z: vec![Vec::new(); num_locations],
+            dem_output_x: vec![Vec::new(); num_locations],
+            dem_output_y: vec![Vec::new(); num_locations],
+            dem_output_z: vec![Vec::new(); num_locations],
         }
     }
 
@@ -676,31 +915,38 @@ impl CompoundRecorder {
             return;
         }
         match pauli {
-            Pauli::X => self.detector_x[loc_idx].push(detector_idx),
-            Pauli::Y => self.detector_y[loc_idx].push(detector_idx),
-            Pauli::Z => self.detector_z[loc_idx].push(detector_idx),
+            Pauli::X => toggle_bucket(&mut self.detector_x[loc_idx], detector_idx),
+            Pauli::Y => toggle_bucket(&mut self.detector_y[loc_idx], detector_idx),
+            Pauli::Z => toggle_bucket(&mut self.detector_z[loc_idx], detector_idx),
             Pauli::I => {}
         }
     }
 
-    fn record_logical(&mut self, loc_idx: usize, pauli: Pauli, logical_idx: u32) {
+    fn record_dem_output(&mut self, loc_idx: usize, pauli: Pauli, dem_output_idx: u32) {
         if loc_idx >= self.num_locations {
             return;
         }
         match pauli {
-            Pauli::X => self.logical_x[loc_idx].push(logical_idx),
-            Pauli::Y => self.logical_y[loc_idx].push(logical_idx),
-            Pauli::Z => self.logical_z[loc_idx].push(logical_idx),
+            Pauli::X => toggle_bucket(&mut self.dem_output_x[loc_idx], dem_output_idx),
+            Pauli::Y => toggle_bucket(&mut self.dem_output_y[loc_idx], dem_output_idx),
+            Pauli::Z => toggle_bucket(&mut self.dem_output_z[loc_idx], dem_output_idx),
             Pauli::I => {}
         }
     }
 
-    fn into_soa(self) -> super::propagator::dag::InfluencesSoA {
+    fn into_soa(mut self) -> super::propagator::dag::InfluencesSoA {
         use super::propagator::dag::InfluencesSoA;
 
         let mut soa = InfluencesSoA::with_capacity(self.num_locations);
 
         for loc_idx in 0..self.num_locations {
+            self.detector_x[loc_idx].sort_unstable();
+            self.detector_y[loc_idx].sort_unstable();
+            self.detector_z[loc_idx].sort_unstable();
+            self.dem_output_x[loc_idx].sort_unstable();
+            self.dem_output_y[loc_idx].sort_unstable();
+            self.dem_output_z[loc_idx].sort_unstable();
+
             // Add detector influences
             for &det in &self.detector_x[loc_idx] {
                 soa.detectors_x.push(det);
@@ -712,15 +958,15 @@ impl CompoundRecorder {
                 soa.detectors_z.push(det);
             }
 
-            // Add logical influences
-            for &log in &self.logical_x[loc_idx] {
-                soa.logicals_x.push(log);
+            // Add DEM-output influences
+            for &dem_output in &self.dem_output_x[loc_idx] {
+                soa.dem_outputs_x.push(dem_output);
             }
-            for &log in &self.logical_y[loc_idx] {
-                soa.logicals_y.push(log);
+            for &dem_output in &self.dem_output_y[loc_idx] {
+                soa.dem_outputs_y.push(dem_output);
             }
-            for &log in &self.logical_z[loc_idx] {
-                soa.logicals_z.push(log);
+            for &dem_output in &self.dem_output_z[loc_idx] {
+                soa.dem_outputs_z.push(dem_output);
             }
 
             soa.finish_location();
@@ -730,9 +976,18 @@ impl CompoundRecorder {
     }
 }
 
+fn toggle_bucket(bucket: &mut Vec<u32>, value: u32) {
+    if let Some(pos) = bucket.iter().position(|&existing| existing == value) {
+        bucket.remove(pos);
+    } else {
+        bucket.push(value);
+    }
+}
+
 #[cfg(test)]
 mod tests {
     use super::*;
+    use crate::fault_tolerance::propagator::DemOutputKind;
     use pecos_quantum::DagCircuit;
 
     #[test]
@@ -801,17 +1056,217 @@ mod tests {
     }
 
     #[test]
-    fn test_with_logical() {
+    fn test_with_tracked_pauli() {
         let mut dag = DagCircuit::new();
         dag.pz(&[2]);
         dag.cx(&[(0, 2)]);
         dag.mz(&[2]);
 
-        let builder = InfluenceBuilder::new(&dag).with_logical_z(vec![0]); // Track Z logical on qubit 0
+        let builder = InfluenceBuilder::new(&dag).with_z(&[0]); // Track Z logical on qubit 0
 
         let map = builder.build();
 
         // Should track the logical
-        assert!(map.influences.max_logical_index().is_some());
+        assert!(map.influences.max_dem_output_index().is_some());
+    }
+
+    #[test]
+    fn test_dem_output_metadata_accepts_pauli_string_and_normalizes_phase() {
+        use pecos_core::{Pauli, QuarterPhase};
+
+        let pauli =
+            PauliString::from_paulis_with_phase(QuarterPhase::MinusI, &[Pauli::X, Pauli::Z]);
+        let metadata = DemOutputMetadata::tracked_pauli(pauli).with_label("xz");
+
+        assert_eq!(metadata.kind, DemOutputKind::TrackedPauli);
+        assert_eq!(metadata.label.as_deref(), Some("xz"));
+        assert_eq!(metadata.pauli.phase(), QuarterPhase::PlusOne);
+        assert_eq!(metadata.pauli.to_sparse_str(), "+X0 Z1");
+    }
+
+    #[test]
+    fn test_circuit_annotation_dem_output_metadata_tracks_observables_and_tracked_paulis() {
+        use pecos_core::pauli::X;
+
+        let mut dag = DagCircuit::new();
+        dag.pz(&[0]);
+        dag.h(&[0]);
+        let meas = dag.mz(&[0]);
+        dag.observable_labeled("record_obs", &[meas[0]]);
+        dag.tracked_pauli_labeled("track_x", X(0));
+
+        let map = InfluenceBuilder::new(&dag)
+            .with_circuit_annotations(&dag)
+            .build();
+
+        // 1 observable (record_obs) + 1 tracked Pauli (track_x) = 2 DEM outputs
+        assert_eq!(map.num_dem_outputs(), 1, "1 observable");
+        assert_eq!(map.num_tracked_paulis(), 1, "1 tracked Pauli");
+        assert_eq!(map.dem_output_metadata.len(), 2);
+
+        // Observable comes first (annotations are processed in order)
+        assert_eq!(map.dem_output_metadata[0].kind, DemOutputKind::Observable);
+        assert_eq!(
+            map.dem_output_metadata[0].label.as_deref(),
+            Some("record_obs")
+        );
+
+        // Tracked Pauli second
+        assert_eq!(map.dem_output_metadata[1].kind, DemOutputKind::TrackedPauli);
+        assert_eq!(map.dem_output_metadata[1].label.as_deref(), Some("track_x"));
+        assert_eq!(map.dem_output_metadata[1].pauli.to_sparse_str(), "+X0");
+    }
+
+    #[test]
+    fn test_observable_measurements_propagate_from_their_own_nodes() {
+        use pecos_quantum::GateType;
+
+        let mut dag = DagCircuit::new();
+        dag.pz(&[0, 1]);
+        let early = dag.mz(&[0]);
+        dag.h(&[0]);
+        let late = dag.mz(&[1]);
+        dag.observable_labeled("split_time_obs", &[early[0], late[0]]);
+
+        let map = InfluenceBuilder::new(&dag)
+            .with_circuit_annotations(&dag)
+            .build();
+
+        assert_eq!(map.num_observables(), 1);
+
+        let post_early_h = map
+            .locations
+            .iter()
+            .enumerate()
+            .find(|(_, loc)| {
+                loc.gate_type == GateType::H
+                    && loc.qubits.first().is_some_and(|q| q.index() == 0)
+                    && !loc.before
+            })
+            .map(|(idx, _)| idx)
+            .expect("H fault location after the early measurement");
+
+        for pauli in [Pauli::X, Pauli::Y, Pauli::Z] {
+            assert!(
+                map.get_observable_indices(post_early_h, pauli.as_u8())
+                    .is_empty(),
+                "faults after an already-recorded measurement must not flip that record"
+            );
+        }
+    }
+
+    #[test]
+    fn test_split_time_observable_fault_before_early_measurement_flips() {
+        // Circuit: PZ(0), PZ(1), MZ(0) [early], H(1), MZ(1) [late]
+        // Observable = MZ(0) XOR MZ(1)
+        //
+        // A prep fault on qubit 0 (after PZ(0), before MZ(0)) should flip the
+        // observable via the early measurement term.
+        use pecos_quantum::GateType;
+
+        let mut dag = DagCircuit::new();
+        dag.pz(&[0, 1]);
+        let early = dag.mz(&[0]);
+        dag.h(&[1]);
+        let late = dag.mz(&[1]);
+        dag.observable_labeled("split_obs", &[early[0], late[0]]);
+
+        let map = InfluenceBuilder::new(&dag)
+            .with_circuit_annotations(&dag)
+            .build();
+
+        assert_eq!(map.num_observables(), 1);
+
+        // Prep fault on qubit 0 (PZ after-gate location) should flip the
+        // observable because it propagates through the early MZ(0).
+        let prep_q0 = map
+            .locations
+            .iter()
+            .enumerate()
+            .find(|(_, loc)| {
+                loc.gate_type == GateType::PZ
+                    && loc.qubits.first().is_some_and(|q| q.index() == 0)
+                    && !loc.before
+            })
+            .map(|(idx, _)| idx)
+            .expect("PZ(0) fault location");
+
+        // X fault after PZ propagates through MZ as a bit flip
+        assert!(
+            !map.get_observable_indices(prep_q0, Pauli::X.as_u8())
+                .is_empty(),
+            "X fault before early measurement should flip observable"
+        );
+    }
+
+    #[test]
+    fn test_split_time_observable_fault_between_measurements_flips_late_only() {
+        // Circuit: PZ(0), PZ(1), MZ(0) [early], H(1), MZ(1) [late]
+        // Observable = MZ(0) XOR MZ(1)
+        //
+        // An H fault on qubit 1 (between the two measurements) should flip the
+        // observable via the late measurement term only.
+        use pecos_quantum::GateType;
+
+        let mut dag = DagCircuit::new();
+        dag.pz(&[0, 1]);
+        let early = dag.mz(&[0]);
+        dag.h(&[1]);
+        let late = dag.mz(&[1]);
+        dag.observable_labeled("split_obs", &[early[0], late[0]]);
+
+        let map = InfluenceBuilder::new(&dag)
+            .with_circuit_annotations(&dag)
+            .build();
+
+        assert_eq!(map.num_observables(), 1);
+
+        // H(1) fault location — between the two measurements, on qubit 1
+        let h_q1 = map
+            .locations
+            .iter()
+            .enumerate()
+            .find(|(_, loc)| {
+                loc.gate_type == GateType::H
+                    && loc.qubits.first().is_some_and(|q| q.index() == 1)
+                    && !loc.before
+            })
+            .map(|(idx, _)| idx)
+            .expect("H(1) fault location");
+
+        // X fault after H(1) becomes Z before MZ(1), which does NOT flip MZ.
+        // Z fault after H(1) becomes X before MZ(1), which DOES flip MZ.
+        assert!(
+            !map.get_observable_indices(h_q1, Pauli::X.as_u8())
+                .is_empty()
+                || !map
+                    .get_observable_indices(h_q1, Pauli::Z.as_u8())
+                    .is_empty(),
+            "at least one Pauli fault between measurements should flip the late term"
+        );
+    }
+
+    #[test]
+    fn test_duplicate_observable_terms_cancel_in_influence_map() {
+        let mut dag = DagCircuit::new();
+        dag.pz(&[0]);
+        dag.h(&[0]);
+        let meas = dag.mz(&[0]);
+        dag.observable_labeled("duplicate_record_obs", &[meas[0], meas[0]]);
+
+        let map = InfluenceBuilder::new(&dag)
+            .with_circuit_annotations(&dag)
+            .build();
+
+        assert_eq!(map.num_observables(), 1);
+        for loc_idx in 0..map.locations.len() {
+            for pauli in [Pauli::X, Pauli::Y, Pauli::Z] {
+                assert!(
+                    map.get_observable_indices(loc_idx, pauli.as_u8())
+                        .is_empty(),
+                    "observable record XOR should cancel duplicate measurement terms"
+                );
+            }
+        }
     }
 }
diff --git a/crates/pecos-qec/src/fault_tolerance/lookup_decoder.rs b/crates/pecos-qec/src/fault_tolerance/lookup_decoder.rs
new file mode 100644
index 000000000..50d828465
--- /dev/null
+++ b/crates/pecos-qec/src/fault_tolerance/lookup_decoder.rs
@@ -0,0 +1,514 @@
+// Copyright 2026 The PECOS Developers
+//
+// Licensed under the Apache License, Version 2.0 (the "License"); you may not use this file except
+// in compliance with the License. You may obtain a copy of the License at
+//
+//     https://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software distributed under the License
+// is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express
+// or implied. See the License for the specific language governing permissions and limitations under
+// the License.
+
+//! Maximum likelihood lookup table decoder.
+//!
+//! Builds a decoder by enumerating fault combinations up to a given weight,
+//! computing their probabilities from a noise model, and for each syndrome
+//! pattern choosing the most likely observable outcome.
+//!
+//! # Example
+//!
+//! ```
+//! use pecos_qec::fault_tolerance::lookup_decoder::LookupDecoder;
+//! use pecos_qec::fault_tolerance::dem_builder::NoiseConfig;
+//! use pecos_qec::fault_tolerance::propagator::dag::DagFaultInfluenceMap;
+//!
+//! let map = DagFaultInfluenceMap::with_capacity(0);
+//! let noise = NoiseConfig::uniform(0.001);
+//!
+//! let decoder = LookupDecoder::build(&map, &noise, 3);
+//! let result = decoder.decode(&[]);
+//! assert!(result.known_syndrome);
+//! assert!(result.corrections.is_empty());
+//! ```
+
+use super::dem_builder::NoiseConfig;
+use super::propagator::dag::{DagFaultInfluenceMap, DagSpacetimeLocation, GateFaultLocation};
+use pecos_core::gate_type::GateType;
+use std::collections::BTreeMap;
+
+/// Maximum likelihood lookup table decoder.
+///
+/// Maps syndrome patterns (sets of fired detectors) to the most likely
+/// observable correction (which observables to flip).
+#[derive(Debug, Clone)]
+pub struct LookupDecoder {
+    /// Syndrome -> most likely observable flip pattern.
+    table: BTreeMap<Vec<u32>, Vec<bool>>,
+    /// Standard observable `L<n>` IDs in correction-vector order.
+    observable_ids: Vec<u32>,
+    /// Maximum fault weight enumerated.
+    max_weight: usize,
+    /// Total probability mass accounted for (weight 0 through `max_weight`).
+    accounted_probability: f64,
+}
+
+/// Result of decoding a syndrome.
+#[derive(Debug, Clone)]
+pub struct DecoderResult {
+    /// Which observables should be flipped (ML correction).
+    pub corrections: Vec<bool>,
+    /// Whether this syndrome was seen during enumeration.
+    pub known_syndrome: bool,
+    /// Whether any detector fired (non-empty syndrome).
+    /// For detection codes (d=2), discard shots where this is true.
+    pub detected: bool,
+}
+
+impl LookupDecoder {
+    /// Build a lookup decoder by enumerating faults up to the given weight.
+    ///
+    /// Uses the standard per-gate circuit noise model: each gate faults with
+    /// probability p, and each non-identity Pauli is equally likely (p/3 for
+    /// 1-qubit, p/15 for 2-qubit). Idle gates with T1/T2 use biased noise.
+    #[must_use]
+    pub fn build(map: &DagFaultInfluenceMap, noise: &NoiseConfig, max_weight: usize) -> Self {
+        let observable_ids = observable_ids(map);
+        let num_observables = observable_ids.len();
+
+        let loc_probs = compute_location_probs(&map.locations, noise);
+        let locs = map.gate_fault_locations();
+
+        // Pre-compute events and no-fault probabilities per gate location.
+        //
+        // For PZ/MZ gates, Z faults are physically no-ops. Their probability
+        // is absorbed into the no-fault probability so the total sums to 1.0.
+        //
+        // The combo probability uses a ratio approach:
+        //   base_prob = product of no_fault(i) over all locations
+        //   combo_prob = base_prob * product of (event_prob / no_fault) for participating locs
+        let mut loc_no_fault_probs: Vec<f64> = Vec::with_capacity(locs.len());
+        let mut loc_events: Vec<Vec<EventData>> = Vec::with_capacity(locs.len());
+
+        for loc in &locs {
+            let p = gate_location_prob(loc, &loc_probs, &map.locations);
+
+            let events = loc.all_events();
+            let num_physical_events = events.len();
+
+            // For idle gates with T1/T2, compute biased per-Pauli probabilities
+            let idle_pauli_probs = if loc.gate_type == GateType::Idle {
+                let duration = map
+                    .locations
+                    .iter()
+                    .find(|l| l.node == loc.node && l.before == loc.before)
+                    .map_or(1, |l| l.idle_duration.max(1));
+                // Duration values are small integers; precision loss is not a concern.
+                #[allow(clippy::cast_precision_loss)]
+                Some(noise.idle_pauli_probs(duration as f64))
+            } else {
+                None
+            };
+
+            let n_qubits = loc.num_qubits();
+            let custom_weights = if idle_pauli_probs.is_some() {
+                None
+            } else if n_qubits == 1 {
+                noise.p1_weights.as_ref()
+            } else {
+                noise.p2_weights.as_ref()
+            };
+
+            let event_probs: Vec<f64> = if let Some(pp) = &idle_pauli_probs {
+                events
+                    .iter()
+                    .map(|event| {
+                        let pauli = event
+                            .pauli
+                            .paulis()
+                            .first()
+                            .map_or(pecos_core::Pauli::I, |&(pa, _)| pa);
+                        match pauli {
+                            pecos_core::Pauli::X => pp.px,
+                            pecos_core::Pauli::Y => pp.py,
+                            pecos_core::Pauli::Z => pp.pz,
+                            pecos_core::Pauli::I => 0.0,
+                        }
+                    })
+                    .collect()
+            } else if let Some(weights) = custom_weights {
+                events
+                    .iter()
+                    .map(|event| p * weights.weight_for(&event.pauli))
+                    .collect()
+            } else {
+                // Event count is a small integer; precision loss is not a concern.
+                #[allow(clippy::cast_precision_loss)]
+                let per_event = if num_physical_events > 0 {
+                    p / num_physical_events as f64
+                } else {
+                    0.0
+                };
+                vec![per_event; events.len()]
+            };
+
+            // No-fault = 1 - sum(event probs), absorbing filtered Paulis
+            let total_event_prob: f64 = event_probs.iter().sum();
+            let no_fault = (1.0 - total_event_prob).max(0.0);
+
+            let event_data: Vec<EventData> = events
+                .into_iter()
+                .zip(event_probs)
+                .map(|(event, prob)| {
+                    let ratio = if no_fault > 0.0 {
+                        prob / no_fault
+                    } else {
+                        prob
+                    };
+                    EventData {
+                        prob: ratio,
+                        detectors: event.detectors,
+                        observable_ids: event
+                            .dem_outputs
+                            .iter()
+                            .filter_map(|&idx| map.observable_id_for_internal_dem_output(idx))
+                            .collect(),
+                    }
+                })
+                .collect();
+
+            loc_no_fault_probs.push(no_fault);
+            loc_events.push(event_data);
+        }
+
+        // Accumulate syndrome probabilities separately from per-observable
+        // correction weights. This keeps probability accounting well-defined
+        // even for detector-only maps with zero observables.
+        let mut syndrome_probabilities: BTreeMap<Vec<u32>, f64> = BTreeMap::new();
+
+        // Accumulate: syndrome -> per-observable (flip_prob, noflip_prob)
+        let mut syndrome_data: BTreeMap<Vec<u32>, Vec<(f64, f64)>> = BTreeMap::new();
+
+        // Base probability: all locations no-fault
+        let base_prob: f64 = loc_no_fault_probs.iter().product();
+
+        // Weight 0: no faults. Empty syndrome, no observable flips.
+        {
+            syndrome_probabilities.insert(Vec::new(), base_prob);
+            let entry = syndrome_data
+                .entry(Vec::new())
+                .or_insert_with(|| vec![(0.0, 0.0); num_observables]);
+            for w in entry.iter_mut() {
+                w.1 += base_prob; // no flip
+            }
+        }
+
+        // Weight 1..max_weight
+        // Start with base_prob (all no-fault). Each event replaces a location's
+        // no-fault factor with the event factor via the pre-computed ratio.
+        let combo_state = ComboState {
+            prob: base_prob,
+            detectors: Vec::new(),
+            observable_ids: Vec::new(),
+        };
+
+        for weight in 1..=max_weight {
+            enumerate_combos(
+                &loc_events,
+                weight,
+                0,
+                &combo_state,
+                &observable_ids,
+                &mut syndrome_probabilities,
+                &mut syndrome_data,
+            );
+        }
+
+        let accounted_probability: f64 = syndrome_probabilities.values().sum();
+
+        // Build ML decision table
+        let table = syndrome_data
+            .into_iter()
+            .map(|(syndrome, weights)| {
+                let corrections: Vec<bool> = weights
+                    .iter()
+                    .map(|&(flip, noflip)| flip > noflip)
+                    .collect();
+                (syndrome, corrections)
+            })
+            .collect();
+
+        Self {
+            table,
+            observable_ids,
+            max_weight,
+            accounted_probability,
+        }
+    }
+
+    /// Decode a syndrome given as detector indices.
+    #[must_use]
+    pub fn decode(&self, syndrome: &[u32]) -> DecoderResult {
+        let mut key: Vec<u32> = syndrome.to_vec();
+        key.sort_unstable();
+        let detected = !key.is_empty();
+
+        if let Some(corrections) = self.table.get(&key) {
+            DecoderResult {
+                corrections: corrections.clone(),
+                known_syndrome: true,
+                detected,
+            }
+        } else {
+            DecoderResult {
+                corrections: vec![false; self.observable_ids.len()],
+                known_syndrome: false,
+                detected,
+            }
+        }
+    }
+
+    /// Decode from a boolean detector vector.
+    #[must_use]
+    pub fn decode_from_bools(&self, detectors: &[bool]) -> DecoderResult {
+        let syndrome: Vec<u32> = detectors
+            .iter()
+            .enumerate()
+            .filter_map(|(i, &fired)| {
+                if fired {
+                    #[allow(clippy::cast_possible_truncation)]
+                    Some(i as u32)
+                } else {
+                    None
+                }
+            })
+            .collect();
+        self.decode(&syndrome)
+    }
+
+    /// Number of distinct syndrome patterns in the table.
+    #[must_use]
+    pub fn num_syndromes(&self) -> usize {
+        self.table.len()
+    }
+
+    /// Maximum fault weight that was enumerated.
+    #[must_use]
+    pub fn max_weight(&self) -> usize {
+        self.max_weight
+    }
+
+    /// Number of observable channels.
+    #[must_use]
+    pub fn num_observables(&self) -> usize {
+        self.observable_ids.len()
+    }
+
+    /// Standard observable `L<n>` IDs in correction-vector order.
+    #[must_use]
+    pub fn observable_ids(&self) -> &[u32] {
+        &self.observable_ids
+    }
+
+    /// Estimated upper bound on the probability mass NOT accounted for
+    /// due to weight truncation.
+    ///
+    /// This bounds the total probability of fault combinations with
+    /// weight > `max_weight`. For low noise rates, this is small.
+    /// If it's large (> 0.01), consider increasing `max_weight`.
+    #[must_use]
+    pub fn truncation_bound(&self) -> f64 {
+        (1.0 - self.accounted_probability).max(0.0)
+    }
+
+    /// Total probability mass accounted for (weights 0 through `max_weight`).
+    ///
+    /// Should be close to 1.0 for low noise rates with sufficient `max_weight`.
+    #[must_use]
+    pub fn accounted_probability(&self) -> f64 {
+        self.accounted_probability
+    }
+}
+
+// ============================================================================
+// Internal types and helpers
+// ============================================================================
+
+struct EventData {
+    prob: f64,
+    detectors: Vec<u32>,
+    observable_ids: Vec<u32>,
+}
+
+#[derive(Clone)]
+struct ComboState {
+    prob: f64,
+    detectors: Vec<u32>,
+    observable_ids: Vec<u32>,
+}
+
+impl ComboState {
+    /// Compose with a new event: XOR detectors/observable IDs, multiply prob.
+    fn compose(&self, event: &EventData) -> Self {
+        let mut detectors = self.detectors.clone();
+        xor_into(&mut detectors, &event.detectors);
+        let mut observable_ids = self.observable_ids.clone();
+        xor_into(&mut observable_ids, &event.observable_ids);
+        Self {
+            prob: self.prob * event.prob,
+            detectors,
+            observable_ids,
+        }
+    }
+}
+
+/// Symmetric difference (XOR) of sorted u32 vecs.
+fn xor_into(acc: &mut Vec<u32>, other: &[u32]) {
+    if other.is_empty() {
+        return;
+    }
+    if acc.is_empty() {
+        acc.extend_from_slice(other);
+        return;
+    }
+    let mut result = Vec::with_capacity(acc.len() + other.len());
+    let (mut i, mut j) = (0, 0);
+    while i < acc.len() && j < other.len() {
+        match acc[i].cmp(&other[j]) {
+            std::cmp::Ordering::Less => {
+                result.push(acc[i]);
+                i += 1;
+            }
+            std::cmp::Ordering::Greater => {
+                result.push(other[j]);
+                j += 1;
+            }
+            std::cmp::Ordering::Equal => {
+                i += 1;
+                j += 1;
+            }
+        }
+    }
+    result.extend_from_slice(&acc[i..]);
+    result.extend_from_slice(&other[j..]);
+    *acc = result;
+}
+
+/// Recursive combination enumeration with probability tracking.
+fn enumerate_combos(
+    loc_events: &[Vec<EventData>],
+    remaining: usize,
+    start_loc: usize,
+    state: &ComboState,
+    observable_ids: &[u32],
+    syndrome_probabilities: &mut BTreeMap<Vec<u32>, f64>,
+    syndrome_data: &mut BTreeMap<Vec<u32>, Vec<(f64, f64)>>,
+) {
+    if remaining == 0 {
+        let mut syndrome = state.detectors.clone();
+        syndrome.sort_unstable();
+
+        *syndrome_probabilities
+            .entry(syndrome.clone())
+            .or_insert(0.0) += state.prob;
+
+        let entry = syndrome_data
+            .entry(syndrome)
+            .or_insert_with(|| vec![(0.0, 0.0); observable_ids.len()]);
+
+        for (&observable_id, weights) in observable_ids.iter().zip(entry.iter_mut()) {
+            let flipped = state.observable_ids.contains(&observable_id);
+            if flipped {
+                weights.0 += state.prob;
+            } else {
+                weights.1 += state.prob;
+            }
+        }
+        return;
+    }
+
+    for loc_idx in start_loc..loc_events.len() {
+        for event in &loc_events[loc_idx] {
+            let next_state = state.compose(event);
+            enumerate_combos(
+                loc_events,
+                remaining - 1,
+                loc_idx + 1,
+                &next_state,
+                observable_ids,
+                syndrome_probabilities,
+                syndrome_data,
+            );
+        }
+    }
+}
+
+/// Compute per-location error probabilities from noise config.
+fn compute_location_probs(locations: &[DagSpacetimeLocation], noise: &NoiseConfig) -> Vec<f64> {
+    super::dem_builder::sampler::compute_location_probs_from_noise(locations, noise)
+}
+
+/// Get the per-qubit error probability for a gate fault location.
+///
+/// Since `gate_fault_locations` groups per-qubit locations, all per-qubit
+/// locations within a gate have the same gate-type-based probability.
+fn gate_location_prob(
+    loc: &GateFaultLocation<'_>,
+    loc_probs: &[f64],
+    all_locations: &[DagSpacetimeLocation],
+) -> f64 {
+    // Find any per-qubit location in the influence map for this gate
+    for (i, l) in all_locations.iter().enumerate() {
+        if l.node == loc.node && l.before == loc.before {
+            return loc_probs[i];
+        }
+    }
+    0.0
+}
+
+fn observable_ids(map: &DagFaultInfluenceMap) -> Vec<u32> {
+    map.observable_ids().into_iter().collect()
+}
+
+#[cfg(test)]
+mod tests {
+    use super::*;
+    use crate::fault_tolerance::InfluenceBuilder;
+    use pecos_core::pauli::X;
+    use pecos_quantum::DagCircuit;
+
+    #[test]
+    fn observable_indices_use_compact_l_namespace_with_tracked_paulis() {
+        let mut dag = DagCircuit::new();
+        dag.pz(&[0]);
+        dag.tracked_pauli_labeled("track_x", X(0));
+        let meas = dag.mz(&[0]);
+        dag.observable_labeled("obs0", &[meas[0]]);
+
+        let map = InfluenceBuilder::new(&dag)
+            .with_circuit_annotations(&dag)
+            .build();
+        assert_eq!(map.num_tracked_paulis(), 1);
+        assert_eq!(map.num_observables(), 1);
+
+        let decoder = LookupDecoder::build(&map, &NoiseConfig::uniform(0.01), 1);
+        assert_eq!(decoder.observable_ids(), &[0]);
+    }
+
+    #[test]
+    fn detector_only_decoder_accounts_probability_without_observables() {
+        let mut dag = DagCircuit::new();
+        dag.pz(&[0, 1]);
+        dag.cx(&[(0, 1)]);
+        let meas = dag.mz(&[1]);
+        dag.detector(&[meas[0]]);
+
+        let map = InfluenceBuilder::new(&dag).build();
+        assert_eq!(map.num_observables(), 0);
+
+        let decoder = LookupDecoder::build(&map, &NoiseConfig::uniform(0.01), 0);
+        assert_eq!(decoder.num_observables(), 0);
+        assert!(decoder.accounted_probability() > 0.0);
+        assert!(decoder.truncation_bound() < 1.0);
+    }
+}
diff --git a/crates/pecos-qec/src/fault_tolerance/noisy_sampler.rs b/crates/pecos-qec/src/fault_tolerance/noisy_sampler.rs
deleted file mode 100644
index 7dca682dd..000000000
--- a/crates/pecos-qec/src/fault_tolerance/noisy_sampler.rs
+++ /dev/null
@@ -1,692 +0,0 @@
-//! Noisy Measurement Sampler using Precomputed Influence Maps
-//!
-//! This module provides efficient sampling of noisy measurement outcomes using
-//! backward-propagated influence maps. Instead of simulating the full circuit
-//! for each shot, we:
-//!
-//! 1. Precompute which fault locations affect which detectors/logicals
-//! 2. For each shot, sample which faults fire
-//! 3. Use O(1) lookups to find which detectors/logicals flip
-//!
-//! This approach is O(shots × `fault_locations`) instead of O(shots × `circuit_depth`),
-//! providing significant speedup for noisy QEC simulations.
-//!
-//! # Example
-//!
-//! ```
-//! use pecos_qec::fault_tolerance::noisy_sampler::{NoisySampler, UniformNoiseModel};
-//! use pecos_qec::fault_tolerance::DagFaultAnalyzer;
-//! use pecos_quantum::DagCircuit;
-//!
-//! // Build a simple circuit
-//! let mut dag = DagCircuit::new();
-//! dag.pz(&[2]);
-//! dag.cx(&[(0, 2)]);
-//! dag.cx(&[(1, 2)]);
-//! dag.mz(&[2]);
-//!
-//! // Build influence map (precomputation)
-//! let analyzer = DagFaultAnalyzer::new(&dag);
-//! let influence_map = analyzer.build_influence_map();
-//!
-//! // Create noise model (uniform depolarizing)
-//! let noise = UniformNoiseModel::depolarizing(0.001);
-//!
-//! // Sample many shots
-//! let mut sampler = NoisySampler::new(&influence_map, noise, 42);
-//! let results = sampler.sample(100);
-//!
-//! // Analyze results
-//! for shot in &results {
-//!     if shot.has_logical_error() {
-//!         // ...
-//!     }
-//! }
-//! ```
-
-use super::propagator::Pauli;
-use super::propagator::dag::DagFaultInfluenceMap;
-use pecos_random::rng_ext::RngProbabilityExt;
-use pecos_random::{PecosRng, Rng};
-use std::collections::BTreeSet;
-
-/// Result from a single shot of noisy sampling.
-#[derive(Debug, Clone)]
-pub struct ShotResult {
-    /// Detectors that flipped (indices into `influence_map.detectors`).
-    pub detector_flips: Vec<u32>,
-    /// Logicals that flipped (indices).
-    pub logical_flips: Vec<u32>,
-    /// Number of faults that fired in this shot.
-    pub fault_count: usize,
-}
-
-impl ShotResult {
-    /// Create an empty result.
-    #[must_use]
-    pub fn new() -> Self {
-        Self {
-            detector_flips: Vec::new(),
-            logical_flips: Vec::new(),
-            fault_count: 0,
-        }
-    }
-
-    /// Check if any logical error occurred.
-    #[inline]
-    #[must_use]
-    pub fn has_logical_error(&self) -> bool {
-        !self.logical_flips.is_empty()
-    }
-
-    /// Check if any syndrome was triggered.
-    #[inline]
-    #[must_use]
-    pub fn has_syndrome(&self) -> bool {
-        !self.detector_flips.is_empty()
-    }
-
-    /// Check if this is an undetectable logical error.
-    #[inline]
-    #[must_use]
-    pub fn is_undetectable_logical_error(&self) -> bool {
-        self.has_logical_error() && !self.has_syndrome()
-    }
-}
-
-impl Default for ShotResult {
-    fn default() -> Self {
-        Self::new()
-    }
-}
-
-/// Trait for noise models that can sample faults at each location.
-pub trait NoiseModel {
-    /// Sample a Pauli fault at the given location.
-    ///
-    /// Returns `Pauli::I` for no fault, or `X/Y/Z` for a fault.
-    fn sample_fault(&mut self, loc_idx: usize, rng: &mut impl Rng) -> Pauli;
-
-    /// Get the total error probability at a location (for statistics).
-    fn error_probability(&self, loc_idx: usize) -> f64;
-}
-
-/// Uniform depolarizing noise model.
-///
-/// Same error probability at every location. With probability p,
-/// applies X, Y, or Z with equal probability (p/3 each).
-#[derive(Debug, Clone)]
-pub struct UniformNoiseModel {
-    /// Total error probability per location.
-    p_error: f64,
-    /// Threshold for error occurrence (`p_error` * `u64::MAX`).
-    threshold: u64,
-}
-
-impl UniformNoiseModel {
-    /// Create a uniform noise model with the given error probability.
-    #[must_use]
-    pub fn new(p_error: f64) -> Self {
-        #[allow(
-            clippy::cast_sign_loss,
-            clippy::cast_possible_truncation,
-            clippy::cast_precision_loss
-        )]
-        // probability in [0,1] so product fits in u64
-        let threshold = (p_error * u64::MAX as f64) as u64;
-        Self { p_error, threshold }
-    }
-
-    /// Create a depolarizing noise model (convenience alias).
-    #[must_use]
-    pub fn depolarizing(p_error: f64) -> Self {
-        Self::new(p_error)
-    }
-}
-
-impl NoiseModel for UniformNoiseModel {
-    fn sample_fault(&mut self, _loc_idx: usize, rng: &mut impl Rng) -> Pauli {
-        let rand = rng.next_u64();
-        if rand < self.threshold {
-            // Error occurred, sample which Pauli
-            match (rng.next_u32() % 3) as u8 {
-                0 => Pauli::X,
-                1 => Pauli::Y,
-                _ => Pauli::Z,
-            }
-        } else {
-            Pauli::I
-        }
-    }
-
-    fn error_probability(&self, _loc_idx: usize) -> f64 {
-        self.p_error
-    }
-}
-
-/// Per-location noise model with different probabilities.
-///
-/// Each location can have different error rates.
-#[derive(Debug, Clone)]
-pub struct PerLocationNoiseModel {
-    /// Error probabilities per location.
-    probabilities: Vec<f64>,
-    /// Precomputed thresholds.
-    thresholds: Vec<u64>,
-}
-
-impl PerLocationNoiseModel {
-    /// Create from a vector of error probabilities (one per location).
-    #[must_use]
-    pub fn new(probabilities: Vec<f64>) -> Self {
-        let thresholds = probabilities
-            .iter()
-            .map(|&p| {
-                #[allow(
-                    clippy::cast_sign_loss,
-                    clippy::cast_possible_truncation,
-                    clippy::cast_precision_loss
-                )]
-                // probability in [0,1] so product fits in u64
-                {
-                    (p * u64::MAX as f64) as u64
-                }
-            })
-            .collect();
-        Self {
-            probabilities,
-            thresholds,
-        }
-    }
-}
-
-impl NoiseModel for PerLocationNoiseModel {
-    fn sample_fault(&mut self, loc_idx: usize, rng: &mut impl Rng) -> Pauli {
-        let threshold = self.thresholds.get(loc_idx).copied().unwrap_or(0);
-        let rand = rng.next_u64();
-        if rand < threshold {
-            match (rng.next_u32() % 3) as u8 {
-                0 => Pauli::X,
-                1 => Pauli::Y,
-                _ => Pauli::Z,
-            }
-        } else {
-            Pauli::I
-        }
-    }
-
-    fn error_probability(&self, loc_idx: usize) -> f64 {
-        self.probabilities.get(loc_idx).copied().unwrap_or(0.0)
-    }
-}
-
-/// Noisy measurement sampler using precomputed influence maps.
-///
-/// This provides efficient sampling by using O(1) lookups from the
-/// influence map instead of full circuit simulation.
-pub struct NoisySampler<'a, N: NoiseModel> {
-    /// Reference to the precomputed influence map.
-    influence_map: &'a DagFaultInfluenceMap,
-    /// Noise model for sampling faults.
-    noise_model: N,
-    /// Random number generator.
-    rng: PecosRng,
-    /// Number of fault locations.
-    num_locations: usize,
-    /// Number of detectors.
-    num_detectors: usize,
-    /// Number of logicals (derived from influence map).
-    num_logicals: usize,
-}
-
-impl<'a, N: NoiseModel> NoisySampler<'a, N> {
-    /// Create a new noisy sampler.
-    ///
-    /// # Arguments
-    /// * `influence_map` - Precomputed influence map from backward propagation
-    /// * `noise_model` - Noise model for sampling faults
-    /// * `seed` - RNG seed for reproducibility
-    pub fn new(influence_map: &'a DagFaultInfluenceMap, noise_model: N, seed: u64) -> Self {
-        let num_locations = influence_map.locations.len();
-        let num_detectors = influence_map.detectors.len();
-
-        // Estimate num_logicals from the influence map
-        // (could be stored explicitly in the map)
-        let num_logicals = influence_map
-            .influences
-            .max_logical_index()
-            .map_or(0, |i| i + 1);
-
-        Self {
-            influence_map,
-            noise_model,
-            rng: PecosRng::seed_from_u64(seed),
-            num_locations,
-            num_detectors,
-            num_logicals,
-        }
-    }
-
-    /// Sample a single shot.
-    pub fn sample_one(&mut self) -> ShotResult {
-        // Track which detectors/logicals have flipped (using XOR)
-        let mut detector_flip_counts: Vec<u32> = vec![0; self.num_detectors];
-        let mut logical_flip_counts: Vec<u32> = vec![0; self.num_logicals.max(1)];
-        let mut fault_count = 0;
-
-        // Sample each fault location
-        for loc_idx in 0..self.num_locations {
-            let pauli = self.noise_model.sample_fault(loc_idx, &mut self.rng);
-
-            if pauli != Pauli::I {
-                fault_count += 1;
-
-                // Get affected detectors (O(1) lookup)
-                let detectors = self
-                    .influence_map
-                    .get_detector_indices(loc_idx, pauli.as_u8());
-                for &det_idx in detectors {
-                    detector_flip_counts[det_idx as usize] ^= 1;
-                }
-
-                // Get affected logicals (O(1) lookup)
-                let logicals = self
-                    .influence_map
-                    .get_logical_indices(loc_idx, pauli.as_u8());
-                for &log_idx in logicals {
-                    if (log_idx as usize) < logical_flip_counts.len() {
-                        logical_flip_counts[log_idx as usize] ^= 1;
-                    }
-                }
-            }
-        }
-
-        // Collect indices that ended up flipped (odd count)
-        let detector_flips: Vec<u32> = detector_flip_counts
-            .iter()
-            .enumerate()
-            .filter(|(_, c)| **c == 1)
-            .map(|(i, _)| {
-                #[allow(clippy::cast_possible_truncation)] // detector index fits in u32
-                {
-                    i as u32
-                }
-            })
-            .collect();
-
-        let logical_flips: Vec<u32> = logical_flip_counts
-            .iter()
-            .enumerate()
-            .filter(|(_, c)| **c == 1)
-            .map(|(i, _)| {
-                #[allow(clippy::cast_possible_truncation)] // logical index fits in u32
-                {
-                    i as u32
-                }
-            })
-            .collect();
-
-        ShotResult {
-            detector_flips,
-            logical_flips,
-            fault_count,
-        }
-    }
-
-    /// Sample multiple shots.
-    pub fn sample(&mut self, num_shots: usize) -> Vec<ShotResult> {
-        (0..num_shots).map(|_| self.sample_one()).collect()
-    }
-
-    /// Sample and compute statistics.
-    pub fn sample_statistics(&mut self, num_shots: usize) -> SamplingStatistics {
-        let mut stats = SamplingStatistics::new();
-
-        for _ in 0..num_shots {
-            let result = self.sample_one();
-            stats.record(&result);
-        }
-
-        stats
-    }
-
-    /// Get the number of fault locations.
-    pub fn num_locations(&self) -> usize {
-        self.num_locations
-    }
-
-    /// Get the number of detectors.
-    pub fn num_detectors(&self) -> usize {
-        self.num_detectors
-    }
-}
-
-/// Statistics from sampling.
-#[derive(Debug, Clone)]
-pub struct SamplingStatistics {
-    /// Total number of shots.
-    pub total_shots: usize,
-    /// Number of shots with logical errors.
-    pub logical_error_count: usize,
-    /// Number of shots with syndromes (detector flips).
-    pub syndrome_count: usize,
-    /// Number of undetectable logical errors.
-    pub undetectable_count: usize,
-    /// Total faults across all shots.
-    pub total_faults: usize,
-}
-
-impl SamplingStatistics {
-    /// Create empty statistics.
-    #[must_use]
-    pub fn new() -> Self {
-        Self {
-            total_shots: 0,
-            logical_error_count: 0,
-            syndrome_count: 0,
-            undetectable_count: 0,
-            total_faults: 0,
-        }
-    }
-
-    /// Record a shot result.
-    pub fn record(&mut self, result: &ShotResult) {
-        self.total_shots += 1;
-        self.total_faults += result.fault_count;
-
-        if result.has_logical_error() {
-            self.logical_error_count += 1;
-        }
-        if result.has_syndrome() {
-            self.syndrome_count += 1;
-        }
-        if result.is_undetectable_logical_error() {
-            self.undetectable_count += 1;
-        }
-    }
-
-    /// Logical error rate.
-    #[must_use]
-    #[allow(clippy::cast_precision_loss)] // rate calculation
-    pub fn logical_error_rate(&self) -> f64 {
-        if self.total_shots == 0 {
-            0.0
-        } else {
-            self.logical_error_count as f64 / self.total_shots as f64
-        }
-    }
-
-    /// Syndrome rate (fraction of shots with non-trivial syndrome).
-    #[must_use]
-    #[allow(clippy::cast_precision_loss)] // rate calculation
-    pub fn syndrome_rate(&self) -> f64 {
-        if self.total_shots == 0 {
-            0.0
-        } else {
-            self.syndrome_count as f64 / self.total_shots as f64
-        }
-    }
-
-    /// Undetectable error rate.
-    #[must_use]
-    #[allow(clippy::cast_precision_loss)] // rate calculation
-    pub fn undetectable_rate(&self) -> f64 {
-        if self.total_shots == 0 {
-            0.0
-        } else {
-            self.undetectable_count as f64 / self.total_shots as f64
-        }
-    }
-
-    /// Average faults per shot.
-    #[must_use]
-    #[allow(clippy::cast_precision_loss)] // rate calculation
-    pub fn average_faults(&self) -> f64 {
-        if self.total_shots == 0 {
-            0.0
-        } else {
-            self.total_faults as f64 / self.total_shots as f64
-        }
-    }
-}
-
-impl Default for SamplingStatistics {
-    fn default() -> Self {
-        Self::new()
-    }
-}
-
-// ============================================================================
-// Optimized Sampler using PecosRng batching and sparse tracking
-// ============================================================================
-
-/// Optimized noisy sampler using `PecosRng` batching and sparse flip tracking.
-///
-/// Key optimizations over [`NoisySampler`]:
-/// 1. Uses `check_probability_indices()` to get sparse list of fault locations
-/// 2. Uses `BTreeSet` for flip tracking instead of dense `Vec<u32>`
-/// 3. Reuses buffers across shots to avoid allocation overhead
-///
-/// For low error rates (p < 0.01), this can be 2-3x faster than the standard sampler.
-pub struct FastNoisySampler<'a> {
-    /// Reference to the precomputed influence map.
-    influence_map: &'a DagFaultInfluenceMap,
-    /// Error probability.
-    p_error: f64,
-    /// Precomputed threshold for probability check.
-    threshold: u64,
-    /// Random number generator (`PecosRng` for batching).
-    rng: PecosRng,
-    /// Number of fault locations.
-    num_locations: usize,
-    /// Number of logicals.
-    num_logicals: usize,
-    /// Reusable buffer for detector flips (sparse).
-    detector_flips_buffer: BTreeSet<u32>,
-    /// Reusable buffer for logical flips (sparse).
-    logical_flips_buffer: BTreeSet<u32>,
-}
-
-impl<'a> FastNoisySampler<'a> {
-    /// Create a new optimized sampler.
-    ///
-    /// # Arguments
-    /// * `influence_map` - Precomputed influence map
-    /// * `p_error` - Uniform depolarizing error probability
-    /// * `seed` - RNG seed
-    #[must_use]
-    pub fn new(influence_map: &'a DagFaultInfluenceMap, p_error: f64, seed: u64) -> Self {
-        let num_locations = influence_map.locations.len();
-        let num_logicals = influence_map
-            .influences
-            .max_logical_index()
-            .map_or(0, |i| i + 1);
-
-        let rng = PecosRng::seed_from_u64(seed);
-        let threshold = rng.probability_threshold(p_error);
-
-        Self {
-            influence_map,
-            p_error,
-            threshold,
-            rng,
-            num_locations,
-            num_logicals,
-            detector_flips_buffer: BTreeSet::new(),
-            logical_flips_buffer: BTreeSet::new(),
-        }
-    }
-
-    /// Sample a single shot using sparse tracking.
-    pub fn sample_one(&mut self) -> ShotResult {
-        // Clear reusable buffers
-        self.detector_flips_buffer.clear();
-        self.logical_flips_buffer.clear();
-
-        // Get sparse list of fault locations using batched RNG
-        let fault_indices = self
-            .rng
-            .check_probability_indices(self.threshold, self.num_locations);
-
-        let fault_count = fault_indices.len();
-
-        // Process only the faulted locations
-        for loc_idx in fault_indices {
-            // Select Pauli type: 0=X, 1=Y, 2=Z
-            let pauli_idx = self.rng.random_index_3();
-            let pauli = match pauli_idx {
-                0 => Pauli::X,
-                1 => Pauli::Y,
-                _ => Pauli::Z,
-            };
-
-            // Toggle affected detectors (XOR via HashSet toggle)
-            let detectors = self
-                .influence_map
-                .get_detector_indices(loc_idx, pauli.as_u8());
-            for &det_idx in detectors {
-                if !self.detector_flips_buffer.remove(&det_idx) {
-                    self.detector_flips_buffer.insert(det_idx);
-                }
-            }
-
-            // Toggle affected logicals
-            let logicals = self
-                .influence_map
-                .get_logical_indices(loc_idx, pauli.as_u8());
-            for &log_idx in logicals {
-                if (log_idx as usize) < self.num_logicals
-                    && !self.logical_flips_buffer.remove(&log_idx)
-                {
-                    self.logical_flips_buffer.insert(log_idx);
-                }
-            }
-        }
-
-        // Collect results
-        let detector_flips: Vec<u32> = self.detector_flips_buffer.iter().copied().collect();
-        let logical_flips: Vec<u32> = self.logical_flips_buffer.iter().copied().collect();
-
-        ShotResult {
-            detector_flips,
-            logical_flips,
-            fault_count,
-        }
-    }
-
-    /// Sample multiple shots.
-    pub fn sample(&mut self, num_shots: usize) -> Vec<ShotResult> {
-        (0..num_shots).map(|_| self.sample_one()).collect()
-    }
-
-    /// Sample and compute statistics.
-    pub fn sample_statistics(&mut self, num_shots: usize) -> SamplingStatistics {
-        let mut stats = SamplingStatistics::new();
-
-        for _ in 0..num_shots {
-            let result = self.sample_one();
-            stats.record(&result);
-        }
-
-        stats
-    }
-
-    /// Get the error probability.
-    #[must_use]
-    pub fn p_error(&self) -> f64 {
-        self.p_error
-    }
-
-    /// Get the number of fault locations.
-    #[must_use]
-    pub fn num_locations(&self) -> usize {
-        self.num_locations
-    }
-}
-
-#[cfg(test)]
-mod tests {
-    use super::*;
-
-    // Mock influence map for testing
-    #[allow(dead_code)]
-    fn create_test_influence_map() -> DagFaultInfluenceMap {
-        DagFaultInfluenceMap::with_capacity(0)
-    }
-
-    #[test]
-    fn test_uniform_noise_model() {
-        let mut noise = UniformNoiseModel::new(0.5);
-        let mut rng = PecosRng::seed_from_u64(42);
-
-        let mut error_count = 0;
-        for _ in 0..1000 {
-            if noise.sample_fault(0, &mut rng) != Pauli::I {
-                error_count += 1;
-            }
-        }
-
-        // Should be roughly 50%
-        assert!(error_count > 400 && error_count < 600);
-    }
-
-    #[test]
-    fn test_per_location_noise_model() {
-        let probs = vec![0.0, 0.5, 1.0];
-        let mut noise = PerLocationNoiseModel::new(probs);
-        let mut rng = PecosRng::seed_from_u64(42);
-
-        // Location 0: never errors
-        for _ in 0..100 {
-            assert_eq!(noise.sample_fault(0, &mut rng), Pauli::I);
-        }
-
-        // Location 2: always errors
-        for _ in 0..100 {
-            assert_ne!(noise.sample_fault(2, &mut rng), Pauli::I);
-        }
-    }
-
-    #[test]
-    fn test_shot_result() {
-        let mut result = ShotResult::new();
-        assert!(!result.has_logical_error());
-        assert!(!result.has_syndrome());
-
-        result.logical_flips.push(0);
-        assert!(result.has_logical_error());
-        assert!(result.is_undetectable_logical_error());
-
-        result.detector_flips.push(0);
-        assert!(!result.is_undetectable_logical_error());
-    }
-
-    #[test]
-    fn test_statistics() {
-        let mut stats = SamplingStatistics::new();
-
-        // Shot with no errors
-        stats.record(&ShotResult::new());
-
-        // Shot with syndrome only
-        let mut shot_with_syndrome = ShotResult::new();
-        shot_with_syndrome.detector_flips.push(0);
-        stats.record(&shot_with_syndrome);
-
-        // Shot with logical error
-        let mut shot_with_logical = ShotResult::new();
-        shot_with_logical.logical_flips.push(0);
-        shot_with_logical.detector_flips.push(1);
-        stats.record(&shot_with_logical);
-
-        // Shot with undetectable logical
-        let mut shot_undetectable = ShotResult::new();
-        shot_undetectable.logical_flips.push(0);
-        stats.record(&shot_undetectable);
-
-        assert_eq!(stats.total_shots, 4);
-        assert_eq!(stats.logical_error_count, 2);
-        assert_eq!(stats.syndrome_count, 2);
-        assert_eq!(stats.undetectable_count, 1);
-    }
-}
diff --git a/crates/pecos-qec/src/fault_tolerance/pauli_prop_checker.rs b/crates/pecos-qec/src/fault_tolerance/pauli_prop_checker.rs
index 7dcedca99..b7cacb7c3 100644
--- a/crates/pecos-qec/src/fault_tolerance/pauli_prop_checker.rs
+++ b/crates/pecos-qec/src/fault_tolerance/pauli_prop_checker.rs
@@ -76,7 +76,7 @@ pub fn detect_input_qubits(circuit: &TickCircuit) -> Vec<usize> {
     let mut prepared_qubits: HashSet<usize> = HashSet::new();
 
     for (_tick_idx, tick) in circuit.iter_ticks() {
-        for gate in tick.gates() {
+        for gate in tick.iter_gate_batches() {
             for &qubit in &gate.qubits {
                 let q = qubit.index();
                 all_qubits.insert(q);
@@ -108,7 +108,7 @@ pub fn detect_ancilla_qubits(circuit: &TickCircuit) -> Vec<usize> {
     let mut prepared_qubits: HashSet<usize> = HashSet::new();
 
     for (_tick_idx, tick) in circuit.iter_ticks() {
-        for gate in tick.gates() {
+        for gate in tick.iter_gate_batches() {
             if gate.gate_type == GateType::PZ {
                 for &qubit in &gate.qubits {
                     prepared_qubits.insert(qubit.index());
@@ -142,7 +142,7 @@ pub fn detect_output_qubits(circuit: &TickCircuit) -> Vec<usize> {
     let mut measured_qubits: HashSet<usize> = HashSet::new();
 
     for (_tick_idx, tick) in circuit.iter_ticks() {
-        for gate in tick.gates() {
+        for gate in tick.iter_gate_batches() {
             for &qubit in &gate.qubits {
                 let q = qubit.index();
                 all_qubits.insert(q);
@@ -191,7 +191,7 @@ impl CircuitIO {
         let mut measured_qubits: HashSet<usize> = HashSet::new();
 
         for (_tick_idx, tick) in circuit.iter_ticks() {
-            for gate in tick.gates() {
+            for gate in tick.iter_gate_batches() {
                 for &qubit in &gate.qubits {
                     let q = qubit.index();
                     all_qubits.insert(q);
@@ -296,8 +296,8 @@ pub fn propagate_fault(circuit: &TickCircuit, fault: &PauliFault) -> PauliProp {
         }
 
         // Apply all gates in this tick
-        for gate in tick.gates() {
-            apply_gate(&mut prop, gate, Direction::Forward);
+        for gate in tick.iter_gate_batches() {
+            apply_gate(&mut prop, gate.as_gate(), Direction::Forward);
         }
     }
 
@@ -335,8 +335,8 @@ pub fn propagate_faults(circuit: &TickCircuit, faults: &FaultConfiguration) -> P
     // Propagate through the circuit from the minimum tick onward
     for (tick_idx, tick) in circuit.iter_ticks() {
         if tick_idx >= min_tick {
-            for gate in tick.gates() {
-                apply_gate(&mut prop, gate, Direction::Forward);
+            for gate in tick.iter_gate_batches() {
+                apply_gate(&mut prop, gate.as_gate(), Direction::Forward);
             }
         }
     }
@@ -1011,7 +1011,7 @@ pub fn extract_measurement_rounds(circuit: &TickCircuit) -> Vec<MeasurementRound
         let mut z_qubits = Vec::new();
         let x_qubits = Vec::new(); // Currently not tracking X-basis measurements
 
-        for gate in tick.gates() {
+        for gate in tick.iter_gate_batches() {
             match gate.gate_type {
                 GateType::MZ | GateType::MeasureFree => {
                     // Z-basis measurement
@@ -1070,7 +1070,7 @@ fn propagate_until_tick(circuit: &TickCircuit, fault: &PauliFault, until_tick: u
         }
 
         // Propagate through all gates in this tick
-        for gate in tick.gates() {
+        for gate in tick.iter_gate_batches() {
             let qubits: Vec<QubitId> = gate.qubits.iter().copied().collect();
             match gate.gate_type {
                 GateType::CX if qubits.len() >= 2 => {
@@ -1083,28 +1083,53 @@ fn propagate_until_tick(circuit: &TickCircuit, fault: &PauliFault, until_tick: u
                     prop.cy(&[(qubits[0], qubits[1])]);
                 }
                 GateType::H => {
-                    for q in &qubits {
-                        prop.h(&[*q]);
-                    }
+                    prop.h(&qubits);
                 }
-                GateType::SZ | GateType::SZdg => {
-                    for q in &qubits {
-                        prop.sz(&[*q]);
-                    }
+                GateType::F => {
+                    prop.f(&qubits);
                 }
-                GateType::SX | GateType::SXdg => {
-                    for q in &qubits {
-                        prop.sx(&[*q]);
-                    }
+                GateType::Fdg => {
+                    prop.fdg(&qubits);
                 }
-                GateType::SY | GateType::SYdg => {
-                    for q in &qubits {
-                        prop.sy(&[*q]);
-                    }
+                GateType::SX => {
+                    prop.sx(&qubits);
+                }
+                GateType::SXdg => {
+                    prop.sxdg(&qubits);
+                }
+                GateType::SY => {
+                    prop.sy(&qubits);
+                }
+                GateType::SYdg => {
+                    prop.sydg(&qubits);
+                }
+                GateType::SZ => {
+                    prop.sz(&qubits);
+                }
+                GateType::SZdg => {
+                    prop.szdg(&qubits);
                 }
                 GateType::SWAP if qubits.len() >= 2 => {
                     prop.swap(&[(qubits[0], qubits[1])]);
                 }
+                GateType::SXX if qubits.len() >= 2 => {
+                    prop.sxx(&[(qubits[0], qubits[1])]);
+                }
+                GateType::SXXdg if qubits.len() >= 2 => {
+                    prop.sxxdg(&[(qubits[0], qubits[1])]);
+                }
+                GateType::SYY if qubits.len() >= 2 => {
+                    prop.syy(&[(qubits[0], qubits[1])]);
+                }
+                GateType::SYYdg if qubits.len() >= 2 => {
+                    prop.syydg(&[(qubits[0], qubits[1])]);
+                }
+                GateType::SZZ if qubits.len() >= 2 => {
+                    prop.szz(&[(qubits[0], qubits[1])]);
+                }
+                GateType::SZZdg if qubits.len() >= 2 => {
+                    prop.szzdg(&[(qubits[0], qubits[1])]);
+                }
                 _ => {}
             }
         }
@@ -2099,8 +2124,8 @@ impl<'a> PauliPropChecker<'a> {
 
                     // Propagate through circuit
                     for (_tick_idx, tick) in self.circuit.iter_ticks() {
-                        for gate in tick.gates() {
-                            apply_gate(&mut prop, gate, Direction::Forward);
+                        for gate in tick.iter_gate_batches() {
+                            apply_gate(&mut prop, gate.as_gate(), Direction::Forward);
                         }
                     }
 
@@ -3576,7 +3601,8 @@ mod tests {
         let mut circuit = TickCircuit::new();
         circuit.tick().pz(&[0, 1, 2]); // Prepare all qubits
         circuit.tick().h(&[0]);
-        circuit.tick().cx(&[(0, 1), (0, 2)]);
+        circuit.tick().cx(&[(0, 1)]);
+        circuit.tick().cx(&[(0, 2)]);
 
         let input_qubits = detect_input_qubits(&circuit);
         assert!(
@@ -4073,7 +4099,8 @@ mod tests {
         let mut circuit = TickCircuit::new();
         circuit.tick().pz(&[0, 1, 2]); // All qubits prepared
         circuit.tick().h(&[0]);
-        circuit.tick().cx(&[(0, 1), (0, 2)]);
+        circuit.tick().cx(&[(0, 1)]);
+        circuit.tick().cx(&[(0, 2)]);
         circuit.tick().mz(&[0, 1, 2]); // All measured
 
         let checker = PauliPropChecker::new(&circuit);
@@ -4097,7 +4124,8 @@ mod tests {
         let mut circuit = TickCircuit::new();
         circuit.tick().pz(&[0, 1, 2]); // All qubits prepared
         circuit.tick().h(&[0]);
-        circuit.tick().cx(&[(0, 1), (0, 2)]);
+        circuit.tick().cx(&[(0, 1)]);
+        circuit.tick().cx(&[(0, 2)]);
         // No measurement - outputs go to next stage
 
         let checker = PauliPropChecker::new(&circuit);
@@ -4169,7 +4197,8 @@ mod tests {
         // Use a simple circuit where we know failures will occur
         let mut circuit = TickCircuit::new();
         circuit.tick().pz(&[2]); // Ancilla
-        circuit.tick().cx(&[(0, 2), (1, 2)]);
+        circuit.tick().cx(&[(0, 2)]);
+        circuit.tick().cx(&[(1, 2)]);
         circuit.tick().mz(&[2]);
 
         let config = FaultCheckConfig::new().with_weight(1).all_paulis();
diff --git a/crates/pecos-qec/src/fault_tolerance/propagator.rs b/crates/pecos-qec/src/fault_tolerance/propagator.rs
index dfed6934b..e35bb7239 100644
--- a/crates/pecos-qec/src/fault_tolerance/propagator.rs
+++ b/crates/pecos-qec/src/fault_tolerance/propagator.rs
@@ -13,9 +13,10 @@
 //! Pauli propagation infrastructure and fault analysis.
 //!
 //! This module provides bidirectional Pauli propagation through quantum circuits,
-//! with specialized support for fault tolerance analysis. By propagating observables
-//! backward from measurements/logicals, we can efficiently determine which faults
-//! affect which detectors:
+//! with specialized support for fault tolerance analysis. By propagating
+//! detector/observable measurement parities and unmeasured tracked Pauli
+//! operators backward through the circuit, we can efficiently determine which
+//! faults affect which outputs:
 //!
 //! 1. **Speed up fault enumeration** - O(1) lookup instead of `O(circuit_depth)` propagation
 //! 2. **Build detector error models** - Direct mapping from faults to detectors
@@ -43,10 +44,17 @@
 //! let analyzer = DagFaultAnalyzer::new(&dag);
 //! let map = analyzer.build_influence_map();
 //!
-//! // O(1) lookup: which measurements does a fault at location L flip?
-//! let (has_syndrome, has_logical) = map.classify_fault(0, 1); // loc 0, X fault
+//! // O(1) lookup: which detector/non-detector outputs does a fault at location L flip?
+//! let (has_syndrome, _flips_non_detector_output) = map.classify_fault(0, 1); // loc 0, X fault
 //! ```
 //!
+//! Observables and tracked Paulis are distinct. Observables are values
+//! observed through measurement-record parities and become standard `L<n>`
+//! outputs in DEM text. Tracked Paulis are Pauli operators annotated at
+//! circuit points; they are not measured and are not applied to the computation.
+//! PECOS records whether each fault anticommutes with, and therefore would flip,
+//! the propagated operator.
+//!
 //! # Concept
 //!
 //! Instead of forward propagation:
@@ -89,14 +97,15 @@ mod checker;
 pub mod dag;
 mod pauli;
 mod tick;
-mod tick_soa;
+mod tick_batched;
 pub mod types;
 
 // Re-export from submodules
 pub use checker::InfluenceBasedChecker;
 pub use dag::{
     BucketRecorder, CsrArray, DagFaultAnalyzer, DagFaultInfluenceMap, DagSpacetimeLocation,
-    FaultLocations, InfluencesSoA, InfluencesSoAStats, SoARecorderBuilder,
+    DemOutputKind, DemOutputMetadata, FaultCombo, FaultComponent, FaultEffect, FaultLocations,
+    GateFaultLocation, InfluencesSoA, InfluencesSoAStats, SoARecorderBuilder,
 };
 pub use pauli::{
     Direction, apply_gate, init_pauli_prop_with_fault, propagate_backward_from_tick,
@@ -104,10 +113,10 @@ pub use pauli::{
     propagate_tick_range,
 };
 pub use tick::TickFaultAnalyzer;
-pub use tick_soa::TickFaultAnalyzerSoA;
+pub use tick_batched::TickFaultAnalyzerBatched;
 pub use types::{
-    DetectorId, DetectorIdx, FaultInfluence, FaultInfluenceMap, LocationId, LogicalId, LogicalIdx,
-    MeasurementId, NodeId, Pauli,
+    DemOutputIdx, DetectorId, DetectorIdx, FaultInfluence, FaultInfluenceMap, LocationId,
+    MeasurementId, NodeId, Pauli, TrackedPauliId, TrackedPauliIdx,
 };
 
 // Internal imports
@@ -199,7 +208,7 @@ pub trait InfluenceRecorder {
 /// clean separation between traversal and recording.
 #[derive(Debug)]
 pub struct PropagationContext<'a> {
-    /// Current Pauli observable being propagated.
+    /// Current Pauli operator being propagated.
     pub prop: PauliProp,
     /// Work buffers for traversal.
     pub buffers: &'a mut PropagatorWorkBuffers,
@@ -218,17 +227,17 @@ impl<'a> PropagationContext<'a> {
         }
     }
 
-    /// Initializes the Pauli observable for a Z-basis measurement.
+    /// Initializes the Pauli operator for a Z-basis measurement.
     pub fn init_z_measurement(&mut self, qubit: usize) {
         self.prop.track_z(&[qubit]);
     }
 
-    /// Initializes the Pauli observable for an X-basis measurement.
+    /// Initializes the Pauli operator for an X-basis measurement.
     pub fn init_x_measurement(&mut self, qubit: usize) {
         self.prop.track_x(&[qubit]);
     }
 
-    /// Initializes the Pauli observable based on measurement basis.
+    /// Initializes the Pauli operator based on measurement basis.
     pub fn init_measurement(&mut self, qubit: usize, basis: u8) {
         if basis == 0 {
             self.prop.track_z(&[qubit]);
@@ -354,7 +363,7 @@ impl InfluenceRecorder for CountingRecorder {
         if obs_x {
             self.by_pauli[3] += 1; // Z fault
         }
-        if obs_x || obs_z {
+        if obs_x ^ obs_z {
             self.by_pauli[2] += 1; // Y fault
         }
     }
@@ -766,8 +775,10 @@ mod tests {
 
         // Get any fault location and check classification
         if let Some((loc, _)) = map.influences.iter().next() {
-            let (has_syndrome, has_logical) = checker.classify(loc, 1); // X fault
-            println!("Location {loc:?}: syndrome={has_syndrome}, logical={has_logical}");
+            let (has_syndrome, flips_tracked_pauli) = checker.classify(loc, 1); // X fault
+            println!(
+                "Location {loc:?}: syndrome={has_syndrome}, tracked_pauli={flips_tracked_pauli}"
+            );
         }
     }
 
@@ -950,33 +961,36 @@ mod tests {
     }
 
     #[test]
-    fn test_backward_vs_forward_with_logicals() {
-        // Test that logical tracking works with backward propagation
+    fn test_backward_vs_forward_with_tracked_paulis() {
+        // Test that tracked-Pauli propagation works with backward propagation
         let mut circuit = TickCircuit::new();
         circuit.tick().pz(&[0, 1, 2]);
         circuit.tick().cx(&[(0, 2)]);
         circuit.tick().cx(&[(1, 2)]);
         circuit.tick().mz(&[2]);
 
-        // Define a simple logical Z = Z0 Z1
-        let logicals: &[(&[usize], &[usize])] = &[(&[], &[0, 1])];
+        // Define a simple tracked Z Pauli = Z0 Z1
+        let tracked_paulis: &[(&[usize], &[usize])] = &[(&[], &[0, 1])];
 
         let propagator = TickFaultAnalyzer::new(&circuit);
-        let map = propagator.build_influence_map_with_logicals(logicals);
+        let map = propagator.build_influence_map_with_tracked_paulis(tracked_paulis);
 
-        // Check that logical tracking is populated
-        assert_eq!(map.logicals.len(), 1);
+        // Check that tracked-Pauli propagation is populated
+        assert_eq!(map.tracked_paulis.len(), 1);
 
-        // X errors on data qubits should flip the logical
-        let mut found_logical_flip = false;
+        // X errors on data qubits should flip the tracked Pauli
+        let mut found_tracked_pauli_flip = false;
         for (loc, influence) in &map.influences {
             if loc.qubits.iter().any(|q| q.index() == 0 || q.index() == 1)
-                && !influence.logicals_for_pauli(1).is_empty()
+                && !influence.tracked_paulis_for_pauli(1).is_empty()
             {
-                found_logical_flip = true;
+                found_tracked_pauli_flip = true;
             }
         }
-        assert!(found_logical_flip, "Should find X errors that flip logical");
+        assert!(
+            found_tracked_pauli_flip,
+            "Should find X errors that flip tracked Pauli"
+        );
     }
 
     #[test]
@@ -1073,6 +1087,149 @@ mod tests {
             .collect()
     }
 
+    fn pauli_prop_from_signature(signature: &[(bool, bool)]) -> PauliProp {
+        let mut prop = PauliProp::new();
+        for (qubit, &(has_x, has_z)) in signature.iter().enumerate() {
+            if has_x {
+                prop.track_x(&[qubit]);
+            }
+            if has_z {
+                prop.track_z(&[qubit]);
+            }
+        }
+        prop
+    }
+
+    fn add_standard_clifford_gate(circuit: &mut TickCircuit, gate_type: GateType) {
+        match gate_type {
+            GateType::I => {
+                circuit.tick().iden(&[0]);
+            }
+            GateType::X => {
+                circuit.tick().x(&[0]);
+            }
+            GateType::Y => {
+                circuit.tick().y(&[0]);
+            }
+            GateType::Z => {
+                circuit.tick().z(&[0]);
+            }
+            GateType::H => {
+                circuit.tick().h(&[0]);
+            }
+            GateType::F => {
+                circuit.tick().f(&[0]);
+            }
+            GateType::Fdg => {
+                circuit.tick().fdg(&[0]);
+            }
+            GateType::SX => {
+                circuit.tick().sx(&[0]);
+            }
+            GateType::SXdg => {
+                circuit.tick().sxdg(&[0]);
+            }
+            GateType::SY => {
+                circuit.tick().sy(&[0]);
+            }
+            GateType::SYdg => {
+                circuit.tick().sydg(&[0]);
+            }
+            GateType::SZ => {
+                circuit.tick().sz(&[0]);
+            }
+            GateType::SZdg => {
+                circuit.tick().szdg(&[0]);
+            }
+            GateType::CX => {
+                circuit.tick().cx(&[(0, 1)]);
+            }
+            GateType::CY => {
+                circuit.tick().cy(&[(0, 1)]);
+            }
+            GateType::CZ => {
+                circuit.tick().cz(&[(0, 1)]);
+            }
+            GateType::SXX => {
+                circuit.tick().sxx(&[(0, 1)]);
+            }
+            GateType::SXXdg => {
+                circuit.tick().sxxdg(&[(0, 1)]);
+            }
+            GateType::SYY => {
+                circuit.tick().syy(&[(0, 1)]);
+            }
+            GateType::SYYdg => {
+                circuit.tick().syydg(&[(0, 1)]);
+            }
+            GateType::SZZ => {
+                circuit.tick().szz(&[(0, 1)]);
+            }
+            GateType::SZZdg => {
+                circuit.tick().szzdg(&[(0, 1)]);
+            }
+            GateType::SWAP => {
+                circuit.tick().swap(&[(0, 1)]);
+            }
+            _ => unreachable!("not a standard Clifford gate: {gate_type:?}"),
+        }
+    }
+
+    fn assert_pauli_signature_after_gate(
+        gate_type: GateType,
+        input: [(bool, bool); 2],
+        expected: [(bool, bool); 2],
+    ) {
+        let mut circuit = TickCircuit::new();
+        add_standard_clifford_gate(&mut circuit, gate_type);
+
+        let mut prop = pauli_prop_from_signature(&input);
+        propagate_through_circuit(&circuit, &mut prop, Direction::Forward);
+
+        assert_eq!(
+            pauli_signature(&prop, &[0, 1]),
+            expected,
+            "{gate_type:?} should map {input:?} to {expected:?} up to Pauli phase"
+        );
+    }
+
+    #[test]
+    fn test_standard_clifford_pauli_conjugation_tables() {
+        const I: (bool, bool) = (false, false);
+        const X: (bool, bool) = (true, false);
+        const Z: (bool, bool) = (false, true);
+        const Y: (bool, bool) = (true, true);
+
+        assert_pauli_signature_after_gate(GateType::H, [X, I], [Z, I]);
+        assert_pauli_signature_after_gate(GateType::H, [Z, I], [X, I]);
+        assert_pauli_signature_after_gate(GateType::F, [X, I], [Y, I]);
+        assert_pauli_signature_after_gate(GateType::F, [Y, I], [Z, I]);
+        assert_pauli_signature_after_gate(GateType::F, [Z, I], [X, I]);
+        assert_pauli_signature_after_gate(GateType::Fdg, [X, I], [Z, I]);
+        assert_pauli_signature_after_gate(GateType::Fdg, [Y, I], [X, I]);
+        assert_pauli_signature_after_gate(GateType::Fdg, [Z, I], [Y, I]);
+        assert_pauli_signature_after_gate(GateType::SX, [Z, I], [Y, I]);
+        assert_pauli_signature_after_gate(GateType::SY, [X, I], [Z, I]);
+        assert_pauli_signature_after_gate(GateType::SZ, [X, I], [Y, I]);
+
+        assert_pauli_signature_after_gate(GateType::CX, [X, I], [X, X]);
+        assert_pauli_signature_after_gate(GateType::CX, [I, Z], [Z, Z]);
+        assert_pauli_signature_after_gate(GateType::CY, [X, I], [X, Y]);
+        assert_pauli_signature_after_gate(GateType::CZ, [X, I], [X, Z]);
+        assert_pauli_signature_after_gate(GateType::SWAP, [X, Z], [Z, X]);
+
+        assert_pauli_signature_after_gate(GateType::SXX, [Z, I], [Y, X]);
+        assert_pauli_signature_after_gate(GateType::SXX, [I, Z], [X, Y]);
+        assert_pauli_signature_after_gate(GateType::SYY, [X, I], [Z, Y]);
+        assert_pauli_signature_after_gate(GateType::SYY, [I, X], [Y, Z]);
+        assert_pauli_signature_after_gate(GateType::SZZ, [X, I], [Y, Z]);
+        assert_pauli_signature_after_gate(GateType::SZZ, [I, X], [Z, Y]);
+
+        assert_pauli_signature_after_gate(GateType::SXXdg, [Z, I], [Y, X]);
+        assert_pauli_signature_after_gate(GateType::SYYdg, [X, I], [Z, Y]);
+        assert_pauli_signature_after_gate(GateType::SZZdg, [X, I], [Y, Z]);
+    }
+
     #[test]
     fn test_rz_propagation_matches_sz() {
         let mut rotated = TickCircuit::new();
diff --git a/crates/pecos-qec/src/fault_tolerance/propagator/checker.rs b/crates/pecos-qec/src/fault_tolerance/propagator/checker.rs
index 58f0bd5d6..6bc14be8f 100644
--- a/crates/pecos-qec/src/fault_tolerance/propagator/checker.rs
+++ b/crates/pecos-qec/src/fault_tolerance/propagator/checker.rs
@@ -35,11 +35,12 @@ impl<'a> InfluenceBasedChecker<'a> {
 
     /// Classifies a fault at the given location with the given Pauli type.
     ///
-    /// For single-qubit locations, returns whether any qubit causes syndrome/logical.
+    /// For single-qubit locations, returns whether any qubit causes syndrome or
+    /// flips a tracked Pauli.
     /// For multi-qubit locations where the same Pauli is applied to all qubits,
     /// use `classify_uniform` which properly handles cancellation effects.
     ///
-    /// Returns (`has_syndrome`, `causes_logical_error`).
+    /// Returns (`has_syndrome`, `flips_tracked_pauli`).
     #[must_use]
     pub fn classify(&self, location: &SpacetimeLocation, pauli: u8) -> (bool, bool) {
         self.influence_map.classify_fault(location, pauli)
@@ -53,7 +54,7 @@ impl<'a> InfluenceBasedChecker<'a> {
     /// For Y faults (single or multi-qubit), we decompose Y = XZ and combine the
     /// X and Z contributions with XOR semantics.
     ///
-    /// Returns (`has_syndrome`, `causes_logical_error`).
+    /// Returns (`has_syndrome`, `flips_tracked_pauli`).
     #[must_use]
     pub fn classify_uniform(&self, location: &SpacetimeLocation, pauli: u8) -> (bool, bool) {
         // Always use multi-qubit logic for Y faults (even single-qubit)
@@ -77,10 +78,10 @@ impl<'a> InfluenceBasedChecker<'a> {
             })
     }
 
-    /// Checks if a fault causes an undetectable logical error.
+    /// Checks if a fault silently flips a tracked Pauli.
     #[must_use]
-    pub fn is_undetectable_logical_error(&self, location: &SpacetimeLocation, pauli: u8) -> bool {
-        let (has_syndrome, has_logical) = self.classify(location, pauli);
-        !has_syndrome && has_logical
+    pub fn is_silent_tracked_pauli_flip(&self, location: &SpacetimeLocation, pauli: u8) -> bool {
+        let (has_syndrome, flips_tracked_pauli) = self.classify(location, pauli);
+        !has_syndrome && flips_tracked_pauli
     }
 }
diff --git a/crates/pecos-qec/src/fault_tolerance/propagator/dag.rs b/crates/pecos-qec/src/fault_tolerance/propagator/dag.rs
index 8f13a49b1..99d164f04 100644
--- a/crates/pecos-qec/src/fault_tolerance/propagator/dag.rs
+++ b/crates/pecos-qec/src/fault_tolerance/propagator/dag.rs
@@ -32,6 +32,26 @@
 //! - [`DagSpacetimeLocation`]: Identifies a fault location in a DAG circuit
 //! - [`DagFaultInfluenceMap`]: Cache-optimized influence map using CSR layout
 //!
+//! # Output Terminology
+//!
+//! The influence map has one detector namespace plus one raw internal
+//! non-detector-output namespace. That raw namespace is only a storage detail:
+//! metadata maps each raw non-detector output to either a standard observable
+//! (`L<n>`) or a PECOS tracked Pauli. Decoder and sampler code should use
+//! [`DagFaultInfluenceMap::observable_ids`],
+//! [`DagFaultInfluenceMap::observable_id_for_internal_dem_output`], and
+//! [`DagFaultInfluenceMap::tracked_pauli_id_for_internal_dem_output`] instead of
+//! assuming raw indices are public `L<n>` IDs.
+//!
+//! Observables and tracked Paulis differ by definition, not just by name.
+//! Observables are values observed through measurement-record parities and are
+//! visible to DEM decoders as standard `L<n>` outputs. Tracked Paulis are
+//! unmeasured Pauli operators annotated at a circuit point, such as logical
+//! operators, stabilizers, or other Paulis of interest; the influence map
+//! records whether a fault anticommutes with, and therefore would flip, the
+//! propagated operator. They are PECOS metadata and are not measurement-record
+//! observables.
+//!
 //! # Example
 //!
 //! ```
@@ -48,18 +68,18 @@
 //! let map = analyzer.build_influence_map();
 //!
 //! // O(1) fault classification
-//! let (has_syndrome, has_logical) = map.classify_fault(0, 1); // loc 0, X fault
+//! let (has_syndrome, _flips_non_detector_output) = map.classify_fault(0, 1); // loc 0, X fault
 //! ```
 
 use super::{
     DagPropagator, DetectorId, Direction, InfluenceRecorder, MeasurementId, Pauli, apply_gate,
 };
-use pecos_core::QubitId;
 use pecos_core::gate_type::GateType;
+use pecos_core::{PauliString, QuarterPhase, QubitId};
 use pecos_quantum::DagCircuit;
 use pecos_simulators::PauliProp;
 use smallvec::SmallVec;
-use std::collections::BinaryHeap;
+use std::collections::{BTreeMap, BTreeSet, BinaryHeap};
 
 /// Reusable work buffers for propagation, avoiding per-call allocation.
 pub struct PropagationBuffers {
@@ -68,6 +88,13 @@ pub struct PropagationBuffers {
     pub heap: BinaryHeap<(usize, usize)>,
 }
 
+struct Phase1Request {
+    meas_node: usize,
+    meas_qubit: usize,
+    basis: u8,
+    detector_idx: usize,
+}
+
 // ============================================================================
 // Fault Locations (SoA Layout)
 // ============================================================================
@@ -179,6 +206,7 @@ impl FaultLocations {
                 qubits: self.qubits[i].iter().map(|&q| QubitId::from(q)).collect(),
                 before: self.before[i],
                 gate_type: self.gate_types[i],
+                idle_duration: 0,
             })
             .collect()
     }
@@ -202,6 +230,8 @@ pub struct DagSpacetimeLocation {
     pub before: bool,
     /// The type of gate at this location.
     pub gate_type: GateType,
+    /// Duration for idle gates (in abstract time units). 0 for non-idle gates.
+    pub idle_duration: u64,
 }
 
 // ============================================================================
@@ -348,14 +378,18 @@ pub struct InfluencesSoA {
     /// Detector indices flipped by Z faults (Pauli=3).
     pub detectors_z: CsrArray,
 
-    /// Logical indices flipped by X faults.
-    pub logicals_x: CsrArray,
+    /// Internal non-detector output indices flipped by X faults.
+    ///
+    /// These raw indices may name either standard observables or PECOS tracked
+    /// operators. Use [`DagFaultInfluenceMap`] metadata helpers to map them into
+    /// the public `L<n>` observable namespace or tracked-Pauli namespace.
+    pub dem_outputs_x: CsrArray,
 
-    /// Logical indices flipped by Y faults.
-    pub logicals_y: CsrArray,
+    /// Internal non-detector output indices flipped by Y faults.
+    pub dem_outputs_y: CsrArray,
 
-    /// Logical indices flipped by Z faults.
-    pub logicals_z: CsrArray,
+    /// Internal non-detector output indices flipped by Z faults.
+    pub dem_outputs_z: CsrArray,
 }
 
 impl InfluencesSoA {
@@ -369,9 +403,9 @@ impl InfluencesSoA {
             detectors_x: CsrArray::with_capacity(num_locations, estimated_data),
             detectors_y: CsrArray::with_capacity(num_locations, estimated_data),
             detectors_z: CsrArray::with_capacity(num_locations, estimated_data),
-            logicals_x: CsrArray::with_capacity(num_locations, estimated_data / 4),
-            logicals_y: CsrArray::with_capacity(num_locations, estimated_data / 4),
-            logicals_z: CsrArray::with_capacity(num_locations, estimated_data / 4),
+            dem_outputs_x: CsrArray::with_capacity(num_locations, estimated_data / 4),
+            dem_outputs_y: CsrArray::with_capacity(num_locations, estimated_data / 4),
+            dem_outputs_z: CsrArray::with_capacity(num_locations, estimated_data / 4),
         }
     }
 
@@ -387,15 +421,21 @@ impl InfluencesSoA {
         }
     }
 
-    /// Returns the logical indices for a location and Pauli type.
+    /// Returns raw internal non-detector output indices for a location and Pauli type.
+    ///
+    /// These indices are not necessarily standard `L<n>` IDs. Callers that
+    /// need public observable IDs should use
+    /// [`DagFaultInfluenceMap::observable_id_for_internal_dem_output`]; callers
+    /// that need tracked-Pauli IDs should use
+    /// [`DagFaultInfluenceMap::tracked_pauli_id_for_internal_dem_output`].
     #[inline]
     #[must_use]
-    pub fn logicals(&self, loc_idx: usize, pauli: Pauli) -> &[u32] {
+    pub fn dem_outputs(&self, loc_idx: usize, pauli: Pauli) -> &[u32] {
         match pauli {
             Pauli::I => &[],
-            Pauli::X => self.logicals_x.row(loc_idx),
-            Pauli::Y => self.logicals_y.row(loc_idx),
-            Pauli::Z => self.logicals_z.row(loc_idx),
+            Pauli::X => self.dem_outputs_x.row(loc_idx),
+            Pauli::Y => self.dem_outputs_y.row(loc_idx),
+            Pauli::Z => self.dem_outputs_z.row(loc_idx),
         }
     }
 
@@ -411,27 +451,27 @@ impl InfluencesSoA {
         }
     }
 
-    /// Returns whether the location has any logical flips for the given Pauli.
+    /// Returns whether the location has any non-detector output flips for the given Pauli.
     #[inline]
     #[must_use]
-    pub fn has_logical_flips(&self, loc_idx: usize, pauli: Pauli) -> bool {
+    pub fn has_dem_output_flips(&self, loc_idx: usize, pauli: Pauli) -> bool {
         match pauli {
             Pauli::I => false,
-            Pauli::X => !self.logicals_x.row_is_empty(loc_idx),
-            Pauli::Y => !self.logicals_y.row_is_empty(loc_idx),
-            Pauli::Z => !self.logicals_z.row_is_empty(loc_idx),
+            Pauli::X => !self.dem_outputs_x.row_is_empty(loc_idx),
+            Pauli::Y => !self.dem_outputs_y.row_is_empty(loc_idx),
+            Pauli::Z => !self.dem_outputs_z.row_is_empty(loc_idx),
         }
     }
 
     /// Classifies a fault at the given location.
     ///
-    /// Returns (`has_syndrome`, `causes_logical_error`).
+    /// Returns (`has_syndrome`, `flips_non_detector_output`).
     #[inline]
     #[must_use]
     pub fn classify(&self, loc_idx: usize, pauli: Pauli) -> (bool, bool) {
         (
             self.has_detector_flips(loc_idx, pauli),
-            self.has_logical_flips(loc_idx, pauli),
+            self.has_dem_output_flips(loc_idx, pauli),
         )
     }
 
@@ -440,9 +480,9 @@ impl InfluencesSoA {
         self.detectors_x.finish_row();
         self.detectors_y.finish_row();
         self.detectors_z.finish_row();
-        self.logicals_x.finish_row();
-        self.logicals_y.finish_row();
-        self.logicals_z.finish_row();
+        self.dem_outputs_x.finish_row();
+        self.dem_outputs_y.finish_row();
+        self.dem_outputs_z.finish_row();
         self.num_locations += 1;
     }
 
@@ -452,17 +492,17 @@ impl InfluencesSoA {
         let offset_bytes = (self.detectors_x.offsets.len()
             + self.detectors_y.offsets.len()
             + self.detectors_z.offsets.len()
-            + self.logicals_x.offsets.len()
-            + self.logicals_y.offsets.len()
-            + self.logicals_z.offsets.len())
+            + self.dem_outputs_x.offsets.len()
+            + self.dem_outputs_y.offsets.len()
+            + self.dem_outputs_z.offsets.len())
             * std::mem::size_of::<u32>();
 
         let data_bytes = (self.detectors_x.data.len()
             + self.detectors_y.data.len()
             + self.detectors_z.data.len()
-            + self.logicals_x.data.len()
-            + self.logicals_y.data.len()
-            + self.logicals_z.data.len())
+            + self.dem_outputs_x.data.len()
+            + self.dem_outputs_y.data.len()
+            + self.dem_outputs_z.data.len())
             * std::mem::size_of::<u32>();
 
         InfluencesSoAStats {
@@ -470,23 +510,25 @@ impl InfluencesSoA {
             total_detector_entries: self.detectors_x.total_elements()
                 + self.detectors_y.total_elements()
                 + self.detectors_z.total_elements(),
-            total_logical_entries: self.logicals_x.total_elements()
-                + self.logicals_y.total_elements()
-                + self.logicals_z.total_elements(),
+            total_dem_output_entries: self.dem_outputs_x.total_elements()
+                + self.dem_outputs_y.total_elements()
+                + self.dem_outputs_z.total_elements(),
             offset_bytes,
             data_bytes,
             total_bytes: offset_bytes + data_bytes,
         }
     }
 
-    /// Returns the maximum logical index found in the influence map, if any.
+    /// Returns the maximum raw non-detector output influence index, if any.
     ///
-    /// This is useful for determining the number of logical operators tracked.
+    /// When metadata is present, callers should use [`Self::num_dem_outputs`]
+    /// for the standard observable `L<n>` namespace and [`Self::num_tracked_paulis`]
+    /// for PECOS tracked Paulis.
     #[must_use]
-    pub fn max_logical_index(&self) -> Option<usize> {
-        let max_x = self.logicals_x.data.iter().max();
-        let max_y = self.logicals_y.data.iter().max();
-        let max_z = self.logicals_z.data.iter().max();
+    pub fn max_dem_output_index(&self) -> Option<usize> {
+        let max_x = self.dem_outputs_x.data.iter().max();
+        let max_y = self.dem_outputs_y.data.iter().max();
+        let max_z = self.dem_outputs_z.data.iter().max();
 
         [max_x, max_y, max_z]
             .into_iter()
@@ -503,8 +545,8 @@ pub struct InfluencesSoAStats {
     pub num_locations: usize,
     /// Total detector entries across all Pauli types.
     pub total_detector_entries: usize,
-    /// Total logical entries across all Pauli types.
-    pub total_logical_entries: usize,
+    /// Total DEM-output entries across all Pauli types.
+    pub total_dem_output_entries: usize,
     /// Bytes used for offset arrays.
     pub offset_bytes: usize,
     /// Bytes used for data arrays.
@@ -529,7 +571,25 @@ pub struct DagFaultInfluenceMap {
     pub detectors: Vec<DetectorId>,
 
     /// All measurements in the circuit (node, qubit, basis).
+    /// Ordered by `MeasId` when gates carry `MeasId` values.
     pub measurements: Vec<(usize, usize, u8)>,
+
+    /// `MeasId` IDs for each measurement, in the same order as `measurements`.
+    /// When populated, `meas_ids[i]` is the stable identity of `measurements[i]`.
+    /// Empty for legacy circuits without `MeasId` on gates.
+    pub meas_ids: Vec<pecos_core::MeasId>,
+
+    /// Optional labels for non-detector parity outputs.
+    /// Indices match the raw non-detector output indices in `influences`.
+    pub dem_output_labels: Vec<Option<String>>,
+
+    /// Optional metadata for non-detector outputs tracked by backward propagation.
+    ///
+    /// These entries may be standard observables or PECOS tracked Paulis.
+    /// The metadata kind is the authority for translating raw influence indices
+    /// into public namespaces; standard observables use compact `L<n>` IDs and
+    /// tracked Paulis use their own compact PECOS-only IDs.
+    pub dem_output_metadata: Vec<DemOutputMetadata>,
 }
 
 impl DagFaultInfluenceMap {
@@ -541,12 +601,15 @@ impl DagFaultInfluenceMap {
             locations: Vec::with_capacity(num_locations),
             detectors: Vec::new(),
             measurements: Vec::new(),
+            meas_ids: Vec::new(),
+            dem_output_labels: Vec::new(),
+            dem_output_metadata: Vec::new(),
         }
     }
 
     /// Classifies a fault at the given location index.
     ///
-    /// Returns (`has_syndrome`, `causes_logical_error`).
+    /// Returns (`has_syndrome`, `flips_non_detector_output`).
     #[inline]
     #[must_use]
     pub fn classify_fault(&self, loc_idx: usize, pauli: u8) -> (bool, bool) {
@@ -560,11 +623,152 @@ impl DagFaultInfluenceMap {
         self.influences.detectors(loc_idx, Pauli::from_u8(pauli))
     }
 
-    /// Returns the logical indices flipped by a fault.
+    /// Returns all raw non-detector output indices flipped by a fault.
+    ///
+    /// Raw indices are an internal storage detail shared by observables and
+    /// tracked Paulis. Prefer [`Self::get_observable_indices`] or
+    /// [`Self::get_tracked_pauli_indices`] when a public namespace is needed.
+    #[inline]
+    #[must_use]
+    pub fn get_dem_output_indices(&self, loc_idx: usize, pauli: u8) -> &[u32] {
+        self.influences.dem_outputs(loc_idx, Pauli::from_u8(pauli))
+    }
+
+    /// Returns the number of standard DEM `L<n>` observable outputs.
+    ///
+    /// This is a DEM-output alias for [`Self::num_observables`]. It does
+    /// not include PECOS tracked Paulis.
+    #[must_use]
+    pub fn num_dem_outputs(&self) -> usize {
+        if self.dem_output_metadata.is_empty() {
+            return self.influences.max_dem_output_index().map_or(0, |i| i + 1);
+        }
+        self.dem_output_metadata
+            .iter()
+            .filter(|metadata| metadata.kind == DemOutputKind::Observable)
+            .count()
+    }
+
+    /// Returns the number of observables.
+    #[must_use]
+    pub fn num_observables(&self) -> usize {
+        self.num_dem_outputs()
+    }
+
+    /// Returns the standard observable `L<n>` IDs present in this map.
+    ///
+    /// Tracked Paulis share internal propagation storage but never appear in
+    /// this set. Public decoder and sampler paths should use this namespace
+    /// rather than raw internal DEM-output indices.
+    #[must_use]
+    pub fn observable_ids(&self) -> BTreeSet<u32> {
+        (0..self.num_dem_outputs())
+            .filter_map(|idx| u32::try_from(idx).ok())
+            .collect()
+    }
+
+    /// Returns the number of PECOS tracked Paulis.
+    #[must_use]
+    pub fn num_tracked_paulis(&self) -> usize {
+        self.dem_output_metadata
+            .iter()
+            .filter(|metadata| metadata.kind == DemOutputKind::TrackedPauli)
+            .count()
+    }
+
+    /// Returns tracked-Pauli output indices flipped by a fault.
+    #[must_use]
+    pub fn get_tracked_pauli_indices(&self, loc_idx: usize, pauli: u8) -> Vec<u32> {
+        let outputs = self.get_dem_output_indices(loc_idx, pauli);
+        outputs
+            .iter()
+            .filter_map(|&idx| self.tracked_pauli_id_for_internal_dem_output(idx))
+            .collect()
+    }
+
+    /// Returns observable output indices flipped by a fault.
+    #[must_use]
+    pub fn get_observable_indices(&self, loc_idx: usize, pauli: u8) -> Vec<u32> {
+        let outputs = self.get_dem_output_indices(loc_idx, pauli);
+        if self.dem_output_metadata.is_empty() {
+            return outputs.to_vec();
+        }
+        outputs
+            .iter()
+            .filter_map(|&idx| self.observable_id_for_internal_dem_output(idx))
+            .collect()
+    }
+
+    /// Map an internal non-detector output index to the standard observable
+    /// `L<n>` ID space.
+    #[must_use]
+    pub fn observable_id_for_internal_dem_output(&self, idx: u32) -> Option<u32> {
+        if self.dem_output_metadata.is_empty() {
+            return Some(idx);
+        }
+        self.output_id_for_kind(idx, DemOutputKind::Observable)
+    }
+
+    /// Map an internal non-detector output index to the PECOS tracked-Pauli
+    /// ID space.
+    #[must_use]
+    pub fn tracked_pauli_id_for_internal_dem_output(&self, idx: u32) -> Option<u32> {
+        self.output_id_for_kind(idx, DemOutputKind::TrackedPauli)
+    }
+
+    /// Returns true if a fault flips any non-detector DEM output.
     #[inline]
     #[must_use]
-    pub fn get_logical_indices(&self, loc_idx: usize, pauli: u8) -> &[u32] {
-        self.influences.logicals(loc_idx, Pauli::from_u8(pauli))
+    pub fn has_dem_output_flips(&self, loc_idx: usize, pauli: u8) -> bool {
+        !self.get_dem_output_indices(loc_idx, pauli).is_empty()
+    }
+
+    /// Returns true if a fault flips any tracked Pauli.
+    #[must_use]
+    pub fn has_tracked_pauli_flips(&self, loc_idx: usize, pauli: u8) -> bool {
+        !self.get_tracked_pauli_indices(loc_idx, pauli).is_empty()
+    }
+
+    /// Returns true if a fault flips any observable.
+    #[must_use]
+    pub fn has_observable_flips(&self, loc_idx: usize, pauli: u8) -> bool {
+        !self.get_observable_indices(loc_idx, pauli).is_empty()
+    }
+
+    /// Returns the label for a detector, if any.
+    #[inline]
+    #[must_use]
+    pub fn detector_label(&self, detector_idx: usize) -> Option<&str> {
+        self.detectors
+            .get(detector_idx)
+            .and_then(|d| d.name.as_deref())
+    }
+
+    /// Returns the label for a DEM output, if any.
+    #[inline]
+    #[must_use]
+    pub fn dem_output_label(&self, dem_output_idx: usize) -> Option<&str> {
+        self.dem_output_labels
+            .get(dem_output_idx)
+            .and_then(|l| l.as_deref())
+    }
+
+    /// Returns metadata for a DEM output, if available.
+    #[inline]
+    #[must_use]
+    pub fn dem_output_metadata(&self, dem_output_idx: usize) -> Option<&DemOutputMetadata> {
+        self.dem_output_metadata.get(dem_output_idx)
+    }
+
+    /// Replace this map's backward-propagated non-detector outputs with
+    /// another map's outputs and metadata.
+    pub fn merge_dem_outputs_from(&mut self, other: &Self) {
+        self.influences.dem_outputs_x = other.influences.dem_outputs_x.clone();
+        self.influences.dem_outputs_y = other.influences.dem_outputs_y.clone();
+        self.influences.dem_outputs_z = other.influences.dem_outputs_z.clone();
+        self.dem_output_labels.clone_from(&other.dem_output_labels);
+        self.dem_output_metadata
+            .clone_from(&other.dem_output_metadata);
     }
 
     /// Returns the location at the given index.
@@ -589,14 +793,19 @@ impl DagFaultInfluenceMap {
 
     /// Export CSR data for GPU use.
     ///
+    /// The exported DEM-output arrays contain only standard observable `L<n>`
+    /// outputs. PECOS tracked Paulis share the internal backward-propagation
+    /// storage but are intentionally filtered out here so decoder-oriented GPU
+    /// code cannot count tracked Paulis as logical errors.
+    ///
     /// Returns all CSR arrays needed to construct a GPU influence sampler:
-    /// (`num_locations`, `num_detectors`, `num_logicals`,
+    /// (`num_locations`, `num_detectors`, `num_dem_outputs`,
     ///  `detector_offsets_x`, `detector_data_x`,
     ///  `detector_offsets_y`, `detector_data_y`,
     ///  `detector_offsets_z`, `detector_data_z`,
-    ///  `logical_offsets_x`, `logical_data_x`,
-    ///  `logical_offsets_y`, `logical_data_y`,
-    ///  `logical_offsets_z`, `logical_data_z`)
+    ///  `dem_output_offsets_x`, `dem_output_data_x`,
+    ///  `dem_output_offsets_y`, `dem_output_data_y`,
+    ///  `dem_output_offsets_z`, `dem_output_data_z`)
     #[allow(clippy::type_complexity)]
     #[must_use]
     pub fn export_csr(
@@ -622,29 +831,715 @@ impl DagFaultInfluenceMap {
         let num_locations = self.locations.len() as u32;
         #[allow(clippy::cast_possible_truncation)] // detector count fits in u32
         let num_detectors = self.detectors.len() as u32;
-        #[allow(clippy::cast_possible_truncation)] // logical index fits in u32
-        let num_logicals = self
-            .influences
-            .max_logical_index()
-            .map_or(0, |i| i as u32 + 1);
+        #[allow(clippy::cast_possible_truncation)] // DEM-output count fits in u32
+        let num_dem_outputs = self.num_dem_outputs() as u32;
+        let (dem_output_offsets_x, dem_output_data_x) =
+            self.observable_csr(&self.influences.dem_outputs_x);
+        let (dem_output_offsets_y, dem_output_data_y) =
+            self.observable_csr(&self.influences.dem_outputs_y);
+        let (dem_output_offsets_z, dem_output_data_z) =
+            self.observable_csr(&self.influences.dem_outputs_z);
+
+        (
+            num_locations,
+            num_detectors,
+            num_dem_outputs,
+            self.influences.detectors_x.offsets.clone(),
+            self.influences.detectors_x.data.clone(),
+            self.influences.detectors_y.offsets.clone(),
+            self.influences.detectors_y.data.clone(),
+            self.influences.detectors_z.offsets.clone(),
+            self.influences.detectors_z.data.clone(),
+            dem_output_offsets_x,
+            dem_output_data_x,
+            dem_output_offsets_y,
+            dem_output_data_y,
+            dem_output_offsets_z,
+            dem_output_data_z,
+        )
+    }
+
+    fn observable_csr(&self, csr: &CsrArray) -> (Vec<u32>, Vec<u32>) {
+        if self.dem_output_metadata.is_empty() {
+            return (csr.offsets.clone(), csr.data.clone());
+        }
+
+        let mut offsets = Vec::with_capacity(csr.offsets.len());
+        let mut data = Vec::new();
+        offsets.push(0);
+        for row_idx in 0..csr.num_rows() {
+            data.extend(
+                csr.row(row_idx)
+                    .iter()
+                    .filter_map(|&idx| self.observable_id_for_internal_dem_output(idx)),
+            );
+            #[allow(clippy::cast_possible_truncation)] // CSR data length fits in u32
+            offsets.push(data.len() as u32);
+        }
+        (offsets, data)
+    }
+
+    fn output_id_for_kind(&self, idx: u32, kind: DemOutputKind) -> Option<u32> {
+        let metadata = self.dem_output_metadata.get(idx as usize)?;
+        if metadata.kind != kind {
+            return None;
+        }
+        #[allow(clippy::cast_possible_truncation)] // filtered output count fits in u32
+        Some(
+            self.dem_output_metadata[..idx as usize]
+                .iter()
+                .filter(|metadata| metadata.kind == kind)
+                .count() as u32,
+        )
+    }
+}
+
+/// Role of a non-detector output under backward Pauli propagation.
+#[derive(Debug, Clone, Copy, PartialEq, Eq, Hash)]
+pub enum DemOutputKind {
+    /// A standard `L<n>` observable defined by measurement records.
+    Observable,
+    /// An unmeasured Pauli-operator annotation, separate from measurement records.
+    TrackedPauli,
+}
+
+impl DemOutputKind {
+    /// Stable string used by PECOS metadata JSON.
+    #[must_use]
+    pub const fn as_str(self) -> &'static str {
+        match self {
+            Self::Observable => "observable",
+            Self::TrackedPauli => "tracked_pauli",
+        }
+    }
+
+    /// Parses a stable PECOS metadata string.
+    #[must_use]
+    pub fn from_metadata_str(kind: &str) -> Option<Self> {
+        match kind {
+            "observable" => Some(Self::Observable),
+            "tracked_pauli" => Some(Self::TrackedPauli),
+            _ => None,
+        }
+    }
+}
+
+/// Metadata for a PECOS non-detector output.
+///
+/// Standard DEM text only has `L<n>` observable markers. PECOS keeps this richer
+/// record alongside the DEM so callers can distinguish those measurement-record
+/// observables from tracked Paulis, which live in a separate
+/// PECOS-only namespace.
+#[derive(Debug, Clone, PartialEq, Eq)]
+pub struct DemOutputMetadata {
+    /// The output role.
+    pub kind: DemOutputKind,
+    /// Pauli string whose flip is tracked.
+    ///
+    /// For observables this is the Pauli associated with the measurement-record
+    /// observable. For tracked Paulis this is the unmeasured tracked Pauli
+    /// annotated at a circuit point.
+    pub pauli: PauliString,
+    /// Optional user label.
+    pub label: Option<String>,
+}
+
+impl DemOutputMetadata {
+    /// Creates DEM output metadata.
+    #[must_use]
+    pub fn new(kind: DemOutputKind, mut pauli: PauliString, label: Option<String>) -> Self {
+        // A tracked Pauli op flip is an anticommutation property; global phase has
+        // no meaning for DEM/sampler output.
+        pauli.set_phase(QuarterPhase::PlusOne);
+        Self { kind, pauli, label }
+    }
+
+    /// Creates metadata for a tracked Pauli.
+    #[must_use]
+    pub fn tracked_pauli(pauli: PauliString) -> Self {
+        Self::new(DemOutputKind::TrackedPauli, pauli, None)
+    }
+
+    /// Creates metadata for an observable.
+    #[must_use]
+    pub fn observable(pauli: PauliString) -> Self {
+        Self::new(DemOutputKind::Observable, pauli, None)
+    }
+
+    /// Sets a user-facing op label.
+    #[must_use]
+    pub fn with_label(mut self, label: impl Into<String>) -> Self {
+        self.label = Some(label.into());
+        self
+    }
+
+    /// Sets an optional user-facing op label.
+    #[must_use]
+    pub fn with_optional_label(mut self, label: Option<String>) -> Self {
+        self.label = label;
+        self
+    }
+}
+
+// ============================================================================
+// Fault Introspection
+// ============================================================================
+
+/// A per-gate fault location with access to all possible fault events.
+///
+/// Each gate at a specific timing (before/after) is one fault location.
+/// Multi-qubit gates have multiple per-qubit sub-locations whose effects
+/// compose via XOR (symmetric difference) for multi-qubit Pauli events.
+///
+/// Borrows the influence map so you can query events directly:
+/// ```
+/// use pecos_qec::fault_tolerance::propagator::dag::DagFaultInfluenceMap;
+///
+/// let map = DagFaultInfluenceMap::with_capacity(0);
+/// for loc in map.gate_fault_locations() {
+///     for event in loc.events() {
+///         println!("{}: dets={:?}", event.pauli, event.detectors);
+///     }
+/// }
+/// ```
+pub struct GateFaultLocation<'a> {
+    map: &'a DagFaultInfluenceMap,
+    /// DAG node index.
+    pub node: usize,
+    /// Gate type.
+    pub gate_type: GateType,
+    /// Qubits this gate acts on.
+    pub qubits: Vec<QubitId>,
+    /// Before (true) or after (false) the gate.
+    pub before: bool,
+    /// Per-qubit location indices in the influence map.
+    qubit_loc_indices: Vec<(usize, usize)>, // (qubit, loc_idx)
+}
+
+/// The effect of a specific fault event (multi-qubit Pauli error).
+#[derive(Debug, Clone)]
+pub struct FaultEffect {
+    /// The multi-qubit Pauli error.
+    pub pauli: pecos_core::PauliString,
+    /// Detector indices that flip.
+    pub detectors: Vec<u32>,
+    /// DEM-output indices that flip.
+    pub dem_outputs: Vec<u32>,
+    /// Raw measurements that flip: `(node, qubit, basis)`.
+    ///
+    /// Derived from the flipped detectors. Each auto-detected detector
+    /// corresponds to one or more measurements; this expands them.
+    pub measurements: Vec<(usize, usize, u8)>,
+}
+
+impl FaultEffect {
+    /// Compose two fault effects (as if both faults occurred).
+    ///
+    /// - Paulis are multiplied (handles same-qubit algebra + tensor product)
+    /// - Detectors, `dem_outputs`, and measurements are XOR'd (symmetric difference)
+    ///
+    /// This is the building block for weight-w fault analysis:
+    /// ```
+    /// use pecos_core::PauliString;
+    /// use pecos_qec::fault_tolerance::propagator::dag::FaultEffect;
+    ///
+    /// let effect_a = FaultEffect {
+    ///     pauli: PauliString::x(0),
+    ///     detectors: vec![0],
+    ///     dem_outputs: vec![],
+    ///     measurements: vec![],
+    /// };
+    /// let effect_b = FaultEffect {
+    ///     pauli: PauliString::z(1),
+    ///     detectors: vec![0, 1],
+    ///     dem_outputs: vec![0],
+    ///     measurements: vec![],
+    /// };
+    /// let w2 = effect_a.compose(&effect_b);
+    /// assert_eq!(w2.detectors, vec![1]);
+    /// assert_eq!(w2.dem_outputs, vec![0]);
+    /// ```
+    #[must_use]
+    pub fn compose(&self, other: &Self) -> Self {
+        let mut pauli = self.pauli.clone() * other.pauli.clone();
+        pauli.set_phase(pecos_core::QuarterPhase::PlusOne);
+
+        let mut detectors = self.detectors.clone();
+        xor_sorted(&mut detectors, &other.detectors);
+
+        let mut dem_outputs = self.dem_outputs.clone();
+        xor_sorted(&mut dem_outputs, &other.dem_outputs);
+
+        let mut measurements = self.measurements.clone();
+        xor_sorted_tuples(&mut measurements, &other.measurements);
+
+        Self {
+            pauli,
+            detectors,
+            dem_outputs,
+            measurements,
+        }
+    }
+}
+
+impl GateFaultLocation<'_> {
+    /// Number of qubits this gate acts on.
+    #[must_use]
+    pub fn num_qubits(&self) -> usize {
+        self.qubits.len()
+    }
+
+    /// All possible fault events at this location.
+    ///
+    /// Only returns multi-qubit Paulis where at least one qubit's
+    /// single-qubit component has a non-trivial effect in the influence
+    /// map. E.g., a measurement-before location might only yield X
+    /// faults since Z before MZ is invisible.
+    #[must_use]
+    pub fn possible_faults(&self) -> Vec<pecos_core::PauliString> {
+        let active = self.active_paulis_per_qubit();
+        if active.is_empty() {
+            return Vec::new();
+        }
+
+        let mut combos: Vec<Vec<(usize, pecos_core::Pauli)>> = vec![vec![]];
+        for &(q, ref paulis) in &active {
+            let mut next = Vec::new();
+            for existing in &combos {
+                next.push(existing.clone());
+                for &p in paulis {
+                    let mut extended = existing.clone();
+                    extended.push((q.index(), p));
+                    next.push(extended);
+                }
+            }
+            combos = next;
+        }
+
+        combos
+            .into_iter()
+            .filter(|c| !c.is_empty())
+            .map(|entries| {
+                pecos_core::PauliString::with_phase_and_paulis(
+                    pecos_core::QuarterPhase::PlusOne,
+                    entries
+                        .iter()
+                        .map(|&(q, p)| (p, QubitId::from(q)))
+                        .collect(),
+                )
+            })
+            .collect()
+    }
+
+    /// All fault events that have non-trivial effects (flip at least one
+    /// detector or logical).
+    #[must_use]
+    pub fn events(&self) -> Vec<FaultEffect> {
+        self.possible_faults()
+            .into_iter()
+            .map(|ps| self.query(&ps))
+            .filter(|e| !e.detectors.is_empty() || !e.dem_outputs.is_empty())
+            .collect()
+    }
+
+    /// All physically possible fault events, including those with no effect.
+    ///
+    /// Use this for probability-correct enumeration (e.g., ML decoder).
+    /// Events with empty detectors and `dem_outputs` are "trivial" faults that
+    /// happen with real probability but don't change any observable.
+    #[must_use]
+    pub fn all_events(&self) -> Vec<FaultEffect> {
+        self.all_physical_paulis()
+            .into_iter()
+            .map(|ps| self.query(&ps))
+            .collect()
+    }
+
+    /// All physically meaningful single-qubit Paulis per qubit, regardless
+    /// of whether they have non-trivial effects in the influence map.
+    ///
+    /// Gate-type filtering applies (PZ/MZ only X/Y) but effect filtering
+    /// does not. This ensures correct probability accounting.
+    fn all_physical_paulis(&self) -> Vec<pecos_core::PauliString> {
+        let physical: &[pecos_core::Pauli] = match self.gate_type {
+            // Z-basis prep/measurement: only X (bit-flip) fault.
+            GateType::PZ | GateType::QAlloc | GateType::MZ | GateType::MeasureFree => {
+                &[pecos_core::Pauli::X]
+            }
+            // Unitary gates: all single-qubit Paulis.
+            _ => &[
+                pecos_core::Pauli::X,
+                pecos_core::Pauli::Y,
+                pecos_core::Pauli::Z,
+            ],
+        };
+
+        // Build all combinations (including I on each qubit)
+        let mut combos: Vec<Vec<(usize, pecos_core::Pauli)>> = vec![vec![]];
+        for &q in &self.qubits {
+            let mut next = Vec::new();
+            for existing in &combos {
+                next.push(existing.clone()); // I on this qubit
+                for &p in physical {
+                    let mut extended = existing.clone();
+                    extended.push((q.index(), p));
+                    next.push(extended);
+                }
+            }
+            combos = next;
+        }
+
+        combos
+            .into_iter()
+            .filter(|c| !c.is_empty())
+            .map(|entries| {
+                pecos_core::PauliString::with_phase_and_paulis(
+                    pecos_core::QuarterPhase::PlusOne,
+                    entries
+                        .iter()
+                        .map(|&(q, p)| (p, QubitId::from(q)))
+                        .collect(),
+                )
+            })
+            .collect()
+    }
+
+    /// Query the effect of a specific multi-qubit Pauli event.
+    #[must_use]
+    pub fn query(&self, pauli: &pecos_core::PauliString) -> FaultEffect {
+        let entries: Vec<(usize, pecos_core::Pauli)> = pauli
+            .paulis()
+            .iter()
+            .map(|&(p, q)| (q.index(), p))
+            .collect();
+        let (detectors, dem_outputs) = self.compose_effects(&entries);
+
+        // Resolve detector indices to raw measurements
+        let measurements = self.resolve_measurements(&detectors);
+
+        FaultEffect {
+            pauli: pauli.clone(),
+            detectors,
+            dem_outputs,
+            measurements,
+        }
+    }
+
+    /// Which single-qubit Paulis are physically meaningful at each qubit.
+    ///
+    /// Filters based on both the influence map (has non-trivial effect) and
+    /// the gate type (Z after PZ is unphysical, Z before MZ is invisible).
+    fn active_paulis_per_qubit(&self) -> Vec<(QubitId, Vec<pecos_core::Pauli>)> {
+        // Determine which Paulis are physical for this gate type
+        let physical_paulis: &[Pauli] = match self.gate_type {
+            // Z-basis prep/measurement: only X (bit-flip) fault.
+            GateType::PZ | GateType::QAlloc | GateType::MZ | GateType::MeasureFree => &[Pauli::X],
+            // Unitary gates: all single-qubit Paulis.
+            _ => &[Pauli::X, Pauli::Y, Pauli::Z],
+        };
+
+        self.qubit_loc_indices
+            .iter()
+            .filter_map(|&(qubit, loc_idx)| {
+                let mut paulis = Vec::new();
+                for &p in physical_paulis {
+                    if self.map.influences.has_detector_flips(loc_idx, p)
+                        || self.map.influences.has_dem_output_flips(loc_idx, p)
+                    {
+                        paulis.push(propagator_to_core_pauli(p));
+                    }
+                }
+                if paulis.is_empty() {
+                    None
+                } else {
+                    Some((QubitId::from(qubit), paulis))
+                }
+            })
+            .collect()
+    }
+
+    /// Compose per-qubit effects via XOR (symmetric difference).
+    fn compose_effects(&self, entries: &[(usize, pecos_core::Pauli)]) -> (Vec<u32>, Vec<u32>) {
+        let mut det_set: Vec<u32> = Vec::new();
+        let mut dem_output_set: Vec<u32> = Vec::new();
+
+        for &(qubit, pauli) in entries {
+            if pauli == pecos_core::Pauli::I {
+                continue;
+            }
+            let prop_pauli = core_to_propagator_pauli(pauli);
+
+            if let Some(&(_, loc_idx)) = self.qubit_loc_indices.iter().find(|&&(q, _)| q == qubit) {
+                let dets = self.map.influences.detectors(loc_idx, prop_pauli);
+                xor_sorted(&mut det_set, dets);
+                let dem_outputs = self.map.influences.dem_outputs(loc_idx, prop_pauli);
+                xor_sorted(&mut dem_output_set, dem_outputs);
+            }
+        }
+
+        (det_set, dem_output_set)
+    }
+
+    /// Resolve detector indices to raw measurement tuples.
+    fn resolve_measurements(&self, detector_indices: &[u32]) -> Vec<(usize, usize, u8)> {
+        let mut measurements = Vec::new();
+        for &det_idx in detector_indices {
+            if let Some(det) = self.map.detectors.get(det_idx as usize) {
+                for meas_id in &det.measurements {
+                    measurements.push((meas_id.tick, meas_id.qubit, meas_id.basis));
+                }
+            }
+        }
+        measurements
+    }
+}
+
+/// Symmetric difference for sorted `(usize, usize, u8)` tuples (measurements).
+fn xor_sorted_tuples(acc: &mut Vec<(usize, usize, u8)>, other: &[(usize, usize, u8)]) {
+    if other.is_empty() {
+        return;
+    }
+    if acc.is_empty() {
+        acc.extend_from_slice(other);
+        return;
+    }
+    let mut result = Vec::with_capacity(acc.len() + other.len());
+    let mut i = 0;
+    let mut j = 0;
+    while i < acc.len() && j < other.len() {
+        match acc[i].cmp(&other[j]) {
+            std::cmp::Ordering::Less => {
+                result.push(acc[i]);
+                i += 1;
+            }
+            std::cmp::Ordering::Greater => {
+                result.push(other[j]);
+                j += 1;
+            }
+            std::cmp::Ordering::Equal => {
+                i += 1;
+                j += 1;
+            }
+        }
+    }
+    result.extend_from_slice(&acc[i..]);
+    result.extend_from_slice(&other[j..]);
+    *acc = result;
+}
+
+/// Convert `pecos_core::Pauli` to the propagator's `Pauli`.
+fn core_to_propagator_pauli(p: pecos_core::Pauli) -> Pauli {
+    match p {
+        pecos_core::Pauli::I => Pauli::I,
+        pecos_core::Pauli::X => Pauli::X,
+        pecos_core::Pauli::Y => Pauli::Y,
+        pecos_core::Pauli::Z => Pauli::Z,
+    }
+}
+
+/// Convert the propagator's `Pauli` to `pecos_core::Pauli`.
+fn propagator_to_core_pauli(p: Pauli) -> pecos_core::Pauli {
+    match p {
+        Pauli::I => pecos_core::Pauli::I,
+        Pauli::X => pecos_core::Pauli::X,
+        Pauli::Y => pecos_core::Pauli::Y,
+        Pauli::Z => pecos_core::Pauli::Z,
+    }
+}
+
+/// Symmetric difference of two sorted u32 slices, mutating `acc` in place.
+fn xor_sorted(acc: &mut Vec<u32>, other: &[u32]) {
+    if other.is_empty() {
+        return;
+    }
+    if acc.is_empty() {
+        acc.extend_from_slice(other);
+        return;
+    }
+    // Build symmetric difference: elements in exactly one of the two sets
+    let mut result = Vec::with_capacity(acc.len() + other.len());
+    let mut i = 0;
+    let mut j = 0;
+    while i < acc.len() && j < other.len() {
+        match acc[i].cmp(&other[j]) {
+            std::cmp::Ordering::Less => {
+                result.push(acc[i]);
+                i += 1;
+            }
+            std::cmp::Ordering::Greater => {
+                result.push(other[j]);
+                j += 1;
+            }
+            std::cmp::Ordering::Equal => {
+                // In both sets -- they cancel (XOR)
+                i += 1;
+                j += 1;
+            }
+        }
+    }
+    result.extend_from_slice(&acc[i..]);
+    result.extend_from_slice(&other[j..]);
+    *acc = result;
+}
+
+impl DagFaultInfluenceMap {
+    /// Group per-qubit locations into per-gate fault locations.
+    ///
+    /// Each returned [`GateFaultLocation`] represents a gate at a specific
+    /// timing (before/after) and supports querying multi-qubit Pauli events.
+    ///
+    /// ```
+    /// use pecos_qec::fault_tolerance::propagator::dag::DagFaultInfluenceMap;
+    ///
+    /// let map = DagFaultInfluenceMap::with_capacity(0);
+    /// for loc in map.gate_fault_locations() {
+    ///     for event in loc.events() {
+    ///         println!("{}: dets={:?} dem_outputs={:?}", event.pauli, event.detectors, event.dem_outputs);
+    ///     }
+    /// }
+    /// ```
+    #[must_use]
+    pub fn gate_fault_locations(&self) -> Vec<GateFaultLocation<'_>> {
+        let mut groups: std::collections::BTreeMap<(usize, bool), Vec<(usize, usize)>> =
+            std::collections::BTreeMap::new();
+
+        for (loc_idx, loc) in self.locations.iter().enumerate() {
+            let key = (loc.node, loc.before);
+            for q in &loc.qubits {
+                groups.entry(key).or_default().push((q.index(), loc_idx));
+            }
+        }
+
+        groups
+            .into_iter()
+            .map(|((node, before), qubit_locs)| {
+                let gate_type = self.locations[qubit_locs[0].1].gate_type;
+                let qubits: Vec<QubitId> =
+                    qubit_locs.iter().map(|&(q, _)| QubitId::from(q)).collect();
+                GateFaultLocation {
+                    map: self,
+                    node,
+                    gate_type,
+                    qubits,
+                    before,
+                    qubit_loc_indices: qubit_locs,
+                }
+            })
+            .collect()
+    }
+}
+
+// ============================================================================
+// Weight-w Fault Enumeration
+// ============================================================================
+
+/// A single component of a multi-fault combination.
+#[derive(Debug, Clone)]
+pub struct FaultComponent {
+    /// Index into `gate_fault_locations()`.
+    pub location_index: usize,
+    /// The fault event at this location.
+    pub event: FaultEffect,
+}
+
+/// A weight-w combination of faults and their combined effect.
+#[derive(Debug, Clone)]
+pub struct FaultCombo {
+    /// The individual (location, event) pairs.
+    pub components: Vec<FaultComponent>,
+    /// Combined effect (XOR of all component effects).
+    pub effect: FaultEffect,
+}
+
+impl DagFaultInfluenceMap {
+    /// Enumerate all weight-w fault combinations, calling `f` for each.
+    ///
+    /// At weight 1, this iterates every fault location and every possible
+    /// fault event. At weight 2, all pairs of (location, event). And so on.
+    ///
+    /// Uses a callback to avoid allocating a potentially huge result vec.
+    ///
+    /// ```
+    /// use pecos_qec::fault_tolerance::propagator::dag::DagFaultInfluenceMap;
+    ///
+    /// let map = DagFaultInfluenceMap::with_capacity(0);
+    /// // Find all undetectable weight-2 errors
+    /// map.for_each_fault_combo(2, |combo| {
+    ///     if !combo.effect.dem_outputs.is_empty() && combo.effect.detectors.is_empty() {
+    ///         println!("Undetectable w=2:");
+    ///         for c in &combo.components {
+    ///             println!("  {} at loc {}", c.event.pauli, c.location_index);
+    ///         }
+    ///     }
+    /// });
+    /// ```
+    pub fn for_each_fault_combo(&self, weight: usize, mut f: impl FnMut(&FaultCombo)) {
+        let locs = self.gate_fault_locations();
+
+        // Pre-compute events for each location
+        let all_events: Vec<Vec<FaultEffect>> =
+            locs.iter().map(GateFaultLocation::events).collect();
+
+        let empty_effect = FaultEffect {
+            pauli: pecos_core::PauliString::identity(),
+            detectors: Vec::new(),
+            dem_outputs: Vec::new(),
+            measurements: Vec::new(),
+        };
 
-        (
-            num_locations,
-            num_detectors,
-            num_logicals,
-            self.influences.detectors_x.offsets.clone(),
-            self.influences.detectors_x.data.clone(),
-            self.influences.detectors_y.offsets.clone(),
-            self.influences.detectors_y.data.clone(),
-            self.influences.detectors_z.offsets.clone(),
-            self.influences.detectors_z.data.clone(),
-            self.influences.logicals_x.offsets.clone(),
-            self.influences.logicals_x.data.clone(),
-            self.influences.logicals_y.offsets.clone(),
-            self.influences.logicals_y.data.clone(),
-            self.influences.logicals_z.offsets.clone(),
-            self.influences.logicals_z.data.clone(),
-        )
+        let mut components = Vec::with_capacity(weight);
+        let mut effects_stack = vec![empty_effect];
+
+        enumerate_combos(
+            &all_events,
+            weight,
+            0, // start_loc
+            &mut components,
+            &mut effects_stack,
+            &mut f,
+        );
+    }
+}
+
+/// Recursive helper for weight-w combination enumeration.
+fn enumerate_combos(
+    all_events: &[Vec<FaultEffect>],
+    remaining: usize,
+    start_loc: usize,
+    components: &mut Vec<FaultComponent>,
+    effects_stack: &mut Vec<FaultEffect>,
+    f: &mut impl FnMut(&FaultCombo),
+) {
+    if remaining == 0 {
+        f(&FaultCombo {
+            components: components.clone(),
+            effect: effects_stack.last().unwrap().clone(),
+        });
+        return;
+    }
+
+    for loc_idx in start_loc..all_events.len() {
+        for event in &all_events[loc_idx] {
+            let combined = effects_stack.last().unwrap().compose(event);
+
+            components.push(FaultComponent {
+                location_index: loc_idx,
+                event: event.clone(),
+            });
+            effects_stack.push(combined);
+
+            enumerate_combos(
+                all_events,
+                remaining - 1,
+                loc_idx + 1, // no repeats
+                components,
+                effects_stack,
+                f,
+            );
+
+            components.pop();
+            effects_stack.pop();
+        }
     }
 }
 
@@ -779,8 +1674,8 @@ impl InfluenceRecorder for BucketRecorder {
         if obs_x {
             self.z_buckets[loc_idx].push(det);
         }
-        // Y fault anticommutes with X or Z observable
-        if obs_x || obs_z {
+        // Y fault anticommutes with X or Z but NOT both (Y commutes with Y)
+        if obs_x ^ obs_z {
             self.y_buckets[loc_idx].push(det);
         }
     }
@@ -873,28 +1768,26 @@ impl<'a> DagFaultAnalyzer<'a> {
 
         for &node in &topo_order {
             if let Some(gate) = propagator.gate(node) {
+                // Skip meta-gates — they don't create fault locations
+                if gate.gate_type.is_meta() {
+                    continue;
+                }
+
                 let is_measurement = matches!(gate.gate_type, GateType::MZ | GateType::MeasureFree);
-                let is_prep = matches!(gate.gate_type, GateType::PZ | GateType::QAlloc);
 
                 // Convert QubitId to usize
                 let qubits: SmallVec<[usize; 2]> =
                     gate.qubits.iter().map(pecos_core::QubitId::index).collect();
 
-                // Create per-qubit fault locations for proper depolarizing noise analysis
+                // Standard circuit noise model: one fault location per gate.
+                //   Measurement: before (X flip before readout)
+                //   All others (prep, unitary, idle): after
+                // Idle gates on non-active qubits provide the missing "before"
+                // coverage that would otherwise require before-gate locations.
+                let before = is_measurement;
                 for &q in &qubits {
                     let single_qubit: SmallVec<[usize; 2]> = smallvec::smallvec![q];
-
-                    if is_measurement {
-                        // Measurements only have before=true locations
-                        locations.push(node, single_qubit, true, gate.gate_type);
-                    } else if is_prep {
-                        // Preps only have before=false locations
-                        locations.push(node, single_qubit, false, gate.gate_type);
-                    } else {
-                        // Regular gates have both before and after locations
-                        locations.push(node, single_qubit.clone(), true, gate.gate_type);
-                        locations.push(node, single_qubit, false, gate.gate_type);
-                    }
+                    locations.push(node, single_qubit, before, gate.gate_type);
                 }
             }
         }
@@ -934,8 +1827,9 @@ impl<'a> DagFaultAnalyzer<'a> {
         map.locations = self.locations.to_dag_spacetime_locations();
 
         // Extract measurements and create detectors
-        let measurements = self.extract_measurements();
+        let (measurements, meas_ids) = self.extract_measurements();
         map.measurements.clone_from(&measurements);
+        map.meas_ids = meas_ids;
 
         for &(node, qubit, basis) in &measurements {
             let measurement_id = MeasurementId {
@@ -946,11 +1840,8 @@ impl<'a> DagFaultAnalyzer<'a> {
             map.detectors.push(DetectorId::single(measurement_id));
         }
 
-        // Use bucket recorder for O(n) construction
-        let mut recorder = BucketRecorder::new(num_locations);
-
-        // Propagate using the generic method with bucket recorder
-        self.propagate_all(&mut recorder);
+        // Use forest propagation: per-ancilla Phase 1/Phase 2 split.
+        let recorder = self.propagate_all_forest();
 
         // Convert buckets to SoA format (O(n) flattening)
         map.influences = recorder.into_soa();
@@ -964,12 +1855,17 @@ impl<'a> DagFaultAnalyzer<'a> {
     /// 1. Topological position (to respect causal dependencies)
     /// 2. Qubit index (to break ties for concurrent/independent measurements)
     ///
-    /// This ensures the measurement ordering matches Stim's convention where
-    /// measurements on lower-indexed qubits appear first when they're in the
-    /// same "layer" of the circuit.
+    /// This gives deterministic measurement ordering where measurements on
+    /// lower-indexed qubits appear first when they are in the same "layer" of
+    /// the circuit.
     #[must_use]
-    pub fn extract_measurements(&self) -> Vec<(usize, usize, u8)> {
-        let mut measurements = Vec::new();
+    /// Extract measurements with optional `MeasId` IDs.
+    ///
+    /// Returns `(measurements, meas_ids)` where:
+    /// - `measurements` is `Vec<(node, qubit, basis)>` in `MeasId` order
+    /// - `meas_ids` is `Vec<MeasId>` (empty for legacy circuits)
+    pub fn extract_measurements(&self) -> (Vec<(usize, usize, u8)>, Vec<pecos_core::MeasId>) {
+        let mut entries = Vec::new(); // (sort_key, qubit, node, basis, Option<MeasId>)
 
         for &node in self.propagator.topo_order() {
             if let Some(gate) = self.propagator.gate(node) {
@@ -978,23 +1874,39 @@ impl<'a> DagFaultAnalyzer<'a> {
                     _ => continue,
                 };
 
-                let topo_pos = self.propagator.topo_position(node);
-                for qubit in &gate.qubits {
-                    // Store (topo_pos, qubit, node, basis) for sorting
-                    measurements.push((topo_pos, qubit.index(), node, basis));
+                if gate.meas_ids.is_empty() {
+                    let topo_pos = self.propagator.topo_position(node);
+                    for qubit in &gate.qubits {
+                        entries.push((topo_pos, qubit.index(), node, basis, None));
+                    }
+                } else {
+                    for (i, qubit) in gate.qubits.iter().enumerate() {
+                        let mr = gate.meas_ids.get(i).copied();
+                        let sort_key = mr.map_or(usize::MAX, pecos_core::MeasId::index);
+                        entries.push((sort_key, qubit.index(), node, basis, mr));
+                    }
                 }
             }
         }
 
-        // Sort by (topological_position, qubit_index) for deterministic ordering
-        // This ensures measurements on lower-indexed qubits come first when concurrent
-        measurements.sort_by_key(|&(topo_pos, qubit, _, _)| (topo_pos, qubit));
+        entries.sort_by_key(|&(sort_key, qubit, _, _, _)| (sort_key, qubit));
 
-        // Return in the expected format: (node, qubit, basis)
-        measurements
+        let has_meas_ids = entries.iter().any(|(_, _, _, _, mr)| mr.is_some());
+        let meas_ids = if has_meas_ids {
+            entries
+                .iter()
+                .map(|(_, _, _, _, mr)| mr.unwrap_or(pecos_core::MeasId(usize::MAX)))
+                .collect()
+        } else {
+            Vec::new()
+        };
+
+        let measurements = entries
             .into_iter()
-            .map(|(_, qubit, node, basis)| (node, qubit, basis))
-            .collect()
+            .map(|(_, qubit, node, basis, _)| (node, qubit, basis))
+            .collect();
+
+        (measurements, meas_ids)
     }
 
     // =========================================================================
@@ -1152,6 +2064,320 @@ impl<'a> DagFaultAnalyzer<'a> {
         }
     }
 
+    // ====================================================================
+    // Forest propagation: per-ancilla Phase 1 / Phase 2 split
+    // ====================================================================
+
+    /// Captured influence entry from Phase 2 (shared tail below PZ).
+    /// Stored with `topo_pos` for prefix slicing across measurements.
+    ///
+    /// Phase 1: propagate from MZ backward through within-round gates,
+    /// stopping at the ancilla's PZ. Records influences normally.
+    /// Returns the PZ node's topo position, or None if no PZ was hit.
+    ///
+    /// After return, `work.heap` still contains data qubit gates below
+    /// the PZ — ready for Phase 2.
+    fn propagate_phase1<R: InfluenceRecorder>(
+        &self,
+        request: &Phase1Request,
+        recorder: &mut R,
+        work: &mut PropagationBuffers,
+        prop: &mut PauliProp,
+    ) -> Option<usize> {
+        let visited = &mut work.visited;
+        let active_qubits = &mut work.active_qubits;
+        let heap = &mut work.heap;
+        visited.fill(false);
+        active_qubits.fill(false);
+        heap.clear();
+
+        *prop = PauliProp::new();
+        if request.basis == 0 {
+            prop.track_z(&[request.meas_qubit]);
+        } else {
+            prop.track_x(&[request.meas_qubit]);
+        }
+
+        let meas_topo_pos = self.propagator.topo_position(request.meas_node);
+        self.record_at_node_generic(
+            request.meas_node,
+            prop,
+            request.detector_idx,
+            recorder,
+            true,
+        );
+
+        if request.meas_qubit <= self.max_qubit() {
+            active_qubits[request.meas_qubit] = true;
+            for (topo_pos, node) in self.propagator.qubit_gates_backward(request.meas_qubit) {
+                if topo_pos < meas_topo_pos && !visited[node] {
+                    visited[node] = true;
+                    heap.push((topo_pos, node));
+                }
+            }
+        }
+
+        while let Some((_, node)) = heap.pop() {
+            if let Some(gate) = self.propagator.gate(node) {
+                let mut was_active = [false; 8];
+                for (j, q) in gate.qubits.iter().enumerate() {
+                    if j < was_active.len() && q.index() <= self.max_qubit() {
+                        was_active[j] = active_qubits[q.index()];
+                    }
+                }
+
+                self.record_at_node_generic(node, prop, request.detector_idx, recorder, false);
+
+                if matches!(gate.gate_type, GateType::PZ | GateType::QAlloc) {
+                    let pz_topo = self.propagator.topo_position(node);
+                    for q in &gate.qubits {
+                        let idx = q.index();
+                        if idx <= self.max_qubit() {
+                            if prop.contains_x(idx) {
+                                prop.track_x(&[idx]);
+                            }
+                            if prop.contains_z(idx) {
+                                prop.track_z(&[idx]);
+                            }
+                            active_qubits[idx] = false;
+                        }
+                    }
+                    // Stop Phase 1 — data qubit gates remain in the heap.
+                    return Some(pz_topo);
+                }
+
+                apply_gate(prop, gate, Direction::Backward);
+                self.record_at_node_generic(node, prop, request.detector_idx, recorder, true);
+
+                let node_topo_pos = self.propagator.topo_position(node);
+                for (j, q) in gate.qubits.iter().enumerate() {
+                    let idx = q.index();
+                    if idx <= self.max_qubit() {
+                        let now_active = prop.contains_x(idx) || prop.contains_z(idx);
+                        let was = j < was_active.len() && was_active[j];
+                        if now_active && !was {
+                            active_qubits[idx] = true;
+                            for (topo_pos, new_node) in self.propagator.qubit_gates_backward(idx) {
+                                if topo_pos < node_topo_pos && !visited[new_node] {
+                                    visited[new_node] = true;
+                                    heap.push((topo_pos, new_node));
+                                }
+                            }
+                        } else if !now_active && was {
+                            active_qubits[idx] = false;
+                        }
+                    }
+                }
+            }
+        }
+        None // No PZ hit (e.g., first round init detectors)
+    }
+
+    /// Phase 2: continue backward propagation from data qubit frontier
+    /// below PZ. Records to `recorder` AND captures the visited node
+    /// sequence for replay.
+    fn propagate_phase2_capture<R: InfluenceRecorder>(
+        &self,
+        detector_idx: usize,
+        recorder: &mut R,
+        work: &mut PropagationBuffers,
+        prop: &mut PauliProp,
+    ) -> Vec<usize> {
+        let mut visited_nodes: Vec<usize> = Vec::new();
+        let visited = &mut work.visited;
+        let active_qubits = &mut work.active_qubits;
+        let heap = &mut work.heap;
+
+        while let Some((_, node)) = heap.pop() {
+            if let Some(gate) = self.propagator.gate(node) {
+                let mut was_active = [false; 8];
+                for (j, q) in gate.qubits.iter().enumerate() {
+                    if j < was_active.len() && q.index() <= self.max_qubit() {
+                        was_active[j] = active_qubits[q.index()];
+                    }
+                }
+
+                self.record_at_node_generic(node, prop, detector_idx, recorder, false);
+                visited_nodes.push(node);
+
+                if matches!(gate.gate_type, GateType::PZ | GateType::QAlloc) {
+                    for q in &gate.qubits {
+                        let idx = q.index();
+                        if idx <= self.max_qubit() {
+                            if prop.contains_x(idx) {
+                                prop.track_x(&[idx]);
+                            }
+                            if prop.contains_z(idx) {
+                                prop.track_z(&[idx]);
+                            }
+                            active_qubits[idx] = false;
+                        }
+                    }
+                    continue;
+                }
+
+                apply_gate(prop, gate, Direction::Backward);
+                self.record_at_node_generic(node, prop, detector_idx, recorder, true);
+
+                let node_topo = self.propagator.topo_position(node);
+                for (j, q) in gate.qubits.iter().enumerate() {
+                    let idx = q.index();
+                    if idx <= self.max_qubit() {
+                        let now_active = prop.contains_x(idx) || prop.contains_z(idx);
+                        let was = j < was_active.len() && was_active[j];
+                        if now_active && !was {
+                            active_qubits[idx] = true;
+                            for (topo_pos, new_node) in self.propagator.qubit_gates_backward(idx) {
+                                if topo_pos < node_topo && !visited[new_node] {
+                                    visited[new_node] = true;
+                                    heap.push((topo_pos, new_node));
+                                }
+                            }
+                        } else if !now_active && was {
+                            active_qubits[idx] = false;
+                        }
+                    }
+                }
+            }
+        }
+        visited_nodes
+    }
+
+    /// Replay Phase 2 using a cached node sequence.
+    ///
+    /// Iterates the captured nodes, re-applies gates backward to the Pauli
+    /// state, and re-records with the correct `obs_x/obs_z` values. No heap
+    /// or visited array needed — just a flat loop over known nodes.
+    fn replay_phase2<R: InfluenceRecorder>(
+        &self,
+        nodes: &[usize],
+        pz_topo: usize,
+        detector_idx: usize,
+        recorder: &mut R,
+        prop: &mut PauliProp,
+    ) {
+        for &node in nodes {
+            if self.propagator.topo_position(node) >= pz_topo {
+                continue;
+            }
+
+            if let Some(gate) = self.propagator.gate(node) {
+                self.record_at_node_generic(node, prop, detector_idx, recorder, false);
+
+                if matches!(gate.gate_type, GateType::PZ | GateType::QAlloc) {
+                    for q in &gate.qubits {
+                        let idx = q.index();
+                        if idx <= self.max_qubit() {
+                            if prop.contains_x(idx) {
+                                prop.track_x(&[idx]);
+                            }
+                            if prop.contains_z(idx) {
+                                prop.track_z(&[idx]);
+                            }
+                        }
+                    }
+                    continue;
+                }
+
+                apply_gate(prop, gate, Direction::Backward);
+                self.record_at_node_generic(node, prop, detector_idx, recorder, true);
+            }
+        }
+    }
+
+    /// Parallel forest propagation: groups measurements by ancilla qubit,
+    /// propagates the latest measurement fully with capture, replays the
+    /// shared tail prefix for earlier measurements.
+    #[must_use]
+    pub fn propagate_all_forest(&self) -> BucketRecorder {
+        use rayon::prelude::*;
+
+        let (measurements, _meas_ids) = self.extract_measurements();
+        let num_locations = self.locations.len();
+
+        // Group measurement indices by qubit (ancilla).
+        let mut by_qubit: BTreeMap<usize, Vec<usize>> = BTreeMap::new();
+        for (det_idx, &(_, qubit, _)) in measurements.iter().enumerate() {
+            by_qubit.entry(qubit).or_default().push(det_idx);
+        }
+
+        // Collect ancilla groups for parallel iteration.
+        let groups: Vec<Vec<usize>> = by_qubit.into_values().collect();
+
+        let per_thread: Vec<BucketRecorder> = groups
+            .par_iter()
+            .map(|det_indices| {
+                let mut recorder = BucketRecorder::new(num_locations);
+                let mut work = PropagationBuffers {
+                    visited: vec![false; self.propagator.max_node() + 1],
+                    active_qubits: vec![false; self.propagator.max_qubit() + 1],
+                    heap: BinaryHeap::with_capacity(64),
+                };
+
+                // Sort by topo position (ascending = earliest first).
+                let mut sorted = det_indices.clone();
+                sorted.sort_by_key(|&i| self.propagator.topo_position(measurements[i].0));
+
+                // Latest measurement: Phase 1 + Phase 2 with capture
+                let Some(&latest) = sorted.last() else {
+                    return recorder;
+                };
+                let (l_node, l_qubit, l_basis) = measurements[latest];
+
+                let mut prop = PauliProp::new();
+
+                let latest_request = Phase1Request {
+                    meas_node: l_node,
+                    meas_qubit: l_qubit,
+                    basis: l_basis,
+                    detector_idx: latest,
+                };
+                let _pz_topo =
+                    self.propagate_phase1(&latest_request, &mut recorder, &mut work, &mut prop);
+                let tail_capture =
+                    self.propagate_phase2_capture(latest, &mut recorder, &mut work, &mut prop);
+
+                // Earlier measurements: Phase 1 + replay tail with correct Pauli state
+                for &det_idx in sorted[..sorted.len() - 1].iter().rev() {
+                    let (m_node, m_qubit, m_basis) = measurements[det_idx];
+
+                    let request = Phase1Request {
+                        meas_node: m_node,
+                        meas_qubit: m_qubit,
+                        basis: m_basis,
+                        detector_idx: det_idx,
+                    };
+                    let pz_topo_i =
+                        self.propagate_phase1(&request, &mut recorder, &mut work, &mut prop);
+
+                    // Replay cached node sequence with correct Pauli state
+                    if let Some(pz_pos) = pz_topo_i {
+                        self.replay_phase2(
+                            &tail_capture,
+                            pz_pos,
+                            det_idx,
+                            &mut recorder,
+                            &mut prop,
+                        );
+                    }
+                }
+
+                recorder
+            })
+            .collect();
+
+        // Merge all recorders
+        let mut merged = BucketRecorder::new(num_locations);
+        for rec in per_thread {
+            for i in 0..num_locations {
+                merged.x_buckets[i].extend(rec.x_buckets[i].iter().copied());
+                merged.y_buckets[i].extend(rec.y_buckets[i].iter().copied());
+                merged.z_buckets[i].extend(rec.z_buckets[i].iter().copied());
+            }
+        }
+        merged
+    }
+
     /// Builds a fault influence map using a custom recorder.
     ///
     /// This is the most flexible method, allowing custom recording strategies.
@@ -1176,7 +2402,7 @@ impl<'a> DagFaultAnalyzer<'a> {
     /// println!("Total influences: {}", recorder.count);
     /// ```
     pub fn propagate_all<R: InfluenceRecorder>(&self, recorder: &mut R) {
-        let measurements = self.extract_measurements();
+        let (measurements, _) = self.extract_measurements();
 
         let mut work = PropagationBuffers {
             visited: vec![false; self.propagator.max_node() + 1],
@@ -1195,6 +2421,55 @@ impl<'a> DagFaultAnalyzer<'a> {
             );
         }
     }
+
+    /// Parallel version: propagates from all measurements using rayon.
+    /// Each thread gets its own `BucketRecorder`, results are merged.
+    #[must_use]
+    pub fn propagate_all_parallel(&self) -> BucketRecorder {
+        use rayon::prelude::*;
+
+        let (measurements, _) = self.extract_measurements();
+        let num_locations = self.locations.len();
+
+        let chunk_size = measurements.len().div_ceil(rayon::current_num_threads());
+
+        let per_thread: Vec<BucketRecorder> = measurements
+            .par_chunks(chunk_size.max(1))
+            .enumerate()
+            .map(|(chunk_idx, chunk)| {
+                let base_idx = chunk_idx * chunk_size;
+                let mut recorder = BucketRecorder::new(num_locations);
+                let mut work = PropagationBuffers {
+                    visited: vec![false; self.propagator.max_node() + 1],
+                    active_qubits: vec![false; self.propagator.max_qubit() + 1],
+                    heap: BinaryHeap::with_capacity(64),
+                };
+
+                for (i, &(node, qubit, basis)) in chunk.iter().enumerate() {
+                    self.propagate_from_measurement_generic(
+                        node,
+                        qubit,
+                        basis,
+                        base_idx + i,
+                        &mut recorder,
+                        &mut work,
+                    );
+                }
+                recorder
+            })
+            .collect();
+
+        // Merge all recorders
+        let mut merged = BucketRecorder::new(num_locations);
+        for rec in per_thread {
+            for i in 0..num_locations {
+                merged.x_buckets[i].extend(rec.x_buckets[i].iter().copied());
+                merged.y_buckets[i].extend(rec.y_buckets[i].iter().copied());
+                merged.z_buckets[i].extend(rec.z_buckets[i].iter().copied());
+            }
+        }
+        merged
+    }
 }
 
 #[cfg(test)]
@@ -1370,12 +2645,14 @@ mod tests {
             qubits: vec![QubitId::from(0)],
             before: true,
             gate_type: GateType::H,
+            idle_duration: 0,
         };
         let loc2 = DagSpacetimeLocation {
             node: 1,
             qubits: vec![QubitId::from(0)],
             before: true,
             gate_type: GateType::H,
+            idle_duration: 0,
         };
         assert!(loc1 < loc2);
     }
@@ -1414,9 +2691,9 @@ mod tests {
         soa.detectors_y.finish_row();
         soa.detectors_z.finish_row();
         soa.detectors_x.finish_row();
-        soa.logicals_x.finish_row();
-        soa.logicals_y.finish_row();
-        soa.logicals_z.finish_row();
+        soa.dem_outputs_x.finish_row();
+        soa.dem_outputs_y.finish_row();
+        soa.dem_outputs_z.finish_row();
         soa.num_locations += 1;
 
         // Location 1: Z flips detector 1
@@ -1424,9 +2701,9 @@ mod tests {
         soa.detectors_y.finish_row();
         soa.detectors_z.push(1);
         soa.detectors_z.finish_row();
-        soa.logicals_x.finish_row();
-        soa.logicals_y.finish_row();
-        soa.logicals_z.finish_row();
+        soa.dem_outputs_x.finish_row();
+        soa.dem_outputs_y.finish_row();
+        soa.dem_outputs_z.finish_row();
         soa.num_locations += 1;
 
         assert!(soa.has_detector_flips(0, Pauli::X));
@@ -1435,6 +2712,106 @@ mod tests {
         assert!(soa.has_detector_flips(1, Pauli::Z));
     }
 
+    #[test]
+    fn test_export_csr_filters_tracked_paulis_from_dem_outputs() {
+        let mut dag = DagCircuit::new();
+        dag.pz(&[0]);
+        dag.h(&[0]);
+
+        let map = crate::fault_tolerance::InfluenceBuilder::new(&dag)
+            .with_z(&[0])
+            .build();
+
+        assert_eq!(map.num_dem_outputs(), 0);
+        assert_eq!(map.num_tracked_paulis(), 1);
+        assert!(
+            map.influences.max_dem_output_index().is_some(),
+            "tracked Pauli should still use internal propagation storage"
+        );
+
+        let (
+            _num_locations,
+            _num_detectors,
+            num_dem_outputs,
+            _detector_offsets_x,
+            _detector_data_x,
+            _detector_offsets_y,
+            _detector_data_y,
+            _detector_offsets_z,
+            _detector_data_z,
+            dem_output_offsets_x,
+            dem_output_data_x,
+            dem_output_offsets_y,
+            dem_output_data_y,
+            dem_output_offsets_z,
+            dem_output_data_z,
+        ) = map.export_csr();
+
+        assert_eq!(num_dem_outputs, 0);
+        assert!(dem_output_data_x.is_empty());
+        assert!(dem_output_data_y.is_empty());
+        assert!(dem_output_data_z.is_empty());
+        assert_eq!(dem_output_offsets_x.len(), map.locations.len() + 1);
+        assert_eq!(dem_output_offsets_y.len(), map.locations.len() + 1);
+        assert_eq!(dem_output_offsets_z.len(), map.locations.len() + 1);
+    }
+
+    #[test]
+    fn test_dem_output_helpers_use_separate_compact_id_spaces() {
+        let mut map = DagFaultInfluenceMap::with_capacity(1);
+        map.locations.push(DagSpacetimeLocation {
+            node: 0,
+            qubits: vec![QubitId(0)],
+            before: false,
+            gate_type: GateType::H,
+            idle_duration: 0,
+        });
+        map.dem_output_metadata = vec![
+            DemOutputMetadata::tracked_pauli(pecos_core::PauliString::xs(&[0])),
+            DemOutputMetadata::observable(pecos_core::PauliString::zs(&[0])),
+            DemOutputMetadata::tracked_pauli(pecos_core::PauliString::zs(&[1])),
+        ];
+
+        map.influences.dem_outputs_x.extend([0, 1, 2]);
+        map.influences.dem_outputs_x.finish_row();
+        map.influences.dem_outputs_y.finish_row();
+        map.influences.dem_outputs_z.finish_row();
+        map.influences.detectors_x.finish_row();
+        map.influences.detectors_y.finish_row();
+        map.influences.detectors_z.finish_row();
+        map.influences.num_locations = 1;
+
+        assert_eq!(map.num_dem_outputs(), 1);
+        assert_eq!(map.num_tracked_paulis(), 2);
+        assert_eq!(map.get_observable_indices(0, Pauli::X.as_u8()), vec![0]);
+        assert_eq!(
+            map.get_tracked_pauli_indices(0, Pauli::X.as_u8()),
+            vec![0, 1]
+        );
+
+        let (
+            _num_locations,
+            _num_detectors,
+            num_dem_outputs,
+            _detector_offsets_x,
+            _detector_data_x,
+            _detector_offsets_y,
+            _detector_data_y,
+            _detector_offsets_z,
+            _detector_data_z,
+            dem_output_offsets_x,
+            dem_output_data_x,
+            _dem_output_offsets_y,
+            _dem_output_data_y,
+            _dem_output_offsets_z,
+            _dem_output_data_z,
+        ) = map.export_csr();
+
+        assert_eq!(num_dem_outputs, 1);
+        assert_eq!(dem_output_offsets_x, vec![0, 1]);
+        assert_eq!(dem_output_data_x, vec![0]);
+    }
+
     // =========================================================================
     // Per-Qubit Fault Location Tests
     // =========================================================================
@@ -1460,11 +2837,11 @@ mod tests {
             .filter(|loc| matches!(loc.gate_type, GateType::CX))
             .collect();
 
-        // Should have 4 locations: before/after for each of 2 qubits
+        // Should have 2 locations: one per qubit (after only)
         assert_eq!(
             cx_locations.len(),
-            4,
-            "CX should have 4 fault locations (before/after x 2 qubits)"
+            2,
+            "CX should have 2 fault locations (1 per qubit, after gate)"
         );
 
         // Each location should have exactly 1 qubit (per-qubit fault model)
@@ -1509,31 +2886,31 @@ mod tests {
 
     #[test]
     fn test_per_qubit_fault_influences() {
-        // Test that per-qubit fault locations correctly track influences
+        // Test that per-qubit fault locations correctly track influences.
+        // In the standard model, faults are AFTER unitary gates.
+        // X on the TARGET after CX(0, 2) flips the Z-measurement on qubit 2.
         let mut dag = DagCircuit::new();
         dag.pz(&[2]); // ancilla
-        dag.cx(&[(0, 2)]); // X on control spreads to target
+        dag.cx(&[(0, 2)]); // X on target flips measurement
         dag.mz(&[2]);
 
         let analyzer = DagFaultAnalyzer::new(&dag);
         let map = analyzer.build_influence_map();
 
-        // X error on data qubit 0 (control of CX) should flip the Z-measurement
-        // because X on control stays on control, but also spreads to target
-        let mut found_data_qubit_influence = false;
+        // X error on target qubit 2 after CX should flip the measurement
+        let mut found_target_influence = false;
         for (loc_idx, loc) in map.locations.iter().enumerate() {
-            // Check data qubit 0 locations
-            if loc.qubits.iter().any(|q| q.index() == 0) {
-                // X fault (pauli=1) should have detector flips
-                if map.influences.has_detector_flips(loc_idx, Pauli::X) {
-                    found_data_qubit_influence = true;
-                }
+            if loc.qubits.iter().any(|q| q.index() == 2)
+                && matches!(loc.gate_type, GateType::CX)
+                && map.influences.has_detector_flips(loc_idx, Pauli::X)
+            {
+                found_target_influence = true;
             }
         }
 
         assert!(
-            found_data_qubit_influence,
-            "X error on data qubit should influence measurement"
+            found_target_influence,
+            "X error on target qubit after CX should influence measurement"
         );
     }
 
diff --git a/crates/pecos-qec/src/fault_tolerance/propagator/pauli.rs b/crates/pecos-qec/src/fault_tolerance/propagator/pauli.rs
index d81932a7c..5b5df18d3 100644
--- a/crates/pecos-qec/src/fault_tolerance/propagator/pauli.rs
+++ b/crates/pecos-qec/src/fault_tolerance/propagator/pauli.rs
@@ -109,6 +109,18 @@ fn apply_named_gate(
         GateType::H => {
             prop.h(qubits);
         }
+        GateType::F => {
+            match direction {
+                Direction::Forward => prop.f(qubits),
+                Direction::Backward => prop.fdg(qubits),
+            };
+        }
+        GateType::Fdg => {
+            match direction {
+                Direction::Forward => prop.fdg(qubits),
+                Direction::Backward => prop.f(qubits),
+            };
+        }
 
         // Non-self-adjoint single-qubit gates - swap with adjoint for backward
         GateType::SX => {
@@ -150,24 +162,36 @@ fn apply_named_gate(
 
         // Self-adjoint two-qubit gates - same in both directions
         GateType::CX => {
-            if qubits.len() >= 2 {
-                prop.cx(&[(qubits[0], qubits[1])]);
-            }
+            let pairs: Vec<_> = qubits
+                .chunks(2)
+                .filter(|c| c.len() == 2)
+                .map(|c| (c[0], c[1]))
+                .collect();
+            prop.cx(&pairs);
         }
         GateType::CY => {
-            if qubits.len() >= 2 {
-                prop.cy(&[(qubits[0], qubits[1])]);
-            }
+            let pairs: Vec<_> = qubits
+                .chunks(2)
+                .filter(|c| c.len() == 2)
+                .map(|c| (c[0], c[1]))
+                .collect();
+            prop.cy(&pairs);
         }
         GateType::CZ => {
-            if qubits.len() >= 2 {
-                prop.cz(&[(qubits[0], qubits[1])]);
-            }
+            let pairs: Vec<_> = qubits
+                .chunks(2)
+                .filter(|c| c.len() == 2)
+                .map(|c| (c[0], c[1]))
+                .collect();
+            prop.cz(&pairs);
         }
         GateType::SWAP => {
-            if qubits.len() >= 2 {
-                prop.swap(&[(qubits[0], qubits[1])]);
-            }
+            let pairs: Vec<_> = qubits
+                .chunks(2)
+                .filter(|c| c.len() == 2)
+                .map(|c| (c[0], c[1]))
+                .collect();
+            prop.swap(&pairs);
         }
 
         // Non-self-adjoint two-qubit Clifford gates - swap with adjoint for backward
@@ -240,15 +264,15 @@ pub fn propagate_through_circuit(
     match direction {
         Direction::Forward => {
             for tick in circuit.ticks() {
-                for gate in tick.gates() {
-                    apply_gate(prop, gate, direction);
+                for gate in tick.iter_gate_batches() {
+                    apply_gate(prop, gate.as_gate(), direction);
                 }
             }
         }
         Direction::Backward => {
             for tick in circuit.ticks().iter().rev() {
-                for gate in tick.gates() {
-                    apply_gate(prop, gate, direction);
+                for gate in tick.iter_gate_batches() {
+                    apply_gate(prop, gate.as_gate(), direction);
                 }
             }
         }
@@ -281,16 +305,16 @@ pub fn propagate_tick_range(
         Direction::Forward => {
             for tick_idx in start..=end {
                 let tick = &circuit.ticks()[tick_idx];
-                for gate in tick.gates() {
-                    apply_gate(prop, gate, direction);
+                for gate in tick.iter_gate_batches() {
+                    apply_gate(prop, gate.as_gate(), direction);
                 }
             }
         }
         Direction::Backward => {
             for tick_idx in (start..=end).rev() {
                 let tick = &circuit.ticks()[tick_idx];
-                for gate in tick.gates() {
-                    apply_gate(prop, gate, direction);
+                for gate in tick.iter_gate_batches() {
+                    apply_gate(prop, gate.as_gate(), direction);
                 }
             }
         }
diff --git a/crates/pecos-qec/src/fault_tolerance/propagator/tick.rs b/crates/pecos-qec/src/fault_tolerance/propagator/tick.rs
index e3513c64f..7e75427b5 100644
--- a/crates/pecos-qec/src/fault_tolerance/propagator/tick.rs
+++ b/crates/pecos-qec/src/fault_tolerance/propagator/tick.rs
@@ -18,7 +18,7 @@
 //! For better performance, consider using [`DagFaultAnalyzer`](super::DagFaultAnalyzer)
 //! with DAG circuits, which provides 5-50x speedup through sparse traversal.
 
-use super::types::{DetectorId, FaultInfluence, FaultInfluenceMap, LogicalId, MeasurementId};
+use super::types::{DetectorId, FaultInfluence, FaultInfluenceMap, MeasurementId, TrackedPauliId};
 use super::{Direction, SpacetimeLocation, apply_gate, extract_spacetime_locations};
 use pecos_core::gate_type::GateType;
 use pecos_quantum::TickCircuit;
@@ -64,7 +64,7 @@ impl<'a> TickFaultAnalyzer<'a> {
         // Find max qubit for active qubit tracking
         let mut max_qubit = 0;
         for tick in circuit.ticks() {
-            for gate in tick.gates() {
+            for gate in tick.iter_gate_batches() {
                 for qubit in &gate.qubits {
                     max_qubit = max_qubit.max(qubit.index());
                 }
@@ -85,20 +85,20 @@ impl<'a> TickFaultAnalyzer<'a> {
     /// creates a lookup table for fault classification.
     #[must_use]
     pub fn build_influence_map(&self) -> FaultInfluenceMap {
-        self.build_influence_map_with_logicals(&[])
+        self.build_influence_map_with_tracked_paulis(&[])
     }
 
-    /// Builds the fault influence map with logical operator tracking.
+    /// Builds the fault influence map with tracked Pauli tracking.
     ///
     /// # Arguments
     ///
-    /// * `logicals` - Logical operators as (`x_positions`, `z_positions`) pairs.
+    /// * `tracked_paulis` - Tracked Paulis as (`x_positions`, `z_positions`) pairs.
     ///   The first element of each pair is the X component positions,
     ///   the second is the Z component positions.
     #[must_use]
-    pub fn build_influence_map_with_logicals(
+    pub fn build_influence_map_with_tracked_paulis(
         &self,
-        logicals: &[(&[usize], &[usize])],
+        tracked_paulis: &[(&[usize], &[usize])],
     ) -> FaultInfluenceMap {
         let mut map = FaultInfluenceMap::new();
 
@@ -112,11 +112,11 @@ impl<'a> TickFaultAnalyzer<'a> {
             map.detectors.push(DetectorId::single(*m));
         }
 
-        // Create logical IDs
-        for (i, _) in logicals.iter().enumerate() {
-            map.logicals.push(LogicalId {
-                logical_qubit: i,
-                observable: 0, // Z observable
+        // Create tracked-Pauli IDs
+        for (i, _) in tracked_paulis.iter().enumerate() {
+            map.tracked_paulis.push(TrackedPauliId {
+                op_index: i,
+                component: 0,
             });
         }
 
@@ -131,13 +131,13 @@ impl<'a> TickFaultAnalyzer<'a> {
             self.propagate_from_measurement(measurement, &mut map);
         }
 
-        // Backward propagate from each logical operator
-        for (i, (x_pos, z_pos)) in logicals.iter().enumerate() {
-            let logical_id = LogicalId {
-                logical_qubit: i,
-                observable: 0,
+        // Backward propagate from each tracked Pauli
+        for (i, (x_pos, z_pos)) in tracked_paulis.iter().enumerate() {
+            let tracked_pauli_id = TrackedPauliId {
+                op_index: i,
+                component: 0,
             };
-            self.propagate_from_logical(x_pos, z_pos, &logical_id, &mut map);
+            self.propagate_from_tracked_pauli(x_pos, z_pos, &tracked_pauli_id, &mut map);
         }
 
         // Build reverse maps
@@ -151,7 +151,7 @@ impl<'a> TickFaultAnalyzer<'a> {
         let mut measurements = Vec::new();
 
         for (tick_idx, tick) in self.circuit.iter_ticks() {
-            for gate in tick.gates() {
+            for gate in tick.iter_gate_batches() {
                 // Currently only Z-basis measurements are supported
                 let basis = match gate.gate_type {
                     GateType::MZ | GateType::MeasureFree => 0, // Z-basis
@@ -229,7 +229,7 @@ impl<'a> TickFaultAnalyzer<'a> {
             // Apply gates at this tick backward - SPARSE: only gates touching active qubits
             if tick_idx < self.circuit.ticks().len() {
                 let tick = &self.circuit.ticks()[tick_idx];
-                for gate in tick.gates() {
+                for gate in tick.iter_gate_batches() {
                     // Check if this gate touches any active qubit
                     let touches_active = gate.qubits.iter().any(|q| {
                         let idx = q.index();
@@ -238,7 +238,7 @@ impl<'a> TickFaultAnalyzer<'a> {
 
                     if touches_active {
                         // Apply gate backward
-                        Self::apply_gate_backward(&mut prop, gate);
+                        Self::apply_gate_backward(&mut prop, gate.as_gate());
 
                         // Update active qubits based on new Pauli state
                         for q in &gate.qubits {
@@ -259,37 +259,37 @@ impl<'a> TickFaultAnalyzer<'a> {
         }
     }
 
-    /// Propagates backward from a logical operator.
+    /// Propagates backward from a tracked Pauli.
     ///
-    /// We propagate the logical OBSERVABLE backward through the circuit.
-    /// An error P at location L flips the logical if P anticommutes with
-    /// the back-propagated observable at L.
+    /// We propagate the tracked Pauli backward through the circuit. An error
+    /// P at location L flips it if P anticommutes with the back-propagated
+    /// operator at L.
     ///
     /// This uses sparse traversal: only gates touching qubits with non-trivial
     /// Paulis are processed, providing significant speedup for circuits with
     /// local connectivity.
-    fn propagate_from_logical(
+    fn propagate_from_tracked_pauli(
         &self,
         x_positions: &[usize],
         z_positions: &[usize],
-        logical_id: &LogicalId,
+        tracked_pauli_id: &TrackedPauliId,
         map: &mut FaultInfluenceMap,
     ) {
-        // Start with the logical observable itself (not swapped)
+        // Start with the tracked Pauli itself (not swapped)
         // The recording function handles anticommutation checking
         let mut prop = PauliProp::new();
 
         // Track active qubits for sparse traversal
         let mut active_qubits = vec![false; self.max_qubit + 1];
 
-        // X positions in logical -> X in prop
+        // X positions in tracked Pauli -> X in prop
         for &q in x_positions {
             prop.track_x(&[q]);
             if q <= self.max_qubit {
                 active_qubits[q] = true;
             }
         }
-        // Z positions in logical -> Z in prop
+        // Z positions in tracked Pauli -> Z in prop
         for &q in z_positions {
             prop.track_z(&[q]);
             if q <= self.max_qubit {
@@ -312,14 +312,14 @@ impl<'a> TickFaultAnalyzer<'a> {
                 tick_idx,
                 &prop,
                 &dummy_detector,
-                Some(logical_id),
+                Some(tracked_pauli_id),
                 map,
                 false,
             );
 
             // Apply gates backward - SPARSE: only gates touching active qubits
             let tick = &self.circuit.ticks()[tick_idx];
-            for gate in tick.gates() {
+            for gate in tick.iter_gate_batches() {
                 // Check if this gate touches any active qubit
                 let touches_active = gate.qubits.iter().any(|q| {
                     let idx = q.index();
@@ -328,7 +328,7 @@ impl<'a> TickFaultAnalyzer<'a> {
 
                 if touches_active {
                     // Apply gate backward
-                    Self::apply_gate_backward(&mut prop, gate);
+                    Self::apply_gate_backward(&mut prop, gate.as_gate());
 
                     // Update active qubits based on new Pauli state
                     for q in &gate.qubits {
@@ -345,7 +345,7 @@ impl<'a> TickFaultAnalyzer<'a> {
                 tick_idx,
                 &prop,
                 &dummy_detector,
-                Some(logical_id),
+                Some(tracked_pauli_id),
                 map,
                 true,
             );
@@ -368,7 +368,7 @@ impl<'a> TickFaultAnalyzer<'a> {
         tick_idx: usize,
         prop: &PauliProp,
         detector: &DetectorId,
-        logical: Option<&LogicalId>,
+        tracked_pauli: Option<&TrackedPauliId>,
         map: &mut FaultInfluenceMap,
         only_before: bool,
     ) {
@@ -400,8 +400,8 @@ impl<'a> TickFaultAnalyzer<'a> {
                     // X fault anticommutes with Z or Y observable
                     let x_flips = obs_z; // Z or Y (both have Z component)
                     if x_flips {
-                        if let Some(log) = logical {
-                            influence.logical_flips[1].push(*log);
+                        if let Some(op) = tracked_pauli {
+                            influence.tracked_pauli_flips[1].push(*op);
                         } else {
                             influence.detector_flips[1].push(detector.clone());
                             influence.measurement_flips[1]
@@ -419,8 +419,8 @@ impl<'a> TickFaultAnalyzer<'a> {
                     // (Z anticommutes with X, Z anticommutes with Y=iXZ)
                     let z_flips = obs_x; // X or Y (both have X component)
                     if z_flips {
-                        if let Some(log) = logical {
-                            influence.logical_flips[3].push(*log);
+                        if let Some(op) = tracked_pauli {
+                            influence.tracked_pauli_flips[3].push(*op);
                         } else {
                             influence.detector_flips[3].push(detector.clone());
                             influence.measurement_flips[3]
@@ -434,12 +434,11 @@ impl<'a> TickFaultAnalyzer<'a> {
                         }
                     }
 
-                    // Y fault = iXZ: Y anticommutes with X, Z, and Y
-                    // Y anticommutes with observable if observable has X or Z component
-                    let y_flips = obs_x || obs_z;
+                    // Y fault: Y anticommutes with X or Z but NOT both (Y commutes with Y)
+                    let y_flips = obs_x ^ obs_z;
                     if y_flips {
-                        if let Some(log) = logical {
-                            influence.logical_flips[2].push(*log);
+                        if let Some(op) = tracked_pauli {
+                            influence.tracked_pauli_flips[2].push(*op);
                         } else {
                             influence.detector_flips[2].push(detector.clone());
                             influence.measurement_flips[2]
@@ -486,7 +485,7 @@ impl<'a> TickFaultAnalyzer<'a> {
         apply_gate(prop, gate, Direction::Backward);
     }
 
-    /// Builds reverse maps (detector -> faults, logical -> faults).
+    /// Builds reverse maps (detector -> faults, tracked Pauli -> faults).
     fn build_reverse_maps(map: &mut FaultInfluenceMap) {
         for (loc, influence) in &map.influences {
             for (pauli, detectors) in influence.detector_flips.iter().enumerate() {
@@ -500,12 +499,12 @@ impl<'a> TickFaultAnalyzer<'a> {
                 }
             }
 
-            for (pauli, logicals) in influence.logical_flips.iter().enumerate() {
+            for (pauli, tracked_paulis) in influence.tracked_pauli_flips.iter().enumerate() {
                 #[allow(clippy::cast_possible_truncation)] // Pauli index 0..2
                 let pauli_u8 = pauli as u8;
-                for logical in logicals {
-                    map.logical_to_faults
-                        .entry(*logical)
+                for tracked_pauli in tracked_paulis {
+                    map.tracked_pauli_to_faults
+                        .entry(*tracked_pauli)
                         .or_default()
                         .push((loc.clone(), pauli_u8));
                 }
diff --git a/crates/pecos-qec/src/fault_tolerance/propagator/tick_soa.rs b/crates/pecos-qec/src/fault_tolerance/propagator/tick_batched.rs
similarity index 60%
rename from crates/pecos-qec/src/fault_tolerance/propagator/tick_soa.rs
rename to crates/pecos-qec/src/fault_tolerance/propagator/tick_batched.rs
index 4fbabc728..388a53ec8 100644
--- a/crates/pecos-qec/src/fault_tolerance/propagator/tick_soa.rs
+++ b/crates/pecos-qec/src/fault_tolerance/propagator/tick_batched.rs
@@ -1,21 +1,21 @@
-//! Optimized DOD-based tick fault analyzer using `TickCircuitSoA`.
+//! Optimized tick fault analyzer using batched `TickCircuit` access.
 //!
-//! This module provides [`TickFaultAnalyzerSoA`] which leverages the Structure of Arrays
-//! layout of [`TickCircuitSoA`] for more cache-efficient fault analysis.
+//! This module provides [`TickFaultAnalyzerBatched`] which uses the batched
+//! full-fidelity command view of [`TickCircuit`] for cache-efficient fault
+//! analysis without requiring a converted circuit representation.
 //!
 //! # Optimizations
 //!
-//! 1. **Raw index access**: Uses u32 indices instead of `GateId` validation
+//! 1. **Raw index access**: Uses local flattened gate indices
 //! 2. **Bitset for visited tracking**: O(1) membership check instead of `Vec::contains`
 //! 3. **Pre-computed tick indexes**: O(1) lookup for gates in each tick
-//! 4. **Sorted qubit gates**: Gates per qubit sorted by tick for efficient backward traversal
-//! 5. **Direct array access**: Skips Option-returning methods in hot loops
+//! 4. **Direct array access**: Skips Option-returning methods in hot loops
 
 use super::SpacetimeLocation;
-use super::types::{DetectorId, FaultInfluence, FaultInfluenceMap, LogicalId, MeasurementId};
-use pecos_core::gate_type::GateType;
-use pecos_quantum::tick_circuit_soa::TickCircuitSoA;
-use pecos_simulators::PauliProp;
+use super::types::{DetectorId, FaultInfluence, FaultInfluenceMap, MeasurementId, TrackedPauliId};
+use pecos_core::{QubitId, gate_type::GateType};
+use pecos_quantum::TickCircuit;
+use pecos_simulators::{CliffordGateable, PauliProp};
 
 // ============================================================================
 // Work Buffers for Reuse
@@ -29,7 +29,7 @@ pub struct AnalyzerWorkBuffers {
     /// Bitset for tracking processed gates in current tick
     processed_gates: Vec<bool>,
     /// Temporary storage for gates to process
-    gates_to_process: Vec<u32>,
+    gates_to_process: Vec<usize>,
 }
 
 impl AnalyzerWorkBuffers {
@@ -62,25 +62,39 @@ impl AnalyzerWorkBuffers {
 }
 
 // ============================================================================
-// Optimized SOA-Based Fault Analyzer
+// Optimized Batched Tick Fault Analyzer
 // ============================================================================
 
-/// Optimized fault analyzer for `TickCircuitSoA`.
+#[derive(Debug, Clone)]
+struct AnalyzerGate {
+    tick: usize,
+    gate_type: GateType,
+    qubits: Vec<QubitId>,
+}
+
+/// Optimized fault analyzer for `TickCircuit`.
 ///
 /// Uses raw indices and bitsets for minimal overhead in hot paths.
-pub struct TickFaultAnalyzerSoA<'a> {
-    circuit: &'a TickCircuitSoA,
+pub struct TickFaultAnalyzerBatched<'a> {
+    circuit: &'a TickCircuit,
+    /// Flattened full-fidelity gate command view.
+    gates: Vec<AnalyzerGate>,
+    /// Pre-computed index: tick -> gate indices
+    tick_gates: Vec<Vec<usize>>,
+    /// Maximum qubit index seen.
+    max_qubit: usize,
     /// Fault locations extracted from the circuit.
     locations: Vec<SpacetimeLocation>,
     /// Pre-computed index: tick -> (`location_index`, before) pairs
     tick_locations: Vec<Vec<(usize, bool)>>,
 }
 
-impl<'a> TickFaultAnalyzerSoA<'a> {
-    /// Creates a new analyzer for the given `SoA` circuit.
+impl<'a> TickFaultAnalyzerBatched<'a> {
+    /// Creates a new analyzer for the given circuit.
     #[must_use]
-    pub fn new(circuit: &'a TickCircuitSoA) -> Self {
-        let locations = Self::extract_spacetime_locations(circuit);
+    pub fn new(circuit: &'a TickCircuit) -> Self {
+        let (gates, tick_gates, max_qubit) = Self::flatten_circuit(circuit);
+        let locations = Self::extract_spacetime_locations(&gates);
 
         // Build tick index for O(1) lookup
         let num_ticks = circuit.num_ticks();
@@ -93,41 +107,60 @@ impl<'a> TickFaultAnalyzerSoA<'a> {
 
         Self {
             circuit,
+            gates,
+            tick_gates,
+            max_qubit,
             locations,
             tick_locations,
         }
     }
 
-    /// Extracts spacetime locations using raw index access.
-    fn extract_spacetime_locations(circuit: &TickCircuitSoA) -> Vec<SpacetimeLocation> {
-        let mut locations = Vec::new();
-        let storage = &circuit.storage;
+    fn flatten_circuit(circuit: &TickCircuit) -> (Vec<AnalyzerGate>, Vec<Vec<usize>>, usize) {
+        let mut gates = Vec::new();
+        let mut tick_gates = vec![Vec::new(); circuit.num_ticks()];
+        let mut max_qubit = 0usize;
 
-        for idx in 0..storage.slot_count() {
-            if !storage.is_occupied(idx) {
-                continue;
+        for (tick, gate) in circuit.iter_gate_batches_with_tick() {
+            let idx = gates.len();
+            let qubits = gate.qubits.to_vec();
+            for qubit in &qubits {
+                max_qubit = max_qubit.max(qubit.index());
+            }
+            if tick >= tick_gates.len() {
+                tick_gates.resize_with(tick + 1, Vec::new);
             }
+            tick_gates[tick].push(idx);
+            gates.push(AnalyzerGate {
+                tick,
+                gate_type: gate.gate_type,
+                qubits,
+            });
+        }
 
-            let gate_type = storage.type_unchecked(idx);
-            let qubits = storage.qubits_unchecked(idx).to_vec();
-            let tick = storage.tick_id_unchecked(idx) as usize;
+        (gates, tick_gates, max_qubit)
+    }
+
+    /// Extracts spacetime locations using raw index access.
+    fn extract_spacetime_locations(gates: &[AnalyzerGate]) -> Vec<SpacetimeLocation> {
+        let mut locations = Vec::new();
 
+        for (idx, gate) in gates.iter().enumerate() {
             // Before location (fault before gate)
             locations.push(SpacetimeLocation {
-                tick,
-                qubits: qubits.clone(),
+                tick: gate.tick,
+                qubits: gate.qubits.clone(),
                 before: true,
-                gate_type,
+                gate_type: gate.gate_type,
                 gate_index: idx,
             });
 
             // After location for most gates (except prep which resets)
-            if !matches!(gate_type, GateType::PZ | GateType::QAlloc) {
+            if !matches!(gate.gate_type, GateType::PZ | GateType::QAlloc) {
                 locations.push(SpacetimeLocation {
-                    tick,
-                    qubits,
+                    tick: gate.tick,
+                    qubits: gate.qubits.clone(),
                     before: false,
-                    gate_type,
+                    gate_type: gate.gate_type,
                     gate_index: idx,
                 });
             }
@@ -145,14 +178,14 @@ impl<'a> TickFaultAnalyzerSoA<'a> {
     /// Builds the complete fault influence map.
     #[must_use]
     pub fn build_influence_map(&self) -> FaultInfluenceMap {
-        self.build_influence_map_with_logicals(&[])
+        self.build_influence_map_with_tracked_paulis(&[])
     }
 
-    /// Builds the fault influence map with logical operator tracking.
+    /// Builds the fault influence map with tracked Pauli tracking.
     #[must_use]
-    pub fn build_influence_map_with_logicals(
+    pub fn build_influence_map_with_tracked_paulis(
         &self,
-        logicals: &[(&[usize], &[usize])],
+        tracked_paulis: &[(&[usize], &[usize])],
     ) -> FaultInfluenceMap {
         let mut map = FaultInfluenceMap::new();
 
@@ -165,11 +198,11 @@ impl<'a> TickFaultAnalyzerSoA<'a> {
             map.detectors.push(DetectorId::single(*m));
         }
 
-        // Create logical IDs
-        for (i, _) in logicals.iter().enumerate() {
-            map.logicals.push(LogicalId {
-                logical_qubit: i,
-                observable: 0,
+        // Create tracked-Pauli IDs
+        for (i, _) in tracked_paulis.iter().enumerate() {
+            map.tracked_paulis.push(TrackedPauliId {
+                op_index: i,
+                component: 0,
             });
         }
 
@@ -180,8 +213,8 @@ impl<'a> TickFaultAnalyzerSoA<'a> {
         }
 
         // Create work buffers
-        let max_qubit = self.circuit.max_qubit();
-        let max_gate = self.circuit.storage.slot_count();
+        let max_qubit = self.max_qubit;
+        let max_gate = self.gates.len();
         let mut buffers = AnalyzerWorkBuffers::new(max_qubit, max_gate);
 
         // Backward propagate from each measurement
@@ -189,16 +222,16 @@ impl<'a> TickFaultAnalyzerSoA<'a> {
             self.propagate_from_measurement_optimized(measurement, &mut map, &mut buffers);
         }
 
-        // Backward propagate from each logical operator
-        for (i, (x_pos, z_pos)) in logicals.iter().enumerate() {
-            let logical_id = LogicalId {
-                logical_qubit: i,
-                observable: 0,
+        // Backward propagate from each tracked Pauli
+        for (i, (x_pos, z_pos)) in tracked_paulis.iter().enumerate() {
+            let tracked_pauli_id = TrackedPauliId {
+                op_index: i,
+                component: 0,
             };
-            self.propagate_from_logical_optimized(
+            self.propagate_from_tracked_pauli_optimized(
                 x_pos,
                 z_pos,
-                &logical_id,
+                &tracked_pauli_id,
                 &mut map,
                 &mut buffers,
             );
@@ -213,25 +246,16 @@ impl<'a> TickFaultAnalyzerSoA<'a> {
     /// Extracts all measurements using raw index access.
     fn extract_measurements(&self) -> Vec<MeasurementId> {
         let mut measurements = Vec::new();
-        let storage = &self.circuit.storage;
-
-        for idx in 0..storage.slot_count() {
-            if !storage.is_occupied(idx) {
-                continue;
-            }
 
-            let gate_type = storage.type_unchecked(idx);
-            let basis = match gate_type {
+        for gate in &self.gates {
+            let basis = match gate.gate_type {
                 GateType::MZ | GateType::MeasureFree => 0, // Z-basis
                 _ => continue,
             };
 
-            let tick = storage.tick_id_unchecked(idx) as usize;
-            let qubits = storage.qubits_unchecked(idx);
-
-            for qubit in qubits {
+            for qubit in &gate.qubits {
                 measurements.push(MeasurementId {
-                    tick,
+                    tick: gate.tick,
                     qubit: qubit.index(),
                     basis,
                 });
@@ -297,25 +321,21 @@ impl<'a> TickFaultAnalyzerSoA<'a> {
         prop: &mut PauliProp,
         buffers: &mut AnalyzerWorkBuffers,
     ) {
-        let storage = &self.circuit.storage;
-
         // Clear processed gates bitset for this tick
         buffers.gates_to_process.clear();
 
         // Get gates in this tick directly from pre-computed index
-        let tick_gates = self.circuit.gates_in_tick_raw(tick_idx);
+        let tick_gates = self
+            .tick_gates
+            .get(tick_idx)
+            .map_or([].as_slice(), Vec::as_slice);
 
         // Find gates that touch active qubits
         for &gate_idx in tick_gates {
-            let idx = gate_idx as usize;
-            if !storage.is_occupied(idx) {
-                continue;
-            }
-
-            let qubits = storage.qubits_unchecked(idx);
+            let gate = &self.gates[gate_idx];
 
             // Check if any qubit is active
-            let touches_active = qubits.iter().any(|q| {
+            let touches_active = gate.qubits.iter().any(|q| {
                 let qi = q.index();
                 qi < buffers.active_qubits.len() && buffers.active_qubits[qi]
             });
@@ -329,7 +349,7 @@ impl<'a> TickFaultAnalyzerSoA<'a> {
         // Note: We iterate by index to avoid borrow conflict
         let num_gates = buffers.gates_to_process.len();
         for i in 0..num_gates {
-            let gate_idx = buffers.gates_to_process[i] as usize;
+            let gate_idx = buffers.gates_to_process[i];
             self.apply_gate_backward_raw(gate_idx, prop, buffers);
         }
     }
@@ -342,50 +362,100 @@ impl<'a> TickFaultAnalyzerSoA<'a> {
         prop: &mut PauliProp,
         buffers: &mut AnalyzerWorkBuffers,
     ) {
-        let storage = &self.circuit.storage;
-        let gate_type = storage.type_unchecked(idx);
-        let qubits = storage.qubits_unchecked(idx);
+        let gate = &self.gates[idx];
+        let gate_type = gate.gate_type;
+        let qubits = gate.qubits.as_slice();
 
         match gate_type {
             GateType::CX if qubits.len() >= 2 => {
-                let control = qubits[0].index();
-                let target = qubits[1].index();
+                for pair in qubits.chunks_exact(2) {
+                    let control = pair[0].index();
+                    let target = pair[1].index();
 
-                let ctrl_x = prop.contains_x(control);
-                let tgt_z = prop.contains_z(target);
+                    let ctrl_x = prop.contains_x(control);
+                    let tgt_z = prop.contains_z(target);
 
-                if ctrl_x {
-                    prop.track_x(&[target]);
-                }
-                if tgt_z {
-                    prop.track_z(&[control]);
-                }
+                    if ctrl_x {
+                        prop.track_x(&[target]);
+                    }
+                    if tgt_z {
+                        prop.track_z(&[control]);
+                    }
 
-                // Update active qubits
-                Self::update_active_qubit(control, prop, buffers);
-                Self::update_active_qubit(target, prop, buffers);
+                    // Update active qubits
+                    Self::update_active_qubit(control, prop, buffers);
+                    Self::update_active_qubit(target, prop, buffers);
+                }
             }
 
             GateType::CZ if qubits.len() >= 2 => {
-                let q0 = qubits[0].index();
-                let q1 = qubits[1].index();
+                for pair in qubits.chunks_exact(2) {
+                    let q0 = pair[0].index();
+                    let q1 = pair[1].index();
 
-                let x0 = prop.contains_x(q0);
-                let x1 = prop.contains_x(q1);
+                    let x0 = prop.contains_x(q0);
+                    let x1 = prop.contains_x(q1);
 
-                if x0 {
-                    prop.track_z(&[q1]);
-                }
-                if x1 {
-                    prop.track_z(&[q0]);
+                    if x0 {
+                        prop.track_z(&[q1]);
+                    }
+                    if x1 {
+                        prop.track_z(&[q0]);
+                    }
+
+                    Self::update_active_qubit(q0, prop, buffers);
+                    Self::update_active_qubit(q1, prop, buffers);
                 }
+            }
 
-                Self::update_active_qubit(q0, prop, buffers);
-                Self::update_active_qubit(q1, prop, buffers);
+            GateType::CY
+            | GateType::SWAP
+            | GateType::SXX
+            | GateType::SXXdg
+            | GateType::SYY
+            | GateType::SYYdg
+            | GateType::SZZ
+            | GateType::SZZdg
+                if qubits.len() >= 2 =>
+            {
+                for pair in qubits.chunks_exact(2) {
+                    let q0 = pair[0];
+                    let q1 = pair[1];
+                    let pair = [(q0, q1)];
+                    match gate_type {
+                        GateType::CY => {
+                            prop.cy(&pair);
+                        }
+                        GateType::SWAP => {
+                            prop.swap(&pair);
+                        }
+                        GateType::SXX => {
+                            prop.sxxdg(&pair);
+                        }
+                        GateType::SXXdg => {
+                            prop.sxx(&pair);
+                        }
+                        GateType::SYY => {
+                            prop.syydg(&pair);
+                        }
+                        GateType::SYYdg => {
+                            prop.syy(&pair);
+                        }
+                        GateType::SZZ => {
+                            prop.szzdg(&pair);
+                        }
+                        GateType::SZZdg => {
+                            prop.szz(&pair);
+                        }
+                        _ => unreachable!(),
+                    }
+                    Self::update_active_qubit(q0.index(), prop, buffers);
+                    Self::update_active_qubit(q1.index(), prop, buffers);
+                }
             }
 
             GateType::H => {
-                if let Some(qid) = qubits.first() {
+                for qid in qubits {
                     let q = qid.index();
                     let has_x = prop.contains_x(q);
                     let has_z = prop.contains_z(q);
@@ -402,8 +472,41 @@ impl<'a> TickFaultAnalyzerSoA<'a> {
                 }
             }
 
+            GateType::SX
+            | GateType::SXdg
+            | GateType::SY
+            | GateType::SYdg
+            | GateType::F
+            | GateType::Fdg => {
+                for qid in qubits {
+                    let q = [QubitId(qid.index())];
+                    match gate_type {
+                        GateType::SX => {
+                            prop.sxdg(&q);
+                        }
+                        GateType::SXdg => {
+                            prop.sx(&q);
+                        }
+                        GateType::SY => {
+                            prop.sydg(&q);
+                        }
+                        GateType::SYdg => {
+                            prop.sy(&q);
+                        }
+                        GateType::F => {
+                            prop.fdg(&q);
+                        }
+                        GateType::Fdg => {
+                            prop.f(&q);
+                        }
+                        _ => unreachable!(),
+                    }
+                    Self::update_active_qubit(qid.index(), prop, buffers);
+                }
+            }
+
             GateType::SZ | GateType::SZdg => {
-                if let Some(qid) = qubits.first() {
+                for qid in qubits {
                     let q = qid.index();
                     let has_x = prop.contains_x(q);
 
@@ -444,12 +547,12 @@ impl<'a> TickFaultAnalyzerSoA<'a> {
         }
     }
 
-    /// Optimized backward propagation from a logical operator.
-    fn propagate_from_logical_optimized(
+    /// Optimized backward propagation from a tracked Pauli.
+    fn propagate_from_tracked_pauli_optimized(
         &self,
         x_positions: &[usize],
         z_positions: &[usize],
-        logical_id: &LogicalId,
+        tracked_pauli_id: &TrackedPauliId,
         map: &mut FaultInfluenceMap,
         buffers: &mut AnalyzerWorkBuffers,
     ) {
@@ -482,7 +585,7 @@ impl<'a> TickFaultAnalyzerSoA<'a> {
                 tick_idx,
                 &prop,
                 &dummy_detector,
-                Some(logical_id),
+                Some(tracked_pauli_id),
                 map,
                 false,
             );
@@ -493,7 +596,7 @@ impl<'a> TickFaultAnalyzerSoA<'a> {
                 tick_idx,
                 &prop,
                 &dummy_detector,
-                Some(logical_id),
+                Some(tracked_pauli_id),
                 map,
                 true,
             );
@@ -507,7 +610,7 @@ impl<'a> TickFaultAnalyzerSoA<'a> {
         tick_idx: usize,
         prop: &PauliProp,
         detector: &DetectorId,
-        logical: Option<&LogicalId>,
+        tracked_pauli: Option<&TrackedPauliId>,
         map: &mut FaultInfluenceMap,
         only_before: bool,
     ) {
@@ -531,8 +634,8 @@ impl<'a> TickFaultAnalyzerSoA<'a> {
                 if let Some(influence) = map.influences.get_mut(loc) {
                     // X fault anticommutes with Z or Y observable
                     if obs_z {
-                        if let Some(log) = logical {
-                            influence.logical_flips[1].push(*log);
+                        if let Some(op) = tracked_pauli {
+                            influence.tracked_pauli_flips[1].push(*op);
                         } else {
                             influence.detector_flips[1].push(detector.clone());
                             influence.measurement_flips[1]
@@ -547,8 +650,8 @@ impl<'a> TickFaultAnalyzerSoA<'a> {
 
                     // Z fault anticommutes with X or Y observable
                     if obs_x {
-                        if let Some(log) = logical {
-                            influence.logical_flips[3].push(*log);
+                        if let Some(op) = tracked_pauli {
+                            influence.tracked_pauli_flips[3].push(*op);
                         } else {
                             influence.detector_flips[3].push(detector.clone());
                             influence.measurement_flips[3]
@@ -561,10 +664,10 @@ impl<'a> TickFaultAnalyzerSoA<'a> {
                         }
                     }
 
-                    // Y fault anticommutes with any non-identity observable
-                    if obs_x || obs_z {
-                        if let Some(log) = logical {
-                            influence.logical_flips[2].push(*log);
+                    // Y fault: anticommutes with X or Z but NOT both (Y commutes with Y)
+                    if obs_x ^ obs_z {
+                        if let Some(op) = tracked_pauli {
+                            influence.tracked_pauli_flips[2].push(*op);
                         } else {
                             influence.detector_flips[2].push(detector.clone());
                             influence.measurement_flips[2]
@@ -595,12 +698,12 @@ impl<'a> TickFaultAnalyzerSoA<'a> {
                 }
             }
 
-            for (pauli, logicals) in influence.logical_flips.iter().enumerate() {
+            for (pauli, tracked_paulis) in influence.tracked_pauli_flips.iter().enumerate() {
                 #[allow(clippy::cast_possible_truncation)] // Pauli index 0..2
                 let pauli_u8 = pauli as u8;
-                for logical in logicals {
-                    map.logical_to_faults
-                        .entry(*logical)
+                for tracked_pauli in tracked_paulis {
+                    map.tracked_pauli_to_faults
+                        .entry(*tracked_pauli)
                         .or_default()
                         .push((loc.clone(), pauli_u8));
                 }
@@ -612,23 +715,16 @@ impl<'a> TickFaultAnalyzerSoA<'a> {
 #[cfg(test)]
 mod tests {
     use super::*;
-    use pecos_quantum::tick_circuit_soa::TickCircuitSoABuilder;
+    use pecos_quantum::TickCircuit;
 
     #[test]
     fn test_basic_analysis() {
-        let mut builder = TickCircuitSoABuilder::new();
-        builder
-            .tick()
-            .pz(&[0, 1])
-            .tick()
-            .h(&[0])
-            .tick()
-            .cx(&[(0, 1)])
-            .tick()
-            .mz(&[0, 1]);
-
-        let circuit = builder.build();
-        let analyzer = TickFaultAnalyzerSoA::new(&circuit);
+        let mut circuit = TickCircuit::new();
+        circuit.tick().pz(&[0, 1]);
+        circuit.tick().h(&[0]);
+        circuit.tick().cx(&[(0, 1)]);
+        circuit.tick().mz(&[0, 1]);
+        let analyzer = TickFaultAnalyzerBatched::new(&circuit);
 
         assert!(!analyzer.locations().is_empty());
 
@@ -640,21 +736,12 @@ mod tests {
 
     #[test]
     fn test_sparse_traversal() {
-        let mut builder = TickCircuitSoABuilder::new();
-        builder
-            .tick()
-            .pz(&[0, 1, 2, 3])
-            .tick()
-            .h(&[0])
-            .h(&[2])
-            .tick()
-            .cx(&[(0, 1)])
-            .cx(&[(2, 3)])
-            .tick()
-            .mz(&[0, 1, 2, 3]);
-
-        let circuit = builder.build();
-        let analyzer = TickFaultAnalyzerSoA::new(&circuit);
+        let mut circuit = TickCircuit::new();
+        circuit.tick().pz(&[0, 1, 2, 3]);
+        circuit.tick().h(&[0]).h(&[2]);
+        circuit.tick().cx(&[(0, 1)]).cx(&[(2, 3)]);
+        circuit.tick().mz(&[0, 1, 2, 3]);
+        let analyzer = TickFaultAnalyzerBatched::new(&circuit);
 
         let map = analyzer.build_influence_map();
 
@@ -663,24 +750,17 @@ mod tests {
     }
 
     #[test]
-    fn test_logical_propagation() {
-        let mut builder = TickCircuitSoABuilder::new();
-        builder
-            .tick()
-            .pz(&[0, 1])
-            .tick()
-            .h(&[0])
-            .tick()
-            .cx(&[(0, 1)])
-            .tick()
-            .mz(&[0, 1]);
-
-        let circuit = builder.build();
-        let analyzer = TickFaultAnalyzerSoA::new(&circuit);
-
-        let logicals = [(&[] as &[usize], &[1usize] as &[usize])];
-        let map = analyzer.build_influence_map_with_logicals(&logicals);
-
-        assert_eq!(map.logicals.len(), 1);
+    fn test_tracked_pauli_propagation() {
+        let mut circuit = TickCircuit::new();
+        circuit.tick().pz(&[0, 1]);
+        circuit.tick().h(&[0]);
+        circuit.tick().cx(&[(0, 1)]);
+        circuit.tick().mz(&[0, 1]);
+        let analyzer = TickFaultAnalyzerBatched::new(&circuit);
+
+        let tracked_paulis = [(&[] as &[usize], &[1usize] as &[usize])];
+        let map = analyzer.build_influence_map_with_tracked_paulis(&tracked_paulis);
+
+        assert_eq!(map.tracked_paulis.len(), 1);
     }
 }
diff --git a/crates/pecos-qec/src/fault_tolerance/propagator/types.rs b/crates/pecos-qec/src/fault_tolerance/propagator/types.rs
index 0998d49b1..a7d6673c0 100644
--- a/crates/pecos-qec/src/fault_tolerance/propagator/types.rs
+++ b/crates/pecos-qec/src/fault_tolerance/propagator/types.rs
@@ -149,12 +149,56 @@ impl From<DetectorIdx> for usize {
     }
 }
 
-/// A logical observable index.
+/// A standard DEM observable `L<n>` output index.
 #[derive(Debug, Clone, Copy, PartialEq, Eq, PartialOrd, Ord, Hash, Default)]
 #[repr(transparent)]
-pub struct LogicalIdx(pub u32);
+pub struct DemOutputIdx(pub u32);
 
-impl LogicalIdx {
+/// A PECOS tracked-Pauli metadata index.
+///
+/// This is intentionally separate from [`DemOutputIdx`]: tracked Paulis are
+/// not standard DEM `L<n>` targets and should not be handed to decoders as
+/// logical observables.
+#[derive(Debug, Clone, Copy, PartialEq, Eq, PartialOrd, Ord, Hash, Default)]
+#[repr(transparent)]
+pub struct TrackedPauliIdx(pub u32);
+
+impl DemOutputIdx {
+    #[inline]
+    #[must_use]
+    pub const fn new(index: u32) -> Self {
+        Self(index)
+    }
+
+    #[inline]
+    #[must_use]
+    pub const fn index(self) -> usize {
+        self.0 as usize
+    }
+
+    #[inline]
+    #[must_use]
+    #[allow(clippy::cast_possible_truncation)] // DEM output index fits in u32
+    pub const fn from_usize(index: usize) -> Self {
+        Self(index as u32)
+    }
+}
+
+impl From<usize> for DemOutputIdx {
+    #[inline]
+    fn from(index: usize) -> Self {
+        Self::from_usize(index)
+    }
+}
+
+impl From<DemOutputIdx> for usize {
+    #[inline]
+    fn from(id: DemOutputIdx) -> Self {
+        id.index()
+    }
+}
+
+impl TrackedPauliIdx {
     #[inline]
     #[must_use]
     pub const fn new(index: u32) -> Self {
@@ -169,22 +213,22 @@ impl LogicalIdx {
 
     #[inline]
     #[must_use]
-    #[allow(clippy::cast_possible_truncation)] // logical index fits in u32
+    #[allow(clippy::cast_possible_truncation)] // tracked-Pauli index fits in u32
     pub const fn from_usize(index: usize) -> Self {
         Self(index as u32)
     }
 }
 
-impl From<usize> for LogicalIdx {
+impl From<usize> for TrackedPauliIdx {
     #[inline]
     fn from(index: usize) -> Self {
         Self::from_usize(index)
     }
 }
 
-impl From<LogicalIdx> for usize {
+impl From<TrackedPauliIdx> for usize {
     #[inline]
-    fn from(id: LogicalIdx) -> Self {
+    fn from(id: TrackedPauliIdx) -> Self {
         id.index()
     }
 }
@@ -287,13 +331,13 @@ impl DetectorId {
     }
 }
 
-/// Unique identifier for a logical observable.
+/// Unique identifier for a tracked Pauli in the older tick influence map.
 #[derive(Debug, Clone, Copy, PartialEq, Eq, PartialOrd, Ord, Hash)]
-pub struct LogicalId {
-    /// Index of the logical qubit.
-    pub logical_qubit: usize,
-    /// Which observable: 0 = Z, 1 = X.
-    pub observable: u8,
+pub struct TrackedPauliId {
+    /// Index of the tracked Pauli.
+    pub op_index: usize,
+    /// Optional Pauli component marker for callers that split X/Z components.
+    pub component: u8,
 }
 
 /// What a single fault location influences.
@@ -305,8 +349,8 @@ pub struct FaultInfluence {
     /// Index 0 is unused (identity fault has no effect).
     pub detector_flips: [Vec<DetectorId>; 4],
 
-    /// Which logical observables this fault flips, indexed by Pauli type.
-    pub logical_flips: [Vec<LogicalId>; 4],
+    /// Which tracked Paulis this fault flips, indexed by Pauli type.
+    pub tracked_pauli_flips: [Vec<TrackedPauliId>; 4],
 
     /// Which raw measurements this fault flips, indexed by Pauli type.
     pub measurement_flips: [Vec<MeasurementId>; 4],
@@ -321,7 +365,7 @@ impl FaultInfluence {
     #[must_use]
     pub fn is_trivial(&self) -> bool {
         self.detector_flips.iter().all(std::vec::Vec::is_empty)
-            && self.logical_flips.iter().all(std::vec::Vec::is_empty)
+            && self.tracked_pauli_flips.iter().all(std::vec::Vec::is_empty)
             && self.measurement_flips.iter().all(std::vec::Vec::is_empty)
     }
 
@@ -334,11 +378,11 @@ impl FaultInfluence {
             .map_or(&[], |v| v.as_slice())
     }
 
-    /// Returns all logicals flipped by a specific Pauli type.
+    /// Returns all tracked Paulis flipped by a specific Pauli type.
     #[inline]
     #[must_use]
-    pub fn logicals_for_pauli(&self, pauli: u8) -> &[LogicalId] {
-        self.logical_flips
+    pub fn tracked_paulis_for_pauli(&self, pauli: u8) -> &[TrackedPauliId] {
+        self.tracked_pauli_flips
             .get(pauli as usize)
             .map_or(&[], |v| v.as_slice())
     }
@@ -356,8 +400,8 @@ pub struct FaultInfluenceMap {
     /// All detectors in the circuit.
     pub detectors: Vec<DetectorId>,
 
-    /// All logical observables being tracked.
-    pub logicals: Vec<LogicalId>,
+    /// All tracked Paulis.
+    pub tracked_paulis: Vec<TrackedPauliId>,
 
     /// All measurements in the circuit.
     pub measurements: Vec<MeasurementId>,
@@ -365,8 +409,8 @@ pub struct FaultInfluenceMap {
     /// Reverse map: for each detector, which fault locations flip it.
     pub detector_to_faults: BTreeMap<DetectorId, Vec<(SpacetimeLocation, u8)>>,
 
-    /// Reverse map: for each logical, which fault locations flip it.
-    pub logical_to_faults: BTreeMap<LogicalId, Vec<(SpacetimeLocation, u8)>>,
+    /// Reverse map: for each tracked Pauli, which fault locations flip it.
+    pub tracked_pauli_to_faults: BTreeMap<TrackedPauliId, Vec<(SpacetimeLocation, u8)>>,
 }
 
 impl FaultInfluenceMap {
@@ -376,10 +420,10 @@ impl FaultInfluenceMap {
         Self {
             influences: BTreeMap::new(),
             detectors: Vec::new(),
-            logicals: Vec::new(),
+            tracked_paulis: Vec::new(),
             measurements: Vec::new(),
             detector_to_faults: BTreeMap::new(),
-            logical_to_faults: BTreeMap::new(),
+            tracked_pauli_to_faults: BTreeMap::new(),
         }
     }
 
@@ -391,14 +435,14 @@ impl FaultInfluenceMap {
 
     /// Quickly classifies a single-qubit fault based on pre-computed influences.
     ///
-    /// Returns (`has_syndrome`, `has_logical_error`) for the given Pauli type.
+    /// Returns (`has_syndrome`, `flips_tracked_pauli`) for the given Pauli type.
     /// For multi-qubit locations, use `classify_multi_qubit_fault` instead.
     #[must_use]
     pub fn classify_fault(&self, location: &SpacetimeLocation, pauli: u8) -> (bool, bool) {
         if let Some(influence) = self.influences.get(location) {
             let has_syndrome = !influence.detectors_for_pauli(pauli).is_empty();
-            let has_logical = !influence.logicals_for_pauli(pauli).is_empty();
-            (has_syndrome, has_logical)
+            let flips_tracked_pauli = !influence.tracked_paulis_for_pauli(pauli).is_empty();
+            (has_syndrome, flips_tracked_pauli)
         } else {
             (false, false)
         }
@@ -413,7 +457,7 @@ impl FaultInfluenceMap {
     /// For Y faults, we decompose Y = XZ and combine the X and Z contributions,
     /// since Y anticommutes with both X and Z components of the observable.
     ///
-    /// Returns (`has_syndrome`, `has_logical_error`).
+    /// Returns (`has_syndrome`, `flips_tracked_pauli`).
     #[must_use]
     pub fn classify_multi_qubit_fault(
         &self,
@@ -458,11 +502,11 @@ impl FaultInfluenceMap {
             // Syndrome = odd number of flips for any detector
             let has_syndrome = detector_flip_counts.values().any(|&count| count % 2 == 1);
 
-            // For logicals, use the same approach
-            // (simplified: just check if any qubit flips logical, proper handling TBD)
-            let has_logical = !influence.logicals_for_pauli(pauli).is_empty();
+            // For tracked Paulis, use the same approach
+            // (simplified: just check if any component flips, proper handling TBD)
+            let flips_tracked_pauli = !influence.tracked_paulis_for_pauli(pauli).is_empty();
 
-            (has_syndrome, has_logical)
+            (has_syndrome, flips_tracked_pauli)
         } else {
             (false, false)
         }
diff --git a/crates/pecos-qec/src/fault_tolerance/targeted_lookup_decoder.rs b/crates/pecos-qec/src/fault_tolerance/targeted_lookup_decoder.rs
new file mode 100644
index 000000000..9df5a9356
--- /dev/null
+++ b/crates/pecos-qec/src/fault_tolerance/targeted_lookup_decoder.rs
@@ -0,0 +1,789 @@
+// Copyright 2026 The PECOS Developers
+//
+// Licensed under the Apache License, Version 2.0 (the "License"); you may not use this file except
+// in compliance with the License. You may obtain a copy of the License at
+//
+//     https://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software distributed under the License
+// is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express
+// or implied. See the License for the specific language governing permissions and limitations under
+// the License.
+
+//! Targeted fault-catalog lookup decoder.
+//!
+//! Answers one detector syndrome at a time by searching the fault catalog,
+//! instead of precomputing a full lookup table for every syndrome.
+//!
+//! Uses odds-space weights for efficient comparison:
+//! - `base_probability = product of all (1 - p_i)`
+//! - `odds_weight(alt) = alt.absolute_probability / (1 - p_i)`
+//! - `configuration_probability = base_probability * product(selected odds_weights)`
+
+use super::fault_sampler::FaultCatalog;
+use std::collections::{BTreeMap, BTreeSet, HashMap};
+
+/// A flattened fault entry for index lookup.
+#[derive(Clone, Debug)]
+struct FaultEntry {
+    /// Index of the physical fault location in the catalog.
+    location_index: usize,
+    /// Detector effect as a sorted set of detector indices (XOR parity).
+    detector_bits: BTreeSet<usize>,
+    /// Observable/logical effect as a sorted set.
+    logical_bits: BTreeSet<usize>,
+    /// Odds-space weight: `absolute_probability / no_fault_probability`.
+    odds_weight: f64,
+}
+
+#[derive(Clone, Copy)]
+struct SearchState<'a> {
+    start_entry: usize,
+    needed: &'a BTreeSet<usize>,
+    used_locations: &'a BTreeSet<usize>,
+    logical_parity: &'a BTreeSet<usize>,
+    odds_product: f64,
+    depth: usize,
+}
+
+/// Result of decoding a single syndrome.
+#[derive(Clone, Debug)]
+pub struct DecodeResult {
+    /// The queried syndrome.
+    pub syndrome: Vec<usize>,
+    /// Accumulated odds-space weights by logical class.
+    /// Multiply by `base_probability` for absolute probabilities.
+    pub logical_weights: BTreeMap<Vec<usize>, f64>,
+    /// The logical class with the highest weight.
+    pub best_logical: Vec<usize>,
+}
+
+/// Targeted fault-catalog lookup decoder.
+///
+/// Searches the fault catalog for explanations of a given detector syndrome,
+/// accumulating odds-space weights by logical class up to `max_faults`
+/// simultaneous fault locations.
+pub struct TargetedLookupDecoder {
+    max_faults: usize,
+    base_prob: f64,
+    entries: Vec<FaultEntry>,
+    /// Index: `detector_bits` -> list of entry indices.
+    by_detector: HashMap<BTreeSet<usize>, Vec<usize>>,
+}
+
+impl TargetedLookupDecoder {
+    /// Build a decoder from a fault catalog.
+    #[must_use]
+    pub fn new(catalog: &FaultCatalog) -> Self {
+        let base_prob: f64 = catalog
+            .locations
+            .iter()
+            .map(|loc| loc.no_fault_probability)
+            .product();
+
+        let mut entries = Vec::new();
+        for (loc_idx, loc) in catalog.locations.iter().enumerate() {
+            for alt in &loc.faults {
+                let odds = if loc.no_fault_probability > 0.0 {
+                    alt.absolute_probability / loc.no_fault_probability
+                } else {
+                    f64::INFINITY
+                };
+                if odds == 0.0 {
+                    continue;
+                }
+                entries.push(FaultEntry {
+                    location_index: loc_idx,
+                    detector_bits: alt.affected_detectors.iter().copied().collect(),
+                    logical_bits: alt.affected_observables.iter().copied().collect(),
+                    odds_weight: odds,
+                });
+            }
+        }
+
+        let mut by_detector: HashMap<BTreeSet<usize>, Vec<usize>> = HashMap::new();
+        for (i, entry) in entries.iter().enumerate() {
+            by_detector
+                .entry(entry.detector_bits.clone())
+                .or_default()
+                .push(i);
+        }
+
+        Self {
+            max_faults: 1,
+            base_prob,
+            entries,
+            by_detector,
+        }
+    }
+
+    /// Set the maximum number of simultaneous fault locations to consider.
+    #[must_use]
+    pub fn max_faults(mut self, max_faults: usize) -> Self {
+        self.max_faults = max_faults;
+        self
+    }
+
+    /// The all-no-fault probability: product of `(1 - p_i)` for all locations.
+    #[must_use]
+    pub fn base_probability(&self) -> f64 {
+        self.base_prob
+    }
+
+    /// Decode a syndrome: find all explanations up to `max_faults` and accumulate
+    /// odds-space weights by logical class.
+    #[must_use]
+    pub fn decode(&self, syndrome: &[usize]) -> DecodeResult {
+        let target: BTreeSet<usize> = syndrome.iter().copied().collect();
+        let mut logical_weights: BTreeMap<Vec<usize>, f64> = BTreeMap::new();
+
+        // k=0: empty syndrome -> empty logical with weight 1
+        if target.is_empty() {
+            *logical_weights.entry(Vec::new()).or_default() += 1.0;
+        }
+
+        // k=1: direct lookup
+        if self.max_faults >= 1
+            && let Some(indices) = self.by_detector.get(&target)
+        {
+            for &i in indices {
+                let e = &self.entries[i];
+                let logical: Vec<usize> = e.logical_bits.iter().copied().collect();
+                *logical_weights.entry(logical).or_default() += e.odds_weight;
+            }
+        }
+
+        // k=2: complement lookup
+        if self.max_faults >= 2 {
+            self.search_k2(&target, &mut logical_weights);
+        }
+
+        // k>=3: recursive exact search
+        if self.max_faults >= 3 {
+            for k in 3..=self.max_faults {
+                self.search_generic(k, &target, &mut logical_weights);
+            }
+        }
+
+        let best_logical = logical_weights
+            .iter()
+            .max_by(|(_, a), (_, b)| a.total_cmp(b))
+            .map(|(logical, _)| logical.clone())
+            .unwrap_or_default();
+
+        DecodeResult {
+            syndrome: syndrome.to_vec(),
+            logical_weights,
+            best_logical,
+        }
+    }
+
+    /// k=2 complement lookup: for each entry `a`, compute
+    /// `needed_b = target XOR a.detectors`,
+    /// then look up entries with that detector effect.
+    fn search_k2(&self, target: &BTreeSet<usize>, logical_weights: &mut BTreeMap<Vec<usize>, f64>) {
+        for (i, a) in self.entries.iter().enumerate() {
+            let needed_b = xor_sets(target, &a.detector_bits);
+            if let Some(b_indices) = self.by_detector.get(&needed_b) {
+                for &j in b_indices {
+                    if j <= i {
+                        continue; // avoid double-counting (ordered pairs)
+                    }
+                    let b = &self.entries[j];
+                    if a.location_index == b.location_index {
+                        continue; // same physical location
+                    }
+                    let logical = xor_sets(&a.logical_bits, &b.logical_bits);
+                    let logical_vec: Vec<usize> = logical.into_iter().collect();
+                    *logical_weights.entry(logical_vec).or_default() +=
+                        a.odds_weight * b.odds_weight;
+                }
+            }
+        }
+    }
+
+    /// Generic exact search for k >= 3. Recursive depth-first with location exclusion.
+    fn search_generic(
+        &self,
+        k: usize,
+        target: &BTreeSet<usize>,
+        logical_weights: &mut BTreeMap<Vec<usize>, f64>,
+    ) {
+        let used_locations = BTreeSet::new();
+        let logical_parity = BTreeSet::new();
+        let state = SearchState {
+            start_entry: 0,
+            needed: target,
+            used_locations: &used_locations,
+            logical_parity: &logical_parity,
+            odds_product: 1.0,
+            depth: 0,
+        };
+        self.search_recursive(k, state, logical_weights);
+    }
+
+    fn search_recursive(
+        &self,
+        k: usize,
+        state: SearchState<'_>,
+        logical_weights: &mut BTreeMap<Vec<usize>, f64>,
+    ) {
+        if state.depth == k {
+            if state.needed.is_empty() {
+                let logical_vec: Vec<usize> = state.logical_parity.iter().copied().collect();
+                *logical_weights.entry(logical_vec).or_default() += state.odds_product;
+            }
+            return;
+        }
+
+        let remaining = k - state.depth;
+        for i in state.start_entry..self.entries.len() {
+            // Check if enough entries remain
+            if self.entries.len() - i < remaining {
+                break;
+            }
+
+            let entry = &self.entries[i];
+
+            // Skip if this location is already used
+            if state.used_locations.contains(&entry.location_index) {
+                continue;
+            }
+
+            let new_needed = xor_sets(state.needed, &entry.detector_bits);
+            let new_logical = xor_sets(state.logical_parity, &entry.logical_bits);
+            let new_odds = state.odds_product * entry.odds_weight;
+
+            let mut new_used = state.used_locations.clone();
+            new_used.insert(entry.location_index);
+
+            let next_state = SearchState {
+                start_entry: i + 1,
+                needed: &new_needed,
+                used_locations: &new_used,
+                logical_parity: &new_logical,
+                odds_product: new_odds,
+                depth: state.depth + 1,
+            };
+            self.search_recursive(k, next_state, logical_weights);
+        }
+    }
+}
+
+/// XOR two sorted sets (symmetric difference).
+fn xor_sets(a: &BTreeSet<usize>, b: &BTreeSet<usize>) -> BTreeSet<usize> {
+    a.symmetric_difference(b).copied().collect()
+}
+
+#[cfg(test)]
+mod tests {
+    use super::*;
+    use crate::fault_tolerance::fault_sampler::{
+        FaultAlternative, FaultCatalog, FaultKind, FaultLocation, StochasticNoiseParams,
+        build_fault_catalog,
+    };
+    use pecos_core::{QubitId, gate_type::GateType};
+    use pecos_quantum::TickCircuit;
+
+    /// Build a tiny circuit: H(0) CX(0,1) H(0) MZ(0) MZ(1)
+    /// with detector D0 = m0 XOR m1 and observable L0 = m1.
+    fn tiny_circuit() -> TickCircuit {
+        let mut tc = TickCircuit::new();
+        tc.tick().h(&[QubitId(0)]);
+        tc.tick().cx(&[(QubitId(0), QubitId(1))]);
+        tc.tick().h(&[QubitId(0)]);
+        tc.tick().mz(&[QubitId(0)]);
+        tc.tick().mz(&[QubitId(1)]);
+        tc.set_meta(
+            "num_measurements",
+            pecos_quantum::Attribute::String("2".to_string()),
+        );
+        tc.set_meta(
+            "detectors",
+            pecos_quantum::Attribute::String(r#"[{"records": [-2, -1]}]"#.to_string()),
+        );
+        tc.set_meta(
+            "observables",
+            pecos_quantum::Attribute::String(r#"[{"records": [-1]}]"#.to_string()),
+        );
+        tc
+    }
+
+    fn tiny_catalog() -> FaultCatalog {
+        let tc = tiny_circuit();
+        let noise = StochasticNoiseParams {
+            p1: 0.003,
+            p2: 0.01,
+            p_meas: 0.005,
+            p_prep: 0.005,
+        };
+        build_fault_catalog(&tc, &noise).unwrap()
+    }
+
+    /// Brute-force reference: enumerate all configurations up to `max_faults`,
+    /// accumulate odds weights by (syndrome, logical).
+    fn brute_force_weights(
+        catalog: &FaultCatalog,
+        max_faults: usize,
+    ) -> BTreeMap<Vec<usize>, BTreeMap<Vec<usize>, f64>> {
+        let base: f64 = catalog
+            .locations
+            .iter()
+            .map(|l| l.no_fault_probability)
+            .product();
+        let mut result: BTreeMap<Vec<usize>, BTreeMap<Vec<usize>, f64>> = BTreeMap::new();
+        for k in 0..=max_faults {
+            for event in catalog.fault_configurations(k) {
+                let odds = if base > 0.0 {
+                    event.configuration_probability / base
+                } else {
+                    0.0
+                };
+                *result
+                    .entry(event.affected_detectors)
+                    .or_default()
+                    .entry(event.affected_observables)
+                    .or_default() += odds;
+            }
+        }
+        result
+    }
+
+    #[test]
+    fn test_k0_empty_syndrome() {
+        let catalog = tiny_catalog();
+        let decoder = TargetedLookupDecoder::new(&catalog).max_faults(0);
+        let result = decoder.decode(&[]);
+        assert_eq!(result.best_logical, Vec::<usize>::new());
+        assert!((result.logical_weights[&vec![]] - 1.0).abs() < 1e-12);
+    }
+
+    #[test]
+    fn test_unparameterized_catalog_has_no_positive_fault_weights() {
+        let catalog = FaultCatalog::from_circuit(&tiny_circuit()).unwrap();
+        let decoder = TargetedLookupDecoder::new(&catalog).max_faults(2);
+
+        let empty = decoder.decode(&[]);
+        assert_eq!(empty.logical_weights.len(), 1);
+        assert!((empty.logical_weights[&vec![]] - 1.0).abs() < 1e-12);
+
+        let non_empty = decoder.decode(&[0]);
+        assert!(
+            non_empty.logical_weights.is_empty(),
+            "zero-probability structural faults must not create zero-weight classes"
+        );
+    }
+
+    #[test]
+    fn test_zero_probability_alternatives_are_ignored() {
+        let catalog = FaultCatalog {
+            locations: vec![
+                FaultLocation {
+                    tick: 0,
+                    gate_index: 0,
+                    gate_type: GateType::H,
+                    qubits: vec![0],
+                    channel: crate::fault_tolerance::fault_sampler::FaultChannel::P1,
+                    channel_probability: 0.0,
+                    no_fault_probability: 1.0,
+                    num_alternatives: 1,
+                    faults: vec![FaultAlternative {
+                        kind: FaultKind::Pauli,
+                        pauli: None,
+                        affected_measurements: Vec::new(),
+                        affected_detectors: vec![0],
+                        affected_observables: vec![9],
+                        affected_tracked_paulis: Vec::new(),
+                        conditional_probability: 1.0,
+                        absolute_probability: 0.0,
+                    }],
+                },
+                FaultLocation {
+                    tick: 1,
+                    gate_index: 0,
+                    gate_type: GateType::MZ,
+                    qubits: vec![0],
+                    channel: crate::fault_tolerance::fault_sampler::FaultChannel::PMeas,
+                    channel_probability: 0.1,
+                    no_fault_probability: 0.9,
+                    num_alternatives: 1,
+                    faults: vec![FaultAlternative {
+                        kind: FaultKind::MeasurementFlip,
+                        pauli: None,
+                        affected_measurements: vec![0],
+                        affected_detectors: vec![0],
+                        affected_observables: Vec::new(),
+                        affected_tracked_paulis: Vec::new(),
+                        conditional_probability: 1.0,
+                        absolute_probability: 0.1,
+                    }],
+                },
+            ],
+        };
+
+        let result = TargetedLookupDecoder::new(&catalog)
+            .max_faults(1)
+            .decode(&[0]);
+
+        assert!(!result.logical_weights.contains_key(&vec![9]));
+        assert_eq!(result.logical_weights.len(), 1);
+        assert!((result.logical_weights[&vec![]] - (0.1 / 0.9)).abs() < 1e-12);
+    }
+
+    #[test]
+    fn test_decode_ignores_tracked_pauli_effects() {
+        let catalog = FaultCatalog {
+            locations: vec![
+                FaultLocation {
+                    tick: 0,
+                    gate_index: 0,
+                    gate_type: GateType::H,
+                    qubits: vec![0],
+                    channel: crate::fault_tolerance::fault_sampler::FaultChannel::P1,
+                    channel_probability: 0.2,
+                    no_fault_probability: 0.8,
+                    num_alternatives: 1,
+                    faults: vec![FaultAlternative {
+                        kind: FaultKind::Pauli,
+                        pauli: None,
+                        affected_measurements: Vec::new(),
+                        affected_detectors: vec![0],
+                        affected_observables: vec![1],
+                        affected_tracked_paulis: vec![0],
+                        conditional_probability: 1.0,
+                        absolute_probability: 0.2,
+                    }],
+                },
+                FaultLocation {
+                    tick: 1,
+                    gate_index: 0,
+                    gate_type: GateType::H,
+                    qubits: vec![1],
+                    channel: crate::fault_tolerance::fault_sampler::FaultChannel::P1,
+                    channel_probability: 0.1,
+                    no_fault_probability: 0.9,
+                    num_alternatives: 1,
+                    faults: vec![FaultAlternative {
+                        kind: FaultKind::Pauli,
+                        pauli: None,
+                        affected_measurements: Vec::new(),
+                        affected_detectors: vec![0],
+                        affected_observables: Vec::new(),
+                        affected_tracked_paulis: vec![3],
+                        conditional_probability: 1.0,
+                        absolute_probability: 0.1,
+                    }],
+                },
+            ],
+        };
+
+        let result = TargetedLookupDecoder::new(&catalog)
+            .max_faults(1)
+            .decode(&[0]);
+
+        assert_eq!(result.best_logical, vec![1]);
+        assert_eq!(result.logical_weights.len(), 2);
+        assert!((result.logical_weights[&vec![1]] - (0.2 / 0.8)).abs() < 1e-12);
+        assert!((result.logical_weights[&vec![]] - (0.1 / 0.9)).abs() < 1e-12);
+    }
+
+    #[test]
+    fn test_unexplainable_syndrome_returns_empty_weights() {
+        let mut tc = TickCircuit::new();
+        tc.tick().mz(&[QubitId(0)]);
+        tc.tick().mz(&[QubitId(1)]);
+        tc.set_meta(
+            "num_measurements",
+            pecos_quantum::Attribute::String("2".into()),
+        );
+        tc.set_meta(
+            "detectors",
+            pecos_quantum::Attribute::String(r#"[{"records":[-2]},{"records":[-1]}]"#.into()),
+        );
+        tc.set_meta("observables", pecos_quantum::Attribute::String("[]".into()));
+
+        let noise = StochasticNoiseParams {
+            p1: 0.0,
+            p2: 0.0,
+            p_meas: 0.01,
+            p_prep: 0.0,
+        };
+        let catalog = build_fault_catalog(&tc, &noise).unwrap();
+
+        let zero_fault_decoder = TargetedLookupDecoder::new(&catalog).max_faults(0);
+        let zero_fault_result = zero_fault_decoder.decode(&[0]);
+        assert!(
+            zero_fault_result.logical_weights.is_empty(),
+            "non-empty syndrome cannot be explained by zero faults"
+        );
+
+        let one_fault_decoder = TargetedLookupDecoder::new(&catalog).max_faults(1);
+        let one_fault_result = one_fault_decoder.decode(&[0, 1]);
+        assert!(
+            one_fault_result.logical_weights.is_empty(),
+            "syndrome [0, 1] requires two distinct measurement faults"
+        );
+    }
+
+    #[test]
+    fn test_k1_matches_brute_force() {
+        let catalog = tiny_catalog();
+        let decoder = TargetedLookupDecoder::new(&catalog).max_faults(1);
+        let bf = brute_force_weights(&catalog, 1);
+
+        for (syndrome, bf_logicals) in &bf {
+            let result = decoder.decode(syndrome);
+            for (logical, &bf_weight) in bf_logicals {
+                let dec_weight = result.logical_weights.get(logical).copied().unwrap_or(0.0);
+                assert!(
+                    (dec_weight - bf_weight).abs() < 1e-12,
+                    "k=1 mismatch for syndrome={syndrome:?} logical={logical:?}: \
+                     decoder={dec_weight} brute_force={bf_weight}"
+                );
+            }
+        }
+    }
+
+    #[test]
+    fn test_k2_matches_brute_force() {
+        let catalog = tiny_catalog();
+        let decoder = TargetedLookupDecoder::new(&catalog).max_faults(2);
+        let bf = brute_force_weights(&catalog, 2);
+
+        for (syndrome, bf_logicals) in &bf {
+            let result = decoder.decode(syndrome);
+            for (logical, &bf_weight) in bf_logicals {
+                let dec_weight = result.logical_weights.get(logical).copied().unwrap_or(0.0);
+                assert!(
+                    (dec_weight - bf_weight).abs() / bf_weight.max(1e-15) < 1e-8,
+                    "k=2 mismatch for syndrome={syndrome:?} logical={logical:?}: \
+                     decoder={dec_weight:.6e} brute_force={bf_weight:.6e}"
+                );
+            }
+        }
+    }
+
+    #[test]
+    fn test_new_clifford_gate_circuit_matches_brute_force() {
+        let mut tc = TickCircuit::new();
+        tc.tick().sx(&[QubitId(0)]);
+        tc.tick().cy(&[(QubitId(0), QubitId(1))]);
+        tc.tick().sxx(&[(QubitId(0), QubitId(1))]);
+        tc.tick().swap(&[(QubitId(0), QubitId(1))]);
+        tc.tick().mz(&[QubitId(0)]);
+        tc.tick().mz(&[QubitId(1)]);
+        tc.set_meta(
+            "num_measurements",
+            pecos_quantum::Attribute::String("2".into()),
+        );
+        tc.set_meta(
+            "detectors",
+            pecos_quantum::Attribute::String(
+                r#"[{"records":[-2]},{"records":[-1]},{"records":[-2,-1]}]"#.into(),
+            ),
+        );
+        tc.set_meta(
+            "observables",
+            pecos_quantum::Attribute::String(r#"[{"records":[-1]}]"#.into()),
+        );
+
+        let noise = StochasticNoiseParams {
+            p1: 0.003,
+            p2: 0.01,
+            p_meas: 0.0,
+            p_prep: 0.0,
+        };
+        let catalog = build_fault_catalog(&tc, &noise).unwrap();
+        assert!(
+            catalog
+                .locations
+                .iter()
+                .any(|loc| loc.gate_type == GateType::SX)
+        );
+        assert!(
+            catalog
+                .locations
+                .iter()
+                .any(|loc| loc.gate_type == GateType::CY)
+        );
+        assert!(
+            catalog
+                .locations
+                .iter()
+                .any(|loc| loc.gate_type == GateType::SXX)
+        );
+        assert!(
+            catalog
+                .locations
+                .iter()
+                .any(|loc| loc.gate_type == GateType::SWAP)
+        );
+
+        let decoder = TargetedLookupDecoder::new(&catalog).max_faults(2);
+        let bf = brute_force_weights(&catalog, 2);
+        for (syndrome, bf_logicals) in &bf {
+            let result = decoder.decode(syndrome);
+            for (logical, &bf_weight) in bf_logicals {
+                let dec_weight = result.logical_weights.get(logical).copied().unwrap_or(0.0);
+                assert!(
+                    (dec_weight - bf_weight).abs() / bf_weight.max(1e-15) < 1e-8,
+                    "new-gate decoder mismatch for syndrome={syndrome:?} logical={logical:?}: \
+                     decoder={dec_weight:.6e} brute_force={bf_weight:.6e}"
+                );
+            }
+        }
+    }
+
+    #[test]
+    fn test_k3_matches_brute_force() {
+        // Very small circuit to keep k=3 tractable
+        let mut tc = TickCircuit::new();
+        tc.tick().h(&[QubitId(0)]);
+        tc.tick().mz(&[QubitId(0)]);
+        tc.set_meta(
+            "num_measurements",
+            pecos_quantum::Attribute::String("1".into()),
+        );
+        tc.set_meta(
+            "detectors",
+            pecos_quantum::Attribute::String(r#"[{"records":[-1]}]"#.into()),
+        );
+        tc.set_meta("observables", pecos_quantum::Attribute::String("[]".into()));
+
+        let noise = StochasticNoiseParams {
+            p1: 0.01,
+            p2: 0.0,
+            p_meas: 0.01,
+            p_prep: 0.01,
+        };
+        let catalog = build_fault_catalog(&tc, &noise).unwrap();
+        let decoder = TargetedLookupDecoder::new(&catalog).max_faults(3);
+        let bf = brute_force_weights(&catalog, 3);
+
+        for (syndrome, bf_logicals) in &bf {
+            let result = decoder.decode(syndrome);
+            for (logical, &bf_weight) in bf_logicals {
+                let dec_weight = result.logical_weights.get(logical).copied().unwrap_or(0.0);
+                assert!(
+                    (dec_weight - bf_weight).abs() / bf_weight.max(1e-15) < 1e-8,
+                    "k=3 mismatch for syndrome={syndrome:?} logical={logical:?}: \
+                     decoder={dec_weight:.6e} brute_force={bf_weight:.6e}"
+                );
+            }
+        }
+    }
+
+    #[test]
+    fn test_cancellation() {
+        // Construct a catalog where syndrome {0} is explained by
+        // {0,1} XOR {1} (two faults cancelling detector 1).
+        let mut tc = TickCircuit::new();
+        tc.tick().h(&[QubitId(0)]);
+        tc.tick().cx(&[(QubitId(0), QubitId(1))]);
+        tc.tick().h(&[QubitId(0)]);
+        tc.tick().mz(&[QubitId(0)]);
+        tc.tick().mz(&[QubitId(1)]);
+        tc.set_meta(
+            "num_measurements",
+            pecos_quantum::Attribute::String("2".into()),
+        );
+        tc.set_meta(
+            "detectors",
+            pecos_quantum::Attribute::String(r#"[{"records":[-2]},{"records":[-1]}]"#.into()),
+        );
+        tc.set_meta("observables", pecos_quantum::Attribute::String("[]".into()));
+
+        let noise = StochasticNoiseParams {
+            p1: 0.01,
+            p2: 0.01,
+            p_meas: 0.01,
+            p_prep: 0.0,
+        };
+        let catalog = build_fault_catalog(&tc, &noise).unwrap();
+        let decoder = TargetedLookupDecoder::new(&catalog).max_faults(2);
+
+        // Check that syndrome [0] has k=2 explanations
+        let result = decoder.decode(&[0]);
+        let bf = brute_force_weights(&catalog, 2);
+        if let Some(bf_logicals) = bf.get(&vec![0]) {
+            for (logical, &bf_weight) in bf_logicals {
+                let dec_weight = result.logical_weights.get(logical).copied().unwrap_or(0.0);
+                assert!(
+                    (dec_weight - bf_weight).abs() / bf_weight.max(1e-15) < 1e-8,
+                    "Cancellation test mismatch"
+                );
+            }
+        }
+    }
+
+    #[test]
+    fn test_same_location_exclusion() {
+        let catalog = tiny_catalog();
+        let decoder = TargetedLookupDecoder::new(&catalog).max_faults(2);
+
+        // Brute force already enforces location exclusion.
+        // Verify decoder matches for all syndromes.
+        let bf = brute_force_weights(&catalog, 2);
+        for (syndrome, bf_logicals) in &bf {
+            let result = decoder.decode(syndrome);
+            for (logical, &bf_weight) in bf_logicals {
+                let dec_weight = result.logical_weights.get(logical).copied().unwrap_or(0.0);
+                assert!(
+                    (dec_weight - bf_weight).abs() / bf_weight.max(1e-15) < 1e-8,
+                    "Location exclusion mismatch at syndrome={syndrome:?}"
+                );
+            }
+        }
+    }
+
+    #[test]
+    fn test_empty_syndrome_with_silent_alternatives() {
+        // Empty-detector alternatives contribute to empty syndrome
+        let catalog = tiny_catalog();
+        let decoder = TargetedLookupDecoder::new(&catalog).max_faults(1);
+        let result = decoder.decode(&[]);
+
+        // k=0 contributes weight 1.0 for empty logical.
+        // k=1 empty-detector alternatives also contribute.
+        assert!(
+            result.logical_weights.contains_key(&vec![]),
+            "Empty logical should appear for empty syndrome"
+        );
+        assert!(
+            *result.logical_weights.get(&vec![]).unwrap() >= 1.0,
+            "Empty-syndrome weight should be >= 1.0 (k=0 contributes 1)"
+        );
+    }
+
+    #[test]
+    fn test_odds_to_absolute_probability() {
+        let catalog = tiny_catalog();
+        let decoder = TargetedLookupDecoder::new(&catalog).max_faults(1);
+        let result = decoder.decode(&[0]);
+
+        // Sum of odds weights * base_probability = sum of configuration_probabilities
+        let total_odds: f64 = result.logical_weights.values().sum();
+        let total_abs = total_odds * decoder.base_probability();
+        assert!(total_abs > 0.0, "Should have nonzero absolute probability");
+        assert!(total_abs < 1.0, "Total probability should be < 1");
+    }
+
+    #[test]
+    fn test_k2_no_double_counting() {
+        let catalog = tiny_catalog();
+        let decoder = TargetedLookupDecoder::new(&catalog).max_faults(2);
+        let bf = brute_force_weights(&catalog, 2);
+
+        // Check EVERY brute-force entry matches decoder exactly
+        for (syndrome, bf_logicals) in &bf {
+            let result = decoder.decode(syndrome);
+            let total_bf: f64 = bf_logicals.values().sum();
+            let total_dec: f64 = result.logical_weights.values().sum();
+            assert!(
+                (total_dec - total_bf).abs() / total_bf.max(1e-15) < 1e-8,
+                "k=2 total weight mismatch at syndrome={syndrome:?}: \
+                 decoder={total_dec:.6e} brute_force={total_bf:.6e}"
+            );
+        }
+    }
+}
diff --git a/crates/pecos-qec/src/lib.rs b/crates/pecos-qec/src/lib.rs
index f42cacc83..50100c2e2 100644
--- a/crates/pecos-qec/src/lib.rs
+++ b/crates/pecos-qec/src/lib.rs
@@ -63,32 +63,38 @@
 //! assert_eq!(analysis.undetectable_logical, 0);
 //! ```
 
+pub mod dem_stab;
 pub mod distance;
 pub mod fault_tolerance;
 pub mod geometry;
 pub mod logical_discovery;
+pub mod mem_stab;
 pub mod stabilizer_code;
 pub mod stabilizer_code_spec;
 pub mod surface;
 
+pub use dem_stab::{DemStabError, DemStabShotBatch, DemStabSim, DemStabSimBuilder};
+pub use mem_stab::{MemStabError, MemStabSim, MemStabSimBuilder};
+
 pub use distance::{
     DistanceResult, DistanceSearchConfig, LogicalOperatorInfo, WeightedPauliIterator,
     calculate_distance, find_min_weight_logicals, find_min_weight_logicals_with_info,
 };
 pub use fault_tolerance::dem_builder::{
-    DecomposedFault, DemBuilder, DemBuilderError, DetectorDef, DetectorErrorModel, FaultMechanism,
-    LogicalObservable, NoiseConfig, combine_probabilities,
+    DecomposedFault, DemBuilder, DemBuilderError, DemOutput, DetectorDef, DetectorErrorModel,
+    FaultMechanism, NoiseConfig, PecosDemMetadataError, combine_probabilities,
 };
 pub use fault_tolerance::{
-    CorrectionResult, DecoderAnalysis, ErrorClass, ErrorCorrectionChecker, ErrorCorrectionConfig,
-    ErrorCorrectionResult, FaultCheckConfig, FaultCheckResult, FaultChecker, FaultClass,
-    FaultConfiguration, FaultToleranceAnalysis, FaultToleranceFailure, LookupTableDecoder,
-    MeasurementRound, PauliFault, PauliFaultIterator, PauliPropChecker, PropagationResult,
-    SpacetimeLocation, StabilizerFlipAnalysis, StabilizerFlipChecker, StabilizerFlips,
-    SyndromeAnalysis, SyndromeClass, SyndromeHistory, SyndromeHistoryAnalysis,
-    SyndromeHistoryResult, anticommutes_with_logical, apply_recovery, classify_fault,
-    extract_measurement_rounds, extract_spacetime_locations, extract_syndrome, get_syndrome_flips,
-    has_syndrome, propagate_fault, propagate_faults, run_circuit_with_faults, run_correction_cycle,
+    CorrectionResult, DecoderAnalysis, DemOutputKind, DemOutputMetadata, ErrorClass,
+    ErrorCorrectionChecker, ErrorCorrectionConfig, ErrorCorrectionResult, FaultCheckConfig,
+    FaultCheckResult, FaultChecker, FaultClass, FaultConfiguration, FaultToleranceAnalysis,
+    FaultToleranceFailure, LookupTableDecoder, MeasurementRound, PauliFault, PauliFaultIterator,
+    PauliPropChecker, PropagationResult, SpacetimeLocation, StabilizerFlipAnalysis,
+    StabilizerFlipChecker, StabilizerFlips, SyndromeAnalysis, SyndromeClass, SyndromeHistory,
+    SyndromeHistoryAnalysis, SyndromeHistoryResult, anticommutes_with_logical, apply_recovery,
+    classify_fault, extract_measurement_rounds, extract_spacetime_locations, extract_syndrome,
+    get_syndrome_flips, has_syndrome, propagate_fault, propagate_faults, run_circuit_with_faults,
+    run_correction_cycle,
 };
 pub use geometry::{CheckSchedule, LogicalOperator, PauliOp, StabilizerCheck, StabilizerColor};
 pub use logical_discovery::{
diff --git a/crates/pecos-qec/src/mem_stab.rs b/crates/pecos-qec/src/mem_stab.rs
new file mode 100644
index 000000000..098a2b419
--- /dev/null
+++ b/crates/pecos-qec/src/mem_stab.rs
@@ -0,0 +1,197 @@
+// Copyright 2026 The PECOS Developers
+//
+// Licensed under the Apache License, Version 2.0 (the "License"); you may not use this file except
+// in compliance with the License. You may obtain a copy of the License at
+//
+//     https://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software distributed under the License
+// is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express
+// or implied. See the License for the specific language governing permissions and limitations under
+// the License.
+
+//! `MemStabSim` -- Clifford + depolarizing-family noise simulator that samples
+//! **raw measurement outcomes** via a Measurement Noise Model (MNM).
+//!
+//! Sibling to [`crate::dem_stab::DemStabSim`]. Same underlying fault-influence
+//! machinery, different aggregation level:
+//!
+//! | | `DemStabSim` | `MemStabSim` |
+//! |---|---|---|
+//! | Output | Detector + observable flips | Raw measurement outcomes |
+//! | Use case | Research batch / decoder input | Classical-engine-facing backend |
+//! | Backing primitive | `DemSampler` (DEM mechanisms) | `MeasurementNoiseModel` (MNM mechanisms) |
+//!
+//! Use `MemStabSim` when a classical control engine needs per-shot raw measurement
+//! records (and will compute its own detectors/observables from them). Use
+//! `DemStabSim` when you just want detector events for a decoder.
+//!
+//! # Scope
+//!
+//! Clifford circuits only, no classical feed-forward. For adaptive circuits use
+//! `sparse_stab` + `pecos-neo` instead. For non-Clifford circuits use `CliffordRz`,
+//! `STN`, or `MAST`.
+//!
+//! # Example
+//!
+//! ```
+//! use pecos_qec::mem_stab::MemStabSim;
+//! use pecos_qec::fault_tolerance::dem_builder::NoiseConfig;
+//! use pecos_quantum::DagCircuit;
+//! use rand::SeedableRng;
+//! use rand::rngs::SmallRng;
+//!
+//! let mut dag = DagCircuit::new();
+//! dag.pz(&[2]);
+//! dag.cx(&[(0, 2)]);
+//! dag.cx(&[(1, 2)]);
+//! dag.mz(&[2]);
+//!
+//! let sim = MemStabSim::builder()
+//!     .circuit(dag)
+//!     .noise(NoiseConfig::uniform(0.01))
+//!     .build()
+//!     .unwrap();
+//!
+//! let mut rng = SmallRng::seed_from_u64(42);
+//! let outcomes = sim.sample(&mut rng);
+//! assert_eq!(outcomes.len(), sim.num_measurements());
+//! ```
+
+use crate::fault_tolerance::dem_builder::{MeasurementNoiseModel, MemBuilder, NoiseConfig};
+use crate::fault_tolerance::propagator::DagFaultAnalyzer;
+use pecos_quantum::DagCircuit;
+use rand::Rng;
+use thiserror::Error;
+
+/// Errors that can occur when building a [`MemStabSim`].
+#[derive(Debug, Error)]
+pub enum MemStabError {
+    /// Builder called without a circuit.
+    #[error("MemStabSim requires a circuit; call .circuit(dag) before .build()")]
+    MissingCircuit,
+}
+
+/// Clifford + depolarizing-family noise simulator that samples raw measurement outcomes.
+///
+/// Built once via [`MemStabSim::builder`], sampled many times via [`Self::sample`] or
+/// [`Self::sample_batch`]. The underlying [`MeasurementNoiseModel`] is constructed
+/// eagerly at build time.
+#[derive(Debug, Clone)]
+pub struct MemStabSim {
+    mnm: MeasurementNoiseModel,
+}
+
+impl MemStabSim {
+    /// Start building a [`MemStabSim`].
+    #[must_use]
+    pub fn builder() -> MemStabSimBuilder {
+        MemStabSimBuilder::default()
+    }
+
+    /// Number of measurements in the compiled circuit.
+    #[must_use]
+    pub fn num_measurements(&self) -> usize {
+        self.mnm.num_measurements
+    }
+
+    /// Number of error mechanisms in the compiled MNM.
+    #[must_use]
+    pub fn num_mechanisms(&self) -> usize {
+        self.mnm.mechanisms.len()
+    }
+
+    /// Access the underlying [`MeasurementNoiseModel`].
+    #[must_use]
+    pub fn mnm(&self) -> &MeasurementNoiseModel {
+        &self.mnm
+    }
+
+    /// Sample one shot of raw measurement outcomes.
+    ///
+    /// Length of the returned vector equals [`Self::num_measurements`].
+    pub fn sample<R: Rng>(&self, rng: &mut R) -> Vec<bool> {
+        self.mnm.sample(rng)
+    }
+
+    /// Sample one shot into a preallocated buffer.
+    ///
+    /// `outcomes` must have length equal to [`Self::num_measurements`]; the buffer
+    /// is cleared before sampling.
+    pub fn sample_into<R: Rng>(&self, outcomes: &mut [bool], rng: &mut R) {
+        self.mnm.sample_into(outcomes, rng);
+    }
+
+    /// Sample `num_shots` independent shots.
+    ///
+    /// Returns a `Vec` of length `num_shots`; each inner vector has length
+    /// [`Self::num_measurements`].
+    #[must_use]
+    pub fn sample_batch<R: Rng>(&self, num_shots: usize, rng: &mut R) -> Vec<Vec<bool>> {
+        let mut out = Vec::with_capacity(num_shots);
+        let mut buf = vec![false; self.num_measurements()];
+        for _ in 0..num_shots {
+            self.mnm.sample_into(&mut buf, rng);
+            out.push(buf.clone());
+        }
+        out
+    }
+}
+
+/// Builder for [`MemStabSim`].
+#[derive(Debug, Default)]
+pub struct MemStabSimBuilder {
+    circuit: Option<DagCircuit>,
+    noise: NoiseConfig,
+    measurement_order: Option<Vec<usize>>,
+}
+
+impl MemStabSimBuilder {
+    /// Set the circuit. Required.
+    #[must_use]
+    pub fn circuit(mut self, dag: DagCircuit) -> Self {
+        self.circuit = Some(dag);
+        self
+    }
+
+    /// Set the noise configuration.
+    #[must_use]
+    pub fn noise(mut self, config: NoiseConfig) -> Self {
+        self.noise = config;
+        self
+    }
+
+    /// Set the measurement order mapping from a `TickCircuit` (advanced).
+    #[must_use]
+    pub fn measurement_order(mut self, order: Vec<usize>) -> Self {
+        self.measurement_order = Some(order);
+        self
+    }
+
+    /// Build the [`MemStabSim`], consuming the builder.
+    ///
+    /// # Errors
+    ///
+    /// Returns [`MemStabError::MissingCircuit`] if no circuit was set.
+    pub fn build(self) -> Result<MemStabSim, MemStabError> {
+        let dag = self.circuit.ok_or(MemStabError::MissingCircuit)?;
+
+        let analyzer = DagFaultAnalyzer::new(&dag);
+        let influence_map = analyzer.build_influence_map();
+
+        let mut builder = MemBuilder::new(&influence_map).with_noise(
+            self.noise.p1,
+            self.noise.p2,
+            self.noise.p_meas,
+            self.noise.p_prep,
+        );
+
+        if let Some(order) = self.measurement_order {
+            builder = builder.with_measurement_order(order);
+        }
+
+        Ok(MemStabSim {
+            mnm: builder.build(),
+        })
+    }
+}
diff --git a/crates/pecos-qec/src/stabilizer_code.rs b/crates/pecos-qec/src/stabilizer_code.rs
index 61c03795e..6f1eb5780 100644
--- a/crates/pecos-qec/src/stabilizer_code.rs
+++ b/crates/pecos-qec/src/stabilizer_code.rs
@@ -128,7 +128,7 @@ impl StabilizerCode {
     ///
     /// ```
     /// use pecos_qec::StabilizerCode;
-    /// use pecos_core::pauli::constructors::*;
+    /// use pecos_core::pauli::*;
     ///
     /// // Repetition code [[3,1]]: logicals are X_L = XXX, Z_L = Z on any qubit
     /// let code = StabilizerCode::repetition(3);
@@ -147,10 +147,10 @@ impl StabilizerCode {
         let mut stab_mat = F2Matrix::zeros(num_generators, 2 * n);
         for (row_idx, stab) in self.group.stabilizers().iter().enumerate() {
             for q in stab.x_positions() {
-                stab_mat.row_mut(row_idx)[q] = 1;
+                stab_mat.set(row_idx, q, 1);
             }
             for q in stab.z_positions() {
-                stab_mat.row_mut(row_idx)[n + q] = 1;
+                stab_mat.set(row_idx, n + q, 1);
             }
         }
         let (stab_rref, stab_pivots) = stab_mat.row_reduce();
@@ -167,7 +167,7 @@ impl StabilizerCode {
             for (row_idx, &pivot_col) in stab_pivots.iter().enumerate() {
                 if v[pivot_col] == 1 {
                     for (col, vi) in v.iter_mut().enumerate() {
-                        *vi ^= stab_rref.row(row_idx)[col];
+                        *vi ^= stab_rref.get(row_idx, col);
                     }
                 }
             }
@@ -182,11 +182,11 @@ impl StabilizerCode {
         if logical_vecs.len() > 1 {
             let mut log_mat = F2Matrix::zeros(logical_vecs.len(), 2 * n);
             for (i, v) in logical_vecs.iter().enumerate() {
-                log_mat.row_mut(i).clone_from(v);
+                log_mat.set_row(i, v);
             }
             let (reduced, _) = log_mat.row_reduce();
             logical_vecs = (0..reduced.num_rows())
-                .map(|i| reduced.row(i).to_vec())
+                .map(|i| reduced.row(i))
                 .filter(|r| r.iter().any(|&b| b != 0))
                 .collect();
         }
@@ -215,7 +215,7 @@ impl StabilizerCode {
     ///
     /// ```
     /// use pecos_qec::StabilizerCode;
-    /// use pecos_core::pauli::constructors::*;
+    /// use pecos_core::pauli::*;
     ///
     /// // Repetition code [[3,1,1]]: distance 1 (logical Z = Z on any single qubit)
     /// let code = StabilizerCode::repetition(3);
@@ -283,7 +283,7 @@ impl StabilizerCode {
     ///
     /// ```
     /// use pecos_qec::StabilizerCode;
-    /// use pecos_core::pauli::constructors::*;
+    /// use pecos_core::pauli::*;
     ///
     /// // Repetition code: ZZI, IZZ on 3 qubits
     /// let code = StabilizerCode::repetition(3);
@@ -347,7 +347,7 @@ impl StabilizerCode {
     /// ```
     #[must_use]
     pub fn repetition(n: usize) -> Self {
-        use pecos_core::pauli::constructors::Zs;
+        use pecos_core::pauli::Zs;
         assert!(
             n >= 2,
             "repetition code requires at least 2 qubits, got {n}"
@@ -377,7 +377,7 @@ impl StabilizerCode {
     /// ```
     #[must_use]
     pub fn steane() -> Self {
-        use pecos_core::pauli::constructors::{Xs, Zs};
+        use pecos_core::pauli::{Xs, Zs};
         let generators = vec![
             Xs([0, 2, 4, 6]),
             Xs([1, 2, 5, 6]),
@@ -411,7 +411,7 @@ impl StabilizerCode {
     /// ```
     #[must_use]
     pub fn five_qubit() -> Self {
-        use pecos_core::pauli::constructors::{X, Z};
+        use pecos_core::pauli::{X, Z};
         let generators = vec![
             X(0) & Z(1) & Z(2) & X(3), // XZZXI
             X(1) & Z(2) & Z(3) & X(4), // IXZZX
@@ -441,7 +441,7 @@ impl StabilizerCode {
     /// ```
     #[must_use]
     pub fn shor() -> Self {
-        use pecos_core::pauli::constructors::{Xs, Zs};
+        use pecos_core::pauli::{Xs, Zs};
         let generators = vec![
             Xs([0, 1]),
             Xs([1, 2]),
@@ -477,7 +477,7 @@ impl StabilizerCode {
     /// ```
     #[must_use]
     pub fn four_two_two() -> Self {
-        use pecos_core::pauli::constructors::{Xs, Zs};
+        use pecos_core::pauli::{Xs, Zs};
         let generators = vec![Xs([0, 1, 2, 3]), Zs([0, 1, 2, 3])];
         Self {
             group: PauliStabilizerGroup::from_generators_unchecked(generators),
@@ -506,7 +506,7 @@ impl StabilizerCode {
     /// ```
     #[must_use]
     pub fn toric(l: usize) -> Self {
-        use pecos_core::pauli::constructors::{Xs, Zs};
+        use pecos_core::pauli::{Xs, Zs};
         assert!(l >= 2, "toric code requires L >= 2, got {l}");
 
         let n = 2 * l * l;
@@ -557,7 +557,7 @@ impl StabilizerCode {
 #[cfg(test)]
 mod tests {
     use super::*;
-    use pecos_core::pauli::constructors::*;
+    use pecos_core::pauli::*;
 
     // ========================================================================
     // Basic code parameter tests
diff --git a/crates/pecos-qec/src/stabilizer_code_spec.rs b/crates/pecos-qec/src/stabilizer_code_spec.rs
index 7c2e4840b..e1d753106 100644
--- a/crates/pecos-qec/src/stabilizer_code_spec.rs
+++ b/crates/pecos-qec/src/stabilizer_code_spec.rs
@@ -938,10 +938,7 @@ impl StabilizerCodeSpecBuilder {
         self
     }
 
-    /// Adds a stabilizer from an `UnitaryRep`.
-    ///
-    /// The operator must be convertible to a `PauliString` (i.e., a Pauli operator
-    /// or tensor product of Pauli operators).
+    /// Adds a stabilizer Pauli operator.
     ///
     /// # Example
     ///
@@ -956,18 +953,9 @@ impl StabilizerCodeSpecBuilder {
     ///     .unwrap();
     /// ```
     ///
-    /// Accepts both `PauliString` and `UnitaryRep` (via `Into<UnitaryRep>`).
-    ///
-    /// # Panics
-    ///
-    /// Panics if the operator cannot be converted to a `PauliString`.
     #[must_use]
-    pub fn check(mut self, op: impl Into<pecos_core::UnitaryRep>) -> Self {
-        let ps = op
-            .into()
-            .try_to_pauli_string()
-            .expect("UnitaryRep must be convertible to PauliString");
-        self.stabilizers.push(ps);
+    pub fn check(mut self, op: impl Into<PauliString>) -> Self {
+        self.stabilizers.push(op.into());
         self
     }
 
@@ -978,20 +966,10 @@ impl StabilizerCodeSpecBuilder {
         self
     }
 
-    /// Adds a logical Z operator.
-    ///
-    /// Accepts both `PauliString` and `UnitaryRep` (via `Into<UnitaryRep>`).
-    ///
-    /// # Panics
-    ///
-    /// Panics if the operator cannot be converted to a `PauliString`.
+    /// Adds a logical Z Pauli operator.
     #[must_use]
-    pub fn logical_z(mut self, op: impl Into<pecos_core::UnitaryRep>) -> Self {
-        let ps = op
-            .into()
-            .try_to_pauli_string()
-            .expect("UnitaryRep must be convertible to PauliString");
-        self.logical_zs.push(ps);
+    pub fn logical_z(mut self, op: impl Into<PauliString>) -> Self {
+        self.logical_zs.push(op.into());
         self
     }
 
@@ -1002,20 +980,10 @@ impl StabilizerCodeSpecBuilder {
         self
     }
 
-    /// Adds a logical X operator.
-    ///
-    /// Accepts both `PauliString` and `UnitaryRep` (via `Into<UnitaryRep>`).
-    ///
-    /// # Panics
-    ///
-    /// Panics if the operator cannot be converted to a `PauliString`.
+    /// Adds a logical X Pauli operator.
     #[must_use]
-    pub fn logical_x(mut self, op: impl Into<pecos_core::UnitaryRep>) -> Self {
-        let ps = op
-            .into()
-            .try_to_pauli_string()
-            .expect("UnitaryRep must be convertible to PauliString");
-        self.logical_xs.push(ps);
+    pub fn logical_x(mut self, op: impl Into<PauliString>) -> Self {
+        self.logical_xs.push(op.into());
         self
     }
 
@@ -1695,7 +1663,7 @@ mod tests {
 
     #[test]
     fn test_stabilizer_group_algebraic_analysis() {
-        use pecos_core::pauli::constructors::*;
+        use pecos_core::pauli::*;
 
         // Use SurfaceCode and convert for algebraic analysis
         let surface = crate::SurfaceCode::rotated(3).unwrap();
@@ -1808,7 +1776,7 @@ mod tests {
 
     #[test]
     fn test_from_stabilizer_code_preserves_explicit_num_qubits() {
-        use pecos_core::pauli::constructors::Z;
+        use pecos_core::pauli::Z;
         use pecos_quantum::PauliStabilizerGroup;
 
         // StabilizerCode with explicit num_qubits > group touches
diff --git a/crates/pecos-qec/tests/dem_sampler_tests.rs b/crates/pecos-qec/tests/dem_sampler_tests.rs
index 46566dd08..f30fcdbe9 100644
--- a/crates/pecos-qec/tests/dem_sampler_tests.rs
+++ b/crates/pecos-qec/tests/dem_sampler_tests.rs
@@ -20,11 +20,10 @@
 //! 3. Consistency with MNM (Measurement Noise Model)
 //! 4. Edge cases and boundary conditions
 
-use pecos_qec::fault_tolerance::dem_builder::{DemSamplerBuilder, MemBuilder};
+use pecos_qec::fault_tolerance::dem_builder::DemSamplerBuilder;
 use pecos_qec::fault_tolerance::propagator::DagFaultAnalyzer;
 use pecos_quantum::DagCircuit;
-use rand::SeedableRng;
-use rand::rngs::SmallRng;
+use pecos_random::PecosRng;
 
 // ============================================================================
 // Test Helpers
@@ -74,12 +73,13 @@ fn test_zero_noise_produces_no_errors() {
         .with_noise(0.0, 0.0, 0.0, 0.0)
         .with_detectors_json(detectors_json)
         .unwrap()
-        .build();
+        .build()
+        .unwrap();
 
     // Zero noise should produce zero mechanisms
     assert_eq!(sampler.num_mechanisms(), 0);
 
-    let mut rng = SmallRng::seed_from_u64(42);
+    let mut rng = PecosRng::seed_from_u64(42);
     let stats = sampler.sample_statistics_with_rng(1000, &mut rng);
 
     assert_eq!(stats.logical_error_count, 0);
@@ -102,13 +102,15 @@ fn test_mechanism_count_scales_with_circuit() {
         .with_noise(0.01, 0.01, 0.01, 0.01)
         .with_detectors_json(r#"[{"id": 0, "records": [-1]}]"#)
         .unwrap()
-        .build();
+        .build()
+        .unwrap();
 
     let sampler2 = DemSamplerBuilder::new(&im2)
         .with_noise(0.01, 0.01, 0.01, 0.01)
         .with_detectors_json(r#"[{"id": 0, "records": [-2]}, {"id": 1, "records": [-1]}]"#)
         .unwrap()
-        .build();
+        .build()
+        .unwrap();
 
     // Larger circuit should have more mechanisms
     assert!(
@@ -129,11 +131,12 @@ fn test_deterministic_sampling_with_seed() {
         .with_noise(0.1, 0.1, 0.1, 0.1)
         .with_detectors_json(detectors_json)
         .unwrap()
-        .build();
+        .build()
+        .unwrap();
 
     // Same seed should produce same results
-    let mut rng1 = SmallRng::seed_from_u64(12345);
-    let mut rng2 = SmallRng::seed_from_u64(12345);
+    let mut rng1 = PecosRng::seed_from_u64(12345);
+    let mut rng2 = PecosRng::seed_from_u64(12345);
 
     let (det1, obs1) = sampler.sample_batch(100, &mut rng1);
     let (det2, obs2) = sampler.sample_batch(100, &mut rng2);
@@ -154,10 +157,11 @@ fn test_different_seeds_produce_different_results() {
         .with_noise(0.1, 0.1, 0.1, 0.1)
         .with_detectors_json(detectors_json)
         .unwrap()
-        .build();
+        .build()
+        .unwrap();
 
-    let mut rng1 = SmallRng::seed_from_u64(12345);
-    let mut rng2 = SmallRng::seed_from_u64(54321);
+    let mut rng1 = PecosRng::seed_from_u64(12345);
+    let mut rng2 = PecosRng::seed_from_u64(54321);
 
     let (det1, _) = sampler.sample_batch(100, &mut rng1);
     let (det2, _) = sampler.sample_batch(100, &mut rng2);
@@ -182,15 +186,17 @@ fn test_syndrome_rate_scales_with_noise() {
         .with_noise(0.001, 0.001, 0.001, 0.001)
         .with_detectors_json(detectors_json)
         .unwrap()
-        .build();
+        .build()
+        .unwrap();
 
     let sampler_high = DemSamplerBuilder::new(&influence_map)
         .with_noise(0.05, 0.05, 0.05, 0.05)
         .with_detectors_json(detectors_json)
         .unwrap()
-        .build();
+        .build()
+        .unwrap();
 
-    let mut rng = SmallRng::seed_from_u64(42);
+    let mut rng = PecosRng::seed_from_u64(42);
 
     let stats_low = sampler_low.sample_statistics_with_rng(10000, &mut rng);
     let stats_high = sampler_high.sample_statistics_with_rng(10000, &mut rng);
@@ -217,9 +223,10 @@ fn test_syndrome_rate_reasonable_magnitude() {
         .with_noise(p, p, p, p)
         .with_detectors_json(detectors_json)
         .unwrap()
-        .build();
+        .build()
+        .unwrap();
 
-    let mut rng = SmallRng::seed_from_u64(42);
+    let mut rng = PecosRng::seed_from_u64(42);
     let stats = sampler.sample_statistics_with_rng(100_000, &mut rng);
 
     // With p=0.01, syndrome rate should be in a reasonable range
@@ -253,17 +260,18 @@ fn test_observable_tracking() {
         .unwrap()
         .with_observables_json(observables_json)
         .unwrap()
-        .build();
+        .build()
+        .unwrap();
 
     assert_eq!(sampler.num_observables(), 1);
 
-    let mut rng = SmallRng::seed_from_u64(42);
+    let mut rng = PecosRng::seed_from_u64(42);
     let stats = sampler.sample_statistics_with_rng(10000, &mut rng);
 
-    // With observable tracking, we should see some logical errors
+    // With observable tracking, we should see some observable errors
     assert!(
         stats.logical_error_rate() > 0.0,
-        "Expected some logical errors with noise"
+        "Expected some observable errors with noise"
     );
 }
 
@@ -281,11 +289,12 @@ fn test_empty_detector_definitions() {
         .with_noise(0.01, 0.01, 0.01, 0.01)
         .with_detectors_json("[]")
         .unwrap()
-        .build();
+        .build()
+        .unwrap();
 
     assert_eq!(sampler.num_detectors(), 0);
 
-    let mut rng = SmallRng::seed_from_u64(42);
+    let mut rng = PecosRng::seed_from_u64(42);
     let (det_events, _) = sampler.sample(&mut rng);
 
     assert!(det_events.is_empty());
@@ -305,12 +314,13 @@ fn test_single_qubit_circuit() {
         .with_noise(0.01, 0.01, 0.01, 0.01)
         .with_detectors_json(r#"[{"id": 0, "records": [-1]}]"#)
         .unwrap()
-        .build();
+        .build()
+        .unwrap();
 
     // Should have mechanisms from prep, H gate, and measurement
     assert!(sampler.num_mechanisms() > 0);
 
-    let mut rng = SmallRng::seed_from_u64(42);
+    let mut rng = PecosRng::seed_from_u64(42);
     let stats = sampler.sample_statistics_with_rng(1000, &mut rng);
 
     // Should produce some syndromes
@@ -327,14 +337,15 @@ fn test_only_measurement_noise() {
         .with_noise(0.0, 0.0, 0.1, 0.0) // Only measurement noise
         .with_detectors_json(r#"[{"id": 0, "records": [-1]}]"#)
         .unwrap()
-        .build();
+        .build()
+        .unwrap();
 
     assert!(
         sampler.num_mechanisms() > 0,
         "Should have mechanisms from measurement noise"
     );
 
-    let mut rng = SmallRng::seed_from_u64(42);
+    let mut rng = PecosRng::seed_from_u64(42);
     let stats = sampler.sample_statistics_with_rng(10000, &mut rng);
 
     // Should produce syndromes from measurement errors
@@ -354,14 +365,15 @@ fn test_only_two_qubit_noise() {
         .with_noise(0.0, 0.1, 0.0, 0.0) // Only two-qubit noise
         .with_detectors_json(r#"[{"id": 0, "records": [-1]}]"#)
         .unwrap()
-        .build();
+        .build()
+        .unwrap();
 
     assert!(
         sampler.num_mechanisms() > 0,
         "Should have mechanisms from two-qubit noise"
     );
 
-    let mut rng = SmallRng::seed_from_u64(42);
+    let mut rng = PecosRng::seed_from_u64(42);
     let stats = sampler.sample_statistics_with_rng(10000, &mut rng);
 
     // Should produce syndromes from CX errors
@@ -384,24 +396,26 @@ fn test_dem_sampler_vs_mnm_mechanism_structure() {
     let p1 = 0.01;
     let p2 = 0.01;
     let p_meas = 0.01;
-    let p_init = 0.01;
-
-    // Build MNM for comparison
-    let mnm = MemBuilder::new(&influence_map)
-        .with_noise(p1, p2, p_meas, p_init)
-        .build();
-
-    // Build DemSampler
-    let sampler = DemSamplerBuilder::new(&influence_map)
-        .with_noise(p1, p2, p_meas, p_init)
-        .with_detectors_json(r#"[{"id": 0, "records": [-1]}]"#)
-        .unwrap()
-        .build();
-
-    // MNM mechanisms are at measurement level, DemSampler at detector level
-    // They should both have non-zero counts
-    assert!(mnm.num_mechanisms() > 0);
-    assert!(sampler.num_mechanisms() > 0);
+    let p_prep = 0.01;
+
+    // DemSampler raw mode (replaces MemBuilder)
+    let raw_sampler = DemSamplerBuilder::new(&influence_map)
+        .with_noise(p1, p2, p_meas, p_prep)
+        .raw_measurements()
+        .build()
+        .unwrap();
+
+    // DemSampler detector mode (replaces DemSamplerBuilder for this use case)
+    let det_records = vec![vec![-1i32]];
+    let det_sampler = DemSamplerBuilder::new(&influence_map)
+        .with_noise(p1, p2, p_meas, p_prep)
+        .with_detectors(det_records, vec![])
+        .build()
+        .unwrap();
+
+    // Both should have non-zero mechanism counts
+    assert!(raw_sampler.num_mechanisms() > 0);
+    assert!(det_sampler.num_mechanisms() > 0);
 }
 
 #[test]
@@ -419,11 +433,12 @@ fn test_multi_detector_circuit() {
         .with_noise(0.01, 0.01, 0.01, 0.01)
         .with_detectors_json(detectors_json)
         .unwrap()
-        .build();
+        .build()
+        .unwrap();
 
     assert_eq!(sampler.num_detectors(), 2);
 
-    let mut rng = SmallRng::seed_from_u64(42);
+    let mut rng = PecosRng::seed_from_u64(42);
     let (det_events, _) = sampler.sample_batch(1000, &mut rng);
 
     // Should get events on both detectors
@@ -448,9 +463,10 @@ fn test_batch_sampling_performance() {
         .with_noise(0.01, 0.01, 0.01, 0.01)
         .with_detectors_json(r#"[{"id": 0, "records": [-2]}, {"id": 1, "records": [-1]}]"#)
         .unwrap()
-        .build();
+        .build()
+        .unwrap();
 
-    let mut rng = SmallRng::seed_from_u64(42);
+    let mut rng = PecosRng::seed_from_u64(42);
 
     // Should be able to sample many shots quickly
     let num_shots = 100_000;
@@ -483,21 +499,22 @@ fn test_statistics_vs_batch_consistency() {
         .unwrap()
         .with_observables_json(observables_json)
         .unwrap()
-        .build();
+        .build()
+        .unwrap();
 
     let num_shots = 10000;
 
     // Sample with statistics method (uses geometric skip)
-    let mut rng1 = SmallRng::seed_from_u64(42);
+    let mut rng1 = PecosRng::seed_from_u64(42);
     let stats = sampler.sample_statistics_with_rng(num_shots, &mut rng1);
 
     // Sample with batch method (uses per-shot threshold)
-    let mut rng2 = SmallRng::seed_from_u64(123); // Different seed since algorithms differ
+    let mut rng2 = PecosRng::seed_from_u64(123); // Different seed since algorithms differ
     let (det_events, obs_flips) = sampler.sample_batch(num_shots, &mut rng2);
 
     // Count from batch results
     let batch_syndromes = det_events.iter().filter(|d| d.iter().any(|&x| x)).count();
-    let batch_logical = obs_flips.iter().filter(|o| o.iter().any(|&x| x)).count();
+    let batch_observable = obs_flips.iter().filter(|o| o.iter().any(|&x| x)).count();
 
     // Should be statistically similar (within 10% relative difference)
     let stats_rate = stats.syndrome_count as f64 / num_shots as f64;
@@ -509,11 +526,11 @@ fn test_statistics_vs_batch_consistency() {
     );
 
     let stats_logical_rate = stats.logical_error_count as f64 / num_shots as f64;
-    let batch_logical_rate = batch_logical as f64 / num_shots as f64;
-    let logical_rel_diff = (stats_logical_rate - batch_logical_rate).abs()
+    let batch_logical_rate = batch_observable as f64 / num_shots as f64;
+    let observable_rel_diff = (stats_logical_rate - batch_logical_rate).abs()
         / stats_logical_rate.max(batch_logical_rate).max(0.001);
     assert!(
-        logical_rel_diff < 0.1,
-        "Logical error rates should be similar: stats={stats_logical_rate:.4} batch={batch_logical_rate:.4} rel_diff={logical_rel_diff:.2}"
+        observable_rel_diff < 0.1,
+        "Logical error rates should be similar: stats={stats_logical_rate:.4} batch={batch_logical_rate:.4} rel_diff={observable_rel_diff:.2}"
     );
 }
diff --git a/crates/pecos-qec/tests/dem_stab_tests.rs b/crates/pecos-qec/tests/dem_stab_tests.rs
new file mode 100644
index 000000000..3b867c711
--- /dev/null
+++ b/crates/pecos-qec/tests/dem_stab_tests.rs
@@ -0,0 +1,156 @@
+// Copyright 2026 The PECOS Developers
+//
+// Licensed under the Apache License, Version 2.0 (the "License"); you may not use this file except
+// in compliance with the License. You may obtain a copy of the License at
+//
+//     https://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software distributed under the License
+// is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express
+// or implied. See the License for the specific language governing permissions and limitations under
+// the License.
+
+//! Integration tests for `DemStabSim`.
+//!
+//! Parity: `DemStabSim` must produce identical shot batches to the raw
+//! `DagFaultAnalyzer` + `DemSamplerBuilder` pipeline given equal inputs and seeds.
+
+use pecos_qec::dem_stab::{DemStabError, DemStabSim};
+use pecos_qec::fault_tolerance::dem_builder::{
+    DemOutput, DemSamplerBuilder, DetectorDef, NoiseConfig,
+};
+use pecos_qec::fault_tolerance::propagator::DagFaultAnalyzer;
+use pecos_quantum::DagCircuit;
+use rand::SeedableRng;
+use rand::rngs::SmallRng;
+
+fn repetition_code_circuit() -> DagCircuit {
+    let mut dag = DagCircuit::new();
+    // 3 data qubits (0, 1, 2), 2 ancillas (3, 4)
+    dag.pz(&[3]);
+    dag.pz(&[4]);
+    dag.cx(&[(0, 3)]);
+    dag.cx(&[(1, 3)]);
+    dag.cx(&[(1, 4)]);
+    dag.cx(&[(2, 4)]);
+    dag.mz(&[3]);
+    dag.mz(&[4]);
+    dag
+}
+
+fn detectors() -> Vec<DetectorDef> {
+    vec![
+        DetectorDef::new(0).with_records([-2]),
+        DetectorDef::new(1).with_records([-1]),
+    ]
+}
+
+fn observables() -> Vec<DemOutput> {
+    vec![DemOutput::new(0).with_records([-2, -1])]
+}
+
+#[test]
+fn builder_rejects_missing_circuit() {
+    let err = DemStabSim::builder().build().unwrap_err();
+    assert!(matches!(err, DemStabError::MissingCircuit));
+}
+
+#[test]
+fn zero_noise_produces_zero_mechanisms() {
+    let sim = DemStabSim::builder()
+        .circuit(repetition_code_circuit())
+        .noise(NoiseConfig::uniform(0.0))
+        .detectors(detectors())
+        .observables(observables())
+        .build()
+        .unwrap();
+
+    assert_eq!(sim.num_mechanisms(), 0);
+    assert_eq!(sim.num_detectors(), 2);
+    assert_eq!(sim.num_observables(), 1);
+}
+
+#[test]
+fn parity_with_raw_pipeline() {
+    let noise = NoiseConfig::uniform(0.01);
+    let shots = 512;
+    let seed = 0xDEAD_BEEF_u64;
+
+    // Path 1: DemStabSim.
+    let sim = DemStabSim::builder()
+        .circuit(repetition_code_circuit())
+        .noise(noise.clone())
+        .detectors(detectors())
+        .observables(observables())
+        .build()
+        .unwrap();
+    let mut rng1 = SmallRng::seed_from_u64(seed);
+    let batch = sim.sample_batch(shots, &mut rng1);
+
+    // Path 2: raw pipeline, identical inputs + identical RNG seed.
+    let dag = repetition_code_circuit();
+    let analyzer = DagFaultAnalyzer::new(&dag);
+    let influence_map = analyzer.build_influence_map();
+    let det_records: Vec<Vec<i32>> = detectors().iter().map(|d| d.records.to_vec()).collect();
+    let obs_records: Vec<Vec<i32>> = observables().iter().map(|o| o.records.to_vec()).collect();
+    let sampler = DemSamplerBuilder::new(&influence_map)
+        .with_noise(noise.p1, noise.p2, noise.p_meas, noise.p_prep)
+        .with_detector_records(det_records)
+        .with_observable_records(obs_records)
+        .build()
+        .unwrap();
+    let mut rng2 = SmallRng::seed_from_u64(seed);
+    let (det_raw, obs_raw) = sampler.sample_batch(shots, &mut rng2);
+
+    assert_eq!(batch.detector_flips, det_raw);
+    assert_eq!(batch.observable_flips, obs_raw);
+}
+
+#[test]
+fn shot_batch_shape_is_correct() {
+    let sim = DemStabSim::builder()
+        .circuit(repetition_code_circuit())
+        .noise(NoiseConfig::uniform(0.005))
+        .detectors(detectors())
+        .observables(observables())
+        .build()
+        .unwrap();
+
+    let mut rng = SmallRng::seed_from_u64(7);
+    let batch = sim.sample_batch(16, &mut rng);
+
+    assert_eq!(batch.detector_flips.len(), 16);
+    assert_eq!(batch.observable_flips.len(), 16);
+    for row in &batch.detector_flips {
+        assert_eq!(row.len(), sim.num_detectors());
+    }
+    for row in &batch.observable_flips {
+        assert_eq!(row.len(), sim.num_observables());
+    }
+}
+
+#[test]
+fn nonzero_noise_yields_some_flips() {
+    // Sanity check: at p=0.1 with 1000 shots we should see plenty of flips.
+    let sim = DemStabSim::builder()
+        .circuit(repetition_code_circuit())
+        .noise(NoiseConfig::uniform(0.1))
+        .detectors(detectors())
+        .observables(observables())
+        .build()
+        .unwrap();
+
+    let mut rng = SmallRng::seed_from_u64(123);
+    let batch = sim.sample_batch(1000, &mut rng);
+
+    let total_det_flips: usize = batch
+        .detector_flips
+        .iter()
+        .map(|row| row.iter().filter(|&&b| b).count())
+        .sum();
+
+    assert!(
+        total_det_flips > 0,
+        "expected some detector flips at p=0.1 over 1000 shots"
+    );
+}
diff --git a/crates/pecos-qec/tests/fault_enumeration_example.rs b/crates/pecos-qec/tests/fault_enumeration_example.rs
new file mode 100644
index 000000000..eb2010a1a
--- /dev/null
+++ b/crates/pecos-qec/tests/fault_enumeration_example.rs
@@ -0,0 +1,793 @@
+// Copyright 2026 The PECOS Developers
+//
+// Licensed under the Apache License, Version 2.0 (the "License"); you may not use this file except
+// in compliance with the License. You may obtain a copy of the License at
+//
+//     https://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software distributed under the License
+// is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express
+// or implied. See the License for the specific language governing permissions and limitations under
+// the License.
+
+// Shot counts and error counters are small integers; precision loss in f64 is not a concern.
+#![allow(clippy::cast_precision_loss)]
+
+//! Example: Repetition code d=3 with 3 rounds of syndrome extraction.
+//!
+//! Demonstrates the full QEC workflow:
+//! 1. Build the circuit with annotations (detectors, observables, tracked Paulis)
+//! 2. Build the fault influence map
+//! 3. Enumerate fault combinations up to weight 3
+//! 4. Classify errors (detectable, undetectable, logical)
+
+use pecos_core::pauli::X;
+use pecos_qec::fault_tolerance::InfluenceBuilder;
+use pecos_quantum::DagCircuit;
+
+/// Build a repetition code d=3 circuit with `num_rounds` syndrome extraction rounds.
+///
+/// Layout:
+///   Data qubits:    0, 1, 2
+///   Z-ancillas:     3 (measures `Z_0` `Z_1`), 4 (measures `Z_1` `Z_2`)
+///
+/// Each round: prep ancillas, CNOT syndrome extraction, measure ancillas.
+/// After the last round: measure all data qubits for final readout.
+fn build_repetition_code(num_rounds: usize) -> DagCircuit {
+    let mut dag = DagCircuit::new();
+
+    // Data qubits
+    let data: Vec<usize> = vec![0, 1, 2];
+    // Ancilla qubits: one per stabilizer
+    let ancilla_01 = 3; // measures Z_0 Z_1
+    let ancilla_12 = 4; // measures Z_1 Z_2
+
+    // Initialize data qubits in |0⟩
+    dag.pz(&data);
+
+    // Track measurements across rounds for detector definitions
+    let mut prev_meas_01 = None;
+    let mut prev_meas_12 = None;
+
+    for round in 0..num_rounds {
+        // Prep ancillas
+        dag.pz(&[ancilla_01, ancilla_12]);
+
+        // Syndrome extraction: CX from data to ancilla
+        // Z_0 Z_1 stabilizer
+        dag.cx(&[(data[0], ancilla_01)]);
+        dag.cx(&[(data[1], ancilla_01)]);
+        // Z_1 Z_2 stabilizer
+        dag.cx(&[(data[1], ancilla_12)]);
+        dag.cx(&[(data[2], ancilla_12)]);
+
+        // Measure ancillas
+        let ms_01 = dag.mz(&[ancilla_01]);
+        let ms_12 = dag.mz(&[ancilla_12]);
+
+        // Detectors
+        if round == 0 {
+            // First round: each measurement should be 0 (fresh code state)
+            dag.detector_labeled(&format!("Z01_r{round}"), &[ms_01[0]]);
+            dag.detector_labeled(&format!("Z12_r{round}"), &[ms_12[0]]);
+        } else {
+            // Subsequent rounds: compare with previous round
+            dag.detector_labeled(&format!("Z01_r{round}"), &[prev_meas_01.unwrap(), ms_01[0]]);
+            dag.detector_labeled(&format!("Z12_r{round}"), &[prev_meas_12.unwrap(), ms_12[0]]);
+        }
+
+        prev_meas_01 = Some(ms_01[0]);
+        prev_meas_12 = Some(ms_12[0]);
+    }
+
+    // Final data qubit measurements
+    let ms_data = dag.mz(&data);
+
+    // Final detectors: compare last syndrome round with data measurements
+    // Z_0 Z_1 from data should match last ancilla measurement
+    dag.detector_labeled(
+        "Z01_final",
+        &[ms_data[0], ms_data[1], prev_meas_01.unwrap()],
+    );
+    // Z_1 Z_2 from data should match last ancilla measurement
+    dag.detector_labeled(
+        "Z12_final",
+        &[ms_data[1], ms_data[2], prev_meas_12.unwrap()],
+    );
+
+    // Observable: logical Z readout = Z_0 (any single data qubit works for rep code)
+    dag.observable_labeled("logical_Z", &[ms_data[0]]);
+
+    // Pauli operator: track logical X = X_0 X_1 X_2
+    dag.tracked_pauli_labeled("logical_X", X(0) & X(1) & X(2));
+
+    dag
+}
+
+#[test]
+fn repetition_code_fault_enumeration() {
+    let dag = build_repetition_code(3);
+
+    println!("Circuit: {} gates", dag.gate_count());
+    println!("Annotations:");
+    for ann in dag.annotations() {
+        let kind = match &ann.kind {
+            pecos_quantum::AnnotationKind::Detector { .. } => "detector",
+            pecos_quantum::AnnotationKind::Observable { .. } => "observable",
+            pecos_quantum::AnnotationKind::TrackedPauli => "tracked_pauli",
+        };
+        let label = ann.label.as_deref().unwrap_or("(none)");
+        println!("  {kind:10} {label:15} {}", ann.pauli);
+    }
+
+    // Build influence map (InfluenceBuilder handles annotations)
+    let map = InfluenceBuilder::new(&dag)
+        .with_circuit_annotations(&dag)
+        .build();
+
+    let locs = map.gate_fault_locations();
+    println!(
+        "\nFault locations: {} (grouped from {} per-qubit locations)",
+        locs.len(),
+        map.locations.len()
+    );
+    println!(
+        "Detectors: {}, DEM outputs: {}",
+        map.detectors.len(),
+        map.influences.max_dem_output_index().map_or(0, |i| i + 1)
+    );
+
+    // Show all fault locations and their possible faults
+    println!("\n--- Fault locations ---");
+    for (i, loc) in locs.iter().enumerate() {
+        let timing = if loc.before { "before" } else { "after" };
+        let qubit_list: Vec<usize> = loc.qubits.iter().map(pecos_core::QubitId::index).collect();
+        let num_faults = loc.possible_faults().len();
+        println!(
+            "  loc {i:2}: {:3?} {timing:6} qubits={qubit_list:?} ({num_faults} faults)",
+            loc.gate_type
+        );
+    }
+
+    // Weight-1 analysis
+    let mut w1_detectable = 0usize;
+    let mut w1_undetectable = 0usize;
+    let mut w1_trivial = 0usize;
+    let mut w1_total = 0usize;
+
+    map.for_each_fault_combo(1, |combo| {
+        w1_total += 1;
+        let has_det = !combo.effect.detectors.is_empty();
+        let has_dem_output = !combo.effect.dem_outputs.is_empty();
+        match (has_det, has_dem_output) {
+            (true, _) => w1_detectable += 1,
+            (false, true) => w1_undetectable += 1,
+            (false, false) => w1_trivial += 1,
+        }
+    });
+    println!("\n--- Weight-1 faults ---");
+    println!("  Total:        {w1_total}");
+    println!("  Detectable:   {w1_detectable}");
+    println!("  Undetectable: {w1_undetectable}");
+    println!("  Trivial:      {w1_trivial}");
+    // The repetition code only detects X errors (via Z stabilizers).
+    // Z errors on data qubits are undetectable -- this is expected.
+    // The undetectable errors flip logical_X (index 1) since Z anticommutes with X.
+    assert!(
+        w1_undetectable > 0,
+        "Z errors should be undetectable in the repetition code"
+    );
+
+    // Weight-2 analysis
+    let mut w2_detectable = 0usize;
+    let mut w2_undetectable = 0usize;
+    let mut w2_trivial = 0usize;
+    let mut w2_total = 0usize;
+
+    map.for_each_fault_combo(2, |combo| {
+        w2_total += 1;
+        let has_det = !combo.effect.detectors.is_empty();
+        let has_dem_output = !combo.effect.dem_outputs.is_empty();
+        match (has_det, has_dem_output) {
+            (true, _) => w2_detectable += 1,
+            (false, true) => w2_undetectable += 1,
+            (false, false) => w2_trivial += 1,
+        }
+    });
+    println!("\n--- Weight-2 faults ---");
+    println!("  Total:        {w2_total}");
+    println!("  Detectable:   {w2_detectable}");
+    println!("  Undetectable: {w2_undetectable}");
+    println!("  Trivial:      {w2_trivial}");
+    // Weight-2 also has undetectable Z errors (Z type is not protected).
+
+    // Weight-3: this is where d=3 codes can have undetectable errors
+    let mut w3_detectable = 0usize;
+    let mut w3_undetectable = 0usize;
+    let mut w3_trivial = 0usize;
+    let mut w3_total = 0usize;
+    let mut w3_undetectable_examples: Vec<String> = Vec::new();
+
+    map.for_each_fault_combo(3, |combo| {
+        w3_total += 1;
+        let has_det = !combo.effect.detectors.is_empty();
+        let has_dem_output = !combo.effect.dem_outputs.is_empty();
+        match (has_det, has_dem_output) {
+            (true, _) => w3_detectable += 1,
+            (false, true) => {
+                w3_undetectable += 1;
+                // Collect first few examples
+                if w3_undetectable_examples.len() < 5 {
+                    let desc: Vec<String> = combo
+                        .components
+                        .iter()
+                        .map(|c| {
+                            let loc = &locs[c.location_index];
+                            let timing = if loc.before { "before" } else { "after" };
+                            format!(
+                                "{} {} {:?} q={:?}",
+                                c.event.pauli,
+                                timing,
+                                loc.gate_type,
+                                loc.qubits
+                                    .iter()
+                                    .map(pecos_core::QubitId::index)
+                                    .collect::<Vec<_>>()
+                            )
+                        })
+                        .collect();
+                    w3_undetectable_examples.push(desc.join(" + "));
+                }
+            }
+            (false, false) => w3_trivial += 1,
+        }
+    });
+    println!("\n--- Weight-3 faults ---");
+    println!("  Total:        {w3_total}");
+    println!("  Detectable:   {w3_detectable}");
+    println!("  Undetectable: {w3_undetectable}");
+    println!("  Trivial:      {w3_trivial}");
+
+    if !w3_undetectable_examples.is_empty() {
+        println!("\n  Example undetectable w=3 errors:");
+        for ex in &w3_undetectable_examples {
+            println!("    {ex}");
+        }
+    }
+
+    // The d=3 repetition code can correct any single fault, so:
+    // - No undetectable errors at w=1 or w=2
+    // - Some undetectable errors at w=3 (this is the code distance)
+    println!("\n--- Summary ---");
+    println!("  The repetition code detects X errors (via Z stabilizers) but not Z errors.");
+    println!("  Undetectable errors at all weights are Z-type faults flipping logical_X.");
+
+    // Also demonstrate single-event introspection
+    println!("\n--- Single event example ---");
+    let first_cx_loc = locs
+        .iter()
+        .find(|l| l.gate_type == pecos_core::gate_type::GateType::CX && !l.before);
+    if let Some(loc) = first_cx_loc {
+        let qubit_list: Vec<usize> = loc.qubits.iter().map(pecos_core::QubitId::index).collect();
+        println!("  CX after, qubits={qubit_list:?}:");
+        for event in loc.events() {
+            if !event.detectors.is_empty() || !event.dem_outputs.is_empty() {
+                println!(
+                    "    {} -> dets={:?} dem_outputs={:?} meas={:?}",
+                    event.pauli, event.detectors, event.dem_outputs, event.measurements
+                );
+            }
+        }
+    }
+}
+
+/// Test that labels are accessible from the influence map during fault introspection.
+#[test]
+fn repetition_code_labels() {
+    let dag = build_repetition_code(1); // 1 round for simplicity
+    let map = InfluenceBuilder::new(&dag)
+        .with_circuit_annotations(&dag)
+        .build();
+
+    // Check DEM-output labels are populated (observables + tracked Paulis)
+    println!("DEM output labels: {:?}", map.dem_output_labels);
+    // 1 observable (logical_Z) + 1 tracked Pauli (logical_X) = 2 labels
+    assert_eq!(map.dem_output_labels.len(), 2);
+    assert_eq!(map.num_dem_outputs(), 1, "1 observable");
+    assert_eq!(map.num_tracked_paulis(), 1, "1 tracked Pauli");
+
+    // Labels accessible via internal index
+    assert_eq!(map.dem_output_label(0), Some("logical_Z"));
+    assert_eq!(map.dem_output_label(1), Some("logical_X"));
+    assert_eq!(map.dem_output_label(99), None);
+
+    // Use labels during fault introspection
+    let locs = map.gate_fault_locations();
+    let mut found_labeled_event = false;
+    for loc in &locs {
+        for event in loc.events() {
+            for &output_idx in &event.dem_outputs {
+                if let Some(label) = map.dem_output_label(output_idx as usize) {
+                    println!("  {} at {:?} flips {label}", event.pauli, loc.gate_type);
+                    found_labeled_event = true;
+                }
+            }
+        }
+    }
+    assert!(
+        found_labeled_event,
+        "Should find at least one labeled logical event"
+    );
+}
+
+/// Demonstrate building a lookup table from the influence map.
+#[test]
+fn repetition_code_lookup_table() {
+    let dag = build_repetition_code(3);
+    let map = InfluenceBuilder::new(&dag)
+        .with_circuit_annotations(&dag)
+        .build();
+
+    // Build lookup: syndrome pattern -> list of possible logical effects
+    let mut lookup: std::collections::BTreeMap<Vec<u32>, Vec<pecos_core::PauliString>> =
+        std::collections::BTreeMap::new();
+
+    // Weight-1 faults define the basic lookup
+    map.for_each_fault_combo(1, |combo| {
+        if !combo.effect.detectors.is_empty() {
+            let mut syndrome = combo.effect.detectors.clone();
+            syndrome.sort_unstable();
+            lookup
+                .entry(syndrome)
+                .or_default()
+                .push(combo.effect.pauli.clone());
+        }
+    });
+
+    println!("Lookup table (weight-1 syndromes):");
+    for (syndrome, faults) in &lookup {
+        println!("  syndrome {syndrome:?} <- {} fault(s)", faults.len());
+    }
+
+    // Verify: each non-trivial weight-1 syndrome maps to a correction
+    assert!(
+        !lookup.is_empty(),
+        "Should have at least one syndrome pattern"
+    );
+}
+
+/// Build an ML lookup table decoder and test it against sampled errors.
+#[test]
+fn repetition_code_ml_decoder() {
+    use pecos_qec::fault_tolerance::dem_builder::{DemSampler, NoiseConfig};
+    use pecos_qec::fault_tolerance::lookup_decoder::LookupDecoder;
+    use rand::SeedableRng;
+
+    let dag = build_repetition_code(3);
+    let noise = NoiseConfig::uniform(0.001);
+
+    // Build influence map
+    let map = InfluenceBuilder::new(&dag)
+        .with_circuit_annotations(&dag)
+        .build();
+
+    // Build ML decoder from fault enumeration up to weight 3
+    let decoder = LookupDecoder::build(&map, &noise, 3);
+
+    println!("ML Decoder:");
+    println!("  Syndrome patterns: {}", decoder.num_syndromes());
+    println!("  Observables:       {}", decoder.num_observables());
+    println!("  Max weight:        {}", decoder.max_weight());
+
+    // Build sampler for testing
+    let sampler = DemSampler::from_circuit(&dag, &noise).unwrap();
+
+    // Sample and decode
+    let mut rng = rand::rngs::SmallRng::seed_from_u64(42);
+    let num_shots = 100_000;
+    let mut _correct = 0usize;
+    let mut total_errors = 0usize;
+    let mut unknown_syndromes = 0usize;
+
+    for _ in 0..num_shots {
+        if let Some(dual) = sampler.sample_dual(&mut rng) {
+            let result = decoder.decode_from_bools(&dual.detector_events);
+            if !result.known_syndrome {
+                unknown_syndromes += 1;
+            }
+
+            // Check: did the decoder's correction fix the logical?
+            // The actual DEM-output outcome is dual.dem_output_flips.
+            // After applying the correction, the residual should be identity.
+            let has_observable_error: bool = dual
+                .dem_output_flips
+                .iter()
+                .zip(&result.corrections)
+                .any(|(&flip, &corr)| flip ^ corr); // residual error
+
+            if has_observable_error {
+                total_errors += 1;
+            } else {
+                _correct += 1;
+            }
+        }
+    }
+
+    let error_rate = total_errors as f64 / num_shots as f64;
+    let raw_error_rate = sampler
+        .sample_statistics(num_shots, 42)
+        .logical_error_rate();
+
+    println!("\n  Shots:             {num_shots}");
+    println!("  Unknown syndromes: {unknown_syndromes}");
+    println!("  Raw observable rate:  {raw_error_rate:.6}");
+    println!("  Decoded error rate:{error_rate:.6}");
+    println!(
+        "  Improvement:       {:.1}x",
+        raw_error_rate / error_rate.max(1e-10)
+    );
+
+    // The decoder should reduce the observable error rate compared to raw
+    // (for the repetition code with Z errors unprotected, improvement is modest
+    // since only X errors are correctable, but it should still help)
+    assert!(
+        total_errors < num_shots,
+        "Decoder should correct at least some errors"
+    );
+}
+
+/// Test decoder correctness: empty syndrome should produce no corrections.
+#[test]
+fn decoder_empty_syndrome() {
+    use pecos_qec::fault_tolerance::dem_builder::NoiseConfig;
+    use pecos_qec::fault_tolerance::lookup_decoder::LookupDecoder;
+
+    let dag = build_repetition_code(1);
+    let noise = NoiseConfig::uniform(0.01);
+    let map = InfluenceBuilder::new(&dag)
+        .with_circuit_annotations(&dag)
+        .build();
+
+    let decoder = LookupDecoder::build(&map, &noise, 2);
+
+    // Empty syndrome = no detectors fired = most likely no error
+    let result = decoder.decode(&[]);
+    assert!(result.known_syndrome, "Empty syndrome should be known");
+    assert!(
+        result.corrections.iter().all(|&c| !c),
+        "Empty syndrome should produce no corrections: {:?}",
+        result.corrections
+    );
+}
+
+/// Test that the decoder table grows with weight, and truncation bound works.
+#[test]
+fn decoder_table_size_and_truncation() {
+    use pecos_qec::fault_tolerance::dem_builder::NoiseConfig;
+    use pecos_qec::fault_tolerance::lookup_decoder::LookupDecoder;
+
+    let dag = build_repetition_code(1);
+    let noise = NoiseConfig::uniform(0.001);
+    let map = InfluenceBuilder::new(&dag)
+        .with_circuit_annotations(&dag)
+        .build();
+
+    let d1 = LookupDecoder::build(&map, &noise, 1);
+    let d2 = LookupDecoder::build(&map, &noise, 2);
+    let d3 = LookupDecoder::build(&map, &noise, 3);
+
+    println!(
+        "Weight 1: {} syndromes, accounted={:.8}, truncation={:.2e}",
+        d1.num_syndromes(),
+        d1.accounted_probability(),
+        d1.truncation_bound()
+    );
+    println!(
+        "Weight 2: {} syndromes, accounted={:.8}, truncation={:.2e}",
+        d2.num_syndromes(),
+        d2.accounted_probability(),
+        d2.truncation_bound()
+    );
+    println!(
+        "Weight 3: {} syndromes, accounted={:.8}, truncation={:.2e}",
+        d3.num_syndromes(),
+        d3.accounted_probability(),
+        d3.truncation_bound()
+    );
+
+    // Higher weight covers more probability mass
+    assert!(d2.accounted_probability() >= d1.accounted_probability());
+    assert!(d3.accounted_probability() >= d2.accounted_probability());
+
+    // At p=0.001, weight-3 should cover essentially all probability mass
+    assert!(
+        d3.truncation_bound() < 1e-6,
+        "Weight 3 at p=0.001 should have negligible truncation: {}",
+        d3.truncation_bound()
+    );
+
+    // Higher weight should discover at least as many syndromes
+    assert!(d2.num_syndromes() >= d1.num_syndromes());
+    assert!(d1.num_syndromes() > 1);
+}
+
+// ============================================================================
+// [[4,2,2]] Code Example
+// ============================================================================
+
+/// Build a [[4,2,2]] code circuit with `num_rounds` of syndrome extraction.
+///
+/// The [[4,2,2]] code:
+///   - 4 data qubits (0-3), 2 ancilla qubits (4-5)
+///   - Stabilizers: `X_0` `X_1` `X_2` `X_3` and `Z_0` `Z_1` `Z_2` `Z_3`
+///   - 2 logical qubits:
+///     - Logical `Z_1` = `Z_0` `Z_1`,  Logical `X_1` = `X_0` `X_2`
+///     - Logical `Z_2` = `Z_0` `Z_2`,  Logical `X_2` = `X_0` `X_1`
+///   - Distance 2: detects any single-qubit error (cannot correct)
+///
+/// X stabilizer measurement (ancilla 4):
+///   Prep |+⟩, CX(ancilla, data) for each data qubit, H, MZ
+///
+/// Z stabilizer measurement (ancilla 5):
+///   Prep |0⟩, CX(data, ancilla) for each data qubit, MZ
+fn build_422_code(num_rounds: usize) -> DagCircuit {
+    let mut dag = DagCircuit::new();
+
+    let data: Vec<usize> = vec![0, 1, 2, 3];
+    let ancilla_x = 4; // measures X_0 X_1 X_2 X_3
+    let ancilla_z = 5; // measures Z_0 Z_1 Z_2 Z_3
+
+    // Initialize data qubits
+    dag.pz(&data);
+
+    let mut prev_meas_x = None;
+    let mut prev_meas_z = None;
+
+    for round in 0..num_rounds {
+        // --- X stabilizer: X_0 X_1 X_2 X_3 ---
+        dag.pz(&[ancilla_x]);
+        dag.h(&[ancilla_x]); // prep |+⟩
+        // CX(ancilla, data) propagates X from ancilla to data
+        dag.cx(&[
+            (ancilla_x, data[0]),
+            (ancilla_x, data[1]),
+            (ancilla_x, data[2]),
+            (ancilla_x, data[3]),
+        ]);
+        dag.h(&[ancilla_x]); // rotate back to Z basis
+        let ms_x = dag.mz(&[ancilla_x]);
+
+        // --- Z stabilizer: Z_0 Z_1 Z_2 Z_3 ---
+        dag.pz(&[ancilla_z]);
+        // CX(data, ancilla) propagates Z from data to ancilla
+        dag.cx(&[
+            (data[0], ancilla_z),
+            (data[1], ancilla_z),
+            (data[2], ancilla_z),
+            (data[3], ancilla_z),
+        ]);
+        let ms_z = dag.mz(&[ancilla_z]);
+
+        // Detectors
+        if round == 0 {
+            // Z stabilizer is deterministic on |0000⟩ (Z eigenstate)
+            dag.detector_labeled(&format!("Sz_r{round}"), &[ms_z[0]]);
+            // X stabilizer is NOT deterministic on |0000⟩ -- no standalone detector.
+            // First X measurement is a random coin flip; only round-to-round
+            // comparisons are valid detectors.
+        } else {
+            dag.detector_labeled(&format!("Sx_r{round}"), &[prev_meas_x.unwrap(), ms_x[0]]);
+            dag.detector_labeled(&format!("Sz_r{round}"), &[prev_meas_z.unwrap(), ms_z[0]]);
+        }
+
+        prev_meas_x = Some(ms_x[0]);
+        prev_meas_z = Some(ms_z[0]);
+    }
+
+    // Final data qubit measurements
+    let ms_data = dag.mz(&data);
+
+    // Final detector: Z stabilizer from data should match last Z-ancilla.
+    // Z_0 Z_1 Z_2 Z_3 is readable from Z-basis data measurements.
+    dag.detector_labeled(
+        "Sz_final",
+        &[
+            ms_data[0],
+            ms_data[1],
+            ms_data[2],
+            ms_data[3],
+            prev_meas_z.unwrap(),
+        ],
+    );
+    // No final X-stabilizer detector: Z-basis data measurements cannot
+    // reconstruct X_0 X_1 X_2 X_3 parity.
+
+    // Observables: logical Z readouts
+    // Logical Z_1 = Z_0 Z_1
+    dag.observable_labeled("logical_Z1", &[ms_data[0], ms_data[1]]);
+    // Logical Z_2 = Z_0 Z_2
+    dag.observable_labeled("logical_Z2", &[ms_data[0], ms_data[2]]);
+
+    // Tracked Paulis: logical X operators
+    // Logical X_1 = X_0 X_2
+    dag.tracked_pauli_labeled("logical_X1", X(0) & X(2));
+    // Logical X_2 = X_0 X_1
+    dag.tracked_pauli_labeled("logical_X2", X(0) & X(1));
+
+    dag
+}
+
+#[test]
+fn code_422_fault_enumeration() {
+    let dag = build_422_code(2);
+
+    println!("[[4,2,2]] Code with 2 rounds");
+    println!("Circuit: {} gates", dag.gate_count());
+    println!("Annotations:");
+    for ann in dag.annotations() {
+        let kind = match &ann.kind {
+            pecos_quantum::AnnotationKind::Detector { .. } => "detector",
+            pecos_quantum::AnnotationKind::Observable { .. } => "observable",
+            pecos_quantum::AnnotationKind::TrackedPauli => "tracked_pauli",
+        };
+        let label = ann.label.as_deref().unwrap_or("(none)");
+        println!("  {kind:10} {label:15} {}", ann.pauli);
+    }
+
+    // Build influence map
+    let map = InfluenceBuilder::new(&dag)
+        .with_circuit_annotations(&dag)
+        .build();
+
+    let locs = map.gate_fault_locations();
+    println!(
+        "\nFault locations: {} (from {} per-qubit locations)",
+        locs.len(),
+        map.locations.len()
+    );
+    println!(
+        "Detectors: {}, DEM outputs: {}",
+        map.detectors.len(),
+        map.influences.max_dem_output_index().map_or(0, |i| i + 1)
+    );
+
+    // Weight-1
+    let mut w1_total = 0usize;
+    let mut w1_detectable = 0usize;
+    let mut w1_undetectable = 0usize;
+    let mut w1_trivial = 0usize;
+
+    map.for_each_fault_combo(1, |combo| {
+        w1_total += 1;
+        let has_det = !combo.effect.detectors.is_empty();
+        let has_dem_output = !combo.effect.dem_outputs.is_empty();
+        match (has_det, has_dem_output) {
+            (true, _) => w1_detectable += 1,
+            (false, true) => {
+                w1_undetectable += 1;
+                if w1_undetectable <= 5 {
+                    let c = &combo.components[0];
+                    let loc = &locs[c.location_index];
+                    let timing = if loc.before { "before" } else { "after" };
+                    println!(
+                        "  UNDET w=1: {} {timing} {:?} q={:?} -> dem_outputs={:?}",
+                        c.event.pauli,
+                        loc.gate_type,
+                        loc.qubits
+                            .iter()
+                            .map(pecos_core::QubitId::index)
+                            .collect::<Vec<_>>(),
+                        combo.effect.dem_outputs,
+                    );
+                }
+            }
+            (false, false) => w1_trivial += 1,
+        }
+    });
+
+    println!("\n--- Weight-1 faults ---");
+    println!("  Total:        {w1_total}");
+    println!("  Detectable:   {w1_detectable}");
+    println!("  Undetectable: {w1_undetectable}");
+    println!("  Trivial:      {w1_trivial}");
+
+    // The [[4,2,2]] code starting from |0000⟩ has partial detection:
+    // - Z stabilizer detects X errors from round 1 (|0000⟩ is Z eigenstate)
+    // - X stabilizer only detects Z errors from round 2 onward (round-to-round)
+    // - First-round Z errors on data qubits are undetectable (no X-stabilizer
+    //   detector in round 1, since |0000⟩ is not an X-stabilizer eigenstate)
+    assert!(w1_total > 0, "Should have fault events");
+    assert!(w1_detectable > 0, "Some faults should be detectable");
+    assert!(w1_undetectable > 0, "First-round Z faults are undetectable");
+}
+
+#[test]
+fn code_422_ml_decoder() {
+    use pecos_qec::fault_tolerance::dem_builder::{DemSampler, NoiseConfig};
+    use pecos_qec::fault_tolerance::lookup_decoder::LookupDecoder;
+    use rand::SeedableRng;
+
+    let dag = build_422_code(2);
+    let noise = NoiseConfig::uniform(0.001);
+
+    let map = InfluenceBuilder::new(&dag)
+        .with_circuit_annotations(&dag)
+        .build();
+
+    // Build ML decoder up to weight 2
+    let decoder = LookupDecoder::build(&map, &noise, 2);
+
+    println!("[[4,2,2]] ML Decoder:");
+    println!("  Syndrome patterns: {}", decoder.num_syndromes());
+    println!("  Observables:       {}", decoder.num_observables());
+
+    // Build sampler
+    let sampler = DemSampler::from_circuit(&dag, &noise).unwrap();
+
+    // Sample and decode
+    let mut rng = rand::rngs::SmallRng::seed_from_u64(42);
+    let num_shots = 100_000;
+    let mut decoded_errors = 0usize;
+    let mut raw_errors = 0usize;
+
+    let mut post_selected_shots = 0usize;
+    let mut post_selected_errors = 0usize;
+
+    for _ in 0..num_shots {
+        if let Some(dual) = sampler.sample_dual(&mut rng) {
+            let result = decoder.decode_from_bools(&dual.detector_events);
+
+            // ML correction
+            let has_residual = dual
+                .dem_output_flips
+                .iter()
+                .zip(&result.corrections)
+                .any(|(&flip, &corr)| flip ^ corr);
+
+            if has_residual {
+                decoded_errors += 1;
+            }
+            if dual.dem_output_flips.iter().any(|&f| f) {
+                raw_errors += 1;
+            }
+
+            // Post-selection: only keep shots with no detectors fired
+            if !result.detected {
+                post_selected_shots += 1;
+                if dual.dem_output_flips.iter().any(|&f| f) {
+                    post_selected_errors += 1;
+                }
+            }
+        }
+    }
+
+    let raw_rate = raw_errors as f64 / num_shots as f64;
+    let decoded_rate = decoded_errors as f64 / num_shots as f64;
+    let ps_rate = if post_selected_shots > 0 {
+        post_selected_errors as f64 / post_selected_shots as f64
+    } else {
+        0.0
+    };
+    let discard_rate = 1.0 - post_selected_shots as f64 / num_shots as f64;
+
+    println!("\n  Shots:                {num_shots}");
+    println!("  Raw observable rate:     {raw_rate:.6}");
+    println!("  ML decoded rate:      {decoded_rate:.6}");
+    println!("  Post-selected rate:   {ps_rate:.6} (discarded {discard_rate:.4})");
+    println!(
+        "  PS improvement:       {:.1}x",
+        raw_rate / ps_rate.max(1e-10)
+    );
+
+    // For the [[4,2,2]] detection code, post-selection should improve the
+    // observable error rate: detected errors are discarded, only undetectable
+    // errors (weight 2+) remain. At p=0.001, this gives ~p^2 rate.
+    assert!(
+        ps_rate < raw_rate || post_selected_shots == 0,
+        "Post-selection should reduce observable error rate"
+    );
+    assert!(
+        decoded_errors < num_shots,
+        "Some shots should decode correctly"
+    );
+}
diff --git a/crates/pecos-qec/tests/idle_noise_tests.rs b/crates/pecos-qec/tests/idle_noise_tests.rs
new file mode 100644
index 000000000..6eebe49d0
--- /dev/null
+++ b/crates/pecos-qec/tests/idle_noise_tests.rs
@@ -0,0 +1,213 @@
+// Copyright 2026 The PECOS Developers
+//
+// Licensed under the Apache License, Version 2.0 (the "License"); you may not use this file except
+// in compliance with the License. You may obtain a copy of the License at
+//
+//     https://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software distributed under the License
+// is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express
+// or implied. See the License for the specific language governing permissions and limitations under
+// the License.
+
+//! Integration tests for idle-gate noise. `GateType::Idle` is a no-op unless
+//! noise is explicitly attached to idle locations via dedicated idle noise or
+//! per-gate idle rates.
+
+use pecos_core::{QubitId, TimeUnits};
+use pecos_qec::fault_tolerance::dem_builder::{
+    DemBuilder, DemSamplerBuilder, NoiseConfig, PerGateTypeNoise,
+};
+use pecos_qec::fault_tolerance::propagator::DagFaultAnalyzer;
+use pecos_quantum::{DagCircuit, GateType};
+
+fn build_idle_then_measure(num_idles: usize) -> DagCircuit {
+    // Prep N qubits, idle each once, measure each. Very simple fixture
+    // to isolate idle-gate contributions.
+    let mut dag = DagCircuit::new();
+    for q in 0..num_idles {
+        dag.pz(&[q]);
+    }
+    for q in 0..num_idles {
+        dag.idle(TimeUnits::new(100), &[q]);
+    }
+    for q in 0..num_idles {
+        dag.mz(&[q]);
+    }
+    dag
+}
+
+#[test]
+fn idle_locations_contribute_mechanisms_when_rates_set() {
+    let dag = build_idle_then_measure(2);
+    let analyzer = DagFaultAnalyzer::new(&dag);
+    let influence = analyzer.build_influence_map();
+
+    // No noise elsewhere; idle rates set only on qubit 0.
+    let q0 = QubitId::from(0usize);
+    let cfg = PerGateTypeNoise::from_base_noise(NoiseConfig::new(0.0, 0.0, 0.0, 0.0))
+        .with_1q_rates_for_qubit(GateType::Idle, q0, [0.001, 0.001, 0.001]);
+    let sim = DemSamplerBuilder::new(&influence)
+        .with_per_gate_noise(cfg)
+        .with_detectors_json(r#"[{"id": 0, "records": [-2]}, {"id": 1, "records": [-1]}]"#)
+        .unwrap()
+        .build()
+        .unwrap();
+
+    // Exactly one location contributes noise (idle on q0). That location
+    // produces X, Y, Z mechanisms, of which X+Y generally both flip the
+    // Z-basis measurement, but aggregation collapses them. Expect at
+    // least one mechanism -> we used to get zero silently.
+    assert!(
+        sim.num_mechanisms() > 0,
+        "idle on q0 should produce at least one mechanism",
+    );
+}
+
+#[test]
+fn idle_rates_absent_means_no_idle_contribution() {
+    // Config provides no Idle rates and uses zero base noise. DEM should have
+    // zero mechanisms: prep/measure are 0 and idle is a no-op by default.
+    let dag = build_idle_then_measure(3);
+    let analyzer = DagFaultAnalyzer::new(&dag);
+    let influence = analyzer.build_influence_map();
+
+    let cfg = PerGateTypeNoise::from_base_noise(NoiseConfig::new(0.0, 0.0, 0.0, 0.0));
+    let sim = DemSamplerBuilder::new(&influence)
+        .with_per_gate_noise(cfg)
+        .with_detectors_json(r#"[{"id": 0, "records": [-3]}, {"id": 1, "records": [-2]}, {"id": 2, "records": [-1]}]"#)
+        .unwrap()
+        .build().unwrap();
+    assert_eq!(sim.num_mechanisms(), 0);
+}
+
+#[test]
+fn per_gate_base_p1_does_not_attach_to_idle() {
+    let dag = build_idle_then_measure(2);
+    let analyzer = DagFaultAnalyzer::new(&dag);
+    let influence = analyzer.build_influence_map();
+
+    let cfg = PerGateTypeNoise::from_base_noise(NoiseConfig::new(0.01, 0.0, 0.0, 0.0));
+    let sim = DemSamplerBuilder::new(&influence)
+        .with_per_gate_noise(cfg)
+        .with_detectors_json(r#"[{"id": 0, "records": [-2]}, {"id": 1, "records": [-1]}]"#)
+        .unwrap()
+        .build()
+        .unwrap();
+
+    assert_eq!(sim.num_mechanisms(), 0);
+}
+
+#[test]
+fn per_gate_base_idle_noise_attaches_to_idle() {
+    let dag = build_idle_then_measure(2);
+    let analyzer = DagFaultAnalyzer::new(&dag);
+    let influence = analyzer.build_influence_map();
+
+    let cfg = PerGateTypeNoise::from_base_noise(NoiseConfig::with_idle(0.01, 0.0, 0.0, 0.0, 0.002));
+    let sim = DemSamplerBuilder::new(&influence)
+        .with_per_gate_noise(cfg)
+        .with_detectors_json(r#"[{"id": 0, "records": [-2]}, {"id": 1, "records": [-1]}]"#)
+        .unwrap()
+        .build()
+        .unwrap();
+
+    assert!(
+        sim.num_mechanisms() > 0,
+        "base p_idle in per-gate config should attach to idle locations",
+    );
+}
+
+#[test]
+fn idle_noise_respects_per_qubit_override() {
+    // q0 gets boosted idle rate; q1 gets zero. Expect exactly one
+    // mechanism from q0's idle.
+    let dag = build_idle_then_measure(2);
+    let analyzer = DagFaultAnalyzer::new(&dag);
+    let influence = analyzer.build_influence_map();
+
+    let q0 = QubitId::from(0usize);
+    let cfg = PerGateTypeNoise::from_base_noise(NoiseConfig::new(0.0, 0.0, 0.0, 0.0))
+        .with_1q_rates(GateType::Idle, [0.0, 0.0, 0.0])
+        .with_1q_rates_for_qubit(GateType::Idle, q0, [0.01, 0.01, 0.01]);
+    let sim = DemSamplerBuilder::new(&influence)
+        .with_per_gate_noise(cfg)
+        .with_detectors_json(r#"[{"id": 0, "records": [-2]}, {"id": 1, "records": [-1]}]"#)
+        .unwrap()
+        .build()
+        .unwrap();
+
+    assert!(sim.num_mechanisms() > 0);
+    // q1's idle at zero rates should not contribute -- only q0's.
+    assert!(sim.max_error_probability() >= 0.01 * 0.5);
+}
+
+#[test]
+fn idle_with_scalar_p1_is_noop() {
+    // Ordinary p1 gate noise should not attach to Idle. Idle is a no-op unless
+    // idle noise is explicitly configured.
+    let dag = build_idle_then_measure(2);
+    let analyzer = DagFaultAnalyzer::new(&dag);
+    let influence = analyzer.build_influence_map();
+
+    let sim = DemSamplerBuilder::new(&influence)
+        .with_noise(0.01, 0.0, 0.0, 0.0)
+        .with_detectors_json(r#"[{"id": 0, "records": [-2]}, {"id": 1, "records": [-1]}]"#)
+        .unwrap()
+        .build()
+        .unwrap();
+
+    assert_eq!(sim.num_mechanisms(), 0);
+}
+
+#[test]
+fn explicit_uniform_idle_noise_is_noisy() {
+    let dag = build_idle_then_measure(2);
+    let analyzer = DagFaultAnalyzer::new(&dag);
+    let influence = analyzer.build_influence_map();
+
+    let sim = DemSamplerBuilder::new(&influence)
+        .with_noise_config(NoiseConfig::with_idle(0.01, 0.0, 0.0, 0.0, 0.002))
+        .with_detectors_json(r#"[{"id": 0, "records": [-2]}, {"id": 1, "records": [-1]}]"#)
+        .unwrap()
+        .build()
+        .unwrap();
+
+    assert!(
+        sim.num_mechanisms() > 0,
+        "explicit p_idle should produce idle-location mechanisms",
+    );
+}
+
+#[test]
+fn dem_builder_scalar_p1_does_not_attach_to_idle() {
+    let dag = build_idle_then_measure(1);
+    let analyzer = DagFaultAnalyzer::new(&dag);
+    let influence = analyzer.build_influence_map();
+
+    let dem = DemBuilder::new(&influence)
+        .with_noise(0.01, 0.0, 0.0, 0.0)
+        .with_detectors_json(r#"[{"id": 0, "records": [-1]}]"#)
+        .unwrap()
+        .build();
+
+    assert_eq!(dem.num_contributions(), 0);
+}
+
+#[test]
+fn dem_builder_explicit_idle_noise_is_noisy() {
+    let dag = build_idle_then_measure(1);
+    let analyzer = DagFaultAnalyzer::new(&dag);
+    let influence = analyzer.build_influence_map();
+
+    let dem = DemBuilder::new(&influence)
+        .with_noise_config(NoiseConfig::with_idle(0.01, 0.0, 0.0, 0.0, 0.002))
+        .with_detectors_json(r#"[{"id": 0, "records": [-1]}]"#)
+        .unwrap()
+        .build();
+
+    assert!(
+        dem.num_contributions() > 0,
+        "explicit p_idle should produce idle-location DEM contributions",
+    );
+}
diff --git a/crates/pecos-qec/tests/mem_stab_tests.rs b/crates/pecos-qec/tests/mem_stab_tests.rs
new file mode 100644
index 000000000..57a7a072e
--- /dev/null
+++ b/crates/pecos-qec/tests/mem_stab_tests.rs
@@ -0,0 +1,142 @@
+// Copyright 2026 The PECOS Developers
+//
+// Licensed under the Apache License, Version 2.0 (the "License"); you may not use this file except
+// in compliance with the License. You may obtain a copy of the License at
+//
+//     https://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software distributed under the License
+// is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express
+// or implied. See the License for the specific language governing permissions and limitations under
+// the License.
+
+//! Integration tests for `MemStabSim`.
+//!
+//! Parity: `MemStabSim` must produce identical raw-measurement shots to the raw
+//! `DagFaultAnalyzer` + `MemBuilder` + `MeasurementNoiseModel` pipeline given equal
+//! inputs and seeds.
+
+use pecos_qec::fault_tolerance::dem_builder::{MemBuilder, NoiseConfig};
+use pecos_qec::fault_tolerance::propagator::DagFaultAnalyzer;
+use pecos_qec::mem_stab::{MemStabError, MemStabSim};
+use pecos_quantum::DagCircuit;
+use rand::SeedableRng;
+use rand::rngs::SmallRng;
+
+fn repetition_code_circuit() -> DagCircuit {
+    let mut dag = DagCircuit::new();
+    dag.pz(&[3]);
+    dag.pz(&[4]);
+    dag.cx(&[(0, 3)]);
+    dag.cx(&[(1, 3)]);
+    dag.cx(&[(1, 4)]);
+    dag.cx(&[(2, 4)]);
+    dag.mz(&[3]);
+    dag.mz(&[4]);
+    dag
+}
+
+#[test]
+fn builder_rejects_missing_circuit() {
+    let err = MemStabSim::builder().build().unwrap_err();
+    assert!(matches!(err, MemStabError::MissingCircuit));
+}
+
+#[test]
+fn zero_noise_produces_zero_mechanisms() {
+    let sim = MemStabSim::builder()
+        .circuit(repetition_code_circuit())
+        .noise(NoiseConfig::uniform(0.0))
+        .build()
+        .unwrap();
+
+    assert_eq!(sim.num_mechanisms(), 0);
+    assert_eq!(sim.num_measurements(), 2);
+}
+
+#[test]
+fn parity_with_raw_pipeline() {
+    let noise = NoiseConfig::uniform(0.01);
+    let shots = 512;
+    let seed = 0xFEED_FACE_u64;
+
+    // Path 1: MemStabSim.
+    let sim = MemStabSim::builder()
+        .circuit(repetition_code_circuit())
+        .noise(noise.clone())
+        .build()
+        .unwrap();
+    let mut rng1 = SmallRng::seed_from_u64(seed);
+    let batch1 = sim.sample_batch(shots, &mut rng1);
+
+    // Path 2: raw pipeline, identical inputs + seed.
+    let dag = repetition_code_circuit();
+    let analyzer = DagFaultAnalyzer::new(&dag);
+    let influence_map = analyzer.build_influence_map();
+    let mnm = MemBuilder::new(&influence_map)
+        .with_noise(noise.p1, noise.p2, noise.p_meas, noise.p_prep)
+        .build();
+    let mut rng2 = SmallRng::seed_from_u64(seed);
+    let mut batch2 = Vec::with_capacity(shots);
+    let mut buf = vec![false; mnm.num_measurements];
+    for _ in 0..shots {
+        mnm.sample_into(&mut buf, &mut rng2);
+        batch2.push(buf.clone());
+    }
+
+    assert_eq!(batch1, batch2);
+}
+
+#[test]
+fn sample_and_sample_batch_agree() {
+    let sim = MemStabSim::builder()
+        .circuit(repetition_code_circuit())
+        .noise(NoiseConfig::uniform(0.02))
+        .build()
+        .unwrap();
+
+    let seed = 0xABCD_EF01_u64;
+    let shots = 32;
+
+    let mut rng_single = SmallRng::seed_from_u64(seed);
+    let singles: Vec<Vec<bool>> = (0..shots).map(|_| sim.sample(&mut rng_single)).collect();
+
+    let mut rng_batch = SmallRng::seed_from_u64(seed);
+    let batch = sim.sample_batch(shots, &mut rng_batch);
+
+    assert_eq!(singles, batch);
+}
+
+#[test]
+fn shot_shape_is_correct() {
+    let sim = MemStabSim::builder()
+        .circuit(repetition_code_circuit())
+        .noise(NoiseConfig::uniform(0.005))
+        .build()
+        .unwrap();
+
+    let mut rng = SmallRng::seed_from_u64(11);
+    let batch = sim.sample_batch(20, &mut rng);
+    assert_eq!(batch.len(), 20);
+    for row in &batch {
+        assert_eq!(row.len(), sim.num_measurements());
+    }
+}
+
+#[test]
+fn nonzero_noise_yields_some_flips() {
+    let sim = MemStabSim::builder()
+        .circuit(repetition_code_circuit())
+        .noise(NoiseConfig::uniform(0.1))
+        .build()
+        .unwrap();
+
+    let mut rng = SmallRng::seed_from_u64(123);
+    let batch = sim.sample_batch(1000, &mut rng);
+
+    let total_flips: usize = batch
+        .iter()
+        .map(|row| row.iter().filter(|&&b| b).count())
+        .sum();
+    assert!(total_flips > 0);
+}
diff --git a/crates/pecos-qec/tests/per_gate_dem_builder_tests.rs b/crates/pecos-qec/tests/per_gate_dem_builder_tests.rs
new file mode 100644
index 000000000..0dbb4775f
--- /dev/null
+++ b/crates/pecos-qec/tests/per_gate_dem_builder_tests.rs
@@ -0,0 +1,199 @@
+// Copyright 2026 The PECOS Developers
+//
+// Licensed under the Apache License, Version 2.0 (the "License"); you may not use this file except
+// in compliance with the License. You may obtain a copy of the License at
+//
+//     https://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software distributed under the License
+// is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express
+// or implied. See the License for the specific language governing permissions and limitations under
+// the License.
+
+//! Integration tests for `DemBuilder::with_per_gate_noise`. Parity with
+//! `DemSamplerBuilder` path + verification that decomposed DEM text
+//! output reflects per-gate-type per-Pauli rates.
+
+use pecos_core::{QubitId, TimeUnits};
+use pecos_qec::fault_tolerance::dem_builder::{DemBuilder, NoiseConfig, PerGateTypeNoise};
+use pecos_qec::fault_tolerance::propagator::DagFaultAnalyzer;
+use pecos_quantum::{DagCircuit, GateType};
+
+fn build_parity_check() -> DagCircuit {
+    let mut dag = DagCircuit::new();
+    dag.pz(&[2]);
+    dag.cx(&[(0, 2)]);
+    dag.cx(&[(1, 2)]);
+    dag.mz(&[2]);
+    dag
+}
+
+#[test]
+fn uniform_equivalent_per_gate_matches_scalar_dem() {
+    // DemBuilder with empty-map PerGateTypeNoise (base noise only) should
+    // produce the same DEM text as scalar `with_noise`.
+    let dag = build_parity_check();
+    let analyzer = DagFaultAnalyzer::new(&dag);
+    let influence = analyzer.build_influence_map();
+
+    let scalar = DemBuilder::new(&influence)
+        .with_noise(0.01, 0.02, 0.005, 0.003)
+        .with_detectors_json(r#"[{"id": 0, "records": [-1]}]"#)
+        .unwrap()
+        .build();
+
+    let per_gate = DemBuilder::new(&influence)
+        .with_per_gate_noise(PerGateTypeNoise::from_base_noise(NoiseConfig::new(
+            0.01, 0.02, 0.005, 0.003,
+        )))
+        .with_detectors_json(r#"[{"id": 0, "records": [-1]}]"#)
+        .unwrap()
+        .build();
+
+    // Both DEMs should contain the same mechanism set with matching probabilities.
+    assert_eq!(scalar.num_contributions(), per_gate.num_contributions());
+    let scalar_text = scalar.to_string();
+    let per_gate_text = per_gate.to_string();
+    // Equal line counts in the text form (mechanism-by-mechanism identical).
+    assert_eq!(
+        scalar_text
+            .lines()
+            .filter(|l| l.starts_with("error("))
+            .count(),
+        per_gate_text
+            .lines()
+            .filter(|l| l.starts_with("error("))
+            .count(),
+        "scalar and uniform-per-gate should produce identical error-line counts:\nscalar:\n{scalar_text}\nper_gate:\n{per_gate_text}",
+    );
+}
+
+#[test]
+fn per_gate_override_produces_decomposed_dem_text() {
+    // Specific per-gate CX rates should appear in the decomposed DEM text.
+    let dag = build_parity_check();
+    let analyzer = DagFaultAnalyzer::new(&dag);
+    let influence = analyzer.build_influence_map();
+
+    let mut rates_2q = [0.0; 15];
+    // IX = index 0, nonzero probability
+    rates_2q[0] = 1e-3;
+    // XX = index 4 ("IX","IY","IZ","XI","XX",...) — high correlated rate
+    rates_2q[4] = 5e-3;
+
+    let cfg = PerGateTypeNoise::from_base_noise(NoiseConfig::new(0.0, 0.0, 0.0, 0.0))
+        .with_2q_rates(GateType::CX, rates_2q);
+
+    let dem = DemBuilder::new(&influence)
+        .with_per_gate_noise(cfg)
+        .with_detectors_json(r#"[{"id": 0, "records": [-1]}]"#)
+        .unwrap()
+        .build();
+
+    let text = dem.to_string_decomposed();
+    let error_lines = text.lines().filter(|l| l.starts_with("error(")).count();
+    assert!(
+        error_lines > 0,
+        "expected per-gate CX rates to produce error lines in decomposed DEM:\n{text}",
+    );
+}
+
+#[test]
+fn per_qubit_cx_override_changes_dem_probabilities() {
+    // Like the sampler-path test: boost CX (0, 2) per-qubit-pair, compare
+    // to baseline where only per-gate-type is set.
+    let dag = build_parity_check();
+    let analyzer = DagFaultAnalyzer::new(&dag);
+    let influence = analyzer.build_influence_map();
+
+    let q0 = QubitId::from(0usize);
+    let q2 = QubitId::from(2usize);
+
+    let cfg_baseline = PerGateTypeNoise::from_base_noise(NoiseConfig::new(0.0, 0.0, 0.0, 0.0))
+        .with_2q_rates(GateType::CX, [1e-4; 15]);
+    let cfg_boost = cfg_baseline
+        .clone()
+        .with_2q_rates_for_qubits(GateType::CX, q0, q2, [1e-3; 15]);
+
+    let baseline = DemBuilder::new(&influence)
+        .with_per_gate_noise(cfg_baseline)
+        .with_detectors_json(r#"[{"id": 0, "records": [-1]}]"#)
+        .unwrap()
+        .build();
+    let boosted = DemBuilder::new(&influence)
+        .with_per_gate_noise(cfg_boost)
+        .with_detectors_json(r#"[{"id": 0, "records": [-1]}]"#)
+        .unwrap()
+        .build();
+
+    // Both produce the same mechanism set (same circuit structure) but
+    // the boosted DEM should have higher-average probabilities in its text.
+    assert_eq!(baseline.num_contributions(), boosted.num_contributions());
+
+    // Parse error-line probabilities and sum them.
+    let sum_probs = |s: &str| -> f64 {
+        s.lines()
+            .filter_map(|l| l.strip_prefix("error("))
+            .filter_map(|inner| inner.split(')').next())
+            .filter_map(|p| p.parse::<f64>().ok())
+            .sum()
+    };
+    let baseline_sum = sum_probs(&baseline.to_string());
+    let boosted_sum = sum_probs(&boosted.to_string());
+    assert!(
+        boosted_sum > 2.0 * baseline_sum,
+        "per-qubit-pair boost should raise probability sum: baseline={baseline_sum} boosted={boosted_sum}",
+    );
+}
+
+#[test]
+fn idle_locations_contribute_to_dem_text() {
+    // Circuit with an idle gate + per-qubit idle rate should produce an
+    // error line for the idle location. Before the Idle routing fix this
+    // test would see zero idle contributions.
+    let mut dag = DagCircuit::new();
+    dag.pz(&[0]);
+    dag.idle(TimeUnits::new(100), &[0]);
+    dag.mz(&[0]);
+    let analyzer = DagFaultAnalyzer::new(&dag);
+    let influence = analyzer.build_influence_map();
+
+    let q0 = QubitId::from(0usize);
+    let cfg = PerGateTypeNoise::from_base_noise(NoiseConfig::new(0.0, 0.0, 0.0, 0.0))
+        .with_1q_rates_for_qubit(GateType::Idle, q0, [0.01, 0.01, 0.01]);
+
+    let dem = DemBuilder::new(&influence)
+        .with_per_gate_noise(cfg)
+        .with_detectors_json(r#"[{"id": 0, "records": [-1]}]"#)
+        .unwrap()
+        .build();
+
+    let text = dem.to_string();
+    assert!(
+        text.contains("error("),
+        "expected idle location to produce an error line:\n{text}",
+    );
+}
+
+#[test]
+fn decomposed_dem_reflects_per_gate_noise() {
+    // DemBuilder's decomposed path uses mark_graphlike_decomposable and
+    // Y-decomposition logic. Verify the text output includes both
+    // direct and decomposed-effect lines when per-gate noise is set.
+    let dag = build_parity_check();
+    let analyzer = DagFaultAnalyzer::new(&dag);
+    let influence = analyzer.build_influence_map();
+
+    let cfg = PerGateTypeNoise::from_base_noise(NoiseConfig::new(0.005, 0.005, 0.005, 0.005));
+    let dem = DemBuilder::new(&influence)
+        .with_per_gate_noise(cfg)
+        .with_detectors_json(r#"[{"id": 0, "records": [-1]}]"#)
+        .unwrap()
+        .build();
+
+    // Both formats should have content.
+    let non_decomposed = dem.to_string();
+    let decomposed = dem.to_string_decomposed();
+    assert!(non_decomposed.contains("error("));
+    assert!(decomposed.contains("error("));
+}
diff --git a/crates/pecos-qec/tests/per_gate_noise_tests.rs b/crates/pecos-qec/tests/per_gate_noise_tests.rs
new file mode 100644
index 000000000..9726c52ad
--- /dev/null
+++ b/crates/pecos-qec/tests/per_gate_noise_tests.rs
@@ -0,0 +1,154 @@
+// Copyright 2026 The PECOS Developers
+//
+// Licensed under the Apache License, Version 2.0 (the "License"); you may not use this file except
+// in compliance with the License. You may obtain a copy of the License at
+//
+//     https://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software distributed under the License
+// is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express
+// or implied. See the License for the specific language governing permissions and limitations under
+// the License.
+
+//! Integration tests for the per-gate-type noise path on
+//! [`DemSamplerBuilder`].
+//!
+//! Verifies:
+//! 1. Uniform-equivalent per-gate spec produces identical mechanisms to
+//!    the scalar `with_noise` path.
+//! 2. Per-gate rates actually override scalar rates for gates in the map.
+//! 3. Fallback uniform rates apply to gate types not in the map.
+
+use pecos_qec::fault_tolerance::dem_builder::{DemSamplerBuilder, NoiseConfig, PerGateTypeNoise};
+use pecos_qec::fault_tolerance::propagator::DagFaultAnalyzer;
+use pecos_quantum::{DagCircuit, GateType};
+
+fn build_parity_check_circuit() -> DagCircuit {
+    let mut dag = DagCircuit::new();
+    dag.pz(&[2]);
+    dag.cx(&[(0, 2)]);
+    dag.cx(&[(1, 2)]);
+    dag.mz(&[2]);
+    dag
+}
+
+#[test]
+fn per_gate_uniform_equivalent_matches_scalar_path() {
+    // Build a PerGateTypeNoise that mimics uniform p1=p2=p_meas=p_prep=0.01.
+    // Expectation: `per_gate.rate_1q()` lookup with an empty map uses
+    // `base.p1 / 3.0` for 1Q, and `base.p2 / 15.0` for 2Q --
+    // which is exactly what the legacy scalar path uses. So the two
+    // builders should produce identical mechanism sets.
+    let dag = build_parity_check_circuit();
+    let analyzer = DagFaultAnalyzer::new(&dag);
+    let influence = analyzer.build_influence_map();
+
+    let p = 0.01;
+    let scalar = DemSamplerBuilder::new(&influence)
+        .with_noise(p, p, p, p)
+        .with_detectors_json(r#"[{"id": 0, "records": [-1]}]"#)
+        .unwrap()
+        .build()
+        .unwrap();
+    let per_gate = DemSamplerBuilder::new(&influence)
+        .with_per_gate_noise(PerGateTypeNoise::from_base_noise(NoiseConfig::uniform(p)))
+        .with_detectors_json(r#"[{"id": 0, "records": [-1]}]"#)
+        .unwrap()
+        .build()
+        .unwrap();
+
+    assert_eq!(
+        scalar.num_mechanisms(),
+        per_gate.num_mechanisms(),
+        "uniform-equivalent per-gate must produce same mechanism count as scalar",
+    );
+}
+
+#[test]
+fn per_gate_override_changes_cx_rate() {
+    // Assign a large explicit CX rate via per_gate, compare against a
+    // scalar baseline with small p2.
+    let dag = build_parity_check_circuit();
+    let analyzer = DagFaultAnalyzer::new(&dag);
+    let influence = analyzer.build_influence_map();
+
+    // Scalar baseline: small p2.
+    let small = DemSamplerBuilder::new(&influence)
+        .with_noise(0.0, 1e-4, 0.0, 0.0)
+        .with_detectors_json(r#"[{"id": 0, "records": [-1]}]"#)
+        .unwrap()
+        .build()
+        .unwrap();
+
+    // Per-gate override: same p2 for CX via map, but 10x larger value.
+    let per_gate = DemSamplerBuilder::new(&influence)
+        .with_per_gate_noise(
+            PerGateTypeNoise::from_base_noise(NoiseConfig::uniform(0.0))
+                .with_2q_rates(GateType::CX, [1e-3; 15]),
+        )
+        .with_detectors_json(r#"[{"id": 0, "records": [-1]}]"#)
+        .unwrap()
+        .build()
+        .unwrap();
+
+    // Per-gate path should produce the same mechanism count (same circuit
+    // structure), but larger aggregate error probabilities.
+    assert_eq!(small.num_mechanisms(), per_gate.num_mechanisms());
+    assert!(
+        per_gate.average_error_probability() > 5.0 * small.average_error_probability(),
+        "10x larger per-CX rate should produce substantially larger avg error \
+         (got per_gate={}, scalar={})",
+        per_gate.average_error_probability(),
+        small.average_error_probability(),
+    );
+}
+
+#[test]
+fn per_gate_base_noise_used_for_unmapped_gate_types() {
+    // Specify H explicitly (rates[X, Y, Z]); CX uses the base noise model.
+    let dag = build_parity_check_circuit();
+    let analyzer = DagFaultAnalyzer::new(&dag);
+    let influence = analyzer.build_influence_map();
+
+    let cfg = PerGateTypeNoise::from_base_noise(NoiseConfig::uniform(0.01))
+        .with_1q_rates(GateType::H, [0.001, 0.001, 0.001]);
+
+    let sim = DemSamplerBuilder::new(&influence)
+        .with_per_gate_noise(cfg)
+        .with_detectors_json(r#"[{"id": 0, "records": [-1]}]"#)
+        .unwrap()
+        .build()
+        .unwrap();
+
+    // Parity-check circuit has no H gate -- all 1Q contributions come
+    // from prep/measurement. Just verify it builds and has mechanisms.
+    assert!(sim.num_mechanisms() > 0);
+}
+
+#[test]
+fn per_gate_asymmetric_2q_rates() {
+    // Set only lambda_IX != 0, everything else zero for CX. Confirms the
+    // sparse rate path (only one of 15 pair rates nonzero) works.
+    let dag = build_parity_check_circuit();
+    let analyzer = DagFaultAnalyzer::new(&dag);
+    let influence = analyzer.build_influence_map();
+
+    let mut rates_2q = [0.0; 15];
+    rates_2q[0] = 0.005; // IX
+    let cfg = PerGateTypeNoise::from_base_noise(NoiseConfig::uniform(0.0))
+        .with_2q_rates(GateType::CX, rates_2q);
+
+    let sim = DemSamplerBuilder::new(&influence)
+        .with_per_gate_noise(cfg)
+        .with_detectors_json(r#"[{"id": 0, "records": [-1]}]"#)
+        .unwrap()
+        .build()
+        .unwrap();
+
+    // With everything else zero, should still produce some mechanisms
+    // (from the single IX contribution at each CX location).
+    assert!(
+        sim.num_mechanisms() > 0,
+        "sparse rates should still produce mechanisms from the IX contribution",
+    );
+}
diff --git a/crates/pecos-qec/tests/per_qubit_measurement_tests.rs b/crates/pecos-qec/tests/per_qubit_measurement_tests.rs
new file mode 100644
index 000000000..aa95c9435
--- /dev/null
+++ b/crates/pecos-qec/tests/per_qubit_measurement_tests.rs
@@ -0,0 +1,166 @@
+// Copyright 2026 The PECOS Developers
+//
+// Licensed under the Apache License, Version 2.0 (the "License"); you may not use this file except
+// in compliance with the License. You may obtain a copy of the License at
+//
+//     https://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software distributed under the License
+// is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express
+// or implied. See the License for the specific language governing permissions and limitations under
+// the License.
+
+//! Integration tests for per-qubit measurement and preparation rates on
+//! [`PerGateTypeNoise`]. Mirrors the per-qubit gate tests but for MZ/PZ
+//! locations.
+
+use pecos_core::QubitId;
+use pecos_qec::fault_tolerance::dem_builder::{DemSamplerBuilder, NoiseConfig, PerGateTypeNoise};
+use pecos_qec::fault_tolerance::propagator::DagFaultAnalyzer;
+use pecos_quantum::DagCircuit;
+
+#[test]
+fn per_qubit_measurement_override_takes_precedence() {
+    // Unit test the lookup layering.
+    let q0 = QubitId::from(0usize);
+    let q1 = QubitId::from(1usize);
+    let mut cfg = PerGateTypeNoise::from_base_noise(NoiseConfig::uniform(0.01));
+    // Explicitly override q0, leave q1 on the base noise model.
+    cfg = cfg.with_measurement_rate(q0, 0.1);
+    assert!((cfg.measurement_rate_on(q0) - 0.1).abs() < 1e-14);
+    assert!((cfg.measurement_rate_on(q1) - 0.01).abs() < 1e-14);
+}
+
+#[test]
+fn per_qubit_init_override_takes_precedence() {
+    let q0 = QubitId::from(0usize);
+    let q1 = QubitId::from(1usize);
+    let mut cfg = PerGateTypeNoise::from_base_noise(NoiseConfig::uniform(0.02));
+    cfg = cfg.with_init_rate(q0, 0.2);
+    assert!((cfg.init_rate_on(q0) - 0.2).abs() < 1e-14);
+    assert!((cfg.init_rate_on(q1) - 0.02).abs() < 1e-14);
+}
+
+fn build_three_ancilla_circuit() -> DagCircuit {
+    // Three prep + measure operations on three different qubits. Each
+    // qubit is only touched once so per-qubit rates affect exactly one
+    // mechanism each.
+    let mut dag = DagCircuit::new();
+    dag.pz(&[0]);
+    dag.pz(&[1]);
+    dag.pz(&[2]);
+    dag.mz(&[0]);
+    dag.mz(&[1]);
+    dag.mz(&[2]);
+    dag
+}
+
+#[test]
+fn per_qubit_measurement_rate_raises_only_targeted_qubit() {
+    // With per-qubit override on qubit 0, and scalar 0 for everyone else,
+    // the total mechanism probability should reflect only the q0
+    // contribution.
+    let dag = build_three_ancilla_circuit();
+    let analyzer = DagFaultAnalyzer::new(&dag);
+    let influence = analyzer.build_influence_map();
+
+    let q0 = QubitId::from(0usize);
+    let cfg_only_q0 = PerGateTypeNoise::from_base_noise(NoiseConfig::new(0.0, 0.0, 0.0, 0.0))
+        .with_measurement_rate(q0, 0.05);
+    let sim_only_q0 = DemSamplerBuilder::new(&influence)
+        .with_per_gate_noise(cfg_only_q0)
+        .with_detectors_json(r#"[{"id": 0, "records": [-3]}, {"id": 1, "records": [-2]}, {"id": 2, "records": [-1]}]"#)
+        .unwrap()
+        .build().unwrap();
+
+    // Baseline: all three qubits at the same rate.
+    let cfg_uniform = PerGateTypeNoise::from_base_noise(NoiseConfig::new(0.0, 0.0, 0.05, 0.0));
+    let sim_uniform = DemSamplerBuilder::new(&influence)
+        .with_per_gate_noise(cfg_uniform)
+        .with_detectors_json(r#"[{"id": 0, "records": [-3]}, {"id": 1, "records": [-2]}, {"id": 2, "records": [-1]}]"#)
+        .unwrap()
+        .build().unwrap();
+
+    // Only q0 has meas noise in `sim_only_q0` => one mechanism.
+    // Uniform has meas noise on all three => three mechanisms.
+    // `average_error_probability` is per-mechanism, so it's the same
+    // in both; what differs is the count.
+    assert_eq!(
+        sim_only_q0.num_mechanisms(),
+        1,
+        "expected exactly one mechanism for per-qubit q0-only override",
+    );
+    assert_eq!(
+        sim_uniform.num_mechanisms(),
+        3,
+        "expected three mechanisms when all qubits share the rate",
+    );
+    // Per-mechanism probability should be the same 0.05 in both cases.
+    let delta =
+        (sim_only_q0.average_error_probability() - sim_uniform.average_error_probability()).abs();
+    assert!(
+        delta < 1e-12,
+        "per-mech probabilities should match: {delta}"
+    );
+}
+
+#[test]
+fn per_qubit_init_rate_raises_only_targeted_qubit() {
+    let dag = build_three_ancilla_circuit();
+    let analyzer = DagFaultAnalyzer::new(&dag);
+    let influence = analyzer.build_influence_map();
+
+    let q1 = QubitId::from(1usize);
+    let cfg_only_q1 = PerGateTypeNoise::from_base_noise(NoiseConfig::new(0.0, 0.0, 0.0, 0.0))
+        .with_init_rate(q1, 0.05);
+    let sim_only_q1 = DemSamplerBuilder::new(&influence)
+        .with_per_gate_noise(cfg_only_q1)
+        .with_detectors_json(r#"[{"id": 0, "records": [-3]}, {"id": 1, "records": [-2]}, {"id": 2, "records": [-1]}]"#)
+        .unwrap()
+        .build().unwrap();
+
+    let cfg_uniform = PerGateTypeNoise::from_base_noise(NoiseConfig::new(0.0, 0.0, 0.0, 0.05));
+    let sim_uniform = DemSamplerBuilder::new(&influence)
+        .with_per_gate_noise(cfg_uniform)
+        .with_detectors_json(r#"[{"id": 0, "records": [-3]}, {"id": 1, "records": [-2]}, {"id": 2, "records": [-1]}]"#)
+        .unwrap()
+        .build().unwrap();
+
+    assert_eq!(
+        sim_only_q1.num_mechanisms(),
+        1,
+        "expected exactly one mechanism for per-qubit q1-only init override",
+    );
+    assert_eq!(
+        sim_uniform.num_mechanisms(),
+        3,
+        "expected three mechanisms when all qubits share the rate",
+    );
+}
+
+#[test]
+fn per_qubit_measurement_path_uses_base_rate_without_overrides() {
+    // A PerGateTypeNoise without any per-qubit measurement rates should
+    // use scalar p_meas exactly.
+    let dag = build_three_ancilla_circuit();
+    let analyzer = DagFaultAnalyzer::new(&dag);
+    let influence = analyzer.build_influence_map();
+
+    let cfg = PerGateTypeNoise::from_base_noise(NoiseConfig::uniform(0.05));
+    let sim_per_gate = DemSamplerBuilder::new(&influence)
+        .with_per_gate_noise(cfg)
+        .with_detectors_json(r#"[{"id": 0, "records": [-3]}, {"id": 1, "records": [-2]}, {"id": 2, "records": [-1]}]"#)
+        .unwrap()
+        .build().unwrap();
+
+    let sim_scalar = DemSamplerBuilder::new(&influence)
+        .with_noise(0.05, 0.05, 0.05, 0.05)
+        .with_detectors_json(r#"[{"id": 0, "records": [-3]}, {"id": 1, "records": [-2]}, {"id": 2, "records": [-1]}]"#)
+        .unwrap()
+        .build().unwrap();
+
+    assert_eq!(sim_per_gate.num_mechanisms(), sim_scalar.num_mechanisms());
+    let delta =
+        (sim_per_gate.average_error_probability() - sim_scalar.average_error_probability()).abs();
+    assert!(delta < 1e-12, "delta {delta} should be near zero");
+}
diff --git a/crates/pecos-qec/tests/per_qubit_noise_tests.rs b/crates/pecos-qec/tests/per_qubit_noise_tests.rs
new file mode 100644
index 000000000..0be609f9c
--- /dev/null
+++ b/crates/pecos-qec/tests/per_qubit_noise_tests.rs
@@ -0,0 +1,158 @@
+// Copyright 2026 The PECOS Developers
+//
+// Licensed under the Apache License, Version 2.0 (the "License"); you may not use this file except
+// in compliance with the License. You may obtain a copy of the License at
+//
+//     https://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software distributed under the License
+// is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express
+// or implied. See the License for the specific language governing permissions and limitations under
+// the License.
+
+//! Integration tests for per-qubit noise variation on top of
+//! [`PerGateTypeNoise`]. Verifies:
+//!
+//! 1. per-qubit rates override per-gate-type defaults for matching qubits.
+//! 2. qubits not in the per-qubit map use the per-gate-type default.
+//! 3. lookup lookup methods (`rate_1q_on`, `rate_2q_on`) layer correctly.
+
+use pecos_core::QubitId;
+use pecos_qec::fault_tolerance::dem_builder::{DemSamplerBuilder, NoiseConfig, PerGateTypeNoise};
+use pecos_qec::fault_tolerance::propagator::DagFaultAnalyzer;
+use pecos_quantum::{DagCircuit, GateType};
+
+fn assert_rate_eq(actual: f64, expected: f64) {
+    assert!(
+        (actual - expected).abs() < 1e-14,
+        "expected rate {expected:.16e}, got {actual:.16e}"
+    );
+}
+
+#[test]
+fn per_qubit_override_takes_precedence_over_per_gate_type() {
+    // Direct unit test of the lookup layering, independent of DemSampler.
+    let q0 = QubitId::from(0usize);
+    let q1 = QubitId::from(1usize);
+    let cfg = PerGateTypeNoise::from_base_noise(NoiseConfig::uniform(0.1))
+        .with_1q_rates(GateType::H, [0.01, 0.02, 0.03])
+        .with_1q_rates_for_qubit(GateType::H, q0, [0.001, 0.002, 0.003]);
+
+    // qubit 0 has per-qubit override
+    assert_rate_eq(cfg.rate_1q_on(GateType::H, q0, 0), 0.001);
+    assert_rate_eq(cfg.rate_1q_on(GateType::H, q0, 1), 0.002);
+    assert_rate_eq(cfg.rate_1q_on(GateType::H, q0, 2), 0.003);
+
+    // qubit 1 uses the per-gate-type default.
+    assert_rate_eq(cfg.rate_1q_on(GateType::H, q1, 0), 0.01);
+    assert_rate_eq(cfg.rate_1q_on(GateType::H, q1, 1), 0.02);
+
+    // Unregistered gate on qubit 0 uses the per-gate-type default (not set),
+    // then to uniform base.p1/3.
+    let uniform_share = 0.1_f64 / 3.0;
+    assert!((cfg.rate_1q_on(GateType::X, q0, 0) - uniform_share).abs() < 1e-14);
+}
+
+#[test]
+fn per_qubit_2q_override_takes_precedence() {
+    let q0 = QubitId::from(0usize);
+    let q1 = QubitId::from(1usize);
+    let q2 = QubitId::from(2usize);
+    let q3 = QubitId::from(3usize);
+
+    let mut per_pair = [0.0; 15];
+    per_pair[0] = 1e-3; // IX
+    let mut gate_default = [0.0; 15];
+    gate_default[0] = 5e-4; // IX
+
+    let cfg = PerGateTypeNoise::from_base_noise(NoiseConfig::uniform(0.0))
+        .with_2q_rates(GateType::CX, gate_default)
+        .with_2q_rates_for_qubits(GateType::CX, q0, q1, per_pair);
+
+    // (q0, q1) uses the specific rates
+    assert_rate_eq(cfg.rate_2q_on(GateType::CX, q0, q1, 0), 1e-3);
+    // (q2, q3) uses the per-gate-type default.
+    assert_rate_eq(cfg.rate_2q_on(GateType::CX, q2, q3, 0), 5e-4);
+    // Different ordered pair (q1, q0): NOT the same as (q0, q1). Falls back.
+    assert_rate_eq(cfg.rate_2q_on(GateType::CX, q1, q0, 0), 5e-4);
+}
+
+fn build_circuit_with_two_cxs() -> DagCircuit {
+    // Two CX gates on different qubit pairs. The per-qubit override
+    // should apply only to the first CX.
+    let mut dag = DagCircuit::new();
+    dag.pz(&[4]);
+    dag.cx(&[(0, 4)]);
+    dag.cx(&[(1, 4)]);
+    dag.mz(&[4]);
+    dag
+}
+
+#[test]
+fn per_qubit_cx_rate_affects_mechanism_probabilities() {
+    // Two CX locations touching different qubit pairs:
+    //   CX on (0, 4): per-qubit rate (10x baseline)
+    //   CX on (1, 4): per-gate-type default rate
+    // Total aggregated error probability should reflect the override.
+    let dag = build_circuit_with_two_cxs();
+    let analyzer = DagFaultAnalyzer::new(&dag);
+    let influence = analyzer.build_influence_map();
+
+    let q0 = QubitId::from(0usize);
+    let q4 = QubitId::from(4usize);
+
+    let baseline_rates = [1e-4; 15];
+    let boosted_rates = [1e-3; 15];
+
+    // Control case: just the baseline.
+    let baseline_cfg = PerGateTypeNoise::from_base_noise(NoiseConfig::uniform(0.0))
+        .with_2q_rates(GateType::CX, baseline_rates);
+    let baseline = DemSamplerBuilder::new(&influence)
+        .with_per_gate_noise(baseline_cfg)
+        .with_detectors_json(r#"[{"id": 0, "records": [-1]}]"#)
+        .unwrap()
+        .build()
+        .unwrap();
+
+    // Override case: boost the (0, 4) pair specifically.
+    let override_cfg = PerGateTypeNoise::from_base_noise(NoiseConfig::uniform(0.0))
+        .with_2q_rates(GateType::CX, baseline_rates)
+        .with_2q_rates_for_qubits(GateType::CX, q0, q4, boosted_rates);
+    let overridden = DemSamplerBuilder::new(&influence)
+        .with_per_gate_noise(override_cfg)
+        .with_detectors_json(r#"[{"id": 0, "records": [-1]}]"#)
+        .unwrap()
+        .build()
+        .unwrap();
+
+    assert_eq!(baseline.num_mechanisms(), overridden.num_mechanisms());
+    // Override should substantially raise average error probability
+    // (one of two CX contributions now 10x the baseline).
+    let avg_base = baseline.average_error_probability();
+    let avg_over = overridden.average_error_probability();
+    assert!(
+        avg_over > 2.0 * avg_base,
+        "expected per-qubit override to raise avg error >>2x, got base={avg_base} over={avg_over}",
+    );
+}
+
+#[test]
+fn per_qubit_path_uses_per_gate_type_rates_without_overrides() {
+    // A config with only per-gate-type rates (no per-qubit overrides)
+    // should still produce mechanisms from the per-gate-type rates.
+    let dag = build_circuit_with_two_cxs();
+    let analyzer = DagFaultAnalyzer::new(&dag);
+    let influence = analyzer.build_influence_map();
+
+    let cfg = PerGateTypeNoise::from_base_noise(NoiseConfig::uniform(0.0))
+        .with_2q_rates(GateType::CX, [1e-3; 15]);
+    let sim = DemSamplerBuilder::new(&influence)
+        .with_per_gate_noise(cfg)
+        .with_detectors_json(r#"[{"id": 0, "records": [-1]}]"#)
+        .unwrap()
+        .build()
+        .unwrap();
+
+    assert!(sim.num_mechanisms() > 0);
+    assert!(sim.average_error_probability() > 0.0);
+}
diff --git a/crates/pecos-qec/tests/stim_dem_export_tests.rs b/crates/pecos-qec/tests/stim_dem_export_tests.rs
new file mode 100644
index 000000000..6c6663e6c
--- /dev/null
+++ b/crates/pecos-qec/tests/stim_dem_export_tests.rs
@@ -0,0 +1,129 @@
+// Copyright 2026 The PECOS Developers
+//
+// Licensed under the Apache License, Version 2.0 (the "License"); you may not use this file except
+// in compliance with the License. You may obtain a copy of the License at
+//
+//     https://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software distributed under the License
+// is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express
+// or implied. See the License for the specific language governing permissions and limitations under
+// the License.
+
+//! Integration tests for Stim-format DEM export from `DemStabSim` with
+//! per-gate noise. Closes the
+//! `~/Repos/pecos-docs/ideas/stim-compat-dem-export.md` gap.
+
+use pecos_core::QubitId;
+use pecos_qec::dem_stab::DemStabSim;
+use pecos_qec::fault_tolerance::dem_builder::{
+    DemOutput, DetectorDef, NoiseConfig, PerGateTypeNoise,
+};
+use pecos_quantum::{DagCircuit, GateType};
+
+fn build_parity_check() -> DagCircuit {
+    let mut dag = DagCircuit::new();
+    dag.pz(&[2]);
+    dag.cx(&[(0, 2)]);
+    dag.cx(&[(1, 2)]);
+    dag.mz(&[2]);
+    dag
+}
+
+#[test]
+fn dem_text_export_with_scalar_noise() {
+    let dag = build_parity_check();
+    let sim = DemStabSim::builder()
+        .circuit(dag)
+        .noise(NoiseConfig::uniform(0.01))
+        .detectors(vec![DetectorDef::new(0).with_records([-1])])
+        .observables(vec![DemOutput::new(0).with_records([-1])])
+        .build()
+        .unwrap();
+
+    let dem = sim.detector_error_model();
+    let text = dem.to_string();
+
+    // Must contain at least one error mechanism.
+    assert!(
+        text.contains("error("),
+        "expected 'error(' line in DEM text:\n{text}"
+    );
+    // Must declare the detector and observable.
+    assert!(text.contains("detector D0"), "missing detector D0:\n{text}");
+    assert!(
+        text.contains("logical_observable L0") || text.contains("observable_include L0"),
+        "missing observable decl:\n{text}",
+    );
+}
+
+#[test]
+fn dem_text_export_with_per_gate_noise() {
+    let dag = build_parity_check();
+    let q0 = QubitId::from(0usize);
+    let q2 = QubitId::from(2usize);
+    let cfg = PerGateTypeNoise::from_base_noise(NoiseConfig::new(0.0, 0.0, 0.001, 0.001))
+        .with_2q_rates(GateType::CX, [1e-3; 15])
+        .with_2q_rates_for_qubits(GateType::CX, q0, q2, [5e-3; 15]);
+    let sim = DemStabSim::builder()
+        .circuit(dag)
+        .per_gate_noise(cfg)
+        .detectors(vec![DetectorDef::new(0).with_records([-1])])
+        .build()
+        .unwrap();
+
+    let dem = sim.detector_error_model();
+    let text = dem.to_string();
+
+    // Should render multiple error mechanisms (CX on (0,2) boosted vs CX on (1,2)).
+    let error_lines = text.matches("error(").count();
+    assert!(
+        error_lines > 0,
+        "expected per-gate-noise path to produce error lines:\n{text}",
+    );
+    assert!(text.contains("detector D0"));
+}
+
+#[test]
+fn dem_round_trip_mechanism_count_matches_sampler() {
+    let dag = build_parity_check();
+    let sim = DemStabSim::builder()
+        .circuit(dag)
+        .noise(NoiseConfig::uniform(0.005))
+        .detectors(vec![DetectorDef::new(0).with_records([-1])])
+        .build()
+        .unwrap();
+
+    let dem = sim.detector_error_model();
+    // The reconstructed DEM should have the same mechanism count as the
+    // sampler (direct contributions).
+    assert_eq!(
+        dem.num_contributions(),
+        sim.num_mechanisms(),
+        "mechanism count should round-trip between sampler and reconstructed DEM"
+    );
+}
+
+#[test]
+fn dem_probabilities_recoverable_from_thresholds() {
+    // Check that the prob → u64 threshold → prob round-trip is close.
+    // Use a small, well-separated set of mechanisms.
+    let dag = build_parity_check();
+    let sim = DemStabSim::builder()
+        .circuit(dag)
+        .noise(NoiseConfig::uniform(0.01))
+        .detectors(vec![DetectorDef::new(0).with_records([-1])])
+        .build()
+        .unwrap();
+
+    let dem = sim.detector_error_model();
+    let text = dem.to_string();
+    // Probabilities recovered should be non-zero and appear in the text
+    // in some form.
+    for line in text.lines().filter(|l| l.starts_with("error(")) {
+        // Parse the prob inside "error(...)".
+        let inner = line.trim_start_matches("error(").split(')').next().unwrap();
+        let p: f64 = inner.parse().unwrap();
+        assert!(p > 0.0 && p < 1.0, "probability out of range: {p}");
+    }
+}
diff --git a/crates/pecos-qec/tests/targeted_tests.rs b/crates/pecos-qec/tests/targeted_tests.rs
new file mode 100644
index 000000000..610be7b27
--- /dev/null
+++ b/crates/pecos-qec/tests/targeted_tests.rs
@@ -0,0 +1,330 @@
+// Copyright 2026 The PECOS Developers
+//
+// Licensed under the Apache License, Version 2.0 (the "License"); you may not use this file except
+// in compliance with the License. You may obtain a copy of the License at
+//
+//     https://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software distributed under the License
+// is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express
+// or implied. See the License for the specific language governing permissions and limitations under
+// the License.
+
+//! Targeted tests for specific features and bug fixes from the annotation/decoder session.
+
+use pecos_core::pauli::{X, Y, Z};
+use pecos_qec::fault_tolerance::InfluenceBuilder;
+use pecos_qec::fault_tolerance::dem_builder::{NoiseConfig, PauliWeights};
+use pecos_qec::fault_tolerance::lookup_decoder::LookupDecoder;
+use pecos_qec::fault_tolerance::propagator::{DagFaultAnalyzer, Pauli};
+use pecos_quantum::DagCircuit;
+
+// ============================================================================
+// Y anticommutation: Y commutes with Y
+// ============================================================================
+
+/// Verify that Y fault does NOT flip a detector when the propagated observable
+/// is also Y on that qubit. {Y, Y} = 2I (commutes), not anticommutes.
+#[test]
+fn y_commutes_with_y() {
+    // Build a circuit where the backward-propagated observable has Y on a qubit.
+    // Backward propagation from MZ through H -> SZ -> H:
+    //   MZ: Z -> backward H: X -> backward SZ: Y -> backward H: Y
+    // So at the first H location, the observable is Y on qubit 0.
+    let mut dag = DagCircuit::new();
+    dag.pz(&[0]);
+    dag.h(&[0]); // observable is Y here (backward from MZ through H,SZ,H)
+    dag.sz(&[0]); // observable is X here (backward from MZ through H,SZ)
+    dag.h(&[0]); // observable is Z here (backward from MZ through H)
+    dag.mz(&[0]);
+
+    let analyzer = DagFaultAnalyzer::new(&dag);
+    let map = analyzer.build_influence_map();
+
+    // Find the first H gate's after-location (node with lowest index)
+    // At this point the backward-propagated observable should have Y on qubit 0.
+    let h_locs: Vec<(
+        usize,
+        &pecos_qec::fault_tolerance::propagator::DagSpacetimeLocation,
+    )> = map
+        .locations
+        .iter()
+        .enumerate()
+        .filter(|(_, loc)| loc.gate_type == pecos_core::gate_type::GateType::H && !loc.before)
+        .collect();
+
+    assert!(h_locs.len() >= 2, "Should have at least 2 H locations");
+    let (first_h_loc, _) = h_locs[0]; // first H (closest to prep)
+
+    // Y fault at first H should NOT flip detector (Y commutes with Y)
+    let y_dets = map.get_detector_indices(first_h_loc, Pauli::Y as u8);
+    assert!(
+        y_dets.is_empty(),
+        "Y fault should not flip detectors when observable is Y on same qubit, got {y_dets:?}"
+    );
+    // But X and Z faults SHOULD flip (both anticommute with Y)
+    let x_dets = map.get_detector_indices(first_h_loc, Pauli::X as u8);
+    let z_dets = map.get_detector_indices(first_h_loc, Pauli::Z as u8);
+    assert!(
+        !x_dets.is_empty() || !z_dets.is_empty(),
+        "X or Z fault should flip detectors when observable is Y"
+    );
+}
+
+// ============================================================================
+// T1/T2 idle noise
+// ============================================================================
+
+/// Verify T1/T2 produces biased noise: P(Z) > P(X) = P(Y).
+#[test]
+fn t1_t2_biased_idle_noise() {
+    let noise = NoiseConfig::new(0.001, 0.01, 0.001, 0.001).set_t1_t2(50_000.0, 30_000.0);
+
+    // 1000 time units of idle
+    let pp = noise.idle_pauli_probs(1000.0);
+
+    // P(X) == P(Y) (from amplitude damping)
+    assert!(
+        (pp.px - pp.py).abs() < 1e-15,
+        "P(X) should equal P(Y): px={}, py={}",
+        pp.px,
+        pp.py
+    );
+
+    // P(Z) > P(X) (dephasing dominates relaxation)
+    assert!(
+        pp.pz > pp.px,
+        "P(Z) should be larger than P(X): pz={}, px={}",
+        pp.pz,
+        pp.px
+    );
+
+    // Total should be reasonable (not > 1)
+    assert!(pp.total() < 1.0, "Total should be < 1: {}", pp.total());
+    assert!(pp.total() > 0.0, "Total should be > 0");
+}
+
+/// Verify uniform depolarizing idle gives equal X/Y/Z.
+#[test]
+fn uniform_idle_noise() {
+    let noise = NoiseConfig::uniform(0.001);
+    let pp = noise.idle_pauli_probs(1.0);
+
+    let eps = 1e-15;
+    assert!((pp.px - pp.py).abs() < eps);
+    assert!((pp.py - pp.pz).abs() < eps);
+    assert!((pp.px - 0.001 / 3.0).abs() < eps);
+}
+
+// ============================================================================
+// PauliWeights
+// ============================================================================
+
+/// Verify custom single-qubit weights change decoder probabilities.
+#[test]
+fn custom_p1_weights_affect_decoder() {
+    let mut dag = DagCircuit::new();
+    dag.pz(&[0, 1]);
+    dag.h(&[0]);
+    dag.cx(&[(0, 1)]);
+    let ms = dag.mz(&[0, 1]);
+    dag.observable(&[ms[0], ms[1]]);
+
+    let map = InfluenceBuilder::new(&dag)
+        .with_circuit_annotations(&dag)
+        .build();
+
+    // Uniform weights
+    let noise_uniform = NoiseConfig::uniform(0.001);
+    let d_uniform = LookupDecoder::build(&map, &noise_uniform, 2);
+
+    // Biased weights: Z only
+    let noise_biased = NoiseConfig::uniform(0.001).set_p1_weights(PauliWeights::from([
+        (X(0), 0.0),
+        (Y(0), 0.0),
+        (Z(0), 1.0),
+    ]));
+    let d_biased = LookupDecoder::build(&map, &noise_biased, 2);
+
+    // Both should build successfully
+    assert!(d_uniform.num_syndromes() > 0);
+    assert!(d_biased.num_syndromes() > 0);
+
+    // Both should account for most probability at p=0.001
+    assert!(
+        d_uniform.accounted_probability() > 0.99,
+        "Uniform: {}",
+        d_uniform.accounted_probability()
+    );
+    assert!(
+        d_biased.accounted_probability() > 0.99,
+        "Biased: {}",
+        d_biased.accounted_probability()
+    );
+}
+
+/// Verify `PauliWeights` validates sum to ~1.0.
+#[test]
+#[should_panic(expected = "must sum to 1.0")]
+fn pauli_weights_validation() {
+    // Should panic: doesn't sum to 1.0
+    let _ = PauliWeights::from([(X(0), 0.5), (Y(0), 0.3)]);
+}
+
+/// Verify `PauliWeights::weight_for` matches by pattern, not qubit ID.
+#[test]
+fn pauli_weights_pattern_matching() {
+    let w = PauliWeights::uniform_2q();
+
+    // X(0) & Z(1) pattern should match regardless of actual qubit IDs
+    let weight = w.weight_for(&(X(0) & Z(1)));
+    assert!((weight - 1.0 / 15.0).abs() < 1e-10);
+
+    // Same pattern from different qubit IDs should also match
+    let weight2 = w.weight_for(&(X(5) & Z(9)));
+    assert!(
+        (weight2 - 1.0 / 15.0).abs() < 1e-10,
+        "Pattern matching should ignore qubit IDs: got {weight2}"
+    );
+}
+
+// ============================================================================
+// Prep-gate propagation stop
+// ============================================================================
+
+/// Verify that faults before a mid-circuit reset don't propagate past it.
+#[test]
+fn prep_gate_stops_propagation() {
+    // Circuit: PZ -> H -> PZ (reset) -> MZ
+    // An X fault after the first H should NOT affect the final measurement
+    // because the second PZ resets qubit 0.
+    let mut dag = DagCircuit::new();
+    dag.pz(&[0]);
+    dag.h(&[0]); // fault here
+    dag.pz(&[0]); // mid-circuit reset -- should block propagation
+    dag.mz(&[0]);
+
+    let map = InfluenceBuilder::new(&dag)
+        .with_circuit_annotations(&dag)
+        .build();
+
+    // Find the H gate's after-location
+    let mut h_has_influence = false;
+    for (loc_idx, loc) in map.locations.iter().enumerate() {
+        if loc.gate_type == pecos_core::gate_type::GateType::H && !loc.before {
+            let x_dets = map.influences.detectors(loc_idx, Pauli::X);
+            let z_dets = map.influences.detectors(loc_idx, Pauli::Z);
+            let y_dets = map.influences.detectors(loc_idx, Pauli::Y);
+            if !x_dets.is_empty() || !z_dets.is_empty() || !y_dets.is_empty() {
+                h_has_influence = true;
+            }
+        }
+    }
+
+    assert!(
+        !h_has_influence,
+        "Faults before mid-circuit PZ should not propagate past the reset"
+    );
+}
+
+/// Verify that faults AFTER a mid-circuit reset DO affect later measurements.
+#[test]
+fn faults_after_reset_propagate() {
+    // Use DagFaultAnalyzer (which creates 1 detector per measurement) to
+    // verify that faults after a reset propagate to the measurement.
+    // Circuit: PZ -> PZ (reset) -> H -> MZ
+    let mut dag = DagCircuit::new();
+    dag.pz(&[0]);
+    dag.pz(&[0]); // mid-circuit reset
+    dag.h(&[0]); // fault here should affect measurement
+    dag.mz(&[0]);
+
+    let analyzer = DagFaultAnalyzer::new(&dag);
+    let map = analyzer.build_influence_map();
+
+    // H gate after-location should have detector influence
+    // (backward from MZ through H: observable is X at H location)
+    let mut h_has_influence = false;
+    for (loc_idx, loc) in map.locations.iter().enumerate() {
+        if loc.gate_type == pecos_core::gate_type::GateType::H && !loc.before {
+            for p in [Pauli::X, Pauli::Y, Pauli::Z] {
+                let dets = map.influences.detectors(loc_idx, p);
+                if !dets.is_empty() {
+                    h_has_influence = true;
+                }
+            }
+        }
+    }
+
+    assert!(
+        h_has_influence,
+        "Faults after mid-circuit PZ should propagate to later measurements"
+    );
+}
+
+// ============================================================================
+// DagCircuit annotation methods
+// ============================================================================
+
+/// Verify `detector()` auto-derives Z Pauli from measurement nodes.
+#[test]
+fn detector_derives_pauli_from_measurements() {
+    let mut dag = DagCircuit::new();
+    dag.pz(&[0, 1]);
+    dag.cx(&[(0, 1)]);
+    let ms = dag.mz(&[0, 1]);
+    dag.detector(&[ms[0], ms[1]]);
+
+    let ann = &dag.annotations()[0];
+    // Pauli should be Z on both measured qubits
+    let paulis = ann.pauli.paulis();
+    assert_eq!(paulis.len(), 2);
+    assert_eq!(paulis[0].0, pecos_core::Pauli::Z);
+    assert_eq!(paulis[1].0, pecos_core::Pauli::Z);
+}
+
+/// Verify `tracked_pauli` normalizes phase to +1.
+#[test]
+fn tracked_pauli_normalizes_phase() {
+    let mut dag = DagCircuit::new();
+    dag.pz(&[0]);
+
+    // -X(0) has phase -1
+    let neg_x = -X(0);
+    assert_ne!(neg_x.get_phase(), pecos_core::QuarterPhase::PlusOne);
+
+    dag.tracked_pauli(neg_x);
+
+    // After storage, phase should be normalized to +1
+    let ann = &dag.annotations()[0];
+    assert_eq!(ann.pauli.get_phase(), pecos_core::QuarterPhase::PlusOne);
+}
+
+/// Verify probability sums to 1.0 with the per-gate noise model.
+#[test]
+fn probability_sums_to_one() {
+    let mut dag = DagCircuit::new();
+    dag.pz(&[0, 1]);
+    dag.h(&[0]);
+    dag.cx(&[(0, 1)]);
+    let ms = dag.mz(&[0, 1]);
+    dag.observable(&[ms[0], ms[1]]);
+
+    let map = InfluenceBuilder::new(&dag)
+        .with_circuit_annotations(&dag)
+        .build();
+
+    let noise = NoiseConfig::uniform(0.001);
+    let decoder = LookupDecoder::build(&map, &noise, 3);
+
+    assert!(
+        decoder.truncation_bound() < 1e-4,
+        "Weight-3 at p=0.001 should have small truncation: {}",
+        decoder.truncation_bound()
+    );
+    assert!(
+        decoder.accounted_probability() > 0.999,
+        "Should account for >99.9% of probability: {}",
+        decoder.accounted_probability()
+    );
+}
diff --git a/crates/pecos-qec/tests/unified_sampler_tests.rs b/crates/pecos-qec/tests/unified_sampler_tests.rs
new file mode 100644
index 000000000..3bdaa2c57
--- /dev/null
+++ b/crates/pecos-qec/tests/unified_sampler_tests.rs
@@ -0,0 +1,483 @@
+// Copyright 2026 The PECOS Developers
+//
+// Licensed under the Apache License, Version 2.0 (the "License"); you may not use this file except
+// in compliance with the License. You may obtain a copy of the License at
+//
+//     https://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software distributed under the License
+// is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express
+// or implied. See the License for the specific language governing permissions and limitations under
+// the License.
+
+//! Verification tests for `DemSampler`.
+//!
+//! These tests ensure the `DemSampler` matches both:
+//! 1. `DemSampler` output (detector-level) for the same seed
+//! 2. raw measurement output (measurement-level) for the same seed
+//! 3. Statistical equivalence across large shot counts
+
+use pecos_qec::fault_tolerance::InfluenceBuilder;
+use pecos_qec::fault_tolerance::dem_builder::DemSamplerBuilder;
+use pecos_qec::fault_tolerance::propagator::DagFaultAnalyzer;
+use pecos_quantum::DagCircuit;
+use pecos_random::PecosRng;
+
+/// Build a repetition code syndrome extraction circuit with the given
+/// number of rounds. Data qubits: 0, 1, 2. Ancilla qubits: 3, 4.
+fn repetition_code_circuit(num_rounds: usize) -> DagCircuit {
+    let mut dag = DagCircuit::new();
+    for _ in 0..num_rounds {
+        dag.pz(&[3]);
+        dag.pz(&[4]);
+        dag.cx(&[(0, 3)]);
+        dag.cx(&[(1, 3)]);
+        dag.cx(&[(1, 4)]);
+        dag.cx(&[(2, 4)]);
+        dag.mz(&[3]);
+        dag.mz(&[4]);
+    }
+    dag
+}
+
+/// Build influence map with logical Z on all data qubits.
+fn build_influence_map(
+    circuit: &DagCircuit,
+) -> pecos_qec::fault_tolerance::propagator::DagFaultInfluenceMap {
+    InfluenceBuilder::new(circuit).with_z(&[0, 1, 2]).build()
+}
+
+// ============================================================================
+// Test 1: DemSampler::from_influence_map matches DemSampler statistics
+// ============================================================================
+
+#[test]
+fn from_influence_map_produces_reasonable_statistics() {
+    let circuit = repetition_code_circuit(3);
+    let influence_map = build_influence_map(&circuit);
+    let seed = 42u64;
+    let num_shots = 50_000;
+
+    let sampler = DemSamplerBuilder::new(&influence_map)
+        .with_noise(0.001, 0.01, 0.005, 0.001)
+        .raw_measurements()
+        .build()
+        .unwrap();
+    let stats = sampler.sample_statistics(num_shots, seed);
+
+    // At these noise levels, we should see some syndromes. The builder above
+    // uses `with_z`, which creates a tracked Pauli, not an observable, so
+    // logical-error statistics and DEM output columns stay empty.
+    assert!(
+        stats.syndrome_rate() > 0.0,
+        "Should have some syndromes at p~0.001-0.01"
+    );
+    assert!(
+        stats.syndrome_rate() < 1.0,
+        "Should not have syndromes on every shot"
+    );
+    assert_eq!(sampler.num_observables(), 0);
+    assert_eq!(sampler.num_tracked_paulis(), 1);
+    assert_eq!(stats.logical_error_count, 0);
+    assert!(stats.dem_output_counts().is_empty());
+}
+
+// ============================================================================
+// Test 2: MNM path produces valid measurement outcomes
+// ============================================================================
+
+#[test]
+fn raw_sampler_produces_valid_measurement_outcomes() {
+    let circuit = repetition_code_circuit(2);
+    let influence_map = build_influence_map(&circuit);
+
+    let sampler = DemSamplerBuilder::new(&influence_map)
+        .with_noise(0.001, 0.01, 0.005, 0.001)
+        .raw_measurements()
+        .build()
+        .unwrap();
+
+    let mut rng = PecosRng::seed_from_u64(42);
+    let (outcomes, _obs) = sampler.sample(&mut rng);
+
+    assert_eq!(outcomes.len(), influence_map.measurements.len());
+}
+
+// ============================================================================
+// Test 3: Zero noise produces zero syndrome for both paths
+// ============================================================================
+
+#[test]
+fn zero_noise_produces_zero_syndrome_both_paths() {
+    let circuit = repetition_code_circuit(3);
+    let influence_map = build_influence_map(&circuit);
+
+    // DemSampler path
+    let sampler = DemSamplerBuilder::new(&influence_map)
+        .with_uniform_noise(0.0)
+        .raw_measurements()
+        .build()
+        .unwrap();
+    let stats = sampler.sample_statistics(1000, 42);
+    assert_eq!(
+        stats.syndrome_count, 0,
+        "DemSampler: zero noise should give zero syndromes"
+    );
+    assert_eq!(
+        stats.logical_error_count, 0,
+        "DemSampler: zero noise should give zero logical errors"
+    );
+
+    // DemSampler raw mode
+    let unified = DemSamplerBuilder::new(&influence_map)
+        .with_uniform_noise(0.0)
+        .raw_measurements()
+        .build()
+        .unwrap();
+    let raw_stats = unified.sample_statistics(1000, 42);
+    assert_eq!(
+        raw_stats.syndrome_count, 0,
+        "Raw: zero noise should give zero syndromes"
+    );
+}
+
+// ============================================================================
+// Test 4: High noise produces high syndrome rate for both paths
+// ============================================================================
+
+#[test]
+fn high_noise_produces_high_syndrome_rate_both_paths() {
+    let circuit = repetition_code_circuit(2);
+    let influence_map = build_influence_map(&circuit);
+    let num_shots = 10_000;
+    let p = 0.1; // 10% error rate — very noisy
+
+    // DemSampler
+    let sampler = DemSamplerBuilder::new(&influence_map)
+        .with_uniform_noise(p)
+        .raw_measurements()
+        .build()
+        .unwrap();
+    let stats = sampler.sample_statistics(num_shots, 42);
+    assert!(
+        stats.syndrome_rate() > 0.1,
+        "DemSampler: high noise should give high syndrome rate, got {}",
+        stats.syndrome_rate()
+    );
+
+    // DemSampler raw mode
+    let unified = DemSamplerBuilder::new(&influence_map)
+        .with_uniform_noise(p)
+        .raw_measurements()
+        .build()
+        .unwrap();
+    let raw_stats = unified.sample_statistics(num_shots, 42);
+    assert!(
+        raw_stats.syndrome_rate() > 0.1,
+        "Raw: high noise should give high syndrome rate, got {}",
+        raw_stats.syndrome_rate()
+    );
+}
+
+// ============================================================================
+// Test 5: DemSampler detector mode matches DemSamplerBuilder statistics
+// ============================================================================
+
+#[test]
+fn detector_mode_matches_dem_sampler_builder() {
+    let circuit = repetition_code_circuit(3);
+    let influence_map = build_influence_map(&circuit);
+
+    let p1 = 0.001;
+    let p2 = 0.01;
+    let p_meas = 0.005;
+    let p_prep = 0.001;
+    let seed = 42u64;
+    let num_shots = 50_000;
+
+    // Simple detector definitions: each measurement as its own detector
+    let num_meas = influence_map.measurements.len();
+    let detector_records: Vec<Vec<i32>> = (0..num_meas)
+        .map(|i| vec![i32::try_from(i).unwrap()])
+        .collect();
+    let observable_records: Vec<Vec<i32>> = vec![];
+
+    // DemSamplerBuilder path
+    let dem_sampler = DemSamplerBuilder::new(&influence_map)
+        .with_noise(p1, p2, p_meas, p_prep)
+        .with_detector_records(detector_records.clone())
+        .with_observable_records(observable_records.clone())
+        .build()
+        .unwrap();
+    let dem_stats = dem_sampler.sample_statistics(num_shots, seed);
+
+    // DemSampler detector mode
+    let dem_sampler = DemSamplerBuilder::new(&influence_map)
+        .with_noise(p1, p2, p_meas, p_prep)
+        .with_detectors(detector_records, observable_records)
+        .build()
+        .unwrap();
+    let raw_stats = dem_sampler.sample_statistics(num_shots, seed);
+
+    // Same seed, same builder → identical statistics
+    assert_eq!(
+        dem_stats.total_shots, raw_stats.total_shots,
+        "Shot count mismatch"
+    );
+    assert_eq!(
+        dem_stats.syndrome_count, raw_stats.syndrome_count,
+        "Syndrome count mismatch: DEM={}, Unified={}",
+        dem_stats.syndrome_count, raw_stats.syndrome_count
+    );
+    assert_eq!(
+        dem_stats.logical_error_count, raw_stats.logical_error_count,
+        "Logical error count mismatch: DEM={}, Unified={}",
+        dem_stats.logical_error_count, raw_stats.logical_error_count
+    );
+}
+
+// ============================================================================
+// Test 6: DemSampler raw mode matches MNM measurement flip statistics
+// ============================================================================
+
+#[test]
+fn raw_sampler_mode_matches_mnm_per_measurement() {
+    let circuit = repetition_code_circuit(2);
+    let influence_map = build_influence_map(&circuit);
+
+    let p = 0.05; // moderate noise for visible statistics
+    let num_shots = 30_000;
+
+    // DemSampler::from_influence_map path: count per-detector flips
+    let num_meas = influence_map.measurements.len();
+    let dem = DemSamplerBuilder::new(&influence_map)
+        .with_uniform_noise(p)
+        .raw_measurements()
+        .build()
+        .unwrap();
+    let mut dem_flip_counts = vec![0u64; num_meas];
+    let mut rng = PecosRng::seed_from_u64(100);
+    for _ in 0..num_shots {
+        let (outcomes, _) = dem.sample(&mut rng);
+        for (i, &flipped) in outcomes.iter().enumerate() {
+            if flipped {
+                dem_flip_counts[i] += 1;
+            }
+        }
+    }
+
+    // DemSampler raw mode: same exercise
+    let sampler = DemSamplerBuilder::new(&influence_map)
+        .with_uniform_noise(p)
+        .raw_measurements()
+        .build()
+        .unwrap();
+    let mut unified_flip_counts = vec![0u64; num_meas];
+    let mut rng2 = PecosRng::seed_from_u64(200);
+    for _ in 0..num_shots {
+        let (outputs, _) = sampler.sample(&mut rng2);
+        for (i, &flipped) in outputs.iter().enumerate() {
+            if flipped {
+                unified_flip_counts[i] += 1;
+            }
+        }
+    }
+
+    // Compare per-measurement flip rates (different seeds -> statistical comparison)
+    for i in 0..num_meas {
+        // Flip counts are at most num_shots (30,000); precision loss is not a concern.
+        #[allow(clippy::cast_precision_loss)]
+        let dem_rate = dem_flip_counts[i] as f64 / f64::from(num_shots);
+        #[allow(clippy::cast_precision_loss)]
+        let unified_rate = unified_flip_counts[i] as f64 / f64::from(num_shots);
+
+        // Allow generous tolerance since different seeds and non-det coin flips add noise
+        assert!(
+            (dem_rate - unified_rate).abs() < 0.1,
+            "Measurement {i} flip rate differs too much: DEM={dem_rate:.4}, Unified={unified_rate:.4}"
+        );
+    }
+}
+
+// ============================================================================
+// Test 7: DemSampler zero noise + detector mode = zero everything
+// ============================================================================
+
+#[test]
+fn unified_zero_noise_detector_mode() {
+    let circuit = repetition_code_circuit(3);
+    let influence_map = build_influence_map(&circuit);
+
+    let num_meas = influence_map.measurements.len();
+    let detector_records: Vec<Vec<i32>> = (0..num_meas)
+        .map(|i| vec![i32::try_from(i).unwrap()])
+        .collect();
+
+    let sampler = DemSamplerBuilder::new(&influence_map)
+        .with_uniform_noise(0.0)
+        .with_detectors(detector_records, vec![])
+        .build()
+        .unwrap();
+
+    let stats = sampler.sample_statistics(1000, 42);
+    assert_eq!(stats.syndrome_count, 0);
+    assert_eq!(stats.logical_error_count, 0);
+}
+
+// ============================================================================
+// Test 8: DemSampler batch output matches single-shot loop
+// ============================================================================
+
+#[test]
+fn unified_batch_matches_single_shot_loop() {
+    let circuit = repetition_code_circuit(2);
+    let influence_map = build_influence_map(&circuit);
+
+    let sampler = DemSamplerBuilder::new(&influence_map)
+        .with_uniform_noise(0.01)
+        .raw_measurements()
+        .build()
+        .unwrap();
+
+    let num_shots = 100;
+    let seed = 42u64;
+
+    // Single-shot loop
+    let mut rng1 = PecosRng::seed_from_u64(seed);
+    let mut single_outputs = Vec::with_capacity(num_shots);
+    for _ in 0..num_shots {
+        let (out, _) = sampler.sample(&mut rng1);
+        single_outputs.push(out);
+    }
+
+    // Batch
+    let mut rng2 = PecosRng::seed_from_u64(seed);
+    let (batch_outputs, _) = sampler.sample_batch(num_shots, &mut rng2);
+
+    // Should match exactly (same seed, same engine)
+    // Note: non-det coin flips may differ between batch and single if
+    // the rng call order differs. This test verifies the mechanism-driven
+    // part matches. For measurements that are ALL deterministic (no non-det
+    // mask set), they should match exactly.
+    // For now, just check lengths match.
+    assert_eq!(single_outputs.len(), batch_outputs.len());
+    assert_eq!(single_outputs[0].len(), batch_outputs[0].len());
+}
+
+// ============================================================================
+// Test 9: Linearly dependent detectors are rejected
+// ============================================================================
+
+#[test]
+fn linearly_dependent_detectors_rejected() {
+    let circuit = repetition_code_circuit(2);
+    let influence_map = build_influence_map(&circuit);
+
+    // Define 3 detectors where the third is XOR of the first two
+    // D0 = m[0], D1 = m[1], D2 = m[0] XOR m[1] = D0 XOR D1 → linearly dependent
+    let detector_records = vec![vec![0i32], vec![1], vec![0, 1]];
+    let observable_records: Vec<Vec<i32>> = vec![];
+
+    let result = DemSamplerBuilder::new(&influence_map)
+        .with_noise(0.001, 0.01, 0.005, 0.001)
+        .with_detectors(detector_records, observable_records)
+        .build();
+
+    assert!(
+        result.is_err(),
+        "Should reject linearly dependent detector definitions"
+    );
+    if let Err(e) = result {
+        let msg = format!("{e}");
+        assert!(
+            msg.contains("linearly independent"),
+            "Error message should mention linear independence, got: {msg}"
+        );
+    }
+}
+
+// ============================================================================
+// Test 10: Valid independent detectors are accepted
+// ============================================================================
+
+#[test]
+fn linearly_independent_detectors_accepted() {
+    let circuit = repetition_code_circuit(2);
+    let influence_map = build_influence_map(&circuit);
+
+    // Two independent detectors: different single measurements
+    let detector_records = vec![vec![0i32], vec![1]];
+    let observable_records: Vec<Vec<i32>> = vec![];
+
+    let result = DemSamplerBuilder::new(&influence_map)
+        .with_noise(0.001, 0.01, 0.005, 0.001)
+        .with_detectors(detector_records, observable_records)
+        .build();
+
+    assert!(
+        result.is_ok(),
+        "Should accept linearly independent detectors"
+    );
+}
+
+// ============================================================================
+// Test 11: In-circuit annotations → dual-output sampling
+// ============================================================================
+
+#[test]
+fn circuit_annotation_dual_output() {
+    let mut dag = DagCircuit::new();
+
+    // 3 rounds for meaningful round-to-round detectors
+    let mut meas_nodes = Vec::new();
+    for _ in 0..3 {
+        dag.pz(&[3, 4]);
+        dag.cx(&[(0, 3)]);
+        dag.cx(&[(1, 3)]);
+        dag.cx(&[(1, 4)]);
+        dag.cx(&[(2, 4)]);
+        let ms = dag.mz(&[3, 4]);
+        meas_nodes.push((ms[0].node, ms[1].node));
+    }
+
+    // Annotate round-to-round detectors (rounds 1-2 and 2-3)
+    dag.detector(&[meas_nodes[0].0, meas_nodes[1].0]); // q3 r1↔r2
+    dag.detector(&[meas_nodes[0].1, meas_nodes[1].1]); // q4 r1↔r2
+    dag.detector(&[meas_nodes[1].0, meas_nodes[2].0]); // q3 r2↔r3
+    dag.detector(&[meas_nodes[1].1, meas_nodes[2].1]); // q4 r2↔r3
+
+    // Build MEASUREMENT-LEVEL influence map (DagFaultAnalyzer, not InfluenceBuilder)
+    // DagFaultAnalyzer creates one "detector" per raw measurement, so
+    // from_influence_map gives raw-measurement-level output suitable for
+    // user-defined detector XOR.
+    let analyzer = DagFaultAnalyzer::new(&dag);
+    let influence_map = analyzer.build_influence_map();
+
+    // Build sampler from annotations
+    let sampler = DemSamplerBuilder::new(&influence_map)
+        .with_uniform_noise(0.05) // high noise for visible effect
+        .with_circuit_annotations(&dag)
+        .build()
+        .unwrap();
+
+    assert!(sampler.num_mechanisms() > 0, "Should have mechanisms");
+
+    // Sample with dual output
+    let mut rng = PecosRng::seed_from_u64(42);
+    let mut det_fired = 0;
+    let num_shots = 10_000;
+    for _ in 0..num_shots {
+        if let Some(result) = sampler.sample_dual(&mut rng)
+            && result.detector_events.iter().any(|&d| d)
+        {
+            det_fired += 1;
+        }
+    }
+
+    let rate = f64::from(det_fired) / f64::from(num_shots);
+    assert!(rate > 0.01, "Detectors should fire with p=0.05, got {rate}");
+    assert!(
+        rate < 0.99,
+        "Detectors should not fire every shot, got {rate}"
+    );
+}
diff --git a/crates/pecos-qis/src/lib.rs b/crates/pecos-qis/src/lib.rs
index cfe7246f0..44478f886 100644
--- a/crates/pecos-qis/src/lib.rs
+++ b/crates/pecos-qis/src/lib.rs
@@ -102,7 +102,6 @@ pub use engine_builder::{QisEngineBuilder, qis_engine};
 
 pub use program::{
     InterfaceChoice, IntoQisInterface, ProgramType, QisEngineProgram, QisInterfaceBuilder,
-    QisInterfaceProvider,
 };
 
 // ============================================================================
@@ -223,36 +222,3 @@ pub fn selene_soft_rz_engine() -> Result<QisEngineBuilder, RuntimeFetchError> {
         .runtime(selene_soft_rz_runtime()?)
         .interface(helios_interface_builder()))
 }
-/// Setup a QIS control engine for a program file (deprecated)
-///
-/// **Deprecated**: This function is deprecated because it relied on implicit runtime selection.
-/// Use `setup_qis_engine_with_runtime` instead and provide an explicit runtime.
-///
-/// # Parameters
-///
-/// - `program_path`: Path to the QIS program file (.ll or .bc)
-///
-/// # Returns
-///
-/// Returns an error directing users to use the explicit runtime version.
-///
-/// # Errors
-/// Always returns an error directing users to use `setup_qis_engine_with_runtime` instead.
-#[deprecated(
-    since = "0.1.1",
-    note = "Use setup_qis_engine_with_runtime with an explicit runtime instead"
-)]
-pub fn setup_qis_engine(
-    _program_path: &Path,
-) -> Result<Box<dyn ClassicalControlEngine>, PecosError> {
-    Err(PecosError::Processing(
-        "setup_qis_engine is deprecated.\n\
-        \n\
-        Please use setup_qis_engine_with_runtime and provide an explicit runtime:\n\
-        \n\
-        use pecos_qis::{setup_qis_engine_with_runtime, selene_simple_runtime};\n\
-        \n\
-        let engine = setup_qis_engine_with_runtime(path, selene_simple_runtime()?)?;"
-            .to_string(),
-    ))
-}
diff --git a/crates/pecos-qis/src/prelude.rs b/crates/pecos-qis/src/prelude.rs
index 3d3b97056..05adeebe0 100644
--- a/crates/pecos-qis/src/prelude.rs
+++ b/crates/pecos-qis/src/prelude.rs
@@ -19,7 +19,6 @@ pub use crate::engine_builder::{QisEngineBuilder, qis_engine};
 // Program types
 pub use crate::program::{
     InterfaceChoice, IntoQisInterface, ProgramType, QisEngineProgram, QisInterfaceBuilder,
-    QisInterfaceProvider,
 };
 
 // Convenience functions
diff --git a/crates/pecos-qis/src/program.rs b/crates/pecos-qis/src/program.rs
index d01775950..1ef2a6ec9 100644
--- a/crates/pecos-qis/src/program.rs
+++ b/crates/pecos-qis/src/program.rs
@@ -10,8 +10,6 @@
 use pecos_core::errors::PecosError;
 use pecos_programs::{Hugr, Qis};
 use pecos_qis_ffi_types::OperationCollector;
-use std::process::Command;
-use tempfile::NamedTempFile;
 
 /// A trait for types that can be converted into a `QisInterface`
 ///
@@ -39,563 +37,6 @@ pub enum ProgramType {
     HugrBytes,
 }
 
-/// Trait for different `QisInterface` implementation strategies
-///
-/// This allows pluggable compilation strategies - Selene Helios compilation
-/// or other future approaches.
-pub trait QisInterfaceProvider: Send + Sync {
-    /// Get the interface (may involve compilation/linking)
-    ///
-    /// # Errors
-    /// Returns an error if the interface cannot be obtained (e.g., compilation/linking failures).
-    fn get_interface(&mut self) -> Result<OperationCollector, PecosError>;
-
-    /// Get provider type for debugging and logging
-    fn provider_type(&self) -> &'static str;
-
-    /// Check if this provider can handle the given program type
-    fn can_handle(&self, program_type: &ProgramType) -> bool;
-
-    /// Get any metadata about the compilation process
-    fn get_metadata(&self) -> std::collections::BTreeMap<String, String> {
-        std::collections::BTreeMap::new()
-    }
-}
-
-/// Selene Helios-based `QisInterface` provider
-///
-/// This provider uses Selene's Helios compiler to compile QIS bitcode
-/// into optimized quantum programs, then converts the result into a `QisInterface`.
-#[derive(Debug)]
-pub struct QisSeleneHeliosInterface {
-    program_data: Vec<u8>,
-    program_type: ProgramType,
-    metadata: std::collections::BTreeMap<String, String>,
-    helios_config: HeliosConfig,
-}
-
-/// Configuration for Selene Helios compilation
-#[derive(Debug, Clone)]
-pub struct HeliosConfig {
-    /// Optimization level (0-3)
-    pub opt_level: u8,
-    /// Target triple for compilation
-    pub target_triple: String,
-    /// Additional compilation flags
-    pub extra_flags: Vec<String>,
-    /// Path to Selene installation
-    pub selene_path: Option<std::path::PathBuf>,
-}
-
-impl Default for HeliosConfig {
-    fn default() -> Self {
-        Self {
-            opt_level: 2,
-            target_triple: "native".to_string(),
-            extra_flags: Vec::new(),
-            selene_path: None,
-        }
-    }
-}
-
-impl QisSeleneHeliosInterface {
-    /// Create a new Selene Helios interface provider from QIS bitcode
-    #[must_use]
-    pub fn from_bitcode(bitcode: Vec<u8>) -> Self {
-        Self::from_bitcode_with_config(bitcode, HeliosConfig::default())
-    }
-
-    /// Create a new Selene Helios interface provider with custom configuration
-    #[must_use]
-    pub fn from_bitcode_with_config(bitcode: Vec<u8>, config: HeliosConfig) -> Self {
-        let mut metadata = std::collections::BTreeMap::new();
-        metadata.insert("bitcode_size".to_string(), bitcode.len().to_string());
-        metadata.insert(
-            "compilation_strategy".to_string(),
-            "selene_helios".to_string(),
-        );
-        metadata.insert("opt_level".to_string(), config.opt_level.to_string());
-
-        Self {
-            program_data: bitcode,
-            program_type: ProgramType::QisBitcode,
-            metadata,
-            helios_config: config,
-        }
-    }
-
-    /// Create a new Selene Helios interface provider from HUGR bytes
-    #[must_use]
-    pub fn from_hugr_bytes(hugr_bytes: Vec<u8>) -> Self {
-        Self::from_hugr_bytes_with_config(hugr_bytes, HeliosConfig::default())
-    }
-
-    /// Create a new Selene Helios interface provider from HUGR bytes with custom configuration
-    #[must_use]
-    pub fn from_hugr_bytes_with_config(hugr_bytes: Vec<u8>, config: HeliosConfig) -> Self {
-        let mut metadata = std::collections::BTreeMap::new();
-        metadata.insert("hugr_size".to_string(), hugr_bytes.len().to_string());
-        metadata.insert(
-            "compilation_strategy".to_string(),
-            "selene_helios".to_string(),
-        );
-        metadata.insert("opt_level".to_string(), config.opt_level.to_string());
-
-        Self {
-            program_data: hugr_bytes,
-            program_type: ProgramType::HugrBytes,
-            metadata,
-            helios_config: config,
-        }
-    }
-
-    /// Create from LLVM IR text by converting to bitcode
-    #[must_use]
-    pub fn from_llvm_ir(llvm_ir: &str) -> Self {
-        #[cfg(feature = "llvm")]
-        {
-            // Convert LLVM IR text to bitcode using inkwell
-            use inkwell::context::Context;
-            use inkwell::targets::{InitializationConfig, Target};
-
-            // Initialize LLVM targets
-            Target::initialize_native(&InitializationConfig::default()).ok();
-
-            let context = Context::create();
-            let bitcode = match context.create_module_from_ir(
-                inkwell::memory_buffer::MemoryBuffer::create_from_memory_range(
-                    llvm_ir.as_bytes(),
-                    "llvm_ir",
-                ),
-            ) {
-                Ok(module) => {
-                    // Write module to bitcode
-                    module.write_bitcode_to_memory().as_slice().to_vec()
-                }
-                Err(e) => {
-                    log::error!("Failed to convert LLVM IR to bitcode: {e}");
-                    // Store the IR text as-is and let Helios handle it
-                    llvm_ir.as_bytes().to_vec()
-                }
-            };
-
-            let mut interface = Self::from_bitcode(bitcode);
-            interface
-                .metadata
-                .insert("original_format".to_string(), "llvm_ir".to_string());
-            interface
-                .metadata
-                .insert("ir_size".to_string(), llvm_ir.len().to_string());
-            interface
-        }
-
-        #[cfg(not(feature = "llvm"))]
-        {
-            // Without LLVM support, store the IR text as-is and let Helios handle it
-            let mut interface = Self::from_bitcode(llvm_ir.as_bytes().to_vec());
-            interface
-                .metadata
-                .insert("original_format".to_string(), "llvm_ir".to_string());
-            interface
-                .metadata
-                .insert("ir_size".to_string(), llvm_ir.len().to_string());
-            interface
-                .metadata
-                .insert("llvm_conversion".to_string(), "skipped".to_string());
-            interface
-        }
-    }
-
-    /// Compile the program using Selene Helios and convert to `QisInterface`
-    fn compile_with_helios(&mut self) -> Result<OperationCollector, PecosError> {
-        log::info!(
-            "Using Selene Helios compilation strategy for {:?}",
-            self.program_type
-        );
-
-        match self.program_type {
-            ProgramType::QisBitcode => {
-                self.compile_bitcode_with_helios()
-            }
-            ProgramType::HugrBytes => {
-                self.compile_hugr_with_helios()
-            }
-            ProgramType::LlvmIr => {
-                Err(PecosError::Generic(
-                    "Selene Helios interface cannot compile LLVM IR text directly.\n\
-                     \n\
-                     The Helios interface is designed for HUGR bytes and QIS bitcode formats.\n\
-                     For LLVM IR text, please convert to bitcode first or use a different interface.\n\
-                     \n\
-                     This is a deprecated code path - modern PECOS uses Selene for all QIS programs.".to_string()
-                ))
-            }
-        }
-    }
-
-    /// Compile QIS bitcode using Selene Helios
-    fn compile_bitcode_with_helios(&mut self) -> Result<OperationCollector, PecosError> {
-        // Compile bitcode to LLVM IR using Selene Helios
-        let _llvm_ir = self.compile_bitcode_to_llvm_ir()?;
-
-        // This old implementation is deprecated - use QisHeliosInterface instead
-        Err(PecosError::Processing(
-            "QisSeleneHeliosInterface is deprecated. Use pecos_qis::QisHeliosInterface instead."
-                .to_string(),
-        ))
-    }
-
-    /// Compile HUGR bytes using Selene Helios
-    fn compile_hugr_with_helios(&mut self) -> Result<OperationCollector, PecosError> {
-        // Use Selene HUGR compiler (no fallback)
-        let _llvm_ir = compile_hugr_with_selene(&self.program_data)?;
-
-        // This old implementation is deprecated - use QisHeliosInterface instead
-        Err(PecosError::Processing(
-            "QisSeleneHeliosInterface is deprecated. Use pecos_qis::QisHeliosInterface instead."
-                .to_string(),
-        ))
-    }
-
-    /// Compile QIS bitcode to LLVM IR using Selene Helios compiler
-    fn compile_bitcode_to_llvm_ir(&mut self) -> Result<String, PecosError> {
-        use std::io::Write;
-        use tempfile::NamedTempFile;
-
-        // Write bitcode to a temporary file
-        let mut bitcode_file = NamedTempFile::new()
-            .map_err(|e| PecosError::Generic(format!("Failed to create temp file: {e}")))?;
-        bitcode_file
-            .write_all(&self.program_data)
-            .map_err(|e| PecosError::Generic(format!("Failed to write bitcode: {e}")))?;
-
-        // Try multiple strategies to find and use Selene Helios
-        self.try_selene_helios_compilation(&bitcode_file)
-    }
-
-    /// Try different strategies for Selene Helios compilation
-    fn try_selene_helios_compilation(
-        &mut self,
-        bitcode_file: &NamedTempFile,
-    ) -> Result<String, PecosError> {
-        let strategy_names = [
-            "Custom Path",
-            "Environment Variable",
-            "Standard Locations",
-            "Conda Environment",
-            "System Installation",
-        ];
-
-        let strategies = [
-            self.try_custom_selene_path(bitcode_file),
-            self.try_env_selene_path(bitcode_file),
-            self.try_standard_selene_locations(bitcode_file),
-            self.try_conda_selene(bitcode_file),
-            self.try_system_selene(bitcode_file),
-        ];
-
-        for (strategy_name, result) in strategy_names.iter().zip(strategies.iter()) {
-            match result {
-                Ok(llvm_ir) => {
-                    log::info!("Selene Helios compilation succeeded using: {strategy_name}");
-                    self.metadata
-                        .insert("helios_strategy".to_string(), (*strategy_name).to_string());
-                    self.metadata
-                        .insert("helios_compilation".to_string(), "success".to_string());
-                    self.metadata
-                        .insert("llvm_ir_size".to_string(), llvm_ir.len().to_string());
-                    return Ok(llvm_ir.clone());
-                }
-                Err(e) => {
-                    log::debug!("Selene Helios strategy '{strategy_name}' failed: {e}");
-                    self.metadata.insert(
-                        format!(
-                            "helios_strategy_{}_error",
-                            strategy_name.to_lowercase().replace(' ', "_")
-                        ),
-                        e.to_string(),
-                    );
-                }
-            }
-        }
-
-        // If all strategies fail, provide helpful error message
-        Err(PecosError::Generic(format!(
-            "Selene Helios compilation failed. Unable to find Selene installation after trying: {}. \n\
-             \n\
-             To use Selene Helios interface, you need to:\n\
-             1. Install Selene (https://github.com/Quantinuum/selene)\n\
-             2. Set SELENE_PATH environment variable to the Selene directory\n\
-             \n\
-             Selene is the only supported interface for QIS programs in modern PECOS.",
-            strategy_names.join(", ")
-        )))
-    }
-
-    /// Try compilation using user-provided Selene path
-    fn try_custom_selene_path(&self, bitcode_file: &NamedTempFile) -> Result<String, PecosError> {
-        let selene_path = self
-            .helios_config
-            .selene_path
-            .as_ref()
-            .ok_or_else(|| PecosError::Generic("No custom Selene path provided".to_string()))?;
-
-        self.run_selene_helios_compiler(selene_path, bitcode_file)
-    }
-
-    /// Try compilation using `SELENE_PATH` environment variable
-    fn try_env_selene_path(&self, bitcode_file: &NamedTempFile) -> Result<String, PecosError> {
-        let selene_path = std::env::var("SELENE_PATH")
-            .map_err(|_| PecosError::Generic("SELENE_PATH not set".to_string()))?;
-
-        let path = std::path::PathBuf::from(selene_path);
-        self.run_selene_helios_compiler(&path, bitcode_file)
-    }
-
-    /// Try compilation using standard Selene installation locations
-    fn try_standard_selene_locations(
-        &self,
-        bitcode_file: &NamedTempFile,
-    ) -> Result<String, PecosError> {
-        let standard_paths = [
-            "/home/ciaranra/Repos/cl_projects/gup/selene",
-            "/opt/selene",
-            "/usr/local/selene",
-            "~/selene",
-            "./selene",
-            "../selene",
-        ];
-
-        for path_str in &standard_paths {
-            let path = std::path::PathBuf::from(path_str);
-            if path.exists() && path.join("selene-compilers/helios/python").exists() {
-                log::debug!("Found Selene at standard location: {}", path.display());
-                return self.run_selene_helios_compiler(&path, bitcode_file);
-            }
-        }
-
-        Err(PecosError::Generic(
-            "No Selene found in standard locations".to_string(),
-        ))
-    }
-
-    /// Try compilation using conda environment
-    fn try_conda_selene(&self, bitcode_file: &NamedTempFile) -> Result<String, PecosError> {
-        // Check if we're in a conda environment with Selene
-        let python_script = r"
-import sys
-try:
-    import selene_helios_compiler
-    print(selene_helios_compiler.__file__)
-except ImportError:
-    sys.exit(1)
-"
-        .to_string();
-
-        let output = Command::new("python3")
-            .arg("-c")
-            .arg(&python_script)
-            .output()
-            .map_err(|e| PecosError::Generic(format!("Failed to check conda Selene: {e}")))?;
-
-        if !output.status.success() {
-            return Err(PecosError::Generic(
-                "Selene not available in conda environment".to_string(),
-            ));
-        }
-
-        // Run compilation directly using available Python module
-        self.run_conda_selene_compilation(bitcode_file)
-    }
-
-    /// Try compilation using system-installed Selene
-    fn try_system_selene(&self, bitcode_file: &NamedTempFile) -> Result<String, PecosError> {
-        // Check if selene-helios command is available in PATH
-        let output = Command::new("which")
-            .arg("selene-helios")
-            .output()
-            .map_err(|_| PecosError::Generic("selene-helios not in PATH".to_string()))?;
-
-        if !output.status.success() {
-            return Err(PecosError::Generic(
-                "selene-helios command not found".to_string(),
-            ));
-        }
-
-        // Use command-line tool
-        self.run_system_selene_compilation(bitcode_file)
-    }
-
-    /// Run Selene Helios compiler from a specific path
-    fn run_selene_helios_compiler(
-        &self,
-        selene_path: &std::path::Path,
-        bitcode_file: &NamedTempFile,
-    ) -> Result<String, PecosError> {
-        let helios_python_path = selene_path.join("selene-compilers/helios/python");
-
-        if !helios_python_path.exists() {
-            return Err(PecosError::Generic(format!(
-                "Selene Helios Python path not found: {}",
-                helios_python_path.display()
-            )));
-        }
-
-        let python_script = format!(
-            r#"
-import sys
-sys.path.insert(0, '{helios_python_path}')
-
-try:
-    from selene_helios_compiler import compile_bitcode_to_llvm_ir
-except ImportError as e:
-    print(f"Failed to import Selene Helios compiler: {{e}}", file=sys.stderr)
-    sys.exit(1)
-
-try:
-    with open('{bitcode_path}', 'rb') as f:
-        bitcode = f.read()
-
-    llvm_ir = compile_bitcode_to_llvm_ir(
-        bitcode,
-        opt_level={opt_level},
-        target_triple='{target_triple}'
-    )
-    print(llvm_ir)
-except Exception as e:
-    print(f"Compilation failed: {{e}}", file=sys.stderr)
-    sys.exit(1)
-"#,
-            helios_python_path = helios_python_path.display(),
-            bitcode_path = bitcode_file.path().display(),
-            opt_level = self.helios_config.opt_level,
-            target_triple = self.helios_config.target_triple
-        );
-
-        let output = Command::new("python3")
-            .arg("-c")
-            .arg(&python_script)
-            .output()
-            .map_err(|e| PecosError::Generic(format!("Failed to run Selene Helios: {e}")))?;
-
-        if !output.status.success() {
-            let stderr = String::from_utf8_lossy(&output.stderr);
-            return Err(PecosError::Generic(format!(
-                "Selene Helios compilation failed: {stderr}"
-            )));
-        }
-
-        let llvm_ir = String::from_utf8(output.stdout)
-            .map_err(|e| PecosError::Generic(format!("Invalid UTF-8 output: {e}")))?;
-
-        log::debug!(
-            "Successfully compiled bitcode using Selene Helios from: {}",
-            selene_path.display()
-        );
-        Ok(llvm_ir.trim().to_string())
-    }
-
-    /// Run Selene Helios compilation using conda environment
-    fn run_conda_selene_compilation(
-        &self,
-        bitcode_file: &NamedTempFile,
-    ) -> Result<String, PecosError> {
-        let python_script = format!(
-            r#"
-import selene_helios_compiler
-
-try:
-    with open('{bitcode_path}', 'rb') as f:
-        bitcode = f.read()
-
-    llvm_ir = selene_helios_compiler.compile_bitcode_to_llvm_ir(
-        bitcode,
-        opt_level={opt_level},
-        target_triple='{target_triple}'
-    )
-    print(llvm_ir)
-except Exception as e:
-    import sys
-    print(f"Conda Selene compilation failed: {{e}}", file=sys.stderr)
-    sys.exit(1)
-"#,
-            bitcode_path = bitcode_file.path().display(),
-            opt_level = self.helios_config.opt_level,
-            target_triple = self.helios_config.target_triple
-        );
-
-        let output = Command::new("python3")
-            .arg("-c")
-            .arg(&python_script)
-            .output()
-            .map_err(|e| PecosError::Generic(format!("Failed to run conda Selene: {e}")))?;
-
-        if !output.status.success() {
-            let stderr = String::from_utf8_lossy(&output.stderr);
-            return Err(PecosError::Generic(format!(
-                "Conda Selene compilation failed: {stderr}"
-            )));
-        }
-
-        let llvm_ir = String::from_utf8(output.stdout)
-            .map_err(|e| PecosError::Generic(format!("Invalid UTF-8 output: {e}")))?;
-
-        Ok(llvm_ir.trim().to_string())
-    }
-
-    /// Run Selene Helios compilation using system command
-    fn run_system_selene_compilation(
-        &self,
-        bitcode_file: &NamedTempFile,
-    ) -> Result<String, PecosError> {
-        let output = Command::new("selene-helios")
-            .arg("compile")
-            .arg("--input")
-            .arg(bitcode_file.path())
-            .arg("--output-format")
-            .arg("llvm-ir")
-            .arg("--opt-level")
-            .arg(self.helios_config.opt_level.to_string())
-            .arg("--target-triple")
-            .arg(&self.helios_config.target_triple)
-            .output()
-            .map_err(|e| PecosError::Generic(format!("Failed to run system Selene: {e}")))?;
-
-        if !output.status.success() {
-            let stderr = String::from_utf8_lossy(&output.stderr);
-            return Err(PecosError::Generic(format!(
-                "System Selene compilation failed: {stderr}"
-            )));
-        }
-
-        let llvm_ir = String::from_utf8(output.stdout)
-            .map_err(|e| PecosError::Generic(format!("Invalid UTF-8 output: {e}")))?;
-
-        Ok(llvm_ir.trim().to_string())
-    }
-}
-
-impl QisInterfaceProvider for QisSeleneHeliosInterface {
-    fn get_interface(&mut self) -> Result<OperationCollector, PecosError> {
-        self.compile_with_helios()
-    }
-
-    fn provider_type(&self) -> &'static str {
-        "Selene Helios"
-    }
-
-    fn can_handle(&self, program_type: &ProgramType) -> bool {
-        matches!(
-            program_type,
-            ProgramType::QisBitcode | ProgramType::HugrBytes
-        )
-    }
-
-    fn get_metadata(&self) -> std::collections::BTreeMap<String, String> {
-        self.metadata.clone()
-    }
-}
-
 /// Implement `IntoQisInterface` for `OperationCollector` itself (identity conversion)
 impl IntoQisInterface for OperationCollector {
     fn into_qis_interface(self) -> Result<OperationCollector, PecosError> {
@@ -811,70 +252,3 @@ impl From<OperationCollector> for QisEngineProgram {
 
 // Tests for program conversion require actual interface implementations
 // and are in the integration test files.
-
-/// Compile HUGR bytes using Selene's compiler
-///
-/// This uses Selene's proven HUGR→LLVM compiler, ensuring proper qubit ID
-/// management and QIS function generation. Returns explicit error if Selene is not available.
-fn compile_hugr_with_selene(hugr_bytes: &[u8]) -> Result<String, PecosError> {
-    log::info!("Compiling HUGR with Selene compiler (required)");
-
-    // Use Selene's Python compiler - no fallbacks
-    compile_hugr_with_selene_python(hugr_bytes).map_err(|e| {
-        PecosError::Generic(format!(
-            "Selene Helios compilation failed: {e}\n\n\
-                To use Helios interface, ensure Selene is installed and available:\n\
-                1. Ensure Selene repository is at ../selene or ../../../selene\n\
-                2. Build Selene compilers: 'cargo build --release' in Selene directory\n\
-                \n\
-                Selene is the only supported interface for QIS programs."
-        ))
-    })
-}
-
-/// Compile HUGR using Selene's Python compiler
-fn compile_hugr_with_selene_python(hugr_bytes: &[u8]) -> Result<String, PecosError> {
-    use std::io::Write;
-    use tempfile::NamedTempFile;
-
-    // Write HUGR bytes to a temporary file
-    let mut hugr_file = NamedTempFile::new()
-        .map_err(|e| PecosError::Generic(format!("Failed to create temp file: {e}")))?;
-    hugr_file
-        .write_all(hugr_bytes)
-        .map_err(|e| PecosError::Generic(format!("Failed to write HUGR bytes: {e}")))?;
-
-    // Call Selene's compiler using Python
-    let output = Command::new("python3")
-        .arg("-c")
-        .arg(format!(
-            r"
-import sys
-sys.path.insert(0, '{}/selene-compilers/hugr_qis/python')
-from selene_hugr_qis_compiler import compile_to_llvm_ir
-
-with open('{}', 'rb') as f:
-    hugr_bytes = f.read()
-
-llvm_ir = compile_to_llvm_ir(hugr_bytes, opt_level=2, target_triple='native')
-print(llvm_ir)
-",
-            "/home/ciaranra/Repos/cl_projects/gup/selene",
-            hugr_file.path().display()
-        ))
-        .output()
-        .map_err(|e| PecosError::Generic(format!("Failed to run Selene compiler: {e}")))?;
-
-    if !output.status.success() {
-        let stderr = String::from_utf8_lossy(&output.stderr);
-        return Err(PecosError::Generic(format!(
-            "Selene compiler failed: {stderr}"
-        )));
-    }
-
-    let llvm_ir = String::from_utf8(output.stdout)
-        .map_err(|e| PecosError::Generic(format!("Invalid UTF-8 output: {e}")))?;
-
-    log::debug!("Successfully compiled HUGR using Selene compiler");
-    Ok(llvm_ir)
-}
diff --git a/crates/pecos-quantum/Cargo.toml b/crates/pecos-quantum/Cargo.toml
index e34b23dc4..cd17ac25f 100644
--- a/crates/pecos-quantum/Cargo.toml
+++ b/crates/pecos-quantum/Cargo.toml
@@ -14,8 +14,10 @@ readme = "README.md"
 [dependencies]
 pecos-core.workspace = true
 pecos-num.workspace = true
+pecos-random.workspace = true
 nalgebra.workspace = true
 num-complex.workspace = true
+serde_json.workspace = true
 smallvec.workspace = true
 tket = { workspace = true, optional = true }
 log.workspace = true
diff --git a/crates/pecos-quantum/examples/style_demo.rs b/crates/pecos-quantum/examples/style_demo.rs
index c3e1b79f7..64703f4cf 100644
--- a/crates/pecos-quantum/examples/style_demo.rs
+++ b/crates/pecos-quantum/examples/style_demo.rs
@@ -482,7 +482,7 @@ fn main() {
     // -- UnitaryRep example --
     html.push_str("<h2>UnitaryRep Algebra</h2>\n");
     {
-        use pecos_core::unitary_rep::{CX, H, T};
+        use pecos_core::unitary::{CX, H, T};
         let circuit = T(1) * CX(0, 1) * H(0);
         let op_renderer = circuit.render_with(2, &default_style);
         write!(
diff --git a/crates/pecos-quantum/src/channel.rs b/crates/pecos-quantum/src/channel.rs
new file mode 100644
index 000000000..430256286
--- /dev/null
+++ b/crates/pecos-quantum/src/channel.rs
@@ -0,0 +1,4585 @@
+// Copyright 2026 The PECOS Developers
+//
+// Licensed under the Apache License, Version 2.0 (the "License"); you may not use this file except
+// in compliance with the License. You may obtain a copy of the License at
+//
+//     https://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software distributed under the License
+// is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express
+// or implied. See the License for the specific language governing permissions and limitations under
+// the License.
+
+//! Sparse Pauli-basis channel and operator representations.
+//!
+//! This module keeps three related representations separate:
+//! - [`PauliSum`] stores arbitrary complex coefficients on Pauli operators.
+//! - [`PauliChannel`] stores real Pauli error probabilities.
+//! - [`DiagonalPtm`] stores real diagonal Pauli-transfer-matrix entries, also
+//!   called Pauli fidelities for Pauli channels.
+//! - [`Ptm`] stores a dense real Pauli-transfer matrix.
+//! - [`KrausOps`] stores a concrete Kraus-operator channel representation.
+//! - [`ChoiMatrix`] stores a concrete Choi representation.
+//! - [`SuperOp`] stores a dense column-stacked superoperator.
+//! - [`ChiMatrix`] stores a process matrix in the Pauli basis.
+//! - [`Stinespring`] stores a Stinespring isometry.
+//!
+//! Pauli-channel probabilities and diagonal PTM entries are connected by an
+//! explicit Walsh-Hadamard transform. They are not the same representation:
+//! probabilities are non-negative and sum to one, while diagonal PTM entries
+//! may be negative.
+
+use std::collections::{BTreeMap, BTreeSet};
+use std::error::Error;
+use std::f64::consts::TAU;
+use std::fmt;
+use std::ops::{Add, Mul};
+
+use nalgebra::{DMatrix, SVD};
+use num_complex::Complex64;
+use pecos_core::{
+    BitmaskStorage, ChannelExpr, Clifford, Pauli, PauliBitmaskSmall, PauliString, Phase as _,
+    UnitaryRep,
+};
+use pecos_random::{Rng, RngExt as _};
+
+use crate::unitary_matrix::to_matrix_with_size;
+
+const DEFAULT_TOLERANCE: f64 = 1e-12;
+
+/// Pauli basis ordering used by channel representations.
+///
+/// The current PECOS channel basis uses lexicographic Pauli digits with
+/// `I=0`, `X=1`, `Y=2`, `Z=3`, and qubit 0 as the least-significant base-4
+/// digit. For two qubits, labels displayed from high qubit to low qubit are:
+/// `II, IX, IY, IZ, XI, XX, XY, XZ, ...`.
+#[derive(Debug, Clone, Copy, PartialEq, Eq, Hash, Default)]
+pub enum PtmBasisOrder {
+    /// Lexicographic Pauli basis with qubit 0 as the fastest-varying digit.
+    #[default]
+    LexicographicLittleEndian,
+}
+
+/// Error returned by channel representation constructors and conversions.
+#[derive(Debug, Clone, PartialEq)]
+pub enum ChannelError {
+    /// The requested number of qubits would overflow a `usize` dimension.
+    DimensionOverflow {
+        /// Number of qubits supplied by the caller.
+        num_qubits: usize,
+    },
+    /// A value was not a valid Pauli basis digit.
+    InvalidBasisDigit {
+        /// Invalid digit.
+        digit: usize,
+    },
+    /// A Pauli-basis index is outside the basis for the requested qubit count.
+    BasisIndexOutOfRange {
+        /// Number of qubits supplied by the caller.
+        num_qubits: usize,
+        /// Basis length for that qubit count.
+        basis_len: usize,
+        /// Invalid index.
+        index: usize,
+    },
+    /// A Pauli term acts outside the declared qubit range.
+    QubitOutOfRange {
+        /// Number of qubits supplied by the caller.
+        num_qubits: usize,
+        /// Highest qubit touched by the offending Pauli term.
+        qubit: usize,
+    },
+    /// Two channel objects act on different numbers of qubits.
+    QubitCountMismatch {
+        /// Expected qubit count.
+        expected: usize,
+        /// Actual qubit count.
+        actual: usize,
+    },
+    /// A coefficient or fidelity is not finite.
+    InvalidCoefficient {
+        /// Offending coefficient.
+        value: Complex64,
+    },
+    /// A `PauliSum` coefficient was not real enough for a probability.
+    NonRealCoefficient {
+        /// Offending coefficient.
+        value: Complex64,
+        /// Allowed imaginary-part tolerance.
+        tolerance: f64,
+    },
+    /// A probability value is invalid for a Pauli channel.
+    InvalidProbability {
+        /// Probability value.
+        value: f64,
+        /// Allowed negative tolerance.
+        tolerance: f64,
+    },
+    /// A probability map does not sum to one within tolerance.
+    ProbabilitySum {
+        /// Observed probability sum.
+        sum: f64,
+        /// Allowed absolute tolerance.
+        tolerance: f64,
+    },
+    /// A dense matrix does not match the expected channel or density-matrix
+    /// shape.
+    InvalidMatrixShape {
+        /// Expected row count.
+        expected_rows: usize,
+        /// Expected column count.
+        expected_cols: usize,
+        /// Actual row count.
+        rows: usize,
+        /// Actual column count.
+        cols: usize,
+    },
+    /// A Kraus channel was constructed without any Kraus operators.
+    EmptyKrausSet,
+    /// A numerical matrix decomposition failed.
+    DecompositionFailed {
+        /// Human-readable reason.
+        reason: String,
+    },
+    /// A channel expression is outside the supported conversion subset.
+    UnsupportedChannelExpr {
+        /// Human-readable reason.
+        reason: String,
+    },
+    /// A repeated subsystem was supplied.
+    DuplicateSubsystem {
+        /// Repeated qubit/subsystem index.
+        qubit: usize,
+    },
+    /// A tomography reconstruction had the wrong number of basis samples.
+    InvalidTomographySampleCount {
+        /// Expected number of operator-basis outputs.
+        expected: usize,
+        /// Actual number of supplied outputs.
+        actual: usize,
+    },
+    /// A tomography input index is outside the experiment design.
+    TomographyInputOutOfRange {
+        /// Number of tomography inputs in the design.
+        num_inputs: usize,
+        /// Invalid input index.
+        index: usize,
+    },
+    /// A computational matrix-unit row/column is outside the Hilbert space.
+    MatrixUnitOutOfRange {
+        /// Hilbert-space dimension.
+        dim: usize,
+        /// Invalid row.
+        row: usize,
+        /// Invalid column.
+        col: usize,
+    },
+}
+
+impl fmt::Display for ChannelError {
+    fn fmt(&self, f: &mut fmt::Formatter<'_>) -> fmt::Result {
+        match self {
+            Self::DimensionOverflow { num_qubits } => write!(
+                f,
+                "Pauli-basis dimension overflows usize for {num_qubits} qubits"
+            ),
+            Self::InvalidBasisDigit { digit } => write!(f, "invalid Pauli basis digit: {digit}"),
+            Self::BasisIndexOutOfRange {
+                num_qubits,
+                basis_len,
+                index,
+            } => write!(
+                f,
+                "Pauli-basis index {index} is outside the {basis_len}-element basis for {num_qubits} qubits"
+            ),
+            Self::QubitOutOfRange { num_qubits, qubit } => write!(
+                f,
+                "Pauli term touches qubit {qubit}, outside declared {num_qubits}-qubit range"
+            ),
+            Self::QubitCountMismatch { expected, actual } => write!(
+                f,
+                "channel qubit count mismatch: expected {expected}, got {actual}"
+            ),
+            Self::InvalidCoefficient { value } => {
+                write!(f, "invalid non-finite coefficient: {value}")
+            }
+            Self::NonRealCoefficient { value, tolerance } => write!(
+                f,
+                "coefficient {value} is not real within tolerance {tolerance}"
+            ),
+            Self::InvalidProbability { value, tolerance } => write!(
+                f,
+                "invalid Pauli-channel probability {value}; tolerance is {tolerance}"
+            ),
+            Self::ProbabilitySum { sum, tolerance } => write!(
+                f,
+                "Pauli-channel probabilities must sum to 1 within tolerance {tolerance}, got {sum}"
+            ),
+            Self::InvalidMatrixShape {
+                expected_rows,
+                expected_cols,
+                rows,
+                cols,
+            } => write!(
+                f,
+                "invalid matrix shape {rows}x{cols}; expected {expected_rows}x{expected_cols}"
+            ),
+            Self::EmptyKrausSet => write!(f, "Kraus channel must contain at least one operator"),
+            Self::DecompositionFailed { reason } => {
+                write!(f, "matrix decomposition failed: {reason}")
+            }
+            Self::UnsupportedChannelExpr { reason } => {
+                write!(f, "unsupported channel expression: {reason}")
+            }
+            Self::DuplicateSubsystem { qubit } => {
+                write!(f, "duplicate subsystem/qubit index: {qubit}")
+            }
+            Self::InvalidTomographySampleCount { expected, actual } => write!(
+                f,
+                "invalid tomography sample count {actual}; expected {expected} operator-basis outputs"
+            ),
+            Self::TomographyInputOutOfRange { num_inputs, index } => write!(
+                f,
+                "tomography input index {index} is outside the {num_inputs}-input design"
+            ),
+            Self::MatrixUnitOutOfRange { dim, row, col } => write!(
+                f,
+                "matrix unit |{row}><{col}| is outside the {dim}-dimensional Hilbert space"
+            ),
+        }
+    }
+}
+
+impl Error for ChannelError {}
+
+/// Returns the number of Pauli basis elements for `num_qubits`.
+///
+/// This is `4^num_qubits`.
+///
+/// # Errors
+///
+/// Returns [`ChannelError::DimensionOverflow`] when `4^num_qubits` does not
+/// fit in `usize`.
+pub fn pauli_basis_len(num_qubits: usize) -> Result<usize, ChannelError> {
+    4usize
+        .checked_pow(
+            num_qubits
+                .try_into()
+                .map_err(|_| ChannelError::DimensionOverflow { num_qubits })?,
+        )
+        .ok_or(ChannelError::DimensionOverflow { num_qubits })
+}
+
+/// Maps a Pauli value to the channel-basis digit `I=0, X=1, Y=2, Z=3`.
+///
+/// This intentionally differs from the internal [`Pauli`] discriminant order,
+/// where `Z` and `Y` are stored in bitmask-friendly order.
+#[must_use]
+pub fn pauli_to_basis_digit(pauli: Pauli) -> usize {
+    match pauli {
+        Pauli::I => 0,
+        Pauli::X => 1,
+        Pauli::Y => 2,
+        Pauli::Z => 3,
+    }
+}
+
+/// Converts a channel-basis digit to a Pauli value.
+///
+/// # Errors
+///
+/// Returns [`ChannelError::InvalidBasisDigit`] when `digit` is not in `0..4`.
+pub fn basis_digit_to_pauli(digit: usize) -> Result<Pauli, ChannelError> {
+    match digit {
+        0 => Ok(Pauli::I),
+        1 => Ok(Pauli::X),
+        2 => Ok(Pauli::Y),
+        3 => Ok(Pauli::Z),
+        _ => Err(ChannelError::InvalidBasisDigit { digit }),
+    }
+}
+
+/// Returns the Pauli basis element at `index`.
+///
+/// The returned vector is indexed by qubit number: element 0 is the Pauli on
+/// qubit 0. Qubit 0 is the fastest-varying base-4 digit.
+///
+/// # Errors
+///
+/// Returns an error when `4^num_qubits` overflows or `index` is outside the
+/// basis.
+pub fn basis_element(num_qubits: usize, index: usize) -> Result<Vec<Pauli>, ChannelError> {
+    let basis_len = pauli_basis_len(num_qubits)?;
+    if index >= basis_len {
+        return Err(ChannelError::BasisIndexOutOfRange {
+            num_qubits,
+            basis_len,
+            index,
+        });
+    }
+
+    let mut remaining = index;
+    let mut paulis = Vec::with_capacity(num_qubits);
+    for _ in 0..num_qubits {
+        paulis.push(basis_digit_to_pauli(remaining & 0b11)?);
+        remaining >>= 2;
+    }
+    Ok(paulis)
+}
+
+/// Returns a display label for a Pauli basis element.
+///
+/// Labels are printed with the highest-numbered qubit first, matching common
+/// ket-label display style. For example, basis index 1 on two qubits is `IX`
+/// because it is identity on qubit 1 and X on qubit 0.
+///
+/// # Errors
+///
+/// Returns an error when `4^num_qubits` overflows or `index` is outside the
+/// basis.
+pub fn basis_label(num_qubits: usize, index: usize) -> Result<String, ChannelError> {
+    let paulis = basis_element(num_qubits, index)?;
+    Ok(paulis
+        .iter()
+        .rev()
+        .map(|pauli| match pauli {
+            Pauli::I => 'I',
+            Pauli::X => 'X',
+            Pauli::Y => 'Y',
+            Pauli::Z => 'Z',
+        })
+        .collect())
+}
+
+/// Returns the Pauli bitmask basis element at `index`.
+///
+/// # Errors
+///
+/// Returns an error when `4^num_qubits` overflows or `index` is outside the
+/// basis.
+pub fn basis_bitmask(num_qubits: usize, index: usize) -> Result<PauliBitmaskSmall, ChannelError> {
+    let paulis = basis_element(num_qubits, index)?;
+    Ok(bitmask_from_paulis(&paulis))
+}
+
+/// Returns the Pauli-basis index for a bitmask in the canonical ordering.
+///
+/// # Errors
+///
+/// Returns [`ChannelError::QubitOutOfRange`] when the bitmask touches a qubit
+/// outside `0..num_qubits`.
+pub fn basis_index(num_qubits: usize, pauli: &PauliBitmaskSmall) -> Result<usize, ChannelError> {
+    pauli_basis_len(num_qubits)?;
+    validate_num_qubits(num_qubits, pauli)?;
+    let mut index = 0usize;
+    for qubit in 0..num_qubits {
+        let digit = match (pauli.has_x(qubit), pauli.has_z(qubit)) {
+            (false, false) => 0,
+            (true, false) => 1,
+            (true, true) => 2,
+            (false, true) => 3,
+        };
+        index += digit << (2 * qubit);
+    }
+    Ok(index)
+}
+
+/// Returns the canonical display label for a bitmask.
+///
+/// # Errors
+///
+/// Returns [`ChannelError::QubitOutOfRange`] when the bitmask touches a qubit
+/// outside `0..num_qubits`.
+pub fn bitmask_label(num_qubits: usize, pauli: &PauliBitmaskSmall) -> Result<String, ChannelError> {
+    basis_label(num_qubits, basis_index(num_qubits, pauli)?)
+}
+
+/// Converts a [`PauliString`] into the phase-free bitmask used by channel
+/// representations.
+///
+/// # Errors
+///
+/// Returns [`ChannelError::QubitOutOfRange`] when the Pauli string touches a
+/// qubit outside `0..num_qubits`.
+pub fn pauli_string_to_bitmask(
+    num_qubits: usize,
+    pauli: &PauliString,
+) -> Result<PauliBitmaskSmall, ChannelError> {
+    let mut out = PauliBitmaskSmall::identity();
+    for (p, q) in pauli.iter_pairs() {
+        let q = q.index();
+        if q >= num_qubits {
+            return Err(ChannelError::QubitOutOfRange {
+                num_qubits,
+                qubit: q,
+            });
+        }
+        match p {
+            Pauli::I => {}
+            Pauli::X => out.x_bits.set_bit(q),
+            Pauli::Y => {
+                out.x_bits.set_bit(q);
+                out.z_bits.set_bit(q);
+            }
+            Pauli::Z => out.z_bits.set_bit(q),
+        }
+    }
+    Ok(out)
+}
+
+/// Sparse complex sum of Pauli operators.
+#[derive(Clone, Debug, PartialEq)]
+pub struct PauliSum {
+    num_qubits: usize,
+    terms: BTreeMap<PauliBitmaskSmall, Complex64>,
+}
+
+impl PauliSum {
+    /// Constructs an empty Pauli sum over `num_qubits`.
+    #[must_use]
+    pub fn new(num_qubits: usize) -> Self {
+        Self {
+            num_qubits,
+            terms: BTreeMap::new(),
+        }
+    }
+
+    /// Constructs a Pauli sum after validating term qubit ranges and
+    /// simplifying near-zero coefficients.
+    ///
+    /// # Errors
+    ///
+    /// Returns an error when any term touches a qubit outside `0..num_qubits`
+    /// or any coefficient is not finite.
+    pub fn try_new(
+        num_qubits: usize,
+        terms: BTreeMap<PauliBitmaskSmall, Complex64>,
+    ) -> Result<Self, ChannelError> {
+        Self::try_new_with_tolerance(num_qubits, terms, DEFAULT_TOLERANCE)
+    }
+
+    /// Constructs a Pauli sum with an explicit zero-dropping tolerance.
+    ///
+    /// # Errors
+    ///
+    /// Returns an error when any term touches a qubit outside `0..num_qubits`
+    /// or any coefficient is not finite.
+    pub fn try_new_with_tolerance(
+        num_qubits: usize,
+        terms: BTreeMap<PauliBitmaskSmall, Complex64>,
+        tolerance: f64,
+    ) -> Result<Self, ChannelError> {
+        let mut out = Self::new(num_qubits);
+        for (pauli, coefficient) in terms {
+            out.add_term_with_tolerance(pauli, coefficient, tolerance)?;
+        }
+        Ok(out)
+    }
+
+    /// Constructs a Pauli sum containing one [`PauliString`].
+    ///
+    /// The `PauliString` phase becomes the complex coefficient. The stored
+    /// Pauli label itself is phase-free.
+    ///
+    /// # Errors
+    ///
+    /// Returns an error when `pauli` touches a qubit outside `0..num_qubits`.
+    pub fn from_pauli_string(num_qubits: usize, pauli: &PauliString) -> Result<Self, ChannelError> {
+        let label = pauli_string_to_bitmask(num_qubits, pauli)?;
+        let coefficient = pauli.phase().to_complex();
+        let mut terms = BTreeMap::new();
+        terms.insert(label, coefficient);
+        Self::try_new(num_qubits, terms)
+    }
+
+    /// Returns the number of qubits represented by this sum.
+    #[must_use]
+    pub fn num_qubits(&self) -> usize {
+        self.num_qubits
+    }
+
+    /// Returns the sparse Pauli terms and complex coefficients.
+    #[must_use]
+    pub fn terms(&self) -> &BTreeMap<PauliBitmaskSmall, Complex64> {
+        &self.terms
+    }
+
+    /// Adds one term, merging with an existing coefficient if needed.
+    ///
+    /// # Errors
+    ///
+    /// Returns an error when `pauli` touches a qubit outside
+    /// `0..self.num_qubits` or `coefficient` is not finite.
+    pub fn add_term(
+        &mut self,
+        pauli: PauliBitmaskSmall,
+        coefficient: Complex64,
+    ) -> Result<(), ChannelError> {
+        self.add_term_with_tolerance(pauli, coefficient, DEFAULT_TOLERANCE)
+    }
+
+    /// Adds one term with an explicit zero-dropping tolerance.
+    ///
+    /// # Errors
+    ///
+    /// Returns an error when `pauli` touches a qubit outside
+    /// `0..self.num_qubits` or `coefficient` is not finite.
+    pub fn add_term_with_tolerance(
+        &mut self,
+        pauli: PauliBitmaskSmall,
+        coefficient: Complex64,
+        tolerance: f64,
+    ) -> Result<(), ChannelError> {
+        validate_num_qubits(self.num_qubits, &pauli)?;
+        validate_complex(coefficient)?;
+        if coefficient.norm() <= tolerance {
+            return Ok(());
+        }
+
+        match self.terms.entry(pauli) {
+            std::collections::btree_map::Entry::Occupied(mut entry) => {
+                *entry.get_mut() += coefficient;
+                if entry.get().norm() <= tolerance {
+                    entry.remove();
+                }
+            }
+            std::collections::btree_map::Entry::Vacant(entry) => {
+                entry.insert(coefficient);
+            }
+        }
+        Ok(())
+    }
+
+    /// Drops near-zero coefficients in-place.
+    pub fn simplify_with_tolerance(&mut self, tolerance: f64) {
+        self.terms
+            .retain(|_, coefficient| coefficient.norm() > tolerance);
+    }
+
+    /// Drops coefficients at the default tolerance and returns the simplified
+    /// sum.
+    #[must_use]
+    pub fn simplify(mut self) -> Self {
+        self.simplify_with_tolerance(DEFAULT_TOLERANCE);
+        self
+    }
+
+    /// Greedily partitions terms into mutually commuting sums.
+    ///
+    /// Coefficients are preserved exactly. The grouping is a graph-coloring
+    /// heuristic on the anticommutation graph, so it is not guaranteed to use
+    /// the minimum possible number of groups.
+    #[must_use]
+    pub fn group_commuting(&self) -> Vec<Self> {
+        let mut groups: Vec<BTreeMap<PauliBitmaskSmall, Complex64>> = Vec::new();
+
+        'next_term: for (pauli, coefficient) in &self.terms {
+            for group in &mut groups {
+                if group.keys().all(|other| pauli.commutes_with(other)) {
+                    group.insert(pauli.clone(), *coefficient);
+                    continue 'next_term;
+                }
+            }
+            groups.push(BTreeMap::from([(pauli.clone(), *coefficient)]));
+        }
+
+        groups
+            .into_iter()
+            .map(|terms| Self {
+                num_qubits: self.num_qubits,
+                terms,
+            })
+            .collect()
+    }
+
+    /// Returns the Pauli conjugation `P * self * P†`.
+    ///
+    /// Pauli conjugation preserves each Pauli label and flips the coefficient
+    /// sign for terms that anticommute with `P`.
+    ///
+    /// # Errors
+    ///
+    /// Returns an error when `pauli` touches a qubit outside this sum's qubit
+    /// range.
+    pub fn conjugated_by_pauli_string(&self, pauli: &PauliString) -> Result<Self, ChannelError> {
+        let label = pauli_string_to_bitmask(self.num_qubits, pauli)?;
+        let mut terms = BTreeMap::new();
+        for (term, coefficient) in &self.terms {
+            let sign = if label.commutes_with(term) { 1.0 } else { -1.0 };
+            terms.insert(term.clone(), *coefficient * sign);
+        }
+        Ok(Self {
+            num_qubits: self.num_qubits,
+            terms,
+        })
+    }
+
+    /// Adds two Pauli sums after validating that they act on the same number
+    /// of qubits.
+    ///
+    /// # Errors
+    ///
+    /// Returns [`ChannelError::QubitCountMismatch`] when the two sums have
+    /// different qubit counts.
+    pub fn try_add(mut self, rhs: Self) -> Result<Self, ChannelError> {
+        if self.num_qubits != rhs.num_qubits {
+            return Err(ChannelError::QubitCountMismatch {
+                expected: self.num_qubits,
+                actual: rhs.num_qubits,
+            });
+        }
+        for (pauli, coefficient) in rhs.terms {
+            self.add_term(pauli, coefficient)?;
+        }
+        Ok(self)
+    }
+
+    /// Returns the trace of the represented operator.
+    ///
+    /// The trace is `identity_coefficient * 2^num_qubits`.
+    ///
+    /// # Errors
+    ///
+    /// Returns [`ChannelError::DimensionOverflow`] when `2^num_qubits` cannot
+    /// fit in `usize`.
+    #[allow(clippy::cast_precision_loss)]
+    pub fn trace(&self) -> Result<Complex64, ChannelError> {
+        let dim = hilbert_dim(self.num_qubits)?;
+        Ok(self
+            .terms
+            .get(&PauliBitmaskSmall::identity())
+            .copied()
+            .unwrap_or_else(|| Complex64::new(0.0, 0.0))
+            * dim as f64)
+    }
+}
+
+impl fmt::Display for PauliSum {
+    fn fmt(&self, f: &mut fmt::Formatter<'_>) -> fmt::Result {
+        if self.terms.is_empty() {
+            return write!(f, "0");
+        }
+        for (idx, (pauli, coefficient)) in self.terms.iter().enumerate() {
+            if idx > 0 {
+                write!(f, " + ")?;
+            }
+            let label = bitmask_label(self.num_qubits, pauli).map_err(|_| fmt::Error)?;
+            write!(f, "({coefficient}){label}")?;
+        }
+        Ok(())
+    }
+}
+
+impl Add for PauliSum {
+    type Output = Self;
+
+    /// Adds two Pauli sums.
+    ///
+    /// # Panics
+    ///
+    /// Panics when the sums have different qubit counts. Use
+    /// [`PauliSum::try_add`] to handle this case without panicking.
+    fn add(self, rhs: Self) -> Self::Output {
+        self.try_add(rhs)
+            .expect("cannot add PauliSum values with different qubit counts")
+    }
+}
+
+impl Mul<Complex64> for PauliSum {
+    type Output = Self;
+
+    fn mul(mut self, rhs: Complex64) -> Self::Output {
+        for coefficient in self.terms.values_mut() {
+            *coefficient *= rhs;
+        }
+        self.simplify()
+    }
+}
+
+impl Mul<PauliSum> for Complex64 {
+    type Output = PauliSum;
+
+    fn mul(self, rhs: PauliSum) -> Self::Output {
+        rhs * self
+    }
+}
+
+impl Mul<f64> for PauliSum {
+    type Output = Self;
+
+    fn mul(self, rhs: f64) -> Self::Output {
+        self * Complex64::new(rhs, 0.0)
+    }
+}
+
+impl Mul<PauliSum> for f64 {
+    type Output = PauliSum;
+
+    fn mul(self, rhs: PauliSum) -> Self::Output {
+        rhs * self
+    }
+}
+
+/// Sparse Pauli error channel represented by probabilities.
+#[derive(Clone, Debug, PartialEq)]
+pub struct PauliChannel {
+    num_qubits: usize,
+    basis_order: PtmBasisOrder,
+    probabilities: BTreeMap<PauliBitmaskSmall, f64>,
+}
+
+impl PauliChannel {
+    /// Constructs a Pauli channel after validating probabilities.
+    ///
+    /// Missing Pauli terms are treated as zero probability. Stored
+    /// probabilities must be finite, non-negative, and sum to one.
+    ///
+    /// # Errors
+    ///
+    /// Returns an error when a term is outside the declared qubit range, a
+    /// probability is non-finite or negative, or probabilities do not sum to
+    /// one.
+    pub fn try_new(
+        num_qubits: usize,
+        probabilities: BTreeMap<PauliBitmaskSmall, f64>,
+    ) -> Result<Self, ChannelError> {
+        Self::try_new_with_tolerance(num_qubits, probabilities, DEFAULT_TOLERANCE)
+    }
+
+    /// Constructs a Pauli channel with an explicit tolerance.
+    ///
+    /// # Errors
+    ///
+    /// Returns an error when a term is outside the declared qubit range, a
+    /// probability is non-finite or negative, or probabilities do not sum to
+    /// one within `tolerance`.
+    pub fn try_new_with_tolerance(
+        num_qubits: usize,
+        probabilities: BTreeMap<PauliBitmaskSmall, f64>,
+        tolerance: f64,
+    ) -> Result<Self, ChannelError> {
+        let mut cleaned = BTreeMap::new();
+        let mut sum = 0.0;
+        for (pauli, probability) in probabilities {
+            validate_num_qubits(num_qubits, &pauli)?;
+            validate_probability(probability, tolerance)?;
+            let probability = if probability.abs() <= tolerance {
+                0.0
+            } else {
+                probability
+            };
+            if probability > 0.0 {
+                cleaned.insert(pauli, probability);
+            }
+            sum += probability;
+        }
+        if (sum - 1.0).abs() > tolerance {
+            return Err(ChannelError::ProbabilitySum { sum, tolerance });
+        }
+        Ok(Self {
+            num_qubits,
+            basis_order: PtmBasisOrder::default(),
+            probabilities: cleaned,
+        })
+    }
+
+    /// Constructs a one-qubit Pauli channel from non-identity probabilities.
+    ///
+    /// # Errors
+    ///
+    /// Returns an error when probabilities are invalid or do not leave a valid
+    /// identity probability.
+    pub fn one_qubit(px: f64, py: f64, pz: f64) -> Result<Self, ChannelError> {
+        let mut probabilities = BTreeMap::new();
+        probabilities.insert(PauliBitmaskSmall::identity(), 1.0 - px - py - pz);
+        probabilities.insert(PauliBitmaskSmall::x(0), px);
+        probabilities.insert(PauliBitmaskSmall::y(0), py);
+        probabilities.insert(PauliBitmaskSmall::z(0), pz);
+        Self::try_new(1, probabilities)
+    }
+
+    /// Converts a real, non-negative [`PauliSum`] into a Pauli channel.
+    ///
+    /// # Errors
+    ///
+    /// Returns an error when any coefficient has a non-negligible imaginary
+    /// part, is negative, or the real coefficients do not sum to one.
+    pub fn from_pauli_sum(sum: &PauliSum) -> Result<Self, ChannelError> {
+        let mut probabilities = BTreeMap::new();
+        for (pauli, coefficient) in sum.terms() {
+            if coefficient.im.abs() > DEFAULT_TOLERANCE {
+                return Err(ChannelError::NonRealCoefficient {
+                    value: *coefficient,
+                    tolerance: DEFAULT_TOLERANCE,
+                });
+            }
+            probabilities.insert(pauli.clone(), coefficient.re);
+        }
+        Self::try_new(sum.num_qubits(), probabilities)
+    }
+
+    /// Constructs a Pauli channel from probabilities keyed by [`PauliString`].
+    ///
+    /// Pauli-string phases are ignored because Pauli channels apply
+    /// `P rho P†`, where global phase cancels. Repeated Pauli keys are
+    /// accumulated before validation.
+    ///
+    /// # Errors
+    ///
+    /// Returns an error when any Pauli string touches a qubit outside
+    /// `0..num_qubits`, a probability is invalid, or probabilities do not sum
+    /// to one.
+    pub fn from_pauli_strings<I>(num_qubits: usize, probabilities: I) -> Result<Self, ChannelError>
+    where
+        I: IntoIterator<Item = (PauliString, f64)>,
+    {
+        let mut terms = BTreeMap::new();
+        for (pauli, probability) in probabilities {
+            let pauli = pauli_string_to_bitmask(num_qubits, &pauli)?;
+            *terms.entry(pauli).or_insert(0.0) += probability;
+        }
+        Self::try_new(num_qubits, terms)
+    }
+
+    /// Converts a symbolic channel expression into a Pauli channel when it is
+    /// a mixture of Pauli unitaries.
+    ///
+    /// This accepts the common constructors for bit-flip, dephasing,
+    /// depolarizing, and general mixed-Pauli channels. Non-Pauli unitary
+    /// mixtures are intentionally rejected instead of silently projecting them.
+    ///
+    /// # Errors
+    ///
+    /// Returns an error when `channel` is not a supported Pauli-unitary
+    /// mixture or when its probabilities are invalid.
+    pub fn from_channel_expr(channel: &ChannelExpr) -> Result<Self, ChannelError> {
+        let num_qubits = channel_num_qubits(channel).max(1);
+        match channel {
+            ChannelExpr::Unitary(unitary) => {
+                let pauli = unitary_rep_to_pauli_bitmask(num_qubits, unitary)?;
+                let mut probabilities = BTreeMap::new();
+                probabilities.insert(pauli, 1.0);
+                Self::try_new(num_qubits, probabilities)
+            }
+            ChannelExpr::MixedUnitary(ops) => {
+                let mut probabilities = BTreeMap::new();
+                for (probability, unitary) in ops {
+                    validate_probability(*probability, DEFAULT_TOLERANCE)?;
+                    let pauli = unitary_rep_to_pauli_bitmask(num_qubits, unitary)?;
+                    *probabilities.entry(pauli).or_insert(0.0) += *probability;
+                }
+                Self::try_new(num_qubits, probabilities)
+            }
+            _ => Err(ChannelError::UnsupportedChannelExpr {
+                reason: "only Pauli-unitary channels can be converted to PauliChannel".to_string(),
+            }),
+        }
+    }
+
+    /// Converts Pauli probabilities to diagonal PTM entries.
+    ///
+    /// # Errors
+    ///
+    /// Returns an error if the Pauli-basis dimension overflows.
+    pub fn to_diagonal_ptm(&self) -> Result<DiagonalPtm, ChannelError> {
+        let basis_len = pauli_basis_len(self.num_qubits)?;
+        let mut fidelities = BTreeMap::new();
+        for basis_index in 0..basis_len {
+            let basis = basis_bitmask(self.num_qubits, basis_index)?;
+            let fidelity = self
+                .probabilities
+                .iter()
+                .map(|(error, probability)| probability * commutation_character(error, &basis))
+                .sum();
+            fidelities.insert(basis, fidelity);
+        }
+        DiagonalPtm::try_new(self.num_qubits, fidelities)
+    }
+
+    /// Converts this Pauli channel to a dense PTM.
+    ///
+    /// # Errors
+    ///
+    /// Returns an error if the Pauli-basis dimension overflows.
+    pub fn to_ptm(&self) -> Result<Ptm, ChannelError> {
+        self.to_diagonal_ptm()?.to_ptm()
+    }
+
+    /// Returns the number of qubits represented by this channel.
+    #[must_use]
+    pub fn num_qubits(&self) -> usize {
+        self.num_qubits
+    }
+
+    /// Returns the PTM basis ordering.
+    #[must_use]
+    pub fn basis_order(&self) -> PtmBasisOrder {
+        self.basis_order
+    }
+
+    /// Returns the sparse probability map.
+    #[must_use]
+    pub fn probabilities(&self) -> &BTreeMap<PauliBitmaskSmall, f64> {
+        &self.probabilities
+    }
+
+    /// Returns the probability of a specific Pauli error.
+    #[must_use]
+    pub fn probability(&self, pauli: &PauliBitmaskSmall) -> f64 {
+        self.probabilities.get(pauli).copied().unwrap_or(0.0)
+    }
+
+    /// Returns the total non-identity probability.
+    #[must_use]
+    pub fn total_error_rate(&self) -> f64 {
+        self.probabilities
+            .iter()
+            .filter(|(pauli, _)| !pauli.is_identity())
+            .map(|(_, probability)| probability)
+            .sum()
+    }
+}
+
+/// Sparse diagonal Pauli transfer matrix.
+#[derive(Clone, Debug, PartialEq)]
+pub struct DiagonalPtm {
+    num_qubits: usize,
+    basis_order: PtmBasisOrder,
+    fidelities: BTreeMap<PauliBitmaskSmall, f64>,
+}
+
+impl DiagonalPtm {
+    /// Constructs a diagonal PTM after validating term qubit ranges.
+    ///
+    /// Missing Pauli terms are treated as zero fidelity.
+    ///
+    /// # Errors
+    ///
+    /// Returns an error when any term is outside the declared qubit range or
+    /// any fidelity is non-finite.
+    pub fn try_new(
+        num_qubits: usize,
+        fidelities: BTreeMap<PauliBitmaskSmall, f64>,
+    ) -> Result<Self, ChannelError> {
+        let mut cleaned = BTreeMap::new();
+        for (pauli, fidelity) in fidelities {
+            validate_num_qubits(num_qubits, &pauli)?;
+            validate_real(fidelity)?;
+            if fidelity.abs() > DEFAULT_TOLERANCE {
+                cleaned.insert(pauli, fidelity);
+            }
+        }
+        Ok(Self {
+            num_qubits,
+            basis_order: PtmBasisOrder::default(),
+            fidelities: cleaned,
+        })
+    }
+
+    /// Converts diagonal PTM entries to Pauli-channel probabilities.
+    ///
+    /// # Errors
+    ///
+    /// Returns an error if the Pauli-basis dimension overflows or the inverse
+    /// Walsh-Hadamard transform does not produce valid probabilities.
+    pub fn to_pauli_channel(&self) -> Result<PauliChannel, ChannelError> {
+        let basis_len = pauli_basis_len(self.num_qubits)?;
+        #[allow(clippy::cast_precision_loss)]
+        let scale = basis_len as f64;
+        let basis: Vec<PauliBitmaskSmall> = (0..basis_len)
+            .map(|basis_index| basis_bitmask(self.num_qubits, basis_index))
+            .collect::<Result<_, _>>()?;
+        let mut probabilities = BTreeMap::new();
+        for error in &basis {
+            let probability: f64 = basis
+                .iter()
+                .map(|basis_element| {
+                    self.fidelity(basis_element) * commutation_character(error, basis_element)
+                })
+                .sum::<f64>()
+                / scale;
+            probabilities.insert(error.clone(), probability);
+        }
+        PauliChannel::try_new(self.num_qubits, probabilities)
+    }
+
+    /// Converts a symbolic Pauli-unitary channel expression to diagonal PTM
+    /// entries.
+    ///
+    /// # Errors
+    ///
+    /// Returns an error when the expression is not a supported Pauli-unitary
+    /// mixture or when probabilities are invalid.
+    pub fn from_channel_expr(channel: &ChannelExpr) -> Result<Self, ChannelError> {
+        PauliChannel::from_channel_expr(channel)?.to_diagonal_ptm()
+    }
+
+    /// Expands this diagonal PTM into a dense PTM matrix.
+    ///
+    /// # Errors
+    ///
+    /// Returns an error if the Pauli-basis dimension overflows.
+    pub fn to_ptm(&self) -> Result<Ptm, ChannelError> {
+        let basis_len = pauli_basis_len(self.num_qubits)?;
+        let mut matrix = DMatrix::zeros(basis_len, basis_len);
+        for basis_idx in 0..basis_len {
+            let basis = basis_bitmask(self.num_qubits, basis_idx)?;
+            matrix[(basis_idx, basis_idx)] = self.fidelity(&basis);
+        }
+        Ptm::try_new(self.num_qubits, matrix)
+    }
+
+    /// Returns the number of qubits represented by this diagonal PTM.
+    #[must_use]
+    pub fn num_qubits(&self) -> usize {
+        self.num_qubits
+    }
+
+    /// Returns the PTM basis ordering.
+    #[must_use]
+    pub fn basis_order(&self) -> PtmBasisOrder {
+        self.basis_order
+    }
+
+    /// Returns the sparse fidelity map.
+    #[must_use]
+    pub fn fidelities(&self) -> &BTreeMap<PauliBitmaskSmall, f64> {
+        &self.fidelities
+    }
+
+    /// Returns the fidelity for a specific Pauli basis element.
+    #[must_use]
+    pub fn fidelity(&self, pauli: &PauliBitmaskSmall) -> f64 {
+        self.fidelities.get(pauli).copied().unwrap_or(0.0)
+    }
+}
+
+/// Dense Pauli transfer matrix in the canonical PECOS Pauli basis.
+///
+/// PTM entries use the normalized convention
+/// `R_ij = (1/d) Tr[P_i E(P_j)]`, where `d = 2^num_qubits`.
+/// Rows index output Paulis, columns index input Paulis.
+#[derive(Clone, Debug, PartialEq)]
+pub struct Ptm {
+    num_qubits: usize,
+    basis_order: PtmBasisOrder,
+    matrix: DMatrix<f64>,
+}
+
+impl Ptm {
+    /// Constructs a dense PTM after validating the structural shape.
+    ///
+    /// # Errors
+    ///
+    /// Returns an error when `matrix` is not `4^num_qubits x 4^num_qubits`
+    /// or contains non-finite entries.
+    pub fn try_new(num_qubits: usize, matrix: DMatrix<f64>) -> Result<Self, ChannelError> {
+        let basis_len = pauli_basis_len(num_qubits)?;
+        if matrix.nrows() != basis_len || matrix.ncols() != basis_len {
+            return Err(ChannelError::InvalidMatrixShape {
+                expected_rows: basis_len,
+                expected_cols: basis_len,
+                rows: matrix.nrows(),
+                cols: matrix.ncols(),
+            });
+        }
+        for value in matrix.iter() {
+            validate_real(*value)?;
+        }
+        Ok(Self {
+            num_qubits,
+            basis_order: PtmBasisOrder::default(),
+            matrix,
+        })
+    }
+
+    /// Constructs the identity channel PTM over `num_qubits`.
+    ///
+    /// # Errors
+    ///
+    /// Returns an error if the Pauli-basis dimension overflows.
+    pub fn identity(num_qubits: usize) -> Result<Self, ChannelError> {
+        let basis_len = pauli_basis_len(num_qubits)?;
+        Self::try_new(num_qubits, DMatrix::identity(basis_len, basis_len))
+    }
+
+    /// Constructs a dense PTM from a diagonal PTM.
+    ///
+    /// # Errors
+    ///
+    /// Returns an error if the Pauli-basis dimension overflows.
+    pub fn from_diagonal_ptm(diagonal: &DiagonalPtm) -> Result<Self, ChannelError> {
+        diagonal.to_ptm()
+    }
+
+    /// Constructs a dense PTM from a Pauli channel.
+    ///
+    /// # Errors
+    ///
+    /// Returns an error if the Pauli-basis dimension overflows.
+    pub fn from_pauli_channel(channel: &PauliChannel) -> Result<Self, ChannelError> {
+        channel.to_ptm()
+    }
+
+    /// Constructs the PTM for a unitary conjugation channel.
+    ///
+    /// # Errors
+    ///
+    /// Returns an error when dimensions overflow or numerical entries have
+    /// significant imaginary components.
+    pub fn from_unitary(unitary: &UnitaryRep, num_qubits: usize) -> Result<Self, ChannelError> {
+        let basis_len = pauli_basis_len(num_qubits)?;
+        let dim = hilbert_dim(num_qubits)?;
+        #[allow(clippy::cast_precision_loss)]
+        let dim_f = dim as f64;
+        let unitary_matrix = to_matrix_with_size(unitary, num_qubits).into_inner();
+        if unitary_matrix.nrows() != dim || unitary_matrix.ncols() != dim {
+            return Err(ChannelError::InvalidMatrixShape {
+                expected_rows: dim,
+                expected_cols: dim,
+                rows: unitary_matrix.nrows(),
+                cols: unitary_matrix.ncols(),
+            });
+        }
+        let unitary_adjoint = unitary_matrix.adjoint();
+        let basis_matrices = pauli_basis_matrices(num_qubits)?;
+        let mut matrix = DMatrix::zeros(basis_len, basis_len);
+        for input_idx in 0..basis_len {
+            let evolved = &unitary_matrix * &basis_matrices[input_idx] * &unitary_adjoint;
+            for output_idx in 0..basis_len {
+                let entry = trace_complex(&(&basis_matrices[output_idx] * &evolved)) / dim_f;
+                if entry.im.abs() > DEFAULT_TOLERANCE {
+                    return Err(ChannelError::NonRealCoefficient {
+                        value: entry,
+                        tolerance: DEFAULT_TOLERANCE,
+                    });
+                }
+                matrix[(output_idx, input_idx)] = entry.re;
+            }
+        }
+        Self::try_new(num_qubits, matrix)
+    }
+
+    /// Converts a symbolic channel expression to a dense PTM when supported.
+    ///
+    /// This supports unitary, mixed-unitary, amplitude-damping, phase-damping,
+    /// tensor, and composed channel expressions that can be represented by
+    /// [`KrausOps`]. Erasure/leakage channels are intentionally rejected until
+    /// PECOS has an explicit flag or extended-Hilbert-space representation.
+    ///
+    /// # Errors
+    ///
+    /// Returns an error when the expression is unsupported or structurally
+    /// invalid.
+    pub fn from_channel_expr(channel: &ChannelExpr) -> Result<Self, ChannelError> {
+        let num_qubits = channel_num_qubits(channel).max(1);
+        match channel {
+            ChannelExpr::Unitary(unitary) => Self::from_unitary(unitary, num_qubits),
+            ChannelExpr::MixedUnitary(ops) => {
+                let basis_len = pauli_basis_len(num_qubits)?;
+                let mut matrix = DMatrix::zeros(basis_len, basis_len);
+                let mut total_probability = 0.0;
+                for (probability, unitary) in ops {
+                    validate_probability(*probability, DEFAULT_TOLERANCE)?;
+                    let unitary_ptm = Self::from_unitary(unitary, num_qubits)?;
+                    matrix += unitary_ptm.matrix * *probability;
+                    total_probability += *probability;
+                }
+                if (total_probability - 1.0).abs() > DEFAULT_TOLERANCE {
+                    return Err(ChannelError::ProbabilitySum {
+                        sum: total_probability,
+                        tolerance: DEFAULT_TOLERANCE,
+                    });
+                }
+                Self::try_new(num_qubits, matrix)
+            }
+            ChannelExpr::AmplitudeDamping { .. }
+            | ChannelExpr::PhaseDamping { .. }
+            | ChannelExpr::Tensor(_)
+            | ChannelExpr::Compose(_) => KrausOps::from_channel_expr(channel)?.to_ptm(),
+            _ => Err(ChannelError::UnsupportedChannelExpr {
+                reason: "dense PTM conversion supports unitary, mixed-unitary, amplitude-damping, phase-damping, tensor, and compose channels".to_string(),
+            }),
+        }
+    }
+
+    /// Returns the number of qubits represented by this PTM.
+    #[must_use]
+    pub fn num_qubits(&self) -> usize {
+        self.num_qubits
+    }
+
+    /// Returns the PTM basis ordering.
+    #[must_use]
+    pub fn basis_order(&self) -> PtmBasisOrder {
+        self.basis_order
+    }
+
+    /// Returns the dense PTM matrix.
+    #[must_use]
+    pub fn matrix(&self) -> &DMatrix<f64> {
+        &self.matrix
+    }
+
+    /// Consumes this PTM and returns its dense matrix.
+    #[must_use]
+    pub fn into_matrix(self) -> DMatrix<f64> {
+        self.matrix
+    }
+
+    /// Returns one PTM entry by row/output and column/input basis indices.
+    #[must_use]
+    pub fn entry(&self, output: usize, input: usize) -> f64 {
+        self.matrix[(output, input)]
+    }
+
+    /// Converts this PTM to a Choi matrix.
+    ///
+    /// # Errors
+    ///
+    /// Returns an error when dimensions overflow or the conversion encounters
+    /// invalid matrix data.
+    pub fn to_choi(&self) -> Result<ChoiMatrix, ChannelError> {
+        ChoiMatrix::from_ptm(self)
+    }
+
+    /// Converts this PTM to Kraus operators through its Choi representation.
+    ///
+    /// # Errors
+    ///
+    /// Returns an error when the Choi conversion or numerical decomposition
+    /// fails.
+    pub fn to_kraus(&self) -> Result<KrausOps, ChannelError> {
+        self.to_choi()?.to_kraus()
+    }
+
+    /// Converts this PTM to a column-stacked superoperator.
+    ///
+    /// # Errors
+    ///
+    /// Returns an error when the conversion through matrix units fails.
+    pub fn to_superop(&self) -> Result<SuperOp, ChannelError> {
+        SuperOp::from_ptm(self)
+    }
+
+    /// Converts this PTM to a Pauli-basis process matrix.
+    ///
+    /// # Errors
+    ///
+    /// Returns an error when the conversion through Choi/Kraus form fails.
+    pub fn to_chi(&self) -> Result<ChiMatrix, ChannelError> {
+        ChiMatrix::from_ptm(self)
+    }
+}
+
+/// Concrete Kraus-operator representation of a quantum channel.
+///
+/// A Kraus channel applies
+/// `E(rho) = sum_k K_k rho K_k†`.
+/// Operators are full `2^n x 2^n` matrices using the same little-endian
+/// computational-basis convention as [`UnitaryMatrix`](crate::UnitaryMatrix).
+#[derive(Clone, Debug, PartialEq)]
+pub struct KrausOps {
+    num_qubits: usize,
+    operators: Vec<DMatrix<Complex64>>,
+}
+
+impl KrausOps {
+    /// Constructs a Kraus representation after structural validation.
+    ///
+    /// This validates only cheap structural properties: non-empty operator
+    /// list, matrix shape, and finite entries. Trace-preservation and complete
+    /// positivity are mathematical properties of the Kraus form; call
+    /// [`Self::is_trace_preserving_with_tolerance`] when that check is needed.
+    ///
+    /// # Errors
+    ///
+    /// Returns an error when the operator list is empty, a matrix has the
+    /// wrong shape, a dimension overflows, or an entry is not finite.
+    pub fn try_new(
+        num_qubits: usize,
+        operators: Vec<DMatrix<Complex64>>,
+    ) -> Result<Self, ChannelError> {
+        if operators.is_empty() {
+            return Err(ChannelError::EmptyKrausSet);
+        }
+        let dim = hilbert_dim(num_qubits)?;
+        for operator in &operators {
+            validate_complex_matrix(operator, dim, dim)?;
+        }
+        Ok(Self {
+            num_qubits,
+            operators,
+        })
+    }
+
+    /// Constructs a one-operator Kraus representation for a unitary channel.
+    ///
+    /// # Errors
+    ///
+    /// Returns an error when the embedded unitary matrix has an invalid shape.
+    pub fn from_unitary(unitary: &UnitaryRep, num_qubits: usize) -> Result<Self, ChannelError> {
+        let operator = to_matrix_with_size(unitary, num_qubits).into_inner();
+        Self::try_new(num_qubits, vec![operator])
+    }
+
+    /// Converts a symbolic channel expression to Kraus operators when
+    /// supported.
+    ///
+    /// Supported variants are unitary, mixed-unitary, amplitude damping, phase
+    /// damping, tensor, and compose. Measurement/preparation gate expressions,
+    /// erasure, and leakage are intentionally rejected because they need
+    /// instrument or flag semantics beyond a simple same-Hilbert-space Kraus
+    /// channel.
+    ///
+    /// # Errors
+    ///
+    /// Returns an error when the expression is unsupported or invalid.
+    pub fn from_channel_expr(channel: &ChannelExpr) -> Result<Self, ChannelError> {
+        let num_qubits = channel_num_qubits(channel).max(1);
+        kraus_from_channel_expr_with_size(channel, num_qubits)
+    }
+
+    /// Converts a symbolic channel expression to Kraus operators embedded in a
+    /// specific system size.
+    ///
+    /// Use this when applying a local channel to a larger simulator state: a
+    /// channel acting on qubit 3 of a 6-qubit system needs 6-qubit Kraus
+    /// matrices, not the minimal 4-qubit representation implied by the highest
+    /// touched qubit.
+    ///
+    /// # Errors
+    ///
+    /// Returns an error when the expression is unsupported, invalid, or touches
+    /// a qubit outside `num_qubits`.
+    pub fn from_channel_expr_with_num_qubits(
+        channel: &ChannelExpr,
+        num_qubits: usize,
+    ) -> Result<Self, ChannelError> {
+        for qubit in channel.qubits() {
+            if qubit >= num_qubits {
+                return Err(ChannelError::QubitOutOfRange { num_qubits, qubit });
+            }
+        }
+        kraus_from_channel_expr_with_size(channel, num_qubits)
+    }
+
+    /// Converts this Kraus channel to a dense PTM.
+    ///
+    /// # Errors
+    ///
+    /// Returns an error when dimensions overflow or a PTM entry has a
+    /// significant imaginary component.
+    pub fn to_ptm(&self) -> Result<Ptm, ChannelError> {
+        let basis_len = pauli_basis_len(self.num_qubits)?;
+        let dim = hilbert_dim(self.num_qubits)?;
+        #[allow(clippy::cast_precision_loss)]
+        let dim_f = dim as f64;
+        let basis_matrices = pauli_basis_matrices(self.num_qubits)?;
+        let mut matrix = DMatrix::zeros(basis_len, basis_len);
+        for input_idx in 0..basis_len {
+            let mut evolved = DMatrix::zeros(dim, dim);
+            for operator in &self.operators {
+                evolved += operator * &basis_matrices[input_idx] * operator.adjoint();
+            }
+            for output_idx in 0..basis_len {
+                let entry = trace_complex(&(&basis_matrices[output_idx] * &evolved)) / dim_f;
+                if entry.im.abs() > DEFAULT_TOLERANCE {
+                    return Err(ChannelError::NonRealCoefficient {
+                        value: entry,
+                        tolerance: DEFAULT_TOLERANCE,
+                    });
+                }
+                matrix[(output_idx, input_idx)] = entry.re;
+            }
+        }
+        Ptm::try_new(self.num_qubits, matrix)
+    }
+
+    /// Converts this Kraus channel to a Choi matrix.
+    ///
+    /// # Errors
+    ///
+    /// Returns an error when dimensions overflow.
+    pub fn to_choi(&self) -> Result<ChoiMatrix, ChannelError> {
+        ChoiMatrix::from_kraus(self)
+    }
+
+    /// Converts this Kraus channel to a column-stacked superoperator.
+    ///
+    /// # Errors
+    ///
+    /// Returns an error when dimensions overflow.
+    pub fn to_superop(&self) -> Result<SuperOp, ChannelError> {
+        SuperOp::from_kraus(self)
+    }
+
+    /// Converts this Kraus channel to a Pauli-basis process matrix.
+    ///
+    /// # Errors
+    ///
+    /// Returns an error when dimensions overflow.
+    pub fn to_chi(&self) -> Result<ChiMatrix, ChannelError> {
+        ChiMatrix::from_kraus(self)
+    }
+
+    /// Converts this Kraus channel to a Stinespring isometry.
+    ///
+    /// # Errors
+    ///
+    /// Returns an error when the stacked Kraus operators are not an isometry.
+    pub fn to_stinespring(&self) -> Result<Stinespring, ChannelError> {
+        Stinespring::from_kraus(self)
+    }
+
+    /// Returns whether `sum_k K_k† K_k = I` within the default tolerance.
+    #[must_use]
+    pub fn is_trace_preserving(&self) -> bool {
+        self.is_trace_preserving_with_tolerance(1e-10)
+    }
+
+    /// Returns whether `sum_k K_k† K_k = I` within `tolerance`.
+    #[must_use]
+    pub fn is_trace_preserving_with_tolerance(&self, tolerance: f64) -> bool {
+        let Ok(dim) = hilbert_dim(self.num_qubits) else {
+            return false;
+        };
+        let mut accumulator = DMatrix::zeros(dim, dim);
+        for operator in &self.operators {
+            accumulator += operator.adjoint() * operator;
+        }
+        let identity = DMatrix::<Complex64>::identity(dim, dim);
+        matrix_max_abs_diff(&accumulator, &identity) <= tolerance
+    }
+
+    /// Returns the number of qubits represented by this channel.
+    #[must_use]
+    pub fn num_qubits(&self) -> usize {
+        self.num_qubits
+    }
+
+    /// Returns the Kraus operators.
+    #[must_use]
+    pub fn operators(&self) -> &[DMatrix<Complex64>] {
+        &self.operators
+    }
+
+    /// Consumes this value and returns the Kraus operators.
+    #[must_use]
+    pub fn into_operators(self) -> Vec<DMatrix<Complex64>> {
+        self.operators
+    }
+}
+
+/// Concrete Choi representation of a quantum channel.
+///
+/// PECOS stores the unnormalized Choi matrix
+/// `J = sum_k vec(K_k) vec(K_k)†`, where `vec` is column-stacking. For a
+/// trace-preserving channel on Hilbert dimension `d`, `Tr(J) = d` and
+/// `Tr_output(J) = I_input`.
+#[derive(Clone, Debug, PartialEq)]
+pub struct ChoiMatrix {
+    num_qubits: usize,
+    matrix: DMatrix<Complex64>,
+}
+
+impl ChoiMatrix {
+    /// Constructs a Choi matrix after structural validation.
+    ///
+    /// This validates only cheap structural properties: shape and finite
+    /// entries. Complete positivity and trace preservation are explicit
+    /// follow-up checks.
+    ///
+    /// # Errors
+    ///
+    /// Returns an error when the matrix shape is not `4^n x 4^n`, dimensions
+    /// overflow, or an entry is not finite.
+    pub fn try_new(num_qubits: usize, matrix: DMatrix<Complex64>) -> Result<Self, ChannelError> {
+        let dim_squared = pauli_basis_len(num_qubits)?;
+        validate_complex_matrix(&matrix, dim_squared, dim_squared)?;
+        Ok(Self { num_qubits, matrix })
+    }
+
+    /// Converts Kraus operators to a Choi matrix.
+    ///
+    /// # Errors
+    ///
+    /// Returns an error when dimensions overflow.
+    pub fn from_kraus(kraus: &KrausOps) -> Result<Self, ChannelError> {
+        let dim = hilbert_dim(kraus.num_qubits)?;
+        let dim_squared = pauli_basis_len(kraus.num_qubits)?;
+        let mut matrix = DMatrix::zeros(dim_squared, dim_squared);
+        for operator in kraus.operators() {
+            for input_col in 0..dim {
+                for output_row in 0..dim {
+                    let row = choi_index(dim, output_row, input_col);
+                    let row_value = operator[(output_row, input_col)];
+                    for input_col_2 in 0..dim {
+                        for output_row_2 in 0..dim {
+                            let col = choi_index(dim, output_row_2, input_col_2);
+                            matrix[(row, col)] +=
+                                row_value * operator[(output_row_2, input_col_2)].conj();
+                        }
+                    }
+                }
+            }
+        }
+        Self::try_new(kraus.num_qubits, matrix)
+    }
+
+    /// Constructs a Choi matrix for a unitary channel.
+    ///
+    /// # Errors
+    ///
+    /// Returns an error when unitary embedding or Choi construction fails.
+    pub fn from_unitary(unitary: &UnitaryRep, num_qubits: usize) -> Result<Self, ChannelError> {
+        KrausOps::from_unitary(unitary, num_qubits)?.to_choi()
+    }
+
+    /// Converts a symbolic channel expression to a Choi matrix when supported.
+    ///
+    /// # Errors
+    ///
+    /// Returns an error when [`KrausOps::from_channel_expr`] rejects the
+    /// expression or Choi construction fails.
+    pub fn from_channel_expr(channel: &ChannelExpr) -> Result<Self, ChannelError> {
+        KrausOps::from_channel_expr(channel)?.to_choi()
+    }
+
+    /// Converts a PTM to a Choi matrix.
+    ///
+    /// # Errors
+    ///
+    /// Returns an error when dimensions overflow.
+    pub fn from_ptm(ptm: &Ptm) -> Result<Self, ChannelError> {
+        let dim = hilbert_dim(ptm.num_qubits)?;
+        let dim_squared = pauli_basis_len(ptm.num_qubits)?;
+        let mut matrix = DMatrix::zeros(dim_squared, dim_squared);
+        for input_row in 0..dim {
+            for input_col in 0..dim {
+                let mut matrix_unit = DMatrix::zeros(dim, dim);
+                matrix_unit[(input_row, input_col)] = Complex64::new(1.0, 0.0);
+                let evolved = apply_ptm_to_operator(ptm, &matrix_unit)?;
+                for output_row in 0..dim {
+                    for output_col in 0..dim {
+                        matrix[(
+                            choi_index(dim, output_row, input_row),
+                            choi_index(dim, output_col, input_col),
+                        )] = evolved[(output_row, output_col)];
+                    }
+                }
+            }
+        }
+        Self::try_new(ptm.num_qubits, matrix)
+    }
+
+    /// Reconstructs a Choi matrix from complete operator-basis tomography data.
+    ///
+    /// `outputs` must contain `d^2` matrices, where `d = 2^num_qubits`.
+    /// Entry `input_row + input_col * d` is the measured/reconstructed output
+    /// operator `E(|input_row><input_col|)`. This is linear-inversion process
+    /// tomography in the computational matrix-unit basis, using PECOS's
+    /// column-stacked Choi convention.
+    ///
+    /// # Errors
+    ///
+    /// Returns an error when dimensions overflow, the sample count is not
+    /// `d^2`, or any output matrix is not `d x d`.
+    pub fn from_matrix_unit_outputs(
+        num_qubits: usize,
+        outputs: &[DMatrix<Complex64>],
+    ) -> Result<Self, ChannelError> {
+        let dim = hilbert_dim(num_qubits)?;
+        let dim_squared = pauli_basis_len(num_qubits)?;
+        if outputs.len() != dim_squared {
+            return Err(ChannelError::InvalidTomographySampleCount {
+                expected: dim_squared,
+                actual: outputs.len(),
+            });
+        }
+
+        let mut matrix = DMatrix::zeros(dim_squared, dim_squared);
+        for input_col in 0..dim {
+            for input_row in 0..dim {
+                let output = &outputs[matrix_unit_index(dim, input_row, input_col)];
+                validate_complex_matrix(output, dim, dim)?;
+                for output_row in 0..dim {
+                    for output_col in 0..dim {
+                        matrix[(
+                            choi_index(dim, output_row, input_row),
+                            choi_index(dim, output_col, input_col),
+                        )] = output[(output_row, output_col)];
+                    }
+                }
+            }
+        }
+        Self::try_new(num_qubits, matrix)
+    }
+
+    /// Converts this Choi matrix to a dense PTM.
+    ///
+    /// # Errors
+    ///
+    /// Returns an error when dimensions overflow or a PTM entry has a
+    /// significant imaginary component.
+    pub fn to_ptm(&self) -> Result<Ptm, ChannelError> {
+        let basis_len = pauli_basis_len(self.num_qubits)?;
+        let dim = hilbert_dim(self.num_qubits)?;
+        #[allow(clippy::cast_precision_loss)]
+        let dim_f = dim as f64;
+        let basis_matrices = pauli_basis_matrices(self.num_qubits)?;
+        let mut matrix = DMatrix::zeros(basis_len, basis_len);
+        for input_idx in 0..basis_len {
+            let evolved = self.apply_to_operator(&basis_matrices[input_idx])?;
+            for output_idx in 0..basis_len {
+                let entry = trace_complex(&(&basis_matrices[output_idx] * &evolved)) / dim_f;
+                if entry.im.abs() > DEFAULT_TOLERANCE {
+                    return Err(ChannelError::NonRealCoefficient {
+                        value: entry,
+                        tolerance: DEFAULT_TOLERANCE,
+                    });
+                }
+                matrix[(output_idx, input_idx)] = entry.re;
+            }
+        }
+        Ptm::try_new(self.num_qubits, matrix)
+    }
+
+    /// Converts this Choi matrix to a Kraus representation using SVD.
+    ///
+    /// For a valid positive-semidefinite Choi matrix, the singular values are
+    /// the Choi eigenvalues and the left singular vectors produce a Kraus
+    /// decomposition. This method reconstructs the Choi matrix from the
+    /// resulting Kraus operators and rejects inputs that are not positive
+    /// semidefinite within the requested tolerance.
+    ///
+    /// # Errors
+    ///
+    /// Returns an error when numerical decomposition fails.
+    pub fn to_kraus(&self) -> Result<KrausOps, ChannelError> {
+        self.to_kraus_with_tolerance(DEFAULT_TOLERANCE)
+    }
+
+    /// Converts this Choi matrix to a column-stacked superoperator.
+    ///
+    /// # Errors
+    ///
+    /// Returns an error when dimensions overflow.
+    pub fn to_superop(&self) -> Result<SuperOp, ChannelError> {
+        SuperOp::from_choi(self)
+    }
+
+    /// Converts this Choi matrix to a Pauli-basis process matrix.
+    ///
+    /// # Errors
+    ///
+    /// Returns an error when conversion through Kraus form fails.
+    pub fn to_chi(&self) -> Result<ChiMatrix, ChannelError> {
+        ChiMatrix::from_choi(self)
+    }
+
+    /// Converts this Choi matrix to Kraus operators with an explicit
+    /// singular-value cutoff.
+    ///
+    /// # Errors
+    ///
+    /// Returns an error when the tolerance is invalid, numerical decomposition
+    /// fails, or the input is not positive semidefinite within tolerance.
+    pub fn to_kraus_with_tolerance(&self, tolerance: f64) -> Result<KrausOps, ChannelError> {
+        if !tolerance.is_finite() || tolerance < 0.0 {
+            return Err(ChannelError::DecompositionFailed {
+                reason: format!("invalid Kraus decomposition tolerance: {tolerance}"),
+            });
+        }
+        let dim = hilbert_dim(self.num_qubits)?;
+        let svd = SVD::new(self.matrix.clone(), true, false);
+        let u = svd.u.ok_or_else(|| ChannelError::DecompositionFailed {
+            reason: "SVD did not return left singular vectors".to_string(),
+        })?;
+        let mut operators = Vec::new();
+        for (idx, singular_value) in svd.singular_values.iter().copied().enumerate() {
+            if singular_value <= tolerance {
+                continue;
+            }
+            let scale = Complex64::new(singular_value.sqrt(), 0.0);
+            let mut operator = DMatrix::zeros(dim, dim);
+            for input_col in 0..dim {
+                for output_row in 0..dim {
+                    operator[(output_row, input_col)] =
+                        u[(choi_index(dim, output_row, input_col), idx)] * scale;
+                }
+            }
+            operators.push(operator);
+        }
+        if operators.is_empty() {
+            operators.push(DMatrix::zeros(dim, dim));
+        }
+        let kraus = KrausOps::try_new(self.num_qubits, operators)?;
+        let recovered = Self::from_kraus(&kraus)?;
+        let reconstruction_tolerance = (10.0 * tolerance).max(1e-10);
+        if matrix_max_abs_diff(recovered.matrix(), &self.matrix) > reconstruction_tolerance {
+            return Err(ChannelError::DecompositionFailed {
+                reason: "Choi matrix is not positive semidefinite within tolerance".to_string(),
+            });
+        }
+        Ok(kraus)
+    }
+
+    /// Applies the represented channel to an operator matrix.
+    ///
+    /// # Errors
+    ///
+    /// Returns an error when the input operator shape is invalid.
+    pub fn apply_to_operator(
+        &self,
+        operator: &DMatrix<Complex64>,
+    ) -> Result<DMatrix<Complex64>, ChannelError> {
+        let dim = hilbert_dim(self.num_qubits)?;
+        validate_complex_matrix(operator, dim, dim)?;
+        let mut out = DMatrix::zeros(dim, dim);
+        for input_row in 0..dim {
+            for input_col in 0..dim {
+                let coefficient = operator[(input_row, input_col)];
+                for output_row in 0..dim {
+                    for output_col in 0..dim {
+                        out[(output_row, output_col)] += coefficient
+                            * self.matrix[(
+                                choi_index(dim, output_row, input_row),
+                                choi_index(dim, output_col, input_col),
+                            )];
+                    }
+                }
+            }
+        }
+        Ok(out)
+    }
+
+    /// Returns the output partial trace `Tr_output(J)`.
+    ///
+    /// With PECOS's column-stacked Choi convention, this equals the input-space
+    /// identity for a trace-preserving channel.
+    ///
+    /// # Errors
+    ///
+    /// Returns an error when the Hilbert-space dimension overflows.
+    pub fn partial_trace_output(&self) -> Result<DMatrix<Complex64>, ChannelError> {
+        let dim = hilbert_dim(self.num_qubits)?;
+        let mut reduced = DMatrix::zeros(dim, dim);
+        for input_row in 0..dim {
+            for input_col in 0..dim {
+                let mut value = Complex64::new(0.0, 0.0);
+                for output in 0..dim {
+                    value += self.matrix[(
+                        choi_index(dim, output, input_row),
+                        choi_index(dim, output, input_col),
+                    )];
+                }
+                reduced[(input_row, input_col)] = value;
+            }
+        }
+        Ok(reduced)
+    }
+
+    /// Returns the input partial trace `Tr_input(J)`.
+    ///
+    /// With PECOS's column-stacked Choi convention, this equals `E(I)` and
+    /// therefore equals the output-space identity for a unital channel.
+    ///
+    /// # Errors
+    ///
+    /// Returns an error when the Hilbert-space dimension overflows.
+    pub fn partial_trace_input(&self) -> Result<DMatrix<Complex64>, ChannelError> {
+        let dim = hilbert_dim(self.num_qubits)?;
+        let mut reduced = DMatrix::zeros(dim, dim);
+        for output_row in 0..dim {
+            for output_col in 0..dim {
+                let mut value = Complex64::new(0.0, 0.0);
+                for input in 0..dim {
+                    value += self.matrix[(
+                        choi_index(dim, output_row, input),
+                        choi_index(dim, output_col, input),
+                    )];
+                }
+                reduced[(output_row, output_col)] = value;
+            }
+        }
+        Ok(reduced)
+    }
+
+    /// Returns whether this Choi matrix is positive semidefinite within the
+    /// default tolerance.
+    #[must_use]
+    pub fn is_completely_positive(&self) -> bool {
+        self.is_completely_positive_with_tolerance(1e-10)
+    }
+
+    /// Returns whether this Choi matrix is positive semidefinite within
+    /// `tolerance`.
+    #[must_use]
+    pub fn is_completely_positive_with_tolerance(&self, tolerance: f64) -> bool {
+        self.to_kraus_with_tolerance(tolerance).is_ok()
+    }
+
+    /// Returns whether this Choi matrix is completely positive and
+    /// trace-preserving within the default tolerance.
+    #[must_use]
+    pub fn is_cptp(&self) -> bool {
+        self.is_cptp_with_tolerance(1e-10)
+    }
+
+    /// Returns whether this Choi matrix is completely positive and
+    /// trace-preserving within `tolerance`.
+    #[must_use]
+    pub fn is_cptp_with_tolerance(&self, tolerance: f64) -> bool {
+        self.is_completely_positive_with_tolerance(tolerance)
+            && self.is_trace_preserving_with_tolerance(tolerance)
+    }
+
+    /// Returns whether `E(I) = I` within the default tolerance.
+    #[must_use]
+    pub fn is_unital(&self) -> bool {
+        self.is_unital_with_tolerance(1e-10)
+    }
+
+    /// Returns whether `E(I) = I` within `tolerance`.
+    #[must_use]
+    pub fn is_unital_with_tolerance(&self, tolerance: f64) -> bool {
+        let Ok(dim) = hilbert_dim(self.num_qubits) else {
+            return false;
+        };
+        let Ok(reduced) = self.partial_trace_input() else {
+            return false;
+        };
+        let identity = DMatrix::<Complex64>::identity(dim, dim);
+        matrix_max_abs_diff(&reduced, &identity) <= tolerance
+    }
+
+    /// Returns whether `Tr_output(J) = I_input` within the default tolerance.
+    #[must_use]
+    pub fn is_trace_preserving(&self) -> bool {
+        self.is_trace_preserving_with_tolerance(1e-10)
+    }
+
+    /// Returns whether `Tr_output(J) = I_input` within `tolerance`.
+    #[must_use]
+    pub fn is_trace_preserving_with_tolerance(&self, tolerance: f64) -> bool {
+        let Ok(dim) = hilbert_dim(self.num_qubits) else {
+            return false;
+        };
+        let Ok(reduced) = self.partial_trace_output() else {
+            return false;
+        };
+        let identity = DMatrix::<Complex64>::identity(dim, dim);
+        matrix_max_abs_diff(&reduced, &identity) <= tolerance
+    }
+
+    /// Returns the number of qubits represented by this Choi matrix.
+    #[must_use]
+    pub fn num_qubits(&self) -> usize {
+        self.num_qubits
+    }
+
+    /// Returns the dense Choi matrix.
+    #[must_use]
+    pub fn matrix(&self) -> &DMatrix<Complex64> {
+        &self.matrix
+    }
+
+    /// Consumes this value and returns the dense Choi matrix.
+    #[must_use]
+    pub fn into_matrix(self) -> DMatrix<Complex64> {
+        self.matrix
+    }
+}
+
+/// Dense column-stacked superoperator representation.
+///
+/// `SuperOp` stores the matrix `S` satisfying `vec(E(A)) = S vec(A)`, where
+/// `vec` uses column-stacking in PECOS's little-endian computational basis.
+#[derive(Clone, Debug, PartialEq)]
+pub struct SuperOp {
+    num_qubits: usize,
+    matrix: DMatrix<Complex64>,
+}
+
+impl SuperOp {
+    /// Constructs a superoperator after structural validation.
+    ///
+    /// # Errors
+    ///
+    /// Returns an error when `matrix` is not `4^n x 4^n` or contains
+    /// non-finite entries.
+    pub fn try_new(num_qubits: usize, matrix: DMatrix<Complex64>) -> Result<Self, ChannelError> {
+        let dim_squared = pauli_basis_len(num_qubits)?;
+        validate_complex_matrix(&matrix, dim_squared, dim_squared)?;
+        Ok(Self { num_qubits, matrix })
+    }
+
+    /// Constructs a superoperator from Kraus operators.
+    ///
+    /// # Errors
+    ///
+    /// Returns an error when dimensions overflow.
+    pub fn from_kraus(kraus: &KrausOps) -> Result<Self, ChannelError> {
+        let dim = hilbert_dim(kraus.num_qubits)?;
+        let dim_squared = pauli_basis_len(kraus.num_qubits)?;
+        let mut matrix = DMatrix::zeros(dim_squared, dim_squared);
+        for input_col in 0..dim {
+            for input_row in 0..dim {
+                let input_idx = matrix_unit_index(dim, input_row, input_col);
+                for output_col in 0..dim {
+                    for output_row in 0..dim {
+                        let output_idx = matrix_unit_index(dim, output_row, output_col);
+                        let mut value = Complex64::new(0.0, 0.0);
+                        for operator in kraus.operators() {
+                            value += operator[(output_row, input_row)]
+                                * operator[(output_col, input_col)].conj();
+                        }
+                        matrix[(output_idx, input_idx)] = value;
+                    }
+                }
+            }
+        }
+        Self::try_new(kraus.num_qubits, matrix)
+    }
+
+    /// Constructs a superoperator from a Choi matrix.
+    ///
+    /// # Errors
+    ///
+    /// Returns an error when dimensions overflow.
+    pub fn from_choi(choi: &ChoiMatrix) -> Result<Self, ChannelError> {
+        let dim = hilbert_dim(choi.num_qubits)?;
+        let dim_squared = pauli_basis_len(choi.num_qubits)?;
+        let mut matrix = DMatrix::zeros(dim_squared, dim_squared);
+        for input_col in 0..dim {
+            for input_row in 0..dim {
+                let input_idx = matrix_unit_index(dim, input_row, input_col);
+                for output_col in 0..dim {
+                    for output_row in 0..dim {
+                        let output_idx = matrix_unit_index(dim, output_row, output_col);
+                        matrix[(output_idx, input_idx)] = choi.matrix()[(
+                            choi_index(dim, output_row, input_row),
+                            choi_index(dim, output_col, input_col),
+                        )];
+                    }
+                }
+            }
+        }
+        Self::try_new(choi.num_qubits, matrix)
+    }
+
+    /// Constructs a superoperator from a PTM.
+    ///
+    /// # Errors
+    ///
+    /// Returns an error when dimensions overflow.
+    pub fn from_ptm(ptm: &Ptm) -> Result<Self, ChannelError> {
+        let dim = hilbert_dim(ptm.num_qubits)?;
+        let dim_squared = pauli_basis_len(ptm.num_qubits)?;
+        let mut matrix = DMatrix::zeros(dim_squared, dim_squared);
+        for input_col in 0..dim {
+            for input_row in 0..dim {
+                let mut input = DMatrix::zeros(dim, dim);
+                input[(input_row, input_col)] = Complex64::new(1.0, 0.0);
+                let output = apply_ptm_to_operator(ptm, &input)?;
+                let input_idx = matrix_unit_index(dim, input_row, input_col);
+                for output_col in 0..dim {
+                    for output_row in 0..dim {
+                        let output_idx = matrix_unit_index(dim, output_row, output_col);
+                        matrix[(output_idx, input_idx)] = output[(output_row, output_col)];
+                    }
+                }
+            }
+        }
+        Self::try_new(ptm.num_qubits, matrix)
+    }
+
+    /// Constructs a superoperator from a supported channel expression.
+    ///
+    /// # Errors
+    ///
+    /// Returns an error when the expression cannot be represented as Kraus
+    /// operators.
+    pub fn from_channel_expr(channel: &ChannelExpr) -> Result<Self, ChannelError> {
+        KrausOps::from_channel_expr(channel)?.to_superop()
+    }
+
+    /// Converts this superoperator to a Choi matrix.
+    ///
+    /// # Errors
+    ///
+    /// Returns an error when dimensions overflow.
+    pub fn to_choi(&self) -> Result<ChoiMatrix, ChannelError> {
+        let dim = hilbert_dim(self.num_qubits)?;
+        let mut matrix = DMatrix::zeros(self.matrix.nrows(), self.matrix.ncols());
+        for input_col in 0..dim {
+            for input_row in 0..dim {
+                let input_idx = matrix_unit_index(dim, input_row, input_col);
+                for output_col in 0..dim {
+                    for output_row in 0..dim {
+                        let output_idx = matrix_unit_index(dim, output_row, output_col);
+                        matrix[(
+                            choi_index(dim, output_row, input_row),
+                            choi_index(dim, output_col, input_col),
+                        )] = self.matrix[(output_idx, input_idx)];
+                    }
+                }
+            }
+        }
+        ChoiMatrix::try_new(self.num_qubits, matrix)
+    }
+
+    /// Converts this superoperator to a PTM.
+    ///
+    /// # Errors
+    ///
+    /// Returns an error when Choi/PTM conversion fails.
+    pub fn to_ptm(&self) -> Result<Ptm, ChannelError> {
+        self.to_choi()?.to_ptm()
+    }
+
+    /// Converts this superoperator to Kraus operators.
+    ///
+    /// # Errors
+    ///
+    /// Returns an error when Choi/Kraus conversion fails.
+    pub fn to_kraus(&self) -> Result<KrausOps, ChannelError> {
+        self.to_choi()?.to_kraus()
+    }
+
+    /// Returns the composition `self ∘ other`, applying `other` first.
+    ///
+    /// # Errors
+    ///
+    /// Returns an error when qubit counts differ.
+    pub fn compose(&self, other: &Self) -> Result<Self, ChannelError> {
+        if self.num_qubits != other.num_qubits {
+            return Err(ChannelError::QubitCountMismatch {
+                expected: self.num_qubits,
+                actual: other.num_qubits,
+            });
+        }
+        Self::try_new(self.num_qubits, &self.matrix * &other.matrix)
+    }
+
+    /// Returns the tensor product of two superoperators.
+    ///
+    /// # Errors
+    ///
+    /// Returns an error when dimensions overflow.
+    pub fn tensor(&self, other: &Self) -> Result<Self, ChannelError> {
+        Self::try_new(
+            self.num_qubits + other.num_qubits,
+            complex_kronecker(&self.matrix, &other.matrix),
+        )
+    }
+
+    /// Returns the number of qubits represented by this superoperator.
+    #[must_use]
+    pub fn num_qubits(&self) -> usize {
+        self.num_qubits
+    }
+
+    /// Returns the dense superoperator matrix.
+    #[must_use]
+    pub fn matrix(&self) -> &DMatrix<Complex64> {
+        &self.matrix
+    }
+
+    /// Consumes this value and returns its dense matrix.
+    #[must_use]
+    pub fn into_matrix(self) -> DMatrix<Complex64> {
+        self.matrix
+    }
+}
+
+/// Pauli-basis process matrix.
+///
+/// `ChiMatrix` stores coefficients `chi_ij` in
+/// `E(rho) = sum_ij chi_ij P_i rho P_j†`, with the same Pauli basis ordering
+/// as [`Ptm`].
+#[derive(Clone, Debug, PartialEq)]
+pub struct ChiMatrix {
+    num_qubits: usize,
+    basis_order: PtmBasisOrder,
+    matrix: DMatrix<Complex64>,
+}
+
+impl ChiMatrix {
+    /// Constructs a chi matrix after structural validation.
+    ///
+    /// # Errors
+    ///
+    /// Returns an error when `matrix` is not `4^n x 4^n` or contains
+    /// non-finite entries.
+    pub fn try_new(num_qubits: usize, matrix: DMatrix<Complex64>) -> Result<Self, ChannelError> {
+        let basis_len = pauli_basis_len(num_qubits)?;
+        validate_complex_matrix(&matrix, basis_len, basis_len)?;
+        Ok(Self {
+            num_qubits,
+            basis_order: PtmBasisOrder::default(),
+            matrix,
+        })
+    }
+
+    /// Constructs a chi matrix from Kraus operators.
+    ///
+    /// # Errors
+    ///
+    /// Returns an error when dimensions overflow.
+    pub fn from_kraus(kraus: &KrausOps) -> Result<Self, ChannelError> {
+        let basis_len = pauli_basis_len(kraus.num_qubits)?;
+        let dim = hilbert_dim(kraus.num_qubits)?;
+        #[allow(clippy::cast_precision_loss)]
+        let dim_f = dim as f64;
+        let basis = pauli_basis_matrices(kraus.num_qubits)?;
+        let mut matrix = DMatrix::zeros(basis_len, basis_len);
+        for operator in kraus.operators() {
+            let coefficients: Vec<Complex64> = basis
+                .iter()
+                .map(|pauli| trace_complex(&(pauli * operator)) / dim_f)
+                .collect();
+            for row in 0..basis_len {
+                for col in 0..basis_len {
+                    matrix[(row, col)] += coefficients[row] * coefficients[col].conj();
+                }
+            }
+        }
+        Self::try_new(kraus.num_qubits, matrix)
+    }
+
+    /// Constructs a chi matrix from a Choi matrix.
+    ///
+    /// # Errors
+    ///
+    /// Returns an error when Choi/Kraus conversion fails.
+    pub fn from_choi(choi: &ChoiMatrix) -> Result<Self, ChannelError> {
+        choi.to_kraus()?.to_chi()
+    }
+
+    /// Constructs a chi matrix from a PTM.
+    ///
+    /// # Errors
+    ///
+    /// Returns an error when PTM/Choi/Kraus conversion fails.
+    pub fn from_ptm(ptm: &Ptm) -> Result<Self, ChannelError> {
+        ptm.to_kraus()?.to_chi()
+    }
+
+    /// Constructs a chi matrix from a supported channel expression.
+    ///
+    /// # Errors
+    ///
+    /// Returns an error when the expression cannot be represented as Kraus
+    /// operators.
+    pub fn from_channel_expr(channel: &ChannelExpr) -> Result<Self, ChannelError> {
+        KrausOps::from_channel_expr(channel)?.to_chi()
+    }
+
+    /// Converts this chi matrix to a Choi matrix.
+    ///
+    /// # Errors
+    ///
+    /// Returns an error when dimensions overflow.
+    pub fn to_choi(&self) -> Result<ChoiMatrix, ChannelError> {
+        let dim_squared = pauli_basis_len(self.num_qubits)?;
+        let basis = pauli_basis_matrices(self.num_qubits)?;
+        let basis_vectors: Vec<DMatrix<Complex64>> = basis.iter().map(vectorize_matrix).collect();
+        let mut matrix = DMatrix::zeros(dim_squared, dim_squared);
+        for row in 0..dim_squared {
+            for col in 0..dim_squared {
+                let coefficient = self.matrix[(row, col)];
+                if coefficient.norm() <= DEFAULT_TOLERANCE {
+                    continue;
+                }
+                matrix += &basis_vectors[row] * basis_vectors[col].adjoint() * coefficient;
+            }
+        }
+        ChoiMatrix::try_new(self.num_qubits, matrix)
+    }
+
+    /// Converts this chi matrix to a PTM.
+    ///
+    /// # Errors
+    ///
+    /// Returns an error when Choi/PTM conversion fails.
+    pub fn to_ptm(&self) -> Result<Ptm, ChannelError> {
+        self.to_choi()?.to_ptm()
+    }
+
+    /// Returns the number of qubits represented by this chi matrix.
+    #[must_use]
+    pub fn num_qubits(&self) -> usize {
+        self.num_qubits
+    }
+
+    /// Returns the PTM basis ordering.
+    #[must_use]
+    pub fn basis_order(&self) -> PtmBasisOrder {
+        self.basis_order
+    }
+
+    /// Returns the dense chi matrix.
+    #[must_use]
+    pub fn matrix(&self) -> &DMatrix<Complex64> {
+        &self.matrix
+    }
+
+    /// Consumes this value and returns its dense matrix.
+    #[must_use]
+    pub fn into_matrix(self) -> DMatrix<Complex64> {
+        self.matrix
+    }
+}
+
+/// Stinespring isometry representation of a quantum channel.
+///
+/// The matrix has shape `(num_kraus * d) x d` and stacks Kraus operators
+/// vertically, where `d = 2^num_qubits`.
+#[derive(Clone, Debug, PartialEq)]
+pub struct Stinespring {
+    num_qubits: usize,
+    environment_dim: usize,
+    isometry: DMatrix<Complex64>,
+}
+
+impl Stinespring {
+    /// Constructs a Stinespring isometry after structural validation.
+    ///
+    /// # Errors
+    ///
+    /// Returns an error when shape or isometry validation fails.
+    pub fn try_new(num_qubits: usize, isometry: DMatrix<Complex64>) -> Result<Self, ChannelError> {
+        let dim = hilbert_dim(num_qubits)?;
+        if isometry.ncols() != dim || isometry.nrows() == 0 || !isometry.nrows().is_multiple_of(dim)
+        {
+            return Err(ChannelError::InvalidMatrixShape {
+                expected_rows: dim,
+                expected_cols: dim,
+                rows: isometry.nrows(),
+                cols: isometry.ncols(),
+            });
+        }
+        validate_complex_matrix(&isometry, isometry.nrows(), dim)?;
+        let identity = DMatrix::<Complex64>::identity(dim, dim);
+        let gram = isometry.adjoint() * &isometry;
+        if matrix_max_abs_diff(&gram, &identity) > 1e-10 {
+            return Err(ChannelError::DecompositionFailed {
+                reason: "Stinespring matrix is not an isometry".to_string(),
+            });
+        }
+        Ok(Self {
+            num_qubits,
+            environment_dim: isometry.nrows() / dim,
+            isometry,
+        })
+    }
+
+    /// Constructs a Stinespring isometry by stacking Kraus operators.
+    ///
+    /// # Errors
+    ///
+    /// Returns an error when the Kraus operators are not trace preserving.
+    pub fn from_kraus(kraus: &KrausOps) -> Result<Self, ChannelError> {
+        let dim = hilbert_dim(kraus.num_qubits)?;
+        let mut isometry = DMatrix::zeros(dim * kraus.operators().len(), dim);
+        for (kraus_idx, operator) in kraus.operators().iter().enumerate() {
+            for row in 0..dim {
+                for col in 0..dim {
+                    isometry[(kraus_idx * dim + row, col)] = operator[(row, col)];
+                }
+            }
+        }
+        Self::try_new(kraus.num_qubits, isometry)
+    }
+
+    /// Converts this Stinespring isometry to Kraus operators.
+    ///
+    /// # Errors
+    ///
+    /// Returns an error when dimensions overflow.
+    pub fn to_kraus(&self) -> Result<KrausOps, ChannelError> {
+        let dim = hilbert_dim(self.num_qubits)?;
+        let operators = (0..self.environment_dim)
+            .map(|kraus_idx| {
+                DMatrix::from_fn(dim, dim, |row, col| {
+                    self.isometry[(kraus_idx * dim + row, col)]
+                })
+            })
+            .collect();
+        KrausOps::try_new(self.num_qubits, operators)
+    }
+
+    /// Converts this Stinespring isometry to a Choi matrix.
+    ///
+    /// # Errors
+    ///
+    /// Returns an error when Kraus/Choi conversion fails.
+    pub fn to_choi(&self) -> Result<ChoiMatrix, ChannelError> {
+        self.to_kraus()?.to_choi()
+    }
+
+    /// Converts this Stinespring isometry to a superoperator.
+    ///
+    /// # Errors
+    ///
+    /// Returns an error when Kraus/superoperator conversion fails.
+    pub fn to_superop(&self) -> Result<SuperOp, ChannelError> {
+        self.to_kraus()?.to_superop()
+    }
+
+    /// Returns the number of qubits represented by this isometry.
+    #[must_use]
+    pub fn num_qubits(&self) -> usize {
+        self.num_qubits
+    }
+
+    /// Returns the environment dimension, equal to the number of Kraus blocks.
+    #[must_use]
+    pub fn environment_dim(&self) -> usize {
+        self.environment_dim
+    }
+
+    /// Returns the dense Stinespring isometry.
+    #[must_use]
+    pub fn isometry(&self) -> &DMatrix<Complex64> {
+        &self.isometry
+    }
+
+    /// Consumes this value and returns its dense isometry.
+    #[must_use]
+    pub fn into_isometry(self) -> DMatrix<Complex64> {
+        self.isometry
+    }
+}
+
+/// Returns the partial trace of a density matrix over selected qubits.
+///
+/// Qubit indexing is little-endian: qubit 0 is the least-significant bit of
+/// the computational-basis index. The returned density matrix keeps the
+/// untraced qubits in ascending qubit-index order.
+///
+/// # Errors
+///
+/// Returns an error when the matrix is not `2^num_qubits x 2^num_qubits`, a
+/// traced qubit is outside range, or a traced qubit is repeated.
+pub fn partial_trace(
+    matrix: &DMatrix<Complex64>,
+    num_qubits: usize,
+    traced_qubits: &[usize],
+) -> Result<DMatrix<Complex64>, ChannelError> {
+    let dim = hilbert_dim(num_qubits)?;
+    if matrix.nrows() != dim || matrix.ncols() != dim {
+        return Err(ChannelError::InvalidMatrixShape {
+            expected_rows: dim,
+            expected_cols: dim,
+            rows: matrix.nrows(),
+            cols: matrix.ncols(),
+        });
+    }
+
+    let mut traced = traced_qubits.to_vec();
+    traced.sort_unstable();
+    for window in traced.windows(2) {
+        if window[0] == window[1] {
+            return Err(ChannelError::DuplicateSubsystem { qubit: window[0] });
+        }
+    }
+    for &qubit in &traced {
+        if qubit >= num_qubits {
+            return Err(ChannelError::QubitOutOfRange { num_qubits, qubit });
+        }
+    }
+
+    let kept: Vec<usize> = (0..num_qubits)
+        .filter(|qubit| traced.binary_search(qubit).is_err())
+        .collect();
+    let out_dim = 1usize << kept.len();
+    let traced_dim = 1usize << traced.len();
+    let mut out = DMatrix::zeros(out_dim, out_dim);
+    for kept_row in 0..out_dim {
+        for kept_col in 0..out_dim {
+            let mut value = Complex64::new(0.0, 0.0);
+            for traced_idx in 0..traced_dim {
+                let row = embed_subsystem_index(&kept, kept_row, &traced, traced_idx);
+                let col = embed_subsystem_index(&kept, kept_col, &traced, traced_idx);
+                value += matrix[(row, col)];
+            }
+            out[(kept_row, kept_col)] = value;
+        }
+    }
+    Ok(out)
+}
+
+/// Returns the computational matrix-unit operator basis.
+///
+/// The returned vector has length `d^2`, where `d = 2^num_qubits`. Entry
+/// `row + col * d` is the matrix unit `|row><col|`. This order is the input
+/// order expected by [`ChoiMatrix::from_matrix_unit_outputs`].
+///
+/// # Errors
+///
+/// Returns an error when the Hilbert-space dimension overflows.
+pub fn matrix_unit_basis(num_qubits: usize) -> Result<Vec<DMatrix<Complex64>>, ChannelError> {
+    let dim = hilbert_dim(num_qubits)?;
+    let dim_squared = pauli_basis_len(num_qubits)?;
+    let mut basis = Vec::with_capacity(dim_squared);
+    for col in 0..dim {
+        for row in 0..dim {
+            let mut matrix = DMatrix::zeros(dim, dim);
+            matrix[(row, col)] = Complex64::new(1.0, 0.0);
+            basis.push(matrix);
+        }
+    }
+    Ok(basis)
+}
+
+/// Metadata for one computational matrix-unit tomography input.
+///
+/// The input operator is `|row><col|`, and `index = row + col * dim`, where
+/// `dim = 2^num_qubits`.
+#[derive(Clone, Copy, Debug, PartialEq, Eq)]
+pub struct MatrixUnitTomographyInput {
+    /// Input index in PECOS matrix-unit tomography order.
+    pub index: usize,
+    /// Ket row of the matrix unit.
+    pub row: usize,
+    /// Bra column of the matrix unit.
+    pub col: usize,
+}
+
+/// Complete linear-inversion process-tomography design.
+///
+/// The current design uses the computational matrix-unit basis. It is useful
+/// for exact channel characterization, simulator validation, and importing
+/// reconstructed channel data. It is not a physical state-preparation recipe;
+/// it records the linear operator basis and the PECOS ordering needed to
+/// reconstruct a [`ChoiMatrix`].
+#[derive(Clone, Debug, PartialEq, Eq)]
+pub struct ProcessTomographyDesign {
+    num_qubits: usize,
+    dim: usize,
+    num_inputs: usize,
+}
+
+impl ProcessTomographyDesign {
+    /// Builds the complete computational matrix-unit design.
+    ///
+    /// # Errors
+    ///
+    /// Returns an error when the Hilbert-space dimension overflows.
+    pub fn matrix_unit(num_qubits: usize) -> Result<Self, ChannelError> {
+        let dim = hilbert_dim(num_qubits)?;
+        let num_inputs = pauli_basis_len(num_qubits)?;
+        Ok(Self {
+            num_qubits,
+            dim,
+            num_inputs,
+        })
+    }
+
+    /// Returns the number of qubits in the characterized channel.
+    #[must_use]
+    pub const fn num_qubits(&self) -> usize {
+        self.num_qubits
+    }
+
+    /// Returns the Hilbert-space dimension `2^num_qubits`.
+    #[must_use]
+    pub const fn dim(&self) -> usize {
+        self.dim
+    }
+
+    /// Returns the number of matrix-unit input operators, `dim^2`.
+    #[must_use]
+    pub const fn num_inputs(&self) -> usize {
+        self.num_inputs
+    }
+
+    /// Returns the index for matrix unit `|row><col|`.
+    ///
+    /// # Errors
+    ///
+    /// Returns an error if `row` or `col` is outside the Hilbert space.
+    pub fn input_index(&self, row: usize, col: usize) -> Result<usize, ChannelError> {
+        if row >= self.dim || col >= self.dim {
+            return Err(ChannelError::MatrixUnitOutOfRange {
+                dim: self.dim,
+                row,
+                col,
+            });
+        }
+        Ok(matrix_unit_index(self.dim, row, col))
+    }
+
+    /// Returns metadata for one matrix-unit input.
+    ///
+    /// # Errors
+    ///
+    /// Returns an error if `index` is outside the design.
+    pub fn input_metadata(&self, index: usize) -> Result<MatrixUnitTomographyInput, ChannelError> {
+        if index >= self.num_inputs {
+            return Err(ChannelError::TomographyInputOutOfRange {
+                num_inputs: self.num_inputs,
+                index,
+            });
+        }
+        Ok(MatrixUnitTomographyInput {
+            index,
+            row: index % self.dim,
+            col: index / self.dim,
+        })
+    }
+
+    /// Returns metadata for all matrix-unit inputs in reconstruction order.
+    #[must_use]
+    pub fn input_metadata_all(&self) -> Vec<MatrixUnitTomographyInput> {
+        (0..self.num_inputs)
+            .map(|index| MatrixUnitTomographyInput {
+                index,
+                row: index % self.dim,
+                col: index / self.dim,
+            })
+            .collect()
+    }
+
+    /// Returns the matrix-unit input operator at `index`.
+    ///
+    /// # Errors
+    ///
+    /// Returns an error if `index` is outside the design.
+    pub fn input_operator(&self, index: usize) -> Result<DMatrix<Complex64>, ChannelError> {
+        let input = self.input_metadata(index)?;
+        let mut matrix = DMatrix::zeros(self.dim, self.dim);
+        matrix[(input.row, input.col)] = Complex64::new(1.0, 0.0);
+        Ok(matrix)
+    }
+
+    /// Returns all matrix-unit input operators in reconstruction order.
+    #[must_use]
+    pub fn input_operators(&self) -> Vec<DMatrix<Complex64>> {
+        (0..self.num_inputs)
+            .map(|index| {
+                let row = index % self.dim;
+                let col = index / self.dim;
+                let mut matrix = DMatrix::zeros(self.dim, self.dim);
+                matrix[(row, col)] = Complex64::new(1.0, 0.0);
+                matrix
+            })
+            .collect()
+    }
+
+    /// Applies `channel` to each design input in reconstruction order.
+    ///
+    /// # Errors
+    ///
+    /// Returns an error when `channel` acts on a different number of qubits or
+    /// if channel application fails.
+    pub fn simulate_outputs(
+        &self,
+        channel: &ChoiMatrix,
+    ) -> Result<Vec<DMatrix<Complex64>>, ChannelError> {
+        if channel.num_qubits() != self.num_qubits {
+            return Err(ChannelError::QubitCountMismatch {
+                expected: self.num_qubits,
+                actual: channel.num_qubits(),
+            });
+        }
+        self.input_operators()
+            .iter()
+            .map(|operator| channel.apply_to_operator(operator))
+            .collect()
+    }
+
+    /// Reconstructs a Choi matrix from outputs ordered by this design.
+    ///
+    /// # Errors
+    ///
+    /// Returns an error when output count or shapes do not match the design.
+    pub fn reconstruct_choi(
+        &self,
+        outputs: &[DMatrix<Complex64>],
+    ) -> Result<ChoiMatrix, ChannelError> {
+        ChoiMatrix::from_matrix_unit_outputs(self.num_qubits, outputs)
+    }
+}
+
+/// Samples a Hilbert-Schmidt random density matrix on `num_qubits` qubits.
+///
+/// This samples a square complex Ginibre matrix `G` and returns
+/// `G G† / Tr(G G†)`. The returned matrix uses the same little-endian
+/// computational-basis order as PECOS's dense matrix helpers.
+///
+/// # Errors
+///
+/// Returns an error when the Hilbert-space dimension overflows.
+pub fn random_density_matrix<R>(
+    rng: &mut R,
+    num_qubits: usize,
+) -> Result<DMatrix<Complex64>, ChannelError>
+where
+    R: Rng + ?Sized,
+{
+    let dim = hilbert_dim(num_qubits)?;
+    random_density_matrix_with_rank(rng, num_qubits, dim)
+}
+
+/// Samples a Hilbert-Schmidt random density matrix with explicit Ginibre rank.
+///
+/// A rank of `1` produces a random pure-state density matrix. Larger ranks
+/// produce mixed states from a `dim x rank` complex Ginibre matrix.
+///
+/// # Errors
+///
+/// Returns an error when the Hilbert-space dimension overflows or `rank == 0`.
+pub fn random_density_matrix_with_rank<R>(
+    rng: &mut R,
+    num_qubits: usize,
+    rank: usize,
+) -> Result<DMatrix<Complex64>, ChannelError>
+where
+    R: Rng + ?Sized,
+{
+    if rank == 0 {
+        return Err(ChannelError::EmptyKrausSet);
+    }
+    let dim = hilbert_dim(num_qubits)?;
+    let ginibre = DMatrix::from_fn(dim, rank, |_, _| standard_complex_normal(rng));
+    let mut rho = &ginibre * ginibre.adjoint();
+    let trace = trace_complex(&rho).re;
+    if trace <= 0.0 || !trace.is_finite() {
+        return Err(ChannelError::DecompositionFailed {
+            reason: "random density matrix has invalid trace".to_string(),
+        });
+    }
+    rho /= Complex64::new(trace, 0.0);
+    Ok(rho)
+}
+
+/// Samples a random CPTP quantum channel in Kraus form.
+///
+/// The implementation samples a random Stinespring isometry by QR-decomposing a
+/// complex Ginibre matrix of shape `(num_kraus * d) x d`, where
+/// `d = 2^num_qubits`, then splits the isometry into `num_kraus` Kraus blocks.
+/// The resulting operators satisfy `sum_k K_k† K_k = I` up to numerical
+/// precision.
+///
+/// # Errors
+///
+/// Returns an error when dimensions overflow or `num_kraus == 0`.
+pub fn random_quantum_channel<R>(
+    rng: &mut R,
+    num_qubits: usize,
+    num_kraus: usize,
+) -> Result<KrausOps, ChannelError>
+where
+    R: Rng + ?Sized,
+{
+    if num_kraus == 0 {
+        return Err(ChannelError::EmptyKrausSet);
+    }
+    let dim = hilbert_dim(num_qubits)?;
+    let rows = dim
+        .checked_mul(num_kraus)
+        .ok_or(ChannelError::DimensionOverflow { num_qubits })?;
+    let ginibre = DMatrix::from_fn(rows, dim, |_, _| standard_complex_normal(rng));
+    let (mut q, r) = ginibre.qr().unpack();
+
+    for col in 0..dim {
+        let diagonal = r[(col, col)];
+        let norm = diagonal.norm();
+        if norm > 0.0 {
+            let phase = diagonal / norm;
+            for row in 0..rows {
+                q[(row, col)] *= phase;
+            }
+        }
+    }
+
+    let operators = (0..num_kraus)
+        .map(|kraus_idx| {
+            let start = kraus_idx * dim;
+            DMatrix::from_fn(dim, dim, |row, col| q[(start + row, col)])
+        })
+        .collect();
+    KrausOps::try_new(num_qubits, operators)
+}
+
+/// Samples a random `num_qubits`-qubit Pauli string.
+///
+/// Each qubit independently receives one of `I, X, Y, Z` with equal
+/// probability. The all-identity Pauli is allowed.
+pub fn random_pauli<R: Rng + ?Sized>(rng: &mut R, num_qubits: usize) -> PauliString {
+    let paulis: Vec<Pauli> = (0..num_qubits)
+        .map(|_| match rng.random_range(0..4) {
+            0 => Pauli::I,
+            1 => Pauli::X,
+            2 => Pauli::Y,
+            _ => Pauli::Z,
+        })
+        .collect();
+    PauliString::from_paulis(&paulis)
+}
+
+/// Samples one of the 24 single-qubit Clifford gate primitives uniformly.
+pub fn random_1q_clifford<R: Rng + ?Sized>(rng: &mut R) -> Clifford {
+    let all = Clifford::all_1q();
+    all[rng.random_range(0..all.len())]
+}
+
+/// Samples one of the standard two-qubit Clifford gate primitives uniformly.
+pub fn random_2q_clifford<R: Rng + ?Sized>(rng: &mut R) -> Clifford {
+    let all = Clifford::all_2q();
+    all[rng.random_range(0..all.len())]
+}
+
+/// Samples one named Clifford gate primitive uniformly from the PECOS Clifford
+/// enum.
+pub fn random_clifford<R: Rng + ?Sized>(rng: &mut R) -> Clifford {
+    let all = Clifford::all();
+    all[rng.random_range(0..all.len())]
+}
+
+fn standard_complex_normal<R: Rng + ?Sized>(rng: &mut R) -> Complex64 {
+    Complex64::new(standard_normal(rng), standard_normal(rng))
+}
+
+fn standard_normal<R: Rng + ?Sized>(rng: &mut R) -> f64 {
+    loop {
+        let u1 = rng.random::<f64>();
+        if u1 > 0.0 {
+            let u2 = rng.random::<f64>();
+            return (-2.0 * u1.ln()).sqrt() * (TAU * u2).cos();
+        }
+    }
+}
+
+fn bitmask_from_paulis(paulis: &[Pauli]) -> PauliBitmaskSmall {
+    let mut out = PauliBitmaskSmall::identity();
+    for (qubit, pauli) in paulis.iter().copied().enumerate() {
+        match pauli {
+            Pauli::I => {}
+            Pauli::X => out.x_bits.set_bit(qubit),
+            Pauli::Y => {
+                out.x_bits.set_bit(qubit);
+                out.z_bits.set_bit(qubit);
+            }
+            Pauli::Z => out.z_bits.set_bit(qubit),
+        }
+    }
+    out
+}
+
+fn channel_num_qubits(channel: &ChannelExpr) -> usize {
+    channel.qubits().into_iter().max().map_or(0, |q| q + 1)
+}
+
+fn bitmask_to_pauli_string(num_qubits: usize, pauli: &PauliBitmaskSmall) -> PauliString {
+    let paulis: Vec<Pauli> = (0..num_qubits)
+        .map(|qubit| match (pauli.has_x(qubit), pauli.has_z(qubit)) {
+            (false, false) => Pauli::I,
+            (true, false) => Pauli::X,
+            (true, true) => Pauli::Y,
+            (false, true) => Pauli::Z,
+        })
+        .collect();
+    PauliString::from_paulis(&paulis)
+}
+
+fn pauli_basis_matrices(num_qubits: usize) -> Result<Vec<DMatrix<Complex64>>, ChannelError> {
+    let basis_len = pauli_basis_len(num_qubits)?;
+    let mut out = Vec::with_capacity(basis_len);
+    for basis_idx in 0..basis_len {
+        let bitmask = basis_bitmask(num_qubits, basis_idx)?;
+        let pauli = bitmask_to_pauli_string(num_qubits, &bitmask);
+        out.push(to_matrix_with_size(&UnitaryRep::Pauli(pauli), num_qubits).into_inner());
+    }
+    Ok(out)
+}
+
+fn apply_ptm_to_operator(
+    ptm: &Ptm,
+    operator: &DMatrix<Complex64>,
+) -> Result<DMatrix<Complex64>, ChannelError> {
+    let dim = hilbert_dim(ptm.num_qubits)?;
+    validate_complex_matrix(operator, dim, dim)?;
+    #[allow(clippy::cast_precision_loss)]
+    let dim_f = dim as f64;
+    let basis_matrices = pauli_basis_matrices(ptm.num_qubits)?;
+    let mut out = DMatrix::zeros(dim, dim);
+    for input_idx in 0..basis_matrices.len() {
+        let coefficient = trace_complex(&(&basis_matrices[input_idx] * operator)) / dim_f;
+        for (output_idx, basis_matrix) in basis_matrices.iter().enumerate() {
+            let output_coefficient = coefficient * ptm.entry(output_idx, input_idx);
+            out += basis_matrix * output_coefficient;
+        }
+    }
+    Ok(out)
+}
+
+fn kraus_from_channel_expr_with_size(
+    channel: &ChannelExpr,
+    num_qubits: usize,
+) -> Result<KrausOps, ChannelError> {
+    match channel {
+        ChannelExpr::Unitary(unitary) => KrausOps::from_unitary(unitary, num_qubits),
+        ChannelExpr::MixedUnitary(ops) => {
+            let mut total_probability = 0.0;
+            let mut operators = Vec::with_capacity(ops.len());
+            for (probability, unitary) in ops {
+                validate_probability(*probability, DEFAULT_TOLERANCE)?;
+                total_probability += *probability;
+                if *probability > DEFAULT_TOLERANCE {
+                    let scale = Complex64::new(probability.sqrt(), 0.0);
+                    operators.push(to_matrix_with_size(unitary, num_qubits).into_inner() * scale);
+                }
+            }
+            if (total_probability - 1.0).abs() > DEFAULT_TOLERANCE {
+                return Err(ChannelError::ProbabilitySum {
+                    sum: total_probability,
+                    tolerance: DEFAULT_TOLERANCE,
+                });
+            }
+            KrausOps::try_new(num_qubits, operators)
+        }
+        ChannelExpr::AmplitudeDamping { gamma, qubit } => {
+            validate_unit_interval(*gamma)?;
+            let sqrt_survival = (1.0 - gamma).sqrt();
+            let sqrt_decay = gamma.sqrt();
+            let k0 = DMatrix::from_row_slice(
+                2,
+                2,
+                &[
+                    Complex64::new(1.0, 0.0),
+                    Complex64::new(0.0, 0.0),
+                    Complex64::new(0.0, 0.0),
+                    Complex64::new(sqrt_survival, 0.0),
+                ],
+            );
+            let k1 = DMatrix::from_row_slice(
+                2,
+                2,
+                &[
+                    Complex64::new(0.0, 0.0),
+                    Complex64::new(sqrt_decay, 0.0),
+                    Complex64::new(0.0, 0.0),
+                    Complex64::new(0.0, 0.0),
+                ],
+            );
+            KrausOps::try_new(
+                num_qubits,
+                vec![
+                    embed_single_qubit_operator(num_qubits, *qubit, &k0)?,
+                    embed_single_qubit_operator(num_qubits, *qubit, &k1)?,
+                ],
+            )
+        }
+        ChannelExpr::PhaseDamping { lambda, qubit } => {
+            validate_unit_interval(*lambda)?;
+            let sqrt_survival = (1.0 - lambda).sqrt();
+            let sqrt_damp = lambda.sqrt();
+            let k0 = DMatrix::from_row_slice(
+                2,
+                2,
+                &[
+                    Complex64::new(1.0, 0.0),
+                    Complex64::new(0.0, 0.0),
+                    Complex64::new(0.0, 0.0),
+                    Complex64::new(sqrt_survival, 0.0),
+                ],
+            );
+            let k1 = DMatrix::from_row_slice(
+                2,
+                2,
+                &[
+                    Complex64::new(0.0, 0.0),
+                    Complex64::new(0.0, 0.0),
+                    Complex64::new(0.0, 0.0),
+                    Complex64::new(sqrt_damp, 0.0),
+                ],
+            );
+            KrausOps::try_new(
+                num_qubits,
+                vec![
+                    embed_single_qubit_operator(num_qubits, *qubit, &k0)?,
+                    embed_single_qubit_operator(num_qubits, *qubit, &k1)?,
+                ],
+            )
+        }
+        ChannelExpr::Tensor(parts) => {
+            if parts.is_empty() {
+                return Err(ChannelError::UnsupportedChannelExpr {
+                    reason: "empty channel tensor has no qubit context".to_string(),
+                });
+            }
+            validate_disjoint_channel_parts(parts)?;
+            let mut operators = vec![DMatrix::<Complex64>::identity(
+                hilbert_dim(num_qubits)?,
+                hilbert_dim(num_qubits)?,
+            )];
+            for part in parts {
+                let part_ops = kraus_from_channel_expr_with_size(part, num_qubits)?;
+                operators = compose_kraus_sets(&operators, part_ops.operators());
+            }
+            KrausOps::try_new(num_qubits, operators)
+        }
+        ChannelExpr::Compose(parts) => {
+            if parts.is_empty() {
+                return Err(ChannelError::UnsupportedChannelExpr {
+                    reason: "empty channel composition has no qubit context".to_string(),
+                });
+            }
+            let dim = hilbert_dim(num_qubits)?;
+            let mut operators = vec![DMatrix::<Complex64>::identity(dim, dim)];
+            for part in parts {
+                let part_ops = kraus_from_channel_expr_with_size(part, num_qubits)?;
+                operators = compose_kraus_sets(&operators, part_ops.operators());
+            }
+            KrausOps::try_new(num_qubits, operators)
+        }
+        ChannelExpr::Gate(_) | ChannelExpr::Erasure { .. } | ChannelExpr::Leakage { .. } => {
+            Err(ChannelError::UnsupportedChannelExpr {
+                reason:
+                    "gate instruments, erasure, and leakage need explicit outcome/flag semantics"
+                        .to_string(),
+            })
+        }
+    }
+}
+
+fn validate_disjoint_channel_parts(parts: &[ChannelExpr]) -> Result<(), ChannelError> {
+    let mut seen = BTreeSet::new();
+    for part in parts {
+        for qubit in part.qubits() {
+            if !seen.insert(qubit) {
+                return Err(ChannelError::DuplicateSubsystem { qubit });
+            }
+        }
+    }
+    Ok(())
+}
+
+fn compose_kraus_sets(
+    current: &[DMatrix<Complex64>],
+    next: &[DMatrix<Complex64>],
+) -> Vec<DMatrix<Complex64>> {
+    let mut out = Vec::with_capacity(current.len() * next.len());
+    for next_op in next {
+        for current_op in current {
+            out.push(next_op * current_op);
+        }
+    }
+    out
+}
+
+fn embed_single_qubit_operator(
+    num_qubits: usize,
+    qubit: usize,
+    local: &DMatrix<Complex64>,
+) -> Result<DMatrix<Complex64>, ChannelError> {
+    if qubit >= num_qubits {
+        return Err(ChannelError::QubitOutOfRange { num_qubits, qubit });
+    }
+    validate_complex_matrix(local, 2, 2)?;
+
+    let dim = hilbert_dim(num_qubits)?;
+    let qubit_mask = 1usize << qubit;
+    let mut out = DMatrix::zeros(dim, dim);
+    for row in 0..dim {
+        for col in 0..dim {
+            if row & !qubit_mask == col & !qubit_mask {
+                let local_row = usize::from((row & qubit_mask) != 0);
+                let local_col = usize::from((col & qubit_mask) != 0);
+                out[(row, col)] = local[(local_row, local_col)];
+            }
+        }
+    }
+    Ok(out)
+}
+
+fn choi_index(dim: usize, output_index: usize, input_index: usize) -> usize {
+    output_index + input_index * dim
+}
+
+fn matrix_unit_index(dim: usize, row: usize, col: usize) -> usize {
+    row + col * dim
+}
+
+fn vectorize_matrix(matrix: &DMatrix<Complex64>) -> DMatrix<Complex64> {
+    DMatrix::from_fn(matrix.nrows() * matrix.ncols(), 1, |idx, _| {
+        let row = idx % matrix.nrows();
+        let col = idx / matrix.nrows();
+        matrix[(row, col)]
+    })
+}
+
+fn complex_kronecker(left: &DMatrix<Complex64>, right: &DMatrix<Complex64>) -> DMatrix<Complex64> {
+    let rows = left.nrows() * right.nrows();
+    let cols = left.ncols() * right.ncols();
+    let mut out = DMatrix::zeros(rows, cols);
+    for left_row in 0..left.nrows() {
+        for left_col in 0..left.ncols() {
+            let scale = left[(left_row, left_col)];
+            for right_row in 0..right.nrows() {
+                for right_col in 0..right.ncols() {
+                    out[(
+                        left_row * right.nrows() + right_row,
+                        left_col * right.ncols() + right_col,
+                    )] = scale * right[(right_row, right_col)];
+                }
+            }
+        }
+    }
+    out
+}
+
+fn trace_complex(matrix: &DMatrix<Complex64>) -> Complex64 {
+    let n = matrix.nrows().min(matrix.ncols());
+    (0..n).map(|idx| matrix[(idx, idx)]).sum()
+}
+
+fn hilbert_dim(num_qubits: usize) -> Result<usize, ChannelError> {
+    2usize
+        .checked_pow(
+            num_qubits
+                .try_into()
+                .map_err(|_| ChannelError::DimensionOverflow { num_qubits })?,
+        )
+        .ok_or(ChannelError::DimensionOverflow { num_qubits })
+}
+
+fn embed_subsystem_index(
+    kept_qubits: &[usize],
+    kept_index: usize,
+    traced_qubits: &[usize],
+    traced_index: usize,
+) -> usize {
+    let mut out = 0usize;
+    for (bit, qubit) in kept_qubits.iter().copied().enumerate() {
+        if ((kept_index >> bit) & 1) != 0 {
+            out |= 1usize << qubit;
+        }
+    }
+    for (bit, qubit) in traced_qubits.iter().copied().enumerate() {
+        if ((traced_index >> bit) & 1) != 0 {
+            out |= 1usize << qubit;
+        }
+    }
+    out
+}
+
+fn unitary_rep_to_pauli_bitmask(
+    num_qubits: usize,
+    unitary: &UnitaryRep,
+) -> Result<PauliBitmaskSmall, ChannelError> {
+    match unitary {
+        unitary if unitary.is_identity() => Ok(PauliBitmaskSmall::identity()),
+        UnitaryRep::Pauli(pauli) => {
+            // Global Pauli phase cancels in the induced channel U rho U†.
+            pauli_string_to_bitmask(num_qubits, pauli)
+        }
+        UnitaryRep::Tensor(parts) => {
+            let mut out = PauliBitmaskSmall::identity();
+            for part in parts {
+                let part_mask = unitary_rep_to_pauli_bitmask(num_qubits, part)?;
+                out = out.multiply(&part_mask);
+            }
+            Ok(out)
+        }
+        _ => Err(ChannelError::UnsupportedChannelExpr {
+            reason: format!("unitary is not a Pauli operator: {unitary:?}"),
+        }),
+    }
+}
+
+fn validate_num_qubits(num_qubits: usize, pauli: &PauliBitmaskSmall) -> Result<(), ChannelError> {
+    if let Some(qubit) = highest_qubit(pauli)
+        && qubit >= num_qubits
+    {
+        return Err(ChannelError::QubitOutOfRange { num_qubits, qubit });
+    }
+    Ok(())
+}
+
+fn highest_qubit(pauli: &PauliBitmaskSmall) -> Option<usize> {
+    [
+        pauli.x_bits.highest_set_bit(),
+        pauli.z_bits.highest_set_bit(),
+    ]
+    .into_iter()
+    .flatten()
+    .max()
+}
+
+fn validate_complex(value: Complex64) -> Result<(), ChannelError> {
+    if value.re.is_finite() && value.im.is_finite() {
+        Ok(())
+    } else {
+        Err(ChannelError::InvalidCoefficient { value })
+    }
+}
+
+fn validate_complex_matrix(
+    matrix: &DMatrix<Complex64>,
+    expected_rows: usize,
+    expected_cols: usize,
+) -> Result<(), ChannelError> {
+    if matrix.nrows() != expected_rows || matrix.ncols() != expected_cols {
+        return Err(ChannelError::InvalidMatrixShape {
+            expected_rows,
+            expected_cols,
+            rows: matrix.nrows(),
+            cols: matrix.ncols(),
+        });
+    }
+    for value in matrix.iter() {
+        validate_complex(*value)?;
+    }
+    Ok(())
+}
+
+fn validate_real(value: f64) -> Result<(), ChannelError> {
+    validate_complex(Complex64::new(value, 0.0))
+}
+
+fn validate_probability(value: f64, tolerance: f64) -> Result<(), ChannelError> {
+    validate_real(value)?;
+    if value < -tolerance {
+        return Err(ChannelError::InvalidProbability { value, tolerance });
+    }
+    Ok(())
+}
+
+fn validate_unit_interval(value: f64) -> Result<(), ChannelError> {
+    validate_probability(value, DEFAULT_TOLERANCE)?;
+    if value > 1.0 + DEFAULT_TOLERANCE {
+        return Err(ChannelError::InvalidProbability {
+            value,
+            tolerance: DEFAULT_TOLERANCE,
+        });
+    }
+    Ok(())
+}
+
+fn matrix_max_abs_diff(a: &DMatrix<Complex64>, b: &DMatrix<Complex64>) -> f64 {
+    if a.shape() != b.shape() {
+        return f64::INFINITY;
+    }
+    a.iter()
+        .zip(b.iter())
+        .map(|(left, right)| (*left - *right).norm())
+        .fold(0.0, f64::max)
+}
+
+fn commutation_character(a: &PauliBitmaskSmall, b: &PauliBitmaskSmall) -> f64 {
+    if a.commutes_with(b) { 1.0 } else { -1.0 }
+}
+
+#[cfg(test)]
+mod tests {
+    use super::*;
+    use pecos_core::op;
+    use pecos_core::unitary;
+    use pecos_core::{Op, QuarterPhase};
+    use pecos_random::PecosRng;
+
+    fn assert_close(a: f64, b: f64) {
+        assert!((a - b).abs() < 1e-10, "{a} != {b}");
+    }
+
+    fn assert_complex_close(a: Complex64, b: Complex64) {
+        assert_close(a.re, b.re);
+        assert_close(a.im, b.im);
+    }
+
+    fn assert_matrix_close(a: &DMatrix<f64>, b: &DMatrix<f64>) {
+        assert_eq!(a.shape(), b.shape());
+        for row in 0..a.nrows() {
+            for col in 0..a.ncols() {
+                assert_close(a[(row, col)], b[(row, col)]);
+            }
+        }
+    }
+
+    fn assert_complex_matrix_close(a: &DMatrix<Complex64>, b: &DMatrix<Complex64>) {
+        assert_eq!(a.shape(), b.shape());
+        for row in 0..a.nrows() {
+            for col in 0..a.ncols() {
+                assert_complex_close(a[(row, col)], b[(row, col)]);
+            }
+        }
+    }
+
+    fn apply_kraus_direct(kraus: &KrausOps, operator: &DMatrix<Complex64>) -> DMatrix<Complex64> {
+        let mut output = DMatrix::zeros(operator.nrows(), operator.ncols());
+        for k in kraus.operators() {
+            output += k * operator * k.adjoint();
+        }
+        output
+    }
+
+    fn direct_superop_from_kraus(kraus: &KrausOps) -> DMatrix<Complex64> {
+        let dim = hilbert_dim(kraus.num_qubits()).unwrap();
+        let dim_squared = dim * dim;
+        let mut matrix = DMatrix::zeros(dim_squared, dim_squared);
+        for input_col in 0..dim {
+            for input_row in 0..dim {
+                let mut input = DMatrix::zeros(dim, dim);
+                input[(input_row, input_col)] = Complex64::new(1.0, 0.0);
+                let output = apply_kraus_direct(kraus, &input);
+                let input_idx = matrix_unit_index(dim, input_row, input_col);
+                for output_col in 0..dim {
+                    for output_row in 0..dim {
+                        let output_idx = matrix_unit_index(dim, output_row, output_col);
+                        matrix[(output_idx, input_idx)] = output[(output_row, output_col)];
+                    }
+                }
+            }
+        }
+        matrix
+    }
+
+    fn direct_ptm_from_kraus(kraus: &KrausOps) -> DMatrix<f64> {
+        let num_qubits = kraus.num_qubits();
+        let basis = pauli_basis_matrices(num_qubits).unwrap();
+        let dim = hilbert_dim(num_qubits).unwrap();
+        #[allow(clippy::cast_precision_loss)]
+        let dim_f = dim as f64;
+        let mut matrix = DMatrix::zeros(basis.len(), basis.len());
+        for input_idx in 0..basis.len() {
+            let evolved = apply_kraus_direct(kraus, &basis[input_idx]);
+            for output_idx in 0..basis.len() {
+                let entry = trace_complex(&(&basis[output_idx] * &evolved)) / dim_f;
+                assert!(
+                    entry.im.abs() < 1e-10,
+                    "PTM oracle produced complex entry {entry}"
+                );
+                matrix[(output_idx, input_idx)] = entry.re;
+            }
+        }
+        matrix
+    }
+
+    fn direct_matrix_unit_outputs(kraus: &KrausOps) -> Vec<DMatrix<Complex64>> {
+        let dim = hilbert_dim(kraus.num_qubits()).unwrap();
+        let mut outputs = Vec::with_capacity(dim * dim);
+        for input_col in 0..dim {
+            for input_row in 0..dim {
+                let mut input = DMatrix::zeros(dim, dim);
+                input[(input_row, input_col)] = Complex64::new(1.0, 0.0);
+                outputs.push(apply_kraus_direct(kraus, &input));
+            }
+        }
+        outputs
+    }
+
+    fn assert_ptm_entry(ptm: &Ptm, output: &str, input: &str, expected: f64) {
+        let output_idx = labels(ptm.num_qubits())
+            .iter()
+            .position(|label| label == output)
+            .unwrap();
+        let input_idx = labels(ptm.num_qubits())
+            .iter()
+            .position(|label| label == input)
+            .unwrap();
+        assert_close(ptm.entry(output_idx, input_idx), expected);
+    }
+
+    fn labels(num_qubits: usize) -> Vec<String> {
+        (0..pauli_basis_len(num_qubits).unwrap())
+            .map(|index| basis_label(num_qubits, index).unwrap())
+            .collect()
+    }
+
+    #[test]
+    fn one_qubit_basis_order_is_independent_of_pauli_discriminants() {
+        assert_eq!(Pauli::Z as u8, 0b10);
+        assert_eq!(Pauli::Y as u8, 0b11);
+
+        assert_eq!(pauli_to_basis_digit(Pauli::I), 0);
+        assert_eq!(pauli_to_basis_digit(Pauli::X), 1);
+        assert_eq!(pauli_to_basis_digit(Pauli::Y), 2);
+        assert_eq!(pauli_to_basis_digit(Pauli::Z), 3);
+
+        assert_eq!(labels(1), ["I", "X", "Y", "Z"]);
+    }
+
+    #[test]
+    fn two_qubit_basis_order_is_little_endian_lexicographic() {
+        assert_eq!(
+            labels(2),
+            [
+                "II", "IX", "IY", "IZ", "XI", "XX", "XY", "XZ", "YI", "YX", "YY", "YZ", "ZI", "ZX",
+                "ZY", "ZZ",
+            ]
+        );
+    }
+
+    #[test]
+    fn basis_bitmask_and_index_round_trip() {
+        for num_qubits in 1..=3 {
+            for index in 0..pauli_basis_len(num_qubits).unwrap() {
+                let pauli = basis_bitmask(num_qubits, index).unwrap();
+                assert_eq!(basis_index(num_qubits, &pauli).unwrap(), index);
+            }
+        }
+    }
+
+    #[test]
+    fn zero_qubit_channel_representations_are_scalar_identity() {
+        let ptm = Ptm::identity(0).unwrap();
+        assert_eq!(ptm.matrix().shape(), (1, 1));
+        assert_close(ptm.entry(0, 0), 1.0);
+
+        let mut probabilities = BTreeMap::new();
+        probabilities.insert(PauliBitmaskSmall::identity(), 1.0);
+        let pauli_channel = PauliChannel::try_new(0, probabilities).unwrap();
+        assert_close(pauli_channel.total_error_rate(), 0.0);
+        assert_matrix_close(pauli_channel.to_ptm().unwrap().matrix(), ptm.matrix());
+
+        let kraus = KrausOps::try_new(
+            0,
+            vec![DMatrix::from_element(1, 1, Complex64::new(1.0, 0.0))],
+        )
+        .unwrap();
+        assert!(kraus.is_trace_preserving());
+
+        let choi = kraus.to_choi().unwrap();
+        assert_eq!(choi.matrix().shape(), (1, 1));
+        assert_complex_close(choi.matrix()[(0, 0)], Complex64::new(1.0, 0.0));
+        assert!(choi.is_cptp());
+
+        let superop = kraus.to_superop().unwrap();
+        assert_eq!(superop.num_qubits(), 0);
+        assert_complex_close(superop.matrix()[(0, 0)], Complex64::new(1.0, 0.0));
+
+        let chi = kraus.to_chi().unwrap();
+        assert_complex_close(chi.matrix()[(0, 0)], Complex64::new(1.0, 0.0));
+
+        let stinespring = kraus.to_stinespring().unwrap();
+        assert_eq!(stinespring.environment_dim(), 1);
+        assert_complex_close(stinespring.isometry()[(0, 0)], Complex64::new(1.0, 0.0));
+    }
+
+    #[test]
+    fn pauli_sum_add_scalar_simplify_and_trace() {
+        let identity = PauliBitmaskSmall::identity();
+        let x0 = PauliBitmaskSmall::x(0);
+
+        let mut a = PauliSum::new(1);
+        a.add_term(identity.clone(), Complex64::new(2.0, 0.0))
+            .unwrap();
+        a.add_term(x0.clone(), Complex64::new(1.0, 0.0)).unwrap();
+
+        let mut b = PauliSum::new(1);
+        b.add_term(x0.clone(), Complex64::new(-1.0, 0.0)).unwrap();
+        b.add_term(PauliBitmaskSmall::z(0), Complex64::new(0.5, 0.0))
+            .unwrap();
+
+        let c = (a + b) * 2.0;
+        assert_eq!(c.terms().len(), 2);
+        assert_complex_close(*c.terms().get(&identity).unwrap(), Complex64::new(4.0, 0.0));
+        assert_complex_close(c.trace().unwrap(), Complex64::new(8.0, 0.0));
+    }
+
+    #[test]
+    fn pauli_sum_trace_reports_dimension_overflow() {
+        let sum = PauliSum::new(usize::MAX);
+        assert_eq!(
+            sum.trace().unwrap_err(),
+            ChannelError::DimensionOverflow {
+                num_qubits: usize::MAX
+            }
+        );
+    }
+
+    #[test]
+    fn pauli_sum_try_add_reports_qubit_mismatch() {
+        let a = PauliSum::new(1);
+        let b = PauliSum::new(2);
+
+        assert_eq!(
+            a.try_add(b).unwrap_err(),
+            ChannelError::QubitCountMismatch {
+                expected: 1,
+                actual: 2
+            }
+        );
+    }
+
+    #[test]
+    fn pauli_sum_try_add_merges_terms_and_drops_cancellations() {
+        let identity = PauliBitmaskSmall::identity();
+        let x0 = PauliBitmaskSmall::x(0);
+        let z0 = PauliBitmaskSmall::z(0);
+
+        let mut a = PauliSum::new(1);
+        a.add_term(identity.clone(), Complex64::new(2.0, 0.0))
+            .unwrap();
+        a.add_term(x0.clone(), Complex64::new(1.0, 0.0)).unwrap();
+
+        let mut b = PauliSum::new(1);
+        b.add_term(x0.clone(), Complex64::new(-1.0, 0.0)).unwrap();
+        b.add_term(z0.clone(), Complex64::new(0.5, 0.0)).unwrap();
+
+        let sum = a.try_add(b).unwrap();
+        assert_eq!(sum.terms().len(), 2);
+        assert!(sum.terms().get(&x0).is_none());
+        assert_complex_close(
+            *sum.terms().get(&identity).unwrap(),
+            Complex64::new(2.0, 0.0),
+        );
+        assert_complex_close(*sum.terms().get(&z0).unwrap(), Complex64::new(0.5, 0.0));
+    }
+
+    #[test]
+    fn pauli_sum_from_pauli_string_preserves_phase_as_coefficient() {
+        let pauli = PauliString::with_phase_and_paulis(
+            QuarterPhase::PlusI,
+            vec![(Pauli::X, 0.into()), (Pauli::Z, 1.into())],
+        );
+        let sum = PauliSum::from_pauli_string(2, &pauli).unwrap();
+        let label = pauli_string_to_bitmask(2, &pauli).unwrap();
+        assert_complex_close(*sum.terms().get(&label).unwrap(), Complex64::new(0.0, 1.0));
+        assert_eq!(bitmask_label(2, &label).unwrap(), "ZX");
+    }
+
+    #[test]
+    fn pauli_string_conjugates_pauli_sum_terms() {
+        let mut sum = PauliSum::new(1);
+        sum.add_term(PauliBitmaskSmall::x(0), Complex64::new(2.0, 0.0))
+            .unwrap();
+        sum.add_term(PauliBitmaskSmall::z(0), Complex64::new(3.0, 0.0))
+            .unwrap();
+
+        let conjugated = sum.conjugated_by_pauli_string(&PauliString::z(0)).unwrap();
+        assert_complex_close(
+            *conjugated.terms().get(&PauliBitmaskSmall::x(0)).unwrap(),
+            Complex64::new(-2.0, 0.0),
+        );
+        assert_complex_close(
+            *conjugated.terms().get(&PauliBitmaskSmall::z(0)).unwrap(),
+            Complex64::new(3.0, 0.0),
+        );
+    }
+
+    #[test]
+    fn pauli_sum_group_commuting_preserves_coefficients() {
+        let mut sum = PauliSum::new(2);
+        sum.add_term(PauliBitmaskSmall::x(0), Complex64::new(2.0, 0.0))
+            .unwrap();
+        sum.add_term(PauliBitmaskSmall::z(0), Complex64::new(3.0, 0.0))
+            .unwrap();
+        sum.add_term(PauliBitmaskSmall::x(1), Complex64::new(5.0, 0.0))
+            .unwrap();
+        sum.add_term(PauliBitmaskSmall::z(1), Complex64::new(7.0, 0.0))
+            .unwrap();
+
+        let groups = sum.group_commuting();
+        assert_eq!(groups.len(), 2);
+        assert_eq!(
+            groups
+                .iter()
+                .map(|group| group.terms().len())
+                .sum::<usize>(),
+            4
+        );
+
+        for group in &groups {
+            for left in group.terms().keys() {
+                for right in group.terms().keys() {
+                    assert!(left.commutes_with(right));
+                }
+            }
+        }
+
+        let recovered: BTreeMap<_, _> = groups
+            .iter()
+            .flat_map(|group| {
+                group
+                    .terms()
+                    .iter()
+                    .map(|(pauli, coeff)| (pauli.clone(), *coeff))
+            })
+            .collect();
+        assert_eq!(recovered, sum.terms().clone());
+    }
+
+    #[test]
+    fn qubit_count_errors_fail_construction() {
+        let mut terms = BTreeMap::new();
+        terms.insert(PauliBitmaskSmall::x(2), Complex64::new(1.0, 0.0));
+        let err = PauliSum::try_new(2, terms).unwrap_err();
+        assert_eq!(
+            err,
+            ChannelError::QubitOutOfRange {
+                num_qubits: 2,
+                qubit: 2
+            }
+        );
+    }
+
+    #[test]
+    fn one_qubit_pauli_channel_round_trips_through_diagonal_ptm() {
+        let channel = PauliChannel::one_qubit(0.1, 0.2, 0.3).unwrap();
+        let diagonal = channel.to_diagonal_ptm().unwrap();
+
+        assert_close(diagonal.fidelity(&PauliBitmaskSmall::identity()), 1.0);
+        assert_close(diagonal.fidelity(&PauliBitmaskSmall::x(0)), 0.0);
+        assert_close(diagonal.fidelity(&PauliBitmaskSmall::y(0)), 0.2);
+        assert_close(diagonal.fidelity(&PauliBitmaskSmall::z(0)), 0.4);
+
+        let recovered = diagonal.to_pauli_channel().unwrap();
+        assert_close(recovered.probability(&PauliBitmaskSmall::identity()), 0.4);
+        assert_close(recovered.probability(&PauliBitmaskSmall::x(0)), 0.1);
+        assert_close(recovered.probability(&PauliBitmaskSmall::y(0)), 0.2);
+        assert_close(recovered.probability(&PauliBitmaskSmall::z(0)), 0.3);
+        assert_close(recovered.total_error_rate(), 0.6);
+    }
+
+    #[test]
+    fn two_qubit_pauli_channel_round_trips_through_diagonal_ptm() {
+        let mut probabilities = BTreeMap::new();
+        probabilities.insert(PauliBitmaskSmall::identity(), 0.7);
+        probabilities.insert(PauliBitmaskSmall::x(0), 0.1);
+        probabilities.insert(PauliBitmaskSmall::z(1), 0.05);
+        probabilities.insert(
+            PauliBitmaskSmall::y(0).multiply(&PauliBitmaskSmall::x(1)),
+            0.15,
+        );
+
+        let channel = PauliChannel::try_new(2, probabilities).unwrap();
+        let recovered = channel
+            .to_diagonal_ptm()
+            .unwrap()
+            .to_pauli_channel()
+            .unwrap();
+
+        assert_close(recovered.probability(&PauliBitmaskSmall::identity()), 0.7);
+        assert_close(recovered.probability(&PauliBitmaskSmall::x(0)), 0.1);
+        assert_close(recovered.probability(&PauliBitmaskSmall::z(1)), 0.05);
+        assert_close(
+            recovered.probability(&PauliBitmaskSmall::y(0).multiply(&PauliBitmaskSmall::x(1))),
+            0.15,
+        );
+    }
+
+    #[test]
+    fn pauli_channel_from_pauli_strings_accumulates_sparse_operator_keys() {
+        use pecos_core::pauli::{I, X, Z};
+
+        let channel = PauliChannel::from_pauli_strings(
+            2,
+            [(I(), 0.5), (X(0) & Z(1), 0.2), (X(0) & Z(1), 0.3)],
+        )
+        .unwrap();
+
+        assert_close(channel.probability(&PauliBitmaskSmall::identity()), 0.5);
+        assert_close(
+            channel.probability(&PauliBitmaskSmall::x(0).multiply(&PauliBitmaskSmall::z(1))),
+            0.5,
+        );
+
+        let err = PauliChannel::from_pauli_strings(1, [(Z(2), 1.0)]).unwrap_err();
+        assert_eq!(
+            err,
+            ChannelError::QubitOutOfRange {
+                num_qubits: 1,
+                qubit: 2
+            }
+        );
+    }
+
+    #[test]
+    fn diagonal_ptm_values_are_not_probabilities() {
+        let mut fidelities = BTreeMap::new();
+        fidelities.insert(PauliBitmaskSmall::identity(), 1.0);
+        fidelities.insert(PauliBitmaskSmall::x(0), -0.5);
+        fidelities.insert(PauliBitmaskSmall::y(0), 0.25);
+        fidelities.insert(PauliBitmaskSmall::z(0), 0.75);
+
+        let diagonal = DiagonalPtm::try_new(1, fidelities.clone()).unwrap();
+        assert_close(diagonal.fidelity(&PauliBitmaskSmall::x(0)), -0.5);
+
+        let err = PauliChannel::try_new(1, fidelities).unwrap_err();
+        assert!(matches!(err, ChannelError::InvalidProbability { .. }));
+    }
+
+    #[test]
+    fn pauli_channel_from_pauli_sum_rejects_complex_or_negative_coefficients() {
+        let mut complex = PauliSum::new(1);
+        complex
+            .add_term(PauliBitmaskSmall::identity(), Complex64::new(1.0, 0.1))
+            .unwrap();
+        assert!(matches!(
+            PauliChannel::from_pauli_sum(&complex).unwrap_err(),
+            ChannelError::NonRealCoefficient { .. }
+        ));
+
+        let mut negative_terms = BTreeMap::new();
+        negative_terms.insert(PauliBitmaskSmall::identity(), -0.1);
+        negative_terms.insert(PauliBitmaskSmall::x(0), 1.1);
+        assert!(matches!(
+            PauliChannel::try_new(1, negative_terms).unwrap_err(),
+            ChannelError::InvalidProbability { .. }
+        ));
+    }
+
+    #[test]
+    fn dense_ptm_identity_channel_is_identity_matrix() {
+        let ptm = Ptm::identity(2).unwrap();
+        assert_eq!(ptm.matrix().nrows(), 16);
+        assert_eq!(ptm.matrix().ncols(), 16);
+        for row in 0..16 {
+            for col in 0..16 {
+                assert_close(ptm.entry(row, col), if row == col { 1.0 } else { 0.0 });
+            }
+        }
+    }
+
+    #[test]
+    fn bit_flip_channel_matches_hand_ptm_and_choi_references() {
+        use pecos_core::pauli::{I, X};
+
+        let p = 0.2;
+        let channel = PauliChannel::from_pauli_strings(1, [(I(), 1.0 - p), (X(0), p)]).unwrap();
+        let ptm = channel.to_ptm().unwrap();
+
+        assert_ptm_entry(&ptm, "I", "I", 1.0);
+        assert_ptm_entry(&ptm, "X", "X", 1.0);
+        assert_ptm_entry(&ptm, "Y", "Y", 1.0 - 2.0 * p);
+        assert_ptm_entry(&ptm, "Z", "Z", 1.0 - 2.0 * p);
+
+        let choi = ptm.to_choi().unwrap();
+        let matrix = choi.matrix();
+        assert_complex_close(matrix[(0, 0)], Complex64::new(1.0 - p, 0.0));
+        assert_complex_close(matrix[(0, 3)], Complex64::new(1.0 - p, 0.0));
+        assert_complex_close(matrix[(3, 0)], Complex64::new(1.0 - p, 0.0));
+        assert_complex_close(matrix[(3, 3)], Complex64::new(1.0 - p, 0.0));
+        assert_complex_close(matrix[(1, 1)], Complex64::new(p, 0.0));
+        assert_complex_close(matrix[(1, 2)], Complex64::new(p, 0.0));
+        assert_complex_close(matrix[(2, 1)], Complex64::new(p, 0.0));
+        assert_complex_close(matrix[(2, 2)], Complex64::new(p, 0.0));
+    }
+
+    #[test]
+    fn depolarizing_channel_matches_hand_diagonal_ptm_reference() {
+        use pecos_core::pauli::{I, X, Y, Z};
+
+        let p = 0.1;
+        let channel = PauliChannel::from_pauli_strings(
+            1,
+            [
+                (I(), 1.0 - p),
+                (X(0), p / 3.0),
+                (Y(0), p / 3.0),
+                (Z(0), p / 3.0),
+            ],
+        )
+        .unwrap();
+        let ptm = channel.to_ptm().unwrap();
+        let non_identity_fidelity = 1.0 - 4.0 * p / 3.0;
+
+        assert_ptm_entry(&ptm, "I", "I", 1.0);
+        assert_ptm_entry(&ptm, "X", "X", non_identity_fidelity);
+        assert_ptm_entry(&ptm, "Y", "Y", non_identity_fidelity);
+        assert_ptm_entry(&ptm, "Z", "Z", non_identity_fidelity);
+    }
+
+    #[test]
+    fn dense_ptm_unitary_conjugation_known_one_qubit_cliffords() {
+        let h = Ptm::from_unitary(&unitary::H(0), 1).unwrap();
+        assert_ptm_entry(&h, "I", "I", 1.0);
+        assert_ptm_entry(&h, "Z", "X", 1.0);
+        assert_ptm_entry(&h, "Y", "Y", -1.0);
+        assert_ptm_entry(&h, "X", "Z", 1.0);
+
+        let s = Ptm::from_unitary(&unitary::SZ(0), 1).unwrap();
+        assert_ptm_entry(&s, "I", "I", 1.0);
+        assert_ptm_entry(&s, "Y", "X", 1.0);
+        assert_ptm_entry(&s, "X", "Y", -1.0);
+        assert_ptm_entry(&s, "Z", "Z", 1.0);
+
+        let x = Ptm::from_unitary(&unitary::X(0), 1).unwrap();
+        assert_ptm_entry(&x, "I", "I", 1.0);
+        assert_ptm_entry(&x, "X", "X", 1.0);
+        assert_ptm_entry(&x, "Y", "Y", -1.0);
+        assert_ptm_entry(&x, "Z", "Z", -1.0);
+    }
+
+    #[test]
+    fn dense_ptm_qubit_order_matches_unitary_matrix_little_endian() {
+        let x0 = Ptm::from_unitary(&(unitary::X(0) & unitary::I(1)), 2).unwrap();
+        assert_ptm_entry(&x0, "IZ", "IZ", -1.0);
+        assert_ptm_entry(&x0, "ZI", "ZI", 1.0);
+
+        let x1 = Ptm::from_unitary(&(unitary::I(0) & unitary::X(1)), 2).unwrap();
+        assert_ptm_entry(&x1, "IZ", "IZ", 1.0);
+        assert_ptm_entry(&x1, "ZI", "ZI", -1.0);
+    }
+
+    #[test]
+    fn invalid_dense_ptm_shape_fails_construction() {
+        let err = Ptm::try_new(1, DMatrix::zeros(3, 3)).unwrap_err();
+        assert!(matches!(err, ChannelError::InvalidMatrixShape { .. }));
+    }
+
+    #[test]
+    fn channel_expr_pauli_channel_conversions_handle_common_constructors() {
+        let Op::Channel(expr) = op::Depolarizing(0.3, 0) else {
+            panic!("expected channel");
+        };
+        let channel = PauliChannel::from_channel_expr(&expr).unwrap();
+        assert_close(channel.probability(&PauliBitmaskSmall::identity()), 0.7);
+        assert_close(channel.probability(&PauliBitmaskSmall::x(0)), 0.1);
+        assert_close(channel.probability(&PauliBitmaskSmall::y(0)), 0.1);
+        assert_close(channel.probability(&PauliBitmaskSmall::z(0)), 0.1);
+
+        let diagonal = DiagonalPtm::from_channel_expr(&expr).unwrap();
+        let dense = Ptm::from_channel_expr(&expr).unwrap();
+        assert_close(dense.entry(0, 0), 1.0);
+        assert_close(
+            dense.entry(1, 1),
+            diagonal.fidelity(&PauliBitmaskSmall::x(0)),
+        );
+    }
+
+    #[test]
+    fn kraus_unitary_ptm_matches_direct_unitary_ptm() {
+        let kraus = KrausOps::from_unitary(&unitary::H(0), 1).unwrap();
+        assert_eq!(kraus.num_qubits(), 1);
+        assert_eq!(kraus.operators().len(), 1);
+        assert!(kraus.is_trace_preserving());
+
+        let from_kraus = kraus.to_ptm().unwrap();
+        let direct = Ptm::from_unitary(&unitary::H(0), 1).unwrap();
+        assert_matrix_close(from_kraus.matrix(), direct.matrix());
+    }
+
+    #[test]
+    fn kraus_mixed_unitary_ptm_matches_pauli_channel_ptm() {
+        let Op::Channel(expr) = op::Depolarizing(0.3, 0) else {
+            panic!("expected channel");
+        };
+        let kraus = KrausOps::from_channel_expr(&expr).unwrap();
+        assert_eq!(kraus.operators().len(), 4);
+        assert!(kraus.is_trace_preserving());
+
+        let from_kraus = kraus.to_ptm().unwrap();
+        let from_pauli = PauliChannel::from_channel_expr(&expr)
+            .unwrap()
+            .to_ptm()
+            .unwrap();
+        assert_matrix_close(from_kraus.matrix(), from_pauli.matrix());
+    }
+
+    #[test]
+    fn amplitude_damping_kraus_and_ptm_have_known_values() {
+        let gamma = 0.25;
+        let Op::Channel(expr) = op::AmplitudeDamping(gamma, 0) else {
+            panic!("expected channel");
+        };
+        let kraus = KrausOps::from_channel_expr(&expr).unwrap();
+        assert_eq!(kraus.operators().len(), 2);
+        assert!(kraus.is_trace_preserving());
+
+        let ptm = Ptm::from_channel_expr(&expr).unwrap();
+        assert_ptm_entry(&ptm, "I", "I", 1.0);
+        assert_ptm_entry(&ptm, "Z", "I", gamma);
+        assert_ptm_entry(&ptm, "X", "X", (1.0 - gamma).sqrt());
+        assert_ptm_entry(&ptm, "Y", "Y", (1.0 - gamma).sqrt());
+        assert_ptm_entry(&ptm, "Z", "Z", 1.0 - gamma);
+    }
+
+    #[test]
+    fn phase_damping_kraus_and_ptm_have_known_values() {
+        let lambda = 0.36;
+        let Op::Channel(expr) = op::PhaseDamping(lambda, 0) else {
+            panic!("expected channel");
+        };
+        let kraus = KrausOps::from_channel_expr(&expr).unwrap();
+        assert_eq!(kraus.operators().len(), 2);
+        assert!(kraus.is_trace_preserving());
+
+        let ptm = Ptm::from_channel_expr(&expr).unwrap();
+        assert_ptm_entry(&ptm, "I", "I", 1.0);
+        assert_ptm_entry(&ptm, "X", "X", (1.0 - lambda).sqrt());
+        assert_ptm_entry(&ptm, "Y", "Y", (1.0 - lambda).sqrt());
+        assert_ptm_entry(&ptm, "Z", "Z", 1.0);
+        assert_ptm_entry(&ptm, "Z", "I", 0.0);
+    }
+
+    #[test]
+    fn kraus_tensor_and_compose_channels_are_trace_preserving() {
+        let tensor = ChannelExpr::Tensor(vec![
+            ChannelExpr::AmplitudeDamping {
+                gamma: 0.2,
+                qubit: 0,
+            },
+            ChannelExpr::PhaseDamping {
+                lambda: 0.3,
+                qubit: 1,
+            },
+        ]);
+        let tensor_kraus = KrausOps::from_channel_expr(&tensor).unwrap();
+        assert_eq!(tensor_kraus.num_qubits(), 2);
+        assert_eq!(tensor_kraus.operators().len(), 4);
+        assert!(tensor_kraus.is_trace_preserving());
+
+        let compose = ChannelExpr::Compose(vec![
+            ChannelExpr::AmplitudeDamping {
+                gamma: 0.2,
+                qubit: 0,
+            },
+            ChannelExpr::PhaseDamping {
+                lambda: 0.3,
+                qubit: 0,
+            },
+        ]);
+        let compose_kraus = KrausOps::from_channel_expr(&compose).unwrap();
+        assert_eq!(compose_kraus.num_qubits(), 1);
+        assert_eq!(compose_kraus.operators().len(), 4);
+        assert!(compose_kraus.is_trace_preserving());
+    }
+
+    #[test]
+    fn kraus_tensor_rejects_manually_constructed_overlapping_subsystems() {
+        let tensor = ChannelExpr::Tensor(vec![
+            pecos_core::channel::BitFlip(0.1, 0),
+            pecos_core::channel::Dephasing(0.2, 0),
+        ]);
+
+        assert!(matches!(
+            KrausOps::from_channel_expr(&tensor),
+            Err(ChannelError::DuplicateSubsystem { qubit: 0 })
+        ));
+    }
+
+    #[test]
+    fn kraus_tensor_and_compose_reject_empty_manual_exprs() {
+        let tensor = ChannelExpr::Tensor(Vec::new());
+        let compose = ChannelExpr::Compose(Vec::new());
+
+        assert!(matches!(
+            KrausOps::from_channel_expr(&tensor),
+            Err(ChannelError::UnsupportedChannelExpr { .. })
+        ));
+        assert!(matches!(
+            KrausOps::from_channel_expr(&compose),
+            Err(ChannelError::UnsupportedChannelExpr { .. })
+        ));
+    }
+
+    #[test]
+    fn kraus_from_channel_expr_can_embed_in_larger_system() {
+        let expr = pecos_core::channel::BitFlip(0.25, 2);
+        let kraus = KrausOps::from_channel_expr_with_num_qubits(&expr, 3).unwrap();
+
+        assert_eq!(kraus.num_qubits(), 3);
+        assert!(kraus.is_trace_preserving());
+        assert!(matches!(
+            KrausOps::from_channel_expr_with_num_qubits(&expr, 2),
+            Err(ChannelError::QubitOutOfRange {
+                num_qubits: 2,
+                qubit: 2
+            })
+        ));
+    }
+
+    #[test]
+    fn pauli_channel_conversion_ignores_global_pauli_phase() {
+        let pauli = PauliString::from_paulis_with_phase(QuarterPhase::PlusI, &[Pauli::X]);
+        let expr = ChannelExpr::Unitary(UnitaryRep::Pauli(pauli));
+
+        let channel = PauliChannel::from_channel_expr(&expr).unwrap();
+        assert_close(channel.probability(&PauliBitmaskSmall::x(0)), 1.0);
+
+        let dense = Ptm::from_channel_expr(&expr).unwrap();
+        assert_ptm_entry(&dense, "X", "X", 1.0);
+        assert_ptm_entry(&dense, "Y", "Y", -1.0);
+        assert_ptm_entry(&dense, "Z", "Z", -1.0);
+    }
+
+    #[test]
+    fn pauli_channel_rejects_non_pauli_channel_conversion() {
+        let Op::Channel(expr) = op::AmplitudeDamping(0.1, 0) else {
+            panic!("expected channel");
+        };
+        assert!(matches!(
+            PauliChannel::from_channel_expr(&expr).unwrap_err(),
+            ChannelError::UnsupportedChannelExpr { .. }
+        ));
+        assert!(Ptm::from_channel_expr(&expr).is_ok());
+    }
+
+    #[test]
+    fn kraus_rejects_channels_with_non_kraus_semantics() {
+        let Op::Gate(gate) = op::MZ(0) else {
+            panic!("expected gate");
+        };
+        let gate_expr = ChannelExpr::Gate(gate);
+        assert!(matches!(
+            KrausOps::from_channel_expr(&gate_expr).unwrap_err(),
+            ChannelError::UnsupportedChannelExpr { .. }
+        ));
+
+        let Op::Channel(erasure) = op::Erasure(0.1, 0) else {
+            panic!("expected channel");
+        };
+        assert!(matches!(
+            KrausOps::from_channel_expr(&erasure).unwrap_err(),
+            ChannelError::UnsupportedChannelExpr { .. }
+        ));
+
+        let Op::Channel(leakage) = op::Leakage(0.1, 0) else {
+            panic!("expected channel");
+        };
+        assert!(matches!(
+            KrausOps::from_channel_expr(&leakage).unwrap_err(),
+            ChannelError::UnsupportedChannelExpr { .. }
+        ));
+    }
+
+    #[test]
+    fn choi_identity_uses_column_stacked_kraus_convention() {
+        let choi = ChoiMatrix::from_unitary(&unitary::I(0), 1).unwrap();
+        assert_eq!(choi.num_qubits(), 1);
+        assert_eq!(choi.matrix().shape(), (4, 4));
+        assert!(choi.is_trace_preserving());
+        assert!(choi.is_completely_positive());
+        assert!(choi.is_cptp());
+        assert!(choi.is_unital());
+        assert_complex_close(trace_complex(choi.matrix()), Complex64::new(2.0, 0.0));
+
+        let mut expected = DMatrix::zeros(4, 4);
+        expected[(0, 0)] = Complex64::new(1.0, 0.0);
+        expected[(0, 3)] = Complex64::new(1.0, 0.0);
+        expected[(3, 0)] = Complex64::new(1.0, 0.0);
+        expected[(3, 3)] = Complex64::new(1.0, 0.0);
+        assert_complex_matrix_close(choi.matrix(), &expected);
+
+        let identity = DMatrix::identity(2, 2);
+        assert_complex_matrix_close(&choi.partial_trace_output().unwrap(), &identity);
+        assert_complex_matrix_close(&choi.partial_trace_input().unwrap(), &identity);
+    }
+
+    #[test]
+    fn choi_tomography_helpers_classify_basic_channels() {
+        let zero = ChoiMatrix::try_new(1, DMatrix::zeros(4, 4)).unwrap();
+        assert!(zero.is_completely_positive());
+        assert!(!zero.is_trace_preserving());
+        assert!(!zero.is_cptp());
+        assert!(!zero.is_unital());
+
+        let Op::Channel(expr) = op::AmplitudeDamping(0.25, 0) else {
+            panic!("expected channel");
+        };
+        let damping = ChoiMatrix::from_channel_expr(&expr).unwrap();
+        assert!(damping.is_completely_positive());
+        assert!(damping.is_trace_preserving());
+        assert!(damping.is_cptp());
+        assert!(!damping.is_unital());
+
+        let mut expected_trace_input = DMatrix::zeros(2, 2);
+        expected_trace_input[(0, 0)] = Complex64::new(1.25, 0.0);
+        expected_trace_input[(1, 1)] = Complex64::new(0.75, 0.0);
+        assert_complex_matrix_close(
+            &damping.partial_trace_input().unwrap(),
+            &expected_trace_input,
+        );
+    }
+
+    #[test]
+    fn choi_transpose_map_is_trace_preserving_unital_but_not_cp() {
+        let mut transpose_choi = DMatrix::zeros(4, 4);
+        transpose_choi[(0, 0)] = Complex64::new(1.0, 0.0);
+        transpose_choi[(1, 2)] = Complex64::new(1.0, 0.0);
+        transpose_choi[(2, 1)] = Complex64::new(1.0, 0.0);
+        transpose_choi[(3, 3)] = Complex64::new(1.0, 0.0);
+        let choi = ChoiMatrix::try_new(1, transpose_choi).unwrap();
+
+        assert!(choi.is_trace_preserving());
+        assert!(choi.is_unital());
+        assert!(!choi.is_completely_positive());
+        assert!(!choi.is_cptp());
+    }
+
+    #[test]
+    fn choi_ptm_round_trip_for_depolarizing_channel() {
+        let Op::Channel(expr) = op::Depolarizing(0.3, 0) else {
+            panic!("expected channel");
+        };
+        let ptm = Ptm::from_channel_expr(&expr).unwrap();
+        let choi = ptm.to_choi().unwrap();
+        assert!(choi.is_trace_preserving());
+
+        let recovered = choi.to_ptm().unwrap();
+        assert_matrix_close(recovered.matrix(), ptm.matrix());
+    }
+
+    #[test]
+    fn choi_round_trips_amplitude_damping_through_kraus_and_ptm() {
+        let Op::Channel(expr) = op::AmplitudeDamping(0.25, 0) else {
+            panic!("expected channel");
+        };
+        let kraus = KrausOps::from_channel_expr(&expr).unwrap();
+        let choi = kraus.to_choi().unwrap();
+        assert!(choi.is_trace_preserving());
+
+        let ptm_from_kraus = kraus.to_ptm().unwrap();
+        let ptm_from_choi = choi.to_ptm().unwrap();
+        assert_matrix_close(ptm_from_choi.matrix(), ptm_from_kraus.matrix());
+
+        let recovered_kraus = choi.to_kraus().unwrap();
+        assert!(recovered_kraus.is_trace_preserving());
+        let recovered_ptm = recovered_kraus.to_ptm().unwrap();
+        assert_matrix_close(recovered_ptm.matrix(), ptm_from_kraus.matrix());
+    }
+
+    #[test]
+    fn ptm_to_kraus_round_trip_for_unitary_channel() {
+        let ptm = Ptm::from_unitary(&unitary::H(0), 1).unwrap();
+        let kraus = ptm.to_kraus().unwrap();
+        assert!(kraus.is_trace_preserving());
+
+        let recovered = kraus.to_ptm().unwrap();
+        assert_matrix_close(recovered.matrix(), ptm.matrix());
+    }
+
+    #[test]
+    fn superop_identity_round_trips_through_channel_representations() {
+        let kraus = KrausOps::from_unitary(&unitary::I(0), 1).unwrap();
+        let superop = SuperOp::from_kraus(&kraus).unwrap();
+        let identity = DMatrix::<Complex64>::identity(4, 4);
+        assert_complex_matrix_close(superop.matrix(), &identity);
+
+        let choi = superop.to_choi().unwrap();
+        let expected_choi = ChoiMatrix::from_kraus(&kraus).unwrap();
+        assert_complex_matrix_close(choi.matrix(), expected_choi.matrix());
+
+        let ptm = superop.to_ptm().unwrap();
+        assert_matrix_close(ptm.matrix(), Ptm::identity(1).unwrap().matrix());
+    }
+
+    #[test]
+    fn superop_choi_round_trip_for_amplitude_damping() {
+        let Op::Channel(expr) = op::AmplitudeDamping(0.25, 0) else {
+            panic!("expected channel");
+        };
+        let kraus = KrausOps::from_channel_expr(&expr).unwrap();
+        let choi = kraus.to_choi().unwrap();
+
+        let superop = SuperOp::from_choi(&choi).unwrap();
+        let recovered = superop.to_choi().unwrap();
+
+        assert_complex_matrix_close(recovered.matrix(), choi.matrix());
+        assert_matrix_close(
+            superop.to_ptm().unwrap().matrix(),
+            kraus.to_ptm().unwrap().matrix(),
+        );
+    }
+
+    #[test]
+    fn superop_ptm_round_trip_for_depolarizing() {
+        let Op::Channel(expr) = op::Depolarizing(0.3, 0) else {
+            panic!("expected channel");
+        };
+        let ptm = Ptm::from_channel_expr(&expr).unwrap();
+
+        let superop = SuperOp::from_ptm(&ptm).unwrap();
+        let recovered = superop.to_ptm().unwrap();
+
+        assert_matrix_close(recovered.matrix(), ptm.matrix());
+    }
+
+    #[test]
+    fn random_channels_match_direct_kraus_oracles_for_small_systems() {
+        for (num_qubits, num_kraus, seed) in [(1, 1, 11), (1, 3, 12), (2, 2, 21), (2, 4, 22)] {
+            let mut rng = PecosRng::seed_from_u64(seed);
+            let kraus = random_quantum_channel(&mut rng, num_qubits, num_kraus).unwrap();
+            assert!(kraus.is_trace_preserving());
+
+            let superop = kraus.to_superop().unwrap();
+            assert_complex_matrix_close(superop.matrix(), &direct_superop_from_kraus(&kraus));
+
+            let ptm = kraus.to_ptm().unwrap();
+            assert_matrix_close(ptm.matrix(), &direct_ptm_from_kraus(&kraus));
+
+            let choi = kraus.to_choi().unwrap();
+            let outputs = direct_matrix_unit_outputs(&kraus);
+            let reconstructed = ChoiMatrix::from_matrix_unit_outputs(num_qubits, &outputs).unwrap();
+            assert_complex_matrix_close(choi.matrix(), reconstructed.matrix());
+
+            for input in matrix_unit_basis(num_qubits).unwrap() {
+                assert_complex_matrix_close(
+                    &choi.apply_to_operator(&input).unwrap(),
+                    &apply_kraus_direct(&kraus, &input),
+                );
+            }
+
+            let stinespring_superop = kraus.to_stinespring().unwrap().to_superop().unwrap();
+            assert_complex_matrix_close(stinespring_superop.matrix(), superop.matrix());
+        }
+    }
+
+    #[test]
+    fn three_qubit_random_channel_matches_direct_oracles() {
+        let mut rng = PecosRng::seed_from_u64(1234);
+        let kraus = random_quantum_channel(&mut rng, 3, 2).unwrap();
+        assert!(kraus.is_trace_preserving());
+
+        let superop = kraus.to_superop().unwrap();
+        assert_eq!(superop.matrix().shape(), (64, 64));
+        assert_complex_matrix_close(superop.matrix(), &direct_superop_from_kraus(&kraus));
+
+        let ptm = kraus.to_ptm().unwrap();
+        assert_eq!(ptm.matrix().shape(), (64, 64));
+        assert_matrix_close(ptm.matrix(), &direct_ptm_from_kraus(&kraus));
+
+        let choi = kraus.to_choi().unwrap();
+        assert_eq!(choi.matrix().shape(), (64, 64));
+        assert!(choi.is_cptp());
+        assert_complex_matrix_close(
+            &choi.partial_trace_output().unwrap(),
+            &DMatrix::identity(8, 8),
+        );
+    }
+
+    #[test]
+    fn superop_compose_and_tensor_follow_matrix_semantics() {
+        let x = KrausOps::from_unitary(&unitary::X(0), 1)
+            .unwrap()
+            .to_superop()
+            .unwrap();
+        let xx = x.compose(&x).unwrap();
+        assert_complex_matrix_close(xx.matrix(), &DMatrix::<Complex64>::identity(4, 4));
+
+        let identity = KrausOps::from_unitary(&unitary::I(0), 1)
+            .unwrap()
+            .to_superop()
+            .unwrap();
+        let tensor = identity.tensor(&identity).unwrap();
+        assert_eq!(tensor.num_qubits(), 2);
+        assert_complex_matrix_close(tensor.matrix(), &DMatrix::<Complex64>::identity(16, 16));
+
+        assert_eq!(
+            identity.compose(&tensor).unwrap_err(),
+            ChannelError::QubitCountMismatch {
+                expected: 1,
+                actual: 2
+            }
+        );
+    }
+
+    #[test]
+    fn stinespring_try_new_rejects_non_isometric_matrix() {
+        let err = Stinespring::try_new(
+            1,
+            DMatrix::from_diagonal_element(2, 2, Complex64::new(2.0, 0.0)),
+        )
+        .unwrap_err();
+
+        assert!(matches!(
+            err,
+            ChannelError::DecompositionFailed { reason } if reason.contains("not an isometry")
+        ));
+    }
+
+    #[test]
+    fn chi_matrix_is_diagonal_for_pauli_mixture() {
+        let expr = ChannelExpr::MixedUnitary(vec![(0.7, unitary::I(0)), (0.3, unitary::X(0))]);
+        let chi = ChiMatrix::from_channel_expr(&expr).unwrap();
+        let identity = basis_index(1, &PauliBitmaskSmall::identity()).unwrap();
+        let x = basis_index(1, &PauliBitmaskSmall::x(0)).unwrap();
+
+        assert_complex_close(chi.matrix()[(identity, identity)], Complex64::new(0.7, 0.0));
+        assert_complex_close(chi.matrix()[(x, x)], Complex64::new(0.3, 0.0));
+        for row in 0..chi.matrix().nrows() {
+            for col in 0..chi.matrix().ncols() {
+                if (row, col) != (identity, identity) && (row, col) != (x, x) {
+                    assert!(chi.matrix()[(row, col)].norm() < 1e-10);
+                }
+            }
+        }
+
+        let recovered = chi.to_ptm().unwrap();
+        let expected = Ptm::from_channel_expr(&expr).unwrap();
+        assert_matrix_close(recovered.matrix(), expected.matrix());
+    }
+
+    #[test]
+    fn chi_matrix_amplitude_damping_has_off_diagonal_terms_and_matches_ptm() {
+        let Op::Channel(expr) = op::AmplitudeDamping(0.25, 0) else {
+            panic!("expected channel");
+        };
+        let kraus = KrausOps::from_channel_expr(&expr).unwrap();
+        let chi = ChiMatrix::from_kraus(&kraus).unwrap();
+
+        let has_off_diagonal = (0..chi.matrix().nrows()).any(|row| {
+            (0..chi.matrix().ncols())
+                .any(|col| row != col && chi.matrix()[(row, col)].norm() > 1e-10)
+        });
+        assert!(
+            has_off_diagonal,
+            "amplitude damping should have off-diagonal chi entries"
+        );
+
+        let recovered = chi.to_ptm().unwrap();
+        let expected = Ptm::from_channel_expr(&expr).unwrap();
+        assert_matrix_close(recovered.matrix(), expected.matrix());
+    }
+
+    #[test]
+    fn chi_choi_round_trip_for_amplitude_damping() {
+        let Op::Channel(expr) = op::AmplitudeDamping(0.25, 0) else {
+            panic!("expected channel");
+        };
+        let kraus = KrausOps::from_channel_expr(&expr).unwrap();
+        let chi = ChiMatrix::from_kraus(&kraus).unwrap();
+
+        let recovered = chi.to_choi().unwrap().to_chi().unwrap();
+
+        assert_complex_matrix_close(recovered.matrix(), chi.matrix());
+    }
+
+    #[test]
+    fn stinespring_round_trips_trace_preserving_kraus_channels() {
+        let Op::Channel(expr) = op::AmplitudeDamping(0.25, 0) else {
+            panic!("expected channel");
+        };
+        let kraus = KrausOps::from_channel_expr(&expr).unwrap();
+        let stinespring = kraus.to_stinespring().unwrap();
+        assert_eq!(stinespring.num_qubits(), 1);
+        assert_eq!(stinespring.environment_dim(), kraus.operators().len());
+
+        let recovered = stinespring.to_kraus().unwrap();
+        let expected_choi = kraus.to_choi().unwrap();
+        let recovered_choi = recovered.to_choi().unwrap();
+        assert_complex_matrix_close(recovered_choi.matrix(), expected_choi.matrix());
+    }
+
+    #[test]
+    fn invalid_choi_shape_fails_construction() {
+        let err = ChoiMatrix::try_new(1, DMatrix::zeros(2, 2)).unwrap_err();
+        assert!(matches!(err, ChannelError::InvalidMatrixShape { .. }));
+    }
+
+    #[test]
+    fn choi_to_kraus_rejects_non_positive_choi_matrix() {
+        let mut matrix = DMatrix::zeros(4, 4);
+        matrix[(0, 0)] = Complex64::new(1.0, 0.0);
+        matrix[(3, 3)] = Complex64::new(-1.0, 0.0);
+        let choi = ChoiMatrix::try_new(1, matrix).unwrap();
+
+        assert!(matches!(
+            choi.to_kraus().unwrap_err(),
+            ChannelError::DecompositionFailed { .. }
+        ));
+    }
+
+    #[test]
+    fn choi_to_kraus_rejects_invalid_tolerance() {
+        let choi = ChoiMatrix::from_unitary(&unitary::I(0), 1).unwrap();
+
+        assert!(matches!(
+            choi.to_kraus_with_tolerance(f64::NAN).unwrap_err(),
+            ChannelError::DecompositionFailed { .. }
+        ));
+        assert!(matches!(
+            choi.to_kraus_with_tolerance(-1e-12).unwrap_err(),
+            ChannelError::DecompositionFailed { .. }
+        ));
+    }
+
+    #[test]
+    fn matrix_unit_basis_uses_column_stacked_order() {
+        let basis = matrix_unit_basis(1).unwrap();
+        assert_eq!(basis.len(), 4);
+        for (idx, (row, col)) in [(0, 0), (1, 0), (0, 1), (1, 1)].into_iter().enumerate() {
+            let mut expected = DMatrix::zeros(2, 2);
+            expected[(row, col)] = Complex64::new(1.0, 0.0);
+            assert_complex_matrix_close(&basis[idx], &expected);
+        }
+    }
+
+    #[test]
+    fn process_tomography_design_exposes_matrix_unit_order() {
+        let design = ProcessTomographyDesign::matrix_unit(1).unwrap();
+        assert_eq!(design.num_qubits(), 1);
+        assert_eq!(design.dim(), 2);
+        assert_eq!(design.num_inputs(), 4);
+        assert_eq!(design.input_index(0, 0).unwrap(), 0);
+        assert_eq!(design.input_index(1, 0).unwrap(), 1);
+        assert_eq!(design.input_index(0, 1).unwrap(), 2);
+        assert_eq!(design.input_index(1, 1).unwrap(), 3);
+
+        let metadata = design.input_metadata_all();
+        assert_eq!(
+            metadata,
+            vec![
+                MatrixUnitTomographyInput {
+                    index: 0,
+                    row: 0,
+                    col: 0
+                },
+                MatrixUnitTomographyInput {
+                    index: 1,
+                    row: 1,
+                    col: 0
+                },
+                MatrixUnitTomographyInput {
+                    index: 2,
+                    row: 0,
+                    col: 1
+                },
+                MatrixUnitTomographyInput {
+                    index: 3,
+                    row: 1,
+                    col: 1
+                },
+            ]
+        );
+
+        let from_design = design.input_operators();
+        let from_free_function = matrix_unit_basis(1).unwrap();
+        for (actual, expected) in from_design.iter().zip(from_free_function.iter()) {
+            assert_complex_matrix_close(actual, expected);
+        }
+    }
+
+    #[test]
+    fn process_tomography_design_reconstructs_channel_outputs() {
+        let Op::Channel(expr) = op::AmplitudeDamping(0.25, 0) else {
+            panic!("expected channel");
+        };
+        let expected = ChoiMatrix::from_channel_expr(&expr).unwrap();
+        let design = ProcessTomographyDesign::matrix_unit(1).unwrap();
+        let outputs = design.simulate_outputs(&expected).unwrap();
+        let reconstructed = design.reconstruct_choi(&outputs).unwrap();
+
+        assert_complex_matrix_close(reconstructed.matrix(), expected.matrix());
+        assert!(reconstructed.is_cptp());
+        assert!(!reconstructed.is_unital());
+    }
+
+    #[test]
+    fn process_tomography_design_reconstructs_two_qubit_tensor_channel() {
+        let tensor = ChannelExpr::Tensor(vec![
+            pecos_core::channel::AmplitudeDamping(0.25, 0),
+            pecos_core::channel::PhaseDamping(0.4, 1),
+        ]);
+        let kraus = KrausOps::from_channel_expr(&tensor).unwrap();
+        let expected = kraus.to_choi().unwrap();
+        let design = ProcessTomographyDesign::matrix_unit(2).unwrap();
+
+        let outputs = direct_matrix_unit_outputs(&kraus);
+        let reconstructed = design.reconstruct_choi(&outputs).unwrap();
+        assert_complex_matrix_close(reconstructed.matrix(), expected.matrix());
+
+        let simulated_outputs = design.simulate_outputs(&expected).unwrap();
+        for (direct, simulated) in outputs.iter().zip(simulated_outputs.iter()) {
+            assert_complex_matrix_close(simulated, direct);
+        }
+    }
+
+    #[test]
+    fn process_tomography_design_rejects_invalid_inputs() {
+        let design = ProcessTomographyDesign::matrix_unit(1).unwrap();
+        assert!(matches!(
+            design.input_metadata(4).unwrap_err(),
+            ChannelError::TomographyInputOutOfRange {
+                num_inputs: 4,
+                index: 4
+            }
+        ));
+        assert!(matches!(
+            design.input_index(2, 0).unwrap_err(),
+            ChannelError::MatrixUnitOutOfRange {
+                dim: 2,
+                row: 2,
+                col: 0
+            }
+        ));
+
+        let two_qubit_channel = ChoiMatrix::from_unitary(&unitary::I(0), 2).unwrap();
+        assert!(matches!(
+            design.simulate_outputs(&two_qubit_channel).unwrap_err(),
+            ChannelError::QubitCountMismatch {
+                expected: 1,
+                actual: 2
+            }
+        ));
+    }
+
+    #[test]
+    fn choi_reconstructs_identity_from_matrix_unit_outputs() {
+        let inputs = matrix_unit_basis(1).unwrap();
+        let reconstructed = ChoiMatrix::from_matrix_unit_outputs(1, &inputs).unwrap();
+        let expected = ChoiMatrix::from_unitary(&unitary::I(0), 1).unwrap();
+
+        assert_complex_matrix_close(reconstructed.matrix(), expected.matrix());
+        assert!(reconstructed.is_cptp());
+        assert!(reconstructed.is_unital());
+    }
+
+    #[test]
+    fn choi_reconstructs_amplitude_damping_from_matrix_unit_outputs() {
+        let Op::Channel(expr) = op::AmplitudeDamping(0.25, 0) else {
+            panic!("expected channel");
+        };
+        let expected = ChoiMatrix::from_channel_expr(&expr).unwrap();
+        let outputs: Vec<DMatrix<Complex64>> = matrix_unit_basis(1)
+            .unwrap()
+            .iter()
+            .map(|operator| expected.apply_to_operator(operator).unwrap())
+            .collect();
+
+        let reconstructed = ChoiMatrix::from_matrix_unit_outputs(1, &outputs).unwrap();
+        assert_complex_matrix_close(reconstructed.matrix(), expected.matrix());
+        assert!(reconstructed.is_cptp());
+        assert!(!reconstructed.is_unital());
+    }
+
+    #[test]
+    fn choi_tomography_rejects_bad_sample_count_and_shape() {
+        let err = ChoiMatrix::from_matrix_unit_outputs(1, &[]).unwrap_err();
+        assert_eq!(
+            err,
+            ChannelError::InvalidTomographySampleCount {
+                expected: 4,
+                actual: 0
+            }
+        );
+
+        let bad_outputs = vec![DMatrix::zeros(2, 2); 3]
+            .into_iter()
+            .chain(std::iter::once(DMatrix::zeros(3, 3)))
+            .collect::<Vec<_>>();
+        assert!(matches!(
+            ChoiMatrix::from_matrix_unit_outputs(1, &bad_outputs).unwrap_err(),
+            ChannelError::InvalidMatrixShape { .. }
+        ));
+    }
+
+    #[test]
+    fn partial_trace_of_bell_state_is_maximally_mixed() {
+        let half = Complex64::new(0.5, 0.0);
+        let mut rho = DMatrix::zeros(4, 4);
+        rho[(0, 0)] = half;
+        rho[(0, 3)] = half;
+        rho[(3, 0)] = half;
+        rho[(3, 3)] = half;
+
+        let reduced = partial_trace(&rho, 2, &[1]).unwrap();
+        assert_eq!(reduced.shape(), (2, 2));
+        assert_complex_close(reduced[(0, 0)], half);
+        assert_complex_close(reduced[(1, 1)], half);
+        assert_complex_close(reduced[(0, 1)], Complex64::new(0.0, 0.0));
+        assert_complex_close(reduced[(1, 0)], Complex64::new(0.0, 0.0));
+    }
+
+    #[test]
+    fn partial_trace_respects_little_endian_qubit_ordering() {
+        let mut rho = DMatrix::zeros(4, 4);
+        rho[(1, 1)] = Complex64::new(1.0, 0.0); // |q1=0, q0=1><...|
+
+        let keep_q0 = partial_trace(&rho, 2, &[1]).unwrap();
+        assert_complex_close(keep_q0[(0, 0)], Complex64::new(0.0, 0.0));
+        assert_complex_close(keep_q0[(1, 1)], Complex64::new(1.0, 0.0));
+
+        let keep_q1 = partial_trace(&rho, 2, &[0]).unwrap();
+        assert_complex_close(keep_q1[(0, 0)], Complex64::new(1.0, 0.0));
+        assert_complex_close(keep_q1[(1, 1)], Complex64::new(0.0, 0.0));
+    }
+
+    #[test]
+    fn random_density_matrix_is_normalized_hermitian_and_reproducible() {
+        let mut rng = PecosRng::seed_from_u64(123);
+        let rho = random_density_matrix(&mut rng, 2).unwrap();
+        assert_eq!(rho.shape(), (4, 4));
+        assert_complex_close(trace_complex(&rho), Complex64::new(1.0, 0.0));
+        assert_complex_matrix_close(&rho, &rho.adjoint());
+
+        let mut same_seed = PecosRng::seed_from_u64(123);
+        let same = random_density_matrix(&mut same_seed, 2).unwrap();
+        assert_complex_matrix_close(&rho, &same);
+
+        let mut different_seed = PecosRng::seed_from_u64(456);
+        let different = random_density_matrix(&mut different_seed, 2).unwrap();
+        assert_ne!(rho, different);
+    }
+
+    #[test]
+    fn random_density_matrix_rank_one_is_pure() {
+        let mut rng = PecosRng::seed_from_u64(123);
+        let rho = random_density_matrix_with_rank(&mut rng, 2, 1).unwrap();
+        let purity = trace_complex(&(&rho * &rho)).re;
+        assert_close(purity, 1.0);
+
+        assert!(matches!(
+            random_density_matrix_with_rank(&mut rng, 1, 0).unwrap_err(),
+            ChannelError::EmptyKrausSet
+        ));
+    }
+
+    #[test]
+    fn random_density_matrix_three_qubit_rank_limited_is_stable() {
+        let mut rng = PecosRng::seed_from_u64(789);
+        let rho = random_density_matrix_with_rank(&mut rng, 3, 3).unwrap();
+        assert_eq!(rho.shape(), (8, 8));
+        assert_complex_close(trace_complex(&rho), Complex64::new(1.0, 0.0));
+        assert_complex_matrix_close(&rho, &rho.adjoint());
+
+        let purity = trace_complex(&(&rho * &rho));
+        assert!(purity.im.abs() < 1e-10);
+        assert!(
+            purity.re > 1.0 / 8.0 - 1e-10 && purity.re <= 1.0 + 1e-10,
+            "unexpected 3-qubit density-matrix purity: {purity}"
+        );
+    }
+
+    #[test]
+    fn random_quantum_channel_is_cptp_and_reproducible() {
+        let mut rng = PecosRng::seed_from_u64(123);
+        let channel = random_quantum_channel(&mut rng, 1, 3).unwrap();
+        assert_eq!(channel.operators().len(), 3);
+        assert!(channel.is_trace_preserving());
+        assert!(channel.to_choi().unwrap().is_cptp());
+
+        let mut same_seed = PecosRng::seed_from_u64(123);
+        let same = random_quantum_channel(&mut same_seed, 1, 3).unwrap();
+        for (left, right) in channel.operators().iter().zip(same.operators()) {
+            assert_complex_matrix_close(left, right);
+        }
+
+        let mut different_seed = PecosRng::seed_from_u64(456);
+        let different = random_quantum_channel(&mut different_seed, 1, 3).unwrap();
+        assert_ne!(channel, different);
+    }
+
+    #[test]
+    fn random_quantum_channel_rejects_zero_kraus_count() {
+        let mut rng = PecosRng::seed_from_u64(123);
+        assert!(matches!(
+            random_quantum_channel(&mut rng, 1, 0).unwrap_err(),
+            ChannelError::EmptyKrausSet
+        ));
+    }
+
+    #[test]
+    fn random_helpers_return_values_from_expected_sets() {
+        let mut rng = PecosRng::seed_from_u64(123);
+        let pauli = random_pauli(&mut rng, 5);
+        assert!(pauli.qubits().into_iter().all(|q| q < 5));
+
+        let c1 = random_1q_clifford(&mut rng);
+        assert!(Clifford::all_1q().contains(&c1));
+
+        let c2 = random_2q_clifford(&mut rng);
+        assert!(Clifford::all_2q().contains(&c2));
+
+        let c = random_clifford(&mut rng);
+        assert!(Clifford::all().contains(&c));
+    }
+}
diff --git a/crates/pecos-quantum/src/circuit_display.rs b/crates/pecos-quantum/src/circuit_display.rs
index 796672126..63a2b69fc 100644
--- a/crates/pecos-quantum/src/circuit_display.rs
+++ b/crates/pecos-quantum/src/circuit_display.rs
@@ -74,7 +74,9 @@ fn gate_symbol(gate_type: GateType) -> &'static str {
         GateType::QFree => "QF",
         GateType::I | GateType::Idle => "I",
         GateType::MeasCrosstalkGlobalPayload | GateType::MeasCrosstalkLocalPayload => "XT",
+        GateType::Channel => "Ch",
         GateType::Custom => "?",
+        GateType::TrackedPauliMeta => "TP",
     }
 }
 
@@ -207,6 +209,7 @@ fn gate_color(gate_type: GateType) -> CellColor {
         | GateType::QAlloc
         | GateType::QFree
         | GateType::Custom
+        | GateType::Channel
         | GateType::MeasCrosstalkGlobalPayload
         | GateType::MeasCrosstalkLocalPayload
         | GateType::CX
@@ -217,7 +220,8 @@ fn gate_color(gate_type: GateType) -> CellColor {
         | GateType::U
         | GateType::R1XY
         | GateType::RXXRYYRZZ
-        | GateType::U2q => CellColor::None,
+        | GateType::U2q
+        | GateType::TrackedPauliMeta => CellColor::None,
     }
 }
 
diff --git a/crates/pecos-quantum/src/dag_circuit.rs b/crates/pecos-quantum/src/dag_circuit.rs
index a052ce158..7086a6dcf 100644
--- a/crates/pecos-quantum/src/dag_circuit.rs
+++ b/crates/pecos-quantum/src/dag_circuit.rs
@@ -17,7 +17,7 @@
 //! This module provides [`DagCircuit`], a directed acyclic graph representation
 //! of quantum circuits where nodes are gates and edges are qubit wires.
 //!
-//! The design follows HUGR and Qiskit's `DAGCircuit`: edges represent qubit wires
+//! The design follows a wire-edge DAG model: edges represent qubit wires
 //! flowing between gates, not just abstract dependencies.
 
 use std::collections::{BTreeMap, BTreeSet};
@@ -126,10 +126,14 @@ impl DagTraversalIndex {
         self.max_qubit + 1
     }
 
-    /// Returns the number of gates.
+    /// Returns the number of gate nodes in the traversal index.
+    ///
+    /// A batched DAG node still contributes one node here. Use
+    /// [`DagCircuit::gate_count`] when you need the number of individual gates
+    /// represented by batched gate nodes.
     #[inline]
     #[must_use]
-    pub fn num_gates(&self) -> usize {
+    pub fn num_gate_nodes(&self) -> usize {
         self.topo_order.len()
     }
 
@@ -313,79 +317,11 @@ impl TraversalWorkBuffers {
     }
 }
 
-/// A handle returned by measurement operations, allowing metadata to be attached.
-///
-/// This follows the simulator pattern where measurements break the chain,
-/// but still allows attaching metadata via `.meta()`.
-///
-/// # Example
-/// ```
-/// use pecos_quantum::{DagCircuit, Attribute};
-///
-/// let mut circuit = DagCircuit::new();
-/// circuit.mz(&[0]).meta("basis", Attribute::String("Z".into()));
-/// circuit.h(&[1]);  // continue building
-/// ```
-pub struct MeasureHandle<'a> {
-    circuit: &'a mut DagCircuit,
-    node: usize,
-}
-
-impl MeasureHandle<'_> {
-    /// Returns the node ID of this measurement.
-    #[inline]
-    #[must_use]
-    pub fn node(&self) -> usize {
-        self.node
-    }
-
-    /// Add metadata to this measurement.
-    ///
-    /// Returns `()` to break the chain, matching simulator behavior.
-    pub fn meta(self, key: &str, value: impl Into<Attribute>) {
-        self.circuit.set_gate_attr(self.node, key, value.into());
-    }
-}
-
-/// Handle returned by preparation operations to allow metadata attachment.
-///
-/// This handle breaks the method chain (unlike regular gates),
-/// but still allows attaching metadata via `.meta()`.
-///
-/// # Example
-/// ```
-/// use pecos_quantum::{DagCircuit, Attribute};
-///
-/// let mut circuit = DagCircuit::new();
-/// circuit.pz(&[0]).meta("reason", Attribute::String("reset".into()));
-/// circuit.h(&[1]);  // continue building
-/// ```
-pub struct PrepHandle<'a> {
-    circuit: &'a mut DagCircuit,
-    node: usize,
-}
-
-impl PrepHandle<'_> {
-    /// Returns the node ID of this preparation.
-    #[inline]
-    #[must_use]
-    pub fn node(&self) -> usize {
-        self.node
-    }
-
-    /// Add metadata to this preparation.
-    ///
-    /// Returns `()` to break the chain.
-    pub fn meta(self, key: &str, value: impl Into<Attribute>) {
-        self.circuit.set_gate_attr(self.node, key, value.into());
-    }
-}
-
 /// A directed acyclic graph representation of a quantum circuit.
 ///
 /// Each node in the DAG represents a quantum gate. Edges represent qubit wires
 /// flowing between gates - each edge is labeled with the [`QubitId`] it carries.
-/// This design follows HUGR and Qiskit's `DAGCircuit`.
+/// This design follows a wire-edge DAG model.
 ///
 /// For a two-qubit gate like CX, there are two incoming edges (one per qubit)
 /// and two outgoing edges.
@@ -416,6 +352,72 @@ impl PrepHandle<'_> {
 /// assert_eq!(circuit.gate_count(), 2);
 /// assert_eq!(circuit.wire_count(), 1);
 /// ```
+/// A measurement reference returned by [`DagCircuit::mz`].
+///
+/// Carries both the DAG node index and the qubit that was measured.
+/// Dereferences to `usize` (the node index) for use in detector/observable
+/// definitions.
+#[derive(Debug, Clone, Copy, PartialEq, Eq, Hash)]
+pub struct MeasRef {
+    /// DAG node index.
+    pub node: usize,
+    /// Qubit that was measured.
+    pub qubit: QubitId,
+}
+
+impl std::ops::Deref for MeasRef {
+    type Target = usize;
+    fn deref(&self) -> &usize {
+        &self.node
+    }
+}
+
+impl From<MeasRef> for usize {
+    fn from(m: MeasRef) -> usize {
+        m.node
+    }
+}
+
+/// The role of a Pauli annotation in the circuit.
+///
+/// All three kinds track the same thing -- whether a Pauli string flips due to
+/// faults. The difference is how the answer is read out and what it means.
+#[derive(Debug, Clone)]
+pub enum AnnotationKind {
+    /// Stabilizer check: the Pauli should be deterministic (flip = error detected).
+    /// Stores measurement node indices for classical readout via XOR, plus
+    /// optional coordinates for visualization/matching.
+    Detector {
+        measurement_nodes: Vec<usize>,
+        coords: Vec<f64>,
+    },
+    /// Logical observable: the Pauli's flip determines a logical outcome.
+    /// Stores measurement node indices for classical readout via XOR.
+    Observable { measurement_nodes: Vec<usize> },
+    /// Tracked Pauli: no measurement readout.
+    /// Position is determined by a `TrackedPauliMeta` node in the DAG.
+    TrackedPauli,
+}
+
+/// A unified Pauli annotation: detectors, observables, and tracked Paulis
+/// are all Pauli strings tracked for flipping via backward propagation.
+///
+/// - **Detectors** are stabilizer checks that should be +1 (noiseless).
+///   Their Pauli is Z on the measured qubits.
+/// - **Observables** are logical operators read out via measurements.
+///   Their Pauli is Z on the measured qubits.
+/// - **Tracked Paulis** are arbitrary Pauli strings with no measurement readout.
+///   Their Pauli is user-specified and their position comes from a meta-gate node.
+#[derive(Debug, Clone)]
+pub struct PauliAnnotation {
+    /// The Pauli string being tracked.
+    pub pauli: pecos_core::PauliString,
+    /// What role this annotation plays.
+    pub kind: AnnotationKind,
+    /// Optional label.
+    pub label: Option<String>,
+}
+
 #[derive(Debug, Clone)]
 pub struct DagCircuit {
     /// The underlying DAG structure.
@@ -430,6 +432,10 @@ pub struct DagCircuit {
     last_node: Option<usize>,
     /// Maximum qubit index seen so far (updated incrementally on gate addition).
     max_qubit: usize,
+    /// Unified Pauli annotations (detectors, observables, and tracked Paulis).
+    annotations: Vec<PauliAnnotation>,
+    /// Measurement labels (`node_index` → label).
+    measurement_labels: BTreeMap<usize, String>,
 }
 
 impl DagCircuit {
@@ -443,6 +449,8 @@ impl DagCircuit {
             qubit_heads: BTreeMap::new(),
             last_node: None,
             max_qubit: 0,
+            annotations: Vec::new(),
+            measurement_labels: BTreeMap::new(),
         }
     }
 
@@ -462,12 +470,14 @@ impl DagCircuit {
             qubit_heads: BTreeMap::new(),
             last_node: None,
             max_qubit: 0,
+            annotations: Vec::new(),
+            measurement_labels: BTreeMap::new(),
         }
     }
 
     // ==================== Gate operations ====================
 
-    /// Adds a gate to the circuit.
+    /// Adds a validated gate to the circuit.
     ///
     /// Returns the node index of the newly added gate.
     /// The gate is not connected to any other gates yet - use [`connect`](Self::connect)
@@ -476,7 +486,27 @@ impl DagCircuit {
     /// # Arguments
     ///
     /// * `gate` - The gate to add
+    ///
+    /// # Panics
+    ///
+    /// Panics if [`Gate::validate`] rejects the gate payload. Use
+    /// [`try_add_gate`](Self::try_add_gate) for fallible insertion.
     pub fn add_gate(&mut self, gate: Gate) -> usize {
+        self.try_add_gate(gate)
+            .unwrap_or_else(|err| panic!("Invalid gate: {err}"))
+    }
+
+    /// Try to add a validated gate to the circuit.
+    ///
+    /// # Errors
+    ///
+    /// Returns an error if [`Gate::validate`] rejects the gate payload.
+    pub fn try_add_gate(&mut self, gate: Gate) -> Result<usize, String> {
+        gate.validate()?;
+        Ok(self.add_gate_unchecked(gate))
+    }
+
+    fn add_gate_unchecked(&mut self, gate: Gate) -> usize {
         let node_idx = self.dag.add_node();
         // Ensure gates vector is large enough
         if node_idx >= self.gates.len() {
@@ -525,8 +555,20 @@ impl DagCircuit {
     }
 
     /// Returns the number of gates in the circuit.
+    ///
+    /// Batched gate nodes count by individual gate. For example, a node carrying
+    /// `Gate::cx(&[(0, 1), (2, 3)])` contributes two gates.
     #[must_use]
     pub fn gate_count(&self) -> usize {
+        self.gates.iter().flatten().map(Gate::num_gates).sum()
+    }
+
+    /// Returns the number of gate nodes stored in the DAG.
+    ///
+    /// A batched node carrying `Gate::cx(&[(0, 1), (2, 3)])` contributes one
+    /// gate node and two gates.
+    #[must_use]
+    pub fn gate_node_count(&self) -> usize {
         self.dag.node_count()
     }
 
@@ -753,7 +795,8 @@ impl DagCircuit {
             .iter()
             .flatten()
             .filter(|g| g.is_single_qubit())
-            .count()
+            .map(Gate::num_gates)
+            .sum()
     }
 
     /// Returns the count of two-qubit gates.
@@ -763,7 +806,8 @@ impl DagCircuit {
             .iter()
             .flatten()
             .filter(|g| g.is_two_qubit())
-            .count()
+            .map(Gate::num_gates)
+            .sum()
     }
 
     /// Returns the count of gates of a specific type.
@@ -773,7 +817,8 @@ impl DagCircuit {
             .iter()
             .flatten()
             .filter(|g| g.gate_type == gate_type)
-            .count()
+            .map(Gate::num_gates)
+            .sum()
     }
 
     // ==================== Topological operations ====================
@@ -1532,9 +1577,7 @@ impl DagCircuit {
 
     // -------------------- Measurement and preparation --------------------
     //
-    // Measurements return MeasureHandle which allows .meta() but breaks
-    // further chaining, matching simulator behavior where mz returns
-    // MeasurementResult instead of &mut Self.
+    // Measurements return Vec<MeasRef> (lightweight Copy handles).
     // Preparations return &mut Self and are chainable.
 
     /// Measure qubit(s) in the Z basis.
@@ -1546,13 +1589,46 @@ impl DagCircuit {
     /// use pecos_quantum::DagCircuit;
     ///
     /// let mut circuit = DagCircuit::new();
-    /// circuit.h(&[0]).mz(&[0, 1]);
+    /// circuit.h(&[0]);
+    /// let nodes = circuit.mz(&[0, 1]);
+    /// assert_eq!(nodes.len(), 2);
     /// ```
-    pub fn mz(&mut self, qubits: &[impl Into<QubitId> + Copy]) -> &mut Self {
-        for &q in qubits {
-            self.add_gate_auto_wire(Gate::mz(&[q]));
-        }
-        self
+    pub fn mz(&mut self, qubits: &[impl Into<QubitId> + Copy]) -> Vec<MeasRef> {
+        qubits
+            .iter()
+            .map(|&q| {
+                let qubit = q.into();
+                let node = self.add_gate_auto_wire(Gate::mz(&[qubit]));
+                MeasRef { node, qubit }
+            })
+            .collect()
+    }
+
+    /// Measure qubits and label them.
+    ///
+    /// Labels are stored on the circuit and flow through to the sampler output.
+    pub fn mz_labeled(&mut self, entries: &[(impl Into<QubitId> + Copy, &str)]) -> Vec<MeasRef> {
+        entries
+            .iter()
+            .map(|&(q, label)| {
+                let qubit = q.into();
+                let node = self.add_gate_auto_wire(Gate::mz(&[qubit]));
+                let mref = MeasRef { node, qubit };
+                self.set_measurement_label(node, label);
+                mref
+            })
+            .collect()
+    }
+
+    /// Set a label on a measurement node.
+    pub fn set_measurement_label(&mut self, node: usize, label: &str) {
+        self.measurement_labels.insert(node, label.to_string());
+    }
+
+    /// Get the label of a measurement node, if any.
+    #[must_use]
+    pub fn measurement_label(&self, node: usize) -> Option<&str> {
+        self.measurement_labels.get(&node).map(String::as_str)
     }
 
     /// Measure and free qubit(s) (destructive measurement).
@@ -1563,6 +1639,224 @@ impl DagCircuit {
         self
     }
 
+    // ========================================================================
+    // Detector and Observable Annotations
+    // ========================================================================
+
+    /// Annotate a detector: a set of measurements whose XOR should be
+    /// deterministic in the noiseless case.
+    ///
+    /// The Pauli string is automatically Z on the measured qubits.
+    ///
+    /// Returns the annotation index.
+    pub fn detector(&mut self, measurements: &[impl Into<usize> + Copy]) -> usize {
+        let meas_nodes: Vec<usize> = measurements.iter().map(|&m| m.into()).collect();
+        let pauli = self.pauli_from_measurement_nodes(&meas_nodes);
+        let idx = self.annotations.len();
+        self.annotations.push(PauliAnnotation {
+            pauli,
+            kind: AnnotationKind::Detector {
+                measurement_nodes: meas_nodes,
+                coords: Vec::new(),
+            },
+            label: None,
+        });
+        idx
+    }
+
+    /// Annotate a labeled detector.
+    pub fn detector_labeled(
+        &mut self,
+        label: &str,
+        measurements: &[impl Into<usize> + Copy],
+    ) -> usize {
+        let meas_nodes: Vec<usize> = measurements.iter().map(|&m| m.into()).collect();
+        let pauli = self.pauli_from_measurement_nodes(&meas_nodes);
+        let idx = self.annotations.len();
+        self.annotations.push(PauliAnnotation {
+            pauli,
+            kind: AnnotationKind::Detector {
+                measurement_nodes: meas_nodes,
+                coords: Vec::new(),
+            },
+            label: Some(label.to_string()),
+        });
+        idx
+    }
+
+    /// Annotate a detector with coordinates.
+    pub fn detector_with_coords(
+        &mut self,
+        measurements: &[impl Into<usize> + Copy],
+        coords: &[f64],
+    ) -> usize {
+        let meas_nodes: Vec<usize> = measurements.iter().map(|&m| m.into()).collect();
+        let pauli = self.pauli_from_measurement_nodes(&meas_nodes);
+        let idx = self.annotations.len();
+        self.annotations.push(PauliAnnotation {
+            pauli,
+            kind: AnnotationKind::Detector {
+                measurement_nodes: meas_nodes,
+                coords: coords.to_vec(),
+            },
+            label: None,
+        });
+        idx
+    }
+
+    /// Annotate a logical observable: a set of measurements whose XOR
+    /// defines whether a logical operator flipped.
+    ///
+    /// The Pauli string is automatically Z on the measured qubits.
+    ///
+    /// Returns the annotation index.
+    pub fn observable(&mut self, measurements: &[impl Into<usize> + Copy]) -> usize {
+        let meas_nodes: Vec<usize> = measurements.iter().map(|&m| m.into()).collect();
+        let pauli = self.pauli_from_measurement_nodes(&meas_nodes);
+        let idx = self.annotations.len();
+        self.annotations.push(PauliAnnotation {
+            pauli,
+            kind: AnnotationKind::Observable {
+                measurement_nodes: meas_nodes,
+            },
+            label: None,
+        });
+        idx
+    }
+
+    /// Annotate a labeled observable.
+    pub fn observable_labeled(
+        &mut self,
+        label: &str,
+        measurements: &[impl Into<usize> + Copy],
+    ) -> usize {
+        let meas_nodes: Vec<usize> = measurements.iter().map(|&m| m.into()).collect();
+        let pauli = self.pauli_from_measurement_nodes(&meas_nodes);
+        let idx = self.annotations.len();
+        self.annotations.push(PauliAnnotation {
+            pauli,
+            kind: AnnotationKind::Observable {
+                measurement_nodes: meas_nodes,
+            },
+            label: Some(label.to_string()),
+        });
+        idx
+    }
+
+    /// Derive a `PauliString` from measurement nodes.
+    /// Z-basis measurements → Z on the measured qubit.
+    fn pauli_from_measurement_nodes(&self, nodes: &[usize]) -> pecos_core::PauliString {
+        let qubits: Vec<usize> = nodes
+            .iter()
+            .filter_map(|&node| {
+                let gate = self.gate(node)?;
+                Some(gate.qubits.iter().map(pecos_core::QubitId::index))
+            })
+            .flatten()
+            .collect();
+        pecos_core::PauliString::zs(&qubits)
+    }
+
+    /// Place a tracked-Pauli meta-gate at this point in the circuit.
+    ///
+    /// This is a **positional** annotation: only faults BEFORE this node
+    /// can flip the tracked Pauli. The meta-gate does not affect quantum state
+    /// -- simulators ignore it.
+    ///
+    /// Accepts a [`PauliString`](pecos_core::PauliString), which supports
+    /// the `X(q) & Y(q) & Z(q)` composition syntax.
+    ///
+    /// Returns the annotation index.
+    ///
+    /// # Example
+    /// ```
+    /// use pecos_quantum::DagCircuit;
+    /// use pecos_core::pauli::{X, Z};
+    ///
+    /// let mut c = DagCircuit::new();
+    /// c.pz(&[0, 1, 2]);
+    /// c.cx(&[(0, 1)]);
+    /// // Place X_0 & Z_1 & Z_2 check HERE -- only faults above can flip it
+    /// c.tracked_pauli(X(0) & Z(1) & Z(2));
+    /// c.cx(&[(1, 2)]);  // faults here don't affect the check
+    /// ```
+    pub fn tracked_pauli(&mut self, mut pauli: pecos_core::PauliString) -> usize {
+        // Phase is irrelevant for flip tracking -- normalize to +1
+        pauli.set_phase(pecos_core::QuarterPhase::PlusOne);
+        let idx = self.annotations.len();
+        self.insert_pauli_meta_gate(&pauli);
+        self.annotations.push(PauliAnnotation {
+            pauli,
+            kind: AnnotationKind::TrackedPauli,
+            label: None,
+        });
+        idx
+    }
+
+    /// Place a labeled tracked-Pauli meta-gate.
+    pub fn tracked_pauli_labeled(
+        &mut self,
+        label: &str,
+        mut pauli: pecos_core::PauliString,
+    ) -> usize {
+        pauli.set_phase(pecos_core::QuarterPhase::PlusOne);
+        let idx = self.annotations.len();
+        self.insert_pauli_meta_gate(&pauli);
+        self.annotations.push(PauliAnnotation {
+            pauli,
+            kind: AnnotationKind::TrackedPauli,
+            label: Some(label.to_string()),
+        });
+        idx
+    }
+
+    /// Insert a `TrackedPauliMeta` gate node into the DAG.
+    fn insert_pauli_meta_gate(&mut self, pauli: &pecos_core::PauliString) {
+        let qubits: Vec<QubitId> = pauli.qubits().into_iter().map(QubitId::from).collect();
+        let gate = Gate::simple(GateType::TrackedPauliMeta, qubits);
+        self.add_gate_auto_wire(gate);
+    }
+
+    /// Get all annotations.
+    #[must_use]
+    pub fn annotations(&self) -> &[PauliAnnotation] {
+        &self.annotations
+    }
+
+    /// Add a pre-built annotation (used for conversion from `TickCircuit`).
+    pub fn add_annotation(&mut self, ann: PauliAnnotation) {
+        // For tracked-Pauli annotations, insert the meta-gate node.
+        if matches!(ann.kind, AnnotationKind::TrackedPauli) {
+            self.insert_pauli_meta_gate(&ann.pauli);
+        }
+        self.annotations.push(ann);
+    }
+
+    /// Get detector annotations.
+    pub fn detectors(&self) -> impl Iterator<Item = &PauliAnnotation> {
+        self.annotations
+            .iter()
+            .filter(|a| matches!(a.kind, AnnotationKind::Detector { .. }))
+    }
+
+    /// Get observable annotations.
+    pub fn observables(&self) -> impl Iterator<Item = &PauliAnnotation> {
+        self.annotations
+            .iter()
+            .filter(|a| matches!(a.kind, AnnotationKind::Observable { .. }))
+    }
+
+    /// Get tracked-Pauli annotations.
+    pub fn tracked_paulis(&self) -> impl Iterator<Item = &PauliAnnotation> {
+        self.annotations
+            .iter()
+            .filter(|a| matches!(a.kind, AnnotationKind::TrackedPauli))
+    }
+
+    // ========================================================================
+    // Preparation Gates
+    // ========================================================================
+
     /// Prepare qubit(s) in the |0> state (Z-basis preparation).
     pub fn pz(&mut self, qubits: &[impl Into<QubitId> + Copy]) -> &mut Self {
         for &q in qubits {
@@ -1918,6 +2212,44 @@ mod tests {
         assert_eq!(circuit.two_qubit_gate_count(), 1);
     }
 
+    #[test]
+    fn test_batched_gate_nodes_count_gates() {
+        let mut circuit = DagCircuit::new();
+
+        circuit.add_gate(Gate::h(&[0, 1, 2, 3]));
+        circuit.add_gate(Gate::cx(&[(0, 1), (2, 3)]));
+
+        assert_eq!(circuit.nodes().len(), 2);
+        assert_eq!(circuit.gate_node_count(), 2);
+        assert_eq!(circuit.gate_count(), 6);
+        assert_eq!(circuit.build_traversal_index().num_gate_nodes(), 2);
+        assert_eq!(circuit.single_qubit_gate_count(), 4);
+        assert_eq!(circuit.two_qubit_gate_count(), 2);
+        assert_eq!(circuit.gate_type_count(GateType::H), 4);
+        assert_eq!(circuit.gate_type_count(GateType::CX), 2);
+    }
+
+    #[test]
+    fn test_separate_compatible_nodes_remain_separate_nodes() {
+        let mut circuit = DagCircuit::new();
+
+        circuit.add_gate(Gate::h(&[0]));
+        circuit.add_gate(Gate::h(&[1]));
+        circuit.add_gate(Gate::cx(&[(2, 3)]));
+        circuit.add_gate(Gate::cx(&[(4, 5)]));
+
+        assert_eq!(circuit.gate_node_count(), 4);
+        assert_eq!(circuit.gate_count(), 4);
+        assert_eq!(circuit.build_traversal_index().num_gate_nodes(), 4);
+        assert_eq!(circuit.gate_type_count(GateType::H), 2);
+        assert_eq!(circuit.gate_type_count(GateType::CX), 2);
+
+        let ticks = crate::TickCircuit::from(&circuit);
+        assert_eq!(ticks.gate_count(), 4);
+        assert_eq!(ticks.gate_batch_count(), 2);
+        assert_eq!(ticks.get_tick(0).unwrap().gate_batch_count(), 2);
+    }
+
     #[test]
     fn test_two_qubit_gate_multiple_wires() {
         let mut circuit = DagCircuit::new();
@@ -2404,10 +2736,9 @@ mod tests {
             .cx(&[(0, 1)])
             .meta("fidelity", Attribute::Float(0.99));
 
-        // Chain meta directly from measurement (mz returns &mut Self)
-        circuit
-            .mz(&[0])
-            .meta("basis", Attribute::String("Z".to_string()));
+        // Measurement returns node indices; use last_node for meta
+        circuit.mz(&[0]);
+        circuit.meta("basis", Attribute::String("Z".to_string()));
 
         assert_eq!(circuit.gate_count(), 3);
 
@@ -2449,22 +2780,21 @@ mod tests {
     }
 
     #[test]
-    fn test_measure_handle_drops_cleanly() {
+    fn test_mz_returns_refs() {
         let mut circuit = DagCircuit::new();
 
-        // MeasureHandle can be ignored (dropped without calling .meta())
         circuit.h(&[0]);
-        circuit.mz(&[0]);
+        let refs = circuit.mz(&[0]);
+        assert_eq!(refs.len(), 1);
         circuit.h(&[1]); // continue building
 
         assert_eq!(circuit.gate_count(), 3);
     }
 
     #[test]
-    fn test_prep_handle_drops_cleanly() {
+    fn test_pz_chainable() {
         let mut circuit = DagCircuit::new();
 
-        // PrepHandle can be ignored (dropped without calling .meta())
         circuit.pz(&[0]);
         circuit.h(&[0]); // continue building
         circuit.mz(&[0]);
@@ -2564,4 +2894,22 @@ mod tests {
         assert_eq!(gate_attrs.get("duration"), Some(&Attribute::Float(50.0)));
         assert_eq!(gate_attrs.get("fidelity"), Some(&Attribute::Float(0.999)));
     }
+
+    #[test]
+    fn test_try_add_gate_rejects_invalid_gate_payload() {
+        let mut circuit = DagCircuit::new();
+        let err = circuit
+            .try_add_gate(Gate::cx(&[(0, 0)]))
+            .expect_err("DAG should reject invalid gate payloads");
+
+        assert!(err.contains("requires distinct qubits"));
+        assert!(circuit.nodes().is_empty());
+    }
+
+    #[test]
+    #[should_panic(expected = "Invalid gate")]
+    fn test_add_gate_panics_on_invalid_gate_payload() {
+        let mut circuit = DagCircuit::new();
+        circuit.add_gate(Gate::cx(&[(0, 0)]));
+    }
 }
diff --git a/crates/pecos-quantum/src/diamond_norm.rs b/crates/pecos-quantum/src/diamond_norm.rs
new file mode 100644
index 000000000..fd36aabd8
--- /dev/null
+++ b/crates/pecos-quantum/src/diamond_norm.rs
@@ -0,0 +1,619 @@
+// Copyright 2026 The PECOS Developers
+//
+// Licensed under the Apache License, Version 2.0 (the "License"); you may not use this file except
+// in compliance with the License. You may obtain a copy of the License at
+//
+//     https://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software distributed under the License
+// is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express
+// or implied. See the License for the specific language governing permissions and limitations under
+// the License.
+
+//! Diamond-norm utilities.
+//!
+//! General channel diamond norm requires solving a semidefinite program. PECOS
+//! does not add an external SDP dependency for that. This module exposes exact
+//! dependency-free cases that are mathematically closed-form today, plus the
+//! linear-algebra pieces needed by a future PECOS-owned general solver.
+
+use std::error::Error;
+use std::fmt;
+
+use nalgebra::DMatrix;
+use num_complex::Complex64;
+
+use crate::channel::{PauliChannel, basis_bitmask, pauli_basis_len};
+
+const DEFAULT_TOLERANCE: f64 = 1e-12;
+
+/// Error returned by diamond-norm linear-algebra helpers.
+#[derive(Debug, Clone, PartialEq)]
+pub enum DiamondNormError {
+    /// A matrix was not square.
+    NonSquareMatrix {
+        /// Row count.
+        rows: usize,
+        /// Column count.
+        cols: usize,
+    },
+    /// A scaled-vector input had the wrong length for the requested matrix.
+    InvalidSvecLength {
+        /// Expected triangular-vector length.
+        expected: usize,
+        /// Actual length.
+        actual: usize,
+    },
+    /// A matrix expected to be symmetric or Hermitian was not within tolerance.
+    NonHermitian {
+        /// Maximum observed entrywise difference from the adjoint/symmetric
+        /// counterpart.
+        max_difference: f64,
+        /// Allowed tolerance.
+        tolerance: f64,
+    },
+    /// A Choi matrix does not match the expected input/output dimensions.
+    InvalidChoiShape {
+        /// Expected row count.
+        expected_rows: usize,
+        /// Expected column count.
+        expected_cols: usize,
+        /// Actual row count.
+        rows: usize,
+        /// Actual column count.
+        cols: usize,
+    },
+    /// Input/output dimensions overflowed a `usize` matrix dimension.
+    DimensionOverflow {
+        /// Input Hilbert-space dimension.
+        dim_in: usize,
+        /// Output Hilbert-space dimension.
+        dim_out: usize,
+    },
+    /// A matrix entry was not finite.
+    NonFiniteEntry,
+    /// Two channel representations act on different Hilbert spaces.
+    QubitCountMismatch {
+        /// Left channel qubit count.
+        left: usize,
+        /// Right channel qubit count.
+        right: usize,
+    },
+    /// Failed to enumerate the Pauli basis for a channel.
+    PauliBasis {
+        /// Underlying reason.
+        reason: String,
+    },
+}
+
+impl fmt::Display for DiamondNormError {
+    fn fmt(&self, f: &mut fmt::Formatter<'_>) -> fmt::Result {
+        match self {
+            Self::NonSquareMatrix { rows, cols } => {
+                write!(f, "matrix must be square, got {rows}x{cols}")
+            }
+            Self::InvalidSvecLength { expected, actual } => write!(
+                f,
+                "invalid scaled-triangle vector length {actual}; expected {expected}"
+            ),
+            Self::NonHermitian {
+                max_difference,
+                tolerance,
+            } => write!(
+                f,
+                "matrix is not Hermitian/symmetric within tolerance {tolerance}; max difference {max_difference}"
+            ),
+            Self::InvalidChoiShape {
+                expected_rows,
+                expected_cols,
+                rows,
+                cols,
+            } => write!(
+                f,
+                "invalid Choi matrix shape {rows}x{cols}; expected {expected_rows}x{expected_cols}"
+            ),
+            Self::DimensionOverflow { dim_in, dim_out } => write!(
+                f,
+                "Choi input/output dimensions overflow usize: dim_in={dim_in}, dim_out={dim_out}"
+            ),
+            Self::NonFiniteEntry => write!(f, "matrix contains a non-finite entry"),
+            Self::QubitCountMismatch { left, right } => write!(
+                f,
+                "channels must act on the same number of qubits, got {left} and {right}"
+            ),
+            Self::PauliBasis { reason } => {
+                write!(f, "failed to enumerate Pauli basis: {reason}")
+            }
+        }
+    }
+}
+
+impl Error for DiamondNormError {}
+
+/// Returns `||left - right||_diamond` for two Pauli channels.
+///
+/// For Pauli channels, the diamond norm of the channel difference is exactly
+/// the L1 distance between the two Pauli probability vectors. Applying the
+/// channel difference to half of a maximally entangled state produces
+/// orthogonal Pauli-labelled Bell states, so no SDP is needed.
+///
+/// # Errors
+///
+/// Returns an error if the channels act on different numbers of qubits or the
+/// Pauli basis size overflows.
+pub fn pauli_channel_diamond_norm(
+    left: &PauliChannel,
+    right: &PauliChannel,
+) -> Result<f64, DiamondNormError> {
+    if left.num_qubits() != right.num_qubits() {
+        return Err(DiamondNormError::QubitCountMismatch {
+            left: left.num_qubits(),
+            right: right.num_qubits(),
+        });
+    }
+    let num_qubits = left.num_qubits();
+    let basis_len = pauli_basis_len(num_qubits).map_err(|err| DiamondNormError::PauliBasis {
+        reason: err.to_string(),
+    })?;
+    let mut total = 0.0;
+    for basis_index in 0..basis_len {
+        let pauli =
+            basis_bitmask(num_qubits, basis_index).map_err(|err| DiamondNormError::PauliBasis {
+                reason: err.to_string(),
+            })?;
+        total += (left.probability(&pauli) - right.probability(&pauli)).abs();
+    }
+    Ok(total)
+}
+
+/// Returns the diamond distance between two Pauli channels.
+///
+/// The diamond distance is `0.5 * ||left - right||_diamond`, matching the
+/// standard trace-distance normalization.
+///
+/// # Errors
+///
+/// Returns an error if [`pauli_channel_diamond_norm`] fails.
+pub fn pauli_channel_diamond_distance(
+    left: &PauliChannel,
+    right: &PauliChannel,
+) -> Result<f64, DiamondNormError> {
+    Ok(0.5 * pauli_channel_diamond_norm(left, right)?)
+}
+
+/// Returns the length of the scaled upper-triangular vector for an `n x n`
+/// symmetric matrix.
+#[must_use]
+pub const fn scaled_psd_triangle_len(n: usize) -> usize {
+    n * (n + 1) / 2
+}
+
+/// Converts a real symmetric matrix to scaled upper-triangular
+/// vector form.
+///
+/// Diagonal entries are stored unchanged. Strict upper-triangular entries are
+/// multiplied by `sqrt(2)`, preserving Frobenius inner products under vector
+/// dot products.
+///
+/// # Errors
+///
+/// Returns an error when `matrix` is not square, contains non-finite values, or
+/// is not symmetric within the default tolerance.
+pub fn svec_real_symmetric(matrix: &DMatrix<f64>) -> Result<Vec<f64>, DiamondNormError> {
+    svec_real_symmetric_with_tolerance(matrix, DEFAULT_TOLERANCE)
+}
+
+/// Converts a real symmetric matrix to scaled upper-triangular vector form
+/// with explicit symmetry tolerance.
+///
+/// # Errors
+///
+/// Returns an error when `matrix` is not square, contains non-finite values, or
+/// is not symmetric within `tolerance`.
+pub fn svec_real_symmetric_with_tolerance(
+    matrix: &DMatrix<f64>,
+    tolerance: f64,
+) -> Result<Vec<f64>, DiamondNormError> {
+    validate_real_symmetric(matrix, tolerance)?;
+    let n = matrix.nrows();
+    let sqrt2 = 2.0_f64.sqrt();
+    let mut out = Vec::with_capacity(scaled_psd_triangle_len(n));
+    for col in 0..n {
+        for row in 0..=col {
+            let scale = if row == col { 1.0 } else { sqrt2 };
+            out.push(matrix[(row, col)] * scale);
+        }
+    }
+    Ok(out)
+}
+
+/// Converts scaled upper-triangular vector form back to a real
+/// symmetric matrix.
+///
+/// # Errors
+///
+/// Returns an error when `data.len()` is not `n * (n + 1) / 2` or a data entry
+/// is not finite.
+pub fn smat_real_symmetric(n: usize, data: &[f64]) -> Result<DMatrix<f64>, DiamondNormError> {
+    let expected = scaled_psd_triangle_len(n);
+    if data.len() != expected {
+        return Err(DiamondNormError::InvalidSvecLength {
+            expected,
+            actual: data.len(),
+        });
+    }
+    let sqrt2 = 2.0_f64.sqrt();
+    let mut out = DMatrix::zeros(n, n);
+    let mut idx = 0;
+    for col in 0..n {
+        for row in 0..=col {
+            let value = data[idx];
+            if !value.is_finite() {
+                return Err(DiamondNormError::NonFiniteEntry);
+            }
+            let unscaled = if row == col { value } else { value / sqrt2 };
+            out[(row, col)] = unscaled;
+            out[(col, row)] = unscaled;
+            idx += 1;
+        }
+    }
+    Ok(out)
+}
+
+/// Embeds a complex Hermitian matrix `A = X + iY` as a real symmetric matrix:
+///
+/// ```text
+/// [ X  -Y ]
+/// [ Y   X ]
+/// ```
+///
+/// This embedding maps complex PSD constraints into real PSD constraints, which
+/// is the representation needed by a real-valued PECOS SDP implementation.
+///
+/// # Errors
+///
+/// Returns an error when `matrix` is not square, contains non-finite values, or
+/// is not Hermitian within the default tolerance.
+pub fn hermitian_to_real_symmetric(
+    matrix: &DMatrix<Complex64>,
+) -> Result<DMatrix<f64>, DiamondNormError> {
+    hermitian_to_real_symmetric_with_tolerance(matrix, DEFAULT_TOLERANCE)
+}
+
+/// Hermitian-to-real-symmetric embedding with explicit tolerance.
+///
+/// # Errors
+///
+/// Returns an error when `matrix` is not square, contains non-finite values, or
+/// is not Hermitian within `tolerance`.
+pub fn hermitian_to_real_symmetric_with_tolerance(
+    matrix: &DMatrix<Complex64>,
+    tolerance: f64,
+) -> Result<DMatrix<f64>, DiamondNormError> {
+    validate_hermitian(matrix, tolerance)?;
+    let n = matrix.nrows();
+    let mut out = DMatrix::zeros(2 * n, 2 * n);
+    for row in 0..n {
+        for col in 0..n {
+            let value = matrix[(row, col)];
+            out[(row, col)] = value.re;
+            out[(row, col + n)] = -value.im;
+            out[(row + n, col)] = value.im;
+            out[(row + n, col + n)] = value.re;
+        }
+    }
+    Ok(out)
+}
+
+/// Converts PECOS's column-stacked Choi convention to the transposed
+/// row-vector convention used by the Watrous diamond-norm SDP objective.
+///
+/// PECOS indexes Choi rows and columns as `output + input * dim_output`.
+/// This helper performs the convention transform used when assembling the
+/// row-vector form of the Watrous SDP:
+///
+/// ```text
+/// reshape(J, (dim_in, dim_out, dim_in, dim_out))
+/// transpose axes (3, 2, 1, 0)
+/// reshape back to a matrix
+/// ```
+///
+/// The result is not a public diamond-norm implementation. It is a tested
+/// convention helper for the future PECOS-owned SDP assembly.
+///
+/// # Errors
+///
+/// Returns an error if `choi` is not `(dim_in * dim_out) x (dim_in * dim_out)`
+/// or if it contains a non-finite entry.
+pub fn choi_to_watrous_row_transpose(
+    choi: &DMatrix<Complex64>,
+    dim_in: usize,
+    dim_out: usize,
+) -> Result<DMatrix<Complex64>, DiamondNormError> {
+    let size = dim_in
+        .checked_mul(dim_out)
+        .ok_or(DiamondNormError::DimensionOverflow { dim_in, dim_out })?;
+    if choi.nrows() != size || choi.ncols() != size {
+        return Err(DiamondNormError::InvalidChoiShape {
+            expected_rows: size,
+            expected_cols: size,
+            rows: choi.nrows(),
+            cols: choi.ncols(),
+        });
+    }
+
+    let mut out = DMatrix::zeros(size, size);
+    for input_row in 0..dim_in {
+        for output_row in 0..dim_out {
+            let src_row = output_row + input_row * dim_out;
+            for input_col in 0..dim_in {
+                for output_col in 0..dim_out {
+                    let src_col = output_col + input_col * dim_out;
+                    let value = choi[(src_row, src_col)];
+                    if !value.re.is_finite() || !value.im.is_finite() {
+                        return Err(DiamondNormError::NonFiniteEntry);
+                    }
+                    let dst_row = input_col + output_col * dim_in;
+                    let dst_col = input_row + output_row * dim_in;
+                    out[(dst_row, dst_col)] = value;
+                }
+            }
+        }
+    }
+    Ok(out)
+}
+
+fn validate_real_symmetric(matrix: &DMatrix<f64>, tolerance: f64) -> Result<(), DiamondNormError> {
+    if matrix.nrows() != matrix.ncols() {
+        return Err(DiamondNormError::NonSquareMatrix {
+            rows: matrix.nrows(),
+            cols: matrix.ncols(),
+        });
+    }
+    let mut max_difference: f64 = 0.0;
+    for row in 0..matrix.nrows() {
+        for col in 0..matrix.ncols() {
+            let value = matrix[(row, col)];
+            if !value.is_finite() {
+                return Err(DiamondNormError::NonFiniteEntry);
+            }
+            max_difference = max_difference.max((value - matrix[(col, row)]).abs());
+        }
+    }
+    if max_difference > tolerance {
+        return Err(DiamondNormError::NonHermitian {
+            max_difference,
+            tolerance,
+        });
+    }
+    Ok(())
+}
+
+fn validate_hermitian(matrix: &DMatrix<Complex64>, tolerance: f64) -> Result<(), DiamondNormError> {
+    if matrix.nrows() != matrix.ncols() {
+        return Err(DiamondNormError::NonSquareMatrix {
+            rows: matrix.nrows(),
+            cols: matrix.ncols(),
+        });
+    }
+    let mut max_difference: f64 = 0.0;
+    for row in 0..matrix.nrows() {
+        for col in 0..matrix.ncols() {
+            let value = matrix[(row, col)];
+            if !value.re.is_finite() || !value.im.is_finite() {
+                return Err(DiamondNormError::NonFiniteEntry);
+            }
+            max_difference = max_difference.max((value - matrix[(col, row)].conj()).norm());
+        }
+    }
+    if max_difference > tolerance {
+        return Err(DiamondNormError::NonHermitian {
+            max_difference,
+            tolerance,
+        });
+    }
+    Ok(())
+}
+
+#[cfg(test)]
+mod tests {
+    use super::*;
+    use std::collections::BTreeMap;
+
+    fn assert_close(left: f64, right: f64) {
+        assert!((left - right).abs() < 1e-12, "{left} != {right}");
+    }
+
+    #[test]
+    fn pauli_channel_diamond_norm_is_l1_probability_distance() {
+        let left = PauliChannel::one_qubit(0.1, 0.2, 0.0).unwrap();
+        let right = PauliChannel::one_qubit(0.0, 0.2, 0.3).unwrap();
+
+        assert_close(pauli_channel_diamond_norm(&left, &right).unwrap(), 0.6);
+        assert_close(pauli_channel_diamond_distance(&left, &right).unwrap(), 0.3);
+    }
+
+    #[test]
+    fn pauli_channel_diamond_norm_includes_absent_terms_as_zero() {
+        let mut left_probs = BTreeMap::new();
+        left_probs.insert(basis_bitmask(2, 0).unwrap(), 0.9);
+        left_probs.insert(basis_bitmask(2, 5).unwrap(), 0.1);
+        let left = PauliChannel::try_new(2, left_probs).unwrap();
+
+        let mut right_probs = BTreeMap::new();
+        right_probs.insert(basis_bitmask(2, 0).unwrap(), 0.8);
+        right_probs.insert(basis_bitmask(2, 10).unwrap(), 0.2);
+        let right = PauliChannel::try_new(2, right_probs).unwrap();
+
+        assert_close(pauli_channel_diamond_norm(&left, &right).unwrap(), 0.4);
+    }
+
+    #[test]
+    fn pauli_channel_diamond_norm_handles_sparse_three_qubit_channels() {
+        let mut left_probs = BTreeMap::new();
+        left_probs.insert(basis_bitmask(3, 0).unwrap(), 0.7);
+        left_probs.insert(basis_bitmask(3, 1).unwrap(), 0.1);
+        left_probs.insert(basis_bitmask(3, 17).unwrap(), 0.2);
+        let left = PauliChannel::try_new(3, left_probs).unwrap();
+
+        let mut right_probs = BTreeMap::new();
+        right_probs.insert(basis_bitmask(3, 0).unwrap(), 0.6);
+        right_probs.insert(basis_bitmask(3, 17).unwrap(), 0.1);
+        right_probs.insert(basis_bitmask(3, 63).unwrap(), 0.3);
+        let right = PauliChannel::try_new(3, right_probs).unwrap();
+
+        assert_close(pauli_channel_diamond_norm(&left, &right).unwrap(), 0.6);
+        assert_close(pauli_channel_diamond_distance(&left, &right).unwrap(), 0.3);
+    }
+
+    #[test]
+    fn pauli_channel_diamond_norm_rejects_qubit_count_mismatch() {
+        let left = PauliChannel::one_qubit(0.1, 0.0, 0.0).unwrap();
+        let mut right_probs = BTreeMap::new();
+        right_probs.insert(basis_bitmask(2, 0).unwrap(), 1.0);
+        let right = PauliChannel::try_new(2, right_probs).unwrap();
+
+        assert!(matches!(
+            pauli_channel_diamond_norm(&left, &right).unwrap_err(),
+            DiamondNormError::QubitCountMismatch { left: 1, right: 2 }
+        ));
+    }
+
+    fn frobenius_inner(left: &DMatrix<f64>, right: &DMatrix<f64>) -> f64 {
+        left.iter().zip(right.iter()).map(|(a, b)| a * b).sum()
+    }
+
+    #[test]
+    fn scaled_triangle_round_trips_real_symmetric_matrix() {
+        let matrix =
+            DMatrix::from_row_slice(3, 3, &[1.0, 2.0, -3.0, 2.0, 5.0, 7.0, -3.0, 7.0, 11.0]);
+        let packed = svec_real_symmetric(&matrix).unwrap();
+        assert_eq!(packed.len(), 6);
+        let recovered = smat_real_symmetric(3, &packed).unwrap();
+        for row in 0..3 {
+            for col in 0..3 {
+                assert_close(recovered[(row, col)], matrix[(row, col)]);
+            }
+        }
+    }
+
+    #[test]
+    fn scaled_triangle_preserves_frobenius_inner_product() {
+        let a = DMatrix::from_row_slice(2, 2, &[1.0, 3.0, 3.0, 2.0]);
+        let b = DMatrix::from_row_slice(2, 2, &[5.0, -7.0, -7.0, 11.0]);
+        let a_vec = svec_real_symmetric(&a).unwrap();
+        let b_vec = svec_real_symmetric(&b).unwrap();
+        let vector_inner: f64 = a_vec.iter().zip(b_vec.iter()).map(|(x, y)| x * y).sum();
+
+        assert_close(vector_inner, frobenius_inner(&a, &b));
+    }
+
+    #[test]
+    fn hermitian_embedding_is_real_symmetric_and_trace_scaled() {
+        let i = Complex64::new(0.0, 1.0);
+        let matrix = DMatrix::from_row_slice(
+            2,
+            2,
+            &[Complex64::new(2.0, 0.0), i, -i, Complex64::new(3.0, 0.0)],
+        );
+        let embedded = hermitian_to_real_symmetric(&matrix).unwrap();
+
+        assert_eq!(embedded.shape(), (4, 4));
+        for row in 0..4 {
+            for col in 0..4 {
+                assert_close(embedded[(row, col)], embedded[(col, row)]);
+            }
+        }
+        assert_close(embedded.trace(), 10.0);
+    }
+
+    #[test]
+    fn choi_to_watrous_row_transpose_matches_reference_axis_permutation() {
+        let choi = DMatrix::from_row_slice(
+            4,
+            4,
+            &[
+                Complex64::new(0.0, 0.0),
+                Complex64::new(1.0, 0.0),
+                Complex64::new(2.0, 0.0),
+                Complex64::new(3.0, 0.0),
+                Complex64::new(4.0, 0.0),
+                Complex64::new(5.0, 0.0),
+                Complex64::new(6.0, 0.0),
+                Complex64::new(7.0, 0.0),
+                Complex64::new(8.0, 0.0),
+                Complex64::new(9.0, 0.0),
+                Complex64::new(10.0, 0.0),
+                Complex64::new(11.0, 0.0),
+                Complex64::new(12.0, 0.0),
+                Complex64::new(13.0, 0.0),
+                Complex64::new(14.0, 0.0),
+                Complex64::new(15.0, 0.0),
+            ],
+        );
+        let converted = choi_to_watrous_row_transpose(&choi, 2, 2).unwrap();
+        let expected = DMatrix::from_row_slice(
+            4,
+            4,
+            &[
+                Complex64::new(0.0, 0.0),
+                Complex64::new(8.0, 0.0),
+                Complex64::new(4.0, 0.0),
+                Complex64::new(12.0, 0.0),
+                Complex64::new(2.0, 0.0),
+                Complex64::new(10.0, 0.0),
+                Complex64::new(6.0, 0.0),
+                Complex64::new(14.0, 0.0),
+                Complex64::new(1.0, 0.0),
+                Complex64::new(9.0, 0.0),
+                Complex64::new(5.0, 0.0),
+                Complex64::new(13.0, 0.0),
+                Complex64::new(3.0, 0.0),
+                Complex64::new(11.0, 0.0),
+                Complex64::new(7.0, 0.0),
+                Complex64::new(15.0, 0.0),
+            ],
+        );
+
+        assert_eq!(converted, expected);
+    }
+
+    #[test]
+    fn helper_validation_rejects_invalid_inputs() {
+        assert!(matches!(
+            svec_real_symmetric(&DMatrix::zeros(2, 3)).unwrap_err(),
+            DiamondNormError::NonSquareMatrix { .. }
+        ));
+
+        let nonsymmetric = DMatrix::from_row_slice(2, 2, &[1.0, 2.0, 3.0, 4.0]);
+        assert!(matches!(
+            svec_real_symmetric(&nonsymmetric).unwrap_err(),
+            DiamondNormError::NonHermitian { .. }
+        ));
+
+        assert!(matches!(
+            smat_real_symmetric(3, &[1.0, 2.0]).unwrap_err(),
+            DiamondNormError::InvalidSvecLength { .. }
+        ));
+
+        let nonhermitian = DMatrix::from_row_slice(
+            2,
+            2,
+            &[
+                Complex64::new(1.0, 0.0),
+                Complex64::new(1.0, 1.0),
+                Complex64::new(1.0, 1.0),
+                Complex64::new(1.0, 0.0),
+            ],
+        );
+        assert!(matches!(
+            hermitian_to_real_symmetric(&nonhermitian).unwrap_err(),
+            DiamondNormError::NonHermitian { .. }
+        ));
+
+        assert!(matches!(
+            choi_to_watrous_row_transpose(&DMatrix::zeros(2, 2), 2, 2).unwrap_err(),
+            DiamondNormError::InvalidChoiShape { .. }
+        ));
+    }
+}
diff --git a/crates/pecos-quantum/src/lib.rs b/crates/pecos-quantum/src/lib.rs
index 949583ce1..44bf47a1b 100644
--- a/crates/pecos-quantum/src/lib.rs
+++ b/crates/pecos-quantum/src/lib.rs
@@ -63,16 +63,18 @@
 //! circuit2.tick().mz(&[0, 1, 2, 3]);    // Measure multiple qubits
 //! ```
 
+pub mod channel;
 mod circuit;
 mod circuit_display;
 mod dag_circuit;
+pub mod diamond_norm;
+pub mod measures;
 pub mod pass;
 pub mod pauli_group;
 pub mod pauli_sequence;
 pub mod pauli_set;
 pub mod stabilizer_group;
 mod tick_circuit;
-pub mod tick_circuit_soa;
 pub mod unitary_matrix;
 
 #[cfg(feature = "hugr")]
@@ -80,15 +82,12 @@ pub mod hugr_convert;
 
 pub use circuit::{Circuit, CircuitMut, GateHandle, GateView};
 pub use dag_circuit::{
-    Attribute, DagCircuit, DagTraversalIndex, MeasureHandle, PrepHandle, TraversalWorkBuffers,
+    AnnotationKind, Attribute, DagCircuit, DagTraversalIndex, MeasRef, PauliAnnotation,
+    TraversalWorkBuffers,
 };
 pub use tick_circuit::{
-    CustomGateError, GateSignatureMismatchError, QubitConflictError, Tick, TickCircuit, TickHandle,
-    TickMeasureHandle, TickPrepHandle,
-};
-pub use tick_circuit_soa::{
-    CircuitIndexes, GateBatch, GateId, GateStorage, MetadataStorage, TickBatches, TickCircuitSoA,
-    TickCircuitSoABuilder, TickGateGroups,
+    CustomGateError, GateSignatureMismatchError, QubitConflictError, Tick, TickCircuit,
+    TickGateError, TickHandle, TickMeasRef, TickMeasureHandle, TickPrepHandle,
 };
 
 // Re-export commonly used types from dependencies
@@ -96,8 +95,31 @@ pub use pecos_core::gate_type::GateType;
 pub use pecos_core::{ClassicalBitId, Gate, QubitId, TimeScale, TimeUnits};
 pub use pecos_num::dag::DagWouldCycleError;
 
+// Concrete channel representation types
+pub use channel::{
+    ChannelError, ChiMatrix, ChoiMatrix, DiagonalPtm, KrausOps, MatrixUnitTomographyInput,
+    PauliChannel, PauliSum, ProcessTomographyDesign, Ptm, PtmBasisOrder, Stinespring, SuperOp,
+    basis_bitmask, basis_digit_to_pauli, basis_element, basis_index, basis_label, bitmask_label,
+    matrix_unit_basis, partial_trace, pauli_basis_len, pauli_string_to_bitmask,
+    pauli_to_basis_digit, random_1q_clifford, random_2q_clifford, random_clifford,
+    random_density_matrix, random_density_matrix_with_rank, random_pauli, random_quantum_channel,
+};
+pub use diamond_norm::{
+    DiamondNormError, choi_to_watrous_row_transpose, hermitian_to_real_symmetric,
+    hermitian_to_real_symmetric_with_tolerance, pauli_channel_diamond_distance,
+    pauli_channel_diamond_norm, scaled_psd_triangle_len, smat_real_symmetric, svec_real_symmetric,
+    svec_real_symmetric_with_tolerance,
+};
+pub use measures::{
+    DensityMatrixPartialTrace, MeasureError, SchmidtTerm, average_gate_fidelity, concurrence,
+    entanglement_of_formation, entropy, entropy_with_base, gate_error, hellinger_distance,
+    hellinger_fidelity, logarithmic_negativity, mutual_information, negativity,
+    partial_trace_qubits, partial_trace_subsystems, process_fidelity, purity,
+    schmidt_decomposition, shannon_entropy, state_fidelity, state_fidelity_with_density_matrix,
+};
+
 // Re-export operator matrix types for convenient method-style matrix conversion
-pub use unitary_matrix::{ToMatrix, UnitaryMatrix};
+pub use unitary_matrix::{ToMatrix, UnitaryMatrix, UnitaryMatrixError, random_unitary};
 
 // Pauli collection and stabilizer group types
 pub use pauli_group::{PauliGroup, PauliGroupError};
diff --git a/crates/pecos-quantum/src/measures.rs b/crates/pecos-quantum/src/measures.rs
new file mode 100644
index 000000000..0943a9ba7
--- /dev/null
+++ b/crates/pecos-quantum/src/measures.rs
@@ -0,0 +1,1490 @@
+// Copyright 2026 The PECOS Developers
+//
+// Licensed under the Apache License, Version 2.0 (the "License"); you may not use this file except
+// in compliance with the License. You may obtain a copy of the License at
+//
+//     https://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software distributed under the License
+// is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express
+// or implied. See the License for the specific language governing permissions and limitations under
+// the License.
+
+//! Standalone quantum information measures.
+//!
+//! Measures are free functions so they can be shared across simulator and
+//! representation types without forcing every backend into a single state API.
+
+use std::error::Error;
+use std::fmt;
+
+use nalgebra::{DMatrix, DVector, SVD, Schur};
+use num_complex::Complex64;
+
+use crate::channel::Ptm;
+
+const DEFAULT_TOLERANCE: f64 = 1e-12;
+
+/// One term in a Schmidt decomposition.
+///
+/// The tuple is `(coefficient, left_vector, right_vector)`.
+pub type SchmidtTerm = (f64, Vec<Complex64>, Vec<Complex64>);
+
+/// Error returned by quantum-information measure functions.
+#[derive(Debug, Clone, PartialEq)]
+pub enum MeasureError {
+    /// The requested Hilbert-space dimension would overflow `usize`.
+    DimensionOverflow {
+        /// Number of qubits supplied by the caller.
+        num_qubits: usize,
+    },
+    /// Two vectors have incompatible lengths.
+    VectorLengthMismatch {
+        /// Left vector length.
+        left: usize,
+        /// Right vector length.
+        right: usize,
+    },
+    /// A matrix is not square.
+    NonSquareMatrix {
+        /// Actual row count.
+        rows: usize,
+        /// Actual column count.
+        cols: usize,
+    },
+    /// A matrix does not have the expected shape.
+    InvalidMatrixShape {
+        /// Expected row count.
+        expected_rows: usize,
+        /// Expected column count.
+        expected_cols: usize,
+        /// Actual row count.
+        rows: usize,
+        /// Actual column count.
+        cols: usize,
+    },
+    /// Two channel/process representations have incompatible qubit counts.
+    QubitCountMismatch {
+        /// Expected qubit count.
+        expected: usize,
+        /// Actual qubit count.
+        actual: usize,
+    },
+    /// A value is not finite.
+    NonFiniteValue {
+        /// Offending value.
+        value: Complex64,
+    },
+    /// A finite complex value was expected to be real within tolerance.
+    NonRealValue {
+        /// Offending value.
+        value: Complex64,
+        /// Allowed imaginary-part tolerance.
+        tolerance: f64,
+    },
+    /// A state vector is not normalized.
+    InvalidStateNorm {
+        /// Observed squared norm.
+        norm_sqr: f64,
+        /// Allowed absolute tolerance.
+        tolerance: f64,
+    },
+    /// A density matrix is not Hermitian within tolerance.
+    NonHermitianMatrix {
+        /// Row index where the mismatch was observed.
+        row: usize,
+        /// Column index where the mismatch was observed.
+        col: usize,
+        /// Observed entry.
+        value: Complex64,
+        /// Conjugate-transposed entry.
+        adjoint_value: Complex64,
+        /// Allowed absolute tolerance.
+        tolerance: f64,
+    },
+    /// A density matrix does not have trace one.
+    InvalidDensityTrace {
+        /// Observed trace.
+        trace: Complex64,
+        /// Allowed absolute tolerance.
+        tolerance: f64,
+    },
+    /// The requested logarithm base is invalid for entropy.
+    InvalidEntropyBase {
+        /// Invalid base.
+        base: f64,
+    },
+    /// A probability is negative or non-finite.
+    InvalidProbability {
+        /// Index of the invalid probability.
+        index: usize,
+        /// Invalid probability value.
+        probability: f64,
+    },
+    /// A probability distribution does not sum to one.
+    InvalidProbabilitySum {
+        /// Observed probability sum.
+        sum: f64,
+        /// Allowed absolute tolerance.
+        tolerance: f64,
+    },
+    /// Subsystem dimensions are invalid for a multipartite measure.
+    InvalidSubsystemDimensions {
+        /// Subsystem dimensions supplied by the caller.
+        dims: Vec<usize>,
+        /// Actual Hilbert-space dimension of the density matrix.
+        matrix_dim: usize,
+    },
+    /// A subsystem index is outside the supplied tensor-factor list.
+    SubsystemOutOfRange {
+        /// Number of subsystems supplied by the caller.
+        num_subsystems: usize,
+        /// Invalid subsystem index.
+        subsystem: usize,
+    },
+    /// A subsystem was listed more than once.
+    DuplicateSubsystem {
+        /// Repeated subsystem index.
+        subsystem: usize,
+    },
+    /// An eigendecomposition did not converge.
+    EigenDecompositionFailed,
+}
+
+impl fmt::Display for MeasureError {
+    fn fmt(&self, f: &mut fmt::Formatter<'_>) -> fmt::Result {
+        match self {
+            Self::DimensionOverflow { num_qubits } => {
+                write!(
+                    f,
+                    "Hilbert-space dimension overflows usize for {num_qubits} qubits"
+                )
+            }
+            Self::VectorLengthMismatch { left, right } => {
+                write!(f, "vector length mismatch: {left} != {right}")
+            }
+            Self::NonSquareMatrix { rows, cols } => {
+                write!(f, "matrix must be square, got {rows}x{cols}")
+            }
+            Self::InvalidMatrixShape {
+                expected_rows,
+                expected_cols,
+                rows,
+                cols,
+            } => write!(
+                f,
+                "invalid matrix shape {rows}x{cols}; expected {expected_rows}x{expected_cols}"
+            ),
+            Self::QubitCountMismatch { expected, actual } => {
+                write!(f, "qubit count mismatch: expected {expected}, got {actual}")
+            }
+            Self::NonFiniteValue { value } => write!(f, "non-finite value: {value}"),
+            Self::NonRealValue { value, tolerance } => write!(
+                f,
+                "value must be real within tolerance {tolerance}, got {value}"
+            ),
+            Self::InvalidStateNorm {
+                norm_sqr,
+                tolerance,
+            } => write!(
+                f,
+                "state vector squared norm must be 1 within tolerance {tolerance}, got {norm_sqr}"
+            ),
+            Self::NonHermitianMatrix {
+                row,
+                col,
+                value,
+                adjoint_value,
+                tolerance,
+            } => write!(
+                f,
+                "matrix is not Hermitian within tolerance {tolerance} at ({row}, {col}): {value} != {adjoint_value}"
+            ),
+            Self::InvalidDensityTrace { trace, tolerance } => write!(
+                f,
+                "density matrix trace must be 1 within tolerance {tolerance}, got {trace}"
+            ),
+            Self::InvalidEntropyBase { base } => {
+                write!(
+                    f,
+                    "entropy logarithm base must be finite, positive, and not 1; got {base}"
+                )
+            }
+            Self::InvalidProbability { index, probability } => write!(
+                f,
+                "probability at index {index} must be finite and non-negative, got {probability}"
+            ),
+            Self::InvalidProbabilitySum { sum, tolerance } => write!(
+                f,
+                "probability distribution must sum to 1 within tolerance {tolerance}, got {sum}"
+            ),
+            Self::InvalidSubsystemDimensions { dims, matrix_dim } => write!(
+                f,
+                "invalid subsystem dimensions {dims:?} for density matrix dimension {matrix_dim}"
+            ),
+            Self::SubsystemOutOfRange {
+                num_subsystems,
+                subsystem,
+            } => write!(
+                f,
+                "subsystem {subsystem} is outside the {num_subsystems}-subsystem tensor product"
+            ),
+            Self::DuplicateSubsystem { subsystem } => {
+                write!(f, "duplicate subsystem index: {subsystem}")
+            }
+            Self::EigenDecompositionFailed => write!(f, "eigendecomposition failed"),
+        }
+    }
+}
+
+impl Error for MeasureError {}
+
+/// Method-style partial trace operations for state density matrices.
+///
+/// This trait is implemented for `DMatrix<Complex64>` because PECOS currently
+/// represents state density matrices as dense complex matrices. The methods
+/// validate that the matrix is a trace-one Hermitian density matrix before
+/// reducing it.
+pub trait DensityMatrixPartialTrace {
+    /// Returns the reduced density matrix after tracing out selected
+    /// tensor-product subsystems.
+    ///
+    /// `dims[i]` is the Hilbert-space dimension of subsystem `i`. Subsystem 0
+    /// is the fastest-varying factor in the computational-basis index.
+    ///
+    /// # Errors
+    ///
+    /// Returns an error when the matrix is not a structurally valid density
+    /// matrix, when `dims` do not match its shape, or when `traced_subsystems`
+    /// contains an out-of-range or repeated subsystem.
+    fn partial_trace(
+        &self,
+        dims: &[usize],
+        traced_subsystems: &[usize],
+    ) -> Result<DMatrix<Complex64>, MeasureError>;
+
+    /// Returns the reduced density matrix after tracing out selected qubits.
+    ///
+    /// Qubit indexing is little-endian: qubit 0 is the least-significant bit
+    /// of the computational-basis index.
+    ///
+    /// # Errors
+    ///
+    /// Returns an error when the matrix is not a structurally valid density
+    /// matrix, when its shape is not `2^num_qubits x 2^num_qubits`, or when
+    /// `traced_qubits` contains an out-of-range or repeated qubit.
+    fn partial_trace_qubits(
+        &self,
+        num_qubits: usize,
+        traced_qubits: &[usize],
+    ) -> Result<DMatrix<Complex64>, MeasureError>;
+}
+
+impl DensityMatrixPartialTrace for DMatrix<Complex64> {
+    fn partial_trace(
+        &self,
+        dims: &[usize],
+        traced_subsystems: &[usize],
+    ) -> Result<DMatrix<Complex64>, MeasureError> {
+        partial_trace_subsystems(self, dims, traced_subsystems)
+    }
+
+    fn partial_trace_qubits(
+        &self,
+        num_qubits: usize,
+        traced_qubits: &[usize],
+    ) -> Result<DMatrix<Complex64>, MeasureError> {
+        partial_trace_qubits(self, num_qubits, traced_qubits)
+    }
+}
+
+/// Returns pure-state fidelity `|<left|right>|^2`.
+///
+/// Both state vectors must have the same length and be normalized.
+///
+/// # Errors
+///
+/// Returns an error when lengths differ, entries are non-finite, or either
+/// vector is not normalized within tolerance.
+pub fn state_fidelity(
+    left: &DVector<Complex64>,
+    right: &DVector<Complex64>,
+) -> Result<f64, MeasureError> {
+    if left.len() != right.len() {
+        return Err(MeasureError::VectorLengthMismatch {
+            left: left.len(),
+            right: right.len(),
+        });
+    }
+    validate_state_vector(left)?;
+    validate_state_vector(right)?;
+    let overlap: Complex64 = left
+        .iter()
+        .zip(right.iter())
+        .map(|(left, right)| left.conj() * right)
+        .sum();
+    Ok(overlap.norm_sqr())
+}
+
+/// Returns fidelity `<psi|rho|psi>` between a density matrix and a pure state.
+///
+/// `rho` must be a trace-one Hermitian density matrix and `psi` must be a
+/// normalized state vector with matching dimension. Positive-semidefinite
+/// validation is intentionally not part of this cheap structural check.
+///
+/// # Errors
+///
+/// Returns an error when dimensions differ or either input is structurally
+/// invalid.
+pub fn state_fidelity_with_density_matrix(
+    rho: &DMatrix<Complex64>,
+    psi: &DVector<Complex64>,
+) -> Result<f64, MeasureError> {
+    validate_density_matrix(rho)?;
+    validate_state_vector(psi)?;
+    if rho.nrows() != psi.len() {
+        return Err(MeasureError::InvalidMatrixShape {
+            expected_rows: psi.len(),
+            expected_cols: psi.len(),
+            rows: rho.nrows(),
+            cols: rho.ncols(),
+        });
+    }
+    let evolved = rho * psi;
+    let value: Complex64 = psi
+        .iter()
+        .zip(evolved.iter())
+        .map(|(left, right)| left.conj() * right)
+        .sum();
+    if value.im.abs() > DEFAULT_TOLERANCE {
+        return Err(MeasureError::NonRealValue {
+            value,
+            tolerance: DEFAULT_TOLERANCE,
+        });
+    }
+    Ok(value.re)
+}
+
+/// Returns density-matrix purity `Tr(rho^2)`.
+///
+/// # Errors
+///
+/// Returns an error when `rho` is not square, finite, Hermitian, and trace one.
+pub fn purity(rho: &DMatrix<Complex64>) -> Result<f64, MeasureError> {
+    validate_density_matrix(rho)?;
+    let value = trace(&(rho * rho));
+    if value.im.abs() > DEFAULT_TOLERANCE {
+        return Err(MeasureError::NonRealValue {
+            value,
+            tolerance: DEFAULT_TOLERANCE,
+        });
+    }
+    Ok(value.re)
+}
+
+/// Returns the von Neumann entropy `-Tr(rho log_2 rho)`.
+///
+/// `rho` must be a positive-semidefinite density matrix. This function
+/// validates the cheap structural conditions (square, finite, Hermitian,
+/// trace one) and computes the entropy from singular values, which equal the
+/// eigenvalues for valid density matrices.
+///
+/// # Errors
+///
+/// Returns an error when `rho` is structurally invalid.
+pub fn entropy(rho: &DMatrix<Complex64>) -> Result<f64, MeasureError> {
+    entropy_with_base(rho, 2.0)
+}
+
+/// Returns the von Neumann entropy `-Tr(rho log_base rho)`.
+///
+/// # Errors
+///
+/// Returns an error when `rho` is structurally invalid or `base` is not finite,
+/// positive, and different from one.
+pub fn entropy_with_base(rho: &DMatrix<Complex64>, base: f64) -> Result<f64, MeasureError> {
+    validate_density_matrix(rho)?;
+    validate_entropy_base(base)?;
+    let svd = SVD::new(rho.clone(), false, false);
+    shannon_entropy(svd.singular_values.as_slice(), base)
+}
+
+/// Returns the Shannon entropy of a probability distribution.
+///
+/// The result is `-sum_i p_i log_base(p_i)`. Zero-probability entries
+/// contribute zero.
+///
+/// # Errors
+///
+/// Returns an error when `base` is invalid, when a probability is negative or
+/// non-finite, or when the probabilities do not sum to one.
+///
+/// # Examples
+///
+/// ```
+/// use pecos_quantum::shannon_entropy;
+///
+/// let entropy = shannon_entropy(&[0.5, 0.5], 2.0).unwrap();
+/// assert!((entropy - 1.0).abs() < 1e-12);
+/// ```
+pub fn shannon_entropy(probabilities: &[f64], base: f64) -> Result<f64, MeasureError> {
+    validate_entropy_base(base)?;
+    validate_probability_distribution(probabilities)?;
+    let log_base = base.ln();
+    Ok(probabilities
+        .iter()
+        .copied()
+        .filter(|probability| *probability > DEFAULT_TOLERANCE)
+        .map(|probability| -probability * probability.ln() / log_base)
+        .sum())
+}
+
+/// Returns normalized process fidelity between two PTMs.
+///
+/// With PECOS's normalized Pauli basis convention, this is
+/// `Tr(R_left^T R_right) / 4^n`. Identity compared with identity gives 1.
+///
+/// # Errors
+///
+/// Returns an error when the PTMs have different qubit counts.
+pub fn process_fidelity(left: &Ptm, right: &Ptm) -> Result<f64, MeasureError> {
+    if left.num_qubits() != right.num_qubits() {
+        return Err(MeasureError::QubitCountMismatch {
+            expected: left.num_qubits(),
+            actual: right.num_qubits(),
+        });
+    }
+    #[allow(clippy::cast_precision_loss)]
+    let basis_len = left.matrix().nrows() as f64;
+    let value: f64 = left
+        .matrix()
+        .iter()
+        .zip(right.matrix().iter())
+        .map(|(left, right)| left * right)
+        .sum::<f64>()
+        / basis_len;
+    Ok(value)
+}
+
+/// Returns average gate fidelity between two PTMs.
+///
+/// This uses `F_avg = (d F_process + 1) / (d + 1)` for Hilbert-space
+/// dimension `d = 2^n`.
+///
+/// # Errors
+///
+/// Returns an error when the PTMs have different qubit counts or the Hilbert
+/// dimension overflows.
+pub fn average_gate_fidelity(left: &Ptm, right: &Ptm) -> Result<f64, MeasureError> {
+    let process = process_fidelity(left, right)?;
+    let dim = hilbert_dim(left.num_qubits())?;
+    #[allow(clippy::cast_precision_loss)]
+    let dim = dim as f64;
+    Ok((dim * process + 1.0) / (dim + 1.0))
+}
+
+/// Returns average gate error `1 - average_gate_fidelity`.
+///
+/// # Errors
+///
+/// Returns an error when [`average_gate_fidelity`] fails.
+pub fn gate_error(left: &Ptm, right: &Ptm) -> Result<f64, MeasureError> {
+    Ok(1.0 - average_gate_fidelity(left, right)?)
+}
+
+/// Returns the two-qubit concurrence of a density matrix.
+///
+/// For a two-qubit state `rho`, this computes Wootters' concurrence using the
+/// spin-flipped matrix `rho_tilde = (Y ⊗ Y) rho* (Y ⊗ Y)` and the square roots
+/// of the eigenvalues of `rho rho_tilde`.
+///
+/// # Errors
+///
+/// Returns an error when `rho` is not a structurally valid 4x4 density matrix,
+/// or when the eigendecomposition fails.
+pub fn concurrence(rho: &DMatrix<Complex64>) -> Result<f64, MeasureError> {
+    validate_density_matrix(rho)?;
+    if rho.nrows() != 4 || rho.ncols() != 4 {
+        return Err(MeasureError::InvalidMatrixShape {
+            expected_rows: 4,
+            expected_cols: 4,
+            rows: rho.nrows(),
+            cols: rho.ncols(),
+        });
+    }
+
+    let yy = pauli_y_tensor_pauli_y();
+    let rho_conj = rho.map(|value| value.conj());
+    let rho_tilde = &yy * rho_conj * yy;
+    let product = rho * rho_tilde;
+    let eigenvalues = Schur::try_new(product, DEFAULT_TOLERANCE, 0)
+        .and_then(|schur| schur.eigenvalues())
+        .ok_or(MeasureError::EigenDecompositionFailed)?;
+
+    let mut roots: Vec<f64> = eigenvalues
+        .iter()
+        .map(|lambda| {
+            if lambda.im.abs() <= 1e-8 {
+                lambda.re.max(0.0).sqrt()
+            } else {
+                lambda.norm().sqrt()
+            }
+        })
+        .collect();
+    roots.sort_by(|a, b| b.total_cmp(a));
+    let value = roots[0] - roots[1] - roots[2] - roots[3];
+    Ok(value.clamp(0.0, 1.0))
+}
+
+/// Returns the two-qubit entanglement of formation.
+///
+/// This is derived from [`concurrence`] as
+/// `h((1 + sqrt(1 - C^2)) / 2)`, where `h` is binary entropy.
+///
+/// # Errors
+///
+/// Returns an error when [`concurrence`] fails.
+pub fn entanglement_of_formation(rho: &DMatrix<Complex64>) -> Result<f64, MeasureError> {
+    let concurrence = concurrence(rho)?;
+    let argument = f64::midpoint(1.0, (1.0 - concurrence * concurrence).max(0.0).sqrt());
+    Ok(binary_entropy(argument))
+}
+
+/// Returns the entanglement negativity of a bipartite or multipartite state.
+///
+/// This computes `(||rho^T_s||_1 - 1) / 2`, where `rho^T_s` is the partial
+/// transpose with respect to `subsystem`.
+///
+/// # Errors
+///
+/// Returns an error when `rho` is not a structurally valid density matrix,
+/// when `dims` do not match its Hilbert-space dimension, or when `subsystem`
+/// is out of range.
+pub fn negativity(
+    rho: &DMatrix<Complex64>,
+    dims: &[usize],
+    subsystem: usize,
+) -> Result<f64, MeasureError> {
+    let partial_transpose = partial_transpose_subsystem(rho, dims, subsystem)?;
+    let trace_norm: f64 = SVD::new(partial_transpose, false, false)
+        .singular_values
+        .iter()
+        .sum();
+    Ok(((trace_norm - 1.0) / 2.0).max(0.0))
+}
+
+/// Returns logarithmic negativity `log2(2 * negativity + 1)`.
+///
+/// # Errors
+///
+/// Returns an error when [`negativity`] fails.
+pub fn logarithmic_negativity(
+    rho: &DMatrix<Complex64>,
+    dims: &[usize],
+    subsystem: usize,
+) -> Result<f64, MeasureError> {
+    Ok((2.0 * negativity(rho, dims, subsystem)? + 1.0).log2())
+}
+
+/// Returns the Schmidt decomposition of a pure state across a bipartition.
+///
+/// `dims[i]` is the dimension of subsystem `i`; subsystem 0 is the
+/// fastest-varying factor. `left_subsystems` selects the left side of the
+/// bipartition. The right side is the sorted complement. Returned terms are
+/// `(coefficient, left_vector, right_vector)` and omit numerically-zero
+/// coefficients.
+///
+/// # Errors
+///
+/// Returns an error when the state is not normalized, when `dims` do not match
+/// the state-vector length, or when `left_subsystems` contains an invalid or
+/// repeated subsystem.
+pub fn schmidt_decomposition(
+    state: &DVector<Complex64>,
+    dims: &[usize],
+    left_subsystems: &[usize],
+) -> Result<Vec<SchmidtTerm>, MeasureError> {
+    validate_state_vector(state)?;
+    validate_state_subsystem_dimensions(state.len(), dims)?;
+    let left = validated_sorted_subsystems(dims, left_subsystems)?;
+    let right: Vec<usize> = (0..dims.len())
+        .filter(|subsystem| left.binary_search(subsystem).is_err())
+        .collect();
+    let left_dim = subsystem_product(dims, &left)?;
+    let right_dim = subsystem_product(dims, &right)?;
+    let strides = subsystem_strides(dims)?;
+
+    let mut matrix = DMatrix::zeros(left_dim, right_dim);
+    for basis_index in 0..state.len() {
+        let left_index = project_subsystem_index(dims, &strides, &left, basis_index);
+        let right_index = project_subsystem_index(dims, &strides, &right, basis_index);
+        matrix[(left_index, right_index)] = state[basis_index];
+    }
+
+    let svd = SVD::new(matrix, true, true);
+    let left_vectors = svd.u.ok_or(MeasureError::EigenDecompositionFailed)?;
+    let right_vectors_adjoint = svd.v_t.ok_or(MeasureError::EigenDecompositionFailed)?;
+
+    Ok(svd
+        .singular_values
+        .iter()
+        .enumerate()
+        .filter(|(_, coefficient)| **coefficient > DEFAULT_TOLERANCE)
+        .map(|(idx, &coefficient)| {
+            let left_vector = left_vectors.column(idx).iter().copied().collect();
+            let right_vector = right_vectors_adjoint
+                .row(idx)
+                .iter()
+                .copied()
+                .map(|value| value.conj())
+                .collect();
+            (coefficient, left_vector, right_vector)
+        })
+        .collect())
+}
+
+/// Returns the reduced density matrix after tracing out selected subsystems.
+///
+/// `dims[i]` is the Hilbert-space dimension of subsystem `i`. Subsystem 0 is
+/// the fastest-varying factor in the computational-basis index, matching PECOS
+/// little-endian qubit ordering. The returned density matrix keeps untraced
+/// subsystems in ascending subsystem-index order.
+///
+/// # Errors
+///
+/// Returns an error when `rho` is not a structurally valid density matrix,
+/// when the product of `dims` does not match `rho`, or when
+/// `traced_subsystems` contains an out-of-range or repeated subsystem.
+pub fn partial_trace_subsystems(
+    rho: &DMatrix<Complex64>,
+    dims: &[usize],
+    traced_subsystems: &[usize],
+) -> Result<DMatrix<Complex64>, MeasureError> {
+    validate_density_matrix(rho)?;
+    validate_subsystem_dimensions(rho, dims)?;
+
+    let mut traced = traced_subsystems.to_vec();
+    traced.sort_unstable();
+    for window in traced.windows(2) {
+        if window[0] == window[1] {
+            return Err(MeasureError::DuplicateSubsystem {
+                subsystem: window[0],
+            });
+        }
+    }
+    for &subsystem in &traced {
+        if subsystem >= dims.len() {
+            return Err(MeasureError::SubsystemOutOfRange {
+                num_subsystems: dims.len(),
+                subsystem,
+            });
+        }
+    }
+
+    let kept: Vec<usize> = (0..dims.len())
+        .filter(|subsystem| traced.binary_search(subsystem).is_err())
+        .collect();
+    let out_dim = subsystem_product(dims, &kept)?;
+    let traced_dim = subsystem_product(dims, &traced)?;
+    let strides = subsystem_strides(dims)?;
+
+    let mut out = DMatrix::zeros(out_dim, out_dim);
+    for kept_row in 0..out_dim {
+        for kept_col in 0..out_dim {
+            let mut value = Complex64::new(0.0, 0.0);
+            for traced_idx in 0..traced_dim {
+                let row =
+                    embed_subsystem_index(dims, &strides, &kept, kept_row, &traced, traced_idx);
+                let col =
+                    embed_subsystem_index(dims, &strides, &kept, kept_col, &traced, traced_idx);
+                value += rho[(row, col)];
+            }
+            out[(kept_row, kept_col)] = value;
+        }
+    }
+    Ok(out)
+}
+
+/// Returns the reduced density matrix after tracing out selected qubits.
+///
+/// Qubit indexing is little-endian: qubit 0 is the least-significant bit of
+/// the computational-basis index. The returned density matrix keeps untraced
+/// qubits in ascending qubit-index order.
+///
+/// # Errors
+///
+/// Returns an error when `rho` is not a structurally valid density matrix, when
+/// its shape is not `2^num_qubits x 2^num_qubits`, or when `traced_qubits`
+/// contains an out-of-range or repeated qubit.
+pub fn partial_trace_qubits(
+    rho: &DMatrix<Complex64>,
+    num_qubits: usize,
+    traced_qubits: &[usize],
+) -> Result<DMatrix<Complex64>, MeasureError> {
+    let dims = vec![2; num_qubits];
+    partial_trace_subsystems(rho, &dims, traced_qubits)
+}
+
+/// Returns bipartite quantum mutual information.
+///
+/// `dims` is `(dim_a, dim_b)`, and `rho` must have shape
+/// `(dim_a * dim_b) x (dim_a * dim_b)`. Subsystem `A` is the fastest-varying
+/// factor in the computational-basis index, matching
+/// [`partial_trace_subsystems`].
+///
+/// # Errors
+///
+/// Returns an error when `rho` is not a structurally valid density matrix, when
+/// `dims` are invalid, or when entropy evaluation fails on a reduced state.
+pub fn mutual_information(
+    rho: &DMatrix<Complex64>,
+    dims: (usize, usize),
+) -> Result<f64, MeasureError> {
+    validate_density_matrix(rho)?;
+    let (dim_a, dim_b) = dims;
+    let Some(total_dim) = dim_a.checked_mul(dim_b) else {
+        return Err(MeasureError::InvalidSubsystemDimensions {
+            dims: vec![dim_a, dim_b],
+            matrix_dim: rho.nrows(),
+        });
+    };
+    if dim_a == 0 || dim_b == 0 || rho.nrows() != total_dim || rho.ncols() != total_dim {
+        return Err(MeasureError::InvalidSubsystemDimensions {
+            dims: vec![dim_a, dim_b],
+            matrix_dim: rho.nrows(),
+        });
+    }
+
+    let rho_a = partial_trace_subsystems(rho, &[dim_a, dim_b], &[1])?;
+    let rho_b = partial_trace_subsystems(rho, &[dim_a, dim_b], &[0])?;
+    Ok(entropy(&rho_a)? + entropy(&rho_b)? - entropy(rho)?)
+}
+
+/// Returns the Hellinger distance between classical probability distributions.
+///
+/// `H(p, q) = sqrt(1 - sum_i sqrt(p_i q_i))`.
+///
+/// # Errors
+///
+/// Returns an error when the vectors have different lengths or either vector is
+/// not a probability distribution.
+pub fn hellinger_distance(left: &[f64], right: &[f64]) -> Result<f64, MeasureError> {
+    if left.len() != right.len() {
+        return Err(MeasureError::VectorLengthMismatch {
+            left: left.len(),
+            right: right.len(),
+        });
+    }
+    validate_probability_distribution(left)?;
+    validate_probability_distribution(right)?;
+    let affinity: f64 = left
+        .iter()
+        .zip(right.iter())
+        .map(|(&left, &right)| (left * right).sqrt())
+        .sum();
+    Ok((1.0 - affinity.clamp(0.0, 1.0)).sqrt())
+}
+
+/// Returns Hellinger fidelity between classical probability distributions.
+///
+/// The value is `(1 - H(p, q)^2)^2`, where `H` is
+/// [`hellinger_distance`].
+///
+/// # Errors
+///
+/// Returns an error when [`hellinger_distance`] fails.
+pub fn hellinger_fidelity(left: &[f64], right: &[f64]) -> Result<f64, MeasureError> {
+    let distance = hellinger_distance(left, right)?;
+    Ok((1.0 - distance * distance).powi(2))
+}
+
+fn validate_state_vector(vector: &DVector<Complex64>) -> Result<(), MeasureError> {
+    let mut norm_sqr = 0.0;
+    for value in vector.iter() {
+        validate_complex(*value)?;
+        norm_sqr += value.norm_sqr();
+    }
+    if (norm_sqr - 1.0).abs() > DEFAULT_TOLERANCE {
+        return Err(MeasureError::InvalidStateNorm {
+            norm_sqr,
+            tolerance: DEFAULT_TOLERANCE,
+        });
+    }
+    Ok(())
+}
+
+fn validate_density_matrix(matrix: &DMatrix<Complex64>) -> Result<(), MeasureError> {
+    if matrix.nrows() != matrix.ncols() {
+        return Err(MeasureError::NonSquareMatrix {
+            rows: matrix.nrows(),
+            cols: matrix.ncols(),
+        });
+    }
+    for value in matrix.iter() {
+        validate_complex(*value)?;
+    }
+    for row in 0..matrix.nrows() {
+        for col in 0..matrix.ncols() {
+            let value = matrix[(row, col)];
+            let adjoint_value = matrix[(col, row)].conj();
+            if (value - adjoint_value).norm() > DEFAULT_TOLERANCE {
+                return Err(MeasureError::NonHermitianMatrix {
+                    row,
+                    col,
+                    value,
+                    adjoint_value,
+                    tolerance: DEFAULT_TOLERANCE,
+                });
+            }
+        }
+    }
+    let trace = trace(matrix);
+    if trace.im.abs() > DEFAULT_TOLERANCE || (trace.re - 1.0).abs() > DEFAULT_TOLERANCE {
+        return Err(MeasureError::InvalidDensityTrace {
+            trace,
+            tolerance: DEFAULT_TOLERANCE,
+        });
+    }
+    Ok(())
+}
+
+fn validate_complex(value: Complex64) -> Result<(), MeasureError> {
+    if value.re.is_finite() && value.im.is_finite() {
+        Ok(())
+    } else {
+        Err(MeasureError::NonFiniteValue { value })
+    }
+}
+
+fn validate_entropy_base(base: f64) -> Result<(), MeasureError> {
+    if base.is_finite() && base > 0.0 && (base - 1.0).abs() > DEFAULT_TOLERANCE {
+        Ok(())
+    } else {
+        Err(MeasureError::InvalidEntropyBase { base })
+    }
+}
+
+fn validate_probability_distribution(probabilities: &[f64]) -> Result<(), MeasureError> {
+    let mut sum = 0.0;
+    for (index, &probability) in probabilities.iter().enumerate() {
+        if !probability.is_finite() || probability < -DEFAULT_TOLERANCE {
+            return Err(MeasureError::InvalidProbability { index, probability });
+        }
+        sum += probability.max(0.0);
+    }
+    if (sum - 1.0).abs() > DEFAULT_TOLERANCE {
+        return Err(MeasureError::InvalidProbabilitySum {
+            sum,
+            tolerance: DEFAULT_TOLERANCE,
+        });
+    }
+    Ok(())
+}
+
+fn trace(matrix: &DMatrix<Complex64>) -> Complex64 {
+    let n = matrix.nrows().min(matrix.ncols());
+    (0..n).map(|idx| matrix[(idx, idx)]).sum()
+}
+
+fn pauli_y_tensor_pauli_y() -> DMatrix<Complex64> {
+    let i = Complex64::new(0.0, 1.0);
+    let minus_i = Complex64::new(0.0, -1.0);
+    let y = DMatrix::from_row_slice(
+        2,
+        2,
+        &[
+            Complex64::new(0.0, 0.0),
+            minus_i,
+            i,
+            Complex64::new(0.0, 0.0),
+        ],
+    );
+    kronecker(&y, &y)
+}
+
+fn kronecker(left: &DMatrix<Complex64>, right: &DMatrix<Complex64>) -> DMatrix<Complex64> {
+    let rows = left.nrows() * right.nrows();
+    let cols = left.ncols() * right.ncols();
+    let mut out = DMatrix::zeros(rows, cols);
+    for left_row in 0..left.nrows() {
+        for left_col in 0..left.ncols() {
+            let scale = left[(left_row, left_col)];
+            for right_row in 0..right.nrows() {
+                for right_col in 0..right.ncols() {
+                    out[(
+                        left_row * right.nrows() + right_row,
+                        left_col * right.ncols() + right_col,
+                    )] = scale * right[(right_row, right_col)];
+                }
+            }
+        }
+    }
+    out
+}
+
+fn validate_subsystem_dimensions(
+    rho: &DMatrix<Complex64>,
+    dims: &[usize],
+) -> Result<(), MeasureError> {
+    let Some(total_dim) =
+        dims.iter().try_fold(
+            1usize,
+            |acc, &dim| {
+                if dim == 0 { None } else { acc.checked_mul(dim) }
+            },
+        )
+    else {
+        return Err(MeasureError::InvalidSubsystemDimensions {
+            dims: dims.to_vec(),
+            matrix_dim: rho.nrows(),
+        });
+    };
+
+    if rho.nrows() == total_dim && rho.ncols() == total_dim {
+        Ok(())
+    } else {
+        Err(MeasureError::InvalidSubsystemDimensions {
+            dims: dims.to_vec(),
+            matrix_dim: rho.nrows(),
+        })
+    }
+}
+
+fn validate_state_subsystem_dimensions(
+    state_len: usize,
+    dims: &[usize],
+) -> Result<(), MeasureError> {
+    let Some(total_dim) =
+        dims.iter().try_fold(
+            1usize,
+            |acc, &dim| {
+                if dim == 0 { None } else { acc.checked_mul(dim) }
+            },
+        )
+    else {
+        return Err(MeasureError::InvalidSubsystemDimensions {
+            dims: dims.to_vec(),
+            matrix_dim: state_len,
+        });
+    };
+
+    if state_len == total_dim {
+        Ok(())
+    } else {
+        Err(MeasureError::InvalidSubsystemDimensions {
+            dims: dims.to_vec(),
+            matrix_dim: state_len,
+        })
+    }
+}
+
+fn validated_sorted_subsystems(
+    dims: &[usize],
+    subsystems: &[usize],
+) -> Result<Vec<usize>, MeasureError> {
+    let mut sorted = subsystems.to_vec();
+    sorted.sort_unstable();
+    for window in sorted.windows(2) {
+        if window[0] == window[1] {
+            return Err(MeasureError::DuplicateSubsystem {
+                subsystem: window[0],
+            });
+        }
+    }
+    for &subsystem in &sorted {
+        if subsystem >= dims.len() {
+            return Err(MeasureError::SubsystemOutOfRange {
+                num_subsystems: dims.len(),
+                subsystem,
+            });
+        }
+    }
+    Ok(sorted)
+}
+
+fn subsystem_product(dims: &[usize], subsystems: &[usize]) -> Result<usize, MeasureError> {
+    subsystems.iter().try_fold(1usize, |acc, &subsystem| {
+        acc.checked_mul(dims[subsystem])
+            .ok_or_else(|| MeasureError::InvalidSubsystemDimensions {
+                dims: dims.to_vec(),
+                matrix_dim: usize::MAX,
+            })
+    })
+}
+
+fn subsystem_strides(dims: &[usize]) -> Result<Vec<usize>, MeasureError> {
+    let mut strides = Vec::with_capacity(dims.len());
+    let mut stride = 1usize;
+    for &dim in dims {
+        strides.push(stride);
+        stride =
+            stride
+                .checked_mul(dim)
+                .ok_or_else(|| MeasureError::InvalidSubsystemDimensions {
+                    dims: dims.to_vec(),
+                    matrix_dim: usize::MAX,
+                })?;
+    }
+    Ok(strides)
+}
+
+fn embed_subsystem_index(
+    dims: &[usize],
+    strides: &[usize],
+    kept_subsystems: &[usize],
+    kept_index: usize,
+    traced_subsystems: &[usize],
+    traced_index: usize,
+) -> usize {
+    let mut index = 0usize;
+    let mut kept_remaining = kept_index;
+    for &subsystem in kept_subsystems {
+        let coord = kept_remaining % dims[subsystem];
+        kept_remaining /= dims[subsystem];
+        index += coord * strides[subsystem];
+    }
+    let mut traced_remaining = traced_index;
+    for &subsystem in traced_subsystems {
+        let coord = traced_remaining % dims[subsystem];
+        traced_remaining /= dims[subsystem];
+        index += coord * strides[subsystem];
+    }
+    index
+}
+
+fn project_subsystem_index(
+    dims: &[usize],
+    strides: &[usize],
+    subsystems: &[usize],
+    basis_index: usize,
+) -> usize {
+    let mut out = 0usize;
+    let mut out_stride = 1usize;
+    for &subsystem in subsystems {
+        let coord = (basis_index / strides[subsystem]) % dims[subsystem];
+        out += coord * out_stride;
+        out_stride *= dims[subsystem];
+    }
+    out
+}
+
+fn partial_transpose_subsystem(
+    rho: &DMatrix<Complex64>,
+    dims: &[usize],
+    subsystem: usize,
+) -> Result<DMatrix<Complex64>, MeasureError> {
+    validate_density_matrix(rho)?;
+    validate_subsystem_dimensions(rho, dims)?;
+    if subsystem >= dims.len() {
+        return Err(MeasureError::SubsystemOutOfRange {
+            num_subsystems: dims.len(),
+            subsystem,
+        });
+    }
+
+    let strides = subsystem_strides(dims)?;
+    let mut out = DMatrix::zeros(rho.nrows(), rho.ncols());
+    for row in 0..rho.nrows() {
+        for col in 0..rho.ncols() {
+            let row_coord = (row / strides[subsystem]) % dims[subsystem];
+            let col_coord = (col / strides[subsystem]) % dims[subsystem];
+            let transposed_row =
+                row - row_coord * strides[subsystem] + col_coord * strides[subsystem];
+            let transposed_col =
+                col - col_coord * strides[subsystem] + row_coord * strides[subsystem];
+            out[(transposed_row, transposed_col)] = rho[(row, col)];
+        }
+    }
+    Ok(out)
+}
+
+fn binary_entropy(probability: f64) -> f64 {
+    let p = probability.clamp(0.0, 1.0);
+    if p <= DEFAULT_TOLERANCE || (1.0 - p) <= DEFAULT_TOLERANCE {
+        0.0
+    } else {
+        -p * p.log2() - (1.0 - p) * (1.0 - p).log2()
+    }
+}
+
+fn hilbert_dim(num_qubits: usize) -> Result<usize, MeasureError> {
+    2usize
+        .checked_pow(
+            num_qubits
+                .try_into()
+                .map_err(|_| MeasureError::DimensionOverflow { num_qubits })?,
+        )
+        .ok_or(MeasureError::DimensionOverflow { num_qubits })
+}
+
+#[cfg(test)]
+mod tests {
+    use super::*;
+    use crate::channel::Ptm;
+    use pecos_core::{Op, op};
+
+    fn assert_close(a: f64, b: f64) {
+        assert!((a - b).abs() < 1e-10, "{a} != {b}");
+    }
+
+    fn ket(values: &[Complex64]) -> DVector<Complex64> {
+        DVector::from_column_slice(values)
+    }
+
+    fn pure_density(psi: &DVector<Complex64>) -> DMatrix<Complex64> {
+        psi * psi.adjoint()
+    }
+
+    fn werner_state(p: f64) -> DMatrix<Complex64> {
+        let bell = ket(&[
+            Complex64::new(1.0 / 2.0_f64.sqrt(), 0.0),
+            Complex64::new(0.0, 0.0),
+            Complex64::new(0.0, 0.0),
+            Complex64::new(1.0 / 2.0_f64.sqrt(), 0.0),
+        ]);
+        pure_density(&bell) * Complex64::new(p, 0.0)
+            + DMatrix::identity(4, 4) * Complex64::new((1.0 - p) / 4.0, 0.0)
+    }
+
+    #[test]
+    fn pure_state_fidelity_matches_known_values() {
+        let zero = ket(&[Complex64::new(1.0, 0.0), Complex64::new(0.0, 0.0)]);
+        let one = ket(&[Complex64::new(0.0, 0.0), Complex64::new(1.0, 0.0)]);
+        let plus = ket(&[
+            Complex64::new(1.0 / 2.0_f64.sqrt(), 0.0),
+            Complex64::new(1.0 / 2.0_f64.sqrt(), 0.0),
+        ]);
+
+        assert_close(state_fidelity(&zero, &zero).unwrap(), 1.0);
+        assert_close(state_fidelity(&zero, &one).unwrap(), 0.0);
+        assert_close(state_fidelity(&zero, &plus).unwrap(), 0.5);
+    }
+
+    #[test]
+    fn state_fidelity_rejects_unnormalized_vectors() {
+        let zero = ket(&[Complex64::new(1.0, 0.0), Complex64::new(0.0, 0.0)]);
+        let bad = ket(&[Complex64::new(1.0, 0.0), Complex64::new(1.0, 0.0)]);
+
+        assert!(matches!(
+            state_fidelity(&zero, &bad).unwrap_err(),
+            MeasureError::InvalidStateNorm { .. }
+        ));
+    }
+
+    #[test]
+    fn density_matrix_purity_and_entropy_match_known_states() {
+        let zero = ket(&[Complex64::new(1.0, 0.0), Complex64::new(0.0, 0.0)]);
+        let pure = pure_density(&zero);
+        let half = Complex64::new(0.5, 0.0);
+        let mixed = DMatrix::from_diagonal_element(2, 2, half);
+
+        assert_close(purity(&pure).unwrap(), 1.0);
+        assert_close(entropy(&pure).unwrap(), 0.0);
+        assert_close(purity(&mixed).unwrap(), 0.5);
+        assert_close(entropy(&mixed).unwrap(), 1.0);
+        assert_close(
+            state_fidelity_with_density_matrix(&mixed, &zero).unwrap(),
+            0.5,
+        );
+    }
+
+    #[test]
+    fn density_matrix_measures_reject_invalid_matrices() {
+        let non_square = DMatrix::from_element(2, 3, Complex64::new(0.0, 0.0));
+        assert!(matches!(
+            purity(&non_square).unwrap_err(),
+            MeasureError::NonSquareMatrix { .. }
+        ));
+
+        let mut non_hermitian = DMatrix::zeros(2, 2);
+        non_hermitian[(0, 0)] = Complex64::new(1.0, 0.0);
+        non_hermitian[(0, 1)] = Complex64::new(0.1, 0.0);
+        assert!(matches!(
+            purity(&non_hermitian).unwrap_err(),
+            MeasureError::NonHermitianMatrix { .. }
+        ));
+    }
+
+    #[test]
+    fn two_qubit_entanglement_measures_match_known_states() {
+        let bell = ket(&[
+            Complex64::new(1.0 / 2.0_f64.sqrt(), 0.0),
+            Complex64::new(0.0, 0.0),
+            Complex64::new(0.0, 0.0),
+            Complex64::new(1.0 / 2.0_f64.sqrt(), 0.0),
+        ]);
+        let bell_rho = pure_density(&bell);
+        assert_close(concurrence(&bell_rho).unwrap(), 1.0);
+        assert_close(entanglement_of_formation(&bell_rho).unwrap(), 1.0);
+        assert_close(mutual_information(&bell_rho, (2, 2)).unwrap(), 2.0);
+
+        let zero_zero = ket(&[
+            Complex64::new(1.0, 0.0),
+            Complex64::new(0.0, 0.0),
+            Complex64::new(0.0, 0.0),
+            Complex64::new(0.0, 0.0),
+        ]);
+        let product = pure_density(&zero_zero);
+        assert_close(concurrence(&product).unwrap(), 0.0);
+        assert_close(entanglement_of_formation(&product).unwrap(), 0.0);
+        assert_close(mutual_information(&product, (2, 2)).unwrap(), 0.0);
+    }
+
+    #[test]
+    fn concurrence_matches_werner_state_threshold_formula() {
+        assert_close(concurrence(&werner_state(0.5)).unwrap(), 0.25);
+        assert_close(concurrence(&werner_state(0.3)).unwrap(), 0.0);
+    }
+
+    #[test]
+    fn entanglement_of_formation_matches_intermediate_werner_state() {
+        let rho = werner_state(0.5);
+        assert_close(concurrence(&rho).unwrap(), 0.25);
+        assert_close(
+            entanglement_of_formation(&rho).unwrap(),
+            0.117_618_873_770_917_81,
+        );
+    }
+
+    #[test]
+    fn negativity_matches_bell_and_product_states() {
+        let bell = ket(&[
+            Complex64::new(1.0 / 2.0_f64.sqrt(), 0.0),
+            Complex64::new(0.0, 0.0),
+            Complex64::new(0.0, 0.0),
+            Complex64::new(1.0 / 2.0_f64.sqrt(), 0.0),
+        ]);
+        let bell_rho = pure_density(&bell);
+        assert_close(negativity(&bell_rho, &[2, 2], 1).unwrap(), 0.5);
+        assert_close(logarithmic_negativity(&bell_rho, &[2, 2], 1).unwrap(), 1.0);
+
+        let product = pure_density(&ket(&[
+            Complex64::new(1.0, 0.0),
+            Complex64::new(0.0, 0.0),
+            Complex64::new(0.0, 0.0),
+            Complex64::new(0.0, 0.0),
+        ]));
+        assert_close(negativity(&product, &[2, 2], 1).unwrap(), 0.0);
+        assert_close(logarithmic_negativity(&product, &[2, 2], 1).unwrap(), 0.0);
+    }
+
+    #[test]
+    fn schmidt_decomposition_matches_bell_and_product_states() {
+        let bell = ket(&[
+            Complex64::new(1.0 / 2.0_f64.sqrt(), 0.0),
+            Complex64::new(0.0, 0.0),
+            Complex64::new(0.0, 0.0),
+            Complex64::new(1.0 / 2.0_f64.sqrt(), 0.0),
+        ]);
+        let bell_terms = schmidt_decomposition(&bell, &[2, 2], &[0]).unwrap();
+        assert_eq!(bell_terms.len(), 2);
+        assert_close(bell_terms[0].0, 1.0 / 2.0_f64.sqrt());
+        assert_close(bell_terms[1].0, 1.0 / 2.0_f64.sqrt());
+
+        let product = ket(&[
+            Complex64::new(1.0, 0.0),
+            Complex64::new(0.0, 0.0),
+            Complex64::new(0.0, 0.0),
+            Complex64::new(0.0, 0.0),
+        ]);
+        let product_terms = schmidt_decomposition(&product, &[2, 2], &[0]).unwrap();
+        assert_eq!(product_terms.len(), 1);
+        assert_close(product_terms[0].0, 1.0);
+    }
+
+    #[test]
+    fn schmidt_decomposition_supports_unequal_bipartition() {
+        let mut ghz = DVector::zeros(8);
+        ghz[0] = Complex64::new(1.0 / 2.0_f64.sqrt(), 0.0);
+        ghz[7] = Complex64::new(1.0 / 2.0_f64.sqrt(), 0.0);
+
+        let terms = schmidt_decomposition(&ghz, &[2, 4], &[0]).unwrap();
+        assert_eq!(terms.len(), 2);
+        assert_close(terms[0].0, 1.0 / 2.0_f64.sqrt());
+        assert_close(terms[1].0, 1.0 / 2.0_f64.sqrt());
+        assert_eq!(terms[0].1.len(), 2);
+        assert_eq!(terms[0].2.len(), 4);
+    }
+
+    #[test]
+    fn mutual_information_accepts_non_qubit_subsystem_dims() {
+        let mut rho = DMatrix::zeros(6, 6);
+        rho[(0, 0)] = Complex64::new(0.5, 0.0);
+        rho[(5, 5)] = Complex64::new(0.5, 0.0);
+
+        assert_close(mutual_information(&rho, (2, 3)).unwrap(), 1.0);
+    }
+
+    #[test]
+    fn shannon_entropy_is_public_distribution_entropy() {
+        assert_close(shannon_entropy(&[0.5, 0.5], 2.0).unwrap(), 1.0);
+        assert_close(shannon_entropy(&[1.0, 0.0], 2.0).unwrap(), 0.0);
+        assert!(matches!(
+            shannon_entropy(&[0.25, 0.25], 2.0).unwrap_err(),
+            MeasureError::InvalidProbabilitySum { .. }
+        ));
+    }
+
+    #[test]
+    fn hellinger_distance_and_fidelity_match_classical_cases() {
+        assert_close(
+            hellinger_distance(&[0.25, 0.75], &[0.25, 0.75]).unwrap(),
+            0.0,
+        );
+        assert_close(
+            hellinger_fidelity(&[0.25, 0.75], &[0.25, 0.75]).unwrap(),
+            1.0,
+        );
+
+        assert_close(hellinger_distance(&[1.0, 0.0], &[0.0, 1.0]).unwrap(), 1.0);
+        assert_close(hellinger_fidelity(&[1.0, 0.0], &[0.0, 1.0]).unwrap(), 0.0);
+    }
+
+    #[test]
+    fn partial_trace_supports_method_and_qubit_forms() {
+        let bell = ket(&[
+            Complex64::new(1.0 / 2.0_f64.sqrt(), 0.0),
+            Complex64::new(0.0, 0.0),
+            Complex64::new(0.0, 0.0),
+            Complex64::new(1.0 / 2.0_f64.sqrt(), 0.0),
+        ]);
+        let bell_rho = pure_density(&bell);
+
+        let reduced_from_method = bell_rho.partial_trace(&[2, 2], &[1]).unwrap();
+        let reduced_from_qubits = partial_trace_qubits(&bell_rho, 2, &[1]).unwrap();
+        let expected = DMatrix::from_diagonal_element(2, 2, Complex64::new(0.5, 0.0));
+
+        assert_close((&reduced_from_method - &expected).norm(), 0.0);
+        assert_close((&reduced_from_qubits - expected).norm(), 0.0);
+    }
+
+    #[test]
+    fn partial_trace_subsystems_accepts_arbitrary_tensor_factors() {
+        let mut state = DVector::zeros(12);
+        state[2] = Complex64::new(1.0 / 2.0_f64.sqrt(), 0.0);
+        state[9] = Complex64::new(1.0 / 2.0_f64.sqrt(), 0.0);
+        let rho = pure_density(&state);
+
+        let reduced = partial_trace_subsystems(&rho, &[2, 3, 2], &[1]).unwrap();
+        let mut expected = DMatrix::zeros(4, 4);
+        expected[(0, 0)] = Complex64::new(0.5, 0.0);
+        expected[(0, 3)] = Complex64::new(0.5, 0.0);
+        expected[(3, 0)] = Complex64::new(0.5, 0.0);
+        expected[(3, 3)] = Complex64::new(0.5, 0.0);
+
+        assert_close((reduced - expected).norm(), 0.0);
+    }
+
+    #[test]
+    fn partial_trace_subsystems_can_trace_noncontiguous_factors() {
+        let mut state = DVector::zeros(12);
+        state[0] = Complex64::new(1.0 / 2.0_f64.sqrt(), 0.0);
+        state[11] = Complex64::new(1.0 / 2.0_f64.sqrt(), 0.0);
+        let rho = pure_density(&state);
+
+        let reduced = partial_trace_subsystems(&rho, &[2, 3, 2], &[0, 2]).unwrap();
+        let mut expected = DMatrix::zeros(3, 3);
+        expected[(0, 0)] = Complex64::new(0.5, 0.0);
+        expected[(2, 2)] = Complex64::new(0.5, 0.0);
+
+        assert_close((reduced - expected).norm(), 0.0);
+    }
+
+    #[test]
+    fn three_qubit_ghz_reductions_have_expected_information() {
+        let mut ghz = DVector::zeros(8);
+        ghz[0] = Complex64::new(1.0 / 2.0_f64.sqrt(), 0.0);
+        ghz[7] = Complex64::new(1.0 / 2.0_f64.sqrt(), 0.0);
+        let rho = pure_density(&ghz);
+
+        let two_qubit_reduction = partial_trace_qubits(&rho, 3, &[2]).unwrap();
+        let mut expected_two_qubit = DMatrix::zeros(4, 4);
+        expected_two_qubit[(0, 0)] = Complex64::new(0.5, 0.0);
+        expected_two_qubit[(3, 3)] = Complex64::new(0.5, 0.0);
+        assert_close((&two_qubit_reduction - &expected_two_qubit).norm(), 0.0);
+        assert_close(entropy(&two_qubit_reduction).unwrap(), 1.0);
+        assert_close(
+            mutual_information(&two_qubit_reduction, (2, 2)).unwrap(),
+            1.0,
+        );
+
+        let one_qubit_reduction = partial_trace_qubits(&rho, 3, &[1, 2]).unwrap();
+        let expected_one_qubit = DMatrix::from_diagonal_element(2, 2, Complex64::new(0.5, 0.0));
+        assert_close((&one_qubit_reduction - expected_one_qubit).norm(), 0.0);
+        assert_close(entropy(&one_qubit_reduction).unwrap(), 1.0);
+    }
+
+    #[test]
+    fn partial_trace_rejects_repeated_or_out_of_range_subsystems() {
+        let mixed = DMatrix::from_diagonal_element(4, 4, Complex64::new(0.25, 0.0));
+        assert!(matches!(
+            partial_trace_subsystems(&mixed, &[2, 2], &[0, 0]).unwrap_err(),
+            MeasureError::DuplicateSubsystem { subsystem: 0 }
+        ));
+        assert!(matches!(
+            partial_trace_subsystems(&mixed, &[2, 2], &[2]).unwrap_err(),
+            MeasureError::SubsystemOutOfRange {
+                num_subsystems: 2,
+                subsystem: 2
+            }
+        ));
+    }
+
+    #[test]
+    fn entanglement_measures_reject_invalid_shapes() {
+        let mixed = DMatrix::from_diagonal_element(2, 2, Complex64::new(0.5, 0.0));
+        assert!(matches!(
+            concurrence(&mixed).unwrap_err(),
+            MeasureError::InvalidMatrixShape { .. }
+        ));
+        assert!(matches!(
+            mutual_information(&mixed, (2, 2)).unwrap_err(),
+            MeasureError::InvalidSubsystemDimensions { .. }
+        ));
+    }
+
+    #[test]
+    fn process_and_average_gate_fidelity_match_depolarizing_channel() {
+        let identity = Ptm::identity(1).unwrap();
+        let Op::Channel(expr) = op::Depolarizing(0.3, 0) else {
+            panic!("expected channel");
+        };
+        let depolarizing = Ptm::from_channel_expr(&expr).unwrap();
+
+        assert_close(process_fidelity(&identity, &identity).unwrap(), 1.0);
+        assert_close(process_fidelity(&depolarizing, &identity).unwrap(), 0.7);
+        assert_close(
+            average_gate_fidelity(&depolarizing, &identity).unwrap(),
+            0.8,
+        );
+        assert_close(gate_error(&depolarizing, &identity).unwrap(), 0.2);
+    }
+
+    #[test]
+    fn process_fidelity_reports_qubit_count_mismatch() {
+        let one_qubit = Ptm::identity(1).unwrap();
+        let two_qubit = Ptm::identity(2).unwrap();
+
+        assert_eq!(
+            process_fidelity(&one_qubit, &two_qubit).unwrap_err(),
+            MeasureError::QubitCountMismatch {
+                expected: 1,
+                actual: 2
+            }
+        );
+        assert_eq!(
+            average_gate_fidelity(&one_qubit, &two_qubit).unwrap_err(),
+            MeasureError::QubitCountMismatch {
+                expected: 1,
+                actual: 2
+            }
+        );
+        assert_eq!(
+            gate_error(&one_qubit, &two_qubit).unwrap_err(),
+            MeasureError::QubitCountMismatch {
+                expected: 1,
+                actual: 2
+            }
+        );
+    }
+}
diff --git a/crates/pecos-quantum/src/operator_matrix.rs b/crates/pecos-quantum/src/operator_matrix.rs
deleted file mode 100644
index 033e20019..000000000
--- a/crates/pecos-quantum/src/operator_matrix.rs
+++ /dev/null
@@ -1,1253 +0,0 @@
-// Copyright 2025 The PECOS Developers
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-//     https://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
-
-//! Matrix representations and operations for quantum operators.
-//!
-//! This module provides functions to convert operators to dense matrices
-//! and perform matrix-level operations like exponential and logarithm.
-//!
-//! # Extension Trait
-//!
-//! The [`ToMatrix`] trait provides a method-style API for converting operators:
-//!
-//! ```
-//! use pecos_quantum::operator_matrix::ToMatrix;
-//! use pecos_core::operator::X;
-//!
-//! let x = X(0);
-//! let matrix = x.to_matrix();  // Method style
-//! ```
-
-use nalgebra::DMatrix;
-use num_complex::Complex64;
-use pecos_core::gate_type::GateType;
-use pecos_core::operator::{Operator, RotationType};
-use pecos_core::{Pauli, PauliString, Phase};
-
-/// Extension trait for converting quantum operators to matrix representations.
-///
-/// This trait is implemented for [`Operator`] and [`PauliString`], providing
-/// a method-style API for matrix conversion.
-///
-/// # Example
-///
-/// ```
-/// use pecos_quantum::operator_matrix::ToMatrix;
-/// use pecos_core::operator::{X, H, CX, Is};
-///
-/// // Single qubit gate
-/// let x_matrix = X(0).to_matrix();
-/// assert_eq!(x_matrix.nrows(), 2);
-///
-/// // Two qubit gate
-/// let cnot_matrix = CX(0, 1).to_matrix();
-/// assert_eq!(cnot_matrix.nrows(), 4);
-///
-/// // For larger matrices, tensor with identities using Is()
-/// let x_extended = X(0) & Is(1..3);  // X on qubit 0 in 3-qubit space
-/// let mat = x_extended.to_matrix();
-/// assert_eq!(mat.nrows(), 8);
-/// ```
-pub trait ToMatrix {
-    /// Converts to a dense matrix representation.
-    ///
-    /// The matrix size is 2^n where n is determined by the maximum qubit index + 1.
-    fn to_matrix(&self) -> DMatrix<Complex64>;
-}
-
-impl ToMatrix for Operator {
-    fn to_matrix(&self) -> DMatrix<Complex64> {
-        to_matrix(self)
-    }
-}
-
-impl ToMatrix for PauliString {
-    fn to_matrix(&self) -> DMatrix<Complex64> {
-        let num_qubits = self.qubits().into_iter().max().map_or(1, |q| q + 1);
-        pauli_string_to_matrix_impl(self, num_qubits)
-    }
-}
-
-/// Converts an `Operator` to its dense matrix representation.
-///
-/// The matrix size is 2^n where n is the number of qubits (determined by
-/// the maximum qubit index + 1).
-///
-/// # Example
-///
-/// ```
-/// use pecos_quantum::operator_matrix::to_matrix;
-/// use pecos_core::operator::X;
-/// use num_complex::Complex64;
-///
-/// let x = X(0);
-/// let matrix = to_matrix(&x);
-///
-/// // X gate matrix: [[0, 1], [1, 0]]
-/// assert_eq!(matrix.nrows(), 2);
-/// assert!((matrix[(0, 1)] - Complex64::new(1.0, 0.0)).norm() < 1e-10);
-/// ```
-#[must_use]
-pub fn to_matrix(op: &Operator) -> DMatrix<Complex64> {
-    let num_qubits = op.qubits().into_iter().max().map_or(1, |q| q + 1);
-    to_matrix_with_size(op, num_qubits)
-}
-
-/// Converts an `Operator` to its dense matrix representation with a specified size.
-///
-/// # Arguments
-/// * `op` - The operator to convert
-/// * `num_qubits` - The number of qubits (matrix will be `2^num_qubits` x `2^num_qubits`)
-#[must_use]
-pub fn to_matrix_with_size(op: &Operator, num_qubits: usize) -> DMatrix<Complex64> {
-    let dim = 1 << num_qubits; // 2^num_qubits
-
-    match op {
-        Operator::Pauli(ps) => pauli_string_to_matrix_impl(ps, num_qubits),
-
-        Operator::Rotation {
-            rotation_type,
-            angle,
-            qubits,
-        } => rotation_to_matrix(*rotation_type, angle.to_radians(), qubits, num_qubits),
-
-        Operator::Gate { gate_type, qubits } => gate_to_matrix(*gate_type, qubits, num_qubits),
-
-        Operator::Tensor(parts) => {
-            // Start with identity, combine each part
-            let mut result = DMatrix::identity(dim, dim);
-            for part in parts {
-                let part_matrix = to_matrix_with_size(part, num_qubits);
-                result = combine_disjoint_operators(&result, &part_matrix);
-            }
-            result
-        }
-
-        Operator::Compose(parts) => {
-            // Matrix multiplication in reverse order (last part applied first)
-            let mut result = DMatrix::identity(dim, dim);
-            for part in parts {
-                let part_matrix = to_matrix_with_size(part, num_qubits);
-                result = part_matrix * result;
-            }
-            result
-        }
-
-        Operator::Adjoint(inner) => {
-            let inner_matrix = to_matrix_with_size(inner, num_qubits);
-            inner_matrix.adjoint()
-        }
-
-        Operator::Phase { phase, inner } => {
-            let inner_matrix = to_matrix_with_size(inner, num_qubits);
-            let phase_factor = Complex64::new(0.0, phase.to_radians()).exp();
-            inner_matrix * phase_factor
-        }
-    }
-}
-
-/// Computes the matrix exponential of an operator: exp(i * op).
-///
-/// This is useful for generating unitaries from Hermitian generators.
-///
-/// # Example
-///
-/// ```
-/// use pecos_quantum::operator_matrix::operator_exp;
-/// use pecos_core::operator::Z;
-/// use num_complex::Complex64;
-/// use std::f64::consts::PI;
-///
-/// // exp(i * pi * Z) = -I
-/// let z = Z(0);
-/// let result = operator_exp(&z, PI);
-/// // Result should be approximately -I
-/// ```
-#[must_use]
-pub fn operator_exp(op: &Operator, theta: f64) -> DMatrix<Complex64> {
-    let matrix = to_matrix(op);
-    let scaled = matrix * Complex64::new(0.0, theta);
-    pecos_num::matrix_exp(&scaled)
-}
-
-/// Computes the matrix logarithm of an operator.
-///
-/// Returns `Some(generator)` where `exp(i * generator) = op`, or `None` if
-/// the computation fails (e.g., for singular matrices).
-///
-/// # Example
-///
-/// ```
-/// use pecos_quantum::operator_matrix::{operator_log, to_matrix};
-/// use pecos_core::operator::X;
-///
-/// let x = X(0);
-/// if let Some(log_x) = operator_log(&x) {
-///     // log_x is the generator such that exp(i * log_x) = X
-/// }
-/// ```
-#[must_use]
-pub fn operator_log(op: &Operator) -> Option<DMatrix<Complex64>> {
-    let matrix = to_matrix(op);
-    let log_matrix = pecos_num::matrix_log(&matrix)?;
-    // Divide by i to get the Hermitian generator
-    Some(log_matrix / Complex64::new(0.0, 1.0))
-}
-
-/// Checks if two operators are equivalent up to a global phase.
-///
-/// Returns `true` if A = e^{i*phi} * B for some real phi.
-///
-/// # Example
-///
-/// ```
-/// use pecos_quantum::operator_matrix::operators_equiv;
-/// use pecos_core::operator::{X, Y, Z};
-///
-/// let x = X(0);
-/// let x2 = X(0);
-/// assert!(operators_equiv(&x, &x2));
-///
-/// let y = Y(0);
-/// assert!(!operators_equiv(&x, &y));
-/// ```
-#[must_use]
-pub fn operators_equiv(a: &Operator, b: &Operator) -> bool {
-    operators_equiv_with_tolerance(a, b, 1e-10)
-}
-
-/// Checks if two operators are equivalent up to a global phase, with custom tolerance.
-#[must_use]
-pub fn operators_equiv_with_tolerance(a: &Operator, b: &Operator, tol: f64) -> bool {
-    let num_qubits_a = a.qubits().into_iter().max().map_or(1, |q| q + 1);
-    let num_qubits_b = b.qubits().into_iter().max().map_or(1, |q| q + 1);
-    let num_qubits = num_qubits_a.max(num_qubits_b);
-
-    let mat_a = to_matrix_with_size(a, num_qubits);
-    let mat_b = to_matrix_with_size(b, num_qubits);
-
-    matrices_equiv_up_to_phase(&mat_a, &mat_b, tol)
-}
-
-/// Checks if two matrices are equal up to a global phase factor.
-fn matrices_equiv_up_to_phase(a: &DMatrix<Complex64>, b: &DMatrix<Complex64>, tol: f64) -> bool {
-    if a.nrows() != b.nrows() || a.ncols() != b.ncols() {
-        return false;
-    }
-
-    // Find the first non-zero element to determine the phase
-    let mut phase: Option<Complex64> = None;
-
-    for i in 0..a.nrows() {
-        for j in 0..a.ncols() {
-            let a_val = a[(i, j)];
-            let b_val = b[(i, j)];
-
-            // Skip near-zero elements
-            if a_val.norm() < tol && b_val.norm() < tol {
-                continue;
-            }
-
-            // If one is zero but not the other, not equivalent
-            if a_val.norm() < tol || b_val.norm() < tol {
-                return false;
-            }
-
-            // Compute the ratio a/b
-            let ratio = a_val / b_val;
-
-            match phase {
-                None => {
-                    // First non-zero element sets the phase
-                    phase = Some(ratio);
-                }
-                Some(p) => {
-                    // Check if this ratio matches the established phase
-                    if (ratio - p).norm() > tol {
-                        return false;
-                    }
-                }
-            }
-        }
-    }
-
-    // Also verify the phase has unit magnitude (global phase factor)
-    if let Some(p) = phase {
-        (p.norm() - 1.0).abs() < tol
-    } else {
-        // Both matrices are zero
-        true
-    }
-}
-
-// --- Helper functions for matrix construction ---
-
-/// Converts a [`PauliString`] to a dense matrix (implementation).
-fn pauli_string_to_matrix_impl(ps: &PauliString, num_qubits: usize) -> DMatrix<Complex64> {
-    let dim = 1 << num_qubits;
-    let mut result = DMatrix::identity(dim, dim);
-
-    // Get the phase
-    let phase = ps.phase().to_complex();
-
-    // Apply each single-qubit Pauli
-    for (pauli, qubit) in ps.iter_pairs() {
-        let q = usize::from(qubit);
-        let pauli_matrix = single_pauli_matrix(pauli);
-        let full_matrix = embed_single_qubit_gate(&pauli_matrix, q, num_qubits);
-        result = full_matrix * result;
-    }
-
-    result * phase
-}
-
-/// Returns the 2x2 matrix for a single Pauli operator.
-fn single_pauli_matrix(pauli: Pauli) -> DMatrix<Complex64> {
-    let zero = Complex64::new(0.0, 0.0);
-    let one = Complex64::new(1.0, 0.0);
-    let i = Complex64::new(0.0, 1.0);
-    let neg_i = Complex64::new(0.0, -1.0);
-    let neg_one = Complex64::new(-1.0, 0.0);
-
-    match pauli {
-        Pauli::I => DMatrix::from_row_slice(2, 2, &[one, zero, zero, one]),
-        Pauli::X => DMatrix::from_row_slice(2, 2, &[zero, one, one, zero]),
-        Pauli::Y => DMatrix::from_row_slice(2, 2, &[zero, neg_i, i, zero]),
-        Pauli::Z => DMatrix::from_row_slice(2, 2, &[one, zero, zero, neg_one]),
-    }
-}
-
-/// Embeds a single-qubit gate into a larger Hilbert space.
-fn embed_single_qubit_gate(
-    gate: &DMatrix<Complex64>,
-    qubit: usize,
-    num_qubits: usize,
-) -> DMatrix<Complex64> {
-    let dim = 1 << num_qubits;
-    let mut result = DMatrix::from_element(dim, dim, Complex64::new(0.0, 0.0));
-
-    for i in 0..dim {
-        for j in 0..dim {
-            // Check if all qubits except `qubit` match
-            let mask = !(1 << qubit);
-            if (i & mask) == (j & mask) {
-                let i_bit = (i >> qubit) & 1;
-                let j_bit = (j >> qubit) & 1;
-                result[(i, j)] = gate[(i_bit, j_bit)];
-            }
-        }
-    }
-
-    result
-}
-
-/// Converts a rotation to a matrix.
-fn rotation_to_matrix(
-    rotation_type: RotationType,
-    angle: f64,
-    qubits: &[usize],
-    num_qubits: usize,
-) -> DMatrix<Complex64> {
-    let half_angle = angle / 2.0;
-    let cos_half = Complex64::new(half_angle.cos(), 0.0);
-    let sin_half = Complex64::new(half_angle.sin(), 0.0);
-    let i = Complex64::new(0.0, 1.0);
-    let neg_i = Complex64::new(0.0, -1.0);
-
-    match rotation_type {
-        RotationType::RX => {
-            // RX(θ) = cos(θ/2)I - i*sin(θ/2)X
-            let gate = DMatrix::from_row_slice(
-                2,
-                2,
-                &[cos_half, neg_i * sin_half, neg_i * sin_half, cos_half],
-            );
-            embed_single_qubit_gate(&gate, qubits[0], num_qubits)
-        }
-        RotationType::RY => {
-            // RY(θ) = cos(θ/2)I - i*sin(θ/2)Y
-            let gate = DMatrix::from_row_slice(2, 2, &[cos_half, -sin_half, sin_half, cos_half]);
-            embed_single_qubit_gate(&gate, qubits[0], num_qubits)
-        }
-        RotationType::RZ => {
-            // RZ(θ) = cos(θ/2)I - i*sin(θ/2)Z = diag(e^{-iθ/2}, e^{iθ/2})
-            let exp_neg = (neg_i * Complex64::new(half_angle, 0.0)).exp();
-            let exp_pos = (i * Complex64::new(half_angle, 0.0)).exp();
-            let zero = Complex64::new(0.0, 0.0);
-            let gate = DMatrix::from_row_slice(2, 2, &[exp_neg, zero, zero, exp_pos]);
-            embed_single_qubit_gate(&gate, qubits[0], num_qubits)
-        }
-        RotationType::RXX | RotationType::RYY | RotationType::RZZ => {
-            // For two-qubit rotations, use matrix exponential
-            let dim = 1 << num_qubits;
-            let generator = match rotation_type {
-                RotationType::RXX => {
-                    two_qubit_pauli_matrix(Pauli::X, Pauli::X, qubits[0], qubits[1], num_qubits)
-                }
-                RotationType::RYY => {
-                    two_qubit_pauli_matrix(Pauli::Y, Pauli::Y, qubits[0], qubits[1], num_qubits)
-                }
-                RotationType::RZZ => {
-                    two_qubit_pauli_matrix(Pauli::Z, Pauli::Z, qubits[0], qubits[1], num_qubits)
-                }
-                _ => DMatrix::identity(dim, dim),
-            };
-            let scaled = generator * Complex64::new(0.0, -half_angle);
-            pecos_num::matrix_exp(&scaled)
-        }
-    }
-}
-
-/// Constructs a two-qubit Pauli tensor product matrix.
-fn two_qubit_pauli_matrix(
-    p1: Pauli,
-    p2: Pauli,
-    q1: usize,
-    q2: usize,
-    num_qubits: usize,
-) -> DMatrix<Complex64> {
-    let m1 = single_pauli_matrix(p1);
-    let m2 = single_pauli_matrix(p2);
-    let e1 = embed_single_qubit_gate(&m1, q1, num_qubits);
-    let e2 = embed_single_qubit_gate(&m2, q2, num_qubits);
-    e1 * e2
-}
-
-/// Converts a gate type to a matrix.
-fn gate_to_matrix(gate_type: GateType, qubits: &[usize], num_qubits: usize) -> DMatrix<Complex64> {
-    let zero = Complex64::new(0.0, 0.0);
-    let one = Complex64::new(1.0, 0.0);
-    let i = Complex64::new(0.0, 1.0);
-    let neg_i = Complex64::new(0.0, -1.0);
-    let neg_one = Complex64::new(-1.0, 0.0);
-    let sqrt2_inv = Complex64::new(1.0 / 2.0_f64.sqrt(), 0.0);
-
-    match gate_type {
-        GateType::I => {
-            let gate = DMatrix::from_row_slice(2, 2, &[one, zero, zero, one]);
-            embed_single_qubit_gate(&gate, qubits[0], num_qubits)
-        }
-        GateType::X => {
-            let gate = DMatrix::from_row_slice(2, 2, &[zero, one, one, zero]);
-            embed_single_qubit_gate(&gate, qubits[0], num_qubits)
-        }
-        GateType::Y => {
-            let gate = DMatrix::from_row_slice(2, 2, &[zero, neg_i, i, zero]);
-            embed_single_qubit_gate(&gate, qubits[0], num_qubits)
-        }
-        GateType::Z => {
-            let gate = DMatrix::from_row_slice(2, 2, &[one, zero, zero, neg_one]);
-            embed_single_qubit_gate(&gate, qubits[0], num_qubits)
-        }
-        GateType::H => {
-            let gate =
-                DMatrix::from_row_slice(2, 2, &[sqrt2_inv, sqrt2_inv, sqrt2_inv, -sqrt2_inv]);
-            embed_single_qubit_gate(&gate, qubits[0], num_qubits)
-        }
-        GateType::SX => {
-            // SX = (1+i)/2 * [[1, -i], [-i, 1]]
-            let factor = Complex64::new(0.5, 0.5);
-            let gate = DMatrix::from_row_slice(
-                2,
-                2,
-                &[factor * one, factor * neg_i, factor * neg_i, factor * one],
-            );
-            embed_single_qubit_gate(&gate, qubits[0], num_qubits)
-        }
-        GateType::SXdg => {
-            let factor = Complex64::new(0.5, -0.5);
-            let gate = DMatrix::from_row_slice(
-                2,
-                2,
-                &[factor * one, factor * i, factor * i, factor * one],
-            );
-            embed_single_qubit_gate(&gate, qubits[0], num_qubits)
-        }
-        GateType::SZ => {
-            // S = diag(1, i)
-            let gate = DMatrix::from_row_slice(2, 2, &[one, zero, zero, i]);
-            embed_single_qubit_gate(&gate, qubits[0], num_qubits)
-        }
-        GateType::SZdg => {
-            let gate = DMatrix::from_row_slice(2, 2, &[one, zero, zero, neg_i]);
-            embed_single_qubit_gate(&gate, qubits[0], num_qubits)
-        }
-        GateType::T => {
-            // T = diag(1, e^{i*pi/4})
-            let exp_pi_4 = Complex64::from_polar(1.0, std::f64::consts::FRAC_PI_4);
-            let gate = DMatrix::from_row_slice(2, 2, &[one, zero, zero, exp_pi_4]);
-            embed_single_qubit_gate(&gate, qubits[0], num_qubits)
-        }
-        GateType::Tdg => {
-            let exp_neg_pi_4 = Complex64::from_polar(1.0, -std::f64::consts::FRAC_PI_4);
-            let gate = DMatrix::from_row_slice(2, 2, &[one, zero, zero, exp_neg_pi_4]);
-            embed_single_qubit_gate(&gate, qubits[0], num_qubits)
-        }
-        GateType::CX => controlled_gate(
-            &single_pauli_matrix(Pauli::X),
-            qubits[0],
-            qubits[1],
-            num_qubits,
-        ),
-        GateType::CY => controlled_gate(
-            &single_pauli_matrix(Pauli::Y),
-            qubits[0],
-            qubits[1],
-            num_qubits,
-        ),
-        GateType::CZ => controlled_gate(
-            &single_pauli_matrix(Pauli::Z),
-            qubits[0],
-            qubits[1],
-            num_qubits,
-        ),
-        GateType::SWAP => swap_matrix(qubits[0], qubits[1], num_qubits),
-        _ => {
-            // Gates not yet implemented: SY, SYdg, U, R1XY, SZZ, SZZdg, CRZ, CCX
-            // Rotation gates (RX, RY, RZ, RXX, RYY, RZZ) should use Operator::Rotation
-            // Prep/Measure gates are not unitary and shouldn't be converted to matrices
-            log::warn!("Gate type {gate_type:?} not implemented in to_matrix, returning identity");
-            let dim = 1 << num_qubits;
-            DMatrix::identity(dim, dim)
-        }
-    }
-}
-
-/// Constructs a controlled gate matrix.
-fn controlled_gate(
-    target_gate: &DMatrix<Complex64>,
-    control: usize,
-    target: usize,
-    num_qubits: usize,
-) -> DMatrix<Complex64> {
-    let dim = 1 << num_qubits;
-    let mut result = DMatrix::identity(dim, dim);
-
-    for i in 0..dim {
-        for j in 0..dim {
-            // Only apply gate when control qubit is 1
-            let control_bit_i = (i >> control) & 1;
-            let control_bit_j = (j >> control) & 1;
-
-            if control_bit_i == 1 && control_bit_j == 1 {
-                // Check if all qubits except target match
-                let mask = !(1 << target);
-                if (i & mask) == (j & mask) {
-                    let i_bit = (i >> target) & 1;
-                    let j_bit = (j >> target) & 1;
-                    result[(i, j)] = target_gate[(i_bit, j_bit)];
-                } else {
-                    result[(i, j)] = Complex64::new(0.0, 0.0);
-                }
-            } else if control_bit_i == control_bit_j && i == j {
-                result[(i, j)] = Complex64::new(1.0, 0.0);
-            } else if control_bit_i != control_bit_j {
-                result[(i, j)] = Complex64::new(0.0, 0.0);
-            }
-        }
-    }
-
-    result
-}
-
-/// Constructs a SWAP gate matrix.
-fn swap_matrix(q1: usize, q2: usize, num_qubits: usize) -> DMatrix<Complex64> {
-    let dim = 1 << num_qubits;
-    let mut result = DMatrix::from_element(dim, dim, Complex64::new(0.0, 0.0));
-
-    for i in 0..dim {
-        // Swap bits at positions q1 and q2
-        let bit1 = (i >> q1) & 1;
-        let bit2 = (i >> q2) & 1;
-
-        let j = if bit1 == bit2 {
-            i
-        } else {
-            // Swap the bits
-            i ^ (1 << q1) ^ (1 << q2)
-        };
-
-        result[(i, j)] = Complex64::new(1.0, 0.0);
-    }
-
-    result
-}
-
-/// Combines two matrices representing operators on disjoint qubits.
-///
-/// When operators act on disjoint qubits, the tensor product in the full Hilbert space
-/// is equivalent to matrix multiplication (since disjoint operators commute).
-fn combine_disjoint_operators(
-    a: &DMatrix<Complex64>,
-    b: &DMatrix<Complex64>,
-) -> DMatrix<Complex64> {
-    a * b
-}
-
-#[cfg(test)]
-mod tests {
-    use super::*;
-    use pecos_core::Angle64;
-    use pecos_core::operator::{CX, H, I, Is, RX, RZ, SWAP, SZ, T, X, Y, Z};
-    use std::f64::consts::PI;
-
-    // --- Basic to_matrix tests ---
-
-    #[test]
-    fn test_pauli_matrices() {
-        let x = X(0);
-        let mat = to_matrix(&x);
-        assert_eq!(mat.nrows(), 2);
-        assert!((mat[(0, 1)] - Complex64::new(1.0, 0.0)).norm() < 1e-10);
-        assert!((mat[(1, 0)] - Complex64::new(1.0, 0.0)).norm() < 1e-10);
-
-        let z = Z(0);
-        let mat = to_matrix(&z);
-        assert!((mat[(0, 0)] - Complex64::new(1.0, 0.0)).norm() < 1e-10);
-        assert!((mat[(1, 1)] - Complex64::new(-1.0, 0.0)).norm() < 1e-10);
-    }
-
-    #[test]
-    fn test_pauli_y() {
-        let y = Y(0);
-        let mat = to_matrix(&y);
-        let i = Complex64::new(0.0, 1.0);
-        assert!((mat[(0, 1)] - (-i)).norm() < 1e-10);
-        assert!((mat[(1, 0)] - i).norm() < 1e-10);
-    }
-
-    #[test]
-    fn test_hadamard() {
-        let h = H(0);
-        let mat = to_matrix(&h);
-        let sqrt2_inv = 1.0 / 2.0_f64.sqrt();
-        assert!((mat[(0, 0)] - Complex64::new(sqrt2_inv, 0.0)).norm() < 1e-10);
-        assert!((mat[(0, 1)] - Complex64::new(sqrt2_inv, 0.0)).norm() < 1e-10);
-        assert!((mat[(1, 0)] - Complex64::new(sqrt2_inv, 0.0)).norm() < 1e-10);
-        assert!((mat[(1, 1)] - Complex64::new(-sqrt2_inv, 0.0)).norm() < 1e-10);
-    }
-
-    #[test]
-    fn test_cnot() {
-        let cx = CX(0, 1);
-        let mat = to_matrix(&cx);
-        assert_eq!(mat.nrows(), 4);
-        // CX with control=0, target=1
-        // |q1 q0> indexing: index = q1*2 + q0
-        // When q0=0 (control off): do nothing
-        // When q0=1 (control on): flip q1
-        // |00> -> |00> (mat[0,0] = 1)
-        // |01> -> |11> (mat[3,1] = 1)
-        // |10> -> |10> (mat[2,2] = 1)
-        // |11> -> |01> (mat[1,3] = 1)
-        assert!((mat[(0, 0)] - Complex64::new(1.0, 0.0)).norm() < 1e-10);
-        assert!((mat[(3, 1)] - Complex64::new(1.0, 0.0)).norm() < 1e-10);
-        assert!((mat[(2, 2)] - Complex64::new(1.0, 0.0)).norm() < 1e-10);
-        assert!((mat[(1, 3)] - Complex64::new(1.0, 0.0)).norm() < 1e-10);
-    }
-
-    #[test]
-    fn test_identity() {
-        let id = I(0);
-        let mat = to_matrix(&id);
-        assert!((mat[(0, 0)] - Complex64::new(1.0, 0.0)).norm() < 1e-10);
-        assert!((mat[(1, 1)] - Complex64::new(1.0, 0.0)).norm() < 1e-10);
-        assert!(mat[(0, 1)].norm() < 1e-10);
-        assert!(mat[(1, 0)].norm() < 1e-10);
-    }
-
-    // --- Rotation matrix tests ---
-
-    #[test]
-    fn test_t_gate_matrix() {
-        let t = T(0);
-        let mat = to_matrix(&t);
-        // T = RZ(π/4) = diag(e^{-iπ/8}, e^{iπ/8})
-        let exp_neg = Complex64::from_polar(1.0, -PI / 8.0);
-        let exp_pos = Complex64::from_polar(1.0, PI / 8.0);
-        assert!((mat[(0, 0)] - exp_neg).norm() < 1e-10);
-        assert!((mat[(1, 1)] - exp_pos).norm() < 1e-10);
-    }
-
-    #[test]
-    fn test_s_gate_matrix() {
-        let s = SZ(0);
-        let mat = to_matrix(&s);
-        // S = RZ(π/2) = diag(e^{-iπ/4}, e^{iπ/4})
-        let exp_neg = Complex64::from_polar(1.0, -PI / 4.0);
-        let exp_pos = Complex64::from_polar(1.0, PI / 4.0);
-        assert!((mat[(0, 0)] - exp_neg).norm() < 1e-10);
-        assert!((mat[(1, 1)] - exp_pos).norm() < 1e-10);
-    }
-
-    #[test]
-    fn test_rx_matrix() {
-        // RX(π) should give X (up to global phase)
-        let rx_pi = RX(Angle64::HALF_TURN, 0);
-        let mat = to_matrix(&rx_pi);
-        let x_mat = to_matrix(&X(0));
-        // RX(π) = -iX, so matrices differ by global phase -i
-        assert!(matrices_equiv_up_to_phase(&mat, &x_mat, 1e-10));
-    }
-
-    #[test]
-    fn test_rz_matrix() {
-        // RZ(π) should give Z (up to global phase)
-        let rz_pi = RZ(Angle64::HALF_TURN, 0);
-        let mat = to_matrix(&rz_pi);
-        let z_mat = to_matrix(&Z(0));
-        assert!(matrices_equiv_up_to_phase(&mat, &z_mat, 1e-10));
-    }
-
-    // --- Tensor product and composition tests ---
-
-    #[test]
-    fn test_tensor_product() {
-        // X ⊗ Z should give a 4x4 matrix
-        let xz = X(0) & Z(1);
-        let mat = to_matrix(&xz);
-        assert_eq!(mat.nrows(), 4);
-
-        // Verify it's the product of embedded X and Z
-        let x_embedded = to_matrix_with_size(&X(0), 2);
-        let z_embedded = to_matrix_with_size(&Z(1), 2);
-        let expected = &x_embedded * &z_embedded;
-        assert!(matrices_equiv_up_to_phase(&mat, &expected, 1e-10));
-    }
-
-    #[test]
-    fn test_composition() {
-        // H * X = XH (matrix multiplication order)
-        let hx = H(0) * X(0);
-        let mat = to_matrix(&hx);
-
-        let h_mat = to_matrix(&H(0));
-        let x_mat = to_matrix(&X(0));
-        let expected = &h_mat * &x_mat;
-        assert!(matrices_equiv_up_to_phase(&mat, &expected, 1e-10));
-    }
-
-    #[test]
-    fn test_adjoint_matrix() {
-        // T† matrix should be conjugate transpose of T
-        let t = T(0);
-        let t_dg = t.dg();
-        let mat_t = to_matrix(&t);
-        let mat_t_dg = to_matrix(&t_dg);
-
-        let expected = mat_t.adjoint();
-        assert!(matrices_equiv_up_to_phase(&mat_t_dg, &expected, 1e-10));
-    }
-
-    #[test]
-    fn test_swap_gate() {
-        let swap = SWAP(0, 1);
-        let mat = to_matrix(&swap);
-        assert_eq!(mat.nrows(), 4);
-
-        // SWAP|00> = |00>, SWAP|01> = |10>, SWAP|10> = |01>, SWAP|11> = |11>
-        assert!((mat[(0, 0)] - Complex64::new(1.0, 0.0)).norm() < 1e-10);
-        assert!((mat[(2, 1)] - Complex64::new(1.0, 0.0)).norm() < 1e-10);
-        assert!((mat[(1, 2)] - Complex64::new(1.0, 0.0)).norm() < 1e-10);
-        assert!((mat[(3, 3)] - Complex64::new(1.0, 0.0)).norm() < 1e-10);
-    }
-
-    // --- operators_equiv tests ---
-
-    #[test]
-    fn test_operators_equiv_same() {
-        let x1 = X(0);
-        let x2 = X(0);
-        assert!(operators_equiv(&x1, &x2));
-    }
-
-    #[test]
-    fn test_operators_equiv_different() {
-        let x = X(0);
-        let y = Y(0);
-        assert!(!operators_equiv(&x, &y));
-    }
-
-    #[test]
-    fn test_operators_equiv_global_phase() {
-        // X and -X differ by global phase -1
-        let x = X(0);
-        let neg_x = pecos_core::operator::phase(Angle64::HALF_TURN) * X(0);
-        assert!(operators_equiv(&x, &neg_x));
-    }
-
-    #[test]
-    fn test_operators_equiv_i_phase() {
-        // X and iX differ by global phase i
-        let x = X(0);
-        let i_x = pecos_core::operator::i * X(0);
-        assert!(operators_equiv(&x, &i_x));
-    }
-
-    // --- operator_exp tests ---
-
-    #[test]
-    fn test_operator_exp_identity() {
-        // exp(i * 0 * X) = I
-        let x = X(0);
-        let result = operator_exp(&x, 0.0);
-        let identity = DMatrix::identity(2, 2);
-        assert!(matrices_equiv_up_to_phase(&result, &identity, 1e-10));
-    }
-
-    #[test]
-    fn test_operator_exp_pauli_pi() {
-        // exp(i * π * Z) = -I
-        let z = Z(0);
-        let result = operator_exp(&z, PI);
-        let neg_identity: DMatrix<Complex64> = DMatrix::identity(2, 2) * Complex64::new(-1.0, 0.0);
-        assert!(matrices_equiv_up_to_phase(&result, &neg_identity, 1e-10));
-    }
-
-    #[test]
-    fn test_operator_exp_pauli_half_pi() {
-        // exp(i * π/2 * X) = i*X = [[0, i], [i, 0]]
-        let x = X(0);
-        let result = operator_exp(&x, PI / 2.0);
-        let i = Complex64::new(0.0, 1.0);
-        let expected = to_matrix(&x) * i;
-        assert!(matrices_equiv_up_to_phase(&result, &expected, 1e-10));
-    }
-
-    // --- operator_log tests ---
-
-    #[test]
-    fn test_operator_log_identity() {
-        // log(I) = 0
-        let id = I(0);
-        let result = operator_log(&id);
-        assert!(result.is_some());
-        let log_mat = result.unwrap();
-        // All elements should be near zero
-        for i in 0..log_mat.nrows() {
-            for j in 0..log_mat.ncols() {
-                assert!(log_mat[(i, j)].norm() < 1e-8);
-            }
-        }
-    }
-
-    #[test]
-    fn test_operator_log_returns_matrix() {
-        // log(T) should exist (T is close to identity)
-        let t = T(0);
-        let result = operator_log(&t);
-        assert!(result.is_some());
-
-        // log(S) should exist
-        let s = SZ(0);
-        let result = operator_log(&s);
-        assert!(result.is_some());
-    }
-
-    // --- to_matrix_with_size tests ---
-
-    #[test]
-    fn test_to_matrix_with_size_embedding() {
-        // X(0) in 3-qubit space should be 8x8
-        let x = X(0);
-        let mat = to_matrix_with_size(&x, 3);
-        assert_eq!(mat.nrows(), 8);
-
-        // Should act as X on qubit 0, identity on others
-        // Check that |000> -> |001>, |001> -> |000>
-        assert!((mat[(1, 0)] - Complex64::new(1.0, 0.0)).norm() < 1e-10);
-        assert!((mat[(0, 1)] - Complex64::new(1.0, 0.0)).norm() < 1e-10);
-    }
-
-    #[test]
-    fn test_to_matrix_preserves_unitarity() {
-        // Verify U * U† = I for various operators
-        let operators = vec![X(0), Y(0), Z(0), H(0), T(0), CX(0, 1)];
-
-        for op in operators {
-            let mat = to_matrix(&op);
-            let product = &mat * mat.adjoint();
-            let identity: DMatrix<Complex64> = DMatrix::identity(mat.nrows(), mat.ncols());
-
-            for i in 0..mat.nrows() {
-                for j in 0..mat.ncols() {
-                    assert!(
-                        (product[(i, j)] - identity[(i, j)]).norm() < 1e-10,
-                        "Unitarity failed for operator at ({i}, {j})"
-                    );
-                }
-            }
-        }
-    }
-
-    // --- Conjugation matrix verification tests ---
-
-    #[test]
-    fn test_conj_matrix_verification() {
-        // Verify A.conj(U) = U * A * U† via matrices
-        let a = X(0);
-        let u = H(0);
-
-        let conj_result = a.conj(&u);
-        let conj_mat = to_matrix(&conj_result);
-
-        // Compute U * A * U† directly
-        let u_mat = to_matrix(&u);
-        let a_mat = to_matrix(&a);
-        let expected = &u_mat * &a_mat * u_mat.adjoint();
-
-        assert!(matrices_equiv_up_to_phase(&conj_mat, &expected, 1e-10));
-    }
-
-    #[test]
-    fn test_conjdg_matrix_verification() {
-        // Verify A.conjdg(U) = U† * A * U via matrices
-        let a = X(0);
-        let u = H(0);
-
-        let conjdg_result = a.conjdg(&u);
-        let conjdg_mat = to_matrix(&conjdg_result);
-
-        // Compute U† * A * U directly
-        let u_mat = to_matrix(&u);
-        let a_mat = to_matrix(&a);
-        let expected = u_mat.adjoint() * &a_mat * &u_mat;
-
-        assert!(matrices_equiv_up_to_phase(&conjdg_mat, &expected, 1e-10));
-    }
-
-    #[test]
-    fn test_conj_sz_gives_y() {
-        // X.conj(SZ) = SZ * X * SZ† should equal Y (up to phase)
-        let x = X(0);
-        let sz = SZ(0);
-
-        let conj_result = x.conj(&sz);
-        let conj_mat = to_matrix(&conj_result);
-
-        let y_mat = to_matrix(&Y(0));
-
-        assert!(matrices_equiv_up_to_phase(&conj_mat, &y_mat, 1e-10));
-    }
-
-    #[test]
-    fn test_conj_conjdg_inverse_via_matrix() {
-        // A.conj(U).conjdg(U) should equal A
-        let a = X(0);
-        let u = T(0);
-
-        let forward = a.clone().conj(&u);
-        let back = forward.conjdg(&u);
-        let back_mat = to_matrix(&back);
-
-        let a_mat = to_matrix(&a);
-
-        assert!(matrices_equiv_up_to_phase(&back_mat, &a_mat, 1e-10));
-    }
-
-    // --- Multi-qubit conjugation tests ---
-
-    #[test]
-    fn test_conj_multi_qubit_stabilizer() {
-        // Two-qubit stabilizer X⊗Z conjugated by CNOT
-        let stabilizer = X(0) & Z(1);
-        let cnot = CX(0, 1);
-
-        let updated = stabilizer.conj(&cnot);
-        let updated_mat = to_matrix(&updated);
-
-        // Compute CNOT * (X⊗Z) * CNOT† directly
-        let cnot_mat = to_matrix(&cnot);
-        let stab_mat = to_matrix(&stabilizer);
-        let expected = &cnot_mat * &stab_mat * cnot_mat.adjoint();
-
-        assert!(matrices_equiv_up_to_phase(&updated_mat, &expected, 1e-10));
-    }
-
-    #[test]
-    fn test_conj_by_two_qubit_gate() {
-        // Single-qubit Pauli conjugated by two-qubit gate
-        let x = X(0);
-        let cnot = CX(0, 1);
-
-        let result = x.conj(&cnot);
-        let result_mat = to_matrix(&result);
-
-        // CNOT * X(0) * CNOT† = X(0) ⊗ X(1) (CNOT propagates X from control to target)
-        let xx = X(0) & X(1);
-        let expected = to_matrix(&xx);
-
-        assert!(matrices_equiv_up_to_phase(&result_mat, &expected, 1e-10));
-    }
-
-    // --- More two-qubit gate tests ---
-
-    #[test]
-    fn test_cz_gate() {
-        // CZ = |0><0| ⊗ I + |1><1| ⊗ Z
-        use pecos_core::operator::CZ;
-        let cz = CZ(0, 1);
-        let mat = to_matrix(&cz);
-
-        // CZ matrix: diag(1, 1, 1, -1)
-        assert!((mat[(0, 0)] - Complex64::new(1.0, 0.0)).norm() < 1e-10);
-        assert!((mat[(1, 1)] - Complex64::new(1.0, 0.0)).norm() < 1e-10);
-        assert!((mat[(2, 2)] - Complex64::new(1.0, 0.0)).norm() < 1e-10);
-        assert!((mat[(3, 3)] - Complex64::new(-1.0, 0.0)).norm() < 1e-10);
-
-        // Off-diagonal should be zero
-        assert!(mat[(0, 1)].norm() < 1e-10);
-        assert!(mat[(1, 2)].norm() < 1e-10);
-    }
-
-    #[test]
-    fn test_cz_symmetric() {
-        // CZ(0,1) should equal CZ(1,0)
-        use pecos_core::operator::CZ;
-        let cz_01 = CZ(0, 1);
-        let cz_10 = CZ(1, 0);
-
-        let mat_01 = to_matrix(&cz_01);
-        let mat_10 = to_matrix(&cz_10);
-
-        assert!(matrices_equiv_up_to_phase(&mat_01, &mat_10, 1e-10));
-    }
-
-    // --- Algebraic identity tests ---
-
-    #[test]
-    fn test_adjoint_of_product() {
-        // (AB)† = B†A†
-        let a = H(0);
-        let b = T(0);
-
-        let ab = a.clone() * b.clone();
-        let ab_dagger = ab.dg();
-        let ab_dagger_mat = to_matrix(&ab_dagger);
-
-        let b_dagger_a_dagger = b.dg() * a.dg();
-        let expected = to_matrix(&b_dagger_a_dagger);
-
-        assert!(matrices_equiv_up_to_phase(&ab_dagger_mat, &expected, 1e-10));
-    }
-
-    #[test]
-    fn test_double_adjoint_identity() {
-        // (A†)† = A
-        let ops = vec![X(0), Y(0), H(0), T(0), CX(0, 1)];
-
-        for op in ops {
-            let double_dagger = op.dg().dg();
-            let original_mat = to_matrix(&op);
-            let double_mat = to_matrix(&double_dagger);
-
-            assert!(matrices_equiv_up_to_phase(
-                &original_mat,
-                &double_mat,
-                1e-10
-            ));
-        }
-    }
-
-    #[test]
-    fn test_tensor_adjoint() {
-        // (A ⊗ B)† = A† ⊗ B†
-        let a = H(0);
-        let b = T(1);
-
-        let tensor = a.clone() & b.clone();
-        let tensor_dagger = tensor.dg();
-        let tensor_dagger_mat = to_matrix(&tensor_dagger);
-
-        let a_dagger_tensor_b_dagger = a.dg() & b.dg();
-        let expected = to_matrix(&a_dagger_tensor_b_dagger);
-
-        assert!(matrices_equiv_up_to_phase(
-            &tensor_dagger_mat,
-            &expected,
-            1e-10
-        ));
-    }
-
-    // --- ToMatrix trait tests ---
-
-    #[test]
-    fn test_to_matrix_trait_method() {
-        // Test that trait method gives same result as standalone function
-        let h = H(0);
-
-        let via_function = to_matrix(&h);
-        let via_trait = h.to_matrix();
-
-        assert_eq!(via_function.nrows(), via_trait.nrows());
-        assert_eq!(via_function.ncols(), via_trait.ncols());
-        for i in 0..via_function.nrows() {
-            for j in 0..via_function.ncols() {
-                assert!((via_function[(i, j)] - via_trait[(i, j)]).norm() < 1e-10);
-            }
-        }
-    }
-
-    #[test]
-    fn test_to_matrix_with_identity_tensor() {
-        // Test using Is() to get larger matrix
-        let x_extended = X(0) & Is(1..3); // X on qubit 0 in 3-qubit space
-
-        let mat = x_extended.to_matrix();
-        assert_eq!(mat.nrows(), 8); // 2^3 = 8
-
-        // Should match the standalone function
-        let expected = to_matrix_with_size(&X(0), 3);
-        assert!(matrices_equiv_up_to_phase(&mat, &expected, 1e-10));
-    }
-
-    #[test]
-    fn test_to_matrix_trait_chaining() {
-        // Verify trait works well with operator chaining
-        let circuit = H(0) * CX(0, 1) * H(0);
-        let mat = circuit.to_matrix();
-
-        assert_eq!(mat.nrows(), 4); // 2 qubits
-
-        // Verify unitarity
-        let product = &mat * mat.adjoint();
-        let identity: DMatrix<Complex64> = DMatrix::identity(4, 4);
-        assert!(matrices_equiv_up_to_phase(&product, &identity, 1e-10));
-    }
-
-    // --- Identity operator ToMatrix tests ---
-
-    #[test]
-    fn test_identity_to_matrix_single_qubit() {
-        // I(0).to_matrix() should be 2x2 identity
-        let mat = I(0).to_matrix();
-        let expected: DMatrix<Complex64> = DMatrix::identity(2, 2);
-
-        assert_eq!(mat.nrows(), 2);
-        assert!(matrices_equiv_up_to_phase(&mat, &expected, 1e-10));
-    }
-
-    #[test]
-    fn test_identity_to_matrix_two_qubits() {
-        // Is(0..=1).to_matrix() should be 4x4 identity
-        let mat = Is(0..=1).to_matrix();
-        let expected: DMatrix<Complex64> = DMatrix::identity(4, 4);
-
-        assert_eq!(mat.nrows(), 4);
-        assert!(matrices_equiv_up_to_phase(&mat, &expected, 1e-10));
-    }
-
-    #[test]
-    fn test_identity_tensor_with_gate() {
-        // X(0) & I(1) should give X tensor I = 4x4 matrix
-        let op = X(0) & I(1);
-        let mat = op.to_matrix();
-
-        assert_eq!(mat.nrows(), 4);
-
-        // Should equal X(0) extended to 2 qubits
-        let expected = to_matrix_with_size(&X(0), 2);
-
-        assert!(matrices_equiv_up_to_phase(&mat, &expected, 1e-10));
-    }
-
-    #[test]
-    fn test_simplify_preserves_tensor_dimension() {
-        // (X(0) & I(1)).simplify() should preserve the 2-qubit space
-        let op = X(0) & I(1);
-        let simplified = op.simplify();
-
-        // Both should produce equivalent 4x4 matrices
-        let orig_mat = op.to_matrix();
-        let simp_mat = simplified.to_matrix();
-
-        assert_eq!(orig_mat.nrows(), 4);
-        assert_eq!(simp_mat.nrows(), 4);
-        assert!(matrices_equiv_up_to_phase(&orig_mat, &simp_mat, 1e-10));
-    }
-
-    // --- PauliString ToMatrix tests ---
-
-    #[test]
-    fn test_pauli_string_to_matrix_single() {
-        use pecos_core::PauliString;
-
-        // Single X Pauli
-        let ps = PauliString::x(0);
-        let mat = ps.to_matrix();
-
-        // Should match X(0).to_matrix()
-        let x_mat = X(0).to_matrix();
-        assert!(matrices_equiv_up_to_phase(&mat, &x_mat, 1e-10));
-    }
-
-    #[test]
-    fn test_pauli_string_to_matrix_multi() {
-        use pecos_core::{Pauli, PauliString};
-
-        // X on qubit 0, Z on qubit 1
-        let ps = PauliString::from_paulis(&[Pauli::X, Pauli::Z]);
-        let mat = ps.to_matrix();
-
-        // Should match (X(0) & Z(1)).to_matrix()
-        let xz = X(0) & Z(1);
-        let expected = xz.to_matrix();
-        assert!(matrices_equiv_up_to_phase(&mat, &expected, 1e-10));
-    }
-
-    #[test]
-    fn test_pauli_string_to_matrix_with_phase() {
-        use pecos_core::{Pauli, PauliString, QuarterPhase};
-
-        // -i * X
-        let ps = PauliString::from_paulis_with_phase(QuarterPhase::MinusI, &[Pauli::X]);
-        let mat = ps.to_matrix();
-
-        // Should be -i times X matrix
-        let x_mat = X(0).to_matrix();
-        let neg_i = Complex64::new(0.0, -1.0);
-        let expected = x_mat * neg_i;
-
-        assert!(matrices_equiv_up_to_phase(&mat, &expected, 1e-10));
-    }
-
-    #[test]
-    fn test_pauli_string_to_matrix_identity() {
-        use pecos_core::PauliString;
-
-        // Identity PauliString - returns 1x1 identity (no qubits)
-        let ps = PauliString::identity();
-        let mat = ps.to_matrix();
-
-        // Identity with no qubits defaults to 1 qubit -> 2x2
-        let identity: DMatrix<Complex64> = DMatrix::identity(2, 2);
-        assert!(matrices_equiv_up_to_phase(&mat, &identity, 1e-10));
-    }
-
-    #[test]
-    fn test_pauli_string_matches_operator_pauli() {
-        use pecos_core::{Pauli, PauliString};
-
-        // Verify PauliString.to_matrix() matches Operator::Pauli.to_matrix()
-        let ps = PauliString::from_paulis(&[Pauli::Y, Pauli::Z]);
-
-        // Convert to Operator::Pauli
-        let op = pecos_core::operator::Operator::Pauli(ps.clone());
-
-        let ps_mat = ps.to_matrix();
-        let op_mat = op.to_matrix();
-
-        assert!(matrices_equiv_up_to_phase(&ps_mat, &op_mat, 1e-10));
-    }
-}
diff --git a/crates/pecos-quantum/src/pass.rs b/crates/pecos-quantum/src/pass.rs
index 7b5546346..98160d49b 100644
--- a/crates/pecos-quantum/src/pass.rs
+++ b/crates/pecos-quantum/src/pass.rs
@@ -23,16 +23,107 @@ use std::collections::{BTreeMap, HashMap, HashSet};
 use pecos_core::gate_type::GateType;
 use pecos_core::{Angle64, Gate, GateQubits, QubitId};
 
-use crate::{Attribute, DagCircuit, TickCircuit};
+use crate::{Attribute, DagCircuit, Tick, TickCircuit};
 
 /// A transformation pass that can be applied to circuits.
+///
+/// Passes transform circuits in-place. For a copy, clone the circuit first:
+///
+/// ```no_run
+/// # use pecos_quantum::pass::{CircuitPass, SimplifyRotations};
+/// # use pecos_quantum::TickCircuit;
+/// # let circuit = TickCircuit::new();
+/// // In-place
+/// let mut tc = circuit;
+/// SimplifyRotations.apply_tick(&mut tc);
+///
+/// // Copy (clone first)
+/// # let original = TickCircuit::new();
+/// let transformed = SimplifyRotations.transform_tick(original);
+/// ```
 pub trait CircuitPass {
-    /// Apply this pass to a [`TickCircuit`].
+    /// Apply this pass to a [`TickCircuit`] in-place.
     fn apply_tick(&self, circuit: &mut TickCircuit);
-    /// Apply this pass to a [`DagCircuit`].
+
+    /// Apply this pass to a [`DagCircuit`] in-place.
     fn apply_dag(&self, circuit: &mut DagCircuit);
+
+    /// Take ownership, transform, return.
+    fn transform_tick(&self, mut circuit: TickCircuit) -> TickCircuit {
+        self.apply_tick(&mut circuit);
+        circuit
+    }
+
+    /// Take ownership, transform, return.
+    fn transform_dag(&self, mut circuit: DagCircuit) -> DagCircuit {
+        self.apply_dag(&mut circuit);
+        circuit
+    }
+}
+
+// ============================================================================
+// Free functions: primary user-facing pass API
+// ============================================================================
+
+/// Lower Clifford-angle rotations to named Clifford gates.
+///
+/// RZ(pi/2) -> SZ, RZ(pi) -> Z, RX(pi/2) -> SX, etc.
+/// Also decomposes two-qubit rotations: RZZ(pi) -> Z+Z.
+pub fn lower_clifford_rotations(circuit: &mut TickCircuit) {
+    SimplifyRotations.apply_tick(circuit);
+}
+
+/// Insert Idle gates after each two-qubit gate on both of its qubits.
+///
+/// Adds Idle(duration) on both qubits of each 2q gate. Models idle noise
+/// during 2q gate execution.
+pub fn insert_idle_after_two_qubit_gates(circuit: &mut TickCircuit, duration: f64) {
+    InsertIdleAfterTwoQubitGates(duration).apply_tick(circuit);
+}
+
+/// Remove identity gates (I, Idle, zero-angle rotations).
+pub fn remove_identity(circuit: &mut TickCircuit) {
+    RemoveIdentity.apply_tick(circuit);
+}
+
+/// Cancel adjacent inverse gate pairs (H-H, S-Sdg, T-Tdg, etc.).
+pub fn cancel_inverses(circuit: &mut TickCircuit) {
+    CancelInverses.apply_tick(circuit);
 }
 
+/// Merge adjacent rotations on the same qubit into a single rotation.
+pub fn merge_adjacent_rotations(circuit: &mut TickCircuit) {
+    MergeAdjacentRotations.apply_tick(circuit);
+}
+
+/// Peephole optimization (rotation merging + Clifford lowering).
+pub fn peephole_optimize(circuit: &mut TickCircuit) {
+    PeepholeOptimize.apply_tick(circuit);
+}
+
+/// Absorb single-qubit basis gates into adjacent preps/measurements.
+pub fn absorb_basis_gates(circuit: &mut TickCircuit) {
+    AbsorbBasisGates.apply_tick(circuit);
+}
+
+/// Compact ticks by ASAP scheduling (merge gates into earlier ticks).
+pub fn compact_ticks(circuit: &mut TickCircuit) {
+    CompactTicks.apply_tick(circuit);
+}
+
+/// Assign `MeasId` to measurement gates that don't have them.
+///
+/// Walks the circuit in tick order and assigns sequential `MeasId`s
+/// to any MZ/MeasureFree gate with empty `meas_ids`. Existing `MeasId`s
+/// are preserved. New IDs continue from the circuit's current counter.
+pub fn assign_missing_meas_ids(circuit: &mut TickCircuit) {
+    AssignMissingMeasIds.apply_tick(circuit);
+}
+
+// ============================================================================
+// Pass trait and pipeline
+// ============================================================================
+
 /// An ordered collection of passes applied sequentially.
 ///
 /// `PassPipeline` itself implements [`CircuitPass`], so pipelines can be
@@ -122,9 +213,70 @@ impl CircuitPass for PassPipeline {
 /// | RYY | pi | Y + Y |
 pub struct SimplifyRotations;
 
+/// Insert Idle gates after each two-qubit gate on both of its qubits.
+///
+/// For each tick containing two-qubit gates, adds a new tick immediately
+/// after with `Idle(duration)` on each qubit involved in a two-qubit gate.
+///
+/// This models the idle noise that qubits experience during two-qubit
+/// gate execution. The noise model applies `RZ(p_idle * duration)` when
+/// it encounters an Idle gate.
+///
+/// The inner value is the idle duration in time units (typically 1.0).
+pub struct InsertIdleAfterTwoQubitGates(pub f64);
+
+impl CircuitPass for InsertIdleAfterTwoQubitGates {
+    fn apply_tick(&self, circuit: &mut TickCircuit) {
+        let duration = self.0;
+        let mut new_ticks = Vec::with_capacity(circuit.ticks().len() * 2);
+
+        // Drain ticks from circuit and rebuild with idle insertions
+        let old_ticks = circuit.take_ticks();
+
+        for tick in old_ticks {
+            let mut idle_qubits: Vec<QubitId> = Vec::new();
+            for gate in tick.iter_gate_batches() {
+                if gate.is_two_qubit() {
+                    for q in &gate.qubits {
+                        if !idle_qubits.contains(q) {
+                            idle_qubits.push(*q);
+                        }
+                    }
+                }
+            }
+
+            new_ticks.push(tick);
+
+            if !idle_qubits.is_empty() {
+                let mut idle_tick = crate::Tick::new();
+                for q in idle_qubits {
+                    idle_tick.add_gate(Gate::idle(duration, vec![q]));
+                }
+                new_ticks.push(idle_tick);
+            }
+        }
+
+        circuit.replace_ticks(new_ticks);
+    }
+
+    fn apply_dag(&self, _circuit: &mut DagCircuit) {
+        // DAG doesn't have tick structure — no-op
+    }
+}
+
 /// Apply an in-place simplification to a gate. Returns `true` if the gate was
 /// simplified (either renamed in place or needs decomposition handling).
 fn simplify_gate_in_place(gate: &mut Gate) -> bool {
+    // R1XY has two angles — handle separately
+    if gate.gate_type == GateType::R1XY && gate.angles.len() == 2 {
+        if let Some(named) = pecos_core::try_simplify_r1xy(gate.angles[0], gate.angles[1]) {
+            gate.gate_type = named;
+            gate.angles.clear();
+            return true;
+        }
+        return false;
+    }
+
     if gate.angles.len() != 1 {
         return false;
     }
@@ -290,6 +442,62 @@ fn peephole_conjugation(middle: &Gate, h_qubit: QubitId) -> Option<(GateType, Ga
     }
 }
 
+fn split_batched_tick_commands(circuit: &mut TickCircuit) {
+    let old_ticks = circuit.take_ticks();
+    let mut new_ticks = Vec::with_capacity(old_ticks.len());
+
+    for old_tick in old_ticks {
+        let mut new_tick = Tick::new();
+        for (key, value) in old_tick.tick_attrs() {
+            new_tick.set_attr(key, value.clone());
+        }
+
+        for batch in old_tick.iter_gate_batches() {
+            let gate = batch.as_gate();
+            let attrs: BTreeMap<String, Attribute> = batch
+                .attrs()
+                .map(|(key, value)| (key.clone(), value.clone()))
+                .collect();
+
+            let split_gates: Vec<Gate> = if batch.gate_count() == 0 {
+                vec![gate.clone()]
+            } else {
+                batch
+                    .iter_gate_instances()
+                    .map(super::tick_circuit::GateInstanceRef::to_gate)
+                    .collect()
+            };
+
+            if split_gates.is_empty() {
+                continue;
+            }
+
+            if split_gates.len() == 1 {
+                let new_idx = new_tick
+                    .try_add_gate_preserving_command(split_gates[0].clone())
+                    .unwrap_or_else(|err| panic!("{err}"));
+                if !attrs.is_empty() {
+                    new_tick.set_gate_attrs(new_idx, attrs);
+                }
+                continue;
+            }
+
+            for split_gate in split_gates {
+                let new_idx = new_tick
+                    .try_add_gate_preserving_command(split_gate)
+                    .unwrap_or_else(|err| panic!("{err}"));
+                if !attrs.is_empty() {
+                    new_tick.set_gate_attrs(new_idx, attrs.clone());
+                }
+            }
+        }
+
+        new_ticks.push(new_tick);
+    }
+
+    circuit.replace_ticks(new_ticks);
+}
+
 impl CircuitPass for SimplifyRotations {
     fn apply_tick(&self, circuit: &mut TickCircuit) {
         for tick in circuit.ticks_mut() {
@@ -297,18 +505,18 @@ impl CircuitPass for SimplifyRotations {
             // We need to know which gate indices to remove and what to add.
             let mut decompositions: Vec<(usize, GateType)> = Vec::new();
 
-            for (i, gate) in tick.gates().iter().enumerate() {
+            for gate in tick.iter_gate_batches() {
                 if gate.angles.len() == 1
                     && let Some(pauli) =
                         pecos_core::half_turn_decomposition(gate.gate_type, gate.angles[0])
                 {
-                    decompositions.push((i, pauli));
+                    decompositions.push((gate.batch_index(), pauli));
                 }
             }
 
             // Process decompositions in reverse order to keep indices valid.
             for &(idx, pauli) in decompositions.iter().rev() {
-                let qubits = tick.gates()[idx].qubits.clone();
+                let qubits = tick.gate_batches()[idx].qubits.clone();
                 // Remove the two-qubit gate, add two single-qubit gates.
                 tick.remove_gate(idx);
                 for pair in qubits.chunks(2) {
@@ -320,8 +528,11 @@ impl CircuitPass for SimplifyRotations {
             }
 
             // Second pass: in-place simplification of remaining gates.
-            for gate in tick.gates_mut() {
-                simplify_gate_in_place(gate);
+            for gate_idx in 0..tick.len() {
+                tick.update_gate_batch(gate_idx, |gate| {
+                    simplify_gate_in_place(gate);
+                })
+                .unwrap_or_else(|err| panic!("{err}"));
             }
         }
     }
@@ -403,7 +614,7 @@ impl CircuitPass for RemoveIdentity {
     fn apply_tick(&self, circuit: &mut TickCircuit) {
         for tick in circuit.ticks_mut() {
             let to_remove: Vec<usize> = tick
-                .gates()
+                .gate_batches()
                 .iter()
                 .enumerate()
                 .filter(|(_, g)| is_identity_gate(g))
@@ -452,13 +663,14 @@ impl CircuitPass for CancelInverses {
         let mut stacks: HashMap<QubitId, Vec<(usize, usize)>> = HashMap::new();
         let mut to_remove: Vec<(usize, usize)> = Vec::new();
 
-        for (ti, tick) in circuit.ticks().iter().enumerate() {
-            for (gi, gate) in tick.gates().iter().enumerate() {
+        for (ti, tick) in circuit.iter_ticks() {
+            for gate in tick.iter_gate_batches() {
+                let gi = gate.batch_index();
                 let qubits: Vec<QubitId> = gate.qubits.iter().copied().collect();
 
                 if let Some((pred_ti, pred_gi)) = check_all_stacks_agree(&stacks, &qubits) {
-                    let pred_gate = &circuit.ticks()[pred_ti].gates()[pred_gi];
-                    if are_inverses(pred_gate, gate) {
+                    let pred_gate = &circuit.ticks()[pred_ti].gate_batches()[pred_gi];
+                    if are_inverses(pred_gate, gate.as_gate()) {
                         for &q in &qubits {
                             if let Some(stack) = stacks.get_mut(&q) {
                                 stack.pop();
@@ -535,15 +747,16 @@ impl CircuitPass for MergeAdjacentRotations {
         let mut angle_adjustments: HashMap<(usize, usize), Angle64> = HashMap::new();
         let mut to_remove: Vec<(usize, usize)> = Vec::new();
 
-        for (ti, tick) in circuit.ticks().iter().enumerate() {
-            for (gi, gate) in tick.gates().iter().enumerate() {
+        for (ti, tick) in circuit.iter_ticks() {
+            for gate in tick.iter_gate_batches() {
+                let gi = gate.batch_index();
                 let qubits: Vec<QubitId> = gate.qubits.iter().copied().collect();
 
                 if is_rotation(gate.gate_type)
                     && gate.angles.len() == 1
                     && let Some((pred_ti, pred_gi)) = check_all_stacks_agree(&stacks, &qubits)
                 {
-                    let pred_gate = &circuit.ticks()[pred_ti].gates()[pred_gi];
+                    let pred_gate = &circuit.ticks()[pred_ti].gate_batches()[pred_gi];
                     if pred_gate.gate_type == gate.gate_type && pred_gate.qubits == gate.qubits {
                         *angle_adjustments
                             .entry((pred_ti, pred_gi))
@@ -563,10 +776,11 @@ impl CircuitPass for MergeAdjacentRotations {
 
         // Apply angle adjustments to surviving gates.
         for (&(ti, gi), &delta) in &angle_adjustments {
-            if let Some(tick) = circuit.get_tick_mut(ti)
-                && let Some(gate) = tick.gates_mut().get_mut(gi)
-            {
-                gate.angles[0] += delta;
+            if let Some(tick) = circuit.get_tick_mut(ti) {
+                tick.update_gate_batch(gi, |gate| {
+                    gate.angles[0] += delta;
+                })
+                .unwrap_or_else(|err| panic!("{err}"));
             }
         }
 
@@ -638,10 +852,13 @@ pub struct PeepholeOptimize;
 
 impl CircuitPass for PeepholeOptimize {
     fn apply_tick(&self, circuit: &mut TickCircuit) {
+        split_batched_tick_commands(circuit);
+
         // Build per-qubit timeline: Vec of (tick_idx, gate_idx) in order.
         let mut timelines: HashMap<QubitId, Vec<(usize, usize)>> = HashMap::new();
-        for (ti, tick) in circuit.ticks().iter().enumerate() {
-            for (gi, gate) in tick.gates().iter().enumerate() {
+        for (ti, tick) in circuit.iter_ticks() {
+            for gate in tick.iter_gate_batches() {
+                let gi = gate.batch_index();
                 for &q in &gate.qubits {
                     timelines.entry(q).or_default().push((ti, gi));
                 }
@@ -671,9 +888,9 @@ impl CircuitPass for PeepholeOptimize {
                     continue;
                 }
 
-                let h1 = &circuit.ticks()[h1_ti].gates()[h1_gi];
-                let mid = &circuit.ticks()[mid_ti].gates()[mid_gi];
-                let h2 = &circuit.ticks()[h2_ti].gates()[h2_gi];
+                let h1 = &circuit.ticks()[h1_ti].gate_batches()[h1_gi];
+                let mid = &circuit.ticks()[mid_ti].gate_batches()[mid_gi];
+                let h2 = &circuit.ticks()[h2_ti].gate_batches()[h2_gi];
 
                 // Both must be single-qubit H on this qubit.
                 if h1.gate_type != GateType::H
@@ -698,11 +915,12 @@ impl CircuitPass for PeepholeOptimize {
 
         // Apply replacements.
         for ((ti, gi), new_gt, new_qubits) in &replacements {
-            if let Some(tick) = circuit.get_tick_mut(*ti)
-                && let Some(gate) = tick.gates_mut().get_mut(*gi)
-            {
-                gate.gate_type = *new_gt;
-                gate.qubits.clone_from(new_qubits);
+            if let Some(tick) = circuit.get_tick_mut(*ti) {
+                tick.update_gate_batch(*gi, |gate| {
+                    gate.gate_type = *new_gt;
+                    gate.qubits.clone_from(new_qubits);
+                })
+                .unwrap_or_else(|err| panic!("{err}"));
             }
         }
 
@@ -834,13 +1052,14 @@ impl CircuitPass for AbsorbBasisGates {
 
         // Forward scan: absorb Z-diagonal gates after Z-preps.
         let mut z_eigenstate: HashSet<QubitId> = HashSet::new();
-        for (ti, tick) in circuit.ticks().iter().enumerate() {
-            for (gi, gate) in tick.gates().iter().enumerate() {
+        for (ti, tick) in circuit.iter_ticks() {
+            for gate in tick.iter_gate_batches() {
+                let gi = gate.batch_index();
                 if is_z_prep(gate.gate_type) {
                     for &q in &gate.qubits {
                         z_eigenstate.insert(q);
                     }
-                } else if is_z_diagonal(gate)
+                } else if is_z_diagonal(gate.as_gate())
                     && gate.qubits.iter().all(|q| z_eigenstate.contains(q))
                 {
                     to_remove.push((ti, gi));
@@ -855,7 +1074,7 @@ impl CircuitPass for AbsorbBasisGates {
         // Backward scan: absorb Z-diagonal gates before Z-measures.
         let mut before_z_measure: HashSet<QubitId> = HashSet::new();
         for (ti, tick) in circuit.ticks().iter().enumerate().rev() {
-            for (gi, gate) in tick.gates().iter().enumerate().rev() {
+            for (gi, gate) in tick.gate_batches().iter().enumerate().rev() {
                 if is_z_measure(gate.gate_type) {
                     for &q in &gate.qubits {
                         before_z_measure.insert(q);
@@ -965,12 +1184,10 @@ impl CircuitPass for CompactTicks {
         // Collect every gate together with its per-gate attributes.
         let mut entries: Vec<(Gate, BTreeMap<String, Attribute>)> = Vec::new();
         for tick in circuit.ticks() {
-            for (gi, gate) in tick.gates().iter().enumerate() {
-                let attrs: BTreeMap<String, Attribute> = tick
-                    .gate_attrs(gi)
-                    .map(|(k, v)| (k.clone(), v.clone()))
-                    .collect();
-                entries.push((gate.clone(), attrs));
+            for gate in tick.iter_gate_batches() {
+                let attrs: BTreeMap<String, Attribute> =
+                    gate.attrs().map(|(k, v)| (k.clone(), v.clone())).collect();
+                entries.push((gate.as_gate().clone(), attrs));
             }
         }
 
@@ -1032,10 +1249,50 @@ impl CircuitPass for CompactTicks {
     }
 }
 
+/// Assign [`MeasId`](pecos_core::MeasId) to measurement gates that don't have them.
+///
+/// Walks the circuit in tick order and assigns sequential IDs to any
+/// measurement gate with empty `meas_ids`. Existing IDs are preserved.
+/// New IDs continue from the circuit's current measurement counter.
+///
+/// Use this on circuits from external sources (QIS trace, Stim import)
+/// that don't assign `MeasId` during construction.
+pub struct AssignMissingMeasIds;
+
+impl CircuitPass for AssignMissingMeasIds {
+    fn apply_tick(&self, circuit: &mut TickCircuit) {
+        let mut next_id = circuit.num_measurements();
+        for tick in circuit.ticks_mut() {
+            for gate_idx in 0..tick.len() {
+                tick.update_gate_batch(gate_idx, |gate| {
+                    let is_measurement =
+                        matches!(gate.gate_type, GateType::MZ | GateType::MeasureFree);
+                    if is_measurement && gate.meas_ids.is_empty() {
+                        for _ in &gate.qubits {
+                            gate.meas_ids.push(pecos_core::MeasId(next_id));
+                            next_id += 1;
+                        }
+                    }
+                })
+                .unwrap_or_else(|err| panic!("{err}"));
+            }
+        }
+        let added = next_id - circuit.num_measurements();
+        if added > 0 {
+            circuit.advance_meas_counter(added);
+        }
+    }
+
+    fn apply_dag(&self, _circuit: &mut DagCircuit) {
+        // No-op: DagCircuit gates are accessed differently.
+    }
+}
+
 #[cfg(test)]
 #[allow(clippy::cast_precision_loss)]
 mod tests {
     use super::*;
+    use pecos_core::MeasId;
 
     // ==================== simplify_rotation unit tests ====================
 
@@ -1202,7 +1459,7 @@ mod tests {
         let mut tc = TickCircuit::new();
         tc.tick().rz(Angle64::QUARTER_TURN, &[0]);
         SimplifyRotations.apply_tick(&mut tc);
-        let gate = &tc.ticks()[0].gates()[0];
+        let gate = &tc.ticks()[0].gate_batches()[0];
         assert_eq!(gate.gate_type, GateType::SZ);
         assert!(gate.angles.is_empty());
     }
@@ -1212,7 +1469,7 @@ mod tests {
         let mut tc = TickCircuit::new();
         tc.tick().rz(Angle64::HALF_TURN, &[0]);
         SimplifyRotations.apply_tick(&mut tc);
-        let gate = &tc.ticks()[0].gates()[0];
+        let gate = &tc.ticks()[0].gate_batches()[0];
         assert_eq!(gate.gate_type, GateType::Z);
         assert!(gate.angles.is_empty());
     }
@@ -1222,7 +1479,7 @@ mod tests {
         let mut tc = TickCircuit::new();
         tc.tick().rx(Angle64::QUARTER_TURN, &[0]);
         SimplifyRotations.apply_tick(&mut tc);
-        let gate = &tc.ticks()[0].gates()[0];
+        let gate = &tc.ticks()[0].gate_batches()[0];
         assert_eq!(gate.gate_type, GateType::SX);
         assert!(gate.angles.is_empty());
     }
@@ -1232,7 +1489,7 @@ mod tests {
         let mut tc = TickCircuit::new();
         tc.tick().ry(Angle64::HALF_TURN, &[0]);
         SimplifyRotations.apply_tick(&mut tc);
-        let gate = &tc.ticks()[0].gates()[0];
+        let gate = &tc.ticks()[0].gate_batches()[0];
         assert_eq!(gate.gate_type, GateType::Y);
         assert!(gate.angles.is_empty());
     }
@@ -1242,7 +1499,7 @@ mod tests {
         let mut tc = TickCircuit::new();
         tc.tick().rzz(Angle64::QUARTER_TURN, &[(0, 1)]);
         SimplifyRotations.apply_tick(&mut tc);
-        let gate = &tc.ticks()[0].gates()[0];
+        let gate = &tc.ticks()[0].gate_batches()[0];
         assert_eq!(gate.gate_type, GateType::SZZ);
         assert!(gate.angles.is_empty());
     }
@@ -1252,10 +1509,14 @@ mod tests {
         let mut tc = TickCircuit::new();
         tc.tick().rzz(Angle64::HALF_TURN, &[(0, 1)]);
         SimplifyRotations.apply_tick(&mut tc);
-        let gates = tc.ticks()[0].gates();
-        assert_eq!(gates.len(), 2);
+        let gates = tc.ticks()[0].gate_batches();
+        assert_eq!(gates.len(), 1);
         assert_eq!(gates[0].gate_type, GateType::Z);
-        assert_eq!(gates[1].gate_type, GateType::Z);
+        assert_eq!(
+            gates[0].qubits.as_slice(),
+            &[QubitId::from(0), QubitId::from(1)]
+        );
+        assert_eq!(gates[0].num_gates(), 2);
     }
 
     #[test]
@@ -1263,10 +1524,14 @@ mod tests {
         let mut tc = TickCircuit::new();
         tc.tick().rxx(Angle64::HALF_TURN, &[(0, 1)]);
         SimplifyRotations.apply_tick(&mut tc);
-        let gates = tc.ticks()[0].gates();
-        assert_eq!(gates.len(), 2);
+        let gates = tc.ticks()[0].gate_batches();
+        assert_eq!(gates.len(), 1);
         assert_eq!(gates[0].gate_type, GateType::X);
-        assert_eq!(gates[1].gate_type, GateType::X);
+        assert_eq!(
+            gates[0].qubits.as_slice(),
+            &[QubitId::from(0), QubitId::from(1)]
+        );
+        assert_eq!(gates[0].num_gates(), 2);
     }
 
     #[test]
@@ -1274,7 +1539,7 @@ mod tests {
         let mut tc = TickCircuit::new();
         tc.tick().rz(Angle64::from_turn_ratio(1, 6), &[0]);
         SimplifyRotations.apply_tick(&mut tc);
-        let gate = &tc.ticks()[0].gates()[0];
+        let gate = &tc.ticks()[0].gate_batches()[0];
         assert_eq!(gate.gate_type, GateType::RZ);
         assert_eq!(gate.angles.len(), 1);
     }
@@ -1284,7 +1549,7 @@ mod tests {
         let mut tc = TickCircuit::new();
         tc.tick().h(&[0]);
         SimplifyRotations.apply_tick(&mut tc);
-        let gate = &tc.ticks()[0].gates()[0];
+        let gate = &tc.ticks()[0].gate_batches()[0];
         assert_eq!(gate.gate_type, GateType::H);
     }
 
@@ -1293,7 +1558,7 @@ mod tests {
         let mut tc = TickCircuit::new();
         tc.tick().rz(Angle64::from_turn_ratio(1, 8), &[0]);
         SimplifyRotations.apply_tick(&mut tc);
-        let gate = &tc.ticks()[0].gates()[0];
+        let gate = &tc.ticks()[0].gate_batches()[0];
         assert_eq!(gate.gate_type, GateType::T);
         assert!(gate.angles.is_empty());
     }
@@ -1508,13 +1773,12 @@ mod tests {
         let mut tick_ops: Vec<UnitaryRep> = Vec::new();
 
         for tick in tc.ticks() {
-            let gates = tick.gates();
-            if gates.is_empty() {
+            if tick.is_empty() {
                 continue;
             }
             let mut gate_ops: Vec<UnitaryRep> = Vec::new();
-            for gate in gates {
-                let op = gate_to_unitary(gate)?;
+            for gate in tick.iter_gate_batches() {
+                let op = gate_to_unitary(gate.as_gate())?;
                 gate_ops.push(op);
             }
             // Tensor all gates in this tick (they act on disjoint qubits).
@@ -1535,7 +1799,19 @@ mod tests {
 
     /// Convert a single `Gate` to an `UnitaryRep`.
     fn gate_to_unitary(gate: &pecos_core::Gate) -> Option<UnitaryRep> {
-        let q0 = gate.qubits.first().copied()?;
+        let arity = gate.gate_type.quantum_arity();
+        let mut ops = Vec::new();
+        for qubits in gate.qubits.chunks(arity) {
+            if qubits.len() != arity {
+                return None;
+            }
+            ops.push(gate_instance_to_unitary(gate, qubits)?);
+        }
+        ops.into_iter().reduce(|a, b| a & b)
+    }
+
+    fn gate_instance_to_unitary(gate: &pecos_core::Gate, qubits: &[QubitId]) -> Option<UnitaryRep> {
+        let q0 = qubits.first().copied()?;
         match gate.gate_type {
             GateType::H => Some(unitary_rep::H(q0)),
             GateType::X => Some(unitary_rep::X(q0)),
@@ -1562,38 +1838,38 @@ mod tests {
                 Some(unitary_rep::RZ(angle, q0))
             }
             GateType::CX => {
-                let q1 = gate.qubits.get(1).copied()?;
+                let q1 = qubits.get(1).copied()?;
                 Some(unitary_rep::CX(q0, q1))
             }
             GateType::CY => {
-                let q1 = gate.qubits.get(1).copied()?;
+                let q1 = qubits.get(1).copied()?;
                 Some(unitary_rep::CY(q0, q1))
             }
             GateType::CZ => {
-                let q1 = gate.qubits.get(1).copied()?;
+                let q1 = qubits.get(1).copied()?;
                 Some(unitary_rep::CZ(q0, q1))
             }
             GateType::RXX => {
-                let q1 = gate.qubits.get(1).copied()?;
+                let q1 = qubits.get(1).copied()?;
                 let angle = *gate.angles.first()?;
                 Some(unitary_rep::RXX(angle, q0, q1))
             }
             GateType::RYY => {
-                let q1 = gate.qubits.get(1).copied()?;
+                let q1 = qubits.get(1).copied()?;
                 let angle = *gate.angles.first()?;
                 Some(unitary_rep::RYY(angle, q0, q1))
             }
             GateType::RZZ => {
-                let q1 = gate.qubits.get(1).copied()?;
+                let q1 = qubits.get(1).copied()?;
                 let angle = *gate.angles.first()?;
                 Some(unitary_rep::RZZ(angle, q0, q1))
             }
             GateType::SZZ => {
-                let q1 = gate.qubits.get(1).copied()?;
+                let q1 = qubits.get(1).copied()?;
                 Some(unitary_rep::SZZ(q0, q1))
             }
             GateType::SZZdg => {
-                let q1 = gate.qubits.get(1).copied()?;
+                let q1 = qubits.get(1).copied()?;
                 Some(unitary_rep::SZZ(q0, q1).dg())
             }
             GateType::I | GateType::Idle => Some(unitary_rep::I(q0)),
@@ -1890,7 +2166,7 @@ mod tests {
         tc.tick();
         tc.ticks_mut()[0].add_gate(Gate::i(&[0]));
         RemoveIdentity.apply_tick(&mut tc);
-        assert!(tc.ticks()[0].gates().is_empty());
+        assert!(tc.ticks()[0].gate_batches().is_empty());
     }
 
     #[test]
@@ -1898,7 +2174,7 @@ mod tests {
         let mut tc = TickCircuit::new();
         tc.tick().rz(Angle64::ZERO, &[0]);
         RemoveIdentity.apply_tick(&mut tc);
-        assert!(tc.ticks()[0].gates().is_empty());
+        assert!(tc.ticks()[0].gate_batches().is_empty());
     }
 
     #[test]
@@ -1906,8 +2182,8 @@ mod tests {
         let mut tc = TickCircuit::new();
         tc.tick().rz(Angle64::QUARTER_TURN, &[0]);
         RemoveIdentity.apply_tick(&mut tc);
-        assert_eq!(tc.ticks()[0].gates().len(), 1);
-        assert_eq!(tc.ticks()[0].gates()[0].gate_type, GateType::RZ);
+        assert_eq!(tc.ticks()[0].gate_batches().len(), 1);
+        assert_eq!(tc.ticks()[0].gate_batches()[0].gate_type, GateType::RZ);
     }
 
     #[test]
@@ -1916,8 +2192,8 @@ mod tests {
         tc.tick().h(&[0]);
         tc.ticks_mut()[0].add_gate(Gate::i(&[1]));
         RemoveIdentity.apply_tick(&mut tc);
-        assert_eq!(tc.ticks()[0].gates().len(), 1);
-        assert_eq!(tc.ticks()[0].gates()[0].gate_type, GateType::H);
+        assert_eq!(tc.ticks()[0].gate_batches().len(), 1);
+        assert_eq!(tc.ticks()[0].gate_batches()[0].gate_type, GateType::H);
     }
 
     // ==================== RemoveIdentity DAG tests ====================
@@ -1966,8 +2242,8 @@ mod tests {
         tc.tick().h(&[0]);
         tc.tick().h(&[0]);
         CancelInverses.apply_tick(&mut tc);
-        assert!(tc.ticks()[0].gates().is_empty());
-        assert!(tc.ticks()[1].gates().is_empty());
+        assert!(tc.ticks()[0].gate_batches().is_empty());
+        assert!(tc.ticks()[1].gate_batches().is_empty());
     }
 
     #[test]
@@ -1976,8 +2252,8 @@ mod tests {
         tc.tick().x(&[0]);
         tc.tick().x(&[0]);
         CancelInverses.apply_tick(&mut tc);
-        assert!(tc.ticks()[0].gates().is_empty());
-        assert!(tc.ticks()[1].gates().is_empty());
+        assert!(tc.ticks()[0].gate_batches().is_empty());
+        assert!(tc.ticks()[1].gate_batches().is_empty());
     }
 
     #[test]
@@ -1987,8 +2263,8 @@ mod tests {
         tc.tick();
         tc.ticks_mut()[1].add_gate(Gate::sxdg(&[0]));
         CancelInverses.apply_tick(&mut tc);
-        assert!(tc.ticks()[0].gates().is_empty());
-        assert!(tc.ticks()[1].gates().is_empty());
+        assert!(tc.ticks()[0].gate_batches().is_empty());
+        assert!(tc.ticks()[1].gate_batches().is_empty());
     }
 
     #[test]
@@ -1998,8 +2274,8 @@ mod tests {
         tc.tick();
         tc.ticks_mut()[1].add_gate(Gate::tdg(&[0]));
         CancelInverses.apply_tick(&mut tc);
-        assert!(tc.ticks()[0].gates().is_empty());
-        assert!(tc.ticks()[1].gates().is_empty());
+        assert!(tc.ticks()[0].gate_batches().is_empty());
+        assert!(tc.ticks()[1].gate_batches().is_empty());
     }
 
     #[test]
@@ -2008,8 +2284,8 @@ mod tests {
         tc.tick().cx(&[(0, 1)]);
         tc.tick().cx(&[(0, 1)]);
         CancelInverses.apply_tick(&mut tc);
-        assert!(tc.ticks()[0].gates().is_empty());
-        assert!(tc.ticks()[1].gates().is_empty());
+        assert!(tc.ticks()[0].gate_batches().is_empty());
+        assert!(tc.ticks()[1].gate_batches().is_empty());
     }
 
     #[test]
@@ -2019,8 +2295,8 @@ mod tests {
         tc.tick().rz(angle, &[0]);
         tc.tick().rz(-angle, &[0]);
         CancelInverses.apply_tick(&mut tc);
-        assert!(tc.ticks()[0].gates().is_empty());
-        assert!(tc.ticks()[1].gates().is_empty());
+        assert!(tc.ticks()[0].gate_batches().is_empty());
+        assert!(tc.ticks()[1].gate_batches().is_empty());
     }
 
     #[test]
@@ -2034,7 +2310,7 @@ mod tests {
         tc.tick().h(&[0]);
         CancelInverses.apply_tick(&mut tc);
         for tick in tc.ticks() {
-            assert!(tick.gates().is_empty());
+            assert!(tick.gate_batches().is_empty());
         }
     }
 
@@ -2046,9 +2322,9 @@ mod tests {
         tc.tick().x(&[0]);
         tc.tick().h(&[0]);
         CancelInverses.apply_tick(&mut tc);
-        assert_eq!(tc.ticks()[0].gates().len(), 1);
-        assert_eq!(tc.ticks()[1].gates().len(), 1);
-        assert_eq!(tc.ticks()[2].gates().len(), 1);
+        assert_eq!(tc.ticks()[0].gate_batches().len(), 1);
+        assert_eq!(tc.ticks()[1].gate_batches().len(), 1);
+        assert_eq!(tc.ticks()[2].gate_batches().len(), 1);
     }
 
     #[test]
@@ -2057,8 +2333,8 @@ mod tests {
         tc.tick().h(&[0]);
         tc.tick().h(&[1]);
         CancelInverses.apply_tick(&mut tc);
-        assert_eq!(tc.ticks()[0].gates().len(), 1);
-        assert_eq!(tc.ticks()[1].gates().len(), 1);
+        assert_eq!(tc.ticks()[0].gate_batches().len(), 1);
+        assert_eq!(tc.ticks()[1].gate_batches().len(), 1);
     }
 
     // ==================== CancelInverses DAG tests ====================
@@ -2107,7 +2383,7 @@ mod tests {
         let gate = tc
             .ticks()
             .iter()
-            .flat_map(super::super::tick_circuit::Tick::gates)
+            .flat_map(super::super::tick_circuit::Tick::gate_batches)
             .next()
             .unwrap();
         assert_eq!(gate.gate_type, GateType::RZ);
@@ -2124,7 +2400,7 @@ mod tests {
         let gate = tc
             .ticks()
             .iter()
-            .flat_map(super::super::tick_circuit::Tick::gates)
+            .flat_map(super::super::tick_circuit::Tick::gate_batches)
             .next()
             .unwrap();
         assert_eq!(gate.gate_type, GateType::RZ);
@@ -2140,7 +2416,7 @@ mod tests {
         let gate = tc
             .ticks()
             .iter()
-            .flat_map(super::super::tick_circuit::Tick::gates)
+            .flat_map(super::super::tick_circuit::Tick::gate_batches)
             .next()
             .unwrap();
         assert_eq!(gate.gate_type, GateType::RZ);
@@ -2156,7 +2432,7 @@ mod tests {
         let gate = tc
             .ticks()
             .iter()
-            .flat_map(super::super::tick_circuit::Tick::gates)
+            .flat_map(super::super::tick_circuit::Tick::gate_batches)
             .next()
             .unwrap();
         assert_eq!(gate.gate_type, GateType::RZZ);
@@ -2298,20 +2574,20 @@ mod tests {
 
     // ==================== Pass effectiveness analysis ====================
 
-    /// Count total gates across all ticks.
-    fn count_gates(tc: &TickCircuit) -> usize {
-        tc.ticks().iter().map(|t| t.gates().len()).sum()
+    /// Count stored gate batches across all ticks.
+    fn count_gate_batches(tc: &TickCircuit) -> usize {
+        tc.ticks().iter().map(|t| t.gate_batches().len()).sum()
     }
 
-    /// Apply the full pipeline and return (before, after) gate counts.
+    /// Apply the full pipeline and return (before, after) gate-batch counts.
     fn pipeline_stats(tc: &mut TickCircuit) -> (usize, usize) {
-        let before = count_gates(tc);
+        let before = count_gate_batches(tc);
         MergeAdjacentRotations.apply_tick(tc);
         RemoveIdentity.apply_tick(tc);
         SimplifyRotations.apply_tick(tc);
         CancelInverses.apply_tick(tc);
         PeepholeOptimize.apply_tick(tc);
-        let after = count_gates(tc);
+        let after = count_gate_batches(tc);
         (before, after)
     }
 
@@ -2348,17 +2624,6 @@ mod tests {
 
         // -- Circuit 3: Inverse cancellation (from circuit composition) --
         let mut c3 = TickCircuit::new();
-        // Subcircuit A applies some basis change
-        c3.tick().h(&[0, 1]);
-        c3.tick().sx(&[0]).t(&[1]);
-        c3.tick().cx(&[(0, 1)]);
-        // Subcircuit B undoes the basis change then does something else
-        c3.tick().cx(&[(0, 1)]);
-        c3.ticks_mut()[3].add_gate(Gate::sxdg(&[0]));
-        c3.ticks_mut()[3].add_gate(Gate::tdg(&[1]));
-        // Wait, this won't cancel because CX is between SX and SXdg on different ticks.
-        // Let me restructure: undo in reverse order
-        let mut c3 = TickCircuit::new();
         c3.tick().h(&[0, 1]);
         c3.tick().t(&[0]).sx(&[1]);
         c3.tick().cx(&[(0, 1)]);
@@ -2509,7 +2774,7 @@ mod tests {
         let gates: Vec<&Gate> = tc
             .ticks()
             .iter()
-            .flat_map(super::super::tick_circuit::Tick::gates)
+            .flat_map(super::super::tick_circuit::Tick::gate_batches)
             .collect();
         assert_eq!(gates.len(), 1);
         assert_eq!(gates[0].gate_type, GateType::CZ);
@@ -2527,7 +2792,7 @@ mod tests {
         let gates: Vec<&Gate> = tc
             .ticks()
             .iter()
-            .flat_map(super::super::tick_circuit::Tick::gates)
+            .flat_map(super::super::tick_circuit::Tick::gate_batches)
             .collect();
         assert_eq!(gates.len(), 1);
         assert_eq!(gates[0].gate_type, GateType::CX);
@@ -2546,7 +2811,7 @@ mod tests {
         let gates: Vec<&Gate> = tc
             .ticks()
             .iter()
-            .flat_map(super::super::tick_circuit::Tick::gates)
+            .flat_map(super::super::tick_circuit::Tick::gate_batches)
             .collect();
         assert_eq!(gates.len(), 3); // unchanged
     }
@@ -2564,7 +2829,7 @@ mod tests {
         let gates: Vec<&Gate> = tc
             .ticks()
             .iter()
-            .flat_map(super::super::tick_circuit::Tick::gates)
+            .flat_map(super::super::tick_circuit::Tick::gate_batches)
             .collect();
         assert_eq!(gates.len(), 3); // X, CZ, Z
         assert_eq!(gates[0].gate_type, GateType::X);
@@ -2572,6 +2837,126 @@ mod tests {
         assert_eq!(gates[2].gate_type, GateType::Z);
     }
 
+    #[test]
+    fn peephole_tick_preserves_metadata_when_splitting_batched_commands() {
+        let mut tc = TickCircuit::new();
+        tc.tick().h(&[1]);
+        tc.tick()
+            .cx(&[(0, 1), (2, 3)])
+            .meta("calibration", Attribute::String("entangler".into()));
+        tc.tick().h(&[1]);
+
+        PeepholeOptimize.apply_tick(&mut tc);
+
+        let middle = tc
+            .ticks()
+            .iter()
+            .find(|tick| !tick.gate_batches().is_empty())
+            .expect("peephole result should keep the middle tick");
+        assert_eq!(middle.len(), 2);
+        assert_eq!(middle.gate_count(), 2);
+
+        let mut saw_rewritten = false;
+        let mut saw_untouched = false;
+        for gate in middle.iter_gate_batches() {
+            assert_eq!(
+                gate.get_attr("calibration"),
+                Some(&Attribute::String("entangler".into()))
+            );
+            match gate.gate_type {
+                GateType::CZ => {
+                    saw_rewritten = true;
+                    assert_eq!(
+                        gate.qubits.as_slice(),
+                        &[QubitId::from(0), QubitId::from(1)]
+                    );
+                }
+                GateType::CX => {
+                    saw_untouched = true;
+                    assert_eq!(
+                        gate.qubits.as_slice(),
+                        &[QubitId::from(2), QubitId::from(3)]
+                    );
+                }
+                other => panic!("unexpected gate after peephole optimization: {other:?}"),
+            }
+        }
+        assert!(saw_rewritten);
+        assert!(saw_untouched);
+    }
+
+    #[test]
+    fn split_batched_tick_commands_preserves_payloads_attrs_and_counters() {
+        let mut tc = TickCircuit::new();
+        let initial_refs = tc.tick().mz(&[0, 1]);
+        assert_eq!(initial_refs[0].record_idx, 0);
+        assert_eq!(initial_refs[1].record_idx, 1);
+        tc.get_tick_mut(0).unwrap().set_gate_attr(
+            0,
+            "role",
+            Attribute::String("measurement".into()),
+        );
+        tc.tick()
+            .cx(&[(2, 3), (4, 5)])
+            .meta("role", Attribute::String("entangler".into()));
+
+        split_batched_tick_commands(&mut tc);
+
+        assert_eq!(tc.num_ticks(), 2);
+        assert_eq!(tc.next_tick_index(), 2);
+        assert_eq!(tc.num_measurements(), 2);
+
+        let meas_tick = tc.get_tick(0).unwrap();
+        assert_eq!(meas_tick.len(), 2);
+        assert_eq!(meas_tick.gate_count(), 2);
+        assert_eq!(
+            meas_tick.gate_batches()[0].qubits.as_slice(),
+            &[QubitId::from(0)]
+        );
+        assert_eq!(
+            meas_tick.gate_batches()[0].meas_ids.as_slice(),
+            &[MeasId(0)]
+        );
+        assert_eq!(
+            meas_tick.gate_batches()[1].qubits.as_slice(),
+            &[QubitId::from(1)]
+        );
+        assert_eq!(
+            meas_tick.gate_batches()[1].meas_ids.as_slice(),
+            &[MeasId(1)]
+        );
+        for batch in meas_tick.iter_gate_batches() {
+            assert_eq!(
+                batch.get_attr("role"),
+                Some(&Attribute::String("measurement".into()))
+            );
+        }
+
+        let entangler_tick = tc.get_tick(1).unwrap();
+        assert_eq!(entangler_tick.len(), 2);
+        assert_eq!(entangler_tick.gate_count(), 2);
+        assert_eq!(
+            entangler_tick.gate_batches()[0].qubits.as_slice(),
+            &[QubitId::from(2), QubitId::from(3)]
+        );
+        assert_eq!(
+            entangler_tick.gate_batches()[1].qubits.as_slice(),
+            &[QubitId::from(4), QubitId::from(5)]
+        );
+        for batch in entangler_tick.iter_gate_batches() {
+            assert_eq!(
+                batch.get_attr("role"),
+                Some(&Attribute::String("entangler".into()))
+            );
+        }
+
+        let later_refs = tc.tick().mz(&[6]);
+        assert_eq!(later_refs[0].record_idx, 2);
+        assert_eq!(later_refs[0].meas_id, MeasId(2));
+        assert_eq!(tc.next_tick_index(), 3);
+        assert_eq!(tc.num_measurements(), 3);
+    }
+
     #[test]
     fn peephole_tick_multiple_patterns() {
         // Two independent H-CX-H patterns
@@ -2583,7 +2968,7 @@ mod tests {
         let gates: Vec<&Gate> = tc
             .ticks()
             .iter()
-            .flat_map(super::super::tick_circuit::Tick::gates)
+            .flat_map(super::super::tick_circuit::Tick::gate_batches)
             .collect();
         assert_eq!(gates.len(), 2);
         assert!(gates.iter().all(|g| g.gate_type == GateType::CZ));
@@ -2904,8 +3289,8 @@ mod tests {
             .then(MergeAdjacentRotations)
             .then(SimplifyRotations);
         pipeline.apply_tick(&mut tc);
-        assert_eq!(count_gates(&tc), 1);
-        assert_eq!(tc.ticks()[0].gates()[0].gate_type, GateType::SZ);
+        assert_eq!(count_gate_batches(&tc), 1);
+        assert_eq!(tc.ticks()[0].gate_batches()[0].gate_type, GateType::SZ);
     }
 
     #[test]
@@ -2929,7 +3314,7 @@ mod tests {
             .then(CancelInverses);
         pipeline.apply_tick(&mut tc);
         // PZ stays, T and both RZs absorbed (after PZ), H+H cancelled, MZ stays
-        assert_eq!(count_gates(&tc), 2); // PZ + MZ
+        assert_eq!(count_gate_batches(&tc), 2); // PZ + MZ
     }
 
     #[test]
@@ -2953,7 +3338,7 @@ mod tests {
         let mut tc = TickCircuit::new();
         tc.tick().h(&[0]);
         pipeline.apply_tick(&mut tc);
-        assert_eq!(count_gates(&tc), 1);
+        assert_eq!(count_gate_batches(&tc), 1);
     }
 
     // ==================== CompactTicks tests ====================
@@ -2978,8 +3363,8 @@ mod tests {
         tc.tick().x(&[0]);
         CompactTicks.apply_tick(&mut tc);
         assert_eq!(tc.num_ticks(), 2);
-        assert_eq!(tc.ticks()[0].gates()[0].gate_type, GateType::H);
-        assert_eq!(tc.ticks()[1].gates()[0].gate_type, GateType::X);
+        assert_eq!(tc.ticks()[0].gate_batches()[0].gate_type, GateType::H);
+        assert_eq!(tc.ticks()[1].gate_batches()[0].gate_type, GateType::X);
     }
 
     #[test]
@@ -2994,7 +3379,7 @@ mod tests {
         assert_eq!(tc.num_ticks(), 3);
         CompactTicks.apply_tick(&mut tc);
         assert_eq!(tc.num_ticks(), 1);
-        assert_eq!(tc.ticks()[0].gates()[0].gate_type, GateType::X);
+        assert_eq!(tc.ticks()[0].gate_batches()[0].gate_type, GateType::X);
     }
 
     #[test]
@@ -3042,9 +3427,9 @@ mod tests {
         tc.tick().sz(&[0]);
         CompactTicks.apply_tick(&mut tc);
         assert_eq!(tc.num_ticks(), 3); // all same qubit, no compaction
-        assert_eq!(tc.ticks()[0].gates()[0].gate_type, GateType::H);
-        assert_eq!(tc.ticks()[1].gates()[0].gate_type, GateType::T);
-        assert_eq!(tc.ticks()[2].gates()[0].gate_type, GateType::SZ);
+        assert_eq!(tc.ticks()[0].gate_batches()[0].gate_type, GateType::H);
+        assert_eq!(tc.ticks()[1].gate_batches()[0].gate_type, GateType::T);
+        assert_eq!(tc.ticks()[2].gate_batches()[0].gate_type, GateType::SZ);
     }
 
     #[test]
@@ -3065,6 +3450,6 @@ mod tests {
         // After absorb+cancel: PZ(0,1), X(0), MZ(0,1)
         // X(0) can't merge with PZ (qubit 0 busy) or MZ (qubit 0 busy).
         assert_eq!(tc.num_ticks(), 3);
-        assert_eq!(count_gates(&tc), 3);
+        assert_eq!(count_gate_batches(&tc), 3);
     }
 }
diff --git a/crates/pecos-quantum/src/pauli_group.rs b/crates/pecos-quantum/src/pauli_group.rs
index bd96fb70f..e3e471f51 100644
--- a/crates/pecos-quantum/src/pauli_group.rs
+++ b/crates/pecos-quantum/src/pauli_group.rs
@@ -39,7 +39,7 @@
 //!
 //! ```
 //! use pecos_quantum::PauliGroup;
-//! use pecos_core::pauli::constructors::*;
+//! use pecos_core::pauli::*;
 //! use pecos_core::pauli::algebra::i;
 //!
 //! // Generators with imaginary phases are allowed
@@ -105,7 +105,7 @@ fn generator_order(phase: QuarterPhase) -> u32 {
 ///
 /// ```
 /// use pecos_quantum::PauliGroup;
-/// use pecos_core::pauli::constructors::*;
+/// use pecos_core::pauli::*;
 /// use pecos_core::pauli::algebra::i;
 ///
 /// // A group with an imaginary-phase generator
@@ -265,15 +265,15 @@ impl PauliGroup {
         for (row_idx, generator) in self.inner.paulis().iter().enumerate() {
             for q in generator.x_positions() {
                 if q < n {
-                    mat.rows[row_idx][q] = 1;
+                    mat.set(row_idx, q, 1);
                 }
             }
             for q in generator.z_positions() {
                 if q < n {
-                    mat.rows[row_idx][n + q] = 1;
+                    mat.set(row_idx, n + q, 1);
                 }
             }
-            mat.rows[row_idx][2 * n + row_idx] = 1;
+            mat.set(row_idx, 2 * n + row_idx, 1);
         }
 
         let (reduced, pivots) = mat.row_reduce();
@@ -295,7 +295,7 @@ impl PauliGroup {
         for (row_idx, &pivot_col) in pivots.iter().enumerate() {
             if target[pivot_col] == 1 {
                 for (col, t) in target.iter_mut().enumerate() {
-                    *t ^= reduced.rows[row_idx][col];
+                    *t ^= reduced.get(row_idx, col);
                 }
             }
         }
@@ -453,9 +453,11 @@ impl PauliGroup {
         self.inner.to_symplectic_matrix()
     }
 
-    /// Returns the commutation matrix (always all-true for a valid group).
+    /// Returns the pairwise anticommutation matrix.
+    ///
+    /// This is always all-zero for a valid commuting group.
     #[must_use]
-    pub fn commutation_matrix(&self) -> Vec<Vec<bool>> {
+    pub fn commutation_matrix(&self) -> F2Matrix {
         self.inner.commutation_matrix()
     }
 
@@ -682,7 +684,7 @@ impl fmt::Display for PauliGroup {
 mod tests {
     use super::*;
     use pecos_core::pauli::algebra::i;
-    use pecos_core::pauli::constructors::*;
+    use pecos_core::pauli::*;
 
     // --- Construction and basic properties ---
 
@@ -1164,14 +1166,15 @@ mod tests {
     // --- commutation_matrix for valid group ---
 
     #[test]
-    fn commutation_matrix_all_true() {
+    fn commutation_matrix_all_zero() {
         let group = PauliGroup::new(vec![X(0), Z(1), X(2)]).unwrap();
         let mat = group.commutation_matrix();
-        for row in &mat {
-            for &val in row {
-                assert!(
-                    val,
-                    "commutation matrix should be all-true for abelian group"
+        for row in 0..mat.num_rows() {
+            for col in 0..mat.num_cols() {
+                assert_eq!(
+                    mat.get(row, col),
+                    0,
+                    "anticommutation matrix should be all-zero for abelian group"
                 );
             }
         }
diff --git a/crates/pecos-quantum/src/pauli_sequence.rs b/crates/pecos-quantum/src/pauli_sequence.rs
index 0c20c31be..355d5fe87 100644
--- a/crates/pecos-quantum/src/pauli_sequence.rs
+++ b/crates/pecos-quantum/src/pauli_sequence.rs
@@ -30,7 +30,7 @@
 //!
 //! ```
 //! use pecos_quantum::PauliSequence;
-//! use pecos_core::pauli::constructors::*;
+//! use pecos_core::pauli::*;
 //!
 //! let paulis = PauliSequence::new(vec![
 //!     Zs(&[0, 1]),
@@ -50,30 +50,45 @@ use pecos_core::{ParsePauliStringError, PauliOperator, PauliString};
 use std::fmt;
 use std::str::FromStr;
 
-/// A binary matrix over GF(2), represented row-major.
+/// A binary matrix over GF(2), represented row-major as packed `u64` words.
 ///
 /// Each row is a 2n-bit vector representing a Pauli string in the binary
 /// symplectic representation: `(x_0, ..., x_{n-1} | z_0, ..., z_{n-1})`
 /// where `x_q = 1` if qubit q has X or Y, and `z_q = 1` if qubit q has Z or Y.
-///
-// TODO: Each bit is stored as a full `u8`. For large codes, consider packing
-// into `u64` words or using a bitvec for 8x memory reduction.
 #[derive(Debug, Clone, PartialEq, Eq)]
 pub struct F2Matrix {
-    pub(crate) rows: Vec<Vec<u8>>,
+    rows: Vec<Vec<u64>>,
     num_cols: usize,
 }
 
 impl F2Matrix {
+    const WORD_BITS: usize = u64::BITS as usize;
+
     /// Creates a new F2 matrix with the given dimensions, initialized to zero.
     #[must_use]
     pub fn zeros(num_rows: usize, num_cols: usize) -> Self {
         Self {
-            rows: vec![vec![0; num_cols]; num_rows],
+            rows: vec![vec![0; Self::num_words(num_cols)]; num_rows],
             num_cols,
         }
     }
 
+    /// Creates an F2 matrix from dense 0/1 rows.
+    ///
+    /// # Panics
+    ///
+    /// Panics if the rows do not all have the same length, or if any entry is
+    /// not 0 or 1.
+    #[must_use]
+    pub fn from_rows(rows: Vec<Vec<u8>>) -> Self {
+        let num_cols = rows.first().map_or(0, Vec::len);
+        let mut mat = Self::zeros(rows.len(), num_cols);
+        for (i, row) in rows.into_iter().enumerate() {
+            mat.set_row(i, &row);
+        }
+        mat
+    }
+
     /// Returns the number of rows.
     #[must_use]
     pub fn num_rows(&self) -> usize {
@@ -88,32 +103,98 @@ impl F2Matrix {
 
     /// Returns a reference to the rows.
     #[must_use]
-    pub fn rows(&self) -> &[Vec<u8>] {
-        &self.rows
+    pub fn rows(&self) -> Vec<Vec<u8>> {
+        (0..self.num_rows()).map(|i| self.row(i)).collect()
+    }
+
+    /// Returns a dense copy of a specific row.
+    #[must_use]
+    pub fn row(&self, i: usize) -> Vec<u8> {
+        (0..self.num_cols).map(|col| self.get(i, col)).collect()
     }
 
-    /// Returns a reference to a specific row.
+    /// Returns the packed words for a row.
     #[must_use]
-    pub fn row(&self, i: usize) -> &[u8] {
+    pub(crate) fn row_words(&self, i: usize) -> &[u64] {
         &self.rows[i]
     }
 
-    /// Returns a mutable reference to a specific row.
-    pub fn row_mut(&mut self, i: usize) -> &mut Vec<u8> {
-        &mut self.rows[i]
+    /// Returns a single matrix entry.
+    ///
+    /// # Panics
+    ///
+    /// Panics if `row` or `col` is out of bounds.
+    #[must_use]
+    pub fn get(&self, row: usize, col: usize) -> u8 {
+        assert!(col < self.num_cols);
+        let (word, mask) = Self::word_mask(col);
+        u8::from((self.rows[row][word] & mask) != 0)
+    }
+
+    /// Sets a single matrix entry.
+    ///
+    /// # Panics
+    ///
+    /// Panics if `row` or `col` is out of bounds, or if `value` is not 0 or 1.
+    pub fn set(&mut self, row: usize, col: usize, value: u8) {
+        assert!(col < self.num_cols);
+        assert!(value <= 1, "F2Matrix entries must be 0 or 1");
+        let (word, mask) = Self::word_mask(col);
+        if value == 0 {
+            self.rows[row][word] &= !mask;
+        } else {
+            self.rows[row][word] |= mask;
+        }
+    }
+
+    /// Replaces one row from a dense 0/1 slice.
+    ///
+    /// # Panics
+    ///
+    /// Panics if the row length does not match `num_cols`, or if any entry is
+    /// not 0 or 1.
+    pub fn set_row(&mut self, row: usize, bits: &[u8]) {
+        assert_eq!(bits.len(), self.num_cols);
+        self.rows[row].fill(0);
+        for (col, &bit) in bits.iter().enumerate() {
+            if bit != 0 {
+                assert_eq!(bit, 1, "F2Matrix entries must be 0 or 1");
+                self.set(row, col, 1);
+            }
+        }
     }
 
     /// Checks if a row is all zeros.
     #[must_use]
     pub fn is_zero_row(&self, i: usize) -> bool {
-        self.rows[i].iter().all(|&b| b == 0)
+        self.rows[i].iter().all(|&word| word == 0)
     }
 
     /// XORs row `src` into row `dst` (row[dst] ^= row[src]).
     fn xor_row(&mut self, dst: usize, src: usize) {
-        // Avoid borrow issues by doing index operations
-        for col in 0..self.num_cols {
-            self.rows[dst][col] ^= self.rows[src][col];
+        if dst == src {
+            self.rows[dst].fill(0);
+            return;
+        }
+        let src_row = self.rows[src].clone();
+        for (dst_word, src_word) in self.rows[dst].iter_mut().zip(src_row) {
+            *dst_word ^= src_word;
+        }
+        self.clear_unused_bits(dst);
+    }
+
+    fn xor_row_into_dense(&self, row: usize, dense: &mut [u8]) {
+        assert_eq!(dense.len(), self.num_cols);
+        for word_idx in 0..self.rows[row].len() {
+            let mut word = self.rows[row][word_idx];
+            while word != 0 {
+                let bit = word.trailing_zeros() as usize;
+                let col = word_idx * Self::WORD_BITS + bit;
+                if col < self.num_cols {
+                    dense[col] ^= 1;
+                }
+                word &= word - 1;
+            }
         }
     }
 
@@ -122,6 +203,40 @@ impl F2Matrix {
         self.rows.swap(a, b);
     }
 
+    fn num_words(num_cols: usize) -> usize {
+        num_cols.div_ceil(Self::WORD_BITS)
+    }
+
+    fn word_mask(col: usize) -> (usize, u64) {
+        let word = col / Self::WORD_BITS;
+        let bit = col % Self::WORD_BITS;
+        (word, 1u64 << bit)
+    }
+
+    fn last_word_mask(&self) -> u64 {
+        let rem = self.num_cols % Self::WORD_BITS;
+        if rem == 0 {
+            u64::MAX
+        } else {
+            (1u64 << rem) - 1
+        }
+    }
+
+    fn clear_unused_bits(&mut self, row: usize) {
+        if self.num_cols == 0 {
+            return;
+        }
+        let mask = self.last_word_mask();
+        if let Some(last) = self.rows[row].last_mut() {
+            *last &= mask;
+        }
+    }
+
+    fn row_has_bit(&self, row: usize, col: usize) -> bool {
+        let (word, mask) = Self::word_mask(col);
+        (self.rows[row][word] & mask) != 0
+    }
+
     /// Performs Gaussian elimination over GF(2), returning the row echelon form
     /// and the pivot column positions.
     ///
@@ -137,7 +252,7 @@ impl F2Matrix {
             // Find a row with a 1 in this column at or below pivot_row
             let mut found = None;
             for row in pivot_row..mat.num_rows() {
-                if mat.rows[row][col] == 1 {
+                if mat.row_has_bit(row, col) {
                     found = Some(row);
                     break;
                 }
@@ -152,7 +267,7 @@ impl F2Matrix {
 
             // Eliminate all other rows with a 1 in this column
             for row in 0..mat.num_rows() {
-                if row != pivot_row && mat.rows[row][col] == 1 {
+                if row != pivot_row && mat.row_has_bit(row, col) {
                     mat.xor_row(row, pivot_row);
                 }
             }
@@ -169,7 +284,7 @@ impl F2Matrix {
     pub fn identity(n: usize) -> Self {
         let mut mat = Self::zeros(n, n);
         for i in 0..n {
-            mat.rows[i][i] = 1;
+            mat.set(i, i, 1);
         }
         mat
     }
@@ -188,9 +303,9 @@ impl F2Matrix {
         let mut aug = Self::zeros(n, 2 * n);
         for i in 0..n {
             for j in 0..n {
-                aug.rows[i][j] = self.rows[i][j];
+                aug.set(i, j, self.get(i, j));
             }
-            aug.rows[i][n + i] = 1;
+            aug.set(i, n + i, 1);
         }
 
         // Row-reduce the augmented matrix.
@@ -199,7 +314,7 @@ impl F2Matrix {
             // Find pivot in this column at or below the diagonal
             let mut found = None;
             for row in col..n {
-                if aug.rows[row][col] == 1 {
+                if aug.row_has_bit(row, col) {
                     found = Some(row);
                     break;
                 }
@@ -212,7 +327,7 @@ impl F2Matrix {
 
             // Eliminate all other rows
             for row in 0..n {
-                if row != col && aug.rows[row][col] == 1 {
+                if row != col && aug.row_has_bit(row, col) {
                     aug.xor_row(row, col);
                 }
             }
@@ -221,7 +336,9 @@ impl F2Matrix {
         // Extract the inverse from the right half
         let mut inv = Self::zeros(n, n);
         for i in 0..n {
-            inv.rows[i] = aug.rows[i][n..2 * n].to_vec();
+            for j in 0..n {
+                inv.set(i, j, aug.get(i, n + j));
+            }
         }
         Some(inv)
     }
@@ -237,13 +354,16 @@ impl F2Matrix {
         let m = self.num_rows();
         let p = other.num_cols;
         let mut result = Self::zeros(m, p);
+        let other_t = other.transpose();
         for i in 0..m {
             for j in 0..p {
-                let mut sum = 0u8;
-                for k in 0..self.num_cols {
-                    sum ^= self.rows[i][k] & other.rows[k][j];
+                let mut parity = 0u32;
+                for (a, b) in self.rows[i].iter().zip(other_t.row_words(j)) {
+                    parity ^= (a & b).count_ones() & 1;
+                }
+                if parity != 0 {
+                    result.set(i, j, 1);
                 }
-                result.rows[i][j] = sum;
             }
         }
         result
@@ -257,7 +377,7 @@ impl F2Matrix {
         let mut result = Self::zeros(n, m);
         for i in 0..m {
             for j in 0..n {
-                result.rows[j][i] = self.rows[i][j];
+                result.set(j, i, self.get(i, j));
             }
         }
         result
@@ -275,7 +395,7 @@ impl F2Matrix {
         let mut aug = Self::zeros(m, n + n);
         for i in 0..m {
             for j in 0..n {
-                aug.rows[i][j] = self.rows[i][j];
+                aug.set(i, j, self.get(i, j));
             }
         }
         // We actually need to work with the transpose to find the right kernel.
@@ -287,12 +407,12 @@ impl F2Matrix {
         let mut at = Self::zeros(n, m + n);
         for i in 0..m {
             for j in 0..n {
-                at.rows[j][i] = self.rows[i][j];
+                at.set(j, i, self.get(i, j));
             }
         }
         // Augment with identity in the right block
         for j in 0..n {
-            at.rows[j][m + j] = 1;
+            at.set(j, m + j, 1);
         }
 
         // Row-reduce A^T
@@ -300,11 +420,11 @@ impl F2Matrix {
 
         // Rows that are zero in the A^T part (columns 0..m) give kernel vectors
         // from the identity part (columns m..m+n).
-        let mut basis = Vec::new();
+        let mut basis: Vec<Vec<u8>> = Vec::new();
         for i in 0..n {
-            if reduced.rows[i][..m].iter().all(|&b| b == 0) {
+            if (0..m).all(|col| reduced.get(i, col) == 0) {
                 // This row's right block is a kernel vector
-                basis.push(reduced.rows[i][m..m + n].to_vec());
+                basis.push((m..m + n).map(|col| reduced.get(i, col)).collect());
             }
         }
 
@@ -316,20 +436,14 @@ impl F2Matrix {
 
         // Handle overcounting: only keep linearly independent vectors
         if basis.len() > 1 {
-            let check = Self {
-                rows: basis.clone(),
-                num_cols: n,
-            };
+            let check = Self::from_rows(basis.clone());
             let (_, _ind_pivots) = check.row_reduce();
             // The first ind_pivots.len() rows of the reduced form are independent
             // but we want the original basis vectors. Since we sorted, just take
             // the independent count. Actually, let's re-reduce properly.
             let (reduced_basis, _) = check.row_reduce();
-            basis = reduced_basis
-                .rows
-                .into_iter()
-                .filter(|r| r.iter().any(|&b| b != 0))
-                .collect();
+            basis = reduced_basis.rows();
+            basis.retain(|r| r.iter().any(|&b| b != 0));
         }
 
         basis
@@ -338,17 +452,17 @@ impl F2Matrix {
 
 impl fmt::Display for F2Matrix {
     fn fmt(&self, f: &mut fmt::Formatter<'_>) -> fmt::Result {
-        for (i, row) in self.rows.iter().enumerate() {
+        for i in 0..self.num_rows() {
             if i > 0 {
                 writeln!(f)?;
             }
             // Show the X block and Z block separated by |
             let n = self.num_cols / 2;
-            for (j, &bit) in row.iter().enumerate() {
+            for j in 0..self.num_cols {
                 if j == n {
                     write!(f, "|")?;
                 }
-                write!(f, "{bit}")?;
+                write!(f, "{}", self.get(i, j))?;
             }
         }
         Ok(())
@@ -374,7 +488,7 @@ impl fmt::Display for F2Matrix {
 ///
 /// ```
 /// use pecos_quantum::PauliSequence;
-/// use pecos_core::pauli::constructors::*;
+/// use pecos_core::pauli::*;
 /// use pecos_core::PauliOperator;
 ///
 /// let gens = PauliSequence::new(vec![
@@ -501,10 +615,10 @@ impl PauliSequence {
 
         for (row_idx, generator) in self.paulis.iter().enumerate() {
             for q in generator.x_positions() {
-                mat.rows[row_idx][q] = 1;
+                mat.set(row_idx, q, 1);
             }
             for q in generator.z_positions() {
-                mat.rows[row_idx][n + q] = 1;
+                mat.set(row_idx, n + q, 1);
             }
         }
 
@@ -519,7 +633,7 @@ impl PauliSequence {
     ///
     /// ```
     /// use pecos_quantum::PauliSequence;
-    /// use pecos_core::pauli::constructors::*;
+    /// use pecos_core::pauli::*;
     ///
     /// // Two independent generators
     /// let gens = PauliSequence::new(vec![Zs(&[0, 1]), Zs(&[1, 2])]);
@@ -545,7 +659,7 @@ impl PauliSequence {
     ///
     /// ```
     /// use pecos_quantum::PauliSequence;
-    /// use pecos_core::pauli::constructors::*;
+    /// use pecos_core::pauli::*;
     ///
     /// let gens = PauliSequence::new(vec![Zs(&[0, 1]), Zs(&[1, 2])]);
     ///
@@ -583,9 +697,7 @@ impl PauliSequence {
         // Eliminate the target using the reduced generators' pivots
         for (row_idx, &pivot_col) in pivots.iter().enumerate() {
             if target[pivot_col] == 1 {
-                for (col, t) in target.iter_mut().enumerate() {
-                    *t ^= reduced.rows[row_idx][col];
-                }
+                reduced.xor_row_into_dense(row_idx, &mut target);
             }
         }
 
@@ -614,12 +726,12 @@ impl PauliSequence {
 
         for (row_idx, generator) in self.paulis.iter().enumerate() {
             for q in generator.x_positions() {
-                mat.rows[row_idx][q] = 1;
+                mat.set(row_idx, q, 1);
             }
             for q in generator.z_positions() {
-                mat.rows[row_idx][n + q] = 1;
+                mat.set(row_idx, n + q, 1);
             }
-            mat.rows[row_idx][2 * n + row_idx] = 1;
+            mat.set(row_idx, 2 * n + row_idx, 1);
         }
 
         let (reduced, pivots) = mat.row_reduce();
@@ -636,9 +748,7 @@ impl PauliSequence {
         // Eliminate the target using the reduced rows
         for (row_idx, &pivot_col) in pivots.iter().enumerate() {
             if target[pivot_col] == 1 {
-                for (col, t) in target.iter_mut().enumerate() {
-                    *t ^= reduced.rows[row_idx][col];
-                }
+                reduced.xor_row_into_dense(row_idx, &mut target);
             }
         }
 
@@ -663,7 +773,7 @@ impl PauliSequence {
     ///
     /// ```
     /// use pecos_quantum::PauliSequence;
-    /// use pecos_core::pauli::constructors::*;
+    /// use pecos_core::pauli::*;
     ///
     /// // Commuting generators
     /// let gens = PauliSequence::new(vec![Zs(&[0, 1]), Zs(&[1, 2])]);
@@ -685,25 +795,63 @@ impl PauliSequence {
         true
     }
 
-    /// Returns the commutation matrix.
+    /// Returns the pairwise anticommutation matrix.
     ///
-    /// `result[i][j]` is `true` if entries `i` and `j` commute, `false` if they anticommute.
-    /// The diagonal is always `true` (every operator commutes with itself).
+    /// Entry `(i, j)` is `1` if entries `i` and `j` anticommute, and `0` if
+    /// they commute. The diagonal is always zero.
     #[must_use]
-    #[allow(clippy::needless_range_loop)] // symmetric update requires indexing both [i][j] and [j][i]
-    pub fn commutation_matrix(&self) -> Vec<Vec<bool>> {
+    pub fn commutation_matrix(&self) -> F2Matrix {
         let k = self.paulis.len();
-        let mut matrix = vec![vec![true; k]; k];
+        let n = self.num_qubits();
+        let (x_rows, z_rows) = self.to_packed_xz_rows(n);
+        let mut matrix = F2Matrix::zeros(k, k);
         for i in 0..k {
             for j in (i + 1)..k {
-                let commutes = self.paulis[i].commutes_with(&self.paulis[j]);
-                matrix[i][j] = commutes;
-                matrix[j][i] = commutes;
+                if symplectic_inner_product(&x_rows[i], &z_rows[i], &x_rows[j], &z_rows[j]) != 0 {
+                    matrix.set(i, j, 1);
+                    matrix.set(j, i, 1);
+                }
             }
         }
         matrix
     }
 
+    /// Greedily partitions the sequence into mutually commuting groups.
+    ///
+    /// The returned groups preserve the input order within each group. This is
+    /// a graph-coloring heuristic on the anticommutation graph, so it is not
+    /// guaranteed to produce the minimum possible number of groups.
+    #[must_use]
+    pub fn group_commuting(&self) -> Vec<PauliSequence> {
+        let anticommutation = self.commutation_matrix();
+        let mut groups: Vec<Vec<usize>> = Vec::new();
+
+        'next_pauli: for pauli_idx in 0..self.paulis.len() {
+            for group in &mut groups {
+                if group
+                    .iter()
+                    .all(|&other_idx| anticommutation.get(pauli_idx, other_idx) == 0)
+                {
+                    group.push(pauli_idx);
+                    continue 'next_pauli;
+                }
+            }
+            groups.push(vec![pauli_idx]);
+        }
+
+        groups
+            .into_iter()
+            .map(|group| {
+                PauliSequence::new(
+                    group
+                        .into_iter()
+                        .map(|idx| self.paulis[idx].clone())
+                        .collect(),
+                )
+            })
+            .collect()
+    }
+
     /// Returns the sequence in row-reduced form.
     ///
     /// This returns a new `PauliSequence` where the Pauli strings are independent
@@ -722,7 +870,7 @@ impl PauliSequence {
         for col in 0..mat.num_cols {
             let mut found = None;
             for row in pivot_row..k {
-                if mat.rows[row][col] == 1 {
+                if mat.get(row, col) == 1 {
                     found = Some(row);
                     break;
                 }
@@ -736,7 +884,7 @@ impl PauliSequence {
             paulis.swap(pivot_row, found_row);
 
             for row in 0..k {
-                if row != pivot_row && mat.rows[row][col] == 1 {
+                if row != pivot_row && mat.get(row, col) == 1 {
                     mat.xor_row(row, pivot_row);
                     let pivot_ps = paulis[pivot_row].clone();
                     paulis[row] = paulis[row].clone() * pivot_ps;
@@ -760,7 +908,7 @@ impl PauliSequence {
     ///
     /// ```
     /// use pecos_quantum::PauliSequence;
-    /// use pecos_core::pauli::constructors::*;
+    /// use pecos_core::pauli::*;
     ///
     /// // Repetition code: ZZI, IZZ on 3 qubits
     /// // Centralizer dimension = 2n - rank = 6 - 2 = 4
@@ -785,12 +933,12 @@ impl PauliSequence {
         for (row_idx, generator) in self.paulis.iter().enumerate() {
             for q in generator.x_positions() {
                 if q < n {
-                    mat.rows[row_idx][q] = 1;
+                    mat.set(row_idx, q, 1);
                 }
             }
             for q in generator.z_positions() {
                 if q < n {
-                    mat.rows[row_idx][n + q] = 1;
+                    mat.set(row_idx, n + q, 1);
                 }
             }
         }
@@ -799,13 +947,42 @@ impl PauliSequence {
         let mut s_omega = F2Matrix::zeros(mat.num_rows(), 2 * n);
         for i in 0..mat.num_rows() {
             for j in 0..n {
-                s_omega.rows[i][j] = mat.rows[i][n + j]; // Z block -> first half
-                s_omega.rows[i][n + j] = mat.rows[i][j]; // X block -> second half
+                s_omega.set(i, j, mat.get(i, n + j)); // Z block -> first half
+                s_omega.set(i, n + j, mat.get(i, j)); // X block -> second half
             }
         }
 
         s_omega.kernel()
     }
+
+    fn to_packed_xz_rows(&self, num_qubits: usize) -> (Vec<Vec<u64>>, Vec<Vec<u64>>) {
+        let num_words = num_qubits.div_ceil(F2Matrix::WORD_BITS);
+        let mut x_rows = vec![vec![0u64; num_words]; self.paulis.len()];
+        let mut z_rows = vec![vec![0u64; num_words]; self.paulis.len()];
+        for (row, pauli) in self.paulis.iter().enumerate() {
+            for q in pauli.x_positions() {
+                if q < num_qubits {
+                    let (word, mask) = F2Matrix::word_mask(q);
+                    x_rows[row][word] |= mask;
+                }
+            }
+            for q in pauli.z_positions() {
+                if q < num_qubits {
+                    let (word, mask) = F2Matrix::word_mask(q);
+                    z_rows[row][word] |= mask;
+                }
+            }
+        }
+        (x_rows, z_rows)
+    }
+}
+
+fn symplectic_inner_product(x_a: &[u64], z_a: &[u64], x_b: &[u64], z_b: &[u64]) -> u8 {
+    let mut parity = 0u32;
+    for (((&xa, &za), &xb), &zb) in x_a.iter().zip(z_a).zip(x_b).zip(z_b) {
+        parity ^= ((xa & zb) ^ (za & xb)).count_ones() & 1;
+    }
+    u8::from(parity != 0)
 }
 
 impl PauliSequence {
@@ -840,7 +1017,7 @@ impl PauliSequence {
     ///
     /// ```
     /// use pecos_quantum::PauliSequence;
-    /// use pecos_core::pauli::constructors::*;
+    /// use pecos_core::pauli::*;
     ///
     /// let seq = PauliSequence::new(vec![X(0) & Z(2), Z(1)]);
     /// assert_eq!(seq.to_sparse_str(), "+X0 Z2\n+Z1");
@@ -911,7 +1088,7 @@ impl fmt::Display for PauliSequence {
 #[cfg(test)]
 mod tests {
     use super::*;
-    use pecos_core::pauli::constructors::*;
+    use pecos_core::pauli::*;
 
     #[test]
     fn test_new() {
@@ -1017,16 +1194,67 @@ mod tests {
         let gens = PauliSequence::new(vec![X(0), Z(0), Y(0)]);
         let cm = gens.commutation_matrix();
         // X,Z anticommute
-        assert!(!cm[0][1]);
-        assert!(!cm[1][0]);
+        assert_eq!(cm.get(0, 1), 1);
+        assert_eq!(cm.get(1, 0), 1);
         // X,Y anticommute
-        assert!(!cm[0][2]);
+        assert_eq!(cm.get(0, 2), 1);
         // Z,Y anticommute
-        assert!(!cm[1][2]);
+        assert_eq!(cm.get(1, 2), 1);
         // Self-commutation
-        assert!(cm[0][0]);
-        assert!(cm[1][1]);
-        assert!(cm[2][2]);
+        assert_eq!(cm.get(0, 0), 0);
+        assert_eq!(cm.get(1, 1), 0);
+        assert_eq!(cm.get(2, 2), 0);
+    }
+
+    #[test]
+    fn test_commutation_matrix_matches_pairwise_across_packed_words() {
+        let gens = PauliSequence::new(vec![
+            X(0),
+            Z(0),
+            X(65) & Z(130),
+            Z(65),
+            Y(130),
+            Zs([0, 65, 130]),
+        ]);
+        let cm = gens.commutation_matrix();
+
+        assert_eq!(cm.num_rows(), gens.len());
+        assert_eq!(cm.num_cols(), gens.len());
+        for i in 0..gens.len() {
+            for j in 0..gens.len() {
+                let expected = u8::from(!gens.paulis()[i].commutes_with(&gens.paulis()[j]));
+                assert_eq!(cm.get(i, j), expected, "entry ({i}, {j})");
+            }
+        }
+    }
+
+    #[test]
+    fn group_commuting_partitions_into_abelian_sequences() {
+        let gens = PauliSequence::new(vec![X(0), Z(0), X(1), Z(1)]);
+        let groups = gens.group_commuting();
+
+        assert_eq!(groups.len(), 2);
+        assert_eq!(groups[0].paulis(), &[X(0), X(1)]);
+        assert_eq!(groups[1].paulis(), &[Z(0), Z(1)]);
+        assert!(groups.iter().all(PauliSequence::is_abelian));
+    }
+
+    #[test]
+    fn group_commuting_handles_empty_single_and_all_commuting_inputs() {
+        let empty = PauliSequence::new(Vec::new());
+        assert!(empty.group_commuting().is_empty());
+
+        let single = PauliSequence::new(vec![X(3)]);
+        let single_groups = single.group_commuting();
+        assert_eq!(single_groups.len(), 1);
+        assert_eq!(single_groups[0].paulis(), &[X(3)]);
+        assert!(single_groups[0].is_abelian());
+
+        let commuting = PauliSequence::new(vec![Z(0), Z(1), Zs([0, 1]), X(2)]);
+        let commuting_groups = commuting.group_commuting();
+        assert_eq!(commuting_groups.len(), 1);
+        assert_eq!(commuting_groups[0].paulis(), commuting.paulis());
+        assert!(commuting_groups[0].is_abelian());
     }
 
     #[test]
@@ -1200,9 +1428,7 @@ mod tests {
     #[test]
     fn test_f2_kernel() {
         // Identity matrix: kernel is empty
-        let mut mat = F2Matrix::zeros(2, 2);
-        mat.rows[0][0] = 1;
-        mat.rows[1][1] = 1;
+        let mat = F2Matrix::from_rows(vec![vec![1, 0], vec![0, 1]]);
         assert!(mat.kernel().is_empty());
 
         // Zero matrix 2x3: kernel dimension = 3
@@ -1213,9 +1439,7 @@ mod tests {
     #[test]
     fn test_f2_kernel_rank_deficient() {
         // [[1,0,0],[1,0,0]]: rank 1, kernel dimension = 3 - 1 = 2
-        let mut mat = F2Matrix::zeros(2, 3);
-        mat.rows[0][0] = 1;
-        mat.rows[1][0] = 1;
+        let mat = F2Matrix::from_rows(vec![vec![1, 0, 0], vec![1, 0, 0]]);
         let kern = mat.kernel();
         assert_eq!(kern.len(), 2);
         // Each kernel vector should satisfy A * v = 0
@@ -1230,9 +1454,7 @@ mod tests {
     #[test]
     fn test_f2_kernel_rectangular() {
         // 1x4 matrix [1,1,0,0]: kernel dim = 3
-        let mut mat = F2Matrix::zeros(1, 4);
-        mat.rows[0][0] = 1;
-        mat.rows[0][1] = 1;
+        let mat = F2Matrix::from_rows(vec![vec![1, 1, 0, 0]]);
         let kern = mat.kernel();
         assert_eq!(kern.len(), 3);
     }
@@ -1304,24 +1526,21 @@ mod tests {
         let seq = PauliSequence::new(vec![Y(0)]);
         let mat = seq.to_symplectic_matrix();
         // For 1 qubit, symplectic vector is [x0, z0]
-        assert_eq!(mat.rows[0], vec![1, 1], "Y should set both x and z bits");
+        assert_eq!(mat.row(0), vec![1, 1], "Y should set both x and z bits");
     }
 
     #[test]
     fn test_f2_matrix_row_reduce_empty() {
         let mat = F2Matrix::zeros(0, 3);
         let (reduced, pivots) = mat.row_reduce();
-        assert!(reduced.rows.is_empty());
+        assert_eq!(reduced.num_rows(), 0);
         assert!(pivots.is_empty());
     }
 
     #[test]
     fn test_f2_matrix_kernel_tall_matrix() {
         // More rows than columns: 3x2 matrix
-        let mut mat = F2Matrix::zeros(3, 2);
-        mat.rows[0] = vec![1, 0];
-        mat.rows[1] = vec![0, 1];
-        mat.rows[2] = vec![1, 1]; // row 2 = row 0 + row 1 (redundant)
+        let mat = F2Matrix::from_rows(vec![vec![1, 0], vec![0, 1], vec![1, 1]]);
         // Full column rank => kernel is empty
         let kern = mat.kernel();
         assert!(
@@ -1333,10 +1552,7 @@ mod tests {
     #[test]
     fn test_f2_matrix_kernel_identity() {
         // Identity matrix: full rank, trivial kernel
-        let mut mat = F2Matrix::zeros(3, 3);
-        mat.rows[0] = vec![1, 0, 0];
-        mat.rows[1] = vec![0, 1, 0];
-        mat.rows[2] = vec![0, 0, 1];
+        let mat = F2Matrix::identity(3);
         let kern = mat.kernel();
         assert!(kern.is_empty());
     }
@@ -1382,9 +1598,7 @@ mod tests {
     #[test]
     fn test_f2_invert_swap_matrix() {
         // Swap rows 0 and 1: [[0,1],[1,0]]
-        let mut m = F2Matrix::zeros(2, 2);
-        m.rows[0][1] = 1;
-        m.rows[1][0] = 1;
+        let m = F2Matrix::from_rows(vec![vec![0, 1], vec![1, 0]]);
         let inv = m.invert().unwrap();
         // Swap is self-inverse
         assert_eq!(inv, m);
@@ -1393,10 +1607,7 @@ mod tests {
     #[test]
     fn test_f2_invert_upper_triangular() {
         // [[1,1],[0,1]] over GF(2) is self-inverse
-        let mut m = F2Matrix::zeros(2, 2);
-        m.rows[0][0] = 1;
-        m.rows[0][1] = 1;
-        m.rows[1][1] = 1;
+        let m = F2Matrix::from_rows(vec![vec![1, 1], vec![0, 1]]);
         let inv = m.invert().unwrap();
         assert_eq!(inv, m);
     }
@@ -1404,9 +1615,7 @@ mod tests {
     #[test]
     fn test_f2_invert_singular() {
         // [[1,1],[1,1]] is singular
-        let mut m = F2Matrix::zeros(2, 2);
-        m.rows[0] = vec![1, 1];
-        m.rows[1] = vec![1, 1];
+        let m = F2Matrix::from_rows(vec![vec![1, 1], vec![1, 1]]);
         assert!(m.invert().is_none());
     }
 
@@ -1419,26 +1628,56 @@ mod tests {
     #[test]
     fn test_f2_mul() {
         // [[1,1],[0,1]] * [[1,0],[1,1]] = [[0,1],[1,1]] over GF(2)
-        let mut a = F2Matrix::zeros(2, 2);
-        a.rows[0] = vec![1, 1];
-        a.rows[1] = vec![0, 1];
-
-        let mut b = F2Matrix::zeros(2, 2);
-        b.rows[0] = vec![1, 0];
-        b.rows[1] = vec![1, 1];
+        let a = F2Matrix::from_rows(vec![vec![1, 1], vec![0, 1]]);
+        let b = F2Matrix::from_rows(vec![vec![1, 0], vec![1, 1]]);
 
         let c = a.mul(&b);
-        assert_eq!(c.rows[0], vec![0, 1]);
-        assert_eq!(c.rows[1], vec![1, 1]);
+        assert_eq!(c.row(0), vec![0, 1]);
+        assert_eq!(c.row(1), vec![1, 1]);
+    }
+
+    #[test]
+    fn test_f2_mul_matches_dense_reference_across_word_boundaries() {
+        fn dense_reference(a: &[Vec<u8>], b: &[Vec<u8>]) -> Vec<Vec<u8>> {
+            let rows = a.len();
+            let inner = b.len();
+            let cols = b.first().map_or(0, Vec::len);
+            let mut out = vec![vec![0; cols]; rows];
+            for i in 0..rows {
+                for j in 0..cols {
+                    let mut bit = 0;
+                    for (k, b_row) in b.iter().enumerate().take(inner) {
+                        bit ^= a[i][k] & b_row[j];
+                    }
+                    out[i][j] = bit;
+                }
+            }
+            out
+        }
+
+        let a_rows: Vec<Vec<u8>> = (0..5)
+            .map(|row| {
+                (0..130)
+                    .map(|col| u8::from((row * 17 + col * 11 + row * col) % 7 < 3))
+                    .collect()
+            })
+            .collect();
+        let b_rows: Vec<Vec<u8>> = (0..130)
+            .map(|row| {
+                (0..7)
+                    .map(|col| u8::from((row * 5 + col * 13 + row * col) % 11 < 5))
+                    .collect()
+            })
+            .collect();
+
+        let packed = F2Matrix::from_rows(a_rows.clone()).mul(&F2Matrix::from_rows(b_rows.clone()));
+        assert_eq!(packed.rows(), dense_reference(&a_rows, &b_rows));
     }
 
     #[test]
     fn test_f2_mul_inverse_gives_identity() {
         // Invertible 3x3 matrix over GF(2)
-        let mut m = F2Matrix::zeros(3, 3);
-        m.rows[0] = vec![1, 1, 0];
-        m.rows[1] = vec![0, 1, 1];
-        m.rows[2] = vec![1, 1, 1];
+        let m = F2Matrix::from_rows(vec![vec![1, 1, 0], vec![0, 1, 1], vec![1, 1, 1]]);
 
         let inv = m.invert().unwrap();
         let product = m.mul(&inv);
@@ -1451,15 +1690,13 @@ mod tests {
 
     #[test]
     fn test_f2_transpose() {
-        let mut m = F2Matrix::zeros(2, 3);
-        m.rows[0] = vec![1, 0, 1];
-        m.rows[1] = vec![0, 1, 0];
+        let m = F2Matrix::from_rows(vec![vec![1, 0, 1], vec![0, 1, 0]]);
         let t = m.transpose();
         assert_eq!(t.num_rows(), 3);
         assert_eq!(t.num_cols(), 2);
-        assert_eq!(t.rows[0], vec![1, 0]);
-        assert_eq!(t.rows[1], vec![0, 1]);
-        assert_eq!(t.rows[2], vec![1, 0]);
+        assert_eq!(t.row(0), vec![1, 0]);
+        assert_eq!(t.row(1), vec![0, 1]);
+        assert_eq!(t.row(2), vec![1, 0]);
     }
 
     // ========================================================================
@@ -1536,16 +1773,15 @@ mod tests {
     #[test]
     fn test_f2_identity_1x1() {
         let id = F2Matrix::identity(1);
-        assert_eq!(id.rows[0], vec![1]);
+        assert_eq!(id.row(0), vec![1]);
     }
 
     #[test]
     fn test_f2_invert_1x1() {
         // [[1]] is invertible
-        let mut m = F2Matrix::zeros(1, 1);
-        m.rows[0] = vec![1];
+        let m = F2Matrix::identity(1);
         let inv = m.invert().unwrap();
-        assert_eq!(inv.rows[0], vec![1]);
+        assert_eq!(inv.row(0), vec![1]);
 
         // [[0]] is not invertible
         let z = F2Matrix::zeros(1, 1);
@@ -1555,10 +1791,7 @@ mod tests {
     #[test]
     fn test_f2_mul_identity() {
         let id = F2Matrix::identity(3);
-        let mut m = F2Matrix::zeros(3, 3);
-        m.rows[0] = vec![1, 1, 0];
-        m.rows[1] = vec![0, 1, 1];
-        m.rows[2] = vec![1, 1, 1];
+        let m = F2Matrix::from_rows(vec![vec![1, 1, 0], vec![0, 1, 1], vec![1, 1, 1]]);
 
         // I * A = A
         assert_eq!(id.mul(&m), m);
@@ -1566,21 +1799,34 @@ mod tests {
         assert_eq!(m.mul(&id), m);
     }
 
+    #[test]
+    fn test_f2_matrix_crosses_multiple_words() {
+        let mut m = F2Matrix::zeros(3, 130);
+        m.set(0, 0, 1);
+        m.set(0, 64, 1);
+        m.set(1, 65, 1);
+        m.set(2, 129, 1);
+
+        assert_eq!(m.get(0, 0), 1);
+        assert_eq!(m.get(0, 64), 1);
+        assert_eq!(m.get(1, 65), 1);
+        assert_eq!(m.get(2, 129), 1);
+        let (_, pivots) = m.row_reduce();
+        assert_eq!(pivots.len(), 3);
+        assert_eq!(m.transpose().transpose(), m);
+    }
+
     #[test]
     fn test_f2_transpose_square() {
-        let mut m = F2Matrix::zeros(2, 2);
-        m.rows[0] = vec![1, 1];
-        m.rows[1] = vec![0, 1];
+        let m = F2Matrix::from_rows(vec![vec![1, 1], vec![0, 1]]);
         let t = m.transpose();
-        assert_eq!(t.rows[0], vec![1, 0]);
-        assert_eq!(t.rows[1], vec![1, 1]);
+        assert_eq!(t.row(0), vec![1, 0]);
+        assert_eq!(t.row(1), vec![1, 1]);
     }
 
     #[test]
     fn test_f2_double_transpose() {
-        let mut m = F2Matrix::zeros(2, 3);
-        m.rows[0] = vec![1, 0, 1];
-        m.rows[1] = vec![0, 1, 0];
+        let m = F2Matrix::from_rows(vec![vec![1, 0, 1], vec![0, 1, 0]]);
         let tt = m.transpose().transpose();
         assert_eq!(tt, m);
     }
@@ -1588,11 +1834,12 @@ mod tests {
     #[test]
     fn test_f2_invert_4x4() {
         // A larger invertible matrix over GF(2)
-        let mut m = F2Matrix::zeros(4, 4);
-        m.rows[0] = vec![1, 0, 0, 1];
-        m.rows[1] = vec![0, 1, 0, 1];
-        m.rows[2] = vec![0, 0, 1, 1];
-        m.rows[3] = vec![1, 1, 1, 0];
+        let m = F2Matrix::from_rows(vec![
+            vec![1, 0, 0, 1],
+            vec![0, 1, 0, 1],
+            vec![0, 0, 1, 1],
+            vec![1, 1, 1, 0],
+        ]);
 
         let inv = m.invert().unwrap();
         assert_eq!(m.mul(&inv), F2Matrix::identity(4));
diff --git a/crates/pecos-quantum/src/pauli_set.rs b/crates/pecos-quantum/src/pauli_set.rs
index 41cdf83e2..8e947b5d6 100644
--- a/crates/pecos-quantum/src/pauli_set.rs
+++ b/crates/pecos-quantum/src/pauli_set.rs
@@ -34,7 +34,7 @@
 //!
 //! ```
 //! use pecos_quantum::PauliSet;
-//! use pecos_core::pauli::constructors::*;
+//! use pecos_core::pauli::*;
 //!
 //! let mut set = PauliSet::new();
 //! set.insert(&X(0));
@@ -112,7 +112,7 @@ impl PauliKey {
 ///
 /// ```
 /// use pecos_quantum::PauliSet;
-/// use pecos_core::pauli::constructors::*;
+/// use pecos_core::pauli::*;
 ///
 /// let a = PauliSet::from_iter([X(0), Z(1), X(0) & Z(1)]);
 /// let b = PauliSet::from_iter([Z(1), Y(2)]);
@@ -233,7 +233,7 @@ impl PauliSet {
     ///
     /// ```
     /// use pecos_quantum::PauliSet;
-    /// use pecos_core::pauli::constructors::*;
+    /// use pecos_core::pauli::*;
     ///
     /// let commuting = PauliSet::from_iter([Zs(&[0, 1]), Zs(&[1, 2])]);
     /// assert!(commuting.is_abelian());
@@ -262,7 +262,7 @@ impl PauliSet {
     ///
     /// ```
     /// use pecos_quantum::PauliSet;
-    /// use pecos_core::pauli::constructors::*;
+    /// use pecos_core::pauli::*;
     ///
     /// let set = PauliSet::from_iter([X(0), Z(1)]);
     /// let s = set.to_sparse_str();
@@ -283,7 +283,7 @@ impl PauliSet {
     ///
     /// ```
     /// use pecos_quantum::PauliSet;
-    /// use pecos_core::pauli::constructors::*;
+    /// use pecos_core::pauli::*;
     ///
     /// let set = PauliSet::from_iter([X(0), Z(1)]);
     /// let s = set.to_dense_str();
@@ -308,7 +308,7 @@ impl FromStr for PauliSet {
     ///
     /// ```
     /// use pecos_quantum::PauliSet;
-    /// use pecos_core::pauli::constructors::*;
+    /// use pecos_core::pauli::*;
     /// use std::str::FromStr;
     ///
     /// let set: PauliSet = "{X0, Z1}".parse().unwrap();
@@ -415,7 +415,7 @@ impl fmt::Display for PauliSet {
 #[cfg(test)]
 mod tests {
     use super::*;
-    use pecos_core::pauli::constructors::*;
+    use pecos_core::pauli::*;
 
     #[test]
     fn test_new_empty() {
diff --git a/crates/pecos-quantum/src/stabilizer_group.rs b/crates/pecos-quantum/src/stabilizer_group.rs
index 856f52523..c62206153 100644
--- a/crates/pecos-quantum/src/stabilizer_group.rs
+++ b/crates/pecos-quantum/src/stabilizer_group.rs
@@ -31,7 +31,7 @@
 //!
 //! ```
 //! use pecos_quantum::PauliStabilizerGroup;
-//! use pecos_core::pauli::constructors::*;
+//! use pecos_core::pauli::*;
 //!
 //! // Repetition code stabilizers
 //! let stab = PauliStabilizerGroup::new(vec![
@@ -94,7 +94,7 @@ impl std::error::Error for PauliStabilizerGroupError {}
 ///
 /// ```
 /// use pecos_quantum::PauliStabilizerGroup;
-/// use pecos_core::pauli::constructors::*;
+/// use pecos_core::pauli::*;
 ///
 /// // 5-qubit code stabilizers: XZZXI, IXZZX, XIXZZ, ZXIXZ
 /// let stab = PauliStabilizerGroup::new(vec![
@@ -245,7 +245,7 @@ impl PauliStabilizerGroup {
     ///
     /// ```
     /// use pecos_quantum::PauliStabilizerGroup;
-    /// use pecos_core::pauli::constructors::*;
+    /// use pecos_core::pauli::*;
     /// use pecos_core::PauliOperator;
     ///
     /// let stab = PauliStabilizerGroup::new(vec![Zs(&[0, 1]), Zs(&[1, 2])]).unwrap();
@@ -284,7 +284,7 @@ impl PauliStabilizerGroup {
     ///
     /// ```
     /// use pecos_quantum::PauliStabilizerGroup;
-    /// use pecos_core::pauli::constructors::*;
+    /// use pecos_core::pauli::*;
     /// use pecos_core::PauliOperator;
     ///
     /// let stab = PauliStabilizerGroup::new(vec![Zs(&[0, 1]), Zs(&[1, 2])]).unwrap();
@@ -315,7 +315,7 @@ impl PauliStabilizerGroup {
     ///
     /// ```
     /// use pecos_quantum::PauliStabilizerGroup;
-    /// use pecos_core::pauli::constructors::*;
+    /// use pecos_core::pauli::*;
     ///
     /// let stab = PauliStabilizerGroup::new(vec![Zs(&[0, 1]), Zs(&[1, 2])]).unwrap();
     /// let elements: Vec<_> = stab.elements().collect();
@@ -332,9 +332,11 @@ impl PauliStabilizerGroup {
         self.inner.to_symplectic_matrix()
     }
 
-    /// Returns the commutation matrix (always all-true for a valid stabilizer group).
+    /// Returns the pairwise anticommutation matrix.
+    ///
+    /// This is always all-zero for a valid stabilizer group.
     #[must_use]
-    pub fn commutation_matrix(&self) -> Vec<Vec<bool>> {
+    pub fn commutation_matrix(&self) -> F2Matrix {
         self.inner.commutation_matrix()
     }
 
@@ -375,7 +377,7 @@ impl PauliStabilizerGroup {
     ///
     /// ```
     /// use pecos_quantum::PauliStabilizerGroup;
-    /// use pecos_core::pauli::constructors::*;
+    /// use pecos_core::pauli::*;
     /// use pecos_core::clifford_rep::CliffordRep;
     ///
     /// // Repetition code stabilizers: ZZ_, _ZZ
@@ -497,7 +499,7 @@ impl fmt::Display for PauliStabilizerGroup {
 #[cfg(test)]
 mod tests {
     use super::*;
-    use pecos_core::pauli::constructors::*;
+    use pecos_core::pauli::*;
     use pecos_core::{Pauli, PauliOperator};
 
     #[test]
@@ -1042,6 +1044,19 @@ mod tests {
         }
     }
 
+    #[test]
+    fn commutation_matrix_delegates_as_all_zero_anticommutation_matrix() {
+        let stab = PauliStabilizerGroup::new(vec![Zs([0, 1]), Zs([1, 2])]).unwrap();
+        let mat = stab.commutation_matrix();
+        assert_eq!(mat.num_rows(), 2);
+        assert_eq!(mat.num_cols(), 2);
+        for row in 0..mat.num_rows() {
+            for col in 0..mat.num_cols() {
+                assert_eq!(mat.get(row, col), 0);
+            }
+        }
+    }
+
     // ========================================================================
     // as_group() accessor
     // ========================================================================
diff --git a/crates/pecos-quantum/src/tick_circuit.rs b/crates/pecos-quantum/src/tick_circuit.rs
index 8b65edeba..dbfc3ed8b 100644
--- a/crates/pecos-quantum/src/tick_circuit.rs
+++ b/crates/pecos-quantum/src/tick_circuit.rs
@@ -40,9 +40,11 @@
 //!
 //! assert_eq!(circuit.num_ticks(), 6);
 //!
-//! // Preps and measurements break the chain but allow .meta():
+//! // Preps break the chain but allow .meta():
 //! circuit.tick().pz(&[0]).meta("reason", pecos_quantum::Attribute::String("init".into()));
-//! circuit.tick().mz(&[0]).meta("basis", pecos_quantum::Attribute::String("Z".into()));
+//! // Measurements return refs for annotations:
+//! let ms = circuit.tick().mz(&[0]);
+//! circuit.detector(&ms);
 //!
 //! // Tick-level metadata: call meta() before adding gates
 //! use pecos_quantum::Attribute;
@@ -58,15 +60,125 @@
 //! circuit3.tick().h(&[0, 1, 2, 3]);       // H on 4 qubits at once
 //! circuit3.tick().cx(&[(0, 1), (2, 3)]);  // 2 CX gates in parallel
 //! circuit3.tick().mz(&[0, 1, 2, 3]);      // Measure all 4 qubits
+//!
+//! assert_eq!(circuit3.gate_count(), 14);       // individual gate applications
+//! assert_eq!(circuit3.gate_batch_count(), 4);  // stored same-type batches
 //! ```
 
 use pecos_core::gate_type::GateType;
-use pecos_core::{Angle64, Gate, GateQubits, GateSignature, QubitId, TimeUnits};
-use std::collections::{BTreeMap, BTreeSet, HashMap};
+use pecos_core::{
+    Angle64, ChannelExpr, Gate, GateMeasIds, GateQubits, GateSignature, MeasId, QubitId, TimeUnits,
+};
+use std::collections::{BTreeMap, BTreeSet};
 
 use crate::Attribute;
-use crate::dag_circuit::DagCircuit;
+use crate::dag_circuit::{AnnotationKind, DagCircuit, PauliAnnotation};
 use std::fmt;
+use std::ops::{Deref, Index};
+
+fn meta_json_array(circuit: &TickCircuit, key: &str) -> Result<Vec<serde_json::Value>, String> {
+    let Some(attr) = circuit.get_meta(key) else {
+        return Ok(Vec::new());
+    };
+    match attr {
+        Attribute::String(s) => {
+            if s.trim().is_empty() {
+                return Ok(Vec::new());
+            }
+            serde_json::from_str::<Vec<serde_json::Value>>(s)
+                .map_err(|e| format!("metadata {key:?} must be a JSON array: {e}"))
+        }
+        Attribute::Json(serde_json::Value::Array(values)) => Ok(values.clone()),
+        _ => Err(format!(
+            "metadata {key:?} must be a JSON array string or JSON array"
+        )),
+    }
+}
+
+fn set_meta_json_array(
+    circuit: &mut TickCircuit,
+    key: &str,
+    values: &[serde_json::Value],
+) -> Result<(), String> {
+    let json =
+        serde_json::to_string(values).map_err(|e| format!("could not serialize {key:?}: {e}"))?;
+    circuit.set_meta(key, Attribute::String(json));
+    Ok(())
+}
+
+fn json_metadata_id(key: &str, id: u64) -> Result<usize, String> {
+    usize::try_from(id).map_err(|_| format!("metadata {key:?} id {id} does not fit usize"))
+}
+
+fn next_metadata_id(values: &[serde_json::Value], key: &str) -> Result<usize, String> {
+    let mut max_id = None;
+    for value in values {
+        if let Some(id) = value.get("id").and_then(serde_json::Value::as_u64) {
+            let id = json_metadata_id(key, id)?;
+            max_id = Some(max_id.map_or(id, |max_id: usize| max_id.max(id)));
+        }
+    }
+    match max_id {
+        Some(max_id) => max_id
+            .checked_add(1)
+            .ok_or_else(|| format!("metadata {key:?} id counter overflow")),
+        None => Ok(values.len()),
+    }
+}
+
+fn metadata_count(values: &[serde_json::Value], key: &str) -> Result<usize, String> {
+    let mut count = values.len();
+    for value in values {
+        if let Some(id) = value.get("id").and_then(serde_json::Value::as_u64) {
+            let next = json_metadata_id(key, id)?
+                .checked_add(1)
+                .ok_or_else(|| format!("metadata {key:?} count overflow"))?;
+            count = count.max(next);
+        }
+    }
+    Ok(count)
+}
+
+fn metadata_count_attr(values: &[serde_json::Value], key: &str) -> Result<Attribute, String> {
+    let count = metadata_count(values, key)?;
+    let count = i64::try_from(count)
+        .map_err(|_| format!("metadata {key:?} count {count} does not fit i64"))?;
+    Ok(Attribute::Int(count))
+}
+
+fn ensure_unique_metadata_id(
+    values: &[serde_json::Value],
+    key: &str,
+    id_name: &str,
+    id: usize,
+) -> Result<(), String> {
+    for value in values {
+        if let Some(existing) = value.get("id").and_then(serde_json::Value::as_u64) {
+            let existing = json_metadata_id(key, existing)?;
+            if existing == id {
+                return Err(format!("{key} metadata already contains {id_name} {id}"));
+            }
+        }
+    }
+    Ok(())
+}
+
+fn observable_id_from_label(label: Option<&str>) -> Result<Option<usize>, String> {
+    let Some(label) = label else {
+        return Ok(None);
+    };
+    let Some(rest) = label.strip_prefix('L') else {
+        return Ok(None);
+    };
+    if rest.is_empty() {
+        return Ok(None);
+    }
+    rest.parse::<usize>().map(Some).map_err(|_| {
+        format!(
+            "observable label {label:?} starts with 'L' but does not contain a valid integer id"
+        )
+    })
+}
 
 /// Error when trying to add a gate that uses a qubit already in use in this tick.
 #[derive(Debug, Clone, PartialEq, Eq)]
@@ -103,6 +215,53 @@ impl fmt::Display for QubitConflictError {
 
 impl std::error::Error for QubitConflictError {}
 
+/// Error when trying to add a gate to a tick.
+#[derive(Debug, Clone, PartialEq, Eq)]
+pub enum TickGateError {
+    /// The gate payload itself is invalid.
+    InvalidGate {
+        /// Validation error from [`Gate::validate`].
+        message: String,
+        /// The tick index where the invalid gate was being inserted.
+        tick_idx: Option<usize>,
+    },
+    /// The gate is valid, but overlaps a qubit already used in this tick.
+    QubitConflict(QubitConflictError),
+}
+
+impl TickGateError {
+    fn set_tick_idx(&mut self, tick_idx: usize) {
+        match self {
+            Self::InvalidGate { tick_idx: idx, .. } => *idx = Some(tick_idx),
+            Self::QubitConflict(err) => err.tick_idx = Some(tick_idx),
+        }
+    }
+}
+
+impl fmt::Display for TickGateError {
+    fn fmt(&self, f: &mut fmt::Formatter<'_>) -> fmt::Result {
+        match self {
+            Self::InvalidGate {
+                message,
+                tick_idx: Some(tick_idx),
+            } => write!(f, "Invalid gate in tick {tick_idx}: {message}"),
+            Self::InvalidGate {
+                message,
+                tick_idx: None,
+            } => write!(f, "Invalid gate: {message}"),
+            Self::QubitConflict(err) => write!(f, "{err}"),
+        }
+    }
+}
+
+impl std::error::Error for TickGateError {}
+
+impl From<QubitConflictError> for TickGateError {
+    fn from(e: QubitConflictError) -> Self {
+        Self::QubitConflict(e)
+    }
+}
+
 /// Error when a custom gate is used with a different signature than previously established.
 #[derive(Debug, Clone, PartialEq, Eq)]
 pub struct GateSignatureMismatchError {
@@ -133,6 +292,7 @@ impl std::error::Error for GateSignatureMismatchError {}
 #[derive(Debug, Clone)]
 pub enum CustomGateError {
     SignatureMismatch(GateSignatureMismatchError),
+    InvalidGate(String),
     QubitConflict(QubitConflictError),
 }
 
@@ -140,6 +300,7 @@ impl fmt::Display for CustomGateError {
     fn fmt(&self, f: &mut fmt::Formatter<'_>) -> fmt::Result {
         match self {
             Self::SignatureMismatch(e) => write!(f, "{e}"),
+            Self::InvalidGate(e) => write!(f, "{e}"),
             Self::QubitConflict(e) => write!(f, "{e}"),
         }
     }
@@ -159,17 +320,301 @@ impl From<QubitConflictError> for CustomGateError {
     }
 }
 
+impl From<TickGateError> for CustomGateError {
+    fn from(e: TickGateError) -> Self {
+        match e {
+            TickGateError::InvalidGate { message, .. } => Self::InvalidGate(message),
+            TickGateError::QubitConflict(err) => Self::QubitConflict(err),
+        }
+    }
+}
+
+#[derive(Debug, Clone, Default)]
+struct TickGateStorage {
+    commands: Vec<Gate>,
+}
+
+impl TickGateStorage {
+    fn len(&self) -> usize {
+        self.commands.len()
+    }
+
+    fn is_empty(&self) -> bool {
+        self.commands.is_empty()
+    }
+
+    fn as_slice(&self) -> &[Gate] {
+        &self.commands
+    }
+
+    fn iter(&self) -> std::slice::Iter<'_, Gate> {
+        self.commands.iter()
+    }
+
+    fn get(&self, idx: usize) -> Option<&Gate> {
+        self.commands.get(idx)
+    }
+
+    fn push(&mut self, gate: Gate) {
+        self.commands.push(gate);
+    }
+
+    fn set(&mut self, idx: usize, gate: Gate) {
+        self.commands[idx] = gate;
+    }
+
+    fn remove(&mut self, idx: usize) -> Gate {
+        self.commands.remove(idx)
+    }
+
+    fn append_batch(&mut self, idx: usize, gate: Gate) {
+        assert!(
+            self.commands[idx].can_batch_with(&gate),
+            "cannot merge incompatible gate batches"
+        );
+        self.commands[idx].append_batch(gate);
+    }
+
+    fn truncate_payload(&mut self, idx: usize, qubit_len: usize, meas_id_len: usize) {
+        self.commands[idx].qubits.truncate(qubit_len);
+        self.commands[idx].meas_ids.truncate(meas_id_len);
+    }
+}
+
+impl Deref for TickGateStorage {
+    type Target = [Gate];
+
+    fn deref(&self) -> &Self::Target {
+        self.as_slice()
+    }
+}
+
+impl Index<usize> for TickGateStorage {
+    type Output = Gate;
+
+    fn index(&self, index: usize) -> &Self::Output {
+        &self.commands[index]
+    }
+}
+
 /// A single time slice containing gates that execute in parallel.
 #[derive(Debug, Clone, Default)]
 pub struct Tick {
-    /// Gates in this tick (all act on disjoint qubits).
-    gates: Vec<Gate>,
-    /// Metadata for each gate, indexed by position in `gates`.
-    gate_attrs: BTreeMap<usize, BTreeMap<String, Attribute>>,
+    /// Gate batches in this tick (all act on disjoint qubits).
+    gate_batches: TickGateStorage,
+    /// Metadata for each gate batch, indexed by position in `gate_batches`.
+    batch_attrs: Vec<Option<BTreeMap<String, Attribute>>>,
     /// Tick-level metadata.
     attrs: BTreeMap<String, Attribute>,
 }
 
+#[derive(Debug, Clone, Copy)]
+struct GateBatchPiece {
+    gate_idx: usize,
+    qubit_start: usize,
+    qubit_len: usize,
+    meas_id_start: usize,
+    meas_id_len: usize,
+}
+
+/// Borrowed view of one stored same-type gate batch in a [`Tick`].
+#[derive(Debug, Clone, Copy)]
+pub struct GateBatchRef<'a> {
+    batch_index: usize,
+    gate: &'a Gate,
+    attrs: Option<&'a BTreeMap<String, Attribute>>,
+}
+
+impl<'a> GateBatchRef<'a> {
+    fn new(
+        batch_index: usize,
+        gate: &'a Gate,
+        attrs: Option<&'a BTreeMap<String, Attribute>>,
+    ) -> Self {
+        Self {
+            batch_index,
+            gate,
+            attrs,
+        }
+    }
+
+    /// Return this batch's index within its tick.
+    #[must_use]
+    pub fn batch_index(self) -> usize {
+        self.batch_index
+    }
+
+    /// Return the underlying stored [`Gate`] batch.
+    #[must_use]
+    pub fn as_gate(self) -> &'a Gate {
+        self.gate
+    }
+
+    /// Return the number of individual gates represented by this batch.
+    #[must_use]
+    pub fn gate_count(self) -> usize {
+        self.gate.num_gates()
+    }
+
+    /// Return the metadata attribute with the given key, if present.
+    #[must_use]
+    pub fn get_attr(self, key: &str) -> Option<&'a Attribute> {
+        self.attrs.and_then(|attrs| attrs.get(key))
+    }
+
+    /// Iterate over metadata attributes attached to this batch.
+    pub fn attrs(self) -> impl Iterator<Item = (&'a String, &'a Attribute)> {
+        self.attrs.into_iter().flat_map(|attrs| attrs.iter())
+    }
+
+    /// Return one individual gate from this batch.
+    #[must_use]
+    pub fn instance(self, instance_index: usize) -> Option<GateInstanceRef<'a>> {
+        let gate_count = self.gate_count();
+        if instance_index >= gate_count {
+            return None;
+        }
+
+        let qubits = if gate_count == 1 {
+            self.gate.qubits.as_slice()
+        } else {
+            let arity = self.gate.quantum_arity();
+            let start = instance_index * arity;
+            let end = start + arity;
+            self.gate.qubits.get(start..end)?
+        };
+
+        let meas_ids = if self.gate.meas_ids.is_empty() {
+            &self.gate.meas_ids[0..0]
+        } else if gate_count == 1 {
+            self.gate.meas_ids.as_slice()
+        } else {
+            if !self.gate.meas_ids.len().is_multiple_of(gate_count) {
+                return None;
+            }
+            let arity = self.gate.meas_ids.len() / gate_count;
+            let start = instance_index * arity;
+            let end = start + arity;
+            self.gate.meas_ids.get(start..end)?
+        };
+
+        Some(GateInstanceRef {
+            batch: self,
+            instance_index,
+            qubits,
+            meas_ids,
+        })
+    }
+
+    /// Iterate over individual gates represented by this batch.
+    pub fn iter_gate_instances(self) -> impl Iterator<Item = GateInstanceRef<'a>> {
+        (0..self.gate_count()).filter_map(move |idx| self.instance(idx))
+    }
+}
+
+impl Deref for GateBatchRef<'_> {
+    type Target = Gate;
+
+    fn deref(&self) -> &Self::Target {
+        self.gate
+    }
+}
+
+/// Borrowed view of one individual gate inside a [`GateBatchRef`].
+#[derive(Debug, Clone, Copy)]
+pub struct GateInstanceRef<'a> {
+    batch: GateBatchRef<'a>,
+    instance_index: usize,
+    qubits: &'a [QubitId],
+    meas_ids: &'a [MeasId],
+}
+
+impl<'a> GateInstanceRef<'a> {
+    /// Return the stored batch this individual gate came from.
+    #[must_use]
+    pub fn batch(self) -> GateBatchRef<'a> {
+        self.batch
+    }
+
+    /// Return the parent batch's index within its tick.
+    #[must_use]
+    pub fn batch_index(self) -> usize {
+        self.batch.batch_index()
+    }
+
+    /// Return this gate's position within its stored batch.
+    #[must_use]
+    pub fn instance_index(self) -> usize {
+        self.instance_index
+    }
+
+    /// Return this individual gate's type.
+    #[must_use]
+    pub fn gate_type(self) -> GateType {
+        self.batch.gate_type
+    }
+
+    /// Return this individual gate's qubit support.
+    #[must_use]
+    pub fn qubits(self) -> &'a [QubitId] {
+        self.qubits
+    }
+
+    /// Return this individual gate's measurement ids, if any.
+    #[must_use]
+    pub fn meas_ids(self) -> &'a [MeasId] {
+        self.meas_ids
+    }
+
+    /// Return this individual gate's rotation angles.
+    #[must_use]
+    pub fn angles(self) -> &'a [Angle64] {
+        self.batch.gate.angles.as_slice()
+    }
+
+    /// Return this individual gate's non-angle parameters.
+    #[must_use]
+    pub fn params(self) -> &'a [f64] {
+        self.batch.gate.params.as_slice()
+    }
+
+    /// Return this individual gate's channel payload, if this is a channel.
+    #[must_use]
+    pub fn channel(self) -> Option<&'a ChannelExpr> {
+        self.batch.gate.channel.as_ref()
+    }
+
+    /// Return the metadata attribute with the given key, if present.
+    #[must_use]
+    pub fn get_attr(self, key: &str) -> Option<&'a Attribute> {
+        self.batch.get_attr(key)
+    }
+
+    /// Iterate over metadata attributes attached to the parent batch.
+    pub fn attrs(self) -> impl Iterator<Item = (&'a String, &'a Attribute)> {
+        self.batch.attrs()
+    }
+
+    /// Materialize this individual gate as an owned [`Gate`].
+    ///
+    /// The returned gate carries this instance's sliced qubits and measurement
+    /// ids, plus the parent batch's gate type, angles, parameters, and channel
+    /// payload. Batch metadata is intentionally not copied into the `Gate`;
+    /// use [`attrs`](Self::attrs) when metadata needs to travel alongside the
+    /// materialized operation.
+    #[must_use]
+    pub fn to_gate(self) -> Gate {
+        Gate {
+            gate_type: self.gate_type(),
+            qubits: self.qubits.iter().copied().collect::<GateQubits>(),
+            angles: self.batch.gate.angles.clone(),
+            params: self.batch.gate.params.clone(),
+            meas_ids: self.meas_ids.iter().copied().collect::<GateMeasIds>(),
+            channel: self.batch.gate.channel.clone(),
+        }
+    }
+}
+
 impl Tick {
     /// Create a new empty tick.
     #[must_use]
@@ -177,53 +622,291 @@ impl Tick {
         Self::default()
     }
 
-    /// Get the number of gates in this tick.
+    /// Get the number of stored gate batches in this tick.
+    ///
+    /// This is the number of stored gate batches. Batched commands such as
+    /// `cx(&[(0, 1), (2, 3)])` count as one stored batch.
     #[must_use]
     pub fn len(&self) -> usize {
-        self.gates.len()
+        self.gate_batches.len()
+    }
+
+    /// Get the number of individual gate applications in this tick.
+    ///
+    /// Batched commands count by the number of gates they represent:
+    /// `h(&[0, 1, 2])` counts as three H gates, and
+    /// `cx(&[(0, 1), (2, 3)])` counts as two CX gates.
+    #[must_use]
+    pub fn gate_count(&self) -> usize {
+        self.gate_batches.iter().map(Gate::num_gates).sum()
+    }
+
+    /// Get the number of compatible gate batches in this tick.
+    ///
+    /// Gates with the same type, parameters, payload shape, and metadata can
+    /// execute as one batch when they differ only by disjoint qubits.
+    #[must_use]
+    pub fn gate_batch_count(&self) -> usize {
+        let mut representative_indices: Vec<usize> = Vec::new();
+        'gate: for (idx, gate) in self.gate_batches.iter().enumerate() {
+            for &rep_idx in &representative_indices {
+                if self.gate_attrs_equivalent(rep_idx, idx)
+                    && self.gate_batches[rep_idx].can_batch_with(gate)
+                {
+                    continue 'gate;
+                }
+            }
+            representative_indices.push(idx);
+        }
+        representative_indices.len()
     }
 
     /// Check if the tick is empty.
     #[must_use]
     pub fn is_empty(&self) -> bool {
-        self.gates.is_empty()
+        self.gate_batches.is_empty()
     }
 
-    /// Get the gates in this tick.
+    /// Get the raw stored gate batches in this tick.
+    ///
+    /// In `TickCircuit`, a stored [`Gate`] command may represent one or more
+    /// individual gates on disjoint qubits. For example,
+    /// `cx(&[(0, 1), (2, 3)])` is one batch containing two gates.
+    ///
+    /// The batches preserve the complete [`Gate`] payload, including
+    /// measurement IDs and typed channel payloads.
+    ///
+    /// Prefer [`iter_gate_batches`](Self::iter_gate_batches) for new read-only
+    /// consumers; it returns [`GateBatchRef`] values that carry the batch index
+    /// and metadata alongside the underlying `Gate`. This raw slice accessor is
+    /// kept for compatibility, storage inspection, and code that intentionally
+    /// needs stable batch indices.
     #[must_use]
-    pub fn gates(&self) -> &[Gate] {
-        &self.gates
+    pub fn gate_batches(&self) -> &[Gate] {
+        self.gate_batches.as_slice()
+    }
+
+    /// Iterate over full-fidelity borrowed gate-batch views in this tick.
+    pub fn iter_gate_batches(&self) -> impl Iterator<Item = GateBatchRef<'_>> {
+        self.gate_batches
+            .iter()
+            .enumerate()
+            .map(|(idx, gate)| GateBatchRef::new(idx, gate, self.normalized_gate_attrs(idx)))
     }
 
-    /// Get mutable access to the gates in this tick.
-    pub fn gates_mut(&mut self) -> &mut [Gate] {
-        &mut self.gates
+    /// Iterate over individual gates expanded from this tick's stored batches.
+    pub fn iter_gate_instances(&self) -> impl Iterator<Item = GateInstanceRef<'_>> {
+        self.iter_gate_batches()
+            .flat_map(GateBatchRef::iter_gate_instances)
     }
 
     /// Add a gate to this tick.
+    ///
+    /// # Panics
+    ///
+    /// Panics if [`Gate::validate`] rejects the gate payload or if the gate
+    /// conflicts with an existing gate in this tick. Use
+    /// [`try_add_gate`](Self::try_add_gate) for fallible insertion.
     pub fn add_gate(&mut self, gate: Gate) -> usize {
-        let idx = self.gates.len();
-        self.gates.push(gate);
+        self.try_add_gate(gate)
+            .unwrap_or_else(|err| panic!("{err}"))
+    }
+
+    fn push_gate_unchecked(&mut self, gate: Gate) -> usize {
+        let idx = self.gate_batches.len();
+        self.gate_batches.push(gate);
+        self.batch_attrs.push(None);
         idx
     }
 
+    fn push_gate_unchecked_piece(&mut self, gate: Gate) -> GateBatchPiece {
+        let qubit_len = gate.qubits.len();
+        let meas_id_len = gate.meas_ids.len();
+        let gate_idx = self.push_gate_unchecked(gate);
+        GateBatchPiece {
+            gate_idx,
+            qubit_start: 0,
+            qubit_len,
+            meas_id_start: 0,
+            meas_id_len,
+        }
+    }
+
+    fn normalized_gate_attrs(&self, gate_idx: usize) -> Option<&BTreeMap<String, Attribute>> {
+        self.batch_attrs
+            .get(gate_idx)
+            .and_then(Option::as_ref)
+            .filter(|attrs| !attrs.is_empty())
+    }
+
+    fn gate_attrs_equivalent(&self, a: usize, b: usize) -> bool {
+        self.normalized_gate_attrs(a) == self.normalized_gate_attrs(b)
+    }
+
+    fn gate_has_no_attrs(&self, gate_idx: usize) -> bool {
+        self.normalized_gate_attrs(gate_idx).is_none()
+    }
+
+    fn compatible_empty_attr_batch(&self, gate: &Gate) -> Option<usize> {
+        self.gate_batches
+            .iter()
+            .enumerate()
+            .find(|(idx, existing)| self.gate_has_no_attrs(*idx) && existing.can_batch_with(gate))
+            .map(|(idx, _)| idx)
+    }
+
+    fn whole_gate_piece(&self, gate_idx: usize) -> GateBatchPiece {
+        let gate = &self.gate_batches[gate_idx];
+        GateBatchPiece {
+            gate_idx,
+            qubit_start: 0,
+            qubit_len: gate.qubits.len(),
+            meas_id_start: 0,
+            meas_id_len: gate.meas_ids.len(),
+        }
+    }
+
+    fn merge_compatible_piece_at(&mut self, piece: GateBatchPiece) -> GateBatchPiece {
+        if piece.gate_idx >= self.gate_batches.len() {
+            return piece;
+        }
+
+        let Some(target_idx) = (0..piece.gate_idx).find(|&idx| {
+            self.gate_attrs_equivalent(idx, piece.gate_idx)
+                && self.gate_batches[idx].can_batch_with(&self.gate_batches[piece.gate_idx])
+        }) else {
+            return piece;
+        };
+
+        let qubit_start = self.gate_batches[target_idx].qubits.len();
+        let meas_id_start = self.gate_batches[target_idx].meas_ids.len();
+        let gate = self.gate_batches[piece.gate_idx].clone();
+        self.gate_batches.append_batch(target_idx, gate);
+        self.remove_gate(piece.gate_idx);
+        GateBatchPiece {
+            gate_idx: target_idx,
+            qubit_start,
+            qubit_len: piece.qubit_len,
+            meas_id_start,
+            meas_id_len: piece.meas_id_len,
+        }
+    }
+
+    fn merge_compatible_gate_at(&mut self, gate_idx: usize) -> usize {
+        if gate_idx >= self.gate_batches.len() {
+            return gate_idx;
+        }
+        self.merge_compatible_piece_at(self.whole_gate_piece(gate_idx))
+            .gate_idx
+    }
+
+    fn isolate_batch_piece(&mut self, piece: GateBatchPiece) -> usize {
+        if piece.gate_idx >= self.gate_batches.len() {
+            return piece.gate_idx;
+        }
+
+        let gate_qubit_len = self.gate_batches[piece.gate_idx].qubits.len();
+        let gate_meas_id_len = self.gate_batches[piece.gate_idx].meas_ids.len();
+        if piece.qubit_start == 0
+            && piece.qubit_len == gate_qubit_len
+            && piece.meas_id_start == 0
+            && piece.meas_id_len == gate_meas_id_len
+        {
+            return piece.gate_idx;
+        }
+
+        assert_eq!(
+            piece.qubit_start + piece.qubit_len,
+            gate_qubit_len,
+            "batched gate metadata can only split the appended suffix"
+        );
+        assert_eq!(
+            piece.meas_id_start + piece.meas_id_len,
+            gate_meas_id_len,
+            "batched gate metadata can only split the appended measurement-id suffix"
+        );
+
+        let mut split_gate = self.gate_batches[piece.gate_idx].clone();
+        split_gate.qubits = self.gate_batches[piece.gate_idx].qubits[piece.qubit_start..].into();
+        split_gate.meas_ids =
+            self.gate_batches[piece.gate_idx].meas_ids[piece.meas_id_start..].into();
+
+        self.gate_batches
+            .truncate_payload(piece.gate_idx, piece.qubit_start, piece.meas_id_start);
+
+        let split_idx = self.push_gate_unchecked(split_gate);
+        if let Some(attrs) = self.normalized_gate_attrs(piece.gate_idx).cloned() {
+            self.batch_attrs[split_idx] = Some(attrs);
+        }
+        split_idx
+    }
+
+    fn set_gate_attr_for_piece(
+        &mut self,
+        piece: GateBatchPiece,
+        key: &str,
+        value: Attribute,
+    ) -> GateBatchPiece {
+        let gate_idx = self.isolate_batch_piece(piece);
+        self.set_gate_attr(gate_idx, key, value);
+        self.merge_compatible_piece_at(self.whole_gate_piece(gate_idx))
+    }
+
+    fn set_gate_attrs_for_piece(
+        &mut self,
+        piece: GateBatchPiece,
+        attrs: BTreeMap<String, Attribute>,
+    ) -> GateBatchPiece {
+        let gate_idx = self.isolate_batch_piece(piece);
+        self.set_gate_attrs(gate_idx, attrs);
+        self.merge_compatible_piece_at(self.whole_gate_piece(gate_idx))
+    }
+
     /// Set metadata on a gate.
-    pub fn set_gate_attr(&mut self, gate_idx: usize, key: &str, value: Attribute) {
-        self.gate_attrs
-            .entry(gate_idx)
-            .or_default()
+    ///
+    /// Returns the gate index.
+    ///
+    /// # Panics
+    ///
+    /// Panics if `gate_idx` is not a valid stored batch index in this tick.
+    pub fn set_gate_attr(&mut self, gate_idx: usize, key: &str, value: Attribute) -> usize {
+        assert!(
+            gate_idx < self.gate_batches.len(),
+            "gate index {gate_idx} out of bounds"
+        );
+        self.batch_attrs[gate_idx]
+            .get_or_insert_with(BTreeMap::new)
             .insert(key.to_string(), value);
+        gate_idx
     }
 
     /// Set multiple metadata attributes on a gate at once.
-    pub fn set_gate_attrs(&mut self, gate_idx: usize, attrs: BTreeMap<String, Attribute>) {
-        self.gate_attrs.entry(gate_idx).or_default().extend(attrs);
+    ///
+    /// Returns the gate index.
+    ///
+    /// # Panics
+    ///
+    /// Panics if `gate_idx` is not a valid stored batch index in this tick.
+    pub fn set_gate_attrs(&mut self, gate_idx: usize, attrs: BTreeMap<String, Attribute>) -> usize {
+        assert!(
+            gate_idx < self.gate_batches.len(),
+            "gate index {gate_idx} out of bounds"
+        );
+        if !attrs.is_empty() {
+            self.batch_attrs[gate_idx]
+                .get_or_insert_with(BTreeMap::new)
+                .extend(attrs);
+        }
+        gate_idx
     }
 
     /// Get metadata from a gate.
     #[must_use]
     pub fn get_gate_attr(&self, gate_idx: usize, key: &str) -> Option<&Attribute> {
-        self.gate_attrs.get(&gate_idx).and_then(|m| m.get(key))
+        self.batch_attrs
+            .get(gate_idx)
+            .and_then(Option::as_ref)
+            .and_then(|m| m.get(key))
     }
 
     /// Set tick-level metadata.
@@ -244,8 +927,9 @@ impl Tick {
 
     /// Get all attributes for a gate.
     pub fn gate_attrs(&self, gate_idx: usize) -> impl Iterator<Item = (&String, &Attribute)> {
-        self.gate_attrs
-            .get(&gate_idx)
+        self.batch_attrs
+            .get(gate_idx)
+            .and_then(Option::as_ref)
             .into_iter()
             .flat_map(|m| m.iter())
     }
@@ -260,7 +944,7 @@ impl Tick {
     /// This is computed lazily by iterating through all gates.
     #[must_use]
     pub fn active_qubits(&self) -> BTreeSet<QubitId> {
-        self.gates
+        self.gate_batches
             .iter()
             .flat_map(|gate| gate.qubits.iter().copied())
             .collect()
@@ -269,7 +953,9 @@ impl Tick {
     /// Check if a specific qubit is already in use in this tick.
     #[must_use]
     pub fn uses_qubit(&self, qubit: QubitId) -> bool {
-        self.gates.iter().any(|gate| gate.qubits.contains(&qubit))
+        self.gate_batches
+            .iter()
+            .any(|gate| gate.qubits.contains(&qubit))
     }
 
     /// Check if any of the given qubits are already in use in this tick.
@@ -285,20 +971,137 @@ impl Tick {
             .collect()
     }
 
-    /// Try to add a gate to this tick, returning an error if any qubit is already in use.
+    /// Try to add a gate to this tick.
     ///
     /// # Errors
     ///
-    /// Returns `QubitConflictError` if any qubit in the gate is already used by another gate in this tick.
-    pub fn try_add_gate(&mut self, gate: Gate) -> Result<usize, QubitConflictError> {
-        let conflicts = self.find_conflicts(&gate.qubits);
+    /// Returns [`TickGateError::InvalidGate`] if the gate payload is invalid, or
+    /// [`TickGateError::QubitConflict`] if any qubit in the gate is already used
+    /// by another gate in this tick.
+    pub(crate) fn try_add_gate_preserving_command(
+        &mut self,
+        gate: Gate,
+    ) -> Result<usize, TickGateError> {
+        gate.validate()
+            .map_err(|message| TickGateError::InvalidGate {
+                message,
+                tick_idx: None,
+            })?;
+        let conflicts = self.find_conflicts(&gate.qubits);
+        if !conflicts.is_empty() {
+            return Err(TickGateError::QubitConflict(QubitConflictError {
+                conflicting_qubits: conflicts,
+                tick_idx: None,
+            }));
+        }
+        Ok(self.push_gate_unchecked(gate))
+    }
+
+    /// Try to add a gate to this tick.
+    ///
+    /// # Errors
+    ///
+    /// Returns [`TickGateError::InvalidGate`] if the gate payload is invalid, or
+    /// [`TickGateError::QubitConflict`] if any qubit in the gate is already used
+    /// by another gate in this tick.
+    pub fn try_add_gate(&mut self, gate: Gate) -> Result<usize, TickGateError> {
+        self.try_add_gate_piece(gate).map(|piece| piece.gate_idx)
+    }
+
+    fn try_add_gate_piece(&mut self, gate: Gate) -> Result<GateBatchPiece, TickGateError> {
+        gate.validate()
+            .map_err(|message| TickGateError::InvalidGate {
+                message,
+                tick_idx: None,
+            })?;
+        let conflicts = self.find_conflicts(&gate.qubits);
         if !conflicts.is_empty() {
-            return Err(QubitConflictError {
+            return Err(TickGateError::QubitConflict(QubitConflictError {
                 conflicting_qubits: conflicts,
                 tick_idx: None,
+            }));
+        }
+        if let Some(gate_idx) = self.compatible_empty_attr_batch(&gate) {
+            let piece = GateBatchPiece {
+                gate_idx,
+                qubit_start: self.gate_batches[gate_idx].qubits.len(),
+                qubit_len: gate.qubits.len(),
+                meas_id_start: self.gate_batches[gate_idx].meas_ids.len(),
+                meas_id_len: gate.meas_ids.len(),
+            };
+            self.gate_batches.append_batch(gate_idx, gate);
+            return Ok(piece);
+        }
+        Ok(self.push_gate_unchecked_piece(gate))
+    }
+
+    /// Replace a stored gate batch while preserving storage invariants.
+    ///
+    /// # Errors
+    ///
+    /// Returns [`TickGateError::InvalidGate`] if `gate_idx` is out of bounds or
+    /// if the replacement gate payload is invalid. Returns
+    /// [`TickGateError::QubitConflict`] if the replacement overlaps another
+    /// command in this tick.
+    pub fn replace_gate_batch(&mut self, gate_idx: usize, gate: Gate) -> Result<(), TickGateError> {
+        if gate_idx >= self.gate_batches.len() {
+            return Err(TickGateError::InvalidGate {
+                message: format!("gate index {gate_idx} out of bounds"),
+                tick_idx: None,
             });
         }
-        Ok(self.add_gate(gate))
+        gate.validate()
+            .map_err(|message| TickGateError::InvalidGate {
+                message,
+                tick_idx: None,
+            })?;
+
+        let mut active = BTreeSet::new();
+        for (idx, existing) in self.gate_batches.iter().enumerate() {
+            if idx == gate_idx {
+                continue;
+            }
+            active.extend(existing.qubits.iter().copied());
+        }
+        let conflicts: Vec<QubitId> = gate
+            .qubits
+            .iter()
+            .filter(|q| active.contains(q))
+            .copied()
+            .collect();
+        if !conflicts.is_empty() {
+            return Err(TickGateError::QubitConflict(QubitConflictError {
+                conflicting_qubits: conflicts,
+                tick_idx: None,
+            }));
+        }
+
+        self.gate_batches.set(gate_idx, gate);
+        Ok(())
+    }
+
+    /// Mutate a stored gate batch through a temporary [`Gate`] value.
+    ///
+    /// The updated gate batch is validated with the same conflict checks as a
+    /// full replacement before it is written back.
+    ///
+    /// # Errors
+    ///
+    /// Propagates the same errors as [`replace_gate_batch`](Self::replace_gate_batch).
+    pub fn update_gate_batch(
+        &mut self,
+        gate_idx: usize,
+        update: impl FnOnce(&mut Gate),
+    ) -> Result<(), TickGateError> {
+        let Some(existing) = self.gate_batches.get(gate_idx) else {
+            return Err(TickGateError::InvalidGate {
+                message: format!("gate index {gate_idx} out of bounds"),
+                tick_idx: None,
+            });
+        };
+        let mut gate = existing.clone();
+        update(&mut gate);
+        self.replace_gate_batch(gate_idx, gate)
     }
 
     /// Remove all gates that use any of the specified qubits.
@@ -324,7 +1127,7 @@ impl Tick {
 
         // Find indices of gates to remove (those using any of the specified qubits)
         let indices_to_remove: Vec<usize> = self
-            .gates
+            .gate_batches
             .iter()
             .enumerate()
             .filter(|(_, gate)| gate.qubits.iter().any(|q| qubits_set.contains(q)))
@@ -339,17 +1142,7 @@ impl Tick {
 
         // Remove gates in reverse order to preserve indices
         for &idx in indices_to_remove.iter().rev() {
-            self.gates.remove(idx);
-        }
-
-        // Rebuild gate_attrs with updated indices
-        let old_attrs = std::mem::take(&mut self.gate_attrs);
-        for (old_idx, attrs) in old_attrs {
-            // Count how many removed indices are before this one
-            let shift = indices_to_remove.iter().filter(|&&i| i < old_idx).count();
-            if !indices_to_remove.contains(&old_idx) {
-                self.gate_attrs.insert(old_idx - shift, attrs);
-            }
+            let _ = self.remove_gate(idx);
         }
 
         removed_count
@@ -374,22 +1167,12 @@ impl Tick {
     /// assert_eq!(tick.len(), 2);  // H and Z remain
     /// ```
     pub fn remove_gate(&mut self, idx: usize) -> Option<Gate> {
-        if idx >= self.gates.len() {
+        if idx >= self.gate_batches.len() {
             return None;
         }
 
-        let gate = self.gates.remove(idx);
-
-        // Rebuild gate_attrs with updated indices
-        let old_attrs = std::mem::take(&mut self.gate_attrs);
-        for (old_idx, attrs) in old_attrs {
-            if old_idx < idx {
-                self.gate_attrs.insert(old_idx, attrs);
-            } else if old_idx > idx {
-                self.gate_attrs.insert(old_idx - 1, attrs);
-            }
-            // Skip old_idx == idx (removed gate's attrs)
-        }
+        let gate = self.gate_batches.remove(idx);
+        self.batch_attrs.remove(idx);
 
         Some(gate)
     }
@@ -425,6 +1208,23 @@ impl Tick {
 /// circuit.tick().cx(&[(0, 1), (2, 3)]);      // Multiple CX gates
 /// circuit.tick().mz(&[0, 1, 2, 3]);          // Measure multiple qubits
 /// ```
+/// Measurement reference in a tick circuit: (`tick_index`, `gate_index`, qubit).
+///
+/// Returned by `mz()` for use in `detector()` and `observable()` annotations.
+#[derive(Debug, Clone, Copy, PartialEq, Eq, Hash)]
+pub struct TickMeasRef {
+    /// Tick index.
+    pub tick: usize,
+    /// Gate index within the tick.
+    pub gate_idx: usize,
+    /// Qubit that was measured.
+    pub qubit: QubitId,
+    /// Measurement record index (cumulative count of MZ qubits in circuit order).
+    pub record_idx: usize,
+    /// Stable measurement result identity (SSA value).
+    pub meas_id: MeasId,
+}
+
 #[derive(Debug, Clone, Default)]
 pub struct TickCircuit {
     /// The sequence of ticks.
@@ -434,7 +1234,45 @@ pub struct TickCircuit {
     /// Circuit-level metadata.
     circuit_attrs: BTreeMap<String, Attribute>,
     /// Gate signatures for custom gate validation (JIT + AOT).
-    gate_signatures: HashMap<String, GateSignature>,
+    gate_signatures: BTreeMap<String, GateSignature>,
+    /// Unified Pauli annotations (detectors, observables, operators).
+    annotations: Vec<PauliAnnotation>,
+    /// Running count of measurement records (incremented by each MZ qubit).
+    next_meas_record: usize,
+}
+
+/// Maps an ideal circuit gate to zero or more channel annotations.
+///
+/// [`TickCircuit::with_noise`] uses this trait to compile an ideal circuit into
+/// an annotated circuit with explicit channel operations interleaved after the
+/// ideal gates that triggered them.
+pub trait GateNoiseModel {
+    /// Returns channel operations that should be placed after `gate`.
+    fn channels_after(&self, gate: &Gate) -> Vec<ChannelExpr>;
+}
+
+impl<F> GateNoiseModel for F
+where
+    F: Fn(&Gate) -> Vec<ChannelExpr>,
+{
+    fn channels_after(&self, gate: &Gate) -> Vec<ChannelExpr> {
+        self(gate)
+    }
+}
+
+fn schedule_channel_gate(noise_ticks: &mut Vec<Tick>, gate: Gate) {
+    let mut pending = Some(gate);
+    for tick in noise_ticks.iter_mut() {
+        let gate_ref = pending.as_ref().expect("pending gate is present");
+        if tick.find_conflicts(&gate_ref.qubits).is_empty() {
+            tick.add_gate(pending.take().expect("pending gate is present"));
+            return;
+        }
+    }
+
+    let mut tick = Tick::new();
+    tick.add_gate(pending.expect("pending gate is present"));
+    noise_ticks.push(tick);
 }
 
 /// Handle to a specific tick for adding gates.
@@ -445,6 +1283,7 @@ pub struct TickHandle<'a> {
     circuit: &'a mut TickCircuit,
     tick_idx: usize,
     last_gate_idx: Option<usize>,
+    last_gate_piece: Option<GateBatchPiece>,
 }
 
 /// Handle returned by preparation operations on a tick.
@@ -454,7 +1293,7 @@ pub struct TickHandle<'a> {
 pub struct TickPrepHandle<'a> {
     circuit: &'a mut TickCircuit,
     tick_idx: usize,
-    gate_idx: usize,
+    gate_piece: GateBatchPiece,
 }
 
 impl TickPrepHandle<'_> {
@@ -463,7 +1302,7 @@ impl TickPrepHandle<'_> {
     /// Returns `()` to break the chain.
     pub fn meta(self, key: &str, value: impl Into<Attribute>) {
         if let Some(tick) = self.circuit.get_tick_mut(self.tick_idx) {
-            tick.set_gate_attr(self.gate_idx, key, value.into());
+            tick.set_gate_attr_for_piece(self.gate_piece, key, value.into());
         }
     }
 
@@ -472,7 +1311,7 @@ impl TickPrepHandle<'_> {
     /// Returns `()` to break the chain.
     pub fn metas(self, attrs: BTreeMap<String, Attribute>) {
         if let Some(tick) = self.circuit.get_tick_mut(self.tick_idx) {
-            tick.set_gate_attrs(self.gate_idx, attrs);
+            tick.set_gate_attrs_for_piece(self.gate_piece, attrs);
         }
     }
 }
@@ -484,7 +1323,7 @@ impl TickPrepHandle<'_> {
 pub struct TickMeasureHandle<'a> {
     circuit: &'a mut TickCircuit,
     tick_idx: usize,
-    gate_idx: usize,
+    gate_piece: GateBatchPiece,
 }
 
 impl TickMeasureHandle<'_> {
@@ -493,7 +1332,7 @@ impl TickMeasureHandle<'_> {
     /// Returns `()` to break the chain.
     pub fn meta(self, key: &str, value: impl Into<Attribute>) {
         if let Some(tick) = self.circuit.get_tick_mut(self.tick_idx) {
-            tick.set_gate_attr(self.gate_idx, key, value.into());
+            tick.set_gate_attr_for_piece(self.gate_piece, key, value.into());
         }
     }
 
@@ -502,7 +1341,7 @@ impl TickMeasureHandle<'_> {
     /// Returns `()` to break the chain.
     pub fn metas(self, attrs: BTreeMap<String, Attribute>) {
         if let Some(tick) = self.circuit.get_tick_mut(self.tick_idx) {
-            tick.set_gate_attrs(self.gate_idx, attrs);
+            tick.set_gate_attrs_for_piece(self.gate_piece, attrs);
         }
     }
 }
@@ -515,7 +1354,9 @@ impl TickCircuit {
             ticks: Vec::new(),
             next_tick: 0,
             circuit_attrs: BTreeMap::new(),
-            gate_signatures: HashMap::new(),
+            gate_signatures: BTreeMap::new(),
+            annotations: Vec::new(),
+            next_meas_record: 0,
         }
     }
 
@@ -525,10 +1366,68 @@ impl TickCircuit {
         self.ticks.len()
     }
 
-    /// Get the total number of gates across all ticks.
+    /// Total number of measurement results produced so far.
+    #[must_use]
+    pub fn num_measurements(&self) -> usize {
+        self.next_meas_record
+    }
+
+    /// Advance the measurement counter by `n` (for external MZ gate construction).
+    pub fn advance_meas_counter(&mut self, n: usize) {
+        self.next_meas_record += n;
+    }
+
+    /// Get the total number of individual gate applications across all ticks.
+    ///
+    /// Batched commands count by individual gate. For example,
+    /// `cx(&[(0, 1), (2, 3)])` contributes two gates.
+    ///
+    /// # Examples
+    ///
+    /// ```
+    /// use pecos_quantum::TickCircuit;
+    ///
+    /// let mut circuit = TickCircuit::new();
+    /// circuit.tick().h(&[0, 1, 2]);
+    /// circuit.tick().cx(&[(0, 1), (2, 3)]);
+    ///
+    /// assert_eq!(circuit.gate_count(), 5);
+    /// assert_eq!(circuit.gate_batch_count(), 2);
+    /// ```
     #[must_use]
     pub fn gate_count(&self) -> usize {
-        self.ticks.iter().map(Tick::len).sum()
+        self.ticks.iter().map(Tick::gate_count).sum()
+    }
+
+    /// Get the total number of compatible gate batches across all ticks.
+    ///
+    /// A batch is a stored command group that can execute together because the
+    /// gates are identical except for disjoint qubit support and compatible
+    /// metadata.
+    ///
+    /// # Examples
+    ///
+    /// ```
+    /// use pecos_quantum::TickCircuit;
+    ///
+    /// let mut circuit = TickCircuit::new();
+    /// circuit.tick().h(&[0]).h(&[1]).cx(&[(2, 3), (4, 5)]);
+    ///
+    /// assert_eq!(circuit.gate_count(), 4);
+    /// assert_eq!(circuit.gate_batch_count(), 2); // one H batch, one CX batch
+    /// ```
+    #[must_use]
+    pub fn gate_batch_count(&self) -> usize {
+        self.ticks.iter().map(Tick::gate_batch_count).sum()
+    }
+
+    /// Convert a per-tick gate index to a global gate index.
+    ///
+    /// Global index = sum of stored gate batches for all ticks before
+    /// `tick_idx` + `gate_idx`.
+    #[must_use]
+    pub fn global_gate_index(&self, tick_idx: usize, gate_idx: usize) -> usize {
+        self.ticks[..tick_idx].iter().map(Tick::len).sum::<usize>() + gate_idx
     }
 
     /// Get a tick by index.
@@ -538,6 +1437,13 @@ impl TickCircuit {
     }
 
     /// Get a mutable tick by index.
+    ///
+    /// Mutating a tick through this handle must preserve the usual
+    /// `TickCircuit` invariants: each stored [`Gate`] must validate, qubits may
+    /// not overlap within a tick, and gate metadata must stay aligned with the
+    /// stored batches. Prefer `Tick` methods such as
+    /// [`Tick::add_gate`], [`Tick::remove_gate`], and
+    /// [`Tick::replace_gate_batch`] over direct structural rewrites.
     pub fn get_tick_mut(&mut self, idx: usize) -> Option<&mut Tick> {
         self.ticks.get_mut(idx)
     }
@@ -548,11 +1454,37 @@ impl TickCircuit {
         &self.ticks
     }
 
-    /// Get mutable access to all ticks.
+    /// Get mutable access to all ticks as a slice.
+    ///
+    /// This is an escape hatch for passes that need to mutate existing ticks in
+    /// place. Do not reorder, insert, or remove ticks through this slice. Keep
+    /// each tick's gate/metadata invariants intact by using `Tick` mutation
+    /// methods rather than editing stored batches directly.
     pub fn ticks_mut(&mut self) -> &mut [Tick] {
         &mut self.ticks
     }
 
+    /// Remove all ticks from this circuit for an internal structural rewrite.
+    ///
+    /// This is crate-private because a partially drained circuit has
+    /// temporarily invalid tick structure. Pair it with
+    /// [`replace_ticks`](Self::replace_ticks) in the same transformation.
+    pub(crate) fn take_ticks(&mut self) -> Vec<Tick> {
+        let ticks = std::mem::take(&mut self.ticks);
+        self.next_tick = 0;
+        ticks
+    }
+
+    /// Replace all ticks after an internal structural rewrite.
+    ///
+    /// Updates `next_tick` to match the replacement length. The caller remains
+    /// responsible for preserving measurement record numbering, annotation
+    /// references, tick ordering, and each tick's gate/metadata alignment.
+    pub(crate) fn replace_ticks(&mut self, ticks: Vec<Tick>) {
+        self.ticks = ticks;
+        self.next_tick = self.ticks.len();
+    }
+
     /// Export as a plain ASCII circuit diagram.
     ///
     /// Produces horizontal qubit-wire lines with gate symbols placed at each
@@ -638,7 +1570,7 @@ impl TickCircuit {
         let layers: Vec<Vec<&pecos_core::Gate>> = self
             .ticks
             .iter()
-            .map(|t| t.gates().iter().collect())
+            .map(|t| t.gate_batches().iter().collect())
             .collect();
         let num_qubits = self.all_qubits().len();
         let header = format!(
@@ -673,6 +1605,7 @@ impl TickCircuit {
             circuit: self,
             tick_idx,
             last_gate_idx: None,
+            last_gate_piece: None,
         }
     }
 
@@ -692,6 +1625,96 @@ impl TickCircuit {
         self.circuit_attrs.get(key)
     }
 
+    /// Add detector metadata defined by measurement-record offsets.
+    ///
+    /// This appends one entry to the circuit-level `"detectors"` JSON metadata
+    /// list and updates `"num_detectors"`. It is intended for circuits whose
+    /// detector definitions are stored in metadata rather than as direct
+    /// [`TickMeasRef`] annotations.
+    ///
+    /// # Errors
+    ///
+    /// Returns an error if existing detector metadata is not a JSON array, if
+    /// JSON serialization fails, or if `detector_id` duplicates an existing
+    /// explicit detector id.
+    pub fn add_detector_metadata(
+        &mut self,
+        records: &[i64],
+        coords: Option<&[f64]>,
+        label: Option<&str>,
+        detector_id: Option<usize>,
+    ) -> Result<usize, String> {
+        let mut detectors = meta_json_array(self, "detectors")?;
+        let id = match detector_id {
+            Some(id) => id,
+            None => next_metadata_id(&detectors, "detectors")?,
+        };
+        ensure_unique_metadata_id(&detectors, "detectors", "detector_id", id)?;
+
+        let mut detector = serde_json::Map::new();
+        detector.insert("id".to_string(), serde_json::json!(id));
+        detector.insert("records".to_string(), serde_json::json!(records));
+        if let Some(coords) = coords {
+            detector.insert("coords".to_string(), serde_json::json!(coords));
+        }
+        if let Some(label) = label {
+            detector.insert("label".to_string(), serde_json::json!(label));
+        }
+        detectors.push(serde_json::Value::Object(detector));
+        set_meta_json_array(self, "detectors", &detectors)?;
+        self.set_meta(
+            "num_detectors",
+            metadata_count_attr(&detectors, "detectors")?,
+        );
+        Ok(id)
+    }
+
+    /// Add observable metadata defined by measurement-record offsets.
+    ///
+    /// Standard observables live in the decoder `L<n>` id space. A label of
+    /// `"L3"` therefore selects observable id 3 unless `observable_id` is
+    /// provided, in which case the two must agree.
+    ///
+    /// # Errors
+    ///
+    /// Returns an error if existing observable metadata is not a JSON array, if
+    /// JSON serialization fails, if the label/id conflict, or if the selected
+    /// id duplicates an existing explicit observable id.
+    pub fn add_observable_metadata(
+        &mut self,
+        records: &[i64],
+        observable_id: Option<usize>,
+        label: Option<&str>,
+    ) -> Result<usize, String> {
+        let mut observables = meta_json_array(self, "observables")?;
+        let label_id = observable_id_from_label(label)?;
+        if let (Some(observable_id), Some(label_id)) = (observable_id, label_id)
+            && observable_id != label_id
+        {
+            return Err(format!(
+                "observable_id={observable_id} conflicts with label id L{label_id}"
+            ));
+        }
+        let id = observable_id
+            .or(label_id)
+            .map_or_else(|| next_metadata_id(&observables, "observables"), Ok)?;
+        ensure_unique_metadata_id(&observables, "observables", "observable_id", id)?;
+
+        let mut observable = serde_json::Map::new();
+        observable.insert("id".to_string(), serde_json::json!(id));
+        observable.insert("records".to_string(), serde_json::json!(records));
+        if let Some(label) = label {
+            observable.insert("label".to_string(), serde_json::json!(label));
+        }
+        observables.push(serde_json::Value::Object(observable));
+        set_meta_json_array(self, "observables", &observables)?;
+        self.set_meta(
+            "num_observables",
+            metadata_count_attr(&observables, "observables")?,
+        );
+        Ok(id)
+    }
+
     /// Get all circuit-level attributes.
     pub fn circuit_attrs(&self) -> impl Iterator<Item = (&String, &Attribute)> {
         self.circuit_attrs.iter()
@@ -755,6 +1778,75 @@ impl TickCircuit {
         self.next_tick = 0;
         self.circuit_attrs.clear();
         self.gate_signatures.clear();
+        self.annotations.clear();
+        self.next_meas_record = 0;
+    }
+
+    /// Try to compile an ideal circuit plus a gate-triggered noise model into
+    /// an annotated circuit containing explicit channel operations.
+    ///
+    /// The original gates are preserved. For each source tick, channel
+    /// operations returned by `noise.channels_after(gate)` are scheduled into
+    /// one or more immediately following ticks while respecting qubit
+    /// conflicts. This produces a concrete inline representation useful for
+    /// inspection, visualization, and simulators that consume interleaved
+    /// channel operations directly.
+    ///
+    /// For measurements, `channels_after` is literal: returned channels are
+    /// placed after the measurement operation. Physical pre-measurement noise
+    /// and classical readout flips should use explicit APIs for those concepts
+    /// instead of being hidden in this post-gate hook.
+    ///
+    /// # Errors
+    ///
+    /// Returns an error if the source circuit already contains channel
+    /// operations. Apply either inline channels or a noise model, not both.
+    pub fn try_with_noise<N: GateNoiseModel>(&self, noise: &N) -> Result<Self, String> {
+        for (tick_idx, tick) in self.iter_ticks() {
+            for gate in tick.iter_gate_batches() {
+                if gate.is_channel() {
+                    let gate_idx = gate.batch_index();
+                    return Err(format!(
+                        "with_noise cannot apply a noise model to a circuit that already contains channel operations (first channel at tick {tick_idx} gate {gate_idx})"
+                    ));
+                }
+            }
+        }
+
+        let mut out = Self::new();
+        out.circuit_attrs.clone_from(&self.circuit_attrs);
+        out.gate_signatures.clone_from(&self.gate_signatures);
+        out.annotations.clone_from(&self.annotations);
+        out.next_meas_record = self.next_meas_record;
+
+        for tick in &self.ticks {
+            out.ticks.push(tick.clone());
+
+            let mut noise_ticks = Vec::new();
+            for gate in tick.iter_gate_batches() {
+                for channel in noise.channels_after(gate.as_gate()) {
+                    schedule_channel_gate(&mut noise_ticks, Gate::channel(channel));
+                }
+            }
+            out.ticks.extend(noise_ticks);
+        }
+
+        out.next_tick = out.ticks.len();
+        Ok(out)
+    }
+
+    /// Compile an ideal circuit plus a gate-triggered noise model into an
+    /// annotated circuit containing explicit channel operations.
+    ///
+    /// This is the convenience form of [`try_with_noise`](Self::try_with_noise).
+    ///
+    /// # Panics
+    ///
+    /// Panics if the source circuit already contains channel operations.
+    #[must_use]
+    pub fn with_noise<N: GateNoiseModel>(&self, noise: &N) -> Self {
+        self.try_with_noise(noise)
+            .expect("with_noise requires an ideal circuit without existing channel operations")
     }
 
     /// Reserve empty ticks in advance.
@@ -825,6 +1917,7 @@ impl TickCircuit {
             circuit: self,
             tick_idx: idx,
             last_gate_idx: None,
+            last_gate_piece: None,
         }
     }
 
@@ -864,6 +1957,7 @@ impl TickCircuit {
             circuit: self,
             tick_idx: idx,
             last_gate_idx: None,
+            last_gate_piece: None,
         }
     }
 
@@ -896,14 +1990,14 @@ impl TickCircuit {
     // --- Gate signature validation ---
 
     /// Import gate signatures in bulk (e.g., from a `GateRegistry`).
-    pub fn import_signatures(&mut self, sigs: &HashMap<String, GateSignature>) {
+    pub fn import_signatures(&mut self, sigs: &BTreeMap<String, GateSignature>) {
         self.gate_signatures
             .extend(sigs.iter().map(|(name, sig)| (name.clone(), sig.clone())));
     }
 
     /// Get read access to the gate signatures.
     #[must_use]
-    pub fn gate_signatures(&self) -> &HashMap<String, GateSignature> {
+    pub fn gate_signatures(&self) -> &BTreeMap<String, GateSignature> {
         &self.gate_signatures
     }
 
@@ -944,49 +2038,41 @@ impl TickCircuit {
 
     // --- Iteration helpers ---
 
-    /// Iterate over all gates in the circuit, across all ticks.
-    ///
-    /// Gates are yielded in tick order, then in order within each tick.
-    ///
-    /// # Examples
-    ///
-    /// ```
-    /// use pecos_quantum::TickCircuit;
+    /// Iterate over full-fidelity gate batches in the circuit.
     ///
-    /// let mut circuit = TickCircuit::new();
-    /// circuit.tick().h(&[0, 1]);
-    /// circuit.tick().cx(&[(0, 1)]);
-    ///
-    /// for gate in circuit.iter_gates() {
-    ///     println!("{:?} on {:?}", gate.gate_type, gate.qubits);
-    /// }
-    /// ```
-    pub fn iter_gates(&self) -> impl Iterator<Item = &Gate> {
-        self.ticks.iter().flat_map(Tick::gates)
+    /// This is the preferred API for consumers that execute or analyze batched
+    /// commands. Each yielded [`Gate`] may represent multiple individual gates
+    /// on disjoint qubits, and carries the full gate payload.
+    pub fn iter_gate_batches(&self) -> impl Iterator<Item = GateBatchRef<'_>> {
+        self.ticks.iter().flat_map(Tick::iter_gate_batches)
     }
 
-    /// Iterate over all gates with their tick index.
-    ///
-    /// Yields `(tick_index, gate)` pairs.
-    ///
-    /// # Examples
-    ///
-    /// ```
-    /// use pecos_quantum::TickCircuit;
-    ///
-    /// let mut circuit = TickCircuit::new();
-    /// circuit.tick().h(&[0]);
-    /// circuit.tick().x(&[0]);
-    ///
-    /// for (tick_idx, gate) in circuit.iter_gates_with_tick() {
-    ///     println!("Tick {}: {:?}", tick_idx, gate.gate_type);
-    /// }
-    /// ```
-    pub fn iter_gates_with_tick(&self) -> impl Iterator<Item = (usize, &Gate)> {
+    /// Returns true if any tick contains an explicit channel operation.
+    #[must_use]
+    pub fn has_channel_operations(&self) -> bool {
+        self.iter_gate_batches().any(|gate| gate.is_channel())
+    }
+
+    /// Iterate over full-fidelity gate batches with their tick index.
+    pub fn iter_gate_batches_with_tick(&self) -> impl Iterator<Item = (usize, GateBatchRef<'_>)> {
         self.ticks
             .iter()
             .enumerate()
-            .flat_map(|(tick_idx, tick)| tick.gates().iter().map(move |gate| (tick_idx, gate)))
+            .flat_map(|(tick_idx, tick)| tick.iter_gate_batches().map(move |gate| (tick_idx, gate)))
+    }
+
+    /// Iterate over individual gates expanded from stored batches.
+    pub fn iter_gate_instances(&self) -> impl Iterator<Item = GateInstanceRef<'_>> {
+        self.ticks.iter().flat_map(Tick::iter_gate_instances)
+    }
+
+    /// Iterate over individual gates with their tick index.
+    pub fn iter_gate_instances_with_tick(
+        &self,
+    ) -> impl Iterator<Item = (usize, GateInstanceRef<'_>)> {
+        self.ticks.iter().enumerate().flat_map(|(tick_idx, tick)| {
+            tick.iter_gate_instances().map(move |gate| (tick_idx, gate))
+        })
     }
 
     /// Iterate over ticks with their index.
@@ -998,7 +2084,8 @@ impl TickCircuit {
     ///
     /// let mut circuit = TickCircuit::new();
     /// circuit.tick().h(&[0, 1, 2]);
-    /// circuit.tick().cx(&[(0, 1), (1, 2)]);
+    /// circuit.tick().cx(&[(0, 1)]);
+    /// circuit.tick().cx(&[(1, 2)]);
     ///
     /// for (tick_idx, tick) in circuit.iter_ticks() {
     ///     println!("Tick {} has {} gates", tick_idx, tick.len());
@@ -1022,10 +2109,14 @@ impl TickCircuit {
     ///
     /// // Get all H gates
     /// let h_gates: Vec<_> = circuit.iter_gates_by_type(GateType::H).collect();
-    /// assert_eq!(h_gates.len(), 1);  // One Gate object with 3 qubits
+    /// assert_eq!(h_gates.len(), 1);  // One H batch with 3 qubits
     /// ```
-    pub fn iter_gates_by_type(&self, gate_type: GateType) -> impl Iterator<Item = &Gate> {
-        self.iter_gates().filter(move |g| g.gate_type == gate_type)
+    pub fn iter_gates_by_type(
+        &self,
+        gate_type: GateType,
+    ) -> impl Iterator<Item = GateBatchRef<'_>> {
+        self.iter_gate_batches()
+            .filter(move |g| g.gate_type == gate_type)
     }
 
     /// Get all qubits used in the circuit.
@@ -1044,14 +2135,16 @@ impl TickCircuit {
     /// ```
     #[must_use]
     pub fn all_qubits(&self) -> BTreeSet<QubitId> {
-        self.iter_gates()
-            .flat_map(|gate| gate.qubits.iter().copied())
+        self.iter_gate_batches()
+            .flat_map(|gate| gate.as_gate().qubits.iter().copied())
             .collect()
     }
 
     /// Count gates by type across the entire circuit.
     ///
-    /// Returns a map from `GateType` to count.
+    /// Returns a map from `GateType` to gate count. Batched commands
+    /// such as `cx(&[(0, 1), (2, 3)])` count as two CX gates even though they
+    /// are stored as one [`Gate`] carrying two disjoint pairs.
     ///
     /// # Examples
     ///
@@ -1060,93 +2153,331 @@ impl TickCircuit {
     /// use pecos_core::gate_type::GateType;
     ///
     /// let mut circuit = TickCircuit::new();
-    /// circuit.tick().h(&[0, 1, 2]);
-    /// circuit.tick().cx(&[(0, 1), (1, 2)]);
+    /// circuit.tick().h(&[0, 1, 2, 3]);
+    /// circuit.tick().cx(&[(0, 1), (2, 3)]);
     ///
     /// let counts = circuit.gate_counts_by_type();
-    /// assert_eq!(counts.get(&GateType::H), Some(&1));  // 1 H gate object (with 3 qubits)
-    /// assert_eq!(counts.get(&GateType::CX), Some(&1)); // 1 CX gate object (with 2 pairs)
+    /// assert_eq!(counts.get(&GateType::H), Some(&4));  // 4 H gates
+    /// assert_eq!(counts.get(&GateType::CX), Some(&2)); // 2 CX gates
     /// ```
     #[must_use]
     pub fn gate_counts_by_type(&self) -> BTreeMap<GateType, usize> {
         let mut counts = BTreeMap::new();
-        for gate in self.iter_gates() {
-            *counts.entry(gate.gate_type).or_insert(0) += 1;
+        for gate in self.iter_gate_batches() {
+            *counts.entry(gate.gate_type).or_insert(0) += gate.num_gates();
         }
         counts
     }
-}
+    // ==================== Annotations ====================
 
-// --- TickHandle - handle for adding gates to a specific tick ---
+    /// Annotate a detector: measurements whose XOR should be deterministic.
+    pub fn detector(&mut self, measurements: &[TickMeasRef]) -> usize {
+        let meas_nodes: Vec<usize> = measurements.iter().map(|m| m.record_idx).collect();
+        let pauli = pecos_core::PauliString::zs(
+            &measurements
+                .iter()
+                .map(|m| m.qubit.index())
+                .collect::<Vec<_>>(),
+        );
+        let idx = self.annotations.len();
+        self.annotations.push(PauliAnnotation {
+            pauli,
+            kind: AnnotationKind::Detector {
+                measurement_nodes: meas_nodes,
+                coords: Vec::new(),
+            },
+            label: None,
+        });
+        idx
+    }
 
-impl<'a> TickHandle<'a> {
-    /// Get the tick index this handle refers to.
+    /// Annotate a labeled detector.
+    pub fn detector_labeled(&mut self, label: &str, measurements: &[TickMeasRef]) -> usize {
+        let idx = self.detector(measurements);
+        self.annotations[idx].label = Some(label.to_string());
+        idx
+    }
+
+    /// Annotate a logical observable.
+    pub fn observable(&mut self, measurements: &[TickMeasRef]) -> usize {
+        let meas_nodes: Vec<usize> = measurements.iter().map(|m| m.record_idx).collect();
+        let pauli = pecos_core::PauliString::zs(
+            &measurements
+                .iter()
+                .map(|m| m.qubit.index())
+                .collect::<Vec<_>>(),
+        );
+        let idx = self.annotations.len();
+        self.annotations.push(PauliAnnotation {
+            pauli,
+            kind: AnnotationKind::Observable {
+                measurement_nodes: meas_nodes,
+            },
+            label: None,
+        });
+        idx
+    }
+
+    /// Annotate a labeled observable.
+    pub fn observable_labeled(&mut self, label: &str, measurements: &[TickMeasRef]) -> usize {
+        let idx = self.observable(measurements);
+        self.annotations[idx].label = Some(label.to_string());
+        idx
+    }
+
+    /// Place a tracked-Pauli annotation.
+    pub fn tracked_pauli(&mut self, mut pauli: pecos_core::PauliString) -> usize {
+        pauli.set_phase(pecos_core::QuarterPhase::PlusOne);
+        let idx = self.annotations.len();
+        self.annotations.push(PauliAnnotation {
+            pauli,
+            kind: AnnotationKind::TrackedPauli,
+            label: None,
+        });
+        idx
+    }
+
+    /// Place a labeled tracked-Pauli annotation.
+    pub fn tracked_pauli_labeled(&mut self, label: &str, pauli: pecos_core::PauliString) -> usize {
+        let idx = self.tracked_pauli(pauli);
+        self.annotations[idx].label = Some(label.to_string());
+        idx
+    }
+
+    /// Get all annotations.
     #[must_use]
-    pub fn index(&self) -> usize {
-        self.tick_idx
+    pub fn annotations(&self) -> &[PauliAnnotation] {
+        &self.annotations
     }
 
-    /// Add a gate to this tick.
+    // ==================== Idle ====================
+
+    /// Insert identity gates for qubits not operated on during each tick.
     ///
-    /// # Panics
+    /// For each tick, finds qubits that are in the circuit's qubit set but
+    /// not actively operated on, and inserts an identity (I) gate. These
+    /// gates receive `p1` noise from the noise model, matching Stim's
+    /// convention of `DEPOLARIZE1` on idle qubits between ticks.
     ///
-    /// Panics if any qubit in the gate is already used by another gate in this tick.
-    /// Use `try_add_gate` for fallible gate addition.
-    fn add_gate(&mut self, gate: Gate) -> &mut Self {
-        match self.circuit.ticks[self.tick_idx].try_add_gate(gate) {
-            Ok(idx) => {
-                self.last_gate_idx = Some(idx);
-                self
-            }
-            Err(mut err) => {
-                err.tick_idx = Some(self.tick_idx);
-                panic!("{}", err);
-            }
-        }
-    }
-
-    /// Try to add a gate to this tick, returning an error if any qubit is already in use.
+    /// This is separate from `GateType::Idle` which represents explicit
+    /// wait operations with duration-dependent `p_idle` noise.
     ///
-    /// # Errors
+    /// # Example
     ///
-    /// Returns `QubitConflictError` if any qubit in the gate is already used by another gate in this tick.
-    pub fn try_add_gate(&mut self, gate: Gate) -> Result<&mut Self, QubitConflictError> {
-        match self.circuit.ticks[self.tick_idx].try_add_gate(gate) {
-            Ok(idx) => {
-                self.last_gate_idx = Some(idx);
-                Ok(self)
-            }
-            Err(mut err) => {
-                err.tick_idx = Some(self.tick_idx);
-                Err(err)
+    /// ```
+    /// use pecos_quantum::TickCircuit;
+    ///
+    /// let mut circuit = TickCircuit::new();
+    /// circuit.tick().h(&[0]);
+    /// circuit.tick().cx(&[(0, 1)]);
+    /// circuit.tick().mz(&[0, 1]);
+    ///
+    /// circuit.fill_idle_gates();
+    /// ```
+    /// Insert Idle gates after each two-qubit gate on both of its qubits.
+    ///
+    /// Delegates to `InsertIdleAfterTwoQubitGates` pass. See [`crate::pass`].
+    pub fn insert_idle_after_two_qubit_gates(&mut self, duration: f64) {
+        use crate::pass::{CircuitPass, InsertIdleAfterTwoQubitGates};
+        InsertIdleAfterTwoQubitGates(duration).apply_tick(self);
+    }
+
+    pub fn fill_idle_gates(&mut self) {
+        let all_qubits = self.all_qubits();
+        if all_qubits.is_empty() {
+            return;
+        }
+
+        for tick in &mut self.ticks {
+            let active = tick.active_qubits();
+            for &q in &all_qubits {
+                if !active.contains(&q) {
+                    // Duration 1 = one tick of idling
+                    let _ = tick.try_add_gate(Gate::idle(1.0, vec![q]));
+                }
             }
         }
     }
 
-    /// Add a gate and return the gate index.
+    /// Compact ticks by merging gates into earlier ticks when possible.
     ///
-    /// # Panics
+    /// ASAP scheduling: walk ticks in order, try to merge each tick's gates
+    /// into the latest tick where all qubits are free. Produces the minimum
+    /// number of ticks for the same gate dependency structure.
     ///
-    /// Panics if any qubit in the gate is already used by another gate in this tick.
-    fn add_gate_get_idx(&mut self, gate: Gate) -> usize {
-        match self.circuit.ticks[self.tick_idx].try_add_gate(gate) {
-            Ok(idx) => {
-                self.last_gate_idx = Some(idx);
-                idx
+    /// This is useful after replaying a serialized trace (e.g., from QIR)
+    /// where each gate gets its own tick even if they could run in parallel.
+    ///
+    /// Gate metadata and tick-level metadata are preserved. Tick-level
+    /// metadata from merged ticks is dropped (the target tick's metadata
+    /// wins).
+    ///
+    /// # Panics
+    ///
+    /// Panics if an existing gate in the circuit fails validation while being
+    /// moved into its compacted tick. Circuits built through `TickCircuit`
+    /// constructors already validate gates at insertion time.
+    ///
+    /// # Example
+    ///
+    /// ```
+    /// use pecos_quantum::TickCircuit;
+    ///
+    /// let mut circuit = TickCircuit::new();
+    /// // Serialized: each gate in its own tick
+    /// circuit.tick().h(&[0]);
+    /// circuit.tick().h(&[1]);
+    /// circuit.tick().cx(&[(0, 1)]);
+    /// assert_eq!(circuit.num_ticks(), 3);
+    ///
+    /// circuit.compact_ticks();
+    /// // H(0) and H(1) merged into one tick; CX(0,1) stays separate
+    /// assert_eq!(circuit.num_ticks(), 2);
+    /// ```
+    pub fn compact_ticks(&mut self) {
+        if self.ticks.len() <= 1 {
+            return;
+        }
+
+        let old_ticks: Vec<Tick> = self.ticks.drain(..).collect();
+        let mut compacted: Vec<Tick> = Vec::new();
+
+        for tick in old_ticks {
+            let mut placed = false;
+
+            // Try to merge into the latest existing tick where all qubits are free.
+            // Walk backwards to find the latest valid target (ASAP scheduling).
+            for target_idx in (0..compacted.len()).rev() {
+                let can_merge = tick.gate_batches.iter().all(|gate| {
+                    gate.qubits
+                        .iter()
+                        .all(|q| !compacted[target_idx].uses_qubit(*q))
+                });
+
+                if can_merge {
+                    // Check that no tick between target+1..end uses any of these qubits
+                    // (would violate ordering).
+                    let all_clear = (target_idx + 1..compacted.len()).all(|between| {
+                        tick.gate_batches.iter().all(|gate| {
+                            gate.qubits
+                                .iter()
+                                .all(|q| !compacted[between].uses_qubit(*q))
+                        })
+                    });
+
+                    if all_clear {
+                        // Move gates and their per-gate metadata into the target tick.
+                        for (gi, gate) in tick.gate_batches.iter().enumerate() {
+                            if let Some(attrs) = tick.normalized_gate_attrs(gi) {
+                                let new_idx = compacted[target_idx]
+                                    .try_add_gate_preserving_command(gate.clone())
+                                    .unwrap_or_else(|err| panic!("{err}"));
+                                compacted[target_idx].set_gate_attrs(new_idx, attrs.clone());
+                                compacted[target_idx].merge_compatible_gate_at(new_idx);
+                            } else {
+                                compacted[target_idx].add_gate(gate.clone());
+                            }
+                        }
+                        placed = true;
+                        break;
+                    }
+                }
+            }
+
+            if !placed {
+                compacted.push(tick);
+            }
+        }
+
+        self.ticks = compacted;
+        self.next_tick = self.ticks.len();
+    }
+}
+
+// --- TickHandle - handle for adding gates to a specific tick ---
+
+impl<'a> TickHandle<'a> {
+    /// Get the tick index this handle refers to.
+    #[must_use]
+    pub fn index(&self) -> usize {
+        self.tick_idx
+    }
+
+    /// Add a gate to this tick.
+    ///
+    /// # Panics
+    ///
+    /// Panics if the gate payload is invalid or any qubit in the gate is
+    /// already used by another gate in this tick.
+    /// Use `try_add_gate` for fallible gate addition.
+    fn add_gate(&mut self, gate: Gate) -> &mut Self {
+        match self.circuit.ticks[self.tick_idx].try_add_gate_piece(gate) {
+            Ok(piece) => {
+                self.last_gate_idx = Some(piece.gate_idx);
+                self.last_gate_piece = Some(piece);
+                self
+            }
+            Err(mut err) => {
+                err.set_tick_idx(self.tick_idx);
+                panic!("{}", err);
+            }
+        }
+    }
+
+    /// Try to add a gate to this tick.
+    ///
+    /// # Errors
+    ///
+    /// Returns [`TickGateError::InvalidGate`] if the gate payload is invalid, or
+    /// [`TickGateError::QubitConflict`] if any qubit in the gate is already used
+    /// by another gate in this tick.
+    pub fn try_add_gate(&mut self, gate: Gate) -> Result<&mut Self, TickGateError> {
+        match self.circuit.ticks[self.tick_idx].try_add_gate_piece(gate) {
+            Ok(piece) => {
+                self.last_gate_idx = Some(piece.gate_idx);
+                self.last_gate_piece = Some(piece);
+                Ok(self)
+            }
+            Err(mut err) => {
+                err.set_tick_idx(self.tick_idx);
+                Err(err)
+            }
+        }
+    }
+
+    /// Add a gate and return the gate index.
+    ///
+    /// # Panics
+    ///
+    /// Panics if the gate payload is invalid or any qubit in the gate is
+    /// already used by another gate in this tick.
+    fn add_gate_get_piece(&mut self, gate: Gate) -> GateBatchPiece {
+        match self.circuit.ticks[self.tick_idx].try_add_gate_piece(gate) {
+            Ok(piece) => {
+                self.last_gate_idx = Some(piece.gate_idx);
+                self.last_gate_piece = Some(piece);
+                piece
             }
             Err(mut err) => {
-                err.tick_idx = Some(self.tick_idx);
+                err.set_tick_idx(self.tick_idx);
                 panic!("{}", err);
             }
         }
     }
 
+    fn add_gate_get_idx(&mut self, gate: Gate) -> usize {
+        self.add_gate_get_piece(gate).gate_idx
+    }
+
     /// Set metadata on the last added gate.
     ///
     /// If no gate has been added yet, sets tick-level metadata instead.
     pub fn meta(&mut self, key: &str, value: impl Into<Attribute>) -> &mut Self {
-        if let Some(gate_idx) = self.last_gate_idx {
-            self.circuit.ticks[self.tick_idx].set_gate_attr(gate_idx, key, value.into());
+        if let Some(piece) = self.last_gate_piece {
+            let piece =
+                self.circuit.ticks[self.tick_idx].set_gate_attr_for_piece(piece, key, value.into());
+            self.last_gate_idx = Some(piece.gate_idx);
+            self.last_gate_piece = Some(piece);
         } else {
             // No gate yet - set tick-level metadata
             self.circuit.ticks[self.tick_idx].set_attr(key, value.into());
@@ -1158,8 +2489,10 @@ impl<'a> TickHandle<'a> {
     ///
     /// If no gate has been added yet, sets tick-level metadata instead.
     pub fn metas(&mut self, attrs: BTreeMap<String, Attribute>) -> &mut Self {
-        if let Some(gate_idx) = self.last_gate_idx {
-            self.circuit.ticks[self.tick_idx].set_gate_attrs(gate_idx, attrs);
+        if let Some(piece) = self.last_gate_piece {
+            let piece = self.circuit.ticks[self.tick_idx].set_gate_attrs_for_piece(piece, attrs);
+            self.last_gate_idx = Some(piece.gate_idx);
+            self.last_gate_piece = Some(piece);
         } else {
             // No gate yet - set tick-level metadata
             self.circuit.ticks[self.tick_idx].set_attrs(attrs);
@@ -1351,6 +2684,14 @@ impl<'a> TickHandle<'a> {
         self.add_gate(Gate::u(theta.into(), phi.into(), lambda.into(), qubits))
     }
 
+    /// Place a typed channel operation in this tick.
+    ///
+    /// This is for annotated/noisy circuits. It does not use custom-gate
+    /// metadata; the channel payload is stored directly on the gate.
+    pub fn channel(&mut self, channel: ChannelExpr) -> &mut Self {
+        self.add_gate(Gate::channel(channel))
+    }
+
     // --- Two-qubit gates ---
 
     /// Apply CNOT (CX) gate(s) to one or more qubit pairs.
@@ -1591,11 +2932,13 @@ impl<'a> TickHandle<'a> {
     /// circuit.tick().pz(&[1, 2, 3]);     // Multiple qubits
     /// ```
     pub fn pz(mut self, qubits: &[impl Into<QubitId> + Copy]) -> TickPrepHandle<'a> {
-        let gate_idx = self.add_gate_get_idx(Gate::pz(qubits));
+        let gate_piece = self.add_gate_get_piece(Gate::pz(qubits));
+        self.last_gate_idx = None;
+        self.last_gate_piece = None;
         TickPrepHandle {
             circuit: self.circuit,
             tick_idx: self.tick_idx,
-            gate_idx,
+            gate_piece,
         }
     }
 
@@ -1613,13 +2956,33 @@ impl<'a> TickHandle<'a> {
     /// circuit.tick().mz(&[0]);           // Single qubit
     /// circuit.tick().mz(&[1, 2, 3]);     // Multiple qubits
     /// ```
-    pub fn mz(mut self, qubits: &[impl Into<QubitId> + Copy]) -> TickMeasureHandle<'a> {
-        let gate_idx = self.add_gate_get_idx(Gate::mz(qubits));
-        TickMeasureHandle {
-            circuit: self.circuit,
-            tick_idx: self.tick_idx,
-            gate_idx,
+    pub fn mz(mut self, qubits: &[impl Into<QubitId> + Copy]) -> Vec<TickMeasRef> {
+        let mut gate = Gate::mz(qubits);
+        let mut refs = Vec::with_capacity(qubits.len());
+        for &q in qubits {
+            let tick_idx = self.tick_idx;
+            let record_idx = self.circuit.next_meas_record;
+            self.circuit.next_meas_record += 1;
+            let mr = MeasId(record_idx);
+            gate.meas_ids.push(mr);
+            refs.push(TickMeasRef {
+                tick: tick_idx,
+                gate_idx: 0, // placeholder, updated below
+                qubit: q.into(),
+                record_idx,
+                meas_id: mr,
+            });
         }
+        let gate_idx = self.add_gate_get_idx(gate);
+        self.last_gate_idx = None;
+        self.last_gate_piece = None;
+        // Fix up gate_idx in refs (needed because we had to build gate before adding)
+        refs.into_iter()
+            .map(|mut r| {
+                r.gate_idx = gate_idx;
+                r
+            })
+            .collect()
     }
 
     /// Measure and free qubit(s) (destructive measurement).
@@ -1634,13 +2997,32 @@ impl<'a> TickHandle<'a> {
     /// let mut circuit = TickCircuit::new();
     /// circuit.tick().mz_free(&[0, 1]);
     /// ```
-    pub fn mz_free(mut self, qubits: &[impl Into<QubitId> + Copy]) -> TickMeasureHandle<'a> {
-        let gate_idx = self.add_gate_get_idx(Gate::mz_free(qubits));
-        TickMeasureHandle {
-            circuit: self.circuit,
-            tick_idx: self.tick_idx,
-            gate_idx,
+    pub fn mz_free(mut self, qubits: &[impl Into<QubitId> + Copy]) -> Vec<TickMeasRef> {
+        let mut gate = Gate::mz_free(qubits);
+        let mut refs = Vec::with_capacity(qubits.len());
+        for &q in qubits {
+            let tick_idx = self.tick_idx;
+            let record_idx = self.circuit.next_meas_record;
+            self.circuit.next_meas_record += 1;
+            let mr = MeasId(record_idx);
+            gate.meas_ids.push(mr);
+            refs.push(TickMeasRef {
+                tick: tick_idx,
+                gate_idx: 0,
+                qubit: q.into(),
+                record_idx,
+                meas_id: mr,
+            });
         }
+        let gate_idx = self.add_gate_get_idx(gate);
+        self.last_gate_idx = None;
+        self.last_gate_piece = None;
+        refs.into_iter()
+            .map(|mut r| {
+                r.gate_idx = gate_idx;
+                r
+            })
+            .collect()
     }
 
     // --- Resource management ---
@@ -1718,20 +3100,21 @@ impl<'a> TickHandle<'a> {
         let qubit_ids: GateQubits = qubits.iter().map(|&q| QubitId::from(q)).collect();
         let gate = Gate::new(GateType::Custom, angles.to_vec(), vec![], qubit_ids);
 
-        match self.circuit.ticks[self.tick_idx].try_add_gate(gate) {
-            Ok(idx) => {
-                self.last_gate_idx = Some(idx);
+        match self.circuit.ticks[self.tick_idx].try_add_gate_piece(gate) {
+            Ok(piece) => {
                 // Auto-store _symbol metadata
-                self.circuit.ticks[self.tick_idx].set_gate_attr(
-                    idx,
+                let piece = self.circuit.ticks[self.tick_idx].set_gate_attr_for_piece(
+                    piece,
                     "_symbol",
                     Attribute::String(name.to_string()),
                 );
+                self.last_gate_idx = Some(piece.gate_idx);
+                self.last_gate_piece = Some(piece);
                 Ok(self)
             }
             Err(mut err) => {
-                err.tick_idx = Some(self.tick_idx);
-                Err(CustomGateError::QubitConflict(err))
+                err.set_tick_idx(self.tick_idx);
+                Err(err.into())
             }
         }
     }
@@ -1759,36 +3142,68 @@ impl From<&DagCircuit> for TickCircuit {
     /// ```
     fn from(dag: &DagCircuit) -> Self {
         let mut tc = TickCircuit::new();
+        let mut dag_node_to_record_indices: BTreeMap<usize, Vec<usize>> = BTreeMap::new();
+        let mut next_meas_record = 0usize;
 
         for layer in dag.layers() {
-            // Allocate a new tick for this layer
-            let tick_idx = {
-                let handle = tc.tick();
-                handle.index()
-            };
-
-            // Add all gates in this layer to the tick
-            if let Some(tick) = tc.get_tick_mut(tick_idx) {
-                for node_id in layer {
-                    if let Some(gate) = dag.gate(node_id) {
-                        let gate_idx = tick.add_gate(gate.clone());
-
-                        // Copy gate attributes
-                        if let Some(attrs) = dag.gate_attrs(node_id) {
-                            for (key, value) in attrs {
-                                tick.set_gate_attr(gate_idx, key, value.clone());
+            let mut layer_ticks = vec![Tick::new()];
+
+            for node_id in layer {
+                if let Some(gate) = dag.gate(node_id) {
+                    let mut gate = gate.clone();
+                    if matches!(
+                        gate.gate_type,
+                        GateType::MZ | GateType::MeasureFree | GateType::MeasureLeaked
+                    ) {
+                        if gate.meas_ids.is_empty() {
+                            let mut records = Vec::with_capacity(gate.qubits.len());
+                            for _ in &gate.qubits {
+                                let record_idx = next_meas_record;
+                                next_meas_record += 1;
+                                gate.meas_ids.push(MeasId(record_idx));
+                                records.push(record_idx);
                             }
+                            dag_node_to_record_indices.insert(node_id, records);
+                        } else {
+                            let records: Vec<usize> =
+                                gate.meas_ids.iter().map(|meas_id| meas_id.0).collect();
+                            if let Some(next) = records.iter().max().map(|record| record + 1) {
+                                next_meas_record = next_meas_record.max(next);
+                            }
+                            dag_node_to_record_indices.insert(node_id, records);
                         }
                     }
+
+                    let target_idx = layer_ticks
+                        .iter()
+                        .position(|tick| tick.find_conflicts(&gate.qubits).is_empty())
+                        .unwrap_or_else(|| {
+                            layer_ticks.push(Tick::new());
+                            layer_ticks.len() - 1
+                        });
+                    let tick = &mut layer_ticks[target_idx];
+                    // Copy gate attributes
+                    if let Some(attrs) = dag.gate_attrs(node_id) {
+                        let gate_idx = tick
+                            .try_add_gate_preserving_command(gate)
+                            .unwrap_or_else(|err| panic!("{err}"));
+                        tick.set_gate_attrs(gate_idx, attrs.clone());
+                        tick.merge_compatible_gate_at(gate_idx);
+                    } else {
+                        tick.add_gate(gate);
+                    }
                 }
             }
+
+            tc.ticks.extend(layer_ticks);
         }
+        tc.next_tick = tc.ticks.len();
+        tc.next_meas_record = next_meas_record;
 
         // Copy circuit-level attributes, restoring tick-level attrs from prefixed keys
         let tick_attr_prefix = "tick[";
         for (key, value) in dag.attrs() {
             if key.starts_with(tick_attr_prefix) {
-                // Parse tick[N].attr_name format
                 if let Some(rest) = key.strip_prefix(tick_attr_prefix)
                     && let Some(bracket_pos) = rest.find(']')
                     && let Ok(tick_idx) = rest[..bracket_pos].parse::<usize>()
@@ -1805,10 +3220,62 @@ impl From<&DagCircuit> for TickCircuit {
             }
         }
 
+        // Transfer annotations, remapping DAG measurement nodes to TickCircuit
+        // measurement record indices. Tracked Paulis have no measurement
+        // readout and keep their Pauli role unchanged.
+        tc.annotations = dag
+            .annotations()
+            .iter()
+            .map(|ann| {
+                let kind = match &ann.kind {
+                    AnnotationKind::Detector {
+                        measurement_nodes,
+                        coords,
+                    } => AnnotationKind::Detector {
+                        measurement_nodes: remap_dag_measurement_nodes(
+                            &dag_node_to_record_indices,
+                            measurement_nodes,
+                        ),
+                        coords: coords.clone(),
+                    },
+                    AnnotationKind::Observable { measurement_nodes } => {
+                        AnnotationKind::Observable {
+                            measurement_nodes: remap_dag_measurement_nodes(
+                                &dag_node_to_record_indices,
+                                measurement_nodes,
+                            ),
+                        }
+                    }
+                    AnnotationKind::TrackedPauli => AnnotationKind::TrackedPauli,
+                };
+                PauliAnnotation {
+                    pauli: ann.pauli.clone(),
+                    kind,
+                    label: ann.label.clone(),
+                }
+            })
+            .collect();
+
         tc
     }
 }
 
+fn remap_dag_measurement_nodes(
+    dag_node_to_record_indices: &BTreeMap<usize, Vec<usize>>,
+    measurement_nodes: &[usize],
+) -> Vec<usize> {
+    measurement_nodes
+        .iter()
+        .flat_map(|node| {
+            dag_node_to_record_indices
+                .get(node)
+                .unwrap_or_else(|| panic!("annotation references non-measurement DAG node {node}"))
+                .iter()
+                .copied()
+        })
+        .collect()
+}
+
 impl From<DagCircuit> for TickCircuit {
     fn from(dag: DagCircuit) -> Self {
         TickCircuit::from(&dag)
@@ -1840,22 +3307,52 @@ impl From<&TickCircuit> for DagCircuit {
         // Track the last node for each qubit to connect wires
         let mut last_node: BTreeMap<QubitId, usize> = BTreeMap::new();
 
-        for (tick_idx, tick) in tc.ticks().iter().enumerate() {
-            for (gate_idx, gate) in tick.gates().iter().enumerate() {
-                let node = dag.add_gate(gate.clone());
+        // Map measurement_record_index -> dag node for annotation transfer
+        let mut meas_record_to_node: BTreeMap<usize, usize> = BTreeMap::new();
+        let mut meas_record_idx = 0usize;
+
+        for (tick_idx, tick) in tc.iter_ticks() {
+            for batch in tick.iter_gate_batches() {
+                // DagCircuit stores individual gate applications. Use the
+                // TickCircuit instance view so qubit/meas-id slicing has one
+                // implementation. Zero-gate metadata batches do not have gate
+                // instances, so keep their stored command as a single DAG node.
+                let split_gates: Vec<Gate> = if batch.gate_count() == 0 {
+                    vec![batch.as_gate().clone()]
+                } else {
+                    batch
+                        .iter_gate_instances()
+                        .map(GateInstanceRef::to_gate)
+                        .collect()
+                };
+
+                let mut split_nodes = Vec::with_capacity(split_gates.len());
+                for split_gate in &split_gates {
+                    let node = dag.add_gate(split_gate.clone());
+                    split_nodes.push(node);
+
+                    // For MZ gates, map each qubit's record to this node
+                    if split_gate.gate_type == GateType::MZ {
+                        for _q in &split_gate.qubits {
+                            meas_record_to_node.insert(meas_record_idx, node);
+                            meas_record_idx += 1;
+                        }
+                    }
 
-                // Connect wires from previous gates on the same qubits
-                for qubit in &gate.qubits {
-                    if let Some(&prev_node) = last_node.get(qubit) {
-                        // Connect previous node to this one on this qubit
-                        let _ = dag.connect(prev_node, node, *qubit);
+                    // Connect wires from previous gates on the same qubits
+                    for qubit in &split_gate.qubits {
+                        if let Some(&prev_node) = last_node.get(qubit) {
+                            let _ = dag.connect(prev_node, node, *qubit);
+                        }
+                        last_node.insert(*qubit, node);
                     }
-                    last_node.insert(*qubit, node);
                 }
 
-                // Copy gate attributes
-                for (key, value) in tick.gate_attrs(gate_idx) {
-                    dag.set_gate_attr(node, key, value.clone());
+                // Copy batch-level gate attributes to every split gate.
+                for (key, value) in batch.attrs() {
+                    for &node in &split_nodes {
+                        dag.set_gate_attr(node, key, value.clone());
+                    }
                 }
             }
 
@@ -1871,6 +3368,40 @@ impl From<&TickCircuit> for DagCircuit {
             dag.set_attr(key.clone(), value.clone());
         }
 
+        // Transfer annotations, remapping measurement record indices to DAG node indices
+        for ann in &tc.annotations {
+            let remapped_kind = match &ann.kind {
+                AnnotationKind::Detector {
+                    measurement_nodes,
+                    coords,
+                } => {
+                    let dag_nodes: Vec<usize> = measurement_nodes
+                        .iter()
+                        .filter_map(|&rec| meas_record_to_node.get(&rec).copied())
+                        .collect();
+                    AnnotationKind::Detector {
+                        measurement_nodes: dag_nodes,
+                        coords: coords.clone(),
+                    }
+                }
+                AnnotationKind::Observable { measurement_nodes } => {
+                    let dag_nodes: Vec<usize> = measurement_nodes
+                        .iter()
+                        .filter_map(|&rec| meas_record_to_node.get(&rec).copied())
+                        .collect();
+                    AnnotationKind::Observable {
+                        measurement_nodes: dag_nodes,
+                    }
+                }
+                AnnotationKind::TrackedPauli => AnnotationKind::TrackedPauli,
+            };
+            dag.add_annotation(PauliAnnotation {
+                pauli: ann.pauli.clone(),
+                kind: remapped_kind,
+                label: ann.label.clone(),
+            });
+        }
+
         dag
     }
 }
@@ -1918,7 +3449,7 @@ mod tests {
         tc.tick().mz(&[0, 1]);
 
         assert_eq!(tc.num_ticks(), 4);
-        assert_eq!(tc.gate_count(), 4); // 1 bulk prep, 1 H, 1 CX, 1 bulk measure
+        assert_eq!(tc.gate_count(), 6); // 2 preps, 1 H, 1 CX, 2 measurements
 
         // Check tick contents
         assert_eq!(tc.get_tick(0).unwrap().len(), 1); // One bulk prep gate
@@ -1928,192 +3459,1494 @@ mod tests {
     }
 
     #[test]
-    fn test_meta_on_gates() {
+    fn test_tick_construction_merges_compatible_gate_batches() {
+        let mut tc = TickCircuit::new();
+        tc.tick().h(&[0]).h(&[1]).cx(&[(2, 3)]).cx(&[(4, 5)]);
+
+        let tick = tc.get_tick(0).unwrap();
+        assert_eq!(tick.len(), 2); // one H batch, one CX batch
+        assert_eq!(tick.gate_count(), 4);
+        assert_eq!(tick.gate_batch_count(), 2);
+        assert_eq!(tc.gate_count(), 4);
+        assert_eq!(tc.gate_batch_count(), 2);
+
+        assert_eq!(tick.gate_batches()[0].gate_type, GateType::H);
+        assert_eq!(
+            tick.gate_batches()[0].qubits.as_slice(),
+            &[QubitId::from(0), QubitId::from(1)]
+        );
+        assert_eq!(tick.gate_batches()[1].gate_type, GateType::CX);
+        assert_eq!(
+            tick.gate_batches()[1].qubits.as_slice(),
+            &[
+                QubitId::from(2),
+                QubitId::from(3),
+                QubitId::from(4),
+                QubitId::from(5)
+            ]
+        );
+    }
+
+    #[test]
+    fn test_tick_replace_gate_batch_updates_stored_views() {
         let mut tc = TickCircuit::new();
+        tc.tick().h(&[0]).h(&[1]);
+
+        let tick = tc.get_tick_mut(0).unwrap();
+        tick.replace_gate_batch(0, Gate::x(&[0, 1]))
+            .expect("same support replacement should be valid");
+
+        assert_eq!(tick.len(), 1);
+        assert_eq!(tick.gate_count(), 2);
+        assert_eq!(tick.gate_batches()[0].gate_type, GateType::X);
+        assert_eq!(
+            tick.gate_batches()[0].qubits.as_slice(),
+            &[QubitId::from(0), QubitId::from(1)]
+        );
+    }
 
+    #[test]
+    fn test_tick_replace_gate_batch_preserves_aligned_attrs() {
+        let mut tc = TickCircuit::new();
         tc.tick()
-            .h(&[0])
-            .meta("duration", Attribute::Float(50.0))
-            .meta("error_rate", Attribute::Float(0.001))
-            .x(&[1])
-            .meta("duration", Attribute::Float(50.0));
+            .h(&[0, 1])
+            .meta("calibration", Attribute::String("old".into()));
+
+        let tick = tc.get_tick_mut(0).unwrap();
+        tick.replace_gate_batch(0, Gate::x(&[0, 1]))
+            .expect("same support replacement should be valid");
+
+        assert_eq!(tick.len(), 1);
+        assert_eq!(tick.gate_batches()[0].gate_type, GateType::X);
+        assert_eq!(
+            tick.get_gate_attr(0, "calibration"),
+            Some(&Attribute::String("old".into()))
+        );
+    }
+
+    #[test]
+    fn test_tick_replace_gate_batch_rejects_overlapping_qubits() {
+        let mut tc = TickCircuit::new();
+        tc.tick().h(&[0]).x(&[1]);
+
+        let tick = tc.get_tick_mut(0).unwrap();
+        let err = tick
+            .replace_gate_batch(0, Gate::z(&[1]))
+            .expect_err("replacement overlaps the X command on q1");
+
+        assert!(matches!(err, TickGateError::QubitConflict(_)));
+        assert_eq!(tick.gate_batches()[0].gate_type, GateType::H);
+        assert_eq!(tick.gate_batches()[1].gate_type, GateType::X);
+    }
+
+    #[test]
+    fn test_tick_update_gate_batch_keeps_measurement_ids_in_sync() {
+        let mut tc = TickCircuit::new();
+        tc.tick().mz(&[0, 1]);
+
+        let tick = tc.get_tick_mut(0).unwrap();
+        tick.update_gate_batch(0, |gate| {
+            gate.meas_ids[0] = MeasId(10);
+            gate.meas_ids[1] = MeasId(11);
+        })
+        .expect("measurement id update should be valid");
+
+        assert_eq!(
+            tick.gate_batches()[0].meas_ids.as_slice(),
+            &[MeasId(10), MeasId(11)]
+        );
+    }
+
+    #[test]
+    fn test_tick_construction_batches_only_same_metadata() {
+        let mut same = TickCircuit::new();
+        {
+            let mut tick = same.tick();
+            tick.h(&[0])
+                .meta("calibration", Attribute::String("a".into()));
+            tick.h(&[1])
+                .meta("calibration", Attribute::String("a".into()));
+        }
+
+        let tick = same.get_tick(0).unwrap();
+        assert_eq!(tick.len(), 1);
+        assert_eq!(tick.gate_count(), 2);
+        assert_eq!(tick.gate_batch_count(), 1);
+        assert_eq!(
+            tick.get_gate_attr(0, "calibration"),
+            Some(&Attribute::String("a".into()))
+        );
+
+        let mut different = TickCircuit::new();
+        {
+            let mut tick = different.tick();
+            tick.h(&[0])
+                .meta("calibration", Attribute::String("a".into()));
+            tick.h(&[1])
+                .meta("calibration", Attribute::String("b".into()));
+        }
+
+        let tick = different.get_tick(0).unwrap();
+        assert_eq!(tick.len(), 2);
+        assert_eq!(tick.gate_count(), 2);
+        assert_eq!(tick.gate_batch_count(), 2);
+    }
+
+    #[test]
+    fn test_tick_construction_metadata_applies_to_last_gate_before_batching() {
+        let mut tc = TickCircuit::new();
+        {
+            let mut tick = tc.tick();
+            tick.h(&[0])
+                .h(&[1])
+                .meta("calibration", Attribute::String("second".into()));
+        }
 
         let tick = tc.get_tick(0).unwrap();
+        assert_eq!(tick.len(), 2);
+        assert_eq!(tick.gate_count(), 2);
+        assert_eq!(tick.gate_batch_count(), 2);
         assert_eq!(
-            tick.get_gate_attr(0, "duration"),
-            Some(&Attribute::Float(50.0))
+            tick.gate_batches()[0].qubits.as_slice(),
+            &[QubitId::from(0)]
         );
         assert_eq!(
-            tick.get_gate_attr(0, "error_rate"),
-            Some(&Attribute::Float(0.001))
+            tick.gate_batches()[1].qubits.as_slice(),
+            &[QubitId::from(1)]
         );
+        assert_eq!(tick.get_gate_attr(0, "calibration"), None);
         assert_eq!(
-            tick.get_gate_attr(1, "duration"),
-            Some(&Attribute::Float(50.0))
+            tick.get_gate_attr(1, "calibration"),
+            Some(&Attribute::String("second".into()))
         );
     }
 
     #[test]
-    fn test_tick_meta() {
+    fn test_tick_construction_multiple_meta_calls_batch_after_completion() {
         let mut tc = TickCircuit::new();
+        {
+            let mut tick = tc.tick();
+            tick.h(&[0])
+                .meta("calibration", Attribute::String("a".into()))
+                .meta("role", Attribute::String("drive".into()));
+            tick.h(&[1])
+                .meta("calibration", Attribute::String("a".into()))
+                .meta("role", Attribute::String("drive".into()));
+        }
 
-        // meta() before any gates = tick-level metadata
-        tc.tick().meta("round", Attribute::Int(0)).h(&[0]);
-        tc.tick().meta("round", Attribute::Int(1)).cx(&[(0, 1)]);
+        let tick = tc.get_tick(0).unwrap();
+        assert_eq!(tick.len(), 1);
+        assert_eq!(tick.gate_count(), 2);
+        assert_eq!(tick.gate_batch_count(), 1);
+        assert_eq!(
+            tick.get_gate_attr(0, "calibration"),
+            Some(&Attribute::String("a".into()))
+        );
+        assert_eq!(
+            tick.get_gate_attr(0, "role"),
+            Some(&Attribute::String("drive".into()))
+        );
+    }
+
+    #[test]
+    fn test_prep_metadata_applies_before_batching() {
+        let mut tc = TickCircuit::new();
+        tc.reserve_ticks(1);
+        tc.tick_at(0).pz(&[0]);
+        tc.tick_at(0)
+            .pz(&[1])
+            .meta("calibration", Attribute::String("second".into()));
 
+        let tick = tc.get_tick(0).unwrap();
+        assert_eq!(tick.len(), 2);
+        assert_eq!(tick.gate_count(), 2);
+        assert_eq!(tick.gate_batch_count(), 2);
+        assert_eq!(tick.get_gate_attr(0, "calibration"), None);
         assert_eq!(
-            tc.get_tick(0).unwrap().get_attr("round"),
-            Some(&Attribute::Int(0))
+            tick.get_gate_attr(1, "calibration"),
+            Some(&Attribute::String("second".into()))
         );
+    }
+
+    #[test]
+    fn test_tick_construction_preserves_measurement_ids_when_batching() {
+        let mut tc = TickCircuit::new();
+        tc.reserve_ticks(1);
+
+        let refs0 = tc.tick_at(0).mz(&[0]);
+        let refs1 = tc.tick_at(0).mz(&[1]);
+
+        let tick = tc.get_tick(0).unwrap();
+        assert_eq!(tick.len(), 1);
+        assert_eq!(tick.gate_count(), 2);
+        assert_eq!(tick.gate_batch_count(), 1);
+        assert_eq!(refs0[0].gate_idx, 0);
+        assert_eq!(refs1[0].gate_idx, 0);
+        assert_eq!(refs0[0].meas_id, MeasId(0));
+        assert_eq!(refs1[0].meas_id, MeasId(1));
         assert_eq!(
-            tc.get_tick(1).unwrap().get_attr("round"),
-            Some(&Attribute::Int(1))
+            tick.gate_batches()[0].meas_ids.as_slice(),
+            &[MeasId(0), MeasId(1)]
         );
     }
 
     #[test]
-    fn test_tick_index() {
+    fn test_measurement_batching_respects_gate_metadata() {
+        let mut same = TickCircuit::new();
+        same.reserve_ticks(1);
+        let refs0 = same.tick_at(0).mz(&[0]);
+        same.get_tick_mut(0).unwrap().set_gate_attr(
+            refs0[0].gate_idx,
+            "basis",
+            Attribute::String("Z".into()),
+        );
+        let refs1 = same.tick_at(0).mz(&[1]);
+        let tick = same.get_tick_mut(0).unwrap();
+        tick.set_gate_attr(refs1[0].gate_idx, "basis", Attribute::String("Z".into()));
+        tick.merge_compatible_gate_at(refs1[0].gate_idx);
+
+        let tick = same.get_tick(0).unwrap();
+        assert_eq!(tick.len(), 1);
+        assert_eq!(tick.gate_count(), 2);
+        assert_eq!(tick.gate_batch_count(), 1);
+        assert_eq!(
+            tick.gate_batches()[0].meas_ids.as_slice(),
+            &[MeasId(0), MeasId(1)]
+        );
+        assert_eq!(
+            tick.get_gate_attr(0, "basis"),
+            Some(&Attribute::String("Z".into()))
+        );
+
+        let mut different = TickCircuit::new();
+        different.reserve_ticks(1);
+        let refs0 = different.tick_at(0).mz(&[0]);
+        different.get_tick_mut(0).unwrap().set_gate_attr(
+            refs0[0].gate_idx,
+            "basis",
+            Attribute::String("Z".into()),
+        );
+        let refs1 = different.tick_at(0).mz(&[1]);
+        let tick = different.get_tick_mut(0).unwrap();
+        tick.set_gate_attr(refs1[0].gate_idx, "basis", Attribute::String("X".into()));
+        tick.merge_compatible_gate_at(refs1[0].gate_idx);
+
+        let tick = different.get_tick(0).unwrap();
+        assert_eq!(tick.len(), 2);
+        assert_eq!(tick.gate_count(), 2);
+        assert_eq!(tick.gate_batch_count(), 2);
+        assert_eq!(tick.gate_batches()[0].meas_ids.as_slice(), &[MeasId(0)]);
+        assert_eq!(tick.gate_batches()[1].meas_ids.as_slice(), &[MeasId(1)]);
+        assert_eq!(
+            tick.get_gate_attr(0, "basis"),
+            Some(&Attribute::String("Z".into()))
+        );
+        assert_eq!(
+            tick.get_gate_attr(1, "basis"),
+            Some(&Attribute::String("X".into()))
+        );
+    }
+
+    #[test]
+    fn test_tick_construction_keeps_different_parameters_in_separate_batches() {
         let mut tc = TickCircuit::new();
+        tc.tick()
+            .rz(Angle64::from_turns(0.25), &[0])
+            .rz(Angle64::from_turns(0.5), &[1]);
 
-        let t0 = tc.tick();
-        assert_eq!(t0.index(), 0);
+        let tick = tc.get_tick(0).unwrap();
+        assert_eq!(tick.len(), 2);
+        assert_eq!(tick.gate_count(), 2);
+        assert_eq!(tick.gate_batch_count(), 2);
+    }
+
+    #[test]
+    fn test_parameterized_gate_batching_counts_and_round_trip() {
+        let mut tc1 = TickCircuit::new();
+        tc1.tick()
+            .rz(Angle64::from_turns(0.25), &[0])
+            .rz(Angle64::from_turns(0.25), &[1])
+            .rz(Angle64::from_turns(0.5), &[2]);
+
+        let tick = tc1.get_tick(0).unwrap();
+        assert_eq!(tick.len(), 2);
+        assert_eq!(tick.gate_count(), 3);
+        assert_eq!(tick.gate_batch_count(), 2);
+        assert_eq!(tc1.gate_count(), 3);
+        assert_eq!(tc1.gate_batch_count(), 2);
+
+        let dag = DagCircuit::from(&tc1);
+        assert_eq!(dag.gate_count(), 3);
+        assert_eq!(dag.gate_node_count(), 3);
+        assert_eq!(dag.gate_type_count(GateType::RZ), 3);
+
+        let tc2 = TickCircuit::from(&dag);
+        let tick = tc2.get_tick(0).unwrap();
+        assert_eq!(tc2.gate_count(), 3);
+        assert_eq!(tc2.gate_batch_count(), 2);
+        assert_eq!(tick.len(), 2);
+        assert_eq!(tick.gate_count(), 3);
+        assert_eq!(tick.gate_batch_count(), 2);
+        assert_eq!(
+            tick.gate_batches()[0].qubits.as_slice(),
+            &[QubitId::from(0), QubitId::from(1)]
+        );
+        assert_eq!(
+            tick.gate_batches()[0].angles,
+            Gate::rz(Angle64::from_turns(0.25), &[0]).angles
+        );
+        assert_eq!(
+            tick.gate_batches()[1].qubits.as_slice(),
+            &[QubitId::from(2)]
+        );
+        assert_eq!(
+            tick.gate_batches()[1].angles,
+            Gate::rz(Angle64::from_turns(0.5), &[2]).angles
+        );
+    }
+
+    #[test]
+    fn test_meta_on_gates() {
+        let mut tc = TickCircuit::new();
+
+        tc.tick()
+            .h(&[0])
+            .meta("duration", Attribute::Float(50.0))
+            .meta("error_rate", Attribute::Float(0.001))
+            .x(&[1])
+            .meta("duration", Attribute::Float(50.0));
+
+        let tick = tc.get_tick(0).unwrap();
+        assert_eq!(
+            tick.get_gate_attr(0, "duration"),
+            Some(&Attribute::Float(50.0))
+        );
+        assert_eq!(
+            tick.get_gate_attr(0, "error_rate"),
+            Some(&Attribute::Float(0.001))
+        );
+        assert_eq!(
+            tick.get_gate_attr(1, "duration"),
+            Some(&Attribute::Float(50.0))
+        );
+    }
+
+    #[test]
+    fn test_tick_meta() {
+        let mut tc = TickCircuit::new();
+
+        // meta() before any gates = tick-level metadata
+        tc.tick().meta("round", Attribute::Int(0)).h(&[0]);
+        tc.tick().meta("round", Attribute::Int(1)).cx(&[(0, 1)]);
+
+        assert_eq!(
+            tc.get_tick(0).unwrap().get_attr("round"),
+            Some(&Attribute::Int(0))
+        );
+        assert_eq!(
+            tc.get_tick(1).unwrap().get_attr("round"),
+            Some(&Attribute::Int(1))
+        );
+    }
+
+    #[test]
+    fn test_tick_index() {
+        let mut tc = TickCircuit::new();
+
+        let t0 = tc.tick();
+        assert_eq!(t0.index(), 0);
+
+        let t1 = tc.tick();
+        assert_eq!(t1.index(), 1);
+
+        assert_eq!(tc.next_tick_index(), 2);
+    }
+
+    #[test]
+    fn test_gates_chain_but_preps_and_meas_break() {
+        let mut tc = TickCircuit::new();
+
+        // Regular gates chain within a tick
+        tc.tick().h(&[0]).x(&[1]).y(&[2]).z(&[3]);
+        tc.tick().cx(&[(0, 1)]).szz(&[(2, 3)]);
+
+        // But preps and measurements break the chain
+        tc.tick().pz(&[0]); // breaks chain
+        tc.tick().mz(&[0]); // breaks chain
+
+        assert_eq!(tc.num_ticks(), 4);
+        assert_eq!(tc.gate_count(), 8);
+    }
+
+    #[test]
+    fn test_prep_and_meas_with_meta() {
+        let mut tc = TickCircuit::new();
+
+        // Preps and measurements allow .meta() before breaking
+        tc.tick()
+            .pz(&[0])
+            .meta("reason", Attribute::String("init".into()));
+        tc.tick().h(&[0]);
+        tc.tick().mz(&[0]);
+        // Attach metadata to the measurement gate directly
+        tc.get_tick_mut(2)
+            .unwrap()
+            .set_gate_attr(0, "basis", Attribute::String("Z".into()));
+
+        assert_eq!(tc.num_ticks(), 3);
+
+        // Check that metadata was attached
+        assert_eq!(
+            tc.get_tick(0).unwrap().get_gate_attr(0, "reason"),
+            Some(&Attribute::String("init".into()))
+        );
+        assert_eq!(
+            tc.get_tick(2).unwrap().get_gate_attr(0, "basis"),
+            Some(&Attribute::String("Z".into()))
+        );
+    }
+
+    #[test]
+    fn test_circuit_meta() {
+        let mut tc = TickCircuit::new();
+        tc.set_meta("name", Attribute::String("bell_state".to_string()));
+        tc.tick().h(&[0]);
+
+        assert_eq!(
+            tc.get_meta("name"),
+            Some(&Attribute::String("bell_state".to_string()))
+        );
+    }
+
+    #[test]
+    fn test_tick_circuit_to_dag_circuit() {
+        let mut tc = TickCircuit::new();
+        tc.set_meta("circuit_name", Attribute::String("test".to_string()));
+
+        // Build a small circuit
+        tc.tick().h(&[0]).x(&[1]); // Tick 0: parallel H and X
+        tc.tick().cx(&[(0, 1)]); // Tick 1: CX
+        tc.tick().h(&[0]); // Tick 2: H
+
+        let dag = DagCircuit::from(&tc);
+
+        // Check gate counts
+        assert_eq!(dag.gate_count(), 4);
+
+        // Check wires: H(0)->CX->H(0), X(1)->CX
+        // So we have 3 wires: H(0)->CX, CX->H(0), X(1)->CX
+        assert_eq!(dag.wire_count(), 3);
+
+        // Check circuit attributes
+        assert_eq!(
+            dag.get_attr("circuit_name"),
+            Some(&Attribute::String("test".to_string()))
+        );
+    }
+
+    #[test]
+    fn test_tick_to_dag_splits_batched_standard_two_qubit_cliffords_as_pairs() {
+        fn add_gate(tc: &mut TickCircuit, gate_type: GateType, pairs: &[(usize, usize)]) {
+            match gate_type {
+                GateType::CX => {
+                    tc.tick().cx(pairs);
+                }
+                GateType::CY => {
+                    tc.tick().cy(pairs);
+                }
+                GateType::CZ => {
+                    tc.tick().cz(pairs);
+                }
+                GateType::SXX => {
+                    tc.tick().sxx(pairs);
+                }
+                GateType::SXXdg => {
+                    tc.tick().sxxdg(pairs);
+                }
+                GateType::SYY => {
+                    tc.tick().syy(pairs);
+                }
+                GateType::SYYdg => {
+                    tc.tick().syydg(pairs);
+                }
+                GateType::SZZ => {
+                    tc.tick().szz(pairs);
+                }
+                GateType::SZZdg => {
+                    tc.tick().szzdg(pairs);
+                }
+                GateType::SWAP => {
+                    tc.tick().swap(pairs);
+                }
+                _ => unreachable!(),
+            }
+        }
+
+        let pair_sets = [
+            [(0usize, 1usize), (2usize, 3usize)],
+            [(4usize, 1usize), (9usize, 2usize)],
+        ];
+
+        for gate_type in [
+            GateType::CX,
+            GateType::CY,
+            GateType::CZ,
+            GateType::SXX,
+            GateType::SXXdg,
+            GateType::SYY,
+            GateType::SYYdg,
+            GateType::SZZ,
+            GateType::SZZdg,
+            GateType::SWAP,
+        ] {
+            for pairs in pair_sets {
+                let mut tc = TickCircuit::new();
+                add_gate(&mut tc, gate_type, &pairs);
+
+                let dag = DagCircuit::from(&tc);
+                let gates: Vec<_> = dag.iter_gates().map(|(_, gate)| gate).collect();
+                assert_eq!(gates.len(), 2, "{gate_type:?} {pairs:?}");
+                assert!(
+                    gates.iter().all(|gate| gate.gate_type == gate_type),
+                    "{gate_type:?} {pairs:?}"
+                );
+                assert!(
+                    gates.iter().all(|gate| gate.qubits.len() == 2),
+                    "{gate_type:?} should remain pairwise in the DAG for {pairs:?}"
+                );
+                for (q0, q1) in pairs {
+                    assert!(
+                        gates.iter().any(|gate| gate
+                            .qubits
+                            .iter()
+                            .copied()
+                            .eq([QubitId(q0), QubitId(q1)])),
+                        "{gate_type:?} should preserve pair ({q0}, {q1})"
+                    );
+                }
+            }
+        }
+    }
+
+    #[test]
+    fn test_dag_circuit_to_tick_circuit() {
+        let mut dag = DagCircuit::new();
+        dag.set_attr("version".to_string(), Attribute::Int(1));
+
+        // Build: H(0) -> CX(0,1)
+        //        X(1) ----^
+        let h = dag.add_gate(Gate::h(&[0]));
+        let x = dag.add_gate(Gate::x(&[1]));
+        let cx = dag.add_gate(Gate::cx(&[(0, 1)]));
+
+        dag.connect(h, cx, QubitId::from(0)).unwrap();
+        dag.connect(x, cx, QubitId::from(1)).unwrap();
+
+        let tc = TickCircuit::from(&dag);
+
+        // H and X are parallel (layer 0), CX depends on both (layer 1)
+        assert_eq!(tc.num_ticks(), 2);
+
+        // First tick should have H and X (order may vary)
+        let tick0 = tc.get_tick(0).unwrap();
+        assert_eq!(tick0.gate_batches().len(), 2);
+
+        // Second tick should have CX
+        let tick1 = tc.get_tick(1).unwrap();
+        assert_eq!(tick1.gate_batches().len(), 1);
+
+        // Check circuit attribute
+        assert_eq!(tc.get_meta("version"), Some(&Attribute::Int(1)));
+    }
+
+    #[test]
+    fn test_round_trip_tick_to_dag_to_tick() {
+        let mut tc1 = TickCircuit::new();
+        tc1.tick().h(&[0]);
+        tc1.tick().cx(&[(0, 1)]);
+        tc1.tick().h(&[1]);
+
+        // Convert to DAG and back
+        let dag = DagCircuit::from(&tc1);
+        let tc2 = TickCircuit::from(&dag);
+
+        // Should have same structure
+        assert_eq!(tc1.num_ticks(), tc2.num_ticks());
+        for i in 0..tc1.num_ticks() {
+            assert_eq!(
+                tc1.get_tick(i).unwrap().gate_batches().len(),
+                tc2.get_tick(i).unwrap().gate_batches().len()
+            );
+        }
+    }
+
+    #[test]
+    fn test_tick_dag_round_trip_preserves_counts_and_metadata_batches() {
+        let mut tc1 = TickCircuit::new();
+        tc1.set_meta("name", Attribute::String("metadata-heavy".into()));
+        tc1.tick()
+            .meta("round", Attribute::Int(0))
+            .h(&[0, 1])
+            .meta("calibration", Attribute::String("h-cal".into()));
+        tc1.tick()
+            .meta("round", Attribute::Int(1))
+            .cx(&[(0, 2), (1, 3)])
+            .meta("calibration", Attribute::String("cx-cal".into()));
+        let ms = tc1.tick().mz(&[0, 1]);
+
+        assert_eq!(tc1.num_ticks(), 3);
+        assert_eq!(tc1.gate_count(), 6);
+        assert_eq!(tc1.gate_batch_count(), 3);
+        assert_eq!(ms[0].meas_id, MeasId(0));
+        assert_eq!(ms[1].meas_id, MeasId(1));
+
+        let dag = DagCircuit::from(&tc1);
+        assert_eq!(dag.gate_count(), 6);
+        assert_eq!(dag.gate_node_count(), 6);
+        assert_eq!(dag.gate_type_count(GateType::H), 2);
+        assert_eq!(dag.gate_type_count(GateType::CX), 2);
+        assert_eq!(dag.gate_type_count(GateType::MZ), 2);
+
+        for (node, gate) in dag.iter_gates() {
+            match gate.gate_type {
+                GateType::H => assert_eq!(
+                    dag.get_gate_attr(node, "calibration"),
+                    Some(&Attribute::String("h-cal".into()))
+                ),
+                GateType::CX => assert_eq!(
+                    dag.get_gate_attr(node, "calibration"),
+                    Some(&Attribute::String("cx-cal".into()))
+                ),
+                _ => {}
+            }
+        }
+
+        let tc2 = TickCircuit::from(&dag);
+        assert_eq!(tc2.num_ticks(), 3);
+        assert_eq!(tc2.gate_count(), 6);
+        assert_eq!(tc2.gate_batch_count(), 3);
+        assert_eq!(
+            tc2.get_meta("name"),
+            Some(&Attribute::String("metadata-heavy".into()))
+        );
+        assert_eq!(
+            tc2.get_tick(0).unwrap().get_attr("round"),
+            Some(&Attribute::Int(0))
+        );
+        assert_eq!(
+            tc2.get_tick(1).unwrap().get_attr("round"),
+            Some(&Attribute::Int(1))
+        );
+
+        let tick0 = tc2.get_tick(0).unwrap();
+        assert_eq!(tick0.len(), 1);
+        assert_eq!(tick0.gate_count(), 2);
+        assert_eq!(tick0.gate_batch_count(), 1);
+        assert_eq!(tick0.gate_batches()[0].gate_type, GateType::H);
+        assert_eq!(
+            tick0.get_gate_attr(0, "calibration"),
+            Some(&Attribute::String("h-cal".into()))
+        );
+
+        let tick1 = tc2.get_tick(1).unwrap();
+        assert_eq!(tick1.len(), 1);
+        assert_eq!(tick1.gate_count(), 2);
+        assert_eq!(tick1.gate_batch_count(), 1);
+        assert_eq!(tick1.gate_batches()[0].gate_type, GateType::CX);
+        assert_eq!(
+            tick1.get_gate_attr(0, "calibration"),
+            Some(&Attribute::String("cx-cal".into()))
+        );
+
+        let tick2 = tc2.get_tick(2).unwrap();
+        assert_eq!(tick2.len(), 1);
+        assert_eq!(tick2.gate_count(), 2);
+        assert_eq!(tick2.gate_batch_count(), 1);
+        assert_eq!(tick2.gate_batches()[0].gate_type, GateType::MZ);
+        assert_eq!(
+            tick2.gate_batches()[0].meas_ids.as_slice(),
+            &[MeasId(0), MeasId(1)]
+        );
+    }
+
+    #[test]
+    fn test_dag_to_tick_preserves_distinct_metadata_batches() {
+        let mut dag = DagCircuit::new();
+        let h0 = dag.add_gate(Gate::h(&[0]));
+        dag.set_gate_attr(h0, "calibration", Attribute::String("a".into()));
+        let h1 = dag.add_gate(Gate::h(&[1]));
+        dag.set_gate_attr(h1, "calibration", Attribute::String("b".into()));
+        let h2 = dag.add_gate(Gate::h(&[2]));
+        dag.set_gate_attr(h2, "calibration", Attribute::String("a".into()));
+
+        let tc = TickCircuit::from(&dag);
+        assert_eq!(tc.gate_count(), 3);
+        assert_eq!(tc.gate_batch_count(), 2);
+
+        let tick = tc.get_tick(0).unwrap();
+        assert_eq!(tick.len(), 2);
+        assert_eq!(tick.gate_count(), 3);
+        assert_eq!(tick.gate_batch_count(), 2);
+        assert_eq!(
+            tick.get_gate_attr(0, "calibration"),
+            Some(&Attribute::String("a".into()))
+        );
+        assert_eq!(
+            tick.get_gate_attr(1, "calibration"),
+            Some(&Attribute::String("b".into()))
+        );
+        assert_eq!(
+            tick.gate_batches()[0].qubits.as_slice(),
+            &[QubitId::from(0), QubitId::from(2)]
+        );
+        assert_eq!(
+            tick.gate_batches()[1].qubits.as_slice(),
+            &[QubitId::from(1)]
+        );
+    }
+
+    #[test]
+    fn test_batched_measurement_metadata_round_trip() {
+        let mut tc1 = TickCircuit::new();
+        let ms = tc1.tick().mz(&[0, 1]);
+        tc1.get_tick_mut(0).unwrap().set_gate_attr(
+            ms[0].gate_idx,
+            "basis",
+            Attribute::String("Z".into()),
+        );
+
+        let dag = DagCircuit::from(&tc1);
+        assert_eq!(dag.gate_count(), 2);
+        assert_eq!(dag.gate_node_count(), 2);
+        for (node, gate) in dag.iter_gates() {
+            assert_eq!(gate.gate_type, GateType::MZ);
+            assert_eq!(
+                dag.get_gate_attr(node, "basis"),
+                Some(&Attribute::String("Z".into()))
+            );
+        }
+
+        let tc2 = TickCircuit::from(&dag);
+        assert_eq!(tc2.gate_count(), 2);
+        assert_eq!(tc2.gate_batch_count(), 1);
+
+        let tick = tc2.get_tick(0).unwrap();
+        assert_eq!(tick.len(), 1);
+        assert_eq!(tick.gate_count(), 2);
+        assert_eq!(tick.gate_batch_count(), 1);
+        assert_eq!(tick.gate_batches()[0].gate_type, GateType::MZ);
+        assert_eq!(
+            tick.gate_batches()[0].meas_ids.as_slice(),
+            &[MeasId(0), MeasId(1)]
+        );
+        assert_eq!(
+            tick.get_gate_attr(0, "basis"),
+            Some(&Attribute::String("Z".into()))
+        );
+    }
+
+    #[test]
+    fn test_channel_gate_counts_as_single_operation_through_round_trip() {
+        let mut tc1 = TickCircuit::new();
+        tc1.tick().channel(
+            pecos_core::channel::Depolarizing(0.1, 0) & pecos_core::channel::Dephasing(0.2, 1),
+        );
+
+        let tick = tc1.get_tick(0).unwrap();
+        assert_eq!(tick.len(), 1);
+        assert_eq!(tick.gate_count(), 1);
+        assert_eq!(tick.gate_batch_count(), 1);
+        assert_eq!(tc1.gate_count(), 1);
+        assert_eq!(tc1.gate_batch_count(), 1);
+        assert_eq!(
+            tick.gate_batches()[0].qubits.as_slice(),
+            &[QubitId::from(0), QubitId::from(1)]
+        );
+
+        let dag = DagCircuit::from(&tc1);
+        assert_eq!(dag.gate_count(), 1);
+        assert_eq!(dag.gate_node_count(), 1);
+        let (_, gate) = dag.iter_gates().next().unwrap();
+        assert!(gate.is_channel());
+        assert_eq!(
+            gate.qubits.as_slice(),
+            &[QubitId::from(0), QubitId::from(1)]
+        );
+
+        let tc2 = TickCircuit::from(&dag);
+        assert_eq!(tc2.gate_count(), 1);
+        assert_eq!(tc2.gate_batch_count(), 1);
+        let gate = &tc2.get_tick(0).unwrap().gate_batches()[0];
+        assert!(gate.is_channel());
+        assert_eq!(
+            gate.qubits.as_slice(),
+            &[QubitId::from(0), QubitId::from(1)]
+        );
+    }
+
+    #[test]
+    fn test_batched_measurement_annotation_records_round_trip() {
+        let mut tc1 = TickCircuit::new();
+        let ms = tc1.tick().mz(&[0, 1]);
+        tc1.detector_labeled("det01", &ms);
+        tc1.observable_labeled("obs1", &[ms[1]]);
+
+        let dag = DagCircuit::from(&tc1);
+        let tc2 = TickCircuit::from(&dag);
+
+        assert_eq!(tc2.num_measurements(), 2);
+        assert_eq!(tc2.annotations().len(), 2);
+        match &tc2.annotations()[0].kind {
+            AnnotationKind::Detector {
+                measurement_nodes, ..
+            } => assert_eq!(measurement_nodes.as_slice(), &[0, 1]),
+            other => panic!("expected detector annotation, got {other:?}"),
+        }
+        match &tc2.annotations()[1].kind {
+            AnnotationKind::Observable { measurement_nodes } => {
+                assert_eq!(measurement_nodes.as_slice(), &[1]);
+            }
+            other => panic!("expected observable annotation, got {other:?}"),
+        }
+
+        let tick = tc2.get_tick(0).unwrap();
+        assert_eq!(
+            tick.gate_batches()[0].meas_ids.as_slice(),
+            &[MeasId(0), MeasId(1)]
+        );
+    }
+
+    #[test]
+    fn test_dag_batched_measurement_node_annotation_expands_to_tick_records() {
+        let mut dag = DagCircuit::new();
+        let node = dag.add_gate(Gate::mz(&[0, 1]));
+        dag.detector_labeled("batched-detector", &[node]);
+
+        let tc = TickCircuit::from(&dag);
+        assert_eq!(tc.num_measurements(), 2);
+        assert_eq!(tc.annotations().len(), 1);
+        match &tc.annotations()[0].kind {
+            AnnotationKind::Detector {
+                measurement_nodes, ..
+            } => assert_eq!(measurement_nodes.as_slice(), &[0, 1]),
+            other => panic!("expected detector annotation, got {other:?}"),
+        }
+
+        let tick = tc.get_tick(0).unwrap();
+        assert_eq!(tick.len(), 1);
+        assert_eq!(tick.gate_batches()[0].gate_type, GateType::MZ);
+        assert_eq!(
+            tick.gate_batches()[0].meas_ids.as_slice(),
+            &[MeasId(0), MeasId(1)]
+        );
+    }
+
+    #[test]
+    fn test_dag_to_tick_preserves_existing_measurement_ids_and_advances_counter() {
+        let mut dag = DagCircuit::new();
+        let mut gate = Gate::mz(&[0]);
+        gate.meas_ids.push(MeasId(5));
+        let node = dag.add_gate(gate);
+        dag.observable_labeled("obs5", &[node]);
+
+        let mut tc = TickCircuit::from(&dag);
+        assert_eq!(tc.num_measurements(), 6);
+        let tick = tc.get_tick(0).unwrap();
+        assert_eq!(tick.gate_batches()[0].meas_ids.as_slice(), &[MeasId(5)]);
+        match &tc.annotations()[0].kind {
+            AnnotationKind::Observable { measurement_nodes } => {
+                assert_eq!(measurement_nodes.as_slice(), &[5]);
+            }
+            other => panic!("expected observable annotation, got {other:?}"),
+        }
+
+        let next = tc.tick().mz(&[1]);
+        assert_eq!(next[0].record_idx, 6);
+        assert_eq!(next[0].meas_id, MeasId(6));
+        assert_eq!(tc.num_measurements(), 7);
+    }
 
-        let t1 = tc.tick();
-        assert_eq!(t1.index(), 1);
+    #[test]
+    #[should_panic(expected = "annotation references non-measurement DAG node")]
+    fn test_dag_to_tick_rejects_annotation_referencing_non_measurement_node() {
+        let mut dag = DagCircuit::new();
+        let h = dag.add_gate(Gate::h(&[0]));
+        dag.detector_labeled("not-a-measurement", &[h]);
 
-        assert_eq!(tc.next_tick_index(), 2);
+        let _ = TickCircuit::from(&dag);
     }
 
     #[test]
-    fn test_gates_chain_but_preps_and_meas_break() {
-        let mut tc = TickCircuit::new();
+    fn test_detector_observable_and_tracked_pauli_remain_distinct_after_round_trip() {
+        use pecos_core::pauli::{X, Z};
 
-        // Regular gates chain within a tick
-        tc.tick().h(&[0]).x(&[1]).y(&[2]).z(&[3]);
-        tc.tick().cx(&[(0, 1)]).szz(&[(2, 3)]);
+        let mut tc1 = TickCircuit::new();
+        tc1.tick().pz(&[0, 1, 2]);
+        let ms = tc1.tick().mz(&[0, 1]);
+        tc1.detector_labeled("detector", &[ms[0]]);
+        tc1.observable_labeled("observable", &[ms[1]]);
+        tc1.tracked_pauli_labeled("tracked", X(0) & Z(2));
+
+        let tc2 = TickCircuit::from(&DagCircuit::from(&tc1));
+        assert_eq!(tc2.annotations().len(), 3);
+
+        assert_eq!(tc2.annotations()[0].label.as_deref(), Some("detector"));
+        match &tc2.annotations()[0].kind {
+            AnnotationKind::Detector {
+                measurement_nodes, ..
+            } => assert_eq!(measurement_nodes.as_slice(), &[0]),
+            other => panic!("expected detector annotation, got {other:?}"),
+        }
 
-        // But preps and measurements break the chain
-        tc.tick().pz(&[0]); // breaks chain
-        tc.tick().mz(&[0]); // breaks chain
+        assert_eq!(tc2.annotations()[1].label.as_deref(), Some("observable"));
+        match &tc2.annotations()[1].kind {
+            AnnotationKind::Observable { measurement_nodes } => {
+                assert_eq!(measurement_nodes.as_slice(), &[1]);
+            }
+            other => panic!("expected observable annotation, got {other:?}"),
+        }
 
-        assert_eq!(tc.num_ticks(), 4);
-        assert_eq!(tc.gate_count(), 8);
+        assert_eq!(tc2.annotations()[2].label.as_deref(), Some("tracked"));
+        assert!(matches!(
+            tc2.annotations()[2].kind,
+            AnnotationKind::TrackedPauli
+        ));
+        assert_eq!(tc2.annotations()[2].pauli, X(0) & Z(2));
     }
 
     #[test]
-    fn test_prep_and_meas_with_meta() {
-        let mut tc = TickCircuit::new();
+    fn test_small_pseudorandom_tick_dag_round_trip_invariants() {
+        fn assert_no_tick_overlaps(circuit: &TickCircuit) {
+            for (tick_idx, tick) in circuit.iter_ticks() {
+                let mut active = BTreeSet::new();
+                for gate in tick.gate_batches() {
+                    gate.validate()
+                        .unwrap_or_else(|err| panic!("invalid gate in tick {tick_idx}: {err}"));
+                    for &qubit in &gate.qubits {
+                        assert!(
+                            active.insert(qubit),
+                            "qubit {qubit:?} appears more than once in tick {tick_idx}"
+                        );
+                    }
+                }
+            }
+        }
 
-        // Preps and measurements allow .meta() before breaking
-        tc.tick()
-            .pz(&[0])
-            .meta("reason", Attribute::String("init".into()));
-        tc.tick().h(&[0]);
-        tc.tick()
-            .mz(&[0])
-            .meta("basis", Attribute::String("Z".into()));
+        fn measurement_ids(circuit: &TickCircuit) -> Vec<MeasId> {
+            circuit
+                .iter_gate_batches()
+                .flat_map(|gate| gate.as_gate().meas_ids.iter().copied())
+                .collect()
+        }
 
-        assert_eq!(tc.num_ticks(), 3);
+        let mut state = 0x5eed_u64;
+        for case_idx in 0..16 {
+            state = state
+                .wrapping_mul(6_364_136_223_846_793_005)
+                .wrapping_add(1);
+            let base = ((state >> 32) as usize % 4) * 10;
+
+            let mut tc1 = TickCircuit::new();
+            tc1.tick()
+                .meta("case", Attribute::Int(case_idx))
+                .h(&[base, base + 1])
+                .meta("role", Attribute::String("prepare".into()));
+
+            if state & 1 == 0 {
+                tc1.tick()
+                    .cx(&[(base, base + 2), (base + 1, base + 3)])
+                    .meta("role", Attribute::String("entangle".into()));
+            } else {
+                tc1.tick()
+                    .rz(Angle64::from_turns(0.25), &[base])
+                    .rz(Angle64::from_turns(0.25), &[base + 1])
+                    .rz(Angle64::from_turns(0.5), &[base + 2]);
+            }
 
-        // Check that metadata was attached
-        assert_eq!(
-            tc.get_tick(0).unwrap().get_gate_attr(0, "reason"),
-            Some(&Attribute::String("init".into()))
-        );
-        assert_eq!(
-            tc.get_tick(2).unwrap().get_gate_attr(0, "basis"),
-            Some(&Attribute::String("Z".into()))
-        );
+            let ms = tc1.tick().mz(&[base, base + 1]);
+            if case_idx % 2 == 0 {
+                tc1.detector_labeled("det", &ms);
+            } else {
+                tc1.observable_labeled("obs", &ms);
+            }
+
+            let tc2 = TickCircuit::from(&DagCircuit::from(&tc1));
+            assert_eq!(tc2.gate_count(), tc1.gate_count());
+            assert_eq!(tc2.num_measurements(), tc1.num_measurements());
+            assert_eq!(tc2.gate_counts_by_type(), tc1.gate_counts_by_type());
+            assert_eq!(measurement_ids(&tc2), measurement_ids(&tc1));
+            assert_eq!(tc2.annotations().len(), tc1.annotations().len());
+            assert_no_tick_overlaps(&tc2);
+        }
     }
 
     #[test]
-    fn test_circuit_meta() {
-        let mut tc = TickCircuit::new();
-        tc.set_meta("name", Attribute::String("bell_state".to_string()));
-        tc.tick().h(&[0]);
+    fn test_pseudorandom_round_trip_preserves_measurement_annotation_details() {
+        use pecos_core::pauli::{X, Y, Z};
+
+        fn annotation_by_label<'a>(circuit: &'a TickCircuit, label: &str) -> &'a PauliAnnotation {
+            circuit
+                .annotations()
+                .iter()
+                .find(|ann| ann.label.as_deref() == Some(label))
+                .unwrap_or_else(|| panic!("missing annotation {label}"))
+        }
 
-        assert_eq!(
-            tc.get_meta("name"),
-            Some(&Attribute::String("bell_state".to_string()))
-        );
-    }
+        let mut state = 0xaced_u64;
+        for case_idx in 0..12 {
+            state = state
+                .wrapping_mul(2_862_933_555_777_941_757)
+                .wrapping_add(3_037_000_493);
+            let base = 20 * case_idx;
+
+            let mut tc1 = TickCircuit::new();
+            tc1.tick().h(&[base, base + 1]).cx(&[(base + 2, base + 3)]);
+            if state & 1 == 0 {
+                tc1.tick().cx(&[(base, base + 2), (base + 1, base + 3)]);
+            } else {
+                tc1.tick()
+                    .rz(Angle64::from_turns(0.25), &[base])
+                    .rz(Angle64::from_turns(0.25), &[base + 1]);
+            }
 
-    #[test]
-    fn test_tick_circuit_to_dag_circuit() {
-        let mut tc = TickCircuit::new();
-        tc.set_meta("circuit_name", Attribute::String("test".to_string()));
+            let measurements = tc1.tick().mz(&[base, base + 1, base + 2]);
+            let detector_records = if state & 2 == 0 {
+                vec![measurements[0], measurements[2]]
+            } else {
+                vec![measurements[1]]
+            };
+            let observable_records = if state & 4 == 0 {
+                vec![measurements[1]]
+            } else {
+                vec![measurements[0], measurements[2]]
+            };
+            let tracked = if state & 8 == 0 {
+                X(base) & Z(base + 3)
+            } else {
+                Y(base + 3)
+            };
 
-        // Build a small circuit
-        tc.tick().h(&[0]).x(&[1]); // Tick 0: parallel H and X
-        tc.tick().cx(&[(0, 1)]); // Tick 1: CX
-        tc.tick().h(&[0]); // Tick 2: H
+            tc1.detector_labeled(&format!("det-{case_idx}"), &detector_records);
+            tc1.observable_labeled(&format!("obs-{case_idx}"), &observable_records);
+            tc1.tracked_pauli_labeled(&format!("track-{case_idx}"), tracked.clone());
 
-        let dag = DagCircuit::from(&tc);
+            let tc2 = TickCircuit::from(&DagCircuit::from(&tc1));
+            assert_eq!(tc2.gate_count(), tc1.gate_count(), "case {case_idx}");
+            assert_eq!(
+                tc2.num_measurements(),
+                tc1.num_measurements(),
+                "case {case_idx}"
+            );
+            assert_eq!(tc2.annotations().len(), 3, "case {case_idx}");
+
+            let det = annotation_by_label(&tc2, &format!("det-{case_idx}"));
+            match &det.kind {
+                AnnotationKind::Detector {
+                    measurement_nodes, ..
+                } => assert_eq!(
+                    measurement_nodes,
+                    &detector_records
+                        .iter()
+                        .map(|m| m.record_idx)
+                        .collect::<Vec<_>>(),
+                    "case {case_idx}"
+                ),
+                other => panic!("expected detector annotation, got {other:?}"),
+            }
 
-        // Check gate counts
-        assert_eq!(dag.gate_count(), 4);
+            let obs = annotation_by_label(&tc2, &format!("obs-{case_idx}"));
+            match &obs.kind {
+                AnnotationKind::Observable { measurement_nodes } => assert_eq!(
+                    measurement_nodes,
+                    &observable_records
+                        .iter()
+                        .map(|m| m.record_idx)
+                        .collect::<Vec<_>>(),
+                    "case {case_idx}"
+                ),
+                other => panic!("expected observable annotation, got {other:?}"),
+            }
 
-        // Check wires: H(0)->CX->H(0), X(1)->CX
-        // So we have 3 wires: H(0)->CX, CX->H(0), X(1)->CX
-        assert_eq!(dag.wire_count(), 3);
+            let track = annotation_by_label(&tc2, &format!("track-{case_idx}"));
+            assert!(matches!(track.kind, AnnotationKind::TrackedPauli));
+            assert_eq!(track.pauli, tracked, "case {case_idx}");
+        }
+    }
 
-        // Check circuit attributes
+    #[test]
+    fn test_all_standard_gate_families_round_trip_through_dag() {
+        use pecos_core::pauli::{X, Z};
+
+        fn channel_payloads(circuit: &TickCircuit) -> Vec<pecos_core::ChannelExpr> {
+            circuit
+                .iter_gate_batches()
+                .filter_map(|gate| gate.channel.clone())
+                .collect()
+        }
+
+        fn nonzero_gate_counts(
+            circuit: &TickCircuit,
+        ) -> std::collections::BTreeMap<GateType, usize> {
+            circuit
+                .gate_counts_by_type()
+                .into_iter()
+                .filter(|(_, count)| *count > 0)
+                .collect()
+        }
+
+        let mut tc1 = TickCircuit::new();
+        tc1.tick()
+            .x(&[0])
+            .y(&[1])
+            .z(&[2])
+            .h(&[3])
+            .sx(&[4])
+            .sxdg(&[5])
+            .sy(&[6])
+            .sydg(&[7])
+            .sz(&[8])
+            .szdg(&[9])
+            .f(&[10])
+            .fdg(&[11])
+            .iden(&[12]);
+        tc1.tick()
+            .cx(&[(20, 21)])
+            .cy(&[(22, 23)])
+            .cz(&[(24, 25)])
+            .sxx(&[(26, 27)])
+            .sxxdg(&[(28, 29)])
+            .syy(&[(30, 31)])
+            .syydg(&[(32, 33)])
+            .szz(&[(34, 35)])
+            .szzdg(&[(36, 37)])
+            .swap(&[(38, 39)]);
+        tc1.tick()
+            .rx(Angle64::from_turns(0.125), &[40])
+            .ry(Angle64::from_turns(0.25), &[41])
+            .rz(Angle64::from_turns(0.375), &[42])
+            .r1xy(Angle64::from_turns(0.125), Angle64::from_turns(0.25), &[43])
+            .u(
+                Angle64::from_turns(0.125),
+                Angle64::from_turns(0.25),
+                Angle64::from_turns(0.375),
+                &[44],
+            );
+        tc1.tick()
+            .channel(pecos_core::channel::Depolarizing(0.01, 50));
+        tc1.tick()
+            .channel(pecos_core::channel::Depolarizing2(0.02, 51, 52));
+        tc1.tick().idle(3u64, &[60]);
+        tc1.tick().pz(&[70, 71]);
+        let ms = tc1.tick().mz(&[70, 71]);
+        tc1.detector_labeled("det-all-gates", &[ms[0]]);
+        tc1.observable_labeled("obs-all-gates", &[ms[1]]);
+        tc1.tracked_pauli_labeled("tracked-all-gates", X(70) & Z(71));
+
+        let tc2 = TickCircuit::from(&DagCircuit::from(&tc1));
+
+        assert_eq!(tc2.gate_count(), tc1.gate_count());
+        assert_eq!(tc2.num_measurements(), tc1.num_measurements());
+        assert_eq!(nonzero_gate_counts(&tc2), nonzero_gate_counts(&tc1));
+        assert_eq!(channel_payloads(&tc2), channel_payloads(&tc1));
+        assert_eq!(tc2.annotations().len(), tc1.annotations().len());
         assert_eq!(
-            dag.get_attr("circuit_name"),
-            Some(&Attribute::String("test".to_string()))
+            tc2.annotations()
+                .iter()
+                .map(|ann| ann.label.as_deref())
+                .collect::<Vec<_>>(),
+            tc1.annotations()
+                .iter()
+                .map(|ann| ann.label.as_deref())
+                .collect::<Vec<_>>()
         );
+        assert!(matches!(
+            tc2.annotations()[0].kind,
+            AnnotationKind::Detector { .. }
+        ));
+        assert!(matches!(
+            tc2.annotations()[1].kind,
+            AnnotationKind::Observable { .. }
+        ));
+        assert!(matches!(
+            tc2.annotations()[2].kind,
+            AnnotationKind::TrackedPauli
+        ));
+        assert!(tc2.has_channel_operations());
     }
 
     #[test]
-    fn test_dag_circuit_to_tick_circuit() {
-        let mut dag = DagCircuit::new();
-        dag.set_attr("version".to_string(), Attribute::Int(1));
+    fn test_seeded_mixed_standard_gate_round_trip_preserves_metadata_annotations_and_batches() {
+        use pecos_core::pauli::{X, Y, Z};
 
-        // Build: H(0) -> CX(0,1)
-        //        X(1) ----^
-        let h = dag.add_gate(Gate::h(&[0]));
-        let x = dag.add_gate(Gate::x(&[1]));
-        let cx = dag.add_gate(Gate::cx(&[(0, 1)]));
+        fn apply_single(tick: &mut TickHandle<'_>, gate_type: GateType, qubit: usize) {
+            match gate_type {
+                GateType::X => {
+                    tick.x(&[qubit]);
+                }
+                GateType::Y => {
+                    tick.y(&[qubit]);
+                }
+                GateType::Z => {
+                    tick.z(&[qubit]);
+                }
+                GateType::H => {
+                    tick.h(&[qubit]);
+                }
+                GateType::SZ => {
+                    tick.sz(&[qubit]);
+                }
+                GateType::SZdg => {
+                    tick.szdg(&[qubit]);
+                }
+                GateType::SX => {
+                    tick.sx(&[qubit]);
+                }
+                GateType::SXdg => {
+                    tick.sxdg(&[qubit]);
+                }
+                GateType::SY => {
+                    tick.sy(&[qubit]);
+                }
+                GateType::SYdg => {
+                    tick.sydg(&[qubit]);
+                }
+                GateType::F => {
+                    tick.f(&[qubit]);
+                }
+                GateType::Fdg => {
+                    tick.fdg(&[qubit]);
+                }
+                other => panic!("unexpected single-qubit gate {other:?}"),
+            }
+        }
 
-        dag.connect(h, cx, QubitId::from(0)).unwrap();
-        dag.connect(x, cx, QubitId::from(1)).unwrap();
+        fn apply_pair(tick: &mut TickHandle<'_>, gate_type: GateType, a: usize, b: usize) {
+            match gate_type {
+                GateType::CX => {
+                    tick.cx(&[(a, b)]);
+                }
+                GateType::CY => {
+                    tick.cy(&[(a, b)]);
+                }
+                GateType::CZ => {
+                    tick.cz(&[(a, b)]);
+                }
+                GateType::SXX => {
+                    tick.sxx(&[(a, b)]);
+                }
+                GateType::SXXdg => {
+                    tick.sxxdg(&[(a, b)]);
+                }
+                GateType::SYY => {
+                    tick.syy(&[(a, b)]);
+                }
+                GateType::SYYdg => {
+                    tick.syydg(&[(a, b)]);
+                }
+                GateType::SZZ => {
+                    tick.szz(&[(a, b)]);
+                }
+                GateType::SZZdg => {
+                    tick.szzdg(&[(a, b)]);
+                }
+                GateType::SWAP => {
+                    tick.swap(&[(a, b)]);
+                }
+                other => panic!("unexpected two-qubit gate {other:?}"),
+            }
+        }
 
-        let tc = TickCircuit::from(&dag);
+        fn nonzero_gate_counts(
+            circuit: &TickCircuit,
+        ) -> std::collections::BTreeMap<GateType, usize> {
+            circuit
+                .gate_counts_by_type()
+                .into_iter()
+                .filter(|(_, count)| *count > 0)
+                .collect()
+        }
 
-        // H and X are parallel (layer 0), CX depends on both (layer 1)
-        assert_eq!(tc.num_ticks(), 2);
+        fn choose_gate(gates: &[GateType], state: u64, shift: u32) -> GateType {
+            let len = u64::try_from(gates.len()).unwrap();
+            let idx = usize::try_from((state >> shift) % len).unwrap();
+            gates[idx]
+        }
 
-        // First tick should have H and X (order may vary)
-        let tick0 = tc.get_tick(0).unwrap();
-        assert_eq!(tick0.gates().len(), 2);
+        const ONE_Q: &[GateType] = &[
+            GateType::X,
+            GateType::Y,
+            GateType::Z,
+            GateType::H,
+            GateType::SZ,
+            GateType::SZdg,
+            GateType::SX,
+            GateType::SXdg,
+            GateType::SY,
+            GateType::SYdg,
+            GateType::F,
+            GateType::Fdg,
+        ];
+        const TWO_Q: &[GateType] = &[
+            GateType::CX,
+            GateType::CY,
+            GateType::CZ,
+            GateType::SXX,
+            GateType::SXXdg,
+            GateType::SYY,
+            GateType::SYYdg,
+            GateType::SZZ,
+            GateType::SZZdg,
+            GateType::SWAP,
+        ];
+
+        let mut state = 0xdecaf_bad5eed_u64;
+        for case_idx in 0..10usize {
+            state = state
+                .wrapping_mul(6_364_136_223_846_793_005)
+                .wrapping_add(1_442_695_040_888_963_407);
+            let base = 100 * case_idx;
+            let one_a = choose_gate(ONE_Q, state, 0);
+            let one_b = choose_gate(ONE_Q, state, 8);
+            let two = choose_gate(TWO_Q, state, 16);
+            let rz_bucket = u8::try_from((state >> 24) & 3).unwrap();
+            let rz_turns = f64::from(rz_bucket + 1) / 8.0;
+
+            let mut tc1 = TickCircuit::new();
+            tc1.set_meta("case", Attribute::Int(i64::try_from(case_idx).unwrap()));
+            {
+                let mut tick = tc1.tick();
+                tick.meta("round", Attribute::Int(0))
+                    .meta("kind", Attribute::String("single".into()));
+                apply_single(&mut tick, one_a, base);
+                apply_single(&mut tick, one_b, base + 1);
+            }
+            {
+                let mut tick = tc1.tick();
+                tick.meta("round", Attribute::Int(1))
+                    .meta("kind", Attribute::String("mixed".into()));
+                apply_pair(&mut tick, two, base + 2, base + 3);
+                tick.rz(Angle64::from_turns(rz_turns), &[base + 4])
+                    .rx(Angle64::from_turns(0.25), &[base + 5]);
+            }
+            tc1.tick()
+                .meta("round", Attribute::Int(2))
+                .channel(pecos_core::channel::Depolarizing(0.01, base + 6));
+            tc1.tick().pz(&[base, base + 1, base + 2]);
+            let measurements = tc1.tick().mz(&[base, base + 1, base + 2]);
+            tc1.detector_labeled(
+                &format!("det-{case_idx}"),
+                &[measurements[0], measurements[2]],
+            );
+            tc1.observable_labeled(&format!("obs-{case_idx}"), &[measurements[1]]);
+            let tracked = if state & (1 << 32) == 0 {
+                X(base) & Z(base + 3)
+            } else {
+                Y(base + 2)
+            };
+            tc1.tracked_pauli_labeled(&format!("tracked-{case_idx}"), tracked.clone());
 
-        // Second tick should have CX
-        let tick1 = tc.get_tick(1).unwrap();
-        assert_eq!(tick1.gates().len(), 1);
+            let tc2 = TickCircuit::from(&DagCircuit::from(&tc1));
 
-        // Check circuit attribute
-        assert_eq!(tc.get_meta("version"), Some(&Attribute::Int(1)));
+            assert_eq!(
+                tc2.get_meta("case"),
+                tc1.get_meta("case"),
+                "case {case_idx}"
+            );
+            assert_eq!(tc2.gate_count(), tc1.gate_count(), "case {case_idx}");
+            assert_eq!(
+                tc2.num_measurements(),
+                tc1.num_measurements(),
+                "case {case_idx}"
+            );
+            assert_eq!(
+                nonzero_gate_counts(&tc2),
+                nonzero_gate_counts(&tc1),
+                "case {case_idx}"
+            );
+            assert_eq!(tc2.annotations().len(), 3, "case {case_idx}");
+            assert_eq!(
+                tc2.annotations()
+                    .iter()
+                    .map(|ann| ann.label.as_deref())
+                    .collect::<Vec<_>>(),
+                tc1.annotations()
+                    .iter()
+                    .map(|ann| ann.label.as_deref())
+                    .collect::<Vec<_>>(),
+                "case {case_idx}"
+            );
+            assert!(matches!(
+                tc2.annotations()[0].kind,
+                AnnotationKind::Detector { .. }
+            ));
+            assert!(matches!(
+                tc2.annotations()[1].kind,
+                AnnotationKind::Observable { .. }
+            ));
+            assert!(matches!(
+                tc2.annotations()[2].kind,
+                AnnotationKind::TrackedPauli
+            ));
+            assert_eq!(tc2.annotations()[2].pauli, tracked, "case {case_idx}");
+            assert!(tc2.has_channel_operations(), "case {case_idx}");
+        }
     }
 
     #[test]
-    fn test_round_trip_tick_to_dag_to_tick() {
-        let mut tc1 = TickCircuit::new();
-        tc1.tick().h(&[0]);
-        tc1.tick().cx(&[(0, 1)]);
-        tc1.tick().h(&[1]);
-
-        // Convert to DAG and back
-        let dag = DagCircuit::from(&tc1);
-        let tc2 = TickCircuit::from(&dag);
+    fn test_batching_invariants_cover_parameters_channels_and_measurements() {
+        let same_rz = Gate::rz(Angle64::from_turns(0.25), &[0]);
+        let same_rz_disjoint = Gate::rz(Angle64::from_turns(0.25), &[1]);
+        let different_rz = Gate::rz(Angle64::from_turns(0.5), &[2]);
+        assert!(same_rz.can_batch_with(&same_rz_disjoint));
+        assert!(!same_rz.can_batch_with(&different_rz));
+
+        let channel0 = Gate::channel(pecos_core::channel::Depolarizing(0.01, 10));
+        let channel1 = Gate::channel(pecos_core::channel::Depolarizing(0.01, 11));
+        assert!(!channel0.can_batch_with(&channel1));
+
+        let mut tick = Tick::new();
+        tick.add_gate(same_rz);
+        tick.add_gate(same_rz_disjoint);
+        tick.merge_compatible_gate_at(1);
+        tick.add_gate(different_rz);
+        tick.add_gate(channel0);
+        tick.add_gate(channel1);
+
+        assert_eq!(tick.gate_count(), 5);
+        assert_eq!(tick.gate_batch_count(), 4);
+        assert_eq!(
+            tick.gate_batches()[0].qubits.as_slice(),
+            &[QubitId::from(0), QubitId::from(1)]
+        );
+        assert!(tick.gate_batches()[2].is_channel());
+        assert!(tick.gate_batches()[3].is_channel());
+
+        let mut meas = TickCircuit::new();
+        meas.reserve_ticks(1);
+        let refs0 = meas.tick_at(0).mz(&[0, 1]);
+        meas.get_tick_mut(0).unwrap().set_gate_attr(
+            refs0[0].gate_idx,
+            "readout_family",
+            Attribute::String("fast".into()),
+        );
+        let refs2 = meas.tick_at(0).mz(&[2]);
+        let tick = meas.get_tick_mut(0).unwrap();
+        tick.set_gate_attr(
+            refs2[0].gate_idx,
+            "readout_family",
+            Attribute::String("slow".into()),
+        );
+        tick.merge_compatible_gate_at(refs2[0].gate_idx);
 
-        // Should have same structure
-        assert_eq!(tc1.num_ticks(), tc2.num_ticks());
-        for i in 0..tc1.num_ticks() {
-            assert_eq!(
-                tc1.get_tick(i).unwrap().gates().len(),
-                tc2.get_tick(i).unwrap().gates().len()
-            );
-        }
+        let tick = meas.get_tick(0).unwrap();
+        assert_eq!(tick.len(), 2);
+        assert_eq!(tick.gate_count(), 3);
+        assert_eq!(tick.gate_batch_count(), 2);
+        assert_eq!(
+            tick.gate_batches()[0].meas_ids.as_slice(),
+            &[MeasId(0), MeasId(1)]
+        );
+        assert_eq!(tick.gate_batches()[1].meas_ids.as_slice(), &[MeasId(2)]);
     }
 
     #[test]
@@ -2230,6 +5063,26 @@ mod tests {
         assert!(handle.try_add_gate(Gate::x(&[1])).is_ok());
     }
 
+    #[test]
+    fn test_batched_two_qubit_gate_accepts_disjoint_pairs_and_rejects_overlap() {
+        let mut tick = Tick::new();
+        assert!(tick.try_add_gate(Gate::cx(&[(0, 1), (2, 3)])).is_ok());
+        assert_eq!(tick.len(), 1);
+        assert_eq!(tick.gate_count(), 2);
+        assert_eq!(tick.gate_batch_count(), 1);
+
+        let err = Tick::new()
+            .try_add_gate(Gate::cx(&[(0, 1), (1, 2)]))
+            .unwrap_err();
+        match err {
+            TickGateError::InvalidGate { message, .. } => {
+                assert!(message.contains("requires distinct qubits"));
+                assert!(message.contains('1'));
+            }
+            TickGateError::QubitConflict(_) => panic!("overlap within one gate command is invalid"),
+        }
+    }
+
     #[test]
     fn test_try_add_gate_conflict() {
         let mut tc = TickCircuit::new();
@@ -2240,11 +5093,12 @@ mod tests {
         let result = handle.try_add_gate(Gate::x(&[0]));
 
         match result {
-            Err(err) => {
+            Err(TickGateError::QubitConflict(err)) => {
                 assert_eq!(err.conflicting_qubits, vec![QubitId::from(0)]);
                 assert_eq!(err.tick_idx, Some(0));
             }
             Ok(_) => panic!("Expected conflict error"),
+            Err(err) => panic!("Expected conflict error, got {err}"),
         }
     }
 
@@ -2272,6 +5126,34 @@ mod tests {
         assert!(result.is_err());
     }
 
+    #[test]
+    fn test_try_add_gate_rejects_invalid_gate_payload_before_storage() {
+        let mut tc = TickCircuit::new();
+        let mut handle = tc.tick();
+        let invalid = Gate::cx(&[(0, 0)]);
+
+        let result = handle.try_add_gate(invalid);
+
+        match result {
+            Err(TickGateError::InvalidGate {
+                message, tick_idx, ..
+            }) => {
+                assert_eq!(tick_idx, Some(0));
+                assert!(message.contains("requires distinct qubits"));
+            }
+            Ok(_) => panic!("Expected invalid-gate error"),
+            Err(err) => panic!("Expected invalid-gate error, got {err}"),
+        }
+        assert!(tc.get_tick(0).unwrap().is_empty());
+    }
+
+    #[test]
+    #[should_panic(expected = "Invalid gate in tick 0")]
+    fn test_tick_handle_panics_on_invalid_gate_payload() {
+        let mut tc = TickCircuit::new();
+        tc.tick().cx(&[(0, 0)]);
+    }
+
     #[test]
     fn test_metas_on_gates() {
         let mut tc = TickCircuit::new();
@@ -2361,19 +5243,67 @@ mod tests {
     #[test]
     fn test_iteration_helpers() {
         let mut tc = TickCircuit::new();
-        tc.tick().h(&[0, 1]);
-        tc.tick().cx(&[(0, 1)]);
-        tc.tick().mz(&[0, 1]);
-
-        // Test iter_gates
-        let gates: Vec<_> = tc.iter_gates().collect();
-        assert_eq!(gates.len(), 3);
+        tc.tick()
+            .h(&[0, 1, 2, 3])
+            .meta("calibration", Attribute::String("h-cal".into()));
+        tc.tick().cx(&[(0, 1), (2, 3)]);
+        tc.tick().mz(&[0, 1, 2, 3]);
 
-        // Test iter_gates_with_tick
-        let gates_with_tick: Vec<_> = tc.iter_gates_with_tick().collect();
-        assert_eq!(gates_with_tick.len(), 3);
-        assert_eq!(gates_with_tick[0].0, 0); // First gate is in tick 0
-        assert_eq!(gates_with_tick[1].0, 1); // Second gate is in tick 1
+        // Test explicit batched views. These preserve full Gate payloads.
+        let batches: Vec<_> = tc.iter_gate_batches().collect();
+        assert_eq!(batches.len(), 3);
+        assert_eq!(batches[0].batch_index(), 0);
+        assert_eq!(batches[0].gate_type, GateType::H);
+        assert_eq!(batches[0].num_gates(), 4);
+        assert_eq!(batches[0].gate_count(), 4);
+        assert_eq!(
+            batches[0].get_attr("calibration"),
+            Some(&Attribute::String("h-cal".into()))
+        );
+        assert_eq!(tc.get_tick(0).unwrap().gate_batches()[0].num_gates(), 4);
+
+        let batches_with_tick: Vec<_> = tc.iter_gate_batches_with_tick().collect();
+        assert_eq!(batches_with_tick.len(), 3);
+        assert_eq!(batches_with_tick[2].0, 2); // Third batch is in tick 2
+        assert_eq!(batches_with_tick[2].1.gate_type, GateType::MZ);
+
+        let instances_with_tick: Vec<_> = tc.iter_gate_instances_with_tick().collect();
+        assert_eq!(instances_with_tick.len(), 10);
+        assert_eq!(instances_with_tick[0].0, 0);
+        assert_eq!(instances_with_tick[0].1.batch_index(), 0);
+        assert_eq!(instances_with_tick[0].1.instance_index(), 0);
+        assert_eq!(instances_with_tick[0].1.gate_type(), GateType::H);
+        assert_eq!(instances_with_tick[0].1.qubits(), &[QubitId::from(0)]);
+        assert_eq!(
+            instances_with_tick[0].1.to_gate().qubits.as_slice(),
+            &[QubitId::from(0)]
+        );
+        assert_eq!(
+            instances_with_tick[0].1.get_attr("calibration"),
+            Some(&Attribute::String("h-cal".into()))
+        );
+        assert_eq!(instances_with_tick[3].1.qubits(), &[QubitId::from(3)]);
+        assert_eq!(instances_with_tick[4].0, 1);
+        assert_eq!(instances_with_tick[4].1.instance_index(), 0);
+        assert_eq!(instances_with_tick[4].1.gate_type(), GateType::CX);
+        assert_eq!(
+            instances_with_tick[4].1.qubits(),
+            &[QubitId::from(0), QubitId::from(1)]
+        );
+        assert_eq!(
+            instances_with_tick[5].1.qubits(),
+            &[QubitId::from(2), QubitId::from(3)]
+        );
+        assert_eq!(instances_with_tick[5].1.instance_index(), 1);
+        assert_eq!(instances_with_tick[6].0, 2);
+        assert_eq!(instances_with_tick[6].1.gate_type(), GateType::MZ);
+        assert_eq!(instances_with_tick[6].1.qubits(), &[QubitId::from(0)]);
+        assert_eq!(instances_with_tick[6].1.meas_ids(), &[MeasId(0)]);
+        assert_eq!(
+            instances_with_tick[6].1.to_gate().meas_ids.as_slice(),
+            &[MeasId(0)]
+        );
+        assert_eq!(instances_with_tick[9].1.meas_ids(), &[MeasId(3)]);
 
         // Test iter_ticks
         let ticks: Vec<_> = tc.iter_ticks().collect();
@@ -2385,15 +5315,128 @@ mod tests {
 
         // Test all_qubits
         let qubits = tc.all_qubits();
-        assert_eq!(qubits.len(), 2);
+        assert_eq!(qubits.len(), 4);
         assert!(qubits.contains(&QubitId::from(0)));
         assert!(qubits.contains(&QubitId::from(1)));
+        assert!(qubits.contains(&QubitId::from(2)));
+        assert!(qubits.contains(&QubitId::from(3)));
 
         // Test gate_counts_by_type
         let counts = tc.gate_counts_by_type();
-        assert_eq!(counts.get(&GateType::H), Some(&1));
-        assert_eq!(counts.get(&GateType::CX), Some(&1));
-        assert_eq!(counts.get(&GateType::MZ), Some(&1));
+        assert_eq!(counts.get(&GateType::H), Some(&4));
+        assert_eq!(counts.get(&GateType::CX), Some(&2));
+        assert_eq!(counts.get(&GateType::MZ), Some(&4));
+    }
+
+    #[test]
+    fn test_gate_instance_to_gate_preserves_payloads_without_attrs() {
+        let angle = Angle64::from_turn_ratio(1, 8);
+        let mut rzz_tick = Tick::new();
+        rzz_tick.add_gate(Gate::rzz(angle, &[(0, 1), (2, 3)]));
+        rzz_tick.set_gate_attr(0, "calibration", Attribute::String("rzz-cal".into()));
+
+        let rzz_instances: Vec<_> = rzz_tick.iter_gate_instances().collect();
+        assert_eq!(rzz_instances.len(), 2);
+        assert_eq!(
+            rzz_instances[0].get_attr("calibration"),
+            Some(&Attribute::String("rzz-cal".into()))
+        );
+        assert_eq!(
+            rzz_instances[0].attrs().count(),
+            1,
+            "batch metadata remains available through the instance view"
+        );
+        assert_eq!(rzz_instances[0].angles(), &[angle]);
+        assert_eq!(
+            rzz_instances[0].to_gate(),
+            Gate::rzz(angle, &[(0usize, 1usize)]),
+            "materialized gates carry sliced support and payload, not attrs"
+        );
+        assert_eq!(
+            rzz_instances[1].to_gate(),
+            Gate::rzz(angle, &[(2usize, 3usize)])
+        );
+
+        let duration = 8.0_f64;
+        let mut idle_tick = Tick::new();
+        idle_tick.add_gate(Gate::idle(
+            duration,
+            vec![QubitId::from(4), QubitId::from(5)],
+        ));
+        let idle_instances: Vec<_> = idle_tick.iter_gate_instances().collect();
+        assert_eq!(idle_instances.len(), 2);
+        let idle_gate = idle_instances[1].to_gate();
+        assert_eq!(idle_gate.gate_type, GateType::Idle);
+        assert_eq!(idle_gate.qubits.as_slice(), &[QubitId::from(5)]);
+        assert_eq!(idle_gate.params.len(), 1);
+        assert_eq!(idle_gate.params[0].to_bits(), duration.to_bits());
+
+        let mut meas_tc = TickCircuit::new();
+        meas_tc.tick().mz(&[8, 9]);
+        let meas_instances: Vec<_> = meas_tc.get_tick(0).unwrap().iter_gate_instances().collect();
+        assert_eq!(meas_instances.len(), 2);
+        assert_eq!(
+            meas_instances[0].to_gate().meas_ids.as_slice(),
+            &[MeasId(0)]
+        );
+        assert_eq!(
+            meas_instances[1].to_gate().meas_ids.as_slice(),
+            &[MeasId(1)]
+        );
+
+        let channel = pecos_core::channel::Depolarizing(0.125, 6);
+        let mut channel_tick = Tick::new();
+        channel_tick.add_gate(Gate::channel(channel.clone()));
+        let channel_instances: Vec<_> = channel_tick.iter_gate_instances().collect();
+        assert_eq!(channel_instances.len(), 1);
+        let channel_gate = channel_instances[0].to_gate();
+        assert_eq!(channel_gate.gate_type, GateType::Channel);
+        assert_eq!(channel_gate.qubits.as_slice(), &[QubitId::from(6)]);
+        assert_eq!(channel_gate.channel.as_ref(), Some(&channel));
+    }
+
+    #[test]
+    fn test_gate_instance_iteration_skips_annotation_batches() {
+        let mut tick = Tick::new();
+        tick.add_gate(Gate::simple(
+            GateType::TrackedPauliMeta,
+            vec![QubitId::from(0), QubitId::from(1)],
+        ));
+
+        let batches: Vec<_> = tick.iter_gate_batches().collect();
+        assert_eq!(batches.len(), 1);
+        assert_eq!(batches[0].gate_count(), 0);
+        assert_eq!(tick.iter_gate_instances().count(), 0);
+    }
+
+    #[test]
+    fn test_tick_to_dag_keeps_zero_gate_metadata_nodes_from_gate_count() {
+        let mut tc = TickCircuit::new();
+        tc.tick().h(&[0]);
+        tc.tick();
+        tc.get_tick_mut(1).unwrap().add_gate(Gate::simple(
+            GateType::TrackedPauliMeta,
+            vec![QubitId::from(1), QubitId::from(2)],
+        ));
+        tc.tick().mz(&[0]);
+
+        let dag = DagCircuit::from(&tc);
+
+        assert_eq!(
+            dag.gate_count(),
+            2,
+            "metadata nodes are not gate applications"
+        );
+        let metadata_nodes: Vec<_> = dag
+            .nodes()
+            .into_iter()
+            .filter(|&node| {
+                dag.gate(node)
+                    .is_some_and(|gate| gate.gate_type == GateType::TrackedPauliMeta)
+            })
+            .collect();
+        assert_eq!(metadata_nodes.len(), 1);
+        assert_eq!(dag.gate(metadata_nodes[0]).unwrap().num_gates(), 0);
     }
 
     #[test]
@@ -2435,6 +5478,82 @@ mod tests {
         assert_eq!(tc.num_ticks(), 1);
     }
 
+    #[test]
+    fn test_reset_clears_annotations_and_measurement_counter() {
+        let mut tc = TickCircuit::new();
+        let first_measurement = tc.tick().mz(&[0]);
+        tc.detector(&first_measurement);
+        tc.observable(&first_measurement);
+        tc.tracked_pauli(pecos_core::pauli::Z(0));
+
+        assert_eq!(tc.num_measurements(), 1);
+        assert_eq!(tc.annotations().len(), 3);
+
+        tc.reset();
+
+        assert_eq!(tc.num_ticks(), 0);
+        assert_eq!(tc.num_measurements(), 0);
+        assert!(tc.annotations().is_empty());
+
+        let reused_measurement = tc.tick().mz(&[1]);
+        assert_eq!(reused_measurement[0].record_idx, 0);
+    }
+
+    #[test]
+    fn test_metadata_helpers_build_detector_and_observable_json() {
+        let mut tc = TickCircuit::new();
+
+        let detector_id = tc
+            .add_detector_metadata(&[-1], Some(&[0.0, 1.0, 2.0]), Some("d0"), None)
+            .unwrap();
+        let observable_id = tc
+            .add_observable_metadata(&[-1, -2], None, Some("L2"))
+            .unwrap();
+
+        assert_eq!(detector_id, 0);
+        assert_eq!(observable_id, 2);
+        assert_eq!(tc.get_meta("num_detectors"), Some(&Attribute::Int(1)));
+        assert_eq!(tc.get_meta("num_observables"), Some(&Attribute::Int(3)));
+
+        let detectors = match tc.get_meta("detectors").unwrap() {
+            Attribute::String(value) => value,
+            other => panic!("expected detectors JSON string, got {other:?}"),
+        };
+        assert_eq!(
+            detectors,
+            r#"[{"coords":[0.0,1.0,2.0],"id":0,"label":"d0","records":[-1]}]"#
+        );
+
+        let observables = match tc.get_meta("observables").unwrap() {
+            Attribute::String(value) => value,
+            other => panic!("expected observables JSON string, got {other:?}"),
+        };
+        assert_eq!(observables, r#"[{"id":2,"label":"L2","records":[-1,-2]}]"#);
+    }
+
+    #[test]
+    fn test_metadata_helpers_reject_conflicts_and_duplicates() {
+        let mut tc = TickCircuit::new();
+
+        let err = tc
+            .add_observable_metadata(&[-1], Some(1), Some("L2"))
+            .unwrap_err();
+        assert!(err.contains("conflicts"));
+
+        tc.add_detector_metadata(&[-1], None, None, Some(7))
+            .unwrap();
+        let err = tc
+            .add_detector_metadata(&[-2], None, None, Some(7))
+            .unwrap_err();
+        assert!(err.contains("already contains detector_id 7"));
+
+        tc.add_observable_metadata(&[-1], Some(3), None).unwrap();
+        let err = tc
+            .add_observable_metadata(&[-2], Some(3), None)
+            .unwrap_err();
+        assert!(err.contains("already contains observable_id 3"));
+    }
+
     #[test]
     fn test_reserve_ticks() {
         let mut tc = TickCircuit::new();
@@ -2467,13 +5586,13 @@ mod tests {
 
         // Check order: H at 0, X at 1, CX at 2
         let tick0 = tc.get_tick(0).unwrap();
-        assert_eq!(tick0.gates()[0].gate_type, GateType::H);
+        assert_eq!(tick0.gate_batches()[0].gate_type, GateType::H);
 
         let tick1 = tc.get_tick(1).unwrap();
-        assert_eq!(tick1.gates()[0].gate_type, GateType::X);
+        assert_eq!(tick1.gate_batches()[0].gate_type, GateType::X);
 
         let tick2 = tc.get_tick(2).unwrap();
-        assert_eq!(tick2.gates()[0].gate_type, GateType::CX);
+        assert_eq!(tick2.gate_batches()[0].gate_type, GateType::CX);
     }
 
     #[test]
@@ -2488,7 +5607,7 @@ mod tests {
 
         // Z should now be at tick 0
         let tick0 = tc.get_tick(0).unwrap();
-        assert_eq!(tick0.gates()[0].gate_type, GateType::Z);
+        assert_eq!(tick0.gate_batches()[0].gate_type, GateType::Z);
     }
 
     #[test]
@@ -2502,7 +5621,7 @@ mod tests {
         assert_eq!(tc.num_ticks(), 2);
 
         let tick1 = tc.get_tick(1).unwrap();
-        assert_eq!(tick1.gates()[0].gate_type, GateType::X);
+        assert_eq!(tick1.gate_batches()[0].gate_type, GateType::X);
     }
 
     #[test]
@@ -2518,9 +5637,18 @@ mod tests {
         assert_eq!(tc.num_ticks(), 3);
 
         // Check each tick has the right gate
-        assert_eq!(tc.get_tick(0).unwrap().gates()[0].gate_type, GateType::H);
-        assert_eq!(tc.get_tick(1).unwrap().gates()[0].gate_type, GateType::X);
-        assert_eq!(tc.get_tick(2).unwrap().gates()[0].gate_type, GateType::CX);
+        assert_eq!(
+            tc.get_tick(0).unwrap().gate_batches()[0].gate_type,
+            GateType::H
+        );
+        assert_eq!(
+            tc.get_tick(1).unwrap().gate_batches()[0].gate_type,
+            GateType::X
+        );
+        assert_eq!(
+            tc.get_tick(2).unwrap().gate_batches()[0].gate_type,
+            GateType::CX
+        );
     }
 
     #[test]
@@ -2564,7 +5692,7 @@ mod tests {
 
         assert_eq!(removed, 2); // H on q0 and CX on q2,q3
         assert_eq!(tick.len(), 1); // Only X on q1 remains
-        assert_eq!(tick.gates()[0].gate_type, GateType::X);
+        assert_eq!(tick.gate_batches()[0].gate_type, GateType::X);
     }
 
     #[test]
@@ -2605,6 +5733,29 @@ mod tests {
         assert!(tick.get_gate_attr(1, "x_attr").is_none());
     }
 
+    #[test]
+    fn test_tick_remove_gate_preserves_aligned_attrs() {
+        let mut tc = TickCircuit::new();
+        tc.tick()
+            .h(&[0])
+            .meta("h_attr", Attribute::Int(1))
+            .x(&[1])
+            .meta("x_attr", Attribute::Int(2))
+            .z(&[2])
+            .meta("z_attr", Attribute::Int(3));
+
+        let tick = tc.get_tick_mut(0).unwrap();
+        let removed = tick.remove_gate(0).expect("H batch should exist");
+
+        assert_eq!(removed.gate_type, GateType::H);
+        assert_eq!(tick.len(), 2);
+        assert_eq!(tick.gate_batches()[0].gate_type, GateType::X);
+        assert_eq!(tick.gate_batches()[1].gate_type, GateType::Z);
+        assert_eq!(tick.get_gate_attr(0, "x_attr"), Some(&Attribute::Int(2)));
+        assert_eq!(tick.get_gate_attr(1, "z_attr"), Some(&Attribute::Int(3)));
+        assert!(tick.get_gate_attr(0, "h_attr").is_none());
+    }
+
     #[test]
     fn test_tick_remove_gate() {
         let mut tc = TickCircuit::new();
@@ -2619,8 +5770,8 @@ mod tests {
         assert_eq!(tick.len(), 2);
 
         // Check remaining gates
-        assert_eq!(tick.gates()[0].gate_type, GateType::H);
-        assert_eq!(tick.gates()[1].gate_type, GateType::Z);
+        assert_eq!(tick.gate_batches()[0].gate_type, GateType::H);
+        assert_eq!(tick.gate_batches()[1].gate_type, GateType::Z);
     }
 
     #[test]
@@ -2634,6 +5785,60 @@ mod tests {
         assert_eq!(tick.len(), 1);
     }
 
+    #[test]
+    fn test_compact_ticks_preserves_and_merges_aligned_batch_attrs() {
+        let mut tc = TickCircuit::new();
+        tc.tick()
+            .h(&[0])
+            .meta("calibration", Attribute::String("shared".into()));
+        tc.tick()
+            .h(&[1])
+            .meta("calibration", Attribute::String("shared".into()));
+
+        tc.compact_ticks();
+
+        assert_eq!(tc.num_ticks(), 1);
+        let tick = tc.get_tick(0).unwrap();
+        assert_eq!(tick.len(), 1);
+        assert_eq!(tick.gate_count(), 2);
+        assert_eq!(tick.gate_batch_count(), 1);
+        assert_eq!(
+            tick.gate_batches()[0].qubits.as_slice(),
+            &[QubitId::from(0), QubitId::from(1)]
+        );
+        assert_eq!(
+            tick.get_gate_attr(0, "calibration"),
+            Some(&Attribute::String("shared".into()))
+        );
+    }
+
+    #[test]
+    fn test_compact_ticks_keeps_different_batch_attrs_separate() {
+        let mut tc = TickCircuit::new();
+        tc.tick()
+            .h(&[0])
+            .meta("calibration", Attribute::String("a".into()));
+        tc.tick()
+            .h(&[1])
+            .meta("calibration", Attribute::String("b".into()));
+
+        tc.compact_ticks();
+
+        assert_eq!(tc.num_ticks(), 1);
+        let tick = tc.get_tick(0).unwrap();
+        assert_eq!(tick.len(), 2);
+        assert_eq!(tick.gate_count(), 2);
+        assert_eq!(tick.gate_batch_count(), 2);
+        assert_eq!(
+            tick.get_gate_attr(0, "calibration"),
+            Some(&Attribute::String("a".into()))
+        );
+        assert_eq!(
+            tick.get_gate_attr(1, "calibration"),
+            Some(&Attribute::String("b".into()))
+        );
+    }
+
     #[test]
     fn test_circuit_discard() {
         let mut tc = TickCircuit::new();
@@ -2734,7 +5939,7 @@ mod tests {
             .expect("should succeed");
 
         let tick = tc.get_tick(0).unwrap();
-        let gate = &tick.gates()[0];
+        let gate = &tick.gate_batches()[0];
         assert_eq!(gate.gate_type, GateType::Custom);
         assert_eq!(gate.angles.len(), 2);
         assert_eq!(gate.angles[0], a1);
@@ -2753,7 +5958,7 @@ mod tests {
     #[test]
     fn test_import_signatures() {
         let mut tc = TickCircuit::new();
-        let mut sigs = HashMap::new();
+        let mut sigs = BTreeMap::new();
         sigs.insert(
             "AOT_GATE".to_string(),
             GateSignature {
@@ -2786,4 +5991,495 @@ mod tests {
         tc.reset();
         assert!(tc.gate_signatures().is_empty());
     }
+
+    #[test]
+    fn test_tick_circuit_annotations() {
+        use pecos_core::pauli::X;
+
+        let mut tc = TickCircuit::new();
+        tc.tick().pz(&[0, 1, 2]);
+        tc.tick().cx(&[(0, 2)]);
+        tc.tick().cx(&[(1, 2)]);
+        let ms = tc.tick().mz(&[2]);
+
+        assert_eq!(ms.len(), 1);
+        assert_eq!(ms[0].qubit, QubitId::from(2));
+
+        tc.detector_labeled("Z_check", &ms);
+        tc.observable_labeled("logical_Z", &ms);
+        tc.tracked_pauli_labeled("logical_X", X(0) & X(1));
+
+        assert_eq!(tc.annotations().len(), 3);
+        assert_eq!(tc.annotations()[0].label.as_deref(), Some("Z_check"));
+        assert_eq!(tc.annotations()[1].label.as_deref(), Some("logical_Z"));
+        assert_eq!(tc.annotations()[2].label.as_deref(), Some("logical_X"));
+    }
+
+    #[test]
+    fn test_tick_to_dag_annotation_transfer() {
+        use pecos_core::pauli::Z;
+
+        let mut tc = TickCircuit::new();
+        tc.tick().pz(&[0, 1, 2]);
+        tc.tick().cx(&[(0, 2)]);
+        tc.tick().cx(&[(1, 2)]);
+        let ms = tc.tick().mz(&[2]);
+        tc.detector_labeled("det0", &ms);
+        tc.observable_labeled("obs0", &ms);
+        tc.tracked_pauli_labeled("op0", Z(0) & Z(1));
+
+        let dag = DagCircuit::from(&tc);
+
+        // Annotations should transfer
+        assert_eq!(dag.annotations().len(), 3);
+        assert_eq!(dag.annotations()[0].label.as_deref(), Some("det0"));
+        assert_eq!(dag.annotations()[1].label.as_deref(), Some("obs0"));
+        assert_eq!(dag.annotations()[2].label.as_deref(), Some("op0"));
+
+        // Kinds preserved
+        assert!(matches!(
+            dag.annotations()[0].kind,
+            crate::dag_circuit::AnnotationKind::Detector { .. }
+        ));
+        assert!(matches!(
+            dag.annotations()[1].kind,
+            crate::dag_circuit::AnnotationKind::Observable { .. }
+        ));
+        assert!(matches!(
+            dag.annotations()[2].kind,
+            crate::dag_circuit::AnnotationKind::TrackedPauli
+        ));
+    }
+
+    #[test]
+    fn test_dag_to_tick_annotation_transfer() {
+        use pecos_core::pauli::X;
+
+        let mut dag = DagCircuit::new();
+        dag.pz(&[0, 1]);
+        dag.cx(&[(0, 1)]);
+        let ms = dag.mz(&[0, 1]);
+        dag.detector_labeled("d0", &[ms[0]]);
+        dag.observable_labeled("o0", &[ms[0], ms[1]]);
+        dag.tracked_pauli_labeled("p0", X(0) & X(1));
+
+        let tc = TickCircuit::from(&dag);
+
+        assert_eq!(tc.annotations().len(), 3);
+        assert_eq!(tc.annotations()[0].label.as_deref(), Some("d0"));
+        assert_eq!(tc.annotations()[1].label.as_deref(), Some("o0"));
+        assert_eq!(tc.annotations()[2].label.as_deref(), Some("p0"));
+    }
+
+    #[test]
+    fn test_annotation_round_trip() {
+        use pecos_core::pauli::X;
+
+        // Build TickCircuit with annotations
+        let mut tc1 = TickCircuit::new();
+        tc1.tick().pz(&[0, 1, 2]);
+        tc1.tick().cx(&[(0, 2)]);
+        tc1.tick().cx(&[(1, 2)]);
+        let ms = tc1.tick().mz(&[2]);
+        tc1.detector_labeled("syndr", &ms);
+        let ms_data = tc1.tick().mz(&[0, 1]);
+        tc1.observable_labeled("log_Z", &ms_data);
+        tc1.tracked_pauli_labeled("log_X", X(0) & X(1));
+
+        // TickCircuit -> DagCircuit -> TickCircuit
+        let dag = DagCircuit::from(&tc1);
+        let tc2 = TickCircuit::from(&dag);
+
+        // Annotation count and labels preserved
+        assert_eq!(tc2.annotations().len(), tc1.annotations().len());
+        for (a1, a2) in tc1.annotations().iter().zip(tc2.annotations()) {
+            assert_eq!(a1.label, a2.label);
+            assert_eq!(a1.pauli, a2.pauli);
+        }
+    }
+
+    #[test]
+    fn test_mz_returns_refs() {
+        let mut tc = TickCircuit::new();
+        tc.tick().pz(&[0, 1]);
+        let ms = tc.tick().mz(&[0, 1]);
+
+        assert_eq!(ms.len(), 2);
+        assert_eq!(ms[0].qubit, QubitId::from(0));
+        assert_eq!(ms[1].qubit, QubitId::from(1));
+        // Both from same tick and gate
+        assert_eq!(ms[0].tick, ms[1].tick);
+        assert_eq!(ms[0].gate_idx, ms[1].gate_idx);
+    }
+
+    #[test]
+    fn test_fill_idle_gates() {
+        let mut tc = TickCircuit::new();
+        tc.tick().h(&[0]); // qubit 1 idle
+        tc.tick().cx(&[(0, 1)]); // none idle
+
+        let count_before = tc.gate_count();
+        tc.fill_idle_gates();
+        let count_after = tc.gate_count();
+
+        // Tick 0: qubit 1 was idle, should get an idle gate
+        assert!(count_after > count_before, "Should have added idle gates");
+    }
+
+    #[test]
+    fn test_channel_gate_is_first_class_tick_operation() {
+        let mut tc = TickCircuit::new();
+        tc.tick()
+            .channel(pecos_core::channel::Depolarizing(0.25, 0));
+
+        let gate = &tc.get_tick(0).unwrap().gate_batches()[0];
+        assert_eq!(gate.gate_type, GateType::Channel);
+        assert_eq!(gate.qubits.as_slice(), &[QubitId::from(0)]);
+        assert!(gate.channel_expr().is_some());
+        assert!(tc.has_channel_operations());
+        assert!(gate.validate().is_ok());
+    }
+
+    #[test]
+    fn test_with_noise_inserts_channel_ticks() {
+        let mut tc = TickCircuit::new();
+        tc.tick().h(&[0]).x(&[1]);
+        tc.tick().cx(&[(0, 1)]);
+
+        let noisy = tc.with_noise(&|gate: &Gate| {
+            gate.qubits
+                .iter()
+                .map(|q| pecos_core::channel::Depolarizing(0.01, q.index()))
+                .collect()
+        });
+
+        assert_eq!(noisy.num_ticks(), 4);
+        assert_eq!(
+            noisy.get_tick(0).unwrap().gate_batches()[0].gate_type,
+            GateType::H
+        );
+        assert!(
+            noisy
+                .get_tick(1)
+                .unwrap()
+                .gate_batches()
+                .iter()
+                .all(Gate::is_channel)
+        );
+        assert_eq!(
+            noisy.get_tick(2).unwrap().gate_batches()[0].gate_type,
+            GateType::CX
+        );
+        assert!(
+            noisy
+                .get_tick(3)
+                .unwrap()
+                .gate_batches()
+                .iter()
+                .all(Gate::is_channel)
+        );
+    }
+
+    #[test]
+    fn test_with_noise_on_batched_source_gate_emits_per_qubit_channels() {
+        use std::cell::{Cell, RefCell};
+
+        let mut tc = TickCircuit::new();
+        tc.tick().h(&[0, 1]);
+
+        let calls = Cell::new(0);
+        let seen_qubits = RefCell::new(Vec::new());
+        let noisy = tc.with_noise(&|gate: &Gate| {
+            calls.set(calls.get() + 1);
+            seen_qubits.borrow_mut().push(gate.qubits.clone());
+            gate.qubits
+                .iter()
+                .map(|qubit| pecos_core::channel::Depolarizing(0.01, qubit.index()))
+                .collect()
+        });
+
+        assert_eq!(calls.get(), 1);
+        assert_eq!(
+            seen_qubits.borrow()[0].as_slice(),
+            &[QubitId::from(0), QubitId::from(1)]
+        );
+        assert_eq!(noisy.num_ticks(), 2);
+        assert_eq!(noisy.get_tick(0).unwrap().gate_count(), 2);
+
+        let noise_tick = noisy.get_tick(1).unwrap();
+        assert_eq!(noise_tick.len(), 2);
+        assert_eq!(noise_tick.gate_count(), 2);
+        assert!(noise_tick.gate_batches().iter().all(Gate::is_channel));
+        assert_eq!(
+            noise_tick.gate_batches()[0].qubits.as_slice(),
+            &[QubitId::from(0)]
+        );
+        assert_eq!(
+            noise_tick.gate_batches()[1].qubits.as_slice(),
+            &[QubitId::from(1)]
+        );
+    }
+
+    #[test]
+    fn test_with_noise_on_batched_measurement_places_channels_after_measurement_tick() {
+        use std::cell::{Cell, RefCell};
+
+        let mut tc = TickCircuit::new();
+        tc.tick().mz(&[0, 1]);
+
+        let calls = Cell::new(0);
+        let seen_measurement_ids = RefCell::new(Vec::new());
+        let noisy = tc.with_noise(&|gate: &Gate| {
+            assert_eq!(gate.gate_type, GateType::MZ);
+            calls.set(calls.get() + 1);
+            seen_measurement_ids
+                .borrow_mut()
+                .extend(gate.meas_ids.iter().copied());
+            gate.qubits
+                .iter()
+                .map(|qubit| pecos_core::channel::Dephasing(0.02, qubit.index()))
+                .collect()
+        });
+
+        assert_eq!(calls.get(), 1);
+        assert_eq!(
+            seen_measurement_ids.borrow().as_slice(),
+            &[MeasId(0), MeasId(1)]
+        );
+        assert_eq!(noisy.num_ticks(), 2);
+
+        let meas_tick = noisy.get_tick(0).unwrap();
+        assert_eq!(meas_tick.gate_batches()[0].gate_type, GateType::MZ);
+        assert_eq!(
+            meas_tick.gate_batches()[0].meas_ids.as_slice(),
+            &[MeasId(0), MeasId(1)]
+        );
+
+        let noise_tick = noisy.get_tick(1).unwrap();
+        assert_eq!(noise_tick.len(), 2);
+        assert!(noise_tick.gate_batches().iter().all(Gate::is_channel));
+        assert_eq!(
+            noise_tick.gate_batches()[0].qubits.as_slice(),
+            &[QubitId::from(0)]
+        );
+        assert_eq!(
+            noise_tick.gate_batches()[1].qubits.as_slice(),
+            &[QubitId::from(1)]
+        );
+    }
+
+    #[test]
+    fn test_with_noise_empty_channels_preserves_tick_structure() {
+        let mut tc = TickCircuit::new();
+        tc.tick().h(&[0]).x(&[1]);
+        tc.tick().cx(&[(0, 1)]);
+        tc.tick().mz(&[0, 1]);
+
+        let noisy = tc.with_noise(&|_: &Gate| Vec::new());
+
+        assert_eq!(noisy.num_ticks(), tc.num_ticks());
+        for tick_idx in 0..tc.num_ticks() {
+            let original = tc.get_tick(tick_idx).unwrap();
+            let copied = noisy.get_tick(tick_idx).unwrap();
+            assert_eq!(copied.gate_batches().len(), original.gate_batches().len());
+            for (copied_gate, original_gate) in
+                copied.gate_batches().iter().zip(original.gate_batches())
+            {
+                assert_eq!(copied_gate.gate_type, original_gate.gate_type);
+                assert_eq!(copied_gate.qubits, original_gate.qubits);
+                assert!(!copied_gate.is_channel());
+            }
+        }
+    }
+
+    #[test]
+    fn test_with_noise_splits_conflicting_channel_ticks() {
+        let mut tc = TickCircuit::new();
+        tc.tick().h(&[0]);
+
+        let noisy = tc.with_noise(&|_: &Gate| {
+            vec![
+                pecos_core::channel::Depolarizing(0.01, 0),
+                pecos_core::channel::Dephasing(0.02, 0),
+            ]
+        });
+
+        assert_eq!(noisy.num_ticks(), 3);
+        assert_eq!(
+            noisy.get_tick(0).unwrap().gate_batches()[0].gate_type,
+            GateType::H
+        );
+
+        let first_noise_tick = noisy.get_tick(1).unwrap();
+        assert_eq!(first_noise_tick.gate_batches().len(), 1);
+        assert!(first_noise_tick.gate_batches()[0].is_channel());
+        assert_eq!(
+            first_noise_tick.gate_batches()[0].qubits.as_slice(),
+            &[QubitId::from(0)]
+        );
+
+        let second_noise_tick = noisy.get_tick(2).unwrap();
+        assert_eq!(second_noise_tick.gate_batches().len(), 1);
+        assert!(second_noise_tick.gate_batches()[0].is_channel());
+        assert_eq!(
+            second_noise_tick.gate_batches()[0].qubits.as_slice(),
+            &[QubitId::from(0)]
+        );
+    }
+
+    #[test]
+    fn test_with_noise_places_measurement_channels_after_measurement_tick() {
+        let mut tc = TickCircuit::new();
+        tc.tick().mz(&[0]);
+
+        let noisy = tc.with_noise(&|gate: &Gate| {
+            if gate.gate_type == GateType::MZ {
+                vec![pecos_core::channel::Dephasing(0.25, 0)]
+            } else {
+                Vec::new()
+            }
+        });
+
+        assert_eq!(noisy.num_ticks(), 2);
+        assert_eq!(
+            noisy.get_tick(0).unwrap().gate_batches()[0].gate_type,
+            GateType::MZ
+        );
+        let channel = &noisy.get_tick(1).unwrap().gate_batches()[0];
+        assert!(channel.is_channel());
+        assert_eq!(channel.qubits.as_slice(), &[QubitId::from(0)]);
+    }
+
+    #[test]
+    fn test_with_noise_packs_disjoint_channels_and_splits_conflicts() {
+        let mut tc = TickCircuit::new();
+        tc.tick().h(&[0]).x(&[1]);
+
+        let noisy = tc.with_noise(&|gate: &Gate| {
+            gate.qubits
+                .iter()
+                .flat_map(|q| {
+                    [
+                        pecos_core::channel::Depolarizing(0.01, q.index()),
+                        pecos_core::channel::Dephasing(0.02, q.index()),
+                    ]
+                })
+                .collect()
+        });
+
+        assert_eq!(noisy.num_ticks(), 3);
+        assert_eq!(noisy.get_tick(1).unwrap().gate_batches().len(), 2);
+        assert_eq!(noisy.get_tick(2).unwrap().gate_batches().len(), 2);
+        assert!(
+            noisy
+                .get_tick(1)
+                .unwrap()
+                .gate_batches()
+                .iter()
+                .all(Gate::is_channel)
+        );
+        assert!(
+            noisy
+                .get_tick(2)
+                .unwrap()
+                .gate_batches()
+                .iter()
+                .all(Gate::is_channel)
+        );
+    }
+
+    #[test]
+    fn test_with_noise_rejects_existing_channel_operations() {
+        let mut tc = TickCircuit::new();
+        tc.tick()
+            .channel(pecos_core::channel::Depolarizing(0.25, 0));
+
+        let err = tc
+            .try_with_noise(&|_: &Gate| vec![pecos_core::channel::Depolarizing(0.01, 0)])
+            .unwrap_err();
+
+        assert!(err.contains("already contains channel operations"));
+        assert!(err.contains("tick 0"));
+        assert!(err.contains("gate 0"));
+    }
+
+    #[test]
+    fn test_meas_record_idx_single_qubit() {
+        let mut tc = TickCircuit::new();
+        let m0 = tc.tick().mz(&[0]);
+        let m1 = tc.tick().mz(&[1]);
+        assert_eq!(m0[0].record_idx, 0);
+        assert_eq!(m1[0].record_idx, 1);
+    }
+
+    #[test]
+    fn test_meas_record_idx_multi_qubit() {
+        let mut tc = TickCircuit::new();
+        let ms = tc.tick().mz(&[0, 1, 2]);
+        assert_eq!(ms[0].record_idx, 0);
+        assert_eq!(ms[1].record_idx, 1);
+        assert_eq!(ms[2].record_idx, 2);
+        // Next measurement continues the count
+        let m2 = tc.tick().mz(&[3]);
+        assert_eq!(m2[0].record_idx, 3);
+    }
+
+    #[test]
+    fn test_detector_uses_record_idx() {
+        // Two qubits measured in one gate: detector referencing each
+        // should get DIFFERENT record indices (not the same gate index).
+        let mut tc = TickCircuit::new();
+        tc.tick().pz(&[0, 1]);
+        let ms = tc.tick().mz(&[0, 1]);
+
+        // Detector on qubit 0's measurement
+        tc.detector(&[ms[0]]);
+        // Detector on qubit 1's measurement
+        tc.detector(&[ms[1]]);
+
+        let anns = tc.annotations();
+        match &anns[0].kind {
+            AnnotationKind::Detector {
+                measurement_nodes, ..
+            } => {
+                assert_eq!(measurement_nodes, &[0], "D0 should reference record 0 (q0)");
+            }
+            _ => panic!("Expected detector"),
+        }
+        match &anns[1].kind {
+            AnnotationKind::Detector {
+                measurement_nodes, ..
+            } => {
+                assert_eq!(measurement_nodes, &[1], "D1 should reference record 1 (q1)");
+            }
+            _ => panic!("Expected detector"),
+        }
+    }
+
+    #[test]
+    fn test_detector_multi_qubit_mz_no_xor_cancel() {
+        // Bug regression: two refs from same multi-qubit MZ gate
+        // used to have the same gate_idx, causing XOR cancellation.
+        // With record_idx they should be distinct.
+        let mut tc = TickCircuit::new();
+        tc.tick().pz(&[0, 1]);
+        let ms = tc.tick().mz(&[0, 1]);
+
+        // Detector comparing both measurements (XOR of records 0 and 1)
+        tc.detector(&[ms[0], ms[1]]);
+
+        let anns = tc.annotations();
+        match &anns[0].kind {
+            AnnotationKind::Detector {
+                measurement_nodes, ..
+            } => {
+                assert_eq!(measurement_nodes.len(), 2);
+                assert_ne!(
+                    measurement_nodes[0], measurement_nodes[1],
+                    "Two qubits from same MZ must have different record indices"
+                );
+            }
+            _ => panic!("Expected detector"),
+        }
+    }
 }
diff --git a/crates/pecos-quantum/src/tick_circuit_soa.rs b/crates/pecos-quantum/src/tick_circuit_soa.rs
deleted file mode 100644
index db9b5e3f0..000000000
--- a/crates/pecos-quantum/src/tick_circuit_soa.rs
+++ /dev/null
@@ -1,1473 +0,0 @@
-//! Data-Oriented Design (DOD) `TickCircuit` implementation.
-//!
-//! This module provides `TickCircuitSoA`, an alternative representation of tick-based
-//! quantum circuits optimized for **batched simulation**.
-//!
-//! # Design Goals
-//!
-//! 1. **Batched gate application**: Gates grouped by type within each tick for batch execution
-//! 2. **Cache-friendly memory layout**: Qubits for same-type gates stored contiguously
-//! 3. **O(1) lookups**: Pre-computed indexes for qubit-to-gate and tick-to-gate queries
-//! 4. **Efficient simulation**: Direct batch calls to simulator without per-gate dispatch
-//!
-//! # Architecture
-//!
-//! ```text
-//! ┌─────────────────────────────────────────────────────────────────┐
-//! │                     TickCircuitSoA                              │
-//! ├─────────────────────────────────────────────────────────────────┤
-//! │  TickGateGroups (simulation-optimized)                          │
-//! │  ├── ticks[0]: [H→[q0,q1], CX→[c0,t0,c1,t1], ...]              │
-//! │  ├── ticks[1]: [Mz→[q0,q1,q2], ...]                            │
-//! │  └── ...                                                        │
-//! ├─────────────────────────────────────────────────────────────────┤
-//! │  GateStorage (SoA layout for individual gate access)            │
-//! │  ├── types:        [H, CX, H, Mz, ...]        (Vec<GateType>)   │
-//! │  ├── tick_ids:     [0, 0, 1, 2, ...]          (Vec<u16>)        │
-//! │  ├── qubit_spans:  [(0,1), (1,3), (3,4), ...] (Vec<(u32,u32)>)  │
-//! │  └── qubits:       [0, 0, 1, 0, ...]          (Vec<QubitId>)    │
-//! ├─────────────────────────────────────────────────────────────────┤
-//! │  CircuitIndexes                                                 │
-//! │  ├── tick_gates:       [[0,1], [2,3], ...]    (Vec<Vec<u32>>)   │
-//! │  ├── qubit_to_gates:   [[0,1], [1], ...]      (Vec<SmallVec>)   │
-//! │  └── max_qubit: usize                                           │
-//! └─────────────────────────────────────────────────────────────────┘
-//! ```
-//!
-//! # Batched Simulation
-//!
-//! The key optimization is grouping gates by type within each tick:
-//!
-//! ```text
-//! // Without batching (gate-by-gate):
-//! for gate in tick.gates():
-//!     match gate.type:
-//!         H  => sim.h(&[gate.qubit])      // 4 separate calls
-//!         H  => sim.h(&[gate.qubit])
-//!         CX => sim.cx(&[c, t])
-//!         CX => sim.cx(&[c, t])
-//!
-//! // With batching (one call per type):
-//! sim.h(&[q0, q1, q2, q3])              // 1 batched call
-//! sim.cx(&[c0, t0, c1, t1])             // 1 batched call
-//! ```
-//!
-//! # Usage
-//!
-//! ```
-//! use pecos_quantum::TickCircuitSoA;
-//!
-//! // Build using the builder pattern
-//! let mut builder = TickCircuitSoA::builder();
-//! builder
-//!     .tick()
-//!         .h(&[0, 1])
-//!         .cx(&[(0, 1)])
-//!     .tick()
-//!         .mz(&[0, 1]);
-//! let circuit = builder.build();
-//! ```
-//!
-//! With a simulator, the batched iteration looks like:
-//!
-//! ```text
-//! for (tick_idx, tick) in circuit.iter_ticks_batched() {
-//!     for batch in tick.iter() {
-//!         match batch.gate_type {
-//!             GateType::H  => sim.h(batch.qubits()),
-//!             GateType::CX => sim.cx(batch.qubits()),
-//!             GateType::MZ => { sim.mz(batch.qubits()); }
-//!             // ...
-//!         }
-//!     }
-//! }
-//! ```
-
-use crate::Attribute;
-use pecos_core::gate_type::GateType;
-use pecos_core::{Angle64, QubitId};
-use smallvec::SmallVec;
-use std::collections::BTreeMap;
-
-// ============================================================================
-// Gate Batching for Simulation
-// ============================================================================
-
-/// A batch of gates of the same type, ready for efficient batch application.
-///
-/// For single-qubit gates, `qubits` contains one qubit per gate instance.
-/// For two-qubit gates, `qubits` contains pairs: `[c0, t0, c1, t1, ...]`.
-#[derive(Debug, Clone)]
-pub struct GateBatch {
-    /// The gate type for all gates in this batch.
-    pub gate_type: GateType,
-    /// Qubits for batch application (contiguous for cache efficiency).
-    /// Single-qubit: `[q0, q1, q2, ...]`
-    /// Two-qubit: `[c0, t0, c1, t1, ...]` (control-target pairs)
-    pub qubits: SmallVec<[QubitId; 16]>,
-    /// Angles for parameterized gates (one per gate instance).
-    pub angles: SmallVec<[Angle64; 4]>,
-    /// Parameters for gates with params (e.g., idle duration).
-    pub params: SmallVec<[f64; 4]>,
-}
-
-impl GateBatch {
-    /// Creates a new empty batch for the given gate type.
-    #[inline]
-    #[must_use]
-    pub fn new(gate_type: GateType) -> Self {
-        Self {
-            gate_type,
-            qubits: SmallVec::new(),
-            angles: SmallVec::new(),
-            params: SmallVec::new(),
-        }
-    }
-
-    /// Returns the qubits for batch application.
-    #[inline]
-    #[must_use]
-    pub fn qubits(&self) -> &[QubitId] {
-        &self.qubits
-    }
-
-    /// Returns the angles for parameterized gates.
-    #[inline]
-    #[must_use]
-    pub fn angles(&self) -> &[Angle64] {
-        &self.angles
-    }
-
-    /// Returns the number of gate instances in this batch.
-    #[inline]
-    #[must_use]
-    pub fn gate_count(&self) -> usize {
-        let arity = self.gate_type.quantum_arity();
-        self.qubits
-            .len()
-            .checked_div(arity)
-            .unwrap_or(self.qubits.len())
-    }
-
-    /// Returns true if the batch is empty.
-    #[inline]
-    #[must_use]
-    pub fn is_empty(&self) -> bool {
-        self.qubits.is_empty()
-    }
-
-    /// Adds a gate's qubits to this batch.
-    #[inline]
-    pub fn add_qubits(&mut self, qubits: &[QubitId]) {
-        self.qubits.extend_from_slice(qubits);
-    }
-
-    /// Adds a gate's angle to this batch.
-    #[inline]
-    pub fn add_angle(&mut self, angle: Angle64) {
-        self.angles.push(angle);
-    }
-}
-
-/// Gates for a single tick, grouped by type for batch application.
-#[derive(Debug, Clone, Default)]
-pub struct TickBatches {
-    /// Gate batches, one per gate type that appears in this tick.
-    /// Ordered by insertion (first gate type seen comes first).
-    pub batches: SmallVec<[GateBatch; 8]>,
-}
-
-impl TickBatches {
-    /// Creates a new empty tick.
-    #[must_use]
-    pub fn new() -> Self {
-        Self::default()
-    }
-
-    /// Returns an iterator over the batches.
-    #[inline]
-    pub fn iter(&self) -> impl Iterator<Item = &GateBatch> {
-        self.batches.iter()
-    }
-
-    /// Returns the number of batches.
-    #[inline]
-    #[must_use]
-    pub fn batch_count(&self) -> usize {
-        self.batches.len()
-    }
-
-    /// Returns the total number of gates in this tick.
-    #[must_use]
-    pub fn gate_count(&self) -> usize {
-        self.batches.iter().map(GateBatch::gate_count).sum()
-    }
-
-    /// Adds a gate to the appropriate batch (creates batch if needed).
-    ///
-    /// # Panics
-    /// Panics if internal batch list is unexpectedly empty after insertion.
-    pub fn add_gate(&mut self, gate_type: GateType, qubits: &[QubitId], angles: &[Angle64]) {
-        // Find or create batch for this gate type
-        let batch = if let Some(batch) = self.batches.iter_mut().find(|b| b.gate_type == gate_type)
-        {
-            batch
-        } else {
-            self.batches.push(GateBatch::new(gate_type));
-            self.batches.last_mut().expect("batch was just pushed")
-        };
-
-        batch.add_qubits(qubits);
-        for &angle in angles {
-            batch.add_angle(angle);
-        }
-    }
-
-    /// Returns the batch for a specific gate type, if present.
-    #[inline]
-    #[must_use]
-    pub fn batch_for_type(&self, gate_type: GateType) -> Option<&GateBatch> {
-        self.batches.iter().find(|b| b.gate_type == gate_type)
-    }
-}
-
-/// Pre-grouped gates by type for each tick, optimized for batched simulation.
-///
-/// This is the primary structure for efficient circuit execution:
-/// - Gates are grouped by type within each tick
-/// - Qubits for same-type gates are stored contiguously
-/// - Enables single batch calls to the simulator per gate type
-#[derive(Debug, Clone, Default)]
-pub struct TickGateGroups {
-    /// For each tick, the batched gates.
-    pub ticks: Vec<TickBatches>,
-    /// Number of ticks.
-    pub num_ticks: usize,
-    /// Maximum qubit index seen.
-    pub max_qubit: usize,
-}
-
-impl TickGateGroups {
-    /// Creates empty gate groups.
-    #[must_use]
-    pub fn new() -> Self {
-        Self::default()
-    }
-
-    /// Returns the number of ticks.
-    #[inline]
-    #[must_use]
-    pub fn num_ticks(&self) -> usize {
-        self.num_ticks
-    }
-
-    /// Returns the batches for a specific tick.
-    #[inline]
-    #[must_use]
-    pub fn tick(&self, tick_idx: usize) -> Option<&TickBatches> {
-        self.ticks.get(tick_idx)
-    }
-
-    /// Returns an iterator over all ticks.
-    #[inline]
-    pub fn iter_ticks(&self) -> impl Iterator<Item = (usize, &TickBatches)> {
-        self.ticks.iter().enumerate()
-    }
-
-    /// Ensures capacity for the given tick index.
-    fn ensure_tick(&mut self, tick_idx: usize) {
-        if tick_idx >= self.ticks.len() {
-            self.ticks.resize_with(tick_idx + 1, TickBatches::new);
-        }
-        self.num_ticks = self.num_ticks.max(tick_idx + 1);
-    }
-
-    /// Adds a gate to the appropriate tick and batch.
-    pub fn add_gate(
-        &mut self,
-        tick_idx: usize,
-        gate_type: GateType,
-        qubits: &[QubitId],
-        angles: &[Angle64],
-    ) {
-        self.ensure_tick(tick_idx);
-        self.ticks[tick_idx].add_gate(gate_type, qubits, angles);
-
-        // Track max qubit
-        for qubit in qubits {
-            self.max_qubit = self.max_qubit.max(qubit.index());
-        }
-    }
-
-    /// Clears all gate groups.
-    pub fn clear(&mut self) {
-        self.ticks.clear();
-        self.num_ticks = 0;
-        self.max_qubit = 0;
-    }
-
-    /// Returns the total number of gates across all ticks.
-    #[must_use]
-    pub fn total_gate_count(&self) -> usize {
-        self.ticks.iter().map(TickBatches::gate_count).sum()
-    }
-}
-
-// ============================================================================
-// Gate ID (Stable, Generational)
-// ============================================================================
-
-/// A stable identifier for a gate in a `TickCircuitSoA`.
-///
-/// Unlike raw indices, `GateId` includes a generation counter that allows
-/// detecting use-after-free when gates are removed. This provides safety
-/// without the overhead of reference counting.
-#[derive(Debug, Clone, Copy, PartialEq, Eq, PartialOrd, Ord, Hash)]
-pub struct GateId {
-    /// Index into the gate storage arrays.
-    index: u32,
-    /// Generation counter for detecting stale IDs.
-    generation: u16,
-}
-
-impl GateId {
-    /// Creates a new `GateId`.
-    #[inline]
-    #[must_use]
-    pub const fn new(index: u32, generation: u16) -> Self {
-        Self { index, generation }
-    }
-
-    /// Returns the raw index (use with caution).
-    #[inline]
-    #[must_use]
-    pub const fn index(self) -> usize {
-        self.index as usize
-    }
-
-    /// Returns the generation.
-    #[inline]
-    #[must_use]
-    pub const fn generation(self) -> u16 {
-        self.generation
-    }
-}
-
-// ============================================================================
-// Gate Storage (SoA Layout)
-// ============================================================================
-
-/// Structure-of-Arrays storage for gate data.
-///
-/// All gates are stored in parallel arrays for cache-friendly access.
-/// Variable-length data (qubits, angles) uses span-based indexing into
-/// contiguous backing arrays.
-#[derive(Debug, Clone, Default)]
-pub struct GateStorage {
-    // Core gate data (one element per gate)
-    /// Gate types (H, CX, Mz, etc.)
-    pub types: Vec<GateType>,
-    /// Which tick each gate belongs to
-    pub tick_ids: Vec<u16>,
-    /// Span (start, end) into the qubits array
-    pub qubit_spans: Vec<(u32, u32)>,
-    /// Span (start, end) into the angles array
-    pub angle_spans: Vec<(u32, u32)>,
-    /// Generation counter for each slot (for `GateId` validation)
-    pub generations: Vec<u16>,
-    /// Whether each slot is occupied (for sparse storage after removals)
-    pub occupied: Vec<bool>,
-
-    // Backing arrays for variable-length data
-    /// All qubits, indexed by `qubit_spans`
-    pub qubits: Vec<QubitId>,
-    /// All angles, indexed by `angle_spans`
-    pub angles: Vec<Angle64>,
-    /// All params (e.g., idle duration), indexed similarly
-    pub param_spans: Vec<(u32, u32)>,
-    pub params: Vec<f64>,
-
-    // Free list for slot reuse after removal
-    free_slots: Vec<u32>,
-}
-
-impl GateStorage {
-    /// Creates empty gate storage.
-    #[must_use]
-    pub fn new() -> Self {
-        Self::default()
-    }
-
-    /// Creates gate storage with pre-allocated capacity.
-    #[must_use]
-    pub fn with_capacity(gate_capacity: usize, qubit_capacity: usize) -> Self {
-        Self {
-            types: Vec::with_capacity(gate_capacity),
-            tick_ids: Vec::with_capacity(gate_capacity),
-            qubit_spans: Vec::with_capacity(gate_capacity),
-            angle_spans: Vec::with_capacity(gate_capacity),
-            generations: Vec::with_capacity(gate_capacity),
-            occupied: Vec::with_capacity(gate_capacity),
-            qubits: Vec::with_capacity(qubit_capacity),
-            angles: Vec::new(),
-            param_spans: Vec::with_capacity(gate_capacity),
-            params: Vec::new(),
-            free_slots: Vec::new(),
-        }
-    }
-
-    /// Returns the number of gates (including removed slots).
-    #[inline]
-    #[must_use]
-    pub fn len(&self) -> usize {
-        self.types.len()
-    }
-
-    /// Returns true if there are no gates.
-    #[inline]
-    #[must_use]
-    pub fn is_empty(&self) -> bool {
-        self.types.is_empty()
-    }
-
-    /// Returns the number of active (non-removed) gates.
-    #[must_use]
-    pub fn active_count(&self) -> usize {
-        self.occupied.iter().filter(|&&o| o).count()
-    }
-
-    /// Adds a gate and returns its ID.
-    pub fn add_gate(
-        &mut self,
-        gate_type: GateType,
-        tick_id: u16,
-        qubits: &[QubitId],
-        angles: &[Angle64],
-        params: &[f64],
-    ) -> GateId {
-        let (index, generation) = if let Some(slot) = self.free_slots.pop() {
-            // Reuse a freed slot
-            let idx = slot as usize;
-            self.generations[idx] = self.generations[idx].wrapping_add(1);
-            self.types[idx] = gate_type;
-            self.tick_ids[idx] = tick_id;
-            self.occupied[idx] = true;
-            (slot, self.generations[idx])
-        } else {
-            // Allocate new slot
-            #[allow(clippy::cast_possible_truncation)] // gate index fits in u32
-            let idx = self.types.len() as u32;
-            self.types.push(gate_type);
-            self.tick_ids.push(tick_id);
-            self.generations.push(0);
-            self.occupied.push(true);
-            // Placeholders for spans - will be set below
-            self.qubit_spans.push((0, 0));
-            self.angle_spans.push((0, 0));
-            self.param_spans.push((0, 0));
-            (idx, 0)
-        };
-
-        let idx = index as usize;
-
-        // Add qubits
-        #[allow(clippy::cast_possible_truncation)] // qubit pool index fits in u32
-        let qubit_start = self.qubits.len() as u32;
-        self.qubits.extend_from_slice(qubits);
-        #[allow(clippy::cast_possible_truncation)] // qubit pool index fits in u32
-        let qubit_end = self.qubits.len() as u32;
-        self.qubit_spans[idx] = (qubit_start, qubit_end);
-
-        // Add angles
-        #[allow(clippy::cast_possible_truncation)] // angle pool index fits in u32
-        let angle_start = self.angles.len() as u32;
-        self.angles.extend_from_slice(angles);
-        #[allow(clippy::cast_possible_truncation)] // angle pool index fits in u32
-        let angle_end = self.angles.len() as u32;
-        self.angle_spans[idx] = (angle_start, angle_end);
-
-        // Add params
-        #[allow(clippy::cast_possible_truncation)] // param pool index fits in u32
-        let param_start = self.params.len() as u32;
-        self.params.extend_from_slice(params);
-        #[allow(clippy::cast_possible_truncation)] // param pool index fits in u32
-        let param_end = self.params.len() as u32;
-        self.param_spans[idx] = (param_start, param_end);
-
-        GateId::new(index, generation)
-    }
-
-    /// Validates that a `GateId` is still valid.
-    #[inline]
-    #[must_use]
-    pub fn is_valid(&self, id: GateId) -> bool {
-        let idx = id.index();
-        idx < self.len() && self.generations[idx] == id.generation() && self.occupied[idx]
-    }
-
-    /// Returns the gate type for a valid ID.
-    #[inline]
-    #[must_use]
-    pub fn gate_type(&self, id: GateId) -> Option<GateType> {
-        if self.is_valid(id) {
-            Some(self.types[id.index()])
-        } else {
-            None
-        }
-    }
-
-    /// Returns the tick ID for a valid gate.
-    #[inline]
-    #[must_use]
-    pub fn tick_id(&self, id: GateId) -> Option<u16> {
-        if self.is_valid(id) {
-            Some(self.tick_ids[id.index()])
-        } else {
-            None
-        }
-    }
-
-    // =========================================================================
-    // Unchecked accessors for hot paths (internal use)
-    // =========================================================================
-
-    /// Returns the gate type without validation. Use only when index is known valid.
-    #[inline]
-    #[must_use]
-    pub fn type_unchecked(&self, idx: usize) -> GateType {
-        self.types[idx]
-    }
-
-    /// Returns the tick ID without validation.
-    #[inline]
-    #[must_use]
-    pub fn tick_id_unchecked(&self, idx: usize) -> u16 {
-        self.tick_ids[idx]
-    }
-
-    /// Returns the qubits without validation.
-    #[inline]
-    #[must_use]
-    pub fn qubits_unchecked(&self, idx: usize) -> &[QubitId] {
-        let (start, end) = self.qubit_spans[idx];
-        &self.qubits[start as usize..end as usize]
-    }
-
-    /// Returns whether the slot is occupied.
-    #[inline]
-    #[must_use]
-    pub fn is_occupied(&self, idx: usize) -> bool {
-        idx < self.occupied.len() && self.occupied[idx]
-    }
-
-    /// Returns the total number of slots (for iteration bounds).
-    #[inline]
-    #[must_use]
-    pub fn slot_count(&self) -> usize {
-        self.types.len()
-    }
-
-    /// Returns the qubits for a valid gate.
-    #[inline]
-    #[must_use]
-    pub fn gate_qubits(&self, id: GateId) -> Option<&[QubitId]> {
-        if self.is_valid(id) {
-            let (start, end) = self.qubit_spans[id.index()];
-            Some(&self.qubits[start as usize..end as usize])
-        } else {
-            None
-        }
-    }
-
-    /// Returns the angles for a valid gate.
-    #[inline]
-    #[must_use]
-    pub fn gate_angles(&self, id: GateId) -> Option<&[Angle64]> {
-        if self.is_valid(id) {
-            let (start, end) = self.angle_spans[id.index()];
-            Some(&self.angles[start as usize..end as usize])
-        } else {
-            None
-        }
-    }
-
-    /// Returns the params for a valid gate.
-    #[inline]
-    #[must_use]
-    pub fn gate_params(&self, id: GateId) -> Option<&[f64]> {
-        if self.is_valid(id) {
-            let (start, end) = self.param_spans[id.index()];
-            Some(&self.params[start as usize..end as usize])
-        } else {
-            None
-        }
-    }
-
-    /// Removes a gate by ID. The slot can be reused.
-    pub fn remove(&mut self, id: GateId) -> bool {
-        if self.is_valid(id) {
-            let idx = id.index();
-            self.occupied[idx] = false;
-            self.free_slots.push(id.index);
-            true
-        } else {
-            false
-        }
-    }
-
-    /// Clears all gates.
-    pub fn clear(&mut self) {
-        self.types.clear();
-        self.tick_ids.clear();
-        self.qubit_spans.clear();
-        self.angle_spans.clear();
-        self.param_spans.clear();
-        self.generations.clear();
-        self.occupied.clear();
-        self.qubits.clear();
-        self.angles.clear();
-        self.params.clear();
-        self.free_slots.clear();
-    }
-
-    /// Iterator over all valid gate IDs.
-    pub fn iter_ids(&self) -> impl Iterator<Item = GateId> + '_ {
-        (0..self.len()).filter_map(move |idx| {
-            if self.occupied[idx] {
-                #[allow(clippy::cast_possible_truncation)] // gate index fits in u32
-                Some(GateId::new(idx as u32, self.generations[idx]))
-            } else {
-                None
-            }
-        })
-    }
-}
-
-// ============================================================================
-// Circuit Indexes
-// ============================================================================
-
-/// Pre-computed indexes for efficient circuit queries.
-///
-/// Uses raw u32 indices instead of `GateIds` for minimal overhead in hot paths.
-#[derive(Debug, Clone, Default)]
-pub struct CircuitIndexes {
-    /// For each tick, the list of gate indices in that tick.
-    /// Using Vec<Vec<u32>> for simplicity; could use CSR format for less allocation.
-    pub tick_gates: Vec<Vec<u32>>,
-
-    /// For each qubit, the list of gate indices that touch it.
-    /// Indexed by qubit index; grows dynamically.
-    /// Uses u32 instead of `GateId` to avoid validation overhead.
-    pub qubit_to_gates: Vec<SmallVec<[u32; 8]>>,
-
-    /// For each qubit, gates sorted by tick (for efficient backward traversal).
-    /// Each entry is (`tick_id`, `gate_idx`).
-    pub qubit_gates_by_tick: Vec<Vec<(u16, u32)>>,
-
-    /// Maximum qubit index seen.
-    pub max_qubit: usize,
-
-    /// Number of ticks.
-    pub num_ticks: usize,
-}
-
-impl CircuitIndexes {
-    /// Creates empty indexes.
-    #[must_use]
-    pub fn new() -> Self {
-        Self::default()
-    }
-
-    /// Ensures the qubit index can accommodate the given qubit.
-    fn ensure_qubit_capacity(&mut self, qubit: usize) {
-        if qubit >= self.qubit_to_gates.len() {
-            self.qubit_to_gates.resize(qubit + 1, SmallVec::new());
-            self.qubit_gates_by_tick.resize(qubit + 1, Vec::new());
-        }
-        self.max_qubit = self.max_qubit.max(qubit);
-    }
-
-    /// Registers a gate in the indexes (using raw index).
-    pub fn register_gate_raw(&mut self, gate_idx: u32, tick_id: u16, qubits: &[QubitId]) {
-        // Add to tick index
-        let tick = tick_id as usize;
-        if tick >= self.tick_gates.len() {
-            self.tick_gates.resize(tick + 1, Vec::new());
-        }
-        self.tick_gates[tick].push(gate_idx);
-        self.num_ticks = self.num_ticks.max(tick + 1);
-
-        // Add to qubit indexes
-        for qubit in qubits {
-            let q = qubit.index();
-            self.ensure_qubit_capacity(q);
-            self.qubit_to_gates[q].push(gate_idx);
-            self.qubit_gates_by_tick[q].push((tick_id, gate_idx));
-        }
-    }
-
-    /// Registers a gate in the qubit index (`GateId` version for compatibility).
-    pub fn register_gate(&mut self, gate_id: GateId, qubits: &[QubitId]) {
-        for qubit in qubits {
-            let q = qubit.index();
-            self.ensure_qubit_capacity(q);
-            self.qubit_to_gates[q].push(gate_id.index);
-        }
-    }
-
-    /// Returns all gate indices touching the given qubit.
-    #[inline]
-    #[must_use]
-    pub fn gates_touching_qubit_raw(&self, qubit: usize) -> &[u32] {
-        if qubit < self.qubit_to_gates.len() {
-            &self.qubit_to_gates[qubit]
-        } else {
-            &[]
-        }
-    }
-
-    /// Returns all gates touching the given qubit (`GateId` version).
-    #[inline]
-    #[must_use]
-    pub fn gates_touching_qubit(&self, _qubit: usize) -> &[GateId] {
-        // Note: This is a bit of a hack - we're reinterpreting u32 as GateId
-        // In practice, for read-only circuits without removal, generation is always 0
-        &[] // Return empty - use gates_touching_qubit_raw instead
-    }
-
-    /// Returns gate indices in a specific tick.
-    #[inline]
-    #[must_use]
-    pub fn gates_in_tick(&self, tick: usize) -> &[u32] {
-        if tick < self.tick_gates.len() {
-            &self.tick_gates[tick]
-        } else {
-            &[]
-        }
-    }
-
-    /// Returns gates on a qubit sorted by tick (for backward traversal).
-    #[inline]
-    #[must_use]
-    pub fn qubit_gates_sorted(&self, qubit: usize) -> &[(u16, u32)] {
-        if qubit < self.qubit_gates_by_tick.len() {
-            &self.qubit_gates_by_tick[qubit]
-        } else {
-            &[]
-        }
-    }
-
-    /// Sorts the `qubit_gates_by_tick` for each qubit (call after building).
-    pub fn finalize(&mut self) {
-        for gates in &mut self.qubit_gates_by_tick {
-            gates.sort_by_key(|&(tick, _)| tick);
-        }
-    }
-
-    /// Clears all indexes.
-    pub fn clear(&mut self) {
-        self.tick_gates.clear();
-        self.qubit_to_gates.clear();
-        self.qubit_gates_by_tick.clear();
-        self.max_qubit = 0;
-        self.num_ticks = 0;
-    }
-
-    /// Rebuilds indexes from gate storage.
-    pub fn rebuild(&mut self, storage: &GateStorage) {
-        self.clear();
-
-        for idx in 0..storage.slot_count() {
-            if storage.is_occupied(idx) {
-                let tick_id = storage.tick_id_unchecked(idx);
-                let qubits = storage.qubits_unchecked(idx);
-                #[allow(clippy::cast_possible_truncation)] // gate index fits in u32
-                self.register_gate_raw(idx as u32, tick_id, qubits);
-            }
-        }
-
-        self.finalize();
-    }
-}
-
-// ============================================================================
-// Metadata Storage
-// ============================================================================
-
-/// Lazy metadata storage - only allocates when metadata is actually used.
-#[derive(Debug, Clone, Default)]
-pub struct MetadataStorage {
-    /// Per-gate attributes.
-    pub gate_attrs: BTreeMap<GateId, BTreeMap<String, Attribute>>,
-    /// Per-tick attributes.
-    pub tick_attrs: Vec<BTreeMap<String, Attribute>>,
-    /// Circuit-level attributes.
-    pub circuit_attrs: BTreeMap<String, Attribute>,
-}
-
-impl MetadataStorage {
-    /// Creates empty metadata storage.
-    #[must_use]
-    pub fn new() -> Self {
-        Self::default()
-    }
-
-    /// Sets a gate attribute.
-    pub fn set_gate_attr(&mut self, gate_id: GateId, key: &str, value: Attribute) {
-        self.gate_attrs
-            .entry(gate_id)
-            .or_default()
-            .insert(key.to_string(), value);
-    }
-
-    /// Gets a gate attribute.
-    #[must_use]
-    pub fn get_gate_attr(&self, gate_id: GateId, key: &str) -> Option<&Attribute> {
-        self.gate_attrs.get(&gate_id).and_then(|m| m.get(key))
-    }
-
-    /// Sets a tick attribute.
-    pub fn set_tick_attr(&mut self, tick: usize, key: &str, value: Attribute) {
-        if tick >= self.tick_attrs.len() {
-            self.tick_attrs.resize(tick + 1, BTreeMap::new());
-        }
-        self.tick_attrs[tick].insert(key.to_string(), value);
-    }
-
-    /// Gets a tick attribute.
-    #[must_use]
-    pub fn get_tick_attr(&self, tick: usize, key: &str) -> Option<&Attribute> {
-        self.tick_attrs.get(tick).and_then(|m| m.get(key))
-    }
-
-    /// Sets a circuit attribute.
-    pub fn set_circuit_attr(&mut self, key: &str, value: Attribute) {
-        self.circuit_attrs.insert(key.to_string(), value);
-    }
-
-    /// Gets a circuit attribute.
-    #[must_use]
-    pub fn get_circuit_attr(&self, key: &str) -> Option<&Attribute> {
-        self.circuit_attrs.get(key)
-    }
-
-    /// Clears all metadata.
-    pub fn clear(&mut self) {
-        self.gate_attrs.clear();
-        self.tick_attrs.clear();
-        self.circuit_attrs.clear();
-    }
-}
-
-// ============================================================================
-// TickCircuitSoA
-// ============================================================================
-
-/// A tick-based quantum circuit optimized for batched simulation.
-///
-/// This is a DOD (Data-Oriented Design) alternative to [`TickCircuit`](crate::TickCircuit)
-/// that provides:
-/// - **Batched simulation**: Gates grouped by type for efficient batch execution
-/// - **Cache-friendly access**: Qubits for same-type gates stored contiguously
-/// - **Individual gate access**: `SoA` storage for analysis workloads
-#[derive(Debug, Clone, Default)]
-pub struct TickCircuitSoA {
-    /// Gates grouped by type for batched simulation (primary interface).
-    pub batched: TickGateGroups,
-    /// Gate data in `SoA` layout (for individual gate access).
-    pub storage: GateStorage,
-    /// Pre-computed indexes.
-    pub indexes: CircuitIndexes,
-    /// Metadata (lazy allocation).
-    pub metadata: MetadataStorage,
-}
-
-impl TickCircuitSoA {
-    /// Creates a new empty circuit.
-    #[must_use]
-    pub fn new() -> Self {
-        Self::default()
-    }
-
-    /// Creates a builder for constructing circuits with a fluent API.
-    #[must_use]
-    pub fn builder() -> TickCircuitSoABuilder {
-        TickCircuitSoABuilder::new()
-    }
-
-    /// Returns the number of ticks.
-    #[inline]
-    #[must_use]
-    pub fn num_ticks(&self) -> usize {
-        self.indexes.num_ticks
-    }
-
-    /// Returns the total number of active gates.
-    #[inline]
-    #[must_use]
-    pub fn gate_count(&self) -> usize {
-        self.storage.active_count()
-    }
-
-    /// Returns the maximum qubit index.
-    #[inline]
-    #[must_use]
-    pub fn max_qubit(&self) -> usize {
-        self.indexes.max_qubit
-    }
-
-    /// Returns the gate type for a gate ID.
-    #[inline]
-    #[must_use]
-    pub fn gate_type(&self, id: GateId) -> Option<GateType> {
-        self.storage.gate_type(id)
-    }
-
-    /// Returns the qubits for a gate ID.
-    #[inline]
-    #[must_use]
-    pub fn gate_qubits(&self, id: GateId) -> Option<&[QubitId]> {
-        self.storage.gate_qubits(id)
-    }
-
-    /// Returns the angles for a gate ID.
-    #[inline]
-    #[must_use]
-    pub fn gate_angles(&self, id: GateId) -> Option<&[Angle64]> {
-        self.storage.gate_angles(id)
-    }
-
-    /// Returns all gates touching a specific qubit.
-    #[inline]
-    #[must_use]
-    pub fn gates_touching_qubit(&self, qubit: usize) -> &[GateId] {
-        self.indexes.gates_touching_qubit(qubit)
-    }
-
-    /// Returns all gate indices touching a specific qubit (optimized, no validation).
-    #[inline]
-    #[must_use]
-    pub fn gates_touching_qubit_raw(&self, qubit: usize) -> &[u32] {
-        self.indexes.gates_touching_qubit_raw(qubit)
-    }
-
-    /// Returns gate indices in a specific tick (optimized, O(1)).
-    #[inline]
-    #[must_use]
-    pub fn gates_in_tick_raw(&self, tick: usize) -> &[u32] {
-        self.indexes.gates_in_tick(tick)
-    }
-
-    /// Returns gates on a qubit sorted by tick (for backward traversal).
-    #[inline]
-    #[must_use]
-    pub fn qubit_gates_sorted(&self, qubit: usize) -> &[(u16, u32)] {
-        self.indexes.qubit_gates_sorted(qubit)
-    }
-
-    /// Validates that a gate ID is still valid.
-    #[inline]
-    #[must_use]
-    pub fn is_valid(&self, id: GateId) -> bool {
-        self.storage.is_valid(id)
-    }
-
-    /// Iterator over all valid gate IDs.
-    pub fn iter_gate_ids(&self) -> impl Iterator<Item = GateId> + '_ {
-        self.storage.iter_ids()
-    }
-
-    /// Iterator over gate IDs in a specific tick.
-    #[allow(clippy::cast_possible_truncation)] // tick index fits in u16
-    pub fn gates_in_tick(&self, tick: usize) -> impl Iterator<Item = GateId> + '_ {
-        self.storage
-            .iter_ids()
-            .filter(move |&id| self.storage.tick_id(id) == Some(tick as u16))
-    }
-
-    // =========================================================================
-    // Batched Simulation API
-    // =========================================================================
-
-    /// Returns an iterator over ticks with batched gates for simulation.
-    ///
-    /// This is the primary API for efficient circuit simulation:
-    /// ```text
-    /// for (tick_idx, tick) in circuit.iter_ticks_batched() {
-    ///     for batch in tick.iter() {
-    ///         match batch.gate_type {
-    ///             GateType::H  => sim.h(batch.qubits()),
-    ///             GateType::CX => sim.cx(batch.qubits()),
-    ///             // ...
-    ///         }
-    ///     }
-    /// }
-    /// ```
-    #[inline]
-    pub fn iter_ticks_batched(&self) -> impl Iterator<Item = (usize, &TickBatches)> {
-        self.batched.iter_ticks()
-    }
-
-    /// Returns the batched gates for a specific tick.
-    #[inline]
-    #[must_use]
-    pub fn tick_batched(&self, tick: usize) -> Option<&TickBatches> {
-        self.batched.tick(tick)
-    }
-
-    /// Returns the number of ticks (from batched representation).
-    #[inline]
-    #[must_use]
-    pub fn num_ticks_batched(&self) -> usize {
-        self.batched.num_ticks()
-    }
-
-    /// Clears the circuit.
-    pub fn clear(&mut self) {
-        self.batched.clear();
-        self.storage.clear();
-        self.indexes.clear();
-        self.metadata.clear();
-    }
-
-    /// Rebuilds indexes after modifications.
-    pub fn rebuild_indexes(&mut self) {
-        self.indexes.rebuild(&self.storage);
-    }
-}
-
-// ============================================================================
-// Builder Pattern
-// ============================================================================
-
-/// Builder for constructing `TickCircuitSoA` with a fluent API.
-#[derive(Debug)]
-pub struct TickCircuitSoABuilder {
-    batched: TickGateGroups,
-    storage: GateStorage,
-    indexes: CircuitIndexes,
-    metadata: MetadataStorage,
-    current_tick: u16,
-    last_gate_id: Option<GateId>,
-}
-
-impl TickCircuitSoABuilder {
-    /// Creates a new builder.
-    #[must_use]
-    pub fn new() -> Self {
-        Self {
-            batched: TickGateGroups::new(),
-            storage: GateStorage::new(),
-            indexes: CircuitIndexes::new(),
-            metadata: MetadataStorage::new(),
-            current_tick: 0,
-            last_gate_id: None,
-        }
-    }
-
-    /// Starts a new tick.
-    pub fn tick(&mut self) -> &mut Self {
-        // Update num_ticks
-        self.indexes.num_ticks = (self.current_tick + 1) as usize;
-        self.current_tick += 1;
-        self.last_gate_id = None;
-        self
-    }
-
-    /// Adds a gate to the current tick.
-    fn add_gate(
-        &mut self,
-        gate_type: GateType,
-        qubits: &[QubitId],
-        angles: &[Angle64],
-        params: &[f64],
-    ) -> &mut Self {
-        let tick = self.current_tick.saturating_sub(1);
-
-        // Add to batched representation (primary for simulation)
-        self.batched
-            .add_gate(tick as usize, gate_type, qubits, angles);
-
-        // Add to SoA storage (for individual gate access)
-        let gate_id = self
-            .storage
-            .add_gate(gate_type, tick, qubits, angles, params);
-
-        // Update indexes
-        self.indexes.register_gate_raw(gate_id.index, tick, qubits);
-        self.last_gate_id = Some(gate_id);
-        self
-    }
-
-    /// Sets metadata on the last added gate (or tick if no gate yet).
-    pub fn meta(&mut self, key: &str, value: impl Into<Attribute>) -> &mut Self {
-        if let Some(gate_id) = self.last_gate_id {
-            self.metadata.set_gate_attr(gate_id, key, value.into());
-        } else {
-            // Set tick-level metadata
-            let tick = self.current_tick.saturating_sub(1) as usize;
-            self.metadata.set_tick_attr(tick, key, value.into());
-        }
-        self
-    }
-
-    /// Builds the final circuit.
-    #[must_use]
-    pub fn build(mut self) -> TickCircuitSoA {
-        // Finalize indexes (sort qubit gates by tick for efficient traversal)
-        self.indexes.finalize();
-        TickCircuitSoA {
-            batched: self.batched,
-            storage: self.storage,
-            indexes: self.indexes,
-            metadata: self.metadata,
-        }
-    }
-
-    // =========================================================================
-    // Gate methods (mirror TickHandle API)
-    // =========================================================================
-
-    /// Apply Hadamard gate(s).
-    pub fn h(&mut self, qubits: &[impl Into<QubitId> + Copy]) -> &mut Self {
-        let qs: Vec<QubitId> = qubits.iter().map(|&q| q.into()).collect();
-        self.add_gate(GateType::H, &qs, &[], &[])
-    }
-
-    /// Apply X gate(s).
-    pub fn x(&mut self, qubits: &[impl Into<QubitId> + Copy]) -> &mut Self {
-        let qs: Vec<QubitId> = qubits.iter().map(|&q| q.into()).collect();
-        self.add_gate(GateType::X, &qs, &[], &[])
-    }
-
-    /// Apply Y gate(s).
-    pub fn y(&mut self, qubits: &[impl Into<QubitId> + Copy]) -> &mut Self {
-        let qs: Vec<QubitId> = qubits.iter().map(|&q| q.into()).collect();
-        self.add_gate(GateType::Y, &qs, &[], &[])
-    }
-
-    /// Apply Z gate(s).
-    pub fn z(&mut self, qubits: &[impl Into<QubitId> + Copy]) -> &mut Self {
-        let qs: Vec<QubitId> = qubits.iter().map(|&q| q.into()).collect();
-        self.add_gate(GateType::Z, &qs, &[], &[])
-    }
-
-    /// Apply SX gate(s).
-    pub fn sx(&mut self, qubits: &[impl Into<QubitId> + Copy]) -> &mut Self {
-        let qs: Vec<QubitId> = qubits.iter().map(|&q| q.into()).collect();
-        self.add_gate(GateType::SX, &qs, &[], &[])
-    }
-
-    /// Apply SY gate(s).
-    pub fn sy(&mut self, qubits: &[impl Into<QubitId> + Copy]) -> &mut Self {
-        let qs: Vec<QubitId> = qubits.iter().map(|&q| q.into()).collect();
-        self.add_gate(GateType::SY, &qs, &[], &[])
-    }
-
-    /// Apply SZ gate(s).
-    pub fn sz(&mut self, qubits: &[impl Into<QubitId> + Copy]) -> &mut Self {
-        let qs: Vec<QubitId> = qubits.iter().map(|&q| q.into()).collect();
-        self.add_gate(GateType::SZ, &qs, &[], &[])
-    }
-
-    /// Apply CX gate(s).
-    pub fn cx(
-        &mut self,
-        pairs: &[(impl Into<QubitId> + Copy, impl Into<QubitId> + Copy)],
-    ) -> &mut Self {
-        let qs: Vec<QubitId> = pairs
-            .iter()
-            .flat_map(|&(c, t)| [c.into(), t.into()])
-            .collect();
-        self.add_gate(GateType::CX, &qs, &[], &[])
-    }
-
-    /// Apply CZ gate(s).
-    pub fn cz(
-        &mut self,
-        pairs: &[(impl Into<QubitId> + Copy, impl Into<QubitId> + Copy)],
-    ) -> &mut Self {
-        let qs: Vec<QubitId> = pairs
-            .iter()
-            .flat_map(|&(a, b)| [a.into(), b.into()])
-            .collect();
-        self.add_gate(GateType::CZ, &qs, &[], &[])
-    }
-
-    /// Prepare qubit(s) in |0⟩.
-    pub fn pz(&mut self, qubits: &[impl Into<QubitId> + Copy]) -> &mut Self {
-        let qs: Vec<QubitId> = qubits.iter().map(|&q| q.into()).collect();
-        self.add_gate(GateType::PZ, &qs, &[], &[])
-    }
-
-    /// Measure qubit(s) in Z basis.
-    pub fn mz(&mut self, qubits: &[impl Into<QubitId> + Copy]) -> &mut Self {
-        let qs: Vec<QubitId> = qubits.iter().map(|&q| q.into()).collect();
-        self.add_gate(GateType::MZ, &qs, &[], &[])
-    }
-}
-
-impl Default for TickCircuitSoABuilder {
-    fn default() -> Self {
-        Self::new()
-    }
-}
-
-// ============================================================================
-// Conversion from TickCircuit
-// ============================================================================
-
-impl From<&crate::TickCircuit> for TickCircuitSoA {
-    fn from(tc: &crate::TickCircuit) -> Self {
-        let mut builder = TickCircuitSoABuilder::new();
-
-        for (tick_idx, tick_data) in tc.iter_ticks() {
-            // Ensure we're at the right tick
-            #[allow(clippy::cast_possible_truncation)] // tick index fits in u16
-            while builder.current_tick <= tick_idx as u16 {
-                builder.tick();
-            }
-
-            for (gate_idx, gate) in tick_data.gates().iter().enumerate() {
-                let qubits: Vec<QubitId> = gate.qubits.to_vec();
-                let angles: Vec<Angle64> = gate.angles.to_vec();
-                let params: Vec<f64> = gate.params.to_vec();
-
-                let tick_num = builder.current_tick.saturating_sub(1);
-
-                // Add to batched representation (primary for simulation)
-                builder
-                    .batched
-                    .add_gate(tick_num as usize, gate.gate_type, &qubits, &angles);
-
-                // Add to SoA storage (for individual gate access)
-                let gate_id =
-                    builder
-                        .storage
-                        .add_gate(gate.gate_type, tick_num, &qubits, &angles, &params);
-                builder.indexes.register_gate(gate_id, &qubits);
-                builder.indexes.num_ticks = builder.indexes.num_ticks.max(tick_num as usize + 1);
-
-                // Copy gate attributes
-                for (key, value) in tick_data.gate_attrs(gate_idx) {
-                    builder.metadata.set_gate_attr(gate_id, key, value.clone());
-                }
-            }
-
-            // Copy tick attributes
-            for (key, value) in tick_data.tick_attrs() {
-                builder.metadata.set_tick_attr(tick_idx, key, value.clone());
-            }
-        }
-
-        // Copy circuit attributes
-        for (key, value) in tc.circuit_attrs() {
-            builder.metadata.set_circuit_attr(key, value.clone());
-        }
-
-        builder.build()
-    }
-}
-
-#[cfg(test)]
-mod tests {
-    use super::*;
-
-    #[test]
-    fn test_basic_construction() {
-        let mut builder = TickCircuitSoA::builder();
-        builder
-            .tick()
-            .pz(&[0, 1])
-            .tick()
-            .h(&[0])
-            .cx(&[(0, 1)])
-            .tick()
-            .mz(&[0, 1]);
-
-        let circuit = builder.build();
-
-        assert_eq!(circuit.num_ticks(), 3);
-        assert_eq!(circuit.gate_count(), 4); // pz, h, cx, mz
-    }
-
-    #[test]
-    fn test_gate_lookup() {
-        let mut builder = TickCircuitSoA::builder();
-        builder.tick().h(&[0]).x(&[1]);
-
-        let circuit = builder.build();
-
-        // Find all gates
-        let gate_ids: Vec<_> = circuit.iter_gate_ids().collect();
-        assert_eq!(gate_ids.len(), 2);
-
-        // Check gate types
-        assert_eq!(circuit.gate_type(gate_ids[0]), Some(GateType::H));
-        assert_eq!(circuit.gate_type(gate_ids[1]), Some(GateType::X));
-
-        // Check qubits
-        assert_eq!(
-            circuit.gate_qubits(gate_ids[0]),
-            Some([QubitId::from(0)].as_slice())
-        );
-        assert_eq!(
-            circuit.gate_qubits(gate_ids[1]),
-            Some([QubitId::from(1)].as_slice())
-        );
-    }
-
-    #[test]
-    fn test_qubit_index() {
-        let mut builder = TickCircuitSoA::builder();
-        builder.tick().h(&[0]).x(&[1]).tick().cx(&[(0, 1)]);
-
-        let circuit = builder.build();
-
-        // Gates on qubit 0: H and CX (using raw accessor for efficiency)
-        let q0_gates = circuit.gates_touching_qubit_raw(0);
-        assert_eq!(q0_gates.len(), 2);
-
-        // Gates on qubit 1: X and CX
-        let q1_gates = circuit.gates_touching_qubit_raw(1);
-        assert_eq!(q1_gates.len(), 2);
-
-        // Gates on qubit 2: none
-        let q2_gates = circuit.gates_touching_qubit_raw(2);
-        assert_eq!(q2_gates.len(), 0);
-    }
-
-    #[test]
-    fn test_metadata() {
-        let mut builder = TickCircuitSoA::builder();
-        builder
-            .tick()
-            .meta("round", Attribute::Int(0))
-            .h(&[0])
-            .meta("duration", Attribute::Float(50.0));
-
-        let circuit = builder.build();
-
-        // Check tick metadata
-        assert_eq!(
-            circuit.metadata.get_tick_attr(0, "round"),
-            Some(&Attribute::Int(0))
-        );
-
-        // Check gate metadata
-        let gate_ids: Vec<_> = circuit.iter_gate_ids().collect();
-        assert_eq!(
-            circuit.metadata.get_gate_attr(gate_ids[0], "duration"),
-            Some(&Attribute::Float(50.0))
-        );
-    }
-
-    #[test]
-    fn test_gate_removal() {
-        let mut builder = TickCircuitSoA::builder();
-        builder.tick().h(&[0]).x(&[1]);
-
-        let mut circuit = builder.build();
-        let gate_ids: Vec<_> = circuit.iter_gate_ids().collect();
-
-        assert_eq!(circuit.gate_count(), 2);
-
-        // Remove first gate
-        assert!(circuit.storage.remove(gate_ids[0]));
-        assert_eq!(circuit.gate_count(), 1);
-
-        // Gate ID is now invalid
-        assert!(!circuit.is_valid(gate_ids[0]));
-        assert!(circuit.is_valid(gate_ids[1]));
-    }
-
-    #[test]
-    fn test_generational_ids() {
-        let mut storage = GateStorage::new();
-
-        // Add and remove a gate
-        let id1 = storage.add_gate(GateType::H, 0, &[QubitId::from(0)], &[], &[]);
-        assert!(storage.is_valid(id1));
-
-        storage.remove(id1);
-        assert!(!storage.is_valid(id1));
-
-        // Add another gate - reuses the slot with new generation
-        let id2 = storage.add_gate(GateType::X, 0, &[QubitId::from(0)], &[], &[]);
-        assert!(storage.is_valid(id2));
-        assert!(!storage.is_valid(id1)); // Old ID still invalid
-
-        // Same index, different generation
-        assert_eq!(id1.index(), id2.index());
-        assert_ne!(id1.generation(), id2.generation());
-    }
-
-    #[test]
-    fn test_batched_simulation_api() {
-        let mut builder = TickCircuitSoA::builder();
-        builder
-            .tick()
-            .pz(&[0, 1, 2, 3]) // 4 preps
-            .tick()
-            .h(&[0, 1]) // 2 H gates
-            .x(&[2, 3]) // 2 X gates
-            .tick()
-            .cx(&[(0, 1), (2, 3)]) // 2 CX gates
-            .tick()
-            .mz(&[0, 1, 2, 3]); // 4 measurements
-
-        let circuit = builder.build();
-
-        // Check tick count
-        assert_eq!(circuit.num_ticks_batched(), 4);
-
-        // Check tick 0: preps batched together
-        let tick0 = circuit.tick_batched(0).unwrap();
-        assert_eq!(tick0.batch_count(), 1);
-        let prep_batch = tick0.batch_for_type(GateType::PZ).unwrap();
-        assert_eq!(prep_batch.qubits().len(), 4);
-        assert_eq!(prep_batch.gate_count(), 4);
-
-        // Check tick 1: H and X are separate batches
-        let tick1 = circuit.tick_batched(1).unwrap();
-        assert_eq!(tick1.batch_count(), 2);
-        let h_batch = tick1.batch_for_type(GateType::H).unwrap();
-        assert_eq!(h_batch.qubits().len(), 2);
-        let x_batch = tick1.batch_for_type(GateType::X).unwrap();
-        assert_eq!(x_batch.qubits().len(), 2);
-
-        // Check tick 2: CX gates batched
-        let tick2 = circuit.tick_batched(2).unwrap();
-        assert_eq!(tick2.batch_count(), 1);
-        let cx_batch = tick2.batch_for_type(GateType::CX).unwrap();
-        assert_eq!(cx_batch.qubits().len(), 4); // 2 pairs = 4 qubits
-        assert_eq!(cx_batch.gate_count(), 2);
-
-        // Check tick 3: measurements batched
-        let tick3 = circuit.tick_batched(3).unwrap();
-        assert_eq!(tick3.batch_count(), 1);
-        let mz_batch = tick3.batch_for_type(GateType::MZ).unwrap();
-        assert_eq!(mz_batch.qubits().len(), 4);
-        assert_eq!(mz_batch.gate_count(), 4);
-    }
-
-    #[test]
-    fn test_iter_ticks_batched() {
-        let mut builder = TickCircuitSoA::builder();
-        builder.tick().h(&[0, 1, 2]).tick().cx(&[(0, 1)]);
-
-        let circuit = builder.build();
-
-        // Iterate and count
-        let mut tick_count = 0;
-        let mut total_batches = 0;
-        for (_tick_idx, tick) in circuit.iter_ticks_batched() {
-            tick_count += 1;
-            total_batches += tick.batch_count();
-        }
-
-        assert_eq!(tick_count, 2);
-        assert_eq!(total_batches, 2); // H batch + CX batch
-    }
-}
diff --git a/crates/pecos-quantum/src/unitary_matrix.rs b/crates/pecos-quantum/src/unitary_matrix.rs
index 5a70072ae..27ffbfeea 100644
--- a/crates/pecos-quantum/src/unitary_matrix.rs
+++ b/crates/pecos-quantum/src/unitary_matrix.rs
@@ -23,7 +23,7 @@
 //!
 //! ```
 //! use pecos_quantum::unitary_matrix::ToMatrix;
-//! use pecos_core::unitary_rep::X;
+//! use pecos_core::unitary::X;
 //!
 //! let x = X(0);
 //! let matrix = x.to_matrix();  // Method style
@@ -31,6 +31,9 @@
 
 use nalgebra::DMatrix;
 use num_complex::Complex64;
+use pecos_random::{Rng, RngExt as _};
+use std::error::Error;
+use std::f64::consts::TAU;
 use std::fmt;
 use std::ops::{BitAnd, Deref, DerefMut, Mul, Neg, Sub};
 use std::sync::LazyLock;
@@ -56,7 +59,7 @@ use pecos_core::{Angle64, Op, Pauli, PauliString, Phase};
 ///
 /// ```
 /// use pecos_quantum::unitary_matrix::{UnitaryMatrix, ToMatrix};
-/// use pecos_core::unitary_rep::{X, Z};
+/// use pecos_core::unitary::{X, Z};
 ///
 /// let mx = X(0).to_matrix();
 /// let mz = Z(0).to_matrix();
@@ -70,6 +73,30 @@ use pecos_core::{Angle64, Op, Pauli, PauliString, Phase};
 #[derive(Debug, Clone, PartialEq)]
 pub struct UnitaryMatrix(pub DMatrix<Complex64>);
 
+/// Error returned by dense unitary-matrix helpers.
+#[derive(Debug, Clone, PartialEq, Eq)]
+pub enum UnitaryMatrixError {
+    /// The requested number of qubits would overflow a dense Hilbert-space
+    /// dimension.
+    DimensionOverflow {
+        /// Number of qubits supplied by the caller.
+        num_qubits: usize,
+    },
+}
+
+impl fmt::Display for UnitaryMatrixError {
+    fn fmt(&self, f: &mut fmt::Formatter<'_>) -> fmt::Result {
+        match self {
+            Self::DimensionOverflow { num_qubits } => write!(
+                f,
+                "dense unitary dimension overflows usize for {num_qubits} qubits"
+            ),
+        }
+    }
+}
+
+impl Error for UnitaryMatrixError {}
+
 impl UnitaryMatrix {
     /// Creates an identity matrix of size `n x n`.
     #[must_use]
@@ -192,6 +219,70 @@ impl UnitaryMatrix {
     }
 }
 
+/// Returns a Haar-random dense unitary on `num_qubits` qubits.
+///
+/// The implementation samples a complex Ginibre matrix, performs QR
+/// decomposition, and fixes the column phases from the `R` diagonal. The output
+/// is a dense matrix in the same little-endian computational-basis convention as
+/// the rest of PECOS's matrix helpers.
+///
+/// # Errors
+///
+/// Returns [`UnitaryMatrixError::DimensionOverflow`] if `2^num_qubits` does not
+/// fit in `usize`.
+pub fn random_unitary<R>(
+    rng: &mut R,
+    num_qubits: usize,
+) -> Result<UnitaryMatrix, UnitaryMatrixError>
+where
+    R: Rng + ?Sized,
+{
+    let dim = dense_hilbert_dim(num_qubits)?;
+    let ginibre = DMatrix::from_fn(dim, dim, |_, _| standard_complex_normal(rng));
+    let (mut q, r) = ginibre.qr().unpack();
+
+    for col in 0..dim {
+        let diagonal = r[(col, col)];
+        let norm = diagonal.norm();
+        if norm > 0.0 {
+            let phase = diagonal / norm;
+            for row in 0..dim {
+                q[(row, col)] *= phase;
+            }
+        }
+    }
+
+    Ok(UnitaryMatrix(q))
+}
+
+fn dense_hilbert_dim(num_qubits: usize) -> Result<usize, UnitaryMatrixError> {
+    let exponent = u32::try_from(num_qubits)
+        .map_err(|_| UnitaryMatrixError::DimensionOverflow { num_qubits })?;
+    2usize
+        .checked_pow(exponent)
+        .ok_or(UnitaryMatrixError::DimensionOverflow { num_qubits })
+}
+
+fn standard_complex_normal<R>(rng: &mut R) -> Complex64
+where
+    R: Rng + ?Sized,
+{
+    Complex64::new(standard_normal(rng), standard_normal(rng))
+}
+
+fn standard_normal<R>(rng: &mut R) -> f64
+where
+    R: Rng + ?Sized,
+{
+    loop {
+        let u1 = rng.random::<f64>();
+        if u1 > 0.0 {
+            let u2 = rng.random::<f64>();
+            return (-2.0 * u1.ln()).sqrt() * (TAU * u2).cos();
+        }
+    }
+}
+
 // --- Canonicalization and cached lookup tables ---
 
 /// Divides all entries by the first nonzero entry (row-major scan).
@@ -1048,7 +1139,7 @@ impl fmt::Display for UnitaryMatrix {
 ///
 /// ```
 /// use pecos_quantum::unitary_matrix::ToMatrix;
-/// use pecos_core::unitary_rep::{X, H, CX, Is};
+/// use pecos_core::unitary::{X, H, CX, Is};
 ///
 /// // Single qubit gate
 /// let x_matrix = X(0).to_matrix();
@@ -1123,13 +1214,17 @@ impl ToMatrix for Unitary {
 }
 
 impl ToMatrix for Op {
-    /// Converts to a matrix. Returns the zero matrix for channels (non-unitary ops).
+    /// Converts to a matrix.
+    ///
+    /// # Panics
+    ///
+    /// Panics for Gate-level or Channel-level operations, which do not have a
+    /// unitary matrix representation.
     fn to_matrix(&self) -> UnitaryMatrix {
         match self.clone().into_unitary() {
             Some(ur) => to_matrix(&ur),
             None => {
-                // Channel ops don't have a unitary matrix
-                panic!("Cannot convert non-unitary Op (Channel) to a matrix")
+                panic!("Cannot convert non-unitary Op (Gate/Channel) to a matrix")
             }
         }
     }
@@ -1144,7 +1239,7 @@ impl ToMatrix for Op {
 ///
 /// ```
 /// use pecos_quantum::unitary_matrix::to_matrix;
-/// use pecos_core::unitary_rep::X;
+/// use pecos_core::unitary::X;
 /// use num_complex::Complex64;
 ///
 /// let x = X(0);
@@ -1170,6 +1265,24 @@ pub fn to_matrix_with_size(op: &UnitaryRep, num_qubits: usize) -> UnitaryMatrix
     UnitaryMatrix(to_matrix_with_size_impl(op, num_qubits))
 }
 
+fn assert_tensor_parts_have_disjoint_support(parts: &[UnitaryRep]) {
+    let mut used = std::collections::BTreeSet::new();
+    for part in parts {
+        let mut overlap = Vec::new();
+        for q in part.qubits() {
+            if used.contains(&q) {
+                overlap.push(q);
+            } else {
+                used.insert(q);
+            }
+        }
+        assert!(
+            overlap.is_empty(),
+            "tensor product requires disjoint unitary support; overlapping qubits: {overlap:?}"
+        );
+    }
+}
+
 /// Internal implementation that returns raw `DMatrix` for recursive use.
 fn to_matrix_with_size_impl(op: &UnitaryRep, num_qubits: usize) -> DMatrix<Complex64> {
     let dim = 1 << num_qubits; // 2^num_qubits
@@ -1211,6 +1324,8 @@ fn to_matrix_with_size_impl(op: &UnitaryRep, num_qubits: usize) -> DMatrix<Compl
         }
 
         UnitaryRep::Tensor(parts) => {
+            assert_tensor_parts_have_disjoint_support(parts);
+
             // Start with identity, combine each part
             let mut result = DMatrix::identity(dim, dim);
             for part in parts {
@@ -1252,7 +1367,7 @@ fn to_matrix_with_size_impl(op: &UnitaryRep, num_qubits: usize) -> DMatrix<Compl
 ///
 /// ```
 /// use pecos_quantum::unitary_matrix::unitary_exp;
-/// use pecos_core::unitary_rep::Z;
+/// use pecos_core::unitary::Z;
 /// use num_complex::Complex64;
 /// use std::f64::consts::PI;
 ///
@@ -1277,7 +1392,7 @@ pub fn unitary_exp(op: &UnitaryRep, theta: f64) -> UnitaryMatrix {
 ///
 /// ```
 /// use pecos_quantum::unitary_matrix::{unitary_log, to_matrix};
-/// use pecos_core::unitary_rep::X;
+/// use pecos_core::unitary::X;
 ///
 /// let x = X(0);
 /// if let Some(log_x) = unitary_log(&x) {
@@ -1300,7 +1415,7 @@ pub fn unitary_log(op: &UnitaryRep) -> Option<DMatrix<Complex64>> {
 ///
 /// ```
 /// use pecos_quantum::unitary_matrix::unitaries_equiv;
-/// use pecos_core::unitary_rep::{X, Y, Z};
+/// use pecos_core::unitary::{X, Y, Z};
 ///
 /// let x = X(0);
 /// let x2 = X(0);
@@ -1834,7 +1949,9 @@ fn gate_to_matrix(gate_type: GateType, qubits: &[usize], num_qubits: usize) -> D
         GateType::Idle
         | GateType::MeasCrosstalkGlobalPayload
         | GateType::MeasCrosstalkLocalPayload
-        | GateType::Custom => {
+        | GateType::Channel
+        | GateType::Custom
+        | GateType::TrackedPauliMeta => {
             panic!("GateType::{gate_type:?} cannot be converted to a unitary matrix")
         }
     }
@@ -1916,6 +2033,7 @@ mod tests {
     use super::*;
     use pecos_core::Angle64;
     use pecos_core::unitary_rep::{CX, H, I, Is, RX, RZ, SWAP, SZ, T, X, Y, Z};
+    use pecos_random::PecosRng;
     use std::f64::consts::PI;
 
     // --- Basic to_matrix tests ---
@@ -2042,6 +2160,40 @@ mod tests {
         assert!(matrices_equiv_up_to_phase(&mat, &expected, 1e-10));
     }
 
+    fn assert_tensor_matrix_matches_embedded_product(
+        lhs: &pecos_core::unitary_rep::UnitaryRep,
+        rhs: &pecos_core::unitary_rep::UnitaryRep,
+        num_qubits: usize,
+    ) {
+        let tensor = lhs.clone() & rhs.clone();
+        let tensor_matrix = to_matrix_with_size(&tensor, num_qubits);
+        let lhs_matrix = to_matrix_with_size(lhs, num_qubits);
+        let rhs_matrix = to_matrix_with_size(rhs, num_qubits);
+        let expected = &lhs_matrix * &rhs_matrix;
+
+        assert!(
+            matrices_equiv_up_to_phase(&tensor_matrix, &expected, 1e-10),
+            "{tensor:?} matrix did not match embedded product"
+        );
+    }
+
+    #[test]
+    fn test_disjoint_tensor_matrix_semantics_across_operator_levels() {
+        assert_tensor_matrix_matches_embedded_product(&X(0), &Z(1), 2);
+        assert_tensor_matrix_matches_embedded_product(&H(0), &SZ(1), 2);
+        assert_tensor_matrix_matches_embedded_product(&H(0), &T(1), 2);
+        assert_tensor_matrix_matches_embedded_product(&CX(0, 2), &T(1), 3);
+        assert_tensor_matrix_matches_embedded_product(&H(3), &CX(0, 2), 4);
+    }
+
+    #[test]
+    #[should_panic(expected = "tensor product requires disjoint unitary support")]
+    fn test_to_matrix_rejects_invalid_overlapping_tensor_node() {
+        let invalid = pecos_core::unitary_rep::UnitaryRep::Tensor(vec![X(0), Z(0)]);
+
+        let _ = to_matrix(&invalid);
+    }
+
     #[test]
     fn test_composition() {
         // H * X = XH (matrix multiplication order)
@@ -3112,6 +3264,32 @@ mod tests {
         assert!(!mat.is_unitary());
     }
 
+    #[test]
+    fn random_unitary_is_unitary_and_seed_reproducible() {
+        let mut rng = PecosRng::seed_from_u64(123);
+        let unitary = random_unitary(&mut rng, 2).unwrap();
+        assert_eq!(unitary.inner().shape(), (4, 4));
+        assert!(unitary.is_unitary_with_tolerance(1e-10));
+
+        let mut same_seed = PecosRng::seed_from_u64(123);
+        let same = random_unitary(&mut same_seed, 2).unwrap();
+        assert_eq!(unitary.inner(), same.inner());
+
+        let mut different_seed = PecosRng::seed_from_u64(456);
+        let different = random_unitary(&mut different_seed, 2).unwrap();
+        assert!(
+            !matrices_approx_equal(unitary.inner(), different.inner(), 1e-8),
+            "different seeds should not produce the same Haar draw"
+        );
+    }
+
+    #[test]
+    fn random_unitary_dimension_overflow_is_reported() {
+        let mut rng = PecosRng::seed_from_u64(123);
+        let err = random_unitary(&mut rng, usize::BITS as usize).unwrap_err();
+        assert!(matches!(err, UnitaryMatrixError::DimensionOverflow { .. }));
+    }
+
     #[test]
     fn try_to_unitary_rxxryyrzz_stress() {
         // Test a grid of angle combinations including edge cases:
diff --git a/crates/pecos-relay-bp/src/core_traits.rs b/crates/pecos-relay-bp/src/core_traits.rs
index ca546425f..208eaeb43 100644
--- a/crates/pecos-relay-bp/src/core_traits.rs
+++ b/crates/pecos-relay-bp/src/core_traits.rs
@@ -21,6 +21,10 @@ impl DecodingResultTrait for DecodingResult {
         self.converged
     }
 
+    fn correction(&self) -> &[u8] {
+        self.decoding.as_slice().unwrap_or(&[])
+    }
+
     fn cost(&self) -> Option<f64> {
         None
     }
diff --git a/crates/pecos-simulators/Cargo.toml b/crates/pecos-simulators/Cargo.toml
index 794ce21b9..b4f4ac594 100644
--- a/crates/pecos-simulators/Cargo.toml
+++ b/crates/pecos-simulators/Cargo.toml
@@ -18,11 +18,6 @@ default = []
 # Do NOT enable for multi-shot workloads where shots are parallelized at the
 # orchestration level - this causes thread oversubscription and hurts throughput.
 parallel = ["rayon"]
-# Enable AVX-512 SIMD operations using f64x8 (512-bit vectors processing 8 f64 at once).
-# Requires AVX-512 capable CPU (Intel Ice Lake+, AMD Zen 4+).
-# Build with: RUSTFLAGS='-C target-feature=+avx512f' cargo build --release --features avx512
-# Provides ~2x theoretical speedup for SIMD-bound operations on supported hardware.
-avx512 = []
 
 [dependencies]
 pecos-core.workspace = true
@@ -30,6 +25,7 @@ pecos-quantum.workspace = true
 pecos-random.workspace = true
 rand.workspace = true
 num-complex.workspace = true
+nalgebra.workspace = true
 smallvec.workspace = true
 wide.workspace = true
 rayon = { version = "1.10", optional = true }
diff --git a/crates/pecos-simulators/src/bitmask_pauli_prop.rs b/crates/pecos-simulators/src/bitmask_pauli_prop.rs
new file mode 100644
index 000000000..2fead22f4
--- /dev/null
+++ b/crates/pecos-simulators/src/bitmask_pauli_prop.rs
@@ -0,0 +1,1173 @@
+// Copyright 2026 The PECOS Developers
+//
+// Licensed under the Apache License, Version 2.0 (the "License"); you may not use this file except
+// in compliance with the License. You may obtain a copy of the License at
+//
+//     https://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software distributed under the License
+// is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express
+// or implied. See the License for the specific language governing permissions and limitations under
+// the License.
+
+//! Bitmask-backed Pauli propagation for hot Clifford fault-analysis paths.
+//!
+//! This type tracks only the binary X/Z support of a propagating Pauli. It
+//! intentionally ignores global phase, matching the fault-catalog use case
+//! where only measurement flips and anticommutation with tracked Paulis
+//! matter.
+
+use crate::clifford_gateable::{CliffordGateable, MeasurementResult};
+use crate::quantum_simulator::QuantumSimulator;
+use pecos_core::{BitmaskStorage, PauliBitmaskSmall, QubitId};
+
+/// Internal phase-free Pauli propagator backed by `PauliBitmaskSmall`.
+///
+/// This is a performance helper for fault analysis and other hot internal
+/// propagation paths. User-facing code should prefer Pauli strings and the
+/// standard simulator APIs.
+#[doc(hidden)]
+#[derive(Clone, Debug)]
+pub struct BitmaskPauliProp {
+    label: PauliBitmaskSmall,
+    num_qubits: usize,
+}
+
+impl Default for BitmaskPauliProp {
+    fn default() -> Self {
+        Self::new()
+    }
+}
+
+impl BitmaskPauliProp {
+    /// Create an empty propagating Pauli with no fixed qubit count.
+    #[must_use]
+    pub fn new() -> Self {
+        Self {
+            label: PauliBitmaskSmall::identity(),
+            num_qubits: 0,
+        }
+    }
+
+    /// Create an empty propagating Pauli with a fixed qubit count for display
+    /// and tests.
+    #[must_use]
+    pub fn with_num_qubits(num_qubits: usize) -> Self {
+        Self {
+            label: PauliBitmaskSmall::identity(),
+            num_qubits,
+        }
+    }
+
+    /// Checks whether the specified qubit has an X component.
+    #[inline]
+    #[must_use]
+    pub fn contains_x(&self, qubit: usize) -> bool {
+        self.label.x_bits.get_bit(qubit)
+    }
+
+    /// Checks whether the specified qubit has a Z component.
+    #[inline]
+    #[must_use]
+    pub fn contains_z(&self, qubit: usize) -> bool {
+        self.label.z_bits.get_bit(qubit)
+    }
+
+    /// Checks whether the specified qubit has a Y component.
+    #[inline]
+    #[must_use]
+    pub fn contains_y(&self, qubit: usize) -> bool {
+        self.contains_x(qubit) && self.contains_z(qubit)
+    }
+
+    /// Toggle X components on the given qubits.
+    #[inline]
+    pub fn track_x(&mut self, qubits: &[usize]) {
+        for &q in qubits {
+            self.label.x_bits.xor_bit(q);
+            self.num_qubits = self.num_qubits.max(q + 1);
+        }
+    }
+
+    /// Toggle Z components on the given qubits.
+    #[inline]
+    pub fn track_z(&mut self, qubits: &[usize]) {
+        for &q in qubits {
+            self.label.z_bits.xor_bit(q);
+            self.num_qubits = self.num_qubits.max(q + 1);
+        }
+    }
+
+    /// Toggle Y components on the given qubits.
+    #[inline]
+    pub fn track_y(&mut self, qubits: &[usize]) {
+        for &q in qubits {
+            self.label.x_bits.xor_bit(q);
+            self.label.z_bits.xor_bit(q);
+            self.num_qubits = self.num_qubits.max(q + 1);
+        }
+    }
+
+    /// Remove all Pauli components from one qubit.
+    #[inline]
+    pub fn clear_qubit(&mut self, qubit: usize) {
+        self.label.x_bits.clear_bit(qubit);
+        self.label.z_bits.clear_bit(qubit);
+    }
+
+    /// True when no X/Z components remain.
+    #[inline]
+    #[must_use]
+    pub fn is_identity(&self) -> bool {
+        self.label.is_identity()
+    }
+
+    /// Number of non-identity single-qubit factors.
+    #[must_use]
+    pub fn weight(&self) -> usize {
+        self.label.weight() as usize
+    }
+
+    /// Dense string representation in qubit-index order.
+    #[must_use]
+    pub fn dense_string(&self) -> String {
+        let mut result = String::with_capacity(self.num_qubits);
+        for q in 0..self.num_qubits {
+            match (self.contains_x(q), self.contains_z(q)) {
+                (false, false) => result.push('I'),
+                (true, false) => result.push('X'),
+                (false, true) => result.push('Z'),
+                (true, true) => result.push('Y'),
+            }
+        }
+        result
+    }
+
+    #[inline]
+    fn set_x_component(&mut self, q: usize, value: bool) {
+        if value {
+            self.label.x_bits.set_bit(q);
+        } else {
+            self.label.x_bits.clear_bit(q);
+        }
+        self.num_qubits = self.num_qubits.max(q + 1);
+    }
+
+    #[inline]
+    fn set_z_component(&mut self, q: usize, value: bool) {
+        if value {
+            self.label.z_bits.set_bit(q);
+        } else {
+            self.label.z_bits.clear_bit(q);
+        }
+        self.num_qubits = self.num_qubits.max(q + 1);
+    }
+
+    #[inline]
+    fn set_components(&mut self, q: usize, x: bool, z: bool) {
+        self.set_x_component(q, x);
+        self.set_z_component(q, z);
+    }
+}
+
+impl QuantumSimulator for BitmaskPauliProp {
+    #[inline]
+    fn reset(&mut self) -> &mut Self {
+        self.label = PauliBitmaskSmall::identity();
+        self
+    }
+
+    fn num_qubits(&self) -> usize {
+        self.num_qubits
+    }
+}
+
+impl CliffordGateable for BitmaskPauliProp {
+    #[inline]
+    fn sz(&mut self, qubits: &[QubitId]) -> &mut Self {
+        for &q in qubits {
+            let q = q.index();
+            if self.contains_x(q) {
+                self.label.z_bits.xor_bit(q);
+            }
+            self.num_qubits = self.num_qubits.max(q + 1);
+        }
+        self
+    }
+
+    #[inline]
+    fn szdg(&mut self, qubits: &[QubitId]) -> &mut Self {
+        self.sz(qubits)
+    }
+
+    #[inline]
+    fn h(&mut self, qubits: &[QubitId]) -> &mut Self {
+        for &q in qubits {
+            let q = q.index();
+            let x = self.contains_x(q);
+            let z = self.contains_z(q);
+            self.set_components(q, z, x);
+        }
+        self
+    }
+
+    #[inline]
+    fn sx(&mut self, qubits: &[QubitId]) -> &mut Self {
+        for &q in qubits {
+            let q = q.index();
+            if self.contains_z(q) {
+                self.label.x_bits.xor_bit(q);
+            }
+            self.num_qubits = self.num_qubits.max(q + 1);
+        }
+        self
+    }
+
+    #[inline]
+    fn sxdg(&mut self, qubits: &[QubitId]) -> &mut Self {
+        self.sx(qubits)
+    }
+
+    #[inline]
+    fn sy(&mut self, qubits: &[QubitId]) -> &mut Self {
+        for &q in qubits {
+            let q = q.index();
+            let x = self.contains_x(q);
+            let z = self.contains_z(q);
+            self.set_components(q, z, x);
+        }
+        self
+    }
+
+    #[inline]
+    fn sydg(&mut self, qubits: &[QubitId]) -> &mut Self {
+        self.sy(qubits)
+    }
+
+    #[inline]
+    fn cx(&mut self, pairs: &[(QubitId, QubitId)]) -> &mut Self {
+        for &(control, target) in pairs {
+            let control = control.index();
+            let target = target.index();
+            let control_x = self.contains_x(control);
+            let target_z = self.contains_z(target);
+            if control_x {
+                self.label.x_bits.xor_bit(target);
+            }
+            if target_z {
+                self.label.z_bits.xor_bit(control);
+            }
+            self.num_qubits = self.num_qubits.max(control.max(target) + 1);
+        }
+        self
+    }
+
+    #[inline]
+    fn cy(&mut self, pairs: &[(QubitId, QubitId)]) -> &mut Self {
+        for &(q1, q2) in pairs {
+            let q1 = q1.index();
+            let q2 = q2.index();
+            let x1 = self.contains_x(q1);
+            let z1 = self.contains_z(q1);
+            let x2 = self.contains_x(q2);
+            let z2 = self.contains_z(q2);
+            self.set_components(q1, x1, z1 ^ x2 ^ z2);
+            self.set_components(q2, x2 ^ x1, z2 ^ x1);
+        }
+        self
+    }
+
+    #[inline]
+    fn cz(&mut self, pairs: &[(QubitId, QubitId)]) -> &mut Self {
+        for &(q1, q2) in pairs {
+            let q1 = q1.index();
+            let q2 = q2.index();
+            let x1 = self.contains_x(q1);
+            let z1 = self.contains_z(q1);
+            let x2 = self.contains_x(q2);
+            let z2 = self.contains_z(q2);
+            self.set_components(q1, x1, z1 ^ x2);
+            self.set_components(q2, x2, z2 ^ x1);
+        }
+        self
+    }
+
+    #[inline]
+    fn sxx(&mut self, pairs: &[(QubitId, QubitId)]) -> &mut Self {
+        for &(q1, q2) in pairs {
+            let q1 = q1.index();
+            let q2 = q2.index();
+            let x1 = self.contains_x(q1);
+            let z1 = self.contains_z(q1);
+            let x2 = self.contains_x(q2);
+            let z2 = self.contains_z(q2);
+            let affected = z1 ^ z2;
+            self.set_components(q1, x1 ^ affected, z1);
+            self.set_components(q2, x2 ^ affected, z2);
+        }
+        self
+    }
+
+    #[inline]
+    fn sxxdg(&mut self, pairs: &[(QubitId, QubitId)]) -> &mut Self {
+        self.sxx(pairs)
+    }
+
+    #[inline]
+    fn syy(&mut self, pairs: &[(QubitId, QubitId)]) -> &mut Self {
+        for &(q1, q2) in pairs {
+            let q1 = q1.index();
+            let q2 = q2.index();
+            let x1 = self.contains_x(q1);
+            let z1 = self.contains_z(q1);
+            let x2 = self.contains_x(q2);
+            let z2 = self.contains_z(q2);
+            self.set_components(q1, x2 ^ z1 ^ z2, x1 ^ x2 ^ z2);
+            self.set_components(q2, x1 ^ z1 ^ z2, x1 ^ x2 ^ z1);
+        }
+        self
+    }
+
+    #[inline]
+    fn syydg(&mut self, pairs: &[(QubitId, QubitId)]) -> &mut Self {
+        self.syy(pairs)
+    }
+
+    #[inline]
+    fn szz(&mut self, pairs: &[(QubitId, QubitId)]) -> &mut Self {
+        for &(q1, q2) in pairs {
+            let q1 = q1.index();
+            let q2 = q2.index();
+            let x1 = self.contains_x(q1);
+            let z1 = self.contains_z(q1);
+            let x2 = self.contains_x(q2);
+            let z2 = self.contains_z(q2);
+            let affected = x1 ^ x2;
+            self.set_components(q1, x1, z1 ^ affected);
+            self.set_components(q2, x2, z2 ^ affected);
+        }
+        self
+    }
+
+    #[inline]
+    fn szzdg(&mut self, pairs: &[(QubitId, QubitId)]) -> &mut Self {
+        self.szz(pairs)
+    }
+
+    #[inline]
+    fn swap(&mut self, pairs: &[(QubitId, QubitId)]) -> &mut Self {
+        for &(q1, q2) in pairs {
+            let q1 = q1.index();
+            let q2 = q2.index();
+            let x1 = self.contains_x(q1);
+            let z1 = self.contains_z(q1);
+            let x2 = self.contains_x(q2);
+            let z2 = self.contains_z(q2);
+            self.set_components(q1, x2, z2);
+            self.set_components(q2, x1, z1);
+        }
+        self
+    }
+
+    #[inline]
+    fn mz(&mut self, qubits: &[QubitId]) -> Vec<MeasurementResult> {
+        qubits
+            .iter()
+            .map(|&q| MeasurementResult {
+                outcome: self.contains_x(q.index()),
+                is_deterministic: true,
+            })
+            .collect()
+    }
+}
+
+#[cfg(test)]
+mod tests {
+    use super::*;
+    use crate::pauli_prop::PauliProp;
+    use pecos_core::QubitId;
+
+    fn all_paulis(num_qubits: usize) -> Vec<String> {
+        let labels = ['I', 'X', 'Y', 'Z'];
+        let mut out = Vec::new();
+        let total = 4usize.pow(num_qubits.try_into().expect("test qubit count fits"));
+        for mut value in 0..total {
+            let mut s = String::with_capacity(num_qubits);
+            for _ in 0..num_qubits {
+                s.push(labels[value % 4]);
+                value /= 4;
+            }
+            out.push(s);
+        }
+        out
+    }
+
+    fn sparse_prop_from_dense(input: &str) -> PauliProp {
+        let mut prop = PauliProp::with_sign_tracking(input.len());
+        for (q, p) in input.chars().enumerate() {
+            match p {
+                'I' => {}
+                'X' => prop.track_x(&[q]),
+                'Y' => prop.track_y(&[q]),
+                'Z' => prop.track_z(&[q]),
+                _ => panic!("invalid Pauli label {p}"),
+            }
+        }
+        prop
+    }
+
+    fn bitmask_prop_from_dense(input: &str) -> BitmaskPauliProp {
+        let mut prop = BitmaskPauliProp::with_num_qubits(input.len());
+        for (q, p) in input.chars().enumerate() {
+            match p {
+                'I' => {}
+                'X' => prop.track_x(&[q]),
+                'Y' => prop.track_y(&[q]),
+                'Z' => prop.track_z(&[q]),
+                _ => panic!("invalid Pauli label {p}"),
+            }
+        }
+        prop
+    }
+
+    fn assert_matches_sparse_1q<F, G>(name: &str, mut apply_sparse: F, mut apply_bitmask: G)
+    where
+        F: FnMut(&mut PauliProp),
+        G: FnMut(&mut BitmaskPauliProp),
+    {
+        for input in all_paulis(1) {
+            let mut sparse = sparse_prop_from_dense(&input);
+            let mut bitmask = bitmask_prop_from_dense(&input);
+            apply_sparse(&mut sparse);
+            apply_bitmask(&mut bitmask);
+            assert_eq!(
+                bitmask.dense_string(),
+                sparse.dense_string(),
+                "{name}: {input}"
+            );
+        }
+    }
+
+    fn assert_matches_sparse_2q<F, G>(name: &str, mut apply_sparse: F, mut apply_bitmask: G)
+    where
+        F: FnMut(&mut PauliProp, &[(QubitId, QubitId)]),
+        G: FnMut(&mut BitmaskPauliProp, &[(QubitId, QubitId)]),
+    {
+        let pair = [(QubitId(0), QubitId(1))];
+        for input in all_paulis(2) {
+            let mut sparse = sparse_prop_from_dense(&input);
+            let mut bitmask = bitmask_prop_from_dense(&input);
+            apply_sparse(&mut sparse, &pair);
+            apply_bitmask(&mut bitmask, &pair);
+            assert_eq!(
+                bitmask.dense_string(),
+                sparse.dense_string(),
+                "{name}: {input}"
+            );
+        }
+    }
+
+    fn assert_matches_sparse_2q_at_pair<F, G>(
+        name: &str,
+        pair: (QubitId, QubitId),
+        num_qubits: usize,
+        mut apply_sparse: F,
+        mut apply_bitmask: G,
+    ) where
+        F: FnMut(&mut PauliProp, &[(QubitId, QubitId)]),
+        G: FnMut(&mut BitmaskPauliProp, &[(QubitId, QubitId)]),
+    {
+        let labels = ['I', 'X', 'Y', 'Z'];
+        let pairs = [pair];
+        for lhs in labels {
+            for rhs in labels {
+                let mut input = vec!['I'; num_qubits];
+                input[pair.0.0] = lhs;
+                input[pair.1.0] = rhs;
+                let input = input.into_iter().collect::<String>();
+
+                let mut sparse = sparse_prop_from_dense(&input);
+                let mut bitmask = bitmask_prop_from_dense(&input);
+                apply_sparse(&mut sparse, &pairs);
+                apply_bitmask(&mut bitmask, &pairs);
+                assert_eq!(
+                    bitmask.dense_string(),
+                    sparse.dense_string(),
+                    "{name}: pair {pair:?}, input {input}"
+                );
+            }
+        }
+    }
+
+    fn assert_phase_free_1q_table<F>(name: &str, mut apply: F, table: &[(&str, &str)])
+    where
+        F: FnMut(&mut BitmaskPauliProp),
+    {
+        for &(input, expected) in table {
+            let mut prop = bitmask_prop_from_dense(input);
+            apply(&mut prop);
+            assert_eq!(prop.dense_string(), expected, "{name}: {input}");
+        }
+    }
+
+    fn assert_phase_free_2q_table<F>(name: &str, mut apply: F, table: &[(&str, &str)])
+    where
+        F: FnMut(&mut BitmaskPauliProp),
+    {
+        for &(input, expected) in table {
+            let mut prop = bitmask_prop_from_dense(input);
+            apply(&mut prop);
+            assert_eq!(prop.dense_string(), expected, "{name}: {input}");
+        }
+    }
+
+    #[test]
+    fn single_qubit_cliffords_match_sparse_pauli_prop() {
+        assert_matches_sparse_1q(
+            "H",
+            |p| {
+                p.h(&[QubitId(0)]);
+            },
+            |p| {
+                p.h(&[QubitId(0)]);
+            },
+        );
+        assert_matches_sparse_1q(
+            "SZ",
+            |p| {
+                p.sz(&[QubitId(0)]);
+            },
+            |p| {
+                p.sz(&[QubitId(0)]);
+            },
+        );
+        assert_matches_sparse_1q(
+            "SZdg",
+            |p| {
+                p.szdg(&[QubitId(0)]);
+            },
+            |p| {
+                p.szdg(&[QubitId(0)]);
+            },
+        );
+        assert_matches_sparse_1q(
+            "SX",
+            |p| {
+                p.sx(&[QubitId(0)]);
+            },
+            |p| {
+                p.sx(&[QubitId(0)]);
+            },
+        );
+        assert_matches_sparse_1q(
+            "SXdg",
+            |p| {
+                p.sxdg(&[QubitId(0)]);
+            },
+            |p| {
+                p.sxdg(&[QubitId(0)]);
+            },
+        );
+        assert_matches_sparse_1q(
+            "SY",
+            |p| {
+                p.sy(&[QubitId(0)]);
+            },
+            |p| {
+                p.sy(&[QubitId(0)]);
+            },
+        );
+        assert_matches_sparse_1q(
+            "SYdg",
+            |p| {
+                p.sydg(&[QubitId(0)]);
+            },
+            |p| {
+                p.sydg(&[QubitId(0)]);
+            },
+        );
+        assert_matches_sparse_1q(
+            "F",
+            |p| {
+                p.f(&[QubitId(0)]);
+            },
+            |p| {
+                p.f(&[QubitId(0)]);
+            },
+        );
+        assert_matches_sparse_1q(
+            "Fdg",
+            |p| {
+                p.fdg(&[QubitId(0)]);
+            },
+            |p| {
+                p.fdg(&[QubitId(0)]);
+            },
+        );
+    }
+
+    #[test]
+    fn standard_cliffords_match_phase_free_pauli_tables() {
+        const PAULI_SELF: &[(&str, &str)] = &[("I", "I"), ("X", "X"), ("Y", "Y"), ("Z", "Z")];
+        const H_SY: &[(&str, &str)] = &[("I", "I"), ("X", "Z"), ("Y", "Y"), ("Z", "X")];
+        const SZ: &[(&str, &str)] = &[("I", "I"), ("X", "Y"), ("Y", "X"), ("Z", "Z")];
+        const SX: &[(&str, &str)] = &[("I", "I"), ("X", "X"), ("Y", "Z"), ("Z", "Y")];
+        const F: &[(&str, &str)] = &[("I", "I"), ("X", "Y"), ("Y", "Z"), ("Z", "X")];
+        const FDG: &[(&str, &str)] = &[("I", "I"), ("X", "Z"), ("Y", "X"), ("Z", "Y")];
+        const CX: &[(&str, &str)] = &[
+            ("XI", "XX"),
+            ("YI", "YX"),
+            ("ZI", "ZI"),
+            ("IX", "IX"),
+            ("IY", "ZY"),
+            ("IZ", "ZZ"),
+        ];
+        const CY: &[(&str, &str)] = &[
+            ("XI", "XY"),
+            ("YI", "YY"),
+            ("ZI", "ZI"),
+            ("IX", "ZX"),
+            ("IY", "IY"),
+            ("IZ", "ZZ"),
+        ];
+        const CZ: &[(&str, &str)] = &[
+            ("XI", "XZ"),
+            ("YI", "YZ"),
+            ("ZI", "ZI"),
+            ("IX", "ZX"),
+            ("IY", "ZY"),
+            ("IZ", "IZ"),
+        ];
+        const SXX: &[(&str, &str)] = &[
+            ("XI", "XI"),
+            ("YI", "ZX"),
+            ("ZI", "YX"),
+            ("IX", "IX"),
+            ("IY", "XZ"),
+            ("IZ", "XY"),
+        ];
+        const SYY: &[(&str, &str)] = &[
+            ("XI", "ZY"),
+            ("YI", "YI"),
+            ("ZI", "XY"),
+            ("IX", "YZ"),
+            ("IY", "IY"),
+            ("IZ", "YX"),
+        ];
+        const SZZ: &[(&str, &str)] = &[
+            ("XI", "YZ"),
+            ("YI", "XZ"),
+            ("ZI", "ZI"),
+            ("IX", "ZY"),
+            ("IY", "ZX"),
+            ("IZ", "IZ"),
+        ];
+        const SWAP: &[(&str, &str)] = &[
+            ("XI", "IX"),
+            ("YI", "IY"),
+            ("ZI", "IZ"),
+            ("IX", "XI"),
+            ("IY", "YI"),
+            ("IZ", "ZI"),
+        ];
+
+        assert_phase_free_1q_table(
+            "X",
+            |p| {
+                p.x(&[QubitId(0)]);
+            },
+            PAULI_SELF,
+        );
+        assert_phase_free_1q_table(
+            "Y",
+            |p| {
+                p.y(&[QubitId(0)]);
+            },
+            PAULI_SELF,
+        );
+        assert_phase_free_1q_table(
+            "Z",
+            |p| {
+                p.z(&[QubitId(0)]);
+            },
+            PAULI_SELF,
+        );
+        assert_phase_free_1q_table(
+            "H",
+            |p| {
+                p.h(&[QubitId(0)]);
+            },
+            H_SY,
+        );
+        assert_phase_free_1q_table(
+            "SZ",
+            |p| {
+                p.sz(&[QubitId(0)]);
+            },
+            SZ,
+        );
+        assert_phase_free_1q_table(
+            "SZdg",
+            |p| {
+                p.szdg(&[QubitId(0)]);
+            },
+            SZ,
+        );
+        assert_phase_free_1q_table(
+            "SX",
+            |p| {
+                p.sx(&[QubitId(0)]);
+            },
+            SX,
+        );
+        assert_phase_free_1q_table(
+            "SXdg",
+            |p| {
+                p.sxdg(&[QubitId(0)]);
+            },
+            SX,
+        );
+        assert_phase_free_1q_table(
+            "SY",
+            |p| {
+                p.sy(&[QubitId(0)]);
+            },
+            H_SY,
+        );
+        assert_phase_free_1q_table(
+            "SYdg",
+            |p| {
+                p.sydg(&[QubitId(0)]);
+            },
+            H_SY,
+        );
+        assert_phase_free_1q_table(
+            "F",
+            |p| {
+                p.f(&[QubitId(0)]);
+            },
+            F,
+        );
+        assert_phase_free_1q_table(
+            "Fdg",
+            |p| {
+                p.fdg(&[QubitId(0)]);
+            },
+            FDG,
+        );
+
+        let pair = [(QubitId(0), QubitId(1))];
+        assert_phase_free_2q_table(
+            "CX",
+            |p| {
+                p.cx(&pair);
+            },
+            CX,
+        );
+        assert_phase_free_2q_table(
+            "CY",
+            |p| {
+                p.cy(&pair);
+            },
+            CY,
+        );
+        assert_phase_free_2q_table(
+            "CZ",
+            |p| {
+                p.cz(&pair);
+            },
+            CZ,
+        );
+        assert_phase_free_2q_table(
+            "SXX",
+            |p| {
+                p.sxx(&pair);
+            },
+            SXX,
+        );
+        assert_phase_free_2q_table(
+            "SXXdg",
+            |p| {
+                p.sxxdg(&pair);
+            },
+            SXX,
+        );
+        assert_phase_free_2q_table(
+            "SYY",
+            |p| {
+                p.syy(&pair);
+            },
+            SYY,
+        );
+        assert_phase_free_2q_table(
+            "SYYdg",
+            |p| {
+                p.syydg(&pair);
+            },
+            SYY,
+        );
+        assert_phase_free_2q_table(
+            "SZZ",
+            |p| {
+                p.szz(&pair);
+            },
+            SZZ,
+        );
+        assert_phase_free_2q_table(
+            "SZZdg",
+            |p| {
+                p.szzdg(&pair);
+            },
+            SZZ,
+        );
+        assert_phase_free_2q_table(
+            "SWAP",
+            |p| {
+                p.swap(&pair);
+            },
+            SWAP,
+        );
+    }
+
+    #[test]
+    fn two_qubit_cliffords_match_sparse_pauli_prop() {
+        assert_matches_sparse_2q(
+            "CX",
+            |p, qs| {
+                p.cx(qs);
+            },
+            |p, qs| {
+                p.cx(qs);
+            },
+        );
+        assert_matches_sparse_2q(
+            "CY",
+            |p, qs| {
+                p.cy(qs);
+            },
+            |p, qs| {
+                p.cy(qs);
+            },
+        );
+        assert_matches_sparse_2q(
+            "CZ",
+            |p, qs| {
+                p.cz(qs);
+            },
+            |p, qs| {
+                p.cz(qs);
+            },
+        );
+        assert_matches_sparse_2q(
+            "SXX",
+            |p, qs| {
+                p.sxx(qs);
+            },
+            |p, qs| {
+                p.sxx(qs);
+            },
+        );
+        assert_matches_sparse_2q(
+            "SXXdg",
+            |p, qs| {
+                p.sxxdg(qs);
+            },
+            |p, qs| {
+                p.sxxdg(qs);
+            },
+        );
+        assert_matches_sparse_2q(
+            "SYY",
+            |p, qs| {
+                p.syy(qs);
+            },
+            |p, qs| {
+                p.syy(qs);
+            },
+        );
+        assert_matches_sparse_2q(
+            "SYYdg",
+            |p, qs| {
+                p.syydg(qs);
+            },
+            |p, qs| {
+                p.syydg(qs);
+            },
+        );
+        assert_matches_sparse_2q(
+            "SZZ",
+            |p, qs| {
+                p.szz(qs);
+            },
+            |p, qs| {
+                p.szz(qs);
+            },
+        );
+        assert_matches_sparse_2q(
+            "SZZdg",
+            |p, qs| {
+                p.szzdg(qs);
+            },
+            |p, qs| {
+                p.szzdg(qs);
+            },
+        );
+        assert_matches_sparse_2q(
+            "SWAP",
+            |p, qs| {
+                p.swap(qs);
+            },
+            |p, qs| {
+                p.swap(qs);
+            },
+        );
+        assert_matches_sparse_2q(
+            "ISWAP",
+            |p, qs| {
+                p.iswap(qs);
+            },
+            |p, qs| {
+                p.iswap(qs);
+            },
+        );
+        assert_matches_sparse_2q(
+            "ISWAPdg",
+            |p, qs| {
+                p.iswapdg(qs);
+            },
+            |p, qs| {
+                p.iswapdg(qs);
+            },
+        );
+    }
+
+    #[test]
+    fn two_qubit_cliffords_match_sparse_pauli_prop_across_word_boundaries() {
+        for pair in [
+            (QubitId(63), QubitId(64)),
+            (QubitId(64), QubitId(63)),
+            (QubitId(64), QubitId(65)),
+        ] {
+            assert_matches_sparse_2q_at_pair(
+                "CX",
+                pair,
+                66,
+                |p, qs| {
+                    p.cx(qs);
+                },
+                |p, qs| {
+                    p.cx(qs);
+                },
+            );
+            assert_matches_sparse_2q_at_pair(
+                "CY",
+                pair,
+                66,
+                |p, qs| {
+                    p.cy(qs);
+                },
+                |p, qs| {
+                    p.cy(qs);
+                },
+            );
+            assert_matches_sparse_2q_at_pair(
+                "CZ",
+                pair,
+                66,
+                |p, qs| {
+                    p.cz(qs);
+                },
+                |p, qs| {
+                    p.cz(qs);
+                },
+            );
+            assert_matches_sparse_2q_at_pair(
+                "SXX",
+                pair,
+                66,
+                |p, qs| {
+                    p.sxx(qs);
+                },
+                |p, qs| {
+                    p.sxx(qs);
+                },
+            );
+            assert_matches_sparse_2q_at_pair(
+                "SXXdg",
+                pair,
+                66,
+                |p, qs| {
+                    p.sxxdg(qs);
+                },
+                |p, qs| {
+                    p.sxxdg(qs);
+                },
+            );
+            assert_matches_sparse_2q_at_pair(
+                "SYY",
+                pair,
+                66,
+                |p, qs| {
+                    p.syy(qs);
+                },
+                |p, qs| {
+                    p.syy(qs);
+                },
+            );
+            assert_matches_sparse_2q_at_pair(
+                "SYYdg",
+                pair,
+                66,
+                |p, qs| {
+                    p.syydg(qs);
+                },
+                |p, qs| {
+                    p.syydg(qs);
+                },
+            );
+            assert_matches_sparse_2q_at_pair(
+                "SZZ",
+                pair,
+                66,
+                |p, qs| {
+                    p.szz(qs);
+                },
+                |p, qs| {
+                    p.szz(qs);
+                },
+            );
+            assert_matches_sparse_2q_at_pair(
+                "SZZdg",
+                pair,
+                66,
+                |p, qs| {
+                    p.szzdg(qs);
+                },
+                |p, qs| {
+                    p.szzdg(qs);
+                },
+            );
+            assert_matches_sparse_2q_at_pair(
+                "SWAP",
+                pair,
+                66,
+                |p, qs| {
+                    p.swap(qs);
+                },
+                |p, qs| {
+                    p.swap(qs);
+                },
+            );
+            assert_matches_sparse_2q_at_pair(
+                "ISWAP",
+                pair,
+                66,
+                |p, qs| {
+                    p.iswap(qs);
+                },
+                |p, qs| {
+                    p.iswap(qs);
+                },
+            );
+            assert_matches_sparse_2q_at_pair(
+                "ISWAPdg",
+                pair,
+                66,
+                |p, qs| {
+                    p.iswapdg(qs);
+                },
+                |p, qs| {
+                    p.iswapdg(qs);
+                },
+            );
+        }
+    }
+
+    #[test]
+    fn word_boundary_propagation_matches_sparse_pauli_prop() {
+        let qubits = [63, 64, 65];
+        let qids = qubits.map(QubitId);
+        let mut sparse = PauliProp::with_sign_tracking(66);
+        let mut bitmask = BitmaskPauliProp::with_num_qubits(66);
+
+        sparse.track_z(&qubits);
+        bitmask.track_z(&qubits);
+        sparse.h(&qids);
+        bitmask.h(&qids);
+
+        assert_eq!(bitmask.dense_string(), sparse.dense_string());
+
+        let sparse_meas = sparse.mz(&qids);
+        let bitmask_meas = bitmask.mz(&qids);
+        assert_eq!(
+            bitmask_meas.iter().map(|m| m.outcome).collect::<Vec<_>>(),
+            sparse_meas.iter().map(|m| m.outcome).collect::<Vec<_>>()
+        );
+        assert_eq!(
+            bitmask_meas
+                .iter()
+                .map(|m| m.is_deterministic)
+                .collect::<Vec<_>>(),
+            sparse_meas
+                .iter()
+                .map(|m| m.is_deterministic)
+                .collect::<Vec<_>>()
+        );
+    }
+
+    #[test]
+    fn sequential_gate_composition_matches_sparse_pauli_prop() {
+        let sequence = |sparse: &mut PauliProp, bitmask: &mut BitmaskPauliProp| {
+            sparse
+                .h(&[QubitId(0)])
+                .sz(&[QubitId(1)])
+                .cx(&[(QubitId(0), QubitId(1))])
+                .sxx(&[(QubitId(1), QubitId(2))])
+                .iswap(&[(QubitId(0), QubitId(2))])
+                .sydg(&[QubitId(2)])
+                .cz(&[(QubitId(2), QubitId(1))])
+                .swap(&[(QubitId(0), QubitId(1))]);
+            bitmask
+                .h(&[QubitId(0)])
+                .sz(&[QubitId(1)])
+                .cx(&[(QubitId(0), QubitId(1))])
+                .sxx(&[(QubitId(1), QubitId(2))])
+                .iswap(&[(QubitId(0), QubitId(2))])
+                .sydg(&[QubitId(2)])
+                .cz(&[(QubitId(2), QubitId(1))])
+                .swap(&[(QubitId(0), QubitId(1))]);
+        };
+
+        for input in all_paulis(3) {
+            let mut sparse = sparse_prop_from_dense(&input);
+            let mut bitmask = bitmask_prop_from_dense(&input);
+            sequence(&mut sparse, &mut bitmask);
+            assert_eq!(
+                bitmask.dense_string(),
+                sparse.dense_string(),
+                "sequential composition: {input}"
+            );
+        }
+    }
+
+    #[test]
+    fn measurement_reset_and_identity_match_fault_catalog_semantics() {
+        let mut prop = BitmaskPauliProp::with_num_qubits(3);
+        prop.track_y(&[1]);
+
+        let meas = prop.mz(&[QubitId(0), QubitId(1), QubitId(2)]);
+        assert_eq!(
+            meas.iter().map(|m| m.outcome).collect::<Vec<_>>(),
+            vec![false, true, false]
+        );
+        assert!(meas.iter().all(|m| m.is_deterministic));
+
+        prop.clear_qubit(1);
+        assert!(prop.is_identity());
+
+        prop.track_z(&[2]);
+        assert_eq!(prop.weight(), 1);
+        prop.reset();
+        assert!(prop.is_identity());
+    }
+}
diff --git a/crates/pecos-simulators/src/circuit_executor.rs b/crates/pecos-simulators/src/circuit_executor.rs
index 219f9178a..18261f0d1 100644
--- a/crates/pecos-simulators/src/circuit_executor.rs
+++ b/crates/pecos-simulators/src/circuit_executor.rs
@@ -12,9 +12,10 @@
 
 //! Batched circuit execution for Clifford simulators.
 //!
-//! This module provides efficient circuit execution using the batched gate groups
-//! from `TickCircuitSoA`. Instead of dispatching each gate individually, gates of
-//! the same type are applied as a single batch call.
+//! This module provides efficient circuit execution using the full-fidelity
+//! batched gate commands stored by `TickCircuit`. Instead of dispatching each
+//! individual gate application, stored batched commands are applied as one
+//! simulator call.
 //!
 //! # Performance Benefits
 //!
@@ -26,15 +27,13 @@
 //!
 //! ```
 //! use pecos_simulators::{SparseStab, CircuitExecutor};
-//! use pecos_quantum::TickCircuitSoA;
+//! use pecos_quantum::TickCircuit;
 //!
-//! let mut builder = TickCircuitSoA::builder();
-//! builder
-//!     .tick().pz(&[0, 1, 2, 3])
-//!     .tick().h(&[0, 1, 2, 3])
-//!     .tick().cx(&[(0, 1), (2, 3)])
-//!     .tick().mz(&[0, 1, 2, 3]);
-//! let circuit = builder.build();
+//! let mut circuit = TickCircuit::new();
+//! circuit.tick().pz(&[0, 1, 2, 3]);
+//! circuit.tick().h(&[0, 1, 2, 3]);
+//! circuit.tick().cx(&[(0, 1), (2, 3)]);
+//! circuit.tick().mz(&[0, 1, 2, 3]);
 //!
 //! let mut sim = SparseStab::new(4);
 //! let executor = CircuitExecutor::new(&circuit);
@@ -42,9 +41,9 @@
 //! ```
 
 use crate::{CliffordGateable, MeasurementResult};
-use pecos_core::QubitId;
 use pecos_core::gate_type::GateType;
-use pecos_quantum::{GateBatch, TickBatches, TickCircuitSoA, TickGateGroups};
+use pecos_core::{Gate, QubitId};
+use pecos_quantum::TickCircuit;
 use smallvec::SmallVec;
 
 /// Convert a flat qubit slice `[c0, t0, c1, t1, ...]` to a vec of pairs.
@@ -55,20 +54,20 @@ fn flat_to_pairs(qubits: &[QubitId]) -> SmallVec<[(QubitId, QubitId); 4]> {
         .collect()
 }
 
-/// Executes a `TickCircuitSoA` on a Clifford simulator using batched operations.
+/// Executes a `TickCircuit` on a Clifford simulator using batched operations.
 ///
-/// This executor leverages the pre-grouped gate batches in `TickCircuitSoA` for
-/// efficient execution with minimal dispatch overhead.
+/// This executor leverages the full-fidelity batched gate commands in
+/// `TickCircuit` for efficient execution with minimal dispatch overhead.
 pub struct CircuitExecutor<'a> {
     /// The circuit to execute.
-    circuit: &'a TickCircuitSoA,
+    circuit: &'a TickCircuit,
 }
 
 impl<'a> CircuitExecutor<'a> {
     /// Creates a new executor for the given circuit.
     #[inline]
     #[must_use]
-    pub fn new(circuit: &'a TickCircuitSoA) -> Self {
+    pub fn new(circuit: &'a TickCircuit) -> Self {
         Self { circuit }
     }
 
@@ -78,66 +77,38 @@ impl<'a> CircuitExecutor<'a> {
     pub fn run<S: CliffordGateable>(&self, sim: &mut S) -> Vec<MeasurementResult> {
         let mut measurements = Vec::new();
 
-        for (_tick_idx, tick) in self.circuit.iter_ticks_batched() {
-            Self::execute_tick(sim, tick, &mut measurements);
+        for (_tick_idx, tick) in self.circuit.iter_ticks() {
+            for batch in tick.iter_gate_batches() {
+                Self::execute_gate_batch(sim, batch.as_gate(), &mut measurements);
+            }
         }
 
         measurements
     }
 
-    /// Runs a single tick on the simulator.
-    #[inline]
-    fn execute_tick<S: CliffordGateable>(
-        sim: &mut S,
-        tick: &TickBatches,
-        measurements: &mut Vec<MeasurementResult>,
-    ) {
-        for batch in tick.iter() {
-            Self::execute_batch(sim, batch, measurements);
-        }
-    }
-
-    /// Executes a single batch of gates.
+    /// Executes a single full-fidelity batched gate command.
     ///
     /// This is the core dispatch function - one match per batch, not per gate.
     #[inline]
-    fn execute_batch<S: CliffordGateable>(
+    fn execute_gate_batch<S: CliffordGateable>(
         sim: &mut S,
-        batch: &GateBatch,
+        batch: &Gate,
         measurements: &mut Vec<MeasurementResult>,
     ) {
-        execute_single_batch(sim, batch, measurements);
+        execute_gate_command(sim, batch, measurements);
     }
 }
 
-/// Executes a `TickGateGroups` directly on a simulator.
-///
-/// This is a simpler interface when you have gate groups but not the full circuit.
-pub fn execute_batched<S: CliffordGateable>(
-    groups: &TickGateGroups,
-    sim: &mut S,
-) -> Vec<MeasurementResult> {
-    let mut measurements = Vec::new();
-
-    for (_tick_idx, tick) in groups.iter_ticks() {
-        for batch in tick.iter() {
-            execute_single_batch(sim, batch, &mut measurements);
-        }
-    }
-
-    measurements
-}
-
-/// Executes a single batch on a simulator.
+/// Executes one full-fidelity `TickCircuit` gate command on a simulator.
 #[inline]
-fn execute_single_batch<S: CliffordGateable>(
+fn execute_gate_command<S: CliffordGateable>(
     sim: &mut S,
-    batch: &GateBatch,
+    gate: &Gate,
     measurements: &mut Vec<MeasurementResult>,
 ) {
-    let qubits = batch.qubits();
+    let qubits = gate.qubits.as_slice();
 
-    match batch.gate_type {
+    match gate.gate_type {
         GateType::I => {
             sim.identity(qubits);
         }
@@ -287,22 +258,15 @@ impl<S: CliffordGateable> GateSystemRegistry<S> {
 mod tests {
     use super::*;
     use crate::SparseStab;
-    use pecos_quantum::TickCircuitSoA;
+    use pecos_quantum::TickCircuit;
 
     #[test]
     fn test_circuit_executor_basic() {
-        let mut builder = TickCircuitSoA::builder();
-        builder
-            .tick()
-            .pz(&[0, 1])
-            .tick()
-            .h(&[0])
-            .tick()
-            .cx(&[(0, 1)])
-            .tick()
-            .mz(&[0, 1]);
-
-        let circuit = builder.build();
+        let mut circuit = TickCircuit::new();
+        circuit.tick().pz(&[0, 1]);
+        circuit.tick().h(&[0]);
+        circuit.tick().cx(&[(0, 1)]);
+        circuit.tick().mz(&[0, 1]);
 
         let mut sim = SparseStab::new(2);
         let executor = CircuitExecutor::new(&circuit);
@@ -315,18 +279,11 @@ mod tests {
     #[test]
     fn test_circuit_executor_batched_gates() {
         // Create a circuit with multiple gates of same type per tick
-        let mut builder = TickCircuitSoA::builder();
-        builder
-            .tick()
-            .pz(&[0, 1, 2, 3]) // 4 preps in one batch
-            .tick()
-            .h(&[0, 1, 2, 3]) // 4 H gates in one batch
-            .tick()
-            .cx(&[(0, 1), (2, 3)]) // 2 CX gates in one batch
-            .tick()
-            .mz(&[0, 1, 2, 3]); // 4 measurements in one batch
-
-        let circuit = builder.build();
+        let mut circuit = TickCircuit::new();
+        circuit.tick().pz(&[0, 1, 2, 3]); // 4 preps in one batch
+        circuit.tick().h(&[0, 1, 2, 3]); // 4 H gates in one batch
+        circuit.tick().cx(&[(0, 1), (2, 3)]); // 2 CX gates in one batch
+        circuit.tick().mz(&[0, 1, 2, 3]); // 4 measurements in one batch
 
         let mut sim = SparseStab::new(4);
         let executor = CircuitExecutor::new(&circuit);
@@ -335,23 +292,4 @@ mod tests {
         // Should have 4 measurements
         assert_eq!(measurements.len(), 4);
     }
-
-    #[test]
-    fn test_execute_batched_function() {
-        let mut builder = TickCircuitSoA::builder();
-        builder
-            .tick()
-            .pz(&[0, 1])
-            .tick()
-            .h(&[0, 1])
-            .tick()
-            .mz(&[0, 1]);
-
-        let circuit = builder.build();
-
-        let mut sim = SparseStab::new(2);
-        let measurements = execute_batched(&circuit.batched, &mut sim);
-
-        assert_eq!(measurements.len(), 2);
-    }
 }
diff --git a/crates/pecos-simulators/src/clifford_matrix_oracle.rs b/crates/pecos-simulators/src/clifford_matrix_oracle.rs
new file mode 100644
index 000000000..b008b98f2
--- /dev/null
+++ b/crates/pecos-simulators/src/clifford_matrix_oracle.rs
@@ -0,0 +1,316 @@
+// Copyright 2026 The PECOS Developers
+// Licensed under the Apache License, Version 2.0
+
+use num_complex::Complex64;
+use std::f64::consts::FRAC_1_SQRT_2;
+
+const MATRIX_EPS: f64 = 1e-9;
+
+#[derive(Clone, Copy, Debug)]
+#[allow(clippy::upper_case_acronyms)]
+pub(crate) enum CliffordMatrixGate {
+    SZdg,
+    F,
+    Fdg,
+    SX,
+    SXdg,
+    SY,
+    SYdg,
+    CX,
+    CY,
+    CZ,
+    SXX,
+    SXXdg,
+    SYY,
+    SYYdg,
+    SZZ,
+    SZZdg,
+    SWAP,
+}
+
+#[derive(Clone, Debug, PartialEq, Eq)]
+pub(crate) struct SignedPauli {
+    pub(crate) sign: i8,
+    pub(crate) pauli: String,
+}
+
+#[derive(Clone, Debug)]
+struct Matrix {
+    n: usize,
+    data: Vec<Complex64>,
+}
+
+impl Matrix {
+    fn from_data(n: usize, data: Vec<Complex64>) -> Self {
+        assert_eq!(data.len(), n * n);
+        Self { n, data }
+    }
+
+    fn zeros(n: usize) -> Self {
+        Self {
+            n,
+            data: vec![Complex64::new(0.0, 0.0); n * n],
+        }
+    }
+
+    fn identity(n: usize) -> Self {
+        let mut matrix = Self::zeros(n);
+        for i in 0..n {
+            matrix.set(i, i, Complex64::new(1.0, 0.0));
+        }
+        matrix
+    }
+
+    fn get(&self, row: usize, col: usize) -> Complex64 {
+        self.data[row * self.n + col]
+    }
+
+    fn set(&mut self, row: usize, col: usize, value: Complex64) {
+        self.data[row * self.n + col] = value;
+    }
+
+    fn add(&self, other: &Self) -> Self {
+        assert_eq!(self.n, other.n);
+        let data = self
+            .data
+            .iter()
+            .zip(other.data.iter())
+            .map(|(a, b)| a + b)
+            .collect();
+        Self::from_data(self.n, data)
+    }
+
+    fn scale(&self, scalar: Complex64) -> Self {
+        let data = self.data.iter().map(|v| scalar * v).collect();
+        Self::from_data(self.n, data)
+    }
+
+    fn mul(&self, other: &Self) -> Self {
+        assert_eq!(self.n, other.n);
+        let mut out = Self::zeros(self.n);
+        for row in 0..self.n {
+            for col in 0..self.n {
+                let mut value = Complex64::new(0.0, 0.0);
+                for k in 0..self.n {
+                    value += self.get(row, k) * other.get(k, col);
+                }
+                out.set(row, col, value);
+            }
+        }
+        out
+    }
+
+    fn dagger(&self) -> Self {
+        let mut out = Self::zeros(self.n);
+        for row in 0..self.n {
+            for col in 0..self.n {
+                out.set(col, row, self.get(row, col).conj());
+            }
+        }
+        out
+    }
+
+    fn approx_eq(&self, other: &Self) -> bool {
+        assert_eq!(self.n, other.n);
+        self.data
+            .iter()
+            .zip(other.data.iter())
+            .all(|(a, b)| (*a - *b).norm() < MATRIX_EPS)
+    }
+}
+
+pub(crate) fn all_pauli_strings(num_qubits: usize) -> Vec<String> {
+    let mut strings = vec![String::new()];
+    for _ in 0..num_qubits {
+        let mut next = Vec::with_capacity(strings.len() * 4);
+        for prefix in &strings {
+            for suffix in ['I', 'X', 'Y', 'Z'] {
+                let mut value = prefix.clone();
+                value.push(suffix);
+                next.push(value);
+            }
+        }
+        strings = next;
+    }
+    strings
+}
+
+pub(crate) fn conjugate_pauli(gate: CliffordMatrixGate, input: &str) -> SignedPauli {
+    let unitary = gate_matrix(gate);
+    let input_matrix = pauli_string_matrix(input);
+    let image = unitary.mul(&input_matrix).mul(&unitary.dagger());
+    classify_signed_pauli(&image, input.len())
+}
+
+fn classify_signed_pauli(image: &Matrix, num_qubits: usize) -> SignedPauli {
+    for pauli in all_pauli_strings(num_qubits) {
+        let matrix = pauli_string_matrix(&pauli);
+        if image.approx_eq(&matrix) {
+            return SignedPauli { sign: 1, pauli };
+        }
+        if image.approx_eq(&matrix.scale(Complex64::new(-1.0, 0.0))) {
+            return SignedPauli { sign: -1, pauli };
+        }
+    }
+    panic!("matrix image is not a signed Pauli");
+}
+
+fn gate_matrix(gate: CliffordMatrixGate) -> Matrix {
+    match gate {
+        CliffordMatrixGate::SZdg => sqrt_pauli_matrix("Z", true),
+        CliffordMatrixGate::F => sqrt_pauli_matrix("Z", false).mul(&sqrt_pauli_matrix("X", false)),
+        CliffordMatrixGate::Fdg => sqrt_pauli_matrix("X", true).mul(&sqrt_pauli_matrix("Z", true)),
+        CliffordMatrixGate::SX => sqrt_pauli_matrix("X", false),
+        CliffordMatrixGate::SXdg => sqrt_pauli_matrix("X", true),
+        CliffordMatrixGate::SY => sqrt_pauli_matrix("Y", false),
+        CliffordMatrixGate::SYdg => sqrt_pauli_matrix("Y", true),
+        CliffordMatrixGate::CX => controlled_x_matrix(),
+        CliffordMatrixGate::CY => controlled_y_matrix(),
+        CliffordMatrixGate::CZ => controlled_z_matrix(),
+        CliffordMatrixGate::SXX => sqrt_pauli_matrix("XX", false),
+        CliffordMatrixGate::SXXdg => sqrt_pauli_matrix("XX", true),
+        CliffordMatrixGate::SYY => sqrt_pauli_matrix("YY", false),
+        CliffordMatrixGate::SYYdg => sqrt_pauli_matrix("YY", true),
+        CliffordMatrixGate::SZZ => sqrt_pauli_matrix("ZZ", false),
+        CliffordMatrixGate::SZZdg => sqrt_pauli_matrix("ZZ", true),
+        CliffordMatrixGate::SWAP => swap_matrix(),
+    }
+}
+
+fn sqrt_pauli_matrix(pauli: &str, adjoint: bool) -> Matrix {
+    let pauli = pauli_string_matrix(pauli);
+    let identity = Matrix::identity(pauli.n);
+    let phase_sign = if adjoint { 1.0 } else { -1.0 };
+    identity
+        .scale(Complex64::new(FRAC_1_SQRT_2, 0.0))
+        .add(&pauli.scale(Complex64::new(0.0, phase_sign * FRAC_1_SQRT_2)))
+}
+
+fn pauli_string_matrix(pauli: &str) -> Matrix {
+    let mut matrix = Matrix::from_data(1, vec![Complex64::new(1.0, 0.0)]);
+    for label in pauli.chars() {
+        matrix = kron(&matrix, &single_pauli_matrix(label));
+    }
+    matrix
+}
+
+fn single_pauli_matrix(label: char) -> Matrix {
+    let one = Complex64::new(1.0, 0.0);
+    let minus_one = Complex64::new(-1.0, 0.0);
+    let zero = Complex64::new(0.0, 0.0);
+    let i = Complex64::new(0.0, 1.0);
+    let minus_i = Complex64::new(0.0, -1.0);
+
+    match label {
+        'I' => Matrix::from_data(2, vec![one, zero, zero, one]),
+        'X' => Matrix::from_data(2, vec![zero, one, one, zero]),
+        'Y' => Matrix::from_data(2, vec![zero, minus_i, i, zero]),
+        'Z' => Matrix::from_data(2, vec![one, zero, zero, minus_one]),
+        _ => panic!("invalid Pauli label {label}"),
+    }
+}
+
+fn kron(left: &Matrix, right: &Matrix) -> Matrix {
+    let n = left.n * right.n;
+    let mut out = Matrix::zeros(n);
+    for lr in 0..left.n {
+        for lc in 0..left.n {
+            for rr in 0..right.n {
+                for rc in 0..right.n {
+                    out.set(
+                        lr * right.n + rr,
+                        lc * right.n + rc,
+                        left.get(lr, lc) * right.get(rr, rc),
+                    );
+                }
+            }
+        }
+    }
+    out
+}
+
+fn controlled_y_matrix() -> Matrix {
+    let one = Complex64::new(1.0, 0.0);
+    let zero = Complex64::new(0.0, 0.0);
+    let i = Complex64::new(0.0, 1.0);
+    let minus_i = Complex64::new(0.0, -1.0);
+    Matrix::from_data(
+        4,
+        vec![
+            one, zero, zero, zero, zero, one, zero, zero, zero, zero, zero, minus_i, zero, zero, i,
+            zero,
+        ],
+    )
+}
+
+fn controlled_x_matrix() -> Matrix {
+    Matrix::from_data(
+        4,
+        vec![
+            Complex64::new(1.0, 0.0),
+            Complex64::new(0.0, 0.0),
+            Complex64::new(0.0, 0.0),
+            Complex64::new(0.0, 0.0),
+            Complex64::new(0.0, 0.0),
+            Complex64::new(1.0, 0.0),
+            Complex64::new(0.0, 0.0),
+            Complex64::new(0.0, 0.0),
+            Complex64::new(0.0, 0.0),
+            Complex64::new(0.0, 0.0),
+            Complex64::new(0.0, 0.0),
+            Complex64::new(1.0, 0.0),
+            Complex64::new(0.0, 0.0),
+            Complex64::new(0.0, 0.0),
+            Complex64::new(1.0, 0.0),
+            Complex64::new(0.0, 0.0),
+        ],
+    )
+}
+
+fn controlled_z_matrix() -> Matrix {
+    Matrix::from_data(
+        4,
+        vec![
+            Complex64::new(1.0, 0.0),
+            Complex64::new(0.0, 0.0),
+            Complex64::new(0.0, 0.0),
+            Complex64::new(0.0, 0.0),
+            Complex64::new(0.0, 0.0),
+            Complex64::new(1.0, 0.0),
+            Complex64::new(0.0, 0.0),
+            Complex64::new(0.0, 0.0),
+            Complex64::new(0.0, 0.0),
+            Complex64::new(0.0, 0.0),
+            Complex64::new(1.0, 0.0),
+            Complex64::new(0.0, 0.0),
+            Complex64::new(0.0, 0.0),
+            Complex64::new(0.0, 0.0),
+            Complex64::new(0.0, 0.0),
+            Complex64::new(-1.0, 0.0),
+        ],
+    )
+}
+
+fn swap_matrix() -> Matrix {
+    Matrix::from_data(
+        4,
+        vec![
+            Complex64::new(1.0, 0.0),
+            Complex64::new(0.0, 0.0),
+            Complex64::new(0.0, 0.0),
+            Complex64::new(0.0, 0.0),
+            Complex64::new(0.0, 0.0),
+            Complex64::new(0.0, 0.0),
+            Complex64::new(1.0, 0.0),
+            Complex64::new(0.0, 0.0),
+            Complex64::new(0.0, 0.0),
+            Complex64::new(1.0, 0.0),
+            Complex64::new(0.0, 0.0),
+            Complex64::new(0.0, 0.0),
+            Complex64::new(0.0, 0.0),
+            Complex64::new(0.0, 0.0),
+            Complex64::new(0.0, 0.0),
+            Complex64::new(1.0, 0.0),
+        ],
+    )
+}
diff --git a/crates/pecos-simulators/src/dense_stab.rs b/crates/pecos-simulators/src/dense_stab.rs
index fc77da9fd..f0f95559a 100644
--- a/crates/pecos-simulators/src/dense_stab.rs
+++ b/crates/pecos-simulators/src/dense_stab.rs
@@ -51,7 +51,7 @@
 
 use crate::{CliffordGateable, MeasurementResult, QuantumSimulator, StabilizerTableauSimulator};
 use core::fmt::Debug;
-use pecos_core::{QubitId, RngManageable};
+use pecos_core::{Pauli, PauliString, Phase, QuarterPhase, QubitId, RngManageable};
 use pecos_random::rng_ext::RngProbabilityExt;
 use pecos_random::{PecosRng, Rng, SeedableRng};
 
@@ -1348,6 +1348,100 @@ impl<R: SeedableRng + Rng + Debug + Clone> StabilizerTableauSimulator for DenseS
 }
 
 impl<R: Rng> DenseStab<R> {
+    fn generator_from_rows(
+        num_qubits: usize,
+        words_per_row: usize,
+        row_x: &[u64],
+        row_z: &[u64],
+        signs_minus: &[u64],
+        signs_i: &[u64],
+        row: usize,
+    ) -> PauliString {
+        let mut phase = match (get_sign(signs_minus, row), get_sign(signs_i, row)) {
+            (false, false) => QuarterPhase::PlusOne,
+            (true, false) => QuarterPhase::MinusOne,
+            (false, true) => QuarterPhase::PlusI,
+            (true, true) => QuarterPhase::MinusI,
+        };
+        let base = row * words_per_row;
+        let mut paulis = Vec::new();
+        let mut num_y_terms = 0usize;
+        for qubit in 0..num_qubits {
+            let word_idx = base + qubit / 64;
+            let bit_mask = 1u64 << (qubit % 64);
+            let in_x = row_x[word_idx] & bit_mask != 0;
+            let in_z = row_z[word_idx] & bit_mask != 0;
+            let pauli = match (in_x, in_z) {
+                (false, false) => continue,
+                (true, false) => Pauli::X,
+                (false, true) => Pauli::Z,
+                (true, true) => {
+                    num_y_terms += 1;
+                    Pauli::Y
+                }
+            };
+            paulis.push((pauli, QubitId::new(qubit)));
+        }
+        for _ in 0..num_y_terms {
+            phase = phase.multiply(&QuarterPhase::MinusI);
+        }
+        PauliString::with_phase_and_paulis(phase, paulis)
+    }
+
+    fn generators_from_rows(
+        &self,
+        row_x: &[u64],
+        row_z: &[u64],
+        signs_minus: &[u64],
+        signs_i: &[u64],
+    ) -> Vec<PauliString> {
+        (0..self.num_qubits)
+            .map(|row| {
+                Self::generator_from_rows(
+                    self.num_qubits,
+                    self.words_per_row,
+                    row_x,
+                    row_z,
+                    signs_minus,
+                    signs_i,
+                    row,
+                )
+            })
+            .collect()
+    }
+
+    /// Extracts the stabilizer generators as a [`PauliStabilizerGroup`].
+    ///
+    /// The dense tableau stores X/Z support plus two sign bits per row. This
+    /// converts that signed row representation into the shared algebraic
+    /// stabilizer type used by state inspection and quantum-info routines.
+    ///
+    /// [`PauliStabilizerGroup`]: pecos_quantum::PauliStabilizerGroup
+    #[must_use]
+    pub fn to_stabilizer_group(&self) -> pecos_quantum::PauliStabilizerGroup {
+        let generators = self.generators_from_rows(
+            &self.stab_row_x,
+            &self.stab_row_z,
+            &self.stab_signs_minus,
+            &self.stab_signs_i,
+        );
+        pecos_quantum::PauliStabilizerGroup::from_generators_unchecked(generators)
+    }
+
+    /// Extracts the destabilizer generators as a [`PauliSequence`].
+    ///
+    /// [`PauliSequence`]: pecos_quantum::PauliSequence
+    #[must_use]
+    pub fn to_destabilizer_sequence(&self) -> pecos_quantum::PauliSequence {
+        let generators = self.generators_from_rows(
+            &self.destab_row_x,
+            &self.destab_row_z,
+            &self.destab_signs_minus,
+            &self.destab_signs_i,
+        );
+        pecos_quantum::PauliSequence::new(generators)
+    }
+
     /// Produces a tableau string from dense bit arrays.
     fn gen_tableau_string(
         num_qubits: usize,
diff --git a/crates/pecos-simulators/src/density_matrix.rs b/crates/pecos-simulators/src/density_matrix.rs
index dce74e0d2..03aca37db 100644
--- a/crates/pecos-simulators/src/density_matrix.rs
+++ b/crates/pecos-simulators/src/density_matrix.rs
@@ -14,11 +14,37 @@ use super::arbitrary_rotation_gateable::ArbitraryRotationGateable;
 use super::clifford_gateable::{CliffordGateable, MeasurementResult};
 use super::quantum_simulator::QuantumSimulator;
 use super::state_vec::StateVec;
-use pecos_core::{Angle64, QubitId, RngManageable};
+use super::state_vec_soa::StateVecSoA;
+use nalgebra::DMatrix;
+use pecos_core::{Angle64, ChannelExpr, QubitId, RngManageable};
+use pecos_quantum::{ChannelError, KrausOps};
 use pecos_random::{PecosRng, Rng, RngExt, SeedableRng};
 
 use core::fmt::{Debug, Display, Formatter, Write};
 use num_complex::Complex64;
+use std::error::Error;
+
+const PURE_STATE_TOLERANCE: f64 = 1e-10;
+
+/// Error returned when converting between simulator state representations.
+#[derive(Clone, Debug, PartialEq)]
+pub enum StateConversionError {
+    /// The density matrix is not rank-1 within the conversion tolerance.
+    MixedDensityMatrix { residual: f64 },
+}
+
+impl Display for StateConversionError {
+    fn fmt(&self, f: &mut Formatter<'_>) -> core::fmt::Result {
+        match self {
+            Self::MixedDensityMatrix { residual } => write!(
+                f,
+                "density matrix is not a pure state; reconstruction residual is {residual}"
+            ),
+        }
+    }
+}
+
+impl Error for StateConversionError {}
 
 /// A quantum state simulator using the density matrix representation via the Choi-Jamiolkowski isomorphism
 ///
@@ -836,6 +862,143 @@ where
 
         self
     }
+
+    /// Apply a symbolic channel expression to this density matrix.
+    ///
+    /// Supported expressions are those convertible to same-Hilbert-space Kraus
+    /// operators: unitary, mixed-unitary, amplitude damping, phase damping,
+    /// tensor, and composition. Erasure, leakage, and gate instruments are
+    /// intentionally rejected because they need extra flag/outcome semantics.
+    ///
+    /// # Errors
+    ///
+    /// Returns an error if the channel expression is unsupported or invalid for
+    /// this simulator's qubit count.
+    pub fn apply_channel_expr(&mut self, channel: &ChannelExpr) -> Result<&mut Self, ChannelError> {
+        let kraus = KrausOps::from_channel_expr_with_num_qubits(channel, self.num_physical_qubits)?;
+        self.apply_kraus_ops(&kraus)
+    }
+
+    /// Apply Kraus operators to this density matrix.
+    ///
+    /// # Errors
+    ///
+    /// Returns an error if the Kraus operators are not defined on the same
+    /// number of qubits as this density matrix.
+    pub fn apply_kraus_ops(&mut self, kraus: &KrausOps) -> Result<&mut Self, ChannelError> {
+        let num_qubits_u32 = u32::try_from(self.num_physical_qubits).map_err(|_| {
+            ChannelError::DimensionOverflow {
+                num_qubits: self.num_physical_qubits,
+            }
+        })?;
+        let dim = 1usize
+            .checked_shl(num_qubits_u32)
+            .ok_or(ChannelError::DimensionOverflow {
+                num_qubits: self.num_physical_qubits,
+            })?;
+        if kraus.num_qubits() != self.num_physical_qubits {
+            let actual_qubits_u32 =
+                u32::try_from(kraus.num_qubits()).map_err(|_| ChannelError::DimensionOverflow {
+                    num_qubits: kraus.num_qubits(),
+                })?;
+            let actual_dim =
+                1usize
+                    .checked_shl(actual_qubits_u32)
+                    .ok_or(ChannelError::DimensionOverflow {
+                        num_qubits: kraus.num_qubits(),
+                    })?;
+            return Err(ChannelError::InvalidMatrixShape {
+                expected_rows: dim,
+                expected_cols: dim,
+                rows: actual_dim,
+                cols: actual_dim,
+            });
+        }
+
+        let rho = self.get_density_matrix();
+        let flat: Vec<Complex64> = rho.iter().flat_map(|row| row.iter().copied()).collect();
+        let rho_matrix = DMatrix::from_row_slice(dim, dim, &flat);
+        let mut evolved = DMatrix::zeros(dim, dim);
+        for operator in kraus.operators() {
+            evolved += operator * &rho_matrix * operator.adjoint();
+        }
+
+        let new_rho: Vec<Vec<Complex64>> = (0..dim)
+            .map(|row| (0..dim).map(|col| evolved[(row, col)]).collect())
+            .collect();
+        self.set_from_density_matrix(&new_rho);
+        Ok(self)
+    }
+}
+
+impl<R> From<&StateVecSoA<R>> for DensityMatrix<R>
+where
+    R: Rng + SeedableRng + Debug + Clone,
+{
+    fn from(state: &StateVecSoA<R>) -> Self {
+        let mut state = state.clone();
+        let amplitudes = state.state();
+        let dim = amplitudes.len();
+        let num_physical_qubits = dim.trailing_zeros() as usize;
+        let mut purification = vec![Complex64::new(0.0, 0.0); dim * dim];
+
+        for (row, amplitude) in amplitudes.iter().enumerate() {
+            purification[row << num_physical_qubits] = *amplitude;
+        }
+
+        Self {
+            num_physical_qubits,
+            state_vector: StateVec::from_state(&purification, state.rng().clone()),
+        }
+    }
+}
+
+impl<R> TryFrom<&DensityMatrix<R>> for Vec<Complex64>
+where
+    R: Rng + SeedableRng + Debug + Clone,
+{
+    type Error = StateConversionError;
+
+    fn try_from(density_matrix: &DensityMatrix<R>) -> Result<Self, Self::Error> {
+        let mut density_matrix = density_matrix.clone();
+        let rho = density_matrix.get_density_matrix();
+        pure_state_from_density_matrix(&rho)
+    }
+}
+
+fn pure_state_from_density_matrix(
+    rho: &[Vec<Complex64>],
+) -> Result<Vec<Complex64>, StateConversionError> {
+    let dim = rho.len();
+    let (pivot, pivot_probability) = rho
+        .iter()
+        .enumerate()
+        .map(|(i, row)| (i, row[i].re.max(0.0)))
+        .max_by(|(_, left), (_, right)| left.total_cmp(right))
+        .unwrap_or((0, 0.0));
+
+    if pivot_probability <= PURE_STATE_TOLERANCE {
+        return Err(StateConversionError::MixedDensityMatrix { residual: 1.0 });
+    }
+
+    let pivot_amplitude = pivot_probability.sqrt();
+    let state: Vec<Complex64> = (0..dim)
+        .map(|row| rho[row][pivot] / pivot_amplitude)
+        .collect();
+
+    let mut residual = 0.0_f64;
+    for row in 0..dim {
+        for col in 0..dim {
+            let reconstructed = state[row] * state[col].conj();
+            residual = residual.max((rho[row][col] - reconstructed).norm());
+        }
+    }
+
+    if residual > PURE_STATE_TOLERANCE {
+        return Err(StateConversionError::MixedDensityMatrix { residual });
+    }
+
+    Ok(state)
 }
 
 impl<R> Display for DensityMatrix<R>
@@ -1322,5 +1485,91 @@ mod tests {
         assert!(dm.is_pure());
     }
 
+    #[test]
+    fn channel_expr_bit_flip_applies_to_density_matrix() {
+        let mut dm = DensityMatrix::new(1);
+        dm.apply_channel_expr(&pecos_core::channel::BitFlip(1.0, 0))
+            .unwrap();
+
+        assert!(dm.probability(0) < 1e-10);
+        assert!((dm.probability(1) - 1.0).abs() < 1e-10);
+    }
+
+    #[test]
+    fn channel_expr_embeds_local_channel_in_larger_density_matrix() {
+        let mut dm = DensityMatrix::new(2);
+        dm.apply_channel_expr(&pecos_core::channel::BitFlip(1.0, 1))
+            .unwrap();
+
+        assert!(dm.probability(0) < 1e-10);
+        assert!((dm.probability(2) - 1.0).abs() < 1e-10);
+    }
+
+    #[test]
+    fn tensor_channel_expr_applies_to_noncontiguous_density_matrix_qubits() {
+        let mut dm = DensityMatrix::new(3);
+        let channel = ChannelExpr::Tensor(vec![
+            pecos_core::channel::BitFlip(1.0, 0),
+            pecos_core::channel::BitFlip(1.0, 2),
+        ]);
+
+        dm.apply_channel_expr(&channel).unwrap();
+
+        assert!(dm.probability(0) < 1e-10);
+        assert!((dm.probability(5) - 1.0).abs() < 1e-10);
+    }
+
+    #[test]
+    fn out_of_range_channel_expr_is_rejected_without_mutating_state() {
+        let mut dm = DensityMatrix::new(2);
+        dm.h(&qid(0)).cx(&[(QubitId(0), QubitId(1))]);
+        let before = dm.get_flattened_density_matrix();
+
+        let err = dm
+            .apply_channel_expr(&pecos_core::channel::BitFlip(0.5, 2))
+            .expect_err("channel should not apply outside the simulator range");
+
+        assert!(matches!(
+            err,
+            ChannelError::QubitOutOfRange {
+                num_qubits: 2,
+                qubit: 2
+            }
+        ));
+        let after = dm.get_flattened_density_matrix();
+        assert_eq!(after, before);
+    }
+
+    #[test]
+    fn state_vector_converts_to_density_matrix_and_back() {
+        let mut state = StateVecSoA::new(2);
+        state.h(&qid(0)).cx(&[(QubitId(0), QubitId(1))]);
+
+        let mut density_matrix = DensityMatrix::from(&state);
+        assert!((density_matrix.probability(0) - 0.5).abs() < 1e-10);
+        assert!(density_matrix.probability(1) < 1e-10);
+        assert!(density_matrix.probability(2) < 1e-10);
+        assert!((density_matrix.probability(3) - 0.5).abs() < 1e-10);
+
+        let recovered = Vec::<Complex64>::try_from(&density_matrix).unwrap();
+        let expected = state.state();
+
+        for (actual, expected) in recovered.iter().zip(expected.iter()) {
+            assert!((*actual - *expected).norm() < 1e-10);
+        }
+    }
+
+    #[test]
+    fn mixed_density_matrix_rejects_state_vector_conversion() {
+        let mut density_matrix = DensityMatrix::new(1);
+        density_matrix.prepare_maximally_mixed();
+
+        let err = Vec::<Complex64>::try_from(&density_matrix).unwrap_err();
+        assert!(matches!(
+            err,
+            StateConversionError::MixedDensityMatrix { .. }
+        ));
+    }
+
     // Additional tests for other gates and operations would be added here
 }
diff --git a/crates/pecos-simulators/src/gens.rs b/crates/pecos-simulators/src/gens.rs
index a53ffbe86..46808a15b 100644
--- a/crates/pecos-simulators/src/gens.rs
+++ b/crates/pecos-simulators/src/gens.rs
@@ -164,8 +164,9 @@ impl GensHybrid {
     #[must_use]
     pub fn generator(&self, i: usize) -> PauliString {
         assert!(i < self.num_generators(), "generator index out of bounds");
-        let phase = self.generator_phase(i);
+        let mut phase = self.generator_phase(i);
         let mut paulis = Vec::new();
+        let mut num_y_terms = 0usize;
         for q in 0..self.num_qubits {
             let has_x = self.row_x[i].contains(q);
             let has_z = self.row_z[i].contains(q);
@@ -173,10 +174,16 @@ impl GensHybrid {
                 (false, false) => continue,
                 (true, false) => Pauli::X,
                 (false, true) => Pauli::Z,
-                (true, true) => Pauli::Y,
+                (true, true) => {
+                    num_y_terms += 1;
+                    Pauli::Y
+                }
             };
             paulis.push((pauli, QubitId::new(q)));
         }
+        for _ in 0..num_y_terms {
+            phase = phase.multiply(&QuarterPhase::MinusI);
+        }
         PauliString::with_phase_and_paulis(phase, paulis)
     }
 
@@ -391,10 +398,11 @@ impl<S: IndexSet> GensGeneric<S> {
     pub fn generator(&self, i: usize) -> PauliString {
         assert!(i < self.num_generators(), "generator index out of bounds");
 
-        let phase = self.generator_phase(i);
+        let mut phase = self.generator_phase(i);
 
         // Collect non-identity Paulis
         let mut paulis = Vec::new();
+        let mut num_y_terms = 0usize;
 
         // Iterate over all qubits and determine the Pauli at each position
         for q in 0..self.num_qubits {
@@ -405,11 +413,17 @@ impl<S: IndexSet> GensGeneric<S> {
                 (false, false) => continue, // Identity, skip
                 (true, false) => Pauli::X,
                 (false, true) => Pauli::Z,
-                (true, true) => Pauli::Y,
+                (true, true) => {
+                    num_y_terms += 1;
+                    Pauli::Y
+                }
             };
 
             paulis.push((pauli, QubitId::new(q)));
         }
+        for _ in 0..num_y_terms {
+            phase = phase.multiply(&QuarterPhase::MinusI);
+        }
 
         PauliString::with_phase_and_paulis(phase, paulis)
     }
diff --git a/crates/pecos-simulators/src/lib.rs b/crates/pecos-simulators/src/lib.rs
index a67d3c4cc..88791d4bd 100644
--- a/crates/pecos-simulators/src/lib.rs
+++ b/crates/pecos-simulators/src/lib.rs
@@ -12,9 +12,13 @@
 
 pub mod arbitrary_rotation_gateable;
 pub mod batched_ops;
+#[doc(hidden)]
+pub mod bitmask_pauli_prop;
 pub mod circuit_executor;
 pub mod clifford_frame;
 pub mod clifford_gateable;
+#[cfg(test)]
+mod clifford_matrix_oracle;
 pub mod clifford_rotation;
 pub mod clifford_test_utils;
 pub mod coin_toss;
@@ -42,6 +46,7 @@ pub mod sparse_stab_y;
 pub mod stabilizer;
 pub mod stabilizer_tableau;
 pub mod stabilizer_test_utils;
+pub mod state_access;
 pub mod state_vec;
 pub mod state_vec_aos;
 pub mod state_vec_soa;
@@ -55,7 +60,9 @@ pub mod symbolic_sparse_stab_bitset;
 
 pub use arbitrary_rotation_gateable::ArbitraryRotationGateable;
 pub use batched_ops::{BatchedOps, CommandBuffer, RawOps};
-pub use circuit_executor::{CircuitExecutor, GateSystem, GateSystemRegistry, execute_batched};
+#[doc(hidden)]
+pub use bitmask_pauli_prop::BitmaskPauliProp;
+pub use circuit_executor::{CircuitExecutor, GateSystem, GateSystemRegistry};
 pub use clifford_gateable::{CliffordGateable, MeasurementResult};
 pub use coin_toss::CoinToss;
 /// Sparse index representation of stabilizer/destabilizer generators.
@@ -100,9 +107,12 @@ pub use sparse_stab_y::{
 };
 pub use stabilizer::Stabilizer;
 pub use stabilizer_tableau::StabilizerTableauSimulator;
+pub use state_access::{
+    DensityMatrixAccess, PauliExpectationAccess, StabilizerStateVectorConversion, StateAccessError,
+    StateInfo, StateSampling, StateVectorAccess, random_statevector,
+};
 // StateVec uses the sparse SoA implementation optimized for QEC workloads.
 // The dense implementation is available as DenseStateVec / StateVecSoA.
-pub use state_vec::StateVec as StateVecOld;
 pub use state_vec_aos::StateVecAoS;
 pub use state_vec_soa::StateVecSoA as DenseStateVec;
 pub use state_vec_soa::StateVecSoA;
diff --git a/crates/pecos-simulators/src/measurement_stress_test_utils.rs b/crates/pecos-simulators/src/measurement_stress_test_utils.rs
index 787c09a0d..336128405 100644
--- a/crates/pecos-simulators/src/measurement_stress_test_utils.rs
+++ b/crates/pecos-simulators/src/measurement_stress_test_utils.rs
@@ -268,8 +268,9 @@ pub fn run_measurement_stress_tests<S: ArbitraryRotationGateable>(sim: &mut S) {
 /// Generate a test that runs the measurement stress suite on a simulator type.
 ///
 /// Usage:
-/// ```ignore
-/// use pecos_simulators::measurement_stress_test_suite;
+/// ```
+/// use pecos_simulators::{StabVec, measurement_stress_test_suite};
+///
 /// measurement_stress_test_suite!(StabVec, 4);
 /// ```
 #[macro_export]
diff --git a/crates/pecos-simulators/src/pauli_prop.rs b/crates/pecos-simulators/src/pauli_prop.rs
index 5927b65db..0a24fef5f 100644
--- a/crates/pecos-simulators/src/pauli_prop.rs
+++ b/crates/pecos-simulators/src/pauli_prop.rs
@@ -372,6 +372,15 @@ impl PauliProp {
         count
     }
 
+    /// Remove all Pauli operators from a specific qubit.
+    ///
+    /// Models reset (PZ) which absorbs any propagating error on that qubit.
+    pub fn clear_qubit(&mut self, qubit: usize) {
+        use pecos_core::sets::set::Set;
+        self.xs.remove(&qubit);
+        self.zs.remove(&qubit);
+    }
+
     /// Checks if this is the identity operator (no Pauli operators on any qubit).
     ///
     /// # Returns
@@ -537,6 +546,23 @@ impl PauliProp {
     pub fn to_dense_string(&self) -> String {
         format!("{}{}", self.sign_string(), self.dense_string())
     }
+
+    fn set_x_component(&mut self, q: usize, value: bool) {
+        if self.contains_x(q) != value {
+            self.track_x(&[q]);
+        }
+    }
+
+    fn set_z_component(&mut self, q: usize, value: bool) {
+        if self.contains_z(q) != value {
+            self.track_z(&[q]);
+        }
+    }
+
+    fn set_components(&mut self, q: usize, x: bool, z: bool) {
+        self.set_x_component(q, x);
+        self.set_z_component(q, z);
+    }
 }
 
 impl fmt::Display for PauliProp {
@@ -573,6 +599,21 @@ impl CliffordGateable for PauliProp {
         self
     }
 
+    /// Applies the adjoint square root of Z gate.
+    ///
+    /// Ignoring global phase, `SZ` and `SZdg` have the same binary Pauli action:
+    /// X <-> Y, Z -> Z.
+    #[inline]
+    fn szdg(&mut self, qubits: &[QubitId]) -> &mut Self {
+        for &q in qubits {
+            let qu = q.index();
+            if self.contains_x(qu) {
+                self.track_z(&[qu]);
+            }
+        }
+        self
+    }
+
     /// Applies the Hadamard (H) gate to the specified qubits.
     ///
     /// The H gate transforms Pauli operators as follows:
@@ -611,6 +652,62 @@ impl CliffordGateable for PauliProp {
         self
     }
 
+    /// Applies the square root of X gate.
+    ///
+    /// Binary Pauli action: X -> X, Z <-> Y.
+    #[inline]
+    fn sx(&mut self, qubits: &[QubitId]) -> &mut Self {
+        for &q in qubits {
+            let qu = q.index();
+            if self.contains_z(qu) {
+                self.track_x(&[qu]);
+            }
+        }
+        self
+    }
+
+    /// Applies the adjoint square root of X gate.
+    ///
+    /// Ignoring global phase, `SX` and `SXdg` have the same binary Pauli action.
+    #[inline]
+    fn sxdg(&mut self, qubits: &[QubitId]) -> &mut Self {
+        for &q in qubits {
+            let qu = q.index();
+            if self.contains_z(qu) {
+                self.track_x(&[qu]);
+            }
+        }
+        self
+    }
+
+    /// Applies the square root of Y gate.
+    ///
+    /// Binary Pauli action: X <-> Z, Y -> Y.
+    #[inline]
+    fn sy(&mut self, qubits: &[QubitId]) -> &mut Self {
+        for &q in qubits {
+            let qu = q.index();
+            let x = self.contains_x(qu);
+            let z = self.contains_z(qu);
+            self.set_components(qu, z, x);
+        }
+        self
+    }
+
+    /// Applies the adjoint square root of Y gate.
+    ///
+    /// Ignoring global phase, `SY` and `SYdg` have the same binary Pauli action.
+    #[inline]
+    fn sydg(&mut self, qubits: &[QubitId]) -> &mut Self {
+        for &q in qubits {
+            let qu = q.index();
+            let x = self.contains_x(qu);
+            let z = self.contains_z(qu);
+            self.set_components(qu, z, x);
+        }
+        self
+    }
+
     /// Applies the controlled-X (CX) gate between pairs of qubits
     ///
     /// The CX gate transforms Pauli operators as follows:
@@ -645,6 +742,160 @@ impl CliffordGateable for PauliProp {
         self
     }
 
+    /// Applies the controlled-Y gate.
+    #[inline]
+    fn cy(&mut self, pairs: &[(QubitId, QubitId)]) -> &mut Self {
+        for &(q1, q2) in pairs {
+            let q1 = q1.index();
+            let q2 = q2.index();
+            let x1 = self.contains_x(q1);
+            let z1 = self.contains_z(q1);
+            let x2 = self.contains_x(q2);
+            let z2 = self.contains_z(q2);
+            self.set_components(q1, x1, z1 ^ x2 ^ z2);
+            self.set_components(q2, x2 ^ x1, z2 ^ x1);
+        }
+        self
+    }
+
+    /// Applies the controlled-Z gate.
+    #[inline]
+    fn cz(&mut self, pairs: &[(QubitId, QubitId)]) -> &mut Self {
+        for &(q1, q2) in pairs {
+            let q1 = q1.index();
+            let q2 = q2.index();
+            let x1 = self.contains_x(q1);
+            let z1 = self.contains_z(q1);
+            let x2 = self.contains_x(q2);
+            let z2 = self.contains_z(q2);
+            self.set_components(q1, x1, z1 ^ x2);
+            self.set_components(q2, x2, z2 ^ x1);
+        }
+        self
+    }
+
+    /// Applies the square root of XX gate.
+    #[inline]
+    fn sxx(&mut self, pairs: &[(QubitId, QubitId)]) -> &mut Self {
+        for &(q1, q2) in pairs {
+            let q1 = q1.index();
+            let q2 = q2.index();
+            let x1 = self.contains_x(q1);
+            let z1 = self.contains_z(q1);
+            let x2 = self.contains_x(q2);
+            let z2 = self.contains_z(q2);
+            let affected = z1 ^ z2;
+            self.set_components(q1, x1 ^ affected, z1);
+            self.set_components(q2, x2 ^ affected, z2);
+        }
+        self
+    }
+
+    /// Applies the adjoint square root of XX gate.
+    ///
+    /// Ignoring global phase, `SXX` and `SXXdg` have the same binary Pauli action.
+    #[inline]
+    fn sxxdg(&mut self, pairs: &[(QubitId, QubitId)]) -> &mut Self {
+        for &(q1, q2) in pairs {
+            let q1 = q1.index();
+            let q2 = q2.index();
+            let x1 = self.contains_x(q1);
+            let z1 = self.contains_z(q1);
+            let x2 = self.contains_x(q2);
+            let z2 = self.contains_z(q2);
+            let affected = z1 ^ z2;
+            self.set_components(q1, x1 ^ affected, z1);
+            self.set_components(q2, x2 ^ affected, z2);
+        }
+        self
+    }
+
+    /// Applies the square root of YY gate.
+    #[inline]
+    fn syy(&mut self, pairs: &[(QubitId, QubitId)]) -> &mut Self {
+        for &(q1, q2) in pairs {
+            let q1 = q1.index();
+            let q2 = q2.index();
+            let x1 = self.contains_x(q1);
+            let z1 = self.contains_z(q1);
+            let x2 = self.contains_x(q2);
+            let z2 = self.contains_z(q2);
+            self.set_components(q1, x2 ^ z1 ^ z2, x1 ^ x2 ^ z2);
+            self.set_components(q2, x1 ^ z1 ^ z2, x1 ^ x2 ^ z1);
+        }
+        self
+    }
+
+    /// Applies the adjoint square root of YY gate.
+    ///
+    /// Ignoring global phase, `SYY` and `SYYdg` have the same binary Pauli action.
+    #[inline]
+    fn syydg(&mut self, pairs: &[(QubitId, QubitId)]) -> &mut Self {
+        for &(q1, q2) in pairs {
+            let q1 = q1.index();
+            let q2 = q2.index();
+            let x1 = self.contains_x(q1);
+            let z1 = self.contains_z(q1);
+            let x2 = self.contains_x(q2);
+            let z2 = self.contains_z(q2);
+            self.set_components(q1, x2 ^ z1 ^ z2, x1 ^ x2 ^ z2);
+            self.set_components(q2, x1 ^ z1 ^ z2, x1 ^ x2 ^ z1);
+        }
+        self
+    }
+
+    /// Applies the square root of ZZ gate.
+    #[inline]
+    fn szz(&mut self, pairs: &[(QubitId, QubitId)]) -> &mut Self {
+        for &(q1, q2) in pairs {
+            let q1 = q1.index();
+            let q2 = q2.index();
+            let x1 = self.contains_x(q1);
+            let z1 = self.contains_z(q1);
+            let x2 = self.contains_x(q2);
+            let z2 = self.contains_z(q2);
+            let affected = x1 ^ x2;
+            self.set_components(q1, x1, z1 ^ affected);
+            self.set_components(q2, x2, z2 ^ affected);
+        }
+        self
+    }
+
+    /// Applies the adjoint square root of ZZ gate.
+    ///
+    /// Ignoring global phase, `SZZ` and `SZZdg` have the same binary Pauli action.
+    #[inline]
+    fn szzdg(&mut self, pairs: &[(QubitId, QubitId)]) -> &mut Self {
+        for &(q1, q2) in pairs {
+            let q1 = q1.index();
+            let q2 = q2.index();
+            let x1 = self.contains_x(q1);
+            let z1 = self.contains_z(q1);
+            let x2 = self.contains_x(q2);
+            let z2 = self.contains_z(q2);
+            let affected = x1 ^ x2;
+            self.set_components(q1, x1, z1 ^ affected);
+            self.set_components(q2, x2, z2 ^ affected);
+        }
+        self
+    }
+
+    /// Applies the SWAP gate.
+    #[inline]
+    fn swap(&mut self, pairs: &[(QubitId, QubitId)]) -> &mut Self {
+        for &(q1, q2) in pairs {
+            let q1 = q1.index();
+            let q2 = q2.index();
+            let x1 = self.contains_x(q1);
+            let z1 = self.contains_z(q1);
+            let x2 = self.contains_x(q2);
+            let z2 = self.contains_z(q2);
+            self.set_components(q1, x2, z2);
+            self.set_components(q2, x1, z1);
+        }
+        self
+    }
+
     /// Performs a Z-basis measurement on the specified qubits.
     ///
     /// This simulates the effect of Pauli operators on measurement due to propagation.
@@ -680,8 +931,106 @@ impl CliffordGateable for PauliProp {
 #[cfg(test)]
 mod tests {
     use super::*;
+    use crate::clifford_matrix_oracle::{CliffordMatrixGate, all_pauli_strings, conjugate_pauli};
     use std::collections::BTreeMap;
 
+    fn prop_from_dense(input: &str) -> PauliProp {
+        let mut prop = PauliProp::with_sign_tracking(input.len());
+        for (q, p) in input.chars().enumerate() {
+            match p {
+                'I' => {}
+                'X' => prop.track_x(&[q]),
+                'Y' => prop.track_y(&[q]),
+                'Z' => prop.track_z(&[q]),
+                _ => panic!("invalid Pauli label {p}"),
+            }
+        }
+        prop
+    }
+
+    fn assert_gate_table<F>(name: &str, table: &[(&str, &str)], mut apply: F)
+    where
+        F: FnMut(&mut PauliProp),
+    {
+        for &(input, expected) in table {
+            let mut prop = prop_from_dense(input);
+            apply(&mut prop);
+            assert_eq!(prop.dense_string(), expected, "{name}: {input}");
+        }
+    }
+
+    fn assert_gate_matches_matrix_oracle<F>(
+        name: &str,
+        gate: CliffordMatrixGate,
+        num_qubits: usize,
+        mut apply: F,
+    ) where
+        F: FnMut(&mut PauliProp),
+    {
+        for input in all_pauli_strings(num_qubits) {
+            let expected = conjugate_pauli(gate, &input);
+            let mut prop = prop_from_dense(&input);
+            apply(&mut prop);
+            assert_eq!(
+                prop.dense_string(),
+                expected.pauli,
+                "{name}: {input}, oracle sign {}",
+                expected.sign
+            );
+        }
+    }
+
+    fn reverse_two_qubit_pauli(pauli: &str) -> String {
+        let labels: Vec<char> = pauli.chars().collect();
+        assert_eq!(labels.len(), 2);
+        [labels[1], labels[0]].into_iter().collect()
+    }
+
+    fn assert_reversed_pair_matches_matrix_oracle<F>(
+        name: &str,
+        gate: CliffordMatrixGate,
+        mut apply: F,
+    ) where
+        F: FnMut(&mut PauliProp, &[(QubitId, QubitId)]),
+    {
+        let reversed_pair = [(QubitId(1), QubitId(0))];
+        for input in all_pauli_strings(2) {
+            let oracle_input = reverse_two_qubit_pauli(&input);
+            let mut expected = conjugate_pauli(gate, &oracle_input);
+            expected.pauli = reverse_two_qubit_pauli(&expected.pauli);
+
+            let mut prop = prop_from_dense(&input);
+            apply(&mut prop, &reversed_pair);
+            assert_eq!(
+                prop.dense_string(),
+                expected.pauli,
+                "{name} reversed pair: {input}, oracle sign {}",
+                expected.sign
+            );
+        }
+    }
+
+    fn assert_two_pair_batch_matches_sequential<F>(name: &str, mut apply: F)
+    where
+        F: FnMut(&mut PauliProp, &[(QubitId, QubitId)]),
+    {
+        let pairs = [(QubitId(0), QubitId(1)), (QubitId(2), QubitId(3))];
+        for input in all_pauli_strings(4) {
+            let mut batched = prop_from_dense(&input);
+            apply(&mut batched, &pairs);
+
+            let mut sequential = prop_from_dense(&input);
+            apply(&mut sequential, &pairs[0..1]);
+            apply(&mut sequential, &pairs[1..2]);
+
+            assert_eq!(
+                batched.dense_string(),
+                sequential.dense_string(),
+                "{name} batched: {input}"
+            );
+        }
+    }
+
     #[test]
     fn test_sign_tracking() {
         let mut sim = PauliProp::with_sign_tracking(4);
@@ -785,4 +1134,265 @@ mod tests {
         // Phase should be -i (X·Z = -iY)
         assert_eq!(sim.sign_string(), "-i");
     }
+
+    #[test]
+    fn test_direct_clifford_gate_binary_truth_tables() {
+        let q0 = QubitId(0);
+        let q1 = QubitId(1);
+        let pair = [(q0, q1)];
+
+        assert_gate_table(
+            "SZdg",
+            &[("I", "I"), ("X", "Y"), ("Y", "X"), ("Z", "Z")],
+            |prop| {
+                prop.szdg(&[q0]);
+            },
+        );
+        assert_gate_table(
+            "SX",
+            &[("I", "I"), ("X", "X"), ("Y", "Z"), ("Z", "Y")],
+            |prop| {
+                prop.sx(&[q0]);
+            },
+        );
+        assert_gate_table(
+            "SXdg",
+            &[("I", "I"), ("X", "X"), ("Y", "Z"), ("Z", "Y")],
+            |prop| {
+                prop.sxdg(&[q0]);
+            },
+        );
+        assert_gate_table(
+            "SY",
+            &[("I", "I"), ("X", "Z"), ("Y", "Y"), ("Z", "X")],
+            |prop| {
+                prop.sy(&[q0]);
+            },
+        );
+        assert_gate_table(
+            "SYdg",
+            &[("I", "I"), ("X", "Z"), ("Y", "Y"), ("Z", "X")],
+            |prop| {
+                prop.sydg(&[q0]);
+            },
+        );
+        assert_gate_table(
+            "CY",
+            &[("XI", "XY"), ("IX", "ZX"), ("ZI", "ZI"), ("IZ", "ZZ")],
+            |prop| {
+                prop.cy(&pair);
+            },
+        );
+        assert_gate_table(
+            "CZ",
+            &[("XI", "XZ"), ("IX", "ZX"), ("ZI", "ZI"), ("IZ", "IZ")],
+            |prop| {
+                prop.cz(&pair);
+            },
+        );
+        assert_gate_table(
+            "SXX",
+            &[("XI", "XI"), ("IX", "IX"), ("ZI", "YX"), ("IZ", "XY")],
+            |prop| {
+                prop.sxx(&pair);
+            },
+        );
+        assert_gate_table(
+            "SXXdg",
+            &[("XI", "XI"), ("IX", "IX"), ("ZI", "YX"), ("IZ", "XY")],
+            |prop| {
+                prop.sxxdg(&pair);
+            },
+        );
+        assert_gate_table(
+            "SYY",
+            &[("XI", "ZY"), ("IX", "YZ"), ("ZI", "XY"), ("IZ", "YX")],
+            |prop| {
+                prop.syy(&pair);
+            },
+        );
+        assert_gate_table(
+            "SYYdg",
+            &[("XI", "ZY"), ("IX", "YZ"), ("ZI", "XY"), ("IZ", "YX")],
+            |prop| {
+                prop.syydg(&pair);
+            },
+        );
+        assert_gate_table(
+            "SZZ",
+            &[("XI", "YZ"), ("IX", "ZY"), ("ZI", "ZI"), ("IZ", "IZ")],
+            |prop| {
+                prop.szz(&pair);
+            },
+        );
+        assert_gate_table(
+            "SZZdg",
+            &[("XI", "YZ"), ("IX", "ZY"), ("ZI", "ZI"), ("IZ", "IZ")],
+            |prop| {
+                prop.szzdg(&pair);
+            },
+        );
+        assert_gate_table(
+            "SWAP",
+            &[("XI", "IX"), ("IX", "XI"), ("ZI", "IZ"), ("IZ", "ZI")],
+            |prop| {
+                prop.swap(&pair);
+            },
+        );
+    }
+
+    #[test]
+    fn test_direct_clifford_gates_match_matrix_oracle_for_all_paulis() {
+        let q0 = QubitId(0);
+        let q1 = QubitId(1);
+        let pair = [(q0, q1)];
+
+        assert_gate_matches_matrix_oracle("CX", CliffordMatrixGate::CX, 2, |prop| {
+            prop.cx(&pair);
+        });
+        assert_gate_matches_matrix_oracle("SZdg", CliffordMatrixGate::SZdg, 1, |prop| {
+            prop.szdg(&[q0]);
+        });
+        assert_gate_matches_matrix_oracle("F", CliffordMatrixGate::F, 1, |prop| {
+            prop.f(&[q0]);
+        });
+        assert_gate_matches_matrix_oracle("Fdg", CliffordMatrixGate::Fdg, 1, |prop| {
+            prop.fdg(&[q0]);
+        });
+        assert_gate_matches_matrix_oracle("SX", CliffordMatrixGate::SX, 1, |prop| {
+            prop.sx(&[q0]);
+        });
+        assert_gate_matches_matrix_oracle("SXdg", CliffordMatrixGate::SXdg, 1, |prop| {
+            prop.sxdg(&[q0]);
+        });
+        assert_gate_matches_matrix_oracle("SY", CliffordMatrixGate::SY, 1, |prop| {
+            prop.sy(&[q0]);
+        });
+        assert_gate_matches_matrix_oracle("SYdg", CliffordMatrixGate::SYdg, 1, |prop| {
+            prop.sydg(&[q0]);
+        });
+        assert_gate_matches_matrix_oracle("CY", CliffordMatrixGate::CY, 2, |prop| {
+            prop.cy(&pair);
+        });
+        assert_gate_matches_matrix_oracle("CZ", CliffordMatrixGate::CZ, 2, |prop| {
+            prop.cz(&pair);
+        });
+        assert_gate_matches_matrix_oracle("SXX", CliffordMatrixGate::SXX, 2, |prop| {
+            prop.sxx(&pair);
+        });
+        assert_gate_matches_matrix_oracle("SXXdg", CliffordMatrixGate::SXXdg, 2, |prop| {
+            prop.sxxdg(&pair);
+        });
+        assert_gate_matches_matrix_oracle("SYY", CliffordMatrixGate::SYY, 2, |prop| {
+            prop.syy(&pair);
+        });
+        assert_gate_matches_matrix_oracle("SYYdg", CliffordMatrixGate::SYYdg, 2, |prop| {
+            prop.syydg(&pair);
+        });
+        assert_gate_matches_matrix_oracle("SZZ", CliffordMatrixGate::SZZ, 2, |prop| {
+            prop.szz(&pair);
+        });
+        assert_gate_matches_matrix_oracle("SZZdg", CliffordMatrixGate::SZZdg, 2, |prop| {
+            prop.szzdg(&pair);
+        });
+        assert_gate_matches_matrix_oracle("SWAP", CliffordMatrixGate::SWAP, 2, |prop| {
+            prop.swap(&pair);
+        });
+    }
+
+    #[test]
+    fn test_two_qubit_gates_reversed_pair_matches_matrix_oracle() {
+        assert_reversed_pair_matches_matrix_oracle("CX", CliffordMatrixGate::CX, |prop, pairs| {
+            prop.cx(pairs);
+        });
+        assert_reversed_pair_matches_matrix_oracle("CY", CliffordMatrixGate::CY, |prop, pairs| {
+            prop.cy(pairs);
+        });
+        assert_reversed_pair_matches_matrix_oracle("CZ", CliffordMatrixGate::CZ, |prop, pairs| {
+            prop.cz(pairs);
+        });
+        assert_reversed_pair_matches_matrix_oracle(
+            "SXX",
+            CliffordMatrixGate::SXX,
+            |prop, pairs| {
+                prop.sxx(pairs);
+            },
+        );
+        assert_reversed_pair_matches_matrix_oracle(
+            "SXXdg",
+            CliffordMatrixGate::SXXdg,
+            |prop, pairs| {
+                prop.sxxdg(pairs);
+            },
+        );
+        assert_reversed_pair_matches_matrix_oracle(
+            "SYY",
+            CliffordMatrixGate::SYY,
+            |prop, pairs| {
+                prop.syy(pairs);
+            },
+        );
+        assert_reversed_pair_matches_matrix_oracle(
+            "SYYdg",
+            CliffordMatrixGate::SYYdg,
+            |prop, pairs| {
+                prop.syydg(pairs);
+            },
+        );
+        assert_reversed_pair_matches_matrix_oracle(
+            "SZZ",
+            CliffordMatrixGate::SZZ,
+            |prop, pairs| {
+                prop.szz(pairs);
+            },
+        );
+        assert_reversed_pair_matches_matrix_oracle(
+            "SZZdg",
+            CliffordMatrixGate::SZZdg,
+            |prop, pairs| {
+                prop.szzdg(pairs);
+            },
+        );
+        assert_reversed_pair_matches_matrix_oracle(
+            "SWAP",
+            CliffordMatrixGate::SWAP,
+            |prop, pairs| {
+                prop.swap(pairs);
+            },
+        );
+    }
+
+    #[test]
+    fn test_two_qubit_gate_batches_match_sequential_pairs() {
+        assert_two_pair_batch_matches_sequential("CX", |prop, pairs| {
+            prop.cx(pairs);
+        });
+        assert_two_pair_batch_matches_sequential("CY", |prop, pairs| {
+            prop.cy(pairs);
+        });
+        assert_two_pair_batch_matches_sequential("CZ", |prop, pairs| {
+            prop.cz(pairs);
+        });
+        assert_two_pair_batch_matches_sequential("SXX", |prop, pairs| {
+            prop.sxx(pairs);
+        });
+        assert_two_pair_batch_matches_sequential("SXXdg", |prop, pairs| {
+            prop.sxxdg(pairs);
+        });
+        assert_two_pair_batch_matches_sequential("SYY", |prop, pairs| {
+            prop.syy(pairs);
+        });
+        assert_two_pair_batch_matches_sequential("SYYdg", |prop, pairs| {
+            prop.syydg(pairs);
+        });
+        assert_two_pair_batch_matches_sequential("SZZ", |prop, pairs| {
+            prop.szz(pairs);
+        });
+        assert_two_pair_batch_matches_sequential("SZZdg", |prop, pairs| {
+            prop.szzdg(pairs);
+        });
+        assert_two_pair_batch_matches_sequential("SWAP", |prop, pairs| {
+            prop.swap(pairs);
+        });
+    }
 }
diff --git a/crates/pecos-simulators/src/quantum_simulator.rs b/crates/pecos-simulators/src/quantum_simulator.rs
index 4b747d0bb..740b45116 100644
--- a/crates/pecos-simulators/src/quantum_simulator.rs
+++ b/crates/pecos-simulators/src/quantum_simulator.rs
@@ -19,7 +19,7 @@ pub trait QuantumSimulator {
     ///
     /// The exact meaning of reset depends on the simulator type:
     /// - For state vector simulators: resets to |0⟩ state
-    /// - For observable propagators: clears tracked operators
+    /// - For observable propagators: clears tracked Paulis
     /// - For stabilizer simulators: resets to trivial stabilizer group
     ///
     /// # Returns
diff --git a/crates/pecos-simulators/src/sparse_stab.rs b/crates/pecos-simulators/src/sparse_stab.rs
index 0432793aa..fd67b16e0 100644
--- a/crates/pecos-simulators/src/sparse_stab.rs
+++ b/crates/pecos-simulators/src/sparse_stab.rs
@@ -301,6 +301,28 @@ where
         self
     }
 
+    /// Extracts the stabilizer generators as a [`PauliStabilizerGroup`].
+    ///
+    /// Converts the simulator's internal tableau into the algebraic
+    /// representation, enabling rank analysis, distance calculation,
+    /// logical operator computation, and other GF(2) operations.
+    ///
+    /// [`PauliStabilizerGroup`]: pecos_quantum::PauliStabilizerGroup
+    #[must_use]
+    pub fn to_stabilizer_group(&self) -> pecos_quantum::PauliStabilizerGroup {
+        let generators = self.stabs.generators();
+        pecos_quantum::PauliStabilizerGroup::from_generators_unchecked(generators)
+    }
+
+    /// Extracts the destabilizer generators as a [`PauliSequence`].
+    ///
+    /// [`PauliSequence`]: pecos_quantum::PauliSequence
+    #[must_use]
+    pub fn to_destabilizer_sequence(&self) -> pecos_quantum::PauliSequence {
+        let generators = self.destabs.generators();
+        pecos_quantum::PauliSequence::new(generators)
+    }
+
     /// Returns generator data as sparse index vectors.
     ///
     /// Returns `(col_x, col_z, row_x, row_z)` where each is a `Vec<Vec<usize>>`.
diff --git a/crates/pecos-simulators/src/stabilizer.rs b/crates/pecos-simulators/src/stabilizer.rs
index b1e1b5bc6..02b7dbb50 100644
--- a/crates/pecos-simulators/src/stabilizer.rs
+++ b/crates/pecos-simulators/src/stabilizer.rs
@@ -112,6 +112,22 @@ impl Stabilizer {
     pub fn gens_data(&self, is_stab: bool) -> crate::GensData {
         self.inner.gens_data(is_stab)
     }
+
+    /// Extracts the stabilizer generators as a [`PauliStabilizerGroup`].
+    ///
+    /// [`PauliStabilizerGroup`]: pecos_quantum::PauliStabilizerGroup
+    #[must_use]
+    pub fn to_stabilizer_group(&self) -> pecos_quantum::PauliStabilizerGroup {
+        self.inner.to_stabilizer_group()
+    }
+
+    /// Extracts the destabilizer generators as a [`PauliSequence`].
+    ///
+    /// [`PauliSequence`]: pecos_quantum::PauliSequence
+    #[must_use]
+    pub fn to_destabilizer_sequence(&self) -> pecos_quantum::PauliSequence {
+        self.inner.to_destabilizer_sequence()
+    }
 }
 
 impl QuantumSimulator for Stabilizer {
diff --git a/crates/pecos-simulators/src/state_access.rs b/crates/pecos-simulators/src/state_access.rs
new file mode 100644
index 000000000..99caa1925
--- /dev/null
+++ b/crates/pecos-simulators/src/state_access.rs
@@ -0,0 +1,1483 @@
+// Copyright 2026 The PECOS Developers
+//
+// Licensed under the Apache License, Version 2.0 (the "License"); you may not use this file except
+// in compliance with the License. You may obtain a copy of the License at
+//
+//     https://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software distributed under the License
+// is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express
+// or implied. See the License for the specific language governing permissions and limitations under
+// the License.
+
+//! Capability traits for inspecting simulator state.
+//!
+//! These traits deliberately describe what a backend can expose, rather than a
+//! single broad "quantum state" interface. A state-vector simulator can provide
+//! amplitudes; a density-matrix simulator can provide matrix elements; symbolic
+//! propagation backends should not pretend to expose either.
+
+use crate::clifford_gateable::{CliffordGateable, MeasurementResult};
+use crate::dense_stab::DenseStab;
+use crate::density_matrix::DensityMatrix;
+use crate::quantum_simulator::QuantumSimulator;
+use crate::sparse_stab::{SparseStabGeneric, SparseStabHybrid};
+use crate::stabilizer::Stabilizer;
+use crate::state_vec_aos::StateVecAoS;
+use crate::state_vec_soa::StateVecSoA;
+use crate::state_vec_soa32::StateVecSoA32;
+use crate::state_vec_sparse_aos::SparseStateVecAoS;
+use crate::state_vec_sparse_soa::SparseStateVecSoA;
+use core::fmt;
+use num_complex::Complex64;
+use pecos_core::{IndexSet, Pauli, PauliString, Phase, QuarterPhase, QubitId};
+use pecos_quantum::PauliStabilizerGroup;
+use pecos_random::{Rng, RngExt as _, SeedableRng};
+use std::error::Error;
+use std::f64::consts::TAU;
+use std::fmt::Debug;
+
+/// Error returned by state-inspection capability traits.
+#[derive(Clone, Debug, PartialEq, Eq)]
+pub enum StateAccessError {
+    /// `2^num_qubits` cannot be represented as a `usize`.
+    DimensionOverflow {
+        /// Number of qubits requested.
+        num_qubits: usize,
+    },
+    /// A computational-basis index is outside the state Hilbert space.
+    BasisIndexOutOfRange {
+        /// Number of qubits in the state.
+        num_qubits: usize,
+        /// Hilbert-space dimension, when representable.
+        dim: usize,
+        /// Offending basis index.
+        index: usize,
+    },
+    /// A Pauli string acts outside the state qubit range.
+    PauliQubitOutOfRange {
+        /// Number of qubits in the state.
+        num_qubits: usize,
+        /// Offending qubit index.
+        qubit: usize,
+    },
+    /// A sampled/measured qubit is outside the state qubit range.
+    QubitOutOfRange {
+        /// Number of qubits in the state.
+        num_qubits: usize,
+        /// Offending qubit index.
+        qubit: usize,
+    },
+    /// A state vector had an unexpected length.
+    InvalidStateVectorLength {
+        /// Expected vector length.
+        expected: usize,
+        /// Actual vector length.
+        actual: usize,
+    },
+    /// A density matrix had an unexpected shape.
+    InvalidDensityMatrixShape {
+        /// Expected row/column count.
+        expected: usize,
+        /// Actual row count.
+        rows: usize,
+        /// Actual column count.
+        cols: usize,
+    },
+    /// Stabilizer generators do not define a unique pure state.
+    NotPureStabilizerState {
+        /// Number of qubits in the represented system.
+        num_qubits: usize,
+        /// Number of supplied stabilizer generators.
+        num_generators: usize,
+        /// Rank of the stabilizer generator span.
+        rank: usize,
+    },
+}
+
+impl fmt::Display for StateAccessError {
+    fn fmt(&self, f: &mut fmt::Formatter<'_>) -> fmt::Result {
+        match self {
+            Self::DimensionOverflow { num_qubits } => {
+                write!(
+                    f,
+                    "Hilbert dimension overflows usize for {num_qubits} qubits"
+                )
+            }
+            Self::BasisIndexOutOfRange {
+                num_qubits,
+                dim,
+                index,
+            } => write!(
+                f,
+                "basis index {index} is outside the {dim}-element Hilbert space for {num_qubits} qubits"
+            ),
+            Self::PauliQubitOutOfRange { num_qubits, qubit } => write!(
+                f,
+                "Pauli string touches qubit {qubit}, outside {num_qubits}-qubit state"
+            ),
+            Self::QubitOutOfRange { num_qubits, qubit } => {
+                write!(f, "qubit {qubit} is outside {num_qubits}-qubit state")
+            }
+            Self::InvalidStateVectorLength { expected, actual } => {
+                write!(
+                    f,
+                    "invalid state-vector length {actual}; expected {expected}"
+                )
+            }
+            Self::InvalidDensityMatrixShape {
+                expected,
+                rows,
+                cols,
+            } => write!(
+                f,
+                "invalid density-matrix shape {rows}x{cols}; expected {expected}x{expected}"
+            ),
+            Self::NotPureStabilizerState {
+                num_qubits,
+                num_generators,
+                rank,
+            } => write!(
+                f,
+                "stabilizer generators do not define a unique pure state for {num_qubits} qubits: {num_generators} generators, rank {rank}"
+            ),
+        }
+    }
+}
+
+impl Error for StateAccessError {}
+
+/// Common metadata for state-inspection capabilities.
+pub trait StateInfo {
+    /// Returns the number of qubits represented by the state.
+    fn num_qubits(&self) -> usize;
+
+    /// Returns the Hilbert-space dimension `2^num_qubits`.
+    ///
+    /// # Errors
+    ///
+    /// Returns [`StateAccessError::DimensionOverflow`] if the dimension cannot
+    /// be represented as a `usize`.
+    fn hilbert_dim(&self) -> Result<usize, StateAccessError> {
+        hilbert_dim(self.num_qubits())
+    }
+}
+
+impl<T> StateInfo for T
+where
+    T: QuantumSimulator,
+{
+    fn num_qubits(&self) -> usize {
+        QuantumSimulator::num_qubits(self)
+    }
+}
+
+/// Returns a Haar-random pure state vector on `num_qubits` qubits.
+///
+/// The vector is sampled by drawing independent complex normal amplitudes and
+/// normalizing them. The output is in little-endian computational-basis order,
+/// matching PECOS's state-vector backends.
+///
+/// # Errors
+///
+/// Returns [`StateAccessError::DimensionOverflow`] if `2^num_qubits` does not
+/// fit in `usize`.
+pub fn random_statevector<R>(
+    rng: &mut R,
+    num_qubits: usize,
+) -> Result<Vec<Complex64>, StateAccessError>
+where
+    R: Rng + ?Sized,
+{
+    let dim = hilbert_dim(num_qubits)?;
+    if dim == 1 {
+        return Ok(vec![Complex64::new(1.0, 0.0)]);
+    }
+
+    loop {
+        let mut state: Vec<Complex64> = (0..dim).map(|_| standard_complex_normal(rng)).collect();
+        let norm_sqr = state_norm_sqr(&state);
+        if norm_sqr > f64::EPSILON {
+            normalize_state_vector(&mut state, norm_sqr);
+            return Ok(state);
+        }
+    }
+}
+
+/// Capability for backends that can expose computational-basis amplitudes.
+pub trait StateVectorAccess: StateInfo {
+    /// Returns one computational-basis amplitude.
+    ///
+    /// # Errors
+    ///
+    /// Returns an error if `basis_state` is outside the Hilbert space.
+    fn amplitude(&mut self, basis_state: usize) -> Result<Complex64, StateAccessError>;
+
+    /// Returns a dense state vector in little-endian computational-basis order.
+    ///
+    /// # Errors
+    ///
+    /// Returns an error if the Hilbert-space dimension overflows.
+    fn state_vector(&mut self) -> Result<Vec<Complex64>, StateAccessError>;
+
+    /// Returns the probability of one computational-basis state.
+    ///
+    /// # Errors
+    ///
+    /// Returns an error if `basis_state` is outside the Hilbert space.
+    fn basis_probability(&mut self, basis_state: usize) -> Result<f64, StateAccessError> {
+        Ok(self.amplitude(basis_state)?.norm_sqr())
+    }
+}
+
+/// Capability for backends that can expose a density matrix.
+pub trait DensityMatrixAccess: StateInfo {
+    /// Returns a dense density matrix in little-endian computational-basis order.
+    ///
+    /// # Errors
+    ///
+    /// Returns an error if the Hilbert-space dimension overflows.
+    fn density_matrix(&mut self) -> Result<Vec<Vec<Complex64>>, StateAccessError>;
+
+    /// Returns one density-matrix element.
+    ///
+    /// The default implementation materializes the full dense density matrix
+    /// and then reads one entry. Backends with cheaper direct element access
+    /// should override this method.
+    ///
+    /// # Errors
+    ///
+    /// Returns an error if either index is outside the Hilbert space.
+    fn density_matrix_element(
+        &mut self,
+        row: usize,
+        col: usize,
+    ) -> Result<Complex64, StateAccessError> {
+        validate_basis_index(self.num_qubits(), row)?;
+        validate_basis_index(self.num_qubits(), col)?;
+        let rho = self.density_matrix()?;
+        Ok(rho[row][col])
+    }
+
+    /// Returns the probability of one computational-basis state.
+    ///
+    /// # Errors
+    ///
+    /// Returns an error if `basis_state` is outside the Hilbert space.
+    fn basis_probability(&mut self, basis_state: usize) -> Result<f64, StateAccessError> {
+        Ok(self.density_matrix_element(basis_state, basis_state)?.re)
+    }
+}
+
+/// Capability for backends that can evaluate Pauli expectation values.
+pub trait PauliExpectationAccess: StateInfo {
+    /// Returns `<P>` for the supplied Pauli string.
+    ///
+    /// The result is complex so callers can also query phased Pauli strings
+    /// such as `i X`. For Hermitian Paulis with real phase, the imaginary part
+    /// should be numerical roundoff only.
+    ///
+    /// # Errors
+    ///
+    /// Returns an error if the Pauli string acts outside the state.
+    fn pauli_expectation(&mut self, pauli: &PauliString) -> Result<Complex64, StateAccessError>;
+}
+
+/// Capability for backends that can sample projective Pauli-basis measurements.
+///
+/// Unlike [`StateVectorAccess`], [`DensityMatrixAccess`], and
+/// [`PauliExpectationAccess`], these methods are not passive inspection:
+/// sampling mutates the backend by collapsing the measured state and may
+/// consume RNG state.
+pub trait StateSampling: StateInfo {
+    /// Samples/measures qubits in the computational (`Z`) basis.
+    ///
+    /// Results use the existing PECOS [`MeasurementResult`] convention:
+    /// `outcome == false` is the `0`/`+Z` outcome and `outcome == true` is
+    /// the `1`/`-Z` outcome.
+    ///
+    /// # Errors
+    ///
+    /// Returns an error if any qubit is outside the state.
+    fn sample_z(&mut self, qubits: &[QubitId]) -> Result<Vec<MeasurementResult>, StateAccessError>;
+
+    /// Samples/measures qubits in the `X` basis.
+    ///
+    /// # Errors
+    ///
+    /// Returns an error if any qubit is outside the state.
+    fn sample_x(&mut self, qubits: &[QubitId]) -> Result<Vec<MeasurementResult>, StateAccessError>;
+
+    /// Samples/measures qubits in the `Y` basis.
+    ///
+    /// # Errors
+    ///
+    /// Returns an error if any qubit is outside the state.
+    fn sample_y(&mut self, qubits: &[QubitId]) -> Result<Vec<MeasurementResult>, StateAccessError>;
+}
+
+/// Capability for stabilizer backends that can materialize a dense state vector.
+///
+/// This is an explicit conversion, not passive inspection. The output has
+/// length `2^num_qubits`, so callers should treat it as an exponential-cost
+/// debugging and interop path rather than the normal way to query stabilizer
+/// states.
+pub trait StabilizerStateVectorConversion: StateInfo {
+    /// Converts the stabilizer state into a dense state vector in little-endian
+    /// computational-basis order.
+    ///
+    /// The returned vector is normalized and has a deterministic global phase:
+    /// the first nonzero amplitude is real and positive.
+    ///
+    /// # Errors
+    ///
+    /// Returns an error if the Hilbert-space dimension overflows or if the
+    /// stabilizer generators do not define a unique pure state.
+    fn to_state_vector(&self) -> Result<Vec<Complex64>, StateAccessError>;
+}
+
+macro_rules! impl_state_sampling {
+    (impl<$($generic:tt),+> for $ty:ty where $($where_clause:tt)*) => {
+        impl<$($generic),+> StateSampling for $ty
+        where
+            $($where_clause)*
+        {
+            fn sample_z(
+                &mut self,
+                qubits: &[QubitId],
+            ) -> Result<Vec<MeasurementResult>, StateAccessError> {
+                sample_z_via_clifford(self, qubits)
+            }
+
+            fn sample_x(
+                &mut self,
+                qubits: &[QubitId],
+            ) -> Result<Vec<MeasurementResult>, StateAccessError> {
+                sample_x_via_clifford(self, qubits)
+            }
+
+            fn sample_y(
+                &mut self,
+                qubits: &[QubitId],
+            ) -> Result<Vec<MeasurementResult>, StateAccessError> {
+                sample_y_via_clifford(self, qubits)
+            }
+        }
+    };
+    (for $ty:ty) => {
+        impl StateSampling for $ty {
+            fn sample_z(
+                &mut self,
+                qubits: &[QubitId],
+            ) -> Result<Vec<MeasurementResult>, StateAccessError> {
+                sample_z_via_clifford(self, qubits)
+            }
+
+            fn sample_x(
+                &mut self,
+                qubits: &[QubitId],
+            ) -> Result<Vec<MeasurementResult>, StateAccessError> {
+                sample_x_via_clifford(self, qubits)
+            }
+
+            fn sample_y(
+                &mut self,
+                qubits: &[QubitId],
+            ) -> Result<Vec<MeasurementResult>, StateAccessError> {
+                sample_y_via_clifford(self, qubits)
+            }
+        }
+    };
+}
+
+impl_state_sampling!(impl<R> for StateVecSoA<R> where R: Rng);
+impl_state_sampling!(impl<R> for SparseStateVecSoA<R> where R: Rng + Debug);
+impl_state_sampling!(impl<R> for StateVecAoS<R> where R: Rng + SeedableRng + Debug);
+impl_state_sampling!(impl<R> for SparseStateVecAoS<R> where R: Rng + Debug);
+impl_state_sampling!(impl<R> for StateVecSoA32<R> where R: Rng);
+impl_state_sampling!(impl<R> for DensityMatrix<R> where R: Rng + SeedableRng + Debug + Clone);
+impl_state_sampling!(impl<S, R> for SparseStabGeneric<S, R> where S: IndexSet, R: Rng + SeedableRng + Debug);
+impl_state_sampling!(impl<R> for SparseStabHybrid<R> where R: Rng + SeedableRng + Debug);
+impl_state_sampling!(for Stabilizer);
+
+impl<S, R> StabilizerStateVectorConversion for SparseStabGeneric<S, R>
+where
+    S: IndexSet,
+    R: Rng + SeedableRng + Debug,
+{
+    fn to_state_vector(&self) -> Result<Vec<Complex64>, StateAccessError> {
+        stabilizer_group_to_state_vector(&self.to_stabilizer_group())
+    }
+}
+
+impl<R> StabilizerStateVectorConversion for SparseStabHybrid<R>
+where
+    R: Rng + SeedableRng + Debug,
+{
+    fn to_state_vector(&self) -> Result<Vec<Complex64>, StateAccessError> {
+        stabilizer_group_to_state_vector(&self.to_stabilizer_group())
+    }
+}
+
+impl<R> StabilizerStateVectorConversion for DenseStab<R>
+where
+    R: Rng + SeedableRng + Debug + Clone,
+{
+    fn to_state_vector(&self) -> Result<Vec<Complex64>, StateAccessError> {
+        stabilizer_group_to_state_vector(&self.to_stabilizer_group())
+    }
+}
+
+impl StabilizerStateVectorConversion for Stabilizer {
+    fn to_state_vector(&self) -> Result<Vec<Complex64>, StateAccessError> {
+        stabilizer_group_to_state_vector(&self.to_stabilizer_group())
+    }
+}
+
+impl<R> StateVectorAccess for StateVecSoA<R>
+where
+    R: Rng,
+{
+    fn amplitude(&mut self, basis_state: usize) -> Result<Complex64, StateAccessError> {
+        validate_basis_index(StateInfo::num_qubits(self), basis_state)?;
+        Ok(self.get_amplitude(basis_state))
+    }
+
+    fn state_vector(&mut self) -> Result<Vec<Complex64>, StateAccessError> {
+        let expected = self.hilbert_dim()?;
+        let state = self.state();
+        validate_state_vector_len(&state, expected)?;
+        Ok(state)
+    }
+
+    fn basis_probability(&mut self, basis_state: usize) -> Result<f64, StateAccessError> {
+        validate_basis_index(StateInfo::num_qubits(self), basis_state)?;
+        Ok(self.probability(basis_state))
+    }
+}
+
+impl<R> PauliExpectationAccess for StateVecSoA<R>
+where
+    R: Rng,
+{
+    fn pauli_expectation(&mut self, pauli: &PauliString) -> Result<Complex64, StateAccessError> {
+        let num_qubits = StateInfo::num_qubits(self);
+        pauli_expectation_from_state_vector(&self.state_vector()?, num_qubits, pauli)
+    }
+}
+
+impl<R> StateVectorAccess for SparseStateVecSoA<R>
+where
+    R: Rng + Debug,
+{
+    fn amplitude(&mut self, basis_state: usize) -> Result<Complex64, StateAccessError> {
+        validate_basis_index(StateInfo::num_qubits(self), basis_state)?;
+        Ok(self.get_amplitude(basis_state))
+    }
+
+    fn state_vector(&mut self) -> Result<Vec<Complex64>, StateAccessError> {
+        let expected = self.hilbert_dim()?;
+        let state = self.state();
+        validate_state_vector_len(&state, expected)?;
+        Ok(state)
+    }
+
+    fn basis_probability(&mut self, basis_state: usize) -> Result<f64, StateAccessError> {
+        validate_basis_index(StateInfo::num_qubits(self), basis_state)?;
+        Ok(self.probability(basis_state))
+    }
+}
+
+impl<R> PauliExpectationAccess for SparseStateVecSoA<R>
+where
+    R: Rng + Debug,
+{
+    fn pauli_expectation(&mut self, pauli: &PauliString) -> Result<Complex64, StateAccessError> {
+        let num_qubits = StateInfo::num_qubits(self);
+        pauli_expectation_from_state_vector(&self.state_vector()?, num_qubits, pauli)
+    }
+}
+
+impl<R> StateVectorAccess for StateVecAoS<R>
+where
+    R: Rng + SeedableRng + Debug,
+{
+    fn amplitude(&mut self, basis_state: usize) -> Result<Complex64, StateAccessError> {
+        validate_basis_index(StateInfo::num_qubits(self), basis_state)?;
+        Ok(self.state()[basis_state])
+    }
+
+    fn state_vector(&mut self) -> Result<Vec<Complex64>, StateAccessError> {
+        let expected = self.hilbert_dim()?;
+        let state = self.state().to_vec();
+        validate_state_vector_len(&state, expected)?;
+        Ok(state)
+    }
+
+    fn basis_probability(&mut self, basis_state: usize) -> Result<f64, StateAccessError> {
+        validate_basis_index(StateInfo::num_qubits(self), basis_state)?;
+        Ok(self.probability(basis_state))
+    }
+}
+
+impl<R> PauliExpectationAccess for StateVecAoS<R>
+where
+    R: Rng + SeedableRng + Debug,
+{
+    fn pauli_expectation(&mut self, pauli: &PauliString) -> Result<Complex64, StateAccessError> {
+        let num_qubits = StateInfo::num_qubits(self);
+        pauli_expectation_from_state_vector(&self.state_vector()?, num_qubits, pauli)
+    }
+}
+
+impl<R> StateVectorAccess for SparseStateVecAoS<R>
+where
+    R: Rng + Debug,
+{
+    fn amplitude(&mut self, basis_state: usize) -> Result<Complex64, StateAccessError> {
+        validate_basis_index(StateInfo::num_qubits(self), basis_state)?;
+        Ok(self.get_amplitude(basis_state))
+    }
+
+    fn state_vector(&mut self) -> Result<Vec<Complex64>, StateAccessError> {
+        let dim = self.hilbert_dim()?;
+        let mut state = vec![Complex64::new(0.0, 0.0); dim];
+        for (basis_state, amp) in state.iter_mut().enumerate() {
+            *amp = self.get_amplitude(basis_state);
+        }
+        Ok(state)
+    }
+}
+
+impl<R> PauliExpectationAccess for SparseStateVecAoS<R>
+where
+    R: Rng + Debug,
+{
+    fn pauli_expectation(&mut self, pauli: &PauliString) -> Result<Complex64, StateAccessError> {
+        let num_qubits = StateInfo::num_qubits(self);
+        pauli_expectation_from_state_vector(&self.state_vector()?, num_qubits, pauli)
+    }
+}
+
+impl<R> StateVectorAccess for StateVecSoA32<R>
+where
+    R: Rng,
+{
+    fn amplitude(&mut self, basis_state: usize) -> Result<Complex64, StateAccessError> {
+        validate_basis_index(StateInfo::num_qubits(self), basis_state)?;
+        let amp = self.get_amplitude(basis_state);
+        Ok(Complex64::new(f64::from(amp.re), f64::from(amp.im)))
+    }
+
+    fn state_vector(&mut self) -> Result<Vec<Complex64>, StateAccessError> {
+        let expected = self.hilbert_dim()?;
+        let state: Vec<Complex64> = self
+            .to_complex_vec()
+            .into_iter()
+            .map(|amp| Complex64::new(f64::from(amp.re), f64::from(amp.im)))
+            .collect();
+        validate_state_vector_len(&state, expected)?;
+        Ok(state)
+    }
+
+    fn basis_probability(&mut self, basis_state: usize) -> Result<f64, StateAccessError> {
+        validate_basis_index(StateInfo::num_qubits(self), basis_state)?;
+        Ok(self.probability(basis_state))
+    }
+}
+
+impl<R> PauliExpectationAccess for StateVecSoA32<R>
+where
+    R: Rng,
+{
+    fn pauli_expectation(&mut self, pauli: &PauliString) -> Result<Complex64, StateAccessError> {
+        let num_qubits = StateInfo::num_qubits(self);
+        pauli_expectation_from_state_vector(&self.state_vector()?, num_qubits, pauli)
+    }
+}
+
+impl<R> DensityMatrixAccess for DensityMatrix<R>
+where
+    R: Rng + SeedableRng + Debug + Clone,
+{
+    fn density_matrix(&mut self) -> Result<Vec<Vec<Complex64>>, StateAccessError> {
+        let expected = self.hilbert_dim()?;
+        let rho = self.get_density_matrix();
+        validate_density_matrix_shape(&rho, expected)?;
+        Ok(rho)
+    }
+
+    fn basis_probability(&mut self, basis_state: usize) -> Result<f64, StateAccessError> {
+        validate_basis_index(StateInfo::num_qubits(self), basis_state)?;
+        Ok(self.probability(basis_state))
+    }
+}
+
+impl<R> PauliExpectationAccess for DensityMatrix<R>
+where
+    R: Rng + SeedableRng + Debug + Clone,
+{
+    fn pauli_expectation(&mut self, pauli: &PauliString) -> Result<Complex64, StateAccessError> {
+        let num_qubits = StateInfo::num_qubits(self);
+        pauli_expectation_from_density_matrix(&self.density_matrix()?, num_qubits, pauli)
+    }
+}
+
+impl<S, R> PauliExpectationAccess for SparseStabGeneric<S, R>
+where
+    S: IndexSet,
+    R: Rng + SeedableRng + Debug,
+{
+    fn pauli_expectation(&mut self, pauli: &PauliString) -> Result<Complex64, StateAccessError> {
+        pauli_expectation_from_stabilizer_group(
+            &self.to_stabilizer_group(),
+            StateInfo::num_qubits(self),
+            pauli,
+        )
+    }
+}
+
+impl<R> PauliExpectationAccess for SparseStabHybrid<R>
+where
+    R: Rng + SeedableRng + Debug,
+{
+    fn pauli_expectation(&mut self, pauli: &PauliString) -> Result<Complex64, StateAccessError> {
+        pauli_expectation_from_stabilizer_group(
+            &self.to_stabilizer_group(),
+            StateInfo::num_qubits(self),
+            pauli,
+        )
+    }
+}
+
+impl<R> PauliExpectationAccess for DenseStab<R>
+where
+    R: Rng + SeedableRng + Debug + Clone,
+{
+    fn pauli_expectation(&mut self, pauli: &PauliString) -> Result<Complex64, StateAccessError> {
+        pauli_expectation_from_stabilizer_group(
+            &self.to_stabilizer_group(),
+            StateInfo::num_qubits(self),
+            pauli,
+        )
+    }
+}
+
+impl PauliExpectationAccess for Stabilizer {
+    fn pauli_expectation(&mut self, pauli: &PauliString) -> Result<Complex64, StateAccessError> {
+        pauli_expectation_from_stabilizer_group(
+            &self.to_stabilizer_group(),
+            StateInfo::num_qubits(self),
+            pauli,
+        )
+    }
+}
+
+fn hilbert_dim(num_qubits: usize) -> Result<usize, StateAccessError> {
+    let shift = u32::try_from(num_qubits)
+        .map_err(|_| StateAccessError::DimensionOverflow { num_qubits })?;
+    if shift >= usize::BITS {
+        return Err(StateAccessError::DimensionOverflow { num_qubits });
+    }
+    Ok(1usize << shift)
+}
+
+fn validate_basis_index(num_qubits: usize, index: usize) -> Result<usize, StateAccessError> {
+    let dim = hilbert_dim(num_qubits)?;
+    if index >= dim {
+        return Err(StateAccessError::BasisIndexOutOfRange {
+            num_qubits,
+            dim,
+            index,
+        });
+    }
+    Ok(dim)
+}
+
+fn validate_pauli_support(num_qubits: usize, pauli: &PauliString) -> Result<(), StateAccessError> {
+    for qubit in pauli.qubits() {
+        if qubit >= num_qubits {
+            return Err(StateAccessError::PauliQubitOutOfRange { num_qubits, qubit });
+        }
+    }
+    Ok(())
+}
+
+fn validate_qubit_support(num_qubits: usize, qubits: &[QubitId]) -> Result<(), StateAccessError> {
+    for qubit in qubits {
+        let q = qubit.index();
+        if q >= num_qubits {
+            return Err(StateAccessError::QubitOutOfRange {
+                num_qubits,
+                qubit: q,
+            });
+        }
+    }
+    Ok(())
+}
+
+fn validate_state_vector_len(state: &[Complex64], expected: usize) -> Result<(), StateAccessError> {
+    if state.len() != expected {
+        return Err(StateAccessError::InvalidStateVectorLength {
+            expected,
+            actual: state.len(),
+        });
+    }
+    Ok(())
+}
+
+fn validate_density_matrix_shape(
+    rho: &[Vec<Complex64>],
+    expected: usize,
+) -> Result<(), StateAccessError> {
+    if rho.len() != expected {
+        return Err(StateAccessError::InvalidDensityMatrixShape {
+            expected,
+            rows: rho.len(),
+            cols: rho.first().map_or(0, Vec::len),
+        });
+    }
+    for row in rho {
+        if row.len() != expected {
+            return Err(StateAccessError::InvalidDensityMatrixShape {
+                expected,
+                rows: rho.len(),
+                cols: row.len(),
+            });
+        }
+    }
+    Ok(())
+}
+
+fn sample_z_via_clifford<T>(
+    backend: &mut T,
+    qubits: &[QubitId],
+) -> Result<Vec<MeasurementResult>, StateAccessError>
+where
+    T: CliffordGateable + StateInfo,
+{
+    validate_qubit_support(StateInfo::num_qubits(backend), qubits)?;
+    Ok(backend.mz(qubits))
+}
+
+fn sample_x_via_clifford<T>(
+    backend: &mut T,
+    qubits: &[QubitId],
+) -> Result<Vec<MeasurementResult>, StateAccessError>
+where
+    T: CliffordGateable + StateInfo,
+{
+    validate_qubit_support(StateInfo::num_qubits(backend), qubits)?;
+    Ok(backend.mx(qubits))
+}
+
+fn sample_y_via_clifford<T>(
+    backend: &mut T,
+    qubits: &[QubitId],
+) -> Result<Vec<MeasurementResult>, StateAccessError>
+where
+    T: CliffordGateable + StateInfo,
+{
+    validate_qubit_support(StateInfo::num_qubits(backend), qubits)?;
+    Ok(backend.my(qubits))
+}
+
+fn stabilizer_group_to_state_vector(
+    group: &PauliStabilizerGroup,
+) -> Result<Vec<Complex64>, StateAccessError> {
+    let num_qubits = group.num_qubits();
+    let num_generators = group.num_generators();
+    let rank = group.rank();
+    if rank != num_qubits {
+        return Err(StateAccessError::NotPureStabilizerState {
+            num_qubits,
+            num_generators,
+            rank,
+        });
+    }
+
+    let dim = hilbert_dim(num_qubits)?;
+    let generators = group.stabilizers();
+    for seed in 0..dim {
+        let mut state = vec![Complex64::new(0.0, 0.0); dim];
+        state[seed] = Complex64::new(1.0, 0.0);
+
+        for generator in generators {
+            validate_pauli_support(num_qubits, generator)?;
+            apply_stabilizer_projector(&mut state, generator);
+            if state_norm_sqr(&state) <= f64::EPSILON {
+                break;
+            }
+        }
+
+        let norm_sqr = state_norm_sqr(&state);
+        if norm_sqr > f64::EPSILON {
+            normalize_state_vector(&mut state, norm_sqr);
+            canonicalize_global_phase(&mut state);
+            return Ok(state);
+        }
+    }
+
+    Err(StateAccessError::NotPureStabilizerState {
+        num_qubits,
+        num_generators,
+        rank,
+    })
+}
+
+fn apply_stabilizer_projector(state: &mut [Complex64], generator: &PauliString) {
+    let input = state.to_vec();
+    state.fill(Complex64::new(0.0, 0.0));
+    for (basis_state, amplitude) in input.iter().copied().enumerate() {
+        state[basis_state] += amplitude * 0.5;
+        if amplitude.norm_sqr() == 0.0 {
+            continue;
+        }
+        let (output_state, coefficient) = pauli_action_on_basis_index(generator, basis_state);
+        state[output_state] += coefficient * amplitude * 0.5;
+    }
+}
+
+fn state_norm_sqr(state: &[Complex64]) -> f64 {
+    state.iter().map(Complex64::norm_sqr).sum()
+}
+
+fn standard_complex_normal<R>(rng: &mut R) -> Complex64
+where
+    R: Rng + ?Sized,
+{
+    Complex64::new(standard_normal(rng), standard_normal(rng))
+}
+
+fn standard_normal<R>(rng: &mut R) -> f64
+where
+    R: Rng + ?Sized,
+{
+    loop {
+        let u1 = rng.random::<f64>();
+        if u1 > 0.0 {
+            let u2 = rng.random::<f64>();
+            return (-2.0 * u1.ln()).sqrt() * (TAU * u2).cos();
+        }
+    }
+}
+
+fn normalize_state_vector(state: &mut [Complex64], norm_sqr: f64) {
+    let scale = norm_sqr.sqrt();
+    for amplitude in state {
+        *amplitude /= scale;
+    }
+}
+
+fn canonicalize_global_phase(state: &mut [Complex64]) {
+    let Some(first_nonzero) = state
+        .iter()
+        .copied()
+        .find(|amplitude| amplitude.norm_sqr() > f64::EPSILON)
+    else {
+        return;
+    };
+    let phase = first_nonzero / Complex64::new(first_nonzero.norm(), 0.0);
+    let correction = phase.conj();
+    for amplitude in state {
+        *amplitude *= correction;
+    }
+}
+
+fn pauli_action_on_basis_index(pauli: &PauliString, basis_state: usize) -> (usize, Complex64) {
+    let mut output = basis_state;
+    let mut coefficient = pauli.phase().to_complex();
+    for (single, qubit) in pauli.iter_pairs() {
+        let q = qubit.index();
+        let bit = (basis_state >> q) & 1;
+        match single {
+            Pauli::I => {}
+            Pauli::X => {
+                output ^= 1usize << q;
+            }
+            Pauli::Y => {
+                output ^= 1usize << q;
+                coefficient *= if bit == 0 {
+                    Complex64::new(0.0, 1.0)
+                } else {
+                    Complex64::new(0.0, -1.0)
+                };
+            }
+            Pauli::Z => {
+                if bit == 1 {
+                    coefficient = -coefficient;
+                }
+            }
+        }
+    }
+    (output, coefficient)
+}
+
+fn pauli_expectation_from_state_vector(
+    state: &[Complex64],
+    num_qubits: usize,
+    pauli: &PauliString,
+) -> Result<Complex64, StateAccessError> {
+    validate_pauli_support(num_qubits, pauli)?;
+    let dim = hilbert_dim(num_qubits)?;
+    validate_state_vector_len(state, dim)?;
+    let mut expectation = Complex64::new(0.0, 0.0);
+    for basis_state in 0..dim {
+        let (output, coefficient) = pauli_action_on_basis_index(pauli, basis_state);
+        expectation += coefficient * state[basis_state] * state[output].conj();
+    }
+    Ok(expectation)
+}
+
+fn pauli_expectation_from_density_matrix(
+    rho: &[Vec<Complex64>],
+    num_qubits: usize,
+    pauli: &PauliString,
+) -> Result<Complex64, StateAccessError> {
+    validate_pauli_support(num_qubits, pauli)?;
+    let dim = hilbert_dim(num_qubits)?;
+    validate_density_matrix_shape(rho, dim)?;
+    let mut expectation = Complex64::new(0.0, 0.0);
+    for (basis_state, rho_row) in rho.iter().enumerate().take(dim) {
+        let (output, coefficient) = pauli_action_on_basis_index(pauli, basis_state);
+        expectation += coefficient * rho_row[output];
+    }
+    Ok(expectation)
+}
+
+fn pauli_expectation_from_stabilizer_group(
+    stabilizers: &PauliStabilizerGroup,
+    num_qubits: usize,
+    pauli: &PauliString,
+) -> Result<Complex64, StateAccessError> {
+    validate_pauli_support(num_qubits, pauli)?;
+
+    let mut positive_body = pauli.clone();
+    positive_body.set_phase(QuarterPhase::PlusOne);
+    if !stabilizers.contains(&positive_body) {
+        return Ok(Complex64::new(0.0, 0.0));
+    }
+
+    let stabilizer_phase = if stabilizers.contains_with_phase(&positive_body) {
+        QuarterPhase::PlusOne
+    } else {
+        QuarterPhase::MinusOne
+    };
+    Ok(pauli
+        .phase()
+        .multiply(&stabilizer_phase.conjugate())
+        .to_complex())
+}
+
+#[cfg(test)]
+mod tests {
+    use super::*;
+    use crate::{
+        CliffordGateable, DenseStab, SparseStab, SparseStabHybrid, Stabilizer, StateVec, qid,
+    };
+    use pecos_core::QubitId;
+    use pecos_core::pauli::algebra::i;
+    use pecos_core::pauli::*;
+    use pecos_random::PecosRng;
+
+    fn assert_close(actual: Complex64, expected: Complex64) {
+        assert!(
+            (actual - expected).norm() < 1e-10,
+            "actual={actual}, expected={expected}"
+        );
+    }
+
+    fn assert_state_vectors_close(actual: &[Complex64], expected: &[Complex64]) {
+        assert_eq!(actual.len(), expected.len());
+        for (index, (&actual_amp, &expected_amp)) in actual.iter().zip(expected).enumerate() {
+            assert!(
+                (actual_amp - expected_amp).norm() < 1e-10,
+                "state-vector mismatch at basis {index}: actual={actual_amp}, expected={expected_amp}"
+            );
+        }
+    }
+
+    #[test]
+    fn state_vector_access_flushes_pending_gates() {
+        let mut state = StateVecSoA::new(1);
+        state.h(&qid(0));
+
+        let amp0 = StateVectorAccess::amplitude(&mut state, 0).unwrap();
+        let amp1 = StateVectorAccess::amplitude(&mut state, 1).unwrap();
+        let expected = 1.0 / 2.0_f64.sqrt();
+        assert_close(amp0, Complex64::new(expected, 0.0));
+        assert_close(amp1, Complex64::new(expected, 0.0));
+        assert!((StateVectorAccess::basis_probability(&mut state, 0).unwrap() - 0.5).abs() < 1e-10);
+    }
+
+    #[test]
+    fn random_statevector_is_normalized_and_seed_reproducible() {
+        let mut rng = PecosRng::seed_from_u64(123);
+        let state = random_statevector(&mut rng, 3).unwrap();
+        assert_eq!(state.len(), 8);
+        assert!((state_norm_sqr(&state) - 1.0).abs() < 1e-12);
+
+        let mut same_seed = PecosRng::seed_from_u64(123);
+        let same = random_statevector(&mut same_seed, 3).unwrap();
+        assert_eq!(state, same);
+
+        let mut different_seed = PecosRng::seed_from_u64(456);
+        let different = random_statevector(&mut different_seed, 3).unwrap();
+        assert_ne!(state, different);
+    }
+
+    #[test]
+    fn random_statevector_zero_qubits_is_scalar_identity_state() {
+        let mut rng = PecosRng::seed_from_u64(123);
+        let state = random_statevector(&mut rng, 0).unwrap();
+        assert_state_vectors_close(&state, &[Complex64::new(1.0, 0.0)]);
+    }
+
+    #[test]
+    fn random_statevector_haar_marginal_is_reasonable() {
+        let mut rng = PecosRng::seed_from_u64(123);
+        let samples = 2_000;
+        let mut p0_sum = 0.0;
+        for _ in 0..samples {
+            let state = random_statevector(&mut rng, 2).unwrap();
+            p0_sum += state[0].norm_sqr();
+        }
+        let mean = p0_sum / f64::from(samples);
+        assert!(
+            (0.22..0.28).contains(&mean),
+            "expected E[|psi_0|^2] near 1/4 for a 4D Haar state, got {mean}"
+        );
+    }
+
+    #[test]
+    fn sparse_state_vector_access_returns_dense_vector() {
+        let mut state = StateVec::new(2);
+        state.x(&qid(1));
+
+        let dense = state.state_vector().unwrap();
+        assert_eq!(dense.len(), 4);
+        assert_close(dense[0], Complex64::new(0.0, 0.0));
+        assert_close(dense[2], Complex64::new(1.0, 0.0));
+    }
+
+    #[test]
+    fn all_state_vector_backends_expose_amplitudes() {
+        let mut dense_soa = StateVecSoA::new(1);
+        let mut dense_aos = StateVecAoS::new(1);
+        let mut sparse_soa = SparseStateVecSoA::new(1);
+        let mut sparse_aos = SparseStateVecAoS::new(1);
+        let mut soa32 = StateVecSoA32::new(1);
+
+        dense_soa.x(&qid(0));
+        dense_aos.x(&qid(0));
+        sparse_soa.x(&qid(0));
+        sparse_aos.x(&qid(0));
+        soa32.x(&qid(0));
+
+        assert_close(dense_soa.amplitude(1).unwrap(), Complex64::new(1.0, 0.0));
+        assert_close(dense_aos.amplitude(1).unwrap(), Complex64::new(1.0, 0.0));
+        assert_close(sparse_soa.amplitude(1).unwrap(), Complex64::new(1.0, 0.0));
+        assert_close(sparse_aos.amplitude(1).unwrap(), Complex64::new(1.0, 0.0));
+        assert_close(soa32.amplitude(1).unwrap(), Complex64::new(1.0, 0.0));
+    }
+
+    #[test]
+    fn state_vector_pauli_expectations_match_known_states() {
+        let mut plus = StateVec::new(1);
+        plus.h(&qid(0));
+
+        assert_close(
+            plus.pauli_expectation(&X(0)).unwrap(),
+            Complex64::new(1.0, 0.0),
+        );
+        assert_close(
+            plus.pauli_expectation(&Z(0)).unwrap(),
+            Complex64::new(0.0, 0.0),
+        );
+        assert_close(
+            plus.pauli_expectation(&(i * X(0))).unwrap(),
+            Complex64::new(0.0, 1.0),
+        );
+    }
+
+    #[test]
+    fn density_matrix_access_and_expectation_match_known_state() {
+        let mut state = DensityMatrix::new(1);
+        state.h(&qid(0));
+
+        let rho = state.density_matrix().unwrap();
+        assert_eq!(rho.len(), 2);
+        assert_close(rho[0][0], Complex64::new(0.5, 0.0));
+        assert_close(rho[0][1], Complex64::new(0.5, 0.0));
+        assert!(
+            (DensityMatrixAccess::basis_probability(&mut state, 0).unwrap() - 0.5).abs() < 1e-10
+        );
+        assert_close(
+            state.pauli_expectation(&X(0)).unwrap(),
+            Complex64::new(1.0, 0.0),
+        );
+        assert_close(
+            state.pauli_expectation(&Z(0)).unwrap(),
+            Complex64::new(0.0, 0.0),
+        );
+    }
+
+    #[test]
+    fn sparse_stab_pauli_expectation_uses_signed_stabilizer_membership() {
+        let mut one = SparseStab::new(1);
+        one.x(&qid(0));
+
+        assert_close(
+            one.pauli_expectation(&Z(0)).unwrap(),
+            Complex64::new(-1.0, 0.0),
+        );
+        assert_close(
+            one.pauli_expectation(&(-Z(0))).unwrap(),
+            Complex64::new(1.0, 0.0),
+        );
+        assert_close(
+            one.pauli_expectation(&(i * Z(0))).unwrap(),
+            Complex64::new(0.0, -1.0),
+        );
+        assert_close(
+            one.pauli_expectation(&X(0)).unwrap(),
+            Complex64::new(0.0, 0.0),
+        );
+    }
+
+    #[test]
+    fn sparse_stab_pauli_expectation_matches_state_vector_for_bell_state() {
+        let mut state_vec = StateVec::new(2);
+        let mut stab = SparseStab::new(2);
+        state_vec.h(&qid(0)).cx(&[(QubitId(0), QubitId(1))]);
+        stab.h(&qid(0)).cx(&[(QubitId(0), QubitId(1))]);
+
+        for pauli in [
+            X(0) & X(1),
+            Y(0) & Y(1),
+            Z(0) & Z(1),
+            X(0) & Z(1),
+            Y(0) & Z(1),
+            X(0) & Y(1),
+            X(0),
+            Z(0),
+        ] {
+            let expected = state_vec.pauli_expectation(&pauli).unwrap();
+            let actual = stab.pauli_expectation(&pauli).unwrap();
+            assert_close(actual, expected);
+        }
+    }
+
+    #[test]
+    fn dense_stab_pauli_expectation_matches_state_vector_for_bell_state() {
+        let mut state_vec = StateVec::new(2);
+        let mut dense = DenseStab::new(2);
+        state_vec.h(&qid(0)).cx(&[(QubitId(0), QubitId(1))]);
+        dense.h(&qid(0)).cx(&[(QubitId(0), QubitId(1))]);
+
+        for pauli in [
+            X(0) & X(1),
+            Y(0) & Y(1),
+            Z(0) & Z(1),
+            X(0) & Z(1),
+            Y(0) & Z(1),
+            X(0) & Y(1),
+            X(0),
+            Z(0),
+        ] {
+            let expected = state_vec.pauli_expectation(&pauli).unwrap();
+            let actual = dense.pauli_expectation(&pauli).unwrap();
+            assert_close(actual, expected);
+        }
+    }
+
+    #[test]
+    fn stabilizer_pauli_expectations_match_state_vector_for_three_qubit_ghz() {
+        let mut state_vec = StateVec::new(3);
+        let mut sparse = SparseStab::new(3);
+        let mut dense = DenseStab::new(3);
+        let pairs = [(QubitId(0), QubitId(1)), (QubitId(0), QubitId(2))];
+        state_vec.h(&qid(0)).cx(&pairs);
+        sparse.h(&qid(0)).cx(&pairs);
+        dense.h(&qid(0)).cx(&pairs);
+
+        for pauli in [
+            X(0) & X(1) & X(2),
+            Z(0) & Z(1),
+            Z(1) & Z(2),
+            Z(0) & Z(2),
+            Y(0) & Y(1) & X(2),
+            X(0),
+            Z(0),
+        ] {
+            let expected = state_vec.pauli_expectation(&pauli).unwrap();
+            let sparse_actual = sparse.pauli_expectation(&pauli).unwrap();
+            let dense_actual = dense.pauli_expectation(&pauli).unwrap();
+            assert_close(sparse_actual, expected);
+            assert_close(dense_actual, expected);
+        }
+    }
+
+    #[test]
+    fn sparse_stab_hybrid_supports_pauli_expectation_access() {
+        let mut plus = SparseStabHybrid::new(1);
+        plus.h(&qid(0));
+
+        assert_close(
+            plus.pauli_expectation(&X(0)).unwrap(),
+            Complex64::new(1.0, 0.0),
+        );
+        assert_close(
+            plus.pauli_expectation(&Z(0)).unwrap(),
+            Complex64::new(0.0, 0.0),
+        );
+        assert_close(
+            plus.pauli_expectation(&(i * X(0))).unwrap(),
+            Complex64::new(0.0, 1.0),
+        );
+    }
+
+    #[test]
+    fn stabilizer_generator_bridge_preserves_y_phase_convention() {
+        let mut sparse = SparseStab::new(1);
+        sparse.h(&qid(0)).sz(&qid(0));
+
+        assert_close(
+            sparse.pauli_expectation(&Y(0)).unwrap(),
+            Complex64::new(1.0, 0.0),
+        );
+        assert_close(
+            sparse.pauli_expectation(&X(0)).unwrap(),
+            Complex64::new(0.0, 0.0),
+        );
+
+        let mut hybrid = SparseStabHybrid::new(1);
+        hybrid.h(&qid(0)).sz(&qid(0));
+        assert_close(
+            hybrid.pauli_expectation(&Y(0)).unwrap(),
+            Complex64::new(1.0, 0.0),
+        );
+
+        let mut dense = DenseStab::new(1);
+        dense.h(&qid(0)).sz(&qid(0));
+        assert_close(
+            dense.pauli_expectation(&Y(0)).unwrap(),
+            Complex64::new(1.0, 0.0),
+        );
+        assert_close(
+            dense.pauli_expectation(&X(0)).unwrap(),
+            Complex64::new(0.0, 0.0),
+        );
+    }
+
+    #[test]
+    fn dense_stab_pauli_expectation_preserves_signed_basis_state() {
+        let mut one = DenseStab::new(1);
+        one.x(&qid(0));
+
+        assert_close(
+            one.pauli_expectation(&Z(0)).unwrap(),
+            Complex64::new(-1.0, 0.0),
+        );
+        assert_close(
+            one.pauli_expectation(&(-Z(0))).unwrap(),
+            Complex64::new(1.0, 0.0),
+        );
+        assert_close(
+            one.pauli_expectation(&(i * Z(0))).unwrap(),
+            Complex64::new(0.0, -1.0),
+        );
+    }
+
+    #[test]
+    fn default_stabilizer_supports_pauli_expectation_access() {
+        let mut bell = Stabilizer::new(2);
+        bell.h(&qid(0)).cx(&[(QubitId(0), QubitId(1))]);
+
+        assert_close(
+            bell.pauli_expectation(&(X(0) & X(1))).unwrap(),
+            Complex64::new(1.0, 0.0),
+        );
+        assert_close(
+            bell.pauli_expectation(&(Z(0) & Z(1))).unwrap(),
+            Complex64::new(1.0, 0.0),
+        );
+        assert_close(
+            bell.pauli_expectation(&Z(0)).unwrap(),
+            Complex64::new(0.0, 0.0),
+        );
+    }
+
+    #[test]
+    fn state_sampling_z_collapses_state_vector() {
+        let mut state = StateVec::new(1);
+        state.h(&qid(0));
+
+        let first = state.sample_z(&qid(0)).unwrap();
+        assert_eq!(first.len(), 1);
+        assert!(!first[0].is_deterministic);
+
+        let second = state.sample_z(&qid(0)).unwrap();
+        assert_eq!(second.len(), 1);
+        assert!(second[0].is_deterministic);
+        assert_eq!(second[0].outcome, first[0].outcome);
+    }
+
+    #[test]
+    fn state_sampling_x_and_y_bases_use_existing_measurement_semantics() {
+        let mut plus = StateVec::new(1);
+        plus.h(&qid(0));
+        let x_result = plus.sample_x(&qid(0)).unwrap();
+        assert!(x_result[0].is_deterministic);
+        assert!(!x_result[0].outcome);
+
+        let mut plus_i = StateVec::new(1);
+        plus_i.h(&qid(0)).sz(&qid(0));
+        let y_result = plus_i.sample_y(&qid(0)).unwrap();
+        assert!(y_result[0].is_deterministic);
+        assert!(!y_result[0].outcome);
+    }
+
+    #[test]
+    fn state_sampling_batch_preserves_requested_qubit_order() {
+        let mut state = StateVec::new(2);
+        state.x(&qid(0));
+
+        let results = state.sample_z(&[QubitId(1), QubitId(0)]).unwrap();
+        assert_eq!(results.len(), 2);
+        assert!(results[0].is_deterministic);
+        assert!(results[1].is_deterministic);
+        assert!(!results[0].outcome);
+        assert!(results[1].outcome);
+    }
+
+    #[test]
+    fn state_sampling_is_available_on_density_matrix_and_stabilizers() {
+        let mut density = DensityMatrix::new(1);
+        density.x(&qid(0));
+        let density_result = density.sample_z(&qid(0)).unwrap();
+        assert!(density_result[0].is_deterministic);
+        assert!(density_result[0].outcome);
+
+        let mut sparse = SparseStab::new(1);
+        sparse.x(&qid(0));
+        let sparse_result = sparse.sample_z(&qid(0)).unwrap();
+        assert!(sparse_result[0].is_deterministic);
+        assert!(sparse_result[0].outcome);
+
+        let mut hybrid = SparseStabHybrid::new(1);
+        hybrid.x(&qid(0));
+        let hybrid_result = hybrid.sample_z(&qid(0)).unwrap();
+        assert!(hybrid_result[0].is_deterministic);
+        assert!(hybrid_result[0].outcome);
+
+        let mut default_stabilizer = Stabilizer::new(1);
+        default_stabilizer.x(&qid(0));
+        let default_result = default_stabilizer.sample_z(&qid(0)).unwrap();
+        assert!(default_result[0].is_deterministic);
+        assert!(default_result[0].outcome);
+    }
+
+    #[test]
+    fn state_access_rejects_out_of_range_queries() {
+        let mut state = StateVec::new(1);
+        assert!(matches!(
+            state.amplitude(2).unwrap_err(),
+            StateAccessError::BasisIndexOutOfRange { .. }
+        ));
+        assert!(matches!(
+            state.pauli_expectation(&X(1)).unwrap_err(),
+            StateAccessError::PauliQubitOutOfRange { .. }
+        ));
+        let sample_result = state.sample_z(&[QubitId(1)]);
+        assert!(matches!(
+            sample_result,
+            Err(StateAccessError::QubitOutOfRange { .. })
+        ));
+
+        let mut rho = DensityMatrix::new(1);
+        assert!(matches!(
+            rho.density_matrix_element(0, 2).unwrap_err(),
+            StateAccessError::BasisIndexOutOfRange { .. }
+        ));
+    }
+
+    #[test]
+    fn sparse_stabilizer_to_state_vector_matches_initial_state() {
+        let sparse = SparseStab::new(2);
+        let dense = sparse.to_state_vector().unwrap();
+
+        assert_state_vectors_close(
+            &dense,
+            &[
+                Complex64::new(1.0, 0.0),
+                Complex64::new(0.0, 0.0),
+                Complex64::new(0.0, 0.0),
+                Complex64::new(0.0, 0.0),
+            ],
+        );
+    }
+
+    #[test]
+    fn sparse_stabilizer_to_state_vector_preserves_signed_basis_state() {
+        let mut sparse = SparseStab::new(1);
+        sparse.x(&qid(0));
+
+        let dense = sparse.to_state_vector().unwrap();
+        assert_state_vectors_close(
+            &dense,
+            &[Complex64::new(0.0, 0.0), Complex64::new(1.0, 0.0)],
+        );
+    }
+
+    #[test]
+    fn sparse_stabilizer_to_state_vector_matches_bell_statevec() {
+        let mut sparse = SparseStab::new(2);
+        sparse.h(&qid(0)).cx(&[(QubitId(0), QubitId(1))]);
+
+        let mut state_vec = StateVec::new(2);
+        state_vec.h(&qid(0)).cx(&[(QubitId(0), QubitId(1))]);
+
+        let dense = sparse.to_state_vector().unwrap();
+        assert_state_vectors_close(&dense, &state_vec.state_vector().unwrap());
+    }
+
+    #[test]
+    fn dense_stabilizer_to_state_vector_matches_ghz_statevec() {
+        let mut dense = DenseStab::new(3);
+        let mut state_vec = StateVec::new(3);
+        let pairs = [(QubitId(0), QubitId(1)), (QubitId(0), QubitId(2))];
+        dense.h(&qid(0)).cx(&pairs);
+        state_vec.h(&qid(0)).cx(&pairs);
+
+        let dense_state = dense.to_state_vector().unwrap();
+        assert_state_vectors_close(&dense_state, &state_vec.state_vector().unwrap());
+    }
+
+    #[test]
+    fn sparse_stabilizer_to_state_vector_preserves_complex_phase_state() {
+        let mut sparse = SparseStab::new(1);
+        sparse.h(&qid(0)).sz(&qid(0));
+
+        let mut state_vec = StateVec::new(1);
+        state_vec.h(&qid(0)).sz(&qid(0));
+
+        let dense = sparse.to_state_vector().unwrap();
+        assert_state_vectors_close(&dense, &state_vec.state_vector().unwrap());
+    }
+
+    #[test]
+    fn stabilizer_to_state_vector_is_available_on_hybrid_and_default_wrapper() {
+        let mut hybrid = SparseStabHybrid::new(2);
+        hybrid.h(&qid(0)).cx(&[(QubitId(0), QubitId(1))]);
+
+        let mut default_stabilizer = Stabilizer::new(2);
+        default_stabilizer
+            .h(&qid(0))
+            .cx(&[(QubitId(0), QubitId(1))]);
+
+        let hybrid_dense = hybrid.to_state_vector().unwrap();
+        let default_dense = default_stabilizer.to_state_vector().unwrap();
+        assert_state_vectors_close(&hybrid_dense, &default_dense);
+    }
+}
diff --git a/crates/pecos-simulators/src/state_vec_soa.rs b/crates/pecos-simulators/src/state_vec_soa.rs
index 600c744d6..9b6b885fd 100644
--- a/crates/pecos-simulators/src/state_vec_soa.rs
+++ b/crates/pecos-simulators/src/state_vec_soa.rs
@@ -4442,11 +4442,11 @@ where
         results
     }
 
-    /// Optimized measure-and-prepare-Z: always prepares |0⟩ state.
+    /// Optimized measure-and-prepare-Z: measures qubit, then prepares |0⟩.
     ///
-    /// This is more efficient than the default implementation because it:
-    /// 1. Always collapses to |0⟩ regardless of measurement outcome
-    /// 2. Avoids the conditional X correction step
+    /// Fuses projection + conditional X into a single pass over the state vector:
+    /// - outcome 0: zero |1⟩ amplitudes, normalize |0⟩ (already in |0⟩)
+    /// - outcome 1: move |1⟩ amplitudes to |0⟩ positions with normalization, zero |1⟩
     #[inline]
     fn mpz(&mut self, qubits: &[QubitId]) -> Vec<MeasurementResult> {
         self.flush();
@@ -4456,28 +4456,37 @@ where
             let q_idx = q.index();
             let step = 1 << q_idx;
 
-            // Calculate probability of measuring |1⟩
             let prob_one = self.probability_one(q_idx);
-
-            // Sample outcome (for the measurement result)
             let outcome = self.rng.bernoulli(prob_one);
             let is_deterministic = !(1e-10..=1.0 - 1e-10).contains(&prob_one);
 
-            // Always prepare |0⟩: zero the |1⟩ amplitudes and normalize |0⟩
-            let norm_factor = 1.0 / (1.0 - prob_one).sqrt();
+            let norm_factor = if outcome {
+                1.0 / prob_one.sqrt()
+            } else {
+                1.0 / (1.0 - prob_one).sqrt()
+            };
 
             if step < 4 {
                 // Scalar path
                 for i in (0..self.real.len()).step_by(step * 2) {
-                    // Normalize |0⟩ states
-                    for j in i..(i + step) {
-                        self.real[j] *= norm_factor;
-                        self.imag[j] *= norm_factor;
-                    }
-                    // Zero |1⟩ states
-                    for j in (i + step)..(i + 2 * step) {
-                        self.real[j] = 0.0;
-                        self.imag[j] = 0.0;
+                    if outcome {
+                        // Move |1⟩ -> |0⟩ with normalization, zero |1⟩
+                        for j in 0..step {
+                            self.real[i + j] = self.real[i + step + j] * norm_factor;
+                            self.imag[i + j] = self.imag[i + step + j] * norm_factor;
+                            self.real[i + step + j] = 0.0;
+                            self.imag[i + step + j] = 0.0;
+                        }
+                    } else {
+                        // Normalize |0⟩, zero |1⟩
+                        for j in 0..step {
+                            self.real[i + j] *= norm_factor;
+                            self.imag[i + j] *= norm_factor;
+                        }
+                        for j in (i + step)..(i + 2 * step) {
+                            self.real[j] = 0.0;
+                            self.imag[j] = 0.0;
+                        }
                     }
                 }
             } else {
@@ -4485,23 +4494,38 @@ where
                 let norm_vec = f64x4::splat(norm_factor);
 
                 for i in (0..self.real.len()).step_by(step * 2) {
-                    // Normalize |0⟩ states
-                    let mut j = i;
-                    while j + 4 <= i + step {
-                        let re = f64x4::from(&self.real[j..j + 4]);
-                        let im = f64x4::from(&self.imag[j..j + 4]);
-                        let scaled_re: [f64; 4] = (norm_vec * re).into();
-                        let scaled_im: [f64; 4] = (norm_vec * im).into();
-                        self.real[j..j + 4].copy_from_slice(&scaled_re);
-                        self.imag[j..j + 4].copy_from_slice(&scaled_im);
-                        j += 4;
-                    }
-                    // Zero |1⟩ states
-                    let mut j = i + step;
-                    while j + 4 <= i + 2 * step {
-                        self.real[j..j + 4].copy_from_slice(&[0.0; 4]);
-                        self.imag[j..j + 4].copy_from_slice(&[0.0; 4]);
-                        j += 4;
+                    if outcome {
+                        // Move |1⟩ -> |0⟩ with normalization, zero |1⟩
+                        let mut j = 0;
+                        while j + 4 <= step {
+                            let re = f64x4::from(&self.real[i + step + j..i + step + j + 4]);
+                            let im = f64x4::from(&self.imag[i + step + j..i + step + j + 4]);
+                            let scaled_re: [f64; 4] = (norm_vec * re).into();
+                            let scaled_im: [f64; 4] = (norm_vec * im).into();
+                            self.real[i + j..i + j + 4].copy_from_slice(&scaled_re);
+                            self.imag[i + j..i + j + 4].copy_from_slice(&scaled_im);
+                            self.real[i + step + j..i + step + j + 4].copy_from_slice(&[0.0; 4]);
+                            self.imag[i + step + j..i + step + j + 4].copy_from_slice(&[0.0; 4]);
+                            j += 4;
+                        }
+                    } else {
+                        // Normalize |0⟩, zero |1⟩
+                        let mut j = i;
+                        while j + 4 <= i + step {
+                            let re = f64x4::from(&self.real[j..j + 4]);
+                            let im = f64x4::from(&self.imag[j..j + 4]);
+                            let scaled_re: [f64; 4] = (norm_vec * re).into();
+                            let scaled_im: [f64; 4] = (norm_vec * im).into();
+                            self.real[j..j + 4].copy_from_slice(&scaled_re);
+                            self.imag[j..j + 4].copy_from_slice(&scaled_im);
+                            j += 4;
+                        }
+                        let mut j = i + step;
+                        while j + 4 <= i + 2 * step {
+                            self.real[j..j + 4].copy_from_slice(&[0.0; 4]);
+                            self.imag[j..j + 4].copy_from_slice(&[0.0; 4]);
+                            j += 4;
+                        }
                     }
                 }
             }
diff --git a/crates/pecos-simulators/src/state_vector_test_utils.rs b/crates/pecos-simulators/src/state_vector_test_utils.rs
index ba3009076..8eb17590c 100644
--- a/crates/pecos-simulators/src/state_vector_test_utils.rs
+++ b/crates/pecos-simulators/src/state_vector_test_utils.rs
@@ -831,6 +831,33 @@ pub fn verify_pz<S: StateVectorSimulator>(sim: &mut S) {
     // After pz, qubit should be in |0⟩
     let result = sim.mz(&qid(0));
     assert!(!result[0].outcome, "pz should prepare |0⟩");
+
+    // PZ on |1⟩: must not produce NaN (regression test for
+    // projection-based mpz override that divided by sqrt(1-prob_one)
+    // where prob_one=1.0)
+    sim.reset();
+    sim.x(&qid(0)); // deterministic |1⟩
+    sim.pz(&qid(0));
+    let amp0 = sim.get_amplitude(0);
+    assert!(
+        !amp0.re.is_nan() && !amp0.im.is_nan(),
+        "pz on |1⟩ must not produce NaN amplitudes"
+    );
+    assert!(
+        (amp0.norm() - 1.0).abs() < TOLERANCE,
+        "After pz on |1⟩, qubit should be in |0⟩ with unit amplitude"
+    );
+    let result = sim.mz(&qid(0));
+    assert!(!result[0].outcome, "pz on |1⟩ should prepare |0⟩");
+
+    // PZ on |0⟩: trivial case, should remain |0⟩
+    sim.reset();
+    sim.pz(&qid(0));
+    let amp0 = sim.get_amplitude(0);
+    assert!(
+        (amp0.norm() - 1.0).abs() < TOLERANCE,
+        "pz on |0⟩ should remain |0⟩"
+    );
 }
 
 /// Verify pnz (prepare |1⟩) operation.
@@ -877,6 +904,39 @@ pub fn verify_pz_multiple_qubits<S: StateVectorSimulator>(sim: &mut S) {
     assert!(result1[0].outcome, "qubit 1 should still be |1⟩");
 }
 
+/// Verify mid-circuit reset pattern: H-CX-MZ-PZ-CX-MZ on a Bell pair.
+///
+/// This is the pattern used in QEC syndrome extraction with ancilla resets.
+/// The bug it catches: if mpz projects onto |0⟩ without proper measurement
+/// sampling + conditional X, subsequent gates after PZ produce wrong results.
+pub fn verify_mid_circuit_reset<S: StateVectorSimulator>(sim: &mut S) {
+    if sim.num_qubits() < 2 {
+        return;
+    }
+
+    // Run many seeds. After H-CX: Bell state (|00⟩+|11⟩)/sqrt(2).
+    // MZ(1) collapses to |00⟩ or |11⟩.
+    // PZ(1) resets q1 to |0⟩: state is |00⟩ or |10⟩.
+    // CX(0,1) re-entangles: |00⟩->|00⟩ or |10⟩->|11⟩.
+    // MZ(1): should always equal first measurement.
+    for seed in 0..100 {
+        let mut s = S::with_seed(2, seed);
+        s.h(&qid(0));
+        s.cx(&qid2(0, 1));
+        let r1 = s.mz(&qid(1));
+        s.pz(&qid(1));
+        s.cx(&qid2(0, 1));
+        let r2 = s.mz(&qid(1));
+        assert_eq!(
+            r1[0].outcome,
+            r2[0].outcome,
+            "seed {seed}: mid-circuit reset: r1={}, r2={} — should match",
+            u8::from(r1[0].outcome),
+            u8::from(r2[0].outcome)
+        );
+    }
+}
+
 /// Verify measurement consistency - measuring the same qubit multiple times.
 pub fn verify_measurement_consistency<S: StateVectorSimulator>(sim: &mut S) {
     // After a measurement, repeated measurements should give the same result
@@ -2627,6 +2687,7 @@ pub fn run_measurement_test_suite<S: StateVectorSimulator>(sim: &mut S) {
     verify_pz(sim);
     verify_pnz(sim);
     verify_pz_multiple_qubits(sim);
+    verify_mid_circuit_reset(sim);
     verify_measurement_consistency(sim);
     verify_mz_detailed(sim);
 }
diff --git a/crates/pecos-simulators/src/symbolic_sparse_stab.rs b/crates/pecos-simulators/src/symbolic_sparse_stab.rs
index 9ca67d26c..36d50d0c5 100644
--- a/crates/pecos-simulators/src/symbolic_sparse_stab.rs
+++ b/crates/pecos-simulators/src/symbolic_sparse_stab.rs
@@ -591,6 +591,139 @@ impl SymbolicSparseStabVecSet {
             .collect()
     }
 
+    /// Prepare qubit in |0⟩ (reset). Does not record a measurement.
+    ///
+    /// Physically: measure Z, discard the outcome, conditionally apply X
+    /// to force the +1 eigenvalue.
+    ///
+    /// Symbolically: project qubit onto +Z eigenstate with empty sign
+    /// (no measurement dependencies). If the qubit is already in a Z
+    /// eigenstate, H rotates it to the X basis first so the non-deterministic
+    /// projection path can properly disentangle it from all other qubits.
+    pub fn pz(&mut self, q: usize) -> &mut Self {
+        if self.stabs.col_x[q].is_empty() {
+            // Qubit is in a Z eigenstate. Rotate to X basis so the
+            // non-deterministic projection correctly disentangles it
+            // and transfers sign information through the stabilizer group.
+            self.h(&[q]);
+        }
+        self.pz_nondeterministic(q);
+        self
+    }
+
+    /// Project qubit onto +Z eigenstate without recording a measurement.
+    ///
+    /// Same Gaussian elimination as `nondeterministic_meas` but does not
+    /// record a measurement or increment the counter. The resulting `Z` on `q`
+    /// stabilizer gets an empty sign (eigenvalue +1).
+    fn pz_nondeterministic(&mut self, q: usize) {
+        let mut anticom_stabs_col = self.stabs.col_x[q].clone();
+        let mut anticom_destabs_col = self.destabs.col_x[q].clone();
+
+        // Find stabilizer to replace (smallest weight)
+        let mut smallest_wt = 2 * self.num_qubits + 2;
+        let mut removed_id: Option<usize> = None;
+
+        for stab_id in &anticom_stabs_col {
+            let weight = self.stabs.row_x[*stab_id].len() + self.stabs.row_z[*stab_id].len();
+            if weight < smallest_wt {
+                smallest_wt = weight;
+                removed_id = Some(*stab_id);
+            }
+        }
+
+        let id = removed_id.expect("col_x[q] was non-empty");
+        anticom_stabs_col.remove(&id);
+        let removed_row_x = self.stabs.row_x[id].clone();
+        let removed_row_z = self.stabs.row_z[id].clone();
+
+        // Phase tracking for anticommuting stabilizers
+        if self.stabs.signs_minus.contains(&id) {
+            self.stabs.signs_minus ^= &anticom_stabs_col;
+        }
+        if self.stabs.signs_i.contains(&id) {
+            self.stabs.signs_i.remove(&id);
+            let gens_common: Vec<_> = self
+                .stabs
+                .signs_i
+                .intersection(&anticom_stabs_col)
+                .copied()
+                .collect();
+            let gens_only_stabs: Vec<_> = anticom_stabs_col
+                .difference(&self.stabs.signs_i)
+                .copied()
+                .collect();
+            for i in gens_common {
+                self.stabs.signs_minus ^= &i;
+                self.stabs.signs_i.remove(&i);
+            }
+            for i in gens_only_stabs {
+                self.stabs.signs_i.insert(i);
+            }
+        }
+
+        // Multiply all other anticommuting stabilizers by the removed one
+        let removed_sign = self.stabs.signs[id].clone();
+        for g in &anticom_stabs_col {
+            self.stabs.signs[*g].multiply_assign(&removed_sign);
+            let num_minuses = removed_row_z.intersection(&self.stabs.row_x[*g]).count();
+            if num_minuses & 1 != 0 {
+                self.stabs.signs_minus ^= g;
+            }
+            self.stabs.row_x[*g] ^= &removed_row_x;
+            self.stabs.row_z[*g] ^= &removed_row_z;
+        }
+
+        // Update column storage for stabilizers
+        for i in &removed_row_x {
+            self.stabs.col_x[*i] ^= &anticom_stabs_col;
+        }
+        for i in &removed_row_z {
+            self.stabs.col_z[*i] ^= &anticom_stabs_col;
+        }
+
+        // Remove old stabilizer
+        for i in &self.stabs.row_x[id] {
+            self.stabs.col_x[*i].remove(&id);
+        }
+        for i in &self.stabs.row_z[id] {
+            self.stabs.col_z[*i].remove(&id);
+        }
+
+        // Replace with Z_q, sign = empty (forced +1 eigenvalue)
+        self.stabs.col_z[q].insert(id);
+        self.stabs.row_x[id].clear();
+        self.stabs.row_z[id].clear();
+        self.stabs.row_z[id].insert(q);
+        self.stabs.signs[id] = SymbolicSign::empty();
+        self.stabs.signs_minus.remove(&id);
+        self.stabs.signs_i.remove(&id);
+
+        // Update destabilizers
+        for i in &self.destabs.row_x[id] {
+            self.destabs.col_x[*i].remove(&id);
+        }
+        for i in &self.destabs.row_z[id] {
+            self.destabs.col_z[*i].remove(&id);
+        }
+
+        anticom_destabs_col.remove(&id);
+        for i in &removed_row_x {
+            self.destabs.col_x[*i].insert(id);
+            self.destabs.col_x[*i] ^= &anticom_destabs_col;
+        }
+        for i in &removed_row_z {
+            self.destabs.col_z[*i].insert(id);
+            self.destabs.col_z[*i] ^= &anticom_destabs_col;
+        }
+        for row in &anticom_destabs_col {
+            self.destabs.row_x[*row] ^= &removed_row_x;
+            self.destabs.row_z[*row] ^= &removed_row_z;
+        }
+        self.destabs.row_x[id] = removed_row_x;
+        self.destabs.row_z[id] = removed_row_z;
+    }
+
     /// Handle a deterministic measurement.
     /// The outcome is determined by combining:
     /// 1. XOR of measurement dependencies from contributing stabilizers
@@ -1283,4 +1416,90 @@ mod tests {
         assert_eq!(history.format_deterministic(), "[m0=1, m1=0]");
         assert_eq!(history.format_nondeterministic(), "[]");
     }
+
+    /// Two-round X-stabilizer check: m1 must depend on m0 across reset.
+    #[test]
+    fn test_pz_two_round_x_check() {
+        use crate::measurement_sampler::MeasurementKind;
+        let mut sim = SymbolicSparseStabVecSet::new(3);
+
+        // Round 1: measure X₁X₂ via ancilla q0
+        sim.h(&[0]).cx(&[(0, 1)]).cx(&[(0, 2)]).h(&[0]);
+        let r0 = sim.mz(&[0]);
+        assert!(!r0[0].is_deterministic, "m0 should be non-det");
+
+        sim.pz(0);
+
+        // Round 2: same stabilizer
+        sim.h(&[0]).cx(&[(0, 1)]).cx(&[(0, 2)]).h(&[0]);
+        let r1 = sim.mz(&[0]);
+
+        assert!(r1[0].is_deterministic, "m1 should be det, got: {}", r1[0]);
+        assert_eq!(format!("{}", r1[0]), "m1=m0");
+
+        let kinds = MeasurementKind::from_history(sim.measurement_history());
+        assert!(matches!(kinds[0], MeasurementKind::Random));
+        assert!(matches!(kinds[1], MeasurementKind::Copy(0)));
+    }
+
+    /// Multi-round X-check: correlations must survive 6 reset cycles.
+    #[test]
+    fn test_pz_six_round_x_check() {
+        use crate::measurement_sampler::MeasurementKind;
+        let mut sim = SymbolicSparseStabVecSet::new(3);
+
+        for _ in 0..6 {
+            sim.h(&[0]).cx(&[(0, 1)]).cx(&[(0, 2)]).h(&[0]);
+            sim.mz(&[0]);
+            sim.pz(0);
+        }
+
+        let kinds = MeasurementKind::from_history(sim.measurement_history());
+        assert_eq!(kinds.len(), 6);
+        assert!(
+            matches!(kinds[0], MeasurementKind::Random),
+            "m0: {:?}",
+            kinds[0]
+        );
+        // All subsequent measurements must depend on a prior measurement
+        for (i, k) in kinds.iter().enumerate().skip(1) {
+            assert!(
+                matches!(k, MeasurementKind::Copy(_)),
+                "m{i} should be Copy, got {k:?}"
+            );
+        }
+    }
+
+    /// After PZ, the reset qubit itself must be fresh (deterministic |0⟩).
+    #[test]
+    fn test_pz_reset_qubit_is_fresh() {
+        let mut sim = SymbolicSparseStabVecSet::new(2);
+
+        // Entangle q0 and q1 via Bell state
+        sim.h(&[0]).cx(&[(0, 1)]);
+        // Measure q0 (non-det)
+        let r = sim.mz(&[0]);
+        assert!(!r[0].is_deterministic);
+
+        // Reset q0
+        sim.pz(0);
+
+        // Measuring q0 again must give deterministic 0 (fresh |0⟩)
+        let r2 = sim.mz(&[0]);
+        assert!(r2[0].is_deterministic, "reset qubit should be det");
+        assert_eq!(format!("{}", r2[0]), "m1=0", "reset qubit should measure 0");
+    }
+
+    /// PZ on a qubit that was never entangled should be a no-op.
+    #[test]
+    fn test_pz_on_fresh_qubit() {
+        let mut sim = SymbolicSparseStabVecSet::new(2);
+
+        // PZ on |0⟩ should not change anything
+        sim.pz(0);
+
+        let r = sim.mz(&[0]);
+        assert!(r[0].is_deterministic);
+        assert_eq!(format!("{}", r[0]), "m0=0");
+    }
 }
diff --git a/crates/pecos-simulators/src/symbolic_sparse_stab_bitset.rs b/crates/pecos-simulators/src/symbolic_sparse_stab_bitset.rs
index 76506cd45..9ec1a8f4e 100644
--- a/crates/pecos-simulators/src/symbolic_sparse_stab_bitset.rs
+++ b/crates/pecos-simulators/src/symbolic_sparse_stab_bitset.rs
@@ -51,6 +51,81 @@ pub struct SymbolicSparseStab {
     measurement_history: MeasurementHistory,
 }
 
+fn xor_intersection_into(a: &BitSet, b: &BitSet, target: &mut BitSet) {
+    for i in a {
+        if b.contains(i) {
+            target.toggle(i);
+        }
+    }
+}
+
+fn mul_i_for(signs_minus: &mut BitSet, signs_i: &mut BitSet, indices: &BitSet) {
+    for i in indices {
+        if signs_i.contains(i) {
+            signs_minus.toggle(i);
+            signs_i.remove(i);
+        } else {
+            signs_i.insert(i);
+        }
+    }
+}
+
+fn mul_minus_i_for(signs_minus: &mut BitSet, signs_i: &mut BitSet, indices: &BitSet) {
+    *signs_minus ^= indices;
+    mul_i_for(signs_minus, signs_i, indices);
+}
+
+fn toggle_col_x(gens: &mut SymbolicGensBitSet, q: usize, affected: &BitSet) {
+    let old = gens.col_x[q].clone();
+    gens.col_x[q] ^= affected;
+    for i in &old {
+        if !gens.col_x[q].contains(i) {
+            gens.row_x[i].remove(q);
+        }
+    }
+    for i in &gens.col_x[q] {
+        if !old.contains(i) {
+            gens.row_x[i].insert(q);
+        }
+    }
+}
+
+fn toggle_col_z(gens: &mut SymbolicGensBitSet, q: usize, affected: &BitSet) {
+    let old = gens.col_z[q].clone();
+    gens.col_z[q] ^= affected;
+    for i in &old {
+        if !gens.col_z[q].contains(i) {
+            gens.row_z[i].remove(q);
+        }
+    }
+    for i in &gens.col_z[q] {
+        if !old.contains(i) {
+            gens.row_z[i].insert(q);
+        }
+    }
+}
+
+fn swap_xz_on(gens: &mut SymbolicGensBitSet, q: usize) {
+    let only_x: Vec<usize> = gens.col_x[q]
+        .iter()
+        .filter(|i| !gens.col_z[q].contains(*i))
+        .collect();
+    let only_z: Vec<usize> = gens.col_z[q]
+        .iter()
+        .filter(|i| !gens.col_x[q].contains(*i))
+        .collect();
+
+    for i in only_x {
+        gens.row_x[i].remove(q);
+        gens.row_z[i].insert(q);
+    }
+    for i in only_z {
+        gens.row_z[i].remove(q);
+        gens.row_x[i].insert(q);
+    }
+    mem::swap(&mut gens.col_x[q], &mut gens.col_z[q]);
+}
+
 impl SymbolicSparseStab {
     /// Create a new BitSet-based symbolic stabilizer simulator.
     #[inline]
@@ -238,6 +313,99 @@ impl SymbolicSparseStab {
         self
     }
 
+    /// Adjoint sqrt of Z gate. X -> -Y, Z -> Z.
+    #[inline]
+    pub fn szdg(&mut self, qubits: &[usize]) -> &mut Self {
+        for &q in qubits {
+            let affected = self.stabs.col_x[q].clone();
+            mul_minus_i_for(
+                &mut self.stabs.signs_minus,
+                &mut self.stabs.signs_i,
+                &affected,
+            );
+
+            for gens in [&mut self.stabs, &mut self.destabs] {
+                let affected = gens.col_x[q].clone();
+                toggle_col_z(gens, q, &affected);
+            }
+        }
+        self
+    }
+
+    /// Sqrt of X gate. X -> X, Z -> -Y.
+    #[inline]
+    pub fn sx(&mut self, qubits: &[usize]) -> &mut Self {
+        for &q in qubits {
+            let affected = self.stabs.col_z[q].clone();
+            mul_minus_i_for(
+                &mut self.stabs.signs_minus,
+                &mut self.stabs.signs_i,
+                &affected,
+            );
+
+            for gens in [&mut self.stabs, &mut self.destabs] {
+                let affected = gens.col_z[q].clone();
+                toggle_col_x(gens, q, &affected);
+            }
+        }
+        self
+    }
+
+    /// Adjoint sqrt of X gate. X -> X, Z -> Y.
+    #[inline]
+    pub fn sxdg(&mut self, qubits: &[usize]) -> &mut Self {
+        for &q in qubits {
+            let affected = self.stabs.col_z[q].clone();
+            mul_i_for(
+                &mut self.stabs.signs_minus,
+                &mut self.stabs.signs_i,
+                &affected,
+            );
+
+            for gens in [&mut self.stabs, &mut self.destabs] {
+                let affected = gens.col_z[q].clone();
+                toggle_col_x(gens, q, &affected);
+            }
+        }
+        self
+    }
+
+    /// Sqrt of Y gate. X -> -Z, Z -> X.
+    #[inline]
+    pub fn sy(&mut self, qubits: &[usize]) -> &mut Self {
+        for &q in qubits {
+            self.stabs.signs_minus ^= &self.stabs.col_x[q];
+            xor_intersection_into(
+                &self.stabs.col_x[q],
+                &self.stabs.col_z[q],
+                &mut self.stabs.signs_minus,
+            );
+
+            for gens in [&mut self.stabs, &mut self.destabs] {
+                swap_xz_on(gens, q);
+            }
+        }
+        self
+    }
+
+    /// Adjoint sqrt of Y gate. X -> Z, Z -> -X.
+    #[inline]
+    pub fn sydg(&mut self, qubits: &[usize]) -> &mut Self {
+        for &q in qubits {
+            self.stabs.signs_minus ^= &self.stabs.col_z[q];
+            xor_intersection_into(
+                &self.stabs.col_x[q],
+                &self.stabs.col_z[q],
+                &mut self.stabs.signs_minus,
+            );
+
+            for gens in [&mut self.stabs, &mut self.destabs] {
+                swap_xz_on(gens, q);
+            }
+        }
+        self
+    }
+
     /// CNOT gate. IX -> IX, XI -> XX, IZ -> ZZ, ZI -> ZI
     #[inline]
     pub fn cx(&mut self, pairs: &[(usize, usize)]) -> &mut Self {
@@ -288,6 +456,256 @@ impl SymbolicSparseStab {
         self
     }
 
+    /// Controlled-Y gate. XI -> XY, IX -> ZX, ZI -> ZI, IZ -> ZZ.
+    #[inline]
+    pub fn cy(&mut self, pairs: &[(usize, usize)]) -> &mut Self {
+        for &(q1, q2) in pairs {
+            // Direct Pauli action, including the target-Y phase for XI.
+            let affected = self.stabs.col_x[q1].clone();
+            let mut both_x = BitSet::new();
+            for g in &self.stabs.col_x[q1] {
+                if self.stabs.col_x[q2].contains(g) {
+                    both_x.insert(g);
+                }
+            }
+            self.stabs.signs_minus ^= &both_x;
+            mul_i_for(
+                &mut self.stabs.signs_minus,
+                &mut self.stabs.signs_i,
+                &affected,
+            );
+
+            for gens in [&mut self.stabs, &mut self.destabs] {
+                let x1 = gens.col_x[q1].clone();
+                let x2 = gens.col_x[q2].clone();
+                let z2 = gens.col_z[q2].clone();
+                toggle_col_x(gens, q2, &x1);
+                toggle_col_z(gens, q2, &x1);
+
+                let mut z1_effect = x2;
+                z1_effect ^= &z2;
+                toggle_col_z(gens, q1, &z1_effect);
+            }
+        }
+        self
+    }
+
+    /// Controlled-Z gate. XI -> XZ, IX -> ZX, ZI -> ZI, IZ -> IZ.
+    #[inline]
+    pub fn cz(&mut self, pairs: &[(usize, usize)]) -> &mut Self {
+        for &(q1, q2) in pairs {
+            xor_intersection_into(
+                &self.stabs.col_x[q1],
+                &self.stabs.col_x[q2],
+                &mut self.stabs.signs_minus,
+            );
+
+            for gens in [&mut self.stabs, &mut self.destabs] {
+                let x1 = gens.col_x[q1].clone();
+                let x2 = gens.col_x[q2].clone();
+                toggle_col_z(gens, q2, &x1);
+                toggle_col_z(gens, q1, &x2);
+            }
+        }
+        self
+    }
+
+    /// Square root of XX gate. XI -> XI, IX -> IX, ZI -> -YX, IZ -> -XY.
+    #[inline]
+    pub fn sxx(&mut self, pairs: &[(usize, usize)]) -> &mut Self {
+        for &(q1, q2) in pairs {
+            let mut affected = self.stabs.col_z[q1].clone();
+            affected ^= &self.stabs.col_z[q2];
+            mul_minus_i_for(
+                &mut self.stabs.signs_minus,
+                &mut self.stabs.signs_i,
+                &affected,
+            );
+
+            for gens in [&mut self.stabs, &mut self.destabs] {
+                let mut affected = gens.col_z[q1].clone();
+                affected ^= &gens.col_z[q2];
+                toggle_col_x(gens, q1, &affected);
+                toggle_col_x(gens, q2, &affected);
+            }
+        }
+        self
+    }
+
+    /// Adjoint square root of XX gate. XI -> XI, IX -> IX, ZI -> YX, IZ -> XY.
+    #[inline]
+    pub fn sxxdg(&mut self, pairs: &[(usize, usize)]) -> &mut Self {
+        for &(q1, q2) in pairs {
+            let mut affected = self.stabs.col_z[q1].clone();
+            affected ^= &self.stabs.col_z[q2];
+            mul_i_for(
+                &mut self.stabs.signs_minus,
+                &mut self.stabs.signs_i,
+                &affected,
+            );
+
+            for gens in [&mut self.stabs, &mut self.destabs] {
+                let mut affected = gens.col_z[q1].clone();
+                affected ^= &gens.col_z[q2];
+                toggle_col_x(gens, q1, &affected);
+                toggle_col_x(gens, q2, &affected);
+            }
+        }
+        self
+    }
+
+    /// Square root of ZZ gate. XI -> YZ, IX -> ZY, ZI -> ZI, IZ -> IZ.
+    #[inline]
+    pub fn szz(&mut self, pairs: &[(usize, usize)]) -> &mut Self {
+        for &(q1, q2) in pairs {
+            let mut affected = self.stabs.col_x[q1].clone();
+            affected ^= &self.stabs.col_x[q2];
+            mul_i_for(
+                &mut self.stabs.signs_minus,
+                &mut self.stabs.signs_i,
+                &affected,
+            );
+
+            for gens in [&mut self.stabs, &mut self.destabs] {
+                let mut affected = gens.col_x[q1].clone();
+                affected ^= &gens.col_x[q2];
+                toggle_col_z(gens, q1, &affected);
+                toggle_col_z(gens, q2, &affected);
+            }
+        }
+        self
+    }
+
+    /// Adjoint square root of ZZ gate. XI -> -YZ, IX -> -ZY, ZI -> ZI, IZ -> IZ.
+    #[inline]
+    pub fn szzdg(&mut self, pairs: &[(usize, usize)]) -> &mut Self {
+        for &(q1, q2) in pairs {
+            let mut affected = self.stabs.col_x[q1].clone();
+            affected ^= &self.stabs.col_x[q2];
+            mul_minus_i_for(
+                &mut self.stabs.signs_minus,
+                &mut self.stabs.signs_i,
+                &affected,
+            );
+
+            for gens in [&mut self.stabs, &mut self.destabs] {
+                let mut affected = gens.col_x[q1].clone();
+                affected ^= &gens.col_x[q2];
+                toggle_col_z(gens, q1, &affected);
+                toggle_col_z(gens, q2, &affected);
+            }
+        }
+        self
+    }
+
+    /// Square root of YY gate.
+    ///
+    /// XI -> -ZY, IX -> -YZ, ZI -> XY, IZ -> YX.
+    #[inline]
+    pub fn syy(&mut self, pairs: &[(usize, usize)]) -> &mut Self {
+        for &(q1, q2) in pairs {
+            self.apply_syy_signs(q1, q2, false);
+            self.apply_syy_bits(q1, q2);
+        }
+        self
+    }
+
+    /// Adjoint square root of YY gate.
+    ///
+    /// XI -> ZY, IX -> YZ, ZI -> -XY, IZ -> -YX.
+    #[inline]
+    pub fn syydg(&mut self, pairs: &[(usize, usize)]) -> &mut Self {
+        for &(q1, q2) in pairs {
+            self.apply_syy_signs(q1, q2, true);
+            self.apply_syy_bits(q1, q2);
+        }
+        self
+    }
+
+    /// SWAP gate. XI -> IX, IX -> XI, ZI -> IZ, IZ -> ZI.
+    #[inline]
+    pub fn swap(&mut self, pairs: &[(usize, usize)]) -> &mut Self {
+        for &(q1, q2) in pairs {
+            for gens in [&mut self.stabs, &mut self.destabs] {
+                let mut affected_x = gens.col_x[q1].clone();
+                affected_x ^= &gens.col_x[q2];
+                toggle_col_x(gens, q1, &affected_x);
+                toggle_col_x(gens, q2, &affected_x);
+
+                let mut affected_z = gens.col_z[q1].clone();
+                affected_z ^= &gens.col_z[q2];
+                toggle_col_z(gens, q1, &affected_z);
+                toggle_col_z(gens, q2, &affected_z);
+            }
+        }
+        self
+    }
+
+    fn apply_syy_bits(&mut self, q1: usize, q2: usize) {
+        for gens in [&mut self.stabs, &mut self.destabs] {
+            let mut affected = gens.col_x[q1].clone();
+            affected ^= &gens.col_z[q1];
+            affected ^= &gens.col_x[q2];
+            affected ^= &gens.col_z[q2];
+            toggle_col_x(gens, q1, &affected);
+            toggle_col_x(gens, q2, &affected);
+            toggle_col_z(gens, q1, &affected);
+            toggle_col_z(gens, q2, &affected);
+        }
+    }
+
+    fn apply_syy_signs(&mut self, q1: usize, q2: usize, adjoint: bool) {
+        let col_x = &self.stabs.col_x;
+        let col_z = &self.stabs.col_z;
+        let signs_minus = &mut self.stabs.signs_minus;
+        let signs_i = &mut self.stabs.signs_i;
+
+        macro_rules! apply_syy_sign {
+            ($g:expr, $x1:expr, $z1:expr, $x2:expr, $z2:expr) => {
+                if ($x1 != $z1) != ($x2 != $z2) {
+                    let use_plus_i = ($z1 != $z2) != adjoint;
+                    if use_plus_i {
+                        mul_i_for(signs_minus, signs_i, &BitSet::single($g));
+                    } else {
+                        mul_minus_i_for(signs_minus, signs_i, &BitSet::single($g));
+                    }
+                }
+            };
+        }
+
+        for g in &col_x[q1] {
+            let x1 = true;
+            let z1 = col_z[q1].contains(g);
+            let x2 = col_x[q2].contains(g);
+            let z2 = col_z[q2].contains(g);
+            apply_syy_sign!(g, x1, z1, x2, z2);
+        }
+        for g in &col_z[q1] {
+            if col_x[q1].contains(g) {
+                continue;
+            }
+            let x1 = false;
+            let z1 = true;
+            let x2 = col_x[q2].contains(g);
+            let z2 = col_z[q2].contains(g);
+            apply_syy_sign!(g, x1, z1, x2, z2);
+        }
+        for g in &col_x[q2] {
+            if col_x[q1].contains(g) || col_z[q1].contains(g) {
+                continue;
+            }
+            let x2 = true;
+            let z2 = col_z[q2].contains(g);
+            apply_syy_sign!(g, false, false, x2, z2);
+        }
+        for g in &col_z[q2] {
+            if col_x[q1].contains(g) || col_z[q1].contains(g) || col_x[q2].contains(g) {
+                continue;
+            }
+            apply_syy_sign!(g, false, false, false, true);
+        }
+    }
+
     // ==================== Measurement ====================
 
     /// Measure qubits in the Z basis.
@@ -308,6 +726,129 @@ impl SymbolicSparseStab {
             .collect()
     }
 
+    /// Prepare qubit in |0⟩ (reset). Does not record a measurement.
+    ///
+    /// See `SymbolicSparseStabVecSet::pz` for detailed documentation.
+    pub fn pz(&mut self, q: usize) -> &mut Self {
+        if self.stabs.col_x[q].is_empty() {
+            self.h(&[q]);
+        }
+        self.pz_nondeterministic(q);
+        self
+    }
+
+    /// Project qubit onto +Z eigenstate without recording a measurement.
+    ///
+    /// Same Gaussian elimination as `nondeterministic_meas` but with
+    /// empty sign and no measurement counter increment.
+    fn pz_nondeterministic(&mut self, q: usize) {
+        let mut anticom_stabs_col = self.stabs.col_x[q].clone();
+        let mut anticom_destabs_col = self.destabs.col_x[q].clone();
+
+        let mut smallest_wt = 2 * self.num_qubits + 2;
+        let mut removed_id: Option<usize> = None;
+
+        for stab_id in &anticom_stabs_col {
+            let weight = self.stabs.row_x[stab_id].len() + self.stabs.row_z[stab_id].len();
+            if weight < smallest_wt {
+                smallest_wt = weight;
+                removed_id = Some(stab_id);
+            }
+        }
+
+        let id = removed_id.expect("col_x[q] was non-empty");
+        anticom_stabs_col.remove(id);
+        let removed_row_x = self.stabs.row_x[id].clone();
+        let removed_row_z = self.stabs.row_z[id].clone();
+
+        if self.stabs.signs_minus.contains(id) {
+            self.stabs.signs_minus ^= &anticom_stabs_col;
+        }
+        if self.stabs.signs_i.contains(id) {
+            self.stabs.signs_i.remove(id);
+            let gens_common: Vec<usize> = self
+                .stabs
+                .signs_i
+                .iter()
+                .filter(|i| anticom_stabs_col.contains(*i))
+                .collect();
+            let gens_only_stabs: Vec<usize> = anticom_stabs_col
+                .iter()
+                .filter(|i| !self.stabs.signs_i.contains(*i))
+                .collect();
+            for i in gens_common {
+                let i_set = BitSet::single(i);
+                self.stabs.signs_minus ^= &i_set;
+                self.stabs.signs_i.remove(i);
+            }
+            for i in gens_only_stabs {
+                self.stabs.signs_i.insert(i);
+            }
+        }
+
+        let removed_sign = self.stabs.signs[id].clone();
+        for g in &anticom_stabs_col {
+            self.stabs.signs[g].multiply_assign(&removed_sign);
+            let mut num_minuses = 0;
+            for z in &removed_row_z {
+                if self.stabs.row_x[g].contains(z) {
+                    num_minuses += 1;
+                }
+            }
+            if num_minuses & 1 != 0 {
+                let g_set = BitSet::single(g);
+                self.stabs.signs_minus ^= &g_set;
+            }
+            self.stabs.row_x[g] ^= &removed_row_x;
+            self.stabs.row_z[g] ^= &removed_row_z;
+        }
+
+        for i in &removed_row_x {
+            self.stabs.col_x[i] ^= &anticom_stabs_col;
+        }
+        for i in &removed_row_z {
+            self.stabs.col_z[i] ^= &anticom_stabs_col;
+        }
+
+        for i in &self.stabs.row_x[id] {
+            self.stabs.col_x[i].remove(id);
+        }
+        for i in &self.stabs.row_z[id] {
+            self.stabs.col_z[i].remove(id);
+        }
+
+        self.stabs.col_z[q].insert(id);
+        self.stabs.row_x[id].clear();
+        self.stabs.row_z[id].clear();
+        self.stabs.row_z[id].insert(q);
+        self.stabs.signs[id] = SymbolicSign::empty();
+        self.stabs.signs_minus.remove(id);
+        self.stabs.signs_i.remove(id);
+
+        for i in &self.destabs.row_x[id] {
+            self.destabs.col_x[i].remove(id);
+        }
+        for i in &self.destabs.row_z[id] {
+            self.destabs.col_z[i].remove(id);
+        }
+
+        anticom_destabs_col.remove(id);
+        for i in &removed_row_x {
+            self.destabs.col_x[i].insert(id);
+            self.destabs.col_x[i] ^= &anticom_destabs_col;
+        }
+        for i in &removed_row_z {
+            self.destabs.col_z[i].insert(id);
+            self.destabs.col_z[i] ^= &anticom_destabs_col;
+        }
+        for row in &anticom_destabs_col {
+            self.destabs.row_x[row] ^= &removed_row_x;
+            self.destabs.row_z[row] ^= &removed_row_z;
+        }
+        self.destabs.row_x[id] = removed_row_x;
+        self.destabs.row_z[id] = removed_row_z;
+    }
+
     /// Handle a deterministic measurement.
     fn deterministic_meas(&mut self, q: usize) -> SymbolicMeasurementResult {
         let index = self.measurement_counter;
@@ -516,6 +1057,322 @@ impl QuantumSimulator for SymbolicSparseStab {
 #[cfg(test)]
 mod tests {
     use super::*;
+    use crate::clifford_matrix_oracle::{
+        CliffordMatrixGate, SignedPauli, all_pauli_strings, conjugate_pauli,
+    };
+
+    fn assert_same_gens(left: &SymbolicGensBitSet, right: &SymbolicGensBitSet) {
+        assert_eq!(left.col_x, right.col_x);
+        assert_eq!(left.col_z, right.col_z);
+        assert_eq!(left.row_x, right.row_x);
+        assert_eq!(left.row_z, right.row_z);
+        assert_eq!(left.signs, right.signs);
+        assert_eq!(left.signs_minus, right.signs_minus);
+        assert_eq!(left.signs_i, right.signs_i);
+    }
+
+    fn assert_same_state(left: &SymbolicSparseStab, right: &SymbolicSparseStab) {
+        assert_same_gens(&left.stabs, &right.stabs);
+        assert_same_gens(&left.destabs, &right.destabs);
+        assert_eq!(left.measurement_counter, right.measurement_counter);
+        assert_eq!(
+            left.measurement_history.as_slice(),
+            right.measurement_history.as_slice()
+        );
+    }
+
+    fn nontrivial_state() -> SymbolicSparseStab {
+        let mut sim = SymbolicSparseStab::new(3);
+        sim.h(&[0, 1]);
+        sim.cx(&[(0, 2), (1, 2)]);
+        sim.sz(&[0, 2]);
+        sim.h(&[2]);
+        sim
+    }
+
+    fn check_direct_gate(
+        apply_direct: impl FnOnce(&mut SymbolicSparseStab),
+        apply_reference: impl FnOnce(&mut SymbolicSparseStab),
+    ) {
+        let mut direct = nontrivial_state();
+        let mut reference = direct.clone();
+        apply_direct(&mut direct);
+        apply_reference(&mut reference);
+        assert_same_state(&direct, &reference);
+    }
+
+    fn row_binary(gens: &SymbolicGensBitSet, row: usize, num_qubits: usize) -> String {
+        let mut dense = String::with_capacity(num_qubits);
+        for q in 0..num_qubits {
+            dense.push(
+                match (gens.row_x[row].contains(q), gens.row_z[row].contains(q)) {
+                    (false, false) => 'I',
+                    (true, false) => 'X',
+                    (false, true) => 'Z',
+                    (true, true) => 'Y',
+                },
+            );
+        }
+        dense
+    }
+
+    fn assert_symbolic_single_qubit_gate_basis(
+        apply: impl FnOnce(&mut SymbolicSparseStab),
+        expected_x: &str,
+        expected_z: &str,
+    ) {
+        let mut sim = SymbolicSparseStab::new(1);
+        apply(&mut sim);
+
+        assert_eq!(row_binary(&sim.destabs, 0, 1), expected_x, "X image");
+        assert_eq!(row_binary(&sim.stabs, 0, 1), expected_z, "Z image");
+    }
+
+    fn assert_symbolic_two_qubit_gate_basis(
+        apply: impl FnOnce(&mut SymbolicSparseStab),
+        expected_xi: &str,
+        expected_ix: &str,
+        expected_zi: &str,
+        expected_iz: &str,
+    ) {
+        let mut sim = SymbolicSparseStab::new(2);
+        apply(&mut sim);
+
+        assert_eq!(row_binary(&sim.destabs, 0, 2), expected_xi, "XI image");
+        assert_eq!(row_binary(&sim.destabs, 1, 2), expected_ix, "IX image");
+        assert_eq!(row_binary(&sim.stabs, 0, 2), expected_zi, "ZI image");
+        assert_eq!(row_binary(&sim.stabs, 1, 2), expected_iz, "IZ image");
+    }
+
+    fn set_stab_row_to_pauli(gens: &mut SymbolicGensBitSet, row: usize, pauli: &str) {
+        let mut y_count = 0usize;
+        for (q, label) in pauli.chars().enumerate() {
+            match label {
+                'I' => {}
+                'X' => {
+                    gens.row_x[row].insert(q);
+                    gens.col_x[q].insert(row);
+                }
+                'Y' => {
+                    y_count += 1;
+                    gens.row_x[row].insert(q);
+                    gens.row_z[row].insert(q);
+                    gens.col_x[q].insert(row);
+                    gens.col_z[q].insert(row);
+                }
+                'Z' => {
+                    gens.row_z[row].insert(q);
+                    gens.col_z[q].insert(row);
+                }
+                _ => panic!("invalid Pauli label {label}"),
+            }
+        }
+
+        match y_count % 4 {
+            0 => {}
+            1 => {
+                gens.signs_i.insert(row);
+            }
+            2 => {
+                gens.signs_minus.insert(row);
+            }
+            3 => {
+                gens.signs_minus.insert(row);
+                gens.signs_i.insert(row);
+            }
+            _ => unreachable!(),
+        }
+    }
+
+    fn signed_stab_row(gens: &SymbolicGensBitSet, row: usize, num_qubits: usize) -> SignedPauli {
+        assert!(
+            gens.signs[row].measurements.is_empty(),
+            "unexpected measurement-dependent sign"
+        );
+        let pauli = row_binary(gens, row, num_qubits);
+        let y_count = pauli.chars().filter(|&label| label == 'Y').count();
+        let internal_phase = usize::from(gens.signs_i.contains(row))
+            + if gens.signs_minus.contains(row) { 2 } else { 0 };
+        let canonical_phase = (internal_phase + 3 * y_count) % 4;
+        assert!(
+            canonical_phase == 0 || canonical_phase == 2,
+            "unexpected non-Hermitian phase i^{canonical_phase} for row {row}"
+        );
+        SignedPauli {
+            sign: if canonical_phase == 2 { -1 } else { 1 },
+            pauli,
+        }
+    }
+
+    fn symbolic_image_for_pauli<F>(num_qubits: usize, input: &str, apply: F) -> SignedPauli
+    where
+        F: FnOnce(&mut SymbolicSparseStab),
+    {
+        let mut sim = SymbolicSparseStab::new(num_qubits);
+        sim.stabs = SymbolicGensBitSet::new(num_qubits);
+        sim.destabs = SymbolicGensBitSet::new(num_qubits);
+        set_stab_row_to_pauli(&mut sim.stabs, 0, input);
+        apply(&mut sim);
+        signed_stab_row(&sim.stabs, 0, num_qubits)
+    }
+
+    fn assert_symbolic_gate_matches_matrix_oracle<F>(
+        name: &str,
+        gate: CliffordMatrixGate,
+        num_qubits: usize,
+        apply: F,
+    ) where
+        F: Fn(&mut SymbolicSparseStab) + Copy,
+    {
+        for input in all_pauli_strings(num_qubits) {
+            let expected = conjugate_pauli(gate, &input);
+            let observed = symbolic_image_for_pauli(num_qubits, &input, apply);
+            assert_eq!(observed, expected, "{name}: {input}");
+        }
+    }
+
+    fn reverse_two_qubit_pauli(pauli: &str) -> String {
+        let labels: Vec<char> = pauli.chars().collect();
+        assert_eq!(labels.len(), 2);
+        [labels[1], labels[0]].into_iter().collect()
+    }
+
+    fn assert_symbolic_reversed_pair_matches_matrix_oracle<F>(
+        name: &str,
+        gate: CliffordMatrixGate,
+        apply: F,
+    ) where
+        F: Fn(&mut SymbolicSparseStab, &[(usize, usize)]) + Copy,
+    {
+        for input in all_pauli_strings(2) {
+            let oracle_input = reverse_two_qubit_pauli(&input);
+            let mut expected = conjugate_pauli(gate, &oracle_input);
+            expected.pauli = reverse_two_qubit_pauli(&expected.pauli);
+
+            let observed = symbolic_image_for_pauli(2, &input, |sim| {
+                apply(sim, &[(1, 0)]);
+            });
+            assert_eq!(observed, expected, "{name} reversed pair: {input}");
+        }
+    }
+
+    fn assert_symbolic_two_pair_batch_matches_sequential<F>(name: &str, apply: F)
+    where
+        F: Fn(&mut SymbolicSparseStab, &[(usize, usize)]) + Copy,
+    {
+        for input in all_pauli_strings(4) {
+            let batched = symbolic_image_for_pauli(4, &input, |sim| {
+                apply(sim, &[(0, 1), (2, 3)]);
+            });
+            let sequential = symbolic_image_for_pauli(4, &input, |sim| {
+                apply(sim, &[(0, 1)]);
+                apply(sim, &[(2, 3)]);
+            });
+            assert_eq!(batched, sequential, "{name} batched: {input}");
+        }
+    }
+
+    fn ref_szdg(sim: &mut SymbolicSparseStab, qs: &[usize]) {
+        sim.z(qs);
+        sim.sz(qs);
+    }
+
+    fn ref_sx(sim: &mut SymbolicSparseStab, qs: &[usize]) {
+        sim.h(qs);
+        sim.sz(qs);
+        sim.h(qs);
+    }
+
+    fn ref_sxdg(sim: &mut SymbolicSparseStab, qs: &[usize]) {
+        sim.h(qs);
+        ref_szdg(sim, qs);
+        sim.h(qs);
+    }
+
+    fn ref_sy(sim: &mut SymbolicSparseStab, qs: &[usize]) {
+        sim.z(qs);
+        sim.h(qs);
+    }
+
+    fn ref_sydg(sim: &mut SymbolicSparseStab, qs: &[usize]) {
+        sim.h(qs);
+        sim.z(qs);
+    }
+
+    fn ref_cy(sim: &mut SymbolicSparseStab, pairs: &[(usize, usize)]) {
+        let targets: Vec<usize> = pairs.iter().map(|&(_, q2)| q2).collect();
+        ref_szdg(sim, &targets);
+        sim.cx(pairs);
+        sim.sz(&targets);
+    }
+
+    fn ref_cz(sim: &mut SymbolicSparseStab, pairs: &[(usize, usize)]) {
+        let targets: Vec<usize> = pairs.iter().map(|&(_, q2)| q2).collect();
+        sim.h(&targets);
+        sim.cx(pairs);
+        sim.h(&targets);
+    }
+
+    fn ref_sxx(sim: &mut SymbolicSparseStab, pairs: &[(usize, usize)]) {
+        let q1s: Vec<usize> = pairs.iter().map(|&(q1, _)| q1).collect();
+        let q2s: Vec<usize> = pairs.iter().map(|&(_, q2)| q2).collect();
+        ref_sx(sim, &q1s);
+        ref_sx(sim, &q2s);
+        ref_sydg(sim, &q1s);
+        sim.cx(pairs);
+        ref_sy(sim, &q1s);
+    }
+
+    fn ref_sxxdg(sim: &mut SymbolicSparseStab, pairs: &[(usize, usize)]) {
+        let q1s: Vec<usize> = pairs.iter().map(|&(q1, _)| q1).collect();
+        let q2s: Vec<usize> = pairs.iter().map(|&(_, q2)| q2).collect();
+        sim.x(&q1s);
+        sim.x(&q2s);
+        ref_sxx(sim, pairs);
+    }
+
+    fn ref_syy(sim: &mut SymbolicSparseStab, pairs: &[(usize, usize)]) {
+        let q1s: Vec<usize> = pairs.iter().map(|&(q1, _)| q1).collect();
+        let q2s: Vec<usize> = pairs.iter().map(|&(_, q2)| q2).collect();
+        ref_szdg(sim, &q1s);
+        ref_szdg(sim, &q2s);
+        ref_sxx(sim, pairs);
+        sim.sz(&q1s);
+        sim.sz(&q2s);
+    }
+
+    fn ref_syydg(sim: &mut SymbolicSparseStab, pairs: &[(usize, usize)]) {
+        let q1s: Vec<usize> = pairs.iter().map(|&(q1, _)| q1).collect();
+        let q2s: Vec<usize> = pairs.iter().map(|&(_, q2)| q2).collect();
+        sim.y(&q1s);
+        sim.y(&q2s);
+        ref_syy(sim, pairs);
+    }
+
+    fn ref_szz(sim: &mut SymbolicSparseStab, pairs: &[(usize, usize)]) {
+        let q1s: Vec<usize> = pairs.iter().map(|&(q1, _)| q1).collect();
+        let q2s: Vec<usize> = pairs.iter().map(|&(_, q2)| q2).collect();
+        sim.h(&q1s);
+        sim.h(&q2s);
+        ref_sxx(sim, pairs);
+        sim.h(&q1s);
+        sim.h(&q2s);
+    }
+
+    fn ref_szzdg(sim: &mut SymbolicSparseStab, pairs: &[(usize, usize)]) {
+        let q1s: Vec<usize> = pairs.iter().map(|&(q1, _)| q1).collect();
+        let q2s: Vec<usize> = pairs.iter().map(|&(_, q2)| q2).collect();
+        sim.z(&q1s);
+        sim.z(&q2s);
+        ref_szz(sim, pairs);
+    }
+
+    fn ref_swap(sim: &mut SymbolicSparseStab, pairs: &[(usize, usize)]) {
+        let reversed: Vec<(usize, usize)> = pairs.iter().map(|&(q1, q2)| (q2, q1)).collect();
+        sim.cx(pairs);
+        sim.cx(&reversed);
+        sim.cx(pairs);
+    }
 
     #[test]
     fn test_bell_state_bitset() {
@@ -552,4 +1409,390 @@ mod tests {
         assert!(r1.outcome.is_empty());
         assert_eq!(r1.index, 1);
     }
+
+    #[test]
+    fn test_direct_clifford_gate_binary_truth_tables() {
+        assert_symbolic_single_qubit_gate_basis(
+            |sim| {
+                sim.szdg(&[0]);
+            },
+            "Y",
+            "Z",
+        );
+        assert_symbolic_single_qubit_gate_basis(
+            |sim| {
+                sim.sx(&[0]);
+            },
+            "X",
+            "Y",
+        );
+        assert_symbolic_single_qubit_gate_basis(
+            |sim| {
+                sim.sxdg(&[0]);
+            },
+            "X",
+            "Y",
+        );
+        assert_symbolic_single_qubit_gate_basis(
+            |sim| {
+                sim.sy(&[0]);
+            },
+            "Z",
+            "X",
+        );
+        assert_symbolic_single_qubit_gate_basis(
+            |sim| {
+                sim.sydg(&[0]);
+            },
+            "Z",
+            "X",
+        );
+        assert_symbolic_two_qubit_gate_basis(
+            |sim| {
+                sim.cy(&[(0, 1)]);
+            },
+            "XY",
+            "ZX",
+            "ZI",
+            "ZZ",
+        );
+        assert_symbolic_two_qubit_gate_basis(
+            |sim| {
+                sim.cz(&[(0, 1)]);
+            },
+            "XZ",
+            "ZX",
+            "ZI",
+            "IZ",
+        );
+        assert_symbolic_two_qubit_gate_basis(
+            |sim| {
+                sim.sxx(&[(0, 1)]);
+            },
+            "XI",
+            "IX",
+            "YX",
+            "XY",
+        );
+        assert_symbolic_two_qubit_gate_basis(
+            |sim| {
+                sim.sxxdg(&[(0, 1)]);
+            },
+            "XI",
+            "IX",
+            "YX",
+            "XY",
+        );
+        assert_symbolic_two_qubit_gate_basis(
+            |sim| {
+                sim.syy(&[(0, 1)]);
+            },
+            "ZY",
+            "YZ",
+            "XY",
+            "YX",
+        );
+        assert_symbolic_two_qubit_gate_basis(
+            |sim| {
+                sim.syydg(&[(0, 1)]);
+            },
+            "ZY",
+            "YZ",
+            "XY",
+            "YX",
+        );
+        assert_symbolic_two_qubit_gate_basis(
+            |sim| {
+                sim.szz(&[(0, 1)]);
+            },
+            "YZ",
+            "ZY",
+            "ZI",
+            "IZ",
+        );
+        assert_symbolic_two_qubit_gate_basis(
+            |sim| {
+                sim.szzdg(&[(0, 1)]);
+            },
+            "YZ",
+            "ZY",
+            "ZI",
+            "IZ",
+        );
+        assert_symbolic_two_qubit_gate_basis(
+            |sim| {
+                sim.swap(&[(0, 1)]);
+            },
+            "IX",
+            "XI",
+            "IZ",
+            "ZI",
+        );
+    }
+
+    #[test]
+    fn test_direct_clifford_gates_match_matrix_oracle_for_all_paulis() {
+        assert_symbolic_gate_matches_matrix_oracle("CX", CliffordMatrixGate::CX, 2, |sim| {
+            sim.cx(&[(0, 1)]);
+        });
+        assert_symbolic_gate_matches_matrix_oracle("SZdg", CliffordMatrixGate::SZdg, 1, |sim| {
+            sim.szdg(&[0]);
+        });
+        assert_symbolic_gate_matches_matrix_oracle("F", CliffordMatrixGate::F, 1, |sim| {
+            sim.sx(&[0]);
+            sim.sz(&[0]);
+        });
+        assert_symbolic_gate_matches_matrix_oracle("Fdg", CliffordMatrixGate::Fdg, 1, |sim| {
+            sim.szdg(&[0]);
+            sim.sxdg(&[0]);
+        });
+        assert_symbolic_gate_matches_matrix_oracle("SX", CliffordMatrixGate::SX, 1, |sim| {
+            sim.sx(&[0]);
+        });
+        assert_symbolic_gate_matches_matrix_oracle("SXdg", CliffordMatrixGate::SXdg, 1, |sim| {
+            sim.sxdg(&[0]);
+        });
+        assert_symbolic_gate_matches_matrix_oracle("SY", CliffordMatrixGate::SY, 1, |sim| {
+            sim.sy(&[0]);
+        });
+        assert_symbolic_gate_matches_matrix_oracle("SYdg", CliffordMatrixGate::SYdg, 1, |sim| {
+            sim.sydg(&[0]);
+        });
+        assert_symbolic_gate_matches_matrix_oracle("CY", CliffordMatrixGate::CY, 2, |sim| {
+            sim.cy(&[(0, 1)]);
+        });
+        assert_symbolic_gate_matches_matrix_oracle("CZ", CliffordMatrixGate::CZ, 2, |sim| {
+            sim.cz(&[(0, 1)]);
+        });
+        assert_symbolic_gate_matches_matrix_oracle("SXX", CliffordMatrixGate::SXX, 2, |sim| {
+            sim.sxx(&[(0, 1)]);
+        });
+        assert_symbolic_gate_matches_matrix_oracle("SXXdg", CliffordMatrixGate::SXXdg, 2, |sim| {
+            sim.sxxdg(&[(0, 1)]);
+        });
+        assert_symbolic_gate_matches_matrix_oracle("SYY", CliffordMatrixGate::SYY, 2, |sim| {
+            sim.syy(&[(0, 1)]);
+        });
+        assert_symbolic_gate_matches_matrix_oracle("SYYdg", CliffordMatrixGate::SYYdg, 2, |sim| {
+            sim.syydg(&[(0, 1)]);
+        });
+        assert_symbolic_gate_matches_matrix_oracle("SZZ", CliffordMatrixGate::SZZ, 2, |sim| {
+            sim.szz(&[(0, 1)]);
+        });
+        assert_symbolic_gate_matches_matrix_oracle("SZZdg", CliffordMatrixGate::SZZdg, 2, |sim| {
+            sim.szzdg(&[(0, 1)]);
+        });
+        assert_symbolic_gate_matches_matrix_oracle("SWAP", CliffordMatrixGate::SWAP, 2, |sim| {
+            sim.swap(&[(0, 1)]);
+        });
+    }
+
+    #[test]
+    fn test_cy_xx_sign_regression() {
+        assert_eq!(
+            symbolic_image_for_pauli(2, "XX", |sim| {
+                sim.cy(&[(0, 1)]);
+            }),
+            SignedPauli {
+                sign: -1,
+                pauli: "YZ".to_string()
+            }
+        );
+    }
+
+    #[test]
+    fn test_two_qubit_gates_reversed_pair_matches_matrix_oracle() {
+        assert_symbolic_reversed_pair_matches_matrix_oracle(
+            "CX",
+            CliffordMatrixGate::CX,
+            |sim, pairs| {
+                sim.cx(pairs);
+            },
+        );
+        assert_symbolic_reversed_pair_matches_matrix_oracle(
+            "CY",
+            CliffordMatrixGate::CY,
+            |sim, pairs| {
+                sim.cy(pairs);
+            },
+        );
+        assert_symbolic_reversed_pair_matches_matrix_oracle(
+            "CZ",
+            CliffordMatrixGate::CZ,
+            |sim, pairs| {
+                sim.cz(pairs);
+            },
+        );
+        assert_symbolic_reversed_pair_matches_matrix_oracle(
+            "SXX",
+            CliffordMatrixGate::SXX,
+            |sim, pairs| {
+                sim.sxx(pairs);
+            },
+        );
+        assert_symbolic_reversed_pair_matches_matrix_oracle(
+            "SXXdg",
+            CliffordMatrixGate::SXXdg,
+            |sim, pairs| {
+                sim.sxxdg(pairs);
+            },
+        );
+        assert_symbolic_reversed_pair_matches_matrix_oracle(
+            "SYY",
+            CliffordMatrixGate::SYY,
+            |sim, pairs| {
+                sim.syy(pairs);
+            },
+        );
+        assert_symbolic_reversed_pair_matches_matrix_oracle(
+            "SYYdg",
+            CliffordMatrixGate::SYYdg,
+            |sim, pairs| {
+                sim.syydg(pairs);
+            },
+        );
+        assert_symbolic_reversed_pair_matches_matrix_oracle(
+            "SZZ",
+            CliffordMatrixGate::SZZ,
+            |sim, pairs| {
+                sim.szz(pairs);
+            },
+        );
+        assert_symbolic_reversed_pair_matches_matrix_oracle(
+            "SZZdg",
+            CliffordMatrixGate::SZZdg,
+            |sim, pairs| {
+                sim.szzdg(pairs);
+            },
+        );
+        assert_symbolic_reversed_pair_matches_matrix_oracle(
+            "SWAP",
+            CliffordMatrixGate::SWAP,
+            |sim, pairs| {
+                sim.swap(pairs);
+            },
+        );
+    }
+
+    #[test]
+    fn test_two_qubit_gate_batches_match_sequential_pairs() {
+        assert_symbolic_two_pair_batch_matches_sequential("CX", |sim, pairs| {
+            sim.cx(pairs);
+        });
+        assert_symbolic_two_pair_batch_matches_sequential("CY", |sim, pairs| {
+            sim.cy(pairs);
+        });
+        assert_symbolic_two_pair_batch_matches_sequential("CZ", |sim, pairs| {
+            sim.cz(pairs);
+        });
+        assert_symbolic_two_pair_batch_matches_sequential("SXX", |sim, pairs| {
+            sim.sxx(pairs);
+        });
+        assert_symbolic_two_pair_batch_matches_sequential("SXXdg", |sim, pairs| {
+            sim.sxxdg(pairs);
+        });
+        assert_symbolic_two_pair_batch_matches_sequential("SYY", |sim, pairs| {
+            sim.syy(pairs);
+        });
+        assert_symbolic_two_pair_batch_matches_sequential("SYYdg", |sim, pairs| {
+            sim.syydg(pairs);
+        });
+        assert_symbolic_two_pair_batch_matches_sequential("SZZ", |sim, pairs| {
+            sim.szz(pairs);
+        });
+        assert_symbolic_two_pair_batch_matches_sequential("SZZdg", |sim, pairs| {
+            sim.szzdg(pairs);
+        });
+        assert_symbolic_two_pair_batch_matches_sequential("SWAP", |sim, pairs| {
+            sim.swap(pairs);
+        });
+    }
+
+    #[test]
+    fn test_direct_clifford_gates_match_reference_sequences() {
+        check_direct_gate(
+            |sim| {
+                sim.szdg(&[0]);
+            },
+            |sim| ref_szdg(sim, &[0]),
+        );
+        check_direct_gate(
+            |sim| {
+                sim.sx(&[0]);
+            },
+            |sim| ref_sx(sim, &[0]),
+        );
+        check_direct_gate(
+            |sim| {
+                sim.sxdg(&[0]);
+            },
+            |sim| ref_sxdg(sim, &[0]),
+        );
+        check_direct_gate(
+            |sim| {
+                sim.sy(&[0]);
+            },
+            |sim| ref_sy(sim, &[0]),
+        );
+        check_direct_gate(
+            |sim| {
+                sim.sydg(&[0]);
+            },
+            |sim| ref_sydg(sim, &[0]),
+        );
+        check_direct_gate(
+            |sim| {
+                sim.cy(&[(0, 1)]);
+            },
+            |sim| ref_cy(sim, &[(0, 1)]),
+        );
+        check_direct_gate(
+            |sim| {
+                sim.cz(&[(0, 1)]);
+            },
+            |sim| ref_cz(sim, &[(0, 1)]),
+        );
+        check_direct_gate(
+            |sim| {
+                sim.sxx(&[(0, 1)]);
+            },
+            |sim| ref_sxx(sim, &[(0, 1)]),
+        );
+        check_direct_gate(
+            |sim| {
+                sim.sxxdg(&[(0, 1)]);
+            },
+            |sim| ref_sxxdg(sim, &[(0, 1)]),
+        );
+        check_direct_gate(
+            |sim| {
+                sim.syy(&[(0, 1)]);
+            },
+            |sim| ref_syy(sim, &[(0, 1)]),
+        );
+        check_direct_gate(
+            |sim| {
+                sim.syydg(&[(0, 1)]);
+            },
+            |sim| ref_syydg(sim, &[(0, 1)]),
+        );
+        check_direct_gate(
+            |sim| {
+                sim.szz(&[(0, 1)]);
+            },
+            |sim| ref_szz(sim, &[(0, 1)]),
+        );
+        check_direct_gate(
+            |sim| {
+                sim.szzdg(&[(0, 1)]);
+            },
+            |sim| ref_szzdg(sim, &[(0, 1)]),
+        );
+        check_direct_gate(
+            |sim| {
+                sim.swap(&[(0, 1)]);
+            },
+            |sim| ref_swap(sim, &[(0, 1)]),
+        );
+    }
 }
diff --git a/crates/pecos-tesseract/build_tesseract.rs b/crates/pecos-tesseract/build_tesseract.rs
index 1c10e3166..9ed16962c 100644
--- a/crates/pecos-tesseract/build_tesseract.rs
+++ b/crates/pecos-tesseract/build_tesseract.rs
@@ -2,6 +2,7 @@
 
 use pecos_build::{Manifest, Result, check_cxx20_toolchain, ensure_dep_ready, report_cache_config};
 use std::env;
+use std::fs;
 use std::path::{Path, PathBuf};
 
 // Use the shared modules from the parent
@@ -52,18 +53,19 @@ pub fn build() -> Result<()> {
     println!("cargo:rustc-link-search=native={}", out_dir.display());
     println!("cargo:rustc-link-lib=static=tesseract-bridge");
 
-    // Get Tesseract and Stim sources (downloads to ~/.pecos/cache/, extracts to ~/.pecos/deps/)
+    // Get Tesseract, Stim, and Boost sources (downloads to ~/.pecos/cache/, extracts to ~/.pecos/deps/)
     let manifest = Manifest::find_and_load_validated()?;
     let tesseract_dir = ensure_dep_ready("tesseract", &manifest)?;
     let stim_dir = ensure_dep_ready("stim", &manifest)?;
+    let boost_dir = ensure_dep_ready("boost", &manifest)?;
 
     // Build using cxx
-    build_cxx_bridge(&tesseract_dir, &stim_dir);
+    build_cxx_bridge(&tesseract_dir, &stim_dir, &boost_dir);
 
     Ok(())
 }
 
-fn build_cxx_bridge(tesseract_dir: &Path, stim_dir: &Path) {
+fn build_cxx_bridge(tesseract_dir: &Path, stim_dir: &Path, boost_dir: &Path) {
     let tesseract_src_dir = tesseract_dir.join("src");
     let stim_src_dir = stim_dir.join("src");
 
@@ -89,11 +91,27 @@ fn build_cxx_bridge(tesseract_dir: &Path, stim_dir: &Path) {
         .file(tesseract_src_dir.join("utils.cc"))
         .file(tesseract_src_dir.join("tesseract.cc"));
 
+    // visualization.cc uses std::min(3ul, vec.size()). On MSVC Win64,
+    // unsigned long is 32-bit and size_t is 64-bit, so std::min template
+    // deduction fails. Patch the source to use size_t{3} instead.
+    let vis_src = tesseract_src_dir.join("visualization.cc");
+    let vis_content = fs::read_to_string(&vis_src).expect("read visualization.cc");
+    if vis_content.contains("std::min(3ul,") {
+        let out_dir = PathBuf::from(env::var("OUT_DIR").unwrap());
+        let patched = out_dir.join("visualization_patched.cc");
+        let fixed = vis_content.replace("std::min(3ul,", "std::min(size_t{3},");
+        fs::write(&patched, fixed).expect("write patched visualization.cc");
+        build.file(patched);
+    } else {
+        build.file(vis_src);
+    }
+
     // Configure build
     build
         .std("c++20")
         .include(&tesseract_src_dir)
         .include(&stim_src_dir)
+        .include(boost_dir)
         .include("include")
         .include("src")
         .define("TESSERACT_BRIDGE_EXPORTS", None);
@@ -146,10 +164,11 @@ fn build_cxx_bridge(tesseract_dir: &Path, stim_dir: &Path) {
             .flag_if_supported("/permissive-")
             .flag_if_supported("/Zc:__cplusplus");
 
-        // Force include standard headers that external libraries assume are available
-        // MSVC is stricter than GCC/Clang about transitive includes
-        build.flag("/FI").flag("array"); // For std::array
-        build.flag("/FI").flag("numeric"); // For std::iota
+        // Force include standard headers that vendored code assumes are
+        // transitively available. MSVC is stricter than GCC/Clang.
+        build.flag("/FI").flag("array");
+        build.flag("/FI").flag("numeric");
+        build.flag("/FI").flag("algorithm");
     }
 
     build.compile("tesseract-bridge");
diff --git a/crates/pecos-tesseract/examples/tesseract_usage.rs b/crates/pecos-tesseract/examples/tesseract_usage.rs
index 7500fc0bb..40b6814c0 100644
--- a/crates/pecos-tesseract/examples/tesseract_usage.rs
+++ b/crates/pecos-tesseract/examples/tesseract_usage.rs
@@ -131,7 +131,6 @@ error(0.0005) D1 D3 L0
         det_beam: 50,
         beam_climbing: true,
         no_revisit_dets: false,
-        at_most_two_errors_per_detector: true,
         verbose: false,
         pqlimit: 10000,
         det_penalty: 0.05,
@@ -161,10 +160,6 @@ error(0.0005) D1 D3 L0
         "  No revisit detectors: {}",
         custom_decoder.no_revisit_dets()
     );
-    println!(
-        "  At most two errors per detector: {}",
-        custom_decoder.at_most_two_errors_per_detector()
-    );
     println!("  Priority queue limit: {}", custom_decoder.pqlimit());
     println!("  Detector penalty: {:.3}", custom_decoder.det_penalty());
 
diff --git a/crates/pecos-tesseract/include/tesseract_bridge.h b/crates/pecos-tesseract/include/tesseract_bridge.h
index 75ea89fea..d87177c86 100644
--- a/crates/pecos-tesseract/include/tesseract_bridge.h
+++ b/crates/pecos-tesseract/include/tesseract_bridge.h
@@ -30,7 +30,6 @@ class TesseractDecoderWrapper {
     uint16_t get_det_beam() const;
     bool get_beam_climbing() const;
     bool get_no_revisit_dets() const;
-    bool get_at_most_two_errors_per_detector() const;
     bool get_verbose() const;
     size_t get_pqlimit() const;
     double get_det_penalty() const;
@@ -74,7 +73,6 @@ size_t get_num_observables(const TesseractDecoderWrapper& decoder);
 uint16_t get_det_beam(const TesseractDecoderWrapper& decoder);
 bool get_beam_climbing(const TesseractDecoderWrapper& decoder);
 bool get_no_revisit_dets(const TesseractDecoderWrapper& decoder);
-bool get_at_most_two_errors_per_detector(const TesseractDecoderWrapper& decoder);
 bool get_verbose(const TesseractDecoderWrapper& decoder);
 size_t get_pqlimit(const TesseractDecoderWrapper& decoder);
 double get_det_penalty(const TesseractDecoderWrapper& decoder);
diff --git a/crates/pecos-tesseract/pecos.toml b/crates/pecos-tesseract/pecos.toml
index 7d0dab5e3..4e7316ed3 100644
--- a/crates/pecos-tesseract/pecos.toml
+++ b/crates/pecos-tesseract/pecos.toml
@@ -4,13 +4,19 @@
 version = 1
 
 [dependencies.stim]
-version = "bd60b73525fd5a9b30839020eb7554ad369e4337"
-url = "https://github.com/quantumlib/Stim/archive/bd60b73525fd5a9b30839020eb7554ad369e4337.tar.gz"
-sha256 = "2a4be24295ce3018d79e08369b31e401a2d33cd8b3a75675d57dac3afd9de37d"
+version = "213275795e49027772bea7c610b6aac3a80583e1"
+url = "https://github.com/quantumlib/Stim/archive/213275795e49027772bea7c610b6aac3a80583e1.tar.gz"
+sha256 = "b63c4ae94494a8819d440757776cf80a829ec1e30454fa7c9b0f670e981938ab"
 description = "Stabilizer simulator for QEC"
 
+[dependencies.boost]
+version = "1.83.0"
+url = "https://archives.boost.io/release/1.83.0/source/boost_1_83_0.tar.bz2"
+sha256 = "6478edfe2f3305127cffe8caf73ea0176c53769f4bf1585be237eb30798c3b8e"
+description = "C++ Boost libraries"
+
 [dependencies.tesseract]
-version = "1d81f0b385b6a9de49ae361d08bd6b5dbcec1773"
-url = "https://github.com/quantumlib/tesseract-decoder/archive/1d81f0b385b6a9de49ae361d08bd6b5dbcec1773.tar.gz"
-sha256 = "0b5d8bfa63bab68ab4882510a96d7e238d598d2ba0e669a8903af142ce276892"
+version = "56dd8d5fee3834ef85ca9475a10e708f7d245bea"
+url = "https://github.com/quantumlib/tesseract-decoder/archive/56dd8d5fee3834ef85ca9475a10e708f7d245bea.tar.gz"
+sha256 = "8736ec264fb9a6310957470ac3c63a6d1ce2a26002821caeb64ad91148893e9e"
 description = "Tesseract decoder"
diff --git a/crates/pecos-tesseract/src/bridge.cpp b/crates/pecos-tesseract/src/bridge.cpp
index 65260dedb..9366bfa63 100644
--- a/crates/pecos-tesseract/src/bridge.cpp
+++ b/crates/pecos-tesseract/src/bridge.cpp
@@ -5,7 +5,9 @@
 #include <memory>
 #include <stdexcept>
 #include <sstream>
-#include <numeric>  // Required for std::iota on MSVC
+#include <numeric>   // Required for std::iota on MSVC
+#include <random>    // std::mt19937, std::shuffle
+#include <algorithm> // std::shuffle
 
 // Include Tesseract headers
 #include "tesseract.h"
@@ -40,28 +42,21 @@ class TesseractDecoderWrapper::Impl {
                           INF_DET_BEAM : static_cast<int>(config_repr.det_beam);
         config.beam_climbing = config_repr.beam_climbing;
         config.no_revisit_dets = config_repr.no_revisit_dets;
-        config.at_most_two_errors_per_detector = config_repr.at_most_two_errors_per_detector;
         config.verbose = config_repr.verbose;
+        config.merge_errors = true;
         config.pqlimit = config_repr.pqlimit;
         config.det_penalty = config_repr.det_penalty;
 
-        // Initialize detector orders with a default ordering
-        if (config.det_orders.empty()) {
-            std::vector<size_t> default_order;
-            size_t num_dets = config.dem.count_detectors();
-            for (size_t i = 0; i < num_dets; ++i) {
-                default_order.push_back(i);
-            }
-            config.det_orders.push_back(default_order);
-        }
+        // Generate BFS-based detector orderings (upstream default).
+        // BFS on the detector graph produces spatially-aware orderings
+        // that help the A* search find short paths faster.
+        config.det_orders = build_det_orders(config.dem, 20, DetOrder::DetBFS, 2384753);
 
         config_ = config;
         decoder_ = std::make_unique<TesseractDecoder>(std::move(config));
     }
 
     DecodingResultRepr decode_detections(const rust::Slice<const uint64_t> detections) {
-        // Use data()+size() instead of begin()/end() iterators to avoid
-        // Xcode 15.4 libc++ pointer_traits incompatibility with cxx iterators in C++20
         std::vector<uint64_t> det_vec(detections.data(), detections.data() + detections.size());
 
         decoder_->decode_to_errors(det_vec);
@@ -72,7 +67,8 @@ class TesseractDecoderWrapper::Impl {
             result.predicted_errors.push_back(err);
         }
 
-        result.observables_mask = decoder_->mask_from_errors(decoder_->predicted_errors_buffer);
+        result.observables_mask = vector_to_u64_mask(
+            decoder_->get_flipped_observables(decoder_->predicted_errors_buffer));
         result.cost = decoder_->cost_from_errors(decoder_->predicted_errors_buffer);
         result.low_confidence = decoder_->low_confidence_flag;
 
@@ -85,7 +81,7 @@ class TesseractDecoderWrapper::Impl {
     ) {
         std::vector<uint64_t> det_vec(detections.data(), detections.data() + detections.size());
 
-        decoder_->decode_to_errors(det_vec, det_order);
+        decoder_->decode_to_errors(det_vec, det_order, config_.det_beam);
 
         DecodingResultRepr result;
         result.predicted_errors = rust::Vec<size_t>();
@@ -93,7 +89,8 @@ class TesseractDecoderWrapper::Impl {
             result.predicted_errors.push_back(err);
         }
 
-        result.observables_mask = decoder_->mask_from_errors(decoder_->predicted_errors_buffer);
+        result.observables_mask = vector_to_u64_mask(
+            decoder_->get_flipped_observables(decoder_->predicted_errors_buffer));
         result.cost = decoder_->cost_from_errors(decoder_->predicted_errors_buffer);
         result.low_confidence = decoder_->low_confidence_flag;
 
@@ -125,10 +122,6 @@ class TesseractDecoderWrapper::Impl {
         return config_.no_revisit_dets;
     }
 
-    bool get_at_most_two_errors_per_detector() const {
-        return config_.at_most_two_errors_per_detector;
-    }
-
     bool get_verbose() const {
         return config_.verbose;
     }
@@ -145,7 +138,7 @@ class TesseractDecoderWrapper::Impl {
         if (error_idx >= decoder_->errors.size()) {
             throw std::out_of_range("Error index out of range");
         }
-        return decoder_->errors[error_idx].probability;
+        return decoder_->errors[error_idx].get_probability();
     }
 
     double get_error_cost(size_t error_idx) const {
@@ -171,31 +164,17 @@ class TesseractDecoderWrapper::Impl {
         if (error_idx >= decoder_->errors.size()) {
             throw std::out_of_range("Error index out of range");
         }
-        return decoder_->errors[error_idx].symptom.observables;
+        return vector_to_u64_mask(decoder_->errors[error_idx].symptom.observables);
     }
 
     uint64_t mask_from_errors(const rust::Slice<const size_t> error_indices) const {
-        // Work around Tesseract bug: functions ignore parameter and use internal buffer
-        // So we calculate the mask ourselves
-        uint64_t mask = 0;
-        for (size_t ei : error_indices) {
-            if (ei < decoder_->errors.size()) {
-                mask ^= decoder_->errors[ei].symptom.observables;
-            }
-        }
-        return mask;
+        std::vector<size_t> indices(error_indices.data(), error_indices.data() + error_indices.size());
+        return vector_to_u64_mask(decoder_->get_flipped_observables(indices));
     }
 
     double cost_from_errors(const rust::Slice<const size_t> error_indices) const {
-        // Work around Tesseract bug: functions ignore parameter and use internal buffer
-        // So we calculate the cost ourselves
-        double total_cost = 0;
-        for (size_t ei : error_indices) {
-            if (ei < decoder_->errors.size()) {
-                total_cost += decoder_->errors[ei].likelihood_cost;
-            }
-        }
-        return total_cost;
+        std::vector<size_t> indices(error_indices.data(), error_indices.data() + error_indices.size());
+        return decoder_->cost_from_errors(indices);
     }
 };
 
@@ -245,9 +224,6 @@ bool TesseractDecoderWrapper::get_no_revisit_dets() const {
     return pimpl_->get_no_revisit_dets();
 }
 
-bool TesseractDecoderWrapper::get_at_most_two_errors_per_detector() const {
-    return pimpl_->get_at_most_two_errors_per_detector();
-}
 
 bool TesseractDecoderWrapper::get_verbose() const {
     return pimpl_->get_verbose();
@@ -345,10 +321,6 @@ bool get_no_revisit_dets(const TesseractDecoderWrapper& decoder) {
     return decoder.get_no_revisit_dets();
 }
 
-bool get_at_most_two_errors_per_detector(const TesseractDecoderWrapper& decoder) {
-    return decoder.get_at_most_two_errors_per_detector();
-}
-
 bool get_verbose(const TesseractDecoderWrapper& decoder) {
     return decoder.get_verbose();
 }
diff --git a/crates/pecos-tesseract/src/bridge.rs b/crates/pecos-tesseract/src/bridge.rs
index f22e68d26..f73a72528 100644
--- a/crates/pecos-tesseract/src/bridge.rs
+++ b/crates/pecos-tesseract/src/bridge.rs
@@ -11,7 +11,6 @@ pub(crate) mod ffi {
         pub det_beam: u16,
         pub beam_climbing: bool,
         pub no_revisit_dets: bool,
-        pub at_most_two_errors_per_detector: bool,
         pub verbose: bool,
         pub pqlimit: usize,
         pub det_penalty: f64,
@@ -80,9 +79,6 @@ pub(crate) mod ffi {
         /// Check if detector revisiting is disabled.
         fn get_no_revisit_dets(decoder: &TesseractDecoderWrapper) -> bool;
 
-        /// Check if at-most-two-errors-per-detector is enabled.
-        fn get_at_most_two_errors_per_detector(decoder: &TesseractDecoderWrapper) -> bool;
-
         /// Check if verbose mode is enabled.
         fn get_verbose(decoder: &TesseractDecoderWrapper) -> bool;
 
diff --git a/crates/pecos-tesseract/src/decoder.rs b/crates/pecos-tesseract/src/decoder.rs
index a58068d28..4962d2163 100644
--- a/crates/pecos-tesseract/src/decoder.rs
+++ b/crates/pecos-tesseract/src/decoder.rs
@@ -45,8 +45,6 @@ pub struct TesseractConfig {
     pub beam_climbing: bool,
     /// Avoid revisiting detectors during search
     pub no_revisit_dets: bool,
-    /// Limit to at most two errors per detector
-    pub at_most_two_errors_per_detector: bool,
     /// Enable verbose output
     pub verbose: bool,
     /// Priority queue size limit
@@ -60,10 +58,9 @@ impl Default for TesseractConfig {
         Self {
             det_beam: u16::MAX, // Infinite beam by default
             beam_climbing: false,
-            no_revisit_dets: false,
-            at_most_two_errors_per_detector: false,
+            no_revisit_dets: true,
             verbose: false,
-            pqlimit: usize::MAX,
+            pqlimit: 200_000,
             det_penalty: 0.0,
         }
     }
@@ -74,12 +71,11 @@ impl TesseractConfig {
     #[must_use]
     pub fn fast() -> Self {
         Self {
-            det_beam: 100,
+            det_beam: 5,
             beam_climbing: true,
             no_revisit_dets: true,
-            at_most_two_errors_per_detector: true,
             verbose: false,
-            pqlimit: 1_000_000,
+            pqlimit: 200_000,
             det_penalty: 0.1,
         }
     }
@@ -91,9 +87,8 @@ impl TesseractConfig {
             det_beam: u16::MAX,
             beam_climbing: false,
             no_revisit_dets: false,
-            at_most_two_errors_per_detector: false,
             verbose: false,
-            pqlimit: usize::MAX,
+            pqlimit: 1_000_000,
             det_penalty: 0.0,
         }
     }
@@ -105,7 +100,6 @@ impl TesseractConfig {
             det_beam: self.det_beam,
             beam_climbing: self.beam_climbing,
             no_revisit_dets: self.no_revisit_dets,
-            at_most_two_errors_per_detector: self.at_most_two_errors_per_detector,
             verbose: self.verbose,
             pqlimit: self.pqlimit,
             det_penalty: self.det_penalty,
@@ -336,12 +330,6 @@ impl TesseractDecoder {
         ffi::get_no_revisit_dets(&self.inner)
     }
 
-    /// Check if at-most-two-errors-per-detector is enabled
-    #[must_use]
-    pub fn at_most_two_errors_per_detector(&self) -> bool {
-        ffi::get_at_most_two_errors_per_detector(&self.inner)
-    }
-
     /// Check if verbose mode is enabled
     #[must_use]
     pub fn verbose(&self) -> bool {
@@ -361,6 +349,24 @@ impl TesseractDecoder {
     }
 }
 
+impl pecos_decoder_core::ObservableDecoder for TesseractDecoder {
+    fn decode_to_observables(
+        &mut self,
+        syndrome: &[u8],
+    ) -> Result<u64, pecos_decoder_core::DecoderError> {
+        let detections: Vec<u64> = syndrome
+            .iter()
+            .enumerate()
+            .filter_map(|(i, &val)| if val != 0 { Some(i as u64) } else { None })
+            .collect();
+        let det_arr = Array1::from_vec(detections);
+        let result = self
+            .decode_detections(&det_arr.view())
+            .map_err(|e| pecos_decoder_core::DecoderError::DecodingFailed(e.to_string()))?;
+        Ok(result.observables_mask)
+    }
+}
+
 impl Decoder for TesseractDecoder {
     type Result = DecodingResult;
     type Error = TesseractError;
@@ -416,10 +422,9 @@ mod tests {
     #[test]
     fn test_tesseract_config_fast() {
         let config = TesseractConfig::fast();
-        assert_eq!(config.det_beam, 100);
+        assert_eq!(config.det_beam, 5);
         assert!(config.beam_climbing);
         assert!(config.no_revisit_dets);
-        assert!(config.at_most_two_errors_per_detector);
     }
 
     #[test]
@@ -428,6 +433,5 @@ mod tests {
         assert_eq!(config.det_beam, u16::MAX);
         assert!(!config.beam_climbing);
         assert!(!config.no_revisit_dets);
-        assert!(!config.at_most_two_errors_per_detector);
     }
 }
diff --git a/crates/pecos-tesseract/tests/tesseract/tesseract_comprehensive_tests.rs b/crates/pecos-tesseract/tests/tesseract/tesseract_comprehensive_tests.rs
index 6ef83e46a..27c49d542 100644
--- a/crates/pecos-tesseract/tests/tesseract/tesseract_comprehensive_tests.rs
+++ b/crates/pecos-tesseract/tests/tesseract/tesseract_comprehensive_tests.rs
@@ -166,7 +166,7 @@ error(0.1) D2 D3
     // Test fast configuration
     let fast_config = TesseractConfig::fast();
     let mut fast_decoder = TesseractDecoder::new(dem, fast_config).unwrap();
-    assert_eq!(fast_decoder.det_beam(), 100);
+    assert_eq!(fast_decoder.det_beam(), 5);
     assert!(fast_decoder.beam_climbing());
 
     // Test accurate configuration
@@ -250,10 +250,9 @@ fn test_configuration_getters() {
     let dem = "error(0.1) D0";
 
     let custom_config = TesseractConfig {
-        det_beam: 50,
+        det_beam: 5,
         beam_climbing: true,
         no_revisit_dets: false,
-        at_most_two_errors_per_detector: true,
         verbose: false,
         pqlimit: 5000,
         det_penalty: 0.05,
@@ -262,10 +261,9 @@ fn test_configuration_getters() {
     let decoder = TesseractDecoder::new(dem, custom_config).unwrap();
 
     // Verify all configuration values
-    assert_eq!(decoder.det_beam(), 50);
+    assert_eq!(decoder.det_beam(), 5);
     assert!(decoder.beam_climbing());
     assert!(!decoder.no_revisit_dets());
-    assert!(decoder.at_most_two_errors_per_detector());
     assert!(!decoder.verbose());
     assert_eq!(decoder.pqlimit(), 5000);
     assert!((decoder.det_penalty() - 0.05).abs() < 0.001);
diff --git a/crates/pecos-tesseract/tests/tesseract/tesseract_tests.rs b/crates/pecos-tesseract/tests/tesseract/tesseract_tests.rs
index bba9578f3..b2b96b62a 100644
--- a/crates/pecos-tesseract/tests/tesseract/tesseract_tests.rs
+++ b/crates/pecos-tesseract/tests/tesseract/tesseract_tests.rs
@@ -9,10 +9,9 @@ fn test_tesseract_config_default() {
     let config = TesseractConfig::default();
     assert_eq!(config.det_beam, u16::MAX);
     assert!(!config.beam_climbing);
-    assert!(!config.no_revisit_dets);
-    assert!(!config.at_most_two_errors_per_detector);
+    assert!(config.no_revisit_dets);
     assert!(!config.verbose);
-    assert_eq!(config.pqlimit, usize::MAX);
+    assert_eq!(config.pqlimit, 200_000);
     assert!(
         config.det_penalty.abs() < f64::EPSILON,
         "det_penalty should be 0.0 but was {}",
@@ -23,12 +22,11 @@ fn test_tesseract_config_default() {
 #[test]
 fn test_tesseract_config_fast() {
     let config = TesseractConfig::fast();
-    assert_eq!(config.det_beam, 100);
+    assert_eq!(config.det_beam, 5);
     assert!(config.beam_climbing);
     assert!(config.no_revisit_dets);
-    assert!(config.at_most_two_errors_per_detector);
     assert!(!config.verbose);
-    assert_eq!(config.pqlimit, 1_000_000);
+    assert_eq!(config.pqlimit, 200_000);
     assert!(
         (config.det_penalty - 0.1).abs() < f64::EPSILON,
         "det_penalty should be 0.1 but was {}",
@@ -42,9 +40,8 @@ fn test_tesseract_config_accurate() {
     assert_eq!(config.det_beam, u16::MAX);
     assert!(!config.beam_climbing);
     assert!(!config.no_revisit_dets);
-    assert!(!config.at_most_two_errors_per_detector);
     assert!(!config.verbose);
-    assert_eq!(config.pqlimit, usize::MAX);
+    assert_eq!(config.pqlimit, 1_000_000);
     assert!(
         config.det_penalty.abs() < f64::EPSILON,
         "det_penalty should be 0.0 but was {}",
@@ -55,20 +52,18 @@ fn test_tesseract_config_accurate() {
 #[test]
 fn test_tesseract_config_to_ffi_repr() {
     let config = TesseractConfig {
-        det_beam: 50,
+        det_beam: 5,
         beam_climbing: true,
         no_revisit_dets: false,
-        at_most_two_errors_per_detector: true,
         verbose: true,
         pqlimit: 5000,
         det_penalty: 0.05,
     };
 
     let ffi_repr = config.to_ffi_repr();
-    assert_eq!(ffi_repr.det_beam, 50);
+    assert_eq!(ffi_repr.det_beam, 5);
     assert!(ffi_repr.beam_climbing);
     assert!(!ffi_repr.no_revisit_dets);
-    assert!(ffi_repr.at_most_two_errors_per_detector);
     assert!(ffi_repr.verbose);
     assert_eq!(ffi_repr.pqlimit, 5000);
     assert!(
diff --git a/crates/pecos-uf-decoder/Cargo.toml b/crates/pecos-uf-decoder/Cargo.toml
new file mode 100644
index 000000000..27b28a9d4
--- /dev/null
+++ b/crates/pecos-uf-decoder/Cargo.toml
@@ -0,0 +1,26 @@
+[package]
+name = "pecos-uf-decoder"
+version.workspace = true
+edition.workspace = true
+readme = "README.md"
+authors.workspace = true
+homepage.workspace = true
+repository.workspace = true
+license.workspace = true
+keywords.workspace = true
+categories.workspace = true
+description = "Fast syndrome-graph Union-Find decoder for PECOS"
+
+[dependencies]
+pecos-decoder-core.workspace = true
+pecos-random.workspace = true
+rayon.workspace = true
+
+[lib]
+name = "pecos_uf_decoder"
+
+[dev-dependencies]
+fastrand.workspace = true
+
+[lints]
+workspace = true
diff --git a/crates/pecos-uf-decoder/examples/profile_decode.rs b/crates/pecos-uf-decoder/examples/profile_decode.rs
new file mode 100644
index 000000000..78bcd54fa
--- /dev/null
+++ b/crates/pecos-uf-decoder/examples/profile_decode.rs
@@ -0,0 +1,144 @@
+// Simple profiling harness for the UF decoder.
+// Run with: cargo run --release --example profile_decode -p pecos-uf-decoder
+
+use pecos_decoder_core::dem::DemMatchingGraph;
+use pecos_uf_decoder::{UfDecoder, UfDecoderConfig};
+use std::time::Instant;
+
+const D3_DEM: &str =
+    include_str!("../../../examples/surface_code_circuits/surface_code_d3_z_stim.dem");
+const D5_DEM: &str =
+    include_str!("../../../examples/surface_code_circuits/surface_code_d5_z_stim.dem");
+
+fn shots_as_f64(num_shots: usize) -> f64 {
+    f64::from(u32::try_from(num_shots).expect("profile shot count fits in u32"))
+}
+
+fn profile_decoder(name: &str, dem: &str, num_shots: usize) {
+    let graph = DemMatchingGraph::from_dem_str(dem).unwrap();
+    let mut dec = UfDecoder::from_matching_graph(&graph, UfDecoderConfig::fast());
+    let num_det = graph.num_detectors;
+
+    // Generate random syndromes
+    let mut rng = fastrand::Rng::with_seed(42);
+    let syndromes: Vec<Vec<u8>> = (0..num_shots)
+        .map(|_| (0..num_det).map(|_| u8::from(rng.f64() < 0.05)).collect())
+        .collect();
+
+    // Warm up
+    for syn in &syndromes[..100.min(num_shots)] {
+        let _ = dec.decode_syndrome(syn);
+    }
+
+    // Time the full batch
+    let t0 = Instant::now();
+    let mut errors = 0u64;
+    for syn in &syndromes {
+        let obs = dec.decode_syndrome(syn);
+        errors += obs;
+    }
+    let elapsed = t0.elapsed();
+
+    let shots = shots_as_f64(num_shots);
+    let per_shot_ns = elapsed.as_secs_f64() * 1.0e9 / shots;
+    let throughput = shots / elapsed.as_secs_f64();
+    println!(
+        "{name:8}: {num_det:3} det, {per_shot_ns:8.0} ns/shot ({:.0} kshots/s), errors={errors}",
+        throughput / 1000.0
+    );
+}
+
+fn profile_phases(name: &str, dem: &str, num_shots: usize) {
+    let graph = DemMatchingGraph::from_dem_str(dem).unwrap();
+    let num_det = graph.num_detectors;
+    let num_edges = graph.edges.len();
+
+    let mut rng = fastrand::Rng::with_seed(42);
+    let syndromes: Vec<Vec<u8>> = (0..num_shots)
+        .map(|_| (0..num_det).map(|_| u8::from(rng.f64() < 0.05)).collect())
+        .collect();
+
+    // Phase 1: measure reset + syndrome loading only
+    let mut dec = UfDecoder::from_matching_graph(&graph, UfDecoderConfig::fast());
+    let t0 = Instant::now();
+    for syn in &syndromes {
+        dec.syndrome_validate(syn); // reset + grow (no peel)
+    }
+    let grow_time = t0.elapsed();
+
+    // Phase 2: measure full decode (reset + grow + peel)
+    let t0 = Instant::now();
+    for syn in &syndromes {
+        let _ = dec.decode_syndrome(syn);
+    }
+    let total_time = t0.elapsed();
+
+    let shots = shots_as_f64(num_shots);
+    let grow_ns = grow_time.as_secs_f64() * 1.0e9 / shots;
+    let total_ns = total_time.as_secs_f64() * 1.0e9 / shots;
+    let peel_ns = total_ns - grow_ns;
+
+    println!(
+        "{name}: {num_det} det, {num_edges} edges | total {total_ns:.0} ns = grow {grow_ns:.0} ns ({:.0}%) + peel {peel_ns:.0} ns ({:.0}%)",
+        grow_ns / total_ns * 100.0,
+        peel_ns / total_ns * 100.0,
+    );
+
+    // Also profile BP+UF if available
+    if let Ok(mut bp_dec) =
+        pecos_uf_decoder::BpUfDecoder::from_dem(dem, pecos_uf_decoder::BpUfConfig::default())
+    {
+        use pecos_decoder_core::ObservableDecoder;
+        let t0 = Instant::now();
+        for syn in &syndromes {
+            let _ = bp_dec.decode_to_observables(syn);
+        }
+        let bp_total = t0.elapsed();
+        let bp_ns = bp_total.as_secs_f64() * 1.0e9 / shots;
+        let bp_only = bp_ns - total_ns; // approximate BP overhead
+        println!(
+            "  BP+UF: {bp_ns:.0} ns/shot total (BP overhead ~{bp_only:.0} ns = {:.0}%)",
+            bp_only / bp_ns * 100.0,
+        );
+    }
+}
+
+const D7_DEM: &str =
+    include_str!("../../../examples/surface_code_circuits/surface_code_d7_z_stim.dem");
+
+fn main() {
+    let num_shots = 100_000;
+
+    println!("=== UF Decoder Profiling ({num_shots} shots) ===");
+    println!();
+
+    profile_decoder("d3", D3_DEM, num_shots);
+    profile_decoder("d5", D5_DEM, num_shots);
+    profile_decoder("d7", D7_DEM, num_shots);
+
+    println!();
+    println!("=== Phase breakdown ===");
+    profile_phases("d3", D3_DEM, num_shots);
+    profile_phases("d5", D5_DEM, num_shots);
+    profile_phases("d7", D7_DEM, num_shots);
+
+    // Also profile with balanced config (Prim MST)
+    println!();
+    println!("=== Balanced (Prim MST) ===");
+    let graph = DemMatchingGraph::from_dem_str(D5_DEM).unwrap();
+    let mut dec = UfDecoder::from_matching_graph(&graph, UfDecoderConfig::balanced());
+    let num_det = graph.num_detectors;
+
+    let mut rng = fastrand::Rng::with_seed(42);
+    let syndromes: Vec<Vec<u8>> = (0..num_shots)
+        .map(|_| (0..num_det).map(|_| u8::from(rng.f64() < 0.05)).collect())
+        .collect();
+
+    let t0 = Instant::now();
+    for syn in &syndromes {
+        let _ = dec.decode_syndrome(syn);
+    }
+    let elapsed = t0.elapsed();
+    let per_shot_ns = elapsed.as_secs_f64() * 1.0e9 / shots_as_f64(num_shots);
+    println!("d5-bal : {num_det:3} det, {per_shot_ns:8.0} ns/shot");
+}
diff --git a/crates/pecos-uf-decoder/src/astar.rs b/crates/pecos-uf-decoder/src/astar.rs
new file mode 100644
index 000000000..1b0b56bc8
--- /dev/null
+++ b/crates/pecos-uf-decoder/src/astar.rs
@@ -0,0 +1,501 @@
+// Copyright 2026 The PECOS Developers
+//
+// Licensed under the Apache License, Version 2.0 (the "License"); you may not use this file except
+// in compliance with the License. You may obtain a copy of the License at
+//
+//     https://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software distributed under the License
+// is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express
+// or implied. See the License for the specific language governing permissions and limitations under
+// the License.
+
+//! A* error-set decoder inspired by Tesseract (Google, arXiv:2503.10988).
+//!
+//! Searches over error mechanism subsets to find the minimum-weight
+//! error set consistent with the syndrome. Uses `DetCost` heuristic
+//! (per-detector minimum mechanism cost) for admissible pruning.
+//!
+//! Key pruning strategies from Tesseract:
+//! - **Canonical expansion**: only expand mechanisms incident to the
+//!   lowest-index unsatisfied detector
+//! - **No-revisit-dets**: skip states with previously-seen residual syndromes
+//! - **Beam**: skip states with too many residual defects
+//! - **PQ limit**: terminate after a fixed number of expansions
+//!
+//! Uses u64 bitsets for compact state representation and fast operations.
+
+use pecos_decoder_core::ObservableDecoder;
+use pecos_decoder_core::dem::DemMatchingGraph;
+use pecos_decoder_core::errors::DecoderError;
+use std::cmp::Reverse;
+use std::collections::{BinaryHeap, HashSet};
+
+/// A mechanism (error) in the DEM.
+struct Mechanism {
+    detectors: Vec<u32>,
+    obs_mask: u64,
+    weight: f64,
+}
+
+/// Configuration for the A* decoder.
+#[derive(Debug, Clone, Copy)]
+pub struct AStarConfig {
+    /// Maximum priority queue pops before terminating.
+    pub pq_limit: usize,
+    /// Beam: skip states with > beam more residual defects than best seen.
+    pub beam: usize,
+}
+
+impl Default for AStarConfig {
+    fn default() -> Self {
+        Self {
+            pq_limit: 50_000,
+            beam: 20,
+        }
+    }
+}
+
+/// Compact bitset for detector/mechanism membership.
+#[derive(Clone, PartialEq, Eq, Hash)]
+struct Bitset {
+    words: Vec<u64>,
+}
+
+impl Bitset {
+    fn new(n: usize) -> Self {
+        Self {
+            words: vec![0u64; n.div_ceil(64)],
+        }
+    }
+
+    fn get(&self, i: usize) -> bool {
+        let (word, bit) = (i / 64, i % 64);
+        word < self.words.len() && (self.words[word] & (1u64 << bit)) != 0
+    }
+
+    fn set(&mut self, i: usize) {
+        let (word, bit) = (i / 64, i % 64);
+        if word < self.words.len() {
+            self.words[word] |= 1u64 << bit;
+        }
+    }
+
+    fn flip(&mut self, i: usize) {
+        let (word, bit) = (i / 64, i % 64);
+        if word < self.words.len() {
+            self.words[word] ^= 1u64 << bit;
+        }
+    }
+
+    fn count_ones(&self) -> usize {
+        self.words.iter().map(|w| w.count_ones() as usize).sum()
+    }
+
+    /// Find the index of the lowest set bit, or None.
+    fn lowest_set(&self) -> Option<usize> {
+        for (wi, &w) in self.words.iter().enumerate() {
+            if w != 0 {
+                return Some(wi * 64 + w.trailing_zeros() as usize);
+            }
+        }
+        None
+    }
+}
+
+/// A* error-set search decoder.
+pub struct AStarDecoder {
+    mechanisms: Vec<Mechanism>,
+    /// Per-detector: list of mechanism indices incident to this detector.
+    det_to_mechs: Vec<Vec<usize>>,
+    num_detectors: usize,
+    num_mechanisms: usize,
+    config: AStarConfig,
+}
+
+/// State in the A* search (compact representation).
+struct SearchState {
+    errors: Bitset,
+    residual: Bitset,
+    num_residual: usize,
+    g_cost: f64,
+    obs_mask: u64,
+    /// Per-detector: how many included errors are incident to this detector.
+    det_error_count: Vec<u8>,
+    /// Mechanisms forbidden by `ByPrecedence`: were available at an earlier
+    /// step but not chosen. Cannot be added in future steps.
+    forbidden: Bitset,
+}
+
+impl AStarDecoder {
+    /// Build from a DEM string (graphlike — 2-detector edges only).
+    ///
+    /// # Errors
+    ///
+    /// Returns `DecoderError` if the DEM is malformed.
+    pub fn from_dem(dem: &str, config: AStarConfig) -> Result<Self, DecoderError> {
+        let graph = DemMatchingGraph::from_dem_str(dem)?;
+        let num_detectors = graph.num_detectors;
+
+        let mut mechanisms = Vec::new();
+        let mut det_to_mechs: Vec<Vec<usize>> = vec![Vec::new(); num_detectors];
+
+        for edge in &graph.edges {
+            let mut detectors = vec![edge.node1];
+            if let Some(n2) = edge.node2 {
+                detectors.push(n2);
+            }
+
+            let obs_mask: u64 = edge
+                .observables
+                .iter()
+                .fold(0u64, |mask, &o| mask | (1 << o));
+
+            let mech_idx = mechanisms.len();
+            for &d in &detectors {
+                if (d as usize) < num_detectors {
+                    det_to_mechs[d as usize].push(mech_idx);
+                }
+            }
+
+            mechanisms.push(Mechanism {
+                detectors,
+                obs_mask,
+                weight: edge.weight,
+            });
+        }
+
+        let num_mechanisms = mechanisms.len();
+
+        Ok(Self {
+            mechanisms,
+            det_to_mechs,
+            num_detectors,
+            num_mechanisms,
+            config,
+        })
+    }
+
+    /// Build from a non-decomposed DEM (preserves hyperedges with 3+ detectors).
+    ///
+    /// This gives the A* search access to the full error structure including
+    /// Y-error correlations that decomposition loses.
+    ///
+    /// # Errors
+    ///
+    /// Returns `DecoderError` if the DEM is malformed.
+    pub fn from_dem_full(dem: &str, config: AStarConfig) -> Result<Self, DecoderError> {
+        use pecos_decoder_core::dem::DemCheckMatrix;
+
+        let dcm = DemCheckMatrix::from_dem_str(dem)
+            .map_err(|e| DecoderError::InvalidGraph(e.to_string()))?;
+        let num_detectors = dcm.num_detectors;
+
+        let mut mechanisms = Vec::new();
+        let mut det_to_mechs: Vec<Vec<usize>> = vec![Vec::new(); num_detectors];
+
+        for m in 0..dcm.num_mechanisms {
+            let p = dcm.error_priors[m];
+            if p <= 0.0 {
+                continue;
+            }
+
+            let detectors: Vec<u32> = (0..dcm.num_detectors)
+                .filter(|&d| dcm.check_matrix[[d, m]] != 0)
+                .map(|d| d as u32)
+                .collect();
+
+            if detectors.is_empty() {
+                continue;
+            }
+
+            let weight = if p < 1.0 { ((1.0 - p) / p).ln() } else { 0.0 };
+
+            let mut obs_mask = 0u64;
+            for o in 0..dcm.num_observables {
+                if dcm.observable_matrix[[o, m]] != 0 {
+                    obs_mask |= 1 << o;
+                }
+            }
+
+            let mech_idx = mechanisms.len();
+            for &d in &detectors {
+                if (d as usize) < num_detectors {
+                    det_to_mechs[d as usize].push(mech_idx);
+                }
+            }
+
+            mechanisms.push(Mechanism {
+                detectors,
+                obs_mask,
+                weight,
+            });
+        }
+
+        let num_mechanisms = mechanisms.len();
+
+        for mechs in &mut det_to_mechs {
+            mechs.sort_by(|&a, &b| {
+                mechanisms[a]
+                    .weight
+                    .partial_cmp(&mechanisms[b].weight)
+                    .unwrap_or(std::cmp::Ordering::Equal)
+            });
+        }
+
+        Ok(Self {
+            mechanisms,
+            det_to_mechs,
+            num_detectors,
+            num_mechanisms,
+            config,
+        })
+    }
+
+    /// Compute `DetCost` heuristic: admissible lower bound on remaining cost.
+    /// Optimized with early exit: mechanisms per detector are pre-sorted by weight,
+    /// so once weight exceeds `current_min` * `max_possible_coverage`, we can stop.
+    fn det_cost(&self, residual: &Bitset, errors: &Bitset) -> f64 {
+        let mut cost = 0.0;
+        for (wi, &w) in residual.words.iter().enumerate() {
+            let mut bits = w;
+            while bits != 0 {
+                let bit = bits.trailing_zeros() as usize;
+                let d = wi * 64 + bit;
+                bits &= bits - 1;
+
+                if d >= self.num_detectors {
+                    break;
+                }
+
+                let mut min_cost = f64::INFINITY;
+                for &m in &self.det_to_mechs[d] {
+                    if errors.get(m) {
+                        continue;
+                    }
+                    let mech = &self.mechanisms[m];
+
+                    // Early skip: if weight / max_coverage >= min_cost, skip.
+                    // max_coverage = number of detectors in this mechanism.
+                    let max_cov = mech.detectors.len() as f64;
+                    if max_cov > 0.0 && mech.weight / max_cov >= min_cost {
+                        continue;
+                    }
+
+                    let coverage = mech
+                        .detectors
+                        .iter()
+                        .filter(|&&dd| {
+                            (dd as usize) < self.num_detectors && residual.get(dd as usize)
+                        })
+                        .count();
+                    if coverage > 0 {
+                        let c = mech.weight / coverage as f64;
+                        if c < min_cost {
+                            min_cost = c;
+                        }
+                    }
+                }
+                if min_cost < f64::INFINITY {
+                    cost += min_cost;
+                }
+            }
+        }
+        cost
+    }
+}
+
+impl ObservableDecoder for AStarDecoder {
+    fn decode_to_observables(&mut self, syndrome: &[u8]) -> Result<u64, DecoderError> {
+        let n = self.num_detectors;
+        let m = self.num_mechanisms;
+
+        // Build initial residual.
+        let mut init_residual = Bitset::new(n);
+        for (i, &v) in syndrome.iter().enumerate() {
+            if v != 0 && i < n {
+                init_residual.set(i);
+            }
+        }
+        let num_defects = init_residual.count_ones();
+        if num_defects == 0 {
+            return Ok(0);
+        }
+
+        // A* priority queue and visited set.
+        let mut pq: BinaryHeap<(Reverse<u64>, usize)> = BinaryHeap::new();
+        let mut states: Vec<SearchState> = Vec::new();
+        let mut visited: HashSet<Bitset> = HashSet::new();
+
+        let init_errors = Bitset::new(m);
+        let init_h = self.det_cost(&init_residual, &init_errors);
+
+        states.push(SearchState {
+            errors: init_errors,
+            residual: init_residual.clone(),
+            num_residual: num_defects,
+            g_cost: 0.0,
+            obs_mask: 0,
+            det_error_count: vec![0u8; n],
+            forbidden: Bitset::new(m),
+        });
+        pq.push((Reverse((0.0_f64 + init_h).to_bits()), 0));
+        visited.insert(init_residual);
+
+        let mut best_obs = 0u64;
+        let best_cost = f64::INFINITY;
+        let mut min_residual = num_defects;
+        let mut pops = 0;
+
+        while let Some((Reverse(_), state_idx)) = pq.pop() {
+            pops += 1;
+            if pops > self.config.pq_limit {
+                break;
+            }
+
+            // Extract state data (avoids borrow conflict).
+            let (s_num_res, s_g_cost, s_obs) = {
+                let s = &states[state_idx];
+                (s.num_residual, s.g_cost, s.obs_mask)
+            };
+
+            if s_num_res == 0 {
+                best_obs = s_obs;
+                break; // A* first solution is optimal (admissible heuristic).
+            }
+
+            if s_num_res > min_residual + self.config.beam {
+                continue;
+            }
+            if s_num_res < min_residual {
+                min_residual = s_num_res;
+            }
+
+            // Clone for expansion.
+            let (s_errors, s_residual, s_det_counts, s_forbidden) = {
+                let s = &states[state_idx];
+                (
+                    s.errors.clone(),
+                    s.residual.clone(),
+                    s.det_error_count.clone(),
+                    s.forbidden.clone(),
+                )
+            };
+
+            let lowest_det = match s_residual.lowest_set() {
+                Some(d) if d < n => d,
+                _ => continue,
+            };
+
+            // Collect candidate mechanisms incident to lowest_det.
+            let candidates: Vec<usize> = self.det_to_mechs[lowest_det]
+                .iter()
+                .copied()
+                .filter(|&mi| !s_errors.get(mi) && !s_forbidden.get(mi))
+                .collect();
+
+            for &mech_idx in &candidates {
+                let mech = &self.mechanisms[mech_idx];
+
+                // AtMostTwo: skip if adding this mechanism would place >2 errors
+                // on any single detector.
+                let at_most_two_ok = mech.detectors.iter().all(|&d| {
+                    let di = d as usize;
+                    di >= n || s_det_counts[di] < 2
+                });
+                if !at_most_two_ok {
+                    continue;
+                }
+
+                let mut new_residual = s_residual.clone();
+                let mut new_num = s_num_res;
+                let mut new_det_counts = s_det_counts.clone();
+                for &d in &mech.detectors {
+                    let di = d as usize;
+                    if di < n {
+                        if new_residual.get(di) {
+                            new_num -= 1;
+                        } else {
+                            new_num += 1;
+                        }
+                        new_residual.flip(di);
+                        new_det_counts[di] += 1;
+                    }
+                }
+
+                // ByPrecedence: all other candidate mechanisms at this step
+                // become forbidden for this child. They were available but not chosen.
+                let mut new_forbidden = s_forbidden.clone();
+                for &other in &candidates {
+                    if other != mech_idx {
+                        new_forbidden.set(other);
+                    }
+                }
+
+                // No-revisit-dets: skip if we've seen this residual before.
+                if !visited.insert(new_residual.clone()) {
+                    continue;
+                }
+
+                let mut new_errors = s_errors.clone();
+                new_errors.set(mech_idx);
+
+                let new_g = s_g_cost + mech.weight;
+                let new_h = self.det_cost(&new_residual, &new_errors);
+                let new_f = new_g + new_h;
+
+                if new_f >= best_cost {
+                    continue;
+                }
+
+                let idx = states.len();
+                states.push(SearchState {
+                    errors: new_errors,
+                    residual: new_residual,
+                    num_residual: new_num,
+                    g_cost: new_g,
+                    obs_mask: s_obs ^ mech.obs_mask,
+                    det_error_count: new_det_counts,
+                    forbidden: new_forbidden,
+                });
+                pq.push((Reverse(new_f.to_bits()), idx));
+            }
+        }
+
+        Ok(best_obs)
+    }
+}
+
+#[cfg(test)]
+mod tests {
+    use super::*;
+
+    const D3_DEM: &str =
+        include_str!("../../../examples/surface_code_circuits/surface_code_d3_z_stim.dem");
+
+    #[test]
+    fn test_astar_construction() {
+        let dec = AStarDecoder::from_dem(D3_DEM, AStarConfig::default());
+        assert!(dec.is_ok());
+    }
+
+    #[test]
+    fn test_astar_no_errors() {
+        let graph = DemMatchingGraph::from_dem_str(D3_DEM).unwrap();
+        let mut dec = AStarDecoder::from_dem(D3_DEM, AStarConfig::default()).unwrap();
+        let obs = dec
+            .decode_to_observables(&vec![0u8; graph.num_detectors])
+            .unwrap();
+        assert_eq!(obs, 0);
+    }
+
+    #[test]
+    fn test_astar_single_defect() {
+        let graph = DemMatchingGraph::from_dem_str(D3_DEM).unwrap();
+        let mut dec = AStarDecoder::from_dem(D3_DEM, AStarConfig::default()).unwrap();
+        let mut syn = vec![0u8; graph.num_detectors];
+        syn[0] = 1;
+        // Should not panic — single defect resolves to boundary.
+        let _obs = dec.decode_to_observables(&syn).unwrap();
+    }
+}
diff --git a/crates/pecos-uf-decoder/src/bp_uf.rs b/crates/pecos-uf-decoder/src/bp_uf.rs
new file mode 100644
index 000000000..0a293ce40
--- /dev/null
+++ b/crates/pecos-uf-decoder/src/bp_uf.rs
@@ -0,0 +1,617 @@
+// Copyright 2026 The PECOS Developers
+//
+// Licensed under the Apache License, Version 2.0 (the "License"); you may not use this file except
+// in compliance with the License. You may obtain a copy of the License at
+//
+//     https://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software distributed under the License
+// is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express
+// or implied. See the License for the specific language governing permissions and limitations under
+// the License.
+
+//! BP+UF hybrid decoder.
+//!
+//! Runs truncated min-sum BP to get per-mechanism soft reliability scores,
+//! then uses those scores to adjust UF edge weights. Mechanisms that BP
+//! identifies as likely errors get lower weights in UF, improving the
+//! quality of the UF clustering.
+//!
+//! This is a three-stage decoder:
+//! 1. **BP stage**: 3-5 iterations of min-sum BP on the check matrix
+//! 2. **Weight adjustment**: map BP posteriors to UF edge weights
+//! 3. **UF stage**: standard weighted UF growth + peeling
+
+use crate::decoder::{UfDecoder, UfDecoderConfig};
+use crate::mini_bp::{self, BpGraph};
+use pecos_decoder_core::correlated_decoder::MatchingDecoder;
+use pecos_decoder_core::dem::{DemCheckMatrix, DemMatchingGraph};
+use pecos_decoder_core::errors::DecoderError;
+
+/// BP message schedule.
+#[derive(Debug, Clone, Copy, Default)]
+pub enum BpSchedule {
+    /// Flooding: update all checks, then all variables. Fast, good for d<=7.
+    #[default]
+    Flooding,
+    /// Serial: after each check update, immediately update connected variables.
+    /// Better convergence on loopy graphs. Slower but maintains threshold at d>=9.
+    Serial,
+}
+
+/// Which graph to run BP on.
+#[derive(Debug, Clone, Copy, Default)]
+pub enum BpGraphType {
+    /// Auto: matching-graph BP at d<=4, Tanner-graph BP at d>=5.
+    /// Gets the best of both worlds at each distance.
+    #[default]
+    Auto,
+    /// Tanner graph from check matrix (decomposed DEM).
+    TannerGraph,
+    /// Matching graph (pairwise detector edges). Simpler topology,
+    /// better convergence. Based on Hack et al. (2026).
+    MatchingGraph,
+}
+
+/// Configuration for the BP+UF hybrid decoder.
+#[derive(Debug, Clone, Copy)]
+pub struct BpUfConfig {
+    /// Number of BP iterations before UF.
+    /// 0 = adaptive (scales with code distance). Default: 0.
+    pub bp_iterations: usize,
+    /// BP message schedule. Default: Flooding (fast, good for d<=7).
+    pub bp_schedule: BpSchedule,
+    /// Which graph to run BP on. Default: `TannerGraph`.
+    pub bp_graph_type: BpGraphType,
+    /// Min-sum scaling factor. Default: 0.625 (normalized min-sum).
+    pub min_sum_scale: f64,
+    /// How much BP posteriors influence UF weights.
+    /// 0.0 = pure UF, 1.0 = fully trust BP. Default: 0.9.
+    pub bp_weight_blend: f64,
+    /// UF decoder config.
+    pub uf_config: UfDecoderConfig,
+}
+
+impl Default for BpUfConfig {
+    fn default() -> Self {
+        Self::balanced()
+    }
+}
+
+impl BpUfConfig {
+    /// Balanced: flooding BP on Tanner graph, good for d=3-7. Fast.
+    #[must_use]
+    pub fn balanced() -> Self {
+        Self {
+            bp_iterations: 0,
+            bp_schedule: BpSchedule::Flooding,
+            bp_graph_type: BpGraphType::Auto,
+            min_sum_scale: 0.625,
+            bp_weight_blend: 0.9,
+            uf_config: UfDecoderConfig::balanced(),
+        }
+    }
+
+    /// Accurate: serial BP, maintains threshold at d=7-11+. Slower.
+    #[must_use]
+    pub fn accurate() -> Self {
+        Self {
+            bp_iterations: 0,
+            bp_schedule: BpSchedule::Serial,
+            bp_graph_type: BpGraphType::Auto,
+            min_sum_scale: 0.625,
+            bp_weight_blend: 0.9,
+            uf_config: UfDecoderConfig::balanced(),
+        }
+    }
+
+    /// Matching-graph BP: run BP on the simpler matching graph.
+    #[must_use]
+    pub fn matching_bp() -> Self {
+        Self {
+            bp_iterations: 0,
+            bp_schedule: BpSchedule::Flooding,
+            bp_graph_type: BpGraphType::MatchingGraph,
+            min_sum_scale: 0.625,
+            bp_weight_blend: 0.9,
+            uf_config: UfDecoderConfig::balanced(),
+        }
+    }
+}
+
+/// BP+UF hybrid decoder.
+pub struct BpUfDecoder {
+    /// Inner UF decoder.
+    uf: UfDecoder,
+    /// Pre-computed sparse BP graph for Tanner graph BP.
+    bp_graph: BpGraph,
+    /// Matching graph (stored for matching-graph BP mode).
+    matching_graph: Option<DemMatchingGraph>,
+    /// Mapping from mechanism index to matching graph edge index.
+    mechanism_to_edge: Vec<Option<usize>>,
+    /// Base edge weights (from DEM, before BP adjustment).
+    base_weights: Vec<f64>,
+    /// BP-adjusted weights (reusable buffer).
+    adjusted_weights: Vec<f64>,
+    /// BP message buffers (reusable across shots).
+    bp_c_to_v: Vec<f64>,
+    bp_v_to_c: Vec<f64>,
+    bp_posterior: Vec<f64>,
+    /// Config.
+    config: BpUfConfig,
+}
+
+impl BpUfDecoder {
+    /// Create from a DEM string.
+    ///
+    /// # Errors
+    ///
+    /// Returns `DecoderError` if the DEM is malformed.
+    pub fn from_dem(dem: &str, config: BpUfConfig) -> Result<Self, DecoderError> {
+        let dcm = DemCheckMatrix::from_dem_str(dem)
+            .map_err(|e| DecoderError::InvalidConfiguration(e.to_string()))?;
+        let graph = DemMatchingGraph::from_dem_str(dem)?;
+        let uf = UfDecoder::from_matching_graph(&graph, config.uf_config);
+
+        // Build mechanism → edge mapping.
+        // Each mechanism in the check matrix corresponds to a column.
+        // The matching graph merges mechanisms by fault ID into edges.
+        // We need to find which edge each mechanism ended up in.
+        //
+        // Approach: for each mechanism, find which detectors it touches,
+        // then find the matching edge connecting those detectors.
+        let mut mechanism_to_edge = vec![None; dcm.num_mechanisms];
+
+        for (m, mechanism_edge) in mechanism_to_edge
+            .iter_mut()
+            .enumerate()
+            .take(dcm.num_mechanisms)
+        {
+            let mut detectors: Vec<u32> = Vec::new();
+            for d in 0..dcm.num_detectors {
+                if dcm.check_matrix[[d, m]] != 0 {
+                    detectors.push(d as u32);
+                }
+            }
+
+            // Match to graph edge by detector pair.
+            match detectors.len() {
+                1 => {
+                    // Boundary edge: one detector.
+                    let d0 = detectors[0];
+                    for (idx, edge) in graph.edges.iter().enumerate() {
+                        if edge.node1 == d0 && edge.node2.is_none() {
+                            *mechanism_edge = Some(idx);
+                            break;
+                        }
+                    }
+                }
+                2 => {
+                    // Internal edge: two detectors.
+                    let (d0, d1) = (detectors[0], detectors[1]);
+                    for (idx, edge) in graph.edges.iter().enumerate() {
+                        if (edge.node1 == d0 && edge.node2 == Some(d1))
+                            || (edge.node1 == d1 && edge.node2 == Some(d0))
+                        {
+                            *mechanism_edge = Some(idx);
+                            break;
+                        }
+                    }
+                }
+                _ => {
+                    // Hyperedge (3+ detectors): skip, no matching graph edge.
+                }
+            }
+        }
+
+        let base_weights: Vec<f64> = graph.edges.iter().map(|e| e.weight).collect();
+        let adjusted_weights = base_weights.clone();
+
+        let bp_graph_data = BpGraph::from_dcm(&dcm);
+        let bp_c_to_v = vec![0.0; bp_graph_data.total_edges];
+        let bp_v_to_c = vec![0.0; bp_graph_data.total_edges];
+        let bp_posterior = Vec::with_capacity(bp_graph_data.num_vars);
+
+        // Always store matching graph (needed for Auto and MatchingGraph modes).
+        let matching_graph_stored = Some(graph);
+
+        Ok(Self {
+            uf,
+            bp_graph: bp_graph_data,
+            matching_graph: matching_graph_stored,
+            mechanism_to_edge,
+            base_weights,
+            adjusted_weights,
+            bp_c_to_v,
+            bp_v_to_c,
+            bp_posterior,
+            config,
+        })
+    }
+}
+
+impl BpUfDecoder {
+    /// Create from two DEMs: non-decomposed for BP, decomposed for matching graph.
+    ///
+    /// The non-decomposed DEM gives BP cleaner soft info (no decomposition
+    /// artifacts). The decomposed DEM gives the matching graph edge structure
+    /// needed for MWPM and correlation tables.
+    ///
+    /// # Errors
+    ///
+    /// Returns `DecoderError` if either DEM is malformed.
+    pub fn from_dual_dem(
+        bp_dem: &str,
+        matching_dem: &str,
+        config: BpUfConfig,
+    ) -> Result<Self, DecoderError> {
+        // BP graph from the non-decomposed DEM.
+        let bp_dcm = DemCheckMatrix::from_dem_str(bp_dem)
+            .map_err(|e| DecoderError::InvalidConfiguration(e.to_string()))?;
+        let bp_graph = BpGraph::from_dcm(&bp_dcm);
+
+        // Matching graph and UF from the decomposed DEM.
+        let match_graph = DemMatchingGraph::from_dem_str(matching_dem)?;
+        let uf = UfDecoder::from_matching_graph(&match_graph, config.uf_config);
+
+        // Map BP mechanisms (non-decomposed) → matching graph edges (decomposed).
+        let mut mechanism_to_edge = vec![None; bp_dcm.num_mechanisms];
+        for (m, mechanism_edge) in mechanism_to_edge
+            .iter_mut()
+            .enumerate()
+            .take(bp_dcm.num_mechanisms)
+        {
+            let mut detectors: Vec<u32> = Vec::new();
+            for d in 0..bp_dcm.num_detectors {
+                if bp_dcm.check_matrix[[d, m]] != 0 {
+                    detectors.push(d as u32);
+                }
+            }
+            match detectors.len() {
+                1 => {
+                    let d0 = detectors[0];
+                    for (idx, edge) in match_graph.edges.iter().enumerate() {
+                        if edge.node1 == d0 && edge.node2.is_none() {
+                            *mechanism_edge = Some(idx);
+                            break;
+                        }
+                    }
+                }
+                2 => {
+                    let (d0, d1) = (detectors[0], detectors[1]);
+                    for (idx, edge) in match_graph.edges.iter().enumerate() {
+                        if (edge.node1 == d0 && edge.node2 == Some(d1))
+                            || (edge.node1 == d1 && edge.node2 == Some(d0))
+                        {
+                            *mechanism_edge = Some(idx);
+                            break;
+                        }
+                    }
+                }
+                _ => {} // Hyperedge
+            }
+        }
+
+        let base_weights: Vec<f64> = match_graph.edges.iter().map(|e| e.weight).collect();
+        let adjusted_weights = base_weights.clone();
+        let total_edges = bp_graph.total_edges;
+
+        Ok(Self {
+            uf,
+            bp_graph,
+            matching_graph: None, // dual_dem mode uses Tanner graph BP
+            mechanism_to_edge,
+            base_weights,
+            adjusted_weights,
+            bp_c_to_v: vec![0.0; total_edges],
+            bp_v_to_c: vec![0.0; total_edges],
+            bp_posterior: Vec::with_capacity(bp_dcm.num_mechanisms),
+            config,
+        })
+    }
+}
+
+impl pecos_decoder_core::bp_matching::BpWeightProvider for BpUfDecoder {
+    fn compute_weights(&mut self, syndrome: &[u8]) -> Vec<f64> {
+        let num_defects = syndrome.iter().filter(|&&v| v != 0).count();
+
+        let iters = if self.config.bp_iterations > 0 {
+            self.config.bp_iterations
+        } else {
+            let d_est = ((self
+                .matching_graph
+                .as_ref()
+                .map_or(self.bp_graph.num_checks, |mg| mg.num_detectors)
+                as f64)
+                / 2.0)
+                .sqrt();
+            match num_defects {
+                2..=3 => (d_est.ceil() as usize).min(3),
+                4..=8 => (d_est.ceil() as usize).min(8),
+                _ => (d_est.ceil() as usize).min(12),
+            }
+        };
+
+        // Estimate code distance from matching graph detectors.
+        // For surface codes: num_detectors ≈ num_stab * num_rounds ≈ d * 2d = 2d²
+        // so d ≈ sqrt(num_detectors / 2).
+        let num_det = self
+            .matching_graph
+            .as_ref()
+            .map_or(self.bp_graph.num_checks, |mg| mg.num_detectors);
+        let d_est = ((num_det as f64) / 2.0).sqrt();
+        let use_matching_graph = match self.config.bp_graph_type {
+            BpGraphType::MatchingGraph => true,
+            BpGraphType::TannerGraph => false,
+            BpGraphType::Auto => d_est < 5.5, // Matching graph at d<=4 (d_est≈4.9 at d=3)
+        };
+
+        if let (true, Some(mg)) = (use_matching_graph, &self.matching_graph) {
+            // Matching-graph BP: simpler topology, better convergence.
+            self.bp_posterior =
+                mini_bp::matching_graph_bp(mg, syndrome, iters, self.config.min_sum_scale);
+            // Matching-graph BP posteriors are already per-edge (no mechanism mapping needed).
+            // Return them directly as weights.
+            let mut weights = self.base_weights.clone();
+            let d_est = ((self
+                .matching_graph
+                .as_ref()
+                .map_or(self.bp_graph.num_checks, |mg| mg.num_detectors)
+                as f64)
+                / 2.0)
+                .sqrt();
+            let selectivity = 0.2 * d_est.max(1.0) / 3.0;
+            for (edge_idx, &posterior) in self.bp_posterior.iter().enumerate() {
+                if edge_idx < weights.len() {
+                    let prior = self.base_weights[edge_idx];
+                    let shift = (posterior - prior).abs();
+                    if shift > selectivity * prior.abs().max(0.1) {
+                        let bp_weight = if posterior > 10.0 {
+                            posterior
+                        } else if posterior < -10.0 {
+                            0.01
+                        } else {
+                            (1.0 + posterior.exp()).ln()
+                        };
+                        let blend = 0.5;
+                        weights[edge_idx] = (1.0 - blend) * prior + blend * bp_weight;
+                    }
+                }
+            }
+            return weights;
+        }
+
+        // At d>=5 with auto mode, selective BP rarely adjusts edges.
+        // Skip BP entirely and return base weights (= FB_correlated behavior).
+        // The correlation table second pass in BpMatchingDecoder handles accuracy.
+        if matches!(self.config.bp_graph_type, BpGraphType::Auto) && d_est >= 5.5 {
+            return self.base_weights.clone();
+        }
+
+        // Tanner-graph BP.
+        self.bp_c_to_v.fill(0.0);
+        self.bp_v_to_c.fill(0.0);
+        let serial = matches!(self.config.bp_schedule, BpSchedule::Serial);
+        mini_bp::min_sum_bp_into(
+            &self.bp_graph,
+            syndrome,
+            iters,
+            self.config.min_sum_scale,
+            serial,
+            &mut self.bp_c_to_v,
+            &mut self.bp_v_to_c,
+            &mut self.bp_posterior,
+        );
+
+        // Selective BP: only adjust edges where BP strongly disagrees with
+        // the DEM prior. This avoids BP noise (which hurts at d>=5) while
+        // capturing genuine syndrome-dependent information for edges where
+        // BP has high confidence.
+        //
+        // An edge is adjusted if |posterior - prior| > threshold * |prior|.
+        // This means BP must shift the LLR by a significant fraction of the
+        // prior to be trusted.
+        let mut weights = self.base_weights.clone();
+        let d_est = ((self
+            .matching_graph
+            .as_ref()
+            .map_or(self.bp_graph.num_checks, |mg| mg.num_detectors) as f64)
+            / 2.0)
+            .sqrt();
+        // Selectivity threshold: higher at large d (BP less reliable).
+        // At d=3: threshold=0.3 (accept moderate BP shifts).
+        // At d=7: threshold=0.8 (only trust strong BP shifts).
+        // At d=11: threshold=1.2 (very selective).
+        let selectivity = 0.2 * d_est.max(1.0) / 3.0;
+
+        for (m, &posterior) in self.bp_posterior.iter().enumerate() {
+            if let Some(edge_idx) = self.mechanism_to_edge[m] {
+                let prior = self.bp_graph.prior_llr[m];
+                let shift = (posterior - prior).abs();
+
+                // Only use BP weight if the shift is large relative to the prior.
+                if shift > selectivity * prior.abs().max(0.1) {
+                    let bp_weight = if posterior > 10.0 {
+                        posterior
+                    } else if posterior < -10.0 {
+                        0.01
+                    } else {
+                        (1.0 + posterior.exp()).ln()
+                    };
+                    // Blend with a moderate factor for selected edges.
+                    let blend = 0.5;
+                    let blended = (1.0 - blend) * self.base_weights[edge_idx] + blend * bp_weight;
+                    weights[edge_idx] = weights[edge_idx].min(blended);
+                }
+            }
+        }
+        weights
+    }
+
+    fn num_edges(&self) -> usize {
+        self.base_weights.len()
+    }
+
+    fn is_trivial(&self, syndrome: &[u8]) -> Option<u64> {
+        self.uf.predecode_clusters(syndrome)
+    }
+}
+
+impl pecos_decoder_core::ObservableDecoder for BpUfDecoder {
+    fn decode_to_observables(&mut self, syndrome: &[u8]) -> Result<u64, DecoderError> {
+        // Fast path: cluster predecoder handles isolated cases without BP.
+        // This catches 0 defects, single defects, and isolated pairs.
+        if let Some(obs) = self.uf.predecode_clusters(syndrome) {
+            return Ok(obs);
+        }
+
+        let num_defects = syndrome.iter().filter(|&&v| v != 0).count();
+
+        // Stage 1: Run truncated BP (reusing pre-allocated buffers).
+        // Adaptive iterations: need enough for messages to propagate
+        // across the graph, but not so many that BP oscillates.
+        let iters = if self.config.bp_iterations > 0 {
+            self.config.bp_iterations
+        } else {
+            // Estimate code distance from detector count.
+            // Surface code: num_detectors ≈ d * num_rounds, num_rounds ≈ 2d
+            // So num_detectors ≈ 2d^2, d ≈ sqrt(num_det / 2)
+            let d_est = ((self
+                .matching_graph
+                .as_ref()
+                .map_or(self.bp_graph.num_checks, |mg| mg.num_detectors)
+                as f64)
+                / 2.0)
+                .sqrt();
+            // Need ~d iterations for full propagation.
+            // Scale down for few defects.
+            let target = d_est.ceil() as usize;
+            match num_defects {
+                2..=3 => target.min(3), // few defects: local info sufficient
+                4..=8 => target.min(8), // moderate: need more propagation
+                _ => target.min(12),    // many defects: full propagation, capped
+            }
+        };
+
+        self.bp_c_to_v.fill(0.0);
+        self.bp_v_to_c.fill(0.0);
+        let serial = matches!(self.config.bp_schedule, BpSchedule::Serial);
+        mini_bp::min_sum_bp_into(
+            &self.bp_graph,
+            syndrome,
+            iters,
+            self.config.min_sum_scale,
+            serial,
+            &mut self.bp_c_to_v,
+            &mut self.bp_v_to_c,
+            &mut self.bp_posterior,
+        );
+        let posteriors = &self.bp_posterior;
+
+        // Stage 2: Adjust UF edge weights using BP posteriors.
+        //
+        // BP posterior is an LLR: positive = likely no error, negative = likely error.
+        // UF weight = ln((1-p)/p): positive, lower = more likely error.
+        // Both are LLRs with the same sign convention.
+        //
+        // The posterior directly replaces the prior LLR as a better estimate.
+        // We blend to avoid over-reliance on BP when it hasn't converged.
+        self.adjusted_weights.copy_from_slice(&self.base_weights);
+
+        let blend = self.config.bp_weight_blend;
+        for (m, &posterior) in posteriors.iter().enumerate() {
+            if let Some(edge_idx) = self.mechanism_to_edge[m] {
+                // Map posterior LLR to positive UF weight.
+                // Positive posterior = unlikely error = high weight.
+                // Negative posterior = likely error = low weight.
+                // Soft mapping: weight = log(1 + exp(posterior)) keeps
+                // weights positive and smooth, approaching 0 for very
+                // negative posteriors and linear for positive ones.
+                let bp_weight = if posterior > 10.0 {
+                    posterior // Avoid overflow in exp
+                } else if posterior < -10.0 {
+                    0.01 // Very likely error
+                } else {
+                    (1.0 + posterior.exp()).ln()
+                };
+                let blended = (1.0 - blend) * self.base_weights[edge_idx] + blend * bp_weight;
+                // Take the minimum across mechanisms for this edge.
+                self.adjusted_weights[edge_idx] = self.adjusted_weights[edge_idx].min(blended);
+            }
+        }
+
+        // Stage 3: Use UF with BP-adjusted weights.
+        let (mask, matched_edges) = self
+            .uf
+            .decode_with_weights(syndrome, &self.adjusted_weights)?;
+
+        // Stage 4 (optional): Second pass -- use first-pass correction to
+        // boost BP priors for matched edges, re-run BP, re-decode.
+        // Only do this when the first pass found a substantial correction
+        // and BP had enough iterations to produce meaningful posteriors.
+        if matched_edges.len() >= 2 && iters >= 4 {
+            let boost = 1.5;
+            for &edge_idx in &matched_edges {
+                if edge_idx < self.adjusted_weights.len() {
+                    self.adjusted_weights[edge_idx] =
+                        (self.adjusted_weights[edge_idx] - boost).max(0.01);
+                }
+            }
+            let (mask2, _) = self
+                .uf
+                .decode_with_weights(syndrome, &self.adjusted_weights)?;
+            return Ok(mask2);
+        }
+
+        Ok(mask)
+    }
+}
+
+#[cfg(test)]
+mod tests {
+    use super::*;
+    use pecos_decoder_core::ObservableDecoder;
+
+    const SIMPLE_DEM: &str = "\
+error(0.1) D0 D1 L0
+error(0.1) D1
+";
+
+    #[test]
+    fn test_bp_uf_construction() {
+        let dec = BpUfDecoder::from_dem(SIMPLE_DEM, BpUfConfig::default());
+        assert!(dec.is_ok());
+    }
+
+    #[test]
+    fn test_bp_uf_no_errors() {
+        let mut dec = BpUfDecoder::from_dem(SIMPLE_DEM, BpUfConfig::default()).unwrap();
+        let obs = dec.decode_to_observables(&[0, 0]).unwrap();
+        assert_eq!(obs, 0);
+    }
+
+    #[test]
+    fn test_bp_uf_with_errors() {
+        let mut dec = BpUfDecoder::from_dem(SIMPLE_DEM, BpUfConfig::default()).unwrap();
+        let obs = dec.decode_to_observables(&[1, 1]).unwrap();
+        assert_eq!(obs, 1); // D0-D1 edge carries L0
+    }
+
+    const D3_DEM: &str =
+        include_str!("../../../examples/surface_code_circuits/surface_code_d3_z_stim.dem");
+
+    #[test]
+    fn test_bp_uf_real_dem() {
+        let mut dec = BpUfDecoder::from_dem(D3_DEM, BpUfConfig::default()).unwrap();
+        // No errors
+        let obs = dec.decode_to_observables(&[0u8; 24]).unwrap();
+        assert_eq!(obs, 0);
+
+        // Random syndromes shouldn't panic
+        let mut rng = fastrand::Rng::with_seed(42);
+        for _ in 0..100 {
+            let syn: Vec<u8> = (0..24).map(|_| u8::from(rng.f64() < 0.05)).collect();
+            let _ = dec.decode_to_observables(&syn).unwrap();
+        }
+    }
+}
diff --git a/crates/pecos-uf-decoder/src/css_decoder.rs b/crates/pecos-uf-decoder/src/css_decoder.rs
new file mode 100644
index 000000000..69baaf239
--- /dev/null
+++ b/crates/pecos-uf-decoder/src/css_decoder.rs
@@ -0,0 +1,382 @@
+// Copyright 2026 The PECOS Developers
+//
+// Licensed under the Apache License, Version 2.0 (the "License"); you may not use this file except
+// in compliance with the License. You may obtain a copy of the License at
+//
+//     https://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software distributed under the License
+// is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express
+// or implied. See the License for the specific language governing permissions and limitations under
+// the License.
+
+//! CSS-aware Union-Find decoder using the UIUF (Union-Intersection) algorithm.
+//!
+//! Exploits the CSS structure of surface codes by running UF independently on
+//! X and Z syndrome graphs, then identifying likely Y errors via intersection
+//! of the two cluster sets. Y errors are promoted to erasures, dramatically
+//! improving accuracy (matching or exceeding MWPM).
+//!
+//! Reference: Tzu-Hao Lin and Ching-Yi Lai, "Union-Intersection Union-Find
+//! Decoder," arXiv:2506.14745 (2025).
+//!
+//! This decoder takes TWO DEM strings (one for X-basis, one for Z-basis) and
+//! decodes them jointly.
+
+use crate::decoder::{UfDecoder, UfDecoderConfig};
+use pecos_decoder_core::dem::{DemMatchingGraph, MatchingEdge};
+use pecos_decoder_core::errors::DecoderError;
+
+/// Compute the quantized spatial midpoint of an edge from detector coordinates.
+///
+/// For UIUF cross-graph matching, we use only the spatial coordinates
+/// (first two dimensions) and ignore time (third dimension), since X and Z
+/// stabilizers are measured at different times but share the same data qubits.
+///
+/// For same-time edges (timelike = measurement errors), the two endpoints
+/// share spatial coords, so the midpoint is just that shared spatial position.
+/// For space edges (data qubit errors), the midpoint is the data qubit's
+/// spatial position.
+///
+/// Quantized to 0.001 resolution for use as a map key.
+fn edge_spatial_midpoint(edge: &MatchingEdge, coords: &[Option<Vec<f64>>]) -> Option<(i64, i64)> {
+    let c1 = coords.get(edge.node1 as usize)?.as_ref()?;
+
+    if let Some(n2) = edge.node2 {
+        let c2 = coords.get(n2 as usize)?.as_ref()?;
+        // Spatial midpoint only (ignore time dimension).
+        let x = ((c1.first().unwrap_or(&0.0) + c2.first().unwrap_or(&0.0)) * 500.0) as i64;
+        let y = ((c1.get(1).unwrap_or(&0.0) + c2.get(1).unwrap_or(&0.0)) * 500.0) as i64;
+        Some((x, y))
+    } else {
+        // Boundary edge.
+        let x = (c1.first().unwrap_or(&0.0) * 1000.0) as i64;
+        let y = (c1.get(1).unwrap_or(&0.0) * 1000.0) as i64;
+        Some((x, y))
+    }
+}
+
+/// Check if an edge is spatial (connects detectors at the same time)
+/// vs timelike (connects detectors at different times).
+/// Only spatial edges correspond to data qubit errors.
+fn is_spatial_edge(edge: &MatchingEdge, coords: &[Option<Vec<f64>>]) -> bool {
+    let Some(c1) = coords.get(edge.node1 as usize).and_then(|c| c.as_ref()) else {
+        return true; // Assume spatial if no coords.
+    };
+    let Some(n2) = edge.node2 else {
+        return true; // Boundary edges are spatial.
+    };
+    let Some(c2) = coords.get(n2 as usize).and_then(|c| c.as_ref()) else {
+        return true;
+    };
+    let t1 = c1.get(2).unwrap_or(&0.0);
+    let t2 = c2.get(2).unwrap_or(&0.0);
+    (t1 - t2).abs() < 0.01 // Same time = spatial edge
+}
+
+/// Mapping of shared qubits between X and Z decoding graphs.
+///
+/// Each entry represents a data qubit that appears as an edge in both
+/// the X and Z matching graphs. During UIUF intersection, if both
+/// edges are covered by clusters, the qubit is marked as an erasure.
+#[derive(Debug, Clone)]
+pub struct QubitEdgeMapping {
+    /// For each shared qubit: `(edge_idx in X graph, edge_idx in Z graph)`.
+    pub pairs: Vec<(usize, usize)>,
+}
+
+/// CSS-aware UF decoder using UIUF intersection.
+///
+/// Wraps two `UfDecoder` instances (X and Z basis) and exploits the
+/// overlap between their cluster sets to identify Y errors.
+pub struct CssUfDecoder {
+    /// UF decoder for X-basis syndromes (decodes Z errors).
+    x_decoder: UfDecoder,
+    /// UF decoder for Z-basis syndromes (decodes X errors).
+    z_decoder: UfDecoder,
+    /// Number of X detectors (split point for concatenated syndromes).
+    x_num_detectors: usize,
+    /// Qubit-to-edge mapping for intersection step.
+    qubit_map: Option<QubitEdgeMapping>,
+}
+
+impl CssUfDecoder {
+    /// Create from two DEM strings (X-basis and Z-basis).
+    ///
+    /// # Errors
+    ///
+    /// Returns `DecoderError` if either DEM is malformed.
+    pub fn from_dems(
+        x_dem: &str,
+        z_dem: &str,
+        config: UfDecoderConfig,
+    ) -> Result<Self, DecoderError> {
+        let x_graph = DemMatchingGraph::from_dem_str(x_dem)?;
+        let z_graph = DemMatchingGraph::from_dem_str(z_dem)?;
+
+        // Auto-detect qubit-edge mapping from detector coordinates.
+        let qubit_map = Self::build_qubit_mapping(&x_graph, &z_graph);
+
+        let x_num_detectors = x_graph.num_detectors;
+        let x_decoder = UfDecoder::from_matching_graph(&x_graph, config);
+        let z_decoder = UfDecoder::from_matching_graph(&z_graph, config);
+
+        Ok(Self {
+            x_decoder,
+            z_decoder,
+            x_num_detectors,
+            qubit_map,
+        })
+    }
+
+    /// Build qubit-edge mapping by matching spatial edge midpoints across graphs.
+    ///
+    /// Only spatial edges (same-time endpoints = data qubit errors) are matched.
+    /// Timelike edges (measurement errors) are excluded since they don't
+    /// correspond to shared data qubits.
+    ///
+    /// The mapping pairs edges in the X and Z graphs whose spatial midpoints
+    /// coincide, identifying the shared data qubit.
+    fn build_qubit_mapping(
+        x_graph: &DemMatchingGraph,
+        z_graph: &DemMatchingGraph,
+    ) -> Option<QubitEdgeMapping> {
+        use std::collections::BTreeMap;
+
+        // Collect spatial edges from X graph, keyed by spatial midpoint.
+        // Multiple X edges can share the same midpoint (different time slices).
+        // We store all of them and match greedily.
+        let mut x_midpoints: BTreeMap<(i64, i64), Vec<usize>> = BTreeMap::new();
+
+        for (idx, edge) in x_graph.edges.iter().enumerate() {
+            if !is_spatial_edge(edge, &x_graph.detector_coords) {
+                continue;
+            }
+            if let Some(mid) = edge_spatial_midpoint(edge, &x_graph.detector_coords) {
+                x_midpoints.entry(mid).or_default().push(idx);
+            }
+        }
+
+        if x_midpoints.is_empty() {
+            return None;
+        }
+
+        // Match Z spatial edges against X midpoints.
+        let mut pairs = Vec::new();
+        let mut used_x: std::collections::BTreeSet<usize> = std::collections::BTreeSet::new();
+
+        for (z_idx, edge) in z_graph.edges.iter().enumerate() {
+            if !is_spatial_edge(edge, &z_graph.detector_coords) {
+                continue;
+            }
+            if let Some(mid) = edge_spatial_midpoint(edge, &z_graph.detector_coords)
+                && let Some(x_candidates) = x_midpoints.get(&mid)
+            {
+                for &x_idx in x_candidates {
+                    if !used_x.contains(&x_idx) {
+                        pairs.push((x_idx, z_idx));
+                        used_x.insert(x_idx);
+                        break;
+                    }
+                }
+            }
+        }
+
+        if pairs.is_empty() {
+            None
+        } else {
+            Some(QubitEdgeMapping { pairs })
+        }
+    }
+
+    /// Number of qubit pairs in the mapping (0 = no mapping, falls back to independent).
+    #[must_use]
+    pub fn num_qubit_pairs(&self) -> usize {
+        self.qubit_map.as_ref().map_or(0, |m| m.pairs.len())
+    }
+
+    /// Set the qubit-to-edge mapping for UIUF intersection.
+    ///
+    /// Each pair `(x_edge_idx, z_edge_idx)` identifies a data qubit
+    /// that appears as an edge in both the X and Z matching graphs.
+    pub fn set_qubit_mapping(&mut self, mapping: QubitEdgeMapping) {
+        self.qubit_map = Some(mapping);
+    }
+
+    /// Decode X and Z syndromes jointly using UIUF.
+    ///
+    /// If a qubit-to-edge mapping is set, uses the full UIUF algorithm
+    /// (intersection to identify Y-error erasures). Otherwise falls back
+    /// to independent UF decoding on each basis.
+    ///
+    /// Returns `(x_obs_mask, z_obs_mask)` -- observable predictions for each basis.
+    ///
+    /// # Errors
+    ///
+    /// Returns `DecoderError` if decoding fails.
+    pub fn decode_css(
+        &mut self,
+        x_syndrome: &[u8],
+        z_syndrome: &[u8],
+    ) -> Result<(u64, u64), DecoderError> {
+        if let Some(mapping) = &self.qubit_map {
+            let pairs = mapping.pairs.clone();
+            Ok(self.decode_uiuf(x_syndrome, z_syndrome, &pairs))
+        } else {
+            // Fallback: independent decoding.
+            let x_obs = self.x_decoder.decode_syndrome(x_syndrome);
+            let z_obs = self.z_decoder.decode_syndrome(z_syndrome);
+            Ok((x_obs, z_obs))
+        }
+    }
+
+    /// Count erasures that the intersection would produce (diagnostic).
+    pub fn count_intersection_erasures(&mut self, x_syndrome: &[u8], z_syndrome: &[u8]) -> usize {
+        if let Some(mapping) = &self.qubit_map {
+            self.x_decoder.syndrome_validate(x_syndrome);
+            self.z_decoder.syndrome_validate(z_syndrome);
+            let mut count = 0;
+            for &(x_edge, z_edge) in &mapping.pairs {
+                let x_covered = self.x_decoder.edge_in_cluster(x_edge);
+                let z_covered = self.z_decoder.edge_in_cluster(z_edge);
+                if x_covered && z_covered {
+                    count += 1;
+                }
+            }
+            count
+        } else {
+            0
+        }
+    }
+
+    /// Full UIUF algorithm.
+    fn decode_uiuf(
+        &mut self,
+        x_syndrome: &[u8],
+        z_syndrome: &[u8],
+        qubit_pairs: &[(usize, usize)],
+    ) -> (u64, u64) {
+        // Phase 1: Syndrome validation (growth only) on each graph.
+        self.x_decoder.syndrome_validate(x_syndrome);
+        self.z_decoder.syndrome_validate(z_syndrome);
+
+        // Phase 2: Intersection -- find edges covered in BOTH graphs.
+        // These correspond to likely Y errors (which trigger both X and Z syndromes).
+        let mut x_erasure_edges: Vec<usize> = Vec::new();
+        let mut z_erasure_edges: Vec<usize> = Vec::new();
+
+        for &(x_edge, z_edge) in qubit_pairs {
+            let x_covered = self.x_decoder.edge_in_cluster(x_edge);
+            let z_covered = self.z_decoder.edge_in_cluster(z_edge);
+            if x_covered && z_covered {
+                // Both graphs have clusters covering this qubit's edge.
+                // Mark as erasure in both graphs for Phase 3.
+                x_erasure_edges.push(x_edge);
+                z_erasure_edges.push(z_edge);
+            }
+        }
+
+        // Phase 3: Augmented UF decode with erasures.
+        // X errors are decoded on Z graph (with Z erasures).
+        // Z errors are decoded on X graph (with X erasures).
+        let x_obs = self
+            .x_decoder
+            .decode_with_erasures(x_syndrome, &x_erasure_edges);
+        let z_obs = self
+            .z_decoder
+            .decode_with_erasures(z_syndrome, &z_erasure_edges);
+
+        (x_obs, z_obs)
+    }
+}
+
+impl pecos_decoder_core::ObservableDecoder for CssUfDecoder {
+    /// Decode a concatenated `[x_syndrome | z_syndrome]` via UIUF.
+    ///
+    /// The syndrome is split at `x_num_detectors` into X and Z parts.
+    /// Returns the XOR of both observable masks.
+    fn decode_to_observables(&mut self, syndrome: &[u8]) -> Result<u64, DecoderError> {
+        let split = self.x_num_detectors;
+        if syndrome.len() < split {
+            return Err(DecoderError::DecodingFailed(format!(
+                "CssUfDecoder: syndrome length {} < x_num_detectors {}",
+                syndrome.len(),
+                split
+            )));
+        }
+        let x_syn = &syndrome[..split];
+        let z_syn = &syndrome[split..];
+        let (x_obs, z_obs) = self.decode_css(x_syn, z_syn)?;
+        Ok(x_obs ^ z_obs)
+    }
+}
+
+#[cfg(test)]
+mod tests {
+    use super::*;
+
+    // Minimal X-basis and Z-basis DEMs for a distance-3 repetition code.
+    const X_DEM: &str = "\
+error(0.01) D0 D1 L0
+error(0.01) D0
+error(0.01) D1
+";
+
+    const Z_DEM: &str = "\
+error(0.01) D0 D1
+error(0.01) D0 L0
+error(0.01) D1
+";
+
+    #[test]
+    fn test_css_construction() {
+        let dec = CssUfDecoder::from_dems(X_DEM, Z_DEM, UfDecoderConfig::default());
+        assert!(dec.is_ok());
+    }
+
+    #[test]
+    fn test_css_no_errors() {
+        let mut dec = CssUfDecoder::from_dems(X_DEM, Z_DEM, UfDecoderConfig::default()).unwrap();
+        let (x_obs, z_obs) = dec.decode_css(&[0, 0], &[0, 0]).unwrap();
+        assert_eq!(x_obs, 0);
+        assert_eq!(z_obs, 0);
+    }
+
+    #[test]
+    fn test_css_with_qubit_mapping() {
+        let mut dec = CssUfDecoder::from_dems(X_DEM, Z_DEM, UfDecoderConfig::default()).unwrap();
+
+        // Set up mapping: edge 0 in X_DEM corresponds to edge 0 in Z_DEM
+        // (same data qubit connecting the two detectors).
+        dec.set_qubit_mapping(QubitEdgeMapping {
+            pairs: vec![(0, 0)],
+        });
+
+        // No errors: should still decode correctly.
+        let (x_obs, z_obs) = dec.decode_css(&[0, 0], &[0, 0]).unwrap();
+        assert_eq!(x_obs, 0);
+        assert_eq!(z_obs, 0);
+
+        // Y-error scenario: both X and Z syndromes have the same defects.
+        // The intersection should identify the qubit as erasure.
+        let (x_obs, z_obs) = dec.decode_css(&[1, 1], &[1, 1]).unwrap();
+        // With erasure, both decoders should handle this correctly.
+        // The exact observable depends on the DEM structure.
+        let _ = (x_obs, z_obs); // Just verify no panic.
+    }
+
+    #[test]
+    fn test_css_independent_decoding() {
+        let mut dec = CssUfDecoder::from_dems(X_DEM, Z_DEM, UfDecoderConfig::default()).unwrap();
+
+        // X syndrome has defects, Z syndrome clean.
+        let (x_obs, z_obs) = dec.decode_css(&[1, 1], &[0, 0]).unwrap();
+        assert_eq!(x_obs, 1); // D0-D1 edge carries L0 in X_DEM
+        assert_eq!(z_obs, 0);
+
+        // Z syndrome has defects, X syndrome clean.
+        let (x_obs, z_obs) = dec.decode_css(&[0, 0], &[1, 1]).unwrap();
+        assert_eq!(x_obs, 0);
+        assert_eq!(z_obs, 0); // D0-D1 edge has no observable in Z_DEM
+    }
+}
diff --git a/crates/pecos-uf-decoder/src/decoder.rs b/crates/pecos-uf-decoder/src/decoder.rs
new file mode 100644
index 000000000..1ce43de0d
--- /dev/null
+++ b/crates/pecos-uf-decoder/src/decoder.rs
@@ -0,0 +1,1306 @@
+// Copyright 2026 The PECOS Developers
+//
+// Licensed under the Apache License, Version 2.0 (the "License"); you may not use this file except
+// in compliance with the License. You may obtain a copy of the License at
+//
+//     https://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software distributed under the License
+// is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express
+// or implied. See the License for the specific language governing permissions and limitations under
+// the License.
+
+//! Syndrome-graph Union-Find decoder implementation.
+//!
+//! The algorithm (Delfosse-Nickerson style):
+//!
+//! 1. Each defect detector starts as its own cluster (odd parity).
+//! 2. Grow all unsatisfied clusters by radius until an edge becomes fusible.
+//!    An edge is fusible when the sum of endpoint radii reaches the edge weight.
+//!    Two growing clusters fuse at half the weight; boundary needs full weight.
+//! 3. Fuse all fusible edges, merging clusters. Parity = XOR of components.
+//! 4. Repeat until all clusters have even parity or contain the boundary.
+//! 5. Peel a spanning forest (BFS from boundary) to extract the correction:
+//!    an edge is in the correction iff its subtree has odd parity.
+//!
+//! All data structures are flat arrays. Zero per-shot allocation after init.
+
+use pecos_decoder_core::correlated_decoder::MatchingDecoder;
+use pecos_decoder_core::dem::DemMatchingGraph;
+use pecos_decoder_core::errors::DecoderError;
+use std::cmp::Reverse;
+use std::collections::BinaryHeap;
+
+/// Edge in the syndrome graph.
+#[derive(Debug, Clone)]
+struct Edge {
+    /// First endpoint node index.
+    node1: u32,
+    /// Second endpoint node index (boundary = `num_detectors`).
+    node2: u32,
+    /// Weight (log-likelihood ratio). Lower = more likely error.
+    weight: f64,
+    /// Observable bitmask for this edge.
+    obs_mask: u64,
+}
+
+/// Peeling strategy for correction extraction.
+#[derive(Debug, Clone, Copy, Default)]
+pub enum PeelingStrategy {
+    /// BFS from boundary. Fastest, slightly less accurate.
+    Bfs,
+    /// Prim's MST from boundary. Uses globally lightest edges.
+    /// Better accuracy, slight heap overhead at small sizes.
+    #[default]
+    PrimMst,
+}
+
+/// Growth strategy for cluster expansion.
+#[derive(Debug, Clone, Copy, Default)]
+pub enum GrowthStrategy {
+    /// Event-driven with priority queue. Weighted growth (1/size).
+    /// Best for larger codes (d >= 7). O(E log E) total.
+    #[default]
+    EventDriven,
+    /// Scan-based: find min increment per round, grow all, fuse.
+    /// Lower constant overhead for small codes (d <= 5).
+    ScanBased,
+}
+
+/// Configuration for the UF decoder.
+///
+/// Use `UfDecoderConfig::fast()`, `::balanced()`, or `::accurate()` for
+/// presets, then override individual fields as needed.
+#[derive(Debug, Clone, Copy)]
+pub struct UfDecoderConfig {
+    /// Maximum growth rounds before giving up (prevents infinite loops).
+    /// 0 = auto (100 * `num_detectors`).
+    pub max_growth_rounds: usize,
+    /// How to build the spanning forest for peeling.
+    pub peeling: PeelingStrategy,
+    /// How to grow clusters.
+    pub growth: GrowthStrategy,
+    /// Enable cluster predecoder for simple syndromes.
+    /// Disable for windowed decoding which needs complete edge tracking.
+    pub predecoder: bool,
+}
+
+impl Default for UfDecoderConfig {
+    fn default() -> Self {
+        Self::fast()
+    }
+}
+
+impl UfDecoderConfig {
+    /// Fast preset: event-driven growth, BFS peeling. Lowest latency.
+    #[must_use]
+    pub fn fast() -> Self {
+        Self {
+            max_growth_rounds: 0,
+            peeling: PeelingStrategy::Bfs,
+            growth: GrowthStrategy::EventDriven,
+            predecoder: true,
+        }
+    }
+
+    /// Balanced preset: event-driven weighted growth, Prim MST peeling.
+    /// Better accuracy, used as inner decoder for two-pass correlated mode.
+    #[must_use]
+    pub fn balanced() -> Self {
+        Self {
+            max_growth_rounds: 0,
+            peeling: PeelingStrategy::PrimMst,
+            growth: GrowthStrategy::EventDriven,
+            predecoder: true,
+        }
+    }
+
+    /// Accurate preset: same as balanced (UIUF accuracy comes from
+    /// the CSS wrapper, not from single-graph config).
+    #[must_use]
+    pub fn accurate() -> Self {
+        Self::balanced()
+    }
+
+    /// Windowed preset: Prim MST peeling, no predecoder (need complete edge tracking).
+    #[must_use]
+    pub fn windowed() -> Self {
+        Self {
+            max_growth_rounds: 0,
+            peeling: PeelingStrategy::PrimMst,
+            growth: GrowthStrategy::EventDriven,
+            predecoder: false,
+        }
+    }
+}
+
+/// Fast syndrome-graph Union-Find decoder.
+pub struct UfDecoder {
+    /// Edges in the syndrome graph.
+    edges: Vec<Edge>,
+    /// CSR adjacency: flat data array of (`edge_index`, `neighbor_node`).
+    adj_data: Vec<(usize, u32)>,
+    /// CSR adjacency: offset[i]..offset[i+1] is the range in `adj_data` for node i.
+    adj_offset: Vec<u32>,
+    /// Number of detectors.
+    num_detectors: usize,
+    /// Config.
+    config: UfDecoderConfig,
+
+    // === Per-shot reusable buffers ===
+    /// Disjoint-set forest: parent[i] = parent of node i.
+    parent: Vec<u32>,
+    /// Rank for union-by-rank.
+    rank: Vec<u8>,
+    /// Cluster parity: true = odd (needs correction).
+    parity: Vec<bool>,
+    /// Whether cluster contains the boundary node (satisfied regardless of parity).
+    has_boundary: Vec<bool>,
+    /// Growth radius of each cluster at `last_growth_time` (tracked at root).
+    radius: Vec<f64>,
+    /// Time when radius was last updated (for lazy computation).
+    last_growth_time: Vec<f64>,
+    /// Cluster size (number of nodes, tracked at root).
+    cluster_size: Vec<u32>,
+    /// Defect flags per detector.
+    is_defect: Vec<bool>,
+
+    // === Scratch buffers (reused across shots to avoid allocation) ===
+    /// Growth event queue.
+    growth_events: BinaryHeap<Reverse<(u64, usize, u32, u32)>>,
+    /// Peeling: tree parent for each node.
+    tree_parent: Vec<Option<(u32, usize)>>,
+    /// Peeling: visited flags.
+    visited: Vec<bool>,
+    /// Peeling: visit order for reverse traversal.
+    visit_order: Vec<u32>,
+    /// Peeling: priority queue for Prim's MST.
+    peel_heap: BinaryHeap<Reverse<(u64, usize, u32, u32)>>,
+    /// Peeling: subtree parity for each node.
+    subtree_parity: Vec<bool>,
+    /// Peeling: correction edge indices.
+    correction_edges: Vec<usize>,
+    /// Weight swap buffer for `decode_with_weights`.
+    weight_swap: Vec<(usize, f64)>,
+}
+
+impl UfDecoder {
+    /// Get the adjacency entries for a node (slice into CSR data).
+    #[inline]
+    fn adj(&self, node: usize) -> &[(usize, u32)] {
+        let start = self.adj_offset[node] as usize;
+        let end = self.adj_offset[node + 1] as usize;
+        &self.adj_data[start..end]
+    }
+
+    /// Build from a `DemMatchingGraph`.
+    #[must_use]
+    pub fn from_matching_graph(graph: &DemMatchingGraph, config: UfDecoderConfig) -> Self {
+        let num_detectors = graph.num_detectors;
+        let num_nodes = num_detectors + 1;
+        let boundary_node = num_detectors as u32;
+
+        let mut edges = Vec::with_capacity(graph.edges.len());
+        // Build temporary adjacency for sorting, then flatten to CSR.
+        let mut temp_adj: Vec<Vec<(usize, u32)>> = vec![Vec::new(); num_nodes];
+
+        for (idx, me) in graph.edges.iter().enumerate() {
+            let n1 = me.node1;
+            let n2 = me.node2.map_or(boundary_node, |n| n);
+
+            let mut obs_mask = 0u64;
+            for &o in &me.observables {
+                obs_mask |= 1 << o;
+            }
+
+            edges.push(Edge {
+                node1: n1,
+                node2: n2,
+                weight: me.weight,
+                obs_mask,
+            });
+
+            temp_adj[n1 as usize].push((idx, n2));
+            temp_adj[n2 as usize].push((idx, n1));
+        }
+
+        // Sort each node's adjacency by weight (lightest first).
+        for adj in &mut temp_adj {
+            adj.sort_by(|a, b| {
+                edges[a.0]
+                    .weight
+                    .partial_cmp(&edges[b.0].weight)
+                    .unwrap_or(std::cmp::Ordering::Equal)
+            });
+        }
+
+        // Flatten to CSR format.
+        let total_entries: usize = temp_adj.iter().map(std::vec::Vec::len).sum();
+        let mut adj_data = Vec::with_capacity(total_entries);
+        let mut adj_offset = Vec::with_capacity(num_nodes + 1);
+        for adj in &temp_adj {
+            adj_offset.push(adj_data.len() as u32);
+            adj_data.extend_from_slice(adj);
+        }
+        adj_offset.push(adj_data.len() as u32);
+
+        Self {
+            edges,
+            adj_data,
+            adj_offset,
+            num_detectors,
+            config,
+            parent: vec![0; num_nodes],
+            rank: vec![0; num_nodes],
+            parity: vec![false; num_nodes],
+            has_boundary: vec![false; num_nodes],
+            radius: vec![0.0; num_nodes],
+            last_growth_time: vec![0.0; num_nodes],
+            cluster_size: vec![1; num_nodes],
+            is_defect: vec![false; num_nodes],
+            growth_events: BinaryHeap::new(),
+            tree_parent: vec![None; num_nodes],
+            visited: vec![false; num_nodes],
+            visit_order: Vec::with_capacity(num_nodes),
+            peel_heap: BinaryHeap::new(),
+            subtree_parity: vec![false; num_nodes],
+            correction_edges: Vec::new(),
+            weight_swap: Vec::new(),
+        }
+    }
+
+    /// Build from a DEM string.
+    ///
+    /// # Errors
+    ///
+    /// Returns `DecoderError` if the DEM is malformed.
+    pub fn from_dem(dem: &str, config: UfDecoderConfig) -> Result<Self, DecoderError> {
+        let graph = DemMatchingGraph::from_dem_str(dem)?;
+        Ok(Self::from_matching_graph(&graph, config))
+    }
+
+    /// Reset per-shot state. Uses bulk fill operations for cache efficiency.
+    fn reset(&mut self) {
+        let boundary = self.num_detectors;
+        let n = boundary + 1;
+        // Bulk-fill each array (SIMD-friendly).
+        for i in 0..n {
+            self.parent[i] = i as u32;
+        }
+        self.rank[..n].fill(0);
+        self.parity[..n].fill(false);
+        self.has_boundary[..n].fill(false);
+        self.has_boundary[boundary] = true;
+        self.radius[..n].fill(0.0);
+        self.last_growth_time[..n].fill(0.0);
+        self.cluster_size[..n].fill(1);
+        self.is_defect[..n].fill(false);
+    }
+
+    /// Find root of node with path halving (one shortcut per step).
+    fn find(&mut self, mut x: u32) -> u32 {
+        while self.parent[x as usize] != x {
+            let grandparent = self.parent[self.parent[x as usize] as usize];
+            self.parent[x as usize] = grandparent;
+            x = grandparent;
+        }
+        x
+    }
+
+    /// Union two clusters. Returns the new root.
+    fn union(&mut self, a: u32, b: u32) -> u32 {
+        let ra = self.find(a);
+        let rb = self.find(b);
+        if ra == rb {
+            return ra;
+        }
+
+        // Union by rank
+        let (root, child) = if self.rank[ra as usize] >= self.rank[rb as usize] {
+            (ra, rb)
+        } else {
+            (rb, ra)
+        };
+
+        self.parent[child as usize] = root;
+        if self.rank[root as usize] == self.rank[child as usize] {
+            self.rank[root as usize] += 1;
+        }
+
+        // XOR parities
+        self.parity[root as usize] ^= self.parity[child as usize];
+        // Propagate boundary membership
+        self.has_boundary[root as usize] |= self.has_boundary[child as usize];
+        // Keep the larger radius
+        self.radius[root as usize] = self.radius[root as usize].max(self.radius[child as usize]);
+        // Sum cluster sizes
+        self.cluster_size[root as usize] += self.cluster_size[child as usize];
+
+        root
+    }
+
+    /// Decode a syndrome and return the observable mask.
+    pub fn decode_syndrome(&mut self, syndrome: &[u8]) -> u64 {
+        // Try cluster-detection predecoder (if enabled).
+        if self.config.predecoder
+            && let Some(obs) = self.predecode_clusters(syndrome)
+        {
+            return obs;
+        }
+
+        // Full decoder path for complex syndromes.
+        self.reset();
+        for (i, &v) in syndrome.iter().enumerate() {
+            if v != 0 && i < self.num_detectors {
+                self.parity[i] = true;
+                self.is_defect[i] = true;
+            }
+        }
+        self.grow_clusters();
+        self.peel_correction()
+    }
+
+    /// Cluster-detection predecoder.
+    ///
+    /// Finds connected components of defects in the matching graph.
+    /// - Size-0 components: no defects, return 0.
+    /// - Size-1 components: match to boundary.
+    /// - Size-2 components (adjacent pair): match directly if their edge
+    ///   is lighter than both boundary alternatives.
+    /// - Size 3+: too complex, fall through to full UF.
+    ///
+    /// This is provably correct: isolated clusters are independent, so
+    /// predecoding them individually gives the same result as joint decoding.
+    #[must_use]
+    pub fn predecode_clusters(&self, syndrome: &[u8]) -> Option<u64> {
+        let boundary = self.num_detectors as u32;
+
+        // Mark defects.
+        // Use is_defect buffer conceptually but don't mutate self.
+        // Instead use a local bitset for small codes.
+        let mut defect_flags = vec![false; self.num_detectors];
+        let mut defect_list: Vec<u32> = Vec::new();
+        for (i, &v) in syndrome.iter().enumerate() {
+            if v != 0 && i < self.num_detectors {
+                defect_flags[i] = true;
+                defect_list.push(i as u32);
+            }
+        }
+
+        if defect_list.is_empty() {
+            return Some(0);
+        }
+
+        // Find connected components of defects.
+        // Two defects are connected if they share an edge in the matching graph.
+        // Use union-find on defect indices (not the full graph -- just defects).
+        let n = defect_list.len();
+        let mut component: Vec<usize> = (0..n).collect(); // parent array
+
+        // For each defect, check if any neighbor is also a defect.
+        for (di, &d) in defect_list.iter().enumerate() {
+            for &(_, neighbor) in self.adj(d as usize) {
+                if neighbor != boundary
+                    && (neighbor as usize) < self.num_detectors
+                    && defect_flags[neighbor as usize]
+                {
+                    // Find the other defect's index in defect_list.
+                    if let Some(ni) = defect_list.iter().position(|&x| x == neighbor) {
+                        // Union di and ni.
+                        let mut ra = di;
+                        while component[ra] != ra {
+                            ra = component[ra];
+                        }
+                        let mut rb = ni;
+                        while component[rb] != rb {
+                            rb = component[rb];
+                        }
+                        if ra != rb {
+                            component[rb] = ra;
+                        }
+                    }
+                }
+            }
+        }
+
+        // Flatten components.
+        for i in 0..n {
+            let mut r = i;
+            while component[r] != r {
+                r = component[r];
+            }
+            component[i] = r;
+        }
+
+        // Count component sizes.
+        let mut comp_size: Vec<usize> = vec![0; n];
+        for &c in &component {
+            comp_size[c] += 1;
+        }
+
+        // Check if any component has 3+ defects -- if so, fall through.
+        for &s in &comp_size {
+            if s >= 3 {
+                return None; // Complex cluster, need full UF.
+            }
+        }
+
+        // All components are size 1 or 2. Predecode each.
+        let mut obs_mask = 0u64;
+        let mut handled = vec![false; n];
+
+        for di in 0..n {
+            if handled[di] {
+                continue;
+            }
+            let root = component[di];
+
+            if comp_size[root] == 1 {
+                // Isolated defect: match to boundary.
+                obs_mask ^= self.predecode_single(defect_list[di]);
+                handled[di] = true;
+            } else if comp_size[root] == 2 {
+                // Find the other defect in this component.
+                let mut ni = None;
+                for (dj, &candidate_root) in component.iter().enumerate().take(n).skip(di + 1) {
+                    if candidate_root == root {
+                        ni = Some(dj);
+                        break;
+                    }
+                }
+                let ni = ni?;
+
+                let d0 = defect_list[di];
+                let d1 = defect_list[ni];
+
+                // Find lightest direct edge and lightest boundary alternatives.
+                let mut direct_w = f64::INFINITY;
+                let mut direct_obs = 0u64;
+                for &(e, nbr) in self.adj(d0 as usize) {
+                    if nbr == d1 && self.edges[e].weight < direct_w {
+                        direct_w = self.edges[e].weight;
+                        direct_obs = self.edges[e].obs_mask;
+                    }
+                }
+
+                let mut b0_w = f64::INFINITY;
+                let mut b0_obs = 0u64;
+                for &(e, nbr) in self.adj(d0 as usize) {
+                    if nbr == boundary && self.edges[e].weight < b0_w {
+                        b0_w = self.edges[e].weight;
+                        b0_obs = self.edges[e].obs_mask;
+                    }
+                }
+
+                let mut b1_w = f64::INFINITY;
+                let mut b1_obs = 0u64;
+                for &(e, nbr) in self.adj(d1 as usize) {
+                    if nbr == boundary && self.edges[e].weight < b1_w {
+                        b1_w = self.edges[e].weight;
+                        b1_obs = self.edges[e].obs_mask;
+                    }
+                }
+
+                // Pick min-weight correction.
+                if direct_w <= b0_w + b1_w {
+                    obs_mask ^= direct_obs;
+                } else {
+                    obs_mask ^= b0_obs ^ b1_obs;
+                }
+
+                handled[di] = true;
+                handled[ni] = true;
+            }
+        }
+
+        Some(obs_mask)
+    }
+
+    /// Predecode: single defect matches to boundary.
+    fn predecode_single(&self, defect: u32) -> u64 {
+        let boundary = self.num_detectors as u32;
+        // Find the lightest boundary edge from this defect.
+        // Adjacency is sorted by weight, so iterate and pick first boundary edge.
+        for &(edge_idx, neighbor) in self.adj(defect as usize) {
+            if neighbor == boundary {
+                return self.edges[edge_idx].obs_mask;
+            }
+        }
+        // No boundary edge found (shouldn't happen for valid surface codes).
+        0
+    }
+
+    /// Returns true if a cluster (given by its root) still needs to grow.
+    fn is_unsatisfied(&self, root: usize) -> bool {
+        self.parity[root] && !self.has_boundary[root]
+    }
+
+    /// Compute the growth rate for a cluster: `1 / size(cluster)`.
+    /// Smaller clusters grow faster, producing better pairings.
+    fn growth_rate(&self, root: usize) -> f64 {
+        1.0 / f64::from(self.cluster_size[root])
+    }
+
+    /// Get the effective radius of a cluster at a given time.
+    /// Uses lazy computation: radius is only updated when queried.
+    fn effective_radius(&self, root: usize, current_time: f64) -> f64 {
+        if self.is_unsatisfied(root) && root != self.num_detectors {
+            let dt = current_time - self.last_growth_time[root];
+            self.radius[root] + dt * self.growth_rate(root)
+        } else {
+            self.radius[root]
+        }
+    }
+
+    /// Materialize the lazy radius for a cluster (update stored value).
+    fn materialize_radius(&mut self, root: usize, current_time: f64) {
+        if self.is_unsatisfied(root) && root != self.num_detectors {
+            let dt = current_time - self.last_growth_time[root];
+            self.radius[root] += dt * self.growth_rate(root);
+        }
+        self.last_growth_time[root] = current_time;
+    }
+
+    /// Compute when edge becomes fusible given current radii and growth rates.
+    /// Returns the absolute time, or 0 if already fusible.
+    fn fusible_time(&self, root_u: usize, root_v: usize, weight: f64, current_time: f64) -> f64 {
+        let r_u = self.effective_radius(root_u, current_time);
+        let r_v = self.effective_radius(root_v, current_time);
+        let gap = weight - r_u - r_v;
+        if gap <= 0.0 {
+            return current_time;
+        }
+
+        let u_grows = self.is_unsatisfied(root_u);
+        let v_grows = self.is_unsatisfied(root_v);
+
+        let combined_rate = if u_grows && v_grows {
+            self.growth_rate(root_u) + self.growth_rate(root_v)
+        } else if u_grows {
+            self.growth_rate(root_u)
+        } else if v_grows {
+            self.growth_rate(root_v)
+        } else {
+            return f64::INFINITY; // neither grows
+        };
+
+        current_time + gap / combined_rate
+    }
+
+    /// Dispatch to the configured growth strategy.
+    fn grow_clusters(&mut self) {
+        match self.config.growth {
+            GrowthStrategy::EventDriven => self.grow_event_driven(),
+            GrowthStrategy::ScanBased => self.grow_scan_based(),
+        }
+    }
+
+    /// Scan-based growth: simple loop, lower overhead for small codes.
+    ///
+    /// Each round: scan all cross-cluster edges to find the minimum growth
+    /// increment, grow all unsatisfied clusters uniformly, then fuse.
+    /// O(R * E) where R is the number of growth rounds.
+    fn grow_scan_based(&mut self) {
+        let boundary = self.num_detectors;
+        let max_rounds = if self.config.max_growth_rounds > 0 {
+            self.config.max_growth_rounds
+        } else {
+            100 * self.num_detectors.max(1)
+        };
+
+        for _round in 0..max_rounds {
+            // Check for any unsatisfied cluster.
+            let mut any_unsatisfied = false;
+            for i in 0..=self.num_detectors {
+                let root = self.find(i as u32) as usize;
+                if root == i && self.is_unsatisfied(root) {
+                    any_unsatisfied = true;
+                    break;
+                }
+            }
+            if !any_unsatisfied {
+                break;
+            }
+
+            // Find the minimum growth increment across all cross-cluster edges.
+            let mut min_increment = f64::INFINITY;
+            for node in 0..=self.num_detectors {
+                let root_u = self.find(node as u32) as usize;
+                if !self.is_unsatisfied(root_u) {
+                    continue;
+                }
+
+                let adj_len = self.adj(node).len();
+                for adj_i in 0..adj_len {
+                    let (edge_idx, neighbor) = self.adj(node)[adj_i];
+                    let root_v = self.find(neighbor) as usize;
+                    if root_u == root_v {
+                        continue;
+                    }
+
+                    let w = self.edges[edge_idx].weight;
+                    let gap = w - self.radius[root_u] - self.radius[root_v];
+                    if gap <= 0.0 {
+                        min_increment = 0.0;
+                        break;
+                    }
+
+                    let v_grows = self.is_unsatisfied(root_v);
+                    let needed = if v_grows { gap / 2.0 } else { gap };
+                    min_increment = min_increment.min(needed);
+                }
+                if min_increment == 0.0 {
+                    break;
+                }
+            }
+
+            if min_increment.is_infinite() {
+                break;
+            }
+
+            // Grow all unsatisfied clusters.
+            for i in 0..=self.num_detectors {
+                let root = self.find(i as u32) as usize;
+                if root == i && self.is_unsatisfied(root) && i != boundary {
+                    self.radius[root] += min_increment;
+                }
+            }
+
+            // Fuse all now-fusible cross-cluster edges.
+            // Collect first to avoid borrow issues.
+            let mut fuse_count = 0;
+            for node in 0..=self.num_detectors {
+                let adj_len = self.adj(node).len();
+                for adj_i in 0..adj_len {
+                    let (_, neighbor) = self.adj(node)[adj_i];
+                    let root_u = self.find(node as u32) as usize;
+                    let root_v = self.find(neighbor) as usize;
+                    if root_u == root_v {
+                        continue;
+                    }
+                    let w = self.edges[self.adj(node)[adj_i].0].weight;
+                    if self.radius[root_u] + self.radius[root_v] >= w - 1e-12 {
+                        self.union(node as u32, neighbor);
+                        fuse_count += 1;
+                    }
+                }
+            }
+            if fuse_count == 0 && min_increment == 0.0 {
+                break; // No progress
+            }
+        }
+    }
+
+    /// Event-driven weighted cluster growth.
+    ///
+    /// Smaller clusters grow faster (rate = 1/size), making nearby small
+    /// clusters fuse before large clusters can absorb them. This improves
+    /// the quality of the UF pairings.
+    ///
+    /// Uses a priority queue with lazy deletion for O(E log E) total work.
+    fn grow_event_driven(&mut self) {
+        self.growth_events.clear();
+
+        // Seed events only from defect nodes (unsatisfied singletons).
+        // At low error rates, this skips ~95% of nodes.
+        for node in 0..self.num_detectors {
+            if !self.is_defect[node] {
+                continue;
+            }
+
+            let adj_len = self.adj(node).len();
+            for adj_i in 0..adj_len {
+                let (edge_idx, neighbor) = self.adj(node)[adj_i];
+                let root_v = self.find(neighbor) as usize;
+                if root_v == node {
+                    continue; // same cluster (shouldn't happen for singletons)
+                }
+
+                let ft = self.fusible_time(node, root_v, self.edges[edge_idx].weight, 0.0);
+                if ft.is_finite() {
+                    self.growth_events.push(Reverse((
+                        ft.to_bits(),
+                        edge_idx,
+                        node as u32,
+                        neighbor,
+                    )));
+                }
+            }
+        }
+
+        let mut current_time: f64;
+        let max_events = if self.config.max_growth_rounds > 0 {
+            self.config.max_growth_rounds
+        } else {
+            1000 * self.edges.len().max(1)
+        };
+        let mut events_processed = 0;
+
+        while let Some(Reverse((time_bits, _edge_idx, a, b))) = self.growth_events.pop() {
+            events_processed += 1;
+            if events_processed > max_events {
+                break;
+            }
+            let event_time = f64::from_bits(time_bits);
+
+            let root_a = self.find(a) as usize;
+            let root_b = self.find(b) as usize;
+            if root_a == root_b {
+                continue;
+            }
+
+            let a_unsat = self.is_unsatisfied(root_a);
+            let b_unsat = self.is_unsatisfied(root_b);
+            if !a_unsat && !b_unsat {
+                continue;
+            }
+
+            current_time = event_time;
+
+            // Materialize radii for the merging clusters (lazy update).
+            self.materialize_radius(root_a, current_time);
+            self.materialize_radius(root_b, current_time);
+
+            // Fuse.
+            let new_root = self.union(a, b) as usize;
+            self.last_growth_time[new_root] = current_time;
+
+            if !self.is_unsatisfied(new_root) {
+                continue;
+            }
+
+            // Re-insert events for edges from the merge nodes with updated times.
+            for &node in &[a, b] {
+                let nu = node as usize;
+                let adj_len = self.adj(nu).len();
+                for adj_i in 0..adj_len {
+                    let (edge_idx, neighbor) = self.adj(nu)[adj_i];
+                    let root_n = self.find(neighbor) as usize;
+                    if root_n == new_root {
+                        continue;
+                    }
+
+                    let ft = self.fusible_time(
+                        new_root,
+                        root_n,
+                        self.edges[edge_idx].weight,
+                        current_time,
+                    );
+                    if ft.is_finite() {
+                        self.growth_events
+                            .push(Reverse((ft.to_bits(), edge_idx, node, neighbor)));
+                    }
+                }
+            }
+        }
+    }
+
+    /// Build a spanning forest and peel to extract the correction.
+    /// Returns `(obs_mask, correction_edge_indices)`.
+    fn peel_correction_with_edges(&mut self) -> (u64, Vec<usize>) {
+        match self.config.peeling {
+            PeelingStrategy::PrimMst => self.peel_prim_mst(),
+            PeelingStrategy::Bfs => self.peel_bfs(),
+        }
+    }
+
+    /// Prim's MST peeling: globally lightest spanning tree. Better accuracy.
+    fn peel_prim_mst(&mut self) -> (u64, Vec<usize>) {
+        let boundary = self.num_detectors;
+
+        self.tree_parent.fill(None);
+        self.visited.fill(false);
+        self.visit_order.clear();
+        self.peel_heap.clear();
+        self.correction_edges.clear();
+
+        for seed in std::iter::once(boundary).chain(0..self.num_detectors) {
+            if self.visited[seed] {
+                continue;
+            }
+            self.visited[seed] = true;
+            self.visit_order.push(seed as u32);
+
+            let adj_len = self.adj(seed).len();
+            for adj_i in 0..adj_len {
+                let (edge_idx, neighbor) = self.adj(seed)[adj_i];
+                if !self.visited[neighbor as usize] {
+                    let w_bits = self.edges[edge_idx].weight.to_bits();
+                    self.peel_heap
+                        .push(Reverse((w_bits, edge_idx, seed as u32, neighbor)));
+                }
+            }
+
+            while let Some(Reverse((_w_bits, edge_idx, from, to))) = self.peel_heap.pop() {
+                let tu = to as usize;
+                if self.visited[tu] {
+                    continue;
+                }
+                let from_root = self.find(from);
+                let to_root = self.find(to);
+                if from_root != to_root {
+                    continue;
+                }
+                self.visited[tu] = true;
+                self.tree_parent[tu] = Some((from, edge_idx));
+                self.visit_order.push(to);
+
+                let adj_len = self.adj(tu).len();
+                for adj_i in 0..adj_len {
+                    let (e_idx, nbr) = self.adj(tu)[adj_i];
+                    if !self.visited[nbr as usize] {
+                        let w_bits = self.edges[e_idx].weight.to_bits();
+                        self.peel_heap.push(Reverse((w_bits, e_idx, to, nbr)));
+                    }
+                }
+            }
+        }
+
+        // Peel: process in reverse visit order (leaves first).
+        self.subtree_parity.fill(false);
+        self.subtree_parity[..self.num_detectors]
+            .copy_from_slice(&self.is_defect[..self.num_detectors]);
+
+        let mut obs_mask = 0u64;
+
+        for i in (0..self.visit_order.len()).rev() {
+            let v = self.visit_order[i];
+            if let Some((parent, edge_idx)) = self.tree_parent[v as usize] {
+                if self.subtree_parity[v as usize] {
+                    obs_mask ^= self.edges[edge_idx].obs_mask;
+                    self.correction_edges.push(edge_idx);
+                }
+                self.subtree_parity[parent as usize] ^= self.subtree_parity[v as usize];
+            }
+        }
+
+        (obs_mask, self.correction_edges.clone())
+    }
+
+    /// BFS peeling: simpler, faster (no heap), slightly less accurate.
+    fn peel_bfs(&mut self) -> (u64, Vec<usize>) {
+        let boundary = self.num_detectors;
+
+        self.tree_parent.fill(None);
+        self.visited.fill(false);
+        self.visit_order.clear();
+        self.correction_edges.clear();
+
+        for seed in std::iter::once(boundary).chain(0..self.num_detectors) {
+            if self.visited[seed] {
+                continue;
+            }
+            self.visited[seed] = true;
+            self.visit_order.push(seed as u32);
+
+            let mut queue_start = self.visit_order.len() - 1;
+            while queue_start < self.visit_order.len() {
+                let v = self.visit_order[queue_start] as usize;
+                queue_start += 1;
+
+                let adj_len = self.adj(v).len();
+                for adj_i in 0..adj_len {
+                    let (edge_idx, neighbor) = self.adj(v)[adj_i];
+                    let nu = neighbor as usize;
+                    if self.visited[nu] {
+                        continue;
+                    }
+                    let v_root = self.find(v as u32);
+                    let n_root = self.find(neighbor);
+                    if v_root != n_root {
+                        continue;
+                    }
+                    self.visited[nu] = true;
+                    self.tree_parent[nu] = Some((v as u32, edge_idx));
+                    self.visit_order.push(neighbor);
+                }
+            }
+        }
+
+        self.subtree_parity.fill(false);
+        self.subtree_parity[..self.num_detectors]
+            .copy_from_slice(&self.is_defect[..self.num_detectors]);
+
+        let mut obs_mask = 0u64;
+        for i in (0..self.visit_order.len()).rev() {
+            let v = self.visit_order[i];
+            if let Some((parent, edge_idx)) = self.tree_parent[v as usize] {
+                if self.subtree_parity[v as usize] {
+                    obs_mask ^= self.edges[edge_idx].obs_mask;
+                    self.correction_edges.push(edge_idx);
+                }
+                self.subtree_parity[parent as usize] ^= self.subtree_parity[v as usize];
+            }
+        }
+
+        (obs_mask, self.correction_edges.clone())
+    }
+
+    /// Peel correction, returning only the observable mask.
+    fn peel_correction(&mut self) -> u64 {
+        self.peel_correction_with_edges().0
+    }
+
+    /// Number of edges in the matching graph.
+    #[must_use]
+    pub fn num_edges(&self) -> usize {
+        self.edges.len()
+    }
+
+    /// Number of detectors.
+    #[must_use]
+    pub fn num_detectors(&self) -> usize {
+        self.num_detectors
+    }
+
+    /// Get the observable mask for an edge.
+    #[must_use]
+    pub fn edge_obs_mask(&self, edge_idx: usize) -> u64 {
+        self.edges.get(edge_idx).map_or(0, |e| e.obs_mask)
+    }
+
+    /// Get node1 of an edge.
+    #[must_use]
+    pub fn edge_node1(&self, edge_idx: usize) -> u32 {
+        self.edges.get(edge_idx).map_or(0, |e| e.node1)
+    }
+
+    /// Get node2 of an edge (boundary = `num_detectors`).
+    #[must_use]
+    pub fn edge_node2(&self, edge_idx: usize) -> u32 {
+        self.edges.get(edge_idx).map_or(0, |e| e.node2)
+    }
+
+    /// Get the weight of an edge (log-likelihood ratio).
+    #[must_use]
+    pub fn edge_weight(&self, edge_idx: usize) -> f64 {
+        self.edges.get(edge_idx).map_or(0.0, |e| e.weight)
+    }
+
+    /// Decode with full UF (no predecoder) and return matched edges.
+    /// Used by windowed decoder which needs complete edge tracking.
+    ///
+    /// # Errors
+    ///
+    /// Returns `DecoderError` if decoding fails.
+    pub fn decode_full_matching(
+        &mut self,
+        syndrome: &[u8],
+    ) -> Result<(u64, Vec<usize>), DecoderError> {
+        self.reset();
+        for (i, &v) in syndrome.iter().enumerate() {
+            if v != 0 && i < self.num_detectors {
+                self.parity[i] = true;
+                self.is_defect[i] = true;
+            }
+        }
+        self.grow_clusters();
+        Ok(self.peel_correction_with_edges())
+    }
+
+    // === UIUF support methods ===
+
+    /// Run syndrome validation (growth phase only, no peeling).
+    ///
+    /// After calling this, the internal cluster state reflects which nodes
+    /// have been merged. Use `edge_in_cluster()` to query which edges are
+    /// covered by clusters.
+    pub fn syndrome_validate(&mut self, syndrome: &[u8]) {
+        self.reset();
+        for (i, &v) in syndrome.iter().enumerate() {
+            if v != 0 && i < self.num_detectors {
+                self.parity[i] = true;
+                self.is_defect[i] = true;
+            }
+        }
+        self.grow_clusters();
+    }
+
+    /// Check if an edge's two endpoints are in the same cluster.
+    ///
+    /// Call after `syndrome_validate()`. Returns true if the edge is
+    /// "covered" by a cluster (both endpoints merged into one component).
+    pub fn edge_in_cluster(&mut self, edge_idx: usize) -> bool {
+        if edge_idx >= self.edges.len() {
+            return false;
+        }
+        let n1 = self.edges[edge_idx].node1;
+        let n2 = self.edges[edge_idx].node2;
+        let root_a = self.find(n1);
+        let root_b = self.find(n2);
+        root_a == root_b
+    }
+
+    /// Decode with pre-seeded erasure edges.
+    ///
+    /// Erasure edges are pre-merged into clusters before growth begins.
+    /// This is used by UIUF Phase 3 after the intersection step identifies
+    /// likely Y errors as erasures.
+    pub fn decode_with_erasures(&mut self, syndrome: &[u8], erasure_edges: &[usize]) -> u64 {
+        self.reset();
+        for (i, &v) in syndrome.iter().enumerate() {
+            if v != 0 && i < self.num_detectors {
+                self.parity[i] = true;
+                self.is_defect[i] = true;
+            }
+        }
+
+        // Pre-merge erasure edges before growth.
+        for &edge_idx in erasure_edges {
+            if edge_idx < self.edges.len() {
+                let n1 = self.edges[edge_idx].node1;
+                let n2 = self.edges[edge_idx].node2;
+                self.union(n1, n2);
+            }
+        }
+
+        self.grow_clusters();
+        self.peel_correction()
+    }
+}
+
+// === Trait implementations ===
+
+impl pecos_decoder_core::ObservableDecoder for UfDecoder {
+    fn decode_to_observables(&mut self, syndrome: &[u8]) -> Result<u64, DecoderError> {
+        Ok(self.decode_syndrome(syndrome))
+    }
+}
+
+impl pecos_decoder_core::correlated_decoder::MatchingDecoder for UfDecoder {
+    fn decode_with_matching(&mut self, syndrome: &[u8]) -> Result<(u64, Vec<usize>), DecoderError> {
+        // Count defects for predecoder.
+        let num_defects = syndrome
+            .iter()
+            .take(self.num_detectors)
+            .filter(|&&v| v != 0)
+            .count() as u32;
+
+        if num_defects == 0 {
+            return Ok((0, Vec::new()));
+        }
+
+        // Cluster predecoder (if enabled). Skipped in windowed mode
+        // because windowed decoding needs complete edge tracking.
+        if self.config.predecoder
+            && let Some(obs) = self.predecode_clusters(syndrome)
+        {
+            return Ok((obs, Vec::new()));
+        }
+
+        // Full decode path.
+        self.reset();
+        for (i, &v) in syndrome.iter().enumerate() {
+            if v != 0 && i < self.num_detectors {
+                self.parity[i] = true;
+                self.is_defect[i] = true;
+            }
+        }
+        self.grow_clusters();
+        Ok(self.peel_correction_with_edges())
+    }
+
+    fn decode_with_weights(
+        &mut self,
+        syndrome: &[u8],
+        weights: &[f64],
+    ) -> Result<(u64, Vec<usize>), DecoderError> {
+        // Temporarily swap in the new weights
+        self.weight_swap.clear();
+        for (i, &w) in weights.iter().enumerate() {
+            if i < self.edges.len() {
+                self.weight_swap.push((i, self.edges[i].weight));
+                self.edges[i].weight = w;
+            }
+        }
+
+        // Note: CSR adjacency sort order is fixed at construction.
+        // The weight swap affects growth event ordering but not correctness.
+        let result = self.decode_with_matching(syndrome);
+
+        // Restore original weights
+        for &(i, w) in &self.weight_swap {
+            self.edges[i].weight = w;
+        }
+
+        result
+    }
+
+    fn num_edges(&self) -> usize {
+        self.edges.len()
+    }
+}
+
+impl pecos_decoder_core::correlated_decoder::EdgeTrackingDecoder for UfDecoder {
+    fn edge_node1(&self, edge_idx: usize) -> u32 {
+        self.edges.get(edge_idx).map_or(0, |e| e.node1)
+    }
+
+    fn edge_node2(&self, edge_idx: usize) -> u32 {
+        self.edges.get(edge_idx).map_or(0, |e| e.node2)
+    }
+
+    fn edge_weight(&self, edge_idx: usize) -> f64 {
+        self.edges.get(edge_idx).map_or(0.0, |e| e.weight)
+    }
+
+    fn edge_obs_mask(&self, edge_idx: usize) -> u64 {
+        self.edges.get(edge_idx).map_or(0, |e| e.obs_mask)
+    }
+
+    fn num_detectors(&self) -> usize {
+        self.num_detectors
+    }
+}
+
+impl pecos_decoder_core::erasure::ObservableErasureDecoder for UfDecoder {
+    fn decode_with_erasures(
+        &mut self,
+        syndrome: &[u8],
+        erasure_edges: &[usize],
+    ) -> Result<u64, DecoderError> {
+        if erasure_edges.is_empty() {
+            // Use MatchingDecoder path directly.
+            use pecos_decoder_core::correlated_decoder::MatchingDecoder;
+            let (obs, _) = self.decode_with_matching(syndrome)?;
+            return Ok(obs);
+        }
+
+        // Set erased edges to weight=0 (certain error), decode, restore.
+        let mut modified_weights = Vec::with_capacity(self.edges.len());
+        for (i, e) in self.edges.iter().enumerate() {
+            if erasure_edges.contains(&i) {
+                modified_weights.push(0.0);
+            } else {
+                modified_weights.push(e.weight);
+            }
+        }
+
+        let (obs, _) = self.decode_with_weights(syndrome, &modified_weights)?;
+        Ok(obs)
+    }
+}
+
+#[cfg(test)]
+mod tests {
+    use super::*;
+
+    const SIMPLE_DEM: &str = "\
+error(0.1) D0 D1 L0
+error(0.1) D1
+";
+
+    const SURFACE_LIKE_DEM: &str = "\
+error(0.01) D0 D1 L0
+error(0.01) D1 D2
+error(0.01) D2
+error(0.01) D0
+";
+
+    #[test]
+    fn test_no_errors() {
+        let mut dec = UfDecoder::from_dem(SIMPLE_DEM, UfDecoderConfig::default()).unwrap();
+        assert_eq!(dec.decode_syndrome(&[0, 0]), 0);
+    }
+
+    #[test]
+    fn test_single_error() {
+        let mut dec = UfDecoder::from_dem(SIMPLE_DEM, UfDecoderConfig::default()).unwrap();
+        // D0 and D1 both triggered -> edge D0-D1 (carries L0)
+        assert_eq!(dec.decode_syndrome(&[1, 1]), 1);
+    }
+
+    #[test]
+    fn test_boundary_error() {
+        let mut dec = UfDecoder::from_dem(SIMPLE_DEM, UfDecoderConfig::default()).unwrap();
+        // Only D1 triggered -> boundary edge (no observable)
+        assert_eq!(dec.decode_syndrome(&[0, 1]), 0);
+    }
+
+    #[test]
+    fn test_multiple_shots() {
+        let mut dec = UfDecoder::from_dem(SIMPLE_DEM, UfDecoderConfig::default()).unwrap();
+        for _ in 0..20 {
+            let _ = dec.decode_syndrome(&[1, 1]);
+            let _ = dec.decode_syndrome(&[0, 1]);
+            let _ = dec.decode_syndrome(&[0, 0]);
+        }
+    }
+
+    #[test]
+    fn test_surface_like() {
+        let mut dec = UfDecoder::from_dem(SURFACE_LIKE_DEM, UfDecoderConfig::default()).unwrap();
+        // D0 triggered -> boundary edge (no observable)
+        assert_eq!(dec.decode_syndrome(&[1, 0, 0]), 0);
+        // D0 and D1 -> edge D0-D1 (L0)
+        assert_eq!(dec.decode_syndrome(&[1, 1, 0]), 1);
+    }
+
+    #[test]
+    fn test_observable_decoder_trait() {
+        use pecos_decoder_core::ObservableDecoder;
+        let mut dec = UfDecoder::from_dem(SIMPLE_DEM, UfDecoderConfig::default()).unwrap();
+        let mask = dec.decode_to_observables(&[1, 1]).unwrap();
+        assert_eq!(mask, 1);
+    }
+
+    #[test]
+    fn test_matching_decoder_trait() {
+        use pecos_decoder_core::correlated_decoder::MatchingDecoder;
+        let mut dec = UfDecoder::from_dem(SIMPLE_DEM, UfDecoderConfig::default()).unwrap();
+        let (mask, _edges) = dec.decode_with_matching(&[1, 1]).unwrap();
+        assert_eq!(mask, 1);
+        // Note: predecoder may return empty edges for simple cases.
+    }
+
+    /// Distance-3 repetition code: 3 data qubits, 2 detectors, 2 rounds.
+    /// Tests a more realistic graph structure with time-like edges.
+    const REP_CODE_D3_DEM: &str = "\
+error(0.01) D0 D1
+error(0.01) D0 L0
+error(0.01) D1
+error(0.001) D0 D2
+error(0.001) D1 D3
+error(0.01) D2 D3
+error(0.01) D2 L0
+error(0.01) D3
+";
+
+    #[test]
+    fn test_rep_code_d3() {
+        let mut dec = UfDecoder::from_dem(REP_CODE_D3_DEM, UfDecoderConfig::default()).unwrap();
+        assert_eq!(dec.num_edges(), 8);
+        assert_eq!(dec.num_detectors(), 4);
+
+        // No defects
+        assert_eq!(dec.decode_syndrome(&[0, 0, 0, 0]), 0);
+
+        // Single data error in round 1: D0 and D1 both fire
+        assert_eq!(dec.decode_syndrome(&[1, 1, 0, 0]), 0);
+
+        // Boundary error: only D0
+        assert_eq!(dec.decode_syndrome(&[1, 0, 0, 0]), 1); // L0
+
+        // Single boundary error round 2: only D2
+        assert_eq!(dec.decode_syndrome(&[0, 0, 1, 0]), 1); // L0
+    }
+
+    #[test]
+    fn test_stress_reuse() {
+        // Verify buffers are correctly reused over many shots
+        let mut dec = UfDecoder::from_dem(REP_CODE_D3_DEM, UfDecoderConfig::default()).unwrap();
+        let syndromes: &[&[u8]] = &[
+            &[0, 0, 0, 0],
+            &[1, 1, 0, 0],
+            &[1, 0, 0, 0],
+            &[0, 1, 0, 0],
+            &[0, 0, 1, 1],
+            &[1, 0, 1, 0],
+        ];
+        for _ in 0..1000 {
+            for syn in syndromes {
+                let _ = dec.decode_syndrome(syn);
+            }
+        }
+    }
+}
diff --git a/crates/pecos-uf-decoder/src/lib.rs b/crates/pecos-uf-decoder/src/lib.rs
new file mode 100644
index 000000000..180bccf56
--- /dev/null
+++ b/crates/pecos-uf-decoder/src/lib.rs
@@ -0,0 +1,51 @@
+// Copyright 2026 The PECOS Developers
+//
+// Licensed under the Apache License, Version 2.0 (the "License"); you may not use this file except
+// in compliance with the License. You may obtain a copy of the License at
+//
+//     https://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software distributed under the License
+// is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express
+// or implied. See the License for the specific language governing permissions and limitations under
+// the License.
+
+//! Fast syndrome-graph Union-Find decoder.
+//!
+//! Purpose-built for surface codes and other QEC codes with matching-graph
+//! structure. Works on the syndrome graph (not the Tanner graph), where nodes
+//! are detectors and edges are error mechanisms.
+//!
+//! Design goals:
+//! - Zero per-shot allocation (reusable flat arrays)
+//! - No locks, no Arc, no hash sets (unlike MWPF's UF)
+//! - Bounded worst-case latency
+//! - Implements `ObservableDecoder` and `MatchingDecoder` for composability
+//!   with `TwoPassDecoder` (correlated decoding)
+
+#![allow(
+    clippy::cast_possible_truncation,
+    clippy::cast_precision_loss,
+    clippy::cast_sign_loss
+)]
+
+pub mod astar;
+pub mod bp_uf;
+pub mod css_decoder;
+pub mod decoder;
+pub mod mini_bp;
+
+pub mod windowed;
+
+// Note: belief_matching (BP → PyMatching MWPM) lives in the Python bindings
+// (fault_tolerance_bindings.rs) since it requires pecos-pymatching which is
+// a C++ FFI crate. This crate stays pure Rust.
+
+pub use astar::{AStarConfig, AStarDecoder};
+pub use bp_uf::{BpSchedule, BpUfConfig, BpUfDecoder};
+pub use css_decoder::{CssUfDecoder, QubitEdgeMapping};
+pub use decoder::{UfDecoder, UfDecoderConfig};
+pub use windowed::{
+    BeamSearchConfig, BeamSearchWindowedDecoder, OverlappingWindowedDecoder,
+    SandwichWindowedDecoder, StreamingWindowedDecoder, WindowedConfig, WindowedDecoder,
+};
diff --git a/crates/pecos-uf-decoder/src/mini_bp.rs b/crates/pecos-uf-decoder/src/mini_bp.rs
new file mode 100644
index 000000000..fd6510c36
--- /dev/null
+++ b/crates/pecos-uf-decoder/src/mini_bp.rs
@@ -0,0 +1,497 @@
+// Copyright 2026 The PECOS Developers
+//
+// Licensed under the Apache License, Version 2.0 (the "License"); you may not use this file except
+// in compliance with the License. You may obtain a copy of the License at
+//
+//     https://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software distributed under the License
+// is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express
+// or implied. See the License for the specific language governing permissions and limitations under
+// the License.
+
+//! Minimal min-sum belief propagation for BP+UF hybrid decoding.
+//!
+//! Runs a few iterations of min-sum BP on the check matrix (Tanner graph)
+//! to produce per-mechanism soft reliability scores. These scores are then
+//! used to adjust UF edge weights for better accuracy.
+//!
+//! This is intentionally minimal -- no normalization, no scheduling tricks.
+//! Just enough BP to extract useful soft information for UF.
+
+use pecos_decoder_core::dem::DemCheckMatrix;
+
+/// Pre-computed sparse structure for BP message passing.
+/// Build once at construction time, reuse across shots.
+/// Uses CSR-style flat arrays for cache-friendly iteration.
+pub struct BpGraph {
+    pub num_checks: usize,
+    pub num_vars: usize,
+    pub prior_llr: Vec<f64>,
+    /// CSR for checks: flat data of (`var_idx`, `msg_array_idx`).
+    check_data: Vec<(u32, u32)>,
+    /// CSR offsets for checks: `check_offset`[c]..`check_offset`[c+1].
+    check_offset: Vec<u32>,
+    /// CSR for vars: flat data of (`check_idx`, `msg_array_idx`).
+    var_data: Vec<(u32, u32)>,
+    /// CSR offsets for vars: `var_offset`[v]..`var_offset`[v+1].
+    var_offset: Vec<u32>,
+    /// Total number of edges in the Tanner graph.
+    pub total_edges: usize,
+}
+
+impl BpGraph {
+    /// Get check entries (CSR slice).
+    #[inline]
+    #[must_use]
+    pub fn check_entries(&self, c: usize) -> &[(u32, u32)] {
+        let s = self.check_offset[c] as usize;
+        let e = self.check_offset[c + 1] as usize;
+        &self.check_data[s..e]
+    }
+
+    /// Get var entries (CSR slice).
+    #[inline]
+    fn var_entries(&self, v: usize) -> &[(u32, u32)] {
+        let s = self.var_offset[v] as usize;
+        let e = self.var_offset[v + 1] as usize;
+        &self.var_data[s..e]
+    }
+
+    /// Build from a `DemCheckMatrix`.
+    #[must_use]
+    pub fn from_dcm(dcm: &DemCheckMatrix) -> Self {
+        let num_checks = dcm.num_detectors;
+        let num_vars = dcm.num_mechanisms;
+
+        let prior_llr: Vec<f64> = dcm
+            .error_priors
+            .iter()
+            .map(|&p| {
+                if p <= 0.0 {
+                    30.0
+                } else if p >= 1.0 {
+                    -30.0
+                } else {
+                    ((1.0 - p) / p).ln()
+                }
+            })
+            .collect();
+
+        // Build temporary adjacency then flatten to CSR.
+        let mut temp_check: Vec<Vec<(u32, u32)>> = vec![Vec::new(); num_checks];
+        let mut temp_var: Vec<Vec<(u32, u32)>> = vec![Vec::new(); num_vars];
+        let mut msg_idx: u32 = 0;
+
+        for (c, check_entries) in temp_check.iter_mut().enumerate().take(num_checks) {
+            for (v, var_entries) in temp_var.iter_mut().enumerate().take(num_vars) {
+                if dcm.check_matrix[[c, v]] != 0 {
+                    check_entries.push((v as u32, msg_idx));
+                    var_entries.push((c as u32, msg_idx));
+                    msg_idx += 1;
+                }
+            }
+        }
+
+        // Flatten check entries.
+        let mut check_data = Vec::new();
+        let mut check_offset = Vec::with_capacity(num_checks + 1);
+        for entries in &temp_check {
+            check_offset.push(check_data.len() as u32);
+            check_data.extend_from_slice(entries);
+        }
+        check_offset.push(check_data.len() as u32);
+
+        // Flatten var entries.
+        let mut var_data = Vec::new();
+        let mut var_offset = Vec::with_capacity(num_vars + 1);
+        for entries in &temp_var {
+            var_offset.push(var_data.len() as u32);
+            var_data.extend_from_slice(entries);
+        }
+        var_offset.push(var_data.len() as u32);
+
+        Self {
+            num_checks,
+            num_vars,
+            prior_llr,
+            check_data,
+            check_offset,
+            var_data,
+            var_offset,
+            total_edges: msg_idx as usize,
+        }
+    }
+}
+
+/// Run min-sum BP on a pre-computed graph and return posterior LLRs per mechanism.
+///
+/// - `graph`: pre-computed sparse BP graph
+/// - `syndrome`: detection events (1 = triggered)
+/// - `num_iterations`: number of BP iterations
+/// - `min_sum_scale`: scaling factor for min-sum messages (0.625 is standard)
+/// - `serial`: if true, use serial schedule (better convergence, slower)
+/// - `c_to_v`, `v_to_c`: reusable message buffers (must be `graph.total_edges` long)
+/// - `posterior`: output buffer (must be `graph.num_vars` long)
+#[allow(clippy::too_many_arguments)] // Hot-path helper takes reusable buffers explicitly.
+pub fn min_sum_bp_into(
+    graph: &BpGraph,
+    syndrome: &[u8],
+    num_iterations: usize,
+    min_sum_scale: f64,
+    serial: bool,
+    c_to_v: &mut [f64],
+    v_to_c: &mut [f64],
+    posterior: &mut Vec<f64>,
+) {
+    let num_checks = graph.num_checks;
+    let num_vars = graph.num_vars;
+
+    // Initialize v→c with priors.
+    for v in 0..num_vars {
+        for &(_c, idx) in graph.var_entries(v) {
+            v_to_c[idx as usize] = graph.prior_llr[v];
+        }
+    }
+
+    // Pre-compute syndrome signs (avoid branch in inner loop).
+    let mut syn_sign = vec![1.0f64; num_checks];
+    for (c, sign) in syn_sign.iter_mut().enumerate() {
+        if c < syndrome.len() && syndrome[c] != 0 {
+            *sign = -1.0;
+        }
+    }
+
+    let damp = 0.25;
+
+    // EWA posterior accumulator.
+    let ewa_weight = 0.3;
+    let mut ewa_posterior = vec![0.0f64; num_vars];
+    ewa_posterior.copy_from_slice(&graph.prior_llr);
+
+    // EWAInit: run BP multiple times, using EWA of previous posteriors
+    // as the prior for the next run. This finds better fixed points.
+    let outer_iterations = if num_iterations >= 6 { 2 } else { 1 };
+    let inner_iterations = if outer_iterations > 1 {
+        num_iterations / outer_iterations
+    } else {
+        num_iterations
+    };
+
+    for outer in 0..outer_iterations {
+        // Re-initialize v→c with current EWA posteriors as priors.
+        if outer > 0 {
+            for (v, &prior) in ewa_posterior.iter().enumerate().take(num_vars) {
+                for &(_c, idx) in graph.var_entries(v) {
+                    v_to_c[idx as usize] = prior;
+                }
+            }
+            c_to_v.fill(0.0);
+        }
+
+        for iter in 0..inner_iterations {
+            for (c, &syndrome_sign) in syn_sign.iter().enumerate().take(num_checks) {
+                let entries = graph.check_entries(c);
+                if entries.len() < 2 {
+                    continue;
+                }
+
+                // Check-to-variable (normalized min-sum).
+                let mut total_sign = syndrome_sign;
+                let mut min1 = f64::INFINITY;
+                let mut min2 = f64::INFINITY;
+                let mut min1_pos = usize::MAX;
+
+                for (pos, &(_v, idx)) in entries.iter().enumerate() {
+                    let msg = v_to_c[idx as usize];
+                    if msg < 0.0 {
+                        total_sign = -total_sign;
+                    }
+                    let abs_msg = msg.abs();
+                    if abs_msg < min1 {
+                        min2 = min1;
+                        min1 = abs_msg;
+                        min1_pos = pos;
+                    } else if abs_msg < min2 {
+                        min2 = abs_msg;
+                    }
+                }
+
+                for (pos, &(_v, idx)) in entries.iter().enumerate() {
+                    let msg_v = v_to_c[idx as usize];
+                    let sign_without_v = total_sign.copysign(total_sign * msg_v);
+                    let min_without_v = if pos == min1_pos { min2 } else { min1 };
+                    c_to_v[idx as usize] = sign_without_v * min_without_v * min_sum_scale;
+                }
+
+                if serial {
+                    // Serial: immediately update v→c for connected variables.
+                    for &(v_idx, _) in entries {
+                        let v = v_idx as usize;
+                        let gamma = damp;
+                        let v_entries = graph.var_entries(v);
+                        let total: f64 = v_entries
+                            .iter()
+                            .map(|&(_c2, idx2)| c_to_v[idx2 as usize])
+                            .sum();
+                        for &(_c2, idx2) in v_entries {
+                            let new_msg = graph.prior_llr[v] + total - c_to_v[idx2 as usize];
+                            v_to_c[idx2 as usize] =
+                                (1.0 - gamma) * new_msg + gamma * v_to_c[idx2 as usize];
+                        }
+                    }
+                }
+            }
+
+            if !serial {
+                // Flooding: batch update all variables after all checks.
+                for (v, &prior) in graph.prior_llr.iter().enumerate().take(num_vars) {
+                    let gamma = damp;
+                    let entries = graph.var_entries(v);
+                    let total: f64 = entries.iter().map(|&(_c, idx)| c_to_v[idx as usize]).sum();
+                    for &(_c, idx) in entries {
+                        let new_msg = prior + total - c_to_v[idx as usize];
+                        v_to_c[idx as usize] =
+                            (1.0 - gamma) * new_msg + gamma * v_to_c[idx as usize];
+                    }
+                }
+            }
+
+            // EWA: blend current iteration's posterior into the running average.
+            let w = if iter == 0 && outer == 0 {
+                1.0
+            } else {
+                ewa_weight
+            };
+            for (v, ewa) in ewa_posterior.iter_mut().enumerate().take(num_vars) {
+                let cur_posterior = graph.prior_llr[v]
+                    + graph
+                        .var_entries(v)
+                        .iter()
+                        .map(|&(_c, idx)| c_to_v[idx as usize])
+                        .sum::<f64>();
+                *ewa = (1.0 - w) * *ewa + w * cur_posterior;
+            }
+        } // end inner iteration loop
+    } // end outer EWAInit loop
+
+    // Use EWA-averaged posteriors (smoothed across all iterations).
+    posterior.clear();
+    posterior.extend_from_slice(&ewa_posterior);
+    // Also include final iteration's raw posterior for variables where
+    // EWA and raw agree in sign (reinforcement).
+    for (v, post) in posterior.iter_mut().enumerate().take(num_vars) {
+        let raw = graph.prior_llr[v]
+            + graph
+                .var_entries(v)
+                .iter()
+                .map(|&(_c, idx)| c_to_v[idx as usize])
+                .sum::<f64>();
+        // If EWA and raw agree, use the one with larger magnitude (more confident).
+        if (*post > 0.0) == (raw > 0.0) && raw.abs() > post.abs() {
+            *post = raw;
+        }
+        // If they disagree, keep EWA (it's more stable).
+    }
+}
+
+/// BP on the matching graph (Hack et al. 2026 style).
+///
+/// Instead of running BP on the Tanner graph (check matrix), run on the
+/// matching graph where:
+/// - Variables = matching graph edges (is this edge in the correction?)
+/// - Factors = detector nodes (parity constraint from syndrome)
+///
+/// The matching graph has simpler topology (no hyperedges, more tree-like),
+/// so BP converges better. Returns per-edge posterior LLRs.
+#[must_use]
+pub fn matching_graph_bp(
+    graph: &pecos_decoder_core::dem::DemMatchingGraph,
+    syndrome: &[u8],
+    num_iterations: usize,
+    min_sum_scale: f64,
+) -> Vec<f64> {
+    let num_nodes = graph.num_detectors + 1; // +1 for boundary
+    let num_edges = graph.edges.len();
+    let boundary = graph.num_detectors;
+
+    // Prior LLRs for each edge.
+    let prior_llr: Vec<f64> = graph.edges.iter().map(|e| e.weight).collect();
+
+    // Build adjacency: for each node, list of incident edges.
+    let mut node_edges: Vec<Vec<usize>> = vec![Vec::new(); num_nodes];
+    for (idx, edge) in graph.edges.iter().enumerate() {
+        node_edges[edge.node1 as usize].push(idx);
+        if let Some(n2) = edge.node2 {
+            node_edges[n2 as usize].push(idx);
+        } else {
+            node_edges[boundary].push(idx);
+        }
+    }
+
+    // Messages: node-to-edge and edge-to-node.
+    // For each (node, edge) pair, store the message index.
+    let mut msg_idx = 0usize;
+    let mut node_msg: Vec<Vec<(usize, usize)>> = vec![Vec::new(); num_nodes]; // node -> [(edge_idx, msg_idx)]
+    let mut edge_msg: Vec<Vec<(usize, usize)>> = vec![Vec::new(); num_edges]; // edge -> [(node_idx, msg_idx)]
+    for (node, edges) in node_edges.iter().enumerate() {
+        for &edge_idx in edges {
+            node_msg[node].push((edge_idx, msg_idx));
+            edge_msg[edge_idx].push((node, msg_idx));
+            msg_idx += 1;
+        }
+    }
+
+    let total_msgs = msg_idx;
+    let mut n_to_e = vec![0.0f64; total_msgs]; // node→edge messages
+    let mut e_to_n = vec![0.0f64; total_msgs]; // edge→node messages
+
+    // Initialize edge→node with prior LLRs.
+    for (edge_idx, entries) in edge_msg.iter().enumerate() {
+        for &(_, midx) in entries {
+            e_to_n[midx] = prior_llr[edge_idx];
+        }
+    }
+
+    // Syndrome sign.
+    let syn_sign: Vec<f64> = (0..num_nodes)
+        .map(|n| {
+            if n < syndrome.len() && syndrome[n] != 0 {
+                -1.0
+            } else {
+                1.0
+            }
+        })
+        .collect();
+
+    let damp = 0.25;
+
+    for _iter in 0..num_iterations {
+        // Node-to-edge (check-to-variable): min-sum update.
+        // Same as Tanner graph BP but on matching graph nodes.
+        for node in 0..num_nodes {
+            let entries = &node_msg[node];
+            if entries.len() < 2 {
+                continue;
+            }
+
+            let mut total_sign = syn_sign[node];
+            let mut min1 = f64::INFINITY;
+            let mut min2 = f64::INFINITY;
+            let mut min1_pos = usize::MAX;
+
+            for (pos, &(_, midx)) in entries.iter().enumerate() {
+                let msg = e_to_n[midx];
+                if msg < 0.0 {
+                    total_sign = -total_sign;
+                }
+                let abs_msg = msg.abs();
+                if abs_msg < min1 {
+                    min2 = min1;
+                    min1 = abs_msg;
+                    min1_pos = pos;
+                } else if abs_msg < min2 {
+                    min2 = abs_msg;
+                }
+            }
+
+            for (pos, &(_, midx)) in entries.iter().enumerate() {
+                let msg_v = e_to_n[midx];
+                let sign_without = total_sign.copysign(total_sign * msg_v);
+                let min_without = if pos == min1_pos { min2 } else { min1 };
+                n_to_e[midx] = sign_without * min_without * min_sum_scale;
+            }
+        }
+
+        // Edge-to-node (variable-to-check): sum incoming + prior.
+        for (edge_idx, entries) in edge_msg.iter().enumerate() {
+            let total: f64 = entries.iter().map(|&(_, midx)| n_to_e[midx]).sum();
+            for &(_, midx) in entries {
+                let new_msg = prior_llr[edge_idx] + total - n_to_e[midx];
+                e_to_n[midx] = (1.0 - damp) * new_msg + damp * e_to_n[midx];
+            }
+        }
+    }
+
+    // Posterior: prior + sum of all node→edge messages.
+    let mut posterior = prior_llr;
+    for (edge_idx, entries) in edge_msg.iter().enumerate() {
+        for &(_, midx) in entries {
+            posterior[edge_idx] += n_to_e[midx];
+        }
+    }
+
+    posterior
+}
+
+/// Convenience wrapper: build graph, run BP, return posteriors.
+#[must_use]
+pub fn min_sum_bp(
+    dcm: &DemCheckMatrix,
+    syndrome: &[u8],
+    num_iterations: usize,
+    min_sum_scale: f64,
+) -> Vec<f64> {
+    let graph = BpGraph::from_dcm(dcm);
+    let mut c_to_v = vec![0.0f64; graph.total_edges];
+    let mut v_to_c = vec![0.0f64; graph.total_edges];
+    let mut posterior = Vec::with_capacity(graph.num_vars);
+    min_sum_bp_into(
+        &graph,
+        syndrome,
+        num_iterations,
+        min_sum_scale,
+        false,
+        &mut c_to_v,
+        &mut v_to_c,
+        &mut posterior,
+    );
+    posterior
+}
+
+#[cfg(test)]
+mod tests {
+    use super::*;
+
+    #[test]
+    fn test_mini_bp_no_syndrome() {
+        // Simple 2-check, 3-mechanism DEM.
+        let dem_str = "\
+error(0.1) D0 D1 L0
+error(0.1) D1
+error(0.05) D0
+";
+        let dcm = DemCheckMatrix::from_dem_str(dem_str).unwrap();
+        let syndrome = vec![0u8; dcm.num_detectors];
+
+        let posterior = min_sum_bp(&dcm, &syndrome, 5, 0.625);
+        assert_eq!(posterior.len(), dcm.num_mechanisms);
+
+        // With no syndrome, all posteriors should be positive (no error likely).
+        for &llr in &posterior {
+            assert!(llr > 0.0, "Expected positive LLR for no-syndrome case");
+        }
+    }
+
+    #[test]
+    fn test_mini_bp_with_syndrome() {
+        let dem_str = "\
+error(0.1) D0 D1 L0
+error(0.1) D1
+error(0.05) D0
+";
+        let dcm = DemCheckMatrix::from_dem_str(dem_str).unwrap();
+        // D0 and D1 both triggered -> mechanism 0 (D0-D1) is likely.
+        let syndrome = vec![1, 1];
+
+        let posterior = min_sum_bp(&dcm, &syndrome, 5, 0.625);
+        assert_eq!(posterior.len(), dcm.num_mechanisms);
+
+        // Mechanism 0 (D0 D1) should have lower (more negative) LLR
+        // since both its checks are triggered.
+        assert!(
+            posterior[0] < posterior[2],
+            "Mechanism touching both triggered checks should be more likely"
+        );
+    }
+}
diff --git a/crates/pecos-uf-decoder/src/windowed.rs b/crates/pecos-uf-decoder/src/windowed.rs
new file mode 100644
index 000000000..8864adaf8
--- /dev/null
+++ b/crates/pecos-uf-decoder/src/windowed.rs
@@ -0,0 +1,1459 @@
+// Copyright 2026 The PECOS Developers
+//
+// Licensed under the Apache License, Version 2.0 (the "License"); you may not use this file except
+// in compliance with the License. You may obtain a copy of the License at
+//
+//     https://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software distributed under the License
+// is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express
+// or implied. See the License for the specific language governing permissions and limitations under
+// the License.
+
+//! Sliding-window decoder for real-time surface code decoding.
+//!
+//! Two modes:
+//!
+//! - **Non-overlapping (`buf=0`)**: sub-DEM per window, any inner decoder,
+//!   observable XOR across windows. Converges to ~1.03x penalty at large r
+//!   (matching Tan et al.). Inner decoder is pluggable via factory.
+//!
+//! - **Overlapping (`buf>0`)**: uses `UfDecoder` for edge tracking. Each
+//!   window is extended by buffer rounds for matching context. Only corrections
+//!   with both endpoints in the core region are committed. No artificial defect
+//!   injection — the buffer just provides graph context (Tan et al.).
+//!
+//! Reference: Tan et al., PRX Quantum 2023 (arXiv:2209.09219).
+
+use pecos_decoder_core::ObservableDecoder;
+use pecos_decoder_core::correlated_decoder::EdgeTrackingDecoder;
+use pecos_decoder_core::dem::DemMatchingGraph;
+use pecos_decoder_core::errors::DecoderError;
+use std::fmt::Write as _;
+
+/// Configuration for the windowed decoder.
+#[derive(Debug, Clone, Copy, Default)]
+pub struct WindowedConfig {
+    /// Commit rounds per window (step size). 0 = auto (code distance).
+    pub step_size: usize,
+    /// Buffer rounds on each side of the core. 0 = non-overlapping.
+    /// Recommended: set equal to code distance for near-zero penalty.
+    pub buffer_size: usize,
+    /// Half-width of Type-2 seam windows in rounds. 0 = auto (step/2).
+    pub seam_half_width: usize,
+    /// Extend core by this many layers into the buffer on each side.
+    /// Committed edges can touch the extended core, capturing more
+    /// boundary corrections. 0 = strict core only (default).
+    pub core_extend: usize,
+    /// Maximum edge weight for Phase-1 commit. Only correction edges
+    /// with weight below this are committed (high-confidence corrections).
+    /// 0.0 = no threshold (commit all core edges, default).
+    pub commit_weight_max: f64,
+}
+
+// =============================================================================
+// Non-overlapping windowed decoder (buf=0)
+// =============================================================================
+
+/// Pre-built window with a generic inner decoder.
+struct PrebuiltWindow {
+    decoder: Box<dyn ObservableDecoder>,
+    local_to_global: Vec<u32>,
+    num_local: usize,
+}
+
+/// Non-overlapping windowed decoder. Any `ObservableDecoder` as inner decoder.
+pub struct WindowedDecoder {
+    windows: Vec<PrebuiltWindow>,
+}
+
+impl WindowedDecoder {
+    /// Create from a DEM string with a decoder factory.
+    ///
+    /// # Errors
+    ///
+    /// Returns `DecoderError` if the DEM is malformed or the factory fails.
+    pub fn from_dem<F>(
+        dem: &str,
+        config: WindowedConfig,
+        mut decoder_factory: F,
+    ) -> Result<Self, DecoderError>
+    where
+        F: FnMut(&str) -> Result<Box<dyn ObservableDecoder>, DecoderError>,
+    {
+        let (det_times, num_detectors, step_size, total_t) = parse_dem_params(dem, &config)?;
+        let mut windows = Vec::new();
+        let mut t_start = 0.0f64;
+
+        while t_start < total_t {
+            let is_last = t_start + 2.0 * step_size as f64 > total_t;
+            let t_end = if is_last {
+                total_t + 1.0
+            } else {
+                t_start + step_size as f64
+            };
+
+            let (local_to_global, window_dem) =
+                extract_window_dem(dem, &det_times, num_detectors, t_start, t_end);
+
+            let num_local = local_to_global.len();
+            if num_local > 0 && !window_dem.is_empty() {
+                let decoder = decoder_factory(&window_dem)?;
+                windows.push(PrebuiltWindow {
+                    decoder,
+                    local_to_global,
+                    num_local,
+                });
+            }
+
+            t_start += step_size as f64;
+        }
+
+        Ok(Self { windows })
+    }
+
+    /// Number of windows.
+    #[must_use]
+    pub fn num_windows(&self) -> usize {
+        self.windows.len()
+    }
+}
+
+impl ObservableDecoder for WindowedDecoder {
+    fn decode_to_observables(&mut self, syndrome: &[u8]) -> Result<u64, DecoderError> {
+        let mut obs_mask = 0u64;
+        for window in &mut self.windows {
+            let mut window_syn = vec![0u8; window.num_local];
+            for (local_id, &global_id) in window.local_to_global.iter().enumerate() {
+                let gid = global_id as usize;
+                if gid < syndrome.len() {
+                    window_syn[local_id] = syndrome[gid];
+                }
+            }
+            obs_mask ^= window.decoder.decode_to_observables(&window_syn)?;
+        }
+        Ok(obs_mask)
+    }
+}
+
+// =============================================================================
+// Overlapping windowed decoder (buf>0, Tan et al.)
+// =============================================================================
+
+/// Pre-built overlapping window with an edge-tracking inner decoder.
+struct OverlappingWindow<D> {
+    decoder: D,
+    local_to_global: Vec<u32>,
+    /// Per local detector: true = core region, false = buffer.
+    is_core: Vec<bool>,
+    num_local: usize,
+}
+
+/// Overlapping windowed decoder using any `EdgeTrackingDecoder` for edge tracking.
+///
+/// Each window is extended by buffer rounds for matching context.
+/// Only core corrections are committed; buffer corrections are discarded.
+pub struct OverlappingWindowedDecoder<D> {
+    windows: Vec<OverlappingWindow<D>>,
+}
+
+impl<D: EdgeTrackingDecoder> OverlappingWindowedDecoder<D> {
+    /// Create from a DEM string with a factory for the inner decoder.
+    ///
+    /// # Errors
+    ///
+    /// Returns `DecoderError` if the DEM is malformed or the factory fails.
+    pub fn from_dem<F>(
+        dem: &str,
+        config: WindowedConfig,
+        mut factory: F,
+    ) -> Result<Self, DecoderError>
+    where
+        F: FnMut(&str) -> Result<D, DecoderError>,
+    {
+        let (det_times, num_detectors, step_size, total_t) = parse_dem_params(dem, &config)?;
+        let buffer_size = config.buffer_size;
+        let mut windows = Vec::new();
+        let mut t_start = 0.0f64;
+
+        while t_start < total_t {
+            let is_last = t_start + 2.0 * step_size as f64 > total_t;
+            let t_core_end = if is_last {
+                total_t + 1.0
+            } else {
+                t_start + step_size as f64
+            };
+            let t_win_start = (t_start - buffer_size as f64).max(0.0);
+            let t_win_end = if is_last {
+                total_t + 1.0
+            } else {
+                t_core_end + buffer_size as f64
+            };
+
+            let (local_to_global, window_dem) =
+                extract_window_dem(dem, &det_times, num_detectors, t_win_start, t_win_end);
+
+            let ext = config.core_extend as f64;
+            let is_core: Vec<bool> = local_to_global
+                .iter()
+                .map(|&gid| {
+                    let t = det_times[gid as usize];
+                    t >= (t_start - ext) && t < (t_core_end + ext)
+                })
+                .collect();
+
+            let num_local = local_to_global.len();
+            if num_local > 0 && !window_dem.is_empty() {
+                let decoder = factory(&window_dem)?;
+                windows.push(OverlappingWindow {
+                    decoder,
+                    local_to_global,
+                    is_core,
+                    num_local,
+                });
+            }
+
+            t_start += step_size as f64;
+        }
+
+        Ok(Self { windows })
+    }
+
+    /// Number of windows.
+    #[must_use]
+    pub fn num_windows(&self) -> usize {
+        self.windows.len()
+    }
+}
+
+impl<D: EdgeTrackingDecoder> ObservableDecoder for OverlappingWindowedDecoder<D> {
+    fn decode_to_observables(&mut self, syndrome: &[u8]) -> Result<u64, DecoderError> {
+        let mut obs_mask = 0u64;
+
+        for window in &mut self.windows {
+            let mut window_syn = vec![0u8; window.num_local];
+            for (local_id, &global_id) in window.local_to_global.iter().enumerate() {
+                let gid = global_id as usize;
+                if gid < syndrome.len() {
+                    window_syn[local_id] = syndrome[gid];
+                }
+            }
+
+            // Use MatchingDecoder trait for edge tracking.
+            let (_, matched_edges) = window.decoder.decode_with_matching(&window_syn)?;
+
+            let boundary = window.num_local as u32;
+            for &edge_idx in &matched_edges {
+                let n1 = window.decoder.edge_node1(edge_idx);
+                let n2 = window.decoder.edge_node2(edge_idx);
+
+                let n1_core = n1 >= boundary
+                    || ((n1 as usize) < window.is_core.len() && window.is_core[n1 as usize]);
+                let n2_core = n2 >= boundary
+                    || ((n2 as usize) < window.is_core.len() && window.is_core[n2 as usize]);
+
+                if n1_core && n2_core {
+                    obs_mask ^= window.decoder.edge_obs_mask(edge_idx);
+                }
+            }
+        }
+
+        Ok(obs_mask)
+    }
+}
+
+// =============================================================================
+// Sandwich windowed decoder (Tan et al. two-phase)
+// =============================================================================
+
+/// Sandwich windowed decoder: two-phase decoding for reduced boundary penalty.
+///
+/// Phase 1 (Type-1): Overlapping windows with core-only commit, same as
+/// `OverlappingWindowedDecoder`. Independent, can run in parallel.
+///
+/// Phase 2 (Type-2): Small seam windows at core boundaries decode the
+/// residual syndrome left by Type-1. The residual is computed as
+/// `original XOR correction_effect` where `correction_effect` tracks
+/// which syndrome bits were flipped by Type-1's committed edges.
+///
+/// This gives Type-2 bidirectional boundary information from both
+/// flanking Type-1 windows, reducing the boundary penalty.
+pub struct SandwichWindowedDecoder<D> {
+    type1_windows: Vec<OverlappingWindow<D>>,
+    residual_decoder: Box<dyn ObservableDecoder>,
+    num_detectors: usize,
+    commit_weight_max: f64,
+}
+
+impl<D: EdgeTrackingDecoder> SandwichWindowedDecoder<D> {
+    /// Create from a DEM string with factories for Phase-1 and Phase-2 decoders.
+    ///
+    /// # Errors
+    ///
+    /// Returns `DecoderError` if the DEM is malformed or factories fail.
+    pub fn from_dem<F1, F2>(
+        dem: &str,
+        config: WindowedConfig,
+        mut phase1_factory: F1,
+        mut phase2_factory: F2,
+    ) -> Result<Self, DecoderError>
+    where
+        F1: FnMut(&str) -> Result<D, DecoderError>,
+        F2: FnMut(&str) -> Result<Box<dyn ObservableDecoder>, DecoderError>,
+    {
+        let (det_times, num_detectors, step_size, total_t) = parse_dem_params(dem, &config)?;
+        let buffer_size = config.buffer_size;
+
+        let mut type1_windows = Vec::new();
+        let mut t_start = 0.0f64;
+
+        while t_start < total_t {
+            let is_last = t_start + 2.0 * step_size as f64 > total_t;
+            let t_core_end = if is_last {
+                total_t + 1.0
+            } else {
+                t_start + step_size as f64
+            };
+            let t_win_start = (t_start - buffer_size as f64).max(0.0);
+            let t_win_end = if is_last {
+                total_t + 1.0
+            } else {
+                t_core_end + buffer_size as f64
+            };
+
+            let (local_to_global, window_dem) =
+                extract_window_dem(dem, &det_times, num_detectors, t_win_start, t_win_end);
+
+            let ext = config.core_extend as f64;
+            let is_core: Vec<bool> = local_to_global
+                .iter()
+                .map(|&gid| {
+                    let t = det_times[gid as usize];
+                    t >= (t_start - ext) && t < (t_core_end + ext)
+                })
+                .collect();
+
+            let num_local = local_to_global.len();
+            if num_local > 0 && !window_dem.is_empty() {
+                let decoder = phase1_factory(&window_dem)?;
+                type1_windows.push(OverlappingWindow {
+                    decoder,
+                    local_to_global,
+                    is_core,
+                    num_local,
+                });
+            }
+
+            t_start += step_size as f64;
+        }
+
+        let residual_decoder = phase2_factory(dem)?;
+
+        Ok(Self {
+            type1_windows,
+            residual_decoder,
+            num_detectors,
+            commit_weight_max: config.commit_weight_max,
+        })
+    }
+
+    /// Number of Type-1 windows.
+    #[must_use]
+    pub fn num_windows(&self) -> usize {
+        self.type1_windows.len()
+    }
+
+    /// Decode with parallel Phase-1 windows using rayon.
+    ///
+    /// Requires `D: Send` for thread safety. Phase-1 windows run on rayon's
+    /// thread pool; Phase-2 residual runs sequentially after.
+    ///
+    /// # Errors
+    ///
+    /// Returns `DecoderError` if any window decoder fails.
+    pub fn decode_parallel(&mut self, syndrome: &[u8]) -> Result<u64, DecoderError>
+    where
+        D: Send,
+    {
+        use rayon::prelude::*;
+
+        let commit_weight_max = self.commit_weight_max;
+        let num_detectors = self.num_detectors;
+
+        // Phase 1: Decode Type-1 windows in parallel.
+        let window_results: Result<Vec<_>, DecoderError> = self
+            .type1_windows
+            .par_iter_mut()
+            .map(|window| {
+                let mut window_syn = vec![0u8; window.num_local];
+                for (local_id, &global_id) in window.local_to_global.iter().enumerate() {
+                    let gid = global_id as usize;
+                    if gid < syndrome.len() {
+                        window_syn[local_id] = syndrome[gid];
+                    }
+                }
+
+                let (_, matched_edges) = window.decoder.decode_with_matching(&window_syn)?;
+
+                let mut obs = 0u64;
+                let mut corrections: Vec<(usize, u8)> = Vec::new();
+                let boundary = window.num_local as u32;
+
+                for &edge_idx in &matched_edges {
+                    let n1 = window.decoder.edge_node1(edge_idx);
+                    let n2 = window.decoder.edge_node2(edge_idx);
+
+                    let n1_core = n1 >= boundary
+                        || ((n1 as usize) < window.is_core.len() && window.is_core[n1 as usize]);
+                    let n2_core = n2 >= boundary
+                        || ((n2 as usize) < window.is_core.len() && window.is_core[n2 as usize]);
+
+                    let weight_ok = commit_weight_max <= 0.0
+                        || window.decoder.edge_weight(edge_idx) <= commit_weight_max;
+
+                    if n1_core && n2_core && weight_ok {
+                        obs ^= window.decoder.edge_obs_mask(edge_idx);
+                        if (n1 as usize) < window.num_local {
+                            corrections.push((window.local_to_global[n1 as usize] as usize, 1));
+                        }
+                        if (n2 as usize) < window.num_local {
+                            corrections.push((window.local_to_global[n2 as usize] as usize, 1));
+                        }
+                    }
+                }
+
+                Ok((obs, corrections))
+            })
+            .collect();
+
+        // Merge results (XOR is order-independent).
+        let mut obs_mask = 0u64;
+        let mut correction_effect = vec![0u8; num_detectors];
+        for (window_obs, corrections) in window_results? {
+            obs_mask ^= window_obs;
+            for (gid, bit) in corrections {
+                correction_effect[gid] ^= bit;
+            }
+        }
+
+        // Phase 2: Residual decode (sequential).
+        let mut residual_syn = vec![0u8; num_detectors];
+        for (i, &s) in syndrome.iter().enumerate() {
+            if i < num_detectors {
+                residual_syn[i] = s ^ correction_effect[i];
+            }
+        }
+        obs_mask ^= self.residual_decoder.decode_to_observables(&residual_syn)?;
+
+        Ok(obs_mask)
+    }
+}
+
+impl<D: EdgeTrackingDecoder> ObservableDecoder for SandwichWindowedDecoder<D> {
+    fn decode_to_observables(&mut self, syndrome: &[u8]) -> Result<u64, DecoderError> {
+        let mut obs_mask = 0u64;
+        let mut correction_effect = vec![0u8; self.num_detectors];
+        let commit_weight_max = self.commit_weight_max;
+
+        // Phase 1: Decode Type-1 windows.
+        for window in &mut self.type1_windows {
+            let mut window_syn = vec![0u8; window.num_local];
+            for (local_id, &global_id) in window.local_to_global.iter().enumerate() {
+                let gid = global_id as usize;
+                if gid < syndrome.len() {
+                    window_syn[local_id] = syndrome[gid];
+                }
+            }
+
+            let (_, matched_edges) = window.decoder.decode_with_matching(&window_syn)?;
+
+            let boundary = window.num_local as u32;
+            for &edge_idx in &matched_edges {
+                let n1 = window.decoder.edge_node1(edge_idx);
+                let n2 = window.decoder.edge_node2(edge_idx);
+
+                let n1_core = n1 >= boundary
+                    || ((n1 as usize) < window.is_core.len() && window.is_core[n1 as usize]);
+                let n2_core = n2 >= boundary
+                    || ((n2 as usize) < window.is_core.len() && window.is_core[n2 as usize]);
+
+                let weight_ok = commit_weight_max <= 0.0
+                    || window.decoder.edge_weight(edge_idx) <= commit_weight_max;
+
+                if n1_core && n2_core && weight_ok {
+                    obs_mask ^= window.decoder.edge_obs_mask(edge_idx);
+
+                    if (n1 as usize) < window.num_local {
+                        let gid = window.local_to_global[n1 as usize] as usize;
+                        correction_effect[gid] ^= 1;
+                    }
+                    if (n2 as usize) < window.num_local {
+                        let gid = window.local_to_global[n2 as usize] as usize;
+                        correction_effect[gid] ^= 1;
+                    }
+                }
+            }
+        }
+
+        // Phase 2: Decode residual syndrome on the full graph.
+        let mut residual_syn = vec![0u8; self.num_detectors];
+        for (i, &s) in syndrome.iter().enumerate() {
+            if i < self.num_detectors {
+                residual_syn[i] = s ^ correction_effect[i];
+            }
+        }
+        obs_mask ^= self.residual_decoder.decode_to_observables(&residual_syn)?;
+
+        Ok(obs_mask)
+    }
+}
+
+// =============================================================================
+// Shared helpers
+// =============================================================================
+
+/// Parse DEM parameters for windowing.
+fn parse_dem_params(
+    dem: &str,
+    config: &WindowedConfig,
+) -> Result<(Vec<f64>, usize, usize, f64), DecoderError> {
+    let graph = DemMatchingGraph::from_dem_str(dem)?;
+    let num_detectors = graph.num_detectors;
+
+    let mut det_times = vec![0.0f64; num_detectors];
+    let mut max_time = 0.0f64;
+    for (i, coord) in graph.detector_coords.iter().enumerate() {
+        if let Some(c) = coord {
+            let t = c.get(2).copied().unwrap_or(0.0);
+            if i < det_times.len() {
+                det_times[i] = t;
+            }
+            if t > max_time {
+                max_time = t;
+            }
+        }
+    }
+
+    let num_rounds = (max_time + 1.0) as usize;
+    let num_stab = num_detectors
+        .checked_div(num_rounds)
+        .unwrap_or(num_detectors);
+    let d_est = ((num_stab as f64).sqrt().ceil() as usize).max(3);
+    let step_size = if config.step_size > 0 {
+        config.step_size
+    } else {
+        d_est
+    };
+    let total_t = num_rounds as f64;
+
+    Ok((det_times, num_detectors, step_size, total_t))
+}
+
+/// Extract a window sub-DEM by filtering the original DEM text.
+///
+/// Detectors in `[t_start, t_end)` are included and remapped to local IDs.
+/// Detectors outside the window are dropped from error mechanisms, creating
+/// implicit boundary edges.
+fn extract_window_dem(
+    dem: &str,
+    det_times: &[f64],
+    num_det: usize,
+    t_start: f64,
+    t_end: f64,
+) -> (Vec<u32>, String) {
+    let mut in_window = vec![false; num_det];
+    let mut local_to_global: Vec<u32> = Vec::new();
+    let mut global_to_local: Vec<Option<u32>> = vec![None; num_det];
+
+    for (i, &t) in det_times.iter().enumerate() {
+        if t >= t_start && t < t_end {
+            in_window[i] = true;
+            global_to_local[i] = Some(local_to_global.len() as u32);
+            local_to_global.push(i as u32);
+        }
+    }
+
+    let mut out = String::new();
+
+    for line in dem.lines() {
+        let trimmed = line.trim();
+        if trimmed.is_empty() || trimmed.starts_with('#') {
+            continue;
+        }
+
+        if trimmed.starts_with("error(") {
+            let Some(close) = trimmed.find(')') else {
+                continue;
+            };
+            let prob_str = &trimmed[6..close];
+            let rest = &trimmed[close + 1..];
+            let tokens: Vec<&str> = rest.split_whitespace().collect();
+
+            // Split by ^ into decomposed segments.
+            let mut segments: Vec<Vec<&str>> = vec![Vec::new()];
+            for tok in &tokens {
+                if *tok == "^" {
+                    segments.push(Vec::new());
+                } else {
+                    segments.last_mut().unwrap().push(tok);
+                }
+            }
+
+            let mut remapped_segments: Vec<String> = Vec::new();
+            for seg in &segments {
+                let mut seg_dets: Vec<String> = Vec::new();
+                let mut seg_obs: Vec<String> = Vec::new();
+                let mut seg_any_in = false;
+
+                for tok in seg {
+                    if let Some(d_str) = tok.strip_prefix('D') {
+                        if let Ok(d) = d_str.parse::<usize>()
+                            && d < num_det
+                            && in_window[d]
+                        {
+                            seg_any_in = true;
+                            if let Some(local) = global_to_local[d] {
+                                seg_dets.push(format!("D{local}"));
+                            }
+                        }
+                    } else if tok.starts_with('L') {
+                        seg_obs.push((*tok).to_string());
+                    }
+                }
+
+                if seg_any_in {
+                    let mut seg_str = seg_dets.join(" ");
+                    for obs in &seg_obs {
+                        seg_str.push(' ');
+                        seg_str.push_str(obs);
+                    }
+                    remapped_segments.push(seg_str);
+                }
+            }
+
+            if !remapped_segments.is_empty() {
+                let _ = write!(out, "error({prob_str}) ");
+                out.push_str(&remapped_segments.join(" ^ "));
+                out.push('\n');
+            }
+        } else if trimmed.starts_with("detector(")
+            && let Some(d_start) = trimmed.rfind('D')
+            && let Ok(d) = trimmed[d_start + 1..].trim().parse::<usize>()
+            && d < num_det
+            && in_window[d]
+            && let Some(local) = global_to_local[d]
+        {
+            let coords_end = trimmed.find(')').unwrap_or(trimmed.len());
+            out.push_str(&trimmed[..=coords_end]);
+            let _ = writeln!(out, " D{local}");
+        }
+    }
+
+    (local_to_global, out)
+}
+
+// =============================================================================
+// Streaming windowed decoder
+// =============================================================================
+
+use std::collections::BTreeMap;
+
+/// Streaming windowed decoder that accepts syndrome data round-by-round.
+///
+/// Precomputes round-to-detector mapping from DEM coordinates. As rounds
+/// arrive via `feed_round`, buffers syndrome data and triggers window
+/// decoding when each window's extended region is complete. Emits partial
+/// observable corrections as windows commit.
+pub struct StreamingWindowedDecoder<D> {
+    /// Prebuilt windows, ordered by start time.
+    windows: Vec<OverlappingWindow<D>>,
+    /// Round number → list of (`local_window_idx`, `local_detector_idx`) for each window.
+    round_to_dets: BTreeMap<usize, Vec<(usize, usize)>>,
+    /// Per-window syndrome buffers.
+    window_syndromes: Vec<Vec<u8>>,
+    /// Round at which each window becomes decodable (all data received).
+    window_ready_round: Vec<usize>,
+    /// Index of next window to decode.
+    next_decode: usize,
+    /// Accumulated observable corrections.
+    accumulated: u64,
+}
+
+impl<D: EdgeTrackingDecoder> StreamingWindowedDecoder<D> {
+    /// Create from a DEM string with factory.
+    ///
+    /// # Errors
+    ///
+    /// Returns `DecoderError` if the DEM is malformed or factory fails.
+    pub fn from_dem<F>(
+        dem: &str,
+        config: WindowedConfig,
+        mut factory: F,
+    ) -> Result<Self, DecoderError>
+    where
+        F: FnMut(&str) -> Result<D, DecoderError>,
+    {
+        let (det_times, num_detectors, step_size, total_t) = parse_dem_params(dem, &config)?;
+        let buffer_size = config.buffer_size;
+
+        // Build windows (same as OverlappingWindowedDecoder).
+        let mut windows = Vec::new();
+        let mut window_ranges: Vec<(f64, f64, f64)> = Vec::new(); // (win_start, win_end, core_end)
+        let mut t_start = 0.0f64;
+
+        while t_start < total_t {
+            let is_last = t_start + 2.0 * step_size as f64 > total_t;
+            let t_core_end = if is_last {
+                total_t + 1.0
+            } else {
+                t_start + step_size as f64
+            };
+            let t_win_start = (t_start - buffer_size as f64).max(0.0);
+            let t_win_end = if is_last {
+                total_t + 1.0
+            } else {
+                t_core_end + buffer_size as f64
+            };
+
+            let (local_to_global, window_dem) =
+                extract_window_dem(dem, &det_times, num_detectors, t_win_start, t_win_end);
+
+            let ext = config.core_extend as f64;
+            let is_core: Vec<bool> = local_to_global
+                .iter()
+                .map(|&gid| {
+                    let t = det_times[gid as usize];
+                    t >= (t_start - ext) && t < (t_core_end + ext)
+                })
+                .collect();
+
+            let num_local = local_to_global.len();
+            if num_local > 0 && !window_dem.is_empty() {
+                let decoder = factory(&window_dem)?;
+                window_ranges.push((t_win_start, t_win_end, t_core_end));
+                windows.push(OverlappingWindow {
+                    decoder,
+                    local_to_global,
+                    is_core,
+                    num_local,
+                });
+            }
+
+            t_start += step_size as f64;
+        }
+
+        // Build round → (window_idx, local_det) mapping.
+        let mut round_to_dets: BTreeMap<usize, Vec<(usize, usize)>> = BTreeMap::new();
+        for (win_idx, window) in windows.iter().enumerate() {
+            for (local_id, &global_id) in window.local_to_global.iter().enumerate() {
+                let round = det_times[global_id as usize] as usize;
+                round_to_dets
+                    .entry(round)
+                    .or_default()
+                    .push((win_idx, local_id));
+            }
+        }
+
+        // Compute when each window has all its data.
+        let window_ready_round: Vec<usize> = window_ranges
+            .iter()
+            .map(|&(_, t_end, _)| (t_end.ceil() as usize).saturating_sub(1))
+            .collect();
+
+        let window_syndromes = windows.iter().map(|w| vec![0u8; w.num_local]).collect();
+
+        Ok(Self {
+            windows,
+            round_to_dets,
+            window_syndromes,
+            window_ready_round,
+            next_decode: 0,
+            accumulated: 0,
+        })
+    }
+
+    /// Decode a ready window and return its observable contribution.
+    fn decode_window(&mut self, win_idx: usize) -> Result<u64, DecoderError> {
+        let window = &mut self.windows[win_idx];
+        let syn = &self.window_syndromes[win_idx];
+
+        let (_, matched_edges) = window.decoder.decode_with_matching(syn)?;
+
+        let mut obs = 0u64;
+        let boundary = window.num_local as u32;
+        for &edge_idx in &matched_edges {
+            let n1 = window.decoder.edge_node1(edge_idx);
+            let n2 = window.decoder.edge_node2(edge_idx);
+
+            let n1_core = n1 >= boundary
+                || ((n1 as usize) < window.is_core.len() && window.is_core[n1 as usize]);
+            let n2_core = n2 >= boundary
+                || ((n2 as usize) < window.is_core.len() && window.is_core[n2 as usize]);
+
+            if n1_core && n2_core {
+                obs ^= window.decoder.edge_obs_mask(edge_idx);
+            }
+        }
+        Ok(obs)
+    }
+}
+
+impl<D: EdgeTrackingDecoder> pecos_decoder_core::streaming::StreamingDecoder
+    for StreamingWindowedDecoder<D>
+{
+    fn feed_round(&mut self, round: usize, detectors: &[(u32, u8)]) -> Result<u64, DecoderError> {
+        // Store detection events into each window's syndrome buffer.
+        for &(det, val) in detectors {
+            if let Some(entries) = self.round_to_dets.get(&round) {
+                for &(win_idx, local_id) in entries {
+                    // Check if this detector matches
+                    if self.windows[win_idx].local_to_global.get(local_id) == Some(&det) {
+                        self.window_syndromes[win_idx][local_id] = val;
+                    }
+                }
+            }
+        }
+
+        // Also store by global detector index for windows that contain this detector.
+        for &(det, val) in detectors {
+            for (win_idx, window) in self.windows.iter().enumerate() {
+                for (local_id, &global_id) in window.local_to_global.iter().enumerate() {
+                    if global_id == det {
+                        self.window_syndromes[win_idx][local_id] = val;
+                    }
+                }
+            }
+        }
+
+        // Check if any window became ready.
+        let mut new_obs = 0u64;
+        while self.next_decode < self.windows.len() {
+            if round < self.window_ready_round[self.next_decode] {
+                break;
+            }
+            new_obs ^= self.decode_window(self.next_decode)?;
+            self.next_decode += 1;
+        }
+
+        self.accumulated ^= new_obs;
+        Ok(new_obs)
+    }
+
+    fn flush(&mut self) -> Result<u64, DecoderError> {
+        let mut new_obs = 0u64;
+        while self.next_decode < self.windows.len() {
+            new_obs ^= self.decode_window(self.next_decode)?;
+            self.next_decode += 1;
+        }
+        self.accumulated ^= new_obs;
+        Ok(new_obs)
+    }
+
+    fn accumulated_obs(&self) -> u64 {
+        self.accumulated
+    }
+
+    fn reset(&mut self) {
+        for syn in &mut self.window_syndromes {
+            syn.fill(0);
+        }
+        self.next_decode = 0;
+        self.accumulated = 0;
+    }
+}
+
+// =============================================================================
+// Beam search windowed decoder
+// =============================================================================
+
+/// Configuration for the beam search windowed decoder.
+#[derive(Debug, Clone, Copy)]
+pub struct BeamSearchConfig {
+    /// Windowed decoder parameters.
+    pub window: WindowedConfig,
+    /// Number of beam hypotheses (K). Default 5.
+    pub beam_width: usize,
+    /// Perturbation sigma for log-normal weight noise. Default 0.5.
+    pub perturbation_sigma: f64,
+    /// RNG seed for reproducibility.
+    pub seed: u64,
+}
+
+impl Default for BeamSearchConfig {
+    fn default() -> Self {
+        Self {
+            window: WindowedConfig::default(),
+            beam_width: 5,
+            perturbation_sigma: 0.5,
+            seed: 42,
+        }
+    }
+}
+
+/// One beam hypothesis: accumulated state from windows processed so far.
+struct Hypothesis {
+    correction_effect: Vec<u8>,
+    obs_mask: u64,
+    total_weight: f64,
+}
+
+/// Per-window storage: K decoders (1 unperturbed + K-1 perturbed).
+struct BeamWindow<D> {
+    decoders: Vec<D>,
+    local_to_global: Vec<u32>,
+    is_core: Vec<bool>,
+    num_local: usize,
+}
+
+/// Beam search windowed decoder.
+///
+/// Maintains K correction hypotheses across window boundaries. Each window
+/// expands K hypotheses × K perturbed decoders = K² candidates, pruned
+/// to K by total correction weight. After all windows, picks the
+/// lowest-weight hypothesis and optionally runs a Phase-2 residual decode.
+///
+/// The key insight: different hypotheses propagate different
+/// `correction_effect` vectors to subsequent windows, so each hypothesis
+/// sees a different modified syndrome. This explores different string
+/// continuations across window boundaries.
+pub struct BeamSearchWindowedDecoder<D> {
+    windows: Vec<BeamWindow<D>>,
+    num_detectors: usize,
+    beam_width: usize,
+    commit_weight_max: f64,
+    residual_decoder: Option<Box<dyn ObservableDecoder>>,
+}
+
+impl<D: EdgeTrackingDecoder> BeamSearchWindowedDecoder<D> {
+    /// Create from a DEM string.
+    ///
+    /// `phase1_factory` builds the inner edge-tracking decoder from a sub-DEM.
+    /// `phase2_factory` (optional) builds the full-graph residual decoder.
+    ///
+    /// # Errors
+    ///
+    /// Returns `DecoderError` if the DEM is malformed or factories fail.
+    pub fn from_dem<F1, F2>(
+        dem: &str,
+        config: BeamSearchConfig,
+        mut phase1_factory: F1,
+        mut phase2_factory: Option<F2>,
+    ) -> Result<Self, DecoderError>
+    where
+        F1: FnMut(&str) -> Result<D, DecoderError>,
+        F2: FnMut(&str) -> Result<Box<dyn ObservableDecoder>, DecoderError>,
+    {
+        let (det_times, num_detectors, step_size, total_t) = parse_dem_params(dem, &config.window)?;
+        let buffer_size = config.window.buffer_size;
+        let k = config.beam_width;
+
+        let mut windows = Vec::new();
+        let mut t_start = 0.0f64;
+
+        while t_start < total_t {
+            let is_last = t_start + 2.0 * step_size as f64 > total_t;
+            let t_core_end = if is_last {
+                total_t + 1.0
+            } else {
+                t_start + step_size as f64
+            };
+            let t_win_start = (t_start - buffer_size as f64).max(0.0);
+            let t_win_end = if is_last {
+                total_t + 1.0
+            } else {
+                t_core_end + buffer_size as f64
+            };
+
+            let (local_to_global, window_dem) =
+                extract_window_dem(dem, &det_times, num_detectors, t_win_start, t_win_end);
+
+            let ext = config.window.core_extend as f64;
+            let is_core: Vec<bool> = local_to_global
+                .iter()
+                .map(|&gid| {
+                    let t = det_times[gid as usize];
+                    t >= (t_start - ext) && t < (t_core_end + ext)
+                })
+                .collect();
+
+            let num_local = local_to_global.len();
+            if num_local > 0 && !window_dem.is_empty() {
+                let mut decoders = Vec::with_capacity(k);
+
+                // Decoder 0: unperturbed anchor
+                decoders.push(phase1_factory(&window_dem)?);
+
+                // Decoders 1..K-1: perturbed weights
+                for member_idx in 1..k {
+                    let mut rng = pecos_random::PecosRng::seed_from_u64(
+                        config.seed.wrapping_add(member_idx as u64),
+                    );
+                    let mut next_f64 = || rng.next_f64();
+                    let perturbed = pecos_decoder_core::perturbed::perturb_dem(
+                        &window_dem,
+                        config.perturbation_sigma,
+                        &mut next_f64,
+                    );
+                    if let Ok(dec) = phase1_factory(&perturbed) {
+                        decoders.push(dec);
+                    }
+                }
+
+                windows.push(BeamWindow {
+                    decoders,
+                    local_to_global,
+                    is_core,
+                    num_local,
+                });
+            }
+
+            t_start += step_size as f64;
+        }
+
+        let residual_decoder = if let Some(ref mut f2) = phase2_factory {
+            Some(f2(dem)?)
+        } else {
+            None
+        };
+
+        Ok(Self {
+            windows,
+            num_detectors,
+            beam_width: k,
+            commit_weight_max: config.window.commit_weight_max,
+            residual_decoder,
+        })
+    }
+
+    /// Number of windows.
+    #[must_use]
+    pub fn num_windows(&self) -> usize {
+        self.windows.len()
+    }
+}
+
+impl<D: EdgeTrackingDecoder> ObservableDecoder for BeamSearchWindowedDecoder<D> {
+    fn decode_to_observables(&mut self, syndrome: &[u8]) -> Result<u64, DecoderError> {
+        let k = self.beam_width;
+        let commit_weight_max = self.commit_weight_max;
+
+        // Initialize beam with K identical empty hypotheses.
+        let mut beam: Vec<Hypothesis> = (0..k)
+            .map(|_| Hypothesis {
+                correction_effect: vec![0u8; self.num_detectors],
+                obs_mask: 0,
+                total_weight: 0.0,
+            })
+            .collect();
+
+        // Process each window: expand K hypotheses × K decoders → prune to K.
+        for window in &mut self.windows {
+            let actual_k = window.decoders.len();
+            let mut candidates: Vec<Hypothesis> = Vec::with_capacity(beam.len() * actual_k);
+
+            // Build window syndrome from the original (Phase-1 windows are
+            // independent — correction_effect is only used for Phase-2 residual).
+            let mut window_syn = vec![0u8; window.num_local];
+            for (local_id, &global_id) in window.local_to_global.iter().enumerate() {
+                let gid = global_id as usize;
+                if gid < syndrome.len() {
+                    window_syn[local_id] = syndrome[gid];
+                }
+            }
+
+            for hyp in &beam {
+                // Decode with each perturbed decoder.
+                for decoder in &mut window.decoders {
+                    let (_, matched_edges) = decoder.decode_with_matching(&window_syn)?;
+
+                    let mut new_obs = hyp.obs_mask;
+                    let mut new_correction = hyp.correction_effect.clone();
+                    let mut new_weight = hyp.total_weight;
+                    let boundary = window.num_local as u32;
+
+                    for &edge_idx in &matched_edges {
+                        let n1 = decoder.edge_node1(edge_idx);
+                        let n2 = decoder.edge_node2(edge_idx);
+
+                        let n1_core = n1 >= boundary
+                            || ((n1 as usize) < window.is_core.len()
+                                && window.is_core[n1 as usize]);
+                        let n2_core = n2 >= boundary
+                            || ((n2 as usize) < window.is_core.len()
+                                && window.is_core[n2 as usize]);
+
+                        let weight_ok = commit_weight_max <= 0.0
+                            || decoder.edge_weight(edge_idx) <= commit_weight_max;
+
+                        if n1_core && n2_core && weight_ok {
+                            new_obs ^= decoder.edge_obs_mask(edge_idx);
+                            new_weight += decoder.edge_weight(edge_idx);
+
+                            if (n1 as usize) < window.num_local {
+                                let gid = window.local_to_global[n1 as usize] as usize;
+                                new_correction[gid] ^= 1;
+                            }
+                            if (n2 as usize) < window.num_local {
+                                let gid = window.local_to_global[n2 as usize] as usize;
+                                new_correction[gid] ^= 1;
+                            }
+                        }
+                    }
+
+                    candidates.push(Hypothesis {
+                        correction_effect: new_correction,
+                        obs_mask: new_obs,
+                        total_weight: new_weight,
+                    });
+                }
+            }
+
+            // Prune: sort by total weight (lower = more likely), dedup, truncate.
+            candidates.sort_by(|a, b| {
+                a.total_weight
+                    .partial_cmp(&b.total_weight)
+                    .unwrap_or(std::cmp::Ordering::Equal)
+            });
+            candidates.dedup_by(|a, b| a.correction_effect == b.correction_effect);
+            candidates.truncate(k);
+            beam = candidates;
+        }
+
+        // Pick the result via majority vote across surviving hypotheses.
+        // Each hypothesis may have a different Phase-1 obs_mask; we also run
+        // Phase-2 on each to get the complete observable prediction.
+        if beam.is_empty() {
+            return Ok(0);
+        }
+
+        // Collect final observable predictions from each hypothesis.
+        let mut predictions: Vec<u64> = Vec::with_capacity(beam.len());
+        if let Some(ref mut residual_dec) = self.residual_decoder {
+            for hyp in &beam {
+                let mut residual_syn = vec![0u8; self.num_detectors];
+                for (i, &s) in syndrome.iter().enumerate() {
+                    if i < self.num_detectors {
+                        residual_syn[i] = s ^ hyp.correction_effect[i];
+                    }
+                }
+                let phase2_obs = residual_dec.decode_to_observables(&residual_syn)?;
+                predictions.push(hyp.obs_mask ^ phase2_obs);
+            }
+        } else {
+            for hyp in &beam {
+                predictions.push(hyp.obs_mask);
+            }
+        }
+
+        // Majority vote across hypotheses (per observable bit).
+        let half = predictions.len() / 2;
+        let mut result = 0u64;
+        for bit in 0..64u32 {
+            let mask = 1u64 << bit;
+            let count = predictions.iter().filter(|&&p| p & mask != 0).count();
+            if count > half {
+                result |= mask;
+            }
+        }
+        Ok(result)
+    }
+}
+
+#[cfg(test)]
+mod tests {
+    use super::*;
+
+    const D3_DEM: &str =
+        include_str!("../../../examples/surface_code_circuits/surface_code_d3_z_stim.dem");
+
+    fn uf_factory(dem: &str) -> Result<Box<dyn ObservableDecoder>, DecoderError> {
+        Ok(Box::new(crate::UfDecoder::from_dem(
+            dem,
+            crate::UfDecoderConfig::fast(),
+        )?))
+    }
+
+    fn uf_edge_factory(dem: &str) -> Result<crate::UfDecoder, DecoderError> {
+        crate::UfDecoder::from_dem(dem, crate::UfDecoderConfig::windowed())
+    }
+
+    #[test]
+    fn test_windowed_construction() {
+        let dec = WindowedDecoder::from_dem(D3_DEM, WindowedConfig::default(), uf_factory);
+        assert!(dec.is_ok());
+        assert!(dec.unwrap().num_windows() > 0);
+    }
+
+    #[test]
+    fn test_windowed_no_errors() {
+        let graph = DemMatchingGraph::from_dem_str(D3_DEM).unwrap();
+        let mut dec =
+            WindowedDecoder::from_dem(D3_DEM, WindowedConfig::default(), uf_factory).unwrap();
+        let obs = dec.decode_to_observables(&vec![0u8; graph.num_detectors]);
+        assert!(obs.is_ok());
+        assert_eq!(obs.unwrap(), 0);
+    }
+
+    #[test]
+    fn test_single_window_matches_full() {
+        let graph = DemMatchingGraph::from_dem_str(D3_DEM).unwrap();
+        let config = WindowedConfig {
+            step_size: 100,
+            buffer_size: 0,
+            ..Default::default()
+        };
+        let mut wdec = WindowedDecoder::from_dem(D3_DEM, config, uf_factory).unwrap();
+        let mut udec = crate::UfDecoder::from_dem(D3_DEM, crate::UfDecoderConfig::fast()).unwrap();
+
+        let syn = vec![0u8; graph.num_detectors];
+        assert_eq!(
+            wdec.decode_to_observables(&syn).unwrap(),
+            udec.decode_to_observables(&syn).unwrap(),
+        );
+    }
+
+    #[test]
+    fn test_overlapping_construction() {
+        let config = WindowedConfig {
+            step_size: 3,
+            buffer_size: 2,
+            ..Default::default()
+        };
+        let dec = OverlappingWindowedDecoder::from_dem(D3_DEM, config, uf_edge_factory);
+        assert!(dec.is_ok());
+        assert!(dec.unwrap().num_windows() > 0);
+    }
+
+    #[test]
+    fn test_overlapping_no_errors() {
+        let graph = DemMatchingGraph::from_dem_str(D3_DEM).unwrap();
+        let config = WindowedConfig {
+            step_size: 3,
+            buffer_size: 2,
+            ..Default::default()
+        };
+        let mut dec =
+            OverlappingWindowedDecoder::from_dem(D3_DEM, config, uf_edge_factory).unwrap();
+        let obs = dec.decode_to_observables(&vec![0u8; graph.num_detectors]);
+        assert!(obs.is_ok());
+        assert_eq!(obs.unwrap(), 0);
+    }
+
+    #[test]
+    fn test_overlapping_single_window() {
+        let graph = DemMatchingGraph::from_dem_str(D3_DEM).unwrap();
+        let config = WindowedConfig {
+            step_size: 100,
+            buffer_size: 5,
+            ..Default::default()
+        };
+        let mut dec =
+            OverlappingWindowedDecoder::from_dem(D3_DEM, config, uf_edge_factory).unwrap();
+        assert_eq!(dec.num_windows(), 1);
+        let syn = vec![0u8; graph.num_detectors];
+        assert_eq!(dec.decode_to_observables(&syn).unwrap(), 0);
+    }
+
+    #[test]
+    fn test_sandwich_construction() {
+        let config = WindowedConfig {
+            step_size: 3,
+            buffer_size: 3,
+            ..Default::default()
+        };
+        let dec = SandwichWindowedDecoder::from_dem(D3_DEM, config, uf_edge_factory, uf_factory);
+        assert!(dec.is_ok());
+        let dec = dec.unwrap();
+        assert!(dec.num_windows() > 0);
+    }
+
+    #[test]
+    fn test_sandwich_no_errors() {
+        let graph = DemMatchingGraph::from_dem_str(D3_DEM).unwrap();
+        let config = WindowedConfig {
+            step_size: 3,
+            buffer_size: 3,
+            ..Default::default()
+        };
+        let mut dec =
+            SandwichWindowedDecoder::from_dem(D3_DEM, config, uf_edge_factory, uf_factory).unwrap();
+        let obs = dec.decode_to_observables(&vec![0u8; graph.num_detectors]);
+        assert!(obs.is_ok());
+        assert_eq!(obs.unwrap(), 0);
+    }
+
+    #[test]
+    fn test_sandwich_parallel_matches_sequential() {
+        let graph = DemMatchingGraph::from_dem_str(D3_DEM).unwrap();
+        let config = WindowedConfig {
+            step_size: 3,
+            buffer_size: 3,
+            ..Default::default()
+        };
+        let mut dec =
+            SandwichWindowedDecoder::from_dem(D3_DEM, config, uf_edge_factory, uf_factory).unwrap();
+
+        let syn = vec![0u8; graph.num_detectors];
+        let seq = dec.decode_to_observables(&syn).unwrap();
+        let par = dec.decode_parallel(&syn).unwrap();
+        assert_eq!(seq, par);
+    }
+
+    #[test]
+    fn test_streaming_construction() {
+        let config = WindowedConfig {
+            step_size: 3,
+            buffer_size: 2,
+            ..Default::default()
+        };
+        let dec = StreamingWindowedDecoder::from_dem(D3_DEM, config, uf_edge_factory);
+        assert!(dec.is_ok());
+    }
+
+    #[test]
+    fn test_streaming_no_errors() {
+        use pecos_decoder_core::streaming::StreamingDecoder;
+
+        let config = WindowedConfig {
+            step_size: 3,
+            buffer_size: 2,
+            ..Default::default()
+        };
+        let mut dec = StreamingWindowedDecoder::from_dem(D3_DEM, config, uf_edge_factory).unwrap();
+
+        // Feed empty rounds — no detectors fire.
+        let graph = DemMatchingGraph::from_dem_str(D3_DEM).unwrap();
+        let max_round = graph
+            .detector_coords
+            .iter()
+            .filter_map(|c| c.as_ref().and_then(|v| v.get(2)).copied())
+            .fold(0.0f64, f64::max) as usize;
+
+        for r in 0..=max_round {
+            dec.feed_round(r, &[]).unwrap();
+        }
+        dec.flush().unwrap();
+        assert_eq!(dec.accumulated_obs(), 0);
+    }
+
+    #[test]
+    fn test_beam_k1_matches_sandwich_nonzero() {
+        // K=1 beam with non-zero syndrome should match sandwich.
+        let graph = DemMatchingGraph::from_dem_str(D3_DEM).unwrap();
+        let wconfig = WindowedConfig {
+            step_size: 3,
+            buffer_size: 3,
+            commit_weight_max: 2.5,
+            ..Default::default()
+        };
+
+        let mut sandwich =
+            SandwichWindowedDecoder::from_dem(D3_DEM, wconfig, uf_edge_factory, uf_factory)
+                .unwrap();
+
+        let bconfig = BeamSearchConfig {
+            window: wconfig,
+            beam_width: 1,
+            perturbation_sigma: 0.0,
+            seed: 42,
+        };
+        let mut beam =
+            BeamSearchWindowedDecoder::from_dem(D3_DEM, bconfig, uf_edge_factory, Some(uf_factory))
+                .unwrap();
+
+        // Test with single-defect syndrome.
+        let mut syn = vec![0u8; graph.num_detectors];
+        syn[0] = 1;
+        let sw_obs = sandwich.decode_to_observables(&syn).unwrap();
+        let bm_obs = beam.decode_to_observables(&syn).unwrap();
+        assert_eq!(
+            sw_obs, bm_obs,
+            "K=1 beam should match sandwich. sw={sw_obs}, bm={bm_obs}"
+        );
+
+        // Test with two defects.
+        syn[0] = 1;
+        syn[1] = 1;
+        let sw_obs = sandwich.decode_to_observables(&syn).unwrap();
+        let bm_obs = beam.decode_to_observables(&syn).unwrap();
+        assert_eq!(
+            sw_obs, bm_obs,
+            "K=1 beam should match sandwich on 2 defects. sw={sw_obs}, bm={bm_obs}"
+        );
+    }
+
+    #[test]
+    fn test_beam_search_construction() {
+        let config = BeamSearchConfig {
+            window: WindowedConfig {
+                step_size: 3,
+                buffer_size: 3,
+                ..Default::default()
+            },
+            beam_width: 3,
+            perturbation_sigma: 0.5,
+            seed: 42,
+        };
+        let dec =
+            BeamSearchWindowedDecoder::from_dem(D3_DEM, config, uf_edge_factory, Some(uf_factory));
+        assert!(dec.is_ok());
+        assert!(dec.unwrap().num_windows() > 0);
+    }
+
+    #[test]
+    fn test_beam_k1_matches_sandwich() {
+        // K=1 beam with no perturbation should match the sandwich decoder.
+        let graph = DemMatchingGraph::from_dem_str(D3_DEM).unwrap();
+        let wconfig = WindowedConfig {
+            step_size: 3,
+            buffer_size: 3,
+            commit_weight_max: 2.5,
+            ..Default::default()
+        };
+
+        // Sandwich
+        let mut sandwich =
+            SandwichWindowedDecoder::from_dem(D3_DEM, wconfig, uf_edge_factory, uf_factory)
+                .unwrap();
+
+        // Beam K=1
+        let bconfig = BeamSearchConfig {
+            window: wconfig,
+            beam_width: 1,
+            perturbation_sigma: 0.0,
+            seed: 42,
+        };
+        let mut beam =
+            BeamSearchWindowedDecoder::from_dem(D3_DEM, bconfig, uf_edge_factory, Some(uf_factory))
+                .unwrap();
+
+        let syn = vec![0u8; graph.num_detectors];
+        let sw_obs = sandwich.decode_to_observables(&syn).unwrap();
+        let bm_obs = beam.decode_to_observables(&syn).unwrap();
+        assert_eq!(
+            sw_obs, bm_obs,
+            "K=1 beam should match sandwich on zero syndrome"
+        );
+    }
+
+    #[test]
+    fn test_beam_search_no_errors() {
+        let graph = DemMatchingGraph::from_dem_str(D3_DEM).unwrap();
+        let config = BeamSearchConfig {
+            window: WindowedConfig {
+                step_size: 3,
+                buffer_size: 3,
+                ..Default::default()
+            },
+            beam_width: 3,
+            perturbation_sigma: 0.5,
+            seed: 42,
+        };
+        let mut dec =
+            BeamSearchWindowedDecoder::from_dem(D3_DEM, config, uf_edge_factory, Some(uf_factory))
+                .unwrap();
+        let obs = dec.decode_to_observables(&vec![0u8; graph.num_detectors]);
+        assert!(obs.is_ok());
+        assert_eq!(obs.unwrap(), 0);
+    }
+}
diff --git a/crates/pecos-uf-decoder/tests/cross_decoder_tests.rs b/crates/pecos-uf-decoder/tests/cross_decoder_tests.rs
new file mode 100644
index 000000000..d7bec84d7
--- /dev/null
+++ b/crates/pecos-uf-decoder/tests/cross_decoder_tests.rs
@@ -0,0 +1,118 @@
+// Copyright 2026 The PECOS Developers
+//
+// Licensed under the Apache License, Version 2.0 (the "License"); you may not use this file except
+// in compliance with the License. You may obtain a copy of the License at
+//
+//     https://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software distributed under the License
+// is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express
+// or implied. See the License for the specific language governing permissions and limitations under
+// the License.
+
+//! Cross-decoder comparison: UF vs itself (consistency checks).
+//!
+//! We can't depend on pecos-pymatching here (C++ build), but we CAN
+//! verify that UF + ensemble composed of UF decoders all agree.
+
+use pecos_decoder_core::ObservableDecoder;
+use pecos_decoder_core::dem::DemMatchingGraph;
+use pecos_decoder_core::ensemble::EnsembleDecoder;
+use pecos_uf_decoder::{UfDecoder, UfDecoderConfig};
+
+const D3_DEM: &str =
+    include_str!("../../../examples/surface_code_circuits/surface_code_d3_z_stim.dem");
+
+/// An ensemble of 3 identical UF decoders must agree with a single UF decoder
+/// on every syndrome (since all members produce the same result, the majority
+/// vote is identical to any single member).
+#[test]
+fn test_ensemble_of_identical_decoders_matches_single() {
+    let graph = DemMatchingGraph::from_dem_str(D3_DEM).unwrap();
+
+    let mut single = UfDecoder::from_matching_graph(&graph, UfDecoderConfig::default());
+    let members: Vec<Box<dyn ObservableDecoder>> = (0..3)
+        .map(|_| {
+            Box::new(UfDecoder::from_matching_graph(
+                &graph,
+                UfDecoderConfig::default(),
+            )) as Box<dyn ObservableDecoder>
+        })
+        .collect();
+    let mut ensemble = EnsembleDecoder::new(members);
+
+    let mut rng = fastrand::Rng::with_seed(123);
+    for _ in 0..500 {
+        let mut syndrome = vec![0u8; graph.num_detectors];
+        for s in &mut syndrome {
+            if rng.f64() < 0.05 {
+                *s = 1;
+            }
+        }
+
+        let single_obs = single.decode_to_observables(&syndrome).unwrap();
+        let ensemble_obs = ensemble.decode_to_observables(&syndrome).unwrap();
+        assert_eq!(
+            single_obs, ensemble_obs,
+            "Ensemble of identical decoders diverged from single decoder"
+        );
+    }
+}
+
+/// Verify the UF decoder produces deterministic results across runs.
+#[test]
+fn test_deterministic_results() {
+    let graph = DemMatchingGraph::from_dem_str(D3_DEM).unwrap();
+
+    let mut dec1 = UfDecoder::from_matching_graph(&graph, UfDecoderConfig::default());
+    let mut dec2 = UfDecoder::from_matching_graph(&graph, UfDecoderConfig::default());
+
+    let mut rng = fastrand::Rng::with_seed(999);
+    for _ in 0..200 {
+        let mut syndrome = vec![0u8; graph.num_detectors];
+        for s in &mut syndrome {
+            if rng.f64() < 0.08 {
+                *s = 1;
+            }
+        }
+
+        let r1 = dec1.decode_to_observables(&syndrome).unwrap();
+        let r2 = dec2.decode_to_observables(&syndrome).unwrap();
+        assert_eq!(r1, r2, "Two identical decoders gave different results");
+    }
+}
+
+/// Test `MatchingDecoder` consistency: `decode_with_matching` and `decode_to_observables`
+/// must agree on the observable mask.
+#[test]
+fn test_matching_agrees_with_observable() {
+    use pecos_decoder_core::correlated_decoder::MatchingDecoder;
+
+    let graph = DemMatchingGraph::from_dem_str(D3_DEM).unwrap();
+    let mut dec = UfDecoder::from_matching_graph(&graph, UfDecoderConfig::default());
+
+    let mut rng = fastrand::Rng::with_seed(777);
+    for _ in 0..200 {
+        let mut syndrome = vec![0u8; graph.num_detectors];
+        for s in &mut syndrome {
+            if rng.f64() < 0.06 {
+                *s = 1;
+            }
+        }
+
+        let obs = dec.decode_to_observables(&syndrome).unwrap();
+
+        // Reset and decode again with matching
+        let (match_obs, edges) = dec.decode_with_matching(&syndrome).unwrap();
+
+        assert_eq!(
+            obs, match_obs,
+            "ObservableDecoder and MatchingDecoder disagree on observable mask"
+        );
+
+        // If there are matched edges, they should be valid indices
+        for &e in &edges {
+            assert!(e < dec.num_edges(), "Edge index {e} out of range");
+        }
+    }
+}
diff --git a/crates/pecos-uf-decoder/tests/integration_tests.rs b/crates/pecos-uf-decoder/tests/integration_tests.rs
new file mode 100644
index 000000000..985a179b9
--- /dev/null
+++ b/crates/pecos-uf-decoder/tests/integration_tests.rs
@@ -0,0 +1,173 @@
+// Copyright 2026 The PECOS Developers
+//
+// Licensed under the Apache License, Version 2.0 (the "License"); you may not use this file except
+// in compliance with the License. You may obtain a copy of the License at
+//
+//     https://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software distributed under the License
+// is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express
+// or implied. See the License for the specific language governing permissions and limitations under
+// the License.
+
+//! Integration tests for the UF decoder using realistic surface code DEMs.
+
+use pecos_decoder_core::ObservableDecoder;
+use pecos_decoder_core::dem::DemMatchingGraph;
+use pecos_uf_decoder::{UfDecoder, UfDecoderConfig};
+
+/// Distance-3 rotated surface code, Z basis, 3 rounds of syndrome extraction.
+/// This is a realistic DEM with 24 detectors and ~100 error mechanisms.
+/// Non-decomposed (for matching graph extraction).
+const D3_SURFACE_CODE_DEM: &str =
+    include_str!("../../../examples/surface_code_circuits/surface_code_d3_z_stim.dem");
+
+/// Check the decoder initializes correctly from a real surface code DEM.
+#[test]
+fn test_real_dem_construction() {
+    let graph = DemMatchingGraph::from_dem_str(D3_SURFACE_CODE_DEM).unwrap();
+    assert!(
+        graph.num_detectors >= 20,
+        "Expected 20+ detectors, got {}",
+        graph.num_detectors
+    );
+    assert!(
+        graph.edges.len() >= 10,
+        "Expected 10+ edges, got {}",
+        graph.edges.len()
+    );
+
+    let dec = UfDecoder::from_matching_graph(&graph, UfDecoderConfig::default());
+    assert_eq!(dec.num_detectors(), graph.num_detectors);
+    assert_eq!(dec.num_edges(), graph.edges.len());
+}
+
+/// Decode the trivial (no-error) syndrome -- should always give observable 0.
+#[test]
+fn test_real_dem_no_errors() {
+    let graph = DemMatchingGraph::from_dem_str(D3_SURFACE_CODE_DEM).unwrap();
+    let mut dec = UfDecoder::from_matching_graph(&graph, UfDecoderConfig::default());
+    let syndrome = vec![0u8; graph.num_detectors];
+    assert_eq!(dec.decode_syndrome(&syndrome), 0);
+}
+
+/// Decode single-defect syndromes (one detector triggered).
+/// Each should produce a valid correction (not panic, not hang).
+#[test]
+fn test_real_dem_single_defects() {
+    let graph = DemMatchingGraph::from_dem_str(D3_SURFACE_CODE_DEM).unwrap();
+    let mut dec = UfDecoder::from_matching_graph(&graph, UfDecoderConfig::default());
+
+    for d in 0..graph.num_detectors {
+        let mut syndrome = vec![0u8; graph.num_detectors];
+        syndrome[d] = 1;
+        // Should not panic or hang. Observable is either 0 or 1.
+        let obs = dec.decode_syndrome(&syndrome);
+        assert!(
+            obs <= 1,
+            "Observable mask {obs} too large for single-observable DEM"
+        );
+    }
+}
+
+/// Decode syndromes with two adjacent defects.
+/// For each edge in the matching graph, set both endpoint detectors and decode.
+#[test]
+fn test_real_dem_adjacent_pairs() {
+    let graph = DemMatchingGraph::from_dem_str(D3_SURFACE_CODE_DEM).unwrap();
+    let mut dec = UfDecoder::from_matching_graph(&graph, UfDecoderConfig::default());
+
+    for edge in &graph.edges {
+        let mut syndrome = vec![0u8; graph.num_detectors];
+        syndrome[edge.node1 as usize] = 1;
+        if let Some(n2) = edge.node2 {
+            syndrome[n2 as usize] = 1;
+        }
+        let obs = dec.decode_syndrome(&syndrome);
+        assert!(obs <= 1, "Observable mask {obs} too large");
+    }
+}
+
+/// Stress test: decode many random syndromes with even number of defects.
+/// Verify the decoder never panics or hangs, and results are in range.
+#[test]
+fn test_real_dem_random_syndromes() {
+    let graph = DemMatchingGraph::from_dem_str(D3_SURFACE_CODE_DEM).unwrap();
+    let mut dec = UfDecoder::from_matching_graph(&graph, UfDecoderConfig::default());
+    let mut rng = fastrand::Rng::with_seed(42);
+
+    for _ in 0..1000 {
+        let mut syndrome = vec![0u8; graph.num_detectors];
+        let mut num_defects = 0;
+        for s in &mut syndrome {
+            if rng.f64() < 0.05 {
+                *s = 1;
+                num_defects += 1;
+            }
+        }
+        // Ensure even number of defects (valid syndrome for surface codes).
+        if num_defects % 2 != 0 && !syndrome.is_empty() {
+            // Flip a random detector to make it even.
+            let idx = rng.usize(..syndrome.len());
+            syndrome[idx] ^= 1;
+        }
+
+        let obs = dec.decode_syndrome(&syndrome);
+        assert!(obs <= 1, "Observable mask {obs} too large");
+    }
+}
+
+/// Test via the `ObservableDecoder` trait (the actual interface used in production).
+#[test]
+fn test_observable_decoder_trait_real_dem() {
+    let graph = DemMatchingGraph::from_dem_str(D3_SURFACE_CODE_DEM).unwrap();
+    let mut dec = UfDecoder::from_matching_graph(&graph, UfDecoderConfig::default());
+    let syndrome = vec![0u8; graph.num_detectors];
+    let result = dec.decode_to_observables(&syndrome);
+    assert!(result.is_ok());
+    assert_eq!(result.unwrap(), 0);
+}
+
+/// Test `MatchingDecoder` trait on real DEM.
+#[test]
+fn test_matching_decoder_trait_real_dem() {
+    use pecos_decoder_core::correlated_decoder::MatchingDecoder;
+    let graph = DemMatchingGraph::from_dem_str(D3_SURFACE_CODE_DEM).unwrap();
+    let mut dec = UfDecoder::from_matching_graph(&graph, UfDecoderConfig::default());
+
+    // Two adjacent defects.
+    let edge = &graph.edges[0];
+    let mut syndrome = vec![0u8; graph.num_detectors];
+    syndrome[edge.node1 as usize] = 1;
+    if let Some(n2) = edge.node2 {
+        syndrome[n2 as usize] = 1;
+    }
+
+    let (obs, _matched_edges) = dec.decode_with_matching(&syndrome).unwrap();
+    assert!(obs <= 1);
+    // Predecoder may handle simple cases without tracking edges.
+    assert!(obs <= 1);
+}
+
+/// Buffer reuse stress test: alternate between zero and non-zero syndromes.
+/// Catches bugs where state leaks between shots.
+#[test]
+fn test_buffer_reuse_correctness() {
+    let graph = DemMatchingGraph::from_dem_str(D3_SURFACE_CODE_DEM).unwrap();
+    let mut dec = UfDecoder::from_matching_graph(&graph, UfDecoderConfig::default());
+    let zero_syndrome = vec![0u8; graph.num_detectors];
+
+    let mut defect_syndrome = vec![0u8; graph.num_detectors];
+    defect_syndrome[0] = 1;
+
+    for _ in 0..500 {
+        // Zero syndrome must always give 0.
+        assert_eq!(
+            dec.decode_syndrome(&zero_syndrome),
+            0,
+            "Buffer leak: non-zero after defect"
+        );
+        // Defect syndrome should give a consistent result.
+        let _ = dec.decode_syndrome(&defect_syndrome);
+    }
+}
diff --git a/crates/pecos/src/lib.rs b/crates/pecos/src/lib.rs
index 44588d851..95244ce20 100644
--- a/crates/pecos/src/lib.rs
+++ b/crates/pecos/src/lib.rs
@@ -57,7 +57,7 @@ pub mod quantum {
     };
     pub use pecos_quantum::{
         Attribute, Circuit, CircuitMut, CustomGateError, DagCircuit, DagWouldCycleError, Gate,
-        GateHandle, GateType, GateView, QubitId, Tick, TickCircuit,
+        GateHandle, GateType, GateView, QubitId, Tick, TickCircuit, TickGateError,
     };
     pub use pecos_quantum::{F2Matrix, PauliSequence, PauliSet, PauliStabilizerGroup};
 }
diff --git a/design/ENGINES_ARCHITECTURE.md b/design/ENGINES_ARCHITECTURE.md
deleted file mode 100644
index 72bfd9133..000000000
--- a/design/ENGINES_ARCHITECTURE.md
+++ /dev/null
@@ -1,3 +0,0 @@
-# Moved to pecos-docs vault
-
-This document has been moved to `~/Repos/pecos-docs/design/engines-architecture.md`.
diff --git a/design/OPERATOR_TYPE_SYSTEM.md b/design/OPERATOR_TYPE_SYSTEM.md
deleted file mode 100644
index 532d2e099..000000000
--- a/design/OPERATOR_TYPE_SYSTEM.md
+++ /dev/null
@@ -1,3 +0,0 @@
-# Moved to pecos-docs vault
-
-This document has been moved to `~/Repos/pecos-docs/design/operator-type-system.md`.
diff --git a/design/QIS_ARCHITECTURE.md b/design/QIS_ARCHITECTURE.md
deleted file mode 100644
index 03331b6a2..000000000
--- a/design/QIS_ARCHITECTURE.md
+++ /dev/null
@@ -1,3 +0,0 @@
-# Moved to pecos-docs vault
-
-This document has been moved to `~/Repos/pecos-docs/design/qis-architecture.md`.
diff --git a/design/STABILIZER_CODE_ARCHITECTURE.md b/design/STABILIZER_CODE_ARCHITECTURE.md
deleted file mode 100644
index b121b1859..000000000
--- a/design/STABILIZER_CODE_ARCHITECTURE.md
+++ /dev/null
@@ -1,3 +0,0 @@
-# Moved to pecos-docs vault
-
-This document has been moved to `~/Repos/pecos-docs/design/stabilizer-code-architecture.md`.
diff --git a/design/circuit-representations.md b/design/circuit-representations.md
deleted file mode 100644
index 746dd7601..000000000
--- a/design/circuit-representations.md
+++ /dev/null
@@ -1,3 +0,0 @@
-# Moved to pecos-docs vault
-
-This document has been moved to `~/Repos/pecos-docs/design/circuit-representations.md`.
diff --git a/design/pecos-cuquantum-plan.md b/design/pecos-cuquantum-plan.md
deleted file mode 100644
index 0a15b3003..000000000
--- a/design/pecos-cuquantum-plan.md
+++ /dev/null
@@ -1,3 +0,0 @@
-# Moved to pecos-docs vault
-
-This document has been moved to `~/Repos/pecos-docs/design/pecos-cuquantum-plan.md`.
diff --git a/design/proposals/byte_message_api_cleanup.md b/design/proposals/byte_message_api_cleanup.md
deleted file mode 100644
index 4725b8e6a..000000000
--- a/design/proposals/byte_message_api_cleanup.md
+++ /dev/null
@@ -1,3 +0,0 @@
-# Moved to pecos-docs vault
-
-This document has been moved to `~/Repos/pecos-docs/design/proposals/byte_message_api_cleanup.md`.
diff --git a/design/proposals/slr-ast.md b/design/proposals/slr-ast.md
deleted file mode 100644
index 2b1cd8130..000000000
--- a/design/proposals/slr-ast.md
+++ /dev/null
@@ -1,3 +0,0 @@
-# Moved to pecos-docs vault
-
-This document has been moved to `~/Repos/pecos-docs/design/proposals/slr-ast.md`.
diff --git a/design/proposals/slr-qubit-allocators.md b/design/proposals/slr-qubit-allocators.md
deleted file mode 100644
index 771ec8d25..000000000
--- a/design/proposals/slr-qubit-allocators.md
+++ /dev/null
@@ -1,3 +0,0 @@
-# Moved to pecos-docs vault
-
-This document has been moved to `~/Repos/pecos-docs/design/proposals/slr-qubit-allocators.md`.
diff --git a/design/python-classical-interpreter-suspected-bugs.md b/design/python-classical-interpreter-suspected-bugs.md
deleted file mode 100644
index 4cc8cbbff..000000000
--- a/design/python-classical-interpreter-suspected-bugs.md
+++ /dev/null
@@ -1,3 +0,0 @@
-# Moved to pecos-docs vault
-
-This document has been moved to `~/Repos/pecos-docs/design/python-classical-interpreter-suspected-bugs.md`.
diff --git a/design/rust-phir-classical-interpreter.md b/design/rust-phir-classical-interpreter.md
deleted file mode 100644
index b48a2d571..000000000
--- a/design/rust-phir-classical-interpreter.md
+++ /dev/null
@@ -1,3 +0,0 @@
-# Moved to pecos-docs vault
-
-This document has been moved to `~/Repos/pecos-docs/design/rust-phir-classical-interpreter-spec.md`.
diff --git a/design/stn_2d_geometry_backend.md b/design/stn_2d_geometry_backend.md
deleted file mode 100644
index 26b9552f0..000000000
--- a/design/stn_2d_geometry_backend.md
+++ /dev/null
@@ -1,3 +0,0 @@
-# Moved to pecos-docs vault
-
-This document has been moved to `~/Repos/pecos-docs/design/stab-tn/2d-geometry-backend.md`.
diff --git a/design/stn_orthogonal_directions.md b/design/stn_orthogonal_directions.md
deleted file mode 100644
index 2c1ebef8c..000000000
--- a/design/stn_orthogonal_directions.md
+++ /dev/null
@@ -1,3 +0,0 @@
-# Moved to pecos-docs vault
-
-This document has been moved to `~/Repos/pecos-docs/design/stab-tn/orthogonal-directions.md`.
diff --git a/docs/README.md b/docs/README.md
index fede603fb..9eab704d6 100644
--- a/docs/README.md
+++ b/docs/README.md
@@ -115,6 +115,7 @@ PECOS is available in multiple languages:
 This documentation is organized to help you get the most out of PECOS:
 
 - **[User Guide](user-guide/getting-started.md)**: Tutorials and guides for using PECOS
+- **[PECOS Concepts](user-guide/pecos-concepts.md)**: Core terminology for detectors, observables, tracked Paulis, gates, and noise
 - **[Concepts](concepts/index.md)**: Physics, math, and algorithms behind the simulators
 - **API Reference**: Detailed API documentation
     - [Python API](https://quantum-pecos.readthedocs.io/en/latest/)
diff --git a/docs/development/DEVELOPMENT.md b/docs/development/DEVELOPMENT.md
index 57dac9ab4..8ecee016e 100644
--- a/docs/development/DEVELOPMENT.md
+++ b/docs/development/DEVELOPMENT.md
@@ -28,15 +28,14 @@ For developers who want to contribute or modify PECOS:
 
 1. Make sure you have [Python](https://www.python.org/downloads/) and [Rust](https://www.rust-lang.org/tools/install) installed for your system.
 
-2. Install all dev tools with a single command:
+2. Install the pre-clone dev tools from crates.io:
    ```sh
-   cargo install --locked uv just pecos
+   cargo install --locked uv just
    ```
 
    This installs:
    - `uv` - Python package manager
    - `just` - Command runner for build tasks
-   - `pecos` - PECOS dev tools (llvm, cuda, rust, python commands)
 
 3. Clone the repository:
    ```sh
@@ -44,7 +43,14 @@ For developers who want to contribute or modify PECOS:
    cd PECOS
    ```
 
-4. Create the development environment:
+4. Install the PECOS developer CLI from the repo:
+   ```sh
+   cargo install --path crates/pecos-cli
+   ```
+
+   This installs the `pecos` binary (llvm, cuda, cuquantum, rust, python, deps commands).
+
+5. Create the development environment:
    ```sh
    uv sync
    ```
@@ -61,7 +67,7 @@ For developers who want to contribute or modify PECOS:
    Combine groups with multiple `--group` flags
    (e.g. `uv sync --group examples --group cuda`).
 
-5. **LLVM 14 Setup (Required for LLVM IR/QIS Support)**
+6. **LLVM 14 Setup (Required for LLVM IR/QIS Support)**
 
    PECOS requires LLVM version 14 for LLVM IR execution features.
 
@@ -73,7 +79,7 @@ For developers who want to contribute or modify PECOS:
 
    For detailed installation instructions for all platforms (macOS, Linux, Windows), see the [**LLVM Setup Guide**](../user-guide/llvm-setup.md).
 
-6. You may wish to explicitly activate the environment for development. To do so:
+7. You may wish to explicitly activate the environment for development. To do so:
 
     === "Linux/Mac"
         ```sh
@@ -85,24 +91,24 @@ For developers who want to contribute or modify PECOS:
         .\.venv\Scripts\activate
         ```
 
-6. Build the project in editable mode
+8. Build the project in editable mode
     ```sh
    just build
    ```
    Other build options: `just build-release` (optimized), `just build-native` (optimized for your CPU).
 
-7. Run all Python and Rust tests:
+9. Run all Python and Rust tests:
    ```sh
    just test
    ```
    Note: Make sure you have run a build command before running tests.
 
-8. Run linters using pre-commit (after [installing it](https://pre-commit.com/)) to make sure all everything is properly linted/formated
-   ```sh
-   just lint
-   ```
+10. Run linters using pre-commit (after [installing it](https://pre-commit.com/)) to make sure all everything is properly linted/formated
+    ```sh
+    just lint
+    ```
 
-9. To deactivate your development venv:
+11. To deactivate your development venv:
     ```sh
     deactivate
     ```
@@ -139,7 +145,7 @@ PECOS uses `~/.pecos/` to store external dependencies and build artifacts that c
 ```
 ~/.pecos/
 ├── llvm/       # LLVM-14 installation (for QIR/LLVM IR execution)
-├── deps/       # Downloaded C++ dependencies (Stim, QuEST, Qulacs, etc.)
+├── deps/       # Downloaded C++ dependencies (Stim, etc.)
 └── cache/      # Build artifacts and intermediate files
 ```
 
diff --git a/docs/development/ast-infrastructure.md b/docs/development/ast-infrastructure.md
index 97c04d192..67496cb84 100644
--- a/docs/development/ast-infrastructure.md
+++ b/docs/development/ast-infrastructure.md
@@ -25,6 +25,8 @@ Converts compiled Guppy programs (HUGR format) to SLR-AST for analysis and code
 
 **Key functions:**
 ```python
+from guppylang import guppy
+from guppylang.std.quantum import h, measure, qubit
 from pecos.circuit_converters.hugr_to_ast import guppy_to_ast, hugr_to_ast
 
 
@@ -145,9 +147,21 @@ print(qasm)
 ### Serialization Round-trip
 
 ```python
+from guppylang import guppy
+from guppylang.std.quantum import h, measure, qubit
+from pecos.circuit_converters.hugr_to_ast import guppy_to_ast
 from pecos.slr.ast.serialize import ast_to_json, json_to_ast
 from pecos.slr.ast.compare import ast_equal
 
+
+@guppy
+def my_circuit() -> bool:
+    q = qubit()
+    h(q)
+    return measure(q)
+
+
+ast = guppy_to_ast(my_circuit)
 json_str = ast_to_json(ast)
 restored = json_to_ast(json_str)
 assert ast_equal(ast, restored)
diff --git a/docs/development/foreign-plugins.md b/docs/development/foreign-plugins.md
index 3d4295ae5..041629656 100644
--- a/docs/development/foreign-plugins.md
+++ b/docs/development/foreign-plugins.md
@@ -98,6 +98,7 @@ class MyDecoder:
 
 # Wrap and use
 decoder = pecos_rslib.PyForeignDecoder(MyDecoder(100, 50))
+syndrome_bytes = bytes(100)
 result = decoder.decode(syndrome_bytes)
 ```
 
@@ -388,7 +389,7 @@ printf("Passed %u/%u tests\n", report.tests_passed, report.tests_run);
 
 ### From Rust
 
-```rust
+```rust,ignore
 let report = pecos_foreign::conformance::run_conformance_tests(&mut sim);
 assert!(report.all_passed());
 ```
@@ -438,10 +439,11 @@ When using foreign simulators with pecos-neo, the `gate_support` module (behind
 `neo` feature flag) automatically configures the `CircuitRunner` decomposition based
 on what the foreign simulator supports:
 
-```rust
+```rust,ignore
 use pecos_foreign::gate_support::configure_runner_for_foreign;
 
-let sim = ForeignSimulator::new(handle, vtable);
+let sim = unsafe { ForeignSimulator::new(handle, vtable, num_qubits) }
+    .expect("foreign simulator vtable must match PECOS");
 let mut runner = configure_runner_for_foreign(&sim);
 // If sim supports rotations: runner uses RX, RZ, RZZ natively
 // Otherwise: Clifford-only, everything decomposes into {SZ, H, CX}
diff --git a/docs/user-guide/circuit-representation.md b/docs/user-guide/circuit-representation.md
index 6a69fcdd9..291ab6d4b 100644
--- a/docs/user-guide/circuit-representation.md
+++ b/docs/user-guide/circuit-representation.md
@@ -245,8 +245,9 @@ Gates can have arbitrary metadata attached:
     # Multiple metadata entries
     circuit.cx([(0, 1)]).meta("duration_ns", 50)
 
-    # Measurements break the chain but still support metadata
-    circuit.mz([0]).meta("basis", "Z")
+    # Measurements return refs (not the circuit), so chain separately
+    circuit.mz([0])
+    circuit.meta("basis", "Z")
     ```
 
 === ":fontawesome-brands-rust: Rust"
@@ -261,8 +262,9 @@ Gates can have arbitrary metadata attached:
     // Multiple metadata entries
     circuit.cx(&[(0, 1)]).meta("duration_ns", Attribute::Int(50));
 
-    // Measurements break the chain but still support metadata
-    circuit.mz(&[0]).meta("basis", Attribute::String("Z".into()));
+    // Measurements return refs (not &mut Self), so chain separately
+    circuit.mz(&[0]);
+    circuit.meta("basis", Attribute::String("Z".into()));
     ```
 
 ### Circuit Analysis
@@ -272,7 +274,10 @@ Gates can have arbitrary metadata attached:
     from pecos.quantum import DagCircuit
 
     circuit = DagCircuit()
-    circuit.h([0]).cx([(0, 1)]).h([1]).cx([(1, 2)]).mz([0]).mz([1]).mz([2])
+    circuit.h([0]).cx([(0, 1)]).h([1]).cx([(1, 2)])
+    circuit.mz([0])
+    circuit.mz([1])
+    circuit.mz([2])
 
     # Basic metrics
     print(f"Total gates: {circuit.gate_count()}")
@@ -391,10 +396,12 @@ A time-sliced circuit representation where gates are organized into discrete tim
 
     print(f"Number of ticks: {circuit.num_ticks()}")
     print(f"Total gates: {circuit.gate_count()}")
+    print(f"Gate batches: {circuit.gate_batch_count()}")
     ```
 
 === ":fontawesome-brands-rust: Rust"
     ```rust
+    use pecos::core::Gate;
     use pecos::quantum::TickCircuit;
 
     let mut circuit = TickCircuit::new();
@@ -410,6 +417,7 @@ A time-sliced circuit representation where gates are organized into discrete tim
 
     println!("Number of ticks: {}", circuit.num_ticks());
     println!("Total gates: {}", circuit.gate_count());
+    println!("Gate batches: {}", circuit.gate_batch_count());
     ```
 
 ### Qubit Conflict Detection
@@ -440,7 +448,9 @@ TickCircuit prevents scheduling conflicting gates in the same tick:
     // tick.cx(&[(0, 1)]);
 
     // Use try_add_gate for fallible operations
-    if let Err(e) = tick.try_add_gate(Gate::cx(&[(0, 1)])) {
+    if let Err(pecos::quantum::TickGateError::QubitConflict(e)) =
+        tick.try_add_gate(Gate::cx(&[(0, 1)]))
+    {
         println!("Conflict on qubits: {:?}", e.conflicting_qubits);
     }
     ```
@@ -646,7 +656,7 @@ A directed acyclic graph with topological ordering and cycle prevention:
 | `cx(pairs)`, `szz(pairs)`, `rzz(theta, pairs)` | Two-qubit gates |
 | `mz(qubits)`, `pz(qubits)` | Measurement and preparation |
 | `meta(key, value)` | Attach metadata to last gate |
-| `gate_count()`, `depth()`, `width()` | Circuit metrics |
+| `gate_count()`, `gate_node_count()`, `depth()`, `width()` | Circuit metrics |
 | `qubits()` | List of qubits used |
 | `topological_order()` | Gates in dependency order |
 | `layers()` | Iterator over parallel gate layers |
@@ -659,7 +669,9 @@ A directed acyclic graph with topological ordering and cycle prevention:
 | `new()` | Create empty circuit |
 | `tick()` | Start a new time step |
 | `num_ticks()` | Number of time steps |
-| `gate_count()` | Total gates across all ticks |
+| `gate_count()` | Total gate applications across all ticks |
+| `gate_batch_count()` | Total stored compatible gate batches across all ticks |
+| `gate_batches()` | Stored gate batches with tick indices |
 | `set_meta(key, value)` | Circuit-level metadata |
 
 ### DAG Methods
diff --git a/docs/user-guide/cli.md b/docs/user-guide/cli.md
index 763badcd6..660b064ce 100644
--- a/docs/user-guide/cli.md
+++ b/docs/user-guide/cli.md
@@ -108,8 +108,6 @@ Compiled Features:
   [x] selene   - Selene QIS runtime
   [x] wasm     - WebAssembly foreign objects
   [ ] llvm     - LLVM/QIS compilation
-  [ ] quest    - QuEST simulator backend
-  [ ] qulacs   - Qulacs simulator backend
 
 Simulators:
   statevector  - Full quantum state simulation (default)
diff --git a/docs/user-guide/cuda-setup.md b/docs/user-guide/cuda-setup.md
index acac008bf..c8f90ddcd 100644
--- a/docs/user-guide/cuda-setup.md
+++ b/docs/user-guide/cuda-setup.md
@@ -319,7 +319,6 @@ pip install quantum-pecos
 | Simulator | Hardware | Qubits | Gates | Speed | Installation |
 |-----------|----------|--------|-------|-------|--------------|
 | StateVec (CPU) | Any | ~25 | All | Baseline | Easy |
-| Qulacs (CPU) | Any | ~28 | All | 2-3x faster | Easy |
 | CuStateVec (Python) | NVIDIA GPU | ~30 | All | 10-50x faster | Medium |
 | CudaStateVec (Rust) | NVIDIA GPU | ~30 | All | 10-50x faster | Complex |
 | CudaStabilizer (Rust) | NVIDIA GPU | 1000s | Clifford only | Very fast | Complex |
@@ -354,18 +353,6 @@ The Rust bindings provide direct cuQuantum integration without Python package de
 - Integration with quantum-pecos's HybridEngine
 - Reproducible simulations with seed support
 
-### Rust GPU Simulators (QuEST)
-
-**Status**: Limited Support (CPU-only with CUDA 13)
-
-- **Engine**: QuEST (Quantum Exact Simulation Toolkit)
-- **CUDA Version**: Requires CUDA 11 or 12 (incompatible with CUDA 13)
-- **Issue**: QuEST uses deprecated `thrust::unary_function` and `thrust::binary_function` classes that were removed in modern CUDA/Thrust versions
-- **Workaround**: Automatically falls back to CPU-only QuEST build
-- **Impact**: Minimal - use CudaStateVec or Python CuStateVec instead
-
-The Rust QuEST simulator is currently incompatible with CUDA 13 due to deprecated thrust classes.
-
 ## Rust cuQuantum Bindings Setup
 
 To use the Rust-based CUDA simulators (CudaStateVec, CudaStabilizer), you need:
@@ -377,6 +364,16 @@ To use the Rust-based CUDA simulators (CudaStateVec, CudaStabilizer), you need:
 
 ### Installing cuQuantum SDK
 
+**Recommended:** use the `pecos` CLI to download and install into `~/.pecos/deps/cuquantum/`:
+
+```bash
+pecos install cuquantum
+```
+
+This mirrors the LLVM setup flow and is the same pattern used by `pecos install llvm` / `pecos install cuda`. The PECOS build system then picks up the install automatically — no environment variables to set.
+
+**Manual install (if you already have cuQuantum or need a specific version):**
+
 1. Download from [NVIDIA cuQuantum](https://developer.nvidia.com/cuquantum-sdk)
 2. Extract to a known location (e.g., `/opt/nvidia/cuquantum`)
 3. Set environment variables:
@@ -511,5 +508,3 @@ To use GPU simulators in PECOS:
 - **For stabilizer simulations**: Use CudaStabilizer (Rust) for 1000s of qubits
 - **For reproducibility**: Rust bindings have full seed support
 - **For density matrices**: Use CuDensityMat (Rust) for open quantum systems
-
-**Note**: If you see warnings about QuEST GPU compilation failing, this is expected with CUDA 13 and does not affect the cuQuantum-based simulators.
diff --git a/docs/user-guide/fault-catalog.md b/docs/user-guide/fault-catalog.md
new file mode 100644
index 000000000..f5a7e2f18
--- /dev/null
+++ b/docs/user-guide/fault-catalog.md
@@ -0,0 +1,590 @@
+# Fault Catalog and Measurement Sampling
+
+## Quick start
+
+If you have a surface code and want to simulate noisy measurements:
+
+<!--setup-->
+```python
+from pecos.qec.surface import SurfacePatch
+from pecos.qec.surface.decode import _build_surface_tick_circuit_for_native_model
+from pecos_rslib_exp import sim_neo, meas_sampling, depolarizing
+
+patch = SurfacePatch.create(distance=3)
+tc = _build_surface_tick_circuit_for_native_model(patch, num_rounds=6, basis="Z")
+
+result = (
+    sim_neo(tc)
+    .quantum(meas_sampling())
+    .noise(depolarizing().p1(0.001).p2(0.01).p_meas(0.005).p_prep(0.005))
+    .shots(10000)
+    .seed(42)
+    .run()
+)
+
+# result[shot] gives measurement outcomes for each shot
+print(f"{len(result)} shots, {len(result[0])} measurements each")
+```
+
+If you want to inspect what faults are possible in that circuit:
+
+<!--continuation; requires-module: pecos_rslib_exp-->
+```python
+from pecos_rslib_exp import fault_catalog
+
+# Build structural catalog (no noise commitment):
+catalog = fault_catalog(tc)
+print(f"{len(catalog)} fault locations")
+
+# Parameterize to get probabilities:
+catalog.with_noise(p1=0.001, p2=0.01, p_meas=0.005, p_prep=0.005)
+```
+
+The rest of this tutorial uses a small hand-built circuit to explain the
+concepts. Everything works the same way with surface codes or any other
+`TickCircuit`.
+
+Note: when using circuit builders like `SurfacePatch`, the detector and
+observable metadata is set automatically. The hand-built examples below
+set metadata explicitly via `set_meta` -- you normally don't need to write
+JSON strings by hand.
+
+## Core model
+
+- Each `FaultLocation` is an independent physical fault mechanism (one per
+  noisy gate in the circuit).
+- Each location has one or more `FaultAlternative`s (e.g., X/Y/Z for a
+  single-qubit depolarizing channel, 15 alternatives for two-qubit).
+- When the location fires, exactly one alternative is chosen uniformly.
+- Each alternative records which measurements, detectors, observables, and
+  tracked Paulis it flips.
+- Multi-fault effects combine by XOR parity.
+
+## Structural vs Parameterized Catalogs
+
+A fault catalog can be built in two ways:
+
+**Structural (no noise):** includes all fault locations for all gate types.
+Probabilities are zero. Use this for topology queries, fault anatomy
+exploration, or as a reusable base for parameter sweeps.
+
+**Parameterized (with noise):** fills in probabilities based on a stochastic
+noise model. Use this for sampling, decoding, and probability-weighted queries.
+
+<!--setup-->
+```python
+from pecos import Z
+from pecos.quantum import TickCircuit
+from pecos_rslib_exp import depolarizing, fault_catalog
+
+circuit = TickCircuit()
+circuit.tick().h([0])
+circuit.tick().mz([0])
+
+circuit.set_meta("num_measurements", "1")
+circuit.set_meta("detectors", '[{"records":[-1]}]')
+circuit.set_meta("observables", '[{"records":[-1]}]')
+
+# Structural -- all locations, zero probabilities:
+catalog = fault_catalog(circuit)
+
+# Parameterize with noise:
+catalog.with_noise(p1=0.03, p2=0.0, p_meas=0.01, p_prep=0.0)
+
+# Or one-shot (structural + parameterize in one call):
+catalog = fault_catalog(circuit, p1=0.03, p2=0.0, p_meas=0.01, p_prep=0.0)
+```
+
+The circuit must have detector and observable metadata (`num_measurements`,
+`detectors`, `observables`). The catalog uses this metadata to map raw
+measurement flips into detector and observable flips. Without metadata,
+structural fields like `affected_detectors` will be empty, but
+`affected_measurements` are still computed from Pauli propagation.
+
+## Re-parameterization
+
+The expensive work (Pauli propagation, detector mapping) is done once during
+construction. Changing noise is cheap -- it just updates probability fields:
+
+<!--continuation-->
+```python
+catalog = fault_catalog(circuit)
+
+# Sweep noise parameters without rebuilding the catalog:
+for p in [0.001, 0.005, 0.01, 0.05]:
+    catalog.with_noise(p1=p * 0.1, p2=p, p_meas=p * 0.5, p_prep=p * 0.5)
+    # ... decode, sample, analyze ...
+
+# Independent copy for parallel comparison:
+catalog_a = catalog.parameterized(p1=0.001, p2=0.01, p_meas=0.005, p_prep=0.005)
+catalog_b = catalog.parameterized(p1=0.01, p2=0.1, p_meas=0.05, p_prep=0.05)
+```
+
+Note: decoders and samplers built from a catalog are snapshots. They read
+probabilities at construction time. Re-parameterizing the catalog does NOT
+update existing decoders or plans.
+
+The returned object is sequence-like:
+
+<!--continuation-->
+```python
+print(len(catalog))
+print(catalog[0])
+print(catalog[-1])
+
+for location in catalog:
+    print(location.tick, location.gate_type, location.channel)
+```
+
+It also exposes the underlying locations list:
+
+```python
+locations = catalog.locations
+```
+
+## Location Fields
+
+Each `FaultLocation` represents one physical fault mechanism.
+
+| Field | Meaning |
+|---|---|
+| `tick` | Tick index in the `TickCircuit` |
+| `gate_index` | Gate index within the tick |
+| `gate_type` | Gate name, such as `"H"`, `"CX"`, or `"MZ"` |
+| `qubits` | Qubits acted on by this gate |
+| `channel` | `"p1"`, `"p2"`, `"p_meas"`, or `"p_prep"` |
+| `channel_probability` | Total probability the mechanism fires (0 if unparameterized) |
+| `no_fault_probability` | `1 - channel_probability` |
+| `num_alternatives` | Number of alternatives at this location, `k_i` |
+| `faults` | List of `FaultAlternative` objects |
+
+Example:
+
+```python
+for loc in catalog:
+    print(
+        loc.tick,
+        loc.gate_type,
+        loc.channel,
+        loc.channel_probability,
+        loc.no_fault_probability,
+        loc.num_alternatives,
+    )
+```
+
+The catalog includes locations with nonzero channel probability even when all
+alternatives have empty detector/observable effects. This is necessary for
+correct probability accounting.
+
+## Alternative Fields
+
+Each `FaultAlternative` is one possible outcome when its parent location fires.
+
+| Field | Meaning |
+|---|---|
+| `kind` | `"pauli"`, `"measurement_flip"`, or `"prep_flip"` |
+| `pauli` | A PECOS `PauliString` for Pauli faults, or `None` |
+| `measurements` | Raw measurement indices flipped |
+| `detectors` | Detector indices flipped |
+| `observables` | Observable indices flipped |
+| `tracked_paulis` | Tracked Pauli indices flipped |
+| `conditional_probability` | `1 / k_i` (structural, does not depend on noise) |
+| `absolute_probability` | `p_i / k_i` (0 if unparameterized) |
+| `channel_probability` | Same `p_i` as the parent location |
+
+The four effect fields (`measurements`, `detectors`, `observables`,
+`tracked_paulis`) are structural -- they depend on the circuit topology, not the
+noise model. They are populated during construction and never change when
+noise is re-parameterized.
+
+Example:
+
+```python
+for loc in catalog:
+    for fault in loc.faults:
+        print(f"  {fault.kind}: {fault.pauli}")
+        print(f"    measurements: {fault.measurements}")
+        print(f"    detectors:    {fault.detectors}")
+        print(f"    observables:  {fault.observables}")
+        print(f"    tracked_paulis:  {fault.tracked_paulis}")
+```
+
+`fault.absolute_probability` is local to one fault location. It is not the
+probability of "this alternative and no other faults in the circuit."
+
+## Probability Semantics
+
+Understanding probabilities matters when you are building decoders, computing
+thresholds, or verifying that a noise model produces the expected error rates.
+
+For location `i`:
+
+```text
+p_i = location.channel_probability
+k_i = location.num_alternatives
+P(no fault at i) = 1 - p_i
+P(specific alternative at i) = p_i / k_i
+```
+
+For a full-circuit configuration:
+
+```text
+configuration_probability
+  = product selected alternatives (p_i / k_i)
+    * product unselected locations (1 - p_i)
+```
+
+For a single selected alternative at location `i`, the full event probability is:
+
+```python
+selected_location_index = 0
+fault = catalog[selected_location_index].faults[0]
+
+event_probability = fault.absolute_probability
+for j, loc in enumerate(catalog.locations):
+    if j != selected_location_index:
+        event_probability *= loc.no_fault_probability
+```
+
+## Lazy k-Fault Configurations
+
+Use `catalog.fault_configurations(k)` to enumerate every way exactly `k`
+faults can occur simultaneously. This is the foundation for building lookup
+decoders, computing truncated ML tables, and analyzing multi-fault error
+patterns.
+
+For `k = 0`, the iterator yields exactly one no-fault configuration. Its
+probability is the product of every location's `no_fault_probability`:
+
+```python
+configs = list(catalog.fault_configurations(0))
+assert len(configs) == 1
+
+no_fault = configs[0]
+assert no_fault.location_indices == []
+assert no_fault.alternative_indices == []
+assert no_fault.measurements == []
+assert no_fault.detectors == []
+assert no_fault.observables == []
+assert no_fault.selected_probability == 1.0
+
+expected = 1.0
+for loc in catalog.locations:
+    expected *= loc.no_fault_probability
+
+assert abs(no_fault.configuration_probability - expected) < 1e-12
+```
+
+For `k > 0`, each yielded `FaultConfiguration` has:
+
+| Field | Meaning |
+|---|---|
+| `location_indices` | Indices into `catalog.locations` |
+| `alternative_indices` | Chosen alternative index for each selected location |
+| `locations` | The selected `FaultLocation` objects |
+| `faults` | The selected `FaultAlternative` objects |
+| `measurements` | XOR-combined measurement effects |
+| `detectors` | XOR-combined detector effects |
+| `observables` | XOR-combined observable effects |
+| `selected_probability` | Product of selected `absolute_probability` values |
+| `configuration_probability` | Selected probability times no-fault probabilities for unselected locations |
+
+The iterator is lazy -- it yields one configuration at a time without
+materializing all combinations up front:
+
+```python
+it = catalog.fault_configurations(1)
+first = next(it)
+
+print(first.location_indices)
+print(first.alternative_indices)
+print(first.detectors)
+print(first.observables)
+print(first.configuration_probability)
+```
+
+## XOR Parity
+
+When multiple faults occur simultaneously, their effects combine by XOR parity.
+If two faults flip the same detector, that detector cancels. This is fundamental
+to QEC -- it's why weight-2 errors can be undetectable even when each individual
+fault triggers detectors.
+
+```python
+for event in catalog.fault_configurations(2):
+    print(event.detectors, event.observables, event.configuration_probability)
+```
+
+This is the right behavior for detector syndromes and logical observable flips.
+It is also why low-weight decoder tests should apply the selected correction and
+check the residual logical by XOR.
+
+## Building a Small Lookup Table
+
+This example builds a complete lookup table in Python by exhaustively
+enumerating fault configurations. This is useful for understanding the API
+and for small circuits. For larger codes, use the Rust `TargetedLookupDecoder`
+which searches on-demand without precomputing all syndromes.
+
+A lookup decoder table groups configuration probability by:
+
+```text
+detector syndrome -> logical observable class -> probability
+```
+
+For a truncated table:
+
+```python
+from collections import defaultdict
+
+
+def add_weight(table, syndrome, logical, probability):
+    table[tuple(syndrome)][tuple(logical)] += probability
+
+
+table = defaultdict(lambda: defaultdict(float))
+
+for k in range(0, 3):
+    for event in catalog.fault_configurations(k):
+        add_weight(
+            table,
+            event.detectors,
+            event.observables,
+            event.configuration_probability,
+        )
+
+decoder = {}
+for syndrome, logical_weights in table.items():
+    best_logical = max(logical_weights.items(), key=lambda item: item[1])[0]
+    decoder[syndrome] = best_logical
+
+
+# Apply the decoder: XOR the event's logical class with the correction
+def xor_sorted(a, b):
+    out = set(a)
+    for item in b:
+        if item in out:
+            out.remove(item)
+        else:
+            out.add(item)
+    return tuple(sorted(out))
+
+
+for event in catalog.fault_configurations(1):
+    correction = decoder[tuple(event.detectors)]
+    residual = xor_sorted(event.observables, correction)
+    print(event.detectors, residual)
+```
+
+## Rust API
+
+The Rust API lives in `pecos-qec`:
+
+<!--setup-->
+```rust
+use pecos_qec::fault_tolerance::fault_sampler::{
+    FaultCatalog, StochasticNoiseParams,
+};
+use pecos_quantum::{Attribute, TickCircuit};
+
+let mut circuit = TickCircuit::new();
+circuit.tick().h(&[0]);
+circuit.tick().mz(&[0]);
+
+circuit.set_meta("num_measurements", Attribute::String("1".into()));
+circuit.set_meta(
+    "detectors",
+    Attribute::String(r#"[{"records":[-1]}]"#.into()),
+);
+circuit.set_meta(
+    "observables",
+    Attribute::String(r#"[{"records":[-1]}]"#.into()),
+);
+
+// Structural catalog (no noise):
+let mut catalog = FaultCatalog::from_circuit(&circuit).unwrap();
+
+// Parameterize:
+let noise = StochasticNoiseParams {
+    p1: 0.03,
+    p2: 0.0,
+    p_meas: 0.01,
+    p_prep: 0.0,
+};
+catalog.with_noise(&noise);
+
+// Or one-shot convenience:
+// let catalog = build_fault_catalog(&circuit, &noise).unwrap();
+```
+
+Iterate locations and alternatives:
+
+<!--continuation-->
+```rust
+for loc in &catalog.locations {
+    println!(
+        "tick={} gate={:?} channel={:?} p={} k={}",
+        loc.tick,
+        loc.gate_type,
+        loc.channel,
+        loc.channel_probability,
+        loc.num_alternatives
+    );
+
+    for fault in &loc.faults {
+        println!(
+            "  {:?} dets={:?} obs={:?} tracked={:?} p_alt={}",
+            fault.kind,
+            fault.affected_detectors,
+            fault.affected_observables,
+            fault.affected_tracked_paulis,
+            fault.absolute_probability
+        );
+    }
+}
+```
+
+Iterate configurations:
+
+<!--continuation-->
+```rust
+for event in catalog.fault_configurations(2) {
+    println!(
+        "locations={:?} alternatives={:?} dets={:?} obs={:?} p={}",
+        event.location_indices,
+        event.alternative_indices,
+        event.affected_detectors,
+        event.affected_observables,
+        event.configuration_probability
+    );
+}
+```
+
+The Rust iterator borrows the catalog and does not materialize all
+configurations up front. On an unparameterized catalog, `fault_configurations(k)`
+for k > 0 yields nothing (all probabilities are zero).
+
+## Fault Anatomy Exploration
+
+The structural catalog (no noise needed) lets you explore every fault event:
+
+<!--expect-output-block-->
+```python
+catalog = fault_catalog(circuit)
+
+# What faults can flip detector D0?
+for loc in catalog:
+    for alt in loc.faults:
+        if 0 in alt.detectors:
+            print(f"D0 flipped by {alt.pauli} at {loc.gate_type}({loc.qubits})")
+
+# Find undetectable weight-2 logical errors:
+catalog.with_noise(p1=0.01, p2=0.05, p_meas=0.01, p_prep=0.01)
+for config in catalog.fault_configurations(2):
+    if config.observables and not config.detectors:
+        print(f"Undetectable: locations {config.location_indices}")
+```
+```output
+D0 flipped by X_0 at H([0])
+D0 flipped by Y_0 at H([0])
+D0 flipped by None at MZ([0])
+```
+
+## Tracked Operators
+
+Tracked Paulis are Pauli strings that the catalog monitors for
+anticommutation with fault events. Unlike observables, they have no
+measurement records -- they are detected by forward Pauli propagation.
+See [PECOS Concepts](pecos-concepts.md) for the full detector, observable,
+and tracked-Pauli distinction.
+
+Add tracked Paulis to a circuit via `tracked_pauli`:
+
+<!--expect-output-block-->
+```python
+tc2 = TickCircuit()
+tc2.tick().h([0])
+tc2.set_meta("num_measurements", "0")
+tc2.set_meta("detectors", "[]")
+tc2.set_meta("observables", "[]")
+# Track Z on qubit 0 -- X and Y faults after H anticommute with Z
+tc2.tracked_pauli(Z(0), label="track_Z0")
+
+cat2 = fault_catalog(tc2, p1=0.01, p2=0.0, p_meas=0.0, p_prep=0.0)
+for loc in cat2:
+    for alt in loc.faults:
+        if alt.tracked_paulis:
+            print(f"{alt.pauli} flips tracked Paulis {alt.tracked_paulis}")
+```
+```output
+X_0 flips tracked Paulis [0]
+Y_0 flips tracked Paulis [0]
+```
+
+No measurement is needed -- the catalog detects that X and Y faults after H
+anticommute with the tracked Z Pauli. This is useful for studying logical
+operator propagation independently of measurement outcomes.
+
+## Raw Measurement Sampling
+
+The `meas_sampling()` backend in `sim_neo` uses the fault catalog internally
+to produce raw measurement bitstrings:
+
+```python
+from pecos_rslib_exp import sim_neo, meas_sampling, depolarizing
+
+result = (
+    sim_neo(circuit)
+    .quantum(meas_sampling())
+    .noise(depolarizing().p1(0.001).p2(0.01).p_meas(0.005).p_prep(0.005))
+    .shots(10000)
+    .seed(42)
+    .run()
+)
+
+# result[shot] gives measurement outcomes for each shot
+for shot in range(len(result)):
+    measurements = list(result[shot])
+```
+
+The sampling architecture:
+- **Ideal values** from symbolic stabilizer simulation (respects measurement
+  correlations across resets)
+- **Physical faults** from geometric skip sampling (O(fired events) per shot)
+- Raw measurement = ideal XOR faults
+
+This is fast (millions of shots per second at small distances) and produces
+the same measurement format as gate-by-gate stabilizer simulation.
+
+## Common Pitfalls
+
+- `fault.absolute_probability` is `p_i / k_i`, not a full-circuit event
+  probability.
+- Empty-effect alternatives (no measurements flipped) are real -- they
+  represent Pauli errors that commute with subsequent measurements. They
+  must stay in the catalog for the correct uniform denominator.
+- `catalog.fault_configurations(k)` means exactly `k` distinct physical
+  locations fire, not at most `k`. Only alternatives with positive
+  `absolute_probability` are yielded. On an unparameterized catalog, k > 0
+  yields nothing. On a parameterized catalog with some channels zeroed,
+  locations from those channels are skipped.
+- Detector and observable metadata must be correct before building the catalog.
+  Missing boundary detectors can make a correct decoder appear to fail.
+- `with_noise()` mutates the catalog in place. Previously held Python
+  references to locations and faults update automatically. Decoders and
+  samplers do NOT update -- they are snapshots.
+- The structural catalog includes ALL locations even when a channel
+  probability is zero. The `meas_sampling()` backend internally filters
+  zero-probability locations when building raw sampling mechanisms.
+
+## Larger Example
+
+The Rust example `examples/surface/d3_fault_catalog_lookup.rs` builds a
+distance-3 surface-code memory experiment, walks `fault_configurations(k)` for
+`k = 0..=2`, and aggregates a truncated lookup decoder table.
+
+Run it from the repository root:
+
+```bash
+cargo run -p pecos-qec --example surface_d3_fault_catalog_lookup
+```
diff --git a/docs/user-guide/fault-tolerance.md b/docs/user-guide/fault-tolerance.md
index dabe5955f..2fff540cf 100644
--- a/docs/user-guide/fault-tolerance.md
+++ b/docs/user-guide/fault-tolerance.md
@@ -33,7 +33,8 @@ A code is **fault-tolerant at weight t** if no weight-t error is an undetectable
 
 ```rust
 use pecos_qec::{StabilizerCodeSpec, StabilizerFlipChecker, ErrorClass};
-use pecos_core::{Xs, Zs, PauliString, QuarterPhase};
+use pecos_core::{PauliString, QuarterPhase};
+use pecos_core::pauli::{Xs, Zs};
 
 // Define a 3-qubit bit-flip code
 let code = StabilizerCodeSpec::builder(3)
@@ -51,8 +52,7 @@ let checker = StabilizerFlipChecker::new(&code);
 
 ```rust
 use pecos_qec::{StabilizerCodeSpec, StabilizerFlipChecker, ErrorClass};
-use pecos_core::{Xs, Zs};
-use pecos_core::pauli::constructors::*;
+use pecos_core::pauli::*;
 
 let code = StabilizerCodeSpec::builder(3)
     .check(Zs([0, 1]))
@@ -80,8 +80,7 @@ For detailed information about which stabilizers and logicals are affected:
 
 ```rust
 use pecos_qec::{StabilizerCodeSpec, StabilizerFlipChecker};
-use pecos_core::{Xs, Zs};
-use pecos_core::pauli::constructors::*;
+use pecos_core::pauli::*;
 
 let code = StabilizerCodeSpec::builder(3)
     .check(Zs([0, 1])).check(Zs([1, 2]))
@@ -102,7 +101,7 @@ Enumerate all weight-t Pauli errors and classify each:
 
 ```rust
 use pecos_qec::{StabilizerCodeSpec, StabilizerFlipChecker};
-use pecos_core::{Xs, Zs};
+use pecos_core::pauli::{Xs, Zs};
 
 let code = StabilizerCodeSpec::builder(3)
     .check(Zs([0, 1])).check(Zs([1, 2]))
@@ -129,7 +128,7 @@ For CSS codes, you can analyze X, Y, and Z errors separately:
 
 ```rust
 use pecos_qec::{StabilizerCodeSpec, StabilizerFlipChecker};
-use pecos_core::{Xs, Zs};
+use pecos_core::pauli::{Xs, Zs};
 
 let code = StabilizerCodeSpec::builder(3)
     .check(Zs([0, 1])).check(Zs([1, 2]))
@@ -279,7 +278,7 @@ use pecos_qec::DemBuilder;
 
 // Build DEM from a fault influence map
 let dem = DemBuilder::new(&influence_map)
-    .with_noise(0.01, 0.01, 0.01, 0.01)  // p1, p2, p_meas, p_init
+    .with_noise(0.01, 0.01, 0.01, 0.01)  // p1, p2, p_meas, p_prep
     .with_detectors_json(detectors_json)?
     .with_observables_json(observables_json)?
     .build();
@@ -296,7 +295,7 @@ The `distance` module provides configurable distance search:
 
 ```rust
 use pecos_qec::{StabilizerCodeSpec, calculate_distance, DistanceSearchConfig};
-use pecos_core::{Xs, Zs};
+use pecos_core::pauli::{Xs, Zs};
 
 let code = StabilizerCodeSpec::builder(7)
     .check(Xs([0, 2, 4, 6]))
@@ -328,7 +327,7 @@ let result = calculate_distance(&code, &DistanceSearchConfig::with_max_weight(5)
 
 ```rust
 use pecos_qec::{StabilizerCodeSpec, find_min_weight_logicals_with_info, DistanceSearchConfig};
-use pecos_core::{Xs, Zs};
+use pecos_core::pauli::{Xs, Zs};
 
 let code = StabilizerCodeSpec::builder(7)
     .check(Xs([0, 2, 4, 6]))
@@ -357,7 +356,7 @@ When you have stabilizer generators but don't know the logical operators, `disco
 
 ```rust
 use pecos_qec::discover_logical_operators;
-use pecos_core::pauli::constructors::Zs;
+use pecos_core::pauli::Zs;
 
 // Define stabilizers for the 3-qubit bit-flip code
 let stabilizers = vec![Zs([0, 1]), Zs([1, 2])];
diff --git a/docs/user-guide/gate-angle-types.md b/docs/user-guide/gate-angle-types.md
index baaab2430..4f29dad83 100644
--- a/docs/user-guide/gate-angle-types.md
+++ b/docs/user-guide/gate-angle-types.md
@@ -119,7 +119,7 @@ The `phase!` and `phase_turn!` macros wrap angles into `PhaseValue` for use with
 
 ```rust
 use pecos_core::{phase, phase_turn};
-use pecos_core::unitary_rep::X;
+use pecos_core::unitary::X;
 
 // Global phase applied to a gate
 let op = phase!(pi / 4) * X(0);      // e^{i*pi/4} * X
diff --git a/docs/user-guide/gates.md b/docs/user-guide/gates.md
index dc8e6937c..57896dbfa 100644
--- a/docs/user-guide/gates.md
+++ b/docs/user-guide/gates.md
@@ -1073,7 +1073,6 @@ These operations measure and then prepare the qubit in a specific eigenstate reg
 |-----------|---------------|-------------------|-------|
 | **SparseStab** | All | None | Default, fastest for QEC |
 | **StateVec** | All | All | Pure Rust state vector |
-| **Qulacs** | All | All | High-performance C++ backend |
 | **CuStateVec** | All | All | GPU-accelerated (requires CUDA) |
 | **MPS** | All | All | Tensor network (requires CUDA) |
 | **PauliProp** | All | None | Error propagation tracking |
diff --git a/docs/user-guide/getting-started.md b/docs/user-guide/getting-started.md
index 3c75832ad..8fbeb2b16 100644
--- a/docs/user-guide/getting-started.md
+++ b/docs/user-guide/getting-started.md
@@ -167,6 +167,7 @@ The Python example uses a state vector simulator, which supports all quantum gat
 ## Next Steps
 
 - **[HUGR & Guppy Simulation](hugr-simulation.md)**: Measurement-based control flow and advanced Guppy features
+- **[PECOS Concepts](pecos-concepts.md)**: Detectors, observables, tracked Paulis, gates, channels, and fault locations
 - **[QASM Simulation](qasm-simulation.md)**: Full QASM simulation API for existing OpenQASM code
 - **[Simulators](simulators.md)**: Choose the right simulation backend
 - **[Noise Model Builders](noise-model-builders.md)**: Add realistic noise to your simulations
@@ -180,7 +181,6 @@ Most users won't need these, but they're available for specialized use cases:
 |---------|-----------------|-------------|
 | **LLVM** (Rust only) | QIR/LLVM IR execution | [LLVM Setup](llvm-setup.md) |
 | **CUDA** | GPU-accelerated simulation | [CUDA Setup](cuda-setup.md) |
-| **QuEST** | Alternative simulator backend | `pip install quantum-pecos[all]` |
 
 !!! tip "Python users"
     Pre-built wheels include LLVM support—no extra setup needed.
diff --git a/docs/user-guide/llvm-setup.md b/docs/user-guide/llvm-setup.md
index c5fa07ffd..3a523ea88 100644
--- a/docs/user-guide/llvm-setup.md
+++ b/docs/user-guide/llvm-setup.md
@@ -23,7 +23,7 @@ If you don't need QIS LLVM IR/QIR execution features, you can skip LLVM installa
 
 ### Option 1: Automatic Installation (Recommended)
 
-Use the `pecos-llvm` CLI tool to automatically download and install LLVM 14.0.6:
+Use the `pecos` CLI (`pecos install llvm`, or `cargo run -p pecos-cli -- install llvm` in a source checkout) to automatically download and install LLVM 14.0.6:
 
 ```bash
 # Install LLVM 14.0.6 to ~/.pecos/deps/llvm-14/ (~400MB, ~5 minutes)
@@ -110,9 +110,9 @@ cargo run -p pecos-cli -- llvm version
 cargo run -p pecos-cli -- llvm find
 ```
 
-## pecos-llvm CLI Reference
+## `pecos llvm` CLI Reference
 
-The `pecos llvm` CLI tool provides several useful commands:
+The `pecos llvm` subcommand provides several useful commands:
 
 ### `install`
 
@@ -214,7 +214,7 @@ LLVM_SYS_140_PREFIX = { value = "/path/to/llvm", force = true }
 
 ### Detection Priority
 
-The `pecos-llvm` tool searches for LLVM 14 in this order:
+The `pecos llvm` tooling searches for LLVM 14 in this order:
 
 1. **Home directory:**
    - Windows: `~/.pecos/deps/llvm-14`
@@ -244,7 +244,7 @@ The `pecos-llvm` tool searches for LLVM 14 in this order:
 
 - Uses `.7z` archives for distribution
 - Pure Rust extraction (no external tools required)
-- Official LLVM Windows installer lacks development files - use `pecos-llvm install` or community packages
+- Official LLVM Windows installer lacks development files - use `pecos install llvm` or community packages
 
 ### Security
 
diff --git a/docs/user-guide/noise-model-builders.md b/docs/user-guide/noise-model-builders.md
index ebe0a1050..02eaf751b 100644
--- a/docs/user-guide/noise-model-builders.md
+++ b/docs/user-guide/noise-model-builders.md
@@ -131,6 +131,17 @@ noise = (
 )
 ```
 
+### Idle Locations
+
+`Idle` gates are timing markers by default. They do not silently inherit
+single-qubit gate noise from `p1` or `with_p1_probability(...)`.
+
+This is intentional: adding an idle location changes circuit timing, while
+adding idle noise changes the physical noise model. To model idle decoherence,
+use an API that explicitly attaches idle noise or an explicit channel to idle
+locations. This keeps scheduling changes from accidentally changing the noise
+model.
+
 ## Common Noise Model Examples
 
 ### Basic Depolarizing Noise
diff --git a/docs/user-guide/pecos-concepts.md b/docs/user-guide/pecos-concepts.md
new file mode 100644
index 000000000..607d9aa97
--- /dev/null
+++ b/docs/user-guide/pecos-concepts.md
@@ -0,0 +1,141 @@
+# PECOS Concepts
+
+PECOS keeps a few related QEC concepts separate because they answer different
+questions. The implementation can share propagation machinery underneath, but
+the public API should make the distinction clear.
+
+## Quick Map
+
+| Concept | Meaning | Typical source | Decoder role |
+|---|---|---|---|
+| Detector | A parity check on measurement records | Measurement record metadata | Syndrome bit |
+| Observable | A measured logical or experiment output | Measurement record metadata | Logical class decoded from the syndrome |
+| Tracked Pauli | A Pauli operator inserted as a non-physical probe | Circuit annotation | Analysis output, ignored by ordinary DEM decoders |
+| Gate | An ideal operation in a circuit | Circuit builder | No noise unless a noise model attaches it |
+| Channel | A physical CPTP map, often noise | Noise model or explicit channel op | Source of stochastic or coherent faults |
+| Fault location | One independent place a modeled fault can occur | Fault catalog | Unit of fault enumeration and sampling |
+
+## Detectors, Observables, and Tracked Operators
+
+**Detectors** are syndrome bits. A detector is defined by a parity expression
+over measurement records, such as "the previous ancilla measurement differs
+from the same check in the prior round." Decoders consume detector flips as the
+syndrome.
+
+**Observables** are measurement-defined experiment outputs. In QEC workflows
+these are often logical measurement outcomes. They are still defined through
+measurement records, so they are things the experiment can observe directly or
+infer from recorded measurement data. Logical error rate terminology in PECOS
+continues to refer to errors in these logical observables.
+
+**Tracked Paulis** are Pauli strings placed at a circuit point as probes.
+They are not measured by that annotation and do not become detector syndrome
+bits. Fault-analysis code asks whether propagated faults anticommute with the
+tracked Pauli at that point. A tracked Pauli might be a logical operator,
+a stabilizer, or another tracked Pauli useful for analysis.
+
+Error events can therefore flip three independent kinds of output:
+
+- detectors: what syndrome bits changed
+- observables: what measured logical or experiment outputs changed
+- tracked Paulis: which tracked Paulis anticommute with the propagated fault
+
+Do not merge observable IDs and tracked-Pauli IDs. Observable `0` is always
+observable `0`; tracked Paulis have their own ID space and their own metadata.
+
+## Operator Construction
+
+Use the most structured representation that fits the situation:
+
+1. Typed constructors, such as `X(0) & Z(3)`, for ordinary code.
+2. Sparse strings, such as `"X0 Z3"`, for compact text input with explicit
+   qubit indices.
+3. Dense strings, such as `"XIIZ"`, for table-like input where character
+   position is the qubit index.
+
+When writing Rust code, the constructor style is the default:
+
+```rust
+use pecos_core::pauli::*;
+use pecos_core::PauliOperator;
+
+let logical_x = X(0) & X(1) & X(2);
+let z_probe = Z(3);
+
+assert_eq!(logical_x.weight(), 3);
+assert!(logical_x.commutes_with(&z_probe));
+```
+
+String parsing is still useful when reading checks, user input, test fixtures,
+or text formats:
+
+```rust
+use pecos_core::{PauliOperator, PauliString};
+
+let stabilizer: PauliString = "Z0 Z1 Z4 Z5".parse().unwrap();
+assert_eq!(stabilizer.weight(), 4);
+```
+
+Python exposes the same idea. Use `X(0) & Z(3)` for inline construction,
+`PauliString.from_sparse_str(...)` for explicit sparse text, and
+`PauliString.from_dense_str(...)` for dense text. `PauliString.from_str(...)`
+auto-detects sparse versus dense notation.
+
+```python
+from pecos.quantum import PauliString, X, Z
+
+probe = X(0) & X(1) & Z(3)
+from_text = PauliString.from_str("X0 X1 Z3")
+
+assert probe == from_text
+assert probe.to_sparse_str() == "+X0 X1 Z3"
+assert probe.to_dense_str() == "+XXIZ"
+```
+
+In Pauli-algebra contexts, `X`, `Y`, and `Z` construct `PauliString` values.
+In circuit-building contexts, use circuit APIs such as `Gate.x(...)`,
+`TickCircuit.tick().x(...)`, or the corresponding builder methods.
+
+## Gates, Channels, Noise, and Idle Locations
+
+A **gate** is an ideal circuit operation. A **channel** is a physical map. Noise
+models attach channels to selected circuit locations.
+
+`Idle` is a scheduling marker unless idle noise is attached explicitly. Adding
+an `Idle` gate records timing structure; it should not silently inherit
+single-qubit gate noise. To model idle decoherence, use a noise model or channel
+API that explicitly targets idle locations.
+
+This keeps two actions separate:
+
+- changing circuit timing: add or remove idle locations
+- changing the physical noise model: attach idle noise explicitly
+
+## DEMs and Fault Catalogs
+
+PECOS detector-error models represent detector and observable effects that
+ordinary decoders consume. PECOS-specific metadata can also carry tracked
+Paulis for analysis, but tracked Paulis are not logical observables and
+ordinary DEM decoders should ignore them.
+
+The fault catalog gives the most detailed per-location view:
+
+- `affected_measurements`: raw measurement flips
+- `affected_detectors`: syndrome flips
+- `affected_observables`: measurement-defined logical or experiment outputs
+- `affected_tracked_paulis`: tracked Paulis flipped by anticommutation
+
+## Recommended Surface-Code Memory Path
+
+For standard surface-code memory experiments:
+
+1. Build the patch and circuit with `SurfacePatch` and the surface circuit
+   builders.
+2. Generate the circuit-level DEM with the surface decoder helpers.
+3. Sample and decode with the native DEM sampler or a matching decoder backend.
+4. Use the fault catalog when you need per-location fault anatomy, targeted
+   lookup decoding, or probability-weighted explanations for a syndrome.
+
+Use the lower-level `TickCircuit`, `DagCircuit`, `DemBuilder`, and fault-catalog
+APIs when you are developing new circuit families, new analysis tools, or new
+decoder integrations.
diff --git a/docs/user-guide/python-pauli-qec.md b/docs/user-guide/python-pauli-qec.md
index b0c72ecfd..9d3e2a27c 100644
--- a/docs/user-guide/python-pauli-qec.md
+++ b/docs/user-guide/python-pauli-qec.md
@@ -52,16 +52,32 @@ assert Pauli.X.to_int() == 1
 ### Pauli Strings
 
 `PauliString` represents a multi-qubit Pauli operator with a phase from {+1, -1, +i, -i}.
+For inline code, prefer constructor syntax such as `X(0) & Z(1)`. Use sparse
+strings like `"X0 Z1"` when text input is useful and dense strings like `"XZ"`
+for compact table-like input.
 
 ```python
-from pecos_rslib import Pauli, PauliString
+from pecos_rslib import Pauli, PauliString, X, Z
 
-# From string notation
-p = PauliString.from_str("XZI")  # X on qubit 0, Z on qubit 1, I on qubit 2
-q = PauliString.from_str("ZXI")
+# Constructor syntax
+p = X(0) & Z(1)
+q = Z(0) & X(1)
 
 # From list of (Pauli, qubit) pairs
-p = PauliString([(Pauli.X, 0), (Pauli.Z, 1)])
+same_p = PauliString([(Pauli.X, 0), (Pauli.Z, 1)])
+assert p == same_p
+
+# From string notation
+sparse_text = PauliString.from_sparse_str("X0 Z1")
+dense_text = PauliString.from_dense_str("XZ")
+auto_detected = PauliString.from_str("X0 Z1")
+assert p == sparse_text
+assert p == dense_text
+assert p == auto_detected
+
+# To string notation
+assert p.to_sparse_str() == "+X0 Z1"
+assert p.to_dense_str() == "+XZ"
 
 # Get components
 print(p.get_paulis())  # [(Pauli.X, 0), (Pauli.Z, 1)]
@@ -74,9 +90,9 @@ print(p)  # Shows sparse representation with non-identity operators
 ### Matrix Representation
 
 ```python
-from pecos_rslib import PauliString
+from pecos_rslib import X, Z
 
-p = PauliString.from_str("XZ")
+p = X(0) & Z(1)
 matrix = p.to_matrix()  # Returns complex matrix as list of lists
 # Each element is a (real, imag) tuple
 ```
@@ -86,11 +102,11 @@ matrix = p.to_matrix()  # Returns complex matrix as list of lists
 `PauliStabilizerGroup` represents a group of mutually commuting Pauli strings with real phases (+1 or -1). This is the standard stabilizer group used in QEC.
 
 ```python
-from pecos_rslib import PauliString, PauliStabilizerGroup
+from pecos_rslib import PauliStabilizerGroup, Z
 
 # Create from generators
-g1 = PauliString.from_str("ZZI")
-g2 = PauliString.from_str("IZZ")
+g1 = Z(0) & Z(1)
+g2 = Z(1) & Z(2)
 group = PauliStabilizerGroup([g1, g2])
 
 # Basic properties
@@ -100,7 +116,7 @@ print(group.num_generators())  # 2
 print(group.is_independent())  # True
 
 # Membership testing (GF(2) span)
-ziz = PauliString.from_str("ZIZ")
+ziz = Z(0) & Z(2)
 print(group.contains(ziz))  # True (ZIZ = ZZI * IZZ)
 print(group.contains_with_phase(ziz))  # True (with correct +1 phase)
 
@@ -124,12 +140,12 @@ group = PauliStabilizerGroup.from_str("Z0 Z1\nZ1 Z2")
 ### Modifying Groups
 
 ```python
-from pecos_rslib import PauliString, PauliStabilizerGroup
+from pecos_rslib import PauliStabilizerGroup, X
 
 group = PauliStabilizerGroup.from_str("ZZI\nIZZ")
 
 # Add a generator (must commute with existing generators)
-group.add_generator(PauliString.from_str("XXX"))
+group.add_generator(X(0) & X(1) & X(2))
 
 # Remove a generator by index
 removed = group.remove_generator(2)  # Returns the removed PauliString
@@ -144,10 +160,10 @@ group.merge(other)
 `PauliSequence` is an ordered list of Pauli strings with no constraints (they can anticommute). Provides GF(2) symplectic analysis.
 
 ```python
-from pecos_rslib import PauliString, PauliSequence
+from pecos_rslib import PauliSequence, X, Y, Z
 
-p1 = PauliString.from_str("XZ")
-p2 = PauliString.from_str("ZX")
+p1 = X(0) & Z(1)
+p2 = Z(0) & X(1)
 seq = PauliSequence([p1, p2])
 
 # Analysis
@@ -156,10 +172,10 @@ print(seq.is_abelian())  # False (XZ and ZX anticommute)
 
 # Commutation matrix
 comm = seq.commutation_matrix()
-# comm[i][j] is True if seq[i] commutes with seq[j]
+# comm[i][j] is 1 if seq[i] anticommutes with seq[j]
 
 # GF(2) membership
-print(seq.contains(PauliString.from_str("YY")))  # True (XZ * ZX = -YY in GF(2) span)
+print(seq.contains(Y(0) & Y(1)))  # True (XZ * ZX = -YY in GF(2) span)
 
 # Row reduction to independent subset
 reduced = seq.row_reduce()
@@ -237,22 +253,22 @@ for op in logicals:
 ### Syndrome Computation
 
 ```python
-from pecos_rslib import StabilizerCode, PauliString
+from pecos_rslib import StabilizerCode, X, Z
 
 code = StabilizerCode.repetition(3)
 
 # X error on qubit 0
-error = PauliString.from_str("XII")
+error = X(0)
 syndrome = code.syndrome(error)
 print(syndrome)  # [True, False] -- triggers first stabilizer
 
 # X error on qubit 1
-error = PauliString.from_str("IXI")
+error = X(1)
 syndrome = code.syndrome(error)
 print(syndrome)  # [True, True] -- triggers both stabilizers
 
 # Z error (undetectable by Z-stabilizers)
-error = PauliString.from_str("ZII")
+error = Z(0)
 syndrome = code.syndrome(error)
 print(syndrome)  # [False, False]
 ```
diff --git a/docs/user-guide/qec-guppy.md b/docs/user-guide/qec-guppy.md
index 078f35d25..5318a6afc 100644
--- a/docs/user-guide/qec-guppy.md
+++ b/docs/user-guide/qec-guppy.md
@@ -205,6 +205,62 @@ prog = make_color_transversal_cnot_d3(num_rounds=1)
 prog = make_surface_transversal_cnot(distance=5, num_rounds=2)
 ```
 
+## Writing Your Own QEC Circuit
+
+You can write QEC circuits directly in Guppy without using the factory functions. Here is a minimal 3-qubit repetition code:
+
+```python
+from guppylang import guppy
+from guppylang.std.builtins import array
+from guppylang.std.quantum import qubit, cx, measure, measure_array
+
+
+@guppy.struct
+class RepSyndrome:
+    """Two-bit syndrome for the 3-qubit repetition code."""
+
+    s: array[bool, 2]
+
+
+@guppy
+def extract_rep_syndrome(data: array[qubit, 3]) -> RepSyndrome:
+    """Measure Z_0 Z_1 and Z_1 Z_2 stabilizers."""
+    a0 = qubit()
+    a1 = qubit()
+
+    # Z_0 Z_1 stabilizer
+    cx(data[0], a0)
+    cx(data[1], a0)
+
+    # Z_1 Z_2 stabilizer
+    cx(data[1], a1)
+    cx(data[2], a1)
+
+    s0 = measure(a0)
+    s1 = measure(a1)
+
+    return RepSyndrome(array(s0, s1))
+
+
+@guppy
+def rep_code_experiment() -> tuple[array[bool, 3], RepSyndrome]:
+    """Run one round of the 3-qubit repetition code."""
+    data = array(qubit(), qubit(), qubit())
+    syndrome = extract_rep_syndrome(data)
+    results = measure_array(data)
+    return results, syndrome
+
+
+# Verify it compiles
+compiled = rep_code_experiment.compile()
+```
+
+Key patterns:
+- `@guppy.struct` defines data types (qubits are linear — they must be consumed)
+- `@guppy` functions can call each other freely
+- Ancilla qubits are allocated with `qubit()` and consumed by `measure()`
+- Use `measure_array()` to measure all qubits in an array at once
+
 ## Generated Code Structure
 
 ```hidden-python
@@ -256,28 +312,20 @@ def measure_z_stab_0(az: qubit, data: array[qubit, 9]) -> bool:
 
 ### Syndrome Extraction
 
-<!--skip: illustrative generated code, not executable-->
+The generated module includes a `syndrome_extraction` function that applies all stabilizer measurements in a parallelized CNOT schedule and returns the syndrome:
+
 ```python
-@guppy
-def syndrome_extraction(
-    surf: SurfaceCode_3x3,
-    ax: qubit,
-    az: qubit,
-) -> Syndrome_3x3:
-    """Extract full syndrome."""
-    # Z stabilizers
-    sz0 = measure_z_stab_0(az, surf.data)
-    sz1 = measure_z_stab_1(az, surf.data)
-    # ...
-
-    # X stabilizers
-    sx0 = measure_x_stab_0(ax, surf.data)
-    sx1 = measure_x_stab_1(ax, surf.data)
-    # ...
-
-    return Syndrome_3x3(array(sx0, sx1, ...), array(sz0, sz1, ...))
+from pecos.guppy import generate_surface_code_module
+
+source = generate_surface_code_module(d=3)
+
+# The generated module contains the full syndrome extraction circuit
+assert "def syndrome_extraction" in source
+assert "Syndrome_3x3" in source
 ```
 
+To see the full generated code, see [Viewing Generated Source](#viewing-generated-source) below.
+
 ## Viewing Generated Source
 
 To see the generated Guppy source code:
diff --git a/docs/user-guide/quantum-info.md b/docs/user-guide/quantum-info.md
new file mode 100644
index 000000000..7c70530d4
--- /dev/null
+++ b/docs/user-guide/quantum-info.md
@@ -0,0 +1,280 @@
+# Quantum Information Primitives
+
+PECOS exposes Rust-backed channel representations and measure functions for
+workflows that connect process characterization to QEC simulation. These APIs
+live at `pecos.quantum_info` in Python and in the `pecos-quantum` crate in Rust.
+
+Use these types when you need exact channel data, validation, or process
+metrics before reducing a model to Pauli rates, a detector error model, or a
+fault catalog.
+
+## Channel Representations
+
+PECOS currently provides seven concrete channel representations:
+
+| Type | Purpose |
+| ---- | ------- |
+| `PauliChannel` | Sparse Pauli error probabilities. |
+| `Ptm` | Dense Pauli transfer matrix. |
+| `KrausOps` | Kraus-operator representation. |
+| `ChoiMatrix` | Choi-matrix representation for channel validation and tomography. |
+| `SuperOp` | Dense column-stacked superoperator. |
+| `ChiMatrix` | Process matrix in the Pauli basis. |
+| `Stinespring` | Stinespring isometry. |
+
+Use the representation that matches the question you are asking:
+
+| Goal | Start with |
+| ---- | ---------- |
+| Small pure-state examples | State vectors |
+| Noisy states and entanglement measures | Density matrices |
+| Operational noise construction | `KrausOps` |
+| Complete positivity, trace preservation, and tomography reconstruction | `ChoiMatrix` |
+| Pauli-basis channel diagnostics | `Ptm` |
+| Sparse stochastic Pauli noise | `PauliChannel` |
+| Environment/isometry models | `Stinespring` |
+
+PECOS uses these conventions consistently:
+
+| Convention | Meaning |
+| ---------- | ------- |
+| Qubit order | Little-endian: qubit 0 is the least-significant computational-basis bit. |
+| Dense Pauli labels | Highest-numbered qubit first, so `IX` on two qubits means I on qubit 1 and X on qubit 0. |
+| Sparse Pauli strings | Constructor and sparse text forms use explicit qubit IDs, e.g. `X(0) & Z(3)` or `"X0 Z3"`. |
+| PTM basis order | Dense Pauli labels in PECOS basis-label order. |
+| Superoperator order | Column-stacked operator vectorization. |
+| Choi matrix | Built from PECOS's column-stacked superoperator convention. A trace-preserving channel has output partial trace equal to identity. |
+| Subsystem order | Subsystem 0 is the fastest-varying tensor factor. Qubit helpers follow the same little-endian rule. |
+
+```python
+from pecos.quantum_info import PauliChannel, process_fidelity
+
+channel = PauliChannel.one_qubit(px=0.001, py=0.0005, pz=0.002)
+print(channel.probabilities())
+print(channel.total_error_rate())
+
+ptm = channel.to_ptm()
+identity = type(ptm).identity(1)
+print(process_fidelity(ptm, identity))
+```
+
+For Pauli channels, PECOS also provides exact dependency-free diamond norm and
+diamond distance helpers:
+
+```python
+from pecos.quantum_info import (
+    PauliChannel,
+    pauli_channel_diamond_distance,
+    pauli_channel_diamond_norm,
+)
+
+left = PauliChannel.one_qubit(0.001, 0.0, 0.0)
+right = PauliChannel.one_qubit(0.0, 0.0, 0.001)
+
+print(pauli_channel_diamond_norm(left, right))
+print(pauli_channel_diamond_distance(left, right))
+```
+
+Arbitrary-channel diamond norm is intentionally not exposed yet. General
+channels require a semidefinite program, and PECOS will only expose that API
+once the solver and SDP assembly live in Rust with PECOS-owned validation. The
+current Rust groundwork covers the exact Pauli-channel formula plus internal
+linear-algebra helpers for future SDP assembly.
+
+For multi-qubit Pauli channels, pass a label-to-probability map:
+
+```python
+from pecos.quantum_info import PauliChannel
+
+from_labels = PauliChannel.from_probabilities(
+    2,
+    {
+        "II": 0.98,
+        "IX": 0.01,
+        "ZI": 0.01,
+    },
+)
+```
+
+You can also use `PauliString` keys when the channel is written in PECOS's typed
+Pauli style:
+
+```python
+from pecos.quantum import X, Z
+from pecos_rslib import PauliString
+from pecos.quantum_info import PauliChannel
+
+from_paulis = PauliChannel.from_probabilities(
+    2,
+    {
+        PauliString.I(): 0.98,
+        X(0): 0.01,
+        Z(1): 0.01,
+    },
+)
+
+assert from_paulis.probabilities() == {
+    "II": 0.98,
+    "IX": 0.01,
+    "ZI": 0.01,
+}
+```
+
+## Choi Validation
+
+`ChoiMatrix` exposes checks that are useful when importing reconstructed
+processes from tomography or generated channels from another model:
+
+```python
+from pecos.quantum_info import Ptm
+
+choi = Ptm.identity(1).to_choi()
+assert choi.is_completely_positive()
+assert choi.is_trace_preserving()
+assert choi.is_cptp()
+assert choi.is_unital()
+
+trace_check = choi.partial_trace_output()
+```
+
+For PECOS's Choi convention, a trace-preserving channel satisfies
+`partial_trace_output() == I`.
+
+## Process Tomography Helpers
+
+`ProcessTomographyDesign.matrix_unit(n)` gives the complete computational
+matrix-unit operator basis used by PECOS Choi reconstruction. This is a
+linear-inversion design for exact channel characterization and simulator
+validation; it is not a physical state-preparation recipe.
+
+```python
+from pecos.quantum_info import ProcessTomographyDesign, Ptm
+
+design = ProcessTomographyDesign.matrix_unit(1)
+assert design.input_metadata_all() == [
+    (0, 0, 0),  # |0><0|
+    (1, 1, 0),  # |1><0|
+    (2, 0, 1),  # |0><1|
+    (3, 1, 1),  # |1><1|
+]
+
+choi = Ptm.identity(1).to_choi()
+outputs = design.simulate_outputs(choi)
+reconstructed = design.reconstruct_choi(outputs)
+assert reconstructed.matrix() == choi.matrix()
+```
+
+Physical process tomography is a separate layer. A physical workflow prepares
+experimentally realizable input states, measures in chosen bases, aggregates
+shot counts, and reconstructs an estimated channel before converting it into
+`Ptm`, `ChoiMatrix`, or another channel representation. The current
+`ProcessTomographyDesign` is the Rust-backed exact reconstruction primitive
+that those higher-level experiment-design helpers should build on.
+
+The dense channel forms convert through the same Rust-backed validation path:
+
+```python
+from pecos.quantum_info import Ptm
+
+ptm = Ptm.identity(1)
+superop = ptm.to_superop()
+chi = ptm.to_chi()
+stinespring = ptm.to_kraus().to_stinespring()
+
+assert superop.to_ptm().matrix() == ptm.matrix()
+assert chi.to_ptm().matrix() == ptm.matrix()
+assert stinespring.to_kraus().is_trace_preserving()
+```
+
+## State and Process Measures
+
+State measures accept Python lists of complex values:
+
+```python
+from pecos.quantum_info import (
+    entropy,
+    hellinger_distance,
+    negativity,
+    partial_trace_qubits,
+    partial_trace_subsystems,
+    purity,
+    schmidt_decomposition,
+    shannon_entropy,
+    state_fidelity,
+)
+
+zero = [1.0 + 0.0j, 0.0 + 0.0j]
+plus = [2.0**-0.5, 2.0**-0.5]
+
+assert state_fidelity(zero, zero) == 1.0
+assert abs(state_fidelity(zero, plus) - 0.5) < 1e-12
+
+rho_zero = [[1.0 + 0.0j, 0.0 + 0.0j], [0.0 + 0.0j, 0.0 + 0.0j]]
+assert purity(rho_zero) == 1.0
+assert entropy(rho_zero) == 0.0
+
+bell = [2.0**-0.5 + 0.0j, 0.0j, 0.0j, 2.0**-0.5 + 0.0j]
+bell_rho = [
+    [0.5 + 0.0j, 0.0j, 0.0j, 0.5 + 0.0j],
+    [0.0j, 0.0j, 0.0j, 0.0j],
+    [0.0j, 0.0j, 0.0j, 0.0j],
+    [0.5 + 0.0j, 0.0j, 0.0j, 0.5 + 0.0j],
+]
+
+assert abs(negativity(bell_rho, [2, 2], 1) - 0.5) < 1e-12
+assert len(schmidt_decomposition(bell, [2, 2], [0])) == 2
+assert partial_trace_qubits(bell_rho, 2, [1]) == [
+    [0.5 + 0.0j, 0.0 + 0.0j],
+    [0.0 + 0.0j, 0.5 + 0.0j],
+]
+assert partial_trace_subsystems(bell_rho, [2, 2], [1]) == [
+    [0.5 + 0.0j, 0.0 + 0.0j],
+    [0.0 + 0.0j, 0.5 + 0.0j],
+]
+
+assert shannon_entropy([0.5, 0.5], 2.0) == 1.0
+assert hellinger_distance([1.0, 0.0], [0.0, 1.0]) == 1.0
+```
+
+Process measures operate on `Ptm` values:
+
+```python
+from pecos.quantum_info import Ptm, average_gate_fidelity, gate_error
+
+ideal = Ptm.identity(1)
+actual = Ptm.identity(1)
+
+assert average_gate_fidelity(actual, ideal) == 1.0
+assert gate_error(actual, ideal) == 0.0
+```
+
+## Random Generators
+
+Seeded random generators are available for tests and examples:
+
+```python
+from pecos.quantum_info import random_density_matrix, random_quantum_channel
+
+rho = random_density_matrix(num_qubits=1, seed=123)
+channel = random_quantum_channel(num_qubits=1, num_kraus=2, seed=123)
+assert channel.is_trace_preserving()
+```
+
+`random_density_matrix` samples Hilbert-Schmidt random density matrices.
+`random_quantum_channel` samples CPTP channels through a random Stinespring
+isometry.
+
+## Relationship to QEC APIs
+
+These channel and measure APIs are exact quantum-information tools. They do not
+replace detector error models, fault catalogs, or decoders. A typical workflow
+is:
+
+1. Characterize or construct a channel as `KrausOps`, `ChoiMatrix`, `Ptm`, or
+   `PauliChannel`.
+2. Validate the channel and compute state or process measures.
+3. Reduce the channel to the noise model needed by a QEC simulation.
+4. Build a DEM or fault catalog and estimate logical error rate with a decoder.
+
+This separation keeps exact channel analysis distinct from the compressed fault
+models used for large-scale QEC studies.
diff --git a/docs/user-guide/quantum-operator-algebra.md b/docs/user-guide/quantum-operator-algebra.md
index 92e3c598d..8e6b9025d 100644
--- a/docs/user-guide/quantum-operator-algebra.md
+++ b/docs/user-guide/quantum-operator-algebra.md
@@ -15,7 +15,7 @@ This guide covers PECOS's quantum operator type system: from single-qubit Paulis
 PECOS organizes quantum operators into a strict hierarchy where each level is a subset of the next:
 
 ```text
-Pauli  ⊂  Clifford  ⊂  Unitary  ⊂  Channel
+Pauli  ⊂  Clifford  ⊂  Unitary  ⊂  Gate  ⊂  Channel
 ```
 
 Each level has its own representation optimized for what it can express:
@@ -25,9 +25,10 @@ Each level has its own representation optimized for what it can express:
 | Pauli | `PauliString` | Tensor products of I, X, Y, Z with phase | Exact commutation, symplectic algebra |
 | Clifford | `CliffordRep` | Gates that map Paulis to Paulis | Fast conjugation via Heisenberg picture |
 | Unitary | `UnitaryRep` | Any unitary (including non-Clifford) | Lazy expression tree with algebraic ops |
-| Channel | `ChannelExpr` | Non-unitary operations (measurement, noise) | Compose and tensor arbitrary operations |
+| Gate | `GateExpr` | Ideal circuit operations (unitary, preparation, measurement, reset) | Compose and tensor circuit operations |
+| Channel | `ChannelExpr` | General CPTP maps and noise/decoherence operations | Compose and tensor arbitrary physical maps |
 
-The unified `Op` type wraps all four and automatically promotes when you combine operators from different levels.
+The unified `Op` type wraps all five and automatically promotes when you combine operators from different levels.
 
 ---
 
@@ -38,7 +39,7 @@ The unified `Op` type wraps all four and automatically promotes when you combine
 The primary Pauli type. Stores a sparse list of non-identity single-qubit Paulis with a global phase from `{+1, -1, +i, -i}`.
 
 ```rust
-use pecos_core::pauli::constructors::*;
+use pecos_core::pauli::*;
 use pecos_core::PauliOperator;
 
 // Single-qubit constructors
@@ -64,7 +65,7 @@ let neg = -X(0);              // -X
 
 ```rust
 use pecos_core::pauli::algebra::i;
-use pecos_core::pauli::constructors::*;
+use pecos_core::pauli::*;
 
 let imag = i * X(0);          // iX
 let neg_imag = -i * Y(1);     // -iY
@@ -73,7 +74,7 @@ let neg_imag = -i * Y(1);     // -iY
 ### Key Operations
 
 ```rust
-use pecos_core::pauli::constructors::*;
+use pecos_core::pauli::*;
 use pecos_core::PauliOperator;
 
 let a = X(0) & Z(1);
@@ -108,12 +109,23 @@ All three implement the `PauliOperator` trait, which provides `multiply()`, `wei
 
 ### Parsing from Strings
 
+Use constructors for ordinary code. Use sparse strings when explicit qubit
+indices make text input clearer, and dense strings when positional notation is
+useful for compact tables.
+
 ```rust
 use pecos_core::PauliString;
 
-let p: PauliString = "XZI".parse().unwrap();    // X(0) & Z(1)
-let q: PauliString = "+XZZXI".parse().unwrap(); // with explicit phase
-let r: PauliString = "-iYX".parse().unwrap();   // -i * Y(0) * X(1)
+let sparse: PauliString = "X0 Z3".parse().unwrap();
+let dense: PauliString = "XIIZ".parse().unwrap();
+let explicit_sparse = PauliString::from_sparse_str("X0 Z3").unwrap();
+let explicit_dense = PauliString::from_dense_str("XIIZ").unwrap();
+
+assert_eq!(sparse, dense);
+assert_eq!(sparse, explicit_sparse);
+assert_eq!(dense, explicit_dense);
+assert_eq!(sparse.to_sparse_str(), "+X0 Z3");
+assert_eq!(sparse.to_dense_str(None), "+XIIZ");
 ```
 
 ---
@@ -126,7 +138,7 @@ Represents a Clifford gate via the Heisenberg picture: how it transforms each Pa
 
 ```rust
 use pecos_core::clifford_rep::CliffordRep;
-use pecos_core::pauli::constructors::*;
+use pecos_core::pauli::*;
 
 // Hadamard on qubit 0: X -> Z, Z -> X
 let h = CliffordRep::h(0);
@@ -155,7 +167,7 @@ The 24 single-qubit Clifford gates and 14 two-qubit entangling gates are also av
 A lazy expression tree that can represent any quantum unitary, including non-Clifford gates (T, arbitrary rotations). Supports composition, tensor products, and adjoint algebraically.
 
 ```rust
-use pecos_core::unitary_rep::*;
+use pecos_core::unitary::*;
 use pecos_core::Angle64;
 
 // Named gates
@@ -183,19 +195,33 @@ let h_all = Hs([0, 1, 2]);            // H on three qubits
 
 ---
 
-## Level 4: Channels (Non-Unitary Operations)
+## Level 4: Gates (Ideal Circuit Operations)
 
-### ChannelExpr
+### GateExpr
 
-Represents non-unitary quantum operations: measurements, preparations, noise channels.
+Represents ideal circuit operations: unitaries, measurements, preparations, resets, and their compositions.
 
 ```rust
 use pecos_core::op::*;
 
-// Measurement and preparation
+// Measurement, preparation, and reset
 let mz = MZ(0);           // Z-basis measurement on qubit 0
 let mx = MX(1);           // X-basis measurement on qubit 1
 let pz = PZ(0);           // Prepare |0> on qubit 0
+let reset = Reset(0);     // Reset to |0>
+assert!(mz.is_gate());
+```
+
+---
+
+## Level 5: Channels (Physical Maps)
+
+### ChannelExpr
+
+Represents general CPTP maps, which PECOS usually uses for noise and decoherence.
+
+```rust
+use pecos_core::op::*;
 
 // Noise channels
 let depol = Depolarizing(0.01, 0);            // 1% depolarizing on qubit 0
@@ -203,18 +229,18 @@ let deph = Dephasing(0.02, 1);                // 2% dephasing on qubit 1
 let amp_damp = AmplitudeDamping(0.05, 0);     // T1 decay
 let phase_damp = PhaseDamping(0.03, 0);       // T2 dephasing
 let erasure = Erasure(0.01, 0);               // Erasure channel
-let reset = Reset(0);                         // Reset to |0>
 let leak = Leakage(0.001, 0);                 // Leakage to non-computational state
 
 // Custom Pauli channel
 let pauli_ch = PauliChannel(0.01, 0.01, 0.01, 0);  // px, py, pz
+assert!(depol.is_channel());
 ```
 
 ---
 
 ## The Unified `Op` Type
 
-`Op` wraps all four levels and automatically promotes when you combine operators:
+`Op` wraps all five levels and automatically promotes when you combine operators:
 
 ```rust
 use pecos_core::op::*;
@@ -231,8 +257,12 @@ assert!(c.is_clifford());
 let u = X(0) & H(3) & T(5);
 assert!(u.is_unitary());
 
-// Adding a measurement promotes to Channel
-let ch = H(0) & MZ(1);
+// Adding a measurement promotes to Gate
+let g = H(0) & MZ(1);
+assert!(g.is_gate());
+
+// Adding noise promotes to Channel
+let ch = g & Depolarizing(0.01, 2);
 assert!(ch.is_channel());
 ```
 
@@ -273,8 +303,8 @@ assert!(m.try_dg().is_none());
 use pecos_core::op::*;
 
 let circuit = CX(0, 3) & H(5);
-assert_eq!(circuit.num_qubits(), 6);     // spans qubits 0..5
-assert_eq!(circuit.qubits(), vec![0, 1, 2, 3, 4, 5]);  // full range
+assert_eq!(circuit.num_qubits(), 6);     // matrix span is qubits 0..5
+assert_eq!(circuit.qubits(), vec![0, 3, 5]);  // actual support
 ```
 
 ---
@@ -299,7 +329,7 @@ An ordered list of Pauli strings with GF(2) symplectic analysis. No commutativit
 
 ```rust
 use pecos_quantum::PauliSequence;
-use pecos_core::pauli::constructors::*;
+use pecos_core::pauli::*;
 
 let seq = PauliSequence::new(vec![
     Zs([0, 1]),
@@ -328,7 +358,7 @@ A set of distinct Pauli strings. Two strings are equal only if they have the sam
 
 ```rust
 use pecos_quantum::PauliSet;
-use pecos_core::pauli::constructors::*;
+use pecos_core::pauli::*;
 
 let mut set = PauliSet::new();
 set.insert(&X(0));
@@ -350,7 +380,7 @@ A commuting subgroup of the Pauli group. Generators may carry any `QuarterPhase`
 
 ```rust
 use pecos_quantum::PauliGroup;
-use pecos_core::pauli::constructors::*;
+use pecos_core::pauli::*;
 use pecos_core::pauli::algebra::i;
 
 // Generators with imaginary phase
@@ -373,7 +403,7 @@ The standard stabilizer group for QEC. All generators must commute and have phas
 
 ```rust
 use pecos_quantum::PauliStabilizerGroup;
-use pecos_core::pauli::constructors::*;
+use pecos_core::pauli::*;
 
 // Repetition code stabilizers
 let stab = PauliStabilizerGroup::new(vec![
@@ -401,7 +431,7 @@ let transformed = stab.apply_clifford(&h);
 
 ```rust
 use pecos_quantum::{PauliSequence, PauliGroup, PauliStabilizerGroup, PauliSet};
-use pecos_core::pauli::constructors::*;
+use pecos_core::pauli::*;
 
 // Upward (widening) -- always succeeds
 let stab = PauliStabilizerGroup::new(vec![Zs([0, 1])]).unwrap();
@@ -429,7 +459,7 @@ The collection types feed into the QEC types in `pecos-qec`:
 ```rust
 use pecos_quantum::PauliStabilizerGroup;
 use pecos_qec::StabilizerCode;
-use pecos_core::pauli::constructors::*;
+use pecos_core::pauli::*;
 
 // Build a stabilizer group
 let group = PauliStabilizerGroup::new(vec![
diff --git a/docs/user-guide/simulators.md b/docs/user-guide/simulators.md
index 5c0f29104..397a497d7 100644
--- a/docs/user-guide/simulators.md
+++ b/docs/user-guide/simulators.md
@@ -82,10 +82,14 @@ fn main() -> Result<(), Box<dyn std::error::Error>> {
 | **StateVec** | State vector | Arbitrary circuits, small systems | None |
 | **StabVec** | Clifford + Rz | Clifford circuits with Z rotations | None |
 | **PauliProp** | Fault tracking | Error propagation analysis | None |
-| **CuStateVec** | State vector (GPU) | Large circuits with GPU | CUDA, cuQuantum |
+| **CuStateVec** | State vector (GPU, Python) | Large circuits with GPU | CUDA, cuQuantum |
+| **CudaStateVec** | State vector (GPU, Rust) | Large circuits, reproducible seeded runs | CUDA, cuQuantum, cuda-rust build |
+| **CudaStabilizer** | Stabilizer (GPU, Rust) | Very large Clifford circuits (1000s of qubits) | CUDA, cuQuantum, cuda-rust build |
 | **MPS** | Tensor network | Low-entanglement circuits | CUDA, cuQuantum |
 | **density_matrix** | Density matrix | Noisy/mixed state simulation | None |
 
+Two additional specialized backends—**SparseStabPy** (pure-Python reference implementation for debugging) and **CoinToss** (random measurement outcomes for testing)—are documented below but rarely used in production.
+
 ## Choosing a Simulator
 
 ```
@@ -110,24 +114,6 @@ fn main() -> Result<(), Box<dyn std::error::Error>> {
                  └── Need mixed states? ──→ density_matrix
 ```
 
-## Setup
-
-The examples below use this Bell state circuit:
-
-```python
-from pecos import sim, Qasm
-
-circuit = """
-OPENQASM 2.0;
-include "qelib1.inc";
-qreg q[2];
-creg c[2];
-h q[0];
-cx q[0], q[1];
-measure q -> c;
-"""
-```
-
 ## Stabilizer Simulators
 
 Stabilizer simulators efficiently simulate **Clifford circuits** (H, S, CNOT, CZ, and similar gates). They scale polynomially with qubit count, making them ideal for quantum error correction.
@@ -395,6 +381,8 @@ Approximate performance characteristics (relative, not absolute):
 | StateVec | ★★★ | ★★★ | 2^n | ~25-30 |
 | StabVec | ★★★★ | Limited to Clifford + Rz | Low | 1000+ |
 | CuStateVec | ★★★★ | ★★★★★ | 2^n (GPU) | ~30-35 |
+| CudaStateVec | ★★★★ | ★★★★★ | 2^n (GPU) | ~30-35 |
+| CudaStabilizer | ★★★★★ | N/A | Low | 1000+ (GPU) |
 | MPS | ★★★ | ★★★ | ~n × chi² | Varies |
 | density_matrix | ★★ | ★★ | 4^n | ~15 |
 
diff --git a/docs/user-guide/stabilizer-codes.md b/docs/user-guide/stabilizer-codes.md
index fff2e13cd..a9907169c 100644
--- a/docs/user-guide/stabilizer-codes.md
+++ b/docs/user-guide/stabilizer-codes.md
@@ -12,7 +12,7 @@ This guide covers working with Pauli strings and stabilizer codes in PECOS's Rus
 - Converting between code types
 
 ```hidden-rust
-use pecos_core::pauli::constructors::*;
+use pecos_core::pauli::*;
 use pecos_core::PauliOperator;
 
 fn main() {
@@ -27,7 +27,7 @@ Pauli strings are the fundamental building block. PECOS provides a concise const
 === ":fontawesome-brands-rust: Rust"
 
     ```rust
-    use pecos_core::pauli::constructors::*;
+    use pecos_core::pauli::*;
 
     // Single-qubit Paulis
     let x0 = X(0);       // X on qubit 0
@@ -51,11 +51,11 @@ Pauli strings are the fundamental building block. PECOS provides a concise const
 === ":fontawesome-brands-python: Python"
 
     ```python
-    from pecos.quantum import PauliString
+    from pecos.quantum import X, Z
 
-    # From string notation
-    p = PauliString.from_str("XZI")
-    q = PauliString.from_str("ZXI")
+    # Constructor notation
+    p = X(0) & Z(1)
+    q = Z(0) & X(1)
 
     # Commutation check
     print(p.commutes_with(q))  # False (anticommute)
@@ -69,7 +69,7 @@ A `StabilizerCode` is defined by its stabilizer generators and a qubit count:
 
     ```rust
     use pecos_qec::StabilizerCode;
-    use pecos_core::pauli::constructors::*;
+    use pecos_core::pauli::*;
 
     // 3-qubit bit-flip repetition code: generators ZZI, IZZ
     let group = pecos_quantum::PauliStabilizerGroup::new(vec![
@@ -165,7 +165,7 @@ Check which stabilizers an error anticommutes with:
 
 ```rust
 use pecos_qec::StabilizerCode;
-use pecos_core::pauli::constructors::*;
+use pecos_core::pauli::*;
 
 let code = StabilizerCode::repetition(3);
 
@@ -208,7 +208,7 @@ When stabilizer generators don't touch all qubits, the explicit `num_qubits` mat
 ```rust
 use pecos_qec::StabilizerCode;
 use pecos_quantum::PauliStabilizerGroup;
-use pecos_core::pauli::constructors::Zs;
+use pecos_core::pauli::Zs;
 
 // ZZ on qubits 0,1 -- but we declare 4 physical qubits
 let group = PauliStabilizerGroup::new(vec![
@@ -227,7 +227,7 @@ For fault tolerance analysis, use `StabilizerCodeSpec`. This stores explicit pai
 
 ```rust
 use pecos_qec::StabilizerCodeSpec;
-use pecos_core::{Xs, Zs};
+use pecos_core::pauli::{Xs, Zs};
 
 // Build a 3-qubit bit-flip code with explicit logicals
 let code = StabilizerCodeSpec::builder(3)
@@ -269,7 +269,7 @@ spec.verify().unwrap();
 
 ```rust
 use pecos_qec::{StabilizerCodeSpec, StabilizerFlipChecker};
-use pecos_core::{Xs, Zs};
+use pecos_core::pauli::{Xs, Zs};
 
 let code = StabilizerCodeSpec::builder(7)
     .check(Xs([0, 2, 4, 6]))
@@ -298,4 +298,4 @@ PECOS separates stabilizer code concerns into layers:
 - **`StabilizerCode`** (pecos-qec): Mathematical code definition, on-demand analysis.
 - **`StabilizerCodeSpec`** (pecos-qec): Operational specification with verification and fault tolerance integration.
 
-For architecture details, see [Stabilizer Code Architecture](../development/STABILIZER_CODE_ARCHITECTURE.md).
+For architecture details, see `design/STABILIZER_CODE_ARCHITECTURE.md` in the repository root.
diff --git a/examples/surface/README.md b/examples/surface/README.md
index 1319554f2..d7bc1afba 100644
--- a/examples/surface/README.md
+++ b/examples/surface/README.md
@@ -6,6 +6,22 @@ This directory contains the current rotated-surface-code memory sweep tooling:
   logical error rate, and writes plots plus optional JSON/HTML reports.
 - `surface_sweep_report.py`: rebuilds an HTML dashboard from already-generated
   sweep artifacts without rerunning simulations.
+- `d3_fault_catalog_lookup.rs`: Rust example that builds a distance-3
+  surface-code memory experiment, enumerates low-weight fault configurations
+  with the fault catalog API, and aggregates a truncated lookup decoder table.
+
+## Rust Fault-Catalog Lookup Example
+
+Run the d=3 lookup-table example from the PECOS repo root:
+
+```bash
+cargo run -p pecos-qec --example surface_d3_fault_catalog_lookup
+```
+
+The expensive loop stays in Rust: for `k = 0..=2`, the example lazily walks
+`catalog.fault_configurations(k)`, XORs detector/tracked-Pauli effects via the
+catalog iterator, and sums `configuration_probability` into a
+`syndrome -> logical -> probability` table.
 
 ## Typical Workflow
 
diff --git a/examples/surface/analyze_data.py b/examples/surface/analyze_data.py
new file mode 100644
index 000000000..93dbf66e1
--- /dev/null
+++ b/examples/surface/analyze_data.py
@@ -0,0 +1,588 @@
+r"""Analyze decoder performance data from JSON shards.
+
+Reads one or more JSON shards produced by ``generate_data.py`` and
+computes:
+  - Decoder comparison tables (LER + timing at each operating point)
+  - Threshold curves (LER vs p for each decoder, grouped by distance)
+  - Per-round fitting (when multiple duration multipliers are present)
+
+Writes an analysis JSON that ``build_report.py`` consumes.
+
+Example:
+    uv run python examples/surface/analyze_data.py results/data.json
+    uv run python examples/surface/analyze_data.py shard1.json shard2.json -o analysis/
+"""
+
+from __future__ import annotations
+
+import argparse
+import json
+import math
+from dataclasses import asdict, dataclass, field
+from pathlib import Path
+
+# -- Analysis data model ------------------------------------------------------
+
+
+@dataclass
+class ComparisonRow:
+    """One decoder's stats at one operating point."""
+
+    decoder: str
+    distance: int
+    basis: str
+    physical_error_rate: float
+    num_rounds: int
+    num_shots: int
+    num_errors: int
+    logical_error_rate: float
+    ci_low: float
+    ci_high: float
+    per_shot_mean: float
+    per_shot_median: float
+    per_shot_p99: float
+    per_shot_max: float
+    quantiles: list[float] = field(default_factory=list)
+
+
+@dataclass
+class ComparisonTable:
+    """All decoder rows for one (distance, p, rounds) point, sorted by LER."""
+
+    distance: int
+    basis: str
+    physical_error_rate: float
+    num_rounds: int
+    num_shots: int
+    rows: list[ComparisonRow]
+
+
+@dataclass
+class ThresholdCurvePoint:
+    """One (p, LER) point on a threshold curve."""
+
+    physical_error_rate: float
+    # LER over d rounds (either projected from fit, or raw at r=2d)
+    logical_error_rate: float
+    ci_low: float
+    ci_high: float
+    num_shots: int
+    num_errors: int
+    # Per-round fitted epsilon (when multiple round counts available)
+    fitted_epsilon: float | None = None
+    fitted_epsilon_ci_low: float | None = None
+    fitted_epsilon_ci_high: float | None = None
+    num_round_points: int = 1
+    # Per-round LER (= fitted_epsilon when fitted, else raw_LER / num_rounds)
+    per_round_ler: float | None = None
+    per_round_ci_low: float | None = None
+    per_round_ci_high: float | None = None
+
+
+@dataclass
+class ThresholdCurve:
+    """LER vs p for one (decoder, distance, basis) combination.
+
+    When multiple round counts are available, the threshold points use
+    fitted per-round epsilon from p_L(r) = 0.5*(1-(1-2*eps)^r).
+    """
+
+    decoder: str
+    distance: int
+    basis: str
+    points: list[ThresholdCurvePoint]
+    uses_fitted_epsilon: bool = False
+
+
+@dataclass
+class DurationCurvePoint:
+    """One (rounds, LER) point on a duration curve."""
+
+    num_rounds: int
+    logical_error_rate: float
+    ci_low: float
+    ci_high: float
+    num_shots: int
+    num_errors: int
+
+
+@dataclass
+class DurationCurve:
+    """LER vs rounds for one (decoder, distance, basis, p) combination."""
+
+    decoder: str
+    distance: int
+    basis: str
+    physical_error_rate: float
+    points: list[DurationCurvePoint]
+
+
+@dataclass
+class ThresholdEstimate:
+    """Estimated threshold from curve crossing for one decoder.
+
+    metric: "per_round" or "d_round" indicating which LER was used for the crossing.
+    """
+
+    decoder: str
+    basis: str
+    estimated_p_th: float
+    d_small: int
+    d_large: int
+    metric: str = "per_round"  # "per_round", "d_round", or "fss"
+    std_error: float | None = None
+
+
+@dataclass
+class AnalysisResult:
+    """Full analysis output."""
+
+    config: dict
+    comparison_tables: list[ComparisonTable] = field(default_factory=list)
+    threshold_curves: list[ThresholdCurve] = field(default_factory=list)
+    duration_curves: list[DurationCurve] = field(default_factory=list)
+    threshold_estimates: list[ThresholdEstimate] = field(default_factory=list)
+
+
+# -- Wilson score interval ----------------------------------------------------
+
+
+def _wilson_ci(n: int, k: int, z: float = 1.96) -> tuple[float, float]:
+    """95% Wilson score confidence interval for binomial proportion."""
+    if n == 0:
+        return 0.0, 0.0
+    p = k / n
+    if p == 0:
+        return 0.0, 1 - (1 - 0.95) ** (1 / n)  # Clopper-Pearson upper for 0 successes
+    if p == 1:
+        return (1 - 0.95) ** (1 / n), 1.0
+    denom = 1 + z * z / n
+    centre = (p + z * z / (2 * n)) / denom
+    half = z * math.sqrt(p * (1 - p) / n + z * z / (4 * n * n)) / denom
+    return max(0.0, centre - half), min(1.0, centre + half)
+
+
+# -- Per-round epsilon fitting ------------------------------------------------
+
+
+def _ler_model(epsilon: float, r: int) -> float:
+    """p_L(r) = 0.5 * (1 - (1 - 2*epsilon)^r)."""
+    if epsilon <= 0 or epsilon >= 0.5:
+        return 0.5
+    return 0.5 * (1.0 - (1.0 - 2.0 * epsilon) ** r)
+
+
+def _fit_epsilon(round_values: list[int], ler_values: list[float]) -> float | None:
+    """Fit per-round epsilon from (rounds, LER) pairs using golden section search.
+
+    Minimises sum of squared residuals of p_L(r) = 0.5*(1-(1-2*eps)^r).
+    Returns None if fitting is not possible.
+    """
+    if not round_values or all(v == 0 for v in ler_values):
+        return None
+
+    def cost(eps: float) -> float:
+        return sum((ler - _ler_model(eps, r)) ** 2 for r, ler in zip(round_values, ler_values, strict=True))
+
+    # Golden section search on [1e-8, 0.499]
+    a, b = 1e-8, 0.499
+    gr = (math.sqrt(5) + 1) / 2
+    for _ in range(80):
+        c = b - (b - a) / gr
+        d = a + (b - a) / gr
+        if cost(c) < cost(d):
+            b = d
+        else:
+            a = c
+    return (a + b) / 2
+
+
+# -- Load and merge shards ----------------------------------------------------
+
+
+def _load_shards(paths: list[Path]) -> tuple[dict, list[dict]]:
+    """Load JSON shards and return (merged_config, all_points)."""
+    all_points = []
+    config = {}
+    for path in paths:
+        data = json.loads(path.read_text())
+        if not config:
+            config = dict(data.get("config", {}))
+        all_points.extend(data.get("points", []))
+
+    # Derive config fields from actual data (shards may cover different subsets)
+    all_decoders = set()
+    all_distances = set()
+    all_error_rates = set()
+    total_shots = 0
+    for pt in all_points:
+        all_distances.add(pt["distance"])
+        all_error_rates.add(pt["physical_error_rate"])
+        total_shots = max(total_shots, pt.get("num_shots", 0))
+        for ds in pt.get("decoder_stats", []):
+            all_decoders.add(ds["decoder"])
+    config["decoders"] = sorted(all_decoders)
+    config["distances"] = sorted(all_distances)
+    config["error_rates"] = sorted(all_error_rates)
+    if total_shots:
+        config["shots"] = total_shots
+    return config, all_points
+
+
+# -- Analysis -----------------------------------------------------------------
+
+
+def analyze(config: dict, points: list[dict]) -> AnalysisResult:
+    """Compute comparison tables and threshold curves from raw data points."""
+    result = AnalysisResult(config=config)
+
+    # Group points by (distance, basis, p, rounds)
+    from collections import defaultdict
+
+    by_cell: dict[tuple, list[dict]] = defaultdict(list)
+    for pt in points:
+        key = (pt["distance"], pt["basis"], pt["physical_error_rate"], pt["num_rounds"])
+        by_cell[key].append(pt)
+
+    # Comparison tables: one per (distance, p, rounds) cell
+    for (d, basis, p, r), cell_points in sorted(by_cell.items()):
+        # Merge decoder stats across shards for same cell
+        decoder_stats: dict[str, dict] = {}
+        total_shots = 0
+        for pt in cell_points:
+            total_shots += pt["num_shots"]
+            for ds in pt.get("decoder_stats", []):
+                name = ds["decoder"]
+                if name not in decoder_stats:
+                    decoder_stats[name] = {
+                        "num_errors": 0,
+                        "num_shots": 0,
+                        "per_shot_mean": ds["per_shot_mean"],
+                        "per_shot_median": ds["per_shot_median"],
+                        "per_shot_p99": ds["per_shot_p99"],
+                        "per_shot_max": ds["per_shot_max"],
+                        "quantiles": ds.get("quantiles", []),
+                    }
+                decoder_stats[name]["num_errors"] += ds["num_errors"]
+                decoder_stats[name]["num_shots"] += pt["num_shots"]
+
+        rows = []
+        for dec_name, stats in decoder_stats.items():
+            n = stats["num_shots"]
+            k = stats["num_errors"]
+            ler = k / n if n > 0 else 0.0
+            ci_lo, ci_hi = _wilson_ci(n, k)
+            rows.append(
+                ComparisonRow(
+                    decoder=dec_name,
+                    distance=d,
+                    basis=basis,
+                    physical_error_rate=p,
+                    num_rounds=r,
+                    num_shots=n,
+                    num_errors=k,
+                    logical_error_rate=ler,
+                    ci_low=ci_lo,
+                    ci_high=ci_hi,
+                    per_shot_mean=stats["per_shot_mean"],
+                    per_shot_median=stats["per_shot_median"],
+                    per_shot_p99=stats["per_shot_p99"],
+                    per_shot_max=stats["per_shot_max"],
+                    quantiles=stats.get("quantiles", []),
+                ),
+            )
+
+        rows.sort(key=lambda r: r.logical_error_rate)
+
+        result.comparison_tables.append(
+            ComparisonTable(
+                distance=d,
+                basis=basis,
+                physical_error_rate=p,
+                num_rounds=r,
+                num_shots=total_shots,
+                rows=rows,
+            ),
+        )
+
+    # Threshold curves: group by (decoder, distance, basis) across all rounds.
+    # For each p, if multiple round counts exist, fit per-round epsilon.
+    # Otherwise, use the raw LER at the single available round count.
+    tc_groups: dict[tuple, dict[float, list[ComparisonRow]]] = defaultdict(lambda: defaultdict(list))
+    for table in result.comparison_tables:
+        for row in table.rows:
+            key = (row.decoder, row.distance, row.basis)
+            tc_groups[key][row.physical_error_rate].append(row)
+
+    for (dec, d, basis), p_to_rows in sorted(tc_groups.items()):
+        curve_points = []
+        has_fitting = False
+        for p in sorted(p_to_rows):
+            rows = p_to_rows[p]
+            if len(rows) >= 2:
+                # Multiple round counts: fit per-round epsilon
+                round_vals = [r.num_rounds for r in rows]
+                ler_vals = [r.logical_error_rate for r in rows]
+                eps = _fit_epsilon(round_vals, ler_vals)
+                if eps is not None:
+                    has_fitting = True
+                    # Project to d-round LER for display
+                    projected_ler = _ler_model(eps, d)
+                    # CI from fitting upper/lower LER bounds
+                    ci_lo_vals = [r.ci_low for r in rows]
+                    ci_hi_vals = [r.ci_high for r in rows]
+                    eps_lo = _fit_epsilon(round_vals, ci_hi_vals)  # higher LER -> higher eps
+                    eps_hi = _fit_epsilon(round_vals, ci_lo_vals)  # lower LER -> lower eps
+                    total_shots = sum(r.num_shots for r in rows)
+                    total_errors = sum(r.num_errors for r in rows)
+                    proj_ci_lo = _ler_model(eps_hi, d) if eps_hi else projected_ler
+                    proj_ci_hi = _ler_model(eps_lo, d) if eps_lo else projected_ler
+                    curve_points.append(
+                        ThresholdCurvePoint(
+                            physical_error_rate=p,
+                            logical_error_rate=projected_ler,
+                            ci_low=proj_ci_lo,
+                            ci_high=proj_ci_hi,
+                            num_shots=total_shots,
+                            num_errors=total_errors,
+                            fitted_epsilon=eps,
+                            fitted_epsilon_ci_low=eps_hi,
+                            fitted_epsilon_ci_high=eps_lo,
+                            num_round_points=len(rows),
+                            per_round_ler=eps,
+                            per_round_ci_low=eps_hi,
+                            per_round_ci_high=eps_lo,
+                        ),
+                    )
+                    continue
+
+            # Single round count: use raw LER, estimate per-round from
+            # p_L(r) = 0.5*(1-(1-2*eps)^r) inverted.
+            row = rows[0]
+            raw_per_round = _fit_epsilon([row.num_rounds], [row.logical_error_rate])
+            raw_pr_lo = _fit_epsilon([row.num_rounds], [row.ci_high])
+            raw_pr_hi = _fit_epsilon([row.num_rounds], [row.ci_low])
+            curve_points.append(
+                ThresholdCurvePoint(
+                    physical_error_rate=row.physical_error_rate,
+                    logical_error_rate=row.logical_error_rate,
+                    ci_low=row.ci_low,
+                    ci_high=row.ci_high,
+                    num_shots=row.num_shots,
+                    num_errors=row.num_errors,
+                    per_round_ler=raw_per_round,
+                    per_round_ci_low=raw_pr_hi,
+                    per_round_ci_high=raw_pr_lo,
+                ),
+            )
+
+        result.threshold_curves.append(
+            ThresholdCurve(
+                decoder=dec,
+                distance=d,
+                basis=basis,
+                points=curve_points,
+                uses_fitted_epsilon=has_fitting,
+            ),
+        )
+
+    # Duration curves: LER vs rounds for each (decoder, distance, basis, p).
+    # Only meaningful when multiple round counts exist per (d, p).
+    dur_groups: dict[tuple, list[ComparisonRow]] = defaultdict(list)
+    for table in result.comparison_tables:
+        for row in table.rows:
+            key = (row.decoder, row.distance, row.basis, row.physical_error_rate)
+            dur_groups[key].append(row)
+
+    for (dec, d, basis, p), rows in sorted(dur_groups.items()):
+        if len(rows) < 2:
+            continue  # need at least 2 round counts
+        dur_points = [
+            DurationCurvePoint(
+                num_rounds=row.num_rounds,
+                logical_error_rate=row.logical_error_rate,
+                ci_low=row.ci_low,
+                ci_high=row.ci_high,
+                num_shots=row.num_shots,
+                num_errors=row.num_errors,
+            )
+            for row in sorted(rows, key=lambda r: r.num_rounds)
+        ]
+        result.duration_curves.append(
+            DurationCurve(
+                decoder=dec,
+                distance=d,
+                basis=basis,
+                physical_error_rate=p,
+                points=dur_points,
+            ),
+        )
+
+    # Threshold estimates: find where smallest/largest distance curves cross.
+    # Compute for both per-round LER and d-round LER.
+    import itertools as _itertools
+
+    # Threshold estimates via FSS fit (Wang-Harrington-Preskill form).
+    # Uses ALL (p, d, per_round_ler) points across ALL distances simultaneously.
+    # Falls back to pairwise crossing only as a seed for the FSS fit.
+    est_groups: dict[tuple, list[ThresholdCurve]] = defaultdict(list)
+    for curve in result.threshold_curves:
+        est_groups[(curve.decoder, curve.basis)].append(curve)
+
+    def _crude_crossing_seed(dec_curves: list[ThresholdCurve]) -> float | None:
+        """Quick pairwise crossing of smallest/largest distance for FSS seed."""
+        distances = sorted({c.distance for c in dec_curves})
+        if len(distances) < 2:
+            return None
+        small = next(c for c in dec_curves if c.distance == distances[0])
+        large = next(c for c in dec_curves if c.distance == distances[-1])
+        small_by_p = {
+            pt.physical_error_rate: (pt.per_round_ler or pt.logical_error_rate)
+            for pt in small.points
+            if (pt.per_round_ler or pt.logical_error_rate) and (pt.per_round_ler or pt.logical_error_rate) > 0
+        }
+        large_by_p = {
+            pt.physical_error_rate: (pt.per_round_ler or pt.logical_error_rate)
+            for pt in large.points
+            if (pt.per_round_ler or pt.logical_error_rate) and (pt.per_round_ler or pt.logical_error_rate) > 0
+        }
+        shared_ps = sorted(set(small_by_p) & set(large_by_p))
+        diffs = [(p, large_by_p[p] - small_by_p[p]) for p in shared_ps]
+        for (p0, diff0), (p1, diff1) in _itertools.pairwise(diffs):
+            if diff0 == 0.0:
+                return p0
+            if diff0 * diff1 < 0.0:
+                t = abs(diff0) / (abs(diff0) + abs(diff1))
+                return math.exp((1.0 - t) * math.log(p0) + t * math.log(p1))
+        return None
+
+    for (dec, basis), dec_curves in sorted(est_groups.items()):
+        distances = sorted({c.distance for c in dec_curves})
+        if len(distances) < 2:
+            continue
+
+        # FSS fit for per-round LER
+        plist_pr, dlist_pr, plog_pr = [], [], []
+        for curve in dec_curves:
+            for pt in curve.points:
+                pr = pt.per_round_ler
+                if pr and pr > 0:
+                    plist_pr.append(pt.physical_error_rate)
+                    dlist_pr.append(curve.distance)
+                    plog_pr.append(pr)
+
+        # FSS fit for d-round LER
+        plist_dr, dlist_dr, plog_dr = [], [], []
+        for curve in dec_curves:
+            for pt in curve.points:
+                lr = pt.logical_error_rate
+                if lr and lr > 0:
+                    plist_dr.append(pt.physical_error_rate)
+                    dlist_dr.append(curve.distance)
+                    plog_dr.append(lr)
+
+        # Crude seed for FSS optimizer
+        seed = _crude_crossing_seed(dec_curves)
+
+        for metric, plist, dlist, plog in [
+            ("fss_per_round", plist_pr, dlist_pr, plog_pr),
+            ("fss_d_round", plist_dr, dlist_dr, plog_dr),
+        ]:
+            if len(plist) < 5 or len(set(dlist)) < 2:
+                continue
+            s = seed if seed is not None else sorted(plist)[len(plist) // 2]
+            fss = _fit_fss_threshold(plist, dlist, plog, seed_threshold=s)
+            if fss is not None:
+                result.threshold_estimates.append(
+                    ThresholdEstimate(
+                        decoder=dec,
+                        basis=basis,
+                        estimated_p_th=fss[0],
+                        d_small=min(distances),
+                        d_large=max(distances),
+                        metric=metric,
+                        std_error=fss[1],
+                    ),
+                )
+
+    return result
+
+
+def _fit_fss_threshold(
+    plist: list[float],
+    dlist: list[int],
+    plog: list[float],
+    *,
+    seed_threshold: float,
+    seed_nu: float = 1.0,
+    window_factor_low: float = 0.4,
+    window_factor_high: float = 2.0,
+) -> tuple[float, float] | None:
+    """Fit the Wang-Harrington-Preskill FSS form using pecos.analysis.threshold_curve.
+
+    Returns (p_th, p_th_std_error) or None if the fit fails.
+    """
+    try:
+        from pecos.analysis.threshold_curve import func as fss_func
+        from pecos.analysis.threshold_curve import threshold_fit
+    except ImportError:
+        return None
+
+    # Filter to a window around the seed threshold
+    low = seed_threshold * window_factor_low
+    high = seed_threshold * window_factor_high
+    indices = [i for i, p in enumerate(plist) if low <= p <= high and plog[i] > 0]
+    if len(indices) < 5 or len({dlist[i] for i in indices}) < 2:
+        return None
+
+    import pecos as pc
+
+    p_arr = pc.array([plist[i] for i in indices])
+    d_arr = pc.array([float(dlist[i]) for i in indices])
+    ler_arr = pc.array([plog[i] for i in indices])
+    mean_ler = float(sum(plog[i] for i in indices) / len(indices))
+    initial = [seed_threshold, seed_nu, mean_ler, 1.0, 1.0]
+
+    try:
+        popt, stdev = threshold_fit(p_arr, d_arr, ler_arr, fss_func, initial)
+    except Exception:
+        return None
+
+    p_th = float(popt[0])
+    p_th_se = float(stdev[0])
+    if p_th <= 0:
+        return None
+    return (p_th, p_th_se)
+
+
+# -- CLI ----------------------------------------------------------------------
+
+
+def main() -> int:
+    """CLI entry point for data analysis."""
+    parser = argparse.ArgumentParser(
+        description=__doc__,
+        formatter_class=argparse.RawDescriptionHelpFormatter,
+    )
+    parser.add_argument("shards", nargs="+", type=Path, help="JSON shard file(s) from generate_data.py")
+    parser.add_argument("-o", "--output-dir", type=str, default=None)
+    args = parser.parse_args()
+
+    config, points = _load_shards(args.shards)
+    print(f"Loaded {len(points)} data points from {len(args.shards)} shard(s)")
+
+    result = analyze(config, points)
+    print(f"  {len(result.comparison_tables)} comparison tables")
+    print(f"  {len(result.threshold_curves)} threshold curves")
+
+    out = Path(args.output_dir) if args.output_dir else args.shards[0].parent
+    out.mkdir(parents=True, exist_ok=True)
+    json_path = out / "analysis.json"
+    json_path.write_text(json.dumps(asdict(result), indent=2))
+    print(f"Wrote {json_path}")
+
+    return 0
+
+
+if __name__ == "__main__":
+    raise SystemExit(main())
diff --git a/examples/surface/brickwork_sweep.py b/examples/surface/brickwork_sweep.py
new file mode 100644
index 000000000..88fe9f01e
--- /dev/null
+++ b/examples/surface/brickwork_sweep.py
@@ -0,0 +1,800 @@
+r"""Brickwork circuit sweep: transversal gate performance across widths, depths, distances.
+
+Generates mirrored brickwork circuits (H + CX) at various configurations,
+decodes with multiple decoders, and writes JSON results that can be fed
+to ``build_report.py`` for HTML/PDF reports.
+
+The mirrored brickwork guarantees output = |0...0>, so logical errors
+are unambiguous.
+
+Decoder names:
+    observable_subgraph:INNER  -- OSD with inner decoder (pymatching, pecos_uf:fast, etc.)
+    logical_circuit:BUDGET:INNER  -- LogicalCircuitDecoder (unlimited, windowed, 10ms, etc.)
+    logical_algorithm:INNER  -- LogicalAlgorithmDecoder (full-circuit, no budget)
+
+Example:
+    uv run python examples/surface/brickwork_sweep.py \
+        --distances 3 5 --widths 2 3 4 --depths 1 2 3 \
+        --error-rates 0.001 0.002 \
+        --decoders observable_subgraph:pymatching \
+        --shots 5000 --output-dir /tmp/brickwork_sweep
+
+    uv run python examples/surface/brickwork_sweep.py \
+        --distances 3 5 --widths 2 3 --depths 1 2 \
+        --error-rates 0.001 \
+        --decoders observable_subgraph:pymatching logical_circuit:windowed:pymatching \
+        --shots 2000 --save-html --open
+"""
+
+from __future__ import annotations
+
+import argparse
+import json
+import random
+import sys
+import time
+from dataclasses import asdict, dataclass, field
+from pathlib import Path
+
+sys.path.insert(0, str(Path(__file__).resolve().parents[2] / "python" / "quantum-pecos" / "src"))
+
+
+# -- Data model ---------------------------------------------------------------
+
+
+@dataclass
+class DecoderResult:
+    decoder: str
+    num_errors: int
+    logical_error_rate: float
+    decode_seconds: float
+
+
+@dataclass
+class BrickworkPoint:
+    distance: int
+    width: int
+    depth: int
+    physical_error_rate: float
+    num_shots: int
+    seed: int
+    sample_seconds: float
+    decoder_results: list[DecoderResult] = field(default_factory=list)
+
+
+@dataclass
+class BrickworkShard:
+    config: dict
+    points: list[BrickworkPoint] = field(default_factory=list)
+    total_seconds: float = 0.0
+
+
+# -- Circuit builder -----------------------------------------------------------
+
+
+def build_mirrored_brickwork(width, depth, seed, patch, rounds=2):
+    """Build a mirrored brickwork circuit (identity, output = |0...0>)."""
+    from pecos.qec.surface import LogicalCircuitBuilder
+
+    nq = patch.geometry.num_data + patch.geometry.num_ancilla
+    rng = random.Random(seed)
+
+    b = LogicalCircuitBuilder()
+    labels = [f"Q{i}" for i in range(width)]
+    for i, label in enumerate(labels):
+        b.add_patch(patch, label, qubit_offset=i * nq)
+
+    eff = dict.fromkeys(labels, "Z")
+    b.add_memory(labels, rounds, "Z")
+
+    ops_forward = []
+    for layer in range(depth):
+        layer_ops = []
+        for label in labels:
+            if rng.random() < 0.5:
+                b.add_transversal_h(label)
+                eff[label] = "X" if eff[label] == "Z" else "Z"
+                layer_ops.append(("H", label))
+        b.add_memory(labels, rounds, basis={label: eff[label] for label in labels})
+
+        offset = layer % 2
+        cx_applied = []
+        for i in range(offset, width - 1, 2):
+            ctrl, tgt = labels[i], labels[i + 1]
+            if eff[ctrl] == eff[tgt]:
+                b.add_transversal_cx(ctrl, tgt)
+                cx_applied.append((ctrl, tgt))
+        if cx_applied:
+            b.add_memory(labels, rounds, basis={label: eff[label] for label in labels})
+            layer_ops.append(("CX", cx_applied))
+        ops_forward.append(layer_ops)
+
+    # Mirror
+    for layer_ops in reversed(ops_forward):
+        for op_type, *args in reversed(layer_ops):
+            if op_type == "CX":
+                for ctrl, tgt in reversed(args[0]):
+                    if eff[ctrl] == eff[tgt]:
+                        b.add_transversal_cx(ctrl, tgt)
+                b.add_memory(labels, rounds, basis={label: eff[label] for label in labels})
+        for op_type, *args in reversed(layer_ops):
+            if op_type == "H":
+                label = args[0]
+                b.add_transversal_h(label)
+                eff[label] = "X" if eff[label] == "Z" else "Z"
+        b.add_memory(labels, rounds, basis={label: eff[label] for label in labels})
+
+    return b
+
+
+def build_t_injection_circuit(distance, _seed, patch, rounds_per_layer):
+    """Build a T-gate injection circuit: memory + T injection + memory."""
+    from pecos.qec.surface import LogicalCircuitBuilder
+
+    nq = patch.geometry.num_data + patch.geometry.num_ancilla
+    b = LogicalCircuitBuilder()
+    b.add_patch(patch, "D", qubit_offset=0)
+    b.add_patch(patch, "A", qubit_offset=nq)
+
+    # Memory → T injection → Memory
+    rounds = max(rounds_per_layer, distance)
+    b.add_memory(["D", "A"], rounds=rounds, basis="Z")
+    b.add_t_via_injection("D", "A", rounds_before=rounds, rounds_after=rounds)
+    return b
+
+
+# -- Sweep --------------------------------------------------------------------
+
+
+def run_sweep(
+    *,
+    distances: list[int],
+    widths: list[int],
+    depths: list[int],
+    error_rates: list[float],
+    decoders: list[str],
+    shots: int,
+    circuit_seed: int,
+    rounds_per_layer: int,
+) -> BrickworkShard:
+    """Run the full brickwork sweep."""
+    from pecos.qec.surface import SurfacePatch
+    from pecos_rslib.qec import ObservableSubgraphDecoder, ParsedDem
+
+    config = {
+        "distances": distances,
+        "widths": widths,
+        "depths": depths,
+        "error_rates": error_rates,
+        "decoders": decoders,
+        "shots": shots,
+        "circuit_seed": circuit_seed,
+        "rounds_per_layer": rounds_per_layer,
+    }
+
+    shard = BrickworkShard(config=config)
+    t_total = time.perf_counter()
+
+    total_cells = len(distances) * len(widths) * len(depths) * len(error_rates)
+    cell_idx = 0
+
+    for d in distances:
+        patch = SurfacePatch.create(distance=d)
+        for w in widths:
+            for depth in depths:
+                # Build circuit once per (d, w, depth) — reuse across error rates
+                b = build_mirrored_brickwork(w, depth, circuit_seed, patch, rounds_per_layer)
+                sc = b.stab_coords()
+
+                for p in error_rates:
+                    cell_idx += 1
+                    print(f"[{cell_idx}/{total_cells}] d={d} w={w} depth={depth} p={p:.4g} ...", end=" ", flush=True)
+
+                    dem_str = b.build_dem(p1=p, p2=p, p_meas=p, p_prep=p)
+
+                    # Sample
+                    t0 = time.perf_counter()
+                    parsed = ParsedDem.from_string(dem_str)
+                    rust_sampler = parsed.to_dem_sampler()
+                    batch = rust_sampler.generate_samples(shots, seed=circuit_seed + cell_idx)
+                    sample_sec = time.perf_counter() - t0
+
+                    point = BrickworkPoint(
+                        distance=d,
+                        width=w,
+                        depth=depth,
+                        physical_error_rate=p,
+                        num_shots=shots,
+                        seed=circuit_seed,
+                        sample_seconds=sample_sec,
+                    )
+
+                    # Decode with each decoder
+                    for decoder_name in decoders:
+                        t0 = time.perf_counter()
+                        if decoder_name.startswith("logical_circuit"):
+                            from pecos_rslib.qec import LogicalCircuitDecoder
+
+                            # Format: logical_circuit:budget:inner
+                            parts = decoder_name.split(":")
+                            budget = parts[1] if len(parts) > 1 else "offline"
+                            inner = parts[2] if len(parts) > 2 else "pymatching"
+                            desc = b.build_algorithm_descriptor(p1=p, p2=p, p_meas=p, p_prep=p)
+                            dec = LogicalCircuitDecoder(desc, budget, inner)
+                            errors = dec.decode_count(batch)
+                        elif decoder_name.startswith("logical_algorithm"):
+                            from pecos_rslib.qec import LogicalAlgorithmDecoder
+
+                            parts = decoder_name.split(":", 1)
+                            inner = parts[1] if len(parts) > 1 else "pymatching"
+                            desc = b.build_algorithm_descriptor(p1=p, p2=p, p_meas=p, p_prep=p)
+                            algo = LogicalAlgorithmDecoder(desc, inner)
+                            errors = algo.decode_count(batch)
+                        elif decoder_name.startswith("observable_subgraph"):
+                            parts = decoder_name.split(":", 1)
+                            inner = parts[1] if len(parts) > 1 else "pymatching"
+                            osd = ObservableSubgraphDecoder(dem_str, sc, inner)
+                            # Use parallel decode for large shot counts
+                            if shots >= 5000:
+                                errors = osd.decode_count_parallel(batch, dem_str, sc, inner)
+                            else:
+                                errors = osd.decode_count(batch)
+                        else:
+                            msg = (
+                                f"Unknown decoder: '{decoder_name}'. "
+                                f"Supported: observable_subgraph:INNER, "
+                                f"logical_circuit:BUDGET:INNER, "
+                                f"logical_algorithm:INNER"
+                            )
+                            raise ValueError(msg)
+                        dec_sec = time.perf_counter() - t0
+                        ler = errors / shots
+
+                        point.decoder_results.append(
+                            DecoderResult(
+                                decoder=decoder_name,
+                                num_errors=errors,
+                                logical_error_rate=ler,
+                                decode_seconds=dec_sec,
+                            ),
+                        )
+
+                    shard.points.append(point)
+                    lers = {r.decoder: f"{r.logical_error_rate:.5f}" for r in point.decoder_results}
+                    print(f"LER={lers}")
+
+    shard.total_seconds = time.perf_counter() - t_total
+    return shard
+
+
+# -- HTML report ---------------------------------------------------------------
+
+
+def write_html_report(shard: BrickworkShard, path: Path, coherent_results=None) -> None:
+    """Write an HTML report from the sweep results."""
+    from collections import defaultdict
+
+    # Group by (width, depth) for each distance
+    tables = defaultdict(list)
+    for pt in shard.points:
+        tables[(pt.distance, pt.physical_error_rate)].append(pt)
+
+    style = """
+        :root {
+          color-scheme: light dark;
+          --bg: #f8fafc; --fg: #0f172a;
+          --hero-bg: linear-gradient(135deg, #e0f2fe, #f8fafc 55%, #dcfce7);
+          --card-bg: white; --card-border: #dbeafe; --card-shadow: rgba(15,23,42,0.05);
+          --meta-bg: rgba(255,255,255,0.82);
+          --muted: #475569; --link: #2563eb;
+          --table-stripe: #f1f5f9; --table-border: #e2e8f0;
+          --good: #16a34a; --warn: #ea580c; --bad: #dc2626;
+        }
+        @media (prefers-color-scheme: dark) {
+          :root {
+            --bg: #0f172a; --fg: #e2e8f0;
+            --hero-bg: linear-gradient(135deg, #1e293b, #0f172a 55%, #1a2e1a);
+            --card-bg: #1e293b; --card-border: #334155; --card-shadow: rgba(0,0,0,0.3);
+            --meta-bg: rgba(30,41,59,0.82);
+            --muted: #94a3b8; --link: #60a5fa;
+            --table-stripe: #0f172a; --table-border: #334155;
+            --good: #4ade80; --warn: #fb923c; --bad: #f87171;
+          }
+        }
+        body {
+          margin: 0;
+          font-family: ui-sans-serif, -apple-system, BlinkMacSystemFont, sans-serif;
+          background: var(--bg); color: var(--fg);
+        }
+        main { max-width: 1100px; margin: 0 auto; padding: 32px 24px 56px; }
+        h1, h2, h3, p { margin-top: 0; }
+        .hero {
+          background: var(--hero-bg);
+          border: 1px solid var(--card-border);
+          border-radius: 20px;
+          padding: 28px 32px;
+          margin-bottom: 24px;
+        }
+        .hero h1 { font-size: 1.6rem; margin-bottom: 0.3em; }
+        .hero p { color: var(--muted); margin: 0; }
+        .meta {
+          display: grid;
+          grid-template-columns: repeat(auto-fit, minmax(180px, 1fr));
+          gap: 12px;
+          margin-top: 18px;
+        }
+        .meta-card {
+          background: var(--meta-bg);
+          border: 1px solid var(--card-border);
+          border-radius: 14px;
+          padding: 14px 16px;
+        }
+        .meta-card strong {
+          display: block; font-size: 0.78rem; text-transform: uppercase;
+          letter-spacing: 0.04em; color: var(--muted); margin-bottom: 4px;
+        }
+        .section {
+          background: var(--card-bg);
+          border: 1px solid var(--card-border);
+          border-radius: 18px;
+          padding: 22px 26px;
+          margin-top: 20px;
+          box-shadow: 0 10px 24px var(--card-shadow);
+          overflow-x: auto;
+        }
+        .section h2 { font-size: 1.15rem; margin-bottom: 0.3em; }
+        .section h3 { font-size: 0.95rem; color: var(--muted); }
+        .section p { font-size: 0.9rem; color: var(--muted); }
+        table { border-collapse: collapse; width: 100%; margin: 12px 0 0; }
+        th, td { padding: 10px 14px; text-align: right; border-bottom: 1px solid var(--table-border); }
+        th {
+          font-size: 0.78rem; text-transform: uppercase;
+          letter-spacing: 0.03em; color: var(--muted); border-bottom-width: 2px;
+        }
+        td:first-child, th:first-child { text-align: left; }
+        tr:nth-child(even) td { background: var(--table-stripe); }
+        .good { color: var(--good); font-weight: 600; }
+        .warn { color: var(--warn); font-weight: 600; }
+        .bad { color: var(--bad); font-weight: 600; }
+        code {
+          font-family: ui-monospace, SFMono-Regular, Menlo, monospace;
+          font-size: 0.85em; background: var(--table-stripe);
+          padding: 0.15em 0.4em; border-radius: 3px;
+        }
+        details.info {
+          background: var(--card-bg);
+          border: 1px solid var(--card-border);
+          border-radius: 18px;
+          margin-top: 20px;
+          box-shadow: 0 10px 24px var(--card-shadow);
+        }
+        details.info > summary {
+          cursor: pointer; font-size: 0.95rem; font-weight: 600;
+          padding: 16px 26px; list-style: none;
+        }
+        details.info > summary::before { content: "\\25B6\\00a0\\00a0"; font-size: 0.75em; }
+        details.info[open] > summary::before { content: "\\25BC\\00a0\\00a0"; }
+        details.info .content {
+          padding: 0 26px 22px; line-height: 1.7; font-size: 0.9rem;
+        }
+        details.info .content h4 { margin: 1em 0 0.3em; }
+    """
+
+    # Build meta cards
+    distances = sorted({pt.distance for pt in shard.points}) if shard.points else []
+    decoders_used = sorted({r.decoder for pt in shard.points for r in pt.decoder_results})
+
+    meta_cards = []
+    if distances:
+        meta_cards.append(
+            f'<div class="meta-card"><strong>Distances</strong>{", ".join(str(d) for d in distances)}</div>',
+        )
+    if decoders_used:
+        meta_cards.append(f'<div class="meta-card"><strong>Decoders</strong>{len(decoders_used)}</div>')
+    if shard.points:
+        meta_cards.append(f'<div class="meta-card"><strong>Shots</strong>{shard.points[0].num_shots:,}</div>')
+    meta_cards.append(f'<div class="meta-card"><strong>Time</strong>{shard.total_seconds:.1f}s</div>')
+
+    html_parts = [
+        "<!doctype html>",
+        '<html lang="en"><head>',
+        '<meta charset="utf-8">',
+        '<meta name="viewport" content="width=device-width, initial-scale=1">',
+        "<title>PECOS Surface Code Report</title>",
+        f"<style>{style}</style>",
+        "</head><body><main>",
+        '<section class="hero">',
+        "<h1>PECOS Surface Code Report</h1>",
+        "<p>Mirrored brickwork circuits, T-gate injection, and coherent noise analysis</p>",
+        f'<div class="meta">{" ".join(meta_cards)}</div>',
+        "</section>",
+        "",
+        '<details class="info"><summary>Decoding Concepts: Throughput, Reaction Time, and Budgets</summary>',
+        '<div class="content">',
+        "<h4>Throughput (avoiding backlog)</h4>",
+        "<p>The decoder must process syndrome data at least as fast as the hardware "
+        "generates it. If syndrome extraction takes T<sub>cycle</sub> per round, the "
+        "decoder must process each round in &le; T<sub>cycle</sub> on average. If it "
+        "falls behind, a <em>backlog</em> accumulates, causing exponential slowdown of "
+        "the quantum computation.</p>",
+        "",
+        "<h4>Reaction time</h4>",
+        "<p>At feed-forward decision points (T-gate injection, magic state consumption), "
+        "the physical hardware waits for the decoder to produce a correction. The "
+        "<em>reaction time</em> is the time available between the last syndrome arriving "
+        "and the correction being applied. For <strong>Clifford-only circuits</strong> "
+        "(like these brickwork circuits), there are no mid-circuit decisions &mdash; the "
+        "Pauli frame is metadata applied at the final measurement. The reaction time is "
+        "effectively unlimited.</p>",
+        "",
+        "<h4>Budget strategies</h4>",
+        "<p>The decoder framework selects a strategy based on the user-specified reaction time budget:</p>",
+        "<ul>",
+        "<li><code>unlimited</code> &mdash; Full-circuit OSD. Maximum accuracy. "
+        "Appropriate for Clifford circuits or offline analysis.</li>",
+        "<li><code>windowed</code> / <code>10ms</code> &mdash; Windowed OSD with "
+        "overlap buffers inside each per-observable subgraph. Bounded latency, full "
+        "accuracy with sufficient overlap.</li>",
+        "<li><code>100us</code> / <code>1us</code> &mdash; Tight budget. Windowed "
+        "without overlap. Accuracy degrades; requires advanced techniques (ghost "
+        "protocol) for improvement.</li>",
+        "</ul>",
+        "",
+        "<h4>Compute hardware</h4>",
+        "<p>The budget is a <em>constraint</em>, not a measurement. A decode that takes "
+        "300&mu;s on a CPU might take 30&mu;s on an FPGA. The strategy doesn't change "
+        "&mdash; only whether it fits within the budget on a given compute platform. "
+        "Profiling on the target hardware determines feasibility.</p>",
+        "",
+        "<h4>References</h4>",
+        "<ul>",
+        "<li>Riverlane + Rigetti (arXiv:2410.05202): 9.6&mu;s response time, backlog definition</li>",
+        "<li>Cain et al. (arXiv:2505.13587): software commitment, &lt;100&mu;s at d=25</li>",
+        "<li>Turner et al. (arXiv:2505.23567): ghost protocol for scalable windowed decoding</li>",
+        "<li>Serra-Peralta et al. (arXiv:2505.13599): per-observable subgraph MWPM</li>",
+        "</ul>",
+        "</div></details>",
+        "",
+    ]
+
+    # Separate brickwork and T-injection points
+    brickwork_tables = defaultdict(list)
+    t_injection_tables = defaultdict(list)
+    for pt in shard.points:
+        if pt.depth == 0:  # T-injection marker
+            t_injection_tables[(pt.distance, pt.physical_error_rate)].append(pt)
+        else:
+            brickwork_tables[(pt.distance, pt.physical_error_rate)].append(pt)
+
+    if brickwork_tables:
+        html_parts.append('<section class="section">')
+        html_parts.append("<h2>Brickwork Circuits (Clifford)</h2>")
+        html_parts.append(
+            "<p>Mirrored random gate sequences (identity operation). "
+            "LER from stochastic depolarizing noise only.</p>",
+        )
+
+    for (d, p), points in sorted(brickwork_tables.items()):
+        html_parts.append(f"<h3>d={d}, p={p}</h3>")
+
+        decoders = sorted({r.decoder for pt in points for r in pt.decoder_results})
+        html_parts.append("<table><tr><th>Width</th><th>Depth</th>")
+        html_parts.extend(f"<th>{dec}</th>" for dec in decoders)
+        html_parts.append("</tr>")
+
+        for pt in sorted(points, key=lambda x: (x.width, x.depth)):
+            html_parts.append(f"<tr><td>{pt.width}</td><td>{pt.depth}</td>")
+            for dec in decoders:
+                r = next((r for r in pt.decoder_results if r.decoder == dec), None)
+                if r:
+                    cls = "good" if r.logical_error_rate < 0.01 else "warn" if r.logical_error_rate < 0.05 else "bad"
+                    html_parts.append(
+                        f'<td class="{cls}">{r.logical_error_rate:.5f} ({r.decode_seconds:.2f}s)</td>',
+                    )
+                else:
+                    html_parts.append("<td>-</td>")
+            html_parts.append("</tr>")
+        html_parts.append("</table>")
+
+    if brickwork_tables:
+        html_parts.append("</section>")
+
+    if t_injection_tables:
+        html_parts.append('<section class="section">')
+        html_parts.append("<h2>T-Gate Injection (Non-Clifford)</h2>")
+        html_parts.append(
+            "<p>T gate via magic state teleportation: "
+            "|T&rang; ancilla + CX + measure + conditional S. "
+            "Feed-forward decision point for the decoder.</p>",
+        )
+
+    for (d, p), points in sorted(t_injection_tables.items()):
+        decoders = sorted({r.decoder for pt in points for r in pt.decoder_results})
+        html_parts.append(f"<h3>d={d}, p={p}</h3>")
+        html_parts.append("<table><tr><th>Circuit</th>")
+        html_parts.extend(f"<th>{dec}</th>" for dec in decoders)
+        html_parts.append("</tr>")
+
+        for pt in points:
+            html_parts.append("<tr><td>T-injection</td>")
+            for dec in decoders:
+                r = next((r for r in pt.decoder_results if r.decoder == dec), None)
+                if r:
+                    cls = "good" if r.logical_error_rate < 0.01 else "warn" if r.logical_error_rate < 0.05 else "bad"
+                    html_parts.append(
+                        f'<td class="{cls}">{r.logical_error_rate:.5f} ({r.decode_seconds:.2f}s)</td>',
+                    )
+                else:
+                    html_parts.append("<td>-</td>")
+            html_parts.append("</tr>")
+        html_parts.append("</table>")
+
+    if t_injection_tables:
+        html_parts.append("</section>")
+
+    # Coherent noise section
+    if coherent_results:
+        html_parts.append('<section class="section">')
+        html_parts.append("<h2>Coherent Idle Noise (X-basis Memory)</h2>")
+        html_parts.append(
+            "<p>RZ(&theta;) rotation on both qubits after each CX gate models "
+            "uncompensated phase accumulation during idle time. Unlike stochastic "
+            "Z errors, coherent rotations accumulate constructively &mdash; the LER "
+            "far exceeds the Pauli-twirled equivalent sin&sup2;(&theta;/2). "
+            "Decoder uses a stochastic-only DEM. Simulated with StateVec.</p>",
+        )
+
+        for (d, p), result in sorted(coherent_results.items()):
+            html_parts.append(f"<h3>d={d}, p_depol={p}</h3>")
+            html_parts.append(
+                "<table><tr>"
+                "<th style='text-align:left'>&theta; (rad)</th>"
+                "<th>sin&sup2;(&theta;/2)</th>"
+                "<th>LER</th>"
+                "<th>&plusmn; SE</th>"
+                "<th>Errors</th>"
+                "<th>vs baseline</th>"
+                "</tr>",
+            )
+            for pt in result.points:
+                cls = "good" if pt.ler < 0.02 else "warn" if pt.ler < 0.05 else "bad"
+                amplification = (
+                    f"{pt.ler / result.points[0].ler:.1f}x" if result.points[0].ler > 0 and pt.p_idle > 0 else ""
+                )
+                html_parts.append(
+                    f'<tr><td style="text-align:left">{pt.p_idle:.3f}</td>'
+                    f"<td>{pt.p_twirled:.5f}</td>"
+                    f'<td class="{cls}">{pt.ler:.4f}</td>'
+                    f"<td>{pt.standard_error:.4f}</td>"
+                    f"<td>{pt.errors}/{pt.shots}</td>"
+                    f"<td>{amplification}</td></tr>",
+                )
+            html_parts.append("</table>")
+
+        html_parts.append("</section>")
+
+    html_parts.append("</main></body></html>")
+    path.write_text("\n".join(html_parts))
+    print(f"Report written to {path}")
+
+
+# -- CLI -----------------------------------------------------------------------
+
+
+def main():
+    parser = argparse.ArgumentParser(description=__doc__, formatter_class=argparse.RawDescriptionHelpFormatter)
+    parser.add_argument("--distances", type=int, nargs="+", default=[3, 5])
+    parser.add_argument("--widths", type=int, nargs="+", default=[2, 3, 4])
+    parser.add_argument("--depths", type=int, nargs="+", default=[1, 2, 3])
+    parser.add_argument(
+        "--scaled-depth",
+        action="store_true",
+        help="Override --depths: set depth=2^((d+1)/2) per distance",
+    )
+    parser.add_argument("--error-rates", type=float, nargs="+", default=[0.001])
+    parser.add_argument("--decoders", nargs="+", default=["observable_subgraph:pymatching"])
+    parser.add_argument("--shots", type=int, default=5000)
+    parser.add_argument("--seed", type=int, default=42)
+    parser.add_argument("--rounds-per-layer", type=int, default=2)
+    parser.add_argument(
+        "--include-t-injection",
+        action="store_true",
+        help="Include T-gate injection circuits (non-Clifford)",
+    )
+    parser.add_argument(
+        "--t-injection-only",
+        action="store_true",
+        help="Only T-gate injection circuits (skip brickwork)",
+    )
+    parser.add_argument(
+        "--include-coherent-noise",
+        action="store_true",
+        help="Include coherent idle noise sweep (RZ after CX)",
+    )
+    parser.add_argument(
+        "--coherent-p-idle",
+        type=float,
+        nargs="+",
+        default=[0.0, 0.01, 0.03, 0.05, 0.07, 0.1],
+        help="Coherent idle RZ angles to sweep",
+    )
+    parser.add_argument("--coherent-shots", type=int, default=None, help="Shots for coherent noise (default: --shots)")
+    parser.add_argument("--output-dir", type=Path, default=Path("/tmp/brickwork_sweep"))
+    parser.add_argument("--save-json", action="store_true")
+    parser.add_argument("--save-html", action="store_true")
+    parser.add_argument("--open", action="store_true")
+    args = parser.parse_args()
+
+    if args.t_injection_only:
+        shard = BrickworkShard(
+            config={
+                "distances": args.distances,
+                "error_rates": args.error_rates,
+                "decoders": args.decoders,
+                "shots": args.shots,
+                "t_injection_only": True,
+            },
+        )
+    elif args.scaled_depth:
+        # Per-distance depth: 2^((d+1)/2) — challenges the decoder proportionally
+        # d=3→4, d=5→8, d=7→16, d=9→32
+        depths = [int(2 ** ((d + 1) / 2)) for d in args.distances]
+        print(f"Scaled depths: {dict(zip(args.distances, depths, strict=False))}")
+
+        all_points = []
+        for d, depth in zip(args.distances, depths, strict=False):
+            partial = run_sweep(
+                distances=[d],
+                widths=args.widths,
+                depths=[depth],
+                error_rates=args.error_rates,
+                decoders=args.decoders,
+                shots=args.shots,
+                circuit_seed=args.seed,
+                rounds_per_layer=args.rounds_per_layer,
+            )
+            all_points.extend(partial.points)
+        shard = BrickworkShard(
+            config={
+                "distances": args.distances,
+                "widths": args.widths,
+                "scaled_depths": dict(zip(args.distances, depths, strict=False)),
+                "error_rates": args.error_rates,
+                "decoders": args.decoders,
+                "shots": args.shots,
+            },
+            points=all_points,
+        )
+    else:
+        shard = run_sweep(
+            distances=args.distances,
+            widths=args.widths,
+            depths=args.depths,
+            error_rates=args.error_rates,
+            decoders=args.decoders,
+            shots=args.shots,
+            circuit_seed=args.seed,
+            rounds_per_layer=args.rounds_per_layer,
+        )
+
+    # T-injection circuits
+    if args.include_t_injection or args.t_injection_only:
+        from pecos.qec.surface import SurfacePatch
+        from pecos_rslib.qec import ObservableSubgraphDecoder, ParsedDem
+
+        print("\n--- T-Injection Circuits ---")
+        for d in args.distances:
+            patch = SurfacePatch.create(distance=d)
+            for p in args.error_rates:
+                b = build_t_injection_circuit(d, args.seed, patch, args.rounds_per_layer)
+                sc = b.stab_coords()
+                dem_str = b.build_dem(p1=p, p2=p, p_meas=p, p_prep=p)
+                parsed = ParsedDem.from_string(dem_str)
+                batch = parsed.to_dem_sampler().generate_samples(args.shots, seed=args.seed)
+
+                point = BrickworkPoint(
+                    distance=d,
+                    width=2,
+                    depth=0,  # depth=0 signals T-injection
+                    physical_error_rate=p,
+                    num_shots=args.shots,
+                    seed=args.seed,
+                    sample_seconds=0,
+                )
+
+                for decoder_name in args.decoders:
+                    t0 = time.perf_counter()
+                    if decoder_name.startswith("logical_circuit"):
+                        from pecos_rslib.qec import LogicalCircuitDecoder
+
+                        parts = decoder_name.split(":")
+                        budget = parts[1] if len(parts) > 1 else "unlimited"
+                        inner = parts[2] if len(parts) > 2 else "pymatching"
+                        desc = b.build_algorithm_descriptor(p1=p, p2=p, p_meas=p, p_prep=p)
+                        dec = LogicalCircuitDecoder(desc, budget, inner)
+                        errors = dec.decode_count(batch)
+                    elif decoder_name.startswith("logical_algorithm"):
+                        from pecos_rslib.qec import LogicalAlgorithmDecoder
+
+                        parts = decoder_name.split(":", 1)
+                        inner = parts[1] if len(parts) > 1 else "pymatching"
+                        desc = b.build_algorithm_descriptor(p1=p, p2=p, p_meas=p, p_prep=p)
+                        algo = LogicalAlgorithmDecoder(desc, inner)
+                        errors = algo.decode_count(batch)
+                    elif decoder_name.startswith("observable_subgraph"):
+                        parts = decoder_name.split(":", 1)
+                        inner = parts[1] if len(parts) > 1 else "pymatching"
+                        osd = ObservableSubgraphDecoder(dem_str, sc, inner)
+                        errors = osd.decode_count(batch)
+                    else:
+                        msg = (
+                            f"Unknown decoder: '{decoder_name}'. "
+                            f"Supported: observable_subgraph:INNER, "
+                            f"logical_circuit:BUDGET:INNER, "
+                            f"logical_algorithm:INNER"
+                        )
+                        raise ValueError(msg)
+                    dec_sec = time.perf_counter() - t0
+                    ler = errors / args.shots
+
+                    point.decoder_results.append(
+                        DecoderResult(
+                            decoder=decoder_name,
+                            num_errors=errors,
+                            logical_error_rate=ler,
+                            decode_seconds=dec_sec,
+                        ),
+                    )
+
+                shard.points.append(point)
+                lers = {r.decoder: f"{r.logical_error_rate:.5f}" for r in point.decoder_results}
+                print(f"d={d} T-injection p={p:.4g} ... LER={lers}")
+
+    # Coherent noise sweep
+    coherent_results = None
+    if args.include_coherent_noise:
+        from coherent_noise_sweep import run_sweep as run_coherent_sweep
+
+        coherent_shots = args.coherent_shots or args.shots
+        # StateVec is limited to d=3 (17 qubits). Skip larger distances.
+        coherent_distances = [d for d in args.distances if d <= 3]
+        if not coherent_distances:
+            print("\n--- Coherent Idle Noise: skipped (StateVec limited to d<=3) ---")
+        else:
+            print("\n--- Coherent Idle Noise ---")
+            coherent_results = {}
+            for d in coherent_distances:
+                for p in args.error_rates:
+                    print(f"d={d} p={p:.4g}:")
+                    result = run_coherent_sweep(
+                        distance=d,
+                        rounds=d,
+                        basis="X",
+                        p_depol=p,
+                        p_idle_values=args.coherent_p_idle,
+                        shots=coherent_shots,
+                        seed=args.seed,
+                        backend="statevec",
+                        lazy_measure=True,
+                        max_bond_dim=128,
+                    )
+                    coherent_results[(d, p)] = result
+
+    args.output_dir.mkdir(parents=True, exist_ok=True)
+
+    if args.save_json:
+        json_path = args.output_dir / "brickwork_sweep_results.json"
+        json_path.write_text(json.dumps(asdict(shard), indent=2))
+        print(f"JSON written to {json_path}")
+
+    if args.save_html or args.open:
+        html_path = args.output_dir / "brickwork_sweep_report.html"
+        write_html_report(shard, html_path, coherent_results=coherent_results)
+        if args.open:
+            import webbrowser
+
+            webbrowser.open(str(html_path))
+
+
+if __name__ == "__main__":
+    main()
diff --git a/examples/surface/build_report.py b/examples/surface/build_report.py
new file mode 100644
index 000000000..ea392b7b6
--- /dev/null
+++ b/examples/surface/build_report.py
@@ -0,0 +1,1588 @@
+r"""Build HTML and/or PDF reports from analysis JSON.
+
+Reads the analysis JSON produced by ``analyze_data.py`` and renders:
+  - HTML report with comparison tables + threshold curve plots (inline SVG)
+  - PDF report with the same content via matplotlib
+
+Example:
+    uv run python examples/surface/build_report.py results/analysis.json --html --pdf
+    uv run python examples/surface/build_report.py results/analysis.json --html --open
+"""
+
+from __future__ import annotations
+
+import argparse
+import html as html_mod
+import json
+import math
+from collections import defaultdict
+from pathlib import Path
+from textwrap import dedent
+
+# -- Load analysis ------------------------------------------------------------
+
+
+def _load_analysis(path: Path) -> dict:
+    return json.loads(path.read_text())
+
+
+# -- Threshold curve SVG (inline) ---------------------------------------------
+
+
+def _sci(v: float) -> str:
+    """Format a value in clean scientific notation for axis labels."""
+    if v == 0:
+        return "0"
+    return f"{v:.1e}"
+
+
+_COLORS = [
+    "#2563eb",  # blue
+    "#dc2626",  # red
+    "#16a34a",  # green
+    "#9333ea",  # purple
+    "#ea580c",  # orange
+    "#0891b2",  # cyan
+    "#be185d",  # pink
+    "#854d0e",  # brown
+]
+
+_DASH_PATTERNS = [
+    "",  # solid
+    "6,3",  # dashed
+    "2,3",  # dotted
+    "8,3,2,3",  # dash-dot
+]
+
+
+def _build_threshold_svg(
+    curves: list[dict],
+    title: str,
+    width: int = 560,
+    height: int = 380,
+    color_by: str = "decoder",
+    threshold_p: float | None = None,
+    y_field: str = "logical_error_rate",
+    y_label: str = "Logical error rate",
+    decoder_color_map: dict[str, str] | None = None,
+    distance_color_map: dict[int, str] | None = None,
+) -> str:
+    """Build an inline SVG plot of LER vs p for multiple (decoder, distance) curves.
+
+    decoder_color_map / distance_color_map: fixed color assignments for
+    consistency across plots. When provided, overrides index-based coloring.
+    y_field: which field on each point to use for y-axis values.
+             Also uses "{y_field}" with "ci_low"/"ci_high" replaced accordingly.
+    threshold_p: if provided, draw a vertical dashed line at this p value.
+    color_by: "decoder" assigns colors by decoder (dashes by distance),
+              "distance" assigns colors by distance (dashes by decoder).
+    """
+    margin = {"top": 45, "right": 160, "bottom": 55, "left": 70}
+    plot_w = width - margin["left"] - margin["right"]
+    plot_h = height - margin["top"] - margin["bottom"]
+
+    # Resolve CI field names based on y_field
+    if y_field == "per_round_ler":
+        ci_lo_field, ci_hi_field = "per_round_ci_low", "per_round_ci_high"
+    else:
+        ci_lo_field, ci_hi_field = "ci_low", "ci_high"
+
+    def _y(pt: dict) -> float:
+        v = pt.get(y_field)
+        return v if v is not None and v > 0 else 0.0
+
+    # Collect all p and y values for axis scaling
+    all_p = []
+    all_ler = []
+    for curve in curves:
+        for pt in curve["points"]:
+            all_p.append(pt["physical_error_rate"])
+            yv = _y(pt)
+            if yv > 0:
+                all_ler.append(yv)
+
+    if not all_p or not all_ler:
+        return f'<svg width="{width}" height="{height}"><text x="50%" y="50%">No data</text></svg>'
+
+    p_vals_pos = [p for p in all_p if p > 0]
+    p_min = min(p_vals_pos) if p_vals_pos else 1e-4
+    p_max = max(p_vals_pos) if p_vals_pos else 1.0
+    ler_min = max(1e-5, min(all_ler) * 0.5)
+    ler_max = min(1.0, max(all_ler) * 2.0)
+
+    # Log scale for both axes
+    log_p_min = math.log10(p_min * 0.8)
+    log_p_max = math.log10(p_max * 1.2)
+    log_ler_min = math.log10(ler_min)
+    log_ler_max = math.log10(ler_max)
+
+    def x_of(p: float) -> float:
+        if p <= 0:
+            return margin["left"]
+        log_p = math.log10(p)
+        frac = (log_p - log_p_min) / (log_p_max - log_p_min) if log_p_max != log_p_min else 0.5
+        return margin["left"] + frac * plot_w
+
+    def y_of(ler: float) -> float:
+        if ler <= 0:
+            return margin["top"] + plot_h
+        log_val = math.log10(ler)
+        frac = (log_val - log_ler_min) / (log_ler_max - log_ler_min) if log_ler_max != log_ler_min else 0.5
+        return margin["top"] + (1 - frac) * plot_h
+
+    parts = [
+        f'<svg xmlns="http://www.w3.org/2000/svg" width="{width}" height="{height}" '
+        f'style="font-family:ui-sans-serif,sans-serif;font-size:11px;">',
+        # Background
+        f'<rect width="{width}" height="{height}" fill="var(--card-bg, white)" rx="8"/>',
+        # Title
+        f'<text x="{width // 2}" y="24" text-anchor="middle" font-size="13" '
+        f'font-weight="600" fill="var(--fg, #0f172a)">{html_mod.escape(title)}</text>',
+    ]
+
+    # Grid lines (horizontal, log scale for y)
+    for exp in range(math.floor(log_ler_min), math.ceil(log_ler_max) + 1):
+        y = y_of(10**exp)
+        if margin["top"] <= y <= margin["top"] + plot_h:
+            parts.append(
+                f'<line x1="{margin["left"]}" y1="{y:.1f}" '
+                f'x2="{margin["left"] + plot_w}" y2="{y:.1f}" '
+                f'stroke="var(--table-border, #e2e8f0)" stroke-width="0.5"/>',
+            )
+            parts.append(
+                f'<text x="{margin["left"] - 8}" y="{y + 4:.1f}" text-anchor="end" '
+                f'fill="var(--muted, #475569)" font-size="10">1e{exp}</text>',
+            )
+
+    # Grid lines (vertical, log scale for x)
+    for exp in range(math.floor(log_p_min), math.ceil(log_p_max) + 1):
+        x = x_of(10**exp)
+        if margin["left"] <= x <= margin["left"] + plot_w:
+            parts.append(
+                f'<line x1="{x:.1f}" y1="{margin["top"]}" '
+                f'x2="{x:.1f}" y2="{margin["top"] + plot_h}" '
+                f'stroke="var(--table-border, #e2e8f0)" stroke-width="0.5"/>',
+            )
+
+    # Axis labels
+    parts.append(
+        f'<text x="{margin["left"] + plot_w // 2}" y="{height - 8}" text-anchor="middle" '
+        f'fill="var(--muted, #475569)" font-size="11">Physical error rate (p)</text>',
+    )
+    parts.append(
+        f'<text x="14" y="{margin["top"] + plot_h // 2}" text-anchor="middle" '
+        f'fill="var(--muted, #475569)" font-size="11" '
+        f'transform="rotate(-90, 14, {margin["top"] + plot_h // 2})">{html_mod.escape(y_label)}</text>',
+    )
+
+    # X-axis tick labels (log-spaced)
+    # Show ticks at 1, 2, 5 * 10^n (standard log-scale subdivisions)
+    x_ticks = set()
+    for exp in range(math.floor(log_p_min) - 1, math.ceil(log_p_max) + 1):
+        for mult in [1.0, 2.0, 5.0]:
+            x_ticks.add(mult * 10.0**exp)
+    # Filter to visible range and limit density
+    visible_ticks = sorted(p for p in x_ticks if p > 0 and log_p_min <= math.log10(p) <= log_p_max)
+    # If too many ticks, keep only powers of 10
+    if len(visible_ticks) > 8:
+        visible_ticks = sorted(p for p in visible_ticks if p == 10.0 ** round(math.log10(p)))
+    for p in visible_ticks:
+        x = x_of(p)
+        parts.append(
+            f'<text x="{x:.1f}" y="{margin["top"] + plot_h + 18}" text-anchor="middle" '
+            f'fill="var(--muted, #475569)" font-size="10">{_sci(p)}</text>',
+        )
+
+    # Plot area border
+    parts.append(
+        f'<rect x="{margin["left"]}" y="{margin["top"]}" '
+        f'width="{plot_w}" height="{plot_h}" '
+        f'fill="none" stroke="var(--table-border, #e2e8f0)"/>',
+    )
+
+    # Threshold vertical line
+    if threshold_p is not None and p_min <= threshold_p <= p_max:
+        tx = x_of(threshold_p)
+        parts.append(
+            f'<line x1="{tx:.1f}" y1="{margin["top"]}" '
+            f'x2="{tx:.1f}" y2="{margin["top"] + plot_h}" '
+            f'stroke="var(--muted, #334155)" stroke-width="1.5" stroke-dasharray="4,3" opacity="0.7"/>',
+        )
+        parts.append(
+            f'<text x="{tx + 4:.1f}" y="{margin["top"] + 12}" '
+            f'fill="var(--muted, #334155)" font-size="9" opacity="0.8">p_th~{_sci(threshold_p)}</text>',
+        )
+
+    # Draw curves
+    decoder_names = list(dict.fromkeys(c["decoder"] for c in curves))
+    distances = sorted({c["distance"] for c in curves})
+
+    legend_y = margin["top"] + 10
+    for curve in sorted(curves, key=lambda c: (decoder_names.index(c["decoder"]), c["distance"])):
+        dec_idx = decoder_names.index(curve["decoder"])
+        dist_idx = distances.index(curve["distance"])
+        if color_by == "distance":
+            color = (distance_color_map or {}).get(curve["distance"], _COLORS[dist_idx % len(_COLORS)])
+            dash = _DASH_PATTERNS[dec_idx % len(_DASH_PATTERNS)]
+        else:
+            color = (decoder_color_map or {}).get(curve["decoder"], _COLORS[dec_idx % len(_COLORS)])
+            dash = _DASH_PATTERNS[dist_idx % len(_DASH_PATTERNS)]
+
+        # CI shaded band (draw first so it's behind everything)
+        band_upper = []
+        band_lower = []
+        for pt in curve["points"]:
+            yv = _y(pt)
+            if yv <= 0:
+                continue
+            ci_lo = pt.get(ci_lo_field) or 0
+            ci_hi = pt.get(ci_hi_field) or 0
+            if ci_lo > 0 and ci_hi > 0:
+                x = x_of(pt["physical_error_rate"])
+                band_upper.append((x, y_of(ci_hi)))
+                band_lower.append((x, y_of(ci_lo)))
+
+        if len(band_upper) >= 2:
+            band_d = " ".join(f"{'M' if i == 0 else 'L'}{x:.1f},{y:.1f}" for i, (x, y) in enumerate(band_upper))
+            for x, y in reversed(band_lower):
+                band_d += f" L{x:.1f},{y:.1f}"
+            band_d += " Z"
+            parts.append(
+                f'<path d="{band_d}" fill="{color}" opacity="0.2" stroke="none"/>',
+            )
+
+        # Center line
+        pts = [(x_of(pt["physical_error_rate"]), y_of(_y(pt))) for pt in curve["points"] if _y(pt) > 0]
+
+        if len(pts) >= 2:
+            path_d = " ".join(f"{'M' if i == 0 else 'L'}{x:.1f},{y:.1f}" for i, (x, y) in enumerate(pts))
+            dash_attr = f' stroke-dasharray="{dash}"' if dash else ""
+            parts.append(
+                f'<path d="{path_d}" fill="none" stroke="{color}" stroke-width="2"{dash_attr}/>',
+            )
+
+        # Data points with CI whiskers
+        for pt in curve["points"]:
+            yv = _y(pt)
+            if yv <= 0:
+                continue
+            x = x_of(pt["physical_error_rate"])
+            y = y_of(yv)
+            parts.append(f'<circle cx="{x:.1f}" cy="{y:.1f}" r="3" fill="{color}"/>')
+            # CI whiskers
+            ci_lo = pt.get(ci_lo_field) or 0
+            ci_hi = pt.get(ci_hi_field) or 0
+            if ci_lo > 0 and ci_hi > 0:
+                y_lo = y_of(ci_lo)
+                y_hi = y_of(ci_hi)
+                parts.append(
+                    f'<line x1="{x:.1f}" y1="{y_lo:.1f}" x2="{x:.1f}" y2="{y_hi:.1f}" '
+                    f'stroke="{color}" stroke-width="1.5" opacity="0.7"/>',
+                )
+
+        # Legend entry
+        label = f"{curve['decoder']} d={curve['distance']}"
+        lx = margin["left"] + plot_w + 12
+        dash_attr = f' stroke-dasharray="{dash}"' if dash else ""
+        parts.append(
+            f'<line x1="{lx}" y1="{legend_y}" x2="{lx + 18}" y2="{legend_y}" '
+            f'stroke="{color}" stroke-width="2"{dash_attr}/>',
+        )
+        parts.append(
+            f'<text x="{lx + 24}" y="{legend_y + 4}" fill="var(--fg, #0f172a)" '
+            f'font-size="10">{html_mod.escape(label)}</text>',
+        )
+        legend_y += 16
+
+    parts.append("</svg>")
+    return "\n".join(parts)
+
+
+def _build_duration_svg(
+    curves: list[dict],
+    title: str,
+    width: int = 560,
+    height: int = 380,
+) -> str:
+    """Build an inline SVG of LER vs rounds for multiple (decoder, distance) curves at fixed p."""
+    margin = {"top": 45, "right": 160, "bottom": 55, "left": 70}
+    plot_w = width - margin["left"] - margin["right"]
+    plot_h = height - margin["top"] - margin["bottom"]
+
+    all_r = []
+    all_ler = []
+    for curve in curves:
+        for pt in curve["points"]:
+            all_r.append(pt["num_rounds"])
+            if pt["logical_error_rate"] > 0:
+                all_ler.append(pt["logical_error_rate"])
+
+    if not all_r or not all_ler:
+        return f'<svg width="{width}" height="{height}"><text x="50%" y="50%">No data</text></svg>'
+
+    r_min, r_max = min(all_r), max(all_r)
+    ler_min = max(1e-5, min(all_ler) * 0.5)
+    ler_max = min(1.0, max(all_ler) * 2.0)
+    log_ler_min = math.log10(ler_min)
+    log_ler_max = math.log10(ler_max)
+
+    def x_of(r: float) -> float:
+        if r_max == r_min:
+            return margin["left"] + plot_w / 2
+        return margin["left"] + (r - r_min) / (r_max - r_min) * plot_w
+
+    def y_of(ler: float) -> float:
+        if ler <= 0:
+            return margin["top"] + plot_h
+        log_val = math.log10(ler)
+        frac = (log_val - log_ler_min) / (log_ler_max - log_ler_min) if log_ler_max != log_ler_min else 0.5
+        return margin["top"] + (1 - frac) * plot_h
+
+    parts = [
+        f'<svg xmlns="http://www.w3.org/2000/svg" width="{width}" height="{height}" '
+        f'style="font-family:ui-sans-serif,sans-serif;font-size:11px;">',
+        f'<rect width="{width}" height="{height}" fill="var(--card-bg, white)" rx="8"/>',
+        f'<text x="{width // 2}" y="24" text-anchor="middle" font-size="13" '
+        f'font-weight="600" fill="var(--fg, #0f172a)">{html_mod.escape(title)}</text>',
+    ]
+
+    # Grid + axis labels
+    for exp in range(math.floor(log_ler_min), math.ceil(log_ler_max) + 1):
+        y = y_of(10**exp)
+        if margin["top"] <= y <= margin["top"] + plot_h:
+            parts.append(
+                f'<line x1="{margin["left"]}" y1="{y:.1f}" '
+                f'x2="{margin["left"] + plot_w}" y2="{y:.1f}" '
+                f'stroke="var(--table-border, #e2e8f0)" stroke-width="0.5"/>',
+            )
+            parts.append(
+                f'<text x="{margin["left"] - 8}" y="{y + 4:.1f}" text-anchor="end" '
+                f'fill="var(--muted, #475569)" font-size="10">1e{exp}</text>',
+            )
+
+    parts.append(
+        f'<text x="{margin["left"] + plot_w // 2}" y="{height - 8}" text-anchor="middle" '
+        f'fill="var(--muted, #475569)" font-size="11">Rounds</text>',
+    )
+    parts.append(
+        f'<text x="14" y="{margin["top"] + plot_h // 2}" text-anchor="middle" '
+        f'fill="var(--muted, #475569)" font-size="11" '
+        f'transform="rotate(-90, 14, {margin["top"] + plot_h // 2})">Logical error rate</text>',
+    )
+
+    for r in sorted(set(all_r)):
+        x = x_of(r)
+        parts.append(
+            f'<text x="{x:.1f}" y="{margin["top"] + plot_h + 18}" text-anchor="middle" '
+            f'fill="var(--muted, #475569)" font-size="10">{r}</text>',
+        )
+
+    parts.append(
+        f'<rect x="{margin["left"]}" y="{margin["top"]}" '
+        f'width="{plot_w}" height="{plot_h}" '
+        f'fill="none" stroke="var(--table-border, #e2e8f0)"/>',
+    )
+
+    # Draw curves
+    legend_y = margin["top"] + 10
+    for curve_idx, curve in enumerate(curves):
+        color = _COLORS[curve_idx % len(_COLORS)]
+        dash = _DASH_PATTERNS[curve_idx // len(_COLORS) % len(_DASH_PATTERNS)]
+
+        pts = [
+            (x_of(pt["num_rounds"]), y_of(pt["logical_error_rate"]))
+            for pt in curve["points"]
+            if pt["logical_error_rate"] > 0
+        ]
+
+        if len(pts) >= 2:
+            path_d = " ".join(f"{'M' if i == 0 else 'L'}{x:.1f},{y:.1f}" for i, (x, y) in enumerate(pts))
+            dash_attr = f' stroke-dasharray="{dash}"' if dash else ""
+            parts.append(
+                f'<path d="{path_d}" fill="none" stroke="{color}" stroke-width="2"{dash_attr}/>',
+            )
+
+        for pt in curve["points"]:
+            if pt["logical_error_rate"] <= 0:
+                continue
+            x = x_of(pt["num_rounds"])
+            y = y_of(pt["logical_error_rate"])
+            parts.append(f'<circle cx="{x:.1f}" cy="{y:.1f}" r="3" fill="{color}"/>')
+            if pt["ci_low"] > 0 and pt["ci_high"] > 0:
+                y_lo = y_of(pt["ci_low"])
+                y_hi = y_of(pt["ci_high"])
+                parts.append(
+                    f'<line x1="{x:.1f}" y1="{y_lo:.1f}" x2="{x:.1f}" y2="{y_hi:.1f}" '
+                    f'stroke="{color}" stroke-width="1.5" opacity="0.7"/>',
+                )
+
+        label = f"{curve['decoder']} d={curve['distance']}"
+        lx = margin["left"] + plot_w + 12
+        dash_attr = f' stroke-dasharray="{dash}"' if dash else ""
+        parts.append(
+            f'<line x1="{lx}" y1="{legend_y}" x2="{lx + 18}" y2="{legend_y}" '
+            f'stroke="{color}" stroke-width="2"{dash_attr}/>',
+        )
+        parts.append(
+            f'<text x="{lx + 24}" y="{legend_y + 4}" fill="var(--fg, #0f172a)" '
+            f'font-size="10">{html_mod.escape(label)}</text>',
+        )
+        legend_y += 16
+
+    parts.append("</svg>")
+    return "\n".join(parts)
+
+
+def _build_timing_svg(
+    tables: list[dict],
+    title: str,
+    width: int = 700,
+    height: int = 400,
+) -> str:
+    """Build a violin plot SVG showing decode time distributions per decoder.
+
+    Uses quantile data from DecodeStats (21 percentiles at 0%, 5%, ..., 100%)
+    to draw symmetric violins on a log-scale horizontal axis.
+    Falls back to box-style whiskers if quantiles are unavailable.
+    """
+    margin = {"top": 45, "right": 30, "bottom": 55, "left": 120}
+    plot_w = width - margin["left"] - margin["right"]
+    plot_h = height - margin["top"] - margin["bottom"]
+
+    # Collect all quantile arrays per decoder (one per operating point).
+    # We'll merge by taking the element-wise geometric mean.
+    decoder_quantiles: dict[str, list[list[float]]] = {}
+    for table in tables:
+        for row in table["rows"]:
+            dec = row["decoder"]
+            q = row.get("quantiles", [])
+            if q and any(v > 0 for v in q):
+                decoder_quantiles.setdefault(dec, []).append(q)
+
+    # Fallback: synthesize quantiles from summary stats
+    if not decoder_quantiles:
+        for table in tables:
+            for row in table["rows"]:
+                dec = row["decoder"]
+                med = row["per_shot_median"]
+                p99 = row["per_shot_p99"]
+                mx = row["per_shot_max"]
+                if med > 0:
+                    q = [med * 0.5] + [med] * 9 + [med] + [med] * 5 + [p99] * 3 + [mx, mx]
+                    decoder_quantiles.setdefault(dec, []).append(q)
+
+    if not decoder_quantiles:
+        return ""
+
+    # Merge quantiles per decoder: geometric mean of each percentile position
+    merged: dict[str, list[float]] = {}
+    for dec, q_list in sorted(decoder_quantiles.items()):
+        n_q = len(q_list[0])
+        result = []
+        for i in range(n_q):
+            vals = [q[i] for q in q_list if i < len(q) and q[i] > 0]
+            if vals:
+                geo_mean = math.exp(sum(math.log(v) for v in vals) / len(vals))
+                result.append(geo_mean)
+            else:
+                result.append(0.0)
+        merged[dec] = result
+
+    decoders = list(merged.keys())
+    all_vals = [v for qs in merged.values() for v in qs if v > 0]
+    if not all_vals:
+        return ""
+
+    val_min = min(all_vals) * 0.3
+    val_max = max(all_vals) * 3.0
+    log_min = math.log10(val_min)
+    log_max = math.log10(val_max)
+
+    def x_of(v: float) -> float:
+        if v <= 0:
+            return margin["left"]
+        frac = (math.log10(v) - log_min) / (log_max - log_min) if log_max != log_min else 0.5
+        return margin["left"] + frac * plot_w
+
+    violin_h = min(60, plot_h / len(decoders) * 0.75)
+    group_h = plot_h / len(decoders)
+
+    parts = [
+        f'<svg xmlns="http://www.w3.org/2000/svg" width="{width}" height="{height}" '
+        f'style="font-family:ui-sans-serif,sans-serif;font-size:11px;">',
+        f'<rect width="{width}" height="{height}" fill="var(--card-bg, white)" rx="8"/>',
+        f'<text x="{width // 2}" y="24" text-anchor="middle" font-size="13" '
+        f'font-weight="600" fill="var(--fg, #0f172a)">{html_mod.escape(title)}</text>',
+    ]
+
+    # Grid lines (log scale)
+    for exp in range(math.floor(log_min), math.ceil(log_max) + 1):
+        x = x_of(10**exp)
+        if margin["left"] <= x <= margin["left"] + plot_w:
+            parts.append(
+                f'<line x1="{x:.1f}" y1="{margin["top"]}" '
+                f'x2="{x:.1f}" y2="{margin["top"] + plot_h}" '
+                f'stroke="var(--table-border, #e2e8f0)" stroke-width="0.5"/>',
+            )
+            parts.append(
+                f'<text x="{x:.1f}" y="{margin["top"] + plot_h + 16}" text-anchor="middle" '
+                f'fill="var(--muted, #475569)" font-size="10">1e{exp}s</text>',
+            )
+
+    parts.append(
+        f'<text x="{margin["left"] + plot_w // 2}" y="{height - 8}" text-anchor="middle" '
+        f'fill="var(--muted, #475569)" font-size="11">Decode time per shot (seconds, log scale)</text>',
+    )
+
+    # Draw violins
+    for di, dec in enumerate(decoders):
+        qs = merged[dec]
+        cy = margin["top"] + di * group_h + group_h / 2
+        color = _COLORS[di % len(_COLORS)]
+
+        # Decoder label
+        parts.append(
+            f'<text x="{margin["left"] - 8}" y="{cy + 4:.1f}" '
+            f'text-anchor="end" fill="var(--fg, #0f172a)" font-size="11">{html_mod.escape(dec)}</text>',
+        )
+
+        # Build violin shape from quantiles.
+        # The "width" at each quantile represents density: wider near the median,
+        # narrower at tails. We use a triangular kernel approximation where
+        # density ~ 1 / (gap between adjacent quantiles in log space).
+        n = len(qs)
+        if n < 3:
+            continue
+
+        # Compute density proxy at each quantile
+        log_qs = [math.log10(max(v, 1e-12)) for v in qs]
+        densities = []
+        for i in range(n):
+            left = log_qs[i] - log_qs[max(0, i - 1)]
+            right = log_qs[min(n - 1, i + 1)] - log_qs[i]
+            gap = left + right
+            densities.append(1.0 / max(gap, 0.01))
+
+        max_density = max(densities) if densities else 1.0
+        half_h = violin_h / 2
+
+        # Build SVG path: top half then bottom half (mirror)
+        top_points = []
+        bot_points = []
+        for i in range(n):
+            if qs[i] <= 0:
+                continue
+            x = x_of(qs[i])
+            dy = (densities[i] / max_density) * half_h
+            top_points.append((x, cy - dy))
+            bot_points.append((x, cy + dy))
+
+        if len(top_points) < 2:
+            continue
+
+        # Build path: top left-to-right, then bottom right-to-left
+        path_parts = [f"M{top_points[0][0]:.1f},{top_points[0][1]:.1f}"]
+        for x, y in top_points[1:]:
+            path_parts.append(f"L{x:.1f},{y:.1f}")
+        for x, y in reversed(bot_points):
+            path_parts.append(f"L{x:.1f},{y:.1f}")
+        path_parts.append("Z")
+
+        parts.append(
+            f'<path d="{" ".join(path_parts)}" fill="{color}" opacity="0.3" stroke="{color}" stroke-width="1"/>',
+        )
+
+        # Median line
+        med_idx = n // 2
+        if qs[med_idx] > 0:
+            mx = x_of(qs[med_idx])
+            dy = (densities[med_idx] / max_density) * half_h
+            parts.append(
+                f'<line x1="{mx:.1f}" y1="{cy - dy:.1f}" '
+                f'x2="{mx:.1f}" y2="{cy + dy:.1f}" '
+                f'stroke="{color}" stroke-width="2"/>',
+            )
+            parts.append(
+                f'<text x="{mx:.1f}" y="{cy - dy - 4:.1f}" text-anchor="middle" '
+                f'fill="var(--fg, #0f172a)" font-size="9">'
+                f"{qs[med_idx]:.1e}s</text>",
+            )
+
+        # p99 marker (index 19 of 21 = 95th percentile is close, use index ~20*0.99=19.8)
+        p99_idx = min(n - 2, int(n * 0.99))
+        if p99_idx < n and qs[p99_idx] > 0:
+            px = x_of(qs[p99_idx])
+            parts.append(
+                f'<line x1="{px:.1f}" y1="{cy - 3:.1f}" '
+                f'x2="{px:.1f}" y2="{cy + 3:.1f}" '
+                f'stroke="{color}" stroke-width="1.5"/>',
+            )
+
+    parts.append("</svg>")
+    return "\n".join(parts)
+
+
+# -- HTML report --------------------------------------------------------------
+
+
+def _shots_summary(tables: list[dict]) -> str:
+    """Summarise shot counts across all comparison table rows."""
+    all_counts = set()
+    for table in tables:
+        for row in table["rows"]:
+            all_counts.add(row["num_shots"])
+    if not all_counts:
+        return "N/A"
+    lo, hi = min(all_counts), max(all_counts)
+    if lo == hi:
+        return str(lo)
+    return f"{lo} -- {hi} per point"
+
+
+def _rounds_summary(tables: list[dict]) -> str:
+    """Summarise round counts per distance, e.g. 'd=3: r=[6,7,9]; d=5: r=[10,12,15]'."""
+    from collections import defaultdict
+
+    rounds_by_d: dict[int, set[int]] = defaultdict(set)
+    for table in tables:
+        rounds_by_d[table["distance"]].add(table["num_rounds"])
+    if not rounds_by_d:
+        return "N/A"
+    lines = []
+    for d in sorted(rounds_by_d):
+        rs = sorted(rounds_by_d[d])
+        lines.append(html_mod.escape(f"d={d}: r=[{', '.join(str(r) for r in rs)}]"))
+    return "<br>".join(lines)
+
+
+def _build_html(analysis: dict) -> str:
+    """Build the full HTML report string."""
+    config = analysis.get("config", {})
+    tables = analysis.get("comparison_tables", [])
+    curves = analysis.get("threshold_curves", [])
+
+    style = dedent("""
+        :root {
+          color-scheme: light dark;
+          --bg: #f8fafc; --fg: #0f172a;
+          --hero-bg: linear-gradient(135deg, #e0f2fe, #f8fafc 55%, #dcfce7);
+          --card-bg: white; --card-border: #dbeafe; --card-shadow: rgba(15,23,42,0.05);
+          --meta-bg: rgba(255,255,255,0.82);
+          --muted: #475569; --link: #2563eb;
+          --table-stripe: #f1f5f9; --table-border: #e2e8f0;
+        }
+        [data-theme="dark"] {
+          --bg: #0f172a; --fg: #e2e8f0;
+          --hero-bg: linear-gradient(135deg, #1e293b, #0f172a 55%, #1a2e1a);
+          --card-bg: #1e293b; --card-border: #334155; --card-shadow: rgba(0,0,0,0.3);
+          --meta-bg: rgba(30,41,59,0.82);
+          --muted: #94a3b8; --link: #60a5fa;
+          --table-stripe: #0f172a; --table-border: #334155;
+        }
+        @media (prefers-color-scheme: dark) {
+          :root:not([data-theme="light"]) {
+            --bg: #0f172a; --fg: #e2e8f0;
+            --hero-bg: linear-gradient(135deg, #1e293b, #0f172a 55%, #1a2e1a);
+            --card-bg: #1e293b; --card-border: #334155; --card-shadow: rgba(0,0,0,0.3);
+            --meta-bg: rgba(30,41,59,0.82);
+            --muted: #94a3b8; --link: #60a5fa;
+            --table-stripe: #0f172a; --table-border: #334155;
+          }
+        }
+        body {
+          margin: 0;
+          font-family: ui-sans-serif, -apple-system, BlinkMacSystemFont, sans-serif;
+          background: var(--bg); color: var(--fg);
+        }
+        main { max-width: 1400px; margin: 0 auto; padding: 32px 24px 56px; }
+        h1, h2, h3, p { margin-top: 0; }
+        .theme-toggle {
+          position: fixed; top: 16px; right: 16px; z-index: 100;
+          background: var(--card-bg); border: 1px solid var(--card-border);
+          border-radius: 8px; padding: 6px 12px; cursor: pointer;
+          color: var(--fg); font-size: 0.85rem; font-weight: 600;
+        }
+        .theme-toggle:hover { opacity: 0.8; }
+        .hero {
+          background: var(--hero-bg);
+          border: 1px solid var(--card-border);
+          border-radius: 20px;
+          padding: 24px;
+          margin-bottom: 24px;
+        }
+        .meta {
+          display: grid;
+          grid-template-columns: repeat(auto-fit, minmax(200px, 1fr));
+          gap: 12px;
+          margin-top: 18px;
+        }
+        .meta-card {
+          background: var(--meta-bg);
+          border: 1px solid var(--card-border);
+          border-radius: 14px;
+          padding: 14px 16px;
+        }
+        .meta-card strong {
+          display: block; font-size: 0.82rem; text-transform: uppercase;
+          letter-spacing: 0.04em; color: var(--muted); margin-bottom: 6px;
+        }
+        .section {
+          background: var(--card-bg);
+          border: 1px solid var(--card-border);
+          border-radius: 18px;
+          padding: 20px 22px;
+          margin-top: 20px;
+          box-shadow: 0 10px 24px var(--card-shadow);
+          overflow-x: auto;
+        }
+        .plots {
+          display: flex;
+          flex-wrap: wrap;
+          gap: 16px;
+          justify-content: center;
+        }
+        table { border-collapse: collapse; width: 100%; margin: 12px 0 0; }
+        th, td { padding: 10px 14px; text-align: right; border-bottom: 1px solid var(--table-border); }
+        th {
+          font-size: 0.82rem; text-transform: uppercase;
+          letter-spacing: 0.03em; color: var(--muted); border-bottom-width: 2px;
+        }
+        td:first-child, th:first-child { text-align: left; }
+        tr:nth-child(even) td { background: var(--table-stripe); }
+        code { font-family: ui-monospace, SFMono-Regular, Menlo, monospace; }
+        details.collapsible { margin-top: 20px; }
+        details.collapsible > summary {
+          cursor: pointer; font-size: 1.1rem; font-weight: 600;
+          padding: 14px 22px;
+          background: var(--card-bg); border: 1px solid var(--card-border);
+          border-radius: 18px;
+          box-shadow: 0 10px 24px var(--card-shadow);
+          list-style: none;
+        }
+        details.collapsible > summary::before { content: "\\25B6  "; font-size: 0.8em; }
+        details.collapsible[open] > summary::before { content: "\\25BC  "; }
+        details.collapsible > .section { margin-top: 8px; }
+    """).strip()
+
+    def meta_card(label: str, value: str, *, raw: bool = False) -> str:
+        val = value if raw else html_mod.escape(value)
+        return f'      <div class="meta-card"><strong>{html_mod.escape(label)}</strong>{val}</div>'
+
+    decoders = config.get("decoders", [])
+    p1s = config.get("p1_scale", 1 / 30)
+    pms = config.get("p_meas_scale", 1 / 3)
+    pps = config.get("p_prep_scale", 1 / 3)
+    noise_str = f"Depolarizing: p1={p1s:.4g}*p, p2=p, p_meas={pms:.4g}*p, p_prep={pps:.4g}*p"
+
+    # Build global color maps for consistency across all plots
+    all_decoders_sorted = sorted({c["decoder"] for c in curves}) if curves else decoders
+    all_distances_sorted = sorted({c["distance"] for c in curves}) if curves else []
+    dec_colors = {d: _COLORS[i % len(_COLORS)] for i, d in enumerate(all_decoders_sorted)}
+    dist_colors = {d: _COLORS[i % len(_COLORS)] for i, d in enumerate(all_distances_sorted)}
+
+    parts = [
+        "<!doctype html>",
+        '<html lang="en">',
+        "<head>",
+        '  <meta charset="utf-8" />',
+        '  <meta name="viewport" content="width=device-width, initial-scale=1" />',
+        "  <title>PECOS Decoder Performance Report</title>",
+        f"  <style>{style}</style>",
+        "</head>",
+        "<body>",
+        '<button id="theme-toggle" class="theme-toggle">Light / Dark</button>',
+        "<main>",
+        '  <section class="hero">',
+        "    <h1>PECOS Decoder Performance Report</h1>",
+        "    <p>Same samples decoded by multiple decoders. LER differences reflect "
+        "decoder quality, not sampling noise.</p>",
+        '    <div class="meta">',
+        meta_card("Decoders", ", ".join(decoders)),
+        meta_card("Distances", ", ".join(str(d) for d in config.get("distances", []))),
+        meta_card("Basis", config.get("basis", "Z")),
+        meta_card("Shots", _shots_summary(tables)),
+        meta_card("Noise Model", noise_str),
+        meta_card("Error Rates (p)", ", ".join(f"{p:.4g}" for p in config.get("error_rates", []))),
+        "    </div>",
+        '    <div class="meta" style="grid-template-columns: 1fr;">',
+        meta_card("Rounds", _rounds_summary(tables), raw=True),
+        "    </div>",
+        "  </section>",
+    ]
+
+    # -- Threshold curves section --
+    if curves:
+        # Group curves by distance and by decoder
+        curves_by_distance: dict[int, list[dict]] = defaultdict(list)
+        curves_by_decoder: dict[str, list[dict]] = defaultdict(list)
+        for curve in curves:
+            curves_by_distance[curve["distance"]].append(curve)
+            curves_by_decoder[curve["decoder"]].append(curve)
+
+        threshold_estimates = analysis.get("threshold_estimates", [])
+        fss_per_round_est = {e["decoder"]: e for e in threshold_estimates if e.get("metric") == "fss_per_round"}
+        fss_d_round_est = {e["decoder"]: e for e in threshold_estimates if e.get("metric") == "fss_d_round"}
+
+        def _threshold_table(estimates: dict) -> list[str]:
+            if not estimates:
+                return []
+            lines = []
+            lines.append("    <table>")
+            lines.append(
+                "      <tr><th>Decoder</th><th>Threshold (FSS fit)</th><th>Distances</th></tr>",
+            )
+            for est in sorted(estimates.values(), key=lambda e: e.get("estimated_p_th", 0), reverse=True):
+                p_th = est["estimated_p_th"]
+                se = est.get("std_error")
+                th_str = f"{_sci(p_th)} +/- {_sci(se)}" if se else f"{_sci(p_th)}"
+                lines.append(
+                    f"      <tr><td>{html_mod.escape(est['decoder'])}</td>"
+                    f"<td>{th_str}</td>"
+                    f"<td>d={est['d_small']} -- d={est['d_large']}</td></tr>",
+                )
+            lines.append("    </table>")
+            return lines
+
+        # === ALWAYS VISIBLE: Per-round LER ===
+
+        # Per-round by distance
+        parts.append('  <div class="section">')
+        parts.append("    <h2>Per-Round Logical Error Rate -- by Distance</h2>")
+        parts.append(
+            "    <p>All decoders compared at each distance. "
+            "Fitted from multiple syndrome extraction rounds per point.</p>",
+        )
+        parts.append('    <div class="plots">')
+        for d in sorted(curves_by_distance):
+            svg = _build_threshold_svg(
+                curves_by_distance[d],
+                title=f"d = {d}",
+                y_field="per_round_ler",
+                y_label="LER per round",
+                decoder_color_map=dec_colors,
+            )
+            parts.append(f"      {svg}")
+        parts.append("    </div>")
+        parts.append("  </div>")
+
+        # Per-round by decoder (threshold view)
+        parts.append('  <div class="section">')
+        parts.append("    <h2>Per-Round Logical Error Rate -- by Decoder</h2>")
+        parts.append(
+            "    <p>Distance scaling for each decoder. "
+            "Curves crossing = threshold (per-round LER is distance-independent at threshold).</p>",
+        )
+        parts.extend(_threshold_table(fss_per_round_est))
+        parts.append('    <div class="plots">')
+        for dec in sorted(curves_by_decoder):
+            est = fss_per_round_est.get(dec)
+            title = dec
+            p_th = None
+            if est:
+                p_th = est["estimated_p_th"]
+                title = f"{dec} (p_th ~ {p_th:.4f})"
+            svg = _build_threshold_svg(
+                curves_by_decoder[dec],
+                title=title,
+                color_by="distance",
+                threshold_p=p_th,
+                y_field="per_round_ler",
+                y_label="LER per round",
+                distance_color_map=dist_colors,
+            )
+            parts.append(f"      {svg}")
+        parts.append("    </div>")
+        parts.append("  </div>")
+
+        # === COLLAPSIBLE: d-round LER ===
+        parts.append('  <details class="collapsible">')
+        parts.append("    <summary>d-Round Logical Error Rate (click to expand)</summary>")
+
+        # d-round by distance
+        parts.append('    <div class="section">')
+        parts.append("      <h3>d-Round LER -- by Distance</h3>")
+        parts.append("      <p>Logical error rate over d rounds of syndrome extraction.</p>")
+        parts.append('      <div class="plots">')
+        for d in sorted(curves_by_distance):
+            svg = _build_threshold_svg(
+                curves_by_distance[d],
+                title=f"d = {d}",
+                y_label="LER (d rounds)",
+                decoder_color_map=dec_colors,
+            )
+            parts.append(f"        {svg}")
+        parts.append("      </div>")
+        parts.append("    </div>")
+
+        # d-round by decoder
+        parts.append('    <div class="section">')
+        parts.append("      <h3>d-Round LER -- by Decoder</h3>")
+        parts.extend(_threshold_table(fss_d_round_est))
+        parts.append('      <div class="plots">')
+        for dec in sorted(curves_by_decoder):
+            est = fss_d_round_est.get(dec)
+            title = dec
+            p_th = None
+            if est:
+                p_th = est["estimated_p_th"]
+                title = f"{dec} (p_th ~ {p_th:.4f})"
+            svg = _build_threshold_svg(
+                curves_by_decoder[dec],
+                title=title,
+                color_by="distance",
+                threshold_p=p_th,
+                y_label="LER (d rounds)",
+                distance_color_map=dist_colors,
+            )
+            parts.append(f"        {svg}")
+        parts.append("      </div>")
+        parts.append("    </div>")
+        parts.append("  </details>")
+
+    # -- Duration curves (collapsible) --
+    duration_curves = analysis.get("duration_curves", [])
+    if duration_curves:
+        # Group by physical_error_rate
+        dur_by_p: dict[float, list[dict]] = defaultdict(list)
+        for dc in duration_curves:
+            dur_by_p[dc["physical_error_rate"]].append(dc)
+
+        parts.append('  <details class="collapsible">')
+        parts.append("    <summary>Duration Curves -- LER vs Rounds (click to expand)</summary>")
+        parts.append('    <div class="section">')
+        parts.append(
+            "      <p>Logical error rate vs number of rounds at fixed physical error rate. "
+            "Shows how LER grows with memory duration.</p>",
+        )
+        parts.append('      <div class="plots">')
+        for p in sorted(dur_by_p):
+            svg = _build_duration_svg(dur_by_p[p], title=f"p = {p:.4g}")
+            parts.append(f"        {svg}")
+        parts.append("      </div>")
+        parts.append("    </div>")
+        parts.append("  </details>")
+
+    # -- Timing comparison section --
+    if tables:
+        err_rates = sorted({t["physical_error_rate"] for t in tables})
+        distances_available = sorted({t["distance"] for t in tables})
+
+        def _violin_plots_for_p(p_val: float) -> list[str]:
+            """Generate violin SVGs for each distance at a given error rate."""
+            svgs = []
+            for d in distances_available:
+                candidates = [t for t in tables if t["distance"] == d and t["physical_error_rate"] == p_val]
+                if not candidates:
+                    continue
+                target_r = 2 * d
+                best = min(candidates, key=lambda t: abs(t["num_rounds"] - target_r))
+                svg = _build_timing_svg(
+                    [best],
+                    title=f"d = {d}, r = {best['num_rounds']}",
+                )
+                svgs.append(svg)
+            return svgs
+
+        # Always-visible: lowest error rate
+        if err_rates:
+            lowest_p = err_rates[0]
+            svgs = _violin_plots_for_p(lowest_p)
+            if svgs:
+                parts.append('  <div class="section">')
+                parts.append(f"    <h2>Decode Speed (p = {lowest_p:.4g})</h2>")
+                parts.append("    <p>Per-shot decode time distribution for each decoder and distance.</p>")
+                parts.append('    <div class="plots">')
+                parts.extend(f"      {svg}" for svg in svgs)
+                parts.append("    </div>")
+                parts.append("  </div>")
+
+        # Collapsible: all other error rates
+        other_rates = [p for p in err_rates if p != err_rates[0]]
+        if other_rates:
+            parts.append('  <details class="collapsible">')
+            parts.append("    <summary>Decode Speed at Other Error Rates (click to expand)</summary>")
+            for p_val in other_rates:
+                svgs = _violin_plots_for_p(p_val)
+                if svgs:
+                    parts.append('    <div class="section">')
+                    parts.append(f"      <h3>p = {p_val:.4g}</h3>")
+                    parts.append('      <div class="plots">')
+                    parts.extend(f"        {svg}" for svg in svgs)
+                    parts.append("      </div>")
+                    parts.append("    </div>")
+            parts.append("  </details>")
+
+    # -- Comparison tables (collapsible) --
+    if tables:
+        parts.append('  <details class="collapsible">')
+        parts.append("    <summary>Detailed Comparison Tables (click to expand)</summary>")
+        for table in tables:
+            d = table["distance"]
+            p = table["physical_error_rate"]
+            r = table["num_rounds"]
+            n = table["num_shots"]
+
+            parts.append('    <div class="section">')
+            parts.append(f"      <h3>d={d}, p={p:.4g}, rounds={r} ({n} shots)</h3>")
+            parts.append("      <table>")
+            parts.append(
+                "        <tr><th>Decoder</th><th>LER (95% CI)</th>"
+                "<th>Median</th><th>p99</th><th>Max</th><th>Throughput</th></tr>",
+            )
+
+            for row in table["rows"]:
+                ler_str = f"{row['logical_error_rate']:.4f} ({row['ci_low']:.4f} - {row['ci_high']:.4f})"
+                sps = row["num_shots"] / row["per_shot_median"] if row["per_shot_median"] > 0 else float("inf")
+                parts.append(
+                    f"        <tr>"
+                    f"<td>{html_mod.escape(row['decoder'])}</td>"
+                    f"<td>{ler_str}</td>"
+                    f"<td>{row['per_shot_median']:.1e} s</td>"
+                    f"<td>{row['per_shot_p99']:.1e} s</td>"
+                    f"<td>{row['per_shot_max']:.1e} s</td>"
+                    f"<td>{sps:.1e} shots/s</td>"
+                    f"</tr>",
+                )
+
+            parts.append("      </table>")
+            parts.append("    </div>")
+        parts.append("  </details>")
+
+    parts.extend(
+        [
+            "</main>",
+            dedent("""
+        <script>
+        (function() {
+          var html = document.documentElement;
+          var btn = document.getElementById('theme-toggle');
+          var stored = localStorage.getItem('pecos-theme');
+          if (stored) html.setAttribute('data-theme', stored);
+          btn.addEventListener('click', function() {
+            var current = html.getAttribute('data-theme');
+            var next = current === 'dark' ? 'light' : 'dark';
+            if (!current) next = 'dark';
+            html.setAttribute('data-theme', next);
+            localStorage.setItem('pecos-theme', next);
+          });
+        })();
+        </script>
+        """).strip(),
+            "</body>",
+            "</html>",
+        ],
+    )
+
+    return "\n".join(parts)
+
+
+# -- PDF report (matplotlib) --------------------------------------------------
+
+
+def _build_pdf(analysis: dict, output_path: Path) -> None:
+    """Build a multi-page PDF report using matplotlib."""
+    import matplotlib.pyplot as plt
+    from matplotlib.backends.backend_pdf import PdfPages
+
+    config = analysis.get("config", {})
+    tables = analysis.get("comparison_tables", [])
+    curves = analysis.get("threshold_curves", [])
+
+    page_size = (11, 8.5)
+
+    with PdfPages(output_path) as pdf:
+        # -- Cover page --
+        fig, ax = plt.subplots(figsize=page_size)
+        ax.axis("off")
+        ax.text(
+            0.5,
+            0.65,
+            "PECOS Decoder Performance Report",
+            transform=ax.transAxes,
+            fontsize=24,
+            ha="center",
+            va="center",
+            fontweight="bold",
+        )
+
+        info_lines = [
+            f"Decoders: {', '.join(config.get('decoders', []))}",
+            f"Distances: {config.get('distances', [])}",
+            f"Error rates: {config.get('error_rates', [])}",
+            f"Shots: {config.get('shots', 'N/A')}",
+            f"Basis: {config.get('basis', 'Z')}",
+        ]
+        ax.text(
+            0.5,
+            0.40,
+            "\n".join(info_lines),
+            transform=ax.transAxes,
+            fontsize=12,
+            ha="center",
+            va="center",
+            family="monospace",
+        )
+        pdf.savefig(fig)
+        plt.close(fig)
+
+        # -- Threshold curve plots --
+        if curves:
+            curves_by_distance: dict[int, list[dict]] = defaultdict(list)
+            curves_by_decoder: dict[str, list[dict]] = defaultdict(list)
+            for curve in curves:
+                curves_by_distance[curve["distance"]].append(curve)
+                curves_by_decoder[curve["decoder"]].append(curve)
+
+            def _plot_curves(
+                ax: plt.Axes,
+                curve_list: list[dict],
+                title: str,
+                color_by: str = "decoder",
+            ) -> None:
+                ax.set_title(title, fontsize=14, fontweight="bold")
+                ax.set_xlabel("Physical error rate (p)")
+                ax.set_ylabel("Logical error rate")
+                ax.set_yscale("log")
+                ax.grid(visible=True, alpha=0.3)
+                decoder_names = list(dict.fromkeys(c["decoder"] for c in curve_list))
+                dists = sorted({c["distance"] for c in curve_list})
+                linestyles = ["-", "--", ":", "-."]
+                for curve in sorted(curve_list, key=lambda c: (decoder_names.index(c["decoder"]), c["distance"])):
+                    pts = [pt for pt in curve["points"] if pt["logical_error_rate"] > 0]
+                    if not pts:
+                        continue
+                    ps = [pt["physical_error_rate"] for pt in pts]
+                    lers = [pt["logical_error_rate"] for pt in pts]
+                    ci_lows = [pt["ci_low"] for pt in pts]
+                    ci_highs = [pt["ci_high"] for pt in pts]
+                    dec_idx = decoder_names.index(curve["decoder"])
+                    dist_idx = dists.index(curve["distance"])
+                    if color_by == "distance":
+                        color = _COLORS[dist_idx % len(_COLORS)]
+                        ls = linestyles[dec_idx % len(linestyles)]
+                    else:
+                        color = _COLORS[dec_idx % len(_COLORS)]
+                        ls = linestyles[dist_idx % len(linestyles)]
+                    label = f"{curve['decoder']} d={curve['distance']}"
+                    ax.plot(ps, lers, marker="o", linestyle=ls, color=color, label=label, markersize=4)
+                    ax.fill_between(ps, ci_lows, ci_highs, color=color, alpha=0.15)
+                ax.legend(fontsize=9, loc="best")
+
+            # Per-distance plots (all decoders)
+            for d in sorted(curves_by_distance):
+                fig, ax = plt.subplots(figsize=page_size)
+                _plot_curves(ax, curves_by_distance[d], f"By Distance -- d = {d}")
+                fig.tight_layout()
+                pdf.savefig(fig)
+                plt.close(fig)
+
+            # Per-decoder plots (all distances -- color by distance, threshold line)
+            threshold_estimates = analysis.get("threshold_estimates", [])
+            est_by_dec = {e["decoder"]: e for e in threshold_estimates}
+            for dec in sorted(curves_by_decoder):
+                fig, ax = plt.subplots(figsize=page_size)
+                est = est_by_dec.get(dec)
+                title = f"By Decoder -- {dec}"
+                if est:
+                    title += f" (p_th ~ {est['estimated_p_th']:.4f})"
+                _plot_curves(ax, curves_by_decoder[dec], title, color_by="distance")
+                if est:
+                    ax.axvline(
+                        est["estimated_p_th"],
+                        color="#334155",
+                        linestyle=":",
+                        linewidth=1.8,
+                        alpha=0.7,
+                        zorder=0,
+                    )
+                fig.tight_layout()
+                pdf.savefig(fig)
+                plt.close(fig)
+
+        # -- Duration curve plots --
+        duration_curves = analysis.get("duration_curves", [])
+        if duration_curves:
+            dur_by_p: dict[float, list[dict]] = defaultdict(list)
+            for dc in duration_curves:
+                dur_by_p[dc["physical_error_rate"]].append(dc)
+
+            for p_val in sorted(dur_by_p):
+                fig, ax = plt.subplots(figsize=page_size)
+                ax.set_title(f"Duration -- p = {p_val:.4g}", fontsize=14, fontweight="bold")
+                ax.set_xlabel("Rounds")
+                ax.set_ylabel("Logical error rate")
+                ax.set_yscale("log")
+                ax.grid(visible=True, alpha=0.3)
+
+                for ci, dc in enumerate(dur_by_p[p_val]):
+                    pts = [pt for pt in dc["points"] if pt["logical_error_rate"] > 0]
+                    if not pts:
+                        continue
+                    rs = [pt["num_rounds"] for pt in pts]
+                    lers = [pt["logical_error_rate"] for pt in pts]
+                    ci_lows = [pt["ci_low"] for pt in pts]
+                    ci_highs = [pt["ci_high"] for pt in pts]
+                    color = _COLORS[ci % len(_COLORS)]
+                    label = f"{dc['decoder']} d={dc['distance']}"
+                    ax.plot(rs, lers, "o-", color=color, label=label, markersize=4)
+                    ax.fill_between(rs, ci_lows, ci_highs, color=color, alpha=0.15)
+
+                ax.legend(fontsize=9, loc="best")
+                fig.tight_layout()
+                pdf.savefig(fig)
+                plt.close(fig)
+
+        # -- Comparison tables as figures --
+        for table in tables:
+            fig, ax = plt.subplots(figsize=page_size)
+            ax.axis("off")
+            ax.set_title(
+                f"d={table['distance']}, p={table['physical_error_rate']:.4g}, "
+                f"rounds={table['num_rounds']} ({table['num_shots']} shots)",
+                fontsize=14,
+                fontweight="bold",
+                pad=20,
+            )
+
+            col_labels = ["Decoder", "LER", "95% CI", "Median", "p99", "Max"]
+            cell_data = [
+                [
+                    row["decoder"],
+                    f"{row['logical_error_rate']:.4f}",
+                    f"{row['ci_low']:.4f} - {row['ci_high']:.4f}",
+                    f"{row['per_shot_median']:.1e} s",
+                    f"{row['per_shot_p99']:.1e} s",
+                    f"{row['per_shot_max']:.1e} s",
+                ]
+                for row in table["rows"]
+            ]
+
+            if cell_data:
+                tbl = ax.table(
+                    cellText=cell_data,
+                    colLabels=col_labels,
+                    loc="center",
+                    cellLoc="center",
+                )
+                tbl.auto_set_font_size(value=False)
+                tbl.set_fontsize(10)
+                tbl.scale(1.0, 1.8)
+
+                # Style header row
+                for j in range(len(col_labels)):
+                    tbl[0, j].set_facecolor("#e2e8f0")
+                    tbl[0, j].set_text_props(fontweight="bold")
+
+            fig.tight_layout()
+            pdf.savefig(fig)
+            plt.close(fig)
+
+
+# -- Markdown report (Obsidian-compatible) ------------------------------------
+
+
+def _build_markdown(analysis: dict, plots_dir: Path) -> str:
+    """Build an Obsidian-compatible Markdown report with standalone SVG plots."""
+    config = analysis.get("config", {})
+    tables = analysis.get("comparison_tables", [])
+    curves = analysis.get("threshold_curves", [])
+
+    decoders = config.get("decoders", [])
+    p1s = config.get("p1_scale", 1 / 30)
+    pms = config.get("p_meas_scale", 1 / 3)
+    pps = config.get("p_prep_scale", 1 / 3)
+    noise_str = f"Depolarizing: p1={p1s:.4g}*p, p2=p, p_meas={pms:.4g}*p, p_prep={pps:.4g}*p"
+
+    # Global color maps
+    all_decoders_sorted = sorted({c["decoder"] for c in curves}) if curves else decoders
+    all_distances_sorted = sorted({c["distance"] for c in curves}) if curves else []
+    dec_colors = {d: _COLORS[i % len(_COLORS)] for i, d in enumerate(all_decoders_sorted)}
+    dist_colors = {d: _COLORS[i % len(_COLORS)] for i, d in enumerate(all_distances_sorted)}
+
+    # Rounds summary
+    rounds_by_d: dict[int, set[int]] = defaultdict(set)
+    for table in tables:
+        rounds_by_d[table["distance"]].add(table["num_rounds"])
+
+    def _save_svg(svg_content: str, name: str) -> str:
+        """Save SVG to plots_dir and return relative path."""
+        filename = f"{name}.svg"
+        (plots_dir / filename).write_text(svg_content)
+        return f"plots/{filename}"
+
+    lines = []
+
+    # -- Frontmatter --
+    lines.append("---")
+    lines.append("title: PECOS Decoder Performance Report")
+    lines.append("tags: [report, surface-code, decoders]")
+    lines.append(f"decoders: [{', '.join(decoders)}]")
+    lines.append(f"distances: [{', '.join(str(d) for d in config.get('distances', []))}]")
+    lines.append(f"date: {__import__('datetime').date.today().isoformat()}")
+    lines.append("---")
+    lines.append("")
+
+    # -- Header --
+    lines.append("# PECOS Decoder Performance Report")
+    lines.append("")
+    lines.append("> [!info] Configuration")
+    lines.append(f"> **Decoders:** {', '.join(decoders)}")
+    lines.append(f"> **Distances:** {', '.join(str(d) for d in config.get('distances', []))}")
+    lines.append(f"> **Error Rates (p):** {', '.join(f'{p:.4g}' for p in config.get('error_rates', []))}")
+    lines.append(f"> **Shots:** {_shots_summary(tables)}")
+    lines.append(f"> **Noise Model:** {noise_str}")
+    lines.append(f"> **Basis:** {config.get('basis', 'Z')}")
+    for d in sorted(rounds_by_d):
+        rs = sorted(rounds_by_d[d])
+        lines.append(f"> **d={d}:** r=[{', '.join(str(r) for r in rs)}]")
+    lines.append("")
+
+    if curves:
+        curves_by_distance: dict[int, list[dict]] = defaultdict(list)
+        curves_by_decoder: dict[str, list[dict]] = defaultdict(list)
+        for curve in curves:
+            curves_by_distance[curve["distance"]].append(curve)
+            curves_by_decoder[curve["decoder"]].append(curve)
+
+        threshold_estimates = analysis.get("threshold_estimates", [])
+        fss_per_round_est = {e["decoder"]: e for e in threshold_estimates if e.get("metric") == "fss_per_round"}
+        fss_d_round_est = {e["decoder"]: e for e in threshold_estimates if e.get("metric") == "fss_d_round"}
+
+        # -- Per-round by distance --
+        lines.append("## Per-Round LER -- by Distance")
+        lines.append("")
+        for d in sorted(curves_by_distance):
+            svg = _build_threshold_svg(
+                curves_by_distance[d],
+                title=f"d = {d}",
+                y_field="per_round_ler",
+                y_label="LER per round",
+                decoder_color_map=dec_colors,
+            )
+            path = _save_svg(svg, f"per_round_by_dist_d{d}")
+            lines.append(f"![d={d}]({path})")
+            lines.append("")
+
+        # -- Per-round by decoder with thresholds --
+        lines.append("## Per-Round LER -- by Decoder")
+        lines.append("")
+
+        if fss_per_round_est:
+            lines.append("### Threshold Estimates (per-round)")
+            lines.append("")
+            lines.append("| Decoder | Threshold | Distances |")
+            lines.append("|---------|-----------|-----------|")
+            lines.extend(
+                f"| {est['decoder']} | {est['estimated_p_th']:.4f} "
+                f"| d={est['d_small']} / d={est['d_large']} crossing |"
+                for est in sorted(fss_per_round_est.values(), key=lambda e: e["estimated_p_th"], reverse=True)
+            )
+            lines.append("")
+
+        for dec in sorted(curves_by_decoder):
+            est = fss_per_round_est.get(dec)
+            title = dec
+            p_th = None
+            if est:
+                p_th = est["estimated_p_th"]
+                title = f"{dec} (p_th ~ {p_th:.4f})"
+            svg = _build_threshold_svg(
+                curves_by_decoder[dec],
+                title=title,
+                color_by="distance",
+                threshold_p=p_th,
+                y_field="per_round_ler",
+                y_label="LER per round",
+                distance_color_map=dist_colors,
+            )
+            path = _save_svg(svg, f"per_round_by_dec_{dec.replace(':', '_')}")
+            lines.append(f"![{dec}]({path})")
+            lines.append("")
+
+        # -- d-round LER (collapsible) --
+        lines.append("> [!note]- d-Round Logical Error Rate (click to expand)")
+        lines.append(">")
+        lines.append("> ### d-Round LER -- by Distance")
+        lines.append(">")
+        for d in sorted(curves_by_distance):
+            svg = _build_threshold_svg(
+                curves_by_distance[d],
+                title=f"d = {d}",
+                y_label="LER (d rounds)",
+                decoder_color_map=dec_colors,
+            )
+            path = _save_svg(svg, f"d_round_by_dist_d{d}")
+            lines.append(f"> ![d={d}]({path})")
+            lines.append(">")
+
+        if fss_d_round_est:
+            lines.append("> ### Threshold Estimates (d-round)")
+            lines.append(">")
+            lines.append("> | Decoder | Threshold | Distances |")
+            lines.append("> |---------|-----------|-----------|")
+            lines.extend(
+                f"> | {est['decoder']} | {est['estimated_p_th']:.4f} "
+                f"| d={est['d_small']} / d={est['d_large']} crossing |"
+                for est in sorted(fss_d_round_est.values(), key=lambda e: e["estimated_p_th"], reverse=True)
+            )
+            lines.append(">")
+
+        for dec in sorted(curves_by_decoder):
+            est = fss_d_round_est.get(dec)
+            title = dec
+            p_th = None
+            if est:
+                p_th = est["estimated_p_th"]
+                title = f"{dec} (p_th ~ {p_th:.4f})"
+            svg = _build_threshold_svg(
+                curves_by_decoder[dec],
+                title=title,
+                color_by="distance",
+                threshold_p=p_th,
+                y_label="LER (d rounds)",
+                distance_color_map=dist_colors,
+            )
+            path = _save_svg(svg, f"d_round_by_dec_{dec.replace(':', '_')}")
+            lines.append(f"> ![{dec}]({path})")
+            lines.append(">")
+        lines.append("")
+
+    # -- Duration curves (collapsible) --
+    duration_curves = analysis.get("duration_curves", [])
+    if duration_curves:
+        dur_by_p: dict[float, list[dict]] = defaultdict(list)
+        for dc in duration_curves:
+            dur_by_p[dc["physical_error_rate"]].append(dc)
+
+        lines.append("> [!note]- Duration Curves -- LER vs Rounds (click to expand)")
+        lines.append(">")
+        for p in sorted(dur_by_p):
+            svg = _build_duration_svg(dur_by_p[p], title=f"p = {p:.4g}")
+            path = _save_svg(svg, f"duration_p{p:.4g}".replace(".", "_"))
+            lines.append(f"> ![p={p:.4g}]({path})")
+            lines.append(">")
+        lines.append("")
+
+    # -- Decode speed --
+    if tables:
+        err_rates = sorted({t["physical_error_rate"] for t in tables})
+        distances_available = sorted({t["distance"] for t in tables})
+
+        if err_rates:
+            lowest_p = err_rates[0]
+            lines.append(f"## Decode Speed (p = {lowest_p:.4g})")
+            lines.append("")
+            for d in distances_available:
+                candidates = [t for t in tables if t["distance"] == d and t["physical_error_rate"] == lowest_p]
+                if not candidates:
+                    continue
+                target_r = 2 * d
+                best = min(candidates, key=lambda t: abs(t["num_rounds"] - target_r))
+                svg = _build_timing_svg([best], title=f"d = {d}, r = {best['num_rounds']}")
+                path = _save_svg(svg, f"timing_d{d}_p{lowest_p:.4g}".replace(".", "_"))
+                lines.append(f"![d={d}]({path})")
+                lines.append("")
+
+        # Other error rates collapsible
+        other_rates = [p for p in err_rates if p != err_rates[0]] if err_rates else []
+        if other_rates:
+            lines.append("> [!note]- Decode Speed at Other Error Rates (click to expand)")
+            lines.append(">")
+            for p_val in other_rates:
+                lines.append(f"> **p = {p_val:.4g}**")
+                lines.append(">")
+                for d in distances_available:
+                    candidates = [t for t in tables if t["distance"] == d and t["physical_error_rate"] == p_val]
+                    if not candidates:
+                        continue
+                    target_r = 2 * d
+                    best = min(candidates, key=lambda t: abs(t["num_rounds"] - target_r))
+                    svg = _build_timing_svg([best], title=f"d = {d}, r = {best['num_rounds']}")
+                    path = _save_svg(svg, f"timing_d{d}_p{p_val:.4g}".replace(".", "_"))
+                    lines.append(f"> ![d={d}]({path})")
+                    lines.append(">")
+            lines.append("")
+
+    # -- Comparison tables (collapsible) --
+    if tables:
+        lines.append("> [!note]- Detailed Comparison Tables (click to expand)")
+        lines.append(">")
+        for table in tables:
+            d = table["distance"]
+            p = table["physical_error_rate"]
+            r = table["num_rounds"]
+            n = table["num_shots"]
+            lines.append(f"> ### d={d}, p={p:.4g}, rounds={r} ({n} shots)")
+            lines.append(">")
+            lines.append("> | Decoder | LER (95% CI) | Median | p99 | Max | Throughput |")
+            lines.append("> |---------|-------------|--------|-----|-----|------------|")
+            for row in table["rows"]:
+                ler_str = f"{row['logical_error_rate']:.4f} ({row['ci_low']:.4f} - {row['ci_high']:.4f})"
+                sps = row["num_shots"] / row["per_shot_median"] if row["per_shot_median"] > 0 else float("inf")
+                lines.append(
+                    f"> | {row['decoder']} | {ler_str} "
+                    f"| {row['per_shot_median']:.1e} s "
+                    f"| {row['per_shot_p99']:.1e} s "
+                    f"| {row['per_shot_max']:.1e} s "
+                    f"| {sps:.1e} shots/s |",
+                )
+            lines.append(">")
+        lines.append("")
+
+    return "\n".join(lines)
+
+
+# -- CLI ----------------------------------------------------------------------
+
+
+def main() -> int:
+    """CLI entry point for report generation."""
+    parser = argparse.ArgumentParser(
+        description=__doc__,
+        formatter_class=argparse.RawDescriptionHelpFormatter,
+    )
+    parser.add_argument("analysis", type=Path, help="Analysis JSON from analyze_data.py")
+    parser.add_argument("--html", action="store_true", help="Generate HTML report")
+    parser.add_argument("--pdf", action="store_true", help="Generate PDF report (requires matplotlib)")
+    parser.add_argument("--markdown", action="store_true", help="Generate Obsidian-compatible Markdown report")
+    parser.add_argument("--open", action="store_true", help="Open HTML report in browser")
+    parser.add_argument("-o", "--output-dir", type=str, default=None)
+    args = parser.parse_args()
+
+    if not args.html and not args.pdf and not args.markdown:
+        args.html = True  # default to HTML
+
+    analysis = _load_analysis(args.analysis)
+
+    out = Path(args.output_dir) if args.output_dir else args.analysis.parent
+    out.mkdir(parents=True, exist_ok=True)
+
+    if args.html:
+        html_path = out / "report.html"
+        html_path.write_text(_build_html(analysis))
+        print(f"Wrote {html_path}")
+
+        if args.open:
+            import webbrowser
+
+            webbrowser.open(html_path.as_uri())
+            print(f"Opened {html_path}")
+
+    if args.pdf:
+        pdf_path = out / "report.pdf"
+        _build_pdf(analysis, pdf_path)
+        print(f"Wrote {pdf_path}")
+
+    if args.markdown:
+        plots_dir = out / "plots"
+        plots_dir.mkdir(parents=True, exist_ok=True)
+        md_path = out / "report.md"
+        md_path.write_text(_build_markdown(analysis, plots_dir))
+        n_plots = len(list(plots_dir.glob("*.svg")))
+        print(f"Wrote {md_path} ({n_plots} SVG plots in {plots_dir}/)")
+
+    return 0
+
+
+if __name__ == "__main__":
+    raise SystemExit(main())
diff --git a/examples/surface/coherent_noise_sweep.py b/examples/surface/coherent_noise_sweep.py
new file mode 100644
index 000000000..1995878c6
--- /dev/null
+++ b/examples/surface/coherent_noise_sweep.py
@@ -0,0 +1,313 @@
+r"""Coherent idle noise sweep: surface code memory with RZ phase accumulation.
+
+Studies the impact of coherent Z-phase noise (RZ rotation after each CX gate)
+on surface code memory experiments. Uses sim_neo for Rust-native simulation
+with composable noise model (depolarizing + coherent idle RZ).
+
+The coherent noise models uncompensated phase accumulation during idle time
+between gates. Unlike stochastic Z errors (which scale as p_z per gate),
+coherent RZ rotations accumulate constructively, causing error rates far
+higher than the Pauli-twirled equivalent sin²(θ/2).
+
+Example:
+    uv run python examples/surface/coherent_noise_sweep.py \
+        --distance 3 --rounds 3 --basis X \
+        --p-depol 0.003 \
+        --p-idle 0.0 0.01 0.03 0.05 0.07 0.1 \
+        --shots 10000 --save-html --open
+"""
+
+from __future__ import annotations
+
+import argparse
+import json
+import math
+import sys
+import time
+from dataclasses import asdict, dataclass, field
+from pathlib import Path
+
+sys.path.insert(0, str(Path(__file__).resolve().parents[2] / "python" / "quantum-pecos" / "src"))
+
+
+@dataclass
+class CoherentNoisePoint:
+    p_idle: float
+    p_twirled: float
+    ler: float
+    errors: int
+    shots: int
+    standard_error: float
+    sim_seconds: float
+    decode_seconds: float
+
+
+@dataclass
+class CoherentNoiseSweep:
+    distance: int
+    rounds: int
+    basis: str
+    p_depol: float
+    backend: str
+    points: list[CoherentNoisePoint] = field(default_factory=list)
+    total_seconds: float = 0.0
+
+
+def run_sweep(
+    *,
+    distance: int,
+    rounds: int,
+    basis: str,
+    p_depol: float,
+    p_idle_values: list[float],
+    shots: int,
+    seed: int,
+    backend: str,
+    lazy_measure: bool,
+    max_bond_dim: int,
+) -> CoherentNoiseSweep:
+    """Run a coherent noise sweep using sim_neo."""
+    from pecos.qec.surface import LogicalCircuitBuilder, SurfacePatch
+    from pecos_rslib.qec import ObservableSubgraphDecoder
+    from pecos_rslib_exp import depolarizing, sim_neo, stab_mps, statevec
+
+    patch = SurfacePatch.create(distance=distance)
+    b = LogicalCircuitBuilder()
+    b.add_patch(patch, "Q0")
+    b.add_memory("Q0", rounds=rounds, basis=basis)
+    tc = b.to_tick_circuit()
+
+    det_json = json.loads(tc.get_meta("detectors"))
+    obs_json = json.loads(tc.get_meta("observables"))
+    num_meas = int(tc.get_meta("num_measurements"))
+    dem_str = b.build_dem(p1=p_depol, p2=p_depol, p_meas=p_depol, p_prep=p_depol)
+    sc = b.stab_coords()
+    osd = ObservableSubgraphDecoder(dem_str, sc, "pymatching")
+
+    sweep = CoherentNoiseSweep(
+        distance=distance,
+        rounds=rounds,
+        basis=basis,
+        p_depol=p_depol,
+        backend=backend,
+    )
+    t_total = time.perf_counter()
+
+    for p_idle in p_idle_values:
+        # Simulate
+        t0 = time.perf_counter()
+        noise = depolarizing().p1(p_depol).p2(p_depol).p_meas(p_depol).p_prep(p_depol).idle_rz(p_idle)
+        builder = sim_neo(tc).noise(noise).shots(shots).seed(seed)
+        if backend == "stabmps":
+            builder = builder.quantum(
+                (
+                    stab_mps().lazy_measure().max_bond_dim(max_bond_dim)
+                    if lazy_measure
+                    else stab_mps().max_bond_dim(max_bond_dim)
+                ),
+            )
+        else:
+            builder = builder.quantum(statevec())
+        results = builder.run()
+        sim_time = time.perf_counter() - t0
+
+        # Decode
+        t0 = time.perf_counter()
+        errors = 0
+        for r in results:
+            meas = list(r)
+            det_events = []
+            for det in det_json:
+                val = 0
+                for rec in det["records"]:
+                    idx = num_meas + rec
+                    if 0 <= idx < len(meas):
+                        val ^= meas[idx]
+                det_events.append(val)
+            obs_mask = 0
+            for obs in obs_json:
+                val = 0
+                for rec in obs["records"]:
+                    idx = num_meas + rec
+                    if 0 <= idx < len(meas):
+                        val ^= meas[idx]
+                if val:
+                    obs_mask |= 1 << obs["id"]
+            pred = osd.decode([int(x) for x in det_events])
+            if pred != obs_mask:
+                errors += 1
+        decode_time = time.perf_counter() - t0
+
+        ler = errors / shots
+        se = math.sqrt(ler * (1 - ler) / shots) if shots > 0 else 0
+        p_twirled = math.sin(p_idle / 2) ** 2
+
+        point = CoherentNoisePoint(
+            p_idle=p_idle,
+            p_twirled=p_twirled,
+            ler=ler,
+            errors=errors,
+            shots=shots,
+            standard_error=se,
+            sim_seconds=sim_time,
+            decode_seconds=decode_time,
+        )
+        sweep.points.append(point)
+        print(
+            f"  p_idle={p_idle:.3f}  sin²(θ/2)={p_twirled:.5f}  "
+            f"LER={ler:.4f} ± {se:.4f}  ({errors}/{shots})  "
+            f"sim={sim_time:.1f}s  decode={decode_time:.1f}s",
+            flush=True,
+        )
+
+    sweep.total_seconds = time.perf_counter() - t_total
+    return sweep
+
+
+def write_html_report(sweep: CoherentNoiseSweep, path: Path) -> None:
+    """Write an HTML report from the sweep results."""
+    html_parts = [
+        "<!DOCTYPE html><html><head>",
+        "<title>Coherent Idle Noise Sweep</title>",
+        "<style>",
+        "body { font-family: sans-serif; margin: 2em; max-width: 900px; }",
+        "table { border-collapse: collapse; margin: 1em 0; }",
+        "th, td { border: 1px solid #ccc; padding: 6px 12px; text-align: right; }",
+        "th { background: #f5f5f5; }",
+        ".good { color: green; } .bad { color: red; }",
+        "details { background: #f8f9fa; border: 1px solid #dee2e6; border-radius: 4px;"
+        " padding: 0.5em 1em; margin: 1em 0; }",
+        "details summary { cursor: pointer; font-weight: bold; padding: 0.5em 0; }",
+        "details .content { padding: 0.5em 0; line-height: 1.6; }",
+        "</style></head><body>",
+        f"<h1>Coherent Idle Noise: {sweep.basis}-basis Memory d={sweep.distance}</h1>",
+        f"<p>Depolarizing: p={sweep.p_depol}, rounds={sweep.rounds}, backend={sweep.backend}</p>",
+        f"<p>Total time: {sweep.total_seconds:.1f}s</p>",
+        "",
+        "<details><summary>About Coherent Idle Noise</summary>",
+        '<div class="content">',
+        "<p>After each two-qubit gate (CX), an RZ(&theta;) rotation is applied to both "
+        "qubits, modeling uncompensated phase accumulation during idle time. Unlike "
+        "stochastic Z errors, coherent rotations accumulate constructively across gates, "
+        "causing logical error rates far higher than the Pauli-twirled equivalent "
+        "sin&sup2;(&theta;/2).</p>",
+        "<p>The decoder uses a stochastic-only DEM (no knowledge of coherent noise). "
+        "The gap between the coherent LER and the twirled LER measures how much the "
+        "decoder is mismatched to the actual noise.</p>",
+        "</div></details>",
+        "",
+        "<h2>Results</h2>",
+        "<table><tr>",
+        "<th>&theta; (rad)</th>",
+        "<th>sin&sup2;(&theta;/2)</th>",
+        "<th>LER</th>",
+        "<th>&plusmn; SE</th>",
+        "<th>Errors</th>",
+        "<th>Shots</th>",
+        "</tr>",
+    ]
+
+    for pt in sweep.points:
+        cls = "good" if pt.ler < 0.05 else "bad"
+        html_parts.append(
+            f"<tr><td>{pt.p_idle:.3f}</td>"
+            f"<td>{pt.p_twirled:.5f}</td>"
+            f'<td class="{cls}">{pt.ler:.4f}</td>'
+            f"<td>{pt.standard_error:.4f}</td>"
+            f"<td>{pt.errors}</td>"
+            f"<td>{pt.shots}</td></tr>",
+        )
+
+    html_parts.append("</table>")
+
+    # Amplification factor
+    if len(sweep.points) >= 2 and sweep.points[0].ler > 0:
+        baseline = sweep.points[0].ler
+        html_parts.append("<h2>Coherent Amplification</h2>")
+        html_parts.append("<table><tr><th>&theta;</th><th>LER / baseline</th><th>LER / twirled</th></tr>")
+        for pt in sweep.points[1:]:
+            ratio = pt.ler / baseline
+            twirl_ratio = pt.ler / pt.p_twirled if pt.p_twirled > 0 else 0
+            html_parts.append(
+                f"<tr><td>{pt.p_idle:.3f}</td><td>{ratio:.1f}x</td><td>{twirl_ratio:.0f}x</td></tr>",
+            )
+        html_parts.append("</table>")
+
+    html_parts.append("</body></html>")
+    path.write_text("\n".join(html_parts))
+    print(f"Report written to {path}")
+
+
+def main():
+    parser = argparse.ArgumentParser(
+        description=__doc__,
+        formatter_class=argparse.RawDescriptionHelpFormatter,
+    )
+    parser.add_argument("--distance", "-d", type=int, default=3)
+    parser.add_argument("--rounds", type=int, default=None, help="Syndrome rounds (default: distance)")
+    parser.add_argument(
+        "--basis",
+        choices=["X", "Z"],
+        default="X",
+        help="Memory basis (default: X, where RZ noise is visible)",
+    )
+    parser.add_argument("--p-depol", type=float, default=0.003)
+    parser.add_argument("--p-idle", type=float, nargs="+", default=[0.0, 0.01, 0.02, 0.03, 0.05, 0.07, 0.1])
+    parser.add_argument("--shots", type=int, default=10000)
+    parser.add_argument("--seed", type=int, default=42)
+    parser.add_argument("--backend", choices=["statevec", "stabmps"], default="statevec")
+    parser.add_argument("--lazy-measure", action="store_true", default=True)
+    parser.add_argument("--max-bond-dim", type=int, default=128)
+    parser.add_argument("--output-dir", type=Path, default=Path("/tmp/coherent_noise"))
+    parser.add_argument("--save-json", action="store_true")
+    parser.add_argument("--save-html", action="store_true")
+    parser.add_argument("--open", action="store_true")
+    args = parser.parse_args()
+
+    if args.rounds is None:
+        args.rounds = args.distance
+
+    print(
+        f"Coherent idle noise sweep: {args.basis}-basis memory d={args.distance}, "
+        f"rounds={args.rounds}, p_depol={args.p_depol}",
+        flush=True,
+    )
+    print(
+        f"Backend: {args.backend}, shots={args.shots}, seed={args.seed}",
+        flush=True,
+    )
+    print(flush=True)
+
+    sweep = run_sweep(
+        distance=args.distance,
+        rounds=args.rounds,
+        basis=args.basis,
+        p_depol=args.p_depol,
+        p_idle_values=args.p_idle,
+        shots=args.shots,
+        seed=args.seed,
+        backend=args.backend,
+        lazy_measure=args.lazy_measure,
+        max_bond_dim=args.max_bond_dim,
+    )
+
+    print(f"\nTotal: {sweep.total_seconds:.1f}s", flush=True)
+
+    args.output_dir.mkdir(parents=True, exist_ok=True)
+
+    if args.save_json:
+        json_path = args.output_dir / "coherent_noise_results.json"
+        json_path.write_text(json.dumps(asdict(sweep), indent=2))
+        print(f"JSON written to {json_path}")
+
+    if args.save_html or args.open:
+        html_path = args.output_dir / "coherent_noise_report.html"
+        write_html_report(sweep, html_path)
+        if args.open:
+            import webbrowser
+
+            webbrowser.open(str(html_path))
+
+
+if __name__ == "__main__":
+    main()
diff --git a/examples/surface/d3_fault_catalog_lookup.rs b/examples/surface/d3_fault_catalog_lookup.rs
new file mode 100644
index 000000000..82b01fe45
--- /dev/null
+++ b/examples/surface/d3_fault_catalog_lookup.rs
@@ -0,0 +1,597 @@
+// Copyright 2026 The PECOS Developers
+// Licensed under the Apache License, Version 2.0
+
+//! Build a truncated maximum-likelihood lookup table from the Rust fault catalog.
+//!
+//! This example keeps the expensive loop in Rust:
+//! - build a d=3 rotated surface-code Z-memory experiment,
+//! - enumerate all k-fault configurations for k <= `max_faults`,
+//! - XOR detector / observable effects via `fault_configurations(k)`,
+//! - aggregate `configuration_probability` into a lookup table.
+//!
+//! The circuit builder below intentionally uses a simple sequential stabilizer
+//! extraction schedule. The point of the example is the fault-catalog lookup
+//! aggregation path, not the optimized surface-code scheduling used by the
+//! larger sweep scripts.
+//!
+//! Run from the PECOS repo root:
+//!
+//! ```text
+//! cargo run -p pecos-qec --example surface_d3_fault_catalog_lookup
+//! ```
+
+use pecos_qec::SurfaceCode;
+use pecos_qec::fault_tolerance::fault_sampler::{
+    FaultCatalog, StochasticNoiseParams, build_fault_catalog,
+};
+use pecos_quantum::{Attribute, TickCircuit, TickMeasRef};
+use std::collections::BTreeMap;
+use std::time::Instant;
+
+type Syndrome = Vec<usize>;
+type Logical = Vec<usize>;
+type LogicalWeights = BTreeMap<Logical, f64>;
+type LookupWeights = BTreeMap<Syndrome, LogicalWeights>;
+
+#[derive(Debug)]
+struct MemoryCircuit {
+    circuit: TickCircuit,
+    num_detectors: usize,
+    num_observables: usize,
+}
+
+fn main() -> Result<(), Box<dyn std::error::Error>> {
+    let distance = 3;
+    let rounds = 3;
+    let max_faults = 2;
+    let p = 0.001;
+
+    let memory = build_d3_z_memory_circuit(rounds)?;
+    let noise = StochasticNoiseParams {
+        p1: p / 10.0,
+        p2: p,
+        p_meas: p,
+        p_prep: p,
+    };
+
+    println!("d={distance} rotated surface-code Z-memory experiment");
+    println!(
+        "rounds={rounds}, detectors={}, observables={}",
+        memory.num_detectors, memory.num_observables
+    );
+    println!(
+        "noise: p1={:.3e}, p2={:.3e}, p_meas={:.3e}, p_prep={:.3e}",
+        noise.p1, noise.p2, noise.p_meas, noise.p_prep
+    );
+
+    let catalog = build_fault_catalog(&memory.circuit, &noise)?;
+    let total_alternatives: usize = catalog
+        .locations
+        .iter()
+        .map(|loc| loc.num_alternatives)
+        .sum();
+
+    println!(
+        "catalog: {} locations, {total_alternatives} single-location alternatives",
+        catalog.locations.len()
+    );
+
+    let started = Instant::now();
+    let (weights, configs_by_weight) = build_lookup_weights(&catalog, max_faults);
+    let decoder = choose_most_likely_logicals(&weights);
+    let elapsed = started.elapsed();
+
+    println!("enumerated configurations:");
+    for (k, count) in configs_by_weight {
+        println!("  k={k}: {count}");
+    }
+    println!(
+        "lookup table: {} syndromes covered, built in {:.3?}",
+        decoder.len(),
+        elapsed
+    );
+
+    print_top_syndromes(&weights, &decoder, 10);
+
+    Ok(())
+}
+
+fn build_lookup_weights(
+    catalog: &FaultCatalog,
+    max_faults: usize,
+) -> (LookupWeights, Vec<(usize, usize)>) {
+    let mut weights: LookupWeights = BTreeMap::new();
+    let mut configs_by_weight = Vec::new();
+
+    for k in 0..=max_faults {
+        let mut count = 0usize;
+        for event in catalog.fault_configurations(k) {
+            add_lookup_weight(
+                &mut weights,
+                event.affected_detectors,
+                event.affected_observables,
+                event.configuration_probability,
+            );
+            count += 1;
+        }
+        configs_by_weight.push((k, count));
+    }
+
+    (weights, configs_by_weight)
+}
+
+fn add_lookup_weight(
+    weights: &mut LookupWeights,
+    syndrome: Syndrome,
+    logical: Logical,
+    probability: f64,
+) {
+    weights
+        .entry(syndrome)
+        .or_default()
+        .entry(logical)
+        .and_modify(|p| *p += probability)
+        .or_insert(probability);
+}
+
+fn choose_most_likely_logicals(weights: &LookupWeights) -> BTreeMap<Syndrome, Logical> {
+    weights
+        .iter()
+        .map(|(syndrome, logical_weights)| {
+            let best_logical = logical_weights
+                .iter()
+                .max_by(|(_, a), (_, b)| a.total_cmp(b))
+                .map(|(logical, _)| logical.clone())
+                .unwrap_or_default();
+            (syndrome.clone(), best_logical)
+        })
+        .collect()
+}
+
+fn print_top_syndromes(
+    weights: &LookupWeights,
+    decoder: &BTreeMap<Syndrome, Logical>,
+    limit: usize,
+) {
+    let mut rows: Vec<_> = weights
+        .iter()
+        .map(|(syndrome, logical_weights)| {
+            let total_p: f64 = logical_weights.values().sum();
+            (total_p, syndrome, logical_weights)
+        })
+        .collect();
+    rows.sort_by(|(a, _, _), (b, _, _)| b.total_cmp(a));
+
+    println!();
+    println!("top {limit} syndrome classes by truncated probability:");
+    for (rank, (total_p, syndrome, logical_weights)) in rows.into_iter().take(limit).enumerate() {
+        let correction = decoder.get(syndrome).cloned().unwrap_or_default();
+        let no_logical = logical_weights.get(&Vec::new()).copied().unwrap_or(0.0);
+        let logical_total = total_p - no_logical;
+        println!(
+            "  {:>2}. syndrome={:?} total={:.6e} logical_weight={:.6e} correction={:?}",
+            rank + 1,
+            syndrome,
+            total_p,
+            logical_total,
+            correction
+        );
+    }
+}
+
+fn build_d3_z_memory_circuit(rounds: usize) -> Result<MemoryCircuit, String> {
+    let code = SurfaceCode::rotated(3)?;
+    let num_data = code.num_data_qubits();
+    let x_ancilla_offset = num_data;
+    let z_ancilla_offset = x_ancilla_offset + code.num_x_stabilizers();
+
+    let x_ancilla = |idx: usize| x_ancilla_offset + idx;
+    let z_ancilla = |idx: usize| z_ancilla_offset + idx;
+
+    let mut circuit = TickCircuit::new();
+    let data_qubits: Vec<usize> = (0..num_data).collect();
+    circuit.tick().pz(&data_qubits);
+
+    let mut x_round_measurements: Vec<Vec<TickMeasRef>> = Vec::with_capacity(rounds);
+    let mut z_round_measurements: Vec<Vec<TickMeasRef>> = Vec::with_capacity(rounds);
+
+    for _round in 0..rounds {
+        let x_ancillas: Vec<usize> = (0..code.num_x_stabilizers()).map(x_ancilla).collect();
+        let z_ancillas: Vec<usize> = (0..code.num_z_stabilizers()).map(z_ancilla).collect();
+
+        circuit.tick().pz(&x_ancillas);
+        circuit.tick().pz(&z_ancillas);
+        circuit.tick().h(&x_ancillas);
+
+        for check in code.x_stabilizers() {
+            let anc = x_ancilla(check.index);
+            for data in check.qubits() {
+                circuit.tick().cx(&[(anc, data)]);
+            }
+        }
+
+        for check in code.z_stabilizers() {
+            let anc = z_ancilla(check.index);
+            for data in check.qubits() {
+                circuit.tick().cx(&[(data, anc)]);
+            }
+        }
+
+        circuit.tick().h(&x_ancillas);
+
+        let x_refs = circuit.tick().mz(&x_ancillas);
+        let z_refs = circuit.tick().mz(&z_ancillas);
+        x_round_measurements.push(x_refs);
+        z_round_measurements.push(z_refs);
+    }
+
+    let final_data_measurements = circuit.tick().mz(&data_qubits);
+    let num_measurements = circuit.num_measurements();
+
+    let mut detectors: Vec<Vec<i32>> = Vec::new();
+
+    // Initial Z-basis boundary detectors: data starts in |0...0>, so the first
+    // Z-check round is deterministic. Without these, an initial data X fault can
+    // flip every repeated Z-check round and the final data parity, cancelling all
+    // later detectors.
+    for &meas_ref in z_round_measurements[0]
+        .iter()
+        .take(code.num_z_stabilizers())
+    {
+        detectors.push(relative_records(num_measurements, &[meas_ref]));
+    }
+
+    // Repeated syndrome detectors: current stabilizer measurement XOR previous
+    // stabilizer measurement. These are deterministic after the first round.
+    for round in 1..rounds {
+        for (&current, &previous) in x_round_measurements[round]
+            .iter()
+            .zip(x_round_measurements[round - 1].iter())
+            .take(code.num_x_stabilizers())
+        {
+            detectors.push(relative_records(num_measurements, &[current, previous]));
+        }
+        for (&current, &previous) in z_round_measurements[round]
+            .iter()
+            .zip(z_round_measurements[round - 1].iter())
+            .take(code.num_z_stabilizers())
+        {
+            detectors.push(relative_records(num_measurements, &[current, previous]));
+        }
+    }
+
+    // Final Z-basis detectors: last Z-stabilizer result XOR the final data
+    // measurements in that stabilizer support.
+    let last_round = rounds - 1;
+    for check in code.z_stabilizers() {
+        let mut refs = vec![z_round_measurements[last_round][check.index]];
+        refs.extend(
+            check
+                .qubits()
+                .into_iter()
+                .map(|q| final_data_measurements[q]),
+        );
+        detectors.push(relative_records(num_measurements, &refs));
+    }
+
+    let logical_z_refs: Vec<TickMeasRef> = code
+        .logical_z()
+        .data_qubits
+        .iter()
+        .map(|&q| final_data_measurements[q])
+        .collect();
+    let observables = vec![relative_records(num_measurements, &logical_z_refs)];
+
+    circuit.set_meta(
+        "num_measurements",
+        Attribute::String(num_measurements.to_string()),
+    );
+    circuit.set_meta("detectors", Attribute::String(records_json(&detectors)));
+    circuit.set_meta("observables", Attribute::String(records_json(&observables)));
+
+    Ok(MemoryCircuit {
+        circuit,
+        num_detectors: detectors.len(),
+        num_observables: observables.len(),
+    })
+}
+
+fn relative_records(num_measurements: usize, refs: &[TickMeasRef]) -> Vec<i32> {
+    let num_measurements = i32::try_from(num_measurements).expect("measurement count fits in i32");
+    refs.iter()
+        .map(|m| {
+            i32::try_from(m.record_idx).expect("measurement record index fits in i32")
+                - num_measurements
+        })
+        .collect()
+}
+
+fn records_json(records: &[Vec<i32>]) -> String {
+    let entries: Vec<String> = records
+        .iter()
+        .map(|rs| {
+            let values = rs.iter().map(i32::to_string).collect::<Vec<_>>().join(",");
+            format!(r#"{{"records":[{values}]}}"#)
+        })
+        .collect();
+    format!("[{}]", entries.join(","))
+}
+
+#[cfg(test)]
+mod tests {
+    use super::*;
+    use pecos_qec::fault_tolerance::targeted_lookup_decoder::TargetedLookupDecoder;
+    use std::collections::BTreeSet;
+
+    #[test]
+    fn accumulates_repeated_logical_weights_for_a_syndrome() {
+        let mut weights = LookupWeights::new();
+
+        add_lookup_weight(&mut weights, vec![1, 3], vec![0], 0.125);
+        add_lookup_weight(&mut weights, vec![1, 3], vec![0], 0.375);
+        add_lookup_weight(&mut weights, vec![1, 3], Vec::new(), 0.250);
+
+        assert_close(weights[&vec![1, 3]][&vec![0]], 0.500);
+        assert_close(weights[&vec![1, 3]][&Vec::new()], 0.250);
+    }
+
+    #[test]
+    fn decoder_picks_most_likely_logical_per_syndrome() {
+        let mut weights = LookupWeights::new();
+
+        add_lookup_weight(&mut weights, Vec::new(), Vec::new(), 0.900);
+        add_lookup_weight(&mut weights, Vec::new(), vec![0], 0.100);
+        add_lookup_weight(&mut weights, vec![2], Vec::new(), 0.200);
+        add_lookup_weight(&mut weights, vec![2], vec![0], 0.700);
+
+        let decoder = choose_most_likely_logicals(&weights);
+
+        assert_eq!(decoder[&Vec::new()], Vec::<usize>::new());
+        assert_eq!(decoder[&vec![2]], vec![0]);
+    }
+
+    #[test]
+    fn small_catalog_lookup_matches_hand_calculation() {
+        let mut circuit = TickCircuit::new();
+        circuit.tick().h(&[0]);
+        circuit.tick().mz(&[0]);
+        circuit.set_meta("num_measurements", Attribute::String("1".to_string()));
+        circuit.set_meta(
+            "detectors",
+            Attribute::String(r#"[{"records":[-1]}]"#.to_string()),
+        );
+        circuit.set_meta(
+            "observables",
+            Attribute::String(r#"[{"records":[-1]}]"#.to_string()),
+        );
+
+        let noise = StochasticNoiseParams {
+            p1: 0.03,
+            p2: 0.0,
+            p_meas: 0.01,
+            p_prep: 0.0,
+        };
+        let catalog = build_fault_catalog(&circuit, &noise).unwrap();
+        let (weights, counts) = build_lookup_weights(&catalog, 1);
+        let decoder = choose_most_likely_logicals(&weights);
+
+        assert_eq!(counts, vec![(0, 1), (1, 4)]);
+
+        // k=0 no fault: 0.97 * 0.99 = 0.9603.
+        // k=1 no-effect H alternative: (0.03 / 3) * 0.99 = 0.0099.
+        assert_close(weights[&Vec::new()][&Vec::new()], 0.9702);
+
+        // k=1 detector+logical events:
+        // two H alternatives flip MZ: 2 * (0.03 / 3) * 0.99 = 0.0198.
+        // one MZ flip: 0.01 * 0.97 = 0.0097.
+        assert_close(weights[&vec![0]][&vec![0]], 0.0295);
+
+        assert_eq!(decoder[&Vec::new()], Vec::<usize>::new());
+        assert_eq!(decoder[&vec![0]], vec![0]);
+    }
+
+    #[test]
+    fn small_catalog_decoder_corrects_every_truncated_event() {
+        let mut circuit = TickCircuit::new();
+        circuit.tick().h(&[0]);
+        circuit.tick().mz(&[0]);
+        circuit.set_meta("num_measurements", Attribute::String("1".to_string()));
+        circuit.set_meta(
+            "detectors",
+            Attribute::String(r#"[{"records":[-1]}]"#.to_string()),
+        );
+        circuit.set_meta(
+            "observables",
+            Attribute::String(r#"[{"records":[-1]}]"#.to_string()),
+        );
+
+        let noise = StochasticNoiseParams {
+            p1: 0.03,
+            p2: 0.0,
+            p_meas: 0.01,
+            p_prep: 0.0,
+        };
+        let catalog = build_fault_catalog(&circuit, &noise).unwrap();
+        let (weights, _) = build_lookup_weights(&catalog, 1);
+        let decoder = choose_most_likely_logicals(&weights);
+
+        let mut decoded = 0usize;
+        for k in 0..=1 {
+            for event in catalog.fault_configurations(k) {
+                let correction = decoder
+                    .get(&event.affected_detectors)
+                    .expect("decoder should cover every truncated syndrome");
+                let residual = xor_parity(&event.affected_observables, correction);
+                assert!(
+                    residual.is_empty(),
+                    "failed to decode syndrome {:?}: event logical {:?}, correction {:?}",
+                    event.affected_detectors,
+                    event.affected_observables,
+                    correction
+                );
+                decoded += 1;
+            }
+        }
+
+        assert_eq!(decoded, 5);
+    }
+
+    #[test]
+    fn d3_surface_lookup_builds_nontrivial_weight_one_table() {
+        let memory = build_d3_z_memory_circuit(3).unwrap();
+        let noise = StochasticNoiseParams {
+            p1: 0.0001,
+            p2: 0.001,
+            p_meas: 0.001,
+            p_prep: 0.001,
+        };
+        let catalog = build_fault_catalog(&memory.circuit, &noise).unwrap();
+        let (weights, counts) = build_lookup_weights(&catalog, 1);
+        let decoder = choose_most_likely_logicals(&weights);
+
+        assert_eq!(memory.num_detectors, 24);
+        assert_eq!(memory.num_observables, 1);
+        assert_eq!(counts[0], (0, 1));
+        assert_eq!(counts[1].0, 1);
+        assert!(counts[1].1 > 1_000);
+        assert!(weights.len() > 10);
+        assert_eq!(decoder[&Vec::new()], Vec::<usize>::new());
+    }
+
+    #[test]
+    fn d3_surface_weight_one_decoder_corrects_weight_one_events() {
+        let memory = build_d3_z_memory_circuit(3).unwrap();
+        let noise = StochasticNoiseParams {
+            p1: 0.0001,
+            p2: 0.001,
+            p_meas: 0.001,
+            p_prep: 0.001,
+        };
+        let catalog = build_fault_catalog(&memory.circuit, &noise).unwrap();
+        let (weights, _) = build_lookup_weights(&catalog, 1);
+        let decoder = choose_most_likely_logicals(&weights);
+
+        let mut checked = 0usize;
+        for k in 0..=1 {
+            for event in catalog.fault_configurations(k) {
+                let correction = decoder
+                    .get(&event.affected_detectors)
+                    .expect("decoder should cover every weight-one syndrome");
+                let residual = xor_parity(&event.affected_observables, correction);
+                assert!(
+                    residual.is_empty(),
+                    "failed to decode syndrome {:?}: event logical {:?}, correction {:?}",
+                    event.affected_detectors,
+                    event.affected_observables,
+                    correction
+                );
+                checked += 1;
+            }
+        }
+
+        assert_eq!(
+            checked,
+            1 + catalog
+                .locations
+                .iter()
+                .map(|loc| loc.num_alternatives)
+                .sum::<usize>()
+        );
+    }
+
+    #[test]
+    fn targeted_decoder_matches_bruteforce_on_real_d3_surface_catalog() {
+        let memory = build_d3_z_memory_circuit(3).unwrap();
+        let noise = StochasticNoiseParams {
+            p1: 0.0001,
+            p2: 0.001,
+            p_meas: 0.001,
+            p_prep: 0.001,
+        };
+        let catalog = build_fault_catalog(&memory.circuit, &noise).unwrap();
+        let decoder = TargetedLookupDecoder::new(&catalog).max_faults(1);
+        let base_probability = decoder.base_probability();
+
+        let mut syndromes = BTreeSet::new();
+        syndromes.insert(Vec::new());
+        for event in catalog.fault_configurations(1) {
+            if !event.affected_detectors.is_empty() {
+                syndromes.insert(event.affected_detectors);
+            }
+            if syndromes.len() >= 8 {
+                break;
+            }
+        }
+        assert!(
+            syndromes.len() >= 4,
+            "surface catalog should expose several non-empty weight-one syndromes"
+        );
+
+        for syndrome in syndromes {
+            let result = decoder.decode(&syndrome);
+            let expected = brute_force_odds_for_syndrome(&catalog, 1, &syndrome, base_probability);
+            assert_eq!(result.syndrome, syndrome);
+            assert_logical_weights_close(&result.logical_weights, &expected);
+
+            let expected_best = expected
+                .iter()
+                .max_by(|(_, a), (_, b)| a.total_cmp(b))
+                .map(|(logical, _)| logical.clone())
+                .unwrap_or_default();
+            assert_eq!(result.best_logical, expected_best);
+        }
+    }
+
+    fn brute_force_odds_for_syndrome(
+        catalog: &FaultCatalog,
+        max_faults: usize,
+        syndrome: &[usize],
+        base_probability: f64,
+    ) -> LogicalWeights {
+        let mut weights = LogicalWeights::new();
+        for k in 0..=max_faults {
+            for event in catalog.fault_configurations(k) {
+                if event.affected_detectors == syndrome {
+                    let odds = event.configuration_probability / base_probability;
+                    weights
+                        .entry(event.affected_observables)
+                        .and_modify(|w| *w += odds)
+                        .or_insert(odds);
+                }
+            }
+        }
+        weights
+    }
+
+    fn assert_logical_weights_close(actual: &LogicalWeights, expected: &LogicalWeights) {
+        assert_eq!(
+            actual.keys().collect::<Vec<_>>(),
+            expected.keys().collect::<Vec<_>>()
+        );
+        for (logical, expected_weight) in expected {
+            let actual_weight = actual[logical];
+            let scale = expected_weight.abs().max(1e-15);
+            assert!(
+                (actual_weight - expected_weight).abs() / scale < 1e-10,
+                "logical={logical:?}: expected {expected_weight:.12e}, got {actual_weight:.12e}"
+            );
+        }
+    }
+
+    fn assert_close(actual: f64, expected: f64) {
+        assert!(
+            (actual - expected).abs() < 1e-12,
+            "expected {expected}, got {actual}"
+        );
+    }
+
+    fn xor_parity(a: &[usize], b: &[usize]) -> Vec<usize> {
+        let mut out = std::collections::BTreeSet::new();
+        for value in a.iter().chain(b.iter()) {
+            if !out.remove(value) {
+                out.insert(*value);
+            }
+        }
+        out.into_iter().collect()
+    }
+}
diff --git a/examples/surface/decoder_comparison.py b/examples/surface/decoder_comparison.py
new file mode 100644
index 000000000..d1b9ea91d
--- /dev/null
+++ b/examples/surface/decoder_comparison.py
@@ -0,0 +1,542 @@
+r"""Decoder comparison: same samples, multiple decoders, one table.
+
+Generates DEM samples once per (distance, error_rate, rounds) point and
+decodes them with every requested decoder. Produces an HTML report with
+comparison tables showing logical error rates and decode throughput.
+
+This is complementary to ``native_dem_threshold_sweep.py`` which produces
+threshold curves. This script answers "which decoder is best at a given
+operating point?" with a controlled experiment (identical samples).
+
+Example:
+    python examples/surface/decoder_comparison.py
+
+    python examples/surface/decoder_comparison.py \\
+        --distances 3 5 7 \\
+        --error-rates 0.004 0.008 \\
+        --shots 2000 \\
+        --decoders pymatching tesseract bp_osd \\
+        --open-html
+"""
+
+from __future__ import annotations
+
+import argparse
+import html
+import json
+import time
+from dataclasses import asdict, dataclass
+from pathlib import Path
+from textwrap import dedent
+from typing import TYPE_CHECKING
+
+if TYPE_CHECKING:
+    from pecos.qec.surface import NoiseModel
+
+
+@dataclass
+class DecoderResult:
+    """Result for one decoder at one operating point."""
+
+    decoder: str
+    distance: int
+    basis: str
+    physical_error_rate: float
+    num_rounds: int
+    num_shots: int
+    num_errors: int
+    logical_error_rate: float
+    decode_seconds: float
+    shots_per_second: float
+    per_shot_median: float = 0.0
+    per_shot_p99: float = 0.0
+    per_shot_max: float = 0.0
+
+
+@dataclass
+class ComparisonPoint:
+    """All decoder results for one (distance, p, rounds) point."""
+
+    distance: int
+    basis: str
+    physical_error_rate: float
+    num_rounds: int
+    num_shots: int
+    sample_seconds: float
+    results: list[DecoderResult]
+
+
+def _build_sampler(
+    distance: int,
+    num_rounds: int,
+    noise: NoiseModel,
+    basis: str,
+    circuit_source: str,
+) -> tuple:
+    """Build the native sampler and get DEM strings."""
+    from pecos.qec.surface import SurfacePatch, build_native_sampler
+    from pecos.qec.surface.decode import SurfaceDecoder, generate_circuit_level_dem_from_builder
+
+    patch = SurfacePatch.create(distance=distance)
+    sampler = build_native_sampler(
+        patch,
+        num_rounds,
+        noise,
+        basis=basis,
+        circuit_source=circuit_source,
+    )
+
+    # Decomposed DEM for MWPM decoders
+    dec = SurfaceDecoder(
+        patch,
+        num_rounds=num_rounds,
+        noise=noise,
+        decoder_type="pymatching",
+        use_circuit_level_dem=True,
+        circuit_level_dem_mode="native_decomposed",
+        circuit_level_dem_source=circuit_source,
+    )
+    dem_decomp = dec.get_dem(basis.upper(), circuit_level=True)
+    dem_decomp = "\n".join(line for line in dem_decomp.split("\n") if not line.startswith("logical_observable"))
+
+    # Full DEM for non-MWPM decoders
+    dem_full = generate_circuit_level_dem_from_builder(
+        patch,
+        num_rounds,
+        noise,
+        basis=basis,
+        decompose_errors=False,
+        circuit_source=circuit_source,
+    )
+    dem_full = "\n".join(line for line in dem_full.split("\n") if not line.startswith("logical_observable"))
+
+    return sampler, dem_decomp, dem_full
+
+
+# Decoders that need decomposed (graphlike) DEMs
+# MWPM decoders get decomposed DEMs. DemMatchingGraph handles fault-ID-aware
+# merging with first-observable-wins (matching PyMatching's INDEPENDENT strategy).
+_MWPM_DECODERS = {
+    "pymatching",
+    "pymatching_uncorrelated",
+    "fusion_blossom",
+    "fusion_blossom_serial",
+    "fusion_blossom_parallel",
+    "pecos_uf",
+    "pecos_uf_correlated",
+    "pecos_uf:balanced",
+    "pecos_uf:fast",
+    "pecos_uf:bp",
+    "windowed",
+}
+
+# All supported decoders
+_ALL_DECODERS = [
+    "pymatching",
+    "pymatching_uncorrelated",
+    "fusion_blossom",
+    "fusion_blossom_serial",
+    "fusion_blossom_parallel",
+    "tesseract",
+    "mwpf",
+    "bp_osd",
+    "union_find",
+    "min_sum_bp",
+    "relay_bp",
+    "pecos_uf",
+    "pecos_uf:balanced",
+    "pecos_uf:bp",
+    "pecos_uf_correlated",  # legacy alias for pecos_uf:balanced
+]
+
+# Decoders where parallel decoding helps
+_SLOW_DECODERS = {"tesseract", "mwpf", "bp_osd", "relay_bp"}
+
+
+def _decoder_base_name(name: str) -> str:
+    """Extract base decoder name, stripping config suffix (e.g. 'mwpf:c=30' -> 'mwpf')."""
+    return name.split(":", maxsplit=1)[0]
+
+
+def run_comparison(
+    *,
+    distances: list[int],
+    error_rates: list[float],
+    decoders: list[str],
+    basis: str,
+    shots: int,
+    seed: int,
+    circuit_source: str,
+    p1_scale: float,
+    p_meas_scale: float,
+    p_prep_scale: float,
+) -> list[ComparisonPoint]:
+    """Run the full comparison and return results."""
+    from pecos.qec.surface import NoiseModel
+
+    points: list[ComparisonPoint] = []
+    total_configs = len(distances) * len(error_rates)
+    config_idx = 0
+
+    for distance in distances:
+        num_rounds = 2 * distance
+        for p in error_rates:
+            config_idx += 1
+            noise = NoiseModel(
+                p1=p * p1_scale,
+                p2=p,
+                p_meas=p * p_meas_scale,
+                p_prep=p * p_prep_scale,
+            )
+
+            print(f"[{config_idx}/{total_configs}] d={distance} p={p:.4g} r={num_rounds} ...")
+
+            sampler, dem_decomp, dem_full = _build_sampler(
+                distance,
+                num_rounds,
+                noise,
+                basis,
+                circuit_source,
+            )
+
+            # Generate samples once
+            t0 = time.perf_counter()
+            sample_batch = sampler.sampler.generate_samples(shots, seed=seed + config_idx)
+            sample_seconds = time.perf_counter() - t0
+
+            results: list[DecoderResult] = []
+            for decoder_name in decoders:
+                base = _decoder_base_name(decoder_name)
+                # Ensemble uses decomposed DEMs (all ensemble members are matching-graph decoders)
+                dem = dem_decomp if base in _MWPM_DECODERS or base == "ensemble" else dem_full
+
+                if base in _SLOW_DECODERS:
+                    stats = sample_batch.decode_stats_parallel(dem, decoder_name)
+                else:
+                    stats = sample_batch.decode_stats(dem, decoder_name)
+
+                results.append(
+                    DecoderResult(
+                        decoder=decoder_name,
+                        distance=distance,
+                        basis=basis.upper(),
+                        physical_error_rate=p,
+                        num_rounds=num_rounds,
+                        num_shots=shots,
+                        num_errors=stats.num_errors,
+                        logical_error_rate=stats.logical_error_rate,
+                        decode_seconds=stats.total_seconds,
+                        shots_per_second=shots / stats.total_seconds if stats.total_seconds > 0 else float("inf"),
+                        per_shot_median=stats.per_shot_median,
+                        per_shot_p99=stats.per_shot_p99,
+                        per_shot_max=stats.per_shot_max,
+                    ),
+                )
+                print(
+                    f"    {decoder_name:14s}: {stats.num_errors:>4d}/{shots}  "
+                    f"LER={stats.logical_error_rate:.4f}  "
+                    f"mean={stats.per_shot_mean:.1e}s  "
+                    f"median={stats.per_shot_median:.1e}s  "
+                    f"p99={stats.per_shot_p99:.1e}s  "
+                    f"max={stats.per_shot_max:.1e}s",
+                )
+
+            points.append(
+                ComparisonPoint(
+                    distance=distance,
+                    basis=basis.upper(),
+                    physical_error_rate=p,
+                    num_rounds=num_rounds,
+                    num_shots=shots,
+                    sample_seconds=sample_seconds,
+                    results=results,
+                ),
+            )
+
+    return points
+
+
+def write_json(path: Path, points: list[ComparisonPoint], config: dict) -> None:
+    """Write results as JSON."""
+    data = {
+        "config": config,
+        "points": [asdict(p) for p in points],
+    }
+    path.write_text(json.dumps(data, indent=2))
+    print(f"Wrote JSON to {path}")
+
+
+def write_html(path: Path, points: list[ComparisonPoint], config: dict) -> None:
+    """Write an HTML report with comparison tables."""
+    style = dedent("""
+        :root {
+          color-scheme: light dark;
+          --bg: #f8fafc; --fg: #0f172a;
+          --hero-bg: linear-gradient(135deg, #e0f2fe, #f8fafc 55%, #dcfce7);
+          --card-bg: white; --card-border: #dbeafe; --card-shadow: rgba(15,23,42,0.05);
+          --meta-bg: rgba(255,255,255,0.82);
+          --muted: #475569; --link: #2563eb;
+          --table-stripe: #f1f5f9; --table-border: #e2e8f0;
+        }
+        [data-theme="dark"] {
+          --bg: #0f172a; --fg: #e2e8f0;
+          --hero-bg: linear-gradient(135deg, #1e293b, #0f172a 55%, #1a2e1a);
+          --card-bg: #1e293b; --card-border: #334155; --card-shadow: rgba(0,0,0,0.3);
+          --meta-bg: rgba(30,41,59,0.82);
+          --muted: #94a3b8; --link: #60a5fa;
+          --table-stripe: #0f172a; --table-border: #334155;
+        }
+        @media (prefers-color-scheme: dark) {
+          :root:not([data-theme="light"]) {
+            --bg: #0f172a; --fg: #e2e8f0;
+            --hero-bg: linear-gradient(135deg, #1e293b, #0f172a 55%, #1a2e1a);
+            --card-bg: #1e293b; --card-border: #334155; --card-shadow: rgba(0,0,0,0.3);
+            --meta-bg: rgba(30,41,59,0.82);
+            --muted: #94a3b8; --link: #60a5fa;
+            --table-stripe: #0f172a; --table-border: #334155;
+          }
+        }
+        body {
+          margin: 0;
+          font-family: ui-sans-serif, -apple-system, BlinkMacSystemFont, sans-serif;
+          background: var(--bg); color: var(--fg);
+        }
+        main { max-width: 1400px; margin: 0 auto; padding: 32px 24px 56px; }
+        h1, h2, h3, p { margin-top: 0; }
+        .theme-toggle {
+          position: fixed; top: 16px; right: 16px; z-index: 100;
+          background: var(--card-bg); border: 1px solid var(--card-border);
+          border-radius: 8px; padding: 6px 12px; cursor: pointer;
+          color: var(--fg); font-size: 0.85rem; font-weight: 600;
+        }
+        .theme-toggle:hover { opacity: 0.8; }
+        .hero {
+          background: var(--hero-bg);
+          border: 1px solid var(--card-border);
+          border-radius: 20px;
+          padding: 24px;
+          margin-bottom: 24px;
+        }
+        .meta {
+          display: grid;
+          grid-template-columns: repeat(auto-fit, minmax(200px, 1fr));
+          gap: 12px;
+          margin-top: 18px;
+        }
+        .meta-card {
+          background: var(--meta-bg);
+          border: 1px solid var(--card-border);
+          border-radius: 14px;
+          padding: 14px 16px;
+        }
+        .meta-card strong {
+          display: block; font-size: 0.82rem; text-transform: uppercase;
+          letter-spacing: 0.04em; color: var(--muted); margin-bottom: 6px;
+        }
+        .section {
+          background: var(--card-bg);
+          border: 1px solid var(--card-border);
+          border-radius: 18px;
+          padding: 20px 22px;
+          margin-top: 20px;
+          box-shadow: 0 10px 24px var(--card-shadow);
+          overflow-x: auto;
+        }
+        table { border-collapse: collapse; width: 100%; margin: 12px 0 0; }
+        th, td { padding: 10px 14px; text-align: right; border-bottom: 1px solid var(--table-border); }
+        th {
+          font-size: 0.82rem; text-transform: uppercase;
+          letter-spacing: 0.03em; color: var(--muted); border-bottom-width: 2px;
+        }
+        td:first-child, th:first-child { text-align: left; }
+        tr:nth-child(even) td { background: var(--table-stripe); }
+        code { font-family: ui-monospace, SFMono-Regular, Menlo, monospace; }
+    """).strip()
+
+    def meta_card(label: str, value: str) -> str:
+        return f'      <div class="meta-card"><strong>{html.escape(label)}</strong>{html.escape(value)}</div>'
+
+    decoders = config.get("decoders", [])
+    p1s = config.get("p1_scale", 1 / 30)
+    pms = config.get("p_meas_scale", 1 / 3)
+    pps = config.get("p_prep_scale", 1 / 3)
+    noise_str = f"p1={p1s:.4g}*p, p2=p, p_meas={pms:.4g}*p, p_prep={pps:.4g}*p"
+    parts = [
+        "<!doctype html>",
+        '<html lang="en">',
+        "<head>",
+        '  <meta charset="utf-8" />',
+        '  <meta name="viewport" content="width=device-width, initial-scale=1" />',
+        "  <title>PECOS Decoder Comparison</title>",
+        f"  <style>{style}</style>",
+        "</head>",
+        "<body>",
+        '<button id="theme-toggle" class="theme-toggle">Light / Dark</button>',
+        "<main>",
+        '  <section class="hero">',
+        "    <h1>PECOS Decoder Comparison</h1>",
+        "    <p>Same samples decoded by multiple decoders. LER differences reflect "
+        "decoder quality, not sampling noise.</p>",
+        '    <div class="meta">',
+        meta_card("Decoders", ", ".join(decoders)),
+        meta_card("Distances", ", ".join(str(d) for d in config.get("distances", []))),
+        meta_card("Error Rates", ", ".join(f"{p:.4g}" for p in config.get("error_rates", []))),
+        meta_card("Shots", str(config.get("shots", 0))),
+        meta_card("Basis", config.get("basis", "Z")),
+        meta_card("Noise Model", noise_str),
+        meta_card("Circuit Source", config.get("circuit_source", "traced_qis")),
+        "    </div>",
+        "  </section>",
+    ]
+
+    # Group by (distance, p)
+    for point in points:
+        d = point.distance
+        p = point.physical_error_rate
+        r = point.num_rounds
+        parts.append('  <div class="section">')
+        parts.append(f"    <h2>d={d}, p={p:.4g}, rounds={r} ({point.num_shots} shots)</h2>")
+
+        parts.append("    <table>")
+        parts.append(
+            "      <tr><th>Decoder</th><th>LER (95% CI)</th><th>Mean</th>"
+            "<th>Median</th><th>p99</th><th>Max</th><th>Throughput</th></tr>",
+        )
+        for res in sorted(point.results, key=lambda r: r.logical_error_rate):
+            mean_s = res.decode_seconds / res.num_shots if res.num_shots > 0 else 0
+            sps = f"{res.shots_per_second:.1e}"
+            ler = res.logical_error_rate
+            n = res.num_shots
+            z = 1.96
+            if n > 0 and 0 < ler < 1:
+                denom = 1 + z * z / n
+                center = (ler + z * z / (2 * n)) / denom
+                half = z * (ler * (1 - ler) / n + z * z / (4 * n * n)) ** 0.5 / denom
+                ci_lo, ci_hi = max(0, center - half), min(1, center + half)
+            elif n > 0:
+                ci_lo, ci_hi = ler, ler
+            else:
+                ci_lo, ci_hi = 0, 0
+            ler_str = f"{ler:.4f} ({ci_lo:.4f} - {ci_hi:.4f})"
+            parts.append(
+                f"      <tr>"
+                f"<td>{html.escape(res.decoder)}</td>"
+                f"<td>{ler_str}</td>"
+                f"<td>{mean_s:.1e} s</td>"
+                f"<td>{res.per_shot_median:.1e} s</td>"
+                f"<td>{res.per_shot_p99:.1e} s</td>"
+                f"<td>{res.per_shot_max:.1e} s</td>"
+                f"<td>{sps} shots/s</td>"
+                f"</tr>",
+            )
+        parts.append("    </table>")
+        parts.append("  </div>")
+
+    parts.extend(
+        [
+            "</main>",
+            dedent("""
+        <script>
+        (function() {
+          var html = document.documentElement;
+          var btn = document.getElementById('theme-toggle');
+          var stored = localStorage.getItem('pecos-theme');
+          if (stored) html.setAttribute('data-theme', stored);
+          btn.addEventListener('click', function() {
+            var current = html.getAttribute('data-theme');
+            var next = current === 'dark' ? 'light' : 'dark';
+            if (!current) next = 'dark';
+            html.setAttribute('data-theme', next);
+            localStorage.setItem('pecos-theme', next);
+          });
+        })();
+        </script>
+        """).strip(),
+            "</body>",
+            "</html>",
+        ],
+    )
+
+    path.write_text("\n".join(parts))
+    print(f"Wrote HTML to {path}")
+
+
+def main() -> int:
+    """CLI entry point for decoder comparison."""
+    parser = argparse.ArgumentParser(description=__doc__, formatter_class=argparse.RawDescriptionHelpFormatter)
+    parser.add_argument("--distances", nargs="+", type=int, default=[3, 5])
+    parser.add_argument("--error-rates", nargs="+", type=float, default=[0.004, 0.008])
+    parser.add_argument("--shots", type=int, default=1000)
+    parser.add_argument("--basis", default="Z")
+    parser.add_argument("--seed", type=int, default=42)
+    parser.add_argument(
+        "--decoders",
+        nargs="+",
+        default=["pymatching", "tesseract", "bp_osd"],
+        help=f"Decoders to compare. Available: {', '.join(_ALL_DECODERS)}",
+    )
+    parser.add_argument("--circuit-source", default="traced_qis", choices=["traced_qis", "abstract"])
+    parser.add_argument("--p1-scale", type=float, default=1.0 / 30.0)
+    parser.add_argument("--p-meas-scale", type=float, default=1.0 / 3.0)
+    parser.add_argument("--p-prep-scale", type=float, default=1.0 / 3.0)
+    parser.add_argument("--output-dir", type=str, default=None)
+    parser.add_argument("--open-html", action="store_true")
+    args = parser.parse_args()
+
+    config = {
+        "distances": sorted(args.distances),
+        "error_rates": sorted(args.error_rates),
+        "shots": args.shots,
+        "basis": args.basis.upper(),
+        "decoders": args.decoders,
+        "circuit_source": args.circuit_source,
+        "p1_scale": args.p1_scale,
+        "p_meas_scale": args.p_meas_scale,
+        "p_prep_scale": args.p_prep_scale,
+    }
+
+    print("PECOS Decoder Comparison")
+    print("=" * 40)
+    for k, v in config.items():
+        print(f"  {k}: {v}")
+    print()
+
+    t0 = time.perf_counter()
+    points = run_comparison(
+        distances=sorted(args.distances),
+        error_rates=sorted(args.error_rates),
+        decoders=args.decoders,
+        basis=args.basis,
+        shots=args.shots,
+        seed=args.seed,
+        circuit_source=args.circuit_source,
+        p1_scale=args.p1_scale,
+        p_meas_scale=args.p_meas_scale,
+        p_prep_scale=args.p_prep_scale,
+    )
+    elapsed = time.perf_counter() - t0
+    print(f"\nTotal time: {elapsed:.1f}s")
+
+    if args.output_dir:
+        out = Path(args.output_dir)
+    else:
+        import tempfile
+
+        out = Path(tempfile.mkdtemp(prefix="pecos_decoder_comparison_"))
+
+    out.mkdir(parents=True, exist_ok=True)
+    write_json(out / "decoder_comparison.json", points, config)
+    html_path = out / "decoder_comparison.html"
+    write_html(html_path, points, config)
+
+    if args.open_html:
+        import webbrowser
+
+        webbrowser.open(html_path.as_uri())
+        print(f"Opened {html_path}")
+
+    return 0
+
+
+if __name__ == "__main__":
+    raise SystemExit(main())
diff --git a/examples/surface/dem_comparison.py b/examples/surface/dem_comparison.py
new file mode 100644
index 000000000..d9b178981
--- /dev/null
+++ b/examples/surface/dem_comparison.py
@@ -0,0 +1,203 @@
+r"""Compare ALL DEM generation methods against simulation ground truth.
+
+Compares per-detector firing rates from:
+  1. Non-EEG DemBuilder (backward Pauli propagation)
+  2. DemSampler.from_circuit (separate DEM path)
+  3. Backward Heisenberg EEG (exact for coherent, handles depol via attenuation)
+  4. stabilizer() simulation (SparseStab, exact for depol, any distance)
+  5. statevec() simulation (exact for everything, limited to small circuits)
+
+Example:
+    uv run python examples/surface/dem_comparison.py
+    uv run python examples/surface/dem_comparison.py -d 2 3 --p 0.005 --shots 20000
+    uv run python examples/surface/dem_comparison.py -d 5 --no-statevec
+"""
+
+from __future__ import annotations
+
+import argparse
+import json
+import math
+import sys
+import time
+from pathlib import Path
+
+sys.path.insert(0, str(Path(__file__).resolve().parents[2] / "python" / "quantum-pecos" / "src"))
+
+
+def run(*, distance, rounds, basis, p, shots, seed, run_statevec):
+    from pecos.qec.surface import LogicalCircuitBuilder, SurfacePatch
+    from pecos_rslib.qec import DagFaultAnalyzer, DemBuilder, DemSampler
+    from pecos_rslib_exp import (
+        depolarizing,
+        exact_detection_rates,
+        sim_neo,
+        stabilizer,
+        statevec,
+    )
+
+    patch = SurfacePatch.create(distance=distance)
+    b = LogicalCircuitBuilder()
+    b.add_patch(patch, "Q0")
+    b.add_memory("Q0", rounds=rounds, basis=basis)
+    tc = b.to_tick_circuit()
+    dag = tc.to_dag_circuit()
+
+    det_json = json.loads(tc.get_meta("detectors"))
+    num_meas = int(tc.get_meta("num_measurements"))
+    num_dets = len(det_json)
+
+    print(f"\n{'='*80}")
+    print(f"d={distance} {basis}-basis, {rounds} rounds, {num_dets} dets, p={p} (depol only)")
+    print(f"{'='*80}")
+
+    def extract_det_rates(results):
+        rates = [0.0] * num_dets
+        for r in results:
+            meas = list(r)
+            for i, det in enumerate(det_json):
+                val = 0
+                for rec in det["records"]:
+                    idx = num_meas + rec
+                    if 0 <= idx < len(meas):
+                        val ^= meas[idx]
+                if val:
+                    rates[i] += 1.0 / len(results)
+        return rates
+
+    # 1. Non-EEG DemBuilder analytical marginals
+    t0 = time.perf_counter()
+    analyzer = DagFaultAnalyzer(dag)
+    influence = analyzer.build_influence_map()
+    dem_obj = (
+        DemBuilder(influence)
+        .with_noise(p1=p, p2=p, p_meas=p, p_prep=p)
+        .with_detectors_json(tc.get_meta("detectors"))
+        .with_observables_json(tc.get_meta("observables"))
+        .with_num_measurements(num_meas)
+        .build()
+    )
+    dem_str = dem_obj.to_string()
+    dem_analytical = [0.0] * num_dets
+    for line in dem_str.strip().split("\n"):
+        if line.startswith("error("):
+            prob = float(line.split("(")[1].split(")")[0])
+            for x in line.split():
+                if x.startswith("D"):
+                    d_id = int(x[1:])
+                    if d_id < num_dets:
+                        dem_analytical[d_id] += prob
+    dem_build_time = time.perf_counter() - t0
+
+    # 2. DemSampler.from_circuit
+    t0 = time.perf_counter()
+    sampler_fc = DemSampler.from_circuit(dag, p1=p, p2=p, p_meas=p, p_prep=p)
+    batch_fc = sampler_fc.generate_samples(num_shots=shots, seed=seed)
+    dem_fc = [0.0] * num_dets
+    for i in range(shots):
+        syn = batch_fc.get_syndrome(i)
+        for dd in range(min(num_dets, len(syn))):
+            if syn[dd]:
+                dem_fc[dd] += 1.0 / shots
+    fc_time = time.perf_counter() - t0
+
+    # 3. Backward Heisenberg
+    t0 = time.perf_counter()
+    heis_results = exact_detection_rates(tc, p1=p, p2=p, p_meas=p, p_prep=p)
+    heis = [0.0] * num_dets
+    for det_id, prob in heis_results:
+        if det_id < num_dets:
+            heis[det_id] = prob
+    heis_time = time.perf_counter() - t0
+
+    # 4. stabilizer() ground truth
+    t0 = time.perf_counter()
+    noise = depolarizing().p1(p).p2(p).p_meas(p).p_prep(p)
+    stab_results = sim_neo(tc).quantum(stabilizer()).noise(noise).shots(shots).seed(seed).run()
+    stab = extract_det_rates(stab_results)
+    stab_time = time.perf_counter() - t0
+
+    # 5. statevec() (optional, small circuits only)
+    sv = None
+    sv_time = 0
+    if run_statevec:
+        t0 = time.perf_counter()
+        sv_results = sim_neo(tc).quantum(statevec()).noise(noise).shots(shots).seed(seed + 1).run()
+        sv = extract_det_rates(sv_results)
+        sv_time = time.perf_counter() - t0
+
+    # Print timing
+    print(
+        f"  DemBuilder: {dem_build_time*1000:.0f}ms, FromCircuit: {fc_time:.2f}s,"
+        f" Heisenberg: {heis_time*1000:.0f}ms, Stabilizer: {stab_time:.2f}s"
+        + (f", StateVec: {sv_time:.1f}s" if sv else ""),
+    )
+
+    # Header
+    cols = ["Det", "DemBuild", "FromCirc", "Heisen", "Stabiliz"]
+    if sv:
+        cols.append("StateVec")
+    cols += ["DB/Stab", "FC/Stab", "H/Stab"]
+    hdr = f"  {cols[0]:>4}"
+    for c in cols[1:]:
+        hdr += f" {c:>10}"
+    print(hdr)
+
+    for dd in range(num_dets):
+        s = stab[dd]
+        if s < 0.001:
+            continue
+
+        math.sqrt(s * (1 - s) / shots)
+        r_db = dem_analytical[dd] / s
+        r_fc = dem_fc[dd] / s
+        r_h = heis[dd] / s
+
+        line = f"  D{dd:>2} {dem_analytical[dd]:>10.6f} {dem_fc[dd]:>10.6f} {heis[dd]:>10.6f} {s:>10.6f}"
+        if sv:
+            line += f" {sv[dd]:>10.6f}"
+        line += f" {r_db:>10.3f} {r_fc:>10.3f} {r_h:>10.3f}"
+
+        flags = []
+        if abs(1 - r_db) > 0.15:
+            flags.append("DB")
+        if abs(1 - r_fc) > 0.15:
+            flags.append("FC")
+        if abs(1 - r_h) > 0.15:
+            flags.append("H")
+        if flags:
+            line += f"  *** {','.join(flags)}"
+        print(line)
+
+
+def main():
+    parser = argparse.ArgumentParser(
+        description=__doc__,
+        formatter_class=argparse.RawDescriptionHelpFormatter,
+    )
+    parser.add_argument("--distance", "-d", type=int, nargs="+", default=[2, 3])
+    parser.add_argument("--rounds", type=int, default=None)
+    parser.add_argument("--basis", choices=["X", "Z"], nargs="+", default=["Z"])
+    parser.add_argument("--p", type=float, nargs="+", default=[0.005])
+    parser.add_argument("--shots", type=int, default=10000)
+    parser.add_argument("--seed", type=int, default=42)
+    parser.add_argument("--no-statevec", action="store_true")
+    args = parser.parse_args()
+
+    for dist in args.distance:
+        for basis in args.basis:
+            for p_val in args.p:
+                rds = args.rounds if args.rounds is not None else dist
+                run(
+                    distance=dist,
+                    rounds=rds,
+                    basis=basis,
+                    p=p_val,
+                    shots=args.shots,
+                    seed=args.seed,
+                    run_statevec=not args.no_statevec and dist <= 3,
+                )
+
+
+if __name__ == "__main__":
+    main()
diff --git a/examples/surface/dem_method_ler_comparison.py b/examples/surface/dem_method_ler_comparison.py
new file mode 100644
index 000000000..84dd7ef28
--- /dev/null
+++ b/examples/surface/dem_method_ler_comparison.py
@@ -0,0 +1,456 @@
+r"""DEM method x decoder LER comparison on traced_qis circuits.
+
+Generates a traced_qis surface code circuit, builds DEMs from multiple
+methods, samples once, and decodes with multiple decoders.  Reports LER
+for each (DEM method, decoder) combination.
+
+DEM methods:
+  1. from_circuit   — non-EEG backward Pauli propagation (stochastic only)
+  2. coherent_exact — EEG backward Heisenberg + L-BFGS fit
+  3. noise_char     — EEG unified (correlations + mechanisms + DEM)
+  4. perturbative   — EEG forward pass (fast, approximate)
+
+Each method produces a raw DEM string.  MWPM decoders (pymatching,
+fusion_blossom) use the standard decomposed DEM from ``from_circuit``
+since they cannot handle hyperedges.  Non-MWPM decoders (tesseract,
+bp_osd) use the raw DEM from each method.
+
+Example:
+    uv run python examples/surface/dem_method_ler_comparison.py
+    uv run python examples/surface/dem_method_ler_comparison.py \
+        --distances 3 5 --shots 50000 --decoders pymatching tesseract
+"""
+
+from __future__ import annotations
+
+import argparse
+import sys
+import time
+from pathlib import Path
+
+sys.path.insert(0, str(Path(__file__).resolve().parents[2] / "python" / "quantum-pecos" / "src"))
+
+# Slow decoders that benefit from parallel decoding
+SLOW_DECODERS = {"tesseract", "bp_osd"}
+
+
+def _decoder_requires_graphlike(decoder: str) -> bool:
+    """Check if a decoder requires graphlike (decomposed) DEMs."""
+    from pecos_rslib.qec import decoder_dem_requirement
+
+    base = decoder.split(":", maxsplit=1)[0]
+    return decoder_dem_requirement(base) == "graphlike"
+
+
+def sim_results_to_sample_batch(results, det_json, obs_json, num_meas):
+    """Convert sim_neo() results to a SampleBatch.
+
+    Computes detection events from detector record XOR definitions,
+    and observable flips from observable record XOR definitions.
+    """
+    import json
+
+    from pecos_rslib.qec import SampleBatch
+
+    dets = det_json if isinstance(det_json, list) else json.loads(det_json)
+    obs = obs_json if isinstance(obs_json, list) else json.loads(obs_json)
+    num_dets = len(dets)
+    len(obs)
+
+    detection_events = []
+    observable_masks = []
+
+    for r in results:
+        meas = list(r)
+
+        # Detection events: XOR of records per detector
+        syn = [0] * num_dets
+        for i, det in enumerate(dets):
+            val = 0
+            for rec in det["records"]:
+                idx = num_meas + rec
+                if 0 <= idx < len(meas):
+                    val ^= meas[idx]
+            syn[i] = val
+        detection_events.append(syn)
+
+        # Observable flips: XOR of records per observable
+        obs_mask = 0
+        for j, ob in enumerate(obs):
+            val = 0
+            for rec in ob["records"]:
+                idx = num_meas + rec
+                if 0 <= idx < len(meas):
+                    val ^= meas[idx]
+            if val:
+                obs_mask |= 1 << j
+        observable_masks.append(obs_mask)
+
+    return SampleBatch(detection_events, observable_masks)
+
+
+def build_tick_circuits(distance: int, num_rounds: int, basis: str):
+    """Build both abstract and traced_qis TickCircuits for a surface code.
+
+    Returns (patch, abstract_tc, traced_tc).
+    EEG methods need the abstract circuit (CX/H gate set).
+    Non-EEG DemBuilder uses the traced circuit (physical gates).
+    """
+    from pecos.qec.surface import SurfacePatch
+    from pecos.qec.surface.decode import _build_surface_tick_circuit_for_native_model
+
+    patch = SurfacePatch.create(distance=distance)
+    abstract_tc = _build_surface_tick_circuit_for_native_model(
+        patch,
+        num_rounds,
+        basis,
+        circuit_source="abstract",
+    )
+    traced_tc = _build_surface_tick_circuit_for_native_model(
+        patch,
+        num_rounds,
+        basis,
+        circuit_source="traced_qis",
+    )
+    return patch, abstract_tc, traced_tc
+
+
+def generate_dems(
+    abstract_tc,
+    _traced_tc,
+    patch,
+    num_rounds,
+    noise_params: dict,
+    basis: str,
+) -> list[tuple[str, str, str | None]]:
+    """Generate DEM strings from all methods.
+
+    EEG methods use the abstract circuit (CX/H gate set).
+    Non-EEG DemBuilder uses the traced circuit (physical Selene gates).
+
+    Returns list of (method_name, raw_dem, decomposed_dem_or_None).
+    decomposed_dem is None when the method cannot produce a graphlike DEM.
+    """
+    from pecos.qec.surface import NoiseModel
+    from pecos.qec.surface.decode import generate_circuit_level_dem_from_builder
+
+    results = []
+
+    noise = NoiseModel(
+        p1=noise_params.get("p1", 0.0),
+        p2=noise_params.get("p2", 0.0),
+        p_meas=noise_params.get("p_meas", 0.0),
+        p_prep=noise_params.get("p_prep", 0.0),
+    )
+
+    # 1. from_circuit on traced (non-EEG, stochastic, physical gates)
+    try:
+        raw = generate_circuit_level_dem_from_builder(
+            patch,
+            num_rounds,
+            noise,
+            basis=basis,
+            decompose_errors=False,
+            circuit_source="traced_qis",
+        )
+        decomp = generate_circuit_level_dem_from_builder(
+            patch,
+            num_rounds,
+            noise,
+            basis=basis,
+            decompose_errors=True,
+            circuit_source="traced_qis",
+        )
+        results.append(("from_circuit_traced", raw, decomp))
+    except Exception as e:
+        print(f"  WARN: from_circuit_traced failed: {e}")
+
+    # 1b. from_circuit on abstract (non-EEG, stochastic, logical gates)
+    try:
+        raw = generate_circuit_level_dem_from_builder(
+            patch,
+            num_rounds,
+            noise,
+            basis=basis,
+            decompose_errors=False,
+            circuit_source="abstract",
+        )
+        decomp = generate_circuit_level_dem_from_builder(
+            patch,
+            num_rounds,
+            noise,
+            basis=basis,
+            decompose_errors=True,
+            circuit_source="abstract",
+        )
+        results.append(("from_circuit_abstract", raw, decomp))
+    except Exception as e:
+        print(f"  WARN: from_circuit_abstract failed: {e}")
+
+    # EEG methods use the abstract circuit (CX/H gate set)
+    # 2. coherent_dem_decomposed (EEG, X/Z Pauli-aware decomposition)
+    try:
+        from pecos_rslib_exp import coherent_dem_decomposed
+
+        raw_dem, decomp_dem = coherent_dem_decomposed(abstract_tc, **noise_params)
+        if raw_dem.strip():
+            results.append(("coherent_decomp", raw_dem, decomp_dem))
+    except Exception as e:
+        print(f"  WARN: coherent_dem_decomposed failed: {e}")
+
+    # 3. noise_characterization (EEG, unified)
+    try:
+        from pecos_rslib_exp import noise_characterization
+
+        _json_str, dem_raw, dem_decomp = noise_characterization(abstract_tc, **noise_params)
+        if dem_raw.strip():
+            results.append(("noise_char", dem_raw, dem_decomp))
+    except Exception as e:
+        print(f"  WARN: noise_characterization failed: {e}")
+
+    # 4. perturbative_dem (EEG, forward)
+    try:
+        from pecos_rslib_exp import perturbative_dem
+
+        dem_raw, dem_decomp = perturbative_dem(abstract_tc, **noise_params)
+        if dem_raw.strip():
+            results.append(("perturbative", dem_raw, dem_decomp))
+    except Exception as e:
+        print(f"  WARN: perturbative_dem failed: {e}")
+
+    return results
+
+
+def _sample_from_sim(tc, noise_params, shots, seed, backend="statevec"):
+    """Sample using sim_neo (captures actual noise including coherent).
+
+    backend: "statevec" (exact, small circuits),
+             "stabilizer" (exact for depol, fast — no coherent idle_rz),
+             "stab_mps" (handles coherent noise, any distance, approximate).
+    """
+    import json
+
+    from pecos_rslib_exp import depolarizing, sim_neo, stab_mps, stabilizer, statevec
+
+    p1 = noise_params.get("p1", 0.0)
+    p2 = noise_params.get("p2", 0.0)
+    p_meas = noise_params.get("p_meas", 0.0)
+    p_prep = noise_params.get("p_prep", 0.0)
+    irz = noise_params.get("idle_rz", 0.0)
+
+    noise = depolarizing().p1(p1).p2(p2).p_meas(p_meas).p_prep(p_prep)
+    if irz > 0:
+        noise = noise.idle_rz(irz)
+
+    if backend == "stabilizer":
+        quantum_backend = stabilizer()
+    elif backend == "stab_mps":
+        quantum_backend = stab_mps()
+    else:
+        quantum_backend = statevec()
+
+    results = sim_neo(tc).quantum(quantum_backend).noise(noise).shots(shots).seed(seed).run()
+
+    det_json = json.loads(tc.get_meta("detectors"))
+    obs_json = json.loads(tc.get_meta("observables"))
+    num_meas = int(tc.get_meta("num_measurements"))
+
+    return sim_results_to_sample_batch(results, det_json, obs_json, num_meas)
+
+
+def strip_logical_observable_lines(dem_str: str) -> str:
+    """Remove logical_observable lines that some decoders choke on."""
+    return "\n".join(line for line in dem_str.split("\n") if not line.startswith("logical_observable"))
+
+
+def run_comparison(
+    *,
+    distances: list[int],
+    noise_configs: list[tuple[str, dict]],
+    decoders: list[str],
+    basis: str,
+    shots: int,
+    seed: int,
+    sample_backend: str,
+):
+    """Run the full DEM method x decoder comparison."""
+    all_results = []
+
+    for distance in distances:
+        num_rounds = 2 * distance
+        for noise_label, noise_params in noise_configs:
+            print(f"\n{'='*72}")
+            print(f"d={distance} {basis}-basis, {num_rounds} rounds, {noise_label}")
+            print(f"  sample_backend={sample_backend}")
+            print(f"{'='*72}")
+
+            # Build both abstract and traced circuits
+            t0 = time.perf_counter()
+            patch, abstract_tc, traced_tc = build_tick_circuits(distance, num_rounds, basis)
+            t_circuit = time.perf_counter() - t0
+            print(f"  Circuits built in {t_circuit:.2f}s")
+
+            sampler_params = {k: v for k, v in noise_params.items() if k in ("p1", "p2", "p_meas", "p_prep")}
+            idle_rz = noise_params.get("idle_rz", 0.0)
+
+            # Generate samples
+            t0 = time.perf_counter()
+            if sample_backend in ("statevec", "stabilizer", "stab_mps"):
+                # Simulator-based sampling
+                batch = _sample_from_sim(
+                    abstract_tc,
+                    noise_params,
+                    shots,
+                    seed,
+                    backend=sample_backend,
+                )
+            else:
+                # DemSampler: fast, stochastic-only sampling
+                from pecos_rslib.qec import DemSampler
+
+                sampler = DemSampler.from_circuit(
+                    traced_tc,
+                    **sampler_params,
+                    idle_rz=idle_rz if idle_rz > 0 else None,
+                )
+                batch = sampler.generate_samples(shots, seed=seed)
+            t_sample = time.perf_counter() - t0
+            print(f"  Sampled {shots} shots in {t_sample:.2f}s")
+
+            # Generate DEMs from all methods
+            t0 = time.perf_counter()
+            dems = generate_dems(abstract_tc, traced_tc, patch, num_rounds, noise_params, basis)
+            t_dems = time.perf_counter() - t0
+            print(f"  Generated {len(dems)} DEMs in {t_dems:.2f}s")
+            for name, dem_str, _decomp in dems:
+                n_lines = len([line for line in dem_str.strip().split("\n") if line.strip()])
+                print(f"    {name}: {n_lines} lines")
+
+            # Build column headers: for raw-capable decoders, show both raw and decomposed
+            columns = []
+            for dec in decoders:
+                if _decoder_requires_graphlike(dec):
+                    columns.append((dec, "decomp"))
+                else:
+                    columns.append((dec, "raw"))
+                    columns.append((dec, "decomp"))
+
+            # Print header
+            print(f"\n  {'DEM Method':<22s}", end="")
+            for dec, dem_type in columns:
+                label = f"{dec}({dem_type[0]})" if dem_type == "raw" else f"{dec}(d)"
+                print(f" | {label:>16s}", end="")
+            print()
+            print(f"  {'-'*22}", end="")
+            for _ in columns:
+                print(f" | {'-'*16}", end="")
+            print()
+
+            for dem_name, dem_raw, dem_decomp in dems:
+                dem_raw_clean = strip_logical_observable_lines(dem_raw)
+                dem_decomp_clean = strip_logical_observable_lines(dem_decomp) if dem_decomp else None
+                print(f"  {dem_name:<22s}", end="", flush=True)
+
+                for decoder, dem_type in columns:
+                    base = decoder.split(":")[0]
+
+                    if dem_type == "decomp" and dem_decomp_clean is None:
+                        # No decomposed DEM available for this method
+                        print(f" | {'N/A':>16s}", end="")
+                        continue
+
+                    dem = dem_raw_clean if dem_type == "raw" else dem_decomp_clean
+
+                    try:
+                        if base in SLOW_DECODERS:
+                            stats = batch.decode_stats_parallel(dem, decoder)
+                        else:
+                            stats = batch.decode_stats(dem, decoder)
+                        ler = stats.logical_error_rate
+                        print(f" | {ler:>16.4f}", end="")
+                        all_results.append(
+                            {
+                                "distance": distance,
+                                "noise": noise_label,
+                                "dem_method": dem_name,
+                                "decoder": decoder,
+                                "dem_type": dem_type,
+                                "num_shots": shots,
+                                "num_errors": stats.num_errors,
+                                "ler": ler,
+                                "decode_s": stats.total_seconds,
+                            },
+                        )
+                    except Exception:
+                        # Decoder can't handle this DEM (e.g., hyperedges in graphlike DEM)
+                        print(f" | {'N/A':>16s}", end="")
+
+                print()
+
+    return all_results
+
+
+def main():
+    parser = argparse.ArgumentParser(
+        description="DEM method x decoder LER comparison on traced_qis circuits",
+    )
+    parser.add_argument("--distances", type=int, nargs="+", default=[3, 5])
+    parser.add_argument("--shots", type=int, default=10_000)
+    parser.add_argument("--basis", default="Z")
+    parser.add_argument("--seed", type=int, default=42)
+    parser.add_argument(
+        "--decoders",
+        nargs="+",
+        default=["pymatching", "fusion_blossom", "tesseract"],
+    )
+    parser.add_argument("--p2", type=float, default=0.005)
+    parser.add_argument("--idle-rz", type=float, default=0.05)
+    parser.add_argument(
+        "--noise",
+        nargs="+",
+        default=["depol", "depol+irz"],
+        choices=["depol", "depol+irz"],
+    )
+    parser.add_argument(
+        "--sample-backend",
+        default="native",
+        choices=["native", "statevec", "stabilizer", "stab_mps"],
+        help="'native' uses DemSampler (fast, stochastic). "
+        "'statevec' uses exact state vector sim (slow, captures coherent). "
+        "'stabilizer' uses stabilizer sim (fast, exact for depolarizing). "
+        "'stab_mps' uses tensor network sim (handles coherent, any distance).",
+    )
+    args = parser.parse_args()
+
+    p2 = args.p2
+    noise_configs = []
+    if "depol" in args.noise:
+        noise_configs.append(
+            (
+                f"depol(p2={p2})",
+                {"p1": p2 / 10, "p2": p2, "p_meas": p2, "p_prep": p2, "idle_rz": 0.0},
+            ),
+        )
+    if "depol+irz" in args.noise:
+        noise_configs.append(
+            (
+                f"depol+irz(p2={p2},irz={args.idle_rz})",
+                {"p1": p2 / 10, "p2": p2, "p_meas": p2, "p_prep": p2, "idle_rz": args.idle_rz},
+            ),
+        )
+
+    results = run_comparison(
+        distances=args.distances,
+        noise_configs=noise_configs,
+        decoders=args.decoders,
+        basis=args.basis,
+        shots=args.shots,
+        seed=args.seed,
+        sample_backend=args.sample_backend,
+    )
+
+    print(f"\n\nTotal results: {len(results)}")
+
+
+if __name__ == "__main__":
+    main()
diff --git a/examples/surface/dem_tutorial.py b/examples/surface/dem_tutorial.py
new file mode 100644
index 000000000..545d66f18
--- /dev/null
+++ b/examples/surface/dem_tutorial.py
@@ -0,0 +1,132 @@
+"""DEM generation tutorial: build circuit, inspect DEM, sample, validate.
+
+Demonstrates the full PECOS DEM pipeline using a d=3 surface code.
+
+Usage:
+    uv run python examples/surface/dem_tutorial.py
+"""
+
+from __future__ import annotations
+
+import json
+import sys
+from pathlib import Path
+
+sys.path.insert(0, str(Path(__file__).resolve().parents[2] / "python" / "quantum-pecos" / "src"))
+
+from pecos.qec.surface import LogicalCircuitBuilder, SurfacePatch
+from pecos_rslib.qec import DemSampler, DetectorErrorModel
+from pecos_rslib_exp import depolarizing, sim_neo, stabilizer
+
+
+def main():
+    # ================================================================
+    # 1. Build a surface code circuit
+    # ================================================================
+    distance = 3
+    patch = SurfacePatch.create(distance=distance)
+    b = LogicalCircuitBuilder()
+    b.add_patch(patch, "Q0")
+    b.add_memory("Q0", rounds=distance, basis="Z")
+    tc = b.to_tick_circuit()
+
+    print(f"Surface code d={distance}, {tc.num_ticks()} ticks")
+    print(
+        f"  {int(tc.get_meta('num_measurements'))} measurements, "
+        f"{len(json.loads(tc.get_meta('detectors')))} detectors",
+    )
+
+    # ================================================================
+    # 2. Inspect measurement IDs on gates
+    # ================================================================
+    # Each MZ gate carries a MeasId — a stable identity for that
+    # measurement result. These persist through all transformations.
+    dag = tc.to_dag_circuit()
+
+    print("\nMeasurement gates (first 5):")
+    shown = 0
+    for node_id in dag.nodes():
+        gate = dag.gate(node_id)
+        if gate and gate.gate_type.name == "MZ" and shown < 5:
+            print(f"  node={node_id}: MZ qubit={list(gate.qubits)} meas_ids={gate.meas_ids}")
+            shown += 1
+
+    # ================================================================
+    # 3. Inspect detector definitions
+    # ================================================================
+    # Detectors reference measurements by both:
+    #   - "records": negative offsets (Stim compatibility)
+    #   - "meas_ids": stable MeasId values (preferred)
+    dets = json.loads(tc.get_meta("detectors"))
+    print(f"\nDetector definitions (first 3 of {len(dets)}):")
+    for det in dets[:3]:
+        print(f"  D{det['id']}: meas_ids={det['meas_ids']}  records={det['records']}")
+
+    # ================================================================
+    # 4. Build and inspect the DEM (one line)
+    # ================================================================
+    p = 0.005
+    dem = DetectorErrorModel.from_circuit(tc, p1=p, p2=p, p_meas=p, p_prep=p)
+    print(f"\nDetectorErrorModel: {dem.num_detectors} detectors, {dem.num_observables} observables")
+
+    dem_str = dem.to_string()
+    error_lines = [line for line in dem_str.split("\n") if line.startswith("error(")]
+    print(f"  {len(error_lines)} DEM events")
+    print("  First 3 events:")
+    for line in error_lines[:3]:
+        print(f"    {line}")
+
+    # ================================================================
+    # 5. Sample from the DEM (one line)
+    # ================================================================
+    shots = 100_000
+    sampler = DemSampler.from_circuit(tc, p1=p, p2=p, p_meas=p, p_prep=p)
+    batch = sampler.generate_samples(num_shots=shots, seed=42)
+
+    # Compute per-detector firing rates from DEM sampling
+    num_dets = len(dets)
+    dem_rates = [0.0] * num_dets
+    for i in range(shots):
+        syn = batch.get_syndrome(i)
+        for d in range(min(num_dets, len(syn))):
+            if syn[d]:
+                dem_rates[d] += 1.0 / shots
+
+    # ================================================================
+    # 6. Validate against stabilizer simulation (ground truth)
+    # ================================================================
+    noise = depolarizing().p1(p).p2(p).p_meas(p).p_prep(p)
+    results = sim_neo(tc).quantum(stabilizer()).noise(noise).shots(shots).seed(42).run()
+
+    num_meas = int(tc.get_meta("num_measurements"))
+    sim_rates = [0.0] * num_dets
+    for r in results:
+        meas = list(r)
+        for i, det in enumerate(dets):
+            val = 0
+            for rec in det["records"]:
+                idx = num_meas + rec
+                if 0 <= idx < len(meas):
+                    val ^= meas[idx]
+            if val:
+                sim_rates[i] += 1.0 / shots
+
+    # ================================================================
+    # 7. Compare
+    # ================================================================
+    print(f"\nPer-detector rates (p={p}, {shots} shots):")
+    print(f"  {'Det':>4} {'DEM':>10} {'Stabilizer':>10} {'Ratio':>7}")
+    max_rel = 0
+    for d in range(num_dets):
+        if sim_rates[d] > 0.003:
+            ratio = dem_rates[d] / sim_rates[d]
+            max_rel = max(max_rel, abs(1 - ratio))
+            print(f"  D{d:>2} {dem_rates[d]:>10.5f} {sim_rates[d]:>10.5f} {ratio:>7.3f}")
+
+    status = "PASS" if max_rel < 0.15 else f"FAIL (max_rel={max_rel*100:.0f}%)"
+    print(f"\nValidation: {status}")
+    print(f"  Max relative error: {max_rel*100:.1f}% (threshold: 15% for {shots} shots)")
+
+
+if __name__ == "__main__":
+    main()
diff --git a/examples/surface/dem_vs_stabilizer.py b/examples/surface/dem_vs_stabilizer.py
new file mode 100644
index 000000000..5a48f938a
--- /dev/null
+++ b/examples/surface/dem_vs_stabilizer.py
@@ -0,0 +1,163 @@
+r"""Compare non-EEG DEM detection rates against stabilizer() ground truth.
+
+Tests per-detector firing rates from:
+  1. DemBuilder analytical marginals (sum of DEM event probabilities)
+  2. DemSampler.from_circuit sampled rates
+  3. stabilizer() simulation (SparseStab ground truth)
+
+Pure depolarizing noise only (no coherent idle_rz).
+
+Example:
+    uv run python examples/surface/dem_vs_stabilizer.py
+    uv run python examples/surface/dem_vs_stabilizer.py -d 2 3 --p 0.005
+"""
+
+from __future__ import annotations
+
+import argparse
+import json
+import math
+import sys
+import time
+from pathlib import Path
+
+sys.path.insert(0, str(Path(__file__).resolve().parents[2] / "python" / "quantum-pecos" / "src"))
+
+
+def run_comparison(*, distance, rounds, basis, p, shots, seed):
+    from pecos.qec.surface import LogicalCircuitBuilder, SurfacePatch
+    from pecos_rslib.qec import DagFaultAnalyzer, DemBuilder, DemSampler
+    from pecos_rslib_exp import depolarizing, sim_neo, stabilizer
+
+    patch = SurfacePatch.create(distance=distance)
+    b = LogicalCircuitBuilder()
+    b.add_patch(patch, "Q0")
+    b.add_memory("Q0", rounds=rounds, basis=basis)
+    tc = b.to_tick_circuit()
+    dag = tc.to_dag_circuit()
+
+    det_json = json.loads(tc.get_meta("detectors"))
+    num_meas = int(tc.get_meta("num_measurements"))
+    num_dets = len(det_json)
+
+    print(f"\n{'='*70}")
+    print(f"d={distance} {basis}-basis, {rounds} rounds, {num_dets} dets, p={p}")
+    print(f"{'='*70}")
+
+    # 1. DemBuilder analytical marginals
+    analyzer = DagFaultAnalyzer(dag)
+    influence = analyzer.build_influence_map()
+    dem_obj = (
+        DemBuilder(influence)
+        .with_noise(p1=p, p2=p, p_meas=p, p_prep=p)
+        .with_detectors_json(tc.get_meta("detectors"))
+        .with_observables_json(tc.get_meta("observables"))
+        .with_num_measurements(num_meas)
+        .build()
+    )
+    dem_str = dem_obj.to_string()
+    analytical = [0.0] * num_dets
+    for line in dem_str.strip().split("\n"):
+        if line.startswith("error("):
+            prob = float(line.split("(")[1].split(")")[0])
+            for x in line.split():
+                if x.startswith("D"):
+                    d_id = int(x[1:])
+                    if d_id < num_dets:
+                        analytical[d_id] += prob
+
+    # 2. DemSampler.from_circuit
+    t0 = time.perf_counter()
+    sampler_fc = DemSampler.from_circuit(dag, p1=p, p2=p, p_meas=p, p_prep=p)
+    batch_fc = sampler_fc.generate_samples(num_shots=shots, seed=seed)
+    dem_fc = [0.0] * num_dets
+    for i in range(shots):
+        syn = batch_fc.get_syndrome(i)
+        for dd in range(min(num_dets, len(syn))):
+            if syn[dd]:
+                dem_fc[dd] += 1.0 / shots
+    fc_time = time.perf_counter() - t0
+
+    # 3. stabilizer() ground truth
+    t0 = time.perf_counter()
+    noise = depolarizing().p1(p).p2(p).p_meas(p).p_prep(p)
+    results = sim_neo(tc).quantum(stabilizer()).noise(noise).shots(shots).seed(seed).run()
+    sim = [0.0] * num_dets
+    for r in results:
+        meas = list(r)
+        for i, det in enumerate(det_json):
+            val = 0
+            for rec in det["records"]:
+                idx = num_meas + rec
+                if 0 <= idx < len(meas):
+                    val ^= meas[idx]
+            if val:
+                sim[i] += 1.0 / shots
+    sim_time = time.perf_counter() - t0
+
+    print(f"  DEM sample: {fc_time:.2f}s, Stabilizer: {sim_time:.2f}s ({shots} shots)")
+    print(
+        f"  {'Det':>4} {'Analytical':>11} {'FromCirc':>10} {'Stabiliz':>10}"
+        f" {'SV_se':>8} {'A/Sim':>7} {'FC/Sim':>7}",
+    )
+
+    max_a_err = 0.0
+    max_fc_err = 0.0
+    flagged = 0
+    for dd in range(num_dets):
+        sv_r = sim[dd]
+        se = math.sqrt(sv_r * (1 - sv_r) / shots) if sv_r > 0 else 0
+
+        if sv_r > 0.002:
+            ra = analytical[dd] / sv_r
+            rf = dem_fc[dd] / sv_r
+            max_a_err = max(max_a_err, abs(1 - ra))
+            max_fc_err = max(max_fc_err, abs(1 - rf))
+        else:
+            ra = float("nan")
+            rf = float("nan")
+
+        flag = ""
+        if sv_r > 0.002 and (abs(1 - ra) > 0.15 or abs(1 - rf) > 0.15):
+            flag = " ***"
+            flagged += 1
+
+        print(
+            f"  D{dd:>2} {analytical[dd]:>11.6f} {dem_fc[dd]:>10.6f} {sv_r:>10.6f}"
+            f" {se:>8.5f} {ra:>7.3f} {rf:>7.3f}{flag}",
+        )
+
+    print(
+        f"  Max deviation: Analytical={max_a_err*100:.1f}%, FromCircuit={max_fc_err*100:.1f}%, flagged={flagged}",
+    )
+
+
+def main():
+    parser = argparse.ArgumentParser(
+        description=__doc__,
+        formatter_class=argparse.RawDescriptionHelpFormatter,
+    )
+    parser.add_argument("--distance", "-d", type=int, nargs="+", default=[2, 3])
+    parser.add_argument("--rounds", type=int, default=None)
+    parser.add_argument("--basis", choices=["X", "Z"], nargs="+", default=["X", "Z"])
+    parser.add_argument("--p", type=float, nargs="+", default=[0.005])
+    parser.add_argument("--shots", type=int, default=10000)
+    parser.add_argument("--seed", type=int, default=42)
+    args = parser.parse_args()
+
+    for dist in args.distance:
+        for basis in args.basis:
+            for p_val in args.p:
+                rds = args.rounds if args.rounds is not None else dist
+                run_comparison(
+                    distance=dist,
+                    rounds=rds,
+                    basis=basis,
+                    p=p_val,
+                    shots=args.shots,
+                    seed=args.seed,
+                )
+
+
+if __name__ == "__main__":
+    main()
diff --git a/examples/surface/eeg_formula_comparison.py b/examples/surface/eeg_formula_comparison.py
new file mode 100644
index 000000000..6b32a607b
--- /dev/null
+++ b/examples/surface/eeg_formula_comparison.py
@@ -0,0 +1,214 @@
+r"""Compare all forward EEG formula variants against backward Heisenberg.
+
+Tests 6 forward EEG configurations:
+  1. Taylor + BCH1 (default)
+  2. SinSquared + BCH1
+  3. ExactCommuting + BCH1
+  4. Taylor + BCH2
+  5. SinSquared + BCH2
+  6. ExactCommuting + BCH2
+
+Against:
+  7. Backward Heisenberg (exact)
+  8. StateVec simulation (ground truth, optional)
+
+Example:
+    uv run python examples/surface/eeg_formula_comparison.py
+    uv run python examples/surface/eeg_formula_comparison.py -d 3 --theta 0.05 --shots 50000
+    uv run python examples/surface/eeg_formula_comparison.py -d 2 3 --no-statevec
+"""
+
+from __future__ import annotations
+
+import argparse
+import json
+import sys
+import time
+from pathlib import Path
+
+sys.path.insert(0, str(Path(__file__).resolve().parents[2] / "python" / "quantum-pecos" / "src"))
+
+CONFIGS = [
+    ("Taylor", "taylor", 1),
+    ("SinSq", "sin_squared", 1),
+    ("ExCom", "exact_commuting", 1),
+    ("ExSubset", "exact_subset", 1),
+]
+
+
+def marginals_from_events(events, num_dets):
+    rates = [0.0] * num_dets
+    for prob, det_ids, _obs_ids in events:
+        for d in det_ids:
+            if d < num_dets:
+                rates[d] += prob
+    return rates
+
+
+def run(*, distance, rounds, basis, theta_values, shots, seed, run_statevec):
+    from pecos.qec.surface import LogicalCircuitBuilder, SurfacePatch
+    from pecos_rslib_exp import eeg_per_detector, exact_detection_rates, perturbative_dem_events
+
+    patch = SurfacePatch.create(distance=distance)
+    b = LogicalCircuitBuilder()
+    b.add_patch(patch, "Q0")
+    b.add_memory("Q0", rounds=rounds, basis=basis)
+    tc = b.to_tick_circuit()
+
+    det_json = json.loads(tc.get_meta("detectors"))
+    num_meas = int(tc.get_meta("num_measurements"))
+    num_dets = len(det_json)
+
+    print(f"\n{'='*80}")
+    print(f"d={distance} {basis}-basis memory, {rounds} rounds, {num_dets} detectors")
+    print(f"{'='*80}")
+
+    for theta in theta_values:
+        print(f"\ntheta = {theta:.4f}")
+
+        # Forward EEG: all 6 configs
+        fwd_marginals = {}
+        for name, h_formula, bch in CONFIGS:
+            t0 = time.perf_counter()
+            events = perturbative_dem_events(tc, idle_rz=theta, h_formula=h_formula, bch_order=bch)
+            dt = time.perf_counter() - t0
+            fwd_marginals[name] = (marginals_from_events(events, num_dets), dt)
+
+        # Per-detector computation (cross-event beta)
+        per_det_marginals = {}
+        for name, h_formula, _ in [
+            ("PD-Taylor", "taylor", 0),
+            ("PD-SinSq", "sin_squared", 0),
+            ("PD-ExCom", "exact_commuting", 0),
+        ]:
+            t0 = time.perf_counter()
+            pd_results = eeg_per_detector(tc, idle_rz=theta, h_formula=h_formula)
+            dt = time.perf_counter() - t0
+            rates = [0.0] * num_dets
+            for det_id, prob in pd_results:
+                if det_id < num_dets:
+                    rates[det_id] = prob
+            per_det_marginals[name] = (rates, dt)
+
+        # Backward Heisenberg (exact)
+        t0 = time.perf_counter()
+        heis_results = exact_detection_rates(tc, idle_rz=theta)
+        heis_time = time.perf_counter() - t0
+        heis = [0.0] * num_dets
+        for det_id, prob in heis_results:
+            if det_id < num_dets:
+                heis[det_id] = prob
+
+        # StateVec (optional ground truth)
+        sv_rate = None
+        if run_statevec:
+            from pecos_rslib_exp import depolarizing, sim_neo, statevec
+
+            t0 = time.perf_counter()
+            noise = depolarizing().idle_rz(theta)
+            results = sim_neo(tc).quantum(statevec()).noise(noise).shots(shots).seed(seed).run()
+            sv_time = time.perf_counter() - t0
+
+            sv_det_count = [0] * num_dets
+            for r in results:
+                meas = list(r)
+                for i, det in enumerate(det_json):
+                    val = 0
+                    for rec in det["records"]:
+                        idx = num_meas + rec
+                        if 0 <= idx < len(meas):
+                            val ^= meas[idx]
+                    if val:
+                        sv_det_count[i] += 1
+            sv_rate = [c / shots for c in sv_det_count]
+
+        # Summary table: max relative error vs Heisenberg for each config
+        print(f"\n  {'Config':<14} {'Time':>8} {'MaxRelErr':>10} {'MeanRelErr':>11} {'MaxAbsErr':>10}")
+        print(f"  {'-'*14} {'-'*8} {'-'*10} {'-'*11} {'-'*10}")
+
+        all_configs = [(name, fwd_marginals[name]) for name, _, _ in CONFIGS]
+        all_configs += [(name, per_det_marginals[name]) for name in ["PD-Taylor", "PD-SinSq", "PD-ExCom"]]
+
+        for name, (rates, dt) in all_configs:
+            max_rel = 0.0
+            sum_rel = 0.0
+            max_abs = 0.0
+            count = 0
+            for d in range(num_dets):
+                if heis[d] > 1e-6:
+                    rel = abs(rates[d] - heis[d]) / heis[d]
+                    max_rel = max(max_rel, rel)
+                    sum_rel += rel
+                    count += 1
+                max_abs = max(max_abs, abs(rates[d] - heis[d]))
+            mean_rel = sum_rel / count if count > 0 else 0
+            print(f"  {name:<14} {dt*1000:>7.1f}ms {max_rel*100:>9.1f}% {mean_rel*100:>10.1f}% {max_abs:>10.6f}")
+
+        print(f"  {'Heisenberg':<14} {heis_time*1000:>7.1f}ms {'(exact)':>10}")
+
+        if sv_rate is not None:
+            # Also compare Heisenberg vs StateVec
+            max_rel_h = 0.0
+            for d in range(num_dets):
+                if sv_rate[d] > 0.01:
+                    max_rel_h = max(max_rel_h, abs(heis[d] - sv_rate[d]) / sv_rate[d])
+            print(f"  {'StateVec':<14} {sv_time:>6.1f}s   H/SV max err: {max_rel_h*100:.1f}%")
+
+        # Per-detector detail (compact — only show non-zero detectors, skip redundant DEM configs)
+        if num_dets <= 40:
+            # Show: Heisenberg, Taylor (DEM), PD-Taylor, PD-ExCom, SV
+            show_configs = [
+                ("Taylor", lambda fwd_marginals=fwd_marginals: fwd_marginals["Taylor"]),
+                ("ExSubset", lambda fwd_marginals=fwd_marginals: fwd_marginals["ExSubset"]),
+                ("PD-Tayl", lambda per_det_marginals=per_det_marginals: per_det_marginals["PD-Taylor"]),
+            ]
+            cols = ["Det", "Heisen"] + [n for n, _ in show_configs]
+            if sv_rate is not None:
+                cols.append("SV")
+            header = f"  {cols[0]:>4} {cols[1]:>10}"
+            for c in cols[2:]:
+                header += f" {c:>10}"
+            print(f"\n{header}")
+
+            for d in range(num_dets):
+                if heis[d] < 1e-8 and all(fn()[0][d] < 1e-8 for _, fn in show_configs):
+                    continue
+                line = f"  D{d:>2} {heis[d]:>10.6f}"
+                for _, fn in show_configs:
+                    rates, _ = fn()
+                    line += f" {rates[d]:>10.6f}"
+                if sv_rate is not None:
+                    line += f" {sv_rate[d]:>10.6f}"
+                print(line)
+
+
+def main():
+    parser = argparse.ArgumentParser(
+        description=__doc__,
+        formatter_class=argparse.RawDescriptionHelpFormatter,
+    )
+    parser.add_argument("--distance", "-d", type=int, nargs="+", default=[2, 3])
+    parser.add_argument("--rounds", type=int, default=None)
+    parser.add_argument("--basis", choices=["X", "Z"], nargs="+", default=["Z"])
+    parser.add_argument("--theta", type=float, nargs="+", default=[0.01, 0.05, 0.1])
+    parser.add_argument("--shots", type=int, default=50000)
+    parser.add_argument("--seed", type=int, default=42)
+    parser.add_argument("--no-statevec", action="store_true")
+    args = parser.parse_args()
+
+    for dist in args.distance:
+        for basis in args.basis:
+            rds = args.rounds if args.rounds is not None else dist
+            run(
+                distance=dist,
+                rounds=rds,
+                basis=basis,
+                theta_values=args.theta,
+                shots=args.shots,
+                seed=args.seed,
+                run_statevec=not args.no_statevec,
+            )
+
+
+if __name__ == "__main__":
+    main()
diff --git a/examples/surface/eeg_vs_statevec.py b/examples/surface/eeg_vs_statevec.py
new file mode 100644
index 000000000..82fd38915
--- /dev/null
+++ b/examples/surface/eeg_vs_statevec.py
@@ -0,0 +1,219 @@
+r"""Compare EEG analytical DEM vs StateVec empirical detection rates.
+
+Three approaches compared:
+  1. Forward EEG (perturbative Taylor/SinSquared formula) — fast, approximate
+  2. Backward Heisenberg (exact coherent + stochastic) — slower build, exact
+  3. StateVec simulation (ground truth) — slow, limited by qubit count
+
+Both EEG approaches produce Stim-format DEM strings that can be sampled
+at ~15M shots/sec via DemSampler.from_dem_string().
+
+Example:
+    uv run python examples/surface/eeg_vs_statevec.py
+    uv run python examples/surface/eeg_vs_statevec.py --distance 3 --basis X --shots 20000
+    uv run python examples/surface/eeg_vs_statevec.py --distance 2 --basis Z --shots 50000
+    uv run python examples/surface/eeg_vs_statevec.py --distance 5 --basis Z --dem-sample
+"""
+
+from __future__ import annotations
+
+import argparse
+import json
+import math
+import sys
+import time
+from pathlib import Path
+
+sys.path.insert(0, str(Path(__file__).resolve().parents[2] / "python" / "quantum-pecos" / "src"))
+
+
+def run_comparison(
+    *,
+    distance: int,
+    rounds: int,
+    basis: str,
+    theta_values: list[float],
+    shots: int,
+    seed: int,
+    dem_sample: bool,
+):
+    from pecos.qec.surface import LogicalCircuitBuilder, SurfacePatch
+    from pecos_rslib_exp import (
+        coherent_dem_exact,
+        depolarizing,
+        exact_detection_rates,
+        perturbative_dem,
+        perturbative_dem_events,
+        sim_neo,
+        statevec,
+    )
+
+    patch = SurfacePatch.create(distance=distance)
+    b = LogicalCircuitBuilder()
+    b.add_patch(patch, "Q0")
+    b.add_memory("Q0", rounds=rounds, basis=basis)
+    tc = b.to_tick_circuit()
+
+    det_json = json.loads(tc.get_meta("detectors"))
+    num_meas = int(tc.get_meta("num_measurements"))
+    num_dets = len(det_json)
+
+    print(f"\n{'='*70}")
+    print(f"d={distance} {basis}-basis memory, {rounds} rounds, {num_dets} detectors, {num_meas} measurements")
+    print(f"{'='*70}")
+
+    for theta in theta_values:
+        print(f"\ntheta = {theta:.4f}")
+
+        # --- Forward EEG DEM (Taylor) ---
+        t0 = time.perf_counter()
+        eeg_events = perturbative_dem_events(tc, idle_rz=theta, h_formula="taylor")
+        eeg_time = time.perf_counter() - t0
+
+        eeg_taylor = [0.0] * num_dets
+        for prob, det_ids, _obs_ids in eeg_events:
+            for d in det_ids:
+                if d < num_dets:
+                    eeg_taylor[d] += prob
+
+        # --- Heisenberg backward propagation ---
+        t0 = time.perf_counter()
+        heis_results = exact_detection_rates(tc, idle_rz=theta)
+        heis_time = time.perf_counter() - t0
+        heis = [0.0] * num_dets
+        for det_id, prob in heis_results:
+            if det_id < num_dets:
+                heis[det_id] = prob
+
+        # --- DEM sampling path (two-stage: build DEM once, sample fast) ---
+        if dem_sample:
+            from pecos_rslib.qec import DemSampler
+
+            # Forward EEG DEM → sampler
+            t0 = time.perf_counter()
+            dem_taylor_str = perturbative_dem(tc, idle_rz=theta)
+            sampler_taylor = DemSampler.from_dem_string(dem_taylor_str)
+            batch_taylor = sampler_taylor.generate_samples(num_shots=shots, seed=seed)
+            taylor_sample_time = time.perf_counter() - t0
+
+            # Heisenberg DEM → sampler
+            t0 = time.perf_counter()
+            dem_heis_str = coherent_dem_exact(tc, idle_rz=theta)
+            sampler_heis = DemSampler.from_dem_string(dem_heis_str)
+            batch_heis = sampler_heis.generate_samples(num_shots=shots, seed=seed)
+            heis_sample_time = time.perf_counter() - t0
+
+            # Compute per-detector rates from DEM samples
+            taylor_dem_rates = [0.0] * num_dets
+            heis_dem_rates = [0.0] * num_dets
+            for i in range(shots):
+                syn_t = batch_taylor.get_syndrome(i)
+                syn_h = batch_heis.get_syndrome(i)
+                for d in range(min(num_dets, len(syn_t))):
+                    if syn_t[d]:
+                        taylor_dem_rates[d] += 1.0 / shots
+                    if syn_h[d]:
+                        heis_dem_rates[d] += 1.0 / shots
+        else:
+            taylor_dem_rates = None
+            heis_dem_rates = None
+            taylor_sample_time = 0
+            heis_sample_time = 0
+
+        # --- StateVec simulation (ground truth) ---
+        t0 = time.perf_counter()
+        noise = depolarizing().idle_rz(theta)
+        results = sim_neo(tc).quantum(statevec()).noise(noise).shots(shots).seed(seed).run()
+        sv_time = time.perf_counter() - t0
+
+        sv_det_count = [0] * num_dets
+        for r in results:
+            meas = list(r)
+            for i, det in enumerate(det_json):
+                val = 0
+                for rec in det["records"]:
+                    idx = num_meas + rec
+                    if 0 <= idx < len(meas):
+                        val ^= meas[idx]
+                if val:
+                    sv_det_count[i] += 1
+
+        sv_det_rate = [c / shots for c in sv_det_count]
+
+        # --- Compare ---
+        print(f"  EEG: {eeg_time*1000:.1f}ms, Heisenberg: {heis_time*1000:.1f}ms")
+        print(f"  StateVec: {sv_time:.1f}s ({shots} shots)")
+        if dem_sample:
+            print(f"  DEM sample: Taylor {taylor_sample_time:.2f}s, Heisenberg {heis_sample_time:.2f}s ({shots} shots)")
+
+        if dem_sample:
+            print(
+                f"  {'Det':>4} {'Taylor':>10} {'Heisen':>10} {'T(DEM)':>10} "
+                f"{'H(DEM)':>10} {'StateVec':>10} {'SV_se':>8} {'T/SV':>7} {'H/SV':>7}",
+            )
+        else:
+            print(f"  {'Det':>4} {'Taylor':>10} {'Heisen':>10} {'StateVec':>10} {'SV_se':>8} {'T/SV':>7} {'H/SV':>7}")
+
+        max_rel_taylor = 0.0
+        max_rel_heis = 0.0
+        for d in range(num_dets):
+            tp = eeg_taylor[d]
+            hp = heis[d]
+            sv_r = sv_det_rate[d]
+            sv_se = math.sqrt(sv_r * (1 - sv_r) / shots) if shots > 0 else 0
+
+            if sv_r > 0.0001:
+                t_ratio = tp / sv_r
+                h_ratio = hp / sv_r
+                max_rel_taylor = max(max_rel_taylor, abs(tp - sv_r) / sv_r)
+                max_rel_heis = max(max_rel_heis, abs(hp - sv_r) / sv_r)
+            else:
+                t_ratio = float("nan")
+                h_ratio = float("nan")
+
+            if dem_sample:
+                td = taylor_dem_rates[d] if taylor_dem_rates else 0
+                hd = heis_dem_rates[d] if heis_dem_rates else 0
+                print(
+                    f"  D{d:>3} {tp:>10.6f} {hp:>10.6f} {td:>10.6f} {hd:>10.6f} "
+                    f"{sv_r:>10.6f} {sv_se:>8.6f} {t_ratio:>7.3f} {h_ratio:>7.3f}",
+                )
+            else:
+                print(
+                    f"  D{d:>3} {tp:>10.6f} {hp:>10.6f} {sv_r:>10.6f} "
+                    f"{sv_se:>8.6f} {t_ratio:>7.3f} {h_ratio:>7.3f}",
+                )
+
+        print(f"  Max rel err: Taylor={max_rel_taylor*100:.1f}%, Heisenberg={max_rel_heis*100:.1f}%")
+
+
+def main():
+    parser = argparse.ArgumentParser(
+        description=__doc__,
+        formatter_class=argparse.RawDescriptionHelpFormatter,
+    )
+    parser.add_argument("--distance", "-d", type=int, nargs="+", default=[2, 3])
+    parser.add_argument("--rounds", type=int, default=None)
+    parser.add_argument("--basis", choices=["X", "Z"], nargs="+", default=["X", "Z"])
+    parser.add_argument("--theta", type=float, nargs="+", default=[0.01, 0.03, 0.05, 0.1])
+    parser.add_argument("--shots", type=int, default=20000)
+    parser.add_argument("--seed", type=int, default=42)
+    parser.add_argument("--dem-sample", action="store_true", help="Also sample from both DEMs and compare rates")
+    args = parser.parse_args()
+
+    for dist in args.distance:
+        for basis in args.basis:
+            rds = args.rounds if args.rounds is not None else dist
+            run_comparison(
+                distance=dist,
+                rounds=rds,
+                basis=basis,
+                theta_values=args.theta,
+                shots=args.shots,
+                seed=args.seed,
+                dem_sample=args.dem_sample,
+            )
+
+
+if __name__ == "__main__":
+    main()
diff --git a/examples/surface/generate_data.py b/examples/surface/generate_data.py
new file mode 100644
index 000000000..1eb99df7b
--- /dev/null
+++ b/examples/surface/generate_data.py
@@ -0,0 +1,346 @@
+r"""Generate decoder performance data for surface code memory experiments.
+
+Samples detection events once per (distance, error_rate, rounds) point,
+then decodes with each requested decoder. Writes a JSON shard that can
+be fed to ``analyze_data.py`` and ``build_report.py``.
+
+Example:
+    uv run python examples/surface/generate_data.py \\
+        --distances 3 5 --error-rates 0.004 0.008 \\
+        --decoders pymatching mwpf tesseract bp_osd \\
+        --shots 5000
+
+    uv run python examples/surface/generate_data.py \\
+        --distances 3 5 7 \\
+        --error-rates 0.002 0.004 0.006 0.008 \\
+        --decoders pymatching mwpf tesseract \\
+        --duration-multipliers 2 2.5 3 \\
+        --shots 2000 --output-dir results/
+"""
+
+from __future__ import annotations
+
+import argparse
+import json
+import time
+from dataclasses import asdict, dataclass, field
+from pathlib import Path
+from typing import TYPE_CHECKING
+
+if TYPE_CHECKING:
+    from pecos.qec.surface import NoiseModel
+
+# -- Data model ---------------------------------------------------------------
+
+
+@dataclass
+class DecoderStats:
+    """Decode statistics for one decoder on one set of samples."""
+
+    decoder: str
+    num_errors: int
+    logical_error_rate: float
+    total_decode_seconds: float
+    per_shot_mean: float
+    per_shot_median: float
+    per_shot_p99: float
+    per_shot_max: float
+    # 21 quantiles at [0%, 5%, 10%, ..., 95%, 100%] for violin plots
+    quantiles: list[float] = field(default_factory=list)
+
+
+@dataclass
+class DataPoint:
+    """Raw data for one (distance, basis, p, rounds, decoder-set) cell."""
+
+    distance: int
+    basis: str
+    physical_error_rate: float
+    num_rounds: int
+    num_shots: int
+    sample_seconds: float
+    decoder_stats: list[DecoderStats] = field(default_factory=list)
+
+
+@dataclass
+class DataShard:
+    """One complete data-generation run. Serialised to JSON."""
+
+    config: dict
+    points: list[DataPoint] = field(default_factory=list)
+    total_seconds: float = 0.0
+
+
+# -- DEM sets for different decoder families ----------------------------------
+
+# MWPM decoders need decomposed (graphlike) DEMs.
+_MWPM_DECODERS = {
+    "pymatching",
+    "pymatching_uncorrelated",
+    "fusion_blossom",
+    "fusion_blossom_serial",
+    "fusion_blossom_parallel",
+}
+
+# Slow decoders benefit from parallel decode.
+_SLOW_DECODERS = {"tesseract", "mwpf", "bp_osd", "relay_bp"}
+
+
+def _decoder_base_name(name: str) -> str:
+    """Strip config suffix: 'mwpf:c=30' -> 'mwpf'."""
+    return name.split(":", maxsplit=1)[0]
+
+
+# -- Sampler + DEM construction -----------------------------------------------
+
+
+def _build_sampler(
+    distance: int,
+    num_rounds: int,
+    noise: NoiseModel,
+    basis: str,
+    circuit_source: str,
+) -> tuple:
+    """Build native sampler and return (sampler, dem_decomposed, dem_full)."""
+    from pecos.qec.surface import SurfacePatch, build_native_sampler
+    from pecos.qec.surface.decode import SurfaceDecoder, generate_circuit_level_dem_from_builder
+
+    patch = SurfacePatch.create(distance=distance)
+    sampler = build_native_sampler(
+        patch,
+        num_rounds,
+        noise,
+        basis=basis,
+        circuit_source=circuit_source,
+    )
+
+    # Decomposed DEM for MWPM decoders
+    dec = SurfaceDecoder(
+        patch,
+        num_rounds=num_rounds,
+        noise=noise,
+        decoder_type="pymatching",
+        use_circuit_level_dem=True,
+        circuit_level_dem_mode="native_decomposed",
+        circuit_level_dem_source=circuit_source,
+    )
+    dem_decomp = dec.get_dem(basis.upper(), circuit_level=True)
+    dem_decomp = "\n".join(line for line in dem_decomp.split("\n") if not line.startswith("logical_observable"))
+
+    # Full DEM for non-MWPM decoders
+    dem_full = generate_circuit_level_dem_from_builder(
+        patch,
+        num_rounds,
+        noise,
+        basis=basis,
+        decompose_errors=False,
+        circuit_source=circuit_source,
+    )
+    dem_full = "\n".join(line for line in dem_full.split("\n") if not line.startswith("logical_observable"))
+
+    return sampler, dem_decomp, dem_full
+
+
+# -- Main generation loop -----------------------------------------------------
+
+
+def generate(
+    *,
+    distances: list[int],
+    error_rates: list[float],
+    decoders: list[str],
+    basis: str,
+    shots: int,
+    seed: int,
+    circuit_source: str,
+    p1_scale: float,
+    p_meas_scale: float,
+    p_prep_scale: float,
+    duration_multipliers: list[float],
+) -> DataShard:
+    """Run the full data generation and return a shard."""
+    from pecos.qec.surface import NoiseModel
+
+    config = {
+        "distances": distances,
+        "error_rates": error_rates,
+        "decoders": decoders,
+        "basis": basis.upper(),
+        "shots": shots,
+        "seed": seed,
+        "circuit_source": circuit_source,
+        "p1_scale": p1_scale,
+        "p_meas_scale": p_meas_scale,
+        "p_prep_scale": p_prep_scale,
+        "duration_multipliers": duration_multipliers,
+    }
+
+    shard = DataShard(config=config)
+    t_start = time.perf_counter()
+
+    # Compute distinct round counts per distance.
+    # For small d, multipliers may collide after truncation.
+    # Ensure at least len(duration_multipliers) distinct round counts
+    # by extending the range upward if needed.
+    rounds_per_d: dict[int, list[int]] = {}
+    for d in distances:
+        seen = set()
+        for mult in duration_multipliers:
+            seen.add(max(2, int(d * mult)))
+        # If we got fewer than requested, fill in consecutive integers from 2*d
+        target = len(duration_multipliers)
+        r_start = 2 * d
+        while len(seen) < target:
+            seen.add(r_start)
+            r_start += 1
+        rounds_per_d[d] = sorted(seen)
+
+    total_cells = sum(len(rounds_per_d[d]) for d in distances) * len(error_rates)
+    cell_idx = 0
+
+    for d in distances:
+        for p in error_rates:
+            noise = NoiseModel(
+                p1=p * p1_scale,
+                p2=p,
+                p_meas=p * p_meas_scale,
+                p_prep=p * p_prep_scale,
+            )
+
+            for num_rounds in rounds_per_d[d]:
+                cell_idx += 1
+                print(f"[{cell_idx}/{total_cells}] d={d} p={p:.4g} r={num_rounds} ...")
+
+                sampler, dem_decomp, dem_full = _build_sampler(
+                    d,
+                    num_rounds,
+                    noise,
+                    basis,
+                    circuit_source,
+                )
+
+                # Sample once
+                t0 = time.perf_counter()
+                batch = sampler.sampler.generate_samples(shots, seed=seed + cell_idx)
+                sample_seconds = time.perf_counter() - t0
+
+                point = DataPoint(
+                    distance=d,
+                    basis=basis.upper(),
+                    physical_error_rate=p,
+                    num_rounds=num_rounds,
+                    num_shots=shots,
+                    sample_seconds=sample_seconds,
+                )
+
+                # Decode with each decoder
+                for decoder_name in decoders:
+                    base = _decoder_base_name(decoder_name)
+                    dem = dem_decomp if base in _MWPM_DECODERS else dem_full
+
+                    if base in _SLOW_DECODERS:
+                        stats = batch.decode_stats_parallel(dem, decoder_name)
+                    else:
+                        stats = batch.decode_stats(dem, decoder_name)
+
+                    point.decoder_stats.append(
+                        DecoderStats(
+                            decoder=decoder_name,
+                            num_errors=stats.num_errors,
+                            logical_error_rate=stats.logical_error_rate,
+                            total_decode_seconds=stats.total_seconds,
+                            per_shot_mean=stats.per_shot_mean,
+                            per_shot_median=stats.per_shot_median,
+                            per_shot_p99=stats.per_shot_p99,
+                            per_shot_max=stats.per_shot_max,
+                            quantiles=list(stats.quantiles),
+                        ),
+                    )
+
+                    print(
+                        f"    {decoder_name:20s}: {stats.num_errors:>4d}/{shots}  "
+                        f"LER={stats.logical_error_rate:.4f}  "
+                        f"median={stats.per_shot_median:.1e}s  "
+                        f"p99={stats.per_shot_p99:.1e}s",
+                    )
+
+                shard.points.append(point)
+
+    shard.total_seconds = time.perf_counter() - t_start
+    return shard
+
+
+# -- CLI ----------------------------------------------------------------------
+
+
+def main() -> int:
+    """CLI entry point for data generation."""
+    parser = argparse.ArgumentParser(
+        description=__doc__,
+        formatter_class=argparse.RawDescriptionHelpFormatter,
+    )
+    parser.add_argument("--distances", nargs="+", type=int, default=[3, 5])
+    parser.add_argument("--error-rates", nargs="+", type=float, default=[0.004, 0.006, 0.008])
+    parser.add_argument(
+        "--decoders",
+        nargs="+",
+        default=["pymatching", "mwpf", "tesseract", "bp_osd"],
+        help="Decoders to run. Use 'mwpf:c=30,t=0.5' for config overrides.",
+    )
+    parser.add_argument("--shots", type=int, default=1000)
+    parser.add_argument("--basis", default="Z")
+    parser.add_argument("--seed", type=int, default=42)
+    parser.add_argument("--circuit-source", default="traced_qis", choices=["traced_qis", "abstract"])
+    parser.add_argument("--p1-scale", type=float, default=1.0 / 30.0)
+    parser.add_argument("--p-meas-scale", type=float, default=1.0 / 3.0)
+    parser.add_argument("--p-prep-scale", type=float, default=1.0 / 3.0)
+    parser.add_argument(
+        "--duration-multipliers",
+        nargs="+",
+        type=float,
+        default=[2.0],
+        help="Round count = distance * multiplier. Use multiple for threshold fitting.",
+    )
+    parser.add_argument("--output-dir", type=str, default=None)
+    args = parser.parse_args()
+
+    print("PECOS Data Generation")
+    print("=" * 40)
+    for k, v in vars(args).items():
+        if k != "output_dir":
+            print(f"  {k}: {v}")
+    print()
+
+    shard = generate(
+        distances=sorted(args.distances),
+        error_rates=sorted(args.error_rates),
+        decoders=args.decoders,
+        basis=args.basis,
+        shots=args.shots,
+        seed=args.seed,
+        circuit_source=args.circuit_source,
+        p1_scale=args.p1_scale,
+        p_meas_scale=args.p_meas_scale,
+        p_prep_scale=args.p_prep_scale,
+        duration_multipliers=sorted(args.duration_multipliers),
+    )
+
+    print(f"\nTotal time: {shard.total_seconds:.1f}s")
+
+    if args.output_dir:
+        out = Path(args.output_dir)
+    else:
+        import tempfile
+
+        out = Path(tempfile.mkdtemp(prefix="pecos_data_"))
+
+    out.mkdir(parents=True, exist_ok=True)
+    json_path = out / "data.json"
+    json_path.write_text(json.dumps(asdict(shard), indent=2))
+    print(f"Wrote {json_path}")
+
+    return 0
+
+
+if __name__ == "__main__":
+    raise SystemExit(main())
diff --git a/examples/surface/ml_lookup_decoder.py b/examples/surface/ml_lookup_decoder.py
new file mode 100644
index 000000000..6fefa9ca2
--- /dev/null
+++ b/examples/surface/ml_lookup_decoder.py
@@ -0,0 +1,254 @@
+"""Maximum likelihood lookup decoder from simulation samples.
+
+For small codes (d=3: 256 syndromes), precomputes the optimal correction
+for every possible syndrome by counting simulation outcomes.  This is the
+provably optimal decoder — useful as a gold standard for validation.
+
+Example:
+    uv run python examples/surface/ml_lookup_decoder.py
+"""
+
+from __future__ import annotations
+
+import argparse
+import sys
+import time
+from collections import defaultdict
+from pathlib import Path
+
+sys.path.insert(0, str(Path(__file__).resolve().parents[2] / "python" / "quantum-pecos" / "src"))
+
+
+def build_lookup_table(batch, num_detectors: int) -> dict[tuple[int, ...], int]:
+    """Build a syndrome -> most_likely_observable_mask lookup table.
+
+    For each unique syndrome observed in the batch, count how often each
+    observable mask occurs. The most common mask is the ML prediction.
+    """
+    # syndrome (as tuple of fired detector indices) -> {obs_mask: count}
+    syndrome_counts: dict[tuple[int, ...], dict[int, int]] = defaultdict(lambda: defaultdict(int))
+
+    for i in range(batch.num_shots):
+        syn = batch.get_syndrome(i)
+        obs = batch.get_observable_mask(i)
+
+        # Convert syndrome to tuple of fired detector indices
+        fired = tuple(d for d in range(min(num_detectors, len(syn))) if syn[d])
+        syndrome_counts[fired][obs] += 1
+
+    # For each syndrome, pick the most likely observable mask
+    table: dict[tuple[int, ...], int] = {}
+    for syndrome, counts in syndrome_counts.items():
+        best_mask = max(counts, key=counts.get)
+        table[syndrome] = best_mask
+
+    return table
+
+
+def decode_with_lookup(batch, table: dict, num_detectors: int) -> tuple[int, int]:
+    """Decode a batch using the lookup table. Returns (num_errors, num_shots)."""
+    errors = 0
+    for i in range(batch.num_shots):
+        syn = batch.get_syndrome(i)
+        obs_true = batch.get_observable_mask(i)
+
+        fired = tuple(d for d in range(min(num_detectors, len(syn))) if syn[d])
+        predicted = table.get(fired, 0)  # default: no correction
+
+        if predicted != obs_true:
+            errors += 1
+
+    return errors, batch.num_shots
+
+
+def main():
+    parser = argparse.ArgumentParser(description="ML lookup decoder from simulation")
+    parser.add_argument("--distance", type=int, default=3)
+    parser.add_argument("--shots", type=int, default=50_000)
+    parser.add_argument("--basis", default="Z")
+    parser.add_argument("--seed", type=int, default=42)
+    parser.add_argument("--p2", type=float, default=0.005)
+    parser.add_argument("--idle-rz", type=float, default=0.0)
+    parser.add_argument(
+        "--sample-backend",
+        default="stabilizer",
+        choices=["stabilizer", "statevec", "native"],
+    )
+    args = parser.parse_args()
+
+    import json
+
+    from pecos.qec.surface import SurfacePatch
+    from pecos.qec.surface.decode import _build_surface_tick_circuit_for_native_model
+
+    patch = SurfacePatch.create(distance=args.distance)
+    num_rounds = 2 * args.distance
+    tc = _build_surface_tick_circuit_for_native_model(
+        patch,
+        num_rounds,
+        args.basis,
+        circuit_source="abstract",
+    )
+
+    num_dets = len(json.loads(tc.get_meta("detectors")))
+    print(f"d={args.distance}, {num_rounds} rounds, {num_dets} detectors, {2**num_dets} possible syndromes")
+
+    noise_params = {
+        "p1": args.p2 / 10,
+        "p2": args.p2,
+        "p_meas": args.p2,
+        "p_prep": args.p2,
+        "idle_rz": args.idle_rz,
+    }
+
+    # Generate training samples
+    print(f"Generating {args.shots} training samples ({args.sample_backend})...")
+    t0 = time.perf_counter()
+
+    if args.sample_backend in ("stabilizer", "statevec"):
+        from pecos_rslib.qec import SampleBatch
+        from pecos_rslib_exp import depolarizing, sim_neo, stabilizer, statevec
+
+        noise = (
+            depolarizing()
+            .p1(noise_params["p1"])
+            .p2(noise_params["p2"])
+            .p_meas(noise_params["p_meas"])
+            .p_prep(noise_params["p_prep"])
+        )
+        if args.idle_rz > 0:
+            noise = noise.idle_rz(args.idle_rz)
+
+        backend = stabilizer() if args.sample_backend == "stabilizer" else statevec()
+        results = sim_neo(tc).quantum(backend).noise(noise).shots(args.shots).seed(args.seed).run()
+
+        det_json = json.loads(tc.get_meta("detectors"))
+        obs_json = json.loads(tc.get_meta("observables"))
+        num_meas = int(tc.get_meta("num_measurements"))
+
+        # Convert to SampleBatch
+        detection_events = []
+        observable_masks = []
+        for r in results:
+            meas = list(r)
+            syn = [0] * num_dets
+            for i, det in enumerate(det_json):
+                val = 0
+                for rec in det["records"]:
+                    idx = num_meas + rec
+                    if 0 <= idx < len(meas):
+                        val ^= meas[idx]
+                syn[i] = val
+            detection_events.append(syn)
+            obs_mask = 0
+            for j, ob in enumerate(obs_json):
+                val = 0
+                for rec in ob["records"]:
+                    idx = num_meas + rec
+                    if 0 <= idx < len(meas):
+                        val ^= meas[idx]
+                if val:
+                    obs_mask |= 1 << j
+            observable_masks.append(obs_mask)
+        train_batch = SampleBatch(detection_events, observable_masks)
+    else:
+        from pecos_rslib.qec import DemSampler
+
+        sampler_params = {k: v for k, v in noise_params.items() if k in ("p1", "p2", "p_meas", "p_prep")}
+        sampler = DemSampler.from_circuit(tc, **sampler_params)
+        train_batch = sampler.generate_samples(args.shots, seed=args.seed)
+
+    t_sample = time.perf_counter() - t0
+    print(f"  Sampled in {t_sample:.2f}s")
+
+    # Build lookup table
+    t0 = time.perf_counter()
+    table = build_lookup_table(train_batch, num_dets)
+    t_build = time.perf_counter() - t0
+    print(f"  Lookup table: {len(table)} unique syndromes seen (of {2**num_dets} possible)")
+    print(f"  Built in {t_build:.4f}s")
+
+    # Test on separate samples
+    test_shots = args.shots
+    print(f"\nGenerating {test_shots} test samples...")
+    if args.sample_backend in ("stabilizer", "statevec"):
+        results2 = sim_neo(tc).quantum(backend).noise(noise).shots(test_shots).seed(args.seed + 1000).run()
+        detection_events2 = []
+        observable_masks2 = []
+        for r in results2:
+            meas = list(r)
+            syn = [0] * num_dets
+            for i, det in enumerate(det_json):
+                val = 0
+                for rec in det["records"]:
+                    idx = num_meas + rec
+                    if 0 <= idx < len(meas):
+                        val ^= meas[idx]
+                syn[i] = val
+            detection_events2.append(syn)
+            obs_mask = 0
+            for j, ob in enumerate(obs_json):
+                val = 0
+                for rec in ob["records"]:
+                    idx = num_meas + rec
+                    if 0 <= idx < len(meas):
+                        val ^= meas[idx]
+                if val:
+                    obs_mask |= 1 << j
+            observable_masks2.append(obs_mask)
+        test_batch = SampleBatch(detection_events2, observable_masks2)
+    else:
+        test_batch = sampler.generate_samples(test_shots, seed=args.seed + 1000)
+
+    # Decode with lookup
+    errors_lookup, n = decode_with_lookup(test_batch, table, num_dets)
+    ler_lookup = errors_lookup / n
+
+    # Compare with pymatching
+    from pecos.qec.surface import NoiseModel
+    from pecos.qec.surface.decode import generate_circuit_level_dem_from_builder
+
+    noise_obj = NoiseModel(
+        p1=noise_params["p1"],
+        p2=noise_params["p2"],
+        p_meas=noise_params["p_meas"],
+        p_prep=noise_params["p_prep"],
+    )
+    dem_decomp = generate_circuit_level_dem_from_builder(
+        patch,
+        num_rounds,
+        noise_obj,
+        basis=args.basis,
+        decompose_errors=True,
+        circuit_source="abstract",
+    )
+    dem_clean = "\n".join(line for line in dem_decomp.split("\n") if not line.startswith("logical_observable"))
+    stats_pm = test_batch.decode_stats(dem_clean, "pymatching")
+
+    # Compare with coherent_dem_decomposed if available
+    try:
+        from pecos_rslib_exp import coherent_dem_decomposed
+
+        _, coherent_decomp = coherent_dem_decomposed(tc, **noise_params)
+        coherent_clean = "\n".join(
+            line for line in coherent_decomp.split("\n") if not line.startswith("logical_observable")
+        )
+        stats_coherent = test_batch.decode_stats(coherent_clean, "pymatching")
+        ler_coherent = stats_coherent.logical_error_rate
+    except Exception:
+        ler_coherent = None
+
+    print(f"\n{'='*60}")
+    print(f"Results (d={args.distance}, p2={args.p2}, irz={args.idle_rz}):")
+    print(f"{'='*60}")
+    print(f"  ML Lookup:                  LER = {ler_lookup:.6f}  ({errors_lookup}/{n})")
+    print(f"  PyMatching (from_circuit):  LER = {stats_pm.logical_error_rate:.6f}  ({stats_pm.num_errors}/{n})")
+    if ler_coherent is not None:
+        print(f"  PyMatching (coherent):      LER = {ler_coherent:.6f}")
+    if stats_pm.logical_error_rate > 0:
+        improvement = (stats_pm.logical_error_rate - ler_lookup) / stats_pm.logical_error_rate * 100
+        print(f"\n  ML Lookup vs PyMatching:    {improvement:+.1f}%")
+
+
+if __name__ == "__main__":
+    main()
diff --git a/examples/surface/native_dem_threshold_sweep.py b/examples/surface/native_dem_threshold_sweep.py
index 4afb371c8..4839a9ad3 100755
--- a/examples/surface/native_dem_threshold_sweep.py
+++ b/examples/surface/native_dem_threshold_sweep.py
@@ -8,8 +8,8 @@
 - direct ``selene_sim`` execution with either Selene ``Stim`` or the PECOS
   Selene stabilizer plugin
 - optional native DEM sampling via ``build_native_sampler(...)``
-- a uniform depolarizing noise model with ``p1 = p2 = p_meas = p_init = p``
-- ``SurfaceDecoder(..., decoder_type="pymatching")`` with PECOS-native DEMs
+- a depolarizing noise model with ``p2 = p``, ``p1 = p/30``, ``p_meas = p_prep = p/3``
+- ``SurfaceDecoder(...)`` with PECOS-native DEMs (PyMatching or Tesseract)
 
 For the ``sim`` backend, decoding is performed relative to a cached noiseless
 reference trajectory from the same Guppy/QIS circuit. This makes the gate-level
@@ -68,6 +68,7 @@
 if TYPE_CHECKING:
     from types import ModuleType
 
+    import numpy as np
     from matplotlib.axes import Axes
     from matplotlib.figure import Figure
     from matplotlib.patches import Rectangle
@@ -231,6 +232,7 @@ class _NativeSamplerRuntime:
     decoder_runtime: _DecoderRuntime
     sampler: Any
     dem_decoder: Any
+    dem_str: str | None = None
 
 
 _CACHED_SELENE_INSTANCES: list[Any] = []
@@ -251,6 +253,11 @@ def _cleanup_cached_selene_instances() -> None:
 
 def _backend_runtime_label(sample_backend: str, native_circuit_source: str = "abstract") -> str:
     """Describe one sampling backend in human-readable terms."""
+    # Handle "backend:decoder" labels from multi-decoder comparison
+    if ":" in sample_backend:
+        base, decoder = sample_backend.split(":", 1)
+        base_label = _backend_runtime_label(base, native_circuit_source)
+        return f"{base_label} [decoder={decoder}]"
     if sample_backend == "sim":
         return (
             "sim(Guppy(...)).classical(selene_engine()).quantum(pecos.stabilizer()) "
@@ -270,7 +277,7 @@ def _backend_runtime_label(sample_backend: str, native_circuit_source: str = "ab
             f"{native_circuit_source} + noiseless reference-trajectory calibration"
         )
     if sample_backend == "native_sampler":
-        return f"build_native_sampler(..., circuit_source={native_circuit_source!r}) + PyMatching on the native DEM"
+        return f"build_native_sampler(..., circuit_source={native_circuit_source!r}) + DEM decoder on the native DEM"
     msg = f"Unknown sample backend: {sample_backend}"
     raise ValueError(msg)
 
@@ -537,6 +544,106 @@ def _surface_patch(distance: int) -> object:
     return SurfacePatch.create(distance=distance)
 
 
+_CHECK_MATRIX_DECODERS = {"bp_osd", "bp_lsd", "union_find", "relay_bp", "min_sum_bp"}
+
+
+def _noise_model_description(args: argparse.Namespace) -> str:
+    """Human-readable noise model string for reports."""
+    p1s = getattr(args, "p1_scale", 1.0 / 30.0)
+    pms = getattr(args, "p_meas_scale", 1.0 / 3.0)
+    pps = getattr(args, "p_prep_scale", 1.0 / 3.0)
+    return f"depolarizing with p1={p1s:.4g}*p, p2=p, p_meas={pms:.4g}*p, p_prep={pps:.4g}*p"
+
+
+def _create_dem_decoder(decoder_type: str, dem_str: str, *, tesseract_beam: int = 5) -> object:
+    """Create a DEM-level decoder from a DEM string.
+
+    Supports MWPM decoders (pymatching), search decoders (tesseract), and
+    check-matrix decoders (bp_osd, bp_lsd, union_find, relay_bp, min_sum_bp)
+    via DemAwareDecoder which extracts the check matrix from the DEM.
+    """
+    if decoder_type == "tesseract":
+        from pecos_rslib.decoders import TesseractDecoder
+
+        dem_filtered = "\n".join(line for line in dem_str.split("\n") if not line.startswith("logical_observable"))
+        return TesseractDecoder.from_dem(dem_filtered, preset="fast", det_beam=tesseract_beam)
+
+    if decoder_type in _CHECK_MATRIX_DECODERS:
+        from pecos_rslib.decoders import DemAwareDecoder
+
+        dem_filtered = "\n".join(line for line in dem_str.split("\n") if not line.startswith("logical_observable"))
+        return DemAwareDecoder.from_dem(dem_filtered, decoder_type=decoder_type)
+
+    from pecos_rslib.decoders import PyMatchingDecoder
+
+    return PyMatchingDecoder.from_dem(dem_str)
+
+
+def _decode_one_shot(dem_decoder: object, events_flat: list[int]) -> object:
+    """Decode one shot using whichever DEM decoder was created.
+
+    Tesseract.decode() wants sparse indices; decode_syndrome() accepts dense vectors.
+    PyMatching.decode() accepts dense vectors directly.
+    """
+    if hasattr(dem_decoder, "decode_syndrome"):
+        return dem_decoder.decode_syndrome(events_flat)
+    return dem_decoder.decode(events_flat)
+
+
+def _decode_all_shots(
+    dem_decoder: object,
+    detection_events: np.ndarray,
+    observable_flips: np.ndarray,
+    num_shots: int,
+) -> int:
+    """Decode all shots using the fastest available path.
+
+    For PyMatching: uses decode_batch with flattened numpy array (no Python loop).
+    For Tesseract: uses decode_batch with parallel rayon workers.
+    For others: falls back to per-shot Python loop.
+
+    Returns the number of logical errors.
+    """
+    import numpy as np
+
+    true_flips = (
+        observable_flips[:, 0].astype(np.uint8)
+        if observable_flips.shape[1] > 0
+        else np.zeros(num_shots, dtype=np.uint8)
+    )
+
+    # PyMatching batch: takes flattened (num_shots * num_detectors) u8 array
+    from pecos_rslib.decoders import PyMatchingDecoder
+
+    if isinstance(dem_decoder, PyMatchingDecoder):
+        flat = detection_events.astype(np.uint8).flatten().tolist()
+        predictions = dem_decoder.decode_batch(flat, num_shots)
+        # Each prediction is a list of observables; check index 0
+        predicted = np.array([p[0] if p else 0 for p in predictions], dtype=np.uint8)
+        return int(np.sum(predicted != true_flips))
+
+    # Tesseract batch: takes list of syndromes, parallel rayon
+    from pecos_rslib.decoders import TesseractDecoder
+
+    if isinstance(dem_decoder, TesseractDecoder):
+        syndromes = [detection_events[i].astype(np.uint8).tolist() for i in range(num_shots)]
+        batch_results = dem_decoder.decode_batch(syndromes)
+        num_errors = 0
+        for shot_idx, result in enumerate(batch_results):
+            predicted_flip = int(result.observables_mask & 1)
+            num_errors += int(predicted_flip != true_flips[shot_idx])
+        return num_errors
+
+    # Fallback: per-shot loop (DemAwareDecoder, etc.)
+    num_errors = 0
+    for shot_idx in range(num_shots):
+        events_flat = detection_events[shot_idx].astype(np.uint8).tolist()
+        decode_result = _decode_one_shot(dem_decoder, events_flat)
+        predicted_flip = _predicted_observable_flip(decode_result)
+        num_errors += int(predicted_flip != true_flips[shot_idx])
+    return num_errors
+
+
 @cache
 def _decoder_runtime(
     distance: int,
@@ -545,6 +652,11 @@ def _decoder_runtime(
     physical_error_rate: float,
     dem_mode: str,
     native_circuit_source: str,
+    decoder_type: str = "pymatching",
+    ancilla_budget: int | None = None,
+    p1_scale: float = 0.1,
+    p_meas_scale: float = 0.5,
+    p_prep_scale: float = 0.5,
 ) -> _DecoderRuntime:
     """Build and cache the expensive native decoder-side objects once."""
     from pecos.qec.surface import NoiseModel, SurfaceDecoder
@@ -552,19 +664,20 @@ def _decoder_runtime(
     basis = basis.upper()
     patch = _surface_patch(distance)
     noise = NoiseModel(
-        p1=physical_error_rate,
+        p1=physical_error_rate * p1_scale,
         p2=physical_error_rate,
-        p_meas=physical_error_rate,
-        p_init=physical_error_rate,
+        p_meas=physical_error_rate * p_meas_scale,
+        p_prep=physical_error_rate * p_prep_scale,
     )
     decoder = SurfaceDecoder(
         patch,
         num_rounds=total_rounds,
         noise=noise,
-        decoder_type="pymatching",
+        decoder_type=decoder_type,
         use_circuit_level_dem=True,
         circuit_level_dem_mode=dem_mode,
         circuit_level_dem_source=native_circuit_source,
+        ancilla_budget=ancilla_budget,
     )
     return _DecoderRuntime(
         patch=patch,
@@ -584,10 +697,15 @@ def _native_sampler_runtime(
     physical_error_rate: float,
     dem_mode: str,
     native_circuit_source: str,
+    decoder_type: str = "pymatching",
+    ancilla_budget: int | None = None,
+    p1_scale: float = 0.1,
+    p_meas_scale: float = 0.5,
+    p_prep_scale: float = 0.5,
 ) -> _NativeSamplerRuntime:
-    """Build and cache the native sampler + PyMatching decoder bundle once."""
+    """Build and cache the native sampler + decoder bundle once."""
     from pecos.qec.surface import build_native_sampler
-    from pecos_rslib.decoders import PyMatchingDecoder
+    from pecos.qec.surface.decode import generate_circuit_level_dem_from_builder
 
     runtime = _decoder_runtime(
         distance,
@@ -596,6 +714,11 @@ def _native_sampler_runtime(
         physical_error_rate,
         dem_mode,
         native_circuit_source,
+        decoder_type=decoder_type,
+        ancilla_budget=ancilla_budget,
+        p1_scale=p1_scale,
+        p_meas_scale=p_meas_scale,
+        p_prep_scale=p_prep_scale,
     )
     sampler = build_native_sampler(
         runtime.patch,
@@ -603,18 +726,35 @@ def _native_sampler_runtime(
         runtime.noise,
         basis=basis,
         circuit_source=native_circuit_source,
+        ancilla_budget=ancilla_budget,
     )
-    dem_str = runtime.decoder.get_dem(basis.upper(), circuit_level=True)
-    dem_decoder = PyMatchingDecoder.from_dem(dem_str)
+    # PyMatching needs decomposed (graph-like) DEMs; Tesseract and check-matrix
+    # decoders handle hyperedges natively and should get the full DEM.
+    if decoder_type == "pymatching":
+        dem_str = runtime.decoder.get_dem(basis.upper(), circuit_level=True)
+    else:
+        dem_str = generate_circuit_level_dem_from_builder(
+            runtime.patch,
+            total_rounds,
+            runtime.noise,
+            basis=basis,
+            decompose_errors=False,
+            circuit_source=native_circuit_source,
+            ancilla_budget=ancilla_budget,
+        )
+    dem_decoder = _create_dem_decoder(decoder_type, dem_str)
     # The traced-QIS sampler stack has a noticeable one-time initialization cost
     # on its first sample. Pay that once when the cached runtime is created so
     # subsequent point evaluations stay on the true steady-state path.
     warm_det_events, _ = sampler.sample(num_shots=1, seed=0)
-    dem_decoder.decode(warm_det_events[0].astype(int).tolist())
+    _decode_one_shot(dem_decoder, warm_det_events[0].astype(int).tolist())
+    # Filter logical_observable lines for decoders that need it
+    dem_str_filtered = "\n".join(line for line in dem_str.split("\n") if not line.startswith("logical_observable"))
     return _NativeSamplerRuntime(
         decoder_runtime=runtime,
         sampler=sampler,
         dem_decoder=dem_decoder,
+        dem_str=dem_str_filtered,
     )
 
 
@@ -694,6 +834,9 @@ def _run_gate_backend_result_dict(
     num_shots: int,
     seed: int,
     timing_sink: dict[str, float] | None = None,
+    p1_scale: float = 0.1,
+    p_meas_scale: float = 0.5,
+    p_prep_scale: float = 0.5,
 ) -> dict[str, list[list[int]]]:
     """Run one gate-level backend and normalize results to a shot-map-like dict."""
     import os
@@ -731,10 +874,10 @@ def run_direct_selene_backend(*, simulator: object) -> dict[str, list[list[int]]
 
         error_model_start = time.perf_counter()
         error_model = DepolarizingErrorModel(
-            p_1q=physical_error_rate,
+            p_1q=physical_error_rate * p1_scale,
             p_2q=physical_error_rate,
-            p_meas=physical_error_rate,
-            p_init=physical_error_rate,
+            p_meas=physical_error_rate * p_meas_scale,
+            p_prep=physical_error_rate * p_prep_scale,
         )
         error_model_seconds = time.perf_counter() - error_model_start
 
@@ -771,7 +914,14 @@ def run_direct_selene_backend(*, simulator: object) -> dict[str, list[list[int]]
     if sample_backend == "sim":
         backend_start = time.perf_counter()
         noise_start = time.perf_counter()
-        noise_model = pecos.depolarizing_noise().with_uniform_probability(physical_error_rate)
+        noise_model = pecos.depolarizing_noise()
+        noise_model.set_probabilities(
+            physical_error_rate * p_prep_scale,  # p_prep
+            physical_error_rate * p_meas_scale,  # p_meas_0
+            physical_error_rate * p_meas_scale,  # p_meas_1
+            physical_error_rate * p1_scale,  # p1 (single-qubit gates)
+            physical_error_rate,  # p2 (two-qubit gates)
+        )
         noise_seconds = time.perf_counter() - noise_start
         program_start = time.perf_counter()
         program = make_surface_code(distance=distance, num_rounds=total_rounds, basis=basis)
@@ -946,6 +1096,12 @@ def _run_memory_point(
     dem_mode: str,
     native_circuit_source: str,
     seed: int,
+    decoder_type: str = "pymatching",
+    backend_label: str | None = None,
+    ancilla_budget: int | None = None,
+    p1_scale: float = 0.1,
+    p_meas_scale: float = 0.5,
+    p_prep_scale: float = 0.5,
 ) -> SweepPoint:
     """Run one surface-memory point and decode it with native PECOS DEMs."""
     import numpy as np
@@ -958,6 +1114,11 @@ def _run_memory_point(
         physical_error_rate,
         dem_mode,
         native_circuit_source,
+        decoder_type=decoder_type,
+        ancilla_budget=ancilla_budget,
+        p1_scale=p1_scale,
+        p_meas_scale=p_meas_scale,
+        p_prep_scale=p_prep_scale,
     )
     patch = decoder_runtime.patch
     num_x_stab = decoder_runtime.num_x_stab
@@ -986,6 +1147,9 @@ def _run_memory_point(
             total_rounds=total_rounds,
             num_shots=num_shots,
             seed=seed,
+            p1_scale=p1_scale,
+            p_meas_scale=p_meas_scale,
+            p_prep_scale=p_prep_scale,
         )
 
         synx_rows = _result_rows_for_key(result_dict, "synx")
@@ -1043,18 +1207,40 @@ def _run_memory_point(
             physical_error_rate,
             dem_mode,
             native_circuit_source,
+            decoder_type=decoder_type,
+            ancilla_budget=ancilla_budget,
+            p1_scale=p1_scale,
+            p_meas_scale=p_meas_scale,
+            p_prep_scale=p_prep_scale,
         )
         sampler = native_runtime.sampler
         dem_decoder = native_runtime.dem_decoder
         detection_events, observable_flips = sampler.sample(num_shots=num_shots, seed=seed)
 
         num_raw_errors = None
-        for shot_idx in range(num_shots):
-            events_flat = detection_events[shot_idx].astype(np.uint8).tolist()
-            decode_result = dem_decoder.decode(events_flat)
-            predicted_flip = _predicted_observable_flip(decode_result)
-            true_flip = int(observable_flips[shot_idx, 0]) if observable_flips.shape[1] > 0 else 0
-            num_logical_errors += int(predicted_flip != true_flip)
+        # Fast path: sample+decode entirely in Rust via ObservableDecoder trait.
+        # The DemSampler keeps all per-shot data in Rust -- nothing crosses to Python.
+        dem_str_for_rust = native_runtime.dem_str
+        rust_sampler = getattr(sampler, "sampler", None)
+        if dem_str_for_rust and rust_sampler and hasattr(rust_sampler, "sample_decode_count"):
+            # Use parallel path for slow decoders (Tesseract, BP+OSD, etc.)
+            if decoder_type != "pymatching" and hasattr(rust_sampler, "sample_decode_count_parallel"):
+                num_logical_errors = rust_sampler.sample_decode_count_parallel(
+                    dem_str_for_rust,
+                    num_shots,
+                    decoder_type,
+                    seed,
+                )
+            else:
+                num_logical_errors = rust_sampler.sample_decode_count(
+                    dem_str_for_rust,
+                    num_shots,
+                    decoder_type,
+                    seed,
+                )
+        else:
+            detection_events, observable_flips = sampler.sample(num_shots=num_shots, seed=seed)
+            num_logical_errors = _decode_all_shots(dem_decoder, detection_events, observable_flips, num_shots)
     else:
         msg = f"Unknown sample backend: {sample_backend}"
         raise ValueError(msg)
@@ -1063,7 +1249,7 @@ def _run_memory_point(
     raw_error_rate = None if num_raw_errors is None else (num_raw_errors / num_shots if num_shots else 0.0)
 
     return SweepPoint(
-        backend=sample_backend,
+        backend=backend_label or sample_backend,
         distance=distance,
         basis=basis.upper(),
         physical_error_rate=physical_error_rate,
@@ -1569,6 +1755,14 @@ def _basis_summary(summaries: list[FitSummary]) -> dict[str, Any]:
             for p, is_suppressed in _suppression_summary(summaries)
         ],
         "background_threshold_crossing": _estimate_threshold(summaries),
+        "background_threshold_crossing_per_round": _estimate_threshold(
+            summaries,
+            metric="fitted_logical_error_rate_per_round",
+        ),
+        "background_threshold_crossing_d_rounds": _estimate_threshold(
+            summaries,
+            metric="fitted_projected_logical_error_rate_over_d_rounds",
+        ),
         "background_threshold_style_global_scaling_fit": None if global_scaling is None else asdict(global_scaling),
     }
 
@@ -1685,7 +1879,7 @@ def _write_json_results(
                 backend: _backend_runtime_label(backend, args.native_circuit_source)
                 for backend in sorted({point.backend for point in points})
             },
-            "noise_model": "uniform depolarizing with p1 = p2 = p_meas = p_init = p",
+            "noise_model": _noise_model_description(args),
             "fit_model": "p_L(r) = 0.5 * (1 - (1 - 2 * epsilon) ** r)",
             "primary_power_law_model": "epsilon_d(p) ~= A_d * p ** c_d",
             "primary_lambda_model": "Lambda_{d/(d+2)}(p) = epsilon_d(p) / epsilon_{d+2}(p)",
@@ -2212,18 +2406,45 @@ def plot_card(plot: DashboardPlot) -> list[str]:
     ]
     style = dedent(
         """
-        :root { color-scheme: light; }
+        :root {
+          color-scheme: light dark;
+          --bg: #f8fafc; --fg: #0f172a;
+          --hero-bg: linear-gradient(135deg, #e0f2fe, #f8fafc 55%, #dcfce7);
+          --hero-border: #cbd5e1;
+          --card-bg: white; --card-border: #dbeafe; --card-shadow: rgba(15,23,42,0.05);
+          --meta-bg: rgba(255,255,255,0.82);
+          --muted: #475569; --link: #2563eb; --link-alt: #0369a1;
+          --header-border: #e2e8f0;
+          --img-bg: white;
+        }
+        [data-theme="dark"] {
+          --bg: #0f172a; --fg: #e2e8f0;
+          --hero-bg: linear-gradient(135deg, #1e293b, #0f172a 55%, #1a2e1a);
+          --hero-border: #334155;
+          --card-bg: #1e293b; --card-border: #334155; --card-shadow: rgba(0,0,0,0.3);
+          --meta-bg: rgba(30,41,59,0.82);
+          --muted: #94a3b8; --link: #60a5fa; --link-alt: #38bdf8;
+          --header-border: #334155;
+          --img-bg: #1e293b;
+        }
         body {
           margin: 0;
           font-family: ui-sans-serif, -apple-system, BlinkMacSystemFont, sans-serif;
-          background: #f8fafc;
-          color: #0f172a;
+          background: var(--bg);
+          color: var(--fg);
         }
         main { max-width: 1500px; margin: 0 auto; padding: 32px 24px 56px; }
         h1, h2, h3, p { margin-top: 0; }
+        .theme-toggle {
+          position: fixed; top: 16px; right: 16px; z-index: 100;
+          background: var(--card-bg); border: 1px solid var(--card-border);
+          border-radius: 8px; padding: 6px 12px; cursor: pointer;
+          color: var(--fg); font-size: 0.85rem; font-weight: 600;
+        }
+        .theme-toggle:hover { opacity: 0.8; }
         .hero {
-          background: linear-gradient(135deg, #e0f2fe, #f8fafc 55%, #dcfce7);
-          border: 1px solid #cbd5e1;
+          background: var(--hero-bg);
+          border: 1px solid var(--hero-border);
           border-radius: 20px;
           padding: 24px;
           margin-bottom: 24px;
@@ -2235,8 +2456,8 @@ def plot_card(plot: DashboardPlot) -> list[str]:
           margin-top: 18px;
         }
         .meta-card {
-          background: rgba(255,255,255,0.82);
-          border: 1px solid #dbeafe;
+          background: var(--meta-bg);
+          border: 1px solid var(--card-border);
           border-radius: 14px;
           padding: 14px 16px;
         }
@@ -2245,7 +2466,7 @@ def plot_card(plot: DashboardPlot) -> list[str]:
           font-size: 0.82rem;
           text-transform: uppercase;
           letter-spacing: 0.04em;
-          color: #475569;
+          color: var(--muted);
           margin-bottom: 6px;
         }
         .section { margin-top: 30px; }
@@ -2255,44 +2476,67 @@ def plot_card(plot: DashboardPlot) -> list[str]:
           gap: 18px;
         }
         .plot-card {
-          background: white;
-          border: 1px solid #dbeafe;
+          background: var(--card-bg);
+          border: 1px solid var(--card-border);
           border-radius: 18px;
           overflow: hidden;
-          box-shadow: 0 10px 24px rgba(15, 23, 42, 0.05);
+          box-shadow: 0 10px 24px var(--card-shadow);
         }
         .plot-card header {
           padding: 16px 18px 10px;
-          border-bottom: 1px solid #e2e8f0;
+          border-bottom: 1px solid var(--header-border);
         }
         .plot-card header p {
           margin-bottom: 0;
-          color: #475569;
+          color: var(--muted);
           font-size: 0.92rem;
         }
-        .plot-card .image-wrap { padding: 14px; background: #fff; }
+        .plot-card .image-wrap { padding: 14px; background: var(--img-bg); }
         .plot-card img {
           width: 100%;
           height: auto;
           display: block;
           border-radius: 12px;
-          background: white;
+          background: var(--img-bg);
         }
         .plot-card footer { padding: 0 18px 16px; font-size: 0.92rem; }
-        .plot-card a {
-          color: #2563eb;
-          text-decoration: none;
-          font-weight: 600;
-        }
+        .plot-card a { color: var(--link); text-decoration: none; font-weight: 600; }
         .plot-card a:hover { text-decoration: underline; }
         .links { margin-top: 14px; display: flex; flex-wrap: wrap; gap: 12px; }
-        .links a {
-          color: #0369a1;
-          text-decoration: none;
-          font-weight: 600;
-        }
+        .links a { color: var(--link-alt); text-decoration: none; font-weight: 600; }
         .links a:hover { text-decoration: underline; }
         code { font-family: ui-monospace, SFMono-Regular, Menlo, monospace; }
+        @media (prefers-color-scheme: dark) {
+          :root:not([data-theme="light"]) {
+            --bg: #0f172a; --fg: #e2e8f0;
+            --hero-bg: linear-gradient(135deg, #1e293b, #0f172a 55%, #1a2e1a);
+            --hero-border: #334155;
+            --card-bg: #1e293b; --card-border: #334155; --card-shadow: rgba(0,0,0,0.3);
+            --meta-bg: rgba(30,41,59,0.82);
+            --muted: #94a3b8; --link: #60a5fa; --link-alt: #38bdf8;
+            --header-border: #334155;
+            --img-bg: #1e293b;
+          }
+        }
+        """,
+    ).strip()
+    theme_script = dedent(
+        """
+        <script>
+        (function() {
+          var html = document.documentElement;
+          var btn = document.getElementById('theme-toggle');
+          var stored = localStorage.getItem('pecos-theme');
+          if (stored) html.setAttribute('data-theme', stored);
+          btn.addEventListener('click', function() {
+            var current = html.getAttribute('data-theme');
+            var next = current === 'dark' ? 'light' : 'dark';
+            if (!current) next = 'dark';
+            html.setAttribute('data-theme', next);
+            localStorage.setItem('pecos-theme', next);
+          });
+        })();
+        </script>
         """,
     ).strip()
     distances_text = ", ".join(str(distance) for distance in sorted(set(args.distances)))
@@ -2321,6 +2565,7 @@ def plot_card(plot: DashboardPlot) -> list[str]:
         "  </style>",
         "</head>",
         "<body>",
+        '<button id="theme-toggle" class="theme-toggle">Light / Dark</button>',
         "<main>",
         '  <section class="hero">',
         "    <h1>PECOS Surface Sweep Dashboard</h1>",
@@ -2337,7 +2582,7 @@ def plot_card(plot: DashboardPlot) -> list[str]:
         meta_card("Shots / Point", html.escape(str(args.shots))),
         meta_card(
             "Noise Model",
-            "uniform depolarizing with <code>p1 = p2 = p_meas = p_init = p</code>",
+            html.escape(_noise_model_description(args)),
         ),
         meta_card(
             "Overall Throughput",
@@ -2369,7 +2614,7 @@ def plot_card(plot: DashboardPlot) -> list[str]:
             parts.extend(plot_card(plot))
         parts.extend(["    </div>", "  </section>"])
 
-    parts.extend(["</main>", "</body>", "</html>"])
+    parts.extend(["</main>", theme_script, "</body>", "</html>"])
     output_path.write_text("\n".join(parts) + "\n")
 
 
@@ -2831,7 +3076,7 @@ def _build_report_cover_figure(
         ("Error Rates", [", ".join(f"{p:.4g}" for p in config.get("error_rates", [])) or "(none)"], 1),
         (
             "Noise Model",
-            ["uniform depolarizing", "p1 = p2 = p_meas = p_init = p"],
+            [config.get("noise_model", "depolarizing")],
             2,
         ),
     ]
@@ -3266,6 +3511,8 @@ def _config_for_report(args: argparse.Namespace) -> dict[str, Any]:
         # appendix page can read the same field from either source.
         "sample_backend_mode": getattr(args, "sample_backend", None),
         "native_circuit_source": getattr(args, "native_circuit_source", None),
+        "decoder": getattr(args, "decoder", ["pymatching"]),
+        "noise_model": _noise_model_description(args),
         "seed": getattr(args, "seed", None),
     }
 
@@ -3307,6 +3554,26 @@ def _parse_args() -> argparse.Namespace:
             "default duration window when --duration-multipliers is not provided."
         ),
     )
+    parser.add_argument(
+        "--p1-scale",
+        type=float,
+        default=1.0 / 30.0,
+        help=(
+            "Scale factor for single-qubit gate error rate relative to p. p1 = p * p1_scale. Default: 1/30 (~0.033)."
+        ),
+    )
+    parser.add_argument(
+        "--p-meas-scale",
+        type=float,
+        default=1.0 / 3.0,
+        help="Scale factor for measurement error rate. p_meas = p * p_meas_scale. Default: 1/3.",
+    )
+    parser.add_argument(
+        "--p-prep-scale",
+        type=float,
+        default=1.0 / 3.0,
+        help="Scale factor for preparation error rate. p_prep = p * p_prep_scale. Default: 1/3.",
+    )
     parser.add_argument(
         "--error-rates",
         nargs="+",
@@ -3344,12 +3611,14 @@ def _parse_args() -> argparse.Namespace:
     parser.add_argument(
         "--native-circuit-source",
         choices=["abstract", "traced_qis"],
-        default="abstract",
+        default="traced_qis",
         help=(
             "Which ideal circuit the native PECOS DEM/sampler path should analyze. "
-            "'abstract' uses the existing high-level surface TickCircuit, while "
-            "'traced_qis' traces the lowered ideal Selene/QIS gate stream and "
-            "replays that exact circuit into the native PECOS analysis."
+            "'traced_qis' (default) traces the lowered ideal Selene/QIS gate stream "
+            "(decomposed into native gates like RZZ+rotations), matching the actual "
+            "hardware gate set. Use this for hardware-realistic threshold estimation. "
+            "'abstract' uses the high-level surface TickCircuit with CX/H gates, "
+            "matching the standard circuit-level noise model from the QEC literature."
         ),
     )
     parser.add_argument(
@@ -3358,6 +3627,28 @@ def _parse_args() -> argparse.Namespace:
         default="native_decomposed",
         help="PECOS native DEM mode. PyMatching typically wants native_decomposed.",
     )
+    parser.add_argument(
+        "--decoder",
+        nargs="+",
+        choices=["pymatching", "tesseract", "bp_osd", "bp_lsd", "union_find", "relay_bp", "min_sum_bp"],
+        default=["pymatching"],
+        help=(
+            "Decoder(s) for circuit-level DEM decoding. Specify multiple to "
+            "compare them side-by-side in plots and reports. Default: pymatching. "
+            "Check-matrix decoders (bp_osd, bp_lsd, union_find, relay_bp, min_sum_bp) "
+            "extract a check matrix from the DEM automatically."
+        ),
+    )
+    parser.add_argument(
+        "--tesseract-beam",
+        type=int,
+        default=5,
+        help=(
+            "Tesseract det_beam parameter (number of detectors to consider in beam search). "
+            "Default: 5 (matches upstream). With BFS orderings, det_beam=5 gives identical "
+            "accuracy to 50 or 100 at d<=5 while being 10x faster."
+        ),
+    )
     parser.add_argument("--seed", type=int, default=12345, help="Base RNG seed for the runtime noise model.")
     parser.add_argument("--save-json", action="store_true", help="Write a JSON artifact with all sweep results.")
     parser.add_argument("--save-svg", action="store_true", help="Write SVG plots for each basis and fitted metric.")
@@ -3396,6 +3687,41 @@ def _parse_args() -> argparse.Namespace:
         default="surface_threshold_sweep",
         help="Filename prefix for optional artifacts.",
     )
+    parser.add_argument(
+        "--refine-threshold",
+        action="store_true",
+        help=(
+            "After the initial sweep, estimate the threshold and automatically "
+            "run a refined sweep with tighter error-rate spacing around it. "
+            "The refinement uses the same distances, bases, and shots."
+        ),
+    )
+    parser.add_argument(
+        "--refine-window",
+        type=float,
+        default=0.5,
+        help=(
+            "Half-width of the refinement window as a fraction of the estimated "
+            "threshold. E.g., 0.5 means sweep from 0.5*p_th to 1.5*p_th. "
+            "Default: 0.5."
+        ),
+    )
+    parser.add_argument(
+        "--refine-points",
+        type=int,
+        default=6,
+        help="Number of error-rate points in the refinement sweep. Default: 6.",
+    )
+    parser.add_argument(
+        "--ancilla-budget",
+        type=int,
+        default=None,
+        help=(
+            "Optional cap on simultaneously live ancilla qubits. When set, the "
+            "circuit builder batches stabilizer measurements to stay within this "
+            "budget. Affects both the abstract and traced_qis circuit sources."
+        ),
+    )
     parser.add_argument(
         "--benchmark-repetitions",
         type=int,
@@ -3419,9 +3745,18 @@ def _parse_args() -> argparse.Namespace:
 }
 
 
-def _resolve_backends(sample_backend: str) -> list[str]:
-    """Resolve ``--sample-backend`` to the concrete list of backends to run."""
-    return _BACKEND_MODE_EXPANSIONS.get(sample_backend, [sample_backend])
+def _resolve_backends(sample_backend: str, decoders: list[str] | None = None) -> list[str]:
+    """Resolve ``--sample-backend`` and ``--decoder`` to the concrete list of backends to run.
+
+    When multiple decoders are given, each base backend is expanded to
+    ``backend:decoder`` pairs so the plotting infrastructure sees them as
+    separate series.  With a single decoder the backend name is unchanged
+    for backwards compatibility.
+    """
+    base = _BACKEND_MODE_EXPANSIONS.get(sample_backend, [sample_backend])
+    if decoders is None or len(decoders) <= 1:
+        return base
+    return [f"{b}:{d}" for b in base for d in decoders]
 
 
 def _resolve_duration_schedule(
@@ -3512,15 +3847,32 @@ def _print_config_banner(
     print(f"executed backends: {backends}")
     print(f"DEM mode         : {args.dem_mode}")
     print(f"native circuit source: {args.native_circuit_source}")
-    print("decoder          : PyMatching via SurfaceDecoder(native PECOS DEM)")
+    decoders = getattr(args, "decoder", ["pymatching"])
+    print(f"decoder(s)       : {', '.join(decoders)} via SurfaceDecoder(native PECOS DEM)")
     for backend in backends:
         print(f"runtime[{backend}]  : {_backend_runtime_label(backend, args.native_circuit_source)}")
-    print("noise model      : depolarizing with p1 = p2 = p_meas = p_init = p")
+    p1s = getattr(args, "p1_scale", 0.1)
+    pms = getattr(args, "p_meas_scale", 0.5)
+    pps = getattr(args, "p_prep_scale", 0.5)
+    print(f"noise model      : depolarizing with p1={p1s}*p, p2=p, p_meas={pms}*p, p_prep={pps}*p")
     print("fit model        : p_L(r) = 0.5 * (1 - (1 - 2 * epsilon) ** r)")
     if output_dir is not None:
         print(f"artifact dir     : {output_dir}")
 
 
+def _parse_backend_decoder(backend: str, args: argparse.Namespace) -> tuple[str, str]:
+    """Split ``backend:decoder`` into base backend and decoder type.
+
+    When a single decoder is configured the backend string has no colon
+    and the decoder comes from ``args.decoder[0]``.
+    """
+    if ":" in backend:
+        base, decoder = backend.split(":", 1)
+        return base, decoder
+    decoders = getattr(args, "decoder", ["pymatching"])
+    return backend, decoders[0] if isinstance(decoders, list) else decoders
+
+
 def _run_one_memory_point(
     args: argparse.Namespace,
     *,
@@ -3532,9 +3884,10 @@ def _run_one_memory_point(
     seed: int,
 ) -> tuple[SweepPoint, dict[str, Any]]:
     """Run one sampling point, print the per-point line, return the point + its timing row."""
+    base_backend, decoder_type = _parse_backend_decoder(backend, args)
     point_start = time.perf_counter()
     point = _run_memory_point(
-        sample_backend=backend,
+        sample_backend=base_backend,
         distance=distance,
         basis=basis,
         physical_error_rate=physical_error_rate,
@@ -3543,6 +3896,12 @@ def _run_one_memory_point(
         dem_mode=args.dem_mode,
         native_circuit_source=args.native_circuit_source,
         seed=seed,
+        decoder_type=decoder_type,
+        backend_label=backend,
+        ancilla_budget=getattr(args, "ancilla_budget", None),
+        p1_scale=getattr(args, "p1_scale", 0.1),
+        p_meas_scale=getattr(args, "p_meas_scale", 0.5),
+        p_prep_scale=getattr(args, "p_prep_scale", 0.5),
     )
     elapsed_seconds = time.perf_counter() - point_start
     naive_per_round = ler_per_round_exp(point.logical_error_rate, point.total_rounds)
@@ -3784,15 +4143,31 @@ def _print_post_sweep_analysis(
                         f"log_rmse={fit.fit_root_mean_square_log_error:.3e}",
                     )
 
-            crossing = _estimate_threshold(basis_summaries)
+            crossing_per_round = _estimate_threshold(
+                basis_summaries,
+                metric="fitted_logical_error_rate_per_round",
+            )
+            crossing_d_rounds = _estimate_threshold(
+                basis_summaries,
+                metric="fitted_projected_logical_error_rate_over_d_rounds",
+            )
             global_scaling_fit = _fit_global_scaling_law(basis_summaries)
-            fss_fit = _fit_fss_threshold(basis_summaries, seed_threshold=crossing)
-            if crossing is not None or global_scaling_fit is not None or fss_fit is not None:
+            # Try FSS fit seeded from both crossings; prefer d-round seed
+            fss_seed = crossing_d_rounds or crossing_per_round
+            fss_fit = _fit_fss_threshold(basis_summaries, seed_threshold=fss_seed)
+            if (
+                crossing_per_round is not None
+                or crossing_d_rounds is not None
+                or global_scaling_fit is not None
+                or fss_fit is not None
+            ):
                 print(f"{basis} basis [{backend}] background threshold-style summary:")
-                if crossing is None:
+                if crossing_per_round is None and crossing_d_rounds is None:
                     print(f"  no d={min(distances)} vs d={max(distances)} crossing was detected on this sweep.")
-                else:
-                    print(f"  approximate threshold crossing from fitted d-round curves: p ~= {crossing:.6g}")
+                if crossing_per_round is not None:
+                    print(f"  per-round epsilon crossing: p ~= {crossing_per_round:.6g}")
+                if crossing_d_rounds is not None:
+                    print(f"  projected d-round crossing: p ~= {crossing_d_rounds:.6g}")
                 if global_scaling_fit is not None:
                     print(
                         "  "
@@ -3830,7 +4205,7 @@ def main() -> int:
 
     distances = sorted(set(args.distances))
     bases = [basis.upper() for basis in args.bases]
-    backends = _resolve_backends(args.sample_backend)
+    backends = _resolve_backends(args.sample_backend, args.decoder)
     duration_multipliers, duration_rounds_by_distance, duration_schedule_description = _resolve_duration_schedule(
         args,
         distances,
@@ -3884,6 +4259,71 @@ def main() -> int:
         fit_summaries=fit_summaries,
     )
 
+    # --- Adaptive threshold refinement ---
+    if args.refine_threshold:
+        # Estimate threshold from the initial sweep
+        threshold_estimates = []
+        for basis in bases:
+            basis_summaries = [s for s in fit_summaries if s.basis == basis]
+            for backend in backends:
+                backend_summaries = [s for s in basis_summaries if s.backend == backend]
+                if not backend_summaries:
+                    continue
+                # Use d-round crossing as initial estimate (more conservative)
+                crossing = _estimate_threshold(
+                    backend_summaries,
+                    metric="fitted_projected_logical_error_rate_over_d_rounds",
+                )
+                if crossing is None:
+                    # Fall back to per-round crossing
+                    crossing = _estimate_threshold(backend_summaries)
+                if crossing is not None:
+                    threshold_estimates.append((backend, basis, crossing))
+
+        if threshold_estimates:
+            # Use the median estimate across all backends/bases
+            median_th = sorted(t[2] for t in threshold_estimates)[len(threshold_estimates) // 2]
+            half_w = args.refine_window
+            p_low = median_th * (1.0 - half_w)
+            p_high = median_th * (1.0 + half_w)
+            n_pts = args.refine_points
+            import numpy as np
+
+            refined_rates = sorted({float(f"{r:.6g}") for r in np.linspace(p_low, p_high, n_pts)})
+            # Exclude rates already in the initial sweep
+            refined_rates = [r for r in refined_rates if r not in error_rates and r > 0]
+
+            if refined_rates:
+                print()
+                print(
+                    f"=== Threshold refinement: {len(refined_rates)} additional points "
+                    f"in [{p_low:.5g}, {p_high:.5g}] around estimate p_th ~= {median_th:.5g} ===",
+                )
+                refine_points, refine_fits, refine_timings = _run_sweep_and_fit(
+                    args,
+                    backends=backends,
+                    distances=distances,
+                    bases=bases,
+                    error_rates=refined_rates,
+                    duration_rounds_by_distance=duration_rounds_by_distance,
+                )
+                # Merge with initial results
+                all_points.extend(refine_points)
+                fit_summaries.extend(refine_fits)
+                point_timings.extend(refine_timings)
+
+                # Re-run analysis with merged data
+                print()
+                print("=== Combined analysis (initial + refinement) ===")
+                _print_post_sweep_analysis(
+                    backends=backends,
+                    bases=bases,
+                    distances=distances,
+                    fit_summaries=fit_summaries,
+                )
+        else:
+            print("\n  No threshold detected -- skipping refinement.")
+
     timing_summary = _timing_summary(
         point_timings,
         total_wall_clock_seconds=time.perf_counter() - sweep_start,
diff --git a/examples/surface/run_full_sweep.sh b/examples/surface/run_full_sweep.sh
new file mode 100755
index 000000000..10757627d
--- /dev/null
+++ b/examples/surface/run_full_sweep.sh
@@ -0,0 +1,117 @@
+#!/bin/bash
+# Run all data generation shards sequentially, then analyze and build reports.
+#
+# Usage:
+#   bash examples/surface/run_full_sweep.sh
+#   bash examples/surface/run_full_sweep.sh --output-dir ~/Repos/pecos-data/reports/surface-code-decoder-comparison
+#
+# Each shard is skipped if its output already exists (re-run safe).
+# Delete a shard's JSON to regenerate it.
+
+set -euo pipefail
+
+OUTPUT_DIR="${1:---output-dir}"
+if [ "$OUTPUT_DIR" = "--output-dir" ]; then
+    OUTPUT_DIR="${2:-/tmp/pecos_sweep}"
+fi
+
+DATA_DIR="$OUTPUT_DIR/data"
+mkdir -p "$DATA_DIR"
+
+GEN="uv run python examples/surface/generate_data.py"
+
+# Common error rates
+LOW_P="0.0004 0.0008 0.001 0.0015"
+MID_P="0.002 0.004 0.006 0.008 0.010 0.012 0.014"
+HIGH_P="0.016 0.018 0.020"
+ALL_P="$LOW_P $MID_P $HIGH_P"
+
+MULTI_ROUNDS="2.0 2.33 2.67 3.0"
+
+run_shard() {
+    local name="$1"
+    shift
+    local outdir="$DATA_DIR/$name"
+    if [ -f "$outdir/data.json" ]; then
+        echo "=== SKIP $name (already exists) ==="
+        return
+    fi
+    echo ""
+    echo "=== $name ==="
+    echo ""
+    $GEN "$@" --output-dir "$outdir"
+}
+
+# --- PyMatching: all distances, all error rates, multi-round ---
+run_shard pm_all_d3579 \
+    --distances 3 5 7 9 \
+    --error-rates $ALL_P \
+    --decoders pymatching \
+    --shots 5000 \
+    --duration-multipliers $MULTI_ROUNDS \
+    --seed 42
+
+# Extra shots at very low p for PyMatching (need more to resolve rare errors)
+run_shard pm_lowp_extra \
+    --distances 3 5 7 9 \
+    --error-rates $LOW_P \
+    --decoders pymatching \
+    --shots 15000 \
+    --duration-multipliers $MULTI_ROUNDS \
+    --seed 142
+
+# --- Tesseract: d=3,5,7 multi-round, d=9 single round ---
+run_shard ts_d357 \
+    --distances 3 5 7 \
+    --error-rates $MID_P $HIGH_P \
+    --decoders tesseract \
+    --shots 5000 \
+    --duration-multipliers $MULTI_ROUNDS \
+    --seed 200
+
+run_shard ts_d9 \
+    --distances 9 \
+    --error-rates $MID_P \
+    --decoders tesseract \
+    --shots 5000 \
+    --duration-multipliers 2.0 \
+    --seed 300
+
+# --- MWPF: d=3,5,7 single round ---
+run_shard mwpf_d357 \
+    --distances 3 5 7 \
+    --error-rates $MID_P $HIGH_P \
+    --decoders mwpf \
+    --shots 5000 \
+    --duration-multipliers 2.0 \
+    --seed 400
+
+# --- BP+OSD: d=3,5,7 single round ---
+run_shard bposd_d357 \
+    --distances 3 5 7 \
+    --error-rates $MID_P $HIGH_P \
+    --decoders bp_osd \
+    --shots 5000 \
+    --duration-multipliers 2.0 \
+    --seed 500
+
+# --- Analyze ---
+echo ""
+echo "=== ANALYZE ==="
+echo ""
+uv run python examples/surface/analyze_data.py \
+    "$DATA_DIR"/*/data.json \
+    -o "$OUTPUT_DIR"
+
+# --- Build reports ---
+echo ""
+echo "=== BUILD REPORTS ==="
+echo ""
+uv run python examples/surface/build_report.py \
+    "$OUTPUT_DIR/analysis.json" \
+    --html --pdf --markdown \
+    -o "$OUTPUT_DIR"
+
+echo ""
+echo "Done. Reports in $OUTPUT_DIR/"
+ls -lh "$OUTPUT_DIR"/report.*
diff --git a/examples/surface/validate_dem_correlations.py b/examples/surface/validate_dem_correlations.py
new file mode 100644
index 000000000..78f84ed9e
--- /dev/null
+++ b/examples/surface/validate_dem_correlations.py
@@ -0,0 +1,307 @@
+# Copyright 2026 The PECOS Developers
+# Licensed under the Apache License, Version 2.0
+
+"""Validate DEM detector correlations against simulation ground truth.
+
+Computes per-round detector flip frequency matrices from both simulation
+and DEM sampling, then compares them element-wise. The matrix diagonal
+gives marginal detection rates; off-diagonal elements give half the
+joint detection probability, capturing the correlated error structure.
+
+Usage:
+    uv run python examples/surface/validate_dem_correlations.py
+    uv run python examples/surface/validate_dem_correlations.py -d 3 5 --shots 100000
+    uv run python examples/surface/validate_dem_correlations.py --circuit-source traced_qis
+    uv run python examples/surface/validate_dem_correlations.py --show-matrices
+"""
+
+from __future__ import annotations
+
+import argparse
+import json
+import sys
+import time
+
+
+def build_circuit(distance, rounds, basis, circuit_source):
+    from pecos.qec.surface import SurfacePatch
+
+    patch = SurfacePatch.create(distance=distance)
+
+    if circuit_source == "traced_qis":
+        from pecos.qec.surface.decode import _build_surface_tick_circuit_for_native_model
+
+        tc = _build_surface_tick_circuit_for_native_model(
+            patch,
+            rounds,
+            basis,
+            circuit_source="traced_qis",
+        )
+        tc.lower_clifford_rotations()
+        tc.assign_missing_meas_ids()
+    else:
+        from pecos.qec.surface import LogicalCircuitBuilder
+
+        b = LogicalCircuitBuilder()
+        b.add_patch(patch, "Q0")
+        b.add_memory("Q0", rounds=rounds, basis=basis)
+        tc = b.to_tick_circuit()
+
+    return tc, patch
+
+
+def simulate_detector_events(tc, noise_kw, shots, seed):
+    """Run simulation and extract per-shot detector event lists."""
+    from pecos_rslib_exp import depolarizing, sim_neo, stabilizer
+
+    noise = depolarizing()
+    for k, v in noise_kw.items():
+        if v > 0:
+            noise = getattr(noise, k)(v)
+
+    det_json = json.loads(tc.get_meta("detectors"))
+    num_meas = int(tc.get_meta("num_measurements"))
+    num_dets = len(det_json)
+
+    results = sim_neo(tc).quantum(stabilizer()).noise(noise).shots(shots).seed(seed).run()
+
+    events = []
+    for r in results:
+        meas = list(r)
+        fired = []
+        for i, det in enumerate(det_json):
+            val = 0
+            for rec in det["records"]:
+                idx = num_meas + rec
+                if 0 <= idx < len(meas):
+                    val ^= meas[idx]
+            if val:
+                fired.append(i)
+        events.append(fired)
+
+    return events, num_dets
+
+
+def dem_detector_events(tc, noise_kw, shots, seed):
+    """Sample from DEM and extract per-shot detector event lists."""
+    from pecos_rslib.qec import DemSampler
+
+    full_kw = {k: noise_kw.get(k, 0.0) for k in ["p1", "p2", "p_meas", "p_prep"]}
+    sampler = DemSampler.from_circuit(tc, **full_kw)
+    batch = sampler.generate_samples(num_shots=shots, seed=seed)
+    num_dets = len(json.loads(tc.get_meta("detectors")))
+
+    events = []
+    for i in range(shots):
+        syn = batch.get_syndrome(i)
+        fired = [d for d in range(min(num_dets, len(syn))) if syn[d]]
+        events.append(fired)
+
+    return events, num_dets
+
+
+def format_matrix(matrix, width=8, precision=5):
+    """Format a matrix as an aligned string."""
+    lines = []
+    for row in matrix:
+        cells = [f"{v:{width}.{precision}f}" for v in row]
+        lines.append("[" + " ".join(cells) + "]")
+    return "\n".join(lines)
+
+
+def run_validation(
+    *,
+    distances,
+    bases,
+    rounds_per_d,
+    shots,
+    seed,
+    circuit_sources,
+    noise_configs,
+    threshold,
+    show_matrices,
+    max_order,
+):
+    from pecos.qec.analysis import (
+        compare_flip_matrices,
+        compare_k_body_rates,
+        detector_flip_matrices_by_round,
+        detector_k_body_rates_by_round,
+    )
+
+    total_pass = 0
+    total_fail = 0
+    failures = []
+
+    for distance in distances:
+        rounds = rounds_per_d if rounds_per_d else distance
+        for basis in bases:
+            for source in circuit_sources:
+                tc, patch = build_circuit(distance, rounds, basis, source)
+                num_dets = len(json.loads(tc.get_meta("detectors")))
+                n_ancilla = len(patch.x_stabilizers) + len(patch.z_stabilizers)
+
+                src_label = f" [{source}]" if len(circuit_sources) > 1 else ""
+                print(f"\n{'=' * 72}")
+                print(
+                    f"d={distance} {basis}-basis{src_label}, {num_dets} detectors, "
+                    f"{n_ancilla} per round, {rounds} rounds",
+                )
+                print(f"{'=' * 72}")
+
+                for noise_label, noise_kw in noise_configs:
+                    t0 = time.perf_counter()
+                    sim_events, nd = simulate_detector_events(tc, noise_kw, shots, seed)
+                    sim_time = time.perf_counter() - t0
+
+                    dem_events, _ = dem_detector_events(tc, noise_kw, shots, seed)
+
+                    # --- Pairwise flip matrices ---
+                    sim_mats = detector_flip_matrices_by_round(sim_events, nd, n_ancilla)
+                    dem_mats = detector_flip_matrices_by_round(dem_events, nd, n_ancilla)
+
+                    all_pass = True
+                    round_results = []
+                    for r_idx, (sm, dm) in enumerate(zip(sim_mats, dem_mats, strict=False)):
+                        max_err, frob_err, worst = compare_flip_matrices(sm, dm)
+                        ok = max_err <= threshold
+                        if not ok:
+                            all_pass = False
+                        round_results.append((r_idx, max_err, frob_err, worst, ok))
+
+                    # --- Higher-order correlations ---
+                    sim_kbody = detector_k_body_rates_by_round(
+                        sim_events,
+                        nd,
+                        n_ancilla,
+                        max_order=max_order,
+                    )
+                    dem_kbody = detector_k_body_rates_by_round(
+                        dem_events,
+                        nd,
+                        n_ancilla,
+                        max_order=max_order,
+                    )
+
+                    kbody_results = []  # (round, order, max_err, rms_err, worst, ok)
+                    for r_idx, (sr, dr) in enumerate(zip(sim_kbody, dem_kbody, strict=False)):
+                        order_stats = compare_k_body_rates(sr, dr, max_order=max_order)
+                        for order, (me, rms, worst_ev) in order_stats.items():
+                            ok = me <= threshold
+                            if not ok:
+                                all_pass = False
+                            kbody_results.append((r_idx, order, me, rms, worst_ev, ok))
+
+                    # Aggregate
+                    worst_round_err = max(rr[1] for rr in round_results)
+                    status = "PASS" if all_pass else "FAIL"
+                    if all_pass:
+                        total_pass += 1
+                    else:
+                        total_fail += 1
+                        failures.append(
+                            f"d={distance} {basis} {source} {noise_label}: {worst_round_err * 100:.0f}%",
+                        )
+
+                    print(f"\n  {noise_label} (sim: {sim_time:.2f}s)  {status}")
+
+                    # Pairwise per-round summary
+                    print("    Pairwise (flip matrices):")
+                    for r_idx, max_err, frob_err, worst, ok in round_results:
+                        flag = "" if ok else " <-- FAIL"
+                        print(
+                            f"      Round {r_idx}: max_rel={max_err * 100:5.1f}%  "
+                            f"frob_rel={frob_err * 100:5.1f}%  "
+                            f"worst={worst}{flag}",
+                        )
+
+                    # Higher-order per-round summary
+                    for order in range(1, max_order + 1):
+                        order_entries = [(r, me, rms, w, ok) for r, o, me, rms, w, ok in kbody_results if o == order]
+                        if not order_entries:
+                            continue
+                        worst_me = max(e[1] for e in order_entries)
+                        avg_rms = sum(e[2] for e in order_entries) / len(order_entries)
+                        label = {
+                            1: "1-body (marginals)",
+                            2: "2-body (pairs)",
+                            3: "3-body (triples)",
+                            4: "4-body (quads)",
+                        }.get(order, f"{order}-body")
+                        any_fail = any(not e[4] for e in order_entries)
+                        flag = " <-- FAIL" if any_fail else ""
+                        print(
+                            f"    {label}: worst_max_rel={worst_me * 100:5.1f}%  "
+                            f"avg_rms_rel={avg_rms * 100:5.1f}%{flag}",
+                        )
+                        if any_fail:
+                            for r, me, _rms, w, ok in order_entries:
+                                if not ok:
+                                    print(f"      Round {r}: max_rel={me * 100:.1f}% worst={w}")
+
+                    if show_matrices and not all_pass:
+                        for r_idx, _max_err, _, _, ok in round_results:
+                            if not ok:
+                                print(f"\n    Round {r_idx} sim:")
+                                print("    " + format_matrix(sim_mats[r_idx]).replace("\n", "\n    "))
+                                print(f"    Round {r_idx} dem:")
+                                print("    " + format_matrix(dem_mats[r_idx]).replace("\n", "\n    "))
+
+    print(f"\n{'=' * 72}")
+    print(f"SUMMARY: {total_pass}/{total_pass + total_fail} passed (threshold: {threshold * 100:.0f}%)")
+    if failures:
+        print("Failures:")
+        for f in failures:
+            print(f"  {f}")
+    print(f"{'=' * 72}")
+
+    return total_fail == 0
+
+
+def main():
+    parser = argparse.ArgumentParser(
+        description="Validate DEM detector correlations against simulation.",
+    )
+    parser.add_argument("--distance", "-d", type=int, nargs="+", default=[2, 3], help="Code distances (default: 2 3)")
+    parser.add_argument("--basis", type=str, nargs="+", default=["Z"], choices=["Z", "X"], help="Bases (default: Z)")
+    parser.add_argument("--rounds", type=int, default=None, help="Syndrome rounds (default: same as distance)")
+    parser.add_argument("--shots", type=int, default=100000, help="Shots per test (default: 100000)")
+    parser.add_argument("--seed", type=int, default=42)
+    parser.add_argument(
+        "--circuit-source",
+        choices=["abstract", "traced_qis", "both"],
+        default="both",
+        help="Circuit pipeline (default: both)",
+    )
+    parser.add_argument("--threshold", type=float, default=0.20, help="Max relative error threshold (default: 0.20)")
+    parser.add_argument("--max-order", type=int, default=3, help="Max correlation order (default: 3)")
+    parser.add_argument("--show-matrices", action="store_true", help="Print matrices for failing rounds")
+
+    args = parser.parse_args()
+
+    sources = ["abstract", "traced_qis"] if args.circuit_source == "both" else [args.circuit_source]
+
+    noise_configs = [
+        ("p_meas=0.01", {"p1": 0.0, "p2": 0.0, "p_meas": 0.01, "p_prep": 0.0}),
+        ("p2=0.01", {"p1": 0.0, "p2": 0.01, "p_meas": 0.0, "p_prep": 0.0}),
+        ("depol", {"p1": 0.001, "p2": 0.01, "p_meas": 0.01, "p_prep": 0.01}),
+        ("strong_depol", {"p1": 0.005, "p2": 0.05, "p_meas": 0.05, "p_prep": 0.05}),
+    ]
+
+    ok = run_validation(
+        distances=args.distance,
+        bases=args.basis,
+        rounds_per_d=args.rounds,
+        shots=args.shots,
+        seed=args.seed,
+        circuit_sources=sources,
+        noise_configs=noise_configs,
+        threshold=args.threshold,
+        show_matrices=args.show_matrices,
+        max_order=args.max_order,
+    )
+    sys.exit(0 if ok else 1)
+
+
+if __name__ == "__main__":
+    main()
diff --git a/examples/surface/validate_dem_generators.py b/examples/surface/validate_dem_generators.py
new file mode 100644
index 000000000..66efd020a
--- /dev/null
+++ b/examples/surface/validate_dem_generators.py
@@ -0,0 +1,396 @@
+r"""Validate ALL DEM generators against stabilizer() ground truth.
+
+Systematically tests each DEM generation path across:
+- Multiple distances (d=2, 3)
+- Both bases (Z, X)
+- Each noise component independently + combined
+- All DEM generators (DemBuilder, from_circuit, exact_detection_rates, perturbative_dem)
+
+Uses sim_neo().quantum(stabilizer()) as ground truth for depolarizing noise.
+
+Example:
+    uv run python examples/surface/validate_dem_generators.py
+    uv run python examples/surface/validate_dem_generators.py --shots 50000
+    uv run python examples/surface/validate_dem_generators.py -d 2 --verbose
+    uv run python examples/surface/validate_dem_generators.py --circuit-source both
+    uv run python examples/surface/validate_dem_generators.py --circuit-source traced_qis
+"""
+
+from __future__ import annotations
+
+import argparse
+import json
+import sys
+import time
+from pathlib import Path
+
+sys.path.insert(0, str(Path(__file__).resolve().parents[2] / "python" / "quantum-pecos" / "src"))
+
+# Noise configurations: each component independently + combined.
+# "ground_truth" specifies which simulator to use:
+#   "stabilizer" for depolarizing (exact, any distance)
+#   "statevec" for coherent noise (exact, limited to small circuits)
+NOISE_CONFIGS = [
+    # Depolarizing components (ground truth: stabilizer)
+    ("p_meas only", {"p_meas": 0.01}, "stabilizer"),
+    ("p_prep only", {"p_prep": 0.01}, "stabilizer"),
+    ("p1 only", {"p1": 0.01}, "stabilizer"),
+    ("p2 only", {"p2": 0.01}, "stabilizer"),
+    ("depol all", {"p1": 0.005, "p2": 0.005, "p_meas": 0.005, "p_prep": 0.005}, "stabilizer"),
+    ("depol strong", {"p1": 0.01, "p2": 0.01, "p_meas": 0.01, "p_prep": 0.01}, "stabilizer"),
+]
+
+# Coherent noise configs (ground truth: statevec, small circuits only)
+COHERENT_CONFIGS = [
+    ("idle_rz only", {"idle_rz": 0.05}, "statevec"),
+    ("rz+depol", {"idle_rz": 0.05, "p1": 0.005, "p2": 0.005, "p_meas": 0.005, "p_prep": 0.005}, "statevec"),
+]
+
+# Threshold for pass/fail (relative error vs stabilizer)
+THRESHOLD = 0.15  # 15% — accounts for statistical noise at moderate shot counts
+
+
+def build_circuit(distance, rounds, basis, circuit_source="abstract", *, fill_idle=False):
+    """Build surface code TickCircuit.
+
+    circuit_source:
+        "abstract" — LogicalCircuitBuilder (direct gate construction)
+        "traced_qis" — Guppy → Selene → QIS trace → TickCircuit
+    fill_idle:
+        Insert Idle(1) gates on inactive qubits each tick. Needed for
+        realistic idle_rz noise (RZ applied when Idle gate is seen).
+    """
+    from pecos.qec.surface import SurfacePatch
+
+    patch = SurfacePatch.create(distance=distance)
+
+    if circuit_source == "traced_qis":
+        from pecos.qec.surface.decode import _build_surface_tick_circuit_for_native_model
+
+        tc = _build_surface_tick_circuit_for_native_model(
+            patch,
+            rounds,
+            basis,
+            circuit_source="traced_qis",
+        )
+        # Compilation passes for traced QIS circuits:
+        tc.lower_clifford_rotations()  # RZ(pi/2) -> SZ, etc.
+        tc.assign_missing_meas_ids()  # Stamp MeasId on MZ gates
+    else:
+        from pecos.qec.surface import LogicalCircuitBuilder
+
+        b = LogicalCircuitBuilder()
+        b.add_patch(patch, "Q0")
+        b.add_memory("Q0", rounds=rounds, basis=basis)
+        tc = b.to_tick_circuit()
+
+    # Optional passes applied to all circuits:
+    if fill_idle:
+        # Insert Idle(1) after 2q gates (for idle_rz noise modeling)
+        tc.insert_idle_after_two_qubit_gates(1.0)
+        # Fill remaining inactive qubits with Idle gates
+        tc.fill_idle_gates()
+
+    return tc
+
+
+def ground_truth_rates(tc, noise_kw, shots, seed, det_json, num_meas, num_dets, simulator="stabilizer"):
+    """Ground truth: simulation with detector extraction."""
+    from pecos_rslib_exp import depolarizing, sim_neo, stabilizer, statevec
+
+    noise = depolarizing()
+    for k, v in noise_kw.items():
+        noise = getattr(noise, k)(v)
+
+    backend = stabilizer() if simulator == "stabilizer" else statevec()
+    results = sim_neo(tc).quantum(backend).noise(noise).shots(shots).seed(seed).run()
+    rates = [0.0] * num_dets
+    for r in results:
+        meas = list(r)
+        for i, det in enumerate(det_json):
+            val = 0
+            for rec in det["records"]:
+                idx = num_meas + rec
+                if 0 <= idx < len(meas):
+                    val ^= meas[idx]
+            if val:
+                rates[i] += 1.0 / shots
+    return rates
+
+
+def full_noise_kw(noise_kw):
+    """Ensure all noise params are present (default 0 for missing)."""
+    result = {
+        "p1": noise_kw.get("p1", 0.0),
+        "p2": noise_kw.get("p2", 0.0),
+        "p_meas": noise_kw.get("p_meas", 0.0),
+        "p_prep": noise_kw.get("p_prep", 0.0),
+    }
+    if "idle_rz" in noise_kw:
+        result["idle_rz"] = noise_kw["idle_rz"]
+    return result
+
+
+def dem_sampler_rates(tc, noise_kw, shots, seed, num_dets):
+    """DemSampler.from_circuit path."""
+    from pecos_rslib.qec import DemSampler
+
+    sampler = DemSampler.from_circuit(tc, **full_noise_kw(noise_kw))
+    batch = sampler.generate_samples(num_shots=shots, seed=seed)
+    rates = [0.0] * num_dets
+    for i in range(shots):
+        syn = batch.get_syndrome(i)
+        for d in range(min(num_dets, len(syn))):
+            if syn[d]:
+                rates[d] += 1.0 / shots
+    return rates
+
+
+def dem_builder_rates(tc, noise_kw, shots, seed, num_dets):
+    """DemBuilder path (explicit, uses .to_sampler())."""
+    from pecos_rslib.qec import DagFaultAnalyzer, DemBuilder
+
+    dag = tc.to_dag_circuit()
+    analyzer = DagFaultAnalyzer(dag)
+    influence = analyzer.build_influence_map()
+    dem = (
+        DemBuilder(influence)
+        .with_noise(**full_noise_kw(noise_kw))
+        .with_detectors_json(tc.get_meta("detectors"))
+        .with_observables_json(tc.get_meta("observables"))
+        .with_num_measurements(int(tc.get_meta("num_measurements")))
+        .build()
+    )
+    sampler = dem.to_sampler()
+    batch = sampler.generate_samples(num_shots=shots, seed=seed)
+    rates = [0.0] * num_dets
+    for i in range(shots):
+        syn = batch.get_syndrome(i)
+        for d in range(min(num_dets, len(syn))):
+            if syn[d]:
+                rates[d] += 1.0 / shots
+    return rates
+
+
+def heisenberg_rates(tc, noise_kw, num_dets):
+    """Backward Heisenberg exact detection rates."""
+    from pecos_rslib_exp import exact_detection_rates
+
+    results = exact_detection_rates(tc, **full_noise_kw(noise_kw))
+    rates = [0.0] * num_dets
+    for det_id, prob in results:
+        if det_id < num_dets:
+            rates[det_id] = prob
+    return rates
+
+
+def perturbative_rates(tc, noise_kw, num_dets):
+    """Forward EEG perturbative marginals."""
+    from pecos_rslib_exp import perturbative_dem_events
+
+    events = perturbative_dem_events(tc, **full_noise_kw(noise_kw))
+    rates = [0.0] * num_dets
+    for prob, dets, _obs in events:
+        for d in dets:
+            if d < num_dets:
+                rates[d] += prob
+    return rates
+
+
+def max_rel_error(test_rates, ref_rates, min_rate=0.003):
+    """Max relative error across detectors with rate > min_rate."""
+    max_err = 0.0
+    for t, r in zip(test_rates, ref_rates, strict=False):
+        if r > min_rate:
+            max_err = max(max_err, abs(t / r - 1))
+    return max_err
+
+
+def run_validation(*, distances, bases, shots, seed, verbose, circuit_sources, fill_idle):
+    total_tests = 0
+    total_pass = 0
+    total_fail = 0
+    failures = []
+
+    # Generators: (name, func, supports_coherent)
+    # from_circuit and DemBuilder only support depolarizing (no idle_rz)
+    generators = [
+        ("from_circuit", dem_sampler_rates, False),
+        ("DemBuilder", dem_builder_rates, False),
+        ("Heisenberg", None, True),
+        ("Perturbative", None, True),
+    ]
+
+    for distance in distances:
+        for basis in bases:
+            for circuit_source in circuit_sources:
+                try:
+                    tc = build_circuit(distance, distance, basis, circuit_source, fill_idle=fill_idle)
+                except Exception as e:
+                    print(f"\n  d={distance} {basis} [{circuit_source}]: SKIP ({e})")
+                    continue
+
+                det_json = json.loads(tc.get_meta("detectors"))
+                num_meas = int(tc.get_meta("num_measurements"))
+                num_dets = len(det_json)
+
+                src_label = f" [{circuit_source}]" if len(circuit_sources) > 1 else ""
+                print(f"\n{'='*72}")
+                print(f"d={distance} {basis}-basis{src_label}, {num_dets} detectors, {num_meas} measurements")
+                print(f"{'='*72}")
+
+                # Combine depolarizing + coherent configs
+                all_configs = list(NOISE_CONFIGS) + list(COHERENT_CONFIGS)
+
+                for noise_label, noise_kw, gt_simulator in all_configs:
+                    is_coherent = "idle_rz" in noise_kw
+
+                    # Ground truth
+                    t0 = time.perf_counter()
+                    try:
+                        ref = ground_truth_rates(
+                            tc,
+                            noise_kw,
+                            shots,
+                            seed,
+                            det_json,
+                            num_meas,
+                            num_dets,
+                            simulator=gt_simulator,
+                        )
+                    except BaseException as e:
+                        if verbose:
+                            print(f"\n  {noise_label}: SKIP ground truth ({type(e).__name__}: {e})")
+                        continue
+                    ref_time = time.perf_counter() - t0
+
+                    if verbose:
+                        print(f"\n  {noise_label} ({gt_simulator}: {ref_time:.2f}s)")
+
+                    for gen_name, gen_func, supports_coherent in generators:
+                        # Skip non-EEG generators for coherent noise
+                        if is_coherent and not supports_coherent:
+                            if verbose:
+                                print(f"    {gen_name:<14}          (skipped: no coherent support)")
+                            continue
+                        t0 = time.perf_counter()
+                        try:
+                            if gen_name == "Heisenberg":
+                                test = heisenberg_rates(tc, noise_kw, num_dets)
+                            elif gen_name == "Perturbative":
+                                test = perturbative_rates(tc, noise_kw, num_dets)
+                            else:
+                                test = gen_func(tc, noise_kw, shots, seed, num_dets)
+                            dt = time.perf_counter() - t0
+
+                            err = max_rel_error(test, ref)
+                            ok = err < THRESHOLD
+                            total_tests += 1
+                            if ok:
+                                total_pass += 1
+                            else:
+                                total_fail += 1
+                                failures.append(
+                                    f"d={distance} {basis} {noise_label} {gen_name}: {err*100:.0f}%",
+                                )
+
+                            status = "PASS" if ok else f"FAIL({err*100:.0f}%)"
+                            if verbose:
+                                print(f"    {gen_name:<14} {dt*1000:>7.0f}ms  {status}")
+                            elif not ok:
+                                print(f"  {noise_label:<14} {gen_name:<14} {status}")
+
+                        except Exception as e:
+                            total_tests += 1
+                            total_fail += 1
+                            failures.append(
+                                f"d={distance} {basis} {noise_label} {gen_name}: ERROR {e}",
+                            )
+                            if verbose:
+                                print(f"    {gen_name:<14}  ERROR: {e}")
+
+                if not verbose:
+                    # Print summary for this config
+                    pass
+
+    # Final summary
+    print(f"\n{'='*72}")
+    print(f"VALIDATION SUMMARY: {total_pass}/{total_tests} passed, {total_fail} failed")
+    print(f"Threshold: {THRESHOLD*100:.0f}% relative error ({shots} shots)")
+    if failures:
+        print("\nFailures:")
+        for f in failures:
+            print(f"  {f}")
+    else:
+        print("\nAll tests passed.")
+    print(f"{'='*72}")
+
+    return total_fail == 0
+
+
+def main():
+    parser = argparse.ArgumentParser(
+        description=__doc__,
+        formatter_class=argparse.RawDescriptionHelpFormatter,
+    )
+    parser.add_argument(
+        "--distance",
+        "-d",
+        type=int,
+        nargs="+",
+        default=[2, 3],
+        help="Code distances to test (default: 2 3)",
+    )
+    parser.add_argument(
+        "--basis",
+        choices=["X", "Z"],
+        nargs="+",
+        default=["Z", "X"],
+        help="Bases to test (default: Z X)",
+    )
+    parser.add_argument(
+        "--shots",
+        type=int,
+        default=20000,
+        help="Shots per test (default: 20000)",
+    )
+    parser.add_argument(
+        "--seed",
+        type=int,
+        default=42,
+    )
+    parser.add_argument(
+        "--verbose",
+        "-v",
+        action="store_true",
+        help="Show per-generator timing and results",
+    )
+    parser.add_argument(
+        "--circuit-source",
+        choices=["abstract", "traced_qis", "both"],
+        default="abstract",
+        help="Circuit construction pipeline (default: abstract)",
+    )
+    parser.add_argument(
+        "--fill-idle",
+        action="store_true",
+        help="Insert Idle(1) gates on inactive qubits (needed for idle_rz noise)",
+    )
+    args = parser.parse_args()
+
+    sources = ["abstract", "traced_qis"] if args.circuit_source == "both" else [args.circuit_source]
+
+    ok = run_validation(
+        distances=args.distance,
+        bases=args.basis,
+        shots=args.shots,
+        seed=args.seed,
+        verbose=args.verbose,
+        circuit_sources=sources,
+        fill_idle=args.fill_idle,
+    )
+    sys.exit(0 if ok else 1)
+
+
+if __name__ == "__main__":
+    main()
diff --git a/examples/surface_code_experiments.ipynb b/examples/surface_code_experiments.ipynb
index 43a38bdbd..40d1ff49f 100644
--- a/examples/surface_code_experiments.ipynb
+++ b/examples/surface_code_experiments.ipynb
@@ -75,7 +75,7 @@
     "NUM_SHOTS = 1000\n",
     "DECODER_TYPES = [\"pymatching\", \"fusion_blossom\"]\n",
     "\n",
-    "# Uniform depolarizing noise: p1 = p2 = p_meas = p_init = p\n",
+    "# Uniform depolarizing noise: p1 = p2 = p_meas = p_prep = p\n",
     "ERROR_RATES = [0.001, 0.002, 0.005, 0.008, 0.01]"
    ]
   },
@@ -542,7 +542,7 @@
     "\n",
     "    for p in ERROR_RATES:\n",
     "        error_model = DepolarizingErrorModel(p_1q=p, p_2q=p, p_meas=p, p_init=p)\n",
-    "        noise = NoiseModel(p1=p, p2=p, p_meas=p, p_init=p)\n",
+    "        noise = NoiseModel(p1=p, p2=p, p_meas=p, p_prep=p)\n",
     "\n",
     "        # Simulate once, decode with all decoders\n",
     "        shots = run_shots(instance, nq, NUM_SHOTS, error_model)\n",
@@ -744,7 +744,7 @@
     "\n",
     "    for p in ERROR_RATES:\n",
     "        error_model = DepolarizingErrorModel(p_1q=p, p_2q=p, p_meas=p, p_init=p)\n",
-    "        noise = NoiseModel(p1=p, p2=p, p_meas=p, p_init=p)\n",
+    "        noise = NoiseModel(p1=p, p2=p, p_meas=p, p_prep=p)\n",
     "\n",
     "        shots = run_shots(instance, nq, NUM_SHOTS, error_model)\n",
     "\n",
diff --git a/examples/surface_code_noisy_decoding.ipynb b/examples/surface_code_noisy_decoding.ipynb
index cabb4a10c..330d661d7 100644
--- a/examples/surface_code_noisy_decoding.ipynb
+++ b/examples/surface_code_noisy_decoding.ipynb
@@ -101,7 +101,7 @@
     }
    },
    "outputs": [],
-   "source": "from typing import Any\n\n\ndef get_logical_qubits(distance: int, basis: str) -> tuple:\n    \"\"\"Get qubits in the logical operator.\"\"\"\n    patch = SurfacePatch.create(distance=distance)\n    if basis == \"Z\":\n        return patch.geometry.logical_z.data_qubits\n    return patch.geometry.logical_x.data_qubits\n\n\ndef run_memory_experiment(\n    distance: int,\n    num_rounds: int,\n    num_shots: int,\n    basis: str,\n    error_model: Any,\n    *,\n    decode: bool = False,\n    decoder_type: str = \"pymatching\",\n) -> dict:\n    \"\"\"Run memory experiment and compute logical error rate.\n\n    For Z-basis: prepare |0_L>, measure in Z basis, check logical Z parity.\n    For X-basis: prepare |+_L>, measure in X basis, check logical X parity.\n\n    Args:\n        distance: Code distance\n        num_rounds: Number of syndrome extraction rounds\n        num_shots: Number of shots to run\n        basis: 'Z' or 'X' basis\n        error_model: Selene error model (IdealErrorModel or DepolarizingErrorModel)\n        decode: If True, use decoding to correct errors\n        decoder_type: Decoder backend ('pymatching', 'fusion_blossom', 'bp_osd', 'bp_lsd', 'union_find', 'tesseract')\n\n    Returns:\n        Dictionary with experiment results\n    \"\"\"\n    patch = SurfacePatch.create(distance=distance)\n    logical_qubits = get_logical_qubits(distance, basis)\n\n    # Create decoder if needed\n    decoder = None\n    if decode:\n        # Extract noise parameters from error model\n        noise = NoiseModel(\n            p1=getattr(error_model, \"p_1q\", 0.01),\n            p2=getattr(error_model, \"p_2q\", 0.01),\n            p_meas=getattr(error_model, \"p_meas\", 0.01),\n            p_init=getattr(error_model, \"p_init\", 0.01),\n        )\n        decoder = SurfaceDecoder(patch, num_rounds=num_rounds, noise=noise, decoder_type=decoder_type)\n\n    # Build circuit\n    num_qubits = get_num_qubits(distance)\n    prog = make_surface_code(distance=distance, num_rounds=num_rounds, basis=basis)\n    hugr_bytes = compile_guppy_to_hugr(prog)\n    instance = build(hugr_bytes, name=f\"surface_d{distance}\")\n\n    # Run\n    num_logical_errors = 0\n    num_raw_errors = 0\n\n    for shot_results in instance.run_shots(\n        simulator=Stim(),\n        n_qubits=num_qubits,\n        n_shots=num_shots,\n        error_model=error_model,\n        runtime=SimpleRuntime(),\n        n_processes=1,\n    ):\n        # Collect all syndromes properly (multiple entries per key)\n        synx_list = []\n        synz_list = []\n        final = None\n\n        for name, values in shot_results:\n            vals = list(values)\n            if name == \"synx\":\n                synx_list.append(np.array(vals, dtype=np.uint8))\n            elif name == \"synz\":\n                synz_list.append(np.array(vals, dtype=np.uint8))\n            elif name == \"final\":\n                final = vals\n\n        if final is None:\n            continue\n\n        # Raw parity check (no decoding)\n        raw_parity = sum(final[q] for q in logical_qubits) % 2\n        if raw_parity != 0:\n            num_raw_errors += 1\n\n        if decode and decoder is not None:\n            final_arr = np.array(final, dtype=np.uint8)\n\n            # Decode based on basis\n            if basis == \"Z\":\n                is_error, _ = decoder.decode_memory_z(synx_list, synz_list, final_arr)\n            else:\n                is_error, _ = decoder.decode_memory_x(synx_list, synz_list, final_arr)\n\n            if is_error:\n                num_logical_errors += 1\n        else:\n            # No decoding - use raw parity\n            if raw_parity != 0:\n                num_logical_errors += 1\n\n    return {\n        \"distance\": distance,\n        \"num_shots\": num_shots,\n        \"num_logical_errors\": num_logical_errors,\n        \"num_raw_errors\": num_raw_errors,\n        \"logical_error_rate\": num_logical_errors / num_shots,\n        \"raw_error_rate\": num_raw_errors / num_shots,\n        \"decoded\": decode,\n        \"decoder_type\": decoder_type if decode else None,\n    }"
+   "source": "from typing import Any\n\n\ndef get_logical_qubits(distance: int, basis: str) -> tuple:\n    \"\"\"Get qubits in the logical operator.\"\"\"\n    patch = SurfacePatch.create(distance=distance)\n    if basis == \"Z\":\n        return patch.geometry.logical_z.data_qubits\n    return patch.geometry.logical_x.data_qubits\n\n\ndef run_memory_experiment(\n    distance: int,\n    num_rounds: int,\n    num_shots: int,\n    basis: str,\n    error_model: Any,\n    *,\n    decode: bool = False,\n    decoder_type: str = \"pymatching\",\n) -> dict:\n    \"\"\"Run memory experiment and compute logical error rate.\n\n    For Z-basis: prepare |0_L>, measure in Z basis, check logical Z parity.\n    For X-basis: prepare |+_L>, measure in X basis, check logical X parity.\n\n    Args:\n        distance: Code distance\n        num_rounds: Number of syndrome extraction rounds\n        num_shots: Number of shots to run\n        basis: 'Z' or 'X' basis\n        error_model: Selene error model (IdealErrorModel or DepolarizingErrorModel)\n        decode: If True, use decoding to correct errors\n        decoder_type: Decoder backend ('pymatching', 'fusion_blossom', 'bp_osd', 'bp_lsd', 'union_find', 'tesseract')\n\n    Returns:\n        Dictionary with experiment results\n    \"\"\"\n    patch = SurfacePatch.create(distance=distance)\n    logical_qubits = get_logical_qubits(distance, basis)\n\n    # Create decoder if needed\n    decoder = None\n    if decode:\n        # Extract noise parameters from error model\n        noise = NoiseModel(\n            p1=getattr(error_model, \"p_1q\", 0.01),\n            p2=getattr(error_model, \"p_2q\", 0.01),\n            p_meas=getattr(error_model, \"p_meas\", 0.01),\n            p_prep=getattr(error_model, \"p_init\", 0.01),\n        )\n        decoder = SurfaceDecoder(patch, num_rounds=num_rounds, noise=noise, decoder_type=decoder_type)\n\n    # Build circuit\n    num_qubits = get_num_qubits(distance)\n    prog = make_surface_code(distance=distance, num_rounds=num_rounds, basis=basis)\n    hugr_bytes = compile_guppy_to_hugr(prog)\n    instance = build(hugr_bytes, name=f\"surface_d{distance}\")\n\n    # Run\n    num_logical_errors = 0\n    num_raw_errors = 0\n\n    for shot_results in instance.run_shots(\n        simulator=Stim(),\n        n_qubits=num_qubits,\n        n_shots=num_shots,\n        error_model=error_model,\n        runtime=SimpleRuntime(),\n        n_processes=1,\n    ):\n        # Collect all syndromes properly (multiple entries per key)\n        synx_list = []\n        synz_list = []\n        final = None\n\n        for name, values in shot_results:\n            vals = list(values)\n            if name == \"synx\":\n                synx_list.append(np.array(vals, dtype=np.uint8))\n            elif name == \"synz\":\n                synz_list.append(np.array(vals, dtype=np.uint8))\n            elif name == \"final\":\n                final = vals\n\n        if final is None:\n            continue\n\n        # Raw parity check (no decoding)\n        raw_parity = sum(final[q] for q in logical_qubits) % 2\n        if raw_parity != 0:\n            num_raw_errors += 1\n\n        if decode and decoder is not None:\n            final_arr = np.array(final, dtype=np.uint8)\n\n            # Decode based on basis\n            if basis == \"Z\":\n                is_error, _ = decoder.decode_memory_z(synx_list, synz_list, final_arr)\n            else:\n                is_error, _ = decoder.decode_memory_x(synx_list, synz_list, final_arr)\n\n            if is_error:\n                num_logical_errors += 1\n        else:\n            # No decoding - use raw parity\n            if raw_parity != 0:\n                num_logical_errors += 1\n\n    return {\n        \"distance\": distance,\n        \"num_shots\": num_shots,\n        \"num_logical_errors\": num_logical_errors,\n        \"num_raw_errors\": num_raw_errors,\n        \"logical_error_rate\": num_logical_errors / num_shots,\n        \"raw_error_rate\": num_raw_errors / num_shots,\n        \"decoded\": decode,\n        \"decoder_type\": decoder_type if decode else None,\n    }"
   },
   {
    "cell_type": "markdown",
@@ -1094,7 +1094,7 @@
     "\n",
     "# Create a decoder configuration\n",
     "patch = SurfacePatch.create(distance=3)\n",
-    "noise = NoiseModel(p1=0.001, p2=0.01, p_meas=0.01, p_init=0.001)\n",
+    "noise = NoiseModel(p1=0.001, p2=0.01, p_meas=0.01, p_prep=0.001)\n",
     "\n",
     "# Generate DEM using PECOS native pipeline\n",
     "tc = generate_tick_circuit_from_patch(patch, num_rounds=3, basis=\"Z\")\n",
@@ -1110,12 +1110,12 @@
     "\n",
     "# Build DEM\n",
     "builder = DemBuilder(influence_map)\n",
-    "builder.with_noise(noise.p1, noise.p2, noise.p_meas, noise.p_init)\n",
+    "builder.with_noise(noise.p1, noise.p2, noise.p_meas, noise.p_prep)\n",
     "builder.with_num_measurements(num_measurements)\n",
     "builder.with_measurement_order(measurement_order)\n",
     "builder.with_detectors_json(detectors_json)\n",
     "if observables_json:\n",
-    "    builder.with_observables_json(observables_json)\n",
+    "    builder.with_tracked_paulis_json(observables_json)\n",
     "\n",
     "pecos_dem = builder.build()\n",
     "\n",
@@ -1535,7 +1535,7 @@
     "    p1=0.001,      # Single-qubit gate error\n",
     "    p2=0.01,       # Two-qubit gate error\n",
     "    p_meas=0.01,   # Measurement error\n",
-    "    p_init=0.001,  # Initialization error\n",
+    "    p_prep=0.001,  # Initialization error\n",
     ")\n",
     "\n",
     "# Parse and generate DEM\n",
@@ -1596,7 +1596,7 @@
     "\n",
     "# Construct DEM\n",
     "builder = DemBuilder(influence_map)\n",
-    "builder.with_noise(p1, p2, p_meas, p_init)\n",
+    "builder.with_noise(p1, p2, p_meas, p_prep)\n",
     "builder.with_detectors_json(tc.get_meta(\"detectors\"))\n",
     "dem = builder.build()\n",
     "\n",
@@ -1650,7 +1650,7 @@
     "    p1=0.001,      # Single-qubit gate error rate\n",
     "    p2=0.01,       # Two-qubit gate error rate\n",
     "    p_meas=0.01,   # Measurement error rate\n",
-    "    p_init=0.001,  # Initialization error rate\n",
+    "    p_prep=0.001,  # Initialization error rate\n",
     ")\n",
     "```"
    ]
diff --git a/examples/surface_code_selene_demo.ipynb b/examples/surface_code_selene_demo.ipynb
index d9b849f24..3844f7882 100644
--- a/examples/surface_code_selene_demo.ipynb
+++ b/examples/surface_code_selene_demo.ipynb
@@ -84,7 +84,7 @@
     "P1 = 4e-5       # Single-qubit gate error\n",
     "P2 = 1e-3       # Two-qubit gate error\n",
     "P_MEAS = 4e-4   # Measurement error\n",
-    "P_INIT = 4e-4   # Initialization error"
+    "P_PREP = 4e-4   # Initialization error"
    ]
   },
   {
@@ -214,7 +214,7 @@
     "print()\n",
     "\n",
     "# 2. Stim circuit (for Stim simulation and DEM generation)\n",
-    "stim_circuit = generate_stim_from_patch(patch, NUM_ROUNDS, BASIS, p1=P1, p2=P2, p_meas=P_MEAS, p_init=P_INIT)\n",
+    "stim_circuit = generate_stim_from_patch(patch, NUM_ROUNDS, BASIS, p1=P1, p2=P2, p_meas=P_MEAS, p_prep=P_PREP)\n",
     "stim_lines = stim_circuit.strip().split(\"\\n\")\n",
     "print(f\"2. Stim circuit: {len(stim_lines)} lines\")\n",
     "print(f\"   Preview: {stim_lines[0]}\")\n",
@@ -668,7 +668,7 @@
     "PECOS provides native DEM generation that works directly with TickCircuit,\n",
     "without requiring Stim as an intermediate step. The workflow is:\n",
     "\n",
-    "1. `SurfacePatch` -> `TickCircuit` (with detector/observable metadata)\n",
+    "1. `SurfacePatch` -> `TickCircuit` (with detector/tracked-Pauli metadata)\n",
     "2. `TickCircuit` -> `DagCircuit` -> `DagFaultAnalyzer` -> `DemBuilder`\n",
     "3. `DemBuilder` -> DEM string (Stim-compatible format)\n",
     "\n",
@@ -709,7 +709,7 @@
     "    p1: float,\n",
     "    p2: float,\n",
     "    p_meas: float,\n",
-    "    p_init: float,\n",
+    "    p_prep: float,\n",
     ") -> \"DetectorErrorModel\":\n",
     "    \"\"\"Generate DEM using PECOS native fault propagation.\n",
     "\n",
@@ -731,12 +731,12 @@
     "\n",
     "    # Build DEM using Rust DemBuilder\n",
     "    builder = DemBuilder(influence_map)\n",
-    "    builder.with_noise(p1, p2, p_meas, p_init)\n",
+    "    builder.with_noise(p1, p2, p_meas, p_prep)\n",
     "    builder.with_num_measurements(num_measurements)\n",
     "    builder.with_measurement_order(measurement_order)\n",
     "    builder.with_detectors_json(detectors_json)\n",
     "    if observables_json:\n",
-    "        builder.with_observables_json(observables_json)\n",
+    "        builder.with_tracked_paulis_json(observables_json)\n",
     "\n",
     "    return builder.build()"
    ]
@@ -773,7 +773,7 @@
     "# Method 1: Via Stim (for reference)\n",
     "noisy_stim = generate_stim_from_patch(\n",
     "    patch, num_rounds=NUM_ROUNDS, basis=BASIS,\n",
-    "    p1=P1, p2=P2, p_meas=P_MEAS, p_init=P_INIT,\n",
+    "    p1=P1, p2=P2, p_meas=P_MEAS, p_prep=P_PREP,\n",
     ")\n",
     "circuit = stim.Circuit(noisy_stim)\n",
     "stim_dem = circuit.detector_error_model(decompose_errors=True)\n",
@@ -788,7 +788,7 @@
     "# Method 2: Native PECOS\n",
     "pecos_dem = generate_pecos_dem(\n",
     "    patch, num_rounds=NUM_ROUNDS, basis=BASIS,\n",
-    "    p1=P1, p2=P2, p_meas=P_MEAS, p_init=P_INIT,\n",
+    "    p1=P1, p2=P2, p_meas=P_MEAS, p_prep=P_PREP,\n",
     ")\n",
     "pecos_raw_str = pecos_dem.to_string()\n",
     "pecos_decomp_str = pecos_dem.to_string_decomposed()\n",
@@ -935,7 +935,7 @@
       "  Stim DEM raw: 2063 lines\n",
       "  Stim DEM decomposed: 2384 lines\n",
       "\n",
-      "Noise parameters: p1=4e-05, p2=0.001, p_meas=0.0004, p_init=0.0004\n",
+      "Noise parameters: p1=4e-05, p2=0.001, p_meas=0.0004, p_prep=0.0004\n",
       "Syndrome rounds: 3\n"
      ]
     }
@@ -969,13 +969,13 @@
     "    # Generate Stim circuit (with noise)\n",
     "    stim_full = generate_stim_from_patch(\n",
     "        patch, num_rounds=NUM_ROUNDS, basis=basis,\n",
-    "        p1=P1, p2=P2, p_meas=P_MEAS, p_init=P_INIT,\n",
+    "        p1=P1, p2=P2, p_meas=P_MEAS, p_prep=P_PREP,\n",
     "    )\n",
     "\n",
     "    # Generate PECOS DEMs (raw and decomposed)\n",
     "    pecos_dem_obj = generate_pecos_dem(\n",
     "        patch, num_rounds=NUM_ROUNDS, basis=basis,\n",
-    "        p1=P1, p2=P2, p_meas=P_MEAS, p_init=P_INIT,\n",
+    "        p1=P1, p2=P2, p_meas=P_MEAS, p_prep=P_PREP,\n",
     "    )\n",
     "    pecos_dem_raw = pecos_dem_obj.to_string()\n",
     "    pecos_dem_decomposed = pecos_dem_obj.to_string_decomposed()\n",
@@ -1005,7 +1005,7 @@
     "    print(f\"  Stim DEM decomposed: {len(stim_dem_decomposed.splitlines())} lines\")\n",
     "    print()\n",
     "\n",
-    "print(f\"Noise parameters: p1={P1}, p2={P2}, p_meas={P_MEAS}, p_init={P_INIT}\")\n",
+    "print(f\"Noise parameters: p1={P1}, p2={P2}, p_meas={P_MEAS}, p_prep={P_PREP}\")\n",
     "print(f\"Syndrome rounds: {NUM_ROUNDS}\")"
    ]
   },
@@ -4527,13 +4527,13 @@
     "    p = SurfacePatch.create(distance=d)\n",
     "\n",
     "    # Stim DEM (decomposed)\n",
-    "    stim_str = generate_stim_from_patch(p, NUM_ROUNDS, BASIS, p1=P1, p2=P2, p_meas=P_MEAS, p_init=P_INIT)\n",
+    "    stim_str = generate_stim_from_patch(p, NUM_ROUNDS, BASIS, p1=P1, p2=P2, p_meas=P_MEAS, p_prep=P_PREP)\n",
     "    c = stim.Circuit(stim_str)\n",
     "    stim_dem = c.detector_error_model(decompose_errors=True)\n",
     "    stim_errors = count_dem_errors(str(stim_dem))\n",
     "\n",
     "    # PECOS DEM (decomposed)\n",
-    "    pecos_dem = generate_pecos_dem(p, NUM_ROUNDS, BASIS, p1=P1, p2=P2, p_meas=P_MEAS, p_init=P_INIT)\n",
+    "    pecos_dem = generate_pecos_dem(p, NUM_ROUNDS, BASIS, p1=P1, p2=P2, p_meas=P_MEAS, p_prep=P_PREP)\n",
     "    pecos_decomposed = pecos_dem.to_string_decomposed()\n",
     "    pecos_errors = count_dem_errors(pecos_decomposed)\n",
     "    pecos_prob = sum_dem_probability(pecos_decomposed)\n",
@@ -4571,7 +4571,7 @@
     "tc = generate_tick_circuit_from_patch(patch, num_rounds=NUM_ROUNDS, basis=BASIS)\n",
     "\n",
     "# One-liner DEM generation from TickCircuit (outputs decomposed format by default)\n",
-    "dem_str = generate_dem_from_tick_circuit(tc, p1=P1, p2=P2, p_meas=P_MEAS, p_init=P_INIT)\n",
+    "dem_str = generate_dem_from_tick_circuit(tc, p1=P1, p2=P2, p_meas=P_MEAS, p_prep=P_PREP)\n",
     "\n",
     "print(\"=== generate_dem_from_tick_circuit output (first 10 error lines) ===\")\n",
     "error_lines = [err_line for err_line in dem_str.split(\"\\n\") if err_line.startswith(\"error(\")]\n",
diff --git a/examples/surface_code_slr_exploration.ipynb b/examples/surface_code_slr_exploration.ipynb
index c2acf6bc6..4af7f0ec4 100644
--- a/examples/surface_code_slr_exploration.ipynb
+++ b/examples/surface_code_slr_exploration.ipynb
@@ -630,7 +630,7 @@
     "\n",
     "4. **Key gaps for parity with circuit builder:**\n",
     "   - No TickCircuit generator\n",
-    "   - No detector/observable annotation support\n",
+    "   - No detector/tracked-Pauli annotation support\n",
     "   - No semantic phase metadata\n",
     "   - No gate-level metadata (labels, stabilizer info)\n",
     "   - No CNOT scheduling in SLR's surface library\n",
diff --git a/examples/surface_code_threshold.ipynb b/examples/surface_code_threshold.ipynb
index f0ae082f3..90e15a997 100644
--- a/examples/surface_code_threshold.ipynb
+++ b/examples/surface_code_threshold.ipynb
@@ -18,7 +18,7 @@
     "\n",
     "**Setup:**\n",
     "- Distances 9, 11, 13, 15 (avoiding finite-size effects)\n",
-    "- Uniform depolarizing noise (p1 = p2 = p_meas = p_init = p)\n",
+    "- Uniform depolarizing noise (p1 = p2 = p_meas = p_prep = p)\n",
     "- 2*d syndrome rounds per distance\n",
     "- Selene simulation with Stim backend\n",
     "\n",
@@ -164,12 +164,12 @@
     "    measurement_order = _extract_measurement_order(tc)\n",
     "\n",
     "    builder = DemBuilder(influence_map)\n",
-    "    builder.with_noise(noise.p1, noise.p2, noise.p_meas, noise.p_init)\n",
+    "    builder.with_noise(noise.p1, noise.p2, noise.p_meas, noise.p_prep)\n",
     "    builder.with_num_measurements(num_measurements)\n",
     "    builder.with_measurement_order(measurement_order)\n",
     "    builder.with_detectors_json(detectors_json)\n",
     "    if observables_json:\n",
-    "        builder.with_observables_json(observables_json)\n",
+    "        builder.with_tracked_paulis_json(observables_json)\n",
     "\n",
     "    dem = builder.build()\n",
     "    return dem.to_string(), dem.to_string_decomposed()\n",
@@ -438,7 +438,7 @@
     "\n",
     "    for p in ERROR_RATES:\n",
     "        error_model = DepolarizingErrorModel(p_1q=p, p_2q=p, p_meas=p, p_init=p)\n",
-    "        noise = NoiseModel(p1=p, p2=p, p_meas=p, p_init=p)\n",
+    "        noise = NoiseModel(p1=p, p2=p, p_meas=p, p_prep=p)\n",
     "\n",
     "        t0 = time.time()\n",
     "        shots = run_shots(instance, nq, NUM_SHOTS, error_model)\n",
@@ -487,7 +487,7 @@
     "\n",
     "    for p in ERROR_RATES:\n",
     "        error_model = DepolarizingErrorModel(p_1q=p, p_2q=p, p_meas=p, p_init=p)\n",
-    "        noise = NoiseModel(p1=p, p2=p, p_meas=p, p_init=p)\n",
+    "        noise = NoiseModel(p1=p, p2=p, p_meas=p, p_prep=p)\n",
     "\n",
     "        t0 = time.time()\n",
     "        shots = run_shots(instance, nq, NUM_SHOTS, error_model)\n",
@@ -646,7 +646,7 @@
     "by comparing 5 decoder/DEM variants, all using PyMatching MWPM.\n",
     "\n",
     "**Setup:**\n",
-    "- Uniform depolarizing noise: p1 = p2 = p_meas = p_init = p\n",
+    "- Uniform depolarizing noise: p1 = p2 = p_meas = p_prep = p\n",
     "- 2*d syndrome rounds per distance\n",
     "- Distances 9-15 to minimize finite-size effects\n",
     "\n",
diff --git a/examples/surface_code_thresholds.ipynb b/examples/surface_code_thresholds.ipynb
index cdde5afb8..2f5050c2e 100644
--- a/examples/surface_code_thresholds.ipynb
+++ b/examples/surface_code_thresholds.ipynb
@@ -339,7 +339,7 @@
     "def generate_code_capacity_dem(patch: SurfacePatch, num_rounds: int, p: float) -> str:\n",
     "    \"\"\"Generate a code-capacity DEM (data errors only, perfect measurements).\"\"\"\n",
     "    # Use phenomenological DEM with p_meas=0\n",
-    "    noise = NoiseModel(p1=0, p2=p, p_meas=0, p_init=0)\n",
+    "    noise = NoiseModel(p1=0, p2=p, p_meas=0, p_prep=0)\n",
     "    return generate_surface_code_dem(patch, num_rounds=1, noise=noise, stab_type=\"Z\")\n",
     "\n",
     "# Test DEM generation\n",
@@ -424,7 +424,7 @@
    "source": [
     "def generate_phenomenological_dem(patch: SurfacePatch, num_rounds: int, p: float) -> str:\n",
     "    \"\"\"Generate a phenomenological DEM (data + measurement errors).\"\"\"\n",
-    "    noise = NoiseModel(p1=0, p2=p, p_meas=p, p_init=0)\n",
+    "    noise = NoiseModel(p1=0, p2=p, p_meas=p, p_prep=0)\n",
     "    return generate_surface_code_dem(patch, num_rounds=num_rounds, noise=noise, stab_type=\"Z\")\n",
     "\n",
     "# Test DEM generation\n",
@@ -510,7 +510,7 @@
     "def generate_circuit_level_dem(patch: SurfacePatch, num_rounds: int, p: float) -> str:\n",
     "    \"\"\"Generate a circuit-level DEM using PECOS native fault propagation.\"\"\"\n",
     "    # Use same error rate for all noise sources (standard depolarizing)\n",
-    "    noise = NoiseModel(p1=p, p2=p, p_meas=p, p_init=p)\n",
+    "    noise = NoiseModel(p1=p, p2=p, p_meas=p, p_prep=p)\n",
     "    return generate_circuit_level_dem_from_builder(patch, num_rounds=num_rounds, noise=noise, basis=\"Z\")\n",
     "\n",
     "# Test DEM generation\n",
diff --git a/exp/pecos-eeg/Cargo.toml b/exp/pecos-eeg/Cargo.toml
new file mode 100644
index 000000000..ceef7c350
--- /dev/null
+++ b/exp/pecos-eeg/Cargo.toml
@@ -0,0 +1,29 @@
+[package]
+name = "pecos-eeg"
+version.workspace = true
+edition.workspace = true
+authors.workspace = true
+homepage.workspace = true
+repository.workspace = true
+license.workspace = true
+keywords.workspace = true
+categories.workspace = true
+description = "EEG-based coherent noise analysis and DEM generation"
+publish = false
+
+[lib]
+crate-type = ["rlib"]
+
+[dependencies]
+pecos-core.workspace = true
+pecos-qec.workspace = true
+pecos-quantum.workspace = true
+pecos-random.workspace = true
+pecos-simulators.workspace = true
+serde_json.workspace = true
+rayon.workspace = true
+smallvec.workspace = true
+thiserror.workspace = true
+
+[lints]
+workspace = true
diff --git a/exp/pecos-eeg/examples/profile_heisenberg.rs b/exp/pecos-eeg/examples/profile_heisenberg.rs
new file mode 100644
index 000000000..2f5d95bcd
--- /dev/null
+++ b/exp/pecos-eeg/examples/profile_heisenberg.rs
@@ -0,0 +1,101 @@
+//! Profile the Heisenberg DEM build.
+//! Usage: cargo run -p pecos-eeg --example `profile_heisenberg` --profile profiling
+//! Perf:  perf record -g -F 4999 -- `target/profiling/examples/profile_heisenberg`
+
+use pecos_core::gate_type::GateType;
+use pecos_core::pauli::pauli_bitmask::BitmaskStorage;
+use pecos_core::{Gate, GateAngles, GateParams, QubitId};
+use pecos_eeg::Bm;
+use std::time::Instant;
+
+fn gate(gt: GateType, qubits: &[usize]) -> Gate {
+    Gate {
+        gate_type: gt,
+        qubits: qubits.iter().map(|&q| QubitId(q)).collect(),
+        angles: GateAngles::new(),
+        params: GateParams::new(),
+        meas_ids: pecos_core::GateMeasIds::new(),
+        channel: None,
+    }
+}
+
+/// Build a single weight-4 X-check plaquette with 4 data + 1 ancilla, N rounds.
+/// This is the hotspot structure in surface codes.
+fn build_weight4_circuit(num_rounds: usize) -> Vec<Gate> {
+    // Data: 0,1,2,3. Ancilla: 4.
+    let mut gates = Vec::new();
+    for q in 0..5 {
+        gates.push(gate(GateType::PZ, &[q]));
+    }
+    for round in 0..num_rounds {
+        gates.push(gate(GateType::H, &[4]));
+        gates.push(gate(GateType::CX, &[4, 0]));
+        gates.push(gate(GateType::CX, &[4, 1]));
+        gates.push(gate(GateType::CX, &[4, 2]));
+        gates.push(gate(GateType::CX, &[4, 3]));
+        gates.push(gate(GateType::H, &[4]));
+        gates.push(gate(GateType::MZ, &[4]));
+        if round < num_rounds - 1 {
+            gates.push(gate(GateType::PZ, &[4]));
+        }
+    }
+    for q in 0..4 {
+        gates.push(gate(GateType::MZ, &[q]));
+    }
+    gates
+}
+
+fn main() {
+    let num_rounds = 8;
+    let gates = build_weight4_circuit(num_rounds);
+    let noise = pecos_eeg::noise::UniformNoise::coherent_only(0.05);
+    let expanded = pecos_eeg::expand::expand_circuit(&gates);
+    let na = 1; // one ancilla
+
+    let mut detectors = Vec::new();
+    for round in 0..(num_rounds - 1) {
+        let m1 = round * na;
+        let m2 = (round + 1) * na;
+        let mut det = Bm::default();
+        det.z_bits.set_bit(expanded.measurement_qubit[m1]);
+        det.z_bits.set_bit(expanded.measurement_qubit[m2]);
+        detectors.push(det);
+    }
+
+    let init_gates: Vec<Gate> = (0..5)
+        .map(|q| pecos_eeg::expand::make_gate(GateType::PZ, &[q]))
+        .collect();
+    let stab =
+        pecos_eeg::stabilizer::StabilizerGroup::from_circuit(&init_gates, expanded.num_qubits);
+
+    eprintln!(
+        "Weight-4 X-check, {num_rounds} rounds, {} expanded qubits, {} detectors",
+        expanded.num_qubits,
+        detectors.len()
+    );
+
+    // Run 20 iterations to get enough samples for perf
+    let iters = 20;
+    let t = Instant::now();
+    for _ in 0..iters {
+        for det in &detectors {
+            let _p = pecos_eeg::heisenberg::heisenberg_detection_probability(
+                &expanded.gates,
+                det,
+                &noise,
+                &stab,
+                0.0,
+            );
+        }
+    }
+    let total = t.elapsed();
+    let calls = u32::try_from(detectors.len() * iters).expect("profile call count fits in u32");
+    let per_det = total.as_secs_f64() * 1000.0 / f64::from(calls);
+    eprintln!(
+        "{iters} iterations x {} dets = {} calls in {:.2}s ({:.2}ms/det)",
+        detectors.len(),
+        detectors.len() * iters,
+        total.as_secs_f64(),
+        per_det
+    );
+}
diff --git a/exp/pecos-eeg/src/builder.rs b/exp/pecos-eeg/src/builder.rs
new file mode 100644
index 000000000..4eaa9cad6
--- /dev/null
+++ b/exp/pecos-eeg/src/builder.rs
@@ -0,0 +1,407 @@
+// Copyright 2026 The PECOS Developers
+//
+// Licensed under the Apache License, Version 2.0
+
+//! EEG DEM builder: TickCircuit + noise → DEM events.
+
+use crate::Bm;
+use crate::circuit::{self, NoiseModel};
+use crate::dem_mapping::{self, DemEntry, Detector, Observable};
+use crate::expand;
+use crate::stabilizer::StabilizerGroup;
+use pecos_core::pauli::pauli_bitmask::BitmaskStorage;
+use pecos_quantum::{AnnotationKind, TickCircuit};
+
+pub struct EegDemBuilder<'a> {
+    tc: &'a TickCircuit,
+    noise: NoiseModel,
+    config: dem_mapping::EegConfig,
+}
+
+impl<'a> EegDemBuilder<'a> {
+    #[must_use]
+    pub fn from_tick_circuit(tc: &'a TickCircuit) -> Self {
+        Self {
+            tc,
+            noise: NoiseModel::coherent_only(0.0),
+            config: dem_mapping::EegConfig::default(),
+        }
+    }
+
+    #[must_use]
+    pub fn noise(mut self, noise: NoiseModel) -> Self {
+        self.noise = noise;
+        self
+    }
+
+    /// Set the full EEG configuration.
+    #[must_use]
+    pub fn config(mut self, config: dem_mapping::EegConfig) -> Self {
+        self.config = config;
+        self
+    }
+
+    /// Use the exact sin^2(h) formula instead of leading-order h^2.
+    #[must_use]
+    pub fn exact_h_formula(mut self) -> Self {
+        self.config.h_formula = dem_mapping::HFormula::SinSquared;
+        self
+    }
+
+    /// Use second-order BCH (includes [H,H] commutator corrections).
+    #[must_use]
+    pub fn bch_order_2(mut self) -> Self {
+        self.config.bch_order = dem_mapping::BchOrder::Second;
+        self
+    }
+
+    #[must_use]
+    pub fn build(&self) -> Vec<DemEntry> {
+        let gates: Vec<pecos_core::Gate> = self
+            .tc
+            .iter_gate_batches()
+            .map(|batch| batch.as_gate().clone())
+            .collect();
+        let expanded = expand::expand_circuit(&gates);
+        let result = circuit::analyze_expanded(&expanded.gates, &self.noise);
+        let (detectors, observables) = build_detectors(self.tc, &expanded);
+
+        // Compute stabilizer group from the EXPANDED circuit (pre-readout).
+        // This includes auxiliary qubits, so beta function checks happen
+        // directly in the expanded frame without lossy frame mapping.
+        // Exclude the final deferred MZ(aux) gates at the end.
+        let expanded_pre_readout = exclude_final_mz(&expanded.gates);
+        let stab_group = StabilizerGroup::from_circuit(&expanded_pre_readout, expanded.num_qubits);
+
+        dem_mapping::build_dem_configured(
+            &result.generators,
+            &detectors,
+            &observables,
+            Some(&stab_group),
+            &self.config,
+        )
+    }
+
+    #[must_use]
+    pub fn build_dem_string(&self) -> String {
+        dem_mapping::format_dem(&self.build())
+    }
+
+    #[must_use]
+    pub fn summary(&self) -> EegSummary {
+        let gates: Vec<pecos_core::Gate> = self
+            .tc
+            .iter_gate_batches()
+            .map(|batch| batch.as_gate().clone())
+            .collect();
+        let expanded = expand::expand_circuit(&gates);
+        let result = circuit::analyze_expanded(&expanded.gates, &self.noise);
+        let (detectors, observables) = build_detectors(self.tc, &expanded);
+
+        let expanded_pre = exclude_final_mz(&expanded.gates);
+        let stab_group = StabilizerGroup::from_circuit(&expanded_pre, expanded.num_qubits);
+        let entries = dem_mapping::build_dem_configured(
+            &result.generators,
+            &detectors,
+            &observables,
+            Some(&stab_group),
+            &self.config,
+        );
+
+        let h_count = result
+            .generators
+            .iter()
+            .filter(|g| g.eeg_type == crate::eeg::EegType::H)
+            .count();
+        let s_count = result
+            .generators
+            .iter()
+            .filter(|g| g.eeg_type == crate::eeg::EegType::S)
+            .count();
+
+        EegSummary {
+            num_original_gates: gates.len(),
+            num_expanded_gates: expanded.gates.len(),
+            num_expanded_qubits: expanded.num_qubits,
+            num_h_generators: h_count,
+            num_s_generators: s_count,
+            num_detectors: detectors.len(),
+            num_observables: observables.len(),
+            num_dem_events: entries.len(),
+            generator_fidelity: result.generator_fidelity(),
+        }
+    }
+}
+
+#[derive(Clone, Debug)]
+pub struct EegSummary {
+    pub num_original_gates: usize,
+    pub num_expanded_gates: usize,
+    pub num_expanded_qubits: usize,
+    pub num_h_generators: usize,
+    pub num_s_generators: usize,
+    pub num_detectors: usize,
+    pub num_observables: usize,
+    pub num_dem_events: usize,
+    /// Generator fidelity: ε_gen = Σ h_P² + Σ |s_P|. DEM error scales as ε_gen^{1.5}.
+    pub generator_fidelity: f64,
+}
+
+/// Strip all trailing MZ gates from the expanded circuit.
+///
+/// The expanded circuit ends with deferred MZ(aux) gates. Stripping them
+/// gives the pre-readout expanded state for stabilizer group computation.
+fn exclude_final_mz(gates: &[pecos_core::Gate]) -> Vec<pecos_core::Gate> {
+    let last_non_mz = gates
+        .iter()
+        .rposition(|g| g.gate_type != pecos_core::gate_type::GateType::MZ);
+    match last_non_mz {
+        Some(idx) => gates[..=idx].to_vec(),
+        None => Vec::new(),
+    }
+}
+
+/// Build detectors for the expanded circuit from TickCircuit annotations.
+///
+/// Each detector is defined by measurement records (negative indices from
+/// the end of the measurement sequence). In the expanded circuit, each
+/// measurement record k maps to a Z-measurement on auxiliary qubit
+/// `expanded.measurement_qubit[k]`.
+///
+/// The detector stabilizer in the expanded circuit is:
+///   Z_{aux_r1} * Z_{aux_r2} * ...
+/// where aux_ri = expanded.measurement_qubit[abs_index(ri)]
+fn build_detectors(
+    tc: &TickCircuit,
+    expanded: &expand::ExpandedCircuit,
+) -> (Vec<Detector>, Vec<Observable>) {
+    let mut detectors = Vec::new();
+    let mut observables = Vec::new();
+    let num_meas = expanded.measurement_qubit.len();
+
+    for annotation in tc.annotations() {
+        match &annotation.kind {
+            AnnotationKind::Detector {
+                measurement_nodes, ..
+            } => {
+                // measurement_nodes are gate indices in the ORIGINAL circuit.
+                // We need to map these to measurement record indices, then
+                // to auxiliary qubits in the expanded circuit.
+                //
+                // The gate indices correspond to MZ gates. Each MZ gate can
+                // measure multiple qubits. We need to find which measurement
+                // record each gate index maps to.
+                //
+                // Strategy: the k-th measurement record corresponds to the
+                // k-th qubit measured across all MZ gates in order. Each
+                // measurement_node is a gate index — we find which measurement
+                // records that gate produced.
+                let bitmask =
+                    measurement_nodes_to_aux_bitmask(measurement_nodes, tc, expanded, num_meas);
+                detectors.push(Detector {
+                    id: detectors.len(),
+                    stabilizer: bitmask,
+                });
+            }
+            AnnotationKind::Observable {
+                measurement_nodes, ..
+            } => {
+                let bitmask =
+                    measurement_nodes_to_aux_bitmask(measurement_nodes, tc, expanded, num_meas);
+                observables.push(Observable {
+                    id: observables.len(),
+                    pauli: bitmask,
+                });
+            }
+            AnnotationKind::TrackedPauli => {}
+        }
+    }
+
+    (detectors, observables)
+}
+
+/// Map measurement record indices to a Z bitmask on auxiliary qubits.
+///
+/// Each measurement_node is a measurement record index (counting all
+/// MZ qubits in circuit order). Maps directly to an auxiliary qubit
+/// in the expanded circuit via `expanded.measurement_qubit[record]`.
+fn measurement_nodes_to_aux_bitmask(
+    measurement_nodes: &[usize],
+    _tc: &TickCircuit,
+    expanded: &expand::ExpandedCircuit,
+    num_meas: usize,
+) -> Bm {
+    let mut bitmask = Bm::default();
+
+    for &record_idx in measurement_nodes {
+        if record_idx < num_meas {
+            let aux_qubit = expanded.measurement_qubit[record_idx];
+            bitmask.z_bits.xor_bit(aux_qubit);
+        }
+    }
+
+    bitmask
+}
+
+#[cfg(test)]
+mod tests {
+    use super::*;
+
+    #[test]
+    fn test_empty_no_noise() {
+        let mut tc = TickCircuit::new();
+        tc.tick().pz(&[0]);
+        tc.tick().mz(&[0]);
+        let entries = EegDemBuilder::from_tick_circuit(&tc)
+            .noise(NoiseModel::coherent_only(0.0))
+            .build();
+        assert!(entries.is_empty());
+    }
+
+    #[test]
+    fn test_summary_coherent() {
+        let mut tc = TickCircuit::new();
+        tc.tick().pz(&[0, 1]);
+        tc.tick().h(&[0]);
+        tc.tick().cx(&[(0, 1)]);
+        tc.tick().mz(&[0, 1]);
+        let summary = EegDemBuilder::from_tick_circuit(&tc)
+            .noise(NoiseModel::coherent_only(0.1))
+            .summary();
+        assert!(summary.num_h_generators > 0);
+        assert_eq!(summary.num_s_generators, 0);
+    }
+
+    #[test]
+    fn test_builder_matches_manual_pipeline() {
+        // Same circuit through builder and manual pipeline should give same DEM
+        let mut tc = TickCircuit::new();
+        tc.tick().pz(&[0, 1]);
+        tc.tick().h(&[0]);
+        tc.tick().cx(&[(0, 1)]);
+        tc.tick().mz(&[0, 1]);
+
+        let noise = NoiseModel::coherent_only(0.05);
+
+        // Builder path
+        let builder_entries = EegDemBuilder::from_tick_circuit(&tc)
+            .noise(noise.clone())
+            .build();
+
+        // Manual path
+        let gates: Vec<pecos_core::Gate> = tc
+            .iter_gate_batches()
+            .map(|batch| batch.as_gate().clone())
+            .collect();
+        let expanded = expand::expand_circuit(&gates);
+        let result = circuit::analyze_expanded(&expanded.gates, &noise);
+
+        let expanded_pre = exclude_final_mz(&expanded.gates);
+        let stab_group = StabilizerGroup::from_circuit(&expanded_pre, expanded.num_qubits);
+
+        let (detectors, observables) = build_detectors(&tc, &expanded);
+        let manual_entries = dem_mapping::build_dem_with_stabilizers(
+            &result.generators,
+            &detectors,
+            &observables,
+            Some(&stab_group),
+        );
+
+        // Same number of entries
+        assert_eq!(
+            builder_entries.len(),
+            manual_entries.len(),
+            "Builder and manual should produce same number of DEM entries"
+        );
+
+        // Same probabilities (order may differ, so sort)
+        let mut bp: Vec<f64> = builder_entries.iter().map(|e| e.probability).collect();
+        let mut mp: Vec<f64> = manual_entries.iter().map(|e| e.probability).collect();
+        bp.sort_by(|a, b| a.partial_cmp(b).unwrap());
+        mp.sort_by(|a, b| a.partial_cmp(b).unwrap());
+        for (b, m) in bp.iter().zip(mp.iter()) {
+            assert!(
+                (b - m).abs() < 1e-15,
+                "Probability mismatch: builder={b}, manual={m}"
+            );
+        }
+    }
+
+    #[test]
+    fn test_no_annotations_empty_dem() {
+        // Without detector/observable annotations, builder should produce empty DEM
+        let mut tc = TickCircuit::new();
+        tc.tick().pz(&[0, 1]);
+        tc.tick().cx(&[(0, 1)]);
+        tc.tick().mz(&[0, 1]);
+
+        let entries = EegDemBuilder::from_tick_circuit(&tc)
+            .noise(NoiseModel::depolarizing(0.01))
+            .build();
+
+        assert!(
+            entries.is_empty(),
+            "No annotations → no detectors → no DEM entries"
+        );
+    }
+
+    #[test]
+    fn test_with_detector_annotations() {
+        // Build a circuit with detector annotations
+        let mut tc = TickCircuit::new();
+        tc.tick().pz(&[0, 1, 2]);
+
+        // Round 1: syndrome extraction
+        tc.tick().cx(&[(0, 2)]);
+        tc.tick().cx(&[(1, 2)]);
+        let m1 = tc.tick().mz(&[2]);
+
+        // Round 2: syndrome extraction
+        tc.tick().pz(&[2]);
+        tc.tick().cx(&[(0, 2)]);
+        tc.tick().cx(&[(1, 2)]);
+        let m2 = tc.tick().mz(&[2]);
+
+        // Detector: compare m1 and m2
+        tc.detector(&[m1[0], m2[0]]);
+
+        // Final readout
+        tc.tick().mz(&[0, 1]);
+
+        let entries = EegDemBuilder::from_tick_circuit(&tc)
+            .noise(NoiseModel::depolarizing(0.01))
+            .build();
+
+        assert!(
+            !entries.is_empty(),
+            "Circuit with detector annotation should produce DEM entries"
+        );
+        for e in &entries {
+            assert!(e.probability > 0.0);
+            assert!(e.probability < 0.5);
+        }
+    }
+
+    #[test]
+    fn test_summary_counts() {
+        let mut tc = TickCircuit::new();
+        tc.tick().pz(&[0, 1, 2]);
+        tc.tick().cx(&[(0, 1)]);
+        tc.tick().cx(&[(1, 2)]);
+        tc.tick().mz(&[0, 1, 2]);
+
+        let summary = EegDemBuilder::from_tick_circuit(&tc)
+            .noise(NoiseModel::depolarizing(0.01).with_idle_rz(0.05))
+            .summary();
+
+        assert!(
+            summary.num_h_generators > 0,
+            "Should have H generators from idle RZ"
+        );
+        assert!(
+            summary.num_s_generators > 0,
+            "Should have S generators from depolarizing"
+        );
+        assert_eq!(summary.num_expanded_qubits, 6, "3 original + 3 aux");
+    }
+}
diff --git a/exp/pecos-eeg/src/circuit.rs b/exp/pecos-eeg/src/circuit.rs
new file mode 100644
index 000000000..fbc4fda73
--- /dev/null
+++ b/exp/pecos-eeg/src/circuit.rs
@@ -0,0 +1,717 @@
+// Copyright 2026 The PECOS Developers
+//
+// Licensed under the Apache License, Version 2.0
+
+//! EEG circuit analysis on the expanded (measurement-deferred) circuit.
+//!
+//! After expansion, the circuit is purely Clifford. Error generators are
+//! propagated straight to the end via Clifford conjugation (no measurement
+//! absorption). At the end, each Pauli P flips measurement k iff P has
+//! X on measurement_qubit[k].
+
+use crate::Bm;
+use crate::eeg::EegType;
+use pecos_core::Gate;
+use pecos_core::gate_type::GateType;
+use pecos_core::pauli::pauli_bitmask::{
+    BitmaskStorage, Conjugated, conjugate_cx, conjugate_cy, conjugate_cz, conjugate_h,
+    conjugate_swap, conjugate_sx, conjugate_sxdg, conjugate_sy, conjugate_sydg, conjugate_sz,
+    conjugate_szdg, conjugate_x, conjugate_y, conjugate_z,
+};
+
+/// Noise model parameters.
+#[derive(Clone, Debug)]
+pub struct NoiseModel {
+    /// Coherent RZ angle (radians) on both qubits after each 2-qubit gate.
+    pub idle_rz: f64,
+    /// Single-qubit depolarizing probability.
+    pub p1: f64,
+    /// Two-qubit depolarizing probability.
+    pub p2: f64,
+    /// Measurement bit-flip probability.
+    pub p_meas: f64,
+    /// Preparation error probability.
+    pub p_prep: f64,
+}
+
+impl NoiseModel {
+    #[must_use]
+    pub fn coherent_only(idle_rz: f64) -> Self {
+        Self {
+            idle_rz,
+            p1: 0.0,
+            p2: 0.0,
+            p_meas: 0.0,
+            p_prep: 0.0,
+        }
+    }
+
+    #[must_use]
+    pub fn depolarizing(p: f64) -> Self {
+        Self {
+            idle_rz: 0.0,
+            p1: p,
+            p2: p,
+            p_meas: p,
+            p_prep: p,
+        }
+    }
+
+    #[must_use]
+    pub fn with_idle_rz(mut self, angle: f64) -> Self {
+        self.idle_rz = angle;
+        self
+    }
+}
+
+/// Identifies the physical noise source that produced a generator.
+#[derive(Clone, Debug, PartialEq, Eq, Hash)]
+pub struct NoiseSource {
+    /// Index of the gate in the expanded circuit that the noise follows.
+    pub gate_index: usize,
+    /// Qubit the noise acts on (for per-qubit noise like idle RZ).
+    pub qubit: usize,
+}
+
+/// A propagated EEG generator at the end of the expanded circuit.
+#[derive(Clone, Debug)]
+pub struct PropagatedEeg {
+    /// EEG type (H, S, C, or A).
+    pub eeg_type: EegType,
+    /// Primary Pauli label at end of circuit.
+    pub label: Bm,
+    /// Second Pauli label for C and A types (None for H and S).
+    pub label2: Option<Bm>,
+    /// Coefficient (rate). For H: includes sign from conjugation. For S: always negative.
+    pub coeff: f64,
+    /// Physical noise source that produced this generator (for sensitivity analysis).
+    pub source: Option<NoiseSource>,
+}
+
+/// Result of EEG analysis on the expanded circuit.
+#[derive(Clone, Debug)]
+pub struct EegAnalysisResult {
+    /// All propagated generators at end of circuit.
+    pub generators: Vec<PropagatedEeg>,
+    /// Number of measurement records.
+    pub num_measurements: usize,
+}
+
+impl EegAnalysisResult {
+    /// Generator fidelity ε_gen = Σ h_P² + Σ |s_P| (Hines Eq. 2/Eq. 6).
+    ///
+    /// Measures the total "size" of the error. The DEM prediction error
+    /// (TVD) scales as ε_gen^{1.5}.
+    #[must_use]
+    pub fn generator_fidelity(&self) -> f64 {
+        let mut eps = 0.0;
+        for g in &self.generators {
+            match g.eeg_type {
+                EegType::H => eps += g.coeff * g.coeff,
+                EegType::S => eps += g.coeff.abs(),
+                _ => {}
+            }
+        }
+        eps
+    }
+}
+
+/// Analyze the expanded circuit with a flexible noise specification.
+///
+/// For each gate, calls `noise.noise_after_gate()` to get generators,
+/// then propagates them to the end via Clifford conjugation.
+///
+/// Expansion gates (QAlloc, expansion CX, expansion PZ) are skipped
+/// for noise injection.
+pub fn analyze_with_noise(
+    gates: &[Gate],
+    noise: &dyn crate::noise::NoiseSpec,
+) -> EegAnalysisResult {
+    let mut generators = Vec::new();
+    let mut num_measurements = 0;
+
+    // Build sets of expansion gate indices
+    let mut expansion_cx_indices = std::collections::HashSet::new();
+    let mut expansion_pz_indices = std::collections::HashSet::new();
+    for i in 1..gates.len() {
+        if gates[i].gate_type == GateType::CX && gates[i - 1].gate_type == GateType::QAlloc {
+            let alloc_q = gates[i - 1].qubits[0].index();
+            if gates[i].qubits.len() >= 2 && gates[i].qubits[1].index() == alloc_q {
+                expansion_cx_indices.insert(i);
+                if i + 1 < gates.len() && gates[i + 1].gate_type == GateType::PZ {
+                    let cx_control = gates[i].qubits[0].index();
+                    if gates[i + 1].qubits.len() == 1
+                        && gates[i + 1].qubits[0].index() == cx_control
+                    {
+                        expansion_pz_indices.insert(i + 1);
+                    }
+                }
+            }
+        }
+    }
+
+    for (i, gate) in gates.iter().enumerate() {
+        let remaining = &gates[i + 1..];
+        let qubits: Vec<usize> = gate.qubits.iter().map(pecos_core::QubitId::index).collect();
+
+        // Skip expansion gates (virtual, not physical)
+        let is_expansion = expansion_cx_indices.contains(&i)
+            || expansion_pz_indices.contains(&i)
+            || gate.gate_type == GateType::QAlloc;
+
+        if !is_expansion {
+            // Get noise generators from the noise specification
+            let injections = noise.noise_after_gate(i, gate.gate_type, &qubits);
+
+            for inj in injections {
+                match inj.eeg_type {
+                    EegType::H => {
+                        let (pl, coeff) = propagate_h(inj.label, inj.rate, remaining);
+                        generators.push(PropagatedEeg {
+                            eeg_type: EegType::H,
+                            label: pl,
+                            label2: None,
+                            coeff,
+                            source: Some(NoiseSource {
+                                gate_index: i,
+                                qubit: qubits.first().copied().unwrap_or(0),
+                            }),
+                        });
+                    }
+                    EegType::S => {
+                        let (pl, _) = propagate_s(inj.label, remaining);
+                        generators.push(PropagatedEeg {
+                            eeg_type: EegType::S,
+                            label: pl,
+                            label2: None,
+                            coeff: inj.rate,
+                            source: None,
+                        });
+                    }
+                    EegType::C | EegType::A => {
+                        if let Some(label2) = inj.label2 {
+                            let (l1, l2, coeff) =
+                                propagate_ca(inj.label, label2, inj.rate, remaining);
+                            generators.push(PropagatedEeg {
+                                eeg_type: inj.eeg_type,
+                                label: l1,
+                                label2: Some(l2),
+                                coeff,
+                                source: None,
+                            });
+                        }
+                    }
+                }
+            }
+        }
+
+        // Handle explicit RZ gates (from the circuit, not noise model)
+        if gate.gate_type == GateType::RZ
+            && let Some(&angle) = gate.angles.first()
+        {
+            for &q in &qubits {
+                let label = Bm::z(q);
+                let (pl, coeff) = propagate_h(label, angle.to_radians() / 2.0, remaining);
+                generators.push(PropagatedEeg {
+                    eeg_type: EegType::H,
+                    label: pl,
+                    label2: None,
+                    coeff,
+                    source: Some(NoiseSource {
+                        gate_index: i,
+                        qubit: q,
+                    }),
+                });
+            }
+        }
+
+        // Count measurements
+        if gate.gate_type == GateType::MZ {
+            num_measurements += qubits.len();
+        }
+    }
+
+    EegAnalysisResult {
+        generators,
+        num_measurements,
+    }
+}
+
+/// Analyze the expanded circuit with the legacy NoiseModel.
+///
+/// Delegates to `analyze_with_noise` using a `UniformNoise` specification.
+#[must_use]
+pub fn analyze_expanded(gates: &[Gate], noise: &NoiseModel) -> EegAnalysisResult {
+    let uniform = crate::noise::UniformNoise {
+        idle_rz: noise.idle_rz,
+        p1: noise.p1,
+        p2: noise.p2,
+        p_meas: noise.p_meas,
+        p_prep: noise.p_prep,
+    };
+    analyze_with_noise(gates, &uniform)
+}
+
+/// Propagate H_P forward: sign changes under Clifford conjugation.
+/// PZ/QAlloc clears all Pauli components on the reset qubit.
+fn propagate_h(mut label: Bm, mut coeff: f64, remaining: &[Gate]) -> (Bm, f64) {
+    for gate in remaining {
+        match gate.gate_type {
+            GateType::PZ | GateType::QAlloc => {
+                // Reset removes any error on this qubit
+                for q in &gate.qubits {
+                    label.x_bits.clear_bit(q.index());
+                    label.z_bits.clear_bit(q.index());
+                }
+            }
+            _ => {
+                if let Some(r) = conjugate_by_gate(&label, gate) {
+                    label = r.label;
+                    if r.sign_negative {
+                        coeff = -coeff;
+                    }
+                }
+            }
+        }
+    }
+    (label, coeff)
+}
+
+/// Propagate C_{P,Q} or A_{P,Q} forward: both labels conjugate, signs multiply.
+/// gamma(C_{P,Q}, U) = s_{U,P} * s_{U,Q}. Same for A.
+/// PZ/QAlloc clears components on both labels.
+fn propagate_ca(
+    mut label1: Bm,
+    mut label2: Bm,
+    mut coeff: f64,
+    remaining: &[Gate],
+) -> (Bm, Bm, f64) {
+    for gate in remaining {
+        match gate.gate_type {
+            GateType::PZ | GateType::QAlloc => {
+                for q in &gate.qubits {
+                    label1.x_bits.clear_bit(q.index());
+                    label1.z_bits.clear_bit(q.index());
+                    label2.x_bits.clear_bit(q.index());
+                    label2.z_bits.clear_bit(q.index());
+                }
+            }
+            _ => {
+                let mut sign = false;
+                if let Some(r) = conjugate_by_gate(&label1, gate) {
+                    label1 = r.label;
+                    if r.sign_negative {
+                        sign = !sign;
+                    }
+                }
+                if let Some(r) = conjugate_by_gate(&label2, gate) {
+                    label2 = r.label;
+                    if r.sign_negative {
+                        sign = !sign;
+                    }
+                }
+                if sign {
+                    coeff = -coeff;
+                }
+            }
+        }
+    }
+    (label1, label2, coeff)
+}
+
+/// Propagate S_P forward: no sign change (gamma(S_P, U) = 1 always).
+/// PZ/QAlloc clears all Pauli components on the reset qubit.
+fn propagate_s(mut label: Bm, remaining: &[Gate]) -> (Bm, f64) {
+    for gate in remaining {
+        match gate.gate_type {
+            GateType::PZ | GateType::QAlloc => {
+                for q in &gate.qubits {
+                    label.x_bits.clear_bit(q.index());
+                    label.z_bits.clear_bit(q.index());
+                }
+            }
+            _ => {
+                if let Some(r) = conjugate_by_gate(&label, gate) {
+                    label = r.label;
+                }
+            }
+        }
+    }
+    (label, 0.0)
+}
+
+fn conjugate_by_gate(label: &Bm, gate: &Gate) -> Option<Conjugated<smallvec::SmallVec<[u64; 8]>>> {
+    if gate.qubits.is_empty() {
+        return None;
+    }
+    let q0 = || gate.qubits[0].index();
+    let q1 = || gate.qubits[1].index();
+    match gate.gate_type {
+        GateType::H => Some(conjugate_h(label, q0())),
+        GateType::SZ => Some(conjugate_sz(label, q0())),
+        GateType::SZdg => Some(conjugate_szdg(label, q0())),
+        GateType::SX => Some(conjugate_sx(label, q0())),
+        GateType::SXdg => Some(conjugate_sxdg(label, q0())),
+        GateType::SY => Some(conjugate_sy(label, q0())),
+        GateType::SYdg => Some(conjugate_sydg(label, q0())),
+        GateType::X => Some(conjugate_x(label, q0())),
+        GateType::Y => Some(conjugate_y(label, q0())),
+        GateType::Z => Some(conjugate_z(label, q0())),
+        GateType::CX => Some(conjugate_cx(label, q0(), q1())),
+        GateType::CY => Some(conjugate_cy(label, q0(), q1())),
+        GateType::CZ => Some(conjugate_cz(label, q0(), q1())),
+        GateType::SWAP => Some(conjugate_swap(label, q0(), q1())),
+        _ => None,
+    }
+}
+
+#[cfg(test)]
+mod tests {
+    use super::*;
+    use pecos_core::{GateAngles, GateParams, QubitId};
+
+    fn gate(gt: GateType, qubits: &[usize]) -> Gate {
+        Gate {
+            gate_type: gt,
+            qubits: qubits.iter().map(|&q| QubitId(q)).collect(),
+            angles: GateAngles::new(),
+            params: GateParams::new(),
+            meas_ids: pecos_core::GateMeasIds::new(),
+            channel: None,
+        }
+    }
+
+    #[test]
+    fn test_rz_rate_is_half_theta() {
+        // Idle RZ(0.1) after CX: rate should be 0.05 (theta/2)
+        // because RZ(theta) = exp(-i*theta*Z/2) → H_Z with rate theta/2
+        let gates = vec![gate(GateType::CX, &[0, 1])];
+        let noise = NoiseModel::coherent_only(0.1);
+        let result = analyze_expanded(&gates, &noise);
+
+        let h_gens: Vec<_> = result
+            .generators
+            .iter()
+            .filter(|g| g.eeg_type == EegType::H)
+            .collect();
+        assert_eq!(h_gens.len(), 2);
+        for g in &h_gens {
+            assert!(
+                (g.coeff.abs() - 0.05).abs() < 1e-10,
+                "Rate should be 0.05 (theta/2), got {}",
+                g.coeff
+            );
+        }
+    }
+
+    #[test]
+    fn test_h_propagation_through_hadamard() {
+        // H_Z after H gate: Z → X, sign positive
+        let gates = vec![gate(GateType::CX, &[0, 1]), gate(GateType::H, &[0])];
+        let noise = NoiseModel::coherent_only(0.1);
+        let result = analyze_expanded(&gates, &noise);
+
+        let q0_gen = result
+            .generators
+            .iter()
+            .find(|g| g.eeg_type == EegType::H && g.label.has_x(0))
+            .expect("Should have H_X on qubit 0");
+        assert!(
+            (q0_gen.coeff - 0.05).abs() < 1e-10,
+            "H: Z→X, rate=theta/2=0.05"
+        );
+    }
+
+    #[test]
+    fn test_sx_propagation() {
+        // SX on qubit 1 after CX: Z1 → -Y1 (sign flip)
+        let gates = vec![gate(GateType::CX, &[0, 1]), gate(GateType::SX, &[1])];
+        let noise = NoiseModel::coherent_only(0.1);
+        let result = analyze_expanded(&gates, &noise);
+
+        // H_Z(1) propagated through SX(1): Z→-Y, coeff flips sign
+        let q1_gen = result
+            .generators
+            .iter()
+            .find(|g| g.eeg_type == EegType::H && g.label.has_x(1) && g.label.has_z(1))
+            .expect("Should have H_Y on qubit 1 after SX");
+        assert!(
+            (q1_gen.coeff + 0.05).abs() < 1e-10,
+            "SX: Z→-Y, sign flips: expected -0.05, got {}",
+            q1_gen.coeff
+        );
+
+        // H_Z(0) should be unaffected by SX on qubit 1
+        let q0_gen = result
+            .generators
+            .iter()
+            .find(|g| g.eeg_type == EegType::H && g.label == Bm::z(0))
+            .expect("Should still have H_Z on qubit 0");
+        assert!((q0_gen.coeff - 0.05).abs() < 1e-10);
+    }
+
+    #[test]
+    fn test_cy_propagation() {
+        // CY after CX: Z on target propagates like CX (Z_t → Z_c Z_t)
+        let gates = vec![gate(GateType::CX, &[0, 1]), gate(GateType::CY, &[0, 1])];
+        let noise = NoiseModel::coherent_only(0.1);
+        let result = analyze_expanded(&gates, &noise);
+
+        // H_Z(1) from CX, propagated through CY: Z_t → Z_c Z_t
+        let zz_gen = result
+            .generators
+            .iter()
+            .find(|g| g.eeg_type == EegType::H && g.label == Bm::z(0).multiply(&Bm::z(1)))
+            .expect("Should have Z0Z1 after CY propagation of Z1");
+        assert!((zz_gen.coeff.abs() - 0.05).abs() < 1e-10);
+    }
+
+    #[test]
+    fn test_sy_propagation() {
+        // SY: X→-Z, Z→X. So H_Z through SY gives H_X with no sign flip
+        let gates = vec![gate(GateType::CX, &[0, 1]), gate(GateType::SY, &[1])];
+        let noise = NoiseModel::coherent_only(0.1);
+        let result = analyze_expanded(&gates, &noise);
+
+        // H_Z(1) through SY(1): Z→X, no sign flip
+        let q1_gen = result
+            .generators
+            .iter()
+            .find(|g| g.eeg_type == EegType::H && g.label == Bm::x(1))
+            .expect("Should have H_X on qubit 1 after SY");
+        assert!(
+            (q1_gen.coeff - 0.05).abs() < 1e-10,
+            "SY: Z→X, no sign: expected 0.05, got {}",
+            q1_gen.coeff
+        );
+    }
+
+    #[test]
+    fn test_pz_clears_propagated_errors() {
+        // Error injected before PZ should be cleared
+        let gates = vec![
+            gate(GateType::CX, &[0, 1]),
+            gate(GateType::PZ, &[1]), // Reset qubit 1
+        ];
+        let noise = NoiseModel::coherent_only(0.1);
+        let result = analyze_expanded(&gates, &noise);
+
+        // H_Z(1) should be cleared by PZ(1)
+        let q1_gens: Vec<_> = result
+            .generators
+            .iter()
+            .filter(|g| g.eeg_type == EegType::H && (g.label.has_x(1) || g.label.has_z(1)))
+            .collect();
+        assert!(
+            q1_gens.is_empty(),
+            "PZ should clear all error components on qubit 1"
+        );
+
+        // H_Z(0) should survive (PZ on qubit 1 doesn't touch qubit 0)
+        let q0_gen = result
+            .generators
+            .iter()
+            .find(|g| g.eeg_type == EegType::H && g.label == Bm::z(0));
+        assert!(q0_gen.is_some(), "H_Z(0) should survive PZ(1)");
+    }
+
+    #[test]
+    fn test_no_noise_no_generators() {
+        let gates = vec![gate(GateType::CX, &[0, 1]), gate(GateType::H, &[0])];
+        let noise = NoiseModel::coherent_only(0.0);
+        let result = analyze_expanded(&gates, &noise);
+        assert!(result.generators.is_empty());
+    }
+
+    #[test]
+    fn test_depol_1q_injects_three_paulis() {
+        // Single-qubit depolarizing on H gate produces S_X, S_Y, S_Z
+        let gates = vec![gate(GateType::H, &[0])];
+        let noise = NoiseModel {
+            idle_rz: 0.0,
+            p1: 0.03,
+            p2: 0.0,
+            p_meas: 0.0,
+            p_prep: 0.0,
+        };
+        let result = analyze_expanded(&gates, &noise);
+
+        let s_gens: Vec<_> = result
+            .generators
+            .iter()
+            .filter(|g| g.eeg_type == EegType::S)
+            .collect();
+        assert_eq!(
+            s_gens.len(),
+            3,
+            "1q depolarizing should inject 3 S generators"
+        );
+        for g in &s_gens {
+            assert!(
+                (g.coeff + 0.01).abs() < 1e-10,
+                "Rate should be -p/3 = -0.01"
+            );
+        }
+    }
+
+    #[test]
+    fn test_depol_2q_injects_fifteen_paulis() {
+        // Two-qubit depolarizing on CX: 15 S generators (3 single + 3 single + 9 tensor)
+        let gates = vec![gate(GateType::CX, &[0, 1])];
+        let noise = NoiseModel {
+            idle_rz: 0.0,
+            p1: 0.0,
+            p2: 0.15,
+            p_meas: 0.0,
+            p_prep: 0.0,
+        };
+        let result = analyze_expanded(&gates, &noise);
+
+        let s_gens: Vec<_> = result
+            .generators
+            .iter()
+            .filter(|g| g.eeg_type == EegType::S)
+            .collect();
+        assert_eq!(
+            s_gens.len(),
+            15,
+            "2q depolarizing should inject 15 S generators"
+        );
+        for g in &s_gens {
+            assert!(
+                (g.coeff + 0.01).abs() < 1e-10,
+                "Rate should be -p/15 = -0.01"
+            );
+        }
+    }
+
+    #[test]
+    fn test_meas_noise_injects_sx() {
+        // Measurement error produces S_X on the measured qubit
+        let gates = vec![gate(GateType::MZ, &[0])];
+        let noise = NoiseModel {
+            idle_rz: 0.0,
+            p1: 0.0,
+            p2: 0.0,
+            p_meas: 0.05,
+            p_prep: 0.0,
+        };
+        let result = analyze_expanded(&gates, &noise);
+
+        let s_gens: Vec<_> = result
+            .generators
+            .iter()
+            .filter(|g| g.eeg_type == EegType::S)
+            .collect();
+        assert_eq!(s_gens.len(), 1);
+        assert_eq!(s_gens[0].label, Bm::x(0));
+        assert!((s_gens[0].coeff + 0.05).abs() < 1e-10);
+    }
+
+    #[test]
+    fn test_prep_noise_injects_sx() {
+        // Preparation error: S_X after PZ
+        let gates = vec![gate(GateType::PZ, &[0])];
+        let noise = NoiseModel {
+            idle_rz: 0.0,
+            p1: 0.0,
+            p2: 0.0,
+            p_meas: 0.0,
+            p_prep: 0.03,
+        };
+        let result = analyze_expanded(&gates, &noise);
+
+        let s_gens: Vec<_> = result
+            .generators
+            .iter()
+            .filter(|g| g.eeg_type == EegType::S)
+            .collect();
+        assert_eq!(s_gens.len(), 1);
+        assert!((s_gens[0].coeff + 0.03).abs() < 1e-10);
+    }
+
+    #[test]
+    fn test_expansion_pz_gets_no_prep_noise() {
+        // Expansion PZ (measurement projection) should NOT inject prep noise.
+        // Circuit: PZ(0,1), H(1), CX(1,0), MZ(1), PZ(1), H(1), CX(1,0), MZ(1), MZ(0)
+        // With p_prep > 0: only the original PZ gates should inject noise.
+        let original_gates = vec![
+            gate(GateType::PZ, &[0]),
+            gate(GateType::PZ, &[1]),
+            gate(GateType::H, &[1]),
+            gate(GateType::CX, &[1, 0]),
+            gate(GateType::MZ, &[1]),
+            gate(GateType::PZ, &[1]), // original reset
+            gate(GateType::H, &[1]),
+            gate(GateType::CX, &[1, 0]),
+            gate(GateType::MZ, &[1]), // last round
+            gate(GateType::MZ, &[0]),
+        ];
+        let expanded = crate::expand::expand_circuit(&original_gates);
+
+        // Count PZ gates in expanded circuit (originals + expansion projections)
+        let all_pz: Vec<_> = expanded
+            .gates
+            .iter()
+            .filter(|g| g.gate_type == GateType::PZ)
+            .collect();
+
+        // With prep noise: count S generators from prep
+        let noise = NoiseModel {
+            idle_rz: 0.0,
+            p1: 0.0,
+            p2: 0.0,
+            p_meas: 0.0,
+            p_prep: 0.1,
+        };
+        let result = analyze_expanded(&expanded.gates, &noise);
+
+        let prep_gens: Vec<_> = result
+            .generators
+            .iter()
+            .filter(|g| g.eeg_type == EegType::S)
+            .collect();
+
+        // Original PZ gates: PZ(0) init, PZ(1) init, PZ(1) reset = 3 PZ with noise
+        // Expansion PZ: should NOT inject noise
+        // Each original PZ injects 1 S generator (S_X)
+        assert_eq!(
+            prep_gens.len(),
+            3,
+            "Only original PZ should inject prep noise, not expansion PZ. \
+             Got {} S generators, total PZ gates in expanded: {}",
+            prep_gens.len(),
+            all_pz.len()
+        );
+    }
+
+    #[test]
+    fn test_expansion_cx_gets_no_noise() {
+        // The CX gates added by expansion (deferred measurement) should not get noise.
+        // Circuit: PZ(0), CX(0,1), MZ(0), MZ(1)
+        // Expanded: PZ(0), CX(0,1), QAlloc(2), CX(0,2), QAlloc(3), CX(1,3), MZ(2), MZ(3)
+        // Only CX(0,1) should get noise, not CX(0,2) or CX(1,3).
+        let gates = vec![
+            gate(GateType::PZ, &[0]),
+            gate(GateType::PZ, &[1]),
+            gate(GateType::CX, &[0, 1]),
+            gate(GateType::MZ, &[0]),
+            gate(GateType::MZ, &[1]),
+        ];
+        let expanded = crate::expand::expand_circuit(&gates);
+        let noise = NoiseModel::coherent_only(0.1);
+        let result = analyze_expanded(&expanded.gates, &noise);
+
+        let h_gens: Vec<_> = result
+            .generators
+            .iter()
+            .filter(|g| g.eeg_type == EegType::H)
+            .collect();
+        // Only 2 H generators from the original CX (one per qubit)
+        assert_eq!(
+            h_gens.len(),
+            2,
+            "Only original CX should get noise, not expansion CX gates"
+        );
+    }
+}
diff --git a/exp/pecos-eeg/src/coherent_dem.rs b/exp/pecos-eeg/src/coherent_dem.rs
new file mode 100644
index 000000000..a3bf21ed5
--- /dev/null
+++ b/exp/pecos-eeg/src/coherent_dem.rs
@@ -0,0 +1,909 @@
+// Copyright 2026 The PECOS Developers
+//
+// Licensed under the Apache License, Version 2.0 (the "License"); you may not use this file except
+// in compliance with the License. You may obtain a copy of the License at
+//
+//     https://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software distributed under the License
+// is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express
+// or implied. See the License for the specific language governing permissions and limitations under
+// the License.
+
+//! Coherent DEM builder via backward Heisenberg mechanism extraction.
+//!
+//! Walks each noise source backward through the circuit to determine its
+//! effective Pauli label at each detector. Groups noise sources by their
+//! effective label (= same DEM mechanism), accumulates coherent amplitudes,
+//! and computes mechanism probabilities.
+//!
+//! For H-type (coherent) noise: amplitudes add, probability = sin²(total).
+//! For S-type (stochastic) noise: rates add, probability = (1-exp(2·total))/2.
+
+use crate::Bm;
+use crate::dem_mapping::{DecomposableDemEntry, DemEntry, DemEvent, Detector, Observable};
+use crate::eeg::EegType;
+use crate::heisenberg::{SparsePauli, sparse_conjugate};
+use crate::noise::NoiseSpec;
+use pecos_core::Gate;
+use pecos_core::pauli::pauli_bitmask::BitmaskStorage;
+use smallvec::SmallVec;
+use std::collections::BTreeMap;
+
+type FittedEventKey = (SmallVec<[usize; 4]>, SmallVec<[usize; 2]>);
+
+/// A noise contribution at a specific gate.
+struct NoiseContribution {
+    /// Effective Pauli label after backward propagation.
+    label: Bm,
+    /// EEG type (H or S).
+    eeg_type: EegType,
+    /// Amplitude or rate.
+    value: f64,
+}
+
+/// Build a coherent DEM by extracting mechanisms from backward propagation.
+///
+/// For each noise injection point in the expanded circuit, propagates
+/// its Pauli label backward to the detector measurement point. Noise
+/// sources that produce the same effective Pauli label are grouped into
+/// a single DEM mechanism with coherently accumulated amplitude.
+///
+/// This gives both correct mechanism structure AND correct coherent
+/// probabilities from a single framework.
+pub fn build_coherent_dem(
+    gates: &[Gate],
+    noise: &dyn NoiseSpec,
+    detectors: &[Detector],
+    observables: &[Observable],
+    expansion_gates: &[bool],
+) -> Vec<DemEntry> {
+    // Step 1: Collect all noise sources and their Pauli labels
+    let mut noise_sources: Vec<(usize, NoiseContribution)> = Vec::new();
+
+    for (gate_idx, gate) in gates.iter().enumerate() {
+        if gate_idx < expansion_gates.len() && expansion_gates[gate_idx] {
+            continue;
+        }
+        let qubits: SmallVec<[usize; 4]> =
+            gate.qubits.iter().map(pecos_core::QubitId::index).collect();
+        let injections = noise.noise_after_gate(gate_idx, gate.gate_type, &qubits);
+
+        for inj in injections {
+            noise_sources.push((
+                gate_idx,
+                NoiseContribution {
+                    label: inj.label.clone(),
+                    eeg_type: inj.eeg_type,
+                    value: inj.rate,
+                },
+            ));
+        }
+    }
+
+    // Step 2: For each noise source, determine which detectors it affects
+    // by checking if its Pauli label, after backward propagation through
+    // the circuit, anticommutes with each detector's stabilizer.
+    //
+    // Rather than propagating each noise label forward (expensive), we use
+    // the detectors' stabilizers propagated backward to each noise location.
+    // For each detector, we run the backward Heisenberg walk and at each
+    // noise source check anticommutation. If the backward-propagated
+    // stabilizer anticommutes with the noise label at that gate, the noise
+    // source affects that detector.
+    //
+    // We compute this per-detector, then group noise sources by which
+    // detectors they affect.
+
+    // For each noise source: which detectors and observables it flips
+    let num_noise = noise_sources.len();
+    let mut noise_det_sets: Vec<SmallVec<[usize; 4]>> = vec![SmallVec::new(); num_noise];
+    let mut noise_obs_sets: Vec<SmallVec<[usize; 2]>> = vec![SmallVec::new(); num_noise];
+
+    // Build gate_index -> noise_source_indices map (shared across all walks)
+    let mut gate_to_noise: BTreeMap<usize, Vec<usize>> = BTreeMap::new();
+    for (ns_idx, (gate_idx, _)) in noise_sources.iter().enumerate() {
+        gate_to_noise.entry(*gate_idx).or_default().push(ns_idx);
+    }
+
+    // Helper: propagate a stabilizer/observable backward and record
+    // which noise sources anticommute with it.
+    let backward_classify = |stabilizer: &Bm| -> Vec<bool> {
+        let mut prop = stabilizer.clone();
+        let mut hits = vec![false; num_noise];
+
+        for gate_idx in (0..gates.len()).rev() {
+            // Check noise sources BEFORE undoing the gate
+            if let Some(ns_indices) = gate_to_noise.get(&gate_idx) {
+                for &ns_idx in ns_indices {
+                    if !prop.commutes_with(&noise_sources[ns_idx].1.label) {
+                        hits[ns_idx] = true;
+                    }
+                }
+            }
+            backward_conjugate_bm(&mut prop, &gates[gate_idx]);
+        }
+
+        hits
+    };
+
+    // Classify: which detectors does each noise source flip?
+    for det in detectors {
+        let hits = backward_classify(&det.stabilizer);
+        for (ns_idx, &hit) in hits.iter().enumerate() {
+            if hit {
+                noise_det_sets[ns_idx].push(det.id);
+            }
+        }
+    }
+
+    // Classify: which observables does each noise source flip?
+    for obs in observables {
+        let hits = backward_classify(&obs.pauli);
+        for (ns_idx, &hit) in hits.iter().enumerate() {
+            if hit {
+                noise_obs_sets[ns_idx].push(obs.id);
+            }
+        }
+    }
+
+    // Step 3: Group noise sources by (detector_set, observable_set, eeg_type, label).
+    //
+    // For H-type: only noise sources with the SAME Pauli label accumulate
+    // coherently. Different labels (e.g., Z on qubit 1 vs Z on qubit 2)
+    // are separate mechanisms even if they flip the same detectors.
+    //
+    // For S-type: same grouping — different Pauli types at the same location
+    // are independent mechanisms.
+    //
+    // After coherent accumulation per label, mechanisms with the same
+    // detector set are combined independently (product formula).
+    let mut h_groups: BTreeMap<(DemEvent, Bm), f64> = BTreeMap::new();
+    let mut s_groups: BTreeMap<(DemEvent, Bm), f64> = BTreeMap::new();
+
+    for (ns_idx, (_, contrib)) in noise_sources.iter().enumerate() {
+        let dets = &noise_det_sets[ns_idx];
+        let obs = &noise_obs_sets[ns_idx];
+        if dets.is_empty() && obs.is_empty() {
+            continue;
+        }
+
+        let event = DemEvent {
+            detectors: dets.clone(),
+            observables: obs.clone(),
+        };
+
+        let key = (event, contrib.label.clone());
+        match contrib.eeg_type {
+            EegType::H => {
+                *h_groups.entry(key).or_insert(0.0) += contrib.value;
+            }
+            EegType::S => {
+                *s_groups.entry(key).or_insert(0.0) += contrib.value;
+            }
+            _ => {}
+        }
+    }
+
+    // Step 4: Compute approximate probabilities per mechanism
+    let mut entries = Vec::new();
+
+    for ((event, _label), total_h) in &h_groups {
+        let prob = total_h.sin().powi(2);
+        if prob > 1e-15 {
+            entries.push(DemEntry {
+                event: event.clone(),
+                probability: prob,
+            });
+        }
+    }
+
+    for ((event, _label), total_s) in &s_groups {
+        let prob = (1.0 - (2.0 * total_s).exp()) / 2.0;
+        if prob.abs() > 1e-15 {
+            entries.push(DemEntry {
+                event: event.clone(),
+                probability: prob.abs(),
+            });
+        }
+    }
+
+    merge_dem_entries(entries)
+}
+
+/// Build a coherent DEM with X/Z decomposition info for MWPM decoders.
+///
+/// Same mechanism extraction as `build_coherent_dem`, but additionally
+/// splits each Pauli label into X-only and Z-only components and checks
+/// anticommutation separately. This produces `DecomposableDemEntry`s
+/// that know which detectors each component flips, enabling proper
+/// graphlike decomposition for pymatching.
+pub fn build_coherent_dem_decomposable(
+    gates: &[Gate],
+    noise: &dyn NoiseSpec,
+    detectors: &[Detector],
+    observables: &[Observable],
+    expansion_gates: &[bool],
+) -> Vec<DecomposableDemEntry> {
+    // Step 1: Collect noise sources (same as build_coherent_dem)
+    let mut noise_sources: Vec<(usize, NoiseContribution)> = Vec::new();
+
+    for (gate_idx, gate) in gates.iter().enumerate() {
+        if gate_idx < expansion_gates.len() && expansion_gates[gate_idx] {
+            continue;
+        }
+        let qubits: SmallVec<[usize; 4]> =
+            gate.qubits.iter().map(pecos_core::QubitId::index).collect();
+        let injections = noise.noise_after_gate(gate_idx, gate.gate_type, &qubits);
+
+        for inj in injections {
+            noise_sources.push((
+                gate_idx,
+                NoiseContribution {
+                    label: inj.label.clone(),
+                    eeg_type: inj.eeg_type,
+                    value: inj.rate,
+                },
+            ));
+        }
+    }
+
+    let num_noise = noise_sources.len();
+
+    // For each noise source: full, X-only, and Z-only detector/observable sets
+    let mut noise_det_sets: Vec<SmallVec<[usize; 4]>> = vec![SmallVec::new(); num_noise];
+    let mut noise_obs_sets: Vec<SmallVec<[usize; 2]>> = vec![SmallVec::new(); num_noise];
+    let mut noise_x_det_sets: Vec<SmallVec<[usize; 4]>> = vec![SmallVec::new(); num_noise];
+    let mut noise_x_obs_sets: Vec<SmallVec<[usize; 2]>> = vec![SmallVec::new(); num_noise];
+    let mut noise_z_det_sets: Vec<SmallVec<[usize; 4]>> = vec![SmallVec::new(); num_noise];
+    let mut noise_z_obs_sets: Vec<SmallVec<[usize; 2]>> = vec![SmallVec::new(); num_noise];
+
+    // Precompute X-only and Z-only labels for each noise source
+    let noise_x_labels: Vec<Bm> = noise_sources
+        .iter()
+        .map(|(_, c)| Bm {
+            x_bits: c.label.x_bits.clone(),
+            ..Default::default()
+        })
+        .collect();
+    let noise_z_labels: Vec<Bm> = noise_sources
+        .iter()
+        .map(|(_, c)| Bm {
+            z_bits: c.label.z_bits.clone(),
+            ..Default::default()
+        })
+        .collect();
+
+    // Build gate -> noise source index map
+    let mut gate_to_noise: BTreeMap<usize, Vec<usize>> = BTreeMap::new();
+    for (ns_idx, (gate_idx, _)) in noise_sources.iter().enumerate() {
+        gate_to_noise.entry(*gate_idx).or_default().push(ns_idx);
+    }
+
+    // Step 2: Backward walk — check anticommutation with full, X-only, Z-only labels
+    let backward_classify_xz = |stabilizer: &Bm| -> (Vec<bool>, Vec<bool>, Vec<bool>) {
+        let mut prop = stabilizer.clone();
+        let mut hits_full = vec![false; num_noise];
+        let mut hits_x = vec![false; num_noise];
+        let mut hits_z = vec![false; num_noise];
+
+        for gate_idx in (0..gates.len()).rev() {
+            if let Some(ns_indices) = gate_to_noise.get(&gate_idx) {
+                for &ns_idx in ns_indices {
+                    // Full anticommutation
+                    if !prop.commutes_with(&noise_sources[ns_idx].1.label) {
+                        hits_full[ns_idx] = true;
+                    }
+                    // X-only: ⟨S, P_X⟩ = S_Z · P_X
+                    // P_X has no Z bits, so anticommutation only from S_Z * P_X
+                    if !noise_x_labels[ns_idx].x_bits.is_zero()
+                        && !prop.commutes_with(&noise_x_labels[ns_idx])
+                    {
+                        hits_x[ns_idx] = true;
+                    }
+                    // Z-only: ⟨S, P_Z⟩ = S_X · P_Z
+                    // P_Z has no X bits, so anticommutation only from S_X * P_Z
+                    if !noise_z_labels[ns_idx].z_bits.is_zero()
+                        && !prop.commutes_with(&noise_z_labels[ns_idx])
+                    {
+                        hits_z[ns_idx] = true;
+                    }
+                }
+            }
+            backward_conjugate_bm(&mut prop, &gates[gate_idx]);
+        }
+
+        (hits_full, hits_x, hits_z)
+    };
+
+    // Classify detectors
+    for det in detectors {
+        let (hits_full, hits_x, hits_z) = backward_classify_xz(&det.stabilizer);
+        for ns_idx in 0..num_noise {
+            if hits_full[ns_idx] {
+                noise_det_sets[ns_idx].push(det.id);
+            }
+            if hits_x[ns_idx] {
+                noise_x_det_sets[ns_idx].push(det.id);
+            }
+            if hits_z[ns_idx] {
+                noise_z_det_sets[ns_idx].push(det.id);
+            }
+        }
+    }
+
+    // Classify observables
+    for obs in observables {
+        let (hits_full, hits_x, hits_z) = backward_classify_xz(&obs.pauli);
+        for ns_idx in 0..num_noise {
+            if hits_full[ns_idx] {
+                noise_obs_sets[ns_idx].push(obs.id);
+            }
+            if hits_x[ns_idx] {
+                noise_x_obs_sets[ns_idx].push(obs.id);
+            }
+            if hits_z[ns_idx] {
+                noise_z_obs_sets[ns_idx].push(obs.id);
+            }
+        }
+    }
+
+    // Step 3: Group by (event, label, eeg_type) — same as build_coherent_dem
+    // but also track X/Z component events
+    let mut h_groups: BTreeMap<(DemEvent, Bm), (f64, DemEvent, DemEvent)> = BTreeMap::new();
+    let mut s_groups: BTreeMap<(DemEvent, Bm), (f64, DemEvent, DemEvent)> = BTreeMap::new();
+
+    for (ns_idx, (_, contrib)) in noise_sources.iter().enumerate() {
+        let dets = &noise_det_sets[ns_idx];
+        let obs = &noise_obs_sets[ns_idx];
+        if dets.is_empty() && obs.is_empty() {
+            continue;
+        }
+
+        let event = DemEvent {
+            detectors: dets.clone(),
+            observables: obs.clone(),
+        };
+        let x_event = DemEvent {
+            detectors: noise_x_det_sets[ns_idx].clone(),
+            observables: noise_x_obs_sets[ns_idx].clone(),
+        };
+        let z_event = DemEvent {
+            detectors: noise_z_det_sets[ns_idx].clone(),
+            observables: noise_z_obs_sets[ns_idx].clone(),
+        };
+
+        let key = (event.clone(), contrib.label.clone());
+        let groups = match contrib.eeg_type {
+            EegType::H => &mut h_groups,
+            EegType::S => &mut s_groups,
+            _ => continue,
+        };
+        groups
+            .entry(key)
+            .and_modify(|(val, _, _)| *val += contrib.value)
+            .or_insert((contrib.value, x_event, z_event));
+    }
+
+    // Step 4: Compute probabilities with decomposition info
+    let mut entries = Vec::new();
+
+    for ((event, _label), (total_h, x_ev, z_ev)) in &h_groups {
+        let prob = total_h.sin().powi(2);
+        if prob > 1e-15 {
+            let has_x = !x_ev.detectors.is_empty() || !x_ev.observables.is_empty();
+            let has_z = !z_ev.detectors.is_empty() || !z_ev.observables.is_empty();
+            entries.push(DecomposableDemEntry {
+                event: event.clone(),
+                probability: prob,
+                x_component: if has_x { Some(x_ev.clone()) } else { None },
+                z_component: if has_z { Some(z_ev.clone()) } else { None },
+            });
+        }
+    }
+
+    for ((event, _label), (total_s, x_ev, z_ev)) in &s_groups {
+        let prob = (1.0 - (2.0 * total_s).exp()) / 2.0;
+        if prob.abs() > 1e-15 {
+            let has_x = !x_ev.detectors.is_empty() || !x_ev.observables.is_empty();
+            let has_z = !z_ev.detectors.is_empty() || !z_ev.observables.is_empty();
+            entries.push(DecomposableDemEntry {
+                event: event.clone(),
+                probability: prob.abs(),
+                x_component: if has_x { Some(x_ev.clone()) } else { None },
+                z_component: if has_z { Some(z_ev.clone()) } else { None },
+            });
+        }
+    }
+
+    // Merge entries with identical combined events
+    merge_decomposable_dem_entries(entries)
+}
+
+fn merge_decomposable_dem_entries(
+    mut entries: Vec<DecomposableDemEntry>,
+) -> Vec<DecomposableDemEntry> {
+    if entries.len() <= 1 {
+        return entries;
+    }
+
+    // Sort by combined event
+    entries.sort_by(|a, b| {
+        a.event
+            .detectors
+            .cmp(&b.event.detectors)
+            .then(a.event.observables.cmp(&b.event.observables))
+    });
+
+    let mut merged = Vec::new();
+    let mut i = 0;
+    while i < entries.len() {
+        let mut entry = entries[i].clone();
+        let mut j = i + 1;
+        while j < entries.len()
+            && entries[j].event.detectors == entry.event.detectors
+            && entries[j].event.observables == entry.event.observables
+        {
+            // Independent combination: p = p1 + p2 - 2*p1*p2
+            entry.probability = entry.probability + entries[j].probability
+                - 2.0 * entry.probability * entries[j].probability;
+            // Keep X/Z components from first entry (they should be consistent
+            // for same-event mechanisms, or we take the first as representative)
+            j += 1;
+        }
+        merged.push(entry);
+        i = j;
+    }
+
+    merged
+}
+
+/// Build a coherent DEM with Heisenberg-exact marginals.
+///
+/// Uses the backward mechanism extraction for structure (which detectors
+/// each noise source flips) and fits mechanism probabilities to match
+/// Heisenberg-exact per-detector marginal rates.
+///
+/// This combines:
+/// - Correct mechanism structure from backward propagation
+/// - Exact marginals from the Heisenberg walk
+/// - Best independent approximation via iterative fitting
+///
+/// The `heisenberg_marginals` parameter should be a slice where
+/// `heisenberg_marginals[det_id] = exact_detection_probability`.
+///
+/// The optional `heisenberg_pairwise` parameter gives exact joint rates
+/// P(Di AND Dj) for detector pairs. When provided, the fit also matches
+/// pairwise correlations, significantly improving 2-body and 3-body accuracy.
+/// Each entry is `((det_i, det_j), joint_probability)`.
+pub fn build_coherent_dem_exact(
+    gates: &[Gate],
+    noise: &dyn NoiseSpec,
+    detectors: &[Detector],
+    observables: &[Observable],
+    expansion_gates: &[bool],
+    heisenberg_marginals: &[f64],
+    heisenberg_pairwise: Option<&[((usize, usize), f64)]>,
+) -> Vec<DemEntry> {
+    // Step 1-3: Get mechanism structure (same as approximate version)
+    let approx = build_coherent_dem(gates, noise, detectors, observables, expansion_gates);
+
+    if approx.is_empty() {
+        return approx;
+    }
+
+    let num_dets = heisenberg_marginals.len();
+
+    // Build incidence: for each detector, which mechanisms affect it
+    let mut det_to_mechs: Vec<Vec<usize>> = vec![Vec::new(); num_dets];
+    for (m, entry) in approx.iter().enumerate() {
+        for &d in &entry.event.detectors {
+            if d < num_dets {
+                det_to_mechs[d].push(m);
+            }
+        }
+    }
+
+    // Extract initial probabilities
+    let mut q: Vec<f64> = approx.iter().map(|e| e.probability).collect();
+    let n_mech = q.len();
+
+    // Precompute mechanism sets for pairwise computation
+    let det_mech_sets: Vec<std::collections::BTreeSet<usize>> = (0..num_dets)
+        .map(|d| det_to_mechs[d].iter().copied().collect())
+        .collect();
+
+    // Compute DEM marginal for detector d
+    let compute_marginal = |q: &[f64], d: usize| -> f64 {
+        let mut prod = 1.0;
+        for &m in &det_to_mechs[d] {
+            prod *= 1.0 - 2.0 * q[m];
+        }
+        (1.0 - prod) / 2.0
+    };
+
+    // L-BFGS optimization in sigmoid-parameterized space.
+    //
+    // Parameterize q_m = 0.499 * sigmoid(x_m) so x_m is unconstrained.
+    // This gives a smooth loss landscape that L-BFGS can navigate efficiently.
+    //
+    // Loss = sum_d (marginal_d - target_d)^2
+    //      + sum_pairs (pairwise_ij - target_ij)^2
+    let pairs: Vec<((usize, usize), f64)> = heisenberg_pairwise
+        .map(<[((usize, usize), f64)]>::to_vec)
+        .unwrap_or_default();
+    let has_pairwise = !pairs.is_empty();
+
+    // Initialize x from q: x = logit(q / 0.499)
+    let mut x: Vec<f64> = q
+        .iter()
+        .map(|&qi| {
+            let s = (qi / 0.499).clamp(1e-10, 1.0 - 1e-10);
+            (s / (1.0 - s)).ln()
+        })
+        .collect();
+
+    let sigmoid = |xi: f64| -> f64 { 0.499 / (1.0 + (-xi).exp()) };
+    let sigmoid_deriv = |xi: f64| -> f64 {
+        let s = 1.0 / (1.0 + (-xi).exp());
+        0.499 * s * (1.0 - s)
+    };
+
+    // Compute loss and gradient in x-space
+    let compute_loss_grad = |x: &[f64]| -> (f64, Vec<f64>) {
+        let q_local: Vec<f64> = x.iter().map(|&xi| sigmoid(xi)).collect();
+        let dq_dx: Vec<f64> = x.iter().map(|&xi| sigmoid_deriv(xi)).collect();
+
+        let mut grad_q = vec![0.0_f64; n_mech];
+        let mut loss = 0.0_f64;
+
+        // Marginal terms
+        for d in 0..num_dets {
+            let current_d = compute_marginal(&q_local, d);
+            let residual = current_d - heisenberg_marginals[d];
+            loss += residual * residual;
+
+            let mut full_prod = 1.0;
+            for &m in &det_to_mechs[d] {
+                full_prod *= 1.0 - 2.0 * q_local[m];
+            }
+            for &m in &det_to_mechs[d] {
+                let factor = 1.0 - 2.0 * q_local[m];
+                if factor.abs() > 1e-30 {
+                    grad_q[m] += 2.0 * residual * full_prod / factor;
+                }
+            }
+        }
+
+        // Pairwise terms
+        if has_pairwise {
+            let full_prods: Vec<f64> = (0..num_dets)
+                .map(|d| {
+                    let mut p = 1.0;
+                    for &m in &det_to_mechs[d] {
+                        p *= 1.0 - 2.0 * q_local[m];
+                    }
+                    p
+                })
+                .collect();
+
+            for &((di, dj), target_p) in &pairs {
+                if di >= num_dets || dj >= num_dets || target_p < 1e-10 {
+                    continue;
+                }
+
+                let prod_i = full_prods[di];
+                let prod_j = full_prods[dj];
+                let mut prod_both = 1.0;
+                for &m in det_mech_sets[di].intersection(&det_mech_sets[dj]) {
+                    prod_both *= 1.0 - 2.0 * q_local[m];
+                }
+                let prod_xor = if prod_both.abs() > 1e-30 {
+                    prod_i * prod_j / (prod_both * prod_both)
+                } else {
+                    0.0
+                };
+
+                let current_p = (1.0 - prod_i - prod_j + prod_xor) / 4.0;
+                let residual = current_p - target_p;
+                loss += residual * residual;
+
+                for &m in det_mech_sets[di].intersection(&det_mech_sets[dj]) {
+                    let factor = 1.0 - 2.0 * q_local[m];
+                    if factor.abs() > 1e-30 {
+                        grad_q[m] += 2.0 * residual * (prod_i + prod_j) / (2.0 * factor);
+                    }
+                }
+                for &m in &det_to_mechs[di] {
+                    if !det_mech_sets[dj].contains(&m) {
+                        let factor = 1.0 - 2.0 * q_local[m];
+                        if factor.abs() > 1e-30 {
+                            grad_q[m] += 2.0 * residual * (prod_i - prod_xor) / (2.0 * factor);
+                        }
+                    }
+                }
+                for &m in &det_to_mechs[dj] {
+                    if !det_mech_sets[di].contains(&m) {
+                        let factor = 1.0 - 2.0 * q_local[m];
+                        if factor.abs() > 1e-30 {
+                            grad_q[m] += 2.0 * residual * (prod_j - prod_xor) / (2.0 * factor);
+                        }
+                    }
+                }
+            }
+        }
+
+        // Chain rule: grad_x = grad_q * dq/dx
+        let grad_x: Vec<f64> = grad_q
+            .iter()
+            .zip(dq_dx.iter())
+            .map(|(&gq, &dx)| gq * dx)
+            .collect();
+
+        (loss, grad_x)
+    };
+
+    // L-BFGS two-loop recursion
+    let m_lbfgs = 10; // history size
+    let mut s_hist: Vec<Vec<f64>> = Vec::new(); // x differences
+    let mut y_hist: Vec<Vec<f64>> = Vec::new(); // gradient differences
+    let mut rho_hist: Vec<f64> = Vec::new();
+
+    let (mut loss, mut grad) = compute_loss_grad(&x);
+
+    for _iter in 0..500 {
+        if loss < 1e-14 {
+            break;
+        }
+
+        // L-BFGS direction: H_k * grad
+        let mut direction = grad.clone();
+
+        // Two-loop recursion
+        let hist_len = s_hist.len();
+        let mut alpha = vec![0.0; hist_len];
+        for i in (0..hist_len).rev() {
+            alpha[i] = rho_hist[i] * dot(&s_hist[i], &direction);
+            for j in 0..n_mech {
+                direction[j] -= alpha[i] * y_hist[i][j];
+            }
+        }
+        // Scale by gamma = s'y / y'y from most recent pair
+        if let (Some(s), Some(y)) = (s_hist.last(), y_hist.last()) {
+            let yy = dot(y, y);
+            if yy > 1e-30 {
+                let gamma = dot(s, y) / yy;
+                for d in &mut direction {
+                    *d *= gamma;
+                }
+            }
+        }
+        for i in 0..hist_len {
+            let beta = rho_hist[i] * dot(&y_hist[i], &direction);
+            for j in 0..n_mech {
+                direction[j] += (alpha[i] - beta) * s_hist[i][j];
+            }
+        }
+
+        // Negate for descent direction
+        for d in &mut direction {
+            *d = -*d;
+        }
+
+        // Backtracking line search (Armijo condition)
+        let dg = dot(&grad, &direction);
+        if dg >= 0.0 {
+            break;
+        } // not a descent direction
+
+        let mut step = 1.0;
+        let c1 = 1e-4;
+        let mut x_new: Vec<f64> = x
+            .iter()
+            .zip(direction.iter())
+            .map(|(&xi, &di)| xi + step * di)
+            .collect();
+        let (mut loss_new, mut grad_new) = compute_loss_grad(&x_new);
+
+        for _ in 0..20 {
+            if loss_new <= loss + c1 * step * dg {
+                break;
+            }
+            step *= 0.5;
+            x_new = x
+                .iter()
+                .zip(direction.iter())
+                .map(|(&xi, &di)| xi + step * di)
+                .collect();
+            let (ln, gn) = compute_loss_grad(&x_new);
+            loss_new = ln;
+            grad_new = gn;
+        }
+
+        // Update L-BFGS history
+        let s_k: Vec<f64> = x_new.iter().zip(x.iter()).map(|(&a, &b)| a - b).collect();
+        let y_k: Vec<f64> = grad_new
+            .iter()
+            .zip(grad.iter())
+            .map(|(&a, &b)| a - b)
+            .collect();
+        let sy = dot(&s_k, &y_k);
+        if sy > 1e-30 {
+            if s_hist.len() >= m_lbfgs {
+                s_hist.remove(0);
+                y_hist.remove(0);
+                rho_hist.remove(0);
+            }
+            s_hist.push(s_k);
+            y_hist.push(y_k);
+            rho_hist.push(1.0 / sy);
+        }
+
+        x = x_new;
+        loss = loss_new;
+        grad = grad_new;
+    }
+
+    // Convert back to q
+    for (m, &xi) in x.iter().enumerate() {
+        q[m] = sigmoid(xi);
+    }
+
+    // Build fitted DEM entries
+    let fitted: Vec<DemEntry> = approx
+        .iter()
+        .zip(q.iter())
+        .filter(|(_, p)| **p > 1e-15)
+        .map(|(entry, p)| DemEntry {
+            event: entry.event.clone(),
+            probability: *p,
+        })
+        .collect();
+
+    merge_dem_entries(fitted)
+}
+
+/// Build a coherent DEM with Heisenberg-exact marginals AND X/Z decomposition.
+///
+/// Combines the exact probability fitting from `build_coherent_dem_exact`
+/// with the X/Z component tracking from `build_coherent_dem_decomposable`.
+pub fn build_coherent_dem_exact_decomposable(
+    gates: &[Gate],
+    noise: &dyn NoiseSpec,
+    detectors: &[Detector],
+    observables: &[Observable],
+    expansion_gates: &[bool],
+    heisenberg_marginals: &[f64],
+    heisenberg_pairwise: Option<&[((usize, usize), f64)]>,
+) -> Vec<DecomposableDemEntry> {
+    // Get X/Z component structure from decomposable builder
+    let decomposable =
+        build_coherent_dem_decomposable(gates, noise, detectors, observables, expansion_gates);
+
+    if decomposable.is_empty() {
+        return decomposable;
+    }
+
+    // Get fitted probabilities from exact builder
+    let fitted = build_coherent_dem_exact(
+        gates,
+        noise,
+        detectors,
+        observables,
+        expansion_gates,
+        heisenberg_marginals,
+        heisenberg_pairwise,
+    );
+
+    // Build lookup: event → fitted probability
+    let mut prob_lookup: BTreeMap<FittedEventKey, f64> = BTreeMap::new();
+    for entry in &fitted {
+        prob_lookup.insert(
+            (
+                entry.event.detectors.clone(),
+                entry.event.observables.clone(),
+            ),
+            entry.probability,
+        );
+    }
+
+    // Combine: X/Z structure from decomposable + fitted probabilities from exact
+    decomposable
+        .into_iter()
+        .filter_map(|mut entry| {
+            let key = (
+                entry.event.detectors.clone(),
+                entry.event.observables.clone(),
+            );
+            if let Some(&fitted_prob) = prob_lookup.get(&key) {
+                entry.probability = fitted_prob;
+                Some(entry)
+            } else if entry.probability > 1e-15 {
+                // Keep original probability if no fitted version (edge case)
+                Some(entry)
+            } else {
+                None
+            }
+        })
+        .collect()
+}
+
+/// Merge DEM entries with the same event via independent combination.
+fn merge_dem_entries(mut entries: Vec<DemEntry>) -> Vec<DemEntry> {
+    entries.sort_by(|a, b| a.event.cmp(&b.event));
+    let mut merged = Vec::new();
+    for entry in entries {
+        if let Some(last) = merged.last_mut() {
+            let last: &mut DemEntry = last;
+            if last.event == entry.event {
+                let p1 = last.probability;
+                let p2 = entry.probability;
+                last.probability = p1 + p2 - 2.0 * p1 * p2;
+                continue;
+            }
+        }
+        merged.push(entry);
+    }
+    merged
+}
+
+/// Dot product of two slices.
+#[inline]
+fn dot(a: &[f64], b: &[f64]) -> f64 {
+    a.iter().zip(b.iter()).map(|(&x, &y)| x * y).sum()
+}
+
+/// Backward-conjugate a Bm stabilizer through a gate (Heisenberg picture).
+///
+/// Converts to SparsePauli, uses the tested sparse_conjugate function
+/// (which already handles adjoint swapping for backward direction),
+/// then converts back. Panics on unsupported gates.
+fn backward_conjugate_bm(prop: &mut Bm, gate: &Gate) {
+    use pecos_core::gate_type::GateType;
+    match gate.gate_type {
+        // Prep/alloc: kill the Pauli on the prepared qubit.
+        // Z-basis prep projects onto |0>, destroying X coherences.
+        // Backward propagation stops here — errors before prep
+        // don't affect measurements after it.
+        GateType::PZ | GateType::QAlloc => {
+            for q in &gate.qubits {
+                let qi = q.index();
+                // Clear both X and Z on this qubit
+                if prop.has_x(qi) {
+                    let mut sp = SparsePauli::from_bm(prop);
+                    sp.clear_x(qi as u16);
+                    *prop = sp.to_bm();
+                }
+                if prop.has_z(qi) {
+                    let mut sp = SparsePauli::from_bm(prop);
+                    sp.clear_z(qi as u16);
+                    *prop = sp.to_bm();
+                }
+            }
+            return;
+        }
+        // Measurement: kill X on measured qubit (Z-basis measurement
+        // is insensitive to Z errors, but X errors flip the result).
+        // For backward propagation, we don't propagate X past MZ.
+        GateType::MZ | GateType::MeasureFree | GateType::MeasureLeaked => {
+            for q in &gate.qubits {
+                let qi = q.index();
+                if prop.has_x(qi) {
+                    let mut sp = SparsePauli::from_bm(prop);
+                    sp.clear_x(qi as u16);
+                    *prop = sp.to_bm();
+                }
+            }
+            return;
+        }
+        GateType::QFree | GateType::I | GateType::Idle => return,
+        _ => {}
+    }
+
+    let mut sp = SparsePauli::from_bm(prop);
+    // sparse_conjugate already applies adjoint swap for backward walk
+    let _sign = sparse_conjugate(&mut sp, gate);
+    // Sign is tracked in the Heisenberg walk's coefficients;
+    // for the Bm-level classification we only need the Pauli structure.
+    *prop = sp.to_bm();
+}
diff --git a/exp/pecos-eeg/src/correlation_table.rs b/exp/pecos-eeg/src/correlation_table.rs
new file mode 100644
index 000000000..ed42f237d
--- /dev/null
+++ b/exp/pecos-eeg/src/correlation_table.rs
@@ -0,0 +1,406 @@
+// Copyright 2026 The PECOS Developers
+//
+// Licensed under the Apache License, Version 2.0 (the "License"); you may not use this file except
+// in compliance with the License. You may obtain a copy of the License at
+//
+//     https://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software distributed under the License
+// is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express
+// or implied. See the License for the specific language governing permissions and limitations under
+// the License.
+
+//! Exact detector correlation tables from backward Heisenberg walks.
+//!
+//! Computes exact k-body joint detection rates using product stabilizer
+//! walks. No DEM approximation — captures all coherent interference.
+//!
+//! For k detectors with stabilizers S1..Sk, the joint detection probability
+//! is computed via inclusion-exclusion:
+//!
+//!   P(D1 AND D2 AND ... AND Dk) = 1/2^k * sum_{T ⊆ {1..k}} (-1)^{k-|T|} <prod_{i in T} Si>
+//!
+//! where <prod Si> is computed by a Heisenberg walk with the product stabilizer.
+//!
+//! Each walk gives one expectation value. The number of walks needed:
+//! - Order 1 (marginals): C(n,1) = n
+//! - Order 2 (pairwise): C(n,2) new walks
+//! - Order 3 (triples): C(n,3) new walks
+//! - Total up to order k: sum_{j=1}^{k} C(n,j)
+
+use crate::Bm;
+use crate::dem_mapping::{Detector, Observable};
+use crate::noise::NoiseSpec;
+use crate::stabilizer::StabilizerGroup;
+use pecos_core::Gate;
+use rayon::iter::{IntoParallelRefIterator, ParallelIterator};
+use std::collections::BTreeMap;
+use std::fmt::Write as _;
+
+/// Exact k-body correlation table for detectors and observables.
+///
+/// Contains two types of correlations:
+/// - **Detector rates**: P(D_i1, ..., D_ik) — joint detection probabilities
+/// - **Detector-observable rates**: P(D_i1, ..., D_ik, L_j) — how detection
+///   patterns relate to logical observable flips (what decoders need)
+pub struct CorrelationTable {
+    /// Detector-only joint rates: sorted det_indices -> probability
+    pub rates: BTreeMap<Vec<usize>, f64>,
+    /// Detector-observable joint rates: (sorted det_indices, obs_id) -> probability.
+    /// P(D_i1 AND ... AND D_ik AND L_j) for each observable j.
+    pub observable_rates: BTreeMap<(Vec<usize>, usize), f64>,
+    /// Maximum correlation order computed (for detectors)
+    pub max_order: usize,
+    /// Number of detectors
+    pub num_detectors: usize,
+    /// Number of observables
+    pub num_observables: usize,
+    /// Number of Heisenberg walks performed
+    pub num_walks: usize,
+}
+
+/// Inputs for exact correlation table construction.
+#[derive(Clone, Copy)]
+pub struct CorrelationTableInput<'a> {
+    /// Circuit gates.
+    pub gates: &'a [Gate],
+    /// Noise model used for exact correlation targets.
+    pub noise: &'a dyn NoiseSpec,
+    /// Detector definitions.
+    pub detectors: &'a [Detector],
+    /// Observable definitions.
+    pub observables: &'a [Observable],
+    /// Initial stabilizer group.
+    pub initial_stab: &'a StabilizerGroup,
+    /// Number of circuit qubits.
+    pub num_qubits: usize,
+    /// Maximum detector/observable correlation order.
+    pub max_order: usize,
+    /// Drop probabilities below this threshold.
+    pub prune_threshold: f64,
+}
+
+impl CorrelationTable {
+    /// Build a graphlike DEM string from the correlation table.
+    ///
+    /// Uses pairwise correlations as edge probabilities for MWPM decoders.
+    /// Each pairwise correlation P(Di AND Dj) - P(Di)*P(Dj) becomes an edge.
+    /// Observable assignment uses P(Di AND Lk) rates.
+    ///
+    /// This bypasses the DEM independent error model — edge weights come
+    /// directly from exact Heisenberg correlations including all coherent
+    /// interference effects.
+    #[must_use]
+    pub fn to_matching_dem(&self) -> String {
+        let mut lines = Vec::new();
+
+        // Get marginals
+        let marginals: BTreeMap<usize, f64> = self
+            .rates
+            .iter()
+            .filter(|(k, _)| k.len() == 1)
+            .map(|(k, &v)| (k[0], v))
+            .collect();
+
+        // Observable marginals per detector: P(Di AND Lk)
+        let mut det_obs: BTreeMap<(usize, usize), f64> = BTreeMap::new();
+        for ((det_ids, obs_id), &prob) in &self.observable_rates {
+            if det_ids.len() == 1 {
+                det_obs.insert((det_ids[0], *obs_id), prob);
+            }
+        }
+
+        // Pairwise edges: excess correlation = P(Di,Dj) - P(Di)*P(Dj)
+        for (key, &joint_prob) in &self.rates {
+            if key.len() != 2 {
+                continue;
+            }
+            let (di, dj) = (key[0], key[1]);
+
+            let pi = marginals.get(&di).copied().unwrap_or(0.0);
+            let pj = marginals.get(&dj).copied().unwrap_or(0.0);
+            let p_excess = joint_prob - pi * pj;
+
+            if p_excess <= 1e-15 {
+                continue;
+            } // no positive correlation
+            let p_edge = p_excess.min(0.499); // clamp for valid weight
+
+            // Determine observable assignment: which Lk is most correlated
+            // with this pair? Use P(Di AND Dj AND Lk) if available,
+            // otherwise no observable.
+            let mut obs_list = Vec::new();
+            for obs_id in 0..self.num_observables {
+                let pair_key = (vec![di, dj], obs_id);
+                if let Some(&p_trio) = self.observable_rates.get(&pair_key) {
+                    // If the trio rate is significant relative to the pair rate,
+                    // this observable is correlated with this edge
+                    if p_trio > joint_prob * 0.1 {
+                        obs_list.push(obs_id);
+                    }
+                }
+            }
+
+            let mut targets = format!("D{di} D{dj}");
+            for o in &obs_list {
+                let _ = write!(targets, " L{o}");
+            }
+            lines.push(format!("error({p_edge:.6e}) {targets}"));
+        }
+
+        // Boundary edges: P(Di AND Lk) - P(Di)*P(Lk)
+        // Approximation: use P(Di AND Lk) directly as boundary edge probability
+        // (represents probability Di fires due to a logical error chain)
+        for obs_id in 0..self.num_observables {
+            for di in 0..self.num_detectors {
+                let p_det_obs = det_obs.get(&(di, obs_id)).copied().unwrap_or(0.0);
+
+                // Check if this detector has significant correlation with the observable
+                // that isn't already explained by pairwise edges
+                if p_det_obs <= 1e-15 {
+                    continue;
+                }
+
+                // Boundary probability: P(Di fires AND it's a logical error)
+                let p_boundary = p_det_obs.min(0.499);
+                if p_boundary <= 1e-15 {
+                    continue;
+                }
+
+                lines.push(format!("error({p_boundary:.6e}) D{di} L{obs_id}"));
+            }
+        }
+
+        lines.join("\n")
+    }
+}
+
+/// Compute exact correlation table up to `max_order` using Heisenberg walks.
+///
+/// Each entry gives the exact joint detection probability for a subset of
+/// detectors, including all coherent interference effects.
+#[must_use]
+pub fn compute_correlation_table(input: CorrelationTableInput<'_>) -> CorrelationTable {
+    let CorrelationTableInput {
+        gates,
+        noise,
+        detectors,
+        observables,
+        initial_stab,
+        num_qubits,
+        max_order,
+        prune_threshold,
+    } = input;
+
+    let n = detectors.len();
+    let n_obs = observables.len();
+    let has_stochastic = true; // conservative; could check noise params
+
+    // Build noise map once, shared across all walks
+    let gate_index = crate::expand::GateIndex::build(gates, num_qubits);
+    let noise_map = if has_stochastic {
+        Some(crate::heisenberg::build_noise_map(
+            gates,
+            noise,
+            &gate_index.expansion_gates,
+        ))
+    } else {
+        None
+    };
+
+    // Helper: run one Heisenberg walk with a given stabilizer.
+    // Uses sparse traversal (heap + gate index) with optional noise map.
+    let walk = |stab: &Bm| -> f64 {
+        crate::heisenberg::heisenberg_sparse(
+            gates,
+            stab,
+            noise,
+            initial_stab,
+            prune_threshold,
+            &gate_index,
+            noise_map.as_deref(),
+        )
+    };
+
+    let mut rates = BTreeMap::new();
+
+    // Cache walk results for product stabilizers: key = sorted det indices
+    let mut walk_cache: BTreeMap<Vec<usize>, f64> = BTreeMap::new();
+
+    // Collect all (indices, product_stabilizer) pairs for parallel walks
+    let mut walk_items: Vec<(Vec<usize>, Bm)> = Vec::new();
+    for order in 1..=max_order.min(n) {
+        for_each_combination_idx(n, order, |indices| {
+            let mut product = detectors[indices[0]].stabilizer.clone();
+            for &idx in &indices[1..] {
+                product = product.multiply(&detectors[idx].stabilizer);
+            }
+            let det_ids: Vec<usize> = indices.iter().map(|&i| detectors[i].id).collect();
+            walk_items.push((det_ids, product));
+        });
+    }
+
+    // Run all walks in parallel
+    let walk_results: Vec<(Vec<usize>, f64)> = walk_items
+        .par_iter()
+        .map(|(det_ids, product)| {
+            let p_walk = walk(product);
+            (det_ids.clone(), p_walk)
+        })
+        .collect();
+
+    let num_walks = walk_results.len();
+    for (det_ids, p_walk) in walk_results {
+        walk_cache.insert(det_ids, p_walk);
+    }
+
+    // Convert walk results to joint detection probabilities via inclusion-exclusion.
+    // P(D_{i1}, ..., D_{ik}) = 1/2^k * sum_{T ⊆ {i1..ik}} (-1)^{k-|T|} * <prod_{j in T} S_j>
+    // where <prod S> = 1 - 2 * walk_result for that product.
+    for order in 1..=max_order.min(n) {
+        for_each_combination_idx(n, order, |indices| {
+            let det_ids: Vec<usize> = indices.iter().map(|&i| detectors[i].id).collect();
+            let k = order;
+
+            let mut prob = 0.0_f64;
+            let inv_2k = 1.0 / (1u64 << k) as f64;
+
+            // Iterate over all subsets T of {0..k-1}
+            for mask in 0..(1u64 << k) {
+                let subset_size = mask.count_ones() as usize;
+                let sign = if subset_size.is_multiple_of(2) {
+                    1.0
+                } else {
+                    -1.0
+                };
+
+                if subset_size == 0 {
+                    // Empty subset: <I> = 1, contribution = (-1)^k * 1
+                    prob += sign;
+                } else {
+                    // Build the subset's detector IDs
+                    let subset_det_ids: Vec<usize> = (0..k)
+                        .filter(|&bit| mask & (1u64 << bit) != 0)
+                        .map(|bit| detectors[indices[bit]].id)
+                        .collect();
+
+                    // Look up the walk result for this subset
+                    if let Some(&p_walk) = walk_cache.get(&subset_det_ids) {
+                        // <prod S> = 1 - 2 * p_walk
+                        let expectation = 1.0 - 2.0 * p_walk;
+                        prob += sign * expectation;
+                    }
+                }
+            }
+
+            prob *= inv_2k;
+            if prob.abs() > 1e-15 {
+                rates.insert(det_ids, prob.max(0.0));
+            }
+        });
+    }
+
+    // Compute detector-observable cross-correlations.
+    // For each observable L_j and each detector subset {D_i1,...,D_ik}:
+    //   P(D_i1,...,D_ik, L_j) via inclusion-exclusion with the observable
+    //   stabilizer included in the product.
+    //
+    // For single detector + observable:
+    //   P(Di, Lj) = 1/4 (1 - <Si> - <Lj> + <Si*Lj>)
+    //
+    // We compute P(Lj) and P(Di, Lj) for each detector-observable pair.
+    let mut observable_rates: BTreeMap<(Vec<usize>, usize), f64> = BTreeMap::new();
+
+    // Collect observable walk items for parallel execution
+    // Items: (obs_id, Option<det_id>, product_stabilizer)
+    let mut obs_walk_items: Vec<(usize, Option<usize>, Bm)> = Vec::new();
+    for obs in observables {
+        obs_walk_items.push((obs.id, None, obs.pauli.clone()));
+        for det in detectors {
+            let product = det.stabilizer.multiply(&obs.pauli);
+            obs_walk_items.push((obs.id, Some(det.id), product));
+        }
+    }
+
+    let obs_walk_results: Vec<(usize, Option<usize>, f64)> = obs_walk_items
+        .par_iter()
+        .map(|(obs_id, det_id, product)| (*obs_id, *det_id, walk(product)))
+        .collect();
+
+    let num_walks = num_walks + obs_walk_results.len();
+
+    // Process observable walk results: marginals first, then pairwise
+    let mut obs_marginals: BTreeMap<usize, f64> = BTreeMap::new();
+    for &(obs_id, det_id, p_walk) in &obs_walk_results {
+        if det_id.is_none() {
+            obs_marginals.insert(obs_id, p_walk);
+            observable_rates.insert((vec![], obs_id), p_walk);
+        }
+    }
+    for &(obs_id, det_id, p_walk) in &obs_walk_results {
+        if let Some(d_id) = det_id {
+            let p_di = walk_cache.get(&vec![d_id]).copied().unwrap_or(0.0);
+            let p_obs = obs_marginals.get(&obs_id).copied().unwrap_or(0.0);
+            let p_joint = (p_di + p_obs - p_walk) / 2.0;
+            if p_joint.abs() > 1e-15 {
+                observable_rates.insert((vec![d_id], obs_id), p_joint.max(0.0));
+            }
+        }
+    }
+
+    CorrelationTable {
+        rates,
+        observable_rates,
+        max_order: max_order.min(n),
+        num_detectors: n,
+        num_observables: n_obs,
+        num_walks,
+    }
+}
+
+/// Iterate over all k-combinations of indices 0..n, calling f with each sorted combination.
+fn for_each_combination_idx(n: usize, k: usize, mut f: impl FnMut(&[usize])) {
+    if k == 0 || n < k {
+        return;
+    }
+    let mut combo = vec![0usize; k];
+    combination_recurse_idx(n, k, 0, 0, &mut combo, &mut f);
+}
+
+fn combination_recurse_idx(
+    n: usize,
+    k: usize,
+    start: usize,
+    depth: usize,
+    combo: &mut [usize],
+    f: &mut impl FnMut(&[usize]),
+) {
+    if depth == k {
+        f(&combo[..k]);
+        return;
+    }
+    let remaining = k - depth;
+    if start + remaining > n {
+        return;
+    }
+    for i in start..=(n - remaining) {
+        combo[depth] = i;
+        combination_recurse_idx(n, k, i + 1, depth + 1, combo, f);
+    }
+}
+
+#[cfg(test)]
+mod tests {
+    use super::*;
+
+    #[test]
+    fn test_combination_idx() {
+        let mut results = Vec::new();
+        for_each_combination_idx(4, 2, |combo| {
+            results.push(combo.to_vec());
+        });
+        assert_eq!(results.len(), 6); // C(4,2) = 6
+        assert_eq!(results[0], vec![0, 1]);
+        assert_eq!(results[5], vec![2, 3]);
+    }
+}
diff --git a/exp/pecos-eeg/src/dem_generator.rs b/exp/pecos-eeg/src/dem_generator.rs
new file mode 100644
index 000000000..f36dd7608
--- /dev/null
+++ b/exp/pecos-eeg/src/dem_generator.rs
@@ -0,0 +1,261 @@
+// Copyright 2026 The PECOS Developers
+//
+// Licensed under the Apache License, Version 2.0 (the "License"); you may not use this file except
+// in compliance with the License. You may obtain a copy of the License at
+//
+//     https://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software distributed under the License
+// is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express
+// or implied. See the License for the specific language governing permissions and limitations under
+// the License.
+
+//! DEM generator trait and implementations.
+//!
+//! Unifies all DEM generation methods behind a single trait. Any generator
+//! can be used as a simulator backend via the meas_sampling path.
+
+use crate::dem_mapping::{DecomposableDemEntry, DemEntry, Detector, Observable};
+use crate::expand::{ExpandedCircuit, GateIndex};
+use crate::noise::NoiseSpec;
+use pecos_core::Gate;
+
+/// Noise parameters for DEM generation (uniform depolarizing + coherent idle).
+#[derive(Clone, Debug)]
+pub struct NoiseParams {
+    pub p1: f64,
+    pub p2: f64,
+    pub p_meas: f64,
+    pub p_prep: f64,
+    pub idle_rz: f64,
+}
+
+/// Input context for DEM generation.
+///
+/// Contains everything a generator needs: expanded circuit, detectors,
+/// observables, and precomputed indices.
+pub struct DemContext<'a> {
+    pub gates: &'a [Gate],
+    pub expanded: &'a ExpandedCircuit,
+    pub gate_index: &'a GateIndex,
+    pub detectors: &'a [Detector],
+    pub observables: &'a [Observable],
+}
+
+/// Output from a DEM generator.
+pub struct DemOutput {
+    /// Raw DEM entries (for tesseract and other hyperedge-capable decoders).
+    pub entries: Vec<DemEntry>,
+    /// Decomposable entries with X/Z provenance (for MWPM decoders).
+    /// None if the generator doesn't support decomposition.
+    pub decomposable: Option<Vec<DecomposableDemEntry>>,
+}
+
+/// Trait for DEM generators.
+///
+/// Any type implementing this can generate a Detector Error Model from
+/// a circuit and noise parameters. Implementations can then be used as
+/// simulator backends via the meas_sampling path.
+pub trait DemGenerator: Send + Sync {
+    /// Generate a DEM from the given context and noise.
+    fn generate(&self, ctx: &DemContext<'_>, noise: &dyn NoiseSpec) -> DemOutput;
+
+    /// Human-readable name for this generator method.
+    fn name(&self) -> &str;
+}
+
+/// Coherent DEM generator (backward Heisenberg mechanism extraction, approximate probabilities).
+///
+/// Fast. Handles coherent noise (idle_rz). Approximate probabilities
+/// (sin^2 for H-type, (1-exp(2s))/2 for S-type).
+pub struct CoherentApprox;
+
+impl DemGenerator for CoherentApprox {
+    fn generate(&self, ctx: &DemContext<'_>, noise: &dyn NoiseSpec) -> DemOutput {
+        let entries = crate::coherent_dem::build_coherent_dem(
+            ctx.gates,
+            noise,
+            ctx.detectors,
+            ctx.observables,
+            &ctx.gate_index.expansion_gates,
+        );
+        let decomposable = crate::coherent_dem::build_coherent_dem_decomposable(
+            ctx.gates,
+            noise,
+            ctx.detectors,
+            ctx.observables,
+            &ctx.gate_index.expansion_gates,
+        );
+        DemOutput {
+            entries,
+            decomposable: Some(decomposable),
+        }
+    }
+
+    fn name(&self) -> &'static str {
+        "coherent_approx"
+    }
+}
+
+/// Coherent DEM generator with Heisenberg-exact probability fitting.
+///
+/// Slower (runs Heisenberg walks for marginals + pairwise). Handles coherent
+/// noise. Exact marginals via L-BFGS fit.
+pub struct CoherentExact {
+    pub prune_threshold: f64,
+}
+
+impl Default for CoherentExact {
+    fn default() -> Self {
+        Self {
+            prune_threshold: 1e-12,
+        }
+    }
+}
+
+impl DemGenerator for CoherentExact {
+    fn generate(&self, ctx: &DemContext<'_>, noise: &dyn NoiseSpec) -> DemOutput {
+        use crate::heisenberg::{build_noise_map, heisenberg_sparse};
+        use crate::stabilizer::StabilizerGroup;
+
+        // Build initial stabilizer group
+        let init_gates: Vec<Gate> = (0..ctx.expanded.num_original_qubits)
+            .map(|q| crate::expand::make_gate(pecos_core::gate_type::GateType::PZ, &[q]))
+            .collect();
+        let stab = StabilizerGroup::from_circuit(&init_gates, ctx.expanded.num_qubits);
+
+        // Heisenberg walks for exact marginals
+        let noise_map = build_noise_map(ctx.gates, noise, &ctx.gate_index.expansion_gates);
+
+        let num_dets = ctx.detectors.iter().map(|d| d.id + 1).max().unwrap_or(0);
+        let mut marginals = vec![0.0_f64; num_dets];
+        for det in ctx.detectors {
+            let p = heisenberg_sparse(
+                ctx.gates,
+                &det.stabilizer,
+                noise,
+                &stab,
+                self.prune_threshold,
+                ctx.gate_index,
+                Some(&noise_map),
+            );
+            if det.id < marginals.len() {
+                marginals[det.id] = p;
+            }
+        }
+
+        // Pairwise rates
+        let mut pairwise: Vec<((usize, usize), f64)> = Vec::new();
+        for i in 0..ctx.detectors.len() {
+            for j in (i + 1)..ctx.detectors.len() {
+                let product = ctx.detectors[i]
+                    .stabilizer
+                    .multiply(&ctx.detectors[j].stabilizer);
+                let p_product = heisenberg_sparse(
+                    ctx.gates,
+                    &product,
+                    noise,
+                    &stab,
+                    self.prune_threshold,
+                    ctx.gate_index,
+                    Some(&noise_map),
+                );
+                let p_joint = (marginals[ctx.detectors[i].id] + marginals[ctx.detectors[j].id]
+                    - p_product)
+                    / 2.0;
+                if p_joint > 1e-10 {
+                    pairwise.push(((ctx.detectors[i].id, ctx.detectors[j].id), p_joint.max(0.0)));
+                }
+            }
+        }
+
+        // Exact-fitted entries
+        let entries = crate::coherent_dem::build_coherent_dem_exact(
+            ctx.gates,
+            noise,
+            ctx.detectors,
+            ctx.observables,
+            &ctx.gate_index.expansion_gates,
+            &marginals,
+            Some(&pairwise),
+        );
+        let decomposable = crate::coherent_dem::build_coherent_dem_exact_decomposable(
+            ctx.gates,
+            noise,
+            ctx.detectors,
+            ctx.observables,
+            &ctx.gate_index.expansion_gates,
+            &marginals,
+            Some(&pairwise),
+        );
+
+        DemOutput {
+            entries,
+            decomposable: Some(decomposable),
+        }
+    }
+
+    fn name(&self) -> &'static str {
+        "coherent_exact"
+    }
+}
+
+/// Perturbative (forward EEG) DEM generator.
+///
+/// Fastest. Uses forward EEG propagation with Taylor approximation.
+/// Approximate probabilities (~50% error for coherent noise).
+pub struct Perturbative;
+
+impl DemGenerator for Perturbative {
+    fn generate(&self, ctx: &DemContext<'_>, noise: &dyn NoiseSpec) -> DemOutput {
+        // Scaffolding imports for future forward-EEG implementation
+        #[allow(unused_imports)]
+        use crate::circuit::analyze_expanded;
+        #[allow(unused_imports)]
+        use crate::dem_mapping::{EegConfig, build_dem_configured, build_dem_decomposable};
+        #[allow(unused_imports)]
+        use crate::noise::UniformNoise;
+
+        // We need to extract params from the NoiseSpec — use a test gate to probe
+        let _ = noise.noise_after_gate(0, pecos_core::gate_type::GateType::H, &[0]);
+
+        // For now, use the coherent_dem path as fallback since forward EEG
+        // requires its own NoiseModel type (not the NoiseSpec trait)
+        let entries = crate::coherent_dem::build_coherent_dem(
+            ctx.gates,
+            noise,
+            ctx.detectors,
+            ctx.observables,
+            &ctx.gate_index.expansion_gates,
+        );
+
+        // Forward EEG would need stabilizer group for proper classification
+        // Use coherent_dem decomposable for now
+        let decomposable = crate::coherent_dem::build_coherent_dem_decomposable(
+            ctx.gates,
+            noise,
+            ctx.detectors,
+            ctx.observables,
+            &ctx.gate_index.expansion_gates,
+        );
+
+        DemOutput {
+            entries,
+            decomposable: Some(decomposable),
+        }
+    }
+
+    fn name(&self) -> &'static str {
+        "perturbative"
+    }
+}
+
+/// Select a DEM generator by method name.
+#[must_use]
+pub fn select_generator(method: &str, _idle_rz: f64) -> Box<dyn DemGenerator> {
+    match method {
+        "coherent_exact" => Box::new(CoherentExact::default()),
+        "perturbative" => Box::new(Perturbative),
+        _ => Box::new(CoherentApprox), // auto/coherent/default fallback
+    }
+}
diff --git a/exp/pecos-eeg/src/dem_mapping.rs b/exp/pecos-eeg/src/dem_mapping.rs
new file mode 100644
index 000000000..8eca6bdb9
--- /dev/null
+++ b/exp/pecos-eeg/src/dem_mapping.rs
@@ -0,0 +1,1784 @@
+// Copyright 2026 The PECOS Developers
+//
+// Licensed under the Apache License, Version 2.0
+
+//! DEM event classification and probability computation.
+//!
+//! Classifies propagated EEG generators by DEM event class (which
+//! detectors each Pauli anticommutes with), then computes event
+//! probabilities using the correct formulas from Hines et al.
+
+use crate::Bm;
+use crate::circuit::PropagatedEeg;
+use crate::eeg::EegType;
+use crate::stabilizer::StabilizerGroup;
+use pecos_core::pauli::pauli_bitmask::BitmaskStorage;
+use pecos_core::{Pauli, PauliString};
+use smallvec::SmallVec;
+use std::collections::BTreeMap;
+use std::fmt::Write as _;
+
+type DetectorSet = SmallVec<[usize; 4]>;
+type ObservableSet = SmallVec<[usize; 2]>;
+type EventKey = (DetectorSet, ObservableSet);
+type XzComponents = (Option<DemEvent>, Option<DemEvent>);
+type GraphlikePieces = Vec<DetectorSet>;
+type DecompMemo = BTreeMap<DetectorSet, Option<GraphlikePieces>>;
+
+/// Controls the H-type probability formula.
+#[derive(Clone, Copy, Debug, Default, PartialEq, Eq)]
+pub enum HFormula {
+    /// p = sum h_j h_k beta (leading-order Taylor). Fast, accurate for small angles.
+    #[default]
+    Taylor,
+    /// p = sin^2(h_eff) applied to the Taylor quadratic form.
+    SinSquared,
+    /// Exact product formula for commuting generators:
+    ///   p = (1/2)(1 - Re(prod_j factor_j))
+    /// where factor_j depends on whether P_j or D·P_j is a stabilizer.
+    /// Captures all orders for the commuting case.
+    ExactCommuting,
+    /// Exact subset sum formula for commuting generators:
+    ///   p = (1/2)(1 - Re(Σ_S i^|S| Π sin · Π cos · ε_S))
+    /// Enumerates all even-size subsets of generators, checks if the
+    /// product (Π_{j∈S} P_j)·D is a stabilizer. Captures all orders of
+    /// multi-body interference. Exact for commuting generators. Cost: O(2^N)
+    /// where N is generators per event. Practical for N ≤ ~25.
+    ExactSubset,
+}
+
+/// BCH order for generator accumulation.
+#[derive(Clone, Copy, Debug, Default, PartialEq, Eq)]
+pub enum BchOrder {
+    /// First-order: G_c = sum G_i. Same-label rates add.
+    #[default]
+    First,
+    /// Second-order: G_c = sum G_i + (1/2) sum [G_i, G_j].
+    /// Adds new H generators from [H_P, H_Q] = 2i H_{PQ} for anticommuting P,Q.
+    /// Also adds Zassenhaus W_2 cross-event [H,S] → C corrections.
+    Second,
+}
+
+/// Configuration for the EEG DEM builder.
+///
+/// Controls all three approximation levels described in the paper:
+/// 1. BCH order (k): how generators from different layers are combined
+/// 2. Zassenhaus order: how the combined generator is split into single-event channels
+///    (coupled to BCH order — Second enables W_2 cross-event terms)
+/// 3. H-type formula: how detection probabilities are estimated from generators
+#[derive(Clone, Copy, Debug)]
+pub struct EegConfig {
+    /// BCH expansion order for combining layer errors (default: First).
+    pub bch_order: BchOrder,
+    /// Formula for H-type detection probability (default: Taylor).
+    pub h_formula: HFormula,
+}
+
+impl Default for EegConfig {
+    fn default() -> Self {
+        Self {
+            bch_order: BchOrder::First,
+            h_formula: HFormula::Taylor,
+        }
+    }
+}
+
+impl EegConfig {
+    /// Create config with default settings (first-order BCH, Taylor formula).
+    #[must_use]
+    pub fn new() -> Self {
+        Self::default()
+    }
+
+    /// Set BCH order to first (default). Same-label rate summation only.
+    #[must_use]
+    pub fn bch_first(mut self) -> Self {
+        self.bch_order = BchOrder::First;
+        self
+    }
+
+    /// Set BCH order to second. Adds [H,H] and [H,S] commutator corrections.
+    #[must_use]
+    pub fn bch_second(mut self) -> Self {
+        self.bch_order = BchOrder::Second;
+        self
+    }
+
+    /// Use leading-order Taylor (h²) for H-type probabilities (default).
+    #[must_use]
+    pub fn taylor(mut self) -> Self {
+        self.h_formula = HFormula::Taylor;
+        self
+    }
+
+    /// Use sin²(h_eff) for H-type probabilities.
+    #[must_use]
+    pub fn sin_squared(mut self) -> Self {
+        self.h_formula = HFormula::SinSquared;
+        self
+    }
+
+    /// Use exact product formula for commuting H-type generators.
+    #[must_use]
+    pub fn exact_commuting(mut self) -> Self {
+        self.h_formula = HFormula::ExactCommuting;
+        self
+    }
+
+    /// Use exact subset-sum formula for commuting H-type generators.
+    /// Captures all orders of multi-body interference. O(2^N) per event.
+    #[must_use]
+    pub fn exact_subset(mut self) -> Self {
+        self.h_formula = HFormula::ExactSubset;
+        self
+    }
+}
+
+/// A detector definition for EEG classification.
+#[derive(Clone, Debug)]
+pub struct Detector {
+    pub id: usize,
+    /// Pauli stabilizer. A Pauli P flips this detector iff P anticommutes with it.
+    pub stabilizer: Bm,
+}
+
+/// A logical observable for EEG classification.
+#[derive(Clone, Debug)]
+pub struct Observable {
+    pub id: usize,
+    pub pauli: Bm,
+}
+
+/// A DEM event: the set of detectors and observables flipped.
+#[derive(Clone, Debug, PartialEq, Eq, PartialOrd, Ord, Hash)]
+pub struct DemEvent {
+    pub detectors: SmallVec<[usize; 4]>,
+    pub observables: SmallVec<[usize; 2]>,
+}
+
+/// A DEM entry: event + probability.
+#[derive(Clone, Debug)]
+pub struct DemEntry {
+    pub event: DemEvent,
+    pub probability: f64,
+}
+
+/// A DEM entry with X/Z decomposition info for MWPM decoders.
+///
+/// When both `x_component` and `z_component` are `Some`, the mechanism
+/// can be output in decomposed form: `error(p) x_targets ^ z_targets`.
+/// When only one is present (pure X or Z error), output directly.
+#[derive(Clone, Debug)]
+pub struct DecomposableDemEntry {
+    /// Combined detector/observable flips (XOR of X and Z components).
+    pub event: DemEvent,
+    /// Mechanism probability.
+    pub probability: f64,
+    /// Detector/observable flips from the X-only component of the Pauli label.
+    /// None if the label has no X part.
+    pub x_component: Option<DemEvent>,
+    /// Detector/observable flips from the Z-only component of the Pauli label.
+    /// None if the label has no Z part.
+    pub z_component: Option<DemEvent>,
+}
+
+/// Convert PauliString to Bm.
+#[must_use]
+pub fn pauli_string_to_bitmask(ps: &PauliString) -> Bm {
+    let mut bm = Bm::default();
+    for &(pauli, qubit) in ps.paulis() {
+        let q = qubit.index();
+        match pauli {
+            Pauli::X => bm.x_bits.set_bit(q),
+            Pauli::Z => bm.z_bits.set_bit(q),
+            Pauli::Y => {
+                bm.x_bits.set_bit(q);
+                bm.z_bits.set_bit(q);
+            }
+            Pauli::I => {}
+        }
+    }
+    bm
+}
+
+/// Classify which detectors and observables a Pauli label anticommutes with.
+fn classify(label: &Bm, detectors: &[Detector], observables: &[Observable]) -> DemEvent {
+    let mut dets = SmallVec::new();
+    for det in detectors {
+        if !label.commutes_with(&det.stabilizer) {
+            dets.push(det.id);
+        }
+    }
+    let mut obs = SmallVec::new();
+    for o in observables {
+        if !label.commutes_with(&o.pauli) {
+            obs.push(o.id);
+        }
+    }
+    DemEvent {
+        detectors: dets,
+        observables: obs,
+    }
+}
+
+/// Classify with X/Z component decomposition.
+///
+/// Returns (combined_event, x_component, z_component) where x_component
+/// is the detectors/observables flipped by the X-only part of the label,
+/// and z_component by the Z-only part.
+fn classify_xz(
+    label: &Bm,
+    detectors: &[Detector],
+    observables: &[Observable],
+) -> (DemEvent, Option<DemEvent>, Option<DemEvent>) {
+    use pecos_core::pauli::pauli_bitmask::BitmaskStorage;
+
+    let has_x = !label.x_bits.is_zero();
+    let has_z = !label.z_bits.is_zero();
+
+    // Build X-only and Z-only labels
+    let x_only = if has_x {
+        Some(Bm {
+            x_bits: label.x_bits.clone(),
+            ..Default::default()
+        })
+    } else {
+        None
+    };
+    let z_only = if has_z {
+        Some(Bm {
+            z_bits: label.z_bits.clone(),
+            ..Default::default()
+        })
+    } else {
+        None
+    };
+
+    let combined = classify(label, detectors, observables);
+
+    let x_event = x_only.map(|x_label| classify(&x_label, detectors, observables));
+    let z_event = z_only.map(|z_label| classify(&z_label, detectors, observables));
+
+    (combined, x_event, z_event)
+}
+
+/// Build a DEM from propagated EEG generators.
+///
+/// Groups generators by DEM event class, then computes probabilities:
+/// - **S-only event**: p = (1/2)(1 - exp(-2 * sum_rates)) [exact]
+/// - **H-only event**: p = sum_j h_j^2 [leading order, diagonal terms]
+///   (Off-diagonal coherent interference captured at second order via beta)
+/// - **Mixed**: S at O(epsilon) + H^2 at O(epsilon^2)
+///
+/// For first-order BCH with leading-order Taylor, the H-only formula uses
+/// only diagonal terms: p = sum_j h_j^2. This is the Pauli-twirled
+/// equivalent. To capture coherent accumulation (off-diagonal terms),
+/// we need to check if pairs of H generators anticommute with the same
+/// detectors AND their product Q_j*Q_k is a stabilizer of |psi>.
+///
+/// For the first implementation, we use the diagonal approximation for H
+/// and the exact formula for S. This gives correct results for stochastic
+/// noise and a Pauli-twirled approximation for coherent noise. The full
+/// coherent formula (with off-diagonal beta terms) is future work.
+#[must_use]
+pub fn build_dem(
+    generators: &[PropagatedEeg],
+    detectors: &[Detector],
+    observables: &[Observable],
+) -> Vec<DemEntry> {
+    build_dem_with_stabilizers(generators, detectors, observables, None)
+}
+
+/// Build DEM with stabilizer group for coherent interference.
+#[must_use]
+pub fn build_dem_with_stabilizers(
+    generators: &[PropagatedEeg],
+    detectors: &[Detector],
+    observables: &[Observable],
+    stabilizer_group: Option<&StabilizerGroup>,
+) -> Vec<DemEntry> {
+    build_dem_inner(
+        generators,
+        detectors,
+        observables,
+        stabilizer_group,
+        HFormula::Taylor,
+        BchOrder::First,
+    )
+}
+
+/// Build DEM with all options via config struct.
+#[must_use]
+pub fn build_dem_configured(
+    generators: &[PropagatedEeg],
+    detectors: &[Detector],
+    observables: &[Observable],
+    stabilizer_group: Option<&StabilizerGroup>,
+    config: &EegConfig,
+) -> Vec<DemEntry> {
+    build_dem_inner(
+        generators,
+        detectors,
+        observables,
+        stabilizer_group,
+        config.h_formula,
+        config.bch_order,
+    )
+}
+
+/// Build DEM with individual options (convenience).
+#[must_use]
+pub fn build_dem_with_options(
+    generators: &[PropagatedEeg],
+    detectors: &[Detector],
+    observables: &[Observable],
+    stabilizer_group: Option<&StabilizerGroup>,
+    h_formula: HFormula,
+    bch_order: BchOrder,
+) -> Vec<DemEntry> {
+    build_dem_inner(
+        generators,
+        detectors,
+        observables,
+        stabilizer_group,
+        h_formula,
+        bch_order,
+    )
+}
+
+fn build_dem_inner(
+    generators: &[PropagatedEeg],
+    detectors: &[Detector],
+    observables: &[Observable],
+    stabilizer_group: Option<&StabilizerGroup>,
+    h_formula: HFormula,
+    bch_order: BchOrder,
+) -> Vec<DemEntry> {
+    // First-order BCH: combine generators with the same Pauli label.
+    // This is where coherent accumulation happens: h1 + h2 for same label.
+    let mut h_by_label: BTreeMap<Bm, f64> = BTreeMap::new();
+    let mut s_by_label: BTreeMap<Bm, f64> = BTreeMap::new();
+
+    // C and A type generators: two labels, first-order contribution.
+    // Key = (label1, label2), value = coefficient.
+    let mut c_generators: Vec<(Bm, Bm, f64)> = Vec::new();
+    let mut a_generators: Vec<(Bm, Bm, f64)> = Vec::new();
+
+    for g in generators {
+        match g.eeg_type {
+            EegType::H => {
+                *h_by_label.entry(g.label.clone()).or_insert(0.0) += g.coeff;
+            }
+            EegType::S => {
+                *s_by_label.entry(g.label.clone()).or_insert(0.0) += g.coeff;
+            }
+            EegType::C => {
+                if let Some(l2) = g.label2.clone() {
+                    c_generators.push((g.label.clone(), l2, g.coeff));
+                }
+            }
+            EegType::A => {
+                if let Some(l2) = g.label2.clone() {
+                    a_generators.push((g.label.clone(), l2, g.coeff));
+                }
+            }
+        }
+    }
+
+    // Second-order BCH: [H_P, H_Q] = -2i H_{PQ} for anticommuting P, Q.
+    // PQ = i^k * R (from multiply_with_phase), so H_{PQ} = i^k * H_R.
+    // BCH coefficient: (1/2) * (-2i) * i^k * h_i * h_j = -i^{k+1} * h_i * h_j.
+    // This can be real or imaginary depending on k.
+    let mut h_bch2_re_by_label: BTreeMap<Bm, f64> = BTreeMap::new();
+    let mut h_imag_by_label: BTreeMap<Bm, f64> = BTreeMap::new();
+
+    if bch_order == BchOrder::Second {
+        let h_entries: Vec<(Bm, f64)> = h_by_label.iter().map(|(l, &c)| (l.clone(), c)).collect();
+
+        for i in 0..h_entries.len() {
+            for j in (i + 1)..h_entries.len() {
+                let (p_i, h_i) = &h_entries[i];
+                let (p_j, h_j) = &h_entries[j];
+
+                if p_i.commutes_with(p_j) {
+                    continue;
+                }
+
+                // PQ = i^k * R. Coefficient: -i^{k+1} * h_i * h_j = i^{k+3} * h_i * h_j.
+                let (product, phase_k) = p_i.multiply_with_phase(p_j);
+                let mag = h_i * h_j;
+                let phase = (phase_k + 3) % 4; // -i^{k+1} = i^{k+3}
+                let (re_coeff, im_coeff) = match phase {
+                    0 => (mag, 0.0),  // 1
+                    1 => (0.0, mag),  // i
+                    2 => (-mag, 0.0), // -1
+                    3 => (0.0, -mag), // -i
+                    _ => unreachable!(),
+                };
+
+                *h_bch2_re_by_label.entry(product.clone()).or_insert(0.0) += re_coeff;
+                *h_imag_by_label.entry(product).or_insert(0.0) += im_coeff;
+            }
+        }
+    }
+
+    // Zassenhaus W_2: cross-event commutators produce generators in new or
+    // existing event classes. These are iteratively decomposed by event class
+    // and their detection contributions computed (paper step 4).
+    //
+    // [H_P, S_Q] = i C_{Q, [Q,P]} → C-type with imaginary coeff i·h·s
+    // [H_P, H_Q] = -i H_{[P,Q]} → H-type with imaginary coeff (already in BCH2 above)
+    // [S_P, S_Q] = 0 → no contribution
+    //
+    // The [H,S] cross-terms produce C-type generators. At leading order,
+    // their purely imaginary coefficients give zero contribution to
+    // detection: Re(i·h·s · β) = 0 for real β. The paper's O(ε^{3/2})
+    // error bound accounts for this.
+    if bch_order == BchOrder::Second {
+        let h_entries: Vec<(Bm, f64)> = h_by_label.iter().map(|(l, &c)| (l.clone(), c)).collect();
+        let s_entries: Vec<(Bm, f64)> = s_by_label.iter().map(|(l, &c)| (l.clone(), c)).collect();
+
+        for (p, _h_coeff) in &h_entries {
+            for (q, _s_coeff) in &s_entries {
+                if p.commutes_with(q) {
+                    continue;
+                }
+
+                // [H_P, S_Q] = i C_{Q, QP} (for anticommuting P,Q: [Q,P]=2QP)
+                // QP = i^k * R (from multiply_with_phase).
+                // Zassenhaus (1/2) factor: coeff = (1/2)·h·s·i·2·i^k = i^{k+1}·h·s
+                // For k=0: purely imaginary → zero real contribution at leading order.
+                // For k≠0: may have real part, but still O(ε^{3/2}).
+                let (qp, _phase) = q.multiply_with_phase(p);
+                c_generators.push((q.clone(), qp, 0.0));
+            }
+        }
+    }
+
+    // Merge real and imaginary H-type generators into complex coefficients.
+    // BCH2 can contribute both real and imaginary parts to generator labels.
+    // Merge BCH2 real parts into h_by_label.
+    for (label, &re) in &h_bch2_re_by_label {
+        *h_by_label.entry(label.clone()).or_insert(0.0) += re;
+    }
+
+    let all_h_labels: std::collections::BTreeSet<Bm> = h_by_label
+        .keys()
+        .chain(h_imag_by_label.keys())
+        .cloned()
+        .collect();
+
+    // Group BCH-combined generators by DEM event class.
+    // Store (real, imag) coefficient pairs per label.
+    let mut h_events: BTreeMap<DemEvent, Vec<(f64, f64)>> = BTreeMap::new();
+    let mut s_events: BTreeMap<DemEvent, Vec<f64>> = BTreeMap::new();
+    let mut event_pauli_labels: BTreeMap<DemEvent, Vec<Bm>> = BTreeMap::new();
+
+    for label in &all_h_labels {
+        let re = h_by_label.get(label).copied().unwrap_or(0.0);
+        let im = h_imag_by_label.get(label).copied().unwrap_or(0.0);
+        if re.abs() < 1e-20 && im.abs() < 1e-20 {
+            continue;
+        }
+        let event = classify(label, detectors, observables);
+        if event.detectors.is_empty() && event.observables.is_empty() {
+            continue;
+        }
+        h_events.entry(event.clone()).or_default().push((re, im));
+        event_pauli_labels
+            .entry(event)
+            .or_default()
+            .push(label.clone());
+    }
+
+    for (label, &coeff) in &s_by_label {
+        let event = classify(label, detectors, observables);
+        if event.detectors.is_empty() && event.observables.is_empty() {
+            continue;
+        }
+        s_events.entry(event).or_default().push(coeff);
+    }
+
+    let mut entries = Vec::new();
+
+    // S-only events: exact formula
+    // p_D = (1/2)(1 - exp(2 * sum_rates))
+    // Note: S rates are negative (e.g., -p/3), so 2*sum is negative,
+    // exp(2*sum) < 1, and p_D > 0.
+    for (event, rates) in &s_events {
+        let sum_rate: f64 = rates.iter().sum();
+        let prob = (1.0 - (2.0 * sum_rate).exp()) / 2.0;
+        if prob.abs() > 1e-15 {
+            entries.push(DemEntry {
+                event: event.clone(),
+                probability: prob.abs(),
+            });
+        }
+    }
+
+    // C-type and A-type first-order contributions.
+    // β(ψ, C_{Q1,Q2}, P) = ±4 if [Q1,Q2]=0, [Q1,P]≠0, [Q2,P]≠0, Q1Q2|ψ⟩=∓|ψ⟩
+    // β(ψ, A_{Q1,Q2}, P) = ±4 if [Q1,Q2]≠0, [Q1,P]≠0, [Q2,P]≠0, iQ1Q2|ψ⟩=±|ψ⟩
+    // These contribute at first order (same as S).
+    if let Some(stab_group) = stabilizer_group {
+        for &(ref q1, ref q2, coeff) in c_generators.iter().chain(a_generators.iter()) {
+            // Classify: both Q1 and Q2 must anticommute with the same detectors
+            let event1 = classify(q1, detectors, observables);
+            let event2 = classify(q2, detectors, observables);
+            if event1 != event2 || (event1.detectors.is_empty() && event1.observables.is_empty()) {
+                continue;
+            }
+            let event = event1;
+
+            // Check commutativity condition
+            let q1_q2_commute = q1.commutes_with(q2);
+            let is_c_type = c_generators.iter().any(|(a, b, _)| a == q1 && b == q2);
+
+            // C requires [Q1,Q2]=0, A requires [Q1,Q2]≠0
+            if is_c_type && !q1_q2_commute {
+                continue;
+            }
+            if !is_c_type && q1_q2_commute {
+                continue;
+            }
+
+            // Check product stabilizer status
+            let product = q1.multiply(q2);
+            let beta = if product.is_identity() {
+                Some(true)
+            } else {
+                stab_group.is_stabilizer(&product)
+            };
+
+            // β = ±4, contribution to p_D = coeff * β / (-2) at first order
+            // (detection probability p = (1/2)(1 - ⟨Q⟩), ⟨Q⟩ ≈ 1 + β·ε)
+            // For C: β = ±4 → p contribution = -coeff * (±4) / 2 = ∓2·coeff
+            // For A: β = ±4 → same
+            if let Some(sign) = beta {
+                let beta_val = if sign { -4.0 } else { 4.0 };
+                // For A-type, the stabilizer check is on iQ1Q2, not Q1Q2.
+                // Since we check Q1Q2, the sign interpretation differs for A.
+                // A: iQ1Q2|ψ⟩=±|ψ⟩ → Q1Q2|ψ⟩=∓i|ψ⟩. For real stabilizer
+                // eigenvalues (±1), this means Q1Q2 is NOT a real stabilizer.
+                // A-type only contributes when iQ1Q2 has eigenvalue ±1,
+                // which means Q1Q2 has eigenvalue ∓i. Skip for now since
+                // stabilizer eigenvalues are always ±1.
+                if !is_c_type {
+                    continue;
+                }
+
+                let prob_contribution = -coeff * beta_val / 2.0;
+                if prob_contribution.abs() > 1e-15 {
+                    if let Some(existing) = entries.iter_mut().find(|e| e.event == event) {
+                        let p_s = existing.probability;
+                        existing.probability =
+                            p_s + prob_contribution.abs() - 2.0 * p_s * prob_contribution.abs();
+                    } else {
+                        entries.push(DemEntry {
+                            event: event.clone(),
+                            probability: prob_contribution.abs(),
+                        });
+                    }
+                }
+            }
+        }
+    }
+
+    // H-only events: full leading-order formula with coherent interference.
+    //
+    // p_D = -(1/4) * sum_{j,k} h_j * h_k * beta(psi, C_{Qj,Qk}, P)
+    //
+    // beta(psi, C_{Q,Q'}, P) = -4 if [Q,Q']=0 and Q*Q'|psi>=+|psi> (stabilizer)
+    //                        = +4 if [Q,Q']=0 and Q*Q'|psi>=-|psi> (anti-stabilizer)
+    //                        = 0 otherwise
+    //
+    // Diagonal terms (j=k): Q*Q=I, always +1 stabilizer → beta=-4 → contributes +h_j^2
+    // Off-diagonal with stabilizer product: contributes +h_j*h_k (constructive)
+    // Off-diagonal with anti-stabilizer: contributes -h_j*h_k (destructive)
+    //
+    // If stabilizer_group is None, fall back to diagonal approximation.
+    for (event, coeffs) in &h_events {
+        // Collect the detector stabilizers for this event (for ExactCommuting)
+        let event_det_stab =
+            if h_formula == HFormula::ExactCommuting || h_formula == HFormula::ExactSubset {
+                // XOR of all detector stabilizers in this event
+                let mut stab = Bm::default();
+                for &d_id in &event.detectors {
+                    if let Some(det) = detectors.iter().find(|d| d.id == d_id) {
+                        stab = stab.multiply(&det.stabilizer);
+                    }
+                }
+                Some(stab)
+            } else {
+                None
+            };
+
+        let prob = if let Some(stab_group) = stabilizer_group {
+            compute_h_probability_full(
+                coeffs,
+                generators,
+                &event_pauli_labels,
+                event,
+                stab_group,
+                h_formula,
+                event_det_stab.as_ref(),
+            )
+        } else {
+            coeffs.iter().map(|&(re, im)| re * re + im * im).sum()
+        };
+        if prob > 1e-15 {
+            if let Some(existing) = entries.iter_mut().find(|e| e.event == *event) {
+                let p_s = existing.probability;
+                existing.probability = p_s + prob - 2.0 * p_s * prob;
+            } else {
+                entries.push(DemEntry {
+                    event: event.clone(),
+                    probability: prob,
+                });
+            }
+        }
+    }
+
+    entries
+}
+
+/// Compute H-type event probability using the full beta function.
+///
+/// p_D = -(1/4) * sum_{j,k} h_j * h_k * beta(psi, C_{Qj,Qk}, P)
+///
+/// For each pair (j,k):
+/// - If [Q_j, Q_k] ≠ 0: beta = 0
+/// - If [Q_j, Q_k] = 0 and Q_j*Q_k is +1 stabilizer: beta = -4 → +h_j*h_k
+/// - If [Q_j, Q_k] = 0 and Q_j*Q_k is -1 stabilizer: beta = +4 → -h_j*h_k
+/// - Otherwise: beta = 0
+fn compute_h_probability_full(
+    coeffs: &[(f64, f64)],
+    _generators: &[PropagatedEeg],
+    event_labels: &BTreeMap<DemEvent, Vec<Bm>>,
+    event: &DemEvent,
+    stab_group: &StabilizerGroup,
+    h_formula: HFormula,
+    det_stabilizer: Option<&Bm>,
+) -> f64 {
+    let Some(labels) = event_labels.get(event) else {
+        return 0.0;
+    };
+
+    let n = coeffs.len();
+
+    // --- ExactCommuting: product formula for commuting generators ---
+    if h_formula == HFormula::ExactCommuting
+        && let Some(det_stab) = det_stabilizer
+    {
+        return compute_exact_commuting(coeffs, labels, stab_group, det_stab);
+    }
+
+    // --- ExactSubset: enumerate all even-size subsets ---
+    if h_formula == HFormula::ExactSubset
+        && let Some(det_stab) = det_stabilizer
+    {
+        return compute_exact_subset(coeffs, labels, stab_group, det_stab);
+    }
+
+    // --- Taylor or SinSquared: quadratic form with beta ---
+    let mut total = 0.0_f64;
+
+    for j in 0..n {
+        for k in 0..n {
+            let (re_j, im_j) = coeffs[j];
+            let (re_k, im_k) = coeffs[k];
+            let re_product = re_j * re_k - im_j * im_k;
+
+            if j == k {
+                total += re_j * re_j + im_j * im_j;
+            } else {
+                let q_j = &labels[j];
+                let q_k = &labels[k];
+
+                if !q_j.commutes_with(q_k) {
+                    continue;
+                }
+
+                let product = q_j.multiply(q_k);
+
+                if product.is_identity() {
+                    total += re_product;
+                    continue;
+                }
+
+                match stab_group.is_stabilizer(&product) {
+                    Some(true) => {
+                        total += re_product;
+                    }
+                    Some(false) => {
+                        total -= re_product;
+                    }
+                    None => {}
+                }
+            }
+        }
+    }
+
+    let total = total.max(0.0);
+
+    match h_formula {
+        HFormula::SinSquared => {
+            let h_eff = total.sqrt();
+            h_eff.sin().powi(2)
+        }
+        HFormula::Taylor | HFormula::ExactCommuting | HFormula::ExactSubset => total,
+    }
+}
+
+/// Exact product formula for commuting H-type generators.
+///
+/// For each generator P_j with rate h_j:
+/// - If P_j is a ±1 stabilizer: factor = exp(±2i h_j) → contributes to phase
+/// - If D·P_j is a ±1 stabilizer: factor = exp(∓2i h_j) → contributes to phase
+/// - Neither: factor = cos(2h_j) → real damping
+///
+/// p_D = (1/2)(1 - Re(prod_j factor_j))
+fn compute_exact_commuting(
+    coeffs: &[(f64, f64)],
+    labels: &[Bm],
+    stab_group: &StabilizerGroup,
+    det_stab: &Bm,
+) -> f64 {
+    let n = coeffs.len();
+    // Accumulate product as (real, imag) complex number
+    let mut prod_re = 1.0_f64;
+    let mut prod_im = 0.0_f64;
+
+    for j in 0..n {
+        let (h_re, h_im) = coeffs[j];
+        // For simplicity, use magnitude of complex coefficient
+        let h = (h_re * h_re + h_im * h_im).sqrt();
+        if h < 1e-20 {
+            continue;
+        }
+
+        let label = &labels[j];
+
+        // Check if P_j is a stabilizer (directly in expanded frame)
+        let p_stab = if label.is_identity() {
+            Some(true)
+        } else {
+            stab_group.is_stabilizer(label)
+        };
+
+        let (factor_re, factor_im) = if let Some(sign) = p_stab {
+            let s = if sign { 1.0 } else { -1.0 };
+            let angle = 2.0 * s * h;
+            (angle.cos(), angle.sin())
+        } else {
+            // Check D·P_j
+            let dp = det_stab.multiply(label);
+            let dp_stab = if dp.is_identity() {
+                Some(true)
+            } else {
+                stab_group.is_stabilizer(&dp)
+            };
+
+            if let Some(sign) = dp_stab {
+                let s = if sign { 1.0 } else { -1.0 };
+                let angle = -2.0 * s * h;
+                (angle.cos(), angle.sin())
+            } else {
+                ((2.0 * h).cos(), 0.0)
+            }
+        };
+
+        // Complex multiply: prod *= factor
+        let new_re = prod_re * factor_re - prod_im * factor_im;
+        let new_im = prod_re * factor_im + prod_im * factor_re;
+        prod_re = new_re;
+        prod_im = new_im;
+    }
+
+    // p_D = (1/2)(1 - Re(product))
+    let prob = 0.5 * (1.0 - prod_re);
+    prob.max(0.0)
+}
+
+/// Exact subset-sum formula for commuting H-type generators.
+///
+/// Enumerates ALL even-size subsets S of generators. For each:
+///   coefficient = i^|S| · Π_{j∈S} sin(2h_j) · Π_{j∉S} cos(2h_j)
+///   eigenvalue  = ε_S = ⟨ψ|(Π_{j∈S} P_j)·D|ψ⟩
+///
+/// p_D = (1/2)(1 - Re(Σ_S coefficient · ε_S))
+///
+/// Only even-|S| subsets contribute to Re (odd powers of i are imaginary).
+/// This captures all orders of multi-body interference. Exact when all
+/// generators commute. Cost: O(2^N) where N = number of generators.
+fn compute_exact_subset(
+    coeffs: &[(f64, f64)],
+    labels: &[Bm],
+    stab_group: &StabilizerGroup,
+    det_stab: &Bm,
+) -> f64 {
+    let n = coeffs.len();
+
+    // Guard: too many generators → fall back to ExactCommuting
+    if n > 25 {
+        return compute_exact_commuting(coeffs, labels, stab_group, det_stab);
+    }
+
+    // Precompute sin(2h_j) and cos(2h_j) for each generator
+    let mut sin2h = Vec::with_capacity(n);
+    let mut cos2h = Vec::with_capacity(n);
+    for &(h_re, h_im) in coeffs.iter().take(n) {
+        let h = (h_re * h_re + h_im * h_im).sqrt();
+        sin2h.push((2.0 * h).sin());
+        cos2h.push((2.0 * h).cos());
+    }
+
+    // The empty set (S = {}) contributes: Π cos(2h_j) · ε_{D}
+    // D itself should be a stabilizer with eigenvalue +1 (no error → ⟨D⟩=1).
+    let all_cos: f64 = cos2h.iter().product();
+
+    let mut sum_re = all_cos; // |S|=0 contribution
+
+    // Enumerate all non-empty even-size subsets via bitmask
+    // For |S| even: i^|S| has Re = (-1)^{|S|/2}
+    let total_subsets = 1u64 << n;
+    for mask in 1..total_subsets {
+        let size = mask.count_ones() as usize;
+        if !size.is_multiple_of(2) {
+            continue; // odd-size subsets have Im(i^|S|) only → Re = 0
+        }
+
+        // Compute product of labels in S, multiplied by det_stab (D)
+        let mut product = det_stab.clone();
+        for (j, label) in labels.iter().enumerate().take(n) {
+            if mask & (1u64 << j) != 0 {
+                product = product.multiply(label);
+            }
+        }
+
+        // Check if this product is a stabilizer
+        let eigenvalue = if product.is_identity() {
+            Some(true)
+        } else {
+            stab_group.is_stabilizer(&product)
+        };
+
+        let epsilon = match eigenvalue {
+            Some(true) => 1.0,
+            Some(false) => -1.0,
+            None => continue, // not a stabilizer, ε=0
+        };
+
+        // Coefficient: (-1)^{|S|/2} · Π_{j∈S} sin(2h_j) · Π_{j∉S} cos(2h_j)
+        let sign = if (size / 2).is_multiple_of(2) {
+            1.0
+        } else {
+            -1.0
+        };
+
+        let mut coeff = sign;
+        for (j, (&sin, &cos)) in sin2h.iter().zip(&cos2h).enumerate().take(n) {
+            if mask & (1u64 << j) != 0 {
+                coeff *= sin;
+            } else {
+                coeff *= cos;
+            }
+        }
+
+        sum_re += coeff * epsilon;
+    }
+
+    let prob = 0.5 * (1.0 - sum_re);
+    prob.max(0.0)
+}
+
+/// Sensitivity matrix M_E for a DEM event E (Hines Eq. 21).
+///
+/// M_E encodes how physical-level Hamiltonian error parameters affect the
+/// probability of event E: p_E = -(1/2) θ^T M_E θ.
+///
+/// The matrix is indexed by `NoiseSource` pairs. Each entry M[i,j] = b_{P,Q_i,Q_j}
+/// where b is the beta coefficient for the generator pair (Q_i, Q_j) and P is
+/// the detector for event E.
+///
+/// Returns: Vec of (source_i, source_j, value) triplets for non-zero entries.
+#[must_use]
+pub fn sensitivity_matrix(
+    generators: &[crate::circuit::PropagatedEeg],
+    detectors: &[Detector],
+    observables: &[Observable],
+    stabilizer_group: Option<&StabilizerGroup>,
+) -> BTreeMap<
+    DemEvent,
+    Vec<(
+        crate::circuit::NoiseSource,
+        crate::circuit::NoiseSource,
+        f64,
+    )>,
+> {
+    use crate::circuit::NoiseSource;
+    use crate::eeg::EegType;
+
+    let mut result = BTreeMap::new();
+
+    // Collect H generators with their sources
+    let h_gens: Vec<_> = generators
+        .iter()
+        .filter(|g| g.eeg_type == EegType::H && g.source.is_some())
+        .collect();
+
+    // Group by event class
+    let mut event_gens: BTreeMap<DemEvent, Vec<(Bm, f64, NoiseSource)>> = BTreeMap::new();
+    for g in &h_gens {
+        let event = classify(&g.label, detectors, observables);
+        if event.detectors.is_empty() && event.observables.is_empty() {
+            continue;
+        }
+        event_gens.entry(event).or_default().push((
+            g.label.clone(),
+            g.coeff,
+            g.source.clone().unwrap(),
+        ));
+    }
+
+    // For each event class, build the sensitivity matrix
+    for (event, gens) in &event_gens {
+        let mut entries = Vec::new();
+
+        for i in 0..gens.len() {
+            for j in 0..gens.len() {
+                let (ref label_i, _coeff_i, ref src_i) = gens[i];
+                let (ref label_j, _coeff_j, ref src_j) = gens[j];
+
+                // Beta coefficient for pair (i,j)
+                let beta_val: f64 = if i == j {
+                    1.0 // diagonal: beta = -4, but -(1/4)*(-4) = 1
+                } else if label_i.commutes_with(label_j) {
+                    let product = label_i.multiply(label_j);
+                    if product.is_identity() {
+                        1.0
+                    } else if let Some(stab) = stabilizer_group {
+                        match stab.is_stabilizer(&product) {
+                            Some(true) => 1.0,
+                            Some(false) => -1.0,
+                            None => 0.0,
+                        }
+                    } else {
+                        0.0
+                    }
+                } else {
+                    0.0
+                };
+
+                if beta_val.abs() > 1e-15_f64 {
+                    entries.push((src_i.clone(), src_j.clone(), beta_val));
+                }
+            }
+        }
+
+        if !entries.is_empty() {
+            result.insert(event.clone(), entries);
+        }
+    }
+
+    result
+}
+
+/// Build a decomposable DEM from propagated EEG generators.
+///
+/// Same as `build_dem_configured` but includes X/Z component decomposition
+/// for each mechanism, enabling proper graphlike decomposition for MWPM decoders.
+#[must_use]
+pub fn build_dem_decomposable(
+    generators: &[PropagatedEeg],
+    detectors: &[Detector],
+    observables: &[Observable],
+    stabilizer_group: Option<&StabilizerGroup>,
+    config: &EegConfig,
+) -> Vec<DecomposableDemEntry> {
+    // First, build the standard DEM entries with the requested config
+    let standard_entries =
+        build_dem_configured(generators, detectors, observables, stabilizer_group, config);
+
+    // Build a map from combined event → (x_component, z_component)
+    // by classifying each unique label's X/Z components.
+    // Multiple generators may contribute to the same event, but their
+    // X/Z classification should be consistent (same combined effect = same decomposition).
+    let mut event_xz: BTreeMap<EventKey, XzComponents> = BTreeMap::new();
+
+    for g in generators {
+        let (combined, x_ev, z_ev) = classify_xz(&g.label, detectors, observables);
+        let key = (combined.detectors.clone(), combined.observables.clone());
+        // First generator for this event wins (they should all agree)
+        event_xz.entry(key).or_insert((x_ev, z_ev));
+    }
+
+    // Convert standard entries to decomposable entries
+    standard_entries
+        .into_iter()
+        .map(|entry| {
+            let key = (
+                entry.event.detectors.clone(),
+                entry.event.observables.clone(),
+            );
+            let (x_comp, z_comp) = event_xz.get(&key).cloned().unwrap_or((None, None));
+            DecomposableDemEntry {
+                event: entry.event,
+                probability: entry.probability,
+                x_component: x_comp,
+                z_component: z_comp,
+            }
+        })
+        .collect()
+}
+
+/// Format DEM entries as a Stim-compatible string.
+#[must_use]
+pub fn format_dem(entries: &[DemEntry]) -> String {
+    let mut lines = Vec::new();
+    for entry in entries {
+        let mut parts = Vec::new();
+        for &d in &entry.event.detectors {
+            parts.push(format!("D{d}"));
+        }
+        for &o in &entry.event.observables {
+            parts.push(format!("L{o}"));
+        }
+        if !parts.is_empty() {
+            lines.push(format!(
+                "error({:.6e}) {}",
+                entry.probability,
+                parts.join(" ")
+            ));
+        }
+    }
+    lines.join("\n")
+}
+
+/// Format a list of decomposable DEM entries into a graphlike DEM string.
+///
+/// Mechanisms with both X and Z components are output as `error(p) x_targets ^ z_targets`.
+/// Single-component mechanisms with ≤ 2 detectors are output directly.
+/// Single-component hyperedges (3+ detectors) are decomposed via a graphlike
+/// index: expressed as XOR of existing graphlike mechanisms. If no decomposition
+/// exists, the mechanism is dropped (cannot be used by MWPM decoders).
+#[must_use]
+pub fn format_dem_decomposed(entries: &[DecomposableDemEntry]) -> String {
+    use std::collections::{BTreeMap, BTreeSet};
+
+    fn format_event(ev: &DemEvent) -> String {
+        let mut parts = Vec::new();
+        for &d in &ev.detectors {
+            parts.push(format!("D{d}"));
+        }
+        for &o in &ev.observables {
+            parts.push(format!("L{o}"));
+        }
+        parts.join(" ")
+    }
+
+    fn is_graphlike(ev: &DemEvent) -> bool {
+        ev.detectors.len() <= 2
+    }
+
+    // Search for decomposition of a hyperedge into XOR of graphlike pieces
+    fn search_decomp(
+        remaining: &DetectorSet,
+        by_det: &[Vec<DetectorSet>],
+        graphlike_set: &BTreeSet<DetectorSet>,
+        memo: &mut DecompMemo,
+    ) -> Option<GraphlikePieces> {
+        if let Some(cached) = memo.get(remaining) {
+            return cached.clone();
+        }
+        if remaining.is_empty() {
+            let r = Some(Vec::new());
+            memo.insert(remaining.clone(), r.clone());
+            return r;
+        }
+        if remaining.len() <= 2 && graphlike_set.contains(remaining) {
+            let r = Some(vec![remaining.clone()]);
+            memo.insert(remaining.clone(), r.clone());
+            return r;
+        }
+
+        let pivot = remaining[0];
+        if pivot >= by_det.len() {
+            memo.insert(remaining.clone(), None);
+            return None;
+        }
+
+        for candidate in &by_det[pivot] {
+            // Candidate detectors must be subset of remaining
+            if !candidate.iter().all(|d| remaining.contains(d)) {
+                continue;
+            }
+            // XOR: remove shared detectors, keep symmetric difference
+            let mut next: SmallVec<[usize; 4]> = SmallVec::new();
+            let mut i = 0;
+            let mut j = 0;
+            let r = remaining;
+            let c = candidate;
+            while i < r.len() && j < c.len() {
+                match r[i].cmp(&c[j]) {
+                    std::cmp::Ordering::Less => {
+                        next.push(r[i]);
+                        i += 1;
+                    }
+                    std::cmp::Ordering::Greater => {
+                        next.push(c[j]);
+                        j += 1;
+                    }
+                    std::cmp::Ordering::Equal => {
+                        i += 1;
+                        j += 1;
+                    }
+                }
+            }
+            while i < r.len() {
+                next.push(r[i]);
+                i += 1;
+            }
+            while j < c.len() {
+                next.push(c[j]);
+                j += 1;
+            }
+
+            if next.len() >= remaining.len() {
+                continue;
+            } // must make progress
+
+            if let Some(suffix) = search_decomp(&next, by_det, graphlike_set, memo) {
+                let mut result = vec![candidate.clone()];
+                result.extend(suffix);
+                result.sort();
+                let r = Some(result);
+                memo.insert(remaining.clone(), r.clone());
+                return r;
+            }
+        }
+
+        memo.insert(remaining.clone(), None);
+        None
+    }
+
+    // Step 1: Collect all graphlike mechanisms (building blocks for decomposition)
+    let mut graphlike_set: BTreeSet<SmallVec<[usize; 4]>> = BTreeSet::new();
+    for entry in entries {
+        if entry.probability <= 0.0 {
+            continue;
+        }
+        // Collect graphlike from X/Z components
+        if let Some(ref x) = entry.x_component
+            && is_graphlike(x)
+            && !x.detectors.is_empty()
+        {
+            graphlike_set.insert(x.detectors.clone());
+        }
+        if let Some(ref z) = entry.z_component
+            && is_graphlike(z)
+            && !z.detectors.is_empty()
+        {
+            graphlike_set.insert(z.detectors.clone());
+        }
+        // Also from combined event
+        if is_graphlike(&entry.event) && !entry.event.detectors.is_empty() {
+            graphlike_set.insert(entry.event.detectors.clone());
+        }
+    }
+
+    // Step 2: Build index for graphlike decomposition search
+    let max_det = graphlike_set
+        .iter()
+        .flat_map(|d| d.iter().copied())
+        .max()
+        .unwrap_or(0);
+    let mut by_det: Vec<Vec<SmallVec<[usize; 4]>>> = vec![Vec::new(); max_det + 1];
+    for g in &graphlike_set {
+        for &d in g {
+            by_det[d].push(g.clone());
+        }
+    }
+
+    // Step 3: Format entries
+    let mut by_targets: BTreeMap<String, f64> = BTreeMap::new();
+    let mut memo: DecompMemo = BTreeMap::new();
+
+    for entry in entries {
+        if entry.probability <= 0.0 {
+            continue;
+        }
+
+        let targets = match (&entry.x_component, &entry.z_component) {
+            (Some(x), Some(z)) if !x.detectors.is_empty() && !z.detectors.is_empty() => {
+                // Both components non-empty: decompose as X ^ Z
+                let x_str = format_event(x);
+                let z_str = format_event(z);
+                if x_str == z_str {
+                    x_str
+                } else {
+                    format!("{x_str} ^ {z_str}")
+                }
+            }
+            (Some(x), _) if !x.detectors.is_empty() || !x.observables.is_empty() => {
+                if is_graphlike(x) {
+                    format_event(x)
+                } else {
+                    // Hyperedge X-only: try graphlike decomposition
+                    match search_decomp(&x.detectors, &by_det, &graphlike_set, &mut memo) {
+                        Some(pieces) => {
+                            let mut parts: Vec<String> = pieces
+                                .iter()
+                                .map(|p| {
+                                    p.iter()
+                                        .map(|d| format!("D{d}"))
+                                        .collect::<Vec<_>>()
+                                        .join(" ")
+                                })
+                                .collect();
+                            // Attach observables to first piece
+                            if !x.observables.is_empty() && !parts.is_empty() {
+                                for &o in &x.observables {
+                                    let _ = write!(&mut parts[0], " L{o}");
+                                }
+                            }
+                            parts.join(" ^ ")
+                        }
+                        None => continue, // drop undecomposable mechanisms
+                    }
+                }
+            }
+            (_, Some(z)) if !z.detectors.is_empty() || !z.observables.is_empty() => {
+                if is_graphlike(z) {
+                    format_event(z)
+                } else {
+                    // Hyperedge Z-only: try graphlike decomposition
+                    match search_decomp(&z.detectors, &by_det, &graphlike_set, &mut memo) {
+                        Some(pieces) => {
+                            let mut parts: Vec<String> = pieces
+                                .iter()
+                                .map(|p| {
+                                    p.iter()
+                                        .map(|d| format!("D{d}"))
+                                        .collect::<Vec<_>>()
+                                        .join(" ")
+                                })
+                                .collect();
+                            if !z.observables.is_empty() && !parts.is_empty() {
+                                for &o in &z.observables {
+                                    let _ = write!(&mut parts[0], " L{o}");
+                                }
+                            }
+                            parts.join(" ^ ")
+                        }
+                        None => continue, // drop undecomposable mechanisms
+                    }
+                }
+            }
+            _ => {
+                if is_graphlike(&entry.event) {
+                    format_event(&entry.event)
+                } else {
+                    // Combined hyperedge without components: try graphlike decomposition
+                    match search_decomp(&entry.event.detectors, &by_det, &graphlike_set, &mut memo)
+                    {
+                        Some(pieces) => {
+                            let mut parts: Vec<String> = pieces
+                                .iter()
+                                .map(|p| {
+                                    p.iter()
+                                        .map(|d| format!("D{d}"))
+                                        .collect::<Vec<_>>()
+                                        .join(" ")
+                                })
+                                .collect();
+                            if !entry.event.observables.is_empty() && !parts.is_empty() {
+                                for &o in &entry.event.observables {
+                                    let _ = write!(&mut parts[0], " L{o}");
+                                }
+                            }
+                            parts.join(" ^ ")
+                        }
+                        None => continue,
+                    }
+                }
+            }
+        };
+
+        if targets.is_empty() {
+            continue;
+        }
+
+        by_targets
+            .entry(targets)
+            .and_modify(|p| {
+                *p = *p + entry.probability - 2.0 * *p * entry.probability;
+            })
+            .or_insert(entry.probability);
+    }
+
+    let mut lines = Vec::new();
+    for (targets, prob) in &by_targets {
+        if *prob > 0.0 {
+            lines.push(format!("error({prob:.6e}) {targets}"));
+        }
+    }
+    lines.join("\n")
+}
+
+#[cfg(test)]
+mod tests {
+    use super::*;
+
+    fn z_det(id: usize, qubits: &[usize]) -> Detector {
+        let mut bm = Bm::default();
+        for &q in qubits {
+            bm.z_bits.set_bit(q);
+        }
+        Detector { id, stabilizer: bm }
+    }
+
+    #[test]
+    fn test_s_only_probability() {
+        // Single S_X with rate -0.01 → p ≈ 0.00995
+        let gens = vec![PropagatedEeg {
+            eeg_type: EegType::S,
+            label: Bm::x(0),
+            label2: None,
+            coeff: -0.01,
+            source: None,
+        }];
+        let dets = vec![z_det(0, &[0])]; // Z0 anticommutes with X0
+        let entries = build_dem(&gens, &dets, &[]);
+
+        assert_eq!(entries.len(), 1);
+        let expected = (1.0 - (-0.02_f64).exp()) / 2.0;
+        assert!((entries[0].probability - expected).abs() < 1e-6);
+    }
+
+    #[test]
+    fn test_h_diagonal_probability() {
+        // H_X with rate 0.1 → p = 0.1^2 = 0.01 (diagonal approx)
+        let gens = vec![PropagatedEeg {
+            eeg_type: EegType::H,
+            label: Bm::x(0),
+            label2: None,
+            coeff: 0.1,
+            source: None,
+        }];
+        let dets = vec![z_det(0, &[0])];
+        let entries = build_dem(&gens, &dets, &[]);
+
+        assert_eq!(entries.len(), 1);
+        assert!((entries[0].probability - 0.01).abs() < 1e-10);
+    }
+
+    #[test]
+    fn test_h_multiple_same_event() {
+        // Two H generators in same event class: rates don't add (diagonal approx)
+        // p = h1^2 + h2^2 (NOT (h1+h2)^2 — that would be coherent accumulation)
+        let gens = vec![
+            PropagatedEeg {
+                eeg_type: EegType::H,
+                label: Bm::x(0),
+                label2: None,
+                coeff: 0.1,
+                source: None,
+            },
+            PropagatedEeg {
+                eeg_type: EegType::H,
+                label: Bm::y(0),
+                label2: None,
+                coeff: 0.05,
+                source: None,
+            },
+        ];
+        let dets = vec![z_det(0, &[0])]; // Both X0 and Y0 anticommute with Z0
+        let entries = build_dem(&gens, &dets, &[]);
+
+        // Diagonal: p = 0.1^2 + 0.05^2 = 0.01 + 0.0025 = 0.0125
+        assert_eq!(entries.len(), 1);
+        assert!((entries[0].probability - 0.0125).abs() < 1e-10);
+    }
+
+    #[test]
+    fn test_z_invisible_to_z_detector() {
+        // H_Z should NOT flip a Z-type detector (Z commutes with Z)
+        let gens = vec![PropagatedEeg {
+            eeg_type: EegType::H,
+            label: Bm::z(0),
+            label2: None,
+            coeff: 0.1,
+            source: None,
+        }];
+        let dets = vec![z_det(0, &[0])];
+        let entries = build_dem(&gens, &dets, &[]);
+
+        assert!(entries.is_empty(), "Z should not flip Z detector");
+    }
+
+    #[test]
+    fn test_bch_same_label_accumulation() {
+        // Two H generators with SAME Pauli label: BCH sums coefficients.
+        // Two H_X(0) with rates 0.1 and 0.05 → combined rate 0.15 → p = 0.15^2
+        let gens = vec![
+            PropagatedEeg {
+                eeg_type: EegType::H,
+                label: Bm::x(0),
+                label2: None,
+                coeff: 0.1,
+                source: None,
+            },
+            PropagatedEeg {
+                eeg_type: EegType::H,
+                label: Bm::x(0),
+                label2: None,
+                coeff: 0.05,
+                source: None,
+            },
+        ];
+        let dets = vec![z_det(0, &[0])];
+        let entries = build_dem(&gens, &dets, &[]);
+
+        // BCH combines: single generator with rate 0.15, p = 0.15^2 = 0.0225
+        assert_eq!(entries.len(), 1);
+        assert!(
+            (entries[0].probability - 0.0225).abs() < 1e-10,
+            "BCH should sum same-label rates: got {}",
+            entries[0].probability
+        );
+    }
+
+    #[test]
+    fn test_beta_constructive_interference() {
+        // Two H generators Q1=X0, Q2=X1 in same event class (both flip Z0Z1).
+        // Q1*Q2 = X0X1. State is |Phi+> Bell state → X0X1 is +1 stabilizer.
+        // Constructive: p = (h1+h2)^2
+        use crate::stabilizer::StabilizerGroup;
+        use pecos_core::gate_type::GateType;
+        use pecos_core::{Gate, GateAngles, GateParams, QubitId};
+
+        fn g(gt: GateType, qs: &[usize]) -> Gate {
+            Gate {
+                gate_type: gt,
+                qubits: qs.iter().map(|&q| QubitId(q)).collect(),
+                angles: GateAngles::new(),
+                params: GateParams::new(),
+                meas_ids: pecos_core::GateMeasIds::new(),
+                channel: None,
+            }
+        }
+
+        let gens = vec![
+            PropagatedEeg {
+                eeg_type: EegType::H,
+                label: Bm::x(0),
+                label2: None,
+                coeff: 0.1,
+                source: None,
+            },
+            PropagatedEeg {
+                eeg_type: EegType::H,
+                label: Bm::x(1),
+                label2: None,
+                coeff: 0.05,
+                source: None,
+            },
+        ];
+        // Z0Z1 detector: X0 and X1 both anticommute with it
+        let dets = vec![Detector {
+            id: 0,
+            stabilizer: Bm::z(0).multiply(&Bm::z(1)),
+        }];
+
+        // |Phi+> = H CX |00> → stabilizers +X0X1, +Z0Z1
+        let stab_group =
+            StabilizerGroup::from_circuit(&[g(GateType::H, &[0]), g(GateType::CX, &[0, 1])], 2);
+
+        let entries = build_dem_with_stabilizers(&gens, &dets, &[], Some(&stab_group));
+
+        assert_eq!(entries.len(), 1);
+        // X0*X1 is +1 stabilizer → constructive: (0.1+0.05)^2 = 0.0225
+        assert!(
+            (entries[0].probability - 0.0225).abs() < 1e-10,
+            "Constructive beta: got {}, expected 0.0225",
+            entries[0].probability
+        );
+    }
+
+    #[test]
+    fn test_beta_destructive_interference() {
+        // Same event class but |Phi-> state → X0X1 is -1 stabilizer.
+        // Destructive: p = (h1-h2)^2
+        use crate::stabilizer::StabilizerGroup;
+        use pecos_core::gate_type::GateType;
+        use pecos_core::{Gate, GateAngles, GateParams, QubitId};
+
+        fn g(gt: GateType, qs: &[usize]) -> Gate {
+            Gate {
+                gate_type: gt,
+                qubits: qs.iter().map(|&q| QubitId(q)).collect(),
+                angles: GateAngles::new(),
+                params: GateParams::new(),
+                meas_ids: pecos_core::GateMeasIds::new(),
+                channel: None,
+            }
+        }
+
+        let gens = vec![
+            PropagatedEeg {
+                eeg_type: EegType::H,
+                label: Bm::x(0),
+                label2: None,
+                coeff: 0.1,
+                source: None,
+            },
+            PropagatedEeg {
+                eeg_type: EegType::H,
+                label: Bm::x(1),
+                label2: None,
+                coeff: 0.05,
+                source: None,
+            },
+        ];
+        let dets = vec![Detector {
+            id: 0,
+            stabilizer: Bm::z(0).multiply(&Bm::z(1)),
+        }];
+
+        // |Phi-> = CX H X |00> → stabilizers -X0X1, +Z0Z1
+        let stab_group = StabilizerGroup::from_circuit(
+            &[
+                g(GateType::X, &[0]),
+                g(GateType::H, &[0]),
+                g(GateType::CX, &[0, 1]),
+            ],
+            2,
+        );
+
+        let entries = build_dem_with_stabilizers(&gens, &dets, &[], Some(&stab_group));
+
+        assert_eq!(entries.len(), 1);
+        // X0*X1 is -1 stabilizer → destructive: (0.1-0.05)^2 = 0.0025
+        assert!(
+            (entries[0].probability - 0.0025).abs() < 1e-10,
+            "Destructive beta: got {}, expected 0.0025",
+            entries[0].probability
+        );
+    }
+
+    #[test]
+    fn test_beta_equal_rates_destructive_cancels() {
+        // h1 = h2 = 0.1, -1 stabilizer product → p = (h1-h2)^2 = 0
+        use crate::stabilizer::StabilizerGroup;
+        use pecos_core::gate_type::GateType;
+        use pecos_core::{Gate, GateAngles, GateParams, QubitId};
+
+        fn g(gt: GateType, qs: &[usize]) -> Gate {
+            Gate {
+                gate_type: gt,
+                qubits: qs.iter().map(|&q| QubitId(q)).collect(),
+                angles: GateAngles::new(),
+                params: GateParams::new(),
+                meas_ids: pecos_core::GateMeasIds::new(),
+                channel: None,
+            }
+        }
+
+        let gens = vec![
+            PropagatedEeg {
+                eeg_type: EegType::H,
+                label: Bm::x(0),
+                label2: None,
+                coeff: 0.1,
+                source: None,
+            },
+            PropagatedEeg {
+                eeg_type: EegType::H,
+                label: Bm::x(1),
+                label2: None,
+                coeff: 0.1,
+                source: None,
+            },
+        ];
+        let dets = vec![Detector {
+            id: 0,
+            stabilizer: Bm::z(0).multiply(&Bm::z(1)),
+        }];
+
+        let stab_group = StabilizerGroup::from_circuit(
+            &[
+                g(GateType::X, &[0]),
+                g(GateType::H, &[0]),
+                g(GateType::CX, &[0, 1]),
+            ],
+            2,
+        );
+
+        let entries = build_dem_with_stabilizers(&gens, &dets, &[], Some(&stab_group));
+
+        // Complete cancellation: p = 0
+        assert!(
+            entries.is_empty(),
+            "Equal-rate destructive interference should cancel completely"
+        );
+    }
+
+    #[test]
+    fn test_beta_no_stabilizer_diagonal() {
+        // When product is NOT in stabilizer group, beta = 0, fall back to diagonal.
+        // X0 and X1 both flip Z0Z1 detector. Product X0X1.
+        // State |00> has stabilizers Z0, Z1. X0X1 is not a stabilizer.
+        use crate::stabilizer::StabilizerGroup;
+
+        let gens = vec![
+            PropagatedEeg {
+                eeg_type: EegType::H,
+                label: Bm::x(0),
+                label2: None,
+                coeff: 0.1,
+                source: None,
+            },
+            PropagatedEeg {
+                eeg_type: EegType::H,
+                label: Bm::x(1),
+                label2: None,
+                coeff: 0.05,
+                source: None,
+            },
+        ];
+        let dets = vec![Detector {
+            id: 0,
+            stabilizer: Bm::z(0).multiply(&Bm::z(1)),
+        }];
+
+        let stab_group = StabilizerGroup::from_circuit(&[], 2);
+
+        let entries = build_dem_with_stabilizers(&gens, &dets, &[], Some(&stab_group));
+
+        assert_eq!(entries.len(), 1);
+        // p = h1^2 + h2^2 = 0.0125 (diagonal only)
+        assert!(
+            (entries[0].probability - 0.0125).abs() < 1e-10,
+            "Non-stabilizer product → diagonal: got {}",
+            entries[0].probability
+        );
+    }
+
+    #[test]
+    fn test_s_exact_formula_multiple() {
+        // Multiple S generators in same event class: exact formula
+        // p = (1/2)(1 - exp(2 * sum_rates))
+        let gens = vec![
+            PropagatedEeg {
+                eeg_type: EegType::S,
+                label: Bm::x(0),
+                label2: None,
+                coeff: -0.01,
+                source: None,
+            },
+            PropagatedEeg {
+                eeg_type: EegType::S,
+                label: Bm::y(0),
+                label2: None,
+                coeff: -0.005,
+                source: None,
+            },
+        ];
+        let dets = vec![z_det(0, &[0])];
+        let entries = build_dem(&gens, &dets, &[]);
+
+        assert_eq!(entries.len(), 1);
+        // sum_rates = -0.01 + -0.005 = -0.015 (same event class, both flip Z0)
+        let expected = (1.0 - (2.0 * -0.015_f64).exp()) / 2.0;
+        assert!((entries[0].probability - expected).abs() < 1e-10);
+    }
+
+    #[test]
+    fn test_observable_classification() {
+        // Generator that flips an observable but no detectors
+        let gens = vec![PropagatedEeg {
+            eeg_type: EegType::H,
+            label: Bm::x(0),
+            label2: None,
+            coeff: 0.1,
+            source: None,
+        }];
+        let dets = vec![z_det(0, &[1])]; // Detector on qubit 1
+        let obs = vec![Observable {
+            id: 0,
+            pauli: Bm::z(0),
+        }]; // Observable Z0
+
+        let entries = build_dem(&gens, &dets, &obs);
+
+        // X0 anticommutes with Z0 (observable) but not with Z1 (detector)
+        assert_eq!(entries.len(), 1);
+        assert!(entries[0].event.detectors.is_empty());
+        assert_eq!(entries[0].event.observables.as_slice(), &[0]);
+    }
+
+    #[test]
+    fn test_bch2_anticommuting_h_generators() {
+        // Two H generators with anticommuting labels: H_X and H_Z on same qubit.
+        // [H_X, H_Z] = -2i H_{XZ} = -2i H_Y → BCH2 adds imaginary H_Y.
+        // BCH coefficient: -i * h_X * h_Z.
+        //
+        // Both X and Z flip the Z detector. Y also flips Z detector.
+        // The imaginary BCH2 generator contributes to probability via
+        // re_product = re_j * re_k - im_j * im_k.
+        //
+        // Diagonal of imaginary generator: |im|² = (h_X * h_Z)².
+        // Cross with real generators: Re(re * (-im)) = re * im (but im is negative).
+        let h_x = 0.1;
+        let h_z = 0.05;
+
+        let gens = vec![
+            PropagatedEeg {
+                eeg_type: EegType::H,
+                label: Bm::x(0),
+                label2: None,
+                coeff: h_x,
+                source: None,
+            },
+            PropagatedEeg {
+                eeg_type: EegType::H,
+                label: Bm::z(0),
+                label2: None,
+                coeff: h_z,
+                source: None,
+            },
+        ];
+        let dets = vec![z_det(0, &[0])]; // Z detector: X and Y anticommute, Z commutes
+
+        // Without BCH2: only X flips detector. p = h_x² = 0.01
+        let entries_k1 =
+            build_dem_with_options(&gens, &dets, &[], None, HFormula::Taylor, BchOrder::First);
+        let p_k1: f64 = entries_k1.iter().map(|e| e.probability).sum();
+        assert!(
+            (p_k1 - h_x * h_x).abs() < 1e-10,
+            "BCH1: p should be h_x² = {}, got {p_k1}",
+            h_x * h_x
+        );
+
+        // With BCH2: adds H_Y with imaginary coeff -i * h_x * h_z.
+        // Y anticommutes with Z detector → flips it.
+        // Diagonal of imaginary Y: (h_x * h_z)² = 0.000025.
+        // Cross-term X with imaginary Y: Re(h_x * (i * h_x * h_z)) = 0 (imaginary × real = imaginary, Re=0)
+        // Wait, im_Y = -h_x * h_z (negative, from sign fix). Cross: re_X * re_Y - im_X * im_Y.
+        // re_X = h_x, im_X = 0. re_Y = 0, im_Y = -h_x*h_z.
+        // re_product = h_x * 0 - 0 * (-h_x*h_z) = 0. Cross-term is zero.
+        // So BCH2 only adds the diagonal of the Y generator: |im_Y|² = (h_x * h_z)² = 0.000025.
+        let entries_k2 =
+            build_dem_with_options(&gens, &dets, &[], None, HFormula::Taylor, BchOrder::Second);
+        let p_k2: f64 = entries_k2.iter().map(|e| e.probability).sum();
+        let expected_k2 = h_x * h_x + (h_x * h_z).powi(2);
+        assert!(
+            (p_k2 - expected_k2).abs() < 1e-10,
+            "BCH2: p should be h_x² + (h_x·h_z)² = {expected_k2}, got {p_k2}"
+        );
+
+        // BCH2 adds a small correction: 0.01 + 0.000025 = 0.010025
+        assert!(p_k2 > p_k1, "BCH2 should add to probability");
+    }
+}
diff --git a/exp/pecos-eeg/src/dem_simulator.rs b/exp/pecos-eeg/src/dem_simulator.rs
new file mode 100644
index 000000000..2493d2efe
--- /dev/null
+++ b/exp/pecos-eeg/src/dem_simulator.rs
@@ -0,0 +1,445 @@
+// Copyright 2026 The PECOS Developers
+//
+// Licensed under the Apache License, Version 2.0 (the "License"); you may not use this file except
+// in compliance with the License. You may obtain a copy of the License at
+//
+//     https://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software distributed under the License
+// is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express
+// or implied. See the License for the specific language governing permissions and limitations under
+// the License.
+
+//! DEM-based simulator: samples from a Detector Error Model and synthesizes
+//! physical measurement bitstrings.
+//!
+//! This module provides the pure Rust implementation of DEM-based simulation.
+//! Given a circuit (as `Vec<Gate>`) and noise parameters, it:
+//! 1. Builds a DEM via the EEG coherent backward mechanism extraction
+//! 2. Samples detection events from the DEM
+//! 3. Synthesizes physical measurement bitstrings matching the circuit's output
+//!
+//! # Performance
+//!
+//! The sampling step uses `ParsedDem::sample()` which is O(mechanisms) per shot.
+//! For bulk sampling, use `to_dem_sampler()` for columnar bit-packed SIMD sampling.
+
+use crate::dem_generator::{DemContext, DemGenerator};
+use crate::expand::{ExpandedCircuit, GateIndex};
+use crate::noise::UniformNoise;
+use pecos_core::Gate;
+use pecos_core::gate_type::GateType;
+use pecos_core::pauli::pauli_bitmask::BitmaskStorage;
+use pecos_qec::fault_tolerance::dem_builder::ParsedDem;
+use pecos_qec::fault_tolerance::fault_sampler::{
+    RawMeasurementPlan, StochasticNoiseParams, symbolic_measurement_history,
+};
+use pecos_quantum::TickCircuit;
+use pecos_random::PecosRng;
+
+/// Metadata needed for measurement synthesis.
+#[derive(Clone, Debug)]
+pub struct CircuitMeasurementMeta {
+    /// Total number of physical measurements in the circuit.
+    pub num_measurements: usize,
+    /// Detector definitions: each is a list of measurement record offsets.
+    /// Offset is relative: absolute_index = num_measurements + offset.
+    pub detector_records: Vec<Vec<i32>>,
+    /// Observable definitions: same format as detectors.
+    pub observable_records: Vec<Vec<i32>>,
+}
+
+/// Result of a DEM simulation run.
+pub struct DemSimulationResult {
+    /// Per-shot measurement bitstrings (same format as gate-by-gate simulators).
+    pub measurements: Vec<Vec<u8>>,
+}
+
+/// Run DEM-based simulation: build DEM, sample, produce measurement bitstrings.
+///
+/// Two modes:
+/// 1. **Stochastic path** (idle_rz == 0): builds a TickCircuit from gates + metadata,
+///    uses `DemSampler::from_tick_circuit` with `OutputMode::RawMeasurements` for
+///    proper non-deterministic handling and maximum performance.
+/// 2. **Coherent path** (idle_rz > 0): uses EEG DemGenerator for DEM, then
+///    ParsedDem sampler + measurement synthesis (EEG handles coherent noise).
+///
+/// # Arguments
+/// * `gates` - Circuit gates (from CommandQueue conversion)
+/// * `noise` - Noise parameters
+/// * `meta` - Circuit measurement metadata (num_measurements, detector/observable records)
+/// * `generator` - Which DEM generator to use (for coherent path)
+/// * `shots` - Number of shots to sample
+/// * `seed` - Random seed
+pub fn run_dem_simulation(
+    gates: &[Gate],
+    noise: &UniformNoise,
+    meta: &CircuitMeasurementMeta,
+    generator: &dyn DemGenerator,
+    shots: usize,
+    seed: u64,
+) -> DemSimulationResult {
+    // Coherent noise: use EEG path (Heisenberg walks handle idle_rz)
+    if noise.idle_rz.abs() > 1e-15 {
+        return run_eeg_path(gates, noise, meta, generator, shots, seed);
+    }
+
+    // Stochastic: use proper DemSampler with raw measurement output
+    try_stochastic_path(gates, noise, meta, shots, seed)
+        .expect("DEM simulation failed: could not build TickCircuit or DemSampler from circuit")
+}
+
+/// Stochastic raw measurement path via RawMeasurementPlan.
+///
+/// Builds a TickCircuit, runs symbolic simulation for MeasurementHistory,
+/// then uses fault_sampler::RawMeasurementPlan for:
+/// - Correct cross-reset measurement correlations (via SymbolicSparseStab PZ)
+/// - Geometric/O(fired) fault sampling
+/// - Raw measurement output matching gate-by-gate simulators
+///
+/// Returns None if idle_rz > 0 (needs EEG path for coherent noise).
+fn try_stochastic_path(
+    gates: &[Gate],
+    noise: &UniformNoise,
+    meta: &CircuitMeasurementMeta,
+    shots: usize,
+    seed: u64,
+) -> Option<DemSimulationResult> {
+    // Only use stochastic path when no coherent noise
+    if noise.idle_rz.abs() > 1e-15 {
+        return None;
+    }
+
+    // Build TickCircuit using typed API (proper measurement record tracking)
+    let mut tc = build_tick_circuit(gates, meta);
+
+    // Compact ticks to reduce DAG complexity (critical for performance)
+    tc.compact_ticks();
+
+    let history = symbolic_measurement_history(&tc).ok()?;
+
+    let noise_params = StochasticNoiseParams {
+        p1: noise.p1,
+        p2: noise.p2,
+        p_meas: noise.p_meas,
+        p_prep: noise.p_prep,
+    };
+    let mechanisms =
+        pecos_qec::fault_tolerance::fault_sampler::build_fault_table(&tc, &noise_params).ok()?;
+    let plan = RawMeasurementPlan::new(&history, mechanisms);
+
+    // Sample raw measurements (columnar, then extract rows)
+    let result = plan.sample(shots, seed);
+    let mut measurements = Vec::with_capacity(shots);
+    for shot in 0..shots {
+        let n = result.num_measurements();
+        let mut meas = Vec::with_capacity(n);
+        for m in 0..n {
+            meas.push(u8::from(result.get(shot, m).0));
+        }
+        measurements.push(meas);
+    }
+
+    Some(DemSimulationResult { measurements })
+}
+
+/// Build a TickCircuit from flat gates + metadata using the typed API.
+///
+/// Uses `.mz()` for measurement gates (properly tracks measurement records),
+/// `.pz()` for prep gates, and `try_add_gate()` for all other gates.
+/// After building all gates, creates detector/observable annotations using
+/// the stored measurement references. This ensures the DagCircuit conversion
+/// and DagFaultAnalyzer see proper structured annotations.
+fn build_tick_circuit(gates: &[Gate], meta: &CircuitMeasurementMeta) -> TickCircuit {
+    use pecos_quantum::{Attribute, TickMeasRef};
+
+    let mut tc = TickCircuit::default();
+    let mut all_meas_refs: Vec<TickMeasRef> = Vec::new();
+
+    for gate in gates {
+        match gate.gate_type {
+            GateType::MZ => {
+                // Use the typed .mz() API to properly track measurement records
+                let qubits: Vec<pecos_core::QubitId> = gate.qubits.iter().copied().collect();
+                let refs = tc.tick().mz(&qubits);
+                all_meas_refs.extend(refs);
+            }
+            GateType::PZ | GateType::QAlloc => {
+                let qubits: Vec<pecos_core::QubitId> = gate.qubits.iter().copied().collect();
+                tc.tick().pz(&qubits);
+            }
+            _ => {
+                let mut tick = tc.tick();
+                let _ = tick.try_add_gate(gate.clone());
+            }
+        }
+    }
+
+    // Create detector annotations from record definitions
+    for records in &meta.detector_records {
+        let det_refs: Vec<TickMeasRef> = records
+            .iter()
+            .filter_map(|&rec| {
+                let abs_idx = (meta.num_measurements as i32 + rec) as usize;
+                all_meas_refs.get(abs_idx).copied()
+            })
+            .collect();
+        if !det_refs.is_empty() {
+            tc.detector(&det_refs);
+        }
+    }
+
+    // Create observable annotations from record definitions
+    for records in &meta.observable_records {
+        let obs_refs: Vec<TickMeasRef> = records
+            .iter()
+            .filter_map(|&rec| {
+                let abs_idx = (meta.num_measurements as i32 + rec) as usize;
+                all_meas_refs.get(abs_idx).copied()
+            })
+            .collect();
+        if !obs_refs.is_empty() {
+            tc.observable(&obs_refs);
+        }
+    }
+
+    // Set metadata (for DemBuilder JSON fallback path)
+    tc.set_meta(
+        "num_measurements",
+        Attribute::String(meta.num_measurements.to_string()),
+    );
+    if let Ok(det_json) = serde_json::to_string(
+        &meta
+            .detector_records
+            .iter()
+            .enumerate()
+            .map(|(id, recs)| serde_json::json!({"id": id, "records": recs}))
+            .collect::<Vec<_>>(),
+    ) {
+        tc.set_meta("detectors", Attribute::String(det_json));
+    }
+    if let Ok(obs_json) = serde_json::to_string(
+        &meta
+            .observable_records
+            .iter()
+            .enumerate()
+            .map(|(id, recs)| serde_json::json!({"id": id, "records": recs}))
+            .collect::<Vec<_>>(),
+    ) {
+        tc.set_meta("observables", Attribute::String(obs_json));
+    }
+
+    tc
+}
+
+/// EEG path: DEM generation + ParsedDem sampling + measurement synthesis.
+///
+/// Used when coherent noise (idle_rz) is present and the stochastic path
+/// cannot capture the noise accurately.
+fn run_eeg_path(
+    gates: &[Gate],
+    noise: &UniformNoise,
+    meta: &CircuitMeasurementMeta,
+    generator: &dyn DemGenerator,
+    shots: usize,
+    seed: u64,
+) -> DemSimulationResult {
+    // Expand circuit for EEG analysis
+    let expanded = crate::expand::expand_circuit(gates);
+    let gate_index = GateIndex::build(&expanded.gates, expanded.num_qubits);
+
+    // Build detectors and observables from metadata
+    let detectors = build_detectors_from_meta(meta, &expanded);
+    let observables = build_observables_from_meta(meta, &expanded);
+
+    // Generate DEM via trait
+    let ctx = DemContext {
+        gates: &expanded.gates,
+        expanded: &expanded,
+        gate_index: &gate_index,
+        detectors: &detectors,
+        observables: &observables,
+    };
+    let output = generator.generate(&ctx, noise);
+    let dem_str = crate::dem_mapping::format_dem(&output.entries);
+
+    // Parse DEM and build sampler
+    let parsed_dem: ParsedDem = dem_str.parse().unwrap_or_else(|_| ParsedDem::new());
+    let sampler = parsed_dem.to_dem_sampler();
+
+    // Build measurement synthesis info
+    let synthesis_info = MeasurementSynthesisInfo::build(meta, &expanded);
+
+    // Sample and synthesize
+    let mut rng = PecosRng::seed_from_u64(seed);
+    let mut measurements = Vec::with_capacity(shots);
+
+    for _ in 0..shots {
+        let (det_events, obs_flips) = sampler.sample(&mut rng);
+        let meas = synthesis_info.synthesize(&det_events, &obs_flips, &mut rng);
+        measurements.push(meas);
+    }
+
+    DemSimulationResult { measurements }
+}
+
+/// Build EEG Detector structs from circuit metadata.
+fn build_detectors_from_meta(
+    meta: &CircuitMeasurementMeta,
+    expanded: &ExpandedCircuit,
+) -> Vec<crate::dem_mapping::Detector> {
+    meta.detector_records
+        .iter()
+        .enumerate()
+        .map(|(id, records)| {
+            let mut bm = crate::Bm::default();
+            for &rec in records {
+                let meas_idx = (meta.num_measurements as i32 + rec) as usize;
+                if meas_idx < expanded.measurement_qubit.len() {
+                    let q = expanded.measurement_qubit[meas_idx];
+                    bm.z_bits.set_bit(q);
+                }
+            }
+            crate::dem_mapping::Detector { id, stabilizer: bm }
+        })
+        .collect()
+}
+
+/// Build EEG Observable structs from circuit metadata.
+fn build_observables_from_meta(
+    meta: &CircuitMeasurementMeta,
+    expanded: &ExpandedCircuit,
+) -> Vec<crate::dem_mapping::Observable> {
+    meta.observable_records
+        .iter()
+        .enumerate()
+        .map(|(id, records)| {
+            let mut bm = crate::Bm::default();
+            for &rec in records {
+                let meas_idx = (meta.num_measurements as i32 + rec) as usize;
+                if meas_idx < expanded.measurement_qubit.len() {
+                    let q = expanded.measurement_qubit[meas_idx];
+                    bm.z_bits.set_bit(q);
+                }
+            }
+            crate::dem_mapping::Observable { id, pauli: bm }
+        })
+        .collect()
+}
+
+/// Precomputed info for synthesizing measurements from detection events.
+struct MeasurementSynthesisInfo {
+    num_meas: usize,
+    /// For each measurement: Some((det_idx, other_meas_idx)) if determined by a detector.
+    /// other_meas_idx == usize::MAX means single-record detector.
+    meas_info: Vec<Option<(usize, usize)>>,
+    /// Which measurements are non-deterministic (need random coin).
+    is_non_det: Vec<bool>,
+    /// Observable measurement assignments: (meas_idx, obs_idx).
+    obs_meas_info: Vec<(usize, usize)>,
+}
+
+impl MeasurementSynthesisInfo {
+    /// Build synthesis info from circuit metadata.
+    fn build(meta: &CircuitMeasurementMeta, _expanded: &ExpandedCircuit) -> Self {
+        let num_meas = meta.num_measurements;
+        let mut meas_info: Vec<Option<(usize, usize)>> = vec![None; num_meas];
+
+        // Build detector -> measurement mapping
+        for (det_idx, records) in meta.detector_records.iter().enumerate() {
+            let abs_records: Vec<usize> = records
+                .iter()
+                .map(|&r| (num_meas as i32 + r) as usize)
+                .filter(|&idx| idx < num_meas)
+                .collect();
+
+            if abs_records.len() == 2 {
+                let (earlier, later) = if abs_records[0] < abs_records[1] {
+                    (abs_records[0], abs_records[1])
+                } else {
+                    (abs_records[1], abs_records[0])
+                };
+                if meas_info[later].is_none() {
+                    meas_info[later] = Some((det_idx, earlier));
+                }
+            } else if abs_records.len() == 1 {
+                let idx = abs_records[0];
+                if meas_info[idx].is_none() {
+                    meas_info[idx] = Some((det_idx, usize::MAX));
+                }
+            }
+        }
+
+        // Identify non-deterministic measurements
+        let mut is_non_det = vec![false; num_meas];
+        for idx in 0..num_meas {
+            if meas_info[idx].is_none() {
+                is_non_det[idx] = true;
+            }
+        }
+        // Also: measurements referenced as "other" by a detector but not assigned themselves
+        for idx in 0..num_meas {
+            if let Some((_, other_idx)) = meas_info[idx]
+                && other_idx != usize::MAX
+                && other_idx < num_meas
+                && meas_info[other_idx].is_none()
+            {
+                is_non_det[other_idx] = true;
+            }
+        }
+
+        // Observable measurement assignments
+        let mut obs_meas_info = Vec::new();
+        for (obs_idx, records) in meta.observable_records.iter().enumerate() {
+            for &rec in records {
+                let idx = (num_meas as i32 + rec) as usize;
+                if idx < num_meas {
+                    obs_meas_info.push((idx, obs_idx));
+                }
+            }
+        }
+
+        Self {
+            num_meas,
+            meas_info,
+            is_non_det,
+            obs_meas_info,
+        }
+    }
+
+    /// Synthesize a measurement bitstring from detection events + observable flips.
+    fn synthesize(&self, det_events: &[bool], obs_flips: &[bool], rng: &mut PecosRng) -> Vec<u8> {
+        let mut meas = vec![0u8; self.num_meas];
+
+        // Random coins for non-deterministic measurements
+        for (idx, bit) in meas.iter_mut().enumerate().take(self.num_meas) {
+            if self.is_non_det[idx] {
+                *bit = u8::from(rng.random_bool(0.5));
+            }
+        }
+
+        // Assign measurements in index order (time order)
+        for idx in 0..self.num_meas {
+            if let Some((det_idx, other_idx)) = self.meas_info[idx] {
+                if det_idx < det_events.len() && det_events[det_idx] {
+                    if other_idx == usize::MAX {
+                        meas[idx] ^= 1;
+                    } else if other_idx < self.num_meas {
+                        meas[idx] = u8::from(det_events[det_idx]) ^ meas[other_idx];
+                    }
+                } else if other_idx != usize::MAX && other_idx < self.num_meas {
+                    meas[idx] = meas[other_idx];
+                }
+            }
+        }
+
+        // Apply observable flips
+        for &(meas_idx, obs_idx) in &self.obs_meas_info {
+            if obs_idx < obs_flips.len() && obs_flips[obs_idx] {
+                meas[meas_idx] ^= 1;
+            }
+        }
+
+        meas
+    }
+}
diff --git a/exp/pecos-eeg/src/eeg.rs b/exp/pecos-eeg/src/eeg.rs
new file mode 100644
index 000000000..1f342f747
--- /dev/null
+++ b/exp/pecos-eeg/src/eeg.rs
@@ -0,0 +1,120 @@
+// Copyright 2026 The PECOS Developers
+//
+// Licensed under the Apache License, Version 2.0
+
+//! EEG types: generator kinds and accumulators.
+
+use crate::Bm;
+use std::collections::BTreeMap;
+
+/// The four types of Elementary Error Generators.
+#[derive(Clone, Copy, Debug, PartialEq, Eq, Hash, PartialOrd, Ord)]
+pub enum EegType {
+    /// Hamiltonian: H_P[rho] = -i[P, rho]. Coherent rotations.
+    H,
+    /// Stochastic: S_P[rho] = P rho P - rho. Pauli errors.
+    S,
+    /// Correlation: C_{P,Q}. Two-Pauli correlations.
+    C,
+    /// Active: A_{P,Q}. Phase-dependent interference.
+    A,
+}
+
+/// A single Elementary Error Generator with coefficient.
+#[derive(Clone, Debug)]
+pub struct Eeg {
+    pub eeg_type: EegType,
+    pub label_p: Bm,
+    pub label_q: Bm,
+    pub coeff: f64,
+}
+
+/// Accumulator for Hamiltonian EEGs (H_P type).
+///
+/// Stores the sum of coefficients for each Pauli label. This is the
+/// first-order BCH result: G_c = Sigma epsilon_P H_P.
+#[derive(Clone, Debug, Default)]
+pub struct HamiltonianAccumulator {
+    generators: BTreeMap<Bm, f64>,
+}
+
+impl HamiltonianAccumulator {
+    #[must_use]
+    pub fn new() -> Self {
+        Self::default()
+    }
+
+    /// Add H_P with coefficient epsilon.
+    /// Accumulates (first-order BCH = sum).
+    pub fn add(&mut self, label: Bm, coeff: f64) {
+        *self.generators.entry(label).or_insert(0.0) += coeff;
+    }
+
+    #[must_use]
+    pub fn len(&self) -> usize {
+        self.generators.len()
+    }
+
+    #[must_use]
+    pub fn is_empty(&self) -> bool {
+        self.generators.is_empty()
+    }
+
+    pub fn iter(&self) -> impl Iterator<Item = (&Bm, &f64)> {
+        self.generators.iter()
+    }
+
+    pub fn prune(&mut self, threshold: f64) {
+        self.generators.retain(|_, c| c.abs() > threshold);
+    }
+}
+
+/// Accumulator for Stochastic EEGs (S_P type).
+///
+/// S-type generators commute, so first-order BCH is exact.
+#[derive(Clone, Debug, Default)]
+pub struct StochasticAccumulator {
+    generators: BTreeMap<Bm, f64>,
+}
+
+impl StochasticAccumulator {
+    #[must_use]
+    pub fn new() -> Self {
+        Self::default()
+    }
+
+    pub fn add(&mut self, label: Bm, coeff: f64) {
+        *self.generators.entry(label).or_insert(0.0) += coeff;
+    }
+
+    #[must_use]
+    pub fn len(&self) -> usize {
+        self.generators.len()
+    }
+
+    #[must_use]
+    pub fn is_empty(&self) -> bool {
+        self.generators.is_empty()
+    }
+
+    pub fn iter(&self) -> impl Iterator<Item = (&Bm, &f64)> {
+        self.generators.iter()
+    }
+}
+
+#[cfg(test)]
+mod tests {
+    use super::*;
+
+    #[test]
+    fn test_hamiltonian_accumulator() {
+        let mut acc = HamiltonianAccumulator::new();
+        acc.add(Bm::z(0), 0.05);
+        acc.add(Bm::z(0), 0.03);
+        acc.add(Bm::x(1), 0.02);
+
+        assert_eq!(acc.len(), 2);
+        let z0 = acc.generators.get(&Bm::z(0)).unwrap();
+        assert!((z0 - 0.08).abs() < 1e-10);
+    }
+}
diff --git a/exp/pecos-eeg/src/expand.rs b/exp/pecos-eeg/src/expand.rs
new file mode 100644
index 000000000..b0d5a7b0f
--- /dev/null
+++ b/exp/pecos-eeg/src/expand.rs
@@ -0,0 +1,468 @@
+// Copyright 2026 The PECOS Developers
+//
+// Licensed under the Apache License, Version 2.0
+
+//! Deferred measurement: expand a circuit by replacing mid-circuit
+//! MZ+PZ with CX to auxiliary qubits, deferring all measurements to the end.
+//!
+//! After expansion, the circuit is purely Clifford (no mid-circuit
+//! measurements), and error generators can be propagated straight through.
+
+use crate::Bm;
+use pecos_core::gate_type::GateType;
+use pecos_core::pauli::pauli_bitmask::BitmaskStorage;
+use pecos_core::{Gate, GateAngles, GateParams, QubitId};
+
+/// Result of circuit expansion.
+pub struct ExpandedCircuit {
+    /// The expanded gate sequence (purely Clifford, no mid-circuit measurements).
+    pub gates: Vec<Gate>,
+    /// Total number of qubits (original + auxiliary).
+    pub num_qubits: usize,
+    /// Number of original qubits.
+    pub num_original_qubits: usize,
+    /// Mapping: measurement record index → auxiliary qubit index.
+    /// measurement_qubit[k] = the auxiliary qubit whose Z-measurement at
+    /// the end gives the k-th measurement record.
+    pub measurement_qubit: Vec<usize>,
+    /// Mapping: measurement record index → original qubit that was measured.
+    /// original_measured_qubit[k] = the qubit in the original circuit that
+    /// the k-th MZ gate acted on.
+    pub original_measured_qubit: Vec<usize>,
+}
+
+/// Expand a circuit by deferring mid-circuit measurements.
+///
+/// For each MZ(q) followed by PZ(q), replaces with:
+/// 1. CX(q, aux) — copy q's state to a fresh auxiliary qubit
+/// 2. PZ(q) — reset q to |0> (kept as-is, since PZ after CX is valid)
+///
+/// All auxiliary qubits are measured at the end via MZ.
+/// Final data measurements (MZ not followed by PZ) are also deferred
+/// to auxiliary qubits for uniformity.
+pub fn expand_circuit(gates: &[Gate]) -> ExpandedCircuit {
+    // First pass: find the max qubit index to know where auxiliaries start
+    let max_qubit = gates
+        .iter()
+        .flat_map(|g| g.qubits.iter())
+        .map(pecos_core::QubitId::index)
+        .max()
+        .unwrap_or(0);
+    let num_original = max_qubit + 1;
+    let mut next_aux = num_original;
+
+    let mut expanded = Vec::with_capacity(gates.len() * 2);
+    let mut measurement_qubit = Vec::new();
+    let mut original_measured_qubit = Vec::new();
+
+    // Identify which MZ gates are mid-circuit (followed by PZ on same qubit)
+    // vs final (not followed by any operation on that qubit, or followed by
+    // a different operation).
+    //
+    // Track ancilla qubits: those with a PZ after the first non-PZ gate.
+    // Only ancilla MZ gets a post-expansion PZ (measurement projection).
+    let mut ancilla_qubits = std::collections::HashSet::new();
+    {
+        let mut past_init = false;
+        for g in gates {
+            if past_init && (g.gate_type == GateType::PZ || g.gate_type == GateType::QAlloc) {
+                for q in &g.qubits {
+                    ancilla_qubits.insert(q.index());
+                }
+            }
+            if g.gate_type != GateType::PZ && g.gate_type != GateType::QAlloc {
+                past_init = true;
+            }
+        }
+    }
+
+    // Strategy: walk gates, when we see MZ(q):
+    //   - Replace with CX(q, aux_new) where aux_new is a fresh auxiliary
+    //   - For ancilla qubits: add PZ(q) to model measurement projection
+    //   - Record that measurement k maps to aux_new
+    //   - The auxiliary qubit is measured at the end
+
+    let mut i = 0;
+    while i < gates.len() {
+        let gate = &gates[i];
+
+        match gate.gate_type {
+            GateType::MZ => {
+                // For each qubit in this MZ gate, create CX to auxiliary
+                for q in &gate.qubits {
+                    let q_idx = q.index();
+                    let aux = next_aux;
+                    next_aux += 1;
+
+                    // Initialize auxiliary: QAlloc(aux)
+                    // Use QAlloc (not PZ) so the noise model can distinguish
+                    // auxiliary initialization from original circuit resets.
+                    expanded.push(make_gate(GateType::QAlloc, &[aux]));
+
+                    // CX(q, aux) — copy measurement info to auxiliary
+                    expanded.push(make_gate(GateType::CX, &[q_idx, aux]));
+
+                    // For ancilla qubits: add PZ to model measurement projection.
+                    // MZ projects to a Z eigenstate, destroying X/Y coherences.
+                    // Without this, the last round's syndrome generators retain
+                    // X on the measured ancilla, creating spurious correlations.
+                    // For intermediate rounds this is redundant (circuit PZ follows).
+                    //
+                    // Data readout MZ does NOT get PZ: data qubit Z components
+                    // must persist for correct generator labels (Z errors are
+                    // invisible to Z-basis readout and must not be cleared).
+                    if ancilla_qubits.contains(&q_idx) {
+                        expanded.push(make_gate(GateType::PZ, &[q_idx]));
+                    }
+
+                    // Record: this measurement maps to the auxiliary qubit
+                    measurement_qubit.push(aux);
+                    original_measured_qubit.push(q_idx);
+                }
+            }
+            GateType::PZ | GateType::QAlloc => {
+                // Keep resets — they re-initialize the qubit for the next round
+                expanded.push(gate.clone());
+            }
+            _ => {
+                // All other gates pass through unchanged
+                expanded.push(gate.clone());
+            }
+        }
+
+        i += 1;
+    }
+
+    // Add final measurements of all auxiliary qubits at the end
+    for &aux in &measurement_qubit {
+        expanded.push(make_gate(GateType::MZ, &[aux]));
+    }
+
+    ExpandedCircuit {
+        gates: expanded,
+        num_qubits: next_aux,
+        num_original_qubits: num_original,
+        measurement_qubit,
+        original_measured_qubit,
+    }
+}
+
+impl ExpandedCircuit {
+    /// Map an expanded-circuit Pauli back to the original circuit frame.
+    ///
+    /// X on auxiliary qubit `aux_k` → X on `original_measured_qubit[k]`
+    /// (because `CX(q, aux)` copies X from control to target: X on aux
+    /// in the expanded circuit corresponds to X on q in the original).
+    ///
+    /// Z on auxiliary qubits is dropped (doesn't correspond to original).
+    /// Components on original qubits pass through unchanged.
+    #[must_use]
+    pub fn map_to_original_frame(&self, p: &Bm) -> Bm {
+        let mut result = Bm::default();
+
+        // Copy components on original qubits directly
+        for q in 0..self.num_original_qubits {
+            if p.has_x(q) {
+                result.x_bits.set_bit(q);
+            }
+            if p.has_z(q) {
+                result.z_bits.set_bit(q);
+            }
+        }
+
+        // Map X on auxiliary qubits to X on original measured qubits
+        for (meas_idx, &aux_q) in self.measurement_qubit.iter().enumerate() {
+            if p.has_x(aux_q) {
+                let orig_q = self.original_measured_qubit[meas_idx];
+                result.x_bits.xor_bit(orig_q); // XOR because same qubit may be measured multiple times
+            }
+            // Z on aux is ignored (measurement projection absorbs Z)
+        }
+
+        result
+    }
+}
+
+/// Precomputed qubit-to-gate index for sparse backward traversal.
+///
+/// For each qubit, stores the gate indices (in the flat gate list) that
+/// touch it, sorted in ascending order. This enables the backward walk
+/// to visit only gates on active qubits instead of scanning all gates.
+pub struct GateIndex {
+    /// qubit_gates[q] = sorted Vec of gate indices touching qubit q.
+    qubit_gates: Vec<Vec<u32>>,
+    /// Which gates are expansion gates (no physical noise).
+    pub expansion_gates: Vec<bool>,
+}
+
+impl GateIndex {
+    /// Build the index from a gate list (typically the expanded circuit).
+    #[must_use]
+    pub fn build(gates: &[Gate], num_qubits: usize) -> Self {
+        let mut qubit_gates = vec![Vec::new(); num_qubits];
+
+        for (i, gate) in gates.iter().enumerate() {
+            for q in &gate.qubits {
+                qubit_gates[q.index()].push(i as u32);
+            }
+        }
+
+        // Identify expansion gates (QAlloc + subsequent CX + PZ)
+        let mut expansion = vec![false; gates.len()];
+        for i in 0..gates.len() {
+            if gates[i].gate_type == GateType::QAlloc {
+                expansion[i] = true;
+            }
+        }
+        for i in 1..gates.len() {
+            if gates[i].gate_type == GateType::CX && gates[i - 1].gate_type == GateType::QAlloc {
+                let alloc_q = gates[i - 1].qubits[0].index();
+                if gates[i].qubits.len() >= 2 && gates[i].qubits[1].index() == alloc_q {
+                    expansion[i] = true;
+                    if i + 1 < gates.len()
+                        && gates[i + 1].gate_type == GateType::PZ
+                        && gates[i + 1].qubits[0].index() == gates[i].qubits[0].index()
+                    {
+                        expansion[i + 1] = true;
+                    }
+                }
+            }
+        }
+
+        Self {
+            qubit_gates,
+            expansion_gates: expansion,
+        }
+    }
+
+    /// Gate indices touching qubit `q` in reverse order (for backward walk).
+    pub fn gates_on_qubit_rev(&self, q: usize) -> impl Iterator<Item = u32> + '_ {
+        self.qubit_gates
+            .get(q)
+            .into_iter()
+            .flat_map(|v| v.iter().copied().rev())
+    }
+
+    /// Is this gate an expansion gate (no physical noise)?
+    #[inline]
+    #[must_use]
+    pub fn is_expansion(&self, gate_idx: usize) -> bool {
+        self.expansion_gates.get(gate_idx).copied().unwrap_or(false)
+    }
+}
+
+#[must_use]
+pub fn make_gate(gt: GateType, qubits: &[usize]) -> Gate {
+    Gate {
+        gate_type: gt,
+        qubits: qubits.iter().map(|&q| QubitId(q)).collect(),
+        angles: GateAngles::new(),
+        params: GateParams::new(),
+        meas_ids: pecos_core::GateMeasIds::new(),
+        channel: None,
+    }
+}
+
+#[cfg(test)]
+mod tests {
+    use super::*;
+
+    fn gate(gt: GateType, qubits: &[usize]) -> Gate {
+        make_gate(gt, qubits)
+    }
+
+    #[test]
+    fn test_expand_simple_mcm() {
+        // PZ(0), H(0), MZ(0), PZ(0), H(0), MZ(0)
+        // Two rounds: measure, reset, measure again
+        let gates = vec![
+            gate(GateType::PZ, &[0]),
+            gate(GateType::H, &[0]),
+            gate(GateType::MZ, &[0]), // → CX(0, aux0)
+            gate(GateType::PZ, &[0]), // reset
+            gate(GateType::H, &[0]),
+            gate(GateType::MZ, &[0]), // → CX(0, aux1)
+        ];
+
+        let expanded = expand_circuit(&gates);
+
+        // Should have 3 qubits: original 0, aux 1, aux 2
+        assert_eq!(expanded.num_original_qubits, 1);
+        assert_eq!(expanded.num_qubits, 3);
+        assert_eq!(expanded.measurement_qubit.len(), 2);
+
+        // No MZ in the middle — only at the end
+        let mid_mz = expanded.gates[..expanded.gates.len() - 2]
+            .iter()
+            .filter(|g| g.gate_type == GateType::MZ)
+            .count();
+        assert_eq!(mid_mz, 0, "No mid-circuit MZ in expanded circuit");
+
+        // Two MZ at the end (one per auxiliary)
+        let end_mz = expanded
+            .gates
+            .iter()
+            .rev()
+            .take_while(|g| g.gate_type == GateType::MZ)
+            .count();
+        assert_eq!(end_mz, 2);
+    }
+
+    #[test]
+    fn test_expand_preserves_cliffords() {
+        let gates = vec![
+            gate(GateType::PZ, &[0, 1]),
+            gate(GateType::H, &[0]),
+            gate(GateType::CX, &[0, 1]),
+        ];
+
+        let expanded = expand_circuit(&gates);
+
+        // No measurements → no expansion needed
+        assert_eq!(expanded.num_qubits, 2);
+        assert_eq!(expanded.measurement_qubit.len(), 0);
+        assert_eq!(expanded.gates.len(), 3); // same gates
+    }
+
+    #[test]
+    fn test_measurement_qubit_mapping() {
+        // 2 qubits, measure both
+        let gates = vec![
+            gate(GateType::PZ, &[0, 1]),
+            gate(GateType::H, &[0]),
+            gate(GateType::CX, &[0, 1]),
+            gate(GateType::MZ, &[0]), // meas record 0 → aux 2
+            gate(GateType::MZ, &[1]), // meas record 1 → aux 3
+        ];
+
+        let expanded = expand_circuit(&gates);
+
+        assert_eq!(expanded.measurement_qubit, vec![2, 3]);
+        assert_eq!(expanded.num_qubits, 4);
+    }
+
+    #[test]
+    fn test_map_to_original_frame_x_on_aux() {
+        // X on auxiliary → X on original measured qubit
+        let gates = vec![
+            gate(GateType::PZ, &[0]),
+            gate(GateType::MZ, &[0]), // meas 0 → aux 1
+        ];
+        let expanded = expand_circuit(&gates);
+
+        // X on aux 1 maps to X on original qubit 0
+        let p = Bm::x(1); // aux qubit
+        let mapped = expanded.map_to_original_frame(&p);
+        assert_eq!(mapped, Bm::x(0));
+    }
+
+    #[test]
+    fn test_map_to_original_frame_z_on_aux_dropped() {
+        // Z on auxiliary is dropped (measurement projection absorbs it)
+        let gates = vec![gate(GateType::PZ, &[0]), gate(GateType::MZ, &[0])];
+        let expanded = expand_circuit(&gates);
+
+        let p = Bm::z(1); // Z on aux
+        let mapped = expanded.map_to_original_frame(&p);
+        assert!(mapped.is_identity(), "Z on aux should be dropped");
+    }
+
+    #[test]
+    fn test_map_to_original_frame_original_passthrough() {
+        // Components on original qubits pass through unchanged
+        let gates = vec![gate(GateType::PZ, &[0, 1]), gate(GateType::MZ, &[0])];
+        let expanded = expand_circuit(&gates);
+
+        let p = Bm::x(0).multiply(&Bm::z(1)); // X0 Z1
+        let mapped = expanded.map_to_original_frame(&p);
+        assert_eq!(mapped, Bm::x(0).multiply(&Bm::z(1)));
+    }
+
+    #[test]
+    fn test_expand_final_only_mz() {
+        // Circuit with only final MZ (no mid-circuit measurement)
+        let gates = vec![
+            gate(GateType::PZ, &[0]),
+            gate(GateType::H, &[0]),
+            gate(GateType::MZ, &[0]),
+        ];
+        let expanded = expand_circuit(&gates);
+
+        // Still creates one aux qubit for the final MZ
+        assert_eq!(expanded.num_qubits, 2);
+        assert_eq!(expanded.measurement_qubit.len(), 1);
+    }
+
+    #[test]
+    fn test_expansion_pz_for_ancilla_mz() {
+        // Circuit: PZ(0,1), H(1), CX(1,0), MZ(1), PZ(1), H(1), CX(1,0), MZ(1), MZ(0)
+        // Qubit 1 is ancilla (has mid-circuit PZ). Qubit 0 is data.
+        // Last-round MZ(1) should get expansion PZ(1).
+        // Final MZ(0) should NOT get expansion PZ.
+        let gates = vec![
+            gate(GateType::PZ, &[0]),
+            gate(GateType::PZ, &[1]),
+            gate(GateType::H, &[1]),
+            gate(GateType::CX, &[1, 0]),
+            gate(GateType::MZ, &[1]), // round 1 syndrome
+            gate(GateType::PZ, &[1]), // reset
+            gate(GateType::H, &[1]),
+            gate(GateType::CX, &[1, 0]),
+            gate(GateType::MZ, &[1]), // round 2 syndrome (last round, no PZ after)
+            gate(GateType::MZ, &[0]), // data readout
+        ];
+
+        let expanded = expand_circuit(&gates);
+
+        // Count PZ/QAlloc gates on qubit 1 in the expanded circuit
+        let resets_on_1: Vec<_> = expanded
+            .gates
+            .iter()
+            .filter(|g| {
+                (g.gate_type == GateType::PZ || g.gate_type == GateType::QAlloc)
+                    && g.qubits.iter().any(|q| q.index() == 1)
+            })
+            .collect();
+
+        // Should have: original PZ(1) init + expansion PZ(1) round 1 + circuit PZ(1) reset
+        //            + expansion PZ(1) round 2 = 4 reset gates on qubit 1
+        eprintln!("Resets on qubit 1: {} gates", resets_on_1.len());
+        assert!(
+            resets_on_1.len() >= 4,
+            "Should have expansion PZ for last-round MZ(1): got {} on q1",
+            resets_on_1.len()
+        );
+
+        // Count resets on qubit 0 in expanded circuit
+        let resets_on_0: Vec<_> = expanded
+            .gates
+            .iter()
+            .filter(|g| {
+                (g.gate_type == GateType::PZ || g.gate_type == GateType::QAlloc)
+                    && g.qubits.iter().any(|q| q.index() == 0)
+            })
+            .collect();
+        // Should have only: original PZ(0) init = 1
+        eprintln!("Resets on qubit 0: {} gates", resets_on_0.len());
+        assert_eq!(
+            resets_on_0.len(),
+            1,
+            "Data qubit should NOT get expansion PZ"
+        );
+    }
+
+    #[test]
+    fn test_expand_multi_round_tracks_original_qubits() {
+        // Two rounds measuring qubit 0: both aux should map back to qubit 0
+        let gates = vec![
+            gate(GateType::PZ, &[0]),
+            gate(GateType::MZ, &[0]),
+            gate(GateType::PZ, &[0]),
+            gate(GateType::MZ, &[0]),
+        ];
+        let expanded = expand_circuit(&gates);
+
+        assert_eq!(expanded.measurement_qubit.len(), 2);
+        assert_eq!(expanded.original_measured_qubit, vec![0, 0]);
+    }
+}
diff --git a/exp/pecos-eeg/src/heisenberg.rs b/exp/pecos-eeg/src/heisenberg.rs
new file mode 100644
index 000000000..c68d9163b
--- /dev/null
+++ b/exp/pecos-eeg/src/heisenberg.rs
@@ -0,0 +1,2748 @@
+// Copyright 2026 The PECOS Developers
+//
+// Licensed under the Apache License, Version 2.0
+
+//! Backward Heisenberg propagation of detectors through noise.
+//!
+//! Computes exact detection probabilities by propagating the detector
+//! observable BACKWARD through the expanded (measurement-deferred) circuit.
+//!
+//! Coherent (H-type) noise: at each source exp(h·H_P), the observable
+//! transforms via unitary conjugation:
+//!   D → cos(2h)·D + i·sin(2h)·P·D  (when D and P anticommute)
+//!   D → D                            (when D and P commute)
+//!
+//! Stochastic (S-type) noise: EEG rate s < 0, physical error
+//! probability p = (1/2)(1 - exp(2s)).  Heisenberg dual:
+//!   D → D          (when D and P commute)
+//!   D → exp(2s)·D  (when D and P anticommute)
+//!
+//! The cost is exponential in the number of anticommuting H-type noise
+//! sources per detector (2^m terms), but this is typically manageable
+//! for QEC circuits (m ~ 5-15). S-type noise does not increase term count.
+//!
+//! Both a Pauli-tracking walk (fast, exact) and a matrix-based method
+//! (exact, limited to ~20 qubits) are provided.
+
+use crate::Bm;
+use crate::noise::NoiseSpec;
+use crate::stabilizer::StabilizerGroup;
+use pecos_core::Gate;
+use pecos_core::gate_type::GateType;
+use pecos_core::pauli::pauli_bitmask::BitmaskStorage;
+use smallvec::SmallVec;
+use std::collections::BinaryHeap;
+
+const CX_PHASE: [[u8; 4]; 4] = [[0, 0, 0, 0], [0, 0, 3, 1], [0, 1, 0, 3], [0, 3, 1, 0]];
+
+fn sign_parity<const N: usize>(signs: [bool; N]) -> bool {
+    signs.into_iter().fold(false, |parity, sign| parity ^ sign)
+}
+
+fn activate_qubit(
+    q: u16,
+    before_gate: u32,
+    active: &mut [bool],
+    visited: &mut [bool],
+    heap: &mut BinaryHeap<u32>,
+    gate_index: &crate::expand::GateIndex,
+) {
+    let qu = q as usize;
+    if qu >= active.len() {
+        return;
+    }
+    active[qu] = true;
+    for gi in gate_index.gates_on_qubit_rev(qu) {
+        if gi >= before_gate {
+            continue;
+        } // already passed
+        let gi_usize = gi as usize;
+        if !visited[gi_usize] {
+            visited[gi_usize] = true;
+            heap.push(gi);
+        }
+    }
+}
+
+/// Precomputed noise for a single gate: H-type injections + batched S-type scale.
+///
+/// Instead of calling `noise_after_gate()` during the walk and processing
+/// 15+ S-type injections individually, we precompute:
+/// - H-type injections (kept as-is, they cause branching)
+/// - A combined S-type scale factor per qubit-support pattern
+///
+/// For uniform 2-qubit depolarizing at rate p: any term with non-identity
+/// on either gate qubit gets scaled by `(1-2p/15)^8` (exactly 8 of 15
+/// Paulis anticommute for any non-identity support). Single-qubit: `(1-2p/3)^2`.
+pub struct PrecomputedGateNoise {
+    /// H-type injections (cause term branching, can't be batched).
+    pub h_injections: SmallVec<[crate::noise::NoiseInjection; 2]>,
+    /// Combined S-type scale for terms with non-identity on qubit 0 only.
+    /// (For 1q gates, this is the full scale. For 2q, see q1_scale/both_scale.)
+    pub q0_scale: f64,
+    /// Qubit 0 index (for S-type fast path).
+    pub q0: u16,
+    /// Combined S-type scale for terms with non-identity on qubit 1 only (2q gates).
+    pub q1_scale: f64,
+    /// Qubit 1 index.
+    pub q1: u16,
+    /// Combined S-type scale for terms with non-identity on BOTH qubits.
+    pub both_scale: f64,
+    /// Number of qubits this gate acts on (0, 1, or 2).
+    pub num_gate_qubits: u8,
+}
+
+/// Build a noise map: precomputed noise for each gate.
+///
+/// Returns `None` for gates with no noise. Expansion gates are mostly
+/// skipped, except expansion CX gates get p_meas noise on their control
+/// qubit (the originally-measured qubit) to model mid-circuit measurement
+/// errors that the expansion would otherwise lose.
+pub fn build_noise_map(
+    gates: &[Gate],
+    noise: &dyn NoiseSpec,
+    expansion_gates: &[bool],
+) -> Vec<Option<PrecomputedGateNoise>> {
+    let mut map = Vec::with_capacity(gates.len());
+
+    for (i, gate) in gates.iter().enumerate() {
+        if i < expansion_gates.len() && expansion_gates[i] {
+            map.push(None);
+            continue;
+        }
+
+        let qubits: SmallVec<[usize; 4]> =
+            gate.qubits.iter().map(pecos_core::QubitId::index).collect();
+        let injections = noise.noise_after_gate(i, gate.gate_type, &qubits);
+
+        if injections.is_empty() {
+            map.push(None);
+            continue;
+        }
+
+        let mut h_inj = SmallVec::new();
+        // Collect S-type rates grouped by which qubits they touch.
+        // We compute a combined scale factor for each support pattern.
+        let mut s_rates_q0_only = Vec::new(); // S noise on q0 only
+        let mut s_rates_q1_only = Vec::new(); // S noise on q1 only
+        let mut s_rates_both = Vec::new(); // S noise on both q0 and q1
+        let mut s_rates_other = Vec::new(); // S noise on other patterns
+
+        let q0 = qubits.first().copied().unwrap_or(0) as u16;
+        let q1 = if qubits.len() >= 2 {
+            qubits[1] as u16
+        } else {
+            q0
+        };
+
+        for inj in &injections {
+            if inj.eeg_type == crate::eeg::EegType::S {
+                let rate = inj.rate;
+                // Classify by qubit support
+                let on_q0 = inj.label.has_x(q0 as usize) || inj.label.has_z(q0 as usize);
+                let on_q1 = qubits.len() >= 2
+                    && (inj.label.has_x(q1 as usize) || inj.label.has_z(q1 as usize));
+
+                // For each S injection with rate s (s < 0), the scale for
+                // anticommuting terms is (1 - 2*(-s)) = (1 + 2s).
+                // We need to count how many of the term's components
+                // anticommute. For a uniform depolarizing model this is
+                // predetermined by the support pattern.
+                //
+                // Instead of trying to batch analytically (which requires
+                // knowing the exact anticommutation count), we accumulate
+                // the log of the scale factors and compute the combined
+                // scale per support pattern.
+                //
+                // For now, just collect individual rates.
+                if on_q0 && !on_q1 {
+                    s_rates_q0_only.push(rate);
+                } else if !on_q0 && on_q1 {
+                    s_rates_q1_only.push(rate);
+                } else if on_q0 && on_q1 {
+                    s_rates_both.push(rate);
+                } else {
+                    s_rates_other.push(rate);
+                }
+            } else {
+                h_inj.push(inj.clone());
+            }
+        }
+
+        // Compute combined scale factors.
+        // A term anticommutes with S_P iff it has non-trivial overlap with P.
+        //
+        // For a term with non-identity on q0 only:
+        //   - Anticommutes with S generators touching q0: all of q0_only + both
+        //   - But WHICH ones anticommute depends on the specific Pauli.
+        //
+        // For uniform depolarizing, the count of anticommuting generators is
+        // deterministic given the support pattern. But for general S noise, we
+        // can't batch — fall back to individual processing.
+        //
+        // Optimization: if ALL S rates are the same (uniform depol), use
+        // closed-form. Otherwise, keep individual injections.
+        let all_s_same_rate = {
+            let all_s: Vec<f64> = s_rates_q0_only
+                .iter()
+                .chain(&s_rates_q1_only)
+                .chain(&s_rates_both)
+                .chain(&s_rates_other)
+                .copied()
+                .collect();
+            !all_s.is_empty() && all_s.iter().all(|&r| (r - all_s[0]).abs() < 1e-20)
+        };
+
+        if all_s_same_rate && s_rates_other.is_empty() {
+            // Uniform depolarizing: use closed-form combined scale.
+            // For any non-identity on q0: 2 of {X,Y,Z} on q0 anticommute.
+            // For single-qubit: 3 S generators, 2 anticommute → scale = (1+2s)^2
+            // For two-qubit: 15 S generators, 8 anticommute for any non-trivial → (1+2s)^8
+            let total_s = s_rates_q0_only.len() + s_rates_q1_only.len() + s_rates_both.len();
+            let s = s_rates_q0_only
+                .first()
+                .or(s_rates_q1_only.first())
+                .or(s_rates_both.first())
+                .copied()
+                .unwrap_or(0.0);
+            let p = -s;
+            let individual_scale = 1.0 - 2.0 * p;
+
+            // Count anticommuting for each support pattern.
+            // For term with non-identity on q0 only:
+            //   anti with q0-only S: 2 out of 3 (if 1q) or 2 out of 3 (for each A⊗I)
+            //   anti with both S: depends on q1 part (commutes since term has I on q1)
+            //   Total for 2q depol: q0_only anti=2 out of 3, both anti=q0 part anti * q1 commutes
+            //   = 2*3 (from 3 A⊗I where 2 of 3 A anticommute on q0, B=I commutes)
+            //   + 0 (from 3 I⊗B)
+            //   + 2*3 (from 9 A⊗B where 2 of 3 A anticommute, B commutes since I on q1)
+            //   Wait, {A, I_term} always commutes for B part. So:
+            //   anti count = (anti on q0) * (total on q1 including I) + (comm on q0) * (anti on q1)
+            //   For term I on q1: anti on q1 = 0.
+            //   So anti count = 2 * 4 + 2 * 0 = 8 for 15 generators (excluding I⊗I).
+            //
+            // Actually, let me just precompute this properly.
+            // For 1q depol (3 generators): non-identity on q → 2 anticommute → (1-2p/3)^2
+            // For 2q depol (15 generators): non-identity on either q → 8 anticommute → (1-2p/15)^8
+            let n_anti = if total_s == 3 {
+                2
+            } else if total_s == 15 {
+                8
+            } else {
+                0
+            };
+            if n_anti == 0 && total_s > 0 {
+                // Non-standard S count (e.g., 1 for p_meas, 1 for p_prep):
+                // can't batch — put in h_injections for individual processing.
+                for inj in &injections {
+                    if inj.eeg_type == crate::eeg::EegType::S {
+                        h_inj.push(inj.clone());
+                    }
+                }
+            }
+            let combined = individual_scale.powi(n_anti);
+
+            map.push(Some(PrecomputedGateNoise {
+                h_injections: h_inj,
+                q0_scale: combined,
+                q0,
+                q1_scale: combined,
+                q1,
+                both_scale: combined,
+                num_gate_qubits: qubits.len().min(2) as u8,
+            }));
+        } else if s_rates_q0_only.is_empty()
+            && s_rates_q1_only.is_empty()
+            && s_rates_both.is_empty()
+            && s_rates_other.is_empty()
+        {
+            // H-type only, no S noise
+            if h_inj.is_empty() {
+                map.push(None);
+            } else {
+                map.push(Some(PrecomputedGateNoise {
+                    h_injections: h_inj,
+                    q0_scale: 1.0,
+                    q0,
+                    q1_scale: 1.0,
+                    q1,
+                    both_scale: 1.0,
+                    num_gate_qubits: qubits.len().min(2) as u8,
+                }));
+            }
+        } else {
+            // Non-uniform S noise: keep individual injections as H-type
+            // (the walk handles them individually).
+            for inj in injections {
+                if inj.eeg_type == crate::eeg::EegType::S {
+                    h_inj.push(inj); // process individually in walk
+                }
+            }
+            map.push(Some(PrecomputedGateNoise {
+                h_injections: h_inj,
+                q0_scale: 1.0,
+                q0,
+                q1_scale: 1.0,
+                q1,
+                both_scale: 1.0,
+                num_gate_qubits: qubits.len().min(2) as u8,
+            }));
+        }
+    }
+
+    map
+}
+
+/// Sparse Pauli: stores only qubits with non-identity Pauli.
+/// For terms touching ~10-20 qubits out of 1000+, this is 10-100x
+/// more compact than a dense bitmask, making clone/cmp/hash O(support).
+///
+/// Stored as sorted lists of qubit indices for X and Z components.
+/// Y on qubit q means q appears in BOTH x_qubits and z_qubits.
+#[derive(Clone, Debug, Default)]
+pub(crate) struct SparsePauli {
+    x_qubits: SmallVec<[u16; 16]>,
+    z_qubits: SmallVec<[u16; 16]>,
+}
+
+impl SparsePauli {
+    pub(crate) fn from_bm(bm: &Bm) -> Self {
+        let mut sp = Self::default();
+        let max_x = bm.x_bits.highest_set_bit().unwrap_or(0);
+        let max_z = bm.z_bits.highest_set_bit().unwrap_or(0);
+        let max_q = max_x.max(max_z);
+        for q in 0..=max_q {
+            if bm.has_x(q) {
+                sp.x_qubits.push(q as u16);
+            }
+            if bm.has_z(q) {
+                sp.z_qubits.push(q as u16);
+            }
+        }
+        sp
+    }
+
+    pub(crate) fn to_bm(&self) -> Bm {
+        let mut bm = Bm::default();
+        for &q in &self.x_qubits {
+            bm.x_bits.set_bit(q as usize);
+        }
+        for &q in &self.z_qubits {
+            bm.z_bits.set_bit(q as usize);
+        }
+        bm
+    }
+
+    #[inline]
+    fn is_identity(&self) -> bool {
+        self.x_qubits.is_empty() && self.z_qubits.is_empty()
+    }
+
+    #[inline]
+    fn has_x(&self, q: u16) -> bool {
+        self.x_qubits.binary_search(&q).is_ok()
+    }
+
+    #[inline]
+    fn has_z(&self, q: u16) -> bool {
+        self.z_qubits.binary_search(&q).is_ok()
+    }
+
+    /// Toggle x-bit at qubit q (insert if missing, remove if present).
+    fn toggle_x(&mut self, q: u16) {
+        match self.x_qubits.binary_search(&q) {
+            Ok(i) => {
+                self.x_qubits.remove(i);
+            }
+            Err(i) => {
+                self.x_qubits.insert(i, q);
+            }
+        }
+    }
+
+    fn toggle_z(&mut self, q: u16) {
+        match self.z_qubits.binary_search(&q) {
+            Ok(i) => {
+                self.z_qubits.remove(i);
+            }
+            Err(i) => {
+                self.z_qubits.insert(i, q);
+            }
+        }
+    }
+
+    /// Remove X at qubit q (for PZ backward: kill if has_x).
+    pub(crate) fn clear_x(&mut self, q: u16) {
+        if let Ok(i) = self.x_qubits.binary_search(&q) {
+            self.x_qubits.remove(i);
+        }
+    }
+
+    pub(crate) fn clear_z(&mut self, q: u16) {
+        if let Ok(i) = self.z_qubits.binary_search(&q) {
+            self.z_qubits.remove(i);
+        }
+    }
+
+    /// Check if this Pauli commutes with a single-qubit Z_q.
+    /// Full commutation check with another SparsePauli.
+    fn commutes_with(&self, other: &Self) -> bool {
+        // Symplectic inner product mod 2:
+        // count = |self.x ∩ other.z| + |self.z ∩ other.x|
+        // Commutes iff count is even.
+        let c1 = sorted_intersection_count(&self.x_qubits, &other.z_qubits);
+        let c2 = sorted_intersection_count(&self.z_qubits, &other.x_qubits);
+        (c1 + c2).is_multiple_of(2)
+    }
+}
+
+impl PartialEq for SparsePauli {
+    fn eq(&self, other: &Self) -> bool {
+        self.x_qubits == other.x_qubits && self.z_qubits == other.z_qubits
+    }
+}
+impl Eq for SparsePauli {}
+
+impl std::hash::Hash for SparsePauli {
+    fn hash<H: std::hash::Hasher>(&self, state: &mut H) {
+        self.x_qubits.as_slice().hash(state);
+        self.z_qubits.as_slice().hash(state);
+    }
+}
+
+impl Ord for SparsePauli {
+    fn cmp(&self, other: &Self) -> std::cmp::Ordering {
+        self.x_qubits
+            .as_slice()
+            .cmp(other.x_qubits.as_slice())
+            .then(self.z_qubits.as_slice().cmp(other.z_qubits.as_slice()))
+    }
+}
+impl PartialOrd for SparsePauli {
+    fn partial_cmp(&self, other: &Self) -> Option<std::cmp::Ordering> {
+        Some(self.cmp(other))
+    }
+}
+
+/// Count elements in the intersection of two sorted slices.
+#[inline]
+fn sorted_intersection_count(a: &[u16], b: &[u16]) -> u32 {
+    let (mut i, mut j) = (0, 0);
+    let mut count = 0u32;
+    while i < a.len() && j < b.len() {
+        match a[i].cmp(&b[j]) {
+            std::cmp::Ordering::Less => i += 1,
+            std::cmp::Ordering::Greater => j += 1,
+            std::cmp::Ordering::Equal => {
+                count += 1;
+                i += 1;
+                j += 1;
+            }
+        }
+    }
+    count
+}
+
+impl SparsePauli {
+    /// Conjugate by Hadamard on qubit q: X↔Z, Y→-Y.
+    fn conjugate_h(&mut self, q: u16) -> bool {
+        let hx = self.has_x(q);
+        let hz = self.has_z(q);
+        if hx != hz {
+            // X→Z or Z→X: swap
+            self.toggle_x(q);
+            self.toggle_z(q);
+        }
+        // Y→-Y: sign flip when both X and Z
+        hx && hz
+    }
+
+    /// Conjugate by CX(control, target). Returns sign_negative.
+    fn conjugate_cx(&mut self, c: u16, t: u16) -> bool {
+        let cx = self.has_x(c);
+        let cz = self.has_z(c);
+        let tx = self.has_x(t);
+        let tz = self.has_z(t);
+        if cx {
+            self.toggle_x(t);
+        }
+        if tz {
+            self.toggle_z(c);
+        }
+        // Sign from phase table (same formula as the fixed conjugate_cx)
+        let pc = u8::from(cx) + 2 * u8::from(cz);
+        let pt = u8::from(tx) + 2 * u8::from(tz);
+        let phase_c = if tz { CX_PHASE[pc as usize][2] } else { 0 };
+        let phase_t = if cx { CX_PHASE[1][pt as usize] } else { 0 };
+        (phase_c + phase_t) % 4 == 2
+    }
+
+    /// Conjugate by CZ(a, b). Returns sign_negative.
+    fn conjugate_cz(&mut self, a: u16, b: u16) -> bool {
+        let ax = self.has_x(a);
+        let bx = self.has_x(b);
+        let az = self.has_z(a);
+        let bz = self.has_z(b);
+        if bx {
+            self.toggle_z(a);
+        }
+        if ax {
+            self.toggle_z(b);
+        }
+        ax && bx && (az != bz)
+    }
+
+    /// Conjugate by Pauli X on qubit q.
+    fn conjugate_pauli_x(&self, q: u16) -> bool {
+        self.has_z(q)
+    }
+    /// Conjugate by Pauli Y on qubit q.
+    fn conjugate_pauli_y(&self, q: u16) -> bool {
+        self.has_x(q) != self.has_z(q)
+    }
+    /// Conjugate by Pauli Z on qubit q.
+    fn conjugate_pauli_z(&self, q: u16) -> bool {
+        self.has_x(q)
+    }
+
+    /// Conjugate by SZ on qubit q: X→Y, Y→-X, Z→Z.
+    fn conjugate_sz(&mut self, q: u16) -> bool {
+        if !self.has_x(q) {
+            return false;
+        }
+        let was_y = self.has_z(q);
+        self.toggle_z(q);
+        was_y
+    }
+
+    /// Conjugate by SZdg on qubit q.
+    fn conjugate_szdg(&mut self, q: u16) -> bool {
+        if !self.has_x(q) {
+            return false;
+        }
+        let was_y = self.has_z(q);
+        self.toggle_z(q);
+        !was_y
+    }
+
+    /// Conjugate by SX on qubit q.
+    fn conjugate_sx(&mut self, q: u16) -> bool {
+        let xq = self.has_x(q);
+        let zq = self.has_z(q);
+        if zq {
+            self.toggle_x(q);
+        }
+        !xq && zq
+    }
+
+    /// Conjugate by SXdg on qubit q.
+    fn conjugate_sxdg(&mut self, q: u16) -> bool {
+        let xq = self.has_x(q);
+        let zq = self.has_z(q);
+        if zq {
+            self.toggle_x(q);
+        }
+        xq && zq
+    }
+
+    /// Conjugate by SY on qubit q.
+    fn conjugate_sy(&mut self, q: u16) -> bool {
+        let xq = self.has_x(q);
+        let zq = self.has_z(q);
+        if xq != zq {
+            self.toggle_x(q);
+            self.toggle_z(q);
+        }
+        xq && !zq
+    }
+
+    /// Conjugate by SYdg on qubit q.
+    fn conjugate_sydg(&mut self, q: u16) -> bool {
+        let xq = self.has_x(q);
+        let zq = self.has_z(q);
+        if xq != zq {
+            self.toggle_x(q);
+            self.toggle_z(q);
+        }
+        !xq && zq
+    }
+
+    /// Conjugate by SWAP(a, b).
+    fn conjugate_swap(&mut self, a: u16, b: u16) {
+        let ax = self.has_x(a);
+        let az = self.has_z(a);
+        let bx = self.has_x(b);
+        let bz = self.has_z(b);
+        // Clear both
+        if ax {
+            self.clear_x(a);
+        }
+        if az {
+            self.clear_z(a);
+        }
+        if bx {
+            self.clear_x(b);
+        }
+        if bz {
+            self.clear_z(b);
+        }
+        // Set swapped
+        if bx {
+            self.toggle_x(a);
+        }
+        if bz {
+            self.toggle_z(a);
+        }
+        if ax {
+            self.toggle_x(b);
+        }
+        if az {
+            self.toggle_z(b);
+        }
+    }
+}
+
+/// Apply backward (Heisenberg) gate conjugation: P → U† P U.
+///
+/// The conjugation methods on `SparsePauli` use the Schrödinger convention
+/// (P → U P U†), so for the backward walk we swap non-self-adjoint gates
+/// to their adjoints: SZ↔SZdg, SX↔SXdg, SY↔SYdg, SZZ↔SZZdg, etc.
+/// Self-adjoint gates (H, X, Y, Z, CX, CZ, SWAP, CY) are unchanged.
+pub(crate) fn sparse_conjugate(p: &mut SparsePauli, gate: &Gate) -> Option<bool> {
+    if gate.qubits.is_empty() {
+        return None;
+    }
+    let q0 = gate.qubits[0].index() as u16;
+    match gate.gate_type {
+        // Self-adjoint single-qubit gates
+        GateType::H => Some(p.conjugate_h(q0)),
+        GateType::X => Some(p.conjugate_pauli_x(q0)),
+        GateType::Y => Some(p.conjugate_pauli_y(q0)),
+        GateType::Z => Some(p.conjugate_pauli_z(q0)),
+        // Non-self-adjoint single-qubit: swap to adjoint for backward
+        GateType::SZ => Some(p.conjugate_szdg(q0)),
+        GateType::SZdg => Some(p.conjugate_sz(q0)),
+        GateType::SX => Some(p.conjugate_sxdg(q0)),
+        GateType::SXdg => Some(p.conjugate_sx(q0)),
+        GateType::SY => Some(p.conjugate_sydg(q0)),
+        GateType::SYdg => Some(p.conjugate_sy(q0)),
+        // Self-adjoint two-qubit gates
+        GateType::CX => {
+            let q1 = gate.qubits[1].index() as u16;
+            Some(p.conjugate_cx(q0, q1))
+        }
+        GateType::CZ => {
+            let q1 = gate.qubits[1].index() as u16;
+            Some(p.conjugate_cz(q0, q1))
+        }
+        GateType::SWAP => {
+            let q1 = gate.qubits[1].index() as u16;
+            p.conjugate_swap(q0, q1);
+            Some(false)
+        }
+        // CY is self-adjoint: CY = SZdg(t) CX(c,t) SZ(t) — chain
+        GateType::CY => {
+            let q1 = gate.qubits[1].index() as u16;
+            let s1 = p.conjugate_sz(q1);
+            let s2 = p.conjugate_cx(q0, q1);
+            let s3 = p.conjugate_szdg(q1);
+            Some(sign_parity([s1, s2, s3]))
+        }
+        // Non-self-adjoint two-qubit: swap to adjoint for backward.
+        // SZZ backward = SZZdg forward = CX(q0,q1) SZdg(q1) CX(q0,q1)
+        GateType::SZZ => {
+            let q1 = gate.qubits[1].index() as u16;
+            let s1 = p.conjugate_cx(q0, q1);
+            let s2 = p.conjugate_szdg(q1);
+            let s3 = p.conjugate_cx(q0, q1);
+            Some(sign_parity([s1, s2, s3]))
+        }
+        // SZZdg backward = SZZ forward = CX(q0,q1) SZ(q1) CX(q0,q1)
+        GateType::SZZdg => {
+            let q1 = gate.qubits[1].index() as u16;
+            let s1 = p.conjugate_cx(q0, q1);
+            let s2 = p.conjugate_sz(q1);
+            let s3 = p.conjugate_cx(q0, q1);
+            Some(sign_parity([s1, s2, s3]))
+        }
+        // SXX backward = SXXdg forward = H(q0) H(q1) SZZdg H(q0) H(q1)
+        GateType::SXX => {
+            let q1 = gate.qubits[1].index() as u16;
+            let s1 = p.conjugate_h(q0);
+            let s2 = p.conjugate_h(q1);
+            let s3 = p.conjugate_cx(q0, q1);
+            let s4 = p.conjugate_szdg(q1);
+            let s5 = p.conjugate_cx(q0, q1);
+            let s6 = p.conjugate_h(q0);
+            let s7 = p.conjugate_h(q1);
+            Some(sign_parity([s1, s2, s3, s4, s5, s6, s7]))
+        }
+        // SXXdg backward = SXX forward
+        GateType::SXXdg => {
+            let q1 = gate.qubits[1].index() as u16;
+            let s1 = p.conjugate_h(q0);
+            let s2 = p.conjugate_h(q1);
+            let s3 = p.conjugate_cx(q0, q1);
+            let s4 = p.conjugate_sz(q1);
+            let s5 = p.conjugate_cx(q0, q1);
+            let s6 = p.conjugate_h(q0);
+            let s7 = p.conjugate_h(q1);
+            Some(sign_parity([s1, s2, s3, s4, s5, s6, s7]))
+        }
+        // SYY backward = SYYdg forward = SX(q0) SX(q1) SZZdg SXdg(q0) SXdg(q1)
+        GateType::SYY => {
+            let q1 = gate.qubits[1].index() as u16;
+            let s1 = p.conjugate_sxdg(q0);
+            let s2 = p.conjugate_sxdg(q1);
+            let s3 = p.conjugate_cx(q0, q1);
+            let s4 = p.conjugate_szdg(q1);
+            let s5 = p.conjugate_cx(q0, q1);
+            let s6 = p.conjugate_sx(q0);
+            let s7 = p.conjugate_sx(q1);
+            Some(sign_parity([s1, s2, s3, s4, s5, s6, s7]))
+        }
+        // SYYdg backward = SYY forward
+        GateType::SYYdg => {
+            let q1 = gate.qubits[1].index() as u16;
+            let s1 = p.conjugate_sx(q0);
+            let s2 = p.conjugate_sx(q1);
+            let s3 = p.conjugate_cx(q0, q1);
+            let s4 = p.conjugate_sz(q1);
+            let s5 = p.conjugate_cx(q0, q1);
+            let s6 = p.conjugate_sxdg(q0);
+            let s7 = p.conjugate_sxdg(q1);
+            Some(sign_parity([s1, s2, s3, s4, s5, s6, s7]))
+        }
+        // Gates that don't conjugate Paulis
+        GateType::PZ
+        | GateType::QAlloc
+        | GateType::QFree
+        | GateType::MZ
+        | GateType::MeasureFree
+        | GateType::MeasureLeaked
+        | GateType::I
+        | GateType::Idle => None,
+        other => panic!("EEG Heisenberg: unsupported gate type {other:?}"),
+    }
+}
+
+/// A term in the Heisenberg-propagated detector expansion.
+#[derive(Clone, Debug)]
+struct HeisenbergTerm {
+    /// Pauli operator (sparse: only stores non-identity qubits).
+    pauli: SparsePauli,
+    /// Complex coefficient (real, imaginary).
+    coeff_re: f64,
+    coeff_im: f64,
+}
+
+/// Compute detection probability via backward Heisenberg propagation.
+///
+/// Operates on the EXPANDED circuit (from [`crate::expand`]). Expansion
+/// gates are automatically detected and skipped for noise injection.
+///
+/// Handles both H-type (coherent) and S-type (stochastic) noise.
+///
+/// # Arguments
+/// * `gates` - The expanded circuit gates
+/// * `detector` - Detector as Z on auxiliary qubit(s) (expanded frame)
+/// * `noise` - Noise specification
+/// * `initial_stab` - Stabilizer group of |0...0⟩
+/// * `prune_threshold` - Drop terms with |coefficient| below this (0 for exact)
+pub fn heisenberg_detection_probability(
+    gates: &[Gate],
+    detector: &Bm,
+    noise: &dyn NoiseSpec,
+    initial_stab: &StabilizerGroup,
+    prune_threshold: f64,
+) -> f64 {
+    heisenberg_windowed(gates, detector, noise, initial_stab, prune_threshold, None)
+}
+
+/// Backward Heisenberg with precomputed noise map and BTreeMap-based merging.
+///
+/// Uses BTreeMap<SparsePauli, (re, im)> for continuous dedup — no separate
+/// merge step. Terms are merged on insert via BTreeMap's O(log n) lookup.
+/// Also uses batched S-type scaling from the precomputed noise map.
+pub fn heisenberg_with_noise_map(
+    gates: &[Gate],
+    detector: &Bm,
+    noise_map: &[Option<PrecomputedGateNoise>],
+    initial_stab: &StabilizerGroup,
+    prune_threshold: f64,
+) -> f64 {
+    let mut terms = vec![HeisenbergTerm {
+        pauli: SparsePauli::from_bm(detector),
+        coeff_re: 1.0,
+        coeff_im: 0.0,
+    }];
+
+    // Conservative active-qubit bitmap
+    let max_qubit = gates
+        .iter()
+        .flat_map(|g| g.qubits.iter())
+        .map(pecos_core::QubitId::index)
+        .max()
+        .unwrap_or(0)
+        + 1;
+    let mut active_qubits = vec![false; max_qubit];
+    for &q in terms[0]
+        .pauli
+        .x_qubits
+        .iter()
+        .chain(terms[0].pauli.z_qubits.iter())
+    {
+        if (q as usize) < active_qubits.len() {
+            active_qubits[q as usize] = true;
+        }
+    }
+
+    let mut last_merge_count = 1usize;
+    let mut sin_branches: Vec<HeisenbergTerm> = Vec::new();
+
+    for i in (0..gates.len()).rev() {
+        let gate = &gates[i];
+        let gate_qs: SmallVec<[u16; 4]> = gate.qubits.iter().map(|q| q.index() as u16).collect();
+
+        let gate_touches_active = gate_qs
+            .iter()
+            .any(|&q| (q as usize) < active_qubits.len() && active_qubits[q as usize]);
+
+        // Look up precomputed noise for this gate
+        let gate_noise = if gate_touches_active {
+            noise_map.get(i).and_then(|n| n.as_ref())
+        } else {
+            None
+        };
+
+        if let Some(gn) = gate_noise {
+            // H-type injections (branching)
+            for inj in &gn.h_injections {
+                match inj.eeg_type {
+                    crate::eeg::EegType::H => {
+                        let h = inj.rate;
+                        if h.abs() < 1e-20 {
+                            continue;
+                        }
+                        let cos2h = (2.0 * h).cos();
+                        let sin2h = (2.0 * h).sin();
+
+                        let single_z_qubit: Option<u16> = if inj.label.x_bits.is_zero() {
+                            inj.label.z_bits.highest_set_bit().map(|q| q as u16)
+                        } else {
+                            None
+                        };
+                        let noise_sparse = if single_z_qubit.is_none() {
+                            Some(SparsePauli::from_bm(&inj.label))
+                        } else {
+                            None
+                        };
+
+                        sin_branches.clear();
+                        let n = terms.len();
+                        for term in terms.iter_mut().take(n) {
+                            let anticommutes = if let Some(q) = single_z_qubit {
+                                term.pauli.has_x(q)
+                            } else {
+                                !term.pauli.commutes_with(noise_sparse.as_ref().unwrap())
+                            };
+                            if anticommutes {
+                                let (sr, si) = (sin2h * term.coeff_re, sin2h * term.coeff_im);
+                                let (dp, total_phase) = if let Some(q) = single_z_qubit {
+                                    let mut dp = term.pauli.clone();
+                                    dp.toggle_z(q);
+                                    let has_x = term.pauli.has_x(q);
+                                    let has_z = term.pauli.has_z(q);
+                                    let phase = if has_x {
+                                        if has_z { 3u8 } else { 1 }
+                                    } else {
+                                        0
+                                    };
+                                    (dp, (phase + 1) % 4)
+                                } else {
+                                    let term_bm = term.pauli.to_bm();
+                                    let (dp_bm, phase_exp) =
+                                        inj.label.multiply_with_phase(&term_bm);
+                                    (SparsePauli::from_bm(&dp_bm), (phase_exp + 1) % 4)
+                                };
+                                let (new_re, new_im) = match total_phase {
+                                    0 => (sr, si),
+                                    1 => (-si, sr),
+                                    2 => (-sr, -si),
+                                    3 => (si, -sr),
+                                    _ => unreachable!(),
+                                };
+                                sin_branches.push(HeisenbergTerm {
+                                    pauli: dp,
+                                    coeff_re: new_re,
+                                    coeff_im: new_im,
+                                });
+                                term.coeff_re *= cos2h;
+                                term.coeff_im *= cos2h;
+                            }
+                        }
+                        // Merge sin branches: try binary search merge if terms
+                        // are still sorted from last merge, else just extend.
+                        for t in sin_branches.drain(..) {
+                            for &q in t.pauli.x_qubits.iter().chain(t.pauli.z_qubits.iter()) {
+                                let qu = q as usize;
+                                if qu < active_qubits.len() {
+                                    active_qubits[qu] = true;
+                                }
+                            }
+                            if last_merge_count == terms.len() {
+                                match terms.binary_search_by(|p| p.pauli.cmp(&t.pauli)) {
+                                    Ok(idx) => {
+                                        terms[idx].coeff_re += t.coeff_re;
+                                        terms[idx].coeff_im += t.coeff_im;
+                                    }
+                                    Err(_) => {
+                                        terms.push(t);
+                                    }
+                                }
+                            } else {
+                                terms.push(t);
+                            }
+                        }
+                    }
+                    crate::eeg::EegType::S => {
+                        // Non-batched S-type (fallback for non-uniform noise)
+                        let s = inj.rate;
+                        if s.abs() < 1e-20 {
+                            continue;
+                        }
+                        let p = -s;
+                        let scale = 1.0 - 2.0 * p;
+                        let single_q: Option<u16> = {
+                            let xq = inj.label.x_bits.highest_set_bit();
+                            let zq = inj.label.z_bits.highest_set_bit();
+                            match (xq, zq) {
+                                (Some(x), None) => Some(x as u16),
+                                (None, Some(z)) => Some(z as u16),
+                                (Some(x), Some(z)) if x == z => Some(x as u16),
+                                _ => None,
+                            }
+                        };
+                        if let Some(q) = single_q {
+                            let has_x_in_noise = inj.label.x_bits.highest_set_bit().is_some();
+                            let has_z_in_noise = inj.label.z_bits.highest_set_bit().is_some();
+                            for term in &mut terms {
+                                let anti = (has_z_in_noise && term.pauli.has_x(q))
+                                    || (has_x_in_noise && term.pauli.has_z(q));
+                                if anti {
+                                    term.coeff_re *= scale;
+                                    term.coeff_im *= scale;
+                                }
+                            }
+                        } else {
+                            let ns = SparsePauli::from_bm(&inj.label);
+                            for term in &mut terms {
+                                if !term.pauli.commutes_with(&ns) {
+                                    term.coeff_re *= scale;
+                                    term.coeff_im *= scale;
+                                }
+                            }
+                        }
+                    }
+                    _ => {}
+                }
+            }
+
+            // Batched S-type: apply combined scale factor
+            let s_scale = gn.q0_scale; // Same for all non-trivial support patterns
+            if (s_scale - 1.0).abs() > 1e-20 {
+                match gn.num_gate_qubits {
+                    1 => {
+                        let q = gn.q0;
+                        for term in &mut terms {
+                            if term.pauli.has_x(q) || term.pauli.has_z(q) {
+                                term.coeff_re *= s_scale;
+                                term.coeff_im *= s_scale;
+                            }
+                        }
+                    }
+                    2 => {
+                        let q0 = gn.q0;
+                        let q1 = gn.q1;
+                        for term in &mut terms {
+                            let on_q0 = term.pauli.has_x(q0) || term.pauli.has_z(q0);
+                            let on_q1 = term.pauli.has_x(q1) || term.pauli.has_z(q1);
+                            if on_q0 || on_q1 {
+                                term.coeff_re *= s_scale;
+                                term.coeff_im *= s_scale;
+                            }
+                        }
+                    }
+                    _ => {}
+                }
+            }
+        }
+
+        // Step 2: Backward Clifford conjugation
+        if !gate_touches_active {
+            continue;
+        }
+
+        match gate.gate_type {
+            GateType::PZ | GateType::QAlloc => {
+                terms.retain(|t| !gate_qs.iter().any(|&qi| t.pauli.has_x(qi)));
+                for t in &mut terms {
+                    for &qi in &gate_qs {
+                        t.pauli.clear_z(qi);
+                    }
+                }
+            }
+            GateType::MZ => {
+                terms.retain(|t| !gate_qs.iter().any(|&qi| t.pauli.has_x(qi)));
+            }
+            _ => {
+                for t in &mut terms {
+                    if let Some(sign_neg) = sparse_conjugate(&mut t.pauli, gate)
+                        && sign_neg
+                    {
+                        t.coeff_re = -t.coeff_re;
+                        t.coeff_im = -t.coeff_im;
+                    }
+                    for &q in t.pauli.x_qubits.iter().chain(t.pauli.z_qubits.iter()) {
+                        let qu = q as usize;
+                        if qu < active_qubits.len() {
+                            active_qubits[qu] = true;
+                        }
+                    }
+                }
+            }
+        }
+
+        // Prune
+        if prune_threshold > 0.0 {
+            let thresh_sq = prune_threshold * prune_threshold;
+            terms.retain(|t| t.coeff_re * t.coeff_re + t.coeff_im * t.coeff_im > thresh_sq);
+        }
+
+        // Merge: sort + dedup. In-place, no allocation, cache-friendly.
+        // For typical term counts (~50-100), this beats both HashMap and
+        // BTreeMap due to zero allocation overhead and sequential access.
+        let should_merge = match gate.gate_type {
+            GateType::PZ | GateType::QAlloc | GateType::MZ => terms.len() > 4,
+            _ => terms.len() > last_merge_count * 2 && terms.len() > 16,
+        };
+        if should_merge {
+            terms.sort_unstable_by(|a, b| a.pauli.cmp(&b.pauli));
+            let mut write = 0;
+            for read in 1..terms.len() {
+                if terms[read].pauli == terms[write].pauli {
+                    terms[write].coeff_re += terms[read].coeff_re;
+                    terms[write].coeff_im += terms[read].coeff_im;
+                } else {
+                    if terms[write].coeff_re.abs() > 1e-30 || terms[write].coeff_im.abs() > 1e-30 {
+                        write += 1;
+                    }
+                    if write < read {
+                        terms.swap(write, read);
+                    }
+                }
+            }
+            let final_len = if !terms.is_empty()
+                && (terms[write].coeff_re.abs() > 1e-30 || terms[write].coeff_im.abs() > 1e-30)
+            {
+                write + 1
+            } else if terms.is_empty() {
+                0
+            } else {
+                write
+            };
+            terms.truncate(final_len);
+            last_merge_count = terms.len().max(1);
+        }
+    }
+
+    // Evaluate
+    let mut expectation_re = 0.0;
+    for term in &terms {
+        let eigenvalue = if term.pauli.is_identity() {
+            1.0
+        } else {
+            let bm = term.pauli.to_bm();
+            match initial_stab.is_stabilizer(&bm) {
+                Some(true) => 1.0,
+                Some(false) => -1.0,
+                None => 0.0,
+            }
+        };
+        expectation_re += term.coeff_re * eigenvalue;
+    }
+    (0.5 * (1.0 - expectation_re)).clamp(0.0, 1.0)
+}
+
+/// Backward Heisenberg with optional gate windowing.
+///
+/// If `gate_window` is `Some((start, end))`, only walks gates in `[start, end)`.
+/// Faster for large circuits but may miss long-range correlations.
+/// Use `None` (or call [`heisenberg_detection_probability`]) for exact results.
+pub fn heisenberg_windowed(
+    gates: &[Gate],
+    detector: &Bm,
+    noise: &dyn NoiseSpec,
+    initial_stab: &StabilizerGroup,
+    prune_threshold: f64,
+    gate_window: Option<(usize, usize)>,
+) -> f64 {
+    // Start with the detector as a single sparse term
+    let mut terms = vec![HeisenbergTerm {
+        pauli: SparsePauli::from_bm(detector),
+        coeff_re: 1.0,
+        coeff_im: 0.0,
+    }];
+
+    // Identify expansion gates (virtual, no physical noise).
+    let expansion_gates = {
+        let mut exp = vec![false; gates.len()];
+        if !gates.is_empty() && gates[0].gate_type == GateType::QAlloc {
+            exp[0] = true;
+        }
+        for i in 1..gates.len() {
+            if gates[i].gate_type == GateType::QAlloc {
+                exp[i] = true;
+            }
+            if gates[i].gate_type == GateType::CX && gates[i - 1].gate_type == GateType::QAlloc {
+                let aq = gates[i - 1].qubits[0].index();
+                if gates[i].qubits.len() >= 2 && gates[i].qubits[1].index() == aq {
+                    exp[i] = true;
+                    if i + 1 < gates.len()
+                        && gates[i + 1].gate_type == GateType::PZ
+                        && gates[i + 1].qubits[0].index() == gates[i].qubits[0].index()
+                    {
+                        exp[i + 1] = true;
+                    }
+                }
+            }
+        }
+        exp
+    };
+
+    let mut last_merge_count = 1usize;
+    // #3: Pre-allocate sin branches buffer, reused across noise sources
+    let mut sin_branches: Vec<HeisenbergTerm> = Vec::new();
+
+    // Conservative active-qubit bitmap: once a qubit is active, stays active.
+    // This avoids the expensive per-term scan for gate relevance.
+    let max_qubit = gates
+        .iter()
+        .flat_map(|g| g.qubits.iter())
+        .map(pecos_core::QubitId::index)
+        .max()
+        .unwrap_or(0)
+        + 1;
+    let mut active_qubits = vec![false; max_qubit];
+    // Seed from detector
+    for &q in terms[0]
+        .pauli
+        .x_qubits
+        .iter()
+        .chain(terms[0].pauli.z_qubits.iter())
+    {
+        if (q as usize) < active_qubits.len() {
+            active_qubits[q as usize] = true;
+        }
+    }
+
+    // Walk backward through the circuit (optionally windowed)
+    let (walk_start, walk_end) = gate_window.unwrap_or((0, gates.len()));
+    for i in (walk_start..walk_end).rev() {
+        let gate = &gates[i];
+        let gate_qs: SmallVec<[u16; 4]> = gate.qubits.iter().map(|q| q.index() as u16).collect();
+
+        // O(1) gate relevance check via bitmap (conservative: may visit some extra gates)
+        let gate_touches_active = gate_qs
+            .iter()
+            .any(|&q| (q as usize) < active_qubits.len() && active_qubits[q as usize]);
+
+        // Step 1: Apply noise adjoint (skip expansion gates).
+        if !expansion_gates[i] && gate_touches_active {
+            let qubits_usize: SmallVec<[usize; 4]> = gate_qs.iter().map(|&q| q as usize).collect();
+            let injections = noise.noise_after_gate(i, gate.gate_type, &qubits_usize);
+
+            for inj in &injections {
+                match inj.eeg_type {
+                    crate::eeg::EegType::H => {
+                        let h = inj.rate;
+                        if h.abs() < 1e-20 {
+                            continue;
+                        }
+
+                        let cos2h = (2.0 * h).cos();
+                        let sin2h = (2.0 * h).sin();
+
+                        let single_z_qubit: Option<u16> = if inj.label.x_bits.is_zero() {
+                            inj.label.z_bits.highest_set_bit().map(|q| q as u16)
+                        } else {
+                            None
+                        };
+                        let noise_sparse = if single_z_qubit.is_none() {
+                            Some(SparsePauli::from_bm(&inj.label))
+                        } else {
+                            None
+                        };
+
+                        // #3: Reuse sin_branches buffer
+                        sin_branches.clear();
+                        let n = terms.len();
+
+                        for term in terms.iter_mut().take(n) {
+                            let anticommutes = if let Some(q) = single_z_qubit {
+                                term.pauli.has_x(q)
+                            } else {
+                                !term.pauli.commutes_with(noise_sparse.as_ref().unwrap())
+                            };
+
+                            if anticommutes {
+                                let (sr, si) = (sin2h * term.coeff_re, sin2h * term.coeff_im);
+
+                                let (dp, total_phase) = if let Some(q) = single_z_qubit {
+                                    let mut dp = term.pauli.clone();
+                                    dp.toggle_z(q);
+                                    let has_x = term.pauli.has_x(q);
+                                    let has_z = term.pauli.has_z(q);
+                                    let phase = if has_x {
+                                        if has_z { 3u8 } else { 1 }
+                                    } else {
+                                        0
+                                    };
+                                    (dp, (phase + 1) % 4)
+                                } else {
+                                    let term_bm = term.pauli.to_bm();
+                                    let (dp_bm, phase_exp) =
+                                        inj.label.multiply_with_phase(&term_bm);
+                                    (SparsePauli::from_bm(&dp_bm), (phase_exp + 1) % 4)
+                                };
+
+                                let (new_re, new_im) = match total_phase {
+                                    0 => (sr, si),
+                                    1 => (-si, sr),
+                                    2 => (-sr, -si),
+                                    3 => (si, -sr),
+                                    _ => unreachable!(),
+                                };
+                                sin_branches.push(HeisenbergTerm {
+                                    pauli: dp,
+                                    coeff_re: new_re,
+                                    coeff_im: new_im,
+                                });
+                                term.coeff_re *= cos2h;
+                                term.coeff_im *= cos2h;
+                            }
+                        }
+
+                        // Update active bitmap BEFORE extending (only scan new branches)
+                        for t in &sin_branches {
+                            for &q in t.pauli.x_qubits.iter().chain(t.pauli.z_qubits.iter()) {
+                                let qu = q as usize;
+                                if qu < active_qubits.len() {
+                                    active_qubits[qu] = true;
+                                }
+                            }
+                        }
+                        terms.append(&mut sin_branches);
+                    }
+                    crate::eeg::EegType::S => {
+                        let s = inj.rate;
+                        if s.abs() < 1e-20 {
+                            continue;
+                        }
+                        let p = -s;
+                        let scale = 1.0 - 2.0 * p;
+                        // For S-type, single-qubit specialization
+                        let single_q: Option<u16> = {
+                            let xq = inj.label.x_bits.highest_set_bit();
+                            let zq = inj.label.z_bits.highest_set_bit();
+                            match (xq, zq) {
+                                (Some(x), None) => Some(x as u16),
+                                (None, Some(z)) => Some(z as u16),
+                                (Some(x), Some(z)) if x == z => Some(x as u16),
+                                _ => None,
+                            }
+                        };
+
+                        if let Some(q) = single_q {
+                            // Single-qubit S noise: check just the one qubit
+                            let has_x_in_noise = inj.label.x_bits.highest_set_bit().is_some();
+                            let has_z_in_noise = inj.label.z_bits.highest_set_bit().is_some();
+                            for term in &mut terms {
+                                // Anticommutes if noise X overlaps term Z or noise Z overlaps term X
+                                let anti = (has_z_in_noise && term.pauli.has_x(q))
+                                    || (has_x_in_noise && term.pauli.has_z(q));
+                                if anti {
+                                    term.coeff_re *= scale;
+                                    term.coeff_im *= scale;
+                                }
+                            }
+                        } else {
+                            let noise_sparse = SparsePauli::from_bm(&inj.label);
+                            for term in &mut terms {
+                                if !term.pauli.commutes_with(&noise_sparse) {
+                                    term.coeff_re *= scale;
+                                    term.coeff_im *= scale;
+                                }
+                            }
+                        }
+                    }
+                    _ => {}
+                }
+
+                if prune_threshold > 0.0 {
+                    terms.retain(|t| {
+                        t.coeff_re * t.coeff_re + t.coeff_im * t.coeff_im
+                            > prune_threshold * prune_threshold
+                    });
+                }
+            }
+        }
+
+        // Step 2: Conjugate backward through the gate.
+        // #2: Skip gates that don't touch active qubits
+        if !gate_touches_active {
+            continue;
+        }
+
+        match gate.gate_type {
+            // #4: Batch PZ/QAlloc — single pass through terms for all qubits
+            GateType::PZ | GateType::QAlloc => {
+                terms.retain(|t| !gate_qs.iter().any(|&qi| t.pauli.has_x(qi)));
+                for t in &mut terms {
+                    for &qi in &gate_qs {
+                        t.pauli.clear_z(qi);
+                    }
+                }
+            }
+            GateType::MZ => {
+                terms.retain(|t| !gate_qs.iter().any(|&qi| t.pauli.has_x(qi)));
+            }
+            _ => {
+                for t in &mut terms {
+                    if let Some(sign_neg) = sparse_conjugate(&mut t.pauli, gate)
+                        && sign_neg
+                    {
+                        t.coeff_re = -t.coeff_re;
+                        t.coeff_im = -t.coeff_im;
+                    }
+                    // Update active bitmap (CX can spread support to new qubits)
+                    for &q in t.pauli.x_qubits.iter().chain(t.pauli.z_qubits.iter()) {
+                        let qu = q as usize;
+                        if qu < active_qubits.len() {
+                            active_qubits[qu] = true;
+                        }
+                    }
+                }
+            }
+        }
+
+        // Merge duplicate Pauli terms by sorting + linear scan.
+        let should_merge = match gate.gate_type {
+            GateType::PZ | GateType::QAlloc | GateType::MZ => terms.len() > 4,
+            _ => terms.len() > last_merge_count * 2 && terms.len() > 16,
+        };
+        if should_merge {
+            terms.sort_unstable_by(|a, b| a.pauli.cmp(&b.pauli));
+            let mut write = 0;
+            for read in 1..terms.len() {
+                if terms[read].pauli == terms[write].pauli {
+                    let re = terms[read].coeff_re;
+                    let im = terms[read].coeff_im;
+                    terms[write].coeff_re += re;
+                    terms[write].coeff_im += im;
+                } else {
+                    if terms[write].coeff_re.abs() > 1e-30 || terms[write].coeff_im.abs() > 1e-30 {
+                        write += 1;
+                    }
+                    if write < read {
+                        terms.swap(write, read);
+                    }
+                }
+            }
+            let final_len =
+                if terms[write].coeff_re.abs() > 1e-30 || terms[write].coeff_im.abs() > 1e-30 {
+                    write + 1
+                } else {
+                    write
+                };
+            terms.truncate(final_len);
+            last_merge_count = terms.len().max(1);
+        }
+    }
+
+    // Evaluate: p_D = (1/2)(1 - Re(Σ c_j ⟨ψ|Q_j|ψ⟩))
+    let mut expectation_re = 0.0;
+
+    for term in &terms {
+        let eigenvalue = if term.pauli.is_identity() {
+            1.0
+        } else {
+            // Convert sparse back to Bm for stabilizer check
+            let bm = term.pauli.to_bm();
+            match initial_stab.is_stabilizer(&bm) {
+                Some(true) => 1.0,
+                Some(false) => -1.0,
+                None => 0.0,
+            }
+        };
+
+        expectation_re += term.coeff_re * eigenvalue;
+    }
+
+    let prob = 0.5 * (1.0 - expectation_re);
+    prob.clamp(0.0, 1.0)
+}
+
+/// Backward Heisenberg with sparse gate traversal via precomputed index.
+///
+/// Instead of iterating all gates, uses a `GateIndex` to visit only gates
+/// on active qubits (qubits in any term's support). Maintains a binary
+/// heap of pending gates and an active qubit set for O(1) relevance checks.
+///
+/// For large circuits (d>=7), this is significantly faster than the linear
+/// scan in [`heisenberg_windowed`] because most gates are irrelevant.
+///
+/// Accepts an optional precomputed noise map. When provided, uses batched
+/// S-type scaling (faster). When `None`, calls `noise.noise_after_gate()`.
+pub fn heisenberg_sparse(
+    gates: &[Gate],
+    detector: &Bm,
+    noise: &dyn NoiseSpec,
+    initial_stab: &StabilizerGroup,
+    prune_threshold: f64,
+    gate_index: &crate::expand::GateIndex,
+    noise_map: Option<&[Option<PrecomputedGateNoise>]>,
+) -> f64 {
+    let mut terms = vec![HeisenbergTerm {
+        pauli: SparsePauli::from_bm(detector),
+        coeff_re: 1.0,
+        coeff_im: 0.0,
+    }];
+
+    // Active qubit set: union of all terms' support.
+    // Use a Vec<bool> for O(1) check (faster than BTreeSet for small qubit counts).
+    let num_qubits = gate_index.expansion_gates.len().min(gates.len()) + 64;
+    let mut active = vec![false; num_qubits.max(1)];
+
+    // Visited gate set: don't add the same gate to the heap twice.
+    let mut visited = vec![false; gates.len()];
+
+    // Populate initial active qubits and heap from detector support.
+    // Max-heap: pops largest gate index first (backward traversal).
+    let mut heap: BinaryHeap<u32> = BinaryHeap::new();
+
+    // Seed from detector — all gates on detector qubits are candidates
+    let total_gates = gates.len() as u32;
+    for &q in &terms[0].pauli.x_qubits {
+        activate_qubit(
+            q,
+            total_gates,
+            &mut active,
+            &mut visited,
+            &mut heap,
+            gate_index,
+        );
+    }
+    for &q in &terms[0].pauli.z_qubits {
+        activate_qubit(
+            q,
+            total_gates,
+            &mut active,
+            &mut visited,
+            &mut heap,
+            gate_index,
+        );
+    }
+
+    let mut last_merge_count = 1usize;
+    let mut sin_branches: Vec<HeisenbergTerm> = Vec::new();
+
+    // Walk backward: pop gates from heap in reverse order (largest index first)
+    while let Some(gate_idx) = heap.pop() {
+        let i = gate_idx as usize;
+        let gate = &gates[i];
+        let gate_qs: SmallVec<[u16; 4]> = gate.qubits.iter().map(|q| q.index() as u16).collect();
+
+        // Step 1: Apply noise adjoint (skip expansion gates).
+        if !gate_index.is_expansion(i) {
+            // Get noise: from precomputed map if available, else dynamic
+            let precomputed = noise_map.and_then(|nm| nm.get(i).and_then(|n| n.as_ref()));
+
+            // Get injections: from noise map or dynamic noise spec
+            let dynamic_injections = if precomputed.is_none() {
+                let qubits_usize: SmallVec<[usize; 4]> =
+                    gate_qs.iter().map(|&q| q as usize).collect();
+                noise.noise_after_gate(i, gate.gate_type, &qubits_usize)
+            } else {
+                Vec::new()
+            };
+            let injections: &[crate::noise::NoiseInjection] = if let Some(gn) = precomputed {
+                &gn.h_injections
+            } else {
+                &dynamic_injections
+            };
+
+            for inj in injections {
+                match inj.eeg_type {
+                    crate::eeg::EegType::H => {
+                        let h = inj.rate;
+                        if h.abs() < 1e-20 {
+                            continue;
+                        }
+
+                        let cos2h = (2.0 * h).cos();
+                        let sin2h = (2.0 * h).sin();
+
+                        let single_z_qubit: Option<u16> = if inj.label.x_bits.is_zero() {
+                            inj.label.z_bits.highest_set_bit().map(|q| q as u16)
+                        } else {
+                            None
+                        };
+                        let noise_sparse = if single_z_qubit.is_none() {
+                            Some(SparsePauli::from_bm(&inj.label))
+                        } else {
+                            None
+                        };
+
+                        sin_branches.clear();
+                        let n = terms.len();
+
+                        for term in terms.iter_mut().take(n) {
+                            let anticommutes = if let Some(q) = single_z_qubit {
+                                term.pauli.has_x(q)
+                            } else {
+                                !term.pauli.commutes_with(noise_sparse.as_ref().unwrap())
+                            };
+
+                            if anticommutes {
+                                let (sr, si) = (sin2h * term.coeff_re, sin2h * term.coeff_im);
+
+                                let (dp, total_phase) = if let Some(q) = single_z_qubit {
+                                    let mut dp = term.pauli.clone();
+                                    dp.toggle_z(q);
+                                    let has_x = term.pauli.has_x(q);
+                                    let has_z = term.pauli.has_z(q);
+                                    let phase = if has_x {
+                                        if has_z { 3u8 } else { 1 }
+                                    } else {
+                                        0
+                                    };
+                                    (dp, (phase + 1) % 4)
+                                } else {
+                                    let term_bm = term.pauli.to_bm();
+                                    let (dp_bm, phase_exp) =
+                                        inj.label.multiply_with_phase(&term_bm);
+                                    (SparsePauli::from_bm(&dp_bm), (phase_exp + 1) % 4)
+                                };
+
+                                let (new_re, new_im) = match total_phase {
+                                    0 => (sr, si),
+                                    1 => (-si, sr),
+                                    2 => (-sr, -si),
+                                    3 => (si, -sr),
+                                    _ => unreachable!(),
+                                };
+
+                                // Check if new term activates new qubits
+                                for &q in &dp.x_qubits {
+                                    activate_qubit(
+                                        q,
+                                        gate_idx,
+                                        &mut active,
+                                        &mut visited,
+                                        &mut heap,
+                                        gate_index,
+                                    );
+                                }
+                                for &q in &dp.z_qubits {
+                                    activate_qubit(
+                                        q,
+                                        gate_idx,
+                                        &mut active,
+                                        &mut visited,
+                                        &mut heap,
+                                        gate_index,
+                                    );
+                                }
+
+                                sin_branches.push(HeisenbergTerm {
+                                    pauli: dp,
+                                    coeff_re: new_re,
+                                    coeff_im: new_im,
+                                });
+                                term.coeff_re *= cos2h;
+                                term.coeff_im *= cos2h;
+                            }
+                        }
+
+                        terms.append(&mut sin_branches);
+                    }
+                    crate::eeg::EegType::S => {
+                        // S-type: process individually. When using noise map,
+                        // the batched scaling below handles the common case,
+                        // but unbatchable S injections are placed in h_injections
+                        // and must be processed here.
+                        let s = inj.rate;
+                        if s.abs() < 1e-20 {
+                            continue;
+                        }
+                        let p = -s;
+                        let scale = 1.0 - 2.0 * p;
+
+                        let single_q: Option<u16> = {
+                            let xq = inj.label.x_bits.highest_set_bit();
+                            let zq = inj.label.z_bits.highest_set_bit();
+                            match (xq, zq) {
+                                (Some(x), None) => Some(x as u16),
+                                (None, Some(z)) => Some(z as u16),
+                                (Some(x), Some(z)) if x == z => Some(x as u16),
+                                _ => None,
+                            }
+                        };
+
+                        if let Some(q) = single_q {
+                            let has_x_in_noise = inj.label.x_bits.highest_set_bit().is_some();
+                            let has_z_in_noise = inj.label.z_bits.highest_set_bit().is_some();
+                            for term in &mut terms {
+                                let anti = (has_z_in_noise && term.pauli.has_x(q))
+                                    || (has_x_in_noise && term.pauli.has_z(q));
+                                if anti {
+                                    term.coeff_re *= scale;
+                                    term.coeff_im *= scale;
+                                }
+                            }
+                        } else {
+                            let noise_sparse = SparsePauli::from_bm(&inj.label);
+                            for term in &mut terms {
+                                if !term.pauli.commutes_with(&noise_sparse) {
+                                    term.coeff_re *= scale;
+                                    term.coeff_im *= scale;
+                                }
+                            }
+                        }
+                    }
+                    _ => {}
+                }
+            }
+
+            // Batched S-type scaling from noise map (much faster than per-injection)
+            if let Some(gn) = precomputed {
+                let s_scale = gn.q0_scale;
+                if (s_scale - 1.0).abs() > 1e-20 {
+                    match gn.num_gate_qubits {
+                        1 => {
+                            let q = gn.q0;
+                            for term in &mut terms {
+                                if term.pauli.has_x(q) || term.pauli.has_z(q) {
+                                    term.coeff_re *= s_scale;
+                                    term.coeff_im *= s_scale;
+                                }
+                            }
+                        }
+                        2 => {
+                            let q0 = gn.q0;
+                            let q1 = gn.q1;
+                            for term in &mut terms {
+                                let on_q0 = term.pauli.has_x(q0) || term.pauli.has_z(q0);
+                                let on_q1 = term.pauli.has_x(q1) || term.pauli.has_z(q1);
+                                if on_q0 || on_q1 {
+                                    term.coeff_re *= s_scale;
+                                    term.coeff_im *= s_scale;
+                                }
+                            }
+                        }
+                        _ => {}
+                    }
+                }
+            }
+        }
+
+        // Step 2: Backward Clifford conjugation.
+        match gate.gate_type {
+            GateType::PZ | GateType::QAlloc => {
+                terms.retain(|t| !gate_qs.iter().any(|&qi| t.pauli.has_x(qi)));
+                for t in &mut terms {
+                    for &qi in &gate_qs {
+                        t.pauli.clear_z(qi);
+                    }
+                }
+            }
+            GateType::MZ => {
+                terms.retain(|t| !gate_qs.iter().any(|&qi| t.pauli.has_x(qi)));
+            }
+            _ => {
+                for t in &mut terms {
+                    if let Some(sign_neg) = sparse_conjugate(&mut t.pauli, gate)
+                        && sign_neg
+                    {
+                        t.coeff_re = -t.coeff_re;
+                        t.coeff_im = -t.coeff_im;
+                    }
+
+                    // Activate any NEW qubits from conjugation (e.g., CX spreads Z)
+                    for &q in t.pauli.x_qubits.iter().chain(t.pauli.z_qubits.iter()) {
+                        activate_qubit(
+                            q,
+                            gate_idx,
+                            &mut active,
+                            &mut visited,
+                            &mut heap,
+                            gate_index,
+                        );
+                    }
+                }
+            }
+        }
+
+        // Prune
+        if prune_threshold > 0.0 {
+            let thresh_sq = prune_threshold * prune_threshold;
+            terms.retain(|t| t.coeff_re * t.coeff_re + t.coeff_im * t.coeff_im > thresh_sq);
+        }
+
+        // Merge duplicate Pauli terms.
+        let should_merge = match gate.gate_type {
+            GateType::PZ | GateType::QAlloc | GateType::MZ => terms.len() > 4,
+            _ => terms.len() > last_merge_count * 2 && terms.len() > 16,
+        };
+        if should_merge {
+            terms.sort_unstable_by(|a, b| a.pauli.cmp(&b.pauli));
+            let mut write = 0;
+            for read in 1..terms.len() {
+                if terms[read].pauli == terms[write].pauli {
+                    let re = terms[read].coeff_re;
+                    let im = terms[read].coeff_im;
+                    terms[write].coeff_re += re;
+                    terms[write].coeff_im += im;
+                } else {
+                    if terms[write].coeff_re.abs() > 1e-30 || terms[write].coeff_im.abs() > 1e-30 {
+                        write += 1;
+                    }
+                    if write < read {
+                        terms.swap(write, read);
+                    }
+                }
+            }
+            let final_len = if !terms.is_empty()
+                && (terms[write].coeff_re.abs() > 1e-30 || terms[write].coeff_im.abs() > 1e-30)
+            {
+                write + 1
+            } else if terms.is_empty() {
+                0
+            } else {
+                write
+            };
+            terms.truncate(final_len);
+            last_merge_count = terms.len().max(1);
+        }
+    }
+
+    // Evaluate
+    let mut expectation_re = 0.0;
+    for term in &terms {
+        let eigenvalue = if term.pauli.is_identity() {
+            1.0
+        } else {
+            let bm = term.pauli.to_bm();
+            match initial_stab.is_stabilizer(&bm) {
+                Some(true) => 1.0,
+                Some(false) => -1.0,
+                None => 0.0,
+            }
+        };
+        expectation_re += term.coeff_re * eigenvalue;
+    }
+
+    let prob = 0.5 * (1.0 - expectation_re);
+    prob.clamp(0.0, 1.0)
+}
+
+/// Convenience: expand an original circuit and compute detection probability.
+pub fn heisenberg_detection_probability_from_circuit(
+    original_gates: &[Gate],
+    detector_meas_indices: &[usize],
+    noise: &dyn NoiseSpec,
+    num_original_qubits: usize,
+    prune_threshold: f64,
+) -> f64 {
+    let expanded = crate::expand::expand_circuit(original_gates);
+
+    let mut detector = Bm::default();
+    for &m in detector_meas_indices {
+        if m < expanded.measurement_qubit.len() {
+            detector.z_bits.set_bit(expanded.measurement_qubit[m]);
+        }
+    }
+
+    let init_gates: Vec<Gate> = (0..num_original_qubits)
+        .map(|q| crate::expand::make_gate(GateType::PZ, &[q]))
+        .collect();
+    let stab = StabilizerGroup::from_circuit(&init_gates, expanded.num_qubits);
+
+    heisenberg_detection_probability(&expanded.gates, &detector, noise, &stab, prune_threshold)
+}
+
+/// Exact detection probability via matrix-based backward Heisenberg.
+///
+/// Computes the backward adjoint using dense 2^n × 2^n complex matrix
+/// multiplication. Exact for any circuit, but limited to ~20 expanded
+/// qubits by memory. Useful as a reference/validation for the faster
+/// Pauli-tracking walk ([`heisenberg_detection_probability_from_circuit`]).
+pub fn heisenberg_exact_from_circuit(
+    original_gates: &[Gate],
+    detector_meas_indices: &[usize],
+    noise: &dyn NoiseSpec,
+    _num_original_qubits: usize,
+) -> f64 {
+    let expanded = crate::expand::expand_circuit(original_gates);
+    let n = expanded.num_qubits;
+
+    assert!(
+        n <= 20,
+        "Matrix Heisenberg requires 2^n memory; {n} qubits is too large. Use the Pauli-tracking walk for approximate results."
+    );
+
+    let dim = 1usize << n;
+
+    // Build detector matrix: diagonal with Z eigenvalues on the detector aux qubits.
+    let mut obs_re = vec![0.0f64; dim * dim];
+    let obs_im = vec![0.0f64; dim * dim];
+    for i in 0..dim {
+        let mut eigenvalue = 1.0f64;
+        for &m in detector_meas_indices {
+            if m < expanded.measurement_qubit.len() {
+                let aux = expanded.measurement_qubit[m];
+                if (i >> aux) & 1 == 1 {
+                    eigenvalue = -eigenvalue;
+                }
+            }
+        }
+        obs_re[i * dim + i] = eigenvalue;
+    }
+
+    // Identify expansion gates
+    let expansion_gates = find_expansion_gates(&expanded.gates);
+
+    // Walk backward, applying adjoints via matrix multiplication.
+    let mut im = obs_im;
+    for idx in (0..expanded.gates.len()).rev() {
+        let g = &expanded.gates[idx];
+        let qs: Vec<usize> = g.qubits.iter().map(pecos_core::QubitId::index).collect();
+
+        // Noise adjoint (skip expansion gates)
+        if !expansion_gates[idx] {
+            let injections = noise.noise_after_gate(idx, g.gate_type, &qs);
+            for inj in &injections {
+                if inj.eeg_type != crate::eeg::EegType::H {
+                    continue;
+                }
+                if inj.rate.abs() < 1e-20 {
+                    continue;
+                }
+                // RZ(θ) on the noise qubit, where θ = 2*rate
+                let theta = 2.0 * inj.rate;
+                // Find which qubit the noise acts on
+                let noise_q = if let Some(q) = inj.label.z_bits.highest_set_bit() {
+                    q
+                } else if let Some(q) = inj.label.x_bits.highest_set_bit() {
+                    q
+                } else {
+                    continue;
+                };
+                matrix_rz_adjoint(&mut obs_re, &mut im, noise_q, theta, n);
+            }
+        }
+
+        // Gate adjoint
+        match g.gate_type {
+            GateType::PZ | GateType::QAlloc => {
+                matrix_pz_adjoint(&mut obs_re, &mut im, qs[0], n);
+            }
+            GateType::MZ => {
+                matrix_mz_adjoint(&mut obs_re, &mut im, qs[0], n);
+            }
+            GateType::H => {
+                matrix_h_adjoint(&mut obs_re, &mut im, qs[0], n);
+            }
+            GateType::CX if qs.len() >= 2 => {
+                matrix_cx_adjoint(&mut obs_re, &mut im, qs[0], qs[1], n);
+            }
+            _ => {}
+        }
+    }
+
+    // ⟨0...0|O_backward|0...0⟩ = obs_re[0]
+    let expectation = obs_re[0];
+    let prob = 0.5 * (1.0 - expectation);
+    prob.clamp(0.0, 1.0)
+}
+
+// --- Matrix helpers for exact Heisenberg ---
+
+fn bit_to_f64(value: usize) -> f64 {
+    f64::from(u8::try_from(value).expect("bit value fits in u8"))
+}
+
+fn matrix_rz_adjoint(re: &mut [f64], im: &mut [f64], q: usize, theta: f64, n: usize) {
+    let dim = 1usize << n;
+    for i in 0..dim {
+        let bi = bit_to_f64((i >> q) & 1);
+        for j in 0..dim {
+            let bj = bit_to_f64((j >> q) & 1);
+            let phase = (bi - bj) * theta;
+            if phase.abs() < 1e-20 {
+                continue;
+            }
+            let (cp, sp) = (phase.cos(), phase.sin());
+            let idx = i * dim + j;
+            let (r, m) = (re[idx], im[idx]);
+            re[idx] = cp * r - sp * m;
+            im[idx] = sp * r + cp * m;
+        }
+    }
+}
+
+fn matrix_pz_adjoint(re: &mut [f64], im: &mut [f64], q: usize, n: usize) {
+    let dim = 1usize << n;
+    let mask = 1usize << q;
+    for i in 0..dim {
+        let iq = (i >> q) & 1;
+        for j in 0..dim {
+            let jq = (j >> q) & 1;
+            let idx = i * dim + j;
+            if iq == jq {
+                let i0 = i & !mask;
+                let j0 = j & !mask;
+                let idx0 = i0 * dim + j0;
+                re[idx] = re[idx0];
+                im[idx] = im[idx0];
+            } else {
+                re[idx] = 0.0;
+                im[idx] = 0.0;
+            }
+        }
+    }
+}
+
+fn matrix_mz_adjoint(re: &mut [f64], im: &mut [f64], q: usize, n: usize) {
+    let dim = 1usize << n;
+    for i in 0..dim {
+        let iq = (i >> q) & 1;
+        for j in 0..dim {
+            let jq = (j >> q) & 1;
+            if iq != jq {
+                let idx = i * dim + j;
+                re[idx] = 0.0;
+                im[idx] = 0.0;
+            }
+        }
+    }
+}
+
+fn matrix_h_adjoint(re: &mut [f64], im: &mut [f64], q: usize, n: usize) {
+    let dim = 1usize << n;
+    let mask = 1usize << q;
+    let mut new_re = vec![0.0f64; dim * dim];
+    let mut new_im = vec![0.0f64; dim * dim];
+    for i in 0..dim {
+        let i0 = i & !mask;
+        let i1 = i | mask;
+        let iq = (i >> q) & 1;
+        for j in 0..dim {
+            let j0 = j & !mask;
+            let j1 = j | mask;
+            let jq = (j >> q) & 1;
+            let mut sr = 0.0;
+            let mut si = 0.0;
+            for a in 0..2usize {
+                for b in 0..2usize {
+                    let ia = if a == 0 { i0 } else { i1 };
+                    let jb = if b == 0 { j0 } else { j1 };
+                    let sign = if (iq * a + b * jq).is_multiple_of(2) {
+                        0.5
+                    } else {
+                        -0.5
+                    };
+                    let idx = ia * dim + jb;
+                    sr += sign * re[idx];
+                    si += sign * im[idx];
+                }
+            }
+            new_re[i * dim + j] = sr;
+            new_im[i * dim + j] = si;
+        }
+    }
+    re.copy_from_slice(&new_re);
+    im.copy_from_slice(&new_im);
+}
+
+fn matrix_cx_adjoint(re: &mut [f64], im: &mut [f64], control: usize, target: usize, n: usize) {
+    let dim = 1usize << n;
+    let cmask = 1usize << control;
+    let tmask = 1usize << target;
+    let cx_perm = |i: usize| -> usize { if (i & cmask) != 0 { i ^ tmask } else { i } };
+    let mut new_re = vec![0.0f64; dim * dim];
+    let mut new_im = vec![0.0f64; dim * dim];
+    for i in 0..dim {
+        let ci = cx_perm(i);
+        for j in 0..dim {
+            let cj = cx_perm(j);
+            new_re[i * dim + j] = re[ci * dim + cj];
+            new_im[i * dim + j] = im[ci * dim + cj];
+        }
+    }
+    re.copy_from_slice(&new_re);
+    im.copy_from_slice(&new_im);
+}
+
+/// Identify expansion gate indices.
+fn find_expansion_gates(gates: &[Gate]) -> Vec<bool> {
+    let mut exp = vec![false; gates.len()];
+    if !gates.is_empty() && gates[0].gate_type == GateType::QAlloc {
+        exp[0] = true;
+    }
+    for i in 1..gates.len() {
+        if gates[i].gate_type == GateType::QAlloc {
+            exp[i] = true;
+        }
+        if gates[i].gate_type == GateType::CX && gates[i - 1].gate_type == GateType::QAlloc {
+            let aq = gates[i - 1].qubits[0].index();
+            if gates[i].qubits.len() >= 2 && gates[i].qubits[1].index() == aq {
+                exp[i] = true;
+                if i + 1 < gates.len()
+                    && gates[i + 1].gate_type == GateType::PZ
+                    && gates[i + 1].qubits[0].index() == gates[i].qubits[0].index()
+                {
+                    exp[i + 1] = true;
+                }
+            }
+        }
+    }
+    exp
+}
+
+#[cfg(test)]
+mod tests {
+    use super::*;
+    use crate::expand;
+    use crate::noise::UniformNoise;
+    use pecos_core::{GateAngles, GateParams, QubitId};
+
+    fn gate(gt: GateType, qubits: &[usize]) -> Gate {
+        Gate {
+            gate_type: gt,
+            qubits: qubits.iter().map(|&q| QubitId(q)).collect(),
+            angles: GateAngles::new(),
+            params: GateParams::new(),
+            meas_ids: pecos_core::GateMeasIds::new(),
+            channel: None,
+        }
+    }
+
+    #[test]
+    fn test_d2_zbasis_heisenberg_original_circuit() {
+        // d=2 Z-basis surface code (2 rounds) — the circuit where forward EEG
+        // has a ~50% gap. Test if Heisenberg closes it.
+        //
+        // Circuit: 7 qubits (0-3 data, 4-6 ancilla)
+        // X-check ancillas: 4, 5 (H, CX, CX, H, MZ)
+        // Z-check ancilla: 6 (CX, CX, MZ)
+        let gates_orig = vec![
+            gate(GateType::PZ, &[0]),
+            gate(GateType::PZ, &[1]),
+            gate(GateType::PZ, &[2]),
+            gate(GateType::PZ, &[3]),
+            gate(GateType::PZ, &[4]),
+            gate(GateType::PZ, &[5]),
+            gate(GateType::PZ, &[6]),
+            // Round 1
+            gate(GateType::H, &[4]),
+            gate(GateType::H, &[5]),
+            gate(GateType::CX, &[1, 6]),
+            gate(GateType::CX, &[5, 3]),
+            gate(GateType::CX, &[3, 6]),
+            gate(GateType::CX, &[5, 2]),
+            gate(GateType::CX, &[4, 1]),
+            gate(GateType::CX, &[0, 6]),
+            gate(GateType::CX, &[4, 0]),
+            gate(GateType::CX, &[2, 6]),
+            gate(GateType::H, &[4]),
+            gate(GateType::H, &[5]),
+            gate(GateType::MZ, &[4]),
+            gate(GateType::MZ, &[5]),
+            gate(GateType::MZ, &[6]),
+            // Reset
+            gate(GateType::PZ, &[4]),
+            gate(GateType::PZ, &[5]),
+            gate(GateType::PZ, &[6]),
+            // Round 2
+            gate(GateType::H, &[4]),
+            gate(GateType::H, &[5]),
+            gate(GateType::CX, &[1, 6]),
+            gate(GateType::CX, &[5, 3]),
+            gate(GateType::CX, &[3, 6]),
+            gate(GateType::CX, &[5, 2]),
+            gate(GateType::CX, &[4, 1]),
+            gate(GateType::CX, &[0, 6]),
+            gate(GateType::CX, &[4, 0]),
+            gate(GateType::CX, &[2, 6]),
+            gate(GateType::H, &[4]),
+            gate(GateType::H, &[5]),
+            gate(GateType::MZ, &[4]),
+            gate(GateType::MZ, &[5]),
+            gate(GateType::MZ, &[6]),
+            // Final data readout
+            gate(GateType::MZ, &[0]),
+            gate(GateType::MZ, &[1]),
+            gate(GateType::MZ, &[2]),
+            gate(GateType::MZ, &[3]),
+        ];
+
+        let expanded = expand::expand_circuit(&gates_orig);
+        let theta = 0.05;
+        let noise = UniformNoise::coherent_only(theta);
+
+        // Initial state stabilizer group: Z on each PZ-initialized qubit.
+        // At circuit start, all original qubits are |0⟩.
+        // (Aux qubits are QAlloc'd later during the circuit.)
+        let init_gates: Vec<Gate> = (0..7).map(|q| gate(GateType::PZ, &[q])).collect();
+        let stab = StabilizerGroup::from_circuit(&init_gates, expanded.num_qubits);
+
+        // D1: ancilla 4 round comparison (Z on aux for meas 0 and meas 3)
+        let aux_m0 = expanded.measurement_qubit[0]; // q4 round 1
+        let aux_m3 = expanded.measurement_qubit[3]; // q4 round 2
+        let mut det1 = Bm::default();
+        det1.z_bits.set_bit(aux_m0);
+        det1.z_bits.set_bit(aux_m3);
+
+        // D2: ancilla 5 round comparison
+        let aux_m1 = expanded.measurement_qubit[1]; // q5 round 1
+        let aux_m4 = expanded.measurement_qubit[4]; // q5 round 2
+        let mut det2 = Bm::default();
+        det2.z_bits.set_bit(aux_m1);
+        det2.z_bits.set_bit(aux_m4);
+
+        // Run Heisenberg for both detectors
+        let p1_heis =
+            heisenberg_detection_probability(&expanded.gates, &det1, &noise, &stab, 1e-10);
+        let p2_heis =
+            heisenberg_detection_probability(&expanded.gates, &det2, &noise, &stab, 1e-10);
+
+        // For comparison: forward EEG
+        let eeg_result = crate::circuit::analyze_with_noise(&expanded.gates, &noise);
+        let dets = vec![
+            crate::dem_mapping::Detector {
+                id: 1,
+                stabilizer: det1,
+            },
+            crate::dem_mapping::Detector {
+                id: 2,
+                stabilizer: det2,
+            },
+        ];
+        let entries = crate::dem_mapping::build_dem_configured(
+            &eeg_result.generators,
+            &dets,
+            &[],
+            Some(&stab),
+            &crate::dem_mapping::EegConfig::default(),
+        );
+        let mut eeg_d1 = 0.0;
+        let mut eeg_d2 = 0.0;
+        for e in &entries {
+            for &d in &e.event.detectors {
+                if d == 1 {
+                    eeg_d1 += e.probability;
+                }
+                if d == 2 {
+                    eeg_d2 += e.probability;
+                }
+            }
+        }
+
+        eprintln!("\nd=2 Z-basis, theta={theta}:");
+        eprintln!("  D1: Heisenberg={p1_heis:.6}, EEG={eeg_d1:.6}");
+        eprintln!("  D2: Heisenberg={p2_heis:.6}, EEG={eeg_d2:.6}");
+
+        // Heisenberg should give DIFFERENT values for D1 and D2
+        // (unlike EEG which gives them equal due to missing time-ordering)
+        if (p1_heis - p2_heis).abs() > 1e-6 {
+            eprintln!("  Heisenberg correctly distinguishes D1 and D2!");
+        }
+    }
+
+    #[test]
+    fn test_single_x_check_heisenberg() {
+        // Simplest X-check: 2 data + 1 ancilla, 2 rounds.
+        // Detector: Z on ancilla (qubit 2) — passes through both MZ(2) gates.
+        // The round-comparison detector fires when the two MZ outcomes differ.
+        let gates_orig = vec![
+            gate(GateType::PZ, &[0]),
+            gate(GateType::PZ, &[1]),
+            gate(GateType::PZ, &[2]),
+            // Round 1
+            gate(GateType::H, &[2]),
+            gate(GateType::CX, &[2, 0]),
+            gate(GateType::CX, &[2, 1]),
+            gate(GateType::H, &[2]),
+            gate(GateType::MZ, &[2]),
+            gate(GateType::PZ, &[2]),
+            // Round 2
+            gate(GateType::H, &[2]),
+            gate(GateType::CX, &[2, 0]),
+            gate(GateType::CX, &[2, 1]),
+            gate(GateType::H, &[2]),
+            gate(GateType::MZ, &[2]),
+        ];
+
+        let theta = 0.05;
+        let noise = UniformNoise::coherent_only(theta);
+
+        // Initial state: Z on each qubit
+        let init_gates: Vec<Gate> = (0..3).map(|q| gate(GateType::PZ, &[q])).collect();
+        let stab = StabilizerGroup::from_circuit(&init_gates, 3);
+
+        // Detector: Z on ancilla qubit 2 (round-comparison)
+        let det = Bm::z(2);
+
+        let p_heis = heisenberg_detection_probability(&gates_orig, &det, &noise, &stab, 0.0);
+
+        eprintln!("\nSimple X-check (original circuit), theta={theta}:");
+        eprintln!("  Heisenberg: {p_heis:.6}");
+    }
+
+    #[test]
+    fn test_bell_parity_exact() {
+        // Bell parity: PZ(0,1), H(0), CX(0,1), H(0), H(1), MZ(0), MZ(1)
+        // Parity detector: Z_0 * Z_1 (on original qubits)
+        // Exact answer: p = sin²(theta)
+        let gates_orig = vec![
+            gate(GateType::PZ, &[0]),
+            gate(GateType::PZ, &[1]),
+            gate(GateType::H, &[0]),
+            gate(GateType::CX, &[0, 1]),
+            gate(GateType::H, &[0]),
+            gate(GateType::H, &[1]),
+            gate(GateType::MZ, &[0]),
+            gate(GateType::MZ, &[1]),
+        ];
+
+        // Parity detector: Z on both measured qubits (original frame)
+        let mut det = Bm::default();
+        det.z_bits.set_bit(0);
+        det.z_bits.set_bit(1);
+
+        // Initial state: Z on each qubit
+        let init_gates: Vec<Gate> = (0..2).map(|q| gate(GateType::PZ, &[q])).collect();
+        let stab = StabilizerGroup::from_circuit(&init_gates, 2);
+
+        for &theta in &[0.01, 0.05, 0.1, 0.2, 0.5] {
+            let noise = UniformNoise::coherent_only(theta);
+
+            let p = heisenberg_detection_probability(&gates_orig, &det, &noise, &stab, 0.0);
+
+            let exact = theta.sin().powi(2);
+            let eeg_taylor = theta * theta; // leading-order EEG
+
+            eprintln!(
+                "theta={theta:.2}: Heisenberg={p:.6}, exact={exact:.6}, Taylor={eeg_taylor:.6}"
+            );
+
+            // Heisenberg should match exact much better than Taylor
+            assert!(
+                (p - exact).abs() < 0.01,
+                "theta={theta}: Heisenberg {p:.6} vs exact {exact:.6}, diff={:.6}",
+                (p - exact).abs()
+            );
+        }
+    }
+
+    #[test]
+    fn test_exact_bell_parity() {
+        // Matrix-based exact Heisenberg should match sin²(θ) perfectly.
+        let gates = vec![
+            gate(GateType::PZ, &[0]),
+            gate(GateType::PZ, &[1]),
+            gate(GateType::H, &[0]),
+            gate(GateType::CX, &[0, 1]),
+            gate(GateType::H, &[0]),
+            gate(GateType::H, &[1]),
+            gate(GateType::MZ, &[0]),
+            gate(GateType::MZ, &[1]),
+        ];
+
+        for &theta in &[0.01, 0.05, 0.1, 0.2, 0.5] {
+            let noise = crate::noise::UniformNoise::coherent_only(theta);
+            let p = heisenberg_exact_from_circuit(&gates, &[0, 1], &noise, 2);
+            let exact = theta.sin().powi(2);
+            assert!(
+                (p - exact).abs() < 1e-10,
+                "theta={theta}: exact_heisenberg {p:.10} vs sin²(θ) {exact:.10}"
+            );
+        }
+    }
+
+    #[test]
+    fn test_exact_2round_xcheck() {
+        // Matrix Heisenberg on the simplest failing case: 2-round, 1 ancilla.
+        // Exact analytical: P = [2 - cos(6θ) - cos(2θ)] / 4.
+        let gates = vec![
+            gate(GateType::PZ, &[0]),
+            gate(GateType::PZ, &[1]),
+            gate(GateType::PZ, &[2]),
+            gate(GateType::H, &[2]),
+            gate(GateType::CX, &[2, 0]),
+            gate(GateType::CX, &[2, 1]),
+            gate(GateType::H, &[2]),
+            gate(GateType::MZ, &[2]),
+            gate(GateType::PZ, &[2]),
+            gate(GateType::H, &[2]),
+            gate(GateType::CX, &[2, 0]),
+            gate(GateType::CX, &[2, 1]),
+            gate(GateType::H, &[2]),
+            gate(GateType::MZ, &[2]),
+        ];
+
+        for &theta in &[0.01, 0.05, 0.1, 0.2] {
+            let noise = crate::noise::UniformNoise::coherent_only(theta);
+            let p = heisenberg_exact_from_circuit(&gates, &[0, 1], &noise, 3);
+            let exact = (2.0 - (6.0 * theta).cos() - (2.0 * theta).cos()) / 4.0;
+            eprintln!("theta={theta:.2}: exact_heisenberg={p:.10}, analytical={exact:.10}");
+            assert!(
+                (p - exact).abs() < 1e-8,
+                "theta={theta}: got {p:.10}, expected {exact:.10}, diff={:.2e}",
+                (p - exact).abs()
+            );
+        }
+    }
+
+    /// Verify heisenberg_sparse produces identical results to heisenberg_windowed,
+    /// and measure the speedup from sparse traversal.
+    #[test]
+    fn test_sparse_matches_windowed_and_timing() {
+        use std::time::Instant;
+
+        // Build a d=2 Z-basis surface code with 2 rounds (same as test above)
+        let gates_orig = vec![
+            gate(GateType::PZ, &[0]),
+            gate(GateType::PZ, &[1]),
+            gate(GateType::PZ, &[2]),
+            gate(GateType::PZ, &[3]),
+            gate(GateType::PZ, &[4]),
+            gate(GateType::PZ, &[5]),
+            gate(GateType::PZ, &[6]),
+            // Round 1
+            gate(GateType::H, &[4]),
+            gate(GateType::H, &[5]),
+            gate(GateType::CX, &[1, 6]),
+            gate(GateType::CX, &[5, 3]),
+            gate(GateType::CX, &[3, 6]),
+            gate(GateType::CX, &[5, 2]),
+            gate(GateType::CX, &[4, 1]),
+            gate(GateType::CX, &[0, 6]),
+            gate(GateType::CX, &[4, 0]),
+            gate(GateType::CX, &[2, 6]),
+            gate(GateType::H, &[4]),
+            gate(GateType::H, &[5]),
+            gate(GateType::MZ, &[4]),
+            gate(GateType::MZ, &[5]),
+            gate(GateType::MZ, &[6]),
+            // Reset + Round 2
+            gate(GateType::PZ, &[4]),
+            gate(GateType::PZ, &[5]),
+            gate(GateType::PZ, &[6]),
+            gate(GateType::H, &[4]),
+            gate(GateType::H, &[5]),
+            gate(GateType::CX, &[1, 6]),
+            gate(GateType::CX, &[5, 3]),
+            gate(GateType::CX, &[3, 6]),
+            gate(GateType::CX, &[5, 2]),
+            gate(GateType::CX, &[4, 1]),
+            gate(GateType::CX, &[0, 6]),
+            gate(GateType::CX, &[4, 0]),
+            gate(GateType::CX, &[2, 6]),
+            gate(GateType::H, &[4]),
+            gate(GateType::H, &[5]),
+            gate(GateType::MZ, &[4]),
+            gate(GateType::MZ, &[5]),
+            gate(GateType::MZ, &[6]),
+        ];
+
+        let expanded = crate::expand::expand_circuit(&gates_orig);
+        let gate_index = crate::expand::GateIndex::build(&expanded.gates, expanded.num_qubits);
+
+        let init_gates: Vec<Gate> = (0..7).map(|q| gate(GateType::PZ, &[q])).collect();
+        let stab =
+            crate::stabilizer::StabilizerGroup::from_circuit(&init_gates, expanded.num_qubits);
+
+        // Test both coherent-only and depolarizing noise
+        let noise_configs: Vec<(&str, crate::noise::UniformNoise)> = vec![
+            (
+                "coherent_only",
+                crate::noise::UniformNoise::coherent_only(0.05),
+            ),
+            (
+                "depolarizing",
+                crate::noise::UniformNoise {
+                    idle_rz: 0.0,
+                    p1: 0.001,
+                    p2: 0.01,
+                    p_meas: 0.001,
+                    p_prep: 0.001,
+                },
+            ),
+            (
+                "combined",
+                crate::noise::UniformNoise {
+                    idle_rz: 0.05,
+                    p1: 0.001,
+                    p2: 0.01,
+                    p_meas: 0.001,
+                    p_prep: 0.001,
+                },
+            ),
+        ];
+
+        for (label, noise) in &noise_configs {
+            let noise_map = build_noise_map(&expanded.gates, noise, &gate_index.expansion_gates);
+
+            // Test all 3 detectors (auxiliary qubits in round 1: meas 0,1,2)
+            for meas_idx in 0..3 {
+                let aux_q = expanded.measurement_qubit[meas_idx];
+                let det = Bm::z(aux_q);
+
+                // Windowed (old path)
+                let start = Instant::now();
+                let p_windowed =
+                    heisenberg_windowed(&expanded.gates, &det, noise, &stab, 1e-12, None);
+                let t_windowed = start.elapsed();
+
+                // Sparse without noise map
+                let start = Instant::now();
+                let p_sparse = heisenberg_sparse(
+                    &expanded.gates,
+                    &det,
+                    noise,
+                    &stab,
+                    1e-12,
+                    &gate_index,
+                    None,
+                );
+                let t_sparse = start.elapsed();
+
+                // Sparse with noise map
+                let start = Instant::now();
+                let p_sparse_nm = heisenberg_sparse(
+                    &expanded.gates,
+                    &det,
+                    noise,
+                    &stab,
+                    1e-12,
+                    &gate_index,
+                    Some(&noise_map),
+                );
+                let t_sparse_nm = start.elapsed();
+
+                // With noise map (old path)
+                let start = Instant::now();
+                let p_nm =
+                    heisenberg_with_noise_map(&expanded.gates, &det, &noise_map, &stab, 1e-12);
+                let t_nm = start.elapsed();
+
+                // Verify exact match
+                let tol = 1e-12;
+                assert!(
+                    (p_windowed - p_sparse).abs() < tol,
+                    "{label} det{meas_idx}: windowed={p_windowed:.15} vs sparse={p_sparse:.15}, diff={:.2e}",
+                    (p_windowed - p_sparse).abs()
+                );
+                assert!(
+                    (p_windowed - p_sparse_nm).abs() < tol,
+                    "{label} det{meas_idx}: windowed={p_windowed:.15} vs sparse+nm={p_sparse_nm:.15}, diff={:.2e}",
+                    (p_windowed - p_sparse_nm).abs()
+                );
+                assert!(
+                    (p_windowed - p_nm).abs() < tol,
+                    "{label} det{meas_idx}: windowed={p_windowed:.15} vs nm={p_nm:.15}, diff={:.2e}",
+                    (p_windowed - p_nm).abs()
+                );
+
+                eprintln!(
+                    "  {label} det{meas_idx}: p={p_windowed:.8} \
+                    windowed={:.1}us sparse={:.1}us sparse+nm={:.1}us nm={:.1}us",
+                    t_windowed.as_secs_f64() * 1e6,
+                    t_sparse.as_secs_f64() * 1e6,
+                    t_sparse_nm.as_secs_f64() * 1e6,
+                    t_nm.as_secs_f64() * 1e6
+                );
+            }
+        }
+    }
+
+    /// Scaling benchmark: sparse vs windowed at d=3..11 repetition codes.
+    ///
+    /// Builds larger circuits and measures per-detector walk time with both
+    /// implementations. Verifies results match exactly.
+    #[test]
+    #[ignore = "benchmark; run manually with --ignored --nocapture"]
+    fn bench_sparse_scaling() {
+        use std::time::Instant;
+
+        let noise = crate::noise::UniformNoise {
+            idle_rz: 0.05,
+            p1: 0.001,
+            p2: 0.01,
+            p_meas: 0.001,
+            p_prep: 0.001,
+        };
+
+        eprintln!("\n=== Sparse vs Windowed scaling (combined noise) ===");
+        eprintln!(
+            "{:>4} {:>6} {:>8} {:>8} {:>6} {:>12} {:>12} {:>8}",
+            "d", "rnds", "gates", "exp_q", "n_det", "windowed_ms", "sparse_ms", "speedup"
+        );
+
+        // Test with increasing circuit sizes.
+        // Repetition codes are 1D — detectors propagate through most gates.
+        // Surface codes are 2D — detectors are local (touch ~8 out of d^2 qubits).
+        // Test both to show where sparsity helps.
+
+        // --- Repetition codes (1D, low sparsity) ---
+        eprintln!("\n--- Repetition codes (1D) ---");
+        let rep_configs: Vec<(usize, usize)> =
+            vec![(5, 3), (5, 10), (9, 3), (9, 10), (13, 3), (13, 10)];
+
+        for &(d, num_rounds) in &rep_configs {
+            let num_data = d;
+            let num_ancilla = d - 1;
+            let num_qubits = num_data + num_ancilla;
+
+            // Build repetition code
+            let mut gates = Vec::new();
+            for q in 0..num_qubits {
+                gates.push(gate(GateType::PZ, &[q]));
+            }
+            for round in 0..num_rounds {
+                for i in 0..num_ancilla {
+                    gates.push(gate(GateType::H, &[num_data + i]));
+                }
+                for i in 0..num_ancilla {
+                    gates.push(gate(GateType::CX, &[num_data + i, i]));
+                }
+                for i in 0..num_ancilla {
+                    gates.push(gate(GateType::CX, &[num_data + i, i + 1]));
+                }
+                for i in 0..num_ancilla {
+                    gates.push(gate(GateType::H, &[num_data + i]));
+                }
+                for i in 0..num_ancilla {
+                    gates.push(gate(GateType::MZ, &[num_data + i]));
+                }
+                if round < num_rounds - 1 {
+                    for i in 0..num_ancilla {
+                        gates.push(gate(GateType::PZ, &[num_data + i]));
+                    }
+                }
+            }
+            for q in 0..num_data {
+                gates.push(gate(GateType::MZ, &[q]));
+            }
+
+            let expanded = crate::expand::expand_circuit(&gates);
+            let gate_index = crate::expand::GateIndex::build(&expanded.gates, expanded.num_qubits);
+            let noise_map = build_noise_map(&expanded.gates, &noise, &gate_index.expansion_gates);
+
+            let init_gates: Vec<Gate> = (0..num_qubits).map(|q| gate(GateType::PZ, &[q])).collect();
+            let stab =
+                crate::stabilizer::StabilizerGroup::from_circuit(&init_gates, expanded.num_qubits);
+
+            // Build detectors: round-to-round comparison
+            let num_detectors = num_ancilla * (num_rounds - 1);
+            let mut detectors = Vec::new();
+            for round in 0..(num_rounds - 1) {
+                for i in 0..num_ancilla {
+                    let m1 = round * num_ancilla + i;
+                    let m2 = (round + 1) * num_ancilla + i;
+                    let aux1 = expanded.measurement_qubit[m1];
+                    let aux2 = expanded.measurement_qubit[m2];
+                    let det_bm = Bm::z(aux1).multiply(&Bm::z(aux2));
+                    detectors.push(det_bm);
+                }
+            }
+
+            // Time windowed (old path)
+            let start = Instant::now();
+            let mut p_windowed = Vec::new();
+            for det in &detectors {
+                p_windowed.push(heisenberg_with_noise_map(
+                    &expanded.gates,
+                    det,
+                    &noise_map,
+                    &stab,
+                    1e-12,
+                ));
+            }
+            let t_windowed = start.elapsed();
+
+            // Time sparse (new path)
+            let start = Instant::now();
+            let mut p_sparse = Vec::new();
+            for det in &detectors {
+                p_sparse.push(heisenberg_sparse(
+                    &expanded.gates,
+                    det,
+                    &noise,
+                    &stab,
+                    1e-12,
+                    &gate_index,
+                    Some(&noise_map),
+                ));
+            }
+            let t_sparse = start.elapsed();
+
+            // Verify exact match
+            for (i, (&pw, &ps)) in p_windowed.iter().zip(p_sparse.iter()).enumerate() {
+                assert!(
+                    (pw - ps).abs() < 1e-12,
+                    "d={d} det{i}: windowed={pw:.15} vs sparse={ps:.15}, diff={:.2e}",
+                    (pw - ps).abs()
+                );
+            }
+
+            let speedup = t_windowed.as_secs_f64() / t_sparse.as_secs_f64();
+            eprintln!(
+                "{d:>4} {num_rounds:>6} {:>8} {:>8} {num_detectors:>6} {:>12.2} {:>12.2} {speedup:>8.1}x",
+                expanded.gates.len(),
+                expanded.num_qubits,
+                t_windowed.as_secs_f64() * 1000.0,
+                t_sparse.as_secs_f64() * 1000.0
+            );
+        }
+
+        // --- 2D grid codes (high sparsity at large d) ---
+        // Each Z-stabilizer checks a plaquette of 4 data qubits using 1 ancilla.
+        // Detectors are local: each touches only 1 ancilla + 4 data qubits.
+        // At d=7: 49 data qubits, 24 Z-stab ancillas, ~500+ expanded gates.
+        // A detector touches ~10 qubits out of ~100+ — high sparsity.
+        eprintln!("\n--- 2D grid codes (surface-code-like) ---");
+        eprintln!(
+            "{:>4} {:>6} {:>8} {:>8} {:>6} {:>12} {:>12} {:>8}",
+            "d", "rnds", "gates", "exp_q", "n_det", "windowed_ms", "sparse_ms", "speedup"
+        );
+
+        for &(d, num_rounds) in &[(3, 2), (5, 2), (7, 2), (9, 2), (7, 5), (9, 5)] {
+            // Build a d x d grid with Z-plaquette stabilizers.
+            // Data qubits: (r, c) for r in 0..d, c in 0..d → index r*d + c
+            // Z-ancillas: one per plaquette, (d-1)*(d-1) total
+            let num_data = d * d;
+            let num_ancilla = (d - 1) * (d - 1);
+            let num_qubits = num_data + num_ancilla;
+            let anc_start = num_data;
+
+            let mut gates = Vec::new();
+            for q in 0..num_qubits {
+                gates.push(gate(GateType::PZ, &[q]));
+            }
+
+            for round in 0..num_rounds {
+                // Z-stabilizer syndrome: CX(data, anc) for each of 4 data qubits
+                // Plaquette (r, c) has corners at data qubits:
+                //   (r, c), (r, c+1), (r+1, c), (r+1, c+1)
+                for r in 0..(d - 1) {
+                    for c in 0..(d - 1) {
+                        let anc = anc_start + r * (d - 1) + c;
+                        let d00 = r * d + c;
+                        let d01 = r * d + c + 1;
+                        let d10 = (r + 1) * d + c;
+                        let d11 = (r + 1) * d + c + 1;
+                        gates.push(gate(GateType::CX, &[d00, anc]));
+                        gates.push(gate(GateType::CX, &[d01, anc]));
+                        gates.push(gate(GateType::CX, &[d10, anc]));
+                        gates.push(gate(GateType::CX, &[d11, anc]));
+                    }
+                }
+                for i in 0..num_ancilla {
+                    gates.push(gate(GateType::MZ, &[anc_start + i]));
+                }
+                if round < num_rounds - 1 {
+                    for i in 0..num_ancilla {
+                        gates.push(gate(GateType::PZ, &[anc_start + i]));
+                    }
+                }
+            }
+            for q in 0..num_data {
+                gates.push(gate(GateType::MZ, &[q]));
+            }
+
+            let expanded = crate::expand::expand_circuit(&gates);
+            let gate_index = crate::expand::GateIndex::build(&expanded.gates, expanded.num_qubits);
+            let noise_map = build_noise_map(&expanded.gates, &noise, &gate_index.expansion_gates);
+
+            let init_gates: Vec<Gate> = (0..num_qubits).map(|q| gate(GateType::PZ, &[q])).collect();
+            let stab =
+                crate::stabilizer::StabilizerGroup::from_circuit(&init_gates, expanded.num_qubits);
+
+            // Build detectors: round-to-round comparison of each ancilla
+            let num_detectors = num_ancilla * (num_rounds - 1);
+            let mut detectors = Vec::new();
+            for round in 0..(num_rounds - 1) {
+                for i in 0..num_ancilla {
+                    let m1 = round * num_ancilla + i;
+                    let m2 = (round + 1) * num_ancilla + i;
+                    let aux1 = expanded.measurement_qubit[m1];
+                    let aux2 = expanded.measurement_qubit[m2];
+                    let det_bm = Bm::z(aux1).multiply(&Bm::z(aux2));
+                    detectors.push(det_bm);
+                }
+            }
+
+            // Time windowed
+            let start = Instant::now();
+            let mut p_windowed = Vec::new();
+            for det in &detectors {
+                p_windowed.push(heisenberg_with_noise_map(
+                    &expanded.gates,
+                    det,
+                    &noise_map,
+                    &stab,
+                    1e-12,
+                ));
+            }
+            let t_windowed = start.elapsed();
+
+            // Time sparse
+            let start = Instant::now();
+            let mut p_sparse = Vec::new();
+            for det in &detectors {
+                p_sparse.push(heisenberg_sparse(
+                    &expanded.gates,
+                    det,
+                    &noise,
+                    &stab,
+                    1e-12,
+                    &gate_index,
+                    Some(&noise_map),
+                ));
+            }
+            let t_sparse = start.elapsed();
+
+            // Verify exact match
+            for (i, (&pw, &ps)) in p_windowed.iter().zip(p_sparse.iter()).enumerate() {
+                assert!(
+                    (pw - ps).abs() < 1e-12,
+                    "grid d={d} det{i}: windowed={pw:.15} vs sparse={ps:.15}, diff={:.2e}",
+                    (pw - ps).abs()
+                );
+            }
+
+            let speedup = t_windowed.as_secs_f64() / t_sparse.as_secs_f64();
+            eprintln!(
+                "{d:>4} {num_rounds:>6} {:>8} {:>8} {num_detectors:>6} {:>12.2} {:>12.2} {speedup:>8.1}x",
+                expanded.gates.len(),
+                expanded.num_qubits,
+                t_windowed.as_secs_f64() * 1000.0,
+                t_sparse.as_secs_f64() * 1000.0
+            );
+        }
+    }
+}
diff --git a/exp/pecos-eeg/src/lib.rs b/exp/pecos-eeg/src/lib.rs
new file mode 100644
index 000000000..61bb7c921
--- /dev/null
+++ b/exp/pecos-eeg/src/lib.rs
@@ -0,0 +1,66 @@
+// Copyright 2026 The PECOS Developers
+//
+// Licensed under the Apache License, Version 2.0 (the "License"); you may not use this file
+// except in compliance with the License. You may obtain a copy of the License at
+//
+//     https://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software distributed under the
+// License is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either
+// express or implied. See the License for the specific language governing permissions and
+// limitations under the License.
+
+// The EEG crate is experimental physics/math code. Its core routines use
+// numerical casts and dense index-based algebra, and the public API is still
+// stabilizing. Keep this list narrow and fix ordinary style lints in code.
+#![allow(
+    clippy::cast_possible_truncation,
+    clippy::cast_possible_wrap,
+    clippy::cast_precision_loss,
+    clippy::cast_sign_loss,
+    clippy::doc_markdown,
+    clippy::missing_errors_doc,
+    clippy::missing_panics_doc
+)]
+
+//! Elementary Error Generator (EEG) analysis for coherent noise.
+//!
+//! Propagates error generators through Clifford circuits and produces
+//! detector error probabilities at polynomial cost. Based on:
+//! - Miller et al. arXiv:2504.15128 (simulation algorithm)
+//! - Hines et al. arXiv:2603.18457 (DEM mapping)
+//!
+//! # Algorithm
+//!
+//! 1. Express noise as sparse EEG generators (H, S, C, A types)
+//! 2. Propagate each generator forward through Clifford gates
+//! 3. Combine via BCH formula (first order = sum)
+//! 4. Classify by DEM event (which detectors each Pauli flips)
+//! 5. Compute detection event probabilities
+
+pub mod builder;
+pub mod circuit;
+pub mod coherent_dem;
+pub mod correlation_table;
+pub mod dem_generator;
+pub mod dem_mapping;
+pub mod dem_simulator;
+pub mod eeg;
+pub mod expand;
+pub mod heisenberg;
+pub mod noise;
+pub mod noise_characterization;
+pub mod noise_compression;
+pub mod propagate;
+pub mod stabilizer;
+pub mod strong_sim;
+
+/// Pauli bitmask type used throughout the EEG crate.
+/// Pauli bitmask type used throughout the EEG crate. Uses SmallVec<[u64; 8]>
+/// for 512 bits inline (zero allocation up to d=9 surface codes), with
+/// automatic heap spillover for larger circuits.
+pub type Bm = pecos_core::PauliBitmaskSmall;
+
+// Re-export key types for convenience
+pub use dem_mapping::{BchOrder, EegConfig, HFormula};
+pub use noise::{NoiseInjection, NoiseSpec, UniformNoise};
diff --git a/exp/pecos-eeg/src/noise.rs b/exp/pecos-eeg/src/noise.rs
new file mode 100644
index 000000000..57df69c18
--- /dev/null
+++ b/exp/pecos-eeg/src/noise.rs
@@ -0,0 +1,220 @@
+// Copyright 2026 The PECOS Developers
+//
+// Licensed under the Apache License, Version 2.0
+
+//! Noise model specification for EEG analysis.
+//!
+//! Defines the [`NoiseSpec`] trait for specifying how noise generators are
+//! injected at each gate in the circuit. The built-in [`UniformNoise`]
+//! applies the same rates to all gates of each type (matching the original
+//! `NoiseModel`). Users can implement custom noise for per-gate control.
+
+use crate::Bm;
+use crate::eeg::EegType;
+use pecos_core::gate_type::GateType;
+
+/// A noise generator to inject at a specific point in the circuit.
+#[derive(Clone, Debug)]
+pub struct NoiseInjection {
+    /// EEG type of the generator.
+    pub eeg_type: EegType,
+    /// Primary Pauli label.
+    pub label: Bm,
+    /// Second label for C/A types.
+    pub label2: Option<Bm>,
+    /// Rate (coefficient).
+    pub rate: f64,
+}
+
+/// Trait for noise models that produce EEG generators at each gate.
+///
+/// Implement this to specify arbitrary per-gate noise. The EEG analysis
+/// calls `noise_after_gate` for each gate in the expanded circuit,
+/// propagates the returned generators to the end, and accumulates them.
+///
+/// The built-in [`UniformNoise`] applies the same rates to all gates of
+/// each type. For per-gate or per-qubit noise, implement this trait
+/// with a custom struct.
+pub trait NoiseSpec: Send + Sync {
+    /// Return noise generators to inject after the gate at `gate_index`.
+    ///
+    /// The `qubits` are the qubit indices of the gate. For 2-qubit gates,
+    /// idle coherent noise is typically injected on both qubits.
+    ///
+    /// Return an empty vec for no noise at this gate.
+    fn noise_after_gate(
+        &self,
+        gate_index: usize,
+        gate_type: GateType,
+        qubits: &[usize],
+    ) -> Vec<NoiseInjection>;
+}
+
+/// Uniform noise model: same rates for all gates of each type.
+///
+/// This is the original `NoiseModel` wrapped as a `NoiseSpec`.
+#[derive(Clone, Debug)]
+pub struct UniformNoise {
+    /// Coherent RZ angle (radians) on both qubits after each 2-qubit gate.
+    pub idle_rz: f64,
+    /// Single-qubit depolarizing probability.
+    pub p1: f64,
+    /// Two-qubit depolarizing probability.
+    pub p2: f64,
+    /// Measurement bit-flip probability.
+    pub p_meas: f64,
+    /// Preparation error probability.
+    pub p_prep: f64,
+}
+
+impl UniformNoise {
+    #[must_use]
+    pub fn coherent_only(idle_rz: f64) -> Self {
+        Self {
+            idle_rz,
+            p1: 0.0,
+            p2: 0.0,
+            p_meas: 0.0,
+            p_prep: 0.0,
+        }
+    }
+
+    #[must_use]
+    pub fn depolarizing(p: f64) -> Self {
+        Self {
+            idle_rz: 0.0,
+            p1: p,
+            p2: p,
+            p_meas: p,
+            p_prep: p,
+        }
+    }
+
+    #[must_use]
+    pub fn with_idle_rz(mut self, angle: f64) -> Self {
+        self.idle_rz = angle;
+        self
+    }
+}
+
+impl NoiseSpec for UniformNoise {
+    fn noise_after_gate(
+        &self,
+        _gate_index: usize,
+        gate_type: GateType,
+        qubits: &[usize],
+    ) -> Vec<NoiseInjection> {
+        let mut injections = Vec::new();
+
+        match gate_type {
+            // Two-qubit gates: idle RZ + depolarizing
+            GateType::CX
+            | GateType::CZ
+            | GateType::CY
+            | GateType::SWAP
+            | GateType::SZZ
+            | GateType::SZZdg
+            | GateType::SXX
+            | GateType::SXXdg
+            | GateType::SYY
+            | GateType::SYYdg => {
+                if self.idle_rz.abs() > 0.0 && qubits.len() >= 2 {
+                    for &q in &qubits[..2] {
+                        injections.push(NoiseInjection {
+                            eeg_type: EegType::H,
+                            label: Bm::z(q),
+                            label2: None,
+                            rate: self.idle_rz / 2.0,
+                        });
+                    }
+                }
+                if self.p2 > 0.0 && qubits.len() >= 2 {
+                    inject_depol_2q(qubits[0], qubits[1], self.p2, &mut injections);
+                }
+            }
+
+            // Single-qubit Clifford: depolarizing
+            GateType::H
+            | GateType::SZ
+            | GateType::SZdg
+            | GateType::SX
+            | GateType::SXdg
+            | GateType::SY
+            | GateType::SYdg
+            | GateType::X
+            | GateType::Y
+            | GateType::Z
+                if self.p1 > 0.0 && !qubits.is_empty() =>
+            {
+                inject_depol_1q(qubits[0], self.p1, &mut injections);
+            }
+
+            // Measurement error
+            GateType::MZ if self.p_meas > 0.0 => {
+                for &q in qubits {
+                    injections.push(NoiseInjection {
+                        eeg_type: EegType::S,
+                        label: Bm::x(q),
+                        label2: None,
+                        rate: -self.p_meas,
+                    });
+                }
+            }
+
+            // Preparation error
+            GateType::PZ if self.p_prep > 0.0 => {
+                for &q in qubits {
+                    injections.push(NoiseInjection {
+                        eeg_type: EegType::S,
+                        label: Bm::x(q),
+                        label2: None,
+                        rate: -self.p_prep,
+                    });
+                }
+            }
+
+            _ => {}
+        }
+
+        injections
+    }
+}
+
+fn inject_depol_1q(q: usize, prob: f64, out: &mut Vec<NoiseInjection>) {
+    let rate = -prob / 3.0;
+    for pf in [Bm::x, Bm::y, Bm::z] {
+        out.push(NoiseInjection {
+            eeg_type: EegType::S,
+            label: pf(q),
+            label2: None,
+            rate,
+        });
+    }
+}
+
+fn inject_depol_2q(qa: usize, qb: usize, prob: f64, out: &mut Vec<NoiseInjection>) {
+    let rate = -prob / 15.0;
+    let pfs = [Bm::x, Bm::y, Bm::z];
+    for &pa in &pfs {
+        out.push(NoiseInjection {
+            eeg_type: EegType::S,
+            label: pa(qa),
+            label2: None,
+            rate,
+        });
+        out.push(NoiseInjection {
+            eeg_type: EegType::S,
+            label: pa(qb),
+            label2: None,
+            rate,
+        });
+        for &pb in &pfs {
+            out.push(NoiseInjection {
+                eeg_type: EegType::S,
+                label: pa(qa).multiply(&pb(qb)),
+                label2: None,
+                rate,
+            });
+        }
+    }
+}
diff --git a/exp/pecos-eeg/src/noise_characterization.rs b/exp/pecos-eeg/src/noise_characterization.rs
new file mode 100644
index 000000000..69dcd529a
--- /dev/null
+++ b/exp/pecos-eeg/src/noise_characterization.rs
@@ -0,0 +1,339 @@
+// Copyright 2026 The PECOS Developers
+//
+// Licensed under the Apache License, Version 2.0 (the "License"); you may not use this file except
+// in compliance with the License. You may obtain a copy of the License at
+//
+//     https://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software distributed under the License
+// is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express
+// or implied. See the License for the specific language governing permissions and limitations under
+// the License.
+
+//! Unified noise characterization: correlations + mechanisms + DEM.
+//!
+//! Outputs use string labels ("D0", "D1", "L0") consistent with Stim format.
+//! Includes detector/observable definitions mapping to MeasIds.
+
+use crate::coherent_dem::build_coherent_dem_exact;
+use crate::correlation_table::{CorrelationTableInput, compute_correlation_table};
+use crate::dem_mapping::{DemEntry, DemEvent, Detector, Observable, format_dem};
+use crate::noise::NoiseSpec;
+use crate::stabilizer::StabilizerGroup;
+use pecos_core::Gate;
+use std::fmt::Write as _;
+
+/// A correlation entry with string labels.
+#[derive(Debug, Clone)]
+pub struct LabeledCorrelation {
+    /// Node labels: "D0", "D1", "L0", etc.
+    pub labels: Vec<String>,
+    /// Joint probability.
+    pub probability: f64,
+}
+
+/// A mechanism in the DEM with string labels.
+#[derive(Debug, Clone)]
+pub struct LabeledMechanism {
+    /// Detectors this mechanism flips: "D0", "D3", etc.
+    pub detectors: Vec<String>,
+    /// Observables this mechanism flips: "L0", etc.
+    pub observables: Vec<String>,
+    /// Fitted probability.
+    pub probability: f64,
+}
+
+/// Definition of a detector or observable in terms of MeasIds.
+#[derive(Debug, Clone)]
+pub struct NodeDefinition {
+    /// Label: "D0", "L0", etc.
+    pub label: String,
+    /// MeasIds that XOR together to produce this node's value.
+    pub meas_ids: Vec<usize>,
+    /// Record offsets (negative, relative to end of measurement record).
+    pub records: Vec<i32>,
+}
+
+/// Complete noise characterization.
+#[derive(Debug, Clone)]
+pub struct NoiseCharacterization {
+    /// Detector and observable definitions (label -> MeasIds).
+    pub definitions: Vec<NodeDefinition>,
+    /// Exact k-body correlations with string labels.
+    pub correlations: Vec<LabeledCorrelation>,
+    /// DEM mechanisms with string labels and fitted probabilities.
+    pub mechanisms: Vec<LabeledMechanism>,
+    /// Decomposable DEM entries with X/Z component info for MWPM decoders.
+    pub decomposable_entries: Vec<crate::dem_mapping::DecomposableDemEntry>,
+    /// Maximum correlation order computed.
+    pub max_order: usize,
+    /// Number of Heisenberg walks performed.
+    pub num_walks: usize,
+}
+
+/// Inputs for building a complete EEG noise characterization.
+#[derive(Clone, Copy)]
+pub struct NoiseCharacterizationInput<'a> {
+    /// Circuit gates.
+    pub gates: &'a [Gate],
+    /// Noise model used for exact Heisenberg correlation targets.
+    pub noise: &'a dyn NoiseSpec,
+    /// Optional alternate noise model used for DEM mechanism structure.
+    pub structure_noise: Option<&'a dyn NoiseSpec>,
+    /// Detector definitions.
+    pub detectors: &'a [Detector],
+    /// Observable definitions.
+    pub observables: &'a [Observable],
+    /// Initial stabilizer group.
+    pub initial_stab: &'a StabilizerGroup,
+    /// Number of circuit qubits.
+    pub num_qubits: usize,
+    /// Maximum correlation order to compute.
+    pub max_order: usize,
+    /// Drop probabilities below this threshold.
+    pub prune_threshold: f64,
+    /// Detector measurement-record definitions.
+    pub detector_meas_ids: &'a [(usize, Vec<usize>, Vec<i32>)],
+    /// Observable measurement-record definitions.
+    pub observable_meas_ids: &'a [(usize, Vec<usize>, Vec<i32>)],
+}
+
+impl NoiseCharacterization {
+    /// Build from circuit + noise model.
+    ///
+    /// `noise` is used for exact Heisenberg correlation targets.
+    /// `structure_noise` (if provided) is used for DEM mechanism extraction —
+    /// useful when passing compressed noise for structure while keeping
+    /// original noise for exact targets. If `None`, uses `noise` for both.
+    #[must_use]
+    pub fn build(input: NoiseCharacterizationInput<'_>) -> Self {
+        let NoiseCharacterizationInput {
+            gates,
+            noise,
+            structure_noise,
+            detectors,
+            observables,
+            initial_stab,
+            num_qubits,
+            max_order,
+            prune_threshold,
+            detector_meas_ids,
+            observable_meas_ids,
+        } = input;
+        let mechanism_noise = structure_noise.unwrap_or(noise);
+
+        // Correlation table (always uses exact noise)
+        let table = compute_correlation_table(CorrelationTableInput {
+            gates,
+            noise,
+            detectors,
+            observables,
+            initial_stab,
+            num_qubits,
+            max_order,
+            prune_threshold,
+        });
+
+        // DEM with fitted probabilities (uses mechanism noise for structure)
+        let num_dets = detectors.len();
+        let mut marginals = vec![0.0_f64; num_dets];
+        for det in detectors {
+            if let Some(&p) = table.rates.get(&vec![det.id])
+                && det.id < num_dets
+            {
+                marginals[det.id] = p;
+            }
+        }
+        let pairwise: Vec<((usize, usize), f64)> = table
+            .rates
+            .iter()
+            .filter(|(k, _)| k.len() == 2)
+            .map(|(k, &v)| ((k[0], k[1]), v))
+            .collect();
+        let gate_index = crate::expand::GateIndex::build(gates, num_qubits);
+        let dem_entries = build_coherent_dem_exact(
+            gates,
+            mechanism_noise,
+            detectors,
+            observables,
+            &gate_index.expansion_gates,
+            &marginals,
+            Some(&pairwise),
+        );
+        let decomposable_entries = crate::coherent_dem::build_coherent_dem_exact_decomposable(
+            gates,
+            mechanism_noise,
+            detectors,
+            observables,
+            &gate_index.expansion_gates,
+            &marginals,
+            Some(&pairwise),
+        );
+
+        // Build definitions
+        let mut definitions = Vec::new();
+        for &(id, ref mids, ref recs) in detector_meas_ids {
+            definitions.push(NodeDefinition {
+                label: format!("D{id}"),
+                meas_ids: mids.clone(),
+                records: recs.clone(),
+            });
+        }
+        for &(id, ref mids, ref recs) in observable_meas_ids {
+            definitions.push(NodeDefinition {
+                label: format!("L{id}"),
+                meas_ids: mids.clone(),
+                records: recs.clone(),
+            });
+        }
+
+        // Build labeled correlations from detector rates
+        let mut correlations = Vec::new();
+        for (key, &prob) in &table.rates {
+            if prob > 1e-15 {
+                let labels: Vec<String> = key.iter().map(|&d| format!("D{d}")).collect();
+                correlations.push(LabeledCorrelation {
+                    labels,
+                    probability: prob,
+                });
+            }
+        }
+        // Add observable correlations
+        for ((det_ids, obs_id), &prob) in &table.observable_rates {
+            if prob > 1e-15 {
+                let mut labels: Vec<String> = det_ids.iter().map(|&d| format!("D{d}")).collect();
+                labels.push(format!("L{obs_id}"));
+                correlations.push(LabeledCorrelation {
+                    labels,
+                    probability: prob,
+                });
+            }
+        }
+
+        // Build labeled mechanisms
+        let mechanisms: Vec<LabeledMechanism> = dem_entries
+            .iter()
+            .filter(|e| e.probability > 1e-15)
+            .map(|e| LabeledMechanism {
+                detectors: e.event.detectors.iter().map(|&d| format!("D{d}")).collect(),
+                observables: e
+                    .event
+                    .observables
+                    .iter()
+                    .map(|&o| format!("L{o}"))
+                    .collect(),
+                probability: e.probability,
+            })
+            .collect();
+
+        NoiseCharacterization {
+            definitions,
+            correlations,
+            mechanisms,
+            decomposable_entries,
+            max_order: table.max_order,
+            num_walks: table.num_walks,
+        }
+    }
+
+    /// Output as Stim DEM string.
+    #[must_use]
+    pub fn to_dem_string(&self) -> String {
+        let entries: Vec<DemEntry> = self
+            .mechanisms
+            .iter()
+            .map(|m| {
+                let dets: Vec<usize> = m
+                    .detectors
+                    .iter()
+                    .map(|s| s[1..].parse().unwrap_or(0))
+                    .collect();
+                let obs: Vec<usize> = m
+                    .observables
+                    .iter()
+                    .map(|s| s[1..].parse().unwrap_or(0))
+                    .collect();
+                DemEntry {
+                    event: DemEvent {
+                        detectors: dets.into_iter().collect(),
+                        observables: obs.into_iter().collect(),
+                    },
+                    probability: m.probability,
+                }
+            })
+            .collect();
+        format_dem(&entries)
+    }
+
+    /// Output as decomposed (graphlike) DEM string for MWPM decoders.
+    ///
+    /// Uses X/Z Pauli-aware decomposition from the backward mechanism
+    /// extraction. Hyperedges are split into X ^ Z components.
+    #[must_use]
+    pub fn to_dem_string_decomposed(&self) -> String {
+        crate::dem_mapping::format_dem_decomposed(&self.decomposable_entries)
+    }
+
+    /// Serialize to JSON.
+    #[must_use]
+    pub fn to_json(&self) -> String {
+        let mut j = String::from("{\n");
+
+        let _ = writeln!(j, "  \"max_order\": {},", self.max_order);
+        let _ = writeln!(j, "  \"num_walks\": {},", self.num_walks);
+
+        // Definitions
+        j.push_str("  \"definitions\": [\n");
+        for (i, def) in self.definitions.iter().enumerate() {
+            let _ = write!(
+                j,
+                "    {{\"label\": \"{}\", \"meas_ids\": {:?}, \"records\": {:?}}}",
+                def.label, def.meas_ids, def.records
+            );
+            if i + 1 < self.definitions.len() {
+                j.push(',');
+            }
+            j.push('\n');
+        }
+        j.push_str("  ],\n");
+
+        // Correlations
+        j.push_str("  \"correlations\": [\n");
+        for (i, c) in self.correlations.iter().enumerate() {
+            let _ = write!(
+                j,
+                "    {{\"nodes\": {:?}, \"probability\": {:.10e}}}",
+                c.labels, c.probability
+            );
+            if i + 1 < self.correlations.len() {
+                j.push(',');
+            }
+            j.push('\n');
+        }
+        j.push_str("  ],\n");
+
+        // Mechanisms
+        j.push_str("  \"mechanisms\": [\n");
+        for (i, m) in self.mechanisms.iter().enumerate() {
+            let mut nodes: Vec<&str> = m
+                .detectors
+                .iter()
+                .map(std::string::String::as_str)
+                .collect();
+            nodes.extend(m.observables.iter().map(std::string::String::as_str));
+            let _ = write!(
+                j,
+                "    {{\"nodes\": {:?}, \"probability\": {:.10e}}}",
+                nodes, m.probability
+            );
+            if i + 1 < self.mechanisms.len() {
+                j.push(',');
+            }
+            j.push('\n');
+        }
+        j.push_str("  ]\n");
+
+        j.push('}');
+        j
+    }
+}
diff --git a/exp/pecos-eeg/src/noise_compression.rs b/exp/pecos-eeg/src/noise_compression.rs
new file mode 100644
index 000000000..a2f09c2e7
--- /dev/null
+++ b/exp/pecos-eeg/src/noise_compression.rs
@@ -0,0 +1,354 @@
+// Copyright 2026 The PECOS Developers
+//
+// Licensed under the Apache License, Version 2.0 (the "License"); you may not use this file except
+// in compliance with the License. You may obtain a copy of the License at
+//
+//     https://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software distributed under the License
+// is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express
+// or implied. See the License for the specific language governing permissions and limitations under
+// the License.
+
+//! Round-boundary noise compression.
+//!
+//! Propagates mid-round fault locations to round boundaries, producing
+//! effective noise sources with accumulated probabilities/amplitudes.
+//!
+//! For stochastic Pauli noise: exact (Paulis compose deterministically).
+//! For coherent noise: accumulates within-round angles exactly.
+//!
+//! This dramatically reduces the number of noise sources:
+//! ~60 mid-round faults per round → ~17 boundary faults (9 data + 8 meas).
+
+use crate::Bm;
+use crate::eeg::EegType;
+use crate::noise::{NoiseInjection, NoiseSpec};
+use pecos_core::Gate;
+use pecos_core::gate_type::GateType;
+use smallvec::SmallVec;
+use std::collections::BTreeMap;
+
+/// An effective noise source at a round boundary.
+#[derive(Debug, Clone)]
+pub struct BoundaryNoise {
+    /// The effective Pauli label at the boundary.
+    pub label: Bm,
+    /// EEG type (H or S).
+    pub eeg_type: EegType,
+    /// Accumulated rate (S-type) or amplitude (H-type).
+    pub value: f64,
+    /// Gate index of the boundary (for position tracking).
+    pub boundary_gate: usize,
+}
+
+/// Result of noise compression.
+pub struct CompressedNoise {
+    /// Effective noise sources at round boundaries.
+    pub boundary_sources: Vec<BoundaryNoise>,
+    /// Measurement noise (kept as-is, not compressed).
+    pub measurement_sources: Vec<(usize, NoiseInjection)>,
+    /// Preparation noise (kept as-is).
+    pub preparation_sources: Vec<(usize, NoiseInjection)>,
+    /// Number of original noise sources before compression.
+    pub original_count: usize,
+    /// Number of compressed sources.
+    pub compressed_count: usize,
+}
+
+/// Compress mid-round noise to round boundaries.
+///
+/// Identifies rounds (PZ/QAlloc → gates → MZ), propagates each
+/// mid-round noise source's Pauli label forward through remaining
+/// gates to the next boundary, and accumulates.
+///
+/// Gate noise (p1, p2) is compressed. Measurement (p_meas) and
+/// preparation (p_prep) noise is kept at its original position.
+pub fn compress_noise_to_boundaries(
+    gates: &[Gate],
+    noise: &dyn NoiseSpec,
+    expansion_gates: &[bool],
+) -> CompressedNoise {
+    let n_gates = gates.len();
+    let max_qubit = gates
+        .iter()
+        .flat_map(|g| g.qubits.iter())
+        .map(pecos_core::QubitId::index)
+        .max()
+        .unwrap_or(0);
+
+    // Step 1: Collect all noise sources
+    let mut all_noise: Vec<(usize, NoiseInjection)> = Vec::new();
+    for (gate_idx, gate) in gates.iter().enumerate() {
+        if gate_idx < expansion_gates.len() && expansion_gates[gate_idx] {
+            continue;
+        }
+        let qubits: SmallVec<[usize; 4]> =
+            gate.qubits.iter().map(pecos_core::QubitId::index).collect();
+        let injections = noise.noise_after_gate(gate_idx, gate.gate_type, &qubits);
+        for inj in injections {
+            all_noise.push((gate_idx, inj));
+        }
+    }
+
+    let original_count = all_noise.len();
+
+    // Step 2: Identify round boundaries.
+    // A boundary is an MZ gate (end of round) or PZ/QAlloc (start of round).
+    // We propagate gate noise forward to the NEXT MZ on the same qubit.
+    let mut measurement_sources = Vec::new();
+    let mut preparation_sources = Vec::new();
+    let mut gate_noise: Vec<(usize, NoiseInjection)> = Vec::new();
+
+    for (gate_idx, inj) in &all_noise {
+        let gate = &gates[*gate_idx];
+        match gate.gate_type {
+            GateType::MZ | GateType::MeasureFree => {
+                measurement_sources.push((*gate_idx, inj.clone()));
+            }
+            GateType::PZ | GateType::QAlloc => {
+                preparation_sources.push((*gate_idx, inj.clone()));
+            }
+            _ => {
+                gate_noise.push((*gate_idx, inj.clone()));
+            }
+        }
+    }
+
+    // Step 3: For each gate noise source, propagate its label forward
+    // through subsequent gates until we hit a round boundary (MZ or PZ).
+    // Group by (boundary_gate, effective_label, eeg_type).
+    let mut boundary_groups: BTreeMap<(usize, Bm, EegType), f64> = BTreeMap::new();
+
+    for (gate_idx, inj) in &gate_noise {
+        let mut label = inj.label.clone();
+
+        // Propagate forward through subsequent gates until we hit a boundary.
+        // The effective noise lives just BEFORE the boundary gate, so we
+        // inject it "after" the last non-boundary gate before it.
+        let mut inject_at = *gate_idx; // default: stay at original position
+        for g in (*gate_idx + 1)..n_gates {
+            match gates[g].gate_type {
+                GateType::MZ | GateType::MeasureFree | GateType::PZ | GateType::QAlloc => {
+                    let noise_qubits: Vec<usize> = label_qubits(&label, max_qubit);
+                    let boundary_qubits: Vec<usize> = gates[g]
+                        .qubits
+                        .iter()
+                        .map(pecos_core::QubitId::index)
+                        .collect();
+                    if noise_qubits.iter().any(|q| boundary_qubits.contains(q)) {
+                        // Inject at the gate just before the boundary
+                        // (inject_at was set to g-1 by the last non-boundary gate)
+                        break;
+                    }
+                }
+                _ => {
+                    // Propagate the label forward through this gate
+                    forward_conjugate_label(&mut label, &gates[g]);
+                    // Only update inject_at for non-expansion gates.
+                    // Expansion gates are invisible to the noise map —
+                    // injecting there would be silently dropped.
+                    if !(g < expansion_gates.len() && expansion_gates[g]) {
+                        inject_at = g;
+                    }
+                }
+            }
+        }
+
+        let key = (inject_at, label.clone(), inj.eeg_type);
+        *boundary_groups.entry(key).or_insert(0.0) += inj.rate;
+    }
+
+    // Step 4: Convert groups to boundary noise sources
+    let boundary_sources: Vec<BoundaryNoise> = boundary_groups
+        .into_iter()
+        .filter(|(_, value)| value.abs() > 1e-20)
+        .map(|((boundary_gate, label, eeg_type), value)| BoundaryNoise {
+            label,
+            eeg_type,
+            value,
+            boundary_gate,
+        })
+        .collect();
+
+    let compressed_count =
+        boundary_sources.len() + measurement_sources.len() + preparation_sources.len();
+
+    CompressedNoise {
+        boundary_sources,
+        measurement_sources,
+        preparation_sources,
+        original_count,
+        compressed_count,
+    }
+}
+
+/// Extract qubits that a Pauli label acts on (up to max_qubit).
+fn label_qubits(label: &Bm, max_qubit: usize) -> Vec<usize> {
+    let mut qubits = Vec::new();
+    for q in 0..=max_qubit {
+        if label.has_x(q) || label.has_z(q) {
+            qubits.push(q);
+        }
+    }
+    qubits
+}
+
+/// Forward-conjugate a Pauli label through a gate (Schrödinger picture).
+///
+/// This is the FORWARD direction: P → U P U†.
+/// For non-self-adjoint gates, we use the forward conjugation directly
+/// (not the adjoint swap used in backward walks).
+fn forward_conjugate_label(label: &mut Bm, gate: &Gate) {
+    use crate::heisenberg::{SparsePauli, sparse_conjugate};
+
+    match gate.gate_type {
+        GateType::PZ
+        | GateType::QAlloc
+        | GateType::QFree
+        | GateType::MZ
+        | GateType::MeasureFree
+        | GateType::MeasureLeaked
+        | GateType::I
+        | GateType::Idle => return,
+        _ => {}
+    }
+
+    // sparse_conjugate uses backward (Heisenberg) convention.
+    // For forward propagation of a Pauli label, we need U P U†.
+    // For self-adjoint gates: same as backward.
+    // For non-self-adjoint: we need to swap the gate to its adjoint
+    // before calling sparse_conjugate (which already swaps for backward).
+    // Two swaps cancel → just call sparse_conjugate on the adjoint gate.
+    //
+    // Simpler: for forward, swap S↔Sdg BEFORE calling sparse_conjugate
+    // (which swaps again for backward), giving net: forward conjugation.
+    //
+    // Actually, sparse_conjugate applies backward convention (swaps non-self-adjoint).
+    // For forward conjugation, we need the opposite swap.
+    // Forward of SZ: SZ P SZdg → same as backward of SZdg.
+    // So forward_conjugate(P, SZ) = sparse_conjugate(P, SZdg).
+    //
+    // For self-adjoint gates: no difference.
+    // For non-self-adjoint: pass the adjoint gate type.
+
+    let adjoint_type = match gate.gate_type {
+        GateType::SZ => GateType::SZdg,
+        GateType::SZdg => GateType::SZ,
+        GateType::SX => GateType::SXdg,
+        GateType::SXdg => GateType::SX,
+        GateType::SY => GateType::SYdg,
+        GateType::SYdg => GateType::SY,
+        GateType::SZZ => GateType::SZZdg,
+        GateType::SZZdg => GateType::SZZ,
+        GateType::SXX => GateType::SXXdg,
+        GateType::SXXdg => GateType::SXX,
+        GateType::SYY => GateType::SYYdg,
+        GateType::SYYdg => GateType::SYY,
+        other => other, // self-adjoint
+    };
+
+    // Build a temporary gate with the adjoint type
+    let adj_gate = Gate {
+        gate_type: adjoint_type,
+        qubits: gate.qubits.clone(),
+        angles: gate.angles.clone(),
+        params: gate.params.clone(),
+        meas_ids: gate.meas_ids.clone(),
+        channel: None,
+    };
+
+    let mut sp = SparsePauli::from_bm(label);
+    let _sign = sparse_conjugate(&mut sp, &adj_gate);
+    *label = sp.to_bm();
+}
+
+/// A `NoiseSpec` adapter that returns compressed boundary noise.
+///
+/// Call `noise_after_gate()` on each gate just like the original noise model,
+/// but mid-round gate noise is empty — all accumulated at boundaries.
+pub struct CompressedNoiseSpec {
+    /// Gate index → noise injections at that gate.
+    gate_noise: BTreeMap<usize, Vec<NoiseInjection>>,
+}
+
+impl CompressedNoiseSpec {
+    /// Build from compressed noise result.
+    #[must_use]
+    pub fn from_compressed(compressed: &CompressedNoise) -> Self {
+        let mut gate_noise: BTreeMap<usize, Vec<NoiseInjection>> = BTreeMap::new();
+
+        // Boundary sources → noise at boundary gate
+        for bn in &compressed.boundary_sources {
+            gate_noise
+                .entry(bn.boundary_gate)
+                .or_default()
+                .push(NoiseInjection {
+                    eeg_type: bn.eeg_type,
+                    label: bn.label.clone(),
+                    label2: None,
+                    rate: bn.value,
+                });
+        }
+
+        // Measurement and prep sources stay at original positions
+        for (gate_idx, inj) in &compressed.measurement_sources {
+            gate_noise.entry(*gate_idx).or_default().push(inj.clone());
+        }
+        for (gate_idx, inj) in &compressed.preparation_sources {
+            gate_noise.entry(*gate_idx).or_default().push(inj.clone());
+        }
+
+        Self { gate_noise }
+    }
+}
+
+impl NoiseSpec for CompressedNoiseSpec {
+    fn noise_after_gate(
+        &self,
+        gate_index: usize,
+        _gate_type: GateType,
+        _qubits: &[usize],
+    ) -> Vec<NoiseInjection> {
+        self.gate_noise
+            .get(&gate_index)
+            .cloned()
+            .unwrap_or_default()
+    }
+}
+
+#[cfg(test)]
+mod tests {
+    use super::*;
+    use crate::noise::UniformNoise;
+
+    #[test]
+    fn test_compression_reduces_count() {
+        // Simple circuit: PZ(0,1), CX(0,1), H(1), CX(0,1), MZ(0,1)
+        let gates = vec![
+            crate::expand::make_gate(GateType::PZ, &[0]),
+            crate::expand::make_gate(GateType::PZ, &[1]),
+            crate::expand::make_gate(GateType::CX, &[0, 1]),
+            crate::expand::make_gate(GateType::H, &[1]),
+            crate::expand::make_gate(GateType::CX, &[0, 1]),
+            crate::expand::make_gate(GateType::MZ, &[0]),
+            crate::expand::make_gate(GateType::MZ, &[1]),
+        ];
+        let noise = UniformNoise {
+            idle_rz: 0.0,
+            p1: 0.001,
+            p2: 0.01,
+            p_meas: 0.01,
+            p_prep: 0.01,
+        };
+        let expansion = vec![false; gates.len()];
+
+        let result = compress_noise_to_boundaries(&gates, &noise, &expansion);
+        assert!(
+            result.compressed_count < result.original_count,
+            "compressed {} should be < original {}",
+            result.compressed_count,
+            result.original_count
+        );
+    }
+}
diff --git a/exp/pecos-eeg/src/propagate.rs b/exp/pecos-eeg/src/propagate.rs
new file mode 100644
index 000000000..23c70ef17
--- /dev/null
+++ b/exp/pecos-eeg/src/propagate.rs
@@ -0,0 +1,11 @@
+// Copyright 2026 The PECOS Developers
+//
+// Licensed under the Apache License, Version 2.0
+
+//! Re-export Clifford conjugation from pecos-core.
+
+pub use pecos_core::pauli::pauli_bitmask::{
+    conjugate_cx, conjugate_cy, conjugate_cz, conjugate_h, conjugate_swap, conjugate_sx,
+    conjugate_sxdg, conjugate_sy, conjugate_sydg, conjugate_sz, conjugate_szdg, conjugate_x,
+    conjugate_y, conjugate_z,
+};
diff --git a/exp/pecos-eeg/src/stabilizer.rs b/exp/pecos-eeg/src/stabilizer.rs
new file mode 100644
index 000000000..e4829fe32
--- /dev/null
+++ b/exp/pecos-eeg/src/stabilizer.rs
@@ -0,0 +1,247 @@
+// Copyright 2026 The PECOS Developers
+//
+// Licensed under the Apache License, Version 2.0
+
+//! Track the stabilizer group of the noiseless output state using SparseStab.
+
+use crate::Bm;
+use pecos_core::gate_type::GateType;
+use pecos_core::pauli::pauli_bitmask::BitmaskStorage;
+use pecos_core::{Gate, QuarterPhase, QubitId};
+use pecos_simulators::{CliffordGateable, SparseStab};
+
+/// The stabilizer group, tracked via SparseStab.
+///
+/// Keeps the full SparseStab (stabilizers + destabilizers) so we can
+/// determine the exact sign (+1 or -1) of stabilizer group elements.
+pub struct StabilizerGroup {
+    sim: SparseStab,
+}
+
+impl StabilizerGroup {
+    /// Run the noiseless circuit on SparseStab.
+    #[must_use]
+    pub fn from_circuit(gates: &[Gate], num_qubits: usize) -> Self {
+        let mut sim = SparseStab::with_seed(num_qubits, 0);
+
+        for gate in gates {
+            let qubits: Vec<QubitId> = gate.qubits.iter().copied().collect();
+            if qubits.is_empty() {
+                continue;
+            }
+
+            match gate.gate_type {
+                GateType::PZ | GateType::QAlloc => {
+                    for &q in &qubits {
+                        sim.pz(&[q]);
+                    }
+                }
+                GateType::H => {
+                    sim.h(&qubits);
+                }
+                GateType::SZ => {
+                    sim.sz(&qubits);
+                }
+                GateType::SZdg => {
+                    sim.szdg(&qubits);
+                }
+                GateType::SX => {
+                    sim.sx(&qubits);
+                }
+                GateType::SXdg => {
+                    sim.sxdg(&qubits);
+                }
+                GateType::SY => {
+                    sim.sy(&qubits);
+                }
+                GateType::SYdg => {
+                    sim.sydg(&qubits);
+                }
+                GateType::X => {
+                    sim.x(&qubits);
+                }
+                GateType::Y => {
+                    sim.y(&qubits);
+                }
+                GateType::Z => {
+                    sim.z(&qubits);
+                }
+                GateType::CX if qubits.len() >= 2 => {
+                    sim.cx(&[(qubits[0], qubits[1])]);
+                }
+                GateType::CY if qubits.len() >= 2 => {
+                    sim.cy(&[(qubits[0], qubits[1])]);
+                }
+                GateType::CZ if qubits.len() >= 2 => {
+                    sim.cz(&[(qubits[0], qubits[1])]);
+                }
+                GateType::SWAP if qubits.len() >= 2 => {
+                    sim.swap(&[(qubits[0], qubits[1])]);
+                }
+                GateType::MZ => {
+                    sim.mz(&qubits);
+                }
+                _ => {}
+            }
+        }
+
+        Self { sim }
+    }
+
+    /// Check if Pauli P is in the stabilizer group and return its sign.
+    ///
+    /// Returns:
+    /// - `Some(true)` if P is a +1 stabilizer
+    /// - `Some(false)` if P is a -1 stabilizer (anti-stabilizer)
+    /// - `None` if P is not in the stabilizer group
+    #[must_use]
+    pub fn is_stabilizer(&self, p: &Bm) -> Option<bool> {
+        if p.is_identity() {
+            return Some(true);
+        }
+
+        let mut x_positions = Vec::new();
+        let mut z_positions = Vec::new();
+        let mut num_ys = 0usize;
+
+        let max_q = match (p.x_bits.highest_set_bit(), p.z_bits.highest_set_bit()) {
+            (None, None) => return Some(true),
+            (Some(a), None) | (None, Some(a)) => a + 1,
+            (Some(a), Some(b)) => a.max(b) + 1,
+        };
+
+        for q in 0..max_q {
+            let has_x = p.has_x(q);
+            let has_z = p.has_z(q);
+            if has_x {
+                x_positions.push(q);
+            }
+            if has_z {
+                z_positions.push(q);
+            }
+            if has_x && has_z {
+                num_ys += 1;
+            }
+        }
+
+        let stabs = self.sim.stabs();
+        let destabs = self.sim.destabs();
+        let phase = stabs.find_pauli_sign(destabs, x_positions, z_positions, num_ys)?;
+
+        match phase {
+            QuarterPhase::PlusOne => Some(true),
+            QuarterPhase::MinusOne => Some(false),
+            _ => None,
+        }
+    }
+}
+
+#[cfg(test)]
+mod tests {
+    use super::*;
+    use pecos_core::{GateAngles, GateParams};
+
+    fn gate(gt: GateType, qubits: &[usize]) -> Gate {
+        Gate {
+            gate_type: gt,
+            qubits: qubits.iter().map(|&q| QubitId(q)).collect(),
+            angles: GateAngles::new(),
+            params: GateParams::new(),
+            meas_ids: pecos_core::GateMeasIds::new(),
+            channel: None,
+        }
+    }
+
+    #[test]
+    fn test_identity_circuit() {
+        let stabs = StabilizerGroup::from_circuit(&[], 1);
+        assert_eq!(stabs.is_stabilizer(&Bm::z(0)), Some(true));
+        assert_eq!(stabs.is_stabilizer(&Bm::x(0)), None);
+    }
+
+    #[test]
+    fn test_h_circuit() {
+        let gates = vec![gate(GateType::H, &[0])];
+        let stabs = StabilizerGroup::from_circuit(&gates, 1);
+        assert_eq!(stabs.is_stabilizer(&Bm::x(0)), Some(true));
+        assert_eq!(stabs.is_stabilizer(&Bm::z(0)), None);
+    }
+
+    #[test]
+    fn test_bell_state() {
+        let gates = vec![gate(GateType::H, &[0]), gate(GateType::CX, &[0, 1])];
+        let stabs = StabilizerGroup::from_circuit(&gates, 2);
+        assert_eq!(
+            stabs.is_stabilizer(&Bm::x(0).multiply(&Bm::x(1))),
+            Some(true)
+        );
+        assert_eq!(
+            stabs.is_stabilizer(&Bm::z(0).multiply(&Bm::z(1))),
+            Some(true)
+        );
+    }
+
+    #[test]
+    fn test_x0x1_after_syndrome_extraction() {
+        let gates = vec![
+            gate(GateType::PZ, &[0]),
+            gate(GateType::PZ, &[1]),
+            gate(GateType::PZ, &[4]),
+            gate(GateType::H, &[4]),
+            gate(GateType::CX, &[4, 1]),
+            gate(GateType::CX, &[4, 0]),
+            gate(GateType::H, &[4]),
+            gate(GateType::MZ, &[4]),
+            gate(GateType::PZ, &[4]),
+        ];
+        let stabs = StabilizerGroup::from_circuit(&gates, 5);
+
+        let x0x1 = Bm::x(0).multiply(&Bm::x(1));
+        assert_eq!(
+            stabs.is_stabilizer(&x0x1),
+            Some(true),
+            "X0*X1 should be stabilizer after syndrome extraction with MZ projection"
+        );
+    }
+
+    #[test]
+    fn test_anti_stabilizer() {
+        // After PZ, Z is +1 stabilizer. -Z should be anti-stabilizer.
+        // But -Z isn't a Pauli label in our system (no phase in Bm).
+        // Instead, apply X to flip the state to |1>, then Z has eigenvalue -1.
+        let gates = vec![gate(GateType::X, &[0])];
+        let stabs = StabilizerGroup::from_circuit(&gates, 1);
+        // Initial state is |0>, X takes it to |1>.
+        // Z|1> = -|1>, so Z is a -1 stabilizer.
+        assert_eq!(
+            stabs.is_stabilizer(&Bm::z(0)),
+            Some(false),
+            "Z should be -1 stabilizer for |1> state"
+        );
+    }
+
+    #[test]
+    fn test_sign_bell_minus() {
+        // |Phi-> = (|00> - |11>)/sqrt(2) = CX H X |00>
+        // X flips to |10>, H gives |−0>, CX gives |Phi->
+        // Stabilizers: -XX, +ZZ
+        let gates = vec![
+            gate(GateType::X, &[0]),
+            gate(GateType::H, &[0]),
+            gate(GateType::CX, &[0, 1]),
+        ];
+        let stabs = StabilizerGroup::from_circuit(&gates, 2);
+        // XX should be -1 stabilizer (the minus Bell state)
+        assert_eq!(
+            stabs.is_stabilizer(&Bm::x(0).multiply(&Bm::x(1))),
+            Some(false),
+            "XX should be -1 stabilizer for |Phi->"
+        );
+        // ZZ should be +1 stabilizer
+        assert_eq!(
+            stabs.is_stabilizer(&Bm::z(0).multiply(&Bm::z(1))),
+            Some(true),
+            "ZZ should be +1 stabilizer for |Phi->"
+        );
+    }
+}
diff --git a/exp/pecos-eeg/src/strong_sim.rs b/exp/pecos-eeg/src/strong_sim.rs
new file mode 100644
index 000000000..13795e3d0
--- /dev/null
+++ b/exp/pecos-eeg/src/strong_sim.rs
@@ -0,0 +1,655 @@
+// Copyright 2026 The PECOS Developers
+//
+// Licensed under the Apache License, Version 2.0
+
+//! Approximate strong simulation using EEG generators.
+//!
+//! Computes approximate outcome probabilities p̃_x for arbitrary bit strings x,
+//! using the first-order Taylor expansion from Miller et al. (Eq. 17):
+//!
+//!   p̃_x = p_x + (1/2^ζ) Σ_G α(ψ,G,x) ε_G + O(ε²)
+//!
+//! where α(ψ,G,x) = 2^ζ Tr(|x⟩⟨x| G[|ψ⟩⟨ψ|]) encodes how each generator
+//! affects the probability of outcome x.
+//!
+//! At first order (l=1), only S-type generators contribute (H-type contributes
+//! at second order). The S-type α is:
+//!   α(x, S_P, ψ) = [x⊕a ∈ support(ψ)] - [x ∈ support(ψ)]
+//! where a is the X-component of P.
+
+use crate::Bm;
+use crate::circuit::PropagatedEeg;
+use crate::eeg::EegType;
+use pecos_core::pauli::pauli_bitmask::BitmaskStorage;
+
+/// Result of approximate strong simulation for a specific outcome.
+#[derive(Clone, Debug)]
+pub struct OutcomeProbability {
+    /// Noiseless probability p_x = |⟨x|ψ⟩|².
+    pub noiseless: f64,
+    /// First-order S-type correction.
+    pub s_correction: f64,
+    /// Second-order H·H correction (via C-type α).
+    pub h_correction: f64,
+    /// Total approximate probability: noiseless + corrections.
+    pub total: f64,
+}
+
+/// Compute the approximate probability of outcome x at first order.
+///
+/// The outcome is a bit string (true = |1⟩, false = |0⟩) for each measured qubit.
+/// The generators should be propagated to the end of the expanded circuit.
+///
+/// At first order, only S-type generators contribute:
+///   α(x, S_P, ψ) = [x⊕a ∈ support] - [x ∈ support]
+/// where a is the X-component of P and "support" is the set of computational
+/// basis states with nonzero amplitude in |ψ⟩.
+///
+/// For a stabilizer state |ψ⟩ on n qubits: x is in the support iff
+/// all stabilizer generators have eigenvalue +1 on |x⟩.
+///
+/// # Arguments
+/// * `generators` - Propagated EEG generators at end of circuit
+/// * `outcome` - Bit string x (one bool per qubit)
+/// * `stabilizers` - Stabilizer generators of |ψ⟩ as Bm
+///
+/// # Limitations
+/// Currently computes first-order (S-type) corrections only. H-type
+/// corrections require second-order computation with phase tracking.
+#[must_use]
+pub fn outcome_probability(
+    generators: &[PropagatedEeg],
+    outcome: &[bool],
+    stabilizers: &[Bm],
+) -> OutcomeProbability {
+    let n = outcome.len();
+
+    // Check if x is in the support of |ψ⟩.
+    // x ∈ support iff ⟨x|S|x⟩ = +1 for all stabilizer generators S.
+    let x_in_support = is_in_support(outcome, stabilizers);
+
+    // Noiseless probability: 1/2^ζ if in support, 0 otherwise.
+    // ζ = n - rank(stabilizer group restricted to Z-diagonal).
+    // For a pure state: ζ = 0 (deterministic), p_x = 0 or 1.
+    // For a projected state: ζ > 0, p_x = 1/2^ζ.
+    let zeta = compute_zeta(n, stabilizers);
+    let noiseless = if x_in_support {
+        1.0 / (1u64 << zeta) as f64
+    } else {
+        0.0
+    };
+
+    // First-order S-type corrections: α(x, S_P, ψ) = [x⊕a ∈ support] - [x ∈ support]
+    let mut s_correction = 0.0;
+    let scale = if zeta > 0 {
+        1.0 / (1u64 << zeta) as f64
+    } else {
+        1.0
+    };
+
+    for g in generators {
+        if g.eeg_type != EegType::S {
+            continue;
+        }
+
+        let x_flipped = flip_outcome(outcome, &g.label);
+        let flipped_in_support = is_in_support(&x_flipped, stabilizers);
+
+        let alpha =
+            (if flipped_in_support { 1.0 } else { 0.0 }) - (if x_in_support { 1.0 } else { 0.0 });
+
+        s_correction += scale * alpha * g.coeff;
+    }
+
+    // Second-order H·H corrections using α(x, C_{P,P'}, ψ).
+    // (1/2) Σ_{P,P'} h_P h_{P'} α(x, C_{P,P'}, ψ)
+    //
+    // For commuting P,P': α(C) = 2 Re(Φ(P,P')) - 2 Re(Φ(PP',I))
+    // For anticommuting P,P': α(C) = 2 Re(Φ(P,P')) (since {P,P'}=0 → Φ(PP',I) cancels)
+    //
+    // Extract stabilizer phases for Φ computation.
+    let stab_phases: Vec<bool> = stabilizers
+        .iter()
+        .map(|_| false) // Default: all +1 stabilizers (sign info not available from Bm)
+        .collect();
+
+    let h_gens: Vec<_> = generators
+        .iter()
+        .filter(|g| g.eeg_type == EegType::H)
+        .collect();
+
+    let mut h_correction = 0.0;
+    for j in 0..h_gens.len() {
+        for k in 0..h_gens.len() {
+            let h_j = h_gens[j].coeff;
+            let h_k = h_gens[k].coeff;
+            let p = &h_gens[j].label;
+            let q = &h_gens[k].label;
+
+            // α(x, C_{P,Q}, ψ) for commuting P,Q:
+            // = 2 Re(Φ(P,Q)) - 2 Re(Φ(PQ,I))
+            let phi_pq = compute_phi(p, q, outcome, stabilizers, &stab_phases);
+            let pq = p.multiply(q);
+            let identity = Bm::default();
+            let phi_pq_i = compute_phi(&pq, &identity, outcome, stabilizers, &stab_phases);
+
+            let alpha = if p.commutes_with(q) {
+                2.0 * phi_pq.0 - 2.0 * phi_pq_i.0
+            } else {
+                // Anticommuting: α(C) = 2 Re(Φ(P,Q))
+                2.0 * phi_pq.0
+            };
+
+            // (1/2) h_j h_k α
+            h_correction += scale * 0.5 * h_j * h_k * alpha;
+        }
+    }
+
+    // First-order C and A type corrections (if any exist directly in generators).
+    let mut ca_correction = 0.0;
+    for g in generators {
+        match g.eeg_type {
+            EegType::C => {
+                if let Some(ref q_label) = g.label2 {
+                    // α(x, C_{P,Q}) = 2 Re(Φ(P,Q)) - Re(Φ(PQ,I) + Φ(QP,I))
+                    let phi_pq = compute_phi(&g.label, q_label, outcome, stabilizers, &stab_phases);
+                    let pq = g.label.multiply(q_label);
+                    let qp = q_label.multiply(&g.label);
+                    let phi_pq_i =
+                        compute_phi(&pq, &Bm::default(), outcome, stabilizers, &stab_phases);
+                    let phi_qp_i =
+                        compute_phi(&qp, &Bm::default(), outcome, stabilizers, &stab_phases);
+                    let alpha = 2.0 * phi_pq.0 - (phi_pq_i.0 + phi_qp_i.0);
+                    ca_correction += scale * g.coeff * alpha;
+                }
+            }
+            EegType::A => {
+                if let Some(ref q_label) = g.label2 {
+                    // α(x, A_{P,Q}) = 2 Im(Φ(Q,P)) + Im(Φ(QP,I) - Φ(PQ,I))
+                    let phi_qp = compute_phi(q_label, &g.label, outcome, stabilizers, &stab_phases);
+                    let qp = q_label.multiply(&g.label);
+                    let pq = g.label.multiply(q_label);
+                    let phi_qp_i =
+                        compute_phi(&qp, &Bm::default(), outcome, stabilizers, &stab_phases);
+                    let phi_pq_i =
+                        compute_phi(&pq, &Bm::default(), outcome, stabilizers, &stab_phases);
+                    let alpha = 2.0 * phi_qp.1 + (phi_qp_i.1 - phi_pq_i.1);
+                    ca_correction += scale * g.coeff * alpha;
+                }
+            }
+            _ => {}
+        }
+    }
+
+    let total = (noiseless + s_correction + h_correction + ca_correction).clamp(0.0, 1.0);
+
+    OutcomeProbability {
+        noiseless,
+        s_correction,
+        h_correction,
+        total,
+    }
+}
+
+/// Compute Φ_{ψ,x}(P,Q) = 2^ζ ⟨x|P|ψ⟩⟨ψ|Q|x⟩ for stabilizer states.
+///
+/// Returns a complex number as (real, imag). Result is in {0, ±1, ±i}.
+///
+/// Uses: Φ(P,Q) = phase(P·S_0·Q) · (-1)^{z_{PS_0Q}·x} when conditions met.
+/// S_0 is any stabilizer with x_part = x_P ⊕ x_Q.
+fn compute_phi(
+    p: &Bm,
+    q: &Bm,
+    outcome: &[bool],
+    stabilizers: &[Bm],
+    stabilizer_phases: &[bool], // true = -1 sign (minus stabilizer)
+) -> (f64, f64) {
+    // ⟨x|P|ψ⟩ is nonzero iff x⊕a_P is in the support of |ψ⟩.
+    // ⟨ψ|Q|x⟩ is nonzero iff x⊕a_Q is in the support.
+    // Both must hold for Φ to be nonzero.
+    let x_flip_p = flip_outcome(outcome, p);
+    if !is_in_support(&x_flip_p, stabilizers) {
+        return (0.0, 0.0);
+    }
+    let x_flip_q = flip_outcome(outcome, q);
+    if !is_in_support(&x_flip_q, stabilizers) {
+        return (0.0, 0.0);
+    }
+
+    // Target X-pattern for S_0: x_P ⊕ x_Q
+    let target_x = p.multiply(q); // product has x_bits = p.x XOR q.x (and z, but we only use x)
+
+    // Find a subset of generators whose X-parts XOR to target_x.x_bits
+    let n = stabilizers.len();
+
+    // Work with full Bm for GF2 ops (only X-part matters)
+    let mut row_x: Vec<Bm> = stabilizers
+        .iter()
+        .map(|s| Bm {
+            x_bits: s.x_bits.clone(),
+            z_bits: smallvec::SmallVec::default(),
+        })
+        .collect();
+
+    let mut selected = vec![false; n];
+    let mut target = Bm {
+        x_bits: target_x.x_bits.clone(),
+        z_bits: smallvec::SmallVec::default(),
+    };
+
+    // GF(2) greedy elimination
+    for bit in 0..outcome.len() {
+        if !target.x_bits.get_bit(bit) {
+            continue;
+        }
+        let found = row_x
+            .iter()
+            .enumerate()
+            .find(|(_, r)| r.x_bits.get_bit(bit));
+        if let Some((row_idx, _)) = found {
+            // Find the original stabilizer index for this row
+            // (rows may have been XOR-modified but indices track the original)
+            selected[row_idx] = true;
+            let pivot = row_x[row_idx].clone();
+            target = target.multiply(&pivot);
+            for (r, row) in row_x.iter_mut().enumerate().take(n) {
+                if r != row_idx && row.x_bits.get_bit(bit) {
+                    let p_clone = pivot.clone();
+                    *row = row.multiply(&p_clone);
+                }
+            }
+        } else {
+            return (0.0, 0.0);
+        }
+    }
+
+    if !target.is_identity() {
+        return (0.0, 0.0);
+    }
+
+    // Build S_0 = product of selected generators
+    let mut s0 = Bm::default();
+    let mut s0_phase: u8 = 0; // i^{s0_phase}
+    let mut s0_sign_minus = false;
+
+    for i in 0..n {
+        if selected[i] {
+            let (prod, phase) = s0.multiply_with_phase(&stabilizers[i]);
+            s0 = prod;
+            s0_phase = (s0_phase + phase) % 4;
+            if stabilizer_phases[i] {
+                s0_sign_minus = !s0_sign_minus;
+            }
+        }
+    }
+
+    // S_0 has sign (-1)^{s0_sign_minus} · i^{s0_phase}
+    // Compute PSQ = P · S_0 · Q
+    let (ps, phase_ps) = p.multiply_with_phase(&s0);
+    let (psq, phase_psq_part) = ps.multiply_with_phase(q);
+    let total_phase = (phase_ps + phase_psq_part + s0_phase) % 4;
+
+    // PSQ should be diagonal (x_part = 0)
+    if !psq.x_bits.is_zero() {
+        return (0.0, 0.0); // Shouldn't happen if solution found correctly
+    }
+
+    // Compute (-1)^{z_{PSQ} · x}
+    let mut dot = 0u32;
+    for (i, &bit) in outcome.iter().enumerate() {
+        if bit && psq.z_bits.get_bit(i) {
+            dot += 1;
+        }
+    }
+    let z_sign: f64 = if dot.is_multiple_of(2) { 1.0 } else { -1.0 };
+
+    // Total sign from S_0 being a (-1)^{sign} stabilizer
+    let stab_sign: f64 = if s0_sign_minus { -1.0 } else { 1.0 };
+
+    // Φ = i^{total_phase} · stab_sign · z_sign
+    let (re, im) = match total_phase {
+        0 => (1.0, 0.0),
+        1 => (0.0, 1.0),
+        2 => (-1.0, 0.0),
+        3 => (0.0, -1.0),
+        _ => unreachable!(),
+    };
+
+    (re * stab_sign * z_sign, im * stab_sign * z_sign)
+}
+
+/// Check if outcome x is in the support of the stabilizer state.
+///
+/// x ∈ support iff for every stabilizer generator S, ⟨x|S|x⟩ = +1.
+/// For S = phase · X^a Z^b: ⟨x|S|x⟩ = phase · δ_{a,0} · (-1)^{b·x}
+/// (since X flips bits, ⟨x|X^a|x⟩ = 0 unless a=0).
+///
+/// Wait: that's only for diagonal stabilizers. For non-diagonal (X or Y
+/// components), ⟨x|S|x⟩ = 0 ≠ +1, so x is not in the support if any
+/// stabilizer has X component. But stabilizer states CAN have X-type
+/// stabilizers and still have x in the support.
+///
+/// The correct check: x is in the support iff for all Z-type stabilizers
+/// (those with no X component), the Z eigenvalue matches.
+fn is_in_support(outcome: &[bool], stabilizers: &[Bm]) -> bool {
+    for stab in stabilizers {
+        // Only Z-type stabilizers constrain the support
+        if !stab.x_bits.is_zero() {
+            continue; // Has X component — doesn't constrain Z-basis support
+        }
+
+        // Z-type stabilizer: eigenvalue = (-1)^{popcount(z_bits & x)}
+        let mut parity = 0u32;
+        for (i, &bit) in outcome.iter().enumerate() {
+            if bit && stab.z_bits.get_bit(i) {
+                parity += 1;
+            }
+        }
+        // Stabilizer eigenvalue should be +1 on support states
+        if !parity.is_multiple_of(2) {
+            return false; // eigenvalue = -1, not in support
+        }
+    }
+    true
+}
+
+/// Flip outcome bits according to the X-component of a Pauli.
+fn flip_outcome(outcome: &[bool], pauli: &Bm) -> Vec<bool> {
+    outcome
+        .iter()
+        .enumerate()
+        .map(|(i, &bit)| if pauli.has_x(i) { !bit } else { bit })
+        .collect()
+}
+
+/// Compute ζ = number of qubits whose Z-basis outcome is non-deterministic.
+///
+/// ζ = n - (number of independent Z-type stabilizer generators).
+fn compute_zeta(n: usize, stabilizers: &[Bm]) -> usize {
+    // Count independent Z-type stabilizers (no X component).
+    // Extract Z-parts as Bm (store z in x_bits for GF2 rank).
+    let z_stabs: Vec<Bm> = stabilizers
+        .iter()
+        .filter(|s| s.x_bits.is_zero())
+        .map(|s| Bm {
+            x_bits: s.z_bits.clone(),
+            z_bits: smallvec::SmallVec::default(),
+        })
+        .collect();
+
+    let rank = gf2_rank_bitmask(&z_stabs, n);
+    n.saturating_sub(rank)
+}
+
+/// GF(2) rank of binary vectors stored as Bm x_bits.
+fn gf2_rank_bitmask(vectors: &[Bm], max_bits: usize) -> usize {
+    let mut rows: Vec<Bm> = vectors.to_vec();
+    let mut rank = 0;
+
+    for bit in 0..max_bits {
+        if rank >= rows.len() {
+            break;
+        }
+        if rows[rank..]
+            .iter()
+            .all(pecos_core::PauliBitmaskGeneric::is_identity)
+        {
+            break;
+        }
+        if let Some(pivot) = rows[rank..].iter().position(|r| r.x_bits.get_bit(bit)) {
+            rows.swap(rank, rank + pivot);
+            let pivot_val = rows[rank].clone();
+            for (r, row) in rows.iter_mut().enumerate() {
+                if r != rank && row.x_bits.get_bit(bit) {
+                    *row = row.multiply(&pivot_val);
+                }
+            }
+            rank += 1;
+        }
+    }
+
+    rank
+}
+
+#[cfg(test)]
+mod tests {
+    use super::*;
+
+    fn xx() -> Bm {
+        Bm::x(0).multiply(&Bm::x(1))
+    }
+    fn zz() -> Bm {
+        Bm::z(0).multiply(&Bm::z(1))
+    }
+
+    #[test]
+    fn test_single_qubit_z_basis() {
+        // |0⟩ state: stabilizer = +Z. Outcome 0 is deterministic.
+        let stabs = vec![Bm::z(0)];
+        let outcome_0 = vec![false]; // |0⟩
+        let outcome_1 = vec![true]; // |1⟩
+
+        assert!(is_in_support(&outcome_0, &stabs));
+        assert!(!is_in_support(&outcome_1, &stabs));
+
+        // With S_X noise: flips |0⟩ to |1⟩
+        let gens = vec![PropagatedEeg {
+            eeg_type: EegType::S,
+            label: Bm::x(0),
+            label2: None,
+            coeff: -0.01,
+            source: None,
+        }];
+
+        let p0 = outcome_probability(&gens, &outcome_0, &stabs);
+        let p1 = outcome_probability(&gens, &outcome_1, &stabs);
+
+        // p(0) ≈ 1 - 0.01 = 0.99 (S_X moves probability from 0 to 1)
+        // p(1) ≈ 0 + 0.01 = 0.01
+        assert!((p0.noiseless - 1.0).abs() < 1e-10);
+        assert!((p0.s_correction - 0.01).abs() < 1e-10);
+        assert!((p0.h_correction).abs() < 1e-10); // no H generators
+        assert!((p0.total - 0.99).abs() < 0.02);
+
+        assert!((p1.noiseless - 0.0).abs() < 1e-10);
+        assert!((p1.s_correction + 0.01).abs() < 1e-10);
+    }
+
+    #[test]
+    fn test_h_type_diagonal_correction() {
+        // |+⟩ state: stabilizer = +X. Z-basis outcomes 0,1 each with prob 1/2.
+        // With H_Z noise (coherent Z rotation): shifts probability from 0 to 1.
+        let stabs = vec![Bm::x(0)]; // |+⟩
+        let outcome_0 = vec![false];
+        let outcome_1 = vec![true];
+
+        let gens = vec![PropagatedEeg {
+            eeg_type: EegType::H,
+            label: Bm::z(0), // H_Z: Z rotation
+            label2: None,
+            coeff: 0.1,
+            source: None,
+        }];
+
+        let p0 = outcome_probability(&gens, &outcome_0, &stabs);
+        let p1 = outcome_probability(&gens, &outcome_1, &stabs);
+
+        // |+⟩ support: {0, 1} with ζ=1. Both outcomes in support.
+        assert!((p0.noiseless - 0.5).abs() < 1e-10);
+        assert!((p1.noiseless - 0.5).abs() < 1e-10);
+
+        // H_Z diagonal α: Z flips no bits (a_Z = 0), so x⊕a = x.
+        // α(S_Z) = [x ∈ supp] - [x ∈ supp] = 0 for Z-type Paulis.
+        // So the H·H diagonal correction via S_P analogy should be 0
+        // (Z has no X component, doesn't flip outcome bits).
+        assert!((p0.h_correction).abs() < 1e-10);
+
+        // H_X noise would flip bits:
+        let gens_x = vec![PropagatedEeg {
+            eeg_type: EegType::H,
+            label: Bm::x(0), // H_X
+            label2: None,
+            coeff: 0.1,
+            source: None,
+        }];
+        let p0x = outcome_probability(&gens_x, &outcome_0, &stabs);
+        // X flips bit: α = [1∈supp] - [0∈supp] = 1-1 = 0 (both in support)
+        // So h_correction = 0 for |+⟩ with H_X too (both outcomes in support)
+        assert!((p0x.h_correction).abs() < 1e-10);
+    }
+
+    #[test]
+    fn test_h_type_shifts_probability() {
+        // |0⟩ state with H_X noise: X flips from |0⟩ to |1⟩
+        let stabs = vec![Bm::z(0)]; // |0⟩
+        let outcome_0 = vec![false];
+        let outcome_1 = vec![true];
+
+        let gens = vec![PropagatedEeg {
+            eeg_type: EegType::H,
+            label: Bm::x(0), // H_X
+            label2: None,
+            coeff: 0.1, // small angle
+            source: None,
+        }];
+
+        let p0 = outcome_probability(&gens, &outcome_0, &stabs);
+        let p1 = outcome_probability(&gens, &outcome_1, &stabs);
+
+        // |0⟩: only outcome 0 is in support.
+        // α(S_X) for outcome 0: [1∈supp] - [0∈supp] = 0-1 = -1
+        // Diagonal H·H: h² · α = 0.01 · (-1) = -0.01
+        assert!((p0.h_correction + 0.01).abs() < 1e-10);
+        assert!((p0.total - 0.99).abs() < 0.02);
+
+        // α(S_X) for outcome 1: [0∈supp] - [1∈supp] = 1-0 = +1
+        // h² · α = 0.01 · 1 = +0.01
+        assert!((p1.h_correction - 0.01).abs() < 1e-10);
+        assert!((p1.total - 0.01).abs() < 0.02);
+    }
+
+    #[test]
+    fn test_bell_state_support() {
+        // |Φ+⟩ = (|00⟩+|11⟩)/√2. Stabilizers: +XX, +ZZ
+        let stabs = vec![xx(), zz()];
+
+        // Support: {00, 11} (Z-type stabilizer ZZ constrains parity)
+        assert!(is_in_support(&[false, false], &stabs)); // 00: ZZ eigenvalue = (-1)^0 = +1
+        assert!(is_in_support(&[true, true], &stabs)); // 11: ZZ eigenvalue = (-1)^2 = +1
+        assert!(!is_in_support(&[false, true], &stabs)); // 01: ZZ eigenvalue = (-1)^1 = -1
+        assert!(!is_in_support(&[true, false], &stabs)); // 10: ZZ eigenvalue = (-1)^1 = -1
+    }
+
+    #[test]
+    fn test_zeta_computation() {
+        // Single qubit |0⟩: 1 Z-type stabilizer, ζ = 1-1 = 0 (deterministic)
+        assert_eq!(compute_zeta(1, &[Bm::z(0)]), 0);
+
+        // Bell state: 1 Z-type stabilizer (ZZ), ζ = 2-1 = 1
+        let bell_stabs = vec![xx(), zz()];
+        assert_eq!(compute_zeta(2, &bell_stabs), 1);
+
+        // |+⟩: 0 Z-type stabilizers, ζ = 1-0 = 1
+        assert_eq!(compute_zeta(1, &[Bm::x(0)]), 1);
+    }
+
+    #[test]
+    fn test_phi_single_qubit() {
+        // |0⟩: stabilizer +Z
+        let stabs = vec![Bm::z(0)];
+        let phases = vec![false]; // +1 stabilizer
+
+        // Φ(I,I) for outcome 0 (in support): should be 1
+        let phi = compute_phi(&Bm::default(), &Bm::default(), &[false], &stabs, &phases);
+        assert!((phi.0 - 1.0).abs() < 1e-10);
+        assert!(phi.1.abs() < 1e-10);
+
+        // Φ(I,I) for outcome 1 (not in support): should be 0
+        let phi = compute_phi(&Bm::default(), &Bm::default(), &[true], &stabs, &phases);
+        assert!(phi.0.abs() < 1e-10);
+
+        // Φ(X,X) for outcome 0: ⟨0|X|0⟩² = 0 (X flips to |1⟩ which is not in support...
+        // wait, x⊕a_X = 1, is |1⟩ in support? No. So Φ = 0.
+        let phi = compute_phi(&Bm::x(0), &Bm::x(0), &[false], &stabs, &phases);
+        assert!(phi.0.abs() < 1e-10);
+
+        // Φ(X,X) for outcome 1: ⟨1|X|0⟩·⟨0|X|1⟩ = ⟨1|1⟩·⟨0|0⟩ = 1
+        // x⊕a_X = 0, which IS in support. So Φ should be 1.
+        let phi = compute_phi(&Bm::x(0), &Bm::x(0), &[true], &stabs, &phases);
+        assert!(
+            (phi.0 - 1.0).abs() < 1e-10,
+            "Phi(X,X) at |1> for |0> state: got {phi:?}"
+        );
+
+        // Φ(Z,I) for outcome 0: ⟨0|Z|0⟩·⟨0|0⟩ = 1·1 = 1
+        let phi = compute_phi(&Bm::z(0), &Bm::default(), &[false], &stabs, &phases);
+        assert!((phi.0 - 1.0).abs() < 1e-10);
+    }
+
+    #[test]
+    fn test_phi_bell_state() {
+        // |Φ+⟩ = (|00⟩+|11⟩)/√2. Stabilizers: +XX, +ZZ. ζ = 1.
+        let stabs = vec![xx(), zz()];
+        let phases = vec![false, false];
+
+        // Φ(I,I) for outcome 00 (in support): 2^ζ · |⟨00|Φ+⟩|² = 2 · 1/2 = 1
+        let phi = compute_phi(
+            &Bm::default(),
+            &Bm::default(),
+            &[false, false],
+            &stabs,
+            &phases,
+        );
+        assert!((phi.0 - 1.0).abs() < 1e-10, "Phi(I,I) at 00: {phi:?}");
+
+        // Φ(I,I) for outcome 01 (not in support): 0
+        let phi = compute_phi(
+            &Bm::default(),
+            &Bm::default(),
+            &[false, true],
+            &stabs,
+            &phases,
+        );
+        assert!(phi.0.abs() < 1e-10);
+
+        // Φ(Z0,I) for outcome 00
+        let phi = compute_phi(&Bm::z(0), &Bm::default(), &[false, false], &stabs, &phases);
+        assert!((phi.0 - 1.0).abs() < 1e-10, "Phi(Z0,I) at 00: {phi:?}");
+
+        // Φ(Z0,I) for outcome 11
+        let phi = compute_phi(&Bm::z(0), &Bm::default(), &[true, true], &stabs, &phases);
+        assert!((phi.0 + 1.0).abs() < 1e-10, "Phi(Z0,I) at 11: {phi:?}");
+    }
+
+    #[test]
+    fn test_bell_state_strong_sim() {
+        // |Φ+⟩ with S_{Z₀} noise (Z error on qubit 0)
+        let stabs = vec![xx(), zz()];
+
+        let gens = vec![PropagatedEeg {
+            eeg_type: EegType::S,
+            label: Bm::z(0), // S_Z on qubit 0
+            label2: None,
+            coeff: -0.01,
+            source: None,
+        }];
+
+        // Noiseless: p(00) = p(11) = 1/2, p(01) = p(10) = 0
+        let p00 = outcome_probability(&gens, &[false, false], &stabs);
+        let p11 = outcome_probability(&gens, &[true, true], &stabs);
+        let p01 = outcome_probability(&gens, &[false, true], &stabs);
+        let p10 = outcome_probability(&gens, &[true, false], &stabs);
+
+        assert!((p00.noiseless - 0.5).abs() < 1e-10);
+        assert!((p11.noiseless - 0.5).abs() < 1e-10);
+        assert!(p01.noiseless.abs() < 1e-10);
+        assert!(p10.noiseless.abs() < 1e-10);
+
+        // S_{Z₀} on |Φ+⟩: Z₀ maps |Φ+⟩ to |Φ-⟩. No Z-basis effect.
+        assert!(
+            p00.s_correction.abs() < 1e-10,
+            "Z error on Bell state: no Z-basis effect"
+        );
+        assert!(p11.s_correction.abs() < 1e-10);
+    }
+}
diff --git a/exp/pecos-eeg/tests/beta_investigation.rs b/exp/pecos-eeg/tests/beta_investigation.rs
new file mode 100644
index 000000000..e06084dcd
--- /dev/null
+++ b/exp/pecos-eeg/tests/beta_investigation.rs
@@ -0,0 +1,180 @@
+// Copyright 2026 The PECOS Developers
+//
+// Licensed under the Apache License, Version 2.0
+
+//! Investigation: why off-diagonal beta terms don't fire for Z-basis.
+
+use pecos_core::gate_type::GateType;
+use pecos_core::{Gate, GateAngles, GateParams, QubitId};
+use pecos_eeg::Bm;
+use pecos_eeg::circuit::{NoiseModel, PropagatedEeg, analyze_expanded};
+use pecos_eeg::eeg::EegType;
+use pecos_eeg::expand;
+use pecos_eeg::stabilizer::StabilizerGroup;
+use pecos_simulators::{CliffordGateable, SparseStab};
+
+fn gate(gt: GateType, qubits: &[usize]) -> Gate {
+    Gate {
+        gate_type: gt,
+        qubits: qubits.iter().map(|&q| QubitId(q)).collect(),
+        angles: GateAngles::new(),
+        params: GateParams::new(),
+        meas_ids: pecos_core::GateMeasIds::new(),
+        channel: None,
+    }
+}
+
+/// Build a minimal Z-basis circuit: 2 data + 1 X-ancilla, 2 rounds.
+fn build_minimal_zbasis() -> Vec<Gate> {
+    vec![
+        // Init
+        gate(GateType::PZ, &[0]),
+        gate(GateType::PZ, &[1]),
+        gate(GateType::PZ, &[2]), // X-ancilla
+        // Round 1
+        gate(GateType::H, &[2]),
+        gate(GateType::CX, &[2, 0]),
+        gate(GateType::CX, &[2, 1]),
+        gate(GateType::H, &[2]),
+        gate(GateType::MZ, &[2]),
+        gate(GateType::PZ, &[2]),
+        // Round 2
+        gate(GateType::H, &[2]),
+        gate(GateType::CX, &[2, 0]),
+        gate(GateType::CX, &[2, 1]),
+        gate(GateType::H, &[2]),
+        gate(GateType::MZ, &[2]),
+        // Final data readout
+        gate(GateType::MZ, &[0]),
+        gate(GateType::MZ, &[1]),
+    ]
+}
+
+#[test]
+fn test_zbasis_generator_labels() {
+    let gates = build_minimal_zbasis();
+    let expanded = expand::expand_circuit(&gates);
+
+    eprintln!(
+        "Expanded circuit: {} qubits ({} original + {} aux)",
+        expanded.num_qubits,
+        expanded.num_original_qubits,
+        expanded.num_qubits - expanded.num_original_qubits
+    );
+    eprintln!("Measurement mapping:");
+    for (i, (&aux, &orig)) in expanded
+        .measurement_qubit
+        .iter()
+        .zip(expanded.original_measured_qubit.iter())
+        .enumerate()
+    {
+        eprintln!("  meas {i}: aux={aux} orig={orig}");
+    }
+
+    let noise = NoiseModel::coherent_only(0.001);
+    let result = analyze_expanded(&expanded.gates, &noise);
+
+    let h_gens: Vec<&PropagatedEeg> = result
+        .generators
+        .iter()
+        .filter(|g| g.eeg_type == EegType::H)
+        .collect();
+
+    eprintln!("\nH generators ({}):", h_gens.len());
+    for (i, g) in h_gens.iter().enumerate() {
+        let orig = expanded.map_to_original_frame(&g.label);
+        eprintln!(
+            "  [{i}] expanded={:?} coeff={:.6} original_frame={:?}",
+            g.label, g.coeff, orig
+        );
+    }
+
+    // Check products of all pairs
+    eprintln!("\nPairwise products:");
+    let stab_group = StabilizerGroup::from_circuit(&gates, expanded.num_original_qubits);
+
+    for j in 0..h_gens.len() {
+        for k in (j + 1)..h_gens.len() {
+            let qj = &h_gens[j].label;
+            let qk = &h_gens[k].label;
+            if !qj.commutes_with(qk) {
+                continue; // Skip anticommuting pairs
+            }
+            let product = qj.multiply(qk);
+            let orig_product = expanded.map_to_original_frame(&product);
+            let is_stab = stab_group.is_stabilizer(&orig_product);
+
+            if is_stab.is_some() || !orig_product.is_identity() {
+                eprintln!(
+                    "  [{j},{k}] commute=true product_orig={orig_product:?} is_stab={is_stab:?}"
+                );
+            }
+        }
+    }
+}
+
+#[test]
+fn test_zbasis_stabilizer_group() {
+    let gates = build_minimal_zbasis();
+    // Exclude final MZ readout — keep syndrome MZ
+    let last_non_mz = gates
+        .iter()
+        .rposition(|g| g.gate_type != GateType::MZ)
+        .unwrap();
+    let gates_pre = &gates[..=last_non_mz];
+    let stab_group = StabilizerGroup::from_circuit(gates_pre, 3);
+
+    // Dump actual generators
+    eprintln!("Stabilizer generators:");
+    // Run SparseStab manually to see generators
+    let mut sim = SparseStab::with_seed(3, 0);
+    for g in gates_pre {
+        let qs: Vec<QubitId> = g.qubits.iter().copied().collect();
+        match g.gate_type {
+            GateType::PZ => {
+                for &q in &qs {
+                    sim.pz(&[q]);
+                }
+            }
+            GateType::H => {
+                sim.h(&qs);
+            }
+            GateType::CX if qs.len() >= 2 => {
+                sim.cx(&[(qs[0], qs[1])]);
+            }
+            GateType::MZ => {
+                let _r = sim.mz(&qs);
+                eprintln!("  MZ({qs:?})");
+            }
+            _ => {}
+        }
+    }
+    let stab_gens = sim.stabs().generators();
+    for (i, g) in stab_gens.iter().enumerate() {
+        eprintln!("  stab[{i}] = {g:?}");
+    }
+
+    // Check what's in the stabilizer group
+    eprintln!("\nStabilizer group membership checks:");
+    let test_paulis = vec![
+        ("X0", Bm::x(0)),
+        ("X1", Bm::x(1)),
+        ("X0X1", Bm::x(0).multiply(&Bm::x(1))),
+        ("Z0", Bm::z(0)),
+        ("Z1", Bm::z(1)),
+        ("Z0Z1", Bm::z(0).multiply(&Bm::z(1))),
+        ("Z2", Bm::z(2)),
+    ];
+
+    for (name, p) in &test_paulis {
+        let result = stab_group.is_stabilizer(p);
+        eprintln!("  {name}: {result:?}");
+    }
+
+    // X0*X1 should be a stabilizer (from X-type syndrome extraction)
+    assert_eq!(
+        stab_group.is_stabilizer(&Bm::x(0).multiply(&Bm::x(1))),
+        Some(true),
+        "X0*X1 should be stabilizer after 2 rounds of X-stabilizer measurement"
+    );
+}
diff --git a/exp/pecos-eeg/tests/generator_trace.rs b/exp/pecos-eeg/tests/generator_trace.rs
new file mode 100644
index 000000000..2158b871a
--- /dev/null
+++ b/exp/pecos-eeg/tests/generator_trace.rs
@@ -0,0 +1,414 @@
+// Copyright 2026 The PECOS Developers
+//
+// Licensed under the Apache License, Version 2.0
+
+//! Trace generator propagation for d=2 Z-basis surface code.
+//! Diagnose why D1 and D2 have identical EEG probabilities
+//! when `StateVec` shows they should differ.
+
+use std::collections::BTreeMap;
+
+use pecos_core::gate_type::GateType;
+use pecos_core::{Gate, GateAngles, GateParams, QubitId};
+use pecos_eeg::Bm;
+use pecos_eeg::circuit::{NoiseModel, analyze_expanded};
+use pecos_eeg::dem_mapping::*;
+use pecos_eeg::eeg::EegType;
+use pecos_eeg::expand;
+use pecos_eeg::stabilizer::StabilizerGroup;
+
+fn gate(gt: GateType, qubits: &[usize]) -> Gate {
+    Gate {
+        gate_type: gt,
+        qubits: qubits.iter().map(|&q| QubitId(q)).collect(),
+        angles: GateAngles::new(),
+        params: GateParams::new(),
+        meas_ids: pecos_core::GateMeasIds::new(),
+        channel: None,
+    }
+}
+
+/// Build the d=2 Z-basis surface code circuit (2 rounds).
+/// Matches what `LogicalCircuitBuilder` produces.
+fn build_d2_zbasis() -> Vec<Gate> {
+    vec![
+        // Init
+        gate(GateType::PZ, &[0]),
+        gate(GateType::PZ, &[1]),
+        gate(GateType::PZ, &[2]),
+        gate(GateType::PZ, &[3]),
+        gate(GateType::PZ, &[4]),
+        gate(GateType::PZ, &[5]),
+        gate(GateType::PZ, &[6]),
+        // Round 1
+        gate(GateType::H, &[4]),
+        gate(GateType::H, &[5]),
+        gate(GateType::CX, &[1, 6]),
+        gate(GateType::CX, &[5, 3]), // tick 3
+        gate(GateType::CX, &[3, 6]),
+        gate(GateType::CX, &[5, 2]), // tick 4
+        gate(GateType::CX, &[4, 1]),
+        gate(GateType::CX, &[0, 6]), // tick 5
+        gate(GateType::CX, &[4, 0]),
+        gate(GateType::CX, &[2, 6]), // tick 6
+        gate(GateType::H, &[4]),
+        gate(GateType::H, &[5]),
+        gate(GateType::MZ, &[4]),
+        gate(GateType::MZ, &[5]),
+        gate(GateType::MZ, &[6]),
+        // Reset
+        gate(GateType::PZ, &[4]),
+        gate(GateType::PZ, &[5]),
+        gate(GateType::PZ, &[6]),
+        // Round 2
+        gate(GateType::H, &[4]),
+        gate(GateType::H, &[5]),
+        gate(GateType::CX, &[1, 6]),
+        gate(GateType::CX, &[5, 3]), // tick 11
+        gate(GateType::CX, &[3, 6]),
+        gate(GateType::CX, &[5, 2]), // tick 12
+        gate(GateType::CX, &[4, 1]),
+        gate(GateType::CX, &[0, 6]), // tick 13
+        gate(GateType::CX, &[4, 0]),
+        gate(GateType::CX, &[2, 6]), // tick 14
+        gate(GateType::H, &[4]),
+        gate(GateType::H, &[5]),
+        gate(GateType::MZ, &[4]),
+        gate(GateType::MZ, &[5]),
+        gate(GateType::MZ, &[6]),
+        // Final data readout
+        gate(GateType::MZ, &[0]),
+        gate(GateType::MZ, &[1]),
+        gate(GateType::MZ, &[2]),
+        gate(GateType::MZ, &[3]),
+    ]
+}
+
+#[test]
+fn trace_d2_zbasis_generators() {
+    let gates = build_d2_zbasis();
+    let expanded = expand::expand_circuit(&gates);
+    let noise = NoiseModel::coherent_only(0.01);
+    let result = analyze_expanded(&expanded.gates, &noise);
+
+    eprintln!(
+        "Expanded: {} qubits ({} orig + {} aux), {} measurements",
+        expanded.num_qubits,
+        expanded.num_original_qubits,
+        expanded.num_qubits - expanded.num_original_qubits,
+        expanded.measurement_qubit.len()
+    );
+
+    eprintln!("\nMeasurement mapping:");
+    for (i, (&aux, &orig)) in expanded
+        .measurement_qubit
+        .iter()
+        .zip(expanded.original_measured_qubit.iter())
+        .enumerate()
+    {
+        eprintln!("  meas[{i}]: aux=q{aux}, orig=q{orig}");
+    }
+
+    // Detectors: D1 = Z_{aux_meas0} * Z_{aux_meas3} (ancilla 4, rounds 1&2)
+    //            D2 = Z_{aux_meas1} * Z_{aux_meas4} (ancilla 5, rounds 1&2)
+    let aux_m0 = expanded.measurement_qubit[0]; // q4 round 1
+    let aux_m1 = expanded.measurement_qubit[1]; // q5 round 1
+    let aux_m3 = expanded.measurement_qubit[3]; // q4 round 2
+    let aux_m4 = expanded.measurement_qubit[4]; // q5 round 2
+
+    let d1_stab = Bm::z(aux_m0).multiply(&Bm::z(aux_m3));
+    let d2_stab = Bm::z(aux_m1).multiply(&Bm::z(aux_m4));
+
+    eprintln!("\nD1 stabilizer: Z on aux q{aux_m0} and q{aux_m3} (ancilla 4 rounds 1&2)");
+    eprintln!("D2 stabilizer: Z on aux q{aux_m1} and q{aux_m4} (ancilla 5 rounds 1&2)");
+
+    let _dets = [
+        Detector {
+            id: 1,
+            stabilizer: d1_stab.clone(),
+        },
+        Detector {
+            id: 2,
+            stabilizer: d2_stab.clone(),
+        },
+    ];
+
+    // Classify each H generator
+    let h_gens: Vec<_> = result
+        .generators
+        .iter()
+        .filter(|g| g.eeg_type == EegType::H)
+        .collect();
+
+    eprintln!("\n{} H generators. Classification:", h_gens.len());
+
+    let mut d1_gens = Vec::new();
+    let mut d2_gens = Vec::new();
+
+    for g in &h_gens {
+        let flips_d1 = !g.label.commutes_with(&d1_stab);
+        let flips_d2 = !g.label.commutes_with(&d2_stab);
+
+        if flips_d1 || flips_d2 {
+            let orig = expanded.map_to_original_frame(&g.label);
+            eprintln!(
+                "  {:?} coeff={:.6} -> orig={:?} flips: D1={} D2={}",
+                g.label, g.coeff, orig, flips_d1, flips_d2
+            );
+
+            if flips_d1 {
+                d1_gens.push((g.label.clone(), g.coeff));
+            }
+            if flips_d2 {
+                d2_gens.push((g.label.clone(), g.coeff));
+            }
+        }
+    }
+
+    eprintln!("\nD1 generators: {} (ancilla 4)", d1_gens.len());
+    for (label, coeff) in &d1_gens {
+        eprintln!("  {label:?} coeff={coeff:.6}");
+    }
+
+    eprintln!("\nD2 generators: {} (ancilla 5)", d2_gens.len());
+    for (label, coeff) in &d2_gens {
+        eprintln!("  {label:?} coeff={coeff:.6}");
+    }
+
+    // After BCH combination (same label → sum coefficients)
+    let mut d1_bch: BTreeMap<Bm, f64> = BTreeMap::new();
+    let mut d2_bch: BTreeMap<Bm, f64> = BTreeMap::new();
+    for (l, c) in &d1_gens {
+        *d1_bch.entry(l.clone()).or_default() += c;
+    }
+    for (l, c) in &d2_gens {
+        *d2_bch.entry(l.clone()).or_default() += c;
+    }
+
+    eprintln!("\nD1 after BCH: {} distinct labels", d1_bch.len());
+    for (l, c) in &d1_bch {
+        eprintln!("  {l:?} rate={c:.6}");
+    }
+
+    eprintln!("\nD2 after BCH: {} distinct labels", d2_bch.len());
+    for (l, c) in &d2_bch {
+        eprintln!("  {l:?} rate={c:.6}");
+    }
+
+    // Verify asymmetry in generator counts
+    assert_ne!(
+        d1_bch.len(),
+        d2_bch.len(),
+        "D1 and D2 should have different numbers of BCH-combined generators"
+    );
+
+    // Compute probabilities manually to trace the beta function
+    let gates_pre = crate::exclude_final_readout(&gates);
+    let stab_group = StabilizerGroup::from_circuit(&gates_pre, expanded.num_original_qubits);
+
+    // Check what the stabilizer group contains
+    eprintln!("\nStabilizer group membership checks:");
+    let test_paulis = vec![
+        ("Z0", Bm::z(0)),
+        ("Z1", Bm::z(1)),
+        ("Z2", Bm::z(2)),
+        ("Z3", Bm::z(3)),
+        ("Z0Z1", Bm::z(0).multiply(&Bm::z(1))),
+        ("Z0Z3", Bm::z(0).multiply(&Bm::z(3))),
+        ("X0X1", Bm::x(0).multiply(&Bm::x(1))),
+    ];
+    for (name, p) in &test_paulis {
+        let result = stab_group.is_stabilizer(p);
+        eprintln!("  {name}: {result:?}");
+    }
+
+    eprintln!("\nPre-readout gates count: {}", gates_pre.len());
+    eprintln!("Original gates count: {}", gates.len());
+
+    // Dump raw SparseStab generators
+    {
+        use pecos_simulators::{CliffordGateable, SparseStab};
+        let mut sim = SparseStab::with_seed(7, 0);
+        for g in &gates_pre {
+            let qs: Vec<QubitId> = g.qubits.iter().copied().collect();
+            if qs.is_empty() {
+                continue;
+            }
+            match g.gate_type {
+                GateType::PZ => {
+                    for &q in &qs {
+                        sim.pz(&[q]);
+                    }
+                }
+                GateType::H => {
+                    sim.h(&qs);
+                }
+                GateType::CX if qs.len() >= 2 => {
+                    sim.cx(&[(qs[0], qs[1])]);
+                }
+                GateType::MZ => {
+                    let _ = sim.mz(&qs);
+                }
+                _ => {}
+            }
+        }
+        let stabs = sim.stabs();
+        let n_gens = stabs.num_generators();
+        eprintln!("\nSparseStab generators ({n_gens}):");
+        for i in 0..n_gens {
+            let ps = stabs.generator(i);
+            let phase = stabs.generator_phase(i);
+            eprintln!("  [{i}] phase={phase:?} {ps}");
+        }
+
+        // Direct test: can find_pauli_sign find Z0?
+        let result = stabs.find_pauli_sign(
+            sim.destabs(),
+            std::iter::empty::<usize>(),
+            std::iter::once(0usize),
+            0,
+        );
+        eprintln!("\nfind_pauli_sign(Z0) WITH MZ = {result:?}");
+
+        // Try without MZ: skip measurements in stabilizer computation
+        let mut sim2 = SparseStab::with_seed(7, 0);
+        for g in &gates_pre {
+            let qs: Vec<QubitId> = g.qubits.iter().copied().collect();
+            if qs.is_empty() {
+                continue;
+            }
+            match g.gate_type {
+                GateType::PZ => {
+                    for &q in &qs {
+                        sim2.pz(&[q]);
+                    }
+                }
+                GateType::H => {
+                    sim2.h(&qs);
+                }
+                GateType::CX if qs.len() >= 2 => {
+                    sim2.cx(&[(qs[0], qs[1])]);
+                }
+                _ => {}
+            }
+        }
+        let stabs2 = sim2.stabs();
+        let result2 = stabs2.find_pauli_sign(
+            sim2.destabs(),
+            std::iter::empty::<usize>(),
+            std::iter::once(0usize),
+            0,
+        );
+        eprintln!("find_pauli_sign(Z0) WITHOUT MZ = {result2:?}");
+
+        // Check X0X1 without MZ
+        let result3 =
+            stabs2.find_pauli_sign(sim2.destabs(), [0usize, 1], std::iter::empty::<usize>(), 0);
+        eprintln!("find_pauli_sign(X0X1) WITHOUT MZ = {result3:?}");
+    }
+
+    // Check: how many qubits in the stabilizer group? And test Z0Z1Z2Z3
+    let z_all = Bm::z(0)
+        .multiply(&Bm::z(1))
+        .multiply(&Bm::z(2))
+        .multiply(&Bm::z(3));
+    eprintln!("Z0Z1Z2Z3: {:?}", stab_group.is_stabilizer(&z_all));
+    let _z01 = Bm::z(0).multiply(&Bm::z(1));
+    let z23 = Bm::z(2).multiply(&Bm::z(3));
+    eprintln!("Z2Z3: {:?}", stab_group.is_stabilizer(&z23));
+    eprintln!(
+        "Z0Z1Z2: {:?}",
+        stab_group.is_stabilizer(&Bm::z(0).multiply(&Bm::z(1)).multiply(&Bm::z(2)))
+    );
+    eprintln!(
+        "Z1Z2: {:?}",
+        stab_group.is_stabilizer(&Bm::z(1).multiply(&Bm::z(2)))
+    );
+
+    for (det_name, bch) in [("D1", &d1_bch), ("D2", &d2_bch)] {
+        let labels: Vec<Bm> = bch.keys().cloned().collect();
+        let coeffs: Vec<f64> = bch.values().copied().collect();
+        let n = labels.len();
+
+        let mut diag = 0.0;
+        let mut offdiag = 0.0;
+        let mut offdiag_zero = 0;
+        let mut offdiag_plus = 0;
+        let mut offdiag_minus = 0;
+        let mut offdiag_anticommute = 0;
+
+        for j in 0..n {
+            diag += coeffs[j] * coeffs[j];
+            for k in (j + 1)..n {
+                if !labels[j].commutes_with(&labels[k]) {
+                    offdiag_anticommute += 1;
+                    continue;
+                }
+                let product = labels[j].multiply(&labels[k]);
+                let orig_product = expanded.map_to_original_frame(&product);
+
+                if orig_product.is_identity() {
+                    offdiag += 2.0 * coeffs[j] * coeffs[k];
+                    offdiag_plus += 1;
+                    continue;
+                }
+                match stab_group.is_stabilizer(&orig_product) {
+                    Some(true) => {
+                        offdiag += 2.0 * coeffs[j] * coeffs[k];
+                        offdiag_plus += 1;
+                    }
+                    Some(false) => {
+                        offdiag -= 2.0 * coeffs[j] * coeffs[k];
+                        offdiag_minus += 1;
+                    }
+                    None => {
+                        offdiag_zero += 1;
+                        eprintln!(
+                            "    beta=0: {:?} * {:?} = {:?} (orig: {:?})",
+                            labels[j], labels[k], product, orig_product
+                        );
+                    }
+                }
+            }
+        }
+
+        let total = diag + offdiag;
+        eprintln!("\n{det_name} probability breakdown:");
+        eprintln!("  Diagonal:     {diag:.8}");
+        eprintln!(
+            "  Off-diagonal: {offdiag:.8} (+{offdiag_plus} pairs, -{offdiag_minus} pairs, 0:{offdiag_zero} pairs, anticommute:{offdiag_anticommute})"
+        );
+        eprintln!("  Total:        {total:.8}");
+    }
+}
+
+fn exclude_final_readout(gates: &[Gate]) -> Vec<Gate> {
+    use pecos_core::gate_type::GateType;
+    let mut ancilla_qubits = std::collections::HashSet::new();
+    let mut past_init = false;
+    for g in gates {
+        if past_init && (g.gate_type == GateType::PZ || g.gate_type == GateType::QAlloc) {
+            for q in &g.qubits {
+                ancilla_qubits.insert(q.index());
+            }
+        }
+        if g.gate_type != GateType::PZ && g.gate_type != GateType::QAlloc {
+            past_init = true;
+        }
+    }
+    let mut end = gates.len();
+    for g in gates.iter().rev() {
+        if g.gate_type != GateType::MZ {
+            break;
+        }
+        if g.qubits
+            .iter()
+            .all(|q| !ancilla_qubits.contains(&q.index()))
+        {
+            end -= 1;
+        } else {
+            break;
+        }
+    }
+    gates[..end].to_vec()
+}
diff --git a/exp/pecos-eeg/tests/stabilizer_audit.rs b/exp/pecos-eeg/tests/stabilizer_audit.rs
new file mode 100644
index 000000000..5e9fcea9c
--- /dev/null
+++ b/exp/pecos-eeg/tests/stabilizer_audit.rs
@@ -0,0 +1,228 @@
+// Copyright 2026 The PECOS Developers
+//
+// Licensed under the Apache License, Version 2.0
+
+//! Audit: does the `StabilizerGroup` correctly identify all stabilizers?
+//! Test by generating all 2^n products of n generators and checking
+//! that `is_stabilizer` returns Some for each.
+
+use pecos_core::gate_type::GateType;
+use pecos_core::{Gate, GateAngles, GateParams, QubitId};
+use pecos_eeg::Bm;
+use pecos_eeg::stabilizer::StabilizerGroup;
+use pecos_simulators::{CliffordGateable, SparseStab};
+
+fn gate(gt: GateType, qubits: &[usize]) -> Gate {
+    Gate {
+        gate_type: gt,
+        qubits: qubits.iter().map(|&q| QubitId(q)).collect(),
+        angles: GateAngles::new(),
+        params: GateParams::new(),
+        meas_ids: pecos_core::GateMeasIds::new(),
+        channel: None,
+    }
+}
+
+/// Extract generators as Bm from `SparseStab`.
+fn extract_generators(sim: &SparseStab) -> Vec<Bm> {
+    let stabs = sim.stabs();
+    let n = stabs.num_generators();
+    let mut gens = Vec::with_capacity(n);
+    for i in 0..n {
+        let ps = stabs.generator(i);
+        gens.push(pecos_eeg::dem_mapping::pauli_string_to_bitmask(&ps));
+    }
+    gens
+}
+
+/// Check that `StabilizerGroup.is_stabilizer` returns Some for ALL products
+/// of the `SparseStab` generators (which are by definition in the group).
+fn audit_stabilizer_group(label: &str, gates: &[Gate], num_qubits: usize) {
+    let stab_group = StabilizerGroup::from_circuit(gates, num_qubits);
+
+    // Also build a raw SparseStab to extract generators
+    let mut sim = SparseStab::with_seed(num_qubits, 0);
+    for g in gates {
+        let qs: Vec<QubitId> = g.qubits.iter().copied().collect();
+        if qs.is_empty() {
+            continue;
+        }
+        match g.gate_type {
+            GateType::PZ | GateType::QAlloc => {
+                for &q in &qs {
+                    sim.pz(&[q]);
+                }
+            }
+            GateType::H => {
+                sim.h(&qs);
+            }
+            GateType::SZ => {
+                sim.sz(&qs);
+            }
+            GateType::SZdg => {
+                sim.szdg(&qs);
+            }
+            GateType::X => {
+                sim.x(&qs);
+            }
+            GateType::Y => {
+                sim.y(&qs);
+            }
+            GateType::Z => {
+                sim.z(&qs);
+            }
+            GateType::CX if qs.len() >= 2 => {
+                sim.cx(&[(qs[0], qs[1])]);
+            }
+            GateType::CZ if qs.len() >= 2 => {
+                sim.cz(&[(qs[0], qs[1])]);
+            }
+            GateType::MZ => {
+                sim.mz(&qs);
+            }
+            _ => {}
+        }
+    }
+
+    let generators = extract_generators(&sim);
+    let n = generators.len();
+
+    eprintln!("\n{label}: {n} generators on {num_qubits} qubits");
+    for (i, g) in generators.iter().enumerate() {
+        eprintln!("  gen[{i}] = {g:?}");
+    }
+
+    // Test all 2^n products (for small n)
+    let max_subsets = if n <= 10 { 1 << n } else { 1024 }; // cap at 1024 for large n
+    let mut failures = Vec::new();
+
+    for mask in 0..max_subsets {
+        let mut product = Bm::default();
+        for (i, generator) in generators.iter().enumerate().take(n) {
+            if mask & (1 << i) != 0 {
+                product = product.multiply(generator);
+            }
+        }
+
+        let result = stab_group.is_stabilizer(&product);
+        if result.is_none() && !product.is_identity() {
+            failures.push((mask, product));
+        }
+    }
+
+    if failures.is_empty() {
+        eprintln!("  OK: all {max_subsets} products correctly identified");
+    } else {
+        eprintln!("  FAILURES: {} products not found:", failures.len());
+        for (mask, product) in &failures {
+            let gens_used: Vec<usize> = (0..n).filter(|&i| mask & (1 << i) != 0).collect();
+            eprintln!("    mask={mask:#06b} gens={gens_used:?} product={product:?}");
+        }
+    }
+
+    assert!(
+        failures.is_empty(),
+        "{label}: {}/{max_subsets} stabilizer products not found by is_stabilizer",
+        failures.len()
+    );
+}
+
+#[test]
+fn audit_simple_states() {
+    // |0>: stabilizer = Z
+    audit_stabilizer_group("|0>", &[], 1);
+
+    // |+>: stabilizer = X
+    audit_stabilizer_group("|+>", &[gate(GateType::H, &[0])], 1);
+
+    // Bell state
+    audit_stabilizer_group(
+        "|Phi+>",
+        &[gate(GateType::H, &[0]), gate(GateType::CX, &[0, 1])],
+        2,
+    );
+}
+
+#[test]
+fn audit_syndrome_extraction() {
+    // Simple 2-qubit Z-check with ancilla: PZ(0,1,2), CX(0,2), CX(1,2), MZ(2)
+    audit_stabilizer_group(
+        "Z-check 2q",
+        &[
+            gate(GateType::PZ, &[0]),
+            gate(GateType::PZ, &[1]),
+            gate(GateType::PZ, &[2]),
+            gate(GateType::CX, &[0, 2]),
+            gate(GateType::CX, &[1, 2]),
+            gate(GateType::MZ, &[2]),
+        ],
+        3,
+    );
+
+    // X-check: H(2), CX(2,0), CX(2,1), H(2), MZ(2)
+    audit_stabilizer_group(
+        "X-check 2q",
+        &[
+            gate(GateType::PZ, &[0]),
+            gate(GateType::PZ, &[1]),
+            gate(GateType::PZ, &[2]),
+            gate(GateType::H, &[2]),
+            gate(GateType::CX, &[2, 0]),
+            gate(GateType::CX, &[2, 1]),
+            gate(GateType::H, &[2]),
+            gate(GateType::MZ, &[2]),
+        ],
+        3,
+    );
+}
+
+#[test]
+fn audit_d2_zbasis_pre_readout() {
+    // d=2 Z-basis surface code, 2 rounds, pre-readout circuit
+    let gates = vec![
+        gate(GateType::PZ, &[0]),
+        gate(GateType::PZ, &[1]),
+        gate(GateType::PZ, &[2]),
+        gate(GateType::PZ, &[3]),
+        gate(GateType::PZ, &[4]),
+        gate(GateType::PZ, &[5]),
+        gate(GateType::PZ, &[6]),
+        // Round 1
+        gate(GateType::H, &[4]),
+        gate(GateType::H, &[5]),
+        gate(GateType::CX, &[1, 6]),
+        gate(GateType::CX, &[5, 3]),
+        gate(GateType::CX, &[3, 6]),
+        gate(GateType::CX, &[5, 2]),
+        gate(GateType::CX, &[4, 1]),
+        gate(GateType::CX, &[0, 6]),
+        gate(GateType::CX, &[4, 0]),
+        gate(GateType::CX, &[2, 6]),
+        gate(GateType::H, &[4]),
+        gate(GateType::H, &[5]),
+        gate(GateType::MZ, &[4]),
+        gate(GateType::MZ, &[5]),
+        gate(GateType::MZ, &[6]),
+        // Reset
+        gate(GateType::PZ, &[4]),
+        gate(GateType::PZ, &[5]),
+        gate(GateType::PZ, &[6]),
+        // Round 2
+        gate(GateType::H, &[4]),
+        gate(GateType::H, &[5]),
+        gate(GateType::CX, &[1, 6]),
+        gate(GateType::CX, &[5, 3]),
+        gate(GateType::CX, &[3, 6]),
+        gate(GateType::CX, &[5, 2]),
+        gate(GateType::CX, &[4, 1]),
+        gate(GateType::CX, &[0, 6]),
+        gate(GateType::CX, &[4, 0]),
+        gate(GateType::CX, &[2, 6]),
+        gate(GateType::H, &[4]),
+        gate(GateType::H, &[5]),
+        gate(GateType::MZ, &[4]),
+        gate(GateType::MZ, &[5]),
+        gate(GateType::MZ, &[6]),
+    ];
+    audit_stabilizer_group("d=2 Z-basis pre-readout", &gates, 7);
+}
diff --git a/exp/pecos-eeg/tests/statevec_comparison.rs b/exp/pecos-eeg/tests/statevec_comparison.rs
new file mode 100644
index 000000000..ed387111f
--- /dev/null
+++ b/exp/pecos-eeg/tests/statevec_comparison.rs
@@ -0,0 +1,1974 @@
+// Copyright 2026 The PECOS Developers
+//
+// Licensed under the Apache License, Version 2.0
+
+//! Ground-truth comparison: EEG analytical DEM vs `StateVec` simulation.
+//!
+//! Uses Bell-state parity circuit where idle RZ noise creates detectable
+//! parity violations. Without noise, MZ parity is always even.
+//! With RZ(θ) noise after CX, P(odd parity) = sin²(θ).
+//! EEG predicts ≈ θ² at leading order.
+
+use pecos_core::gate_type::GateType;
+use pecos_core::pauli::pauli_bitmask::BitmaskStorage;
+use pecos_core::{Angle64, Gate, GateAngles, GateParams, QubitId};
+use pecos_eeg::Bm;
+use pecos_eeg::circuit::{NoiseModel, analyze_expanded};
+use pecos_eeg::dem_mapping::{Detector, build_dem_with_stabilizers};
+use pecos_eeg::expand;
+use pecos_eeg::noise::UniformNoise;
+use pecos_eeg::stabilizer::StabilizerGroup;
+use pecos_simulators::{ArbitraryRotationGateable, CliffordGateable, StateVec};
+
+fn gate(gt: GateType, qubits: &[usize]) -> Gate {
+    Gate {
+        gate_type: gt,
+        qubits: qubits.iter().map(|&q| QubitId(q)).collect(),
+        angles: GateAngles::new(),
+        params: GateParams::new(),
+        meas_ids: pecos_core::GateMeasIds::new(),
+        channel: None,
+    }
+}
+
+fn qid(q: usize) -> QubitId {
+    QubitId(q)
+}
+
+fn u64_to_f64(value: u64) -> f64 {
+    f64::from(u32::try_from(value).expect("test sample count fits in u32"))
+}
+
+fn usize_to_f64(value: usize) -> f64 {
+    f64::from(u32::try_from(value).expect("test dimension fits in u32"))
+}
+
+fn bit_to_f64(value: usize) -> f64 {
+    f64::from(u8::try_from(value).expect("bit value fits in u8"))
+}
+
+// ============================================================
+// Shared helpers for EEG analysis and StateVec simulation
+// ============================================================
+
+/// Run EEG on a gate list with a parity detector over all measurements.
+fn eeg_detection_prob(gates: &[Gate], theta: f64) -> f64 {
+    let expanded = expand::expand_circuit(gates);
+    let noise = NoiseModel::coherent_only(theta);
+    let result = analyze_expanded(&expanded.gates, &noise);
+
+    // Parity detector: Z on all auxiliary qubits
+    let mut det_stab = Bm::default();
+    for &aux in &expanded.measurement_qubit {
+        det_stab.z_bits.set_bit(aux);
+    }
+    let det = Detector {
+        id: 0,
+        stabilizer: det_stab,
+    };
+
+    // Stabilizer group from expanded circuit (strip trailing deferred MZ)
+    let exp_pre: Vec<_> = {
+        let last = expanded
+            .gates
+            .iter()
+            .rposition(|g| g.gate_type != GateType::MZ)
+            .unwrap();
+        expanded.gates[..=last].to_vec()
+    };
+    let stab_group = StabilizerGroup::from_circuit(&exp_pre, expanded.num_qubits);
+
+    let entries = build_dem_with_stabilizers(&result.generators, &[det], &[], Some(&stab_group));
+
+    entries.iter().map(|e| e.probability).sum()
+}
+
+/// Run EEG with per-round detectors, return per-detector probabilities.
+fn eeg_per_round_probs(gates: &[Gate], theta: f64, num_rounds: usize) -> Vec<f64> {
+    let expanded = expand::expand_circuit(gates);
+    let noise = NoiseModel::coherent_only(theta);
+    let result = analyze_expanded(&expanded.gates, &noise);
+
+    // One detector per round (Z on that round's aux qubit)
+    let dets: Vec<Detector> = (0..num_rounds)
+        .map(|r| {
+            let aux = expanded.measurement_qubit[r];
+            Detector {
+                id: r,
+                stabilizer: Bm::z(aux),
+            }
+        })
+        .collect();
+
+    // Stabilizer group from expanded circuit (strip trailing deferred MZ)
+    let exp_pre: Vec<_> = {
+        let last = expanded
+            .gates
+            .iter()
+            .rposition(|g| g.gate_type != GateType::MZ)
+            .unwrap();
+        expanded.gates[..=last].to_vec()
+    };
+    let stab_group = StabilizerGroup::from_circuit(&exp_pre, expanded.num_qubits);
+
+    let entries = build_dem_with_stabilizers(&result.generators, &dets, &[], Some(&stab_group));
+
+    let mut probs = vec![0.0; num_rounds];
+    for e in &entries {
+        for &d in &e.event.detectors {
+            probs[d] += e.probability;
+        }
+    }
+    probs
+}
+
+/// Bell-state parity circuit:
+///   PZ(0,1), H(0), CX(0,1), [idle RZ], H(0), H(1), MZ(0), MZ(1)
+///
+/// Without noise: |Φ+> → H⊗H → |Φ+> → MZ parity always even.
+/// With RZ(θ) on both qubits: P(odd parity) = sin²(θ) ≈ θ² at leading order.
+#[test]
+fn test_eeg_vs_statevec_bell_parity() {
+    let theta = 0.05;
+    let num_shots = 100_000;
+
+    // --- EEG analytical path ---
+    let gates = vec![
+        gate(GateType::PZ, &[0]),
+        gate(GateType::PZ, &[1]),
+        gate(GateType::H, &[0]),
+        gate(GateType::CX, &[0, 1]),
+        // idle RZ(θ) on both qubits is implicit in noise model
+        gate(GateType::H, &[0]),
+        gate(GateType::H, &[1]),
+        gate(GateType::MZ, &[0]),
+        gate(GateType::MZ, &[1]),
+    ];
+
+    let expanded = expand::expand_circuit(&gates);
+    let noise = NoiseModel::coherent_only(theta);
+    let result = analyze_expanded(&expanded.gates, &noise);
+
+    // Parity detector: Z_aux0 * Z_aux1
+    assert_eq!(expanded.measurement_qubit.len(), 2);
+    let aux0 = expanded.measurement_qubit[0];
+    let aux1 = expanded.measurement_qubit[1];
+    let mut det_stab = Bm::default();
+    det_stab.z_bits.set_bit(aux0);
+    det_stab.z_bits.set_bit(aux1);
+    let det = Detector {
+        id: 0,
+        stabilizer: det_stab,
+    };
+
+    // Pre-readout stabilizer group (exclude final MZ gates)
+    // Stabilizer group from expanded circuit (strip trailing deferred MZ)
+    let exp_pre: Vec<_> = {
+        let last = expanded
+            .gates
+            .iter()
+            .rposition(|g| g.gate_type != GateType::MZ)
+            .unwrap();
+        expanded.gates[..=last].to_vec()
+    };
+    let stab_group = StabilizerGroup::from_circuit(&exp_pre, expanded.num_qubits);
+
+    let entries = build_dem_with_stabilizers(&result.generators, &[det], &[], Some(&stab_group));
+
+    let eeg_prob: f64 = entries.iter().map(|e| e.probability).sum();
+
+    // --- StateVec simulation path ---
+    let mut odd_parity_count = 0u64;
+    let mut sim = StateVec::new(2);
+
+    for _ in 0..num_shots {
+        sim.pz(&[qid(0), qid(1)]);
+        sim.h(&[qid(0)]);
+        sim.cx(&[(qid(0), qid(1))]);
+
+        // Idle RZ noise (same as EEG coherent_only model)
+        sim.rz(Angle64::from_radians(theta), &[qid(0)]);
+        sim.rz(Angle64::from_radians(theta), &[qid(1)]);
+
+        sim.h(&[qid(0)]);
+        sim.h(&[qid(1)]);
+
+        let r = sim.mz(&[qid(0), qid(1)]);
+        if r[0].outcome != r[1].outcome {
+            odd_parity_count += 1;
+        }
+    }
+
+    let sv_rate = u64_to_f64(odd_parity_count) / f64::from(num_shots);
+    let sv_stderr = (sv_rate * (1.0 - sv_rate) / f64::from(num_shots)).sqrt();
+    let exact = theta.sin().powi(2);
+
+    eprintln!("theta = {theta}");
+    eprintln!("EEG:     {eeg_prob:.6}");
+    eprintln!("StateVec: {sv_rate:.6} +/- {sv_stderr:.6}");
+    eprintln!("Exact:   {exact:.6}");
+
+    // EEG should match StateVec within statistical noise + perturbative error.
+    // At θ=0.05: exact=sin²(0.05)≈0.002499, EEG leading-order≈θ²≈0.0025
+    // Perturbative error is O(θ⁴) ≈ 6.25e-6, well within statistical noise.
+    let diff = (eeg_prob - sv_rate).abs();
+    let tolerance = 5.0 * sv_stderr + theta.powi(4); // 5σ + perturbative bound
+    assert!(
+        diff < tolerance,
+        "EEG ({eeg_prob:.6}) vs StateVec ({sv_rate:.6}): diff={diff:.6} > tol={tolerance:.6}"
+    );
+}
+
+/// Same comparison at larger angle to verify scaling.
+#[test]
+fn test_eeg_vs_statevec_larger_angle() {
+    let theta = 0.1;
+    let num_shots = 100_000;
+
+    let gates = vec![
+        gate(GateType::PZ, &[0]),
+        gate(GateType::PZ, &[1]),
+        gate(GateType::H, &[0]),
+        gate(GateType::CX, &[0, 1]),
+        gate(GateType::H, &[0]),
+        gate(GateType::H, &[1]),
+        gate(GateType::MZ, &[0]),
+        gate(GateType::MZ, &[1]),
+    ];
+
+    let expanded = expand::expand_circuit(&gates);
+    let noise = NoiseModel::coherent_only(theta);
+    let result = analyze_expanded(&expanded.gates, &noise);
+
+    let aux0 = expanded.measurement_qubit[0];
+    let aux1 = expanded.measurement_qubit[1];
+    let mut det_stab = Bm::default();
+    det_stab.z_bits.set_bit(aux0);
+    det_stab.z_bits.set_bit(aux1);
+    let det = Detector {
+        id: 0,
+        stabilizer: det_stab,
+    };
+
+    // Stabilizer group from expanded circuit (strip trailing deferred MZ)
+    let exp_pre: Vec<_> = {
+        let last = expanded
+            .gates
+            .iter()
+            .rposition(|g| g.gate_type != GateType::MZ)
+            .unwrap();
+        expanded.gates[..=last].to_vec()
+    };
+    let stab_group = StabilizerGroup::from_circuit(&exp_pre, expanded.num_qubits);
+
+    let entries = build_dem_with_stabilizers(&result.generators, &[det], &[], Some(&stab_group));
+
+    let eeg_prob: f64 = entries.iter().map(|e| e.probability).sum();
+
+    let mut odd_parity_count = 0u64;
+    let mut sim = StateVec::new(2);
+
+    for _ in 0..num_shots {
+        sim.pz(&[qid(0), qid(1)]);
+        sim.h(&[qid(0)]);
+        sim.cx(&[(qid(0), qid(1))]);
+        sim.rz(Angle64::from_radians(theta), &[qid(0)]);
+        sim.rz(Angle64::from_radians(theta), &[qid(1)]);
+        sim.h(&[qid(0)]);
+        sim.h(&[qid(1)]);
+        let r = sim.mz(&[qid(0), qid(1)]);
+        if r[0].outcome != r[1].outcome {
+            odd_parity_count += 1;
+        }
+    }
+
+    let sv_rate = u64_to_f64(odd_parity_count) / f64::from(num_shots);
+    let sv_stderr = (sv_rate * (1.0 - sv_rate) / f64::from(num_shots)).sqrt();
+    let exact = theta.sin().powi(2);
+
+    eprintln!("theta = {theta}");
+    eprintln!("EEG:      {eeg_prob:.6}");
+    eprintln!("StateVec: {sv_rate:.6} +/- {sv_stderr:.6}");
+    eprintln!("Exact:    {exact:.6}");
+
+    // At θ=0.1: exact≈0.00998, EEG≈θ²≈0.01, perturbative error≈O(θ⁴)≈0.0001
+    // Allow larger tolerance for bigger angle
+    let diff = (eeg_prob - sv_rate).abs();
+    let tolerance = 5.0 * sv_stderr + 2.0 * theta.powi(4);
+    assert!(
+        diff < tolerance,
+        "EEG ({eeg_prob:.6}) vs StateVec ({sv_rate:.6}): diff={diff:.6} > tol={tolerance:.6}"
+    );
+}
+
+// ============================================================
+// Benchmark sweeps (run with: cargo test -p pecos-eeg --test statevec_comparison -- --ignored --nocapture)
+// ============================================================
+
+/// Sweep theta for the Bell parity circuit.
+/// Exact answer: sin²(θ). EEG leading-order: θ².
+#[test]
+#[ignore = "benchmark sweep; run manually with --ignored --nocapture"]
+fn bench_bell_parity_theta_sweep() {
+    let num_shots = 200_000;
+
+    let gates = vec![
+        gate(GateType::PZ, &[0]),
+        gate(GateType::PZ, &[1]),
+        gate(GateType::H, &[0]),
+        gate(GateType::CX, &[0, 1]),
+        gate(GateType::H, &[0]),
+        gate(GateType::H, &[1]),
+        gate(GateType::MZ, &[0]),
+        gate(GateType::MZ, &[1]),
+    ];
+
+    eprintln!("\n=== Bell parity: EEG vs StateVec vs Exact ===");
+    eprintln!(
+        "{:>8} {:>10} {:>10} {:>10} {:>10} {:>10}",
+        "theta", "EEG", "StateVec", "SV_stderr", "Exact", "EEG/Exact"
+    );
+
+    for &theta in &[0.01, 0.02, 0.05, 0.1, 0.15, 0.2, 0.3, 0.5] {
+        let eeg_prob = eeg_detection_prob(&gates, theta);
+
+        let mut odd = 0u64;
+        let mut sim = StateVec::new(2);
+        for _ in 0..num_shots {
+            sim.pz(&[qid(0), qid(1)]);
+            sim.h(&[qid(0)]);
+            sim.cx(&[(qid(0), qid(1))]);
+            sim.rz(Angle64::from_radians(theta), &[qid(0)]);
+            sim.rz(Angle64::from_radians(theta), &[qid(1)]);
+            sim.h(&[qid(0)]);
+            sim.h(&[qid(1)]);
+            let r = sim.mz(&[qid(0), qid(1)]);
+            if r[0].outcome != r[1].outcome {
+                odd += 1;
+            }
+        }
+
+        let sv = u64_to_f64(odd) / f64::from(num_shots);
+        let se = (sv * (1.0 - sv) / f64::from(num_shots)).sqrt();
+        let exact = theta.sin().powi(2);
+        let ratio = if exact > 1e-10 {
+            eeg_prob / exact
+        } else {
+            f64::NAN
+        };
+
+        eprintln!(
+            "{theta:>8.3} {eeg_prob:>10.6} {sv:>10.6} {se:>10.6} {exact:>10.6} {ratio:>10.4}"
+        );
+    }
+}
+
+/// Multi-round X-check: 2 data qubits, 1 ancilla, N rounds of X-check with reset.
+/// Data prepared in |++>, ancilla measures X0*X1 each round.
+#[test]
+#[ignore = "benchmark sweep; run manually with --ignored --nocapture"]
+fn bench_x_check_multi_round() {
+    let num_shots = 200_000;
+
+    eprintln!("\n=== Multi-round X-check (2 data + 1 ancilla) ===");
+
+    for &num_rounds in &[1, 2, 3, 4] {
+        // Build circuit: PZ(0,1,2), H(0), H(1), then N rounds of X-check
+        let mut gates = vec![
+            gate(GateType::PZ, &[0]),
+            gate(GateType::PZ, &[1]),
+            gate(GateType::PZ, &[2]),
+            gate(GateType::H, &[0]),
+            gate(GateType::H, &[1]),
+        ];
+
+        for _ in 0..num_rounds {
+            gates.push(gate(GateType::H, &[2]));
+            gates.push(gate(GateType::CX, &[2, 0]));
+            gates.push(gate(GateType::CX, &[2, 1]));
+            gates.push(gate(GateType::H, &[2]));
+            gates.push(gate(GateType::MZ, &[2]));
+            gates.push(gate(GateType::PZ, &[2]));
+        }
+        // Remove trailing PZ (no reset after last round)
+        gates.pop();
+
+        for &theta in &[0.01, 0.05, 0.1] {
+            let eeg_probs = eeg_per_round_probs(&gates, theta, num_rounds);
+
+            // StateVec: run circuit with idle RZ after each CX
+            let mut round_detections = vec![0u64; num_rounds];
+            let mut sim = StateVec::new(3);
+
+            for _ in 0..num_shots {
+                sim.pz(&[qid(0), qid(1), qid(2)]);
+                sim.h(&[qid(0)]);
+                sim.h(&[qid(1)]);
+
+                for (round, round_detection) in
+                    round_detections.iter_mut().enumerate().take(num_rounds)
+                {
+                    sim.h(&[qid(2)]);
+                    sim.cx(&[(qid(2), qid(0))]);
+                    sim.rz(Angle64::from_radians(theta), &[qid(0)]);
+                    sim.rz(Angle64::from_radians(theta), &[qid(2)]);
+                    sim.cx(&[(qid(2), qid(1))]);
+                    sim.rz(Angle64::from_radians(theta), &[qid(1)]);
+                    sim.rz(Angle64::from_radians(theta), &[qid(2)]);
+                    sim.h(&[qid(2)]);
+                    let r = sim.mz(&[qid(2)]);
+                    if r[0].outcome {
+                        *round_detection += 1;
+                    }
+                    if round < num_rounds - 1 {
+                        sim.pz(&[qid(2)]);
+                    }
+                }
+            }
+
+            let sv_rates: Vec<f64> = round_detections
+                .iter()
+                .map(|&d| u64_to_f64(d) / f64::from(num_shots))
+                .collect();
+
+            eprintln!("\nrounds={num_rounds}, theta={theta}:");
+            for r in 0..num_rounds {
+                let se = (sv_rates[r] * (1.0 - sv_rates[r]) / f64::from(num_shots)).sqrt();
+                let ratio = if sv_rates[r] > 1e-10 {
+                    eeg_probs[r] / sv_rates[r]
+                } else {
+                    f64::NAN
+                };
+                eprintln!(
+                    "  D{r}: EEG={:.6} SV={:.6}+/-{:.6} ratio={:.4}",
+                    eeg_probs[r], sv_rates[r], se, ratio
+                );
+            }
+        }
+    }
+}
+
+/// Z-basis: data in |00>, Z-check measures Z0*Z1. Coherent RZ noise.
+/// Z errors commute with Z measurements, so the X-propagated components matter.
+#[test]
+#[ignore = "benchmark sweep; run manually with --ignored --nocapture"]
+fn bench_z_basis_check() {
+    let num_shots = 200_000;
+
+    eprintln!("\n=== Z-basis parity check (CX syndrome extraction) ===");
+    eprintln!(
+        "{:>8} {:>10} {:>10} {:>10} {:>10}",
+        "theta", "EEG", "StateVec", "SV_stderr", "EEG/SV"
+    );
+
+    // Z-check: CX(0,2), CX(1,2), MZ(2). Ancilla 2 measures Z0*Z1 parity.
+    // For |00>: Z0Z1|00> = +|00>, deterministic 0.
+    // RZ noise creates Z errors which don't flip Z-checks directly,
+    // but the CX propagation can create cross-terms.
+    let gates = vec![
+        gate(GateType::PZ, &[0]),
+        gate(GateType::PZ, &[1]),
+        gate(GateType::PZ, &[2]),
+        gate(GateType::CX, &[0, 2]),
+        gate(GateType::CX, &[1, 2]),
+        gate(GateType::MZ, &[2]),
+    ];
+
+    for &theta in &[0.01, 0.05, 0.1, 0.2, 0.3] {
+        let expanded = expand::expand_circuit(&gates);
+        let noise = NoiseModel::coherent_only(theta);
+        let result = analyze_expanded(&expanded.gates, &noise);
+
+        let aux = expanded.measurement_qubit[0];
+        let det = Detector {
+            id: 0,
+            stabilizer: Bm::z(aux),
+        };
+        let gates_pre = &gates[..gates.len() - 1];
+        let stab_group = StabilizerGroup::from_circuit(gates_pre, expanded.num_original_qubits);
+        let entries =
+            build_dem_with_stabilizers(&result.generators, &[det], &[], Some(&stab_group));
+        let eeg_prob: f64 = entries.iter().map(|e| e.probability).sum();
+
+        // StateVec
+        let mut det_count = 0u64;
+        let mut sim = StateVec::new(3);
+        for _ in 0..num_shots {
+            sim.pz(&[qid(0), qid(1), qid(2)]);
+            sim.cx(&[(qid(0), qid(2))]);
+            sim.rz(Angle64::from_radians(theta), &[qid(0)]);
+            sim.rz(Angle64::from_radians(theta), &[qid(2)]);
+            sim.cx(&[(qid(1), qid(2))]);
+            sim.rz(Angle64::from_radians(theta), &[qid(1)]);
+            sim.rz(Angle64::from_radians(theta), &[qid(2)]);
+            let r = sim.mz(&[qid(2)]);
+            if r[0].outcome {
+                det_count += 1;
+            }
+        }
+
+        let sv = u64_to_f64(det_count) / f64::from(num_shots);
+        let se = (sv * (1.0 - sv) / f64::from(num_shots)).sqrt();
+        let ratio = if sv > 1e-10 { eeg_prob / sv } else { f64::NAN };
+
+        eprintln!("{theta:>8.3} {eeg_prob:>10.6} {sv:>10.6} {se:>10.6} {ratio:>10.4}");
+    }
+}
+
+// ============================================================
+// Repetition code comparison: EEG vs Heisenberg vs StateVec
+// ============================================================
+
+/// Build an X-check repetition code circuit.
+///
+/// d data qubits, d-1 ancillas measuring `X_i` * X_{i+1} using
+/// H-CX-CX-H on ancilla (sensitive to Z errors from coherent RZ noise).
+/// `num_rounds` syndrome extraction rounds with reset.
+/// Returns (gates, `num_qubits`, ancilla indices).
+fn build_repetition_code(d: usize, num_rounds: usize) -> (Vec<Gate>, usize, Vec<usize>) {
+    let num_data = d;
+    let num_ancilla = d - 1;
+    let num_qubits = num_data + num_ancilla;
+
+    // Ancilla i checks X_{i} * X_{i+1}, located at qubit index d + i
+    let ancilla_start = num_data;
+
+    let mut gates = Vec::new();
+
+    // Initialize all qubits
+    for q in 0..num_qubits {
+        gates.push(gate(GateType::PZ, &[q]));
+    }
+
+    for round in 0..num_rounds {
+        // X-check: H(anc), CX(anc, data_i), CX(anc, data_{i+1}), H(anc), MZ(anc)
+        for i in 0..num_ancilla {
+            gates.push(gate(GateType::H, &[ancilla_start + i]));
+        }
+        for i in 0..num_ancilla {
+            let anc = ancilla_start + i;
+            gates.push(gate(GateType::CX, &[anc, i]));
+        }
+        for i in 0..num_ancilla {
+            let anc = ancilla_start + i;
+            gates.push(gate(GateType::CX, &[anc, i + 1]));
+        }
+        for i in 0..num_ancilla {
+            gates.push(gate(GateType::H, &[ancilla_start + i]));
+        }
+
+        // Measure ancillas
+        for i in 0..num_ancilla {
+            gates.push(gate(GateType::MZ, &[ancilla_start + i]));
+        }
+
+        // Reset ancillas (except last round)
+        if round < num_rounds - 1 {
+            for i in 0..num_ancilla {
+                gates.push(gate(GateType::PZ, &[ancilla_start + i]));
+            }
+        }
+    }
+
+    // Final data readout
+    for q in 0..num_data {
+        gates.push(gate(GateType::MZ, &[q]));
+    }
+
+    let ancillas: Vec<usize> = (0..num_ancilla).map(|i| ancilla_start + i).collect();
+    (gates, num_qubits, ancillas)
+}
+
+/// Repetition code: compare EEG (forward), Heisenberg (backward), and `StateVec`.
+#[test]
+#[ignore = "benchmark sweep; run manually with --ignored --nocapture"]
+fn bench_repetition_code_comparison() {
+    use pecos_eeg::dem_mapping::EegConfig;
+    use pecos_eeg::heisenberg::heisenberg_detection_probability_from_circuit;
+
+    let num_shots = 500_000;
+    let theta = 0.05;
+
+    eprintln!("\n=== Repetition code: EEG vs Heisenberg vs StateVec ===");
+    eprintln!("theta = {theta}, shots = {num_shots}");
+
+    for &d in &[3, 5] {
+        for &num_rounds in &[2, 3] {
+            let (gates, num_qubits, ancillas) = build_repetition_code(d, num_rounds);
+            let num_ancilla = ancillas.len();
+
+            // Measurement record layout: round 0 ancillas, round 1 ancillas, ..., data readout
+            // Round comparison detectors: meas[round*num_ancilla + i] XOR meas[(round+1)*num_ancilla + i]
+            let num_detectors = num_ancilla * (num_rounds - 1);
+
+            eprintln!(
+                "\n  d={d}, rounds={num_rounds}, qubits={num_qubits}, detectors={num_detectors}"
+            );
+
+            // --- EEG forward ---
+            let expanded = expand::expand_circuit(&gates);
+            let noise_model = NoiseModel::coherent_only(theta);
+            let noise_spec = UniformNoise::coherent_only(theta);
+            let result = analyze_expanded(&expanded.gates, &noise_model);
+
+            let mut dets = Vec::new();
+            for round in 0..(num_rounds - 1) {
+                for i in 0..num_ancilla {
+                    let m1 = round * num_ancilla + i;
+                    let m2 = (round + 1) * num_ancilla + i;
+                    let aux1 = expanded.measurement_qubit[m1];
+                    let aux2 = expanded.measurement_qubit[m2];
+                    let mut stab = Bm::default();
+                    stab.z_bits.set_bit(aux1);
+                    stab.z_bits.set_bit(aux2);
+                    dets.push(Detector {
+                        id: dets.len(),
+                        stabilizer: stab,
+                    });
+                }
+            }
+
+            let exp_pre: Vec<_> = {
+                let last = expanded
+                    .gates
+                    .iter()
+                    .rposition(|g| g.gate_type != GateType::MZ)
+                    .unwrap();
+                expanded.gates[..=last].to_vec()
+            };
+            let stab_group = StabilizerGroup::from_circuit(&exp_pre, expanded.num_qubits);
+
+            let entries = pecos_eeg::dem_mapping::build_dem_configured(
+                &result.generators,
+                &dets,
+                &[],
+                Some(&stab_group),
+                &EegConfig::default(),
+            );
+
+            let mut eeg_probs = vec![0.0; num_detectors];
+            for e in &entries {
+                for &det_id in &e.event.detectors {
+                    if det_id < num_detectors {
+                        eeg_probs[det_id] += e.probability;
+                    }
+                }
+            }
+
+            // --- Heisenberg backward ---
+            let mut heis_probs = vec![0.0; num_detectors];
+            for round in 0..(num_rounds - 1) {
+                for i in 0..num_ancilla {
+                    let det_idx = round * num_ancilla + i;
+                    let m1 = round * num_ancilla + i;
+                    let m2 = (round + 1) * num_ancilla + i;
+                    heis_probs[det_idx] = heisenberg_detection_probability_from_circuit(
+                        &gates,
+                        &[m1, m2],
+                        &noise_spec,
+                        num_qubits,
+                        1e-12,
+                    );
+                }
+            }
+
+            // --- StateVec simulation ---
+            let mut sv_counts = vec![0u64; num_detectors];
+            let mut sim = StateVec::new(num_qubits);
+
+            for _ in 0..num_shots {
+                // Initialize
+                let all_qubits: Vec<_> = (0..num_qubits).map(qid).collect();
+                sim.pz(&all_qubits);
+
+                let mut meas_outcomes = Vec::new();
+
+                for round in 0..num_rounds {
+                    // X-check: H(anc), CX(anc, data_i), CX(anc, data_{i+1}), H(anc)
+                    let anc_qubits: Vec<_> = ancillas.iter().map(|&a| qid(a)).collect();
+                    sim.h(&anc_qubits);
+
+                    for (i, &anc) in ancillas.iter().enumerate().take(num_ancilla) {
+                        sim.cx(&[(qid(anc), qid(i))]);
+                        sim.rz(Angle64::from_radians(theta), &[qid(anc)]);
+                        sim.rz(Angle64::from_radians(theta), &[qid(i)]);
+                    }
+                    for (i, &anc) in ancillas.iter().enumerate().take(num_ancilla) {
+                        sim.cx(&[(qid(anc), qid(i + 1))]);
+                        sim.rz(Angle64::from_radians(theta), &[qid(anc)]);
+                        sim.rz(Angle64::from_radians(theta), &[qid(i + 1)]);
+                    }
+
+                    sim.h(&anc_qubits);
+
+                    // Measure ancillas
+                    for &anc in ancillas.iter().take(num_ancilla) {
+                        let r = sim.mz(&[qid(anc)]);
+                        meas_outcomes.push(r[0].outcome);
+                    }
+
+                    // Reset (except last round)
+                    if round < num_rounds - 1 {
+                        sim.pz(&anc_qubits);
+                    }
+                }
+
+                // Count detector firings (round comparison)
+                for round in 0..(num_rounds - 1) {
+                    for i in 0..num_ancilla {
+                        let m1 = round * num_ancilla + i;
+                        let m2 = (round + 1) * num_ancilla + i;
+                        if meas_outcomes[m1] != meas_outcomes[m2] {
+                            sv_counts[round * num_ancilla + i] += 1;
+                        }
+                    }
+                }
+            }
+
+            // Print comparison
+            eprintln!(
+                "  {:>6} {:>10} {:>10} {:>10} {:>10} {:>10}",
+                "Det", "EEG", "Heisen", "StateVec", "SV_err", "H/SV"
+            );
+            for det_idx in 0..num_detectors {
+                let sv_rate = u64_to_f64(sv_counts[det_idx]) / f64::from(num_shots);
+                let sv_err = (sv_rate * (1.0 - sv_rate) / f64::from(num_shots)).sqrt();
+                let ratio = if sv_rate > 1e-10 {
+                    heis_probs[det_idx] / sv_rate
+                } else {
+                    f64::NAN
+                };
+                let round = det_idx / num_ancilla;
+                let anc = det_idx % num_ancilla;
+                eprintln!(
+                    "  R{round}A{anc} {:>10.6} {:>10.6} {:>10.6} {:>10.6} {:>10.4}",
+                    eeg_probs[det_idx], heis_probs[det_idx], sv_rate, sv_err, ratio
+                );
+            }
+        }
+    }
+}
+
+/// KEY DIAGNOSTIC: Compare original-circuit `StateVec`, expanded-circuit `StateVec`,
+/// and Heisenberg for the simplest failing case (weight-2, 2 rounds, 3 qubits).
+///
+/// If expanded SV matches original SV: expansion is correct, Heisenberg has a bug.
+/// If expanded SV differs: expansion is wrong.
+#[test]
+#[ignore = "benchmark sweep; run manually with --ignored --nocapture"]
+fn bench_expansion_equivalence() {
+    use pecos_eeg::heisenberg::heisenberg_detection_probability_from_circuit;
+
+    let num_shots = 1_000_000;
+    let theta = 0.05;
+
+    eprintln!("\n=== Expansion equivalence: 3 qubits, 2 rounds ===");
+
+    // Original circuit with mid-circuit measurement
+    let gates_orig = vec![
+        gate(GateType::PZ, &[0]),
+        gate(GateType::PZ, &[1]),
+        gate(GateType::PZ, &[2]),
+        gate(GateType::H, &[2]),
+        gate(GateType::CX, &[2, 0]),
+        gate(GateType::CX, &[2, 1]),
+        gate(GateType::H, &[2]),
+        gate(GateType::MZ, &[2]),
+        gate(GateType::PZ, &[2]),
+        gate(GateType::H, &[2]),
+        gate(GateType::CX, &[2, 0]),
+        gate(GateType::CX, &[2, 1]),
+        gate(GateType::H, &[2]),
+        gate(GateType::MZ, &[2]),
+    ];
+
+    // Expand the circuit
+    let expanded = expand::expand_circuit(&gates_orig);
+    eprintln!(
+        "Expanded: {} gates, {} qubits",
+        expanded.gates.len(),
+        expanded.num_qubits
+    );
+    eprintln!("Measurement map: {:?}", expanded.measurement_qubit);
+    for (i, g) in expanded.gates.iter().enumerate() {
+        let qs: Vec<usize> = g.qubits.iter().map(pecos_core::QubitId::index).collect();
+        eprintln!("  [{i:2}] {:?}({qs:?})", g.gate_type);
+    }
+
+    // --- Heisenberg on expanded circuit ---
+    let noise = UniformNoise::coherent_only(theta);
+    let h_p = heisenberg_detection_probability_from_circuit(&gates_orig, &[0, 1], &noise, 3, 0.0);
+
+    // --- StateVec on ORIGINAL circuit (with mid-circuit measurements) ---
+    let mut orig_det = 0u64;
+    {
+        let mut sim = StateVec::new(3);
+        for _ in 0..num_shots {
+            sim.pz(&[qid(0), qid(1), qid(2)]);
+            let mut outs = [false; 2];
+            for (r, out) in outs.iter_mut().enumerate() {
+                sim.h(&[qid(2)]);
+                sim.cx(&[(qid(2), qid(0))]);
+                sim.rz(Angle64::from_radians(theta), &[qid(2)]);
+                sim.rz(Angle64::from_radians(theta), &[qid(0)]);
+                sim.cx(&[(qid(2), qid(1))]);
+                sim.rz(Angle64::from_radians(theta), &[qid(1)]);
+                sim.rz(Angle64::from_radians(theta), &[qid(2)]);
+                sim.h(&[qid(2)]);
+                *out = sim.mz(&[qid(2)])[0].outcome;
+                if r == 0 {
+                    sim.pz(&[qid(2)]);
+                }
+            }
+            if outs[0] != outs[1] {
+                orig_det += 1;
+            }
+        }
+    }
+    let sv_orig = u64_to_f64(orig_det) / f64::from(num_shots);
+
+    // --- StateVec on EXPANDED circuit (no mid-circuit measurements) ---
+    let mut exp_det = 0u64;
+    {
+        let num_exp_q = expanded.num_qubits;
+        let mut sim = StateVec::new(num_exp_q);
+        for _ in 0..num_shots {
+            // Execute the expanded circuit gate by gate
+            let all_q: Vec<_> = (0..num_exp_q).map(qid).collect();
+            sim.pz(&all_q);
+
+            for (i, g) in expanded.gates.iter().enumerate() {
+                let qs: Vec<usize> = g.qubits.iter().map(pecos_core::QubitId::index).collect();
+
+                // Skip expansion gates for noise (same logic as Heisenberg)
+                let is_exp_gate = {
+                    let is_qalloc = g.gate_type == pecos_core::gate_type::GateType::QAlloc;
+                    let is_exp_cx = i > 0
+                        && g.gate_type == pecos_core::gate_type::GateType::CX
+                        && expanded.gates[i - 1].gate_type
+                            == pecos_core::gate_type::GateType::QAlloc
+                        && expanded.gates[i - 1].qubits[0].index()
+                            == qs.get(1).copied().unwrap_or(999);
+                    let is_exp_pz = i > 1
+                        && g.gate_type == pecos_core::gate_type::GateType::PZ
+                        && expanded.gates[i - 1].gate_type == pecos_core::gate_type::GateType::CX
+                        && expanded.gates[i - 2].gate_type
+                            == pecos_core::gate_type::GateType::QAlloc;
+                    is_qalloc || is_exp_cx || is_exp_pz
+                };
+
+                match g.gate_type {
+                    pecos_core::gate_type::GateType::PZ
+                    | pecos_core::gate_type::GateType::QAlloc => {
+                        for &q in &qs {
+                            sim.pz(&[qid(q)]);
+                        }
+                    }
+                    pecos_core::gate_type::GateType::H => {
+                        for &q in &qs {
+                            sim.h(&[qid(q)]);
+                        }
+                    }
+                    pecos_core::gate_type::GateType::CX if qs.len() >= 2 => {
+                        sim.cx(&[(qid(qs[0]), qid(qs[1]))]);
+                    }
+                    _ => {}
+                }
+
+                // Add noise after non-expansion CX gates
+                if !is_exp_gate
+                    && (g.gate_type == pecos_core::gate_type::GateType::CX)
+                    && qs.len() >= 2
+                {
+                    sim.rz(Angle64::from_radians(theta), &[qid(qs[0])]);
+                    sim.rz(Angle64::from_radians(theta), &[qid(qs[1])]);
+                }
+            }
+
+            // Measure the two aux qubits
+            let aux0 = expanded.measurement_qubit[0];
+            let aux1 = expanded.measurement_qubit[1];
+            let r0 = sim.mz(&[qid(aux0)])[0].outcome;
+            let r1 = sim.mz(&[qid(aux1)])[0].outcome;
+            if r0 != r1 {
+                exp_det += 1;
+            }
+        }
+    }
+    let sv_exp = u64_to_f64(exp_det) / f64::from(num_shots);
+
+    // Exact analytical
+    let exact = (2.0 - (6.0 * theta).cos() - (2.0 * theta).cos()) / 4.0;
+
+    let se_orig = (sv_orig * (1.0 - sv_orig) / f64::from(num_shots)).sqrt();
+    let se_exp = (sv_exp * (1.0 - sv_exp) / f64::from(num_shots)).sqrt();
+
+    eprintln!("\nResults:");
+    eprintln!("  Exact analytical:    {exact:.6}");
+    eprintln!("  SV original circuit: {sv_orig:.6} +/- {se_orig:.6}");
+    eprintln!("  SV expanded circuit: {sv_exp:.6} +/- {se_exp:.6}");
+    eprintln!("  Heisenberg:          {h_p:.6}");
+    eprintln!("  H/Exact = {:.4}", h_p / exact);
+    eprintln!("  SVexp/SVorig = {:.4}", sv_exp / sv_orig);
+}
+
+/// Ground truth: compute the backward Heisenberg via DIRECT MATRIX MULTIPLICATION
+/// on the expanded circuit. This bypasses the Pauli-tracking backward walk entirely.
+///
+/// The detection probability is:
+///   p = (1 - <0...0| `O_backward` |0...0>) / 2
+/// where `O_backward` = `E_1`† ... `E_n†(D)`
+///
+/// We compute `O_backward` as a 2^n × 2^n matrix by multiplying the adjoint
+/// of each gate/noise channel, then evaluate the diagonal element.
+#[test]
+#[ignore = "benchmark sweep; run manually with --ignored --nocapture"]
+fn bench_matrix_heisenberg() {
+    use pecos_eeg::heisenberg::heisenberg_detection_probability_from_circuit;
+
+    let theta = 0.05;
+    let n = 5; // qubits: q0,q1 data, q2 ancilla, q3 aux R1, q4 aux R2
+    let dim = 1 << n; // 32
+
+    // The expanded circuit gates (from bench_expansion_equivalence)
+    let gates_orig = vec![
+        gate(GateType::PZ, &[0]),
+        gate(GateType::PZ, &[1]),
+        gate(GateType::PZ, &[2]),
+        gate(GateType::H, &[2]),
+        gate(GateType::CX, &[2, 0]),
+        gate(GateType::CX, &[2, 1]),
+        gate(GateType::H, &[2]),
+        gate(GateType::MZ, &[2]),
+        gate(GateType::PZ, &[2]),
+        gate(GateType::H, &[2]),
+        gate(GateType::CX, &[2, 0]),
+        gate(GateType::CX, &[2, 1]),
+        gate(GateType::H, &[2]),
+        gate(GateType::MZ, &[2]),
+    ];
+    let expanded = expand::expand_circuit(&gates_orig);
+
+    // Build the detector matrix: Z_3 * Z_4
+    // Z_q has eigenvalue +1 for |0> and -1 for |1>
+    let mut obs = vec![0.0f64; dim * dim]; // real part (obs is Hermitian diagonal for Pauli Z)
+    for i in 0..dim {
+        let bit3 = (i >> 3) & 1;
+        let bit4 = (i >> 4) & 1;
+        let z3 = if bit3 == 0 { 1.0 } else { -1.0 };
+        let z4 = if bit4 == 0 { 1.0 } else { -1.0 };
+        obs[i * dim + i] = z3 * z4;
+    }
+
+    // Now apply the adjoint of each gate/noise channel in REVERSE order.
+    // For unitary U: O → U† O U
+    // For PZ_q (reset): O → <0_q| O |0_q> tensored with I_q (extract q=0 block)
+    // For noise RZ(θ): O → RZ†(θ) O RZ(θ) (unitary conjugation)
+    // For MZ_q: O → project to Z eigenstates (diagonal on q)
+
+    // Helper: build a gate matrix for the full n-qubit space
+    // We work with real+imaginary pairs: obs_re[i*dim+j], obs_im[i*dim+j]
+    let mut obs_re = vec![0.0f64; dim * dim];
+    let mut obs_im = vec![0.0f64; dim * dim];
+    for i in 0..dim {
+        let bit3 = (i >> 3) & 1;
+        let bit4 = (i >> 4) & 1;
+        obs_re[i * dim + i] = if bit3 == bit4 { 1.0 } else { -1.0 };
+    }
+
+    // Process gates in reverse order
+    let exp_gates_set = {
+        let mut s = std::collections::HashSet::new();
+        // Detect expansion gates (same logic as heisenberg.rs)
+        for i in 1..expanded.gates.len() {
+            if expanded.gates[i].gate_type == pecos_core::gate_type::GateType::QAlloc {
+                s.insert(i);
+            }
+            if expanded.gates[i].gate_type == pecos_core::gate_type::GateType::CX
+                && expanded.gates[i - 1].gate_type == pecos_core::gate_type::GateType::QAlloc
+            {
+                let aq = expanded.gates[i - 1].qubits[0].index();
+                if expanded.gates[i].qubits.len() >= 2 && expanded.gates[i].qubits[1].index() == aq
+                {
+                    s.insert(i);
+                    if i + 1 < expanded.gates.len()
+                        && expanded.gates[i + 1].gate_type == pecos_core::gate_type::GateType::PZ
+                        && expanded.gates[i + 1].qubits[0].index()
+                            == expanded.gates[i].qubits[0].index()
+                    {
+                        s.insert(i + 1);
+                    }
+                }
+            }
+        }
+        s
+    };
+
+    for idx in (0..expanded.gates.len()).rev() {
+        let g = &expanded.gates[idx];
+        let qs: Vec<usize> = g.qubits.iter().map(pecos_core::QubitId::index).collect();
+
+        // Apply noise adjoint (if not expansion gate)
+        if !exp_gates_set.contains(&idx) && g.gate_type == pecos_core::gate_type::GateType::CX {
+            // idle_rz on both qubits
+            for &q in &qs {
+                apply_rz_adjoint(&mut obs_re, &mut obs_im, q, theta, n);
+            }
+        }
+
+        // Apply gate adjoint
+        match g.gate_type {
+            pecos_core::gate_type::GateType::PZ | pecos_core::gate_type::GateType::QAlloc => {
+                // PZ†(O) = <0_q| O |0_q> ⊗ I_q
+                // This zeros all matrix elements where q is in state |1>
+                // and copies q=0 block to the full matrix
+                apply_pz_adjoint(&mut obs_re, &mut obs_im, qs[0], n);
+            }
+            pecos_core::gate_type::GateType::MZ => {
+                // MZ†(O) = Σ_m |m><m| O |m><m| (decohere in Z basis)
+                apply_mz_adjoint(&mut obs_re, &mut obs_im, qs[0], n);
+            }
+            pecos_core::gate_type::GateType::H => {
+                apply_h_adjoint(&mut obs_re, &mut obs_im, qs[0], n);
+            }
+            pecos_core::gate_type::GateType::CX => {
+                apply_cx_adjoint(&mut obs_re, &mut obs_im, qs[0], qs[1], n);
+            }
+            _ => {}
+        }
+    }
+
+    // Evaluate <0...0| O_backward |0...0>
+    let expectation = obs_re[0]; // |0...0> is index 0
+    let matrix_detection = 0.5 * (1.0 - expectation);
+
+    // Step-by-step matrix trace: print <0|O|0> after each gate
+    // Re-run with printing
+    {
+        let mut tr_re = vec![0.0f64; dim * dim];
+        let mut tr_im = vec![0.0f64; dim * dim];
+        for i in 0..dim {
+            let bit3 = (i >> 3) & 1;
+            let bit4 = (i >> 4) & 1;
+            tr_re[i * dim + i] = if bit3 == bit4 { 1.0 } else { -1.0 };
+        }
+
+        eprintln!("\n  Step-by-step <0|O|0> comparison (matrix vs walk):");
+        eprintln!(
+            "  {:>4} {:>20} {:>12}",
+            "Gate", "Description", "Matrix<0|O|0>"
+        );
+
+        for idx in (0..expanded.gates.len()).rev() {
+            let g = &expanded.gates[idx];
+            let qs: Vec<usize> = g.qubits.iter().map(pecos_core::QubitId::index).collect();
+            let is_exp = exp_gates_set.contains(&idx);
+
+            if !is_exp && g.gate_type == pecos_core::gate_type::GateType::CX && qs.len() >= 2 {
+                for &q in &qs {
+                    apply_rz_adjoint(&mut tr_re, &mut tr_im, q, theta, n);
+                }
+            }
+
+            match g.gate_type {
+                pecos_core::gate_type::GateType::PZ | pecos_core::gate_type::GateType::QAlloc => {
+                    apply_pz_adjoint(&mut tr_re, &mut tr_im, qs[0], n);
+                }
+                pecos_core::gate_type::GateType::MZ => {
+                    apply_mz_adjoint(&mut tr_re, &mut tr_im, qs[0], n);
+                }
+                pecos_core::gate_type::GateType::H => {
+                    apply_h_adjoint(&mut tr_re, &mut tr_im, qs[0], n);
+                }
+                pecos_core::gate_type::GateType::CX => {
+                    apply_cx_adjoint(&mut tr_re, &mut tr_im, qs[0], qs[1], n);
+                }
+                _ => {}
+            }
+
+            let e = tr_re[0];
+            let tag = if is_exp { " [EXP]" } else { "" };
+            eprintln!("  [{idx:>2}] {:?}({qs:?}){tag}: {e:.10}", g.gate_type);
+        }
+    }
+
+    // Heisenberg backward walk
+    let noise = UniformNoise::coherent_only(theta);
+    let h_p = heisenberg_detection_probability_from_circuit(&gates_orig, &[0, 1], &noise, 3, 0.0);
+
+    // Exact analytical
+    let exact = (2.0 - (6.0 * theta).cos() - (2.0 * theta).cos()) / 4.0;
+
+    eprintln!("\n=== Matrix Heisenberg ground truth ===");
+    eprintln!("  Exact analytical:     {exact:.10}");
+    eprintln!("  Matrix Heisenberg:    {matrix_detection:.10}");
+    eprintln!("  Backward walk:        {h_p:.10}");
+    eprintln!("  Matrix/Exact:         {:.6}", matrix_detection / exact);
+    eprintln!("  Walk/Matrix:          {:.6}", h_p / matrix_detection);
+}
+
+// Matrix helpers for n-qubit system
+fn apply_rz_adjoint(re: &mut [f64], im: &mut [f64], q: usize, theta: f64, n: usize) {
+    let dim = 1 << n;
+    // For each matrix element O[i,j]:
+    // New O[i,j] = e^{i(b_i - b_j)θ/2} · O[i,j]
+    // where b_i = bit q of i (0 → phase -θ/2, 1 → phase +θ/2)
+    for i in 0..dim {
+        let bi = bit_to_f64((i >> q) & 1); // 0 or 1
+        for j in 0..dim {
+            let bj = bit_to_f64((j >> q) & 1);
+            let phase = (bi - bj) * theta; // phase angle
+            if phase.abs() < 1e-20 {
+                continue;
+            }
+            let cp = phase.cos();
+            let sp = phase.sin();
+            let idx = i * dim + j;
+            let r = re[idx];
+            let m = im[idx];
+            re[idx] = cp * r - sp * m;
+            im[idx] = sp * r + cp * m;
+        }
+    }
+}
+
+fn apply_pz_adjoint(re: &mut [f64], im: &mut [f64], q: usize, n: usize) {
+    // PZ†(O) = Σ_m |m⟩⟨0| O |0⟩⟨m| where K_m = |0⟩⟨m|
+    // Matrix elements: [PZ†(O)]_{ij} = δ(i_q, j_q) · O_{(i with q=0), (j with q=0)}
+    // Off-diagonal elements (where qubit q differs) are ZERO.
+    let dim = 1 << n;
+    let mask = 1 << q;
+    for i in 0..dim {
+        let iq = (i >> q) & 1;
+        for j in 0..dim {
+            let jq = (j >> q) & 1;
+            let idx = i * dim + j;
+            if iq == jq {
+                let i0 = i & !mask;
+                let j0 = j & !mask;
+                let idx0 = i0 * dim + j0;
+                re[idx] = re[idx0];
+                im[idx] = im[idx0];
+            } else {
+                re[idx] = 0.0;
+                im[idx] = 0.0;
+            }
+        }
+    }
+}
+
+fn apply_mz_adjoint(re: &mut [f64], im: &mut [f64], q: usize, n: usize) {
+    let dim = 1 << n;
+    for i in 0..dim {
+        let bi = (i >> q) & 1;
+        for j in 0..dim {
+            let bj = (j >> q) & 1;
+            if bi != bj {
+                let idx = i * dim + j;
+                re[idx] = 0.0;
+                im[idx] = 0.0;
+            }
+        }
+    }
+}
+
+fn apply_h_adjoint(re: &mut [f64], im: &mut [f64], q: usize, n: usize) {
+    // H† O H = H O H (H is self-adjoint)
+    // H|0> = (|0>+|1>)/√2, H|1> = (|0>-|1>)/√2
+    let dim = 1 << n;
+    let mask = 1 << q;
+    // For each pair (i, i^mask), apply the 2x2 Hadamard conjugation
+    // O' = H ⊗ I · O · H ⊗ I
+    // This swaps/combines rows and columns corresponding to bit q
+    let mut new_re = vec![0.0; dim * dim];
+    let mut new_im = vec![0.0; dim * dim];
+    for i in 0..dim {
+        for j in 0..dim {
+            // new O[i,j] = Σ_{a,b} H[i_q,a] O[i_with_a, j_with_b] H[b, j_q]
+            let i0 = i & !mask;
+            let i1 = i | mask;
+            let j0 = j & !mask;
+            let j1 = j | mask;
+            let iq = (i >> q) & 1;
+            let jq = (j >> q) & 1;
+            // H[0,0]=1/√2, H[0,1]=1/√2, H[1,0]=1/√2, H[1,1]=-1/√2
+            // H[x,y] = (1/√2)(-1)^{xy}
+            // H[iq,a]*H[b,jq] = (1/2)(-1)^{iq*a+b*jq}
+            let mut sum_r = 0.0;
+            let mut sum_i = 0.0;
+            for a in 0..2usize {
+                for b in 0..2usize {
+                    let ia = if a == 0 { i0 } else { i1 };
+                    let jb = if b == 0 { j0 } else { j1 };
+                    let idx = ia * dim + jb;
+                    let sign = if (iq * a + b * jq).is_multiple_of(2) {
+                        1.0
+                    } else {
+                        -1.0
+                    };
+                    let c = 0.5 * sign;
+                    sum_r += c * re[idx];
+                    sum_i += c * im[idx];
+                }
+            }
+            new_re[i * dim + j] = sum_r;
+            new_im[i * dim + j] = sum_i;
+        }
+    }
+    re.copy_from_slice(&new_re);
+    im.copy_from_slice(&new_im);
+}
+
+fn apply_cx_adjoint(re: &mut [f64], im: &mut [f64], control: usize, target: usize, n: usize) {
+    // CX† O CX = CX O CX (CX is self-adjoint)
+    // CX flips target when control=1: CX|c,t> = |c, c⊕t>
+    let dim = 1 << n;
+    let cmask = 1 << control;
+    let tmask = 1 << target;
+    // CX permutation: state index i maps to i ^ (tmask if control bit set)
+    let cx_perm = |i: usize| -> usize { if (i & cmask) != 0 { i ^ tmask } else { i } };
+    // O' = CX · O · CX: new O[i,j] = O[CX(i), CX(j)]
+    let mut new_re = vec![0.0; dim * dim];
+    let mut new_im = vec![0.0; dim * dim];
+    for i in 0..dim {
+        let ci = cx_perm(i);
+        for j in 0..dim {
+            let cj = cx_perm(j);
+            new_re[i * dim + j] = re[ci * dim + cj];
+            new_im[i * dim + j] = im[ci * dim + cj];
+        }
+    }
+    re.copy_from_slice(&new_re);
+    im.copy_from_slice(&new_im);
+}
+
+/// Per-noise-source attribution: which noise sources does the backward walk miss?
+///
+/// Enable one noise source at a time and compare matrix vs backward walk.
+#[test]
+#[ignore = "benchmark sweep; run manually with --ignored --nocapture"]
+fn bench_per_noise_attribution() {
+    use pecos_eeg::heisenberg::heisenberg_detection_probability_from_circuit;
+
+    let theta = 0.05;
+    let n = 5;
+    let dim = 1 << n;
+
+    let gates_orig = vec![
+        gate(GateType::PZ, &[0]),
+        gate(GateType::PZ, &[1]),
+        gate(GateType::PZ, &[2]),
+        gate(GateType::H, &[2]),
+        gate(GateType::CX, &[2, 0]),
+        gate(GateType::CX, &[2, 1]),
+        gate(GateType::H, &[2]),
+        gate(GateType::MZ, &[2]),
+        gate(GateType::PZ, &[2]),
+        gate(GateType::H, &[2]),
+        gate(GateType::CX, &[2, 0]),
+        gate(GateType::CX, &[2, 1]),
+        gate(GateType::H, &[2]),
+        gate(GateType::MZ, &[2]),
+    ];
+    let expanded = expand::expand_circuit(&gates_orig);
+
+    // Noise source locations in expanded circuit:
+    // Gate 4: CX(2,0) R1 → noise on q2 and q0
+    // Gate 5: CX(2,1) R1 → noise on q2 and q1
+    // Gate 12: CX(2,0) R2 → noise on q2 and q0
+    // Gate 13: CX(2,1) R2 → noise on q2 and q1
+    let noise_sources = [
+        (4, 2, "R1 CX(2,0) Z2"),
+        (4, 0, "R1 CX(2,0) Z0"),
+        (5, 2, "R1 CX(2,1) Z2"),
+        (5, 1, "R1 CX(2,1) Z1"),
+        (12, 2, "R2 CX(2,0) Z2"),
+        (12, 0, "R2 CX(2,0) Z0"),
+        (13, 2, "R2 CX(2,1) Z2"),
+        (13, 1, "R2 CX(2,1) Z1"),
+    ];
+
+    eprintln!("\n=== Per-noise-source attribution ===");
+    eprintln!(
+        "{:>25} {:>12} {:>12} {:>8}",
+        "Source", "Matrix", "Walk", "Ratio"
+    );
+
+    for &(gate_idx, qubit, label) in &noise_sources {
+        // Matrix computation with only this one noise source
+        let mut obs_re = vec![0.0f64; dim * dim];
+        let mut obs_im = vec![0.0f64; dim * dim];
+        for i in 0..dim {
+            let bit3 = (i >> 3) & 1;
+            let bit4 = (i >> 4) & 1;
+            obs_re[i * dim + i] = if bit3 == bit4 { 1.0 } else { -1.0 };
+        }
+
+        // Process gates in reverse, only applying noise for the specified source
+        for idx in (0..expanded.gates.len()).rev() {
+            let g = &expanded.gates[idx];
+            let qs: Vec<usize> = g.qubits.iter().map(pecos_core::QubitId::index).collect();
+
+            // Noise: only the specified source
+            if idx == gate_idx {
+                apply_rz_adjoint(&mut obs_re, &mut obs_im, qubit, theta, n);
+            }
+
+            // Gate adjoint (always)
+            match g.gate_type {
+                pecos_core::gate_type::GateType::PZ | pecos_core::gate_type::GateType::QAlloc => {
+                    apply_pz_adjoint(&mut obs_re, &mut obs_im, qs[0], n);
+                }
+                pecos_core::gate_type::GateType::MZ => {
+                    apply_mz_adjoint(&mut obs_re, &mut obs_im, qs[0], n);
+                }
+                pecos_core::gate_type::GateType::H => {
+                    apply_h_adjoint(&mut obs_re, &mut obs_im, qs[0], n);
+                }
+                pecos_core::gate_type::GateType::CX => {
+                    apply_cx_adjoint(&mut obs_re, &mut obs_im, qs[0], qs[1], n);
+                }
+                _ => {}
+            }
+        }
+
+        let matrix_p = 0.5 * (1.0 - obs_re[0]);
+
+        // Backward walk: use a custom noise spec that only injects at the specified source
+        // (We can't easily do this with the public API, so just report the matrix result.)
+        eprintln!("{label:>25} {matrix_p:>12.8} {:>12} {:>8}", "-", "-");
+    }
+
+    // Also show all-noise results
+    let mut obs_re = vec![0.0f64; dim * dim];
+    let mut obs_im = vec![0.0f64; dim * dim];
+    for i in 0..dim {
+        let bit3 = (i >> 3) & 1;
+        let bit4 = (i >> 4) & 1;
+        obs_re[i * dim + i] = if bit3 == bit4 { 1.0 } else { -1.0 };
+    }
+    for idx in (0..expanded.gates.len()).rev() {
+        let g = &expanded.gates[idx];
+        let qs: Vec<usize> = g.qubits.iter().map(pecos_core::QubitId::index).collect();
+        if g.gate_type == pecos_core::gate_type::GateType::CX && qs.len() >= 2 {
+            // Check if expansion gate
+            let is_exp = idx > 0
+                && expanded.gates[idx - 1].gate_type == pecos_core::gate_type::GateType::QAlloc
+                && expanded.gates[idx - 1].qubits[0].index() == qs[1];
+            if !is_exp {
+                apply_rz_adjoint(&mut obs_re, &mut obs_im, qs[0], theta, n);
+                apply_rz_adjoint(&mut obs_re, &mut obs_im, qs[1], theta, n);
+            }
+        }
+        match g.gate_type {
+            pecos_core::gate_type::GateType::PZ | pecos_core::gate_type::GateType::QAlloc => {
+                apply_pz_adjoint(&mut obs_re, &mut obs_im, qs[0], n);
+            }
+            pecos_core::gate_type::GateType::MZ => {
+                apply_mz_adjoint(&mut obs_re, &mut obs_im, qs[0], n);
+            }
+            pecos_core::gate_type::GateType::H => {
+                apply_h_adjoint(&mut obs_re, &mut obs_im, qs[0], n);
+            }
+            pecos_core::gate_type::GateType::CX => {
+                apply_cx_adjoint(&mut obs_re, &mut obs_im, qs[0], qs[1], n);
+            }
+            _ => {}
+        }
+    }
+    let matrix_all = 0.5 * (1.0 - obs_re[0]);
+    let noise = UniformNoise::coherent_only(theta);
+    let walk_all =
+        heisenberg_detection_probability_from_circuit(&gates_orig, &[0, 1], &noise, 3, 0.0);
+    eprintln!(
+        "{:>25} {:>12.8} {:>12.8} {:>8.4}",
+        "ALL",
+        matrix_all,
+        walk_all,
+        walk_all / matrix_all
+    );
+}
+
+/// Isolate weight-2 vs weight-4 X-check, single vs multi-round.
+#[test]
+#[ignore = "benchmark sweep; run manually with --ignored --nocapture"]
+fn bench_weight_isolation() {
+    use pecos_eeg::heisenberg::heisenberg_detection_probability_from_circuit;
+
+    let num_shots = 500_000;
+    let theta = 0.05;
+
+    eprintln!("\n=== Weight isolation: single ancilla, no shared qubits ===");
+    eprintln!("theta = {theta}, shots = {num_shots}\n");
+
+    // ---- Weight-2, 1 round: H(2), CX(2,0), CX(2,1), H(2), MZ(2) ----
+    {
+        let gates = vec![
+            gate(GateType::PZ, &[0]),
+            gate(GateType::PZ, &[1]),
+            gate(GateType::PZ, &[2]),
+            gate(GateType::H, &[2]),
+            gate(GateType::CX, &[2, 0]),
+            gate(GateType::CX, &[2, 1]),
+            gate(GateType::H, &[2]),
+            gate(GateType::MZ, &[2]),
+        ];
+        let noise = UniformNoise::coherent_only(theta);
+        let h_p = heisenberg_detection_probability_from_circuit(&gates, &[0], &noise, 3, 0.0);
+
+        let mut det = 0u64;
+        let mut sim = StateVec::new(3);
+        for _ in 0..num_shots {
+            sim.pz(&[qid(0), qid(1), qid(2)]);
+            sim.h(&[qid(2)]);
+            sim.cx(&[(qid(2), qid(0))]);
+            sim.rz(Angle64::from_radians(theta), &[qid(2)]);
+            sim.rz(Angle64::from_radians(theta), &[qid(0)]);
+            sim.cx(&[(qid(2), qid(1))]);
+            sim.rz(Angle64::from_radians(theta), &[qid(1)]);
+            sim.rz(Angle64::from_radians(theta), &[qid(2)]);
+            sim.h(&[qid(2)]);
+            if sim.mz(&[qid(2)])[0].outcome {
+                det += 1;
+            }
+        }
+        let sv = u64_to_f64(det) / f64::from(num_shots);
+        let se = (sv * (1.0 - sv) / f64::from(num_shots)).sqrt();
+        eprintln!(
+            "Wt-2 1rnd:  H={h_p:.6}  SV={sv:.6}+/-{se:.6}  H/SV={:.4}",
+            if sv > 1e-10 { h_p / sv } else { f64::NAN }
+        );
+    }
+
+    // ---- Weight-2, 2 rounds: round comparison ----
+    {
+        let gates = vec![
+            gate(GateType::PZ, &[0]),
+            gate(GateType::PZ, &[1]),
+            gate(GateType::PZ, &[2]),
+            gate(GateType::H, &[2]),
+            gate(GateType::CX, &[2, 0]),
+            gate(GateType::CX, &[2, 1]),
+            gate(GateType::H, &[2]),
+            gate(GateType::MZ, &[2]),
+            gate(GateType::PZ, &[2]),
+            gate(GateType::H, &[2]),
+            gate(GateType::CX, &[2, 0]),
+            gate(GateType::CX, &[2, 1]),
+            gate(GateType::H, &[2]),
+            gate(GateType::MZ, &[2]),
+        ];
+        let noise = UniformNoise::coherent_only(theta);
+        let h_p = heisenberg_detection_probability_from_circuit(&gates, &[0, 1], &noise, 3, 0.0);
+
+        let mut det = 0u64;
+        let mut sim = StateVec::new(3);
+        for _ in 0..num_shots {
+            sim.pz(&[qid(0), qid(1), qid(2)]);
+            let mut outs = [false; 2];
+            for (r, out) in outs.iter_mut().enumerate() {
+                sim.h(&[qid(2)]);
+                sim.cx(&[(qid(2), qid(0))]);
+                sim.rz(Angle64::from_radians(theta), &[qid(2)]);
+                sim.rz(Angle64::from_radians(theta), &[qid(0)]);
+                sim.cx(&[(qid(2), qid(1))]);
+                sim.rz(Angle64::from_radians(theta), &[qid(1)]);
+                sim.rz(Angle64::from_radians(theta), &[qid(2)]);
+                sim.h(&[qid(2)]);
+                *out = sim.mz(&[qid(2)])[0].outcome;
+                if r == 0 {
+                    sim.pz(&[qid(2)]);
+                }
+            }
+            if outs[0] != outs[1] {
+                det += 1;
+            }
+        }
+        let sv = u64_to_f64(det) / f64::from(num_shots);
+        let se = (sv * (1.0 - sv) / f64::from(num_shots)).sqrt();
+        eprintln!(
+            "Wt-2 2rnd:  H={h_p:.6}  SV={sv:.6}+/-{se:.6}  H/SV={:.4}",
+            if sv > 1e-10 { h_p / sv } else { f64::NAN }
+        );
+    }
+
+    // ---- Weight-4, 1 round ----
+    {
+        let gates = vec![
+            gate(GateType::PZ, &[0]),
+            gate(GateType::PZ, &[1]),
+            gate(GateType::PZ, &[2]),
+            gate(GateType::PZ, &[3]),
+            gate(GateType::PZ, &[4]),
+            gate(GateType::H, &[4]),
+            gate(GateType::CX, &[4, 0]),
+            gate(GateType::CX, &[4, 1]),
+            gate(GateType::CX, &[4, 2]),
+            gate(GateType::CX, &[4, 3]),
+            gate(GateType::H, &[4]),
+            gate(GateType::MZ, &[4]),
+        ];
+        let noise = UniformNoise::coherent_only(theta);
+        let h_p = heisenberg_detection_probability_from_circuit(&gates, &[0], &noise, 5, 0.0);
+
+        let mut det = 0u64;
+        let mut sim = StateVec::new(5);
+        for _ in 0..num_shots {
+            sim.pz(&[qid(0), qid(1), qid(2), qid(3), qid(4)]);
+            sim.h(&[qid(4)]);
+            for &d in &[0usize, 1, 2, 3] {
+                sim.cx(&[(qid(4), qid(d))]);
+                sim.rz(Angle64::from_radians(theta), &[qid(4)]);
+                sim.rz(Angle64::from_radians(theta), &[qid(d)]);
+            }
+            sim.h(&[qid(4)]);
+            if sim.mz(&[qid(4)])[0].outcome {
+                det += 1;
+            }
+        }
+        let sv = u64_to_f64(det) / f64::from(num_shots);
+        let se = (sv * (1.0 - sv) / f64::from(num_shots)).sqrt();
+        eprintln!(
+            "Wt-4 1rnd:  H={h_p:.6}  SV={sv:.6}+/-{se:.6}  H/SV={:.4}",
+            if sv > 1e-10 { h_p / sv } else { f64::NAN }
+        );
+    }
+
+    // ---- Weight-4, 2 rounds ----
+    {
+        let gates = vec![
+            gate(GateType::PZ, &[0]),
+            gate(GateType::PZ, &[1]),
+            gate(GateType::PZ, &[2]),
+            gate(GateType::PZ, &[3]),
+            gate(GateType::PZ, &[4]),
+            gate(GateType::H, &[4]),
+            gate(GateType::CX, &[4, 0]),
+            gate(GateType::CX, &[4, 1]),
+            gate(GateType::CX, &[4, 2]),
+            gate(GateType::CX, &[4, 3]),
+            gate(GateType::H, &[4]),
+            gate(GateType::MZ, &[4]),
+            gate(GateType::PZ, &[4]),
+            gate(GateType::H, &[4]),
+            gate(GateType::CX, &[4, 0]),
+            gate(GateType::CX, &[4, 1]),
+            gate(GateType::CX, &[4, 2]),
+            gate(GateType::CX, &[4, 3]),
+            gate(GateType::H, &[4]),
+            gate(GateType::MZ, &[4]),
+        ];
+        let noise = UniformNoise::coherent_only(theta);
+        let h_p = heisenberg_detection_probability_from_circuit(&gates, &[0, 1], &noise, 5, 0.0);
+
+        let mut det = 0u64;
+        let mut sim = StateVec::new(5);
+        for _ in 0..num_shots {
+            sim.pz(&[qid(0), qid(1), qid(2), qid(3), qid(4)]);
+            let mut outs = [false; 2];
+            for (r, out) in outs.iter_mut().enumerate() {
+                sim.h(&[qid(4)]);
+                for &d in &[0usize, 1, 2, 3] {
+                    sim.cx(&[(qid(4), qid(d))]);
+                    sim.rz(Angle64::from_radians(theta), &[qid(4)]);
+                    sim.rz(Angle64::from_radians(theta), &[qid(d)]);
+                }
+                sim.h(&[qid(4)]);
+                *out = sim.mz(&[qid(4)])[0].outcome;
+                if r == 0 {
+                    sim.pz(&[qid(4)]);
+                }
+            }
+            if outs[0] != outs[1] {
+                det += 1;
+            }
+        }
+        let sv = u64_to_f64(det) / f64::from(num_shots);
+        let se = (sv * (1.0 - sv) / f64::from(num_shots)).sqrt();
+        eprintln!(
+            "Wt-4 2rnd:  H={h_p:.6}  SV={sv:.6}+/-{se:.6}  H/SV={:.4}",
+            if sv > 1e-10 { h_p / sv } else { f64::NAN }
+        );
+    }
+
+    eprintln!();
+    // ---- 2 weight-2 ancillas sharing a data qubit, 2 rounds ----
+    {
+        let gates = vec![
+            gate(GateType::PZ, &[0]),
+            gate(GateType::PZ, &[1]),
+            gate(GateType::PZ, &[2]),
+            gate(GateType::PZ, &[3]),
+            gate(GateType::PZ, &[4]),
+            // Round 1
+            gate(GateType::H, &[3]),
+            gate(GateType::H, &[4]),
+            gate(GateType::CX, &[3, 0]),
+            gate(GateType::CX, &[4, 1]),
+            gate(GateType::CX, &[3, 1]),
+            gate(GateType::CX, &[4, 2]),
+            gate(GateType::H, &[3]),
+            gate(GateType::H, &[4]),
+            gate(GateType::MZ, &[3]),
+            gate(GateType::MZ, &[4]),
+            gate(GateType::PZ, &[3]),
+            gate(GateType::PZ, &[4]),
+            // Round 2
+            gate(GateType::H, &[3]),
+            gate(GateType::H, &[4]),
+            gate(GateType::CX, &[3, 0]),
+            gate(GateType::CX, &[4, 1]),
+            gate(GateType::CX, &[3, 1]),
+            gate(GateType::CX, &[4, 2]),
+            gate(GateType::H, &[3]),
+            gate(GateType::H, &[4]),
+            gate(GateType::MZ, &[3]),
+            gate(GateType::MZ, &[4]),
+        ];
+        let noise = UniformNoise::coherent_only(theta);
+        let h_a0 = heisenberg_detection_probability_from_circuit(&gates, &[0, 2], &noise, 5, 0.0);
+        let h_a1 = heisenberg_detection_probability_from_circuit(&gates, &[1, 3], &noise, 5, 0.0);
+
+        let mut a0 = 0u64;
+        let mut a1 = 0u64;
+        let mut sim = StateVec::new(5);
+        for _ in 0..num_shots {
+            sim.pz(&[qid(0), qid(1), qid(2), qid(3), qid(4)]);
+            let mut outs = [false; 4]; // [r0a0, r0a1, r1a0, r1a1]
+            for (r, out_pair) in outs.chunks_mut(2).enumerate() {
+                sim.h(&[qid(3), qid(4)]);
+                sim.cx(&[(qid(3), qid(0))]);
+                sim.rz(Angle64::from_radians(theta), &[qid(3)]);
+                sim.rz(Angle64::from_radians(theta), &[qid(0)]);
+                sim.cx(&[(qid(4), qid(1))]);
+                sim.rz(Angle64::from_radians(theta), &[qid(4)]);
+                sim.rz(Angle64::from_radians(theta), &[qid(1)]);
+                sim.cx(&[(qid(3), qid(1))]);
+                sim.rz(Angle64::from_radians(theta), &[qid(3)]);
+                sim.rz(Angle64::from_radians(theta), &[qid(1)]);
+                sim.cx(&[(qid(4), qid(2))]);
+                sim.rz(Angle64::from_radians(theta), &[qid(4)]);
+                sim.rz(Angle64::from_radians(theta), &[qid(2)]);
+                sim.h(&[qid(3), qid(4)]);
+                out_pair[0] = sim.mz(&[qid(3)])[0].outcome;
+                out_pair[1] = sim.mz(&[qid(4)])[0].outcome;
+                if r == 0 {
+                    sim.pz(&[qid(3), qid(4)]);
+                }
+            }
+            if outs[0] != outs[2] {
+                a0 += 1;
+            }
+            if outs[1] != outs[3] {
+                a1 += 1;
+            }
+        }
+        let sv0 = u64_to_f64(a0) / f64::from(num_shots);
+        let sv1 = u64_to_f64(a1) / f64::from(num_shots);
+        let se0 = (sv0 * (1.0 - sv0) / f64::from(num_shots)).sqrt();
+        let se1 = (sv1 * (1.0 - sv1) / f64::from(num_shots)).sqrt();
+        eprintln!(
+            "Shared A0:  H={h_a0:.6}  SV={sv0:.6}+/-{se0:.6}  H/SV={:.4}",
+            if sv0 > 1e-10 { h_a0 / sv0 } else { f64::NAN }
+        );
+        eprintln!(
+            "Shared A1:  H={h_a1:.6}  SV={sv1:.6}+/-{se1:.6}  H/SV={:.4}",
+            if sv1 > 1e-10 { h_a1 / sv1 } else { f64::NAN }
+        );
+    }
+}
+
+/// Measure how Heisenberg backward walk cost scales with surface code distance and rounds.
+///
+/// The backward walk creates 2^m terms where m is the number of anticommuting
+/// noise sources per detector. For larger codes, m grows, making the walk
+/// exponentially more expensive.
+///
+/// We measure ALL round-comparison detectors and report per-detector timing,
+/// since boundary detectors (ancilla 0/last) only couple to 2 CX gates while
+/// bulk detectors (middle ancillas) couple to 4, seeing more noise sources.
+#[test]
+#[ignore = "benchmark sweep; run manually with --ignored --nocapture"]
+fn bench_heisenberg_scaling() {
+    use pecos_eeg::heisenberg::heisenberg_detection_probability_from_circuit;
+    use std::time::Instant;
+
+    let theta = 0.05;
+
+    // --- Part 1: Vary distance at fixed rounds=2 ---
+    eprintln!("\n=== Heisenberg scaling: distance sweep (rounds=2, all detectors) ===");
+    eprintln!(
+        "{:>4} {:>10} {:>14} {:>6} {:>18} {:>12} {:>12} {:>12}",
+        "d", "num_qubits", "expanded_q", "n_det", "max_prob", "max_ms", "total_ms", "per_det_ms"
+    );
+
+    for &d in &[3, 5, 7, 9] {
+        let num_rounds = 2;
+        let (gates, num_qubits, _ancillas) = build_repetition_code(d, num_rounds);
+        let num_ancilla = d - 1;
+        let num_detectors = num_ancilla; // rounds-1 == 1 comparison per ancilla
+
+        let expanded = expand::expand_circuit(&gates);
+        let noise = UniformNoise::coherent_only(theta);
+
+        let mut max_prob = 0.0f64;
+        let mut max_ms = 0.0f64;
+        let mut total_ms = 0.0f64;
+
+        eprintln!("  d={d} per-detector detail:");
+        eprintln!("    {:>6} {:>18} {:>12}", "det", "prob", "time_ms");
+
+        for i in 0..num_detectors {
+            // Round comparison: meas record i (round 0) vs i + num_ancilla (round 1)
+            let m1 = i;
+            let m2 = i + num_ancilla;
+
+            let start = Instant::now();
+            let prob = heisenberg_detection_probability_from_circuit(
+                &gates,
+                &[m1, m2],
+                &noise,
+                num_qubits,
+                0.0,
+            );
+            let elapsed_ms = start.elapsed().as_secs_f64() * 1000.0;
+
+            eprintln!("    {i:>6} {prob:>18.10} {elapsed_ms:>12.2}");
+
+            max_prob = max_prob.max(prob);
+            max_ms = max_ms.max(elapsed_ms);
+            total_ms += elapsed_ms;
+        }
+
+        let per_det = total_ms / usize_to_f64(num_detectors);
+        eprintln!(
+            "{d:>4} {num_qubits:>10} {:>14} {num_detectors:>6} {max_prob:>18.10} {max_ms:>12.2} {total_ms:>12.2} {per_det:>12.2}",
+            expanded.num_qubits
+        );
+    }
+
+    // --- Part 2: Vary rounds at fixed d=3 ---
+    eprintln!("\n=== Heisenberg scaling: rounds sweep (d=3, all detectors) ===");
+    eprintln!(
+        "{:>6} {:>10} {:>14} {:>6} {:>18} {:>12} {:>12} {:>12}",
+        "rounds",
+        "num_qubits",
+        "expanded_q",
+        "n_det",
+        "max_prob",
+        "max_ms",
+        "total_ms",
+        "per_det_ms"
+    );
+
+    for &num_rounds in &[2, 3, 4, 5] {
+        let d = 3;
+        let (gates, num_qubits, _ancillas) = build_repetition_code(d, num_rounds);
+        let num_ancilla = d - 1;
+        // Round comparison detectors: (num_rounds - 1) comparisons per ancilla
+        let num_detectors = num_ancilla * (num_rounds - 1);
+
+        let expanded = expand::expand_circuit(&gates);
+        let noise = UniformNoise::coherent_only(theta);
+
+        let mut max_prob = 0.0f64;
+        let mut max_ms = 0.0f64;
+        let mut total_ms = 0.0f64;
+
+        eprintln!("  rounds={num_rounds} per-detector detail:");
+        eprintln!("    {:>6} {:>18} {:>12}", "det", "prob", "time_ms");
+
+        for round in 0..(num_rounds - 1) {
+            for i in 0..num_ancilla {
+                let m1 = round * num_ancilla + i;
+                let m2 = (round + 1) * num_ancilla + i;
+
+                let start = Instant::now();
+                let prob = heisenberg_detection_probability_from_circuit(
+                    &gates,
+                    &[m1, m2],
+                    &noise,
+                    num_qubits,
+                    0.0,
+                );
+                let elapsed_ms = start.elapsed().as_secs_f64() * 1000.0;
+
+                eprintln!("    R{round}A{i} {prob:>18.10} {elapsed_ms:>12.2}");
+
+                max_prob = max_prob.max(prob);
+                max_ms = max_ms.max(elapsed_ms);
+                total_ms += elapsed_ms;
+            }
+        }
+
+        let per_det = total_ms / usize_to_f64(num_detectors);
+        eprintln!(
+            "{num_rounds:>6} {num_qubits:>10} {:>14} {num_detectors:>6} {max_prob:>18.10} {max_ms:>12.2} {total_ms:>12.2} {per_det:>12.2}",
+            expanded.num_qubits
+        );
+    }
+}
+
+/// Combined coherent + stochastic noise on a Wt-2 2-round X-check circuit.
+///
+/// Uses `idle_rz=0.05` (coherent RZ after each CX) plus `p_meas=0.003`
+/// (measurement bit-flip). The Heisenberg walk handles both H-type and
+/// S-type generators in a single backward pass.
+///
+/// `StateVec` applies identical noise: RZ(theta) on both qubits after each
+/// CX, and flips the MZ outcome with probability `p_meas`.
+///
+/// Detector: round-comparison (meas[0] XOR meas[1]).
+#[test]
+#[ignore = "benchmark sweep; run manually with --ignored --nocapture"]
+fn bench_combined_noise() {
+    use pecos_eeg::heisenberg::heisenberg_detection_probability_from_circuit;
+    use pecos_random::PecosRng;
+    use pecos_random::rng_ext::RngProbabilityExt;
+
+    let idle_rz = 0.05;
+    let p_meas = 0.003;
+    let num_shots = 500_000;
+
+    eprintln!("\n=== Combined coherent + stochastic noise: Wt-2 2-round X-check ===");
+    eprintln!("idle_rz = {idle_rz}, p_meas = {p_meas}, shots = {num_shots}\n");
+
+    // ---- Build the circuit: 2 data (q0,q1) + 1 ancilla (q2), 2 rounds ----
+    let gates = vec![
+        gate(GateType::PZ, &[0]),
+        gate(GateType::PZ, &[1]),
+        gate(GateType::PZ, &[2]),
+        // Round 1
+        gate(GateType::H, &[2]),
+        gate(GateType::CX, &[2, 0]),
+        gate(GateType::CX, &[2, 1]),
+        gate(GateType::H, &[2]),
+        gate(GateType::MZ, &[2]),
+        gate(GateType::PZ, &[2]),
+        // Round 2
+        gate(GateType::H, &[2]),
+        gate(GateType::CX, &[2, 0]),
+        gate(GateType::CX, &[2, 1]),
+        gate(GateType::H, &[2]),
+        gate(GateType::MZ, &[2]),
+    ];
+
+    // ---- Heisenberg walk with combined noise ----
+    let noise = UniformNoise {
+        idle_rz,
+        p1: 0.0,
+        p2: 0.0,
+        p_meas,
+        p_prep: 0.0,
+    };
+    // Detector = Z on meas[0] * Z on meas[1] (round comparison)
+    let h_p = heisenberg_detection_probability_from_circuit(&gates, &[0, 1], &noise, 3, 0.0);
+
+    // ---- Also compute coherent-only and meas-only for decomposition ----
+    let noise_coh = UniformNoise::coherent_only(idle_rz);
+    let h_coh = heisenberg_detection_probability_from_circuit(&gates, &[0, 1], &noise_coh, 3, 0.0);
+
+    let noise_meas = UniformNoise {
+        idle_rz: 0.0,
+        p1: 0.0,
+        p2: 0.0,
+        p_meas,
+        p_prep: 0.0,
+    };
+    let h_meas =
+        heisenberg_detection_probability_from_circuit(&gates, &[0, 1], &noise_meas, 3, 0.0);
+
+    // ---- StateVec simulation with matching noise ----
+    let mut rng = PecosRng::seed_from_u64(12345);
+    let meas_threshold = rng.probability_threshold(p_meas);
+
+    let mut det = 0u64;
+    let mut sim = StateVec::new(3);
+    for _ in 0..num_shots {
+        sim.pz(&[qid(0), qid(1), qid(2)]);
+        let mut outs = [false; 2];
+        for (r, out_slot) in outs.iter_mut().enumerate() {
+            sim.h(&[qid(2)]);
+            // CX(2,0) + idle RZ noise
+            sim.cx(&[(qid(2), qid(0))]);
+            sim.rz(Angle64::from_radians(idle_rz), &[qid(2)]);
+            sim.rz(Angle64::from_radians(idle_rz), &[qid(0)]);
+            // CX(2,1) + idle RZ noise
+            sim.cx(&[(qid(2), qid(1))]);
+            sim.rz(Angle64::from_radians(idle_rz), &[qid(1)]);
+            sim.rz(Angle64::from_radians(idle_rz), &[qid(2)]);
+            sim.h(&[qid(2)]);
+            // MZ with measurement error
+            let mut outcome = sim.mz(&[qid(2)])[0].outcome;
+            if rng.check_probability(meas_threshold) {
+                outcome = !outcome;
+            }
+            *out_slot = outcome;
+            if r == 0 {
+                sim.pz(&[qid(2)]);
+            }
+        }
+        if outs[0] != outs[1] {
+            det += 1;
+        }
+    }
+    let sv = u64_to_f64(det) / f64::from(num_shots);
+    let se = (sv * (1.0 - sv) / f64::from(num_shots)).sqrt();
+    let ratio = if sv > 1e-10 { h_p / sv } else { f64::NAN };
+
+    eprintln!("Heisenberg (combined): {h_p:.6}");
+    eprintln!("Heisenberg (coh only): {h_coh:.6}");
+    eprintln!("Heisenberg (meas only):{h_meas:.6}");
+    eprintln!("StateVec:              {sv:.6} +/- {se:.6}");
+    eprintln!("H/SV ratio:            {ratio:.4}");
+    eprintln!();
+
+    // ---- Sweep p_meas to see how combined noise scales ----
+    eprintln!(
+        "{:>8} {:>10} {:>10} {:>10} {:>10}",
+        "p_meas", "H_comb", "SV", "SV_stderr", "H/SV"
+    );
+
+    for &pm in &[0.0, 0.001, 0.003, 0.005, 0.01, 0.02, 0.05] {
+        let n = UniformNoise {
+            idle_rz,
+            p1: 0.0,
+            p2: 0.0,
+            p_meas: pm,
+            p_prep: 0.0,
+        };
+        let hp = heisenberg_detection_probability_from_circuit(&gates, &[0, 1], &n, 3, 0.0);
+
+        let pm_threshold = rng.probability_threshold(pm);
+        let mut d = 0u64;
+        for _ in 0..num_shots {
+            sim.pz(&[qid(0), qid(1), qid(2)]);
+            let mut os = [false; 2];
+            for (r, out_slot) in os.iter_mut().enumerate() {
+                sim.h(&[qid(2)]);
+                sim.cx(&[(qid(2), qid(0))]);
+                sim.rz(Angle64::from_radians(idle_rz), &[qid(2)]);
+                sim.rz(Angle64::from_radians(idle_rz), &[qid(0)]);
+                sim.cx(&[(qid(2), qid(1))]);
+                sim.rz(Angle64::from_radians(idle_rz), &[qid(1)]);
+                sim.rz(Angle64::from_radians(idle_rz), &[qid(2)]);
+                sim.h(&[qid(2)]);
+                let mut out = sim.mz(&[qid(2)])[0].outcome;
+                if rng.check_probability(pm_threshold) {
+                    out = !out;
+                }
+                *out_slot = out;
+                if r == 0 {
+                    sim.pz(&[qid(2)]);
+                }
+            }
+            if os[0] != os[1] {
+                d += 1;
+            }
+        }
+        let s = u64_to_f64(d) / f64::from(num_shots);
+        let e = (s * (1.0 - s) / f64::from(num_shots)).sqrt();
+        let r = if s > 1e-10 { hp / s } else { f64::NAN };
+        eprintln!("{pm:>8.4} {hp:>10.6} {s:>10.6} {e:>10.6} {r:>10.4}");
+    }
+}
diff --git a/exp/pecos-eeg/tests/strong_sim_validation.rs b/exp/pecos-eeg/tests/strong_sim_validation.rs
new file mode 100644
index 000000000..b6e3434c0
--- /dev/null
+++ b/exp/pecos-eeg/tests/strong_sim_validation.rs
@@ -0,0 +1,279 @@
+// Copyright 2026 The PECOS Developers
+//
+// Licensed under the Apache License, Version 2.0
+
+//! Validation tests for approximate strong simulation.
+
+use pecos_eeg::Bm;
+use pecos_eeg::circuit::PropagatedEeg;
+use pecos_eeg::eeg::EegType;
+use pecos_eeg::strong_sim::outcome_probability;
+
+/// H-type correction: |0⟩ with `H_X` gives p(1) = h² at leading order.
+/// Cross-check: exact p(1) = sin²(h).
+#[test]
+fn test_h_correction_matches_exact() {
+    let stabs = vec![Bm::z(0)];
+
+    for &h in &[0.01, 0.05, 0.1, 0.2] {
+        let gens = vec![PropagatedEeg {
+            eeg_type: EegType::H,
+            label: Bm::x(0),
+            label2: None,
+            coeff: h,
+            source: None,
+        }];
+
+        let p1 = outcome_probability(&gens, &[true], &stabs);
+        let exact = h.sin().powi(2);
+
+        // EEG gives h², which ≈ sin²(h) for small h
+        assert!(
+            (p1.total - h * h).abs() < 1e-10,
+            "h={h}: EEG p(1)={:.6} expected h²={:.6}",
+            p1.total,
+            h * h
+        );
+
+        // Check closeness to exact
+        let rel_err = (p1.total - exact).abs() / exact;
+        eprintln!(
+            "h={h:.2}: EEG={:.6} exact={exact:.6} rel_err={rel_err:.4}",
+            p1.total
+        );
+        if h <= 0.1 {
+            assert!(rel_err < 0.02, "h={h}: relative error {rel_err:.4} > 2%");
+        }
+    }
+}
+
+/// Probability conservation: p(0) + p(1) = 1 at leading order for H-type.
+#[test]
+fn test_h_probability_conservation() {
+    let stabs = vec![Bm::z(0)];
+    let h = 0.1;
+
+    let gens = vec![PropagatedEeg {
+        eeg_type: EegType::H,
+        label: Bm::x(0),
+        label2: None,
+        coeff: h,
+        source: None,
+    }];
+
+    let p0 = outcome_probability(&gens, &[false], &stabs);
+    let p1 = outcome_probability(&gens, &[true], &stabs);
+    let sum = p0.total + p1.total;
+
+    assert!(
+        (sum - 1.0).abs() < 0.001,
+        "p(0)+p(1) = {sum:.6}, expected ≈ 1.0"
+    );
+}
+
+/// Bell state: H_{Z0} noise should NOT affect Z-basis measurement probabilities.
+/// (Z commutes with Z-basis measurements.)
+#[test]
+fn test_bell_h_z_invisible() {
+    let stabs = vec![
+        Bm::x(0).multiply(&Bm::x(1)), // XX
+        Bm::z(0).multiply(&Bm::z(1)), // ZZ
+    ];
+
+    let gens = vec![PropagatedEeg {
+        eeg_type: EegType::H,
+        label: Bm::z(0),
+        label2: None,
+        coeff: 0.1,
+        source: None,
+    }];
+
+    // Z₀ has no X component → no bit flips → α(S_Z) = 0 for all outcomes
+    // H correction should be zero for all outcomes
+    for outcome in &[
+        vec![false, false],
+        vec![true, true],
+        vec![false, true],
+        vec![true, false],
+    ] {
+        let p = outcome_probability(&gens, outcome, &stabs);
+        assert!(
+            p.h_correction.abs() < 1e-10,
+            "H_Z should be invisible: outcome={outcome:?} h_corr={}",
+            p.h_correction
+        );
+    }
+}
+
+/// Bell state: H_{X0} shifts probability between {00,11} and {01,10}.
+#[test]
+fn test_bell_h_x_shifts() {
+    let stabs = vec![
+        Bm::x(0).multiply(&Bm::x(1)), // XX
+        Bm::z(0).multiply(&Bm::z(1)), // ZZ
+    ];
+    let h = 0.05;
+
+    let gens = vec![PropagatedEeg {
+        eeg_type: EegType::H,
+        label: Bm::x(0),
+        label2: None,
+        coeff: h,
+        source: None,
+    }];
+
+    let p00 = outcome_probability(&gens, &[false, false], &stabs);
+    let p11 = outcome_probability(&gens, &[true, true], &stabs);
+    let p01 = outcome_probability(&gens, &[false, true], &stabs);
+    let p10 = outcome_probability(&gens, &[true, false], &stabs);
+
+    eprintln!(
+        "Bell + H_X0: p00={:.6} p11={:.6} p01={:.6} p10={:.6}",
+        p00.total, p11.total, p01.total, p10.total
+    );
+
+    // X0 flips qubit 0: maps {00,11} ↔ {10,01}
+    // H_X creates probability at {01,10} from {00,11}
+    // p(01) and p(10) should be > 0 (increased from noiseless 0)
+    assert!(p01.h_correction > 0.0, "p(01) should increase");
+    assert!(p10.h_correction > 0.0, "p(10) should increase");
+
+    // p(00) and p(11) should decrease
+    assert!(p00.h_correction < 0.0, "p(00) should decrease");
+    assert!(p11.h_correction < 0.0, "p(11) should decrease");
+
+    // Conservation: total ≈ 1
+    let sum = p00.total + p11.total + p01.total + p10.total;
+    assert!((sum - 1.0).abs() < 0.01, "Conservation: sum={sum:.6}");
+
+    // Symmetry: p(01) = p(10) (X0 on symmetric Bell state)
+    assert!(
+        (p01.total - p10.total).abs() < 1e-10,
+        "Symmetry: p01={:.6} p10={:.6}",
+        p01.total,
+        p10.total
+    );
+}
+
+/// Multiple H generators: verify the off-diagonal Φ correctly accounts
+/// for cross-generator interference.
+#[test]
+fn test_two_h_generators_interference() {
+    // |0⟩ with H_X rate h1 and H_Y rate h2
+    let stabs = vec![Bm::z(0)];
+    let h1 = 0.05;
+    let h2 = 0.03;
+
+    let gens = vec![
+        PropagatedEeg {
+            eeg_type: EegType::H,
+            label: Bm::x(0),
+            label2: None,
+            coeff: h1,
+            source: None,
+        },
+        PropagatedEeg {
+            eeg_type: EegType::H,
+            label: Bm::y(0),
+            label2: None,
+            coeff: h2,
+            source: None,
+        },
+    ];
+
+    let p0 = outcome_probability(&gens, &[false], &stabs);
+    let p1 = outcome_probability(&gens, &[true], &stabs);
+
+    // Diagonal: h1² + h2² for p(1)
+    let diagonal = h1 * h1 + h2 * h2;
+
+    // X and Y both flip (both have X component set).
+    // Diagonal H·H: both contribute +h² to p(1).
+    // Off-diagonal: X·Y = iZ (anticommuting), so C_{X,Y} has α contribution
+    // from the off-diagonal Φ computation.
+    eprintln!(
+        "Two H gens: p0={:.6} p1={:.6} diagonal={diagonal:.6}",
+        p0.total, p1.total
+    );
+
+    // p(1) should be at least the diagonal
+    assert!(
+        p1.total >= diagonal * 0.9,
+        "p(1)={:.6} should be ≥ diagonal {diagonal:.6}",
+        p1.total
+    );
+
+    // Conservation
+    assert!((p0.total + p1.total - 1.0).abs() < 0.01);
+}
+
+/// C-type first-order α: directly construct a C generator and verify.
+#[test]
+fn test_c_type_alpha() {
+    // |0⟩ with C_{X,X} = 2S_X. Should give same result as S_X at double rate.
+    let stabs = vec![Bm::z(0)];
+    let c = 0.005;
+
+    let gens = vec![PropagatedEeg {
+        eeg_type: EegType::C,
+        label: Bm::x(0),
+        label2: Some(Bm::x(0)),
+        coeff: c,
+        source: None,
+    }];
+
+    let p0 = outcome_probability(&gens, &[false], &stabs);
+    let p1 = outcome_probability(&gens, &[true], &stabs);
+
+    // C_{X,X} = 2S_X. α(C_{X,X}) at outcome 0:
+    // Φ(X,X) at 0 = 0 (flipped not in support), Φ(I,I) = 1.
+    // Φ(XX,I) = Φ(I,I) = 1.
+    // α = 2*Re(0) - Re(1 + 1) = -2.
+    // Correction: c * α = 0.005 * (-2) = -0.01.
+    // But wait — with the scale factor for pure state (ζ=0): scale=1.
+    // So ca_correction = 1 * 0.005 * (-2) = -0.01.
+    // p(0) = 1 + (-0.01) = 0.99.
+
+    eprintln!("C-type: p0={:.6} p1={:.6}", p0.total, p1.total);
+    assert!(
+        (p0.total - 0.99).abs() < 0.02,
+        "p(0) ≈ 0.99: got {:.6}",
+        p0.total
+    );
+    assert!(p1.total > 0.0, "p(1) should be positive");
+}
+
+/// A-type α: construct an A generator. For stabilizer states, A-type
+/// typically gives zero (requires iQ1Q2 to be stabilizer eigenvalue).
+#[test]
+fn test_a_type_alpha_zero_for_stabilizer() {
+    // |0⟩ with A_{X,Z}: iXZ = iY. Is iY|0⟩ = ±|0⟩? Y|0⟩ = i|1⟩, so iY|0⟩ = -|1⟩.
+    // Not an eigenstate → α(A) should be 0 for both outcomes.
+    let stabs = vec![Bm::z(0)];
+
+    let gens = vec![PropagatedEeg {
+        eeg_type: EegType::A,
+        label: Bm::x(0),
+        label2: Some(Bm::z(0)),
+        coeff: 0.01,
+        source: None,
+    }];
+
+    let p0 = outcome_probability(&gens, &[false], &stabs);
+    let p1 = outcome_probability(&gens, &[true], &stabs);
+
+    // A-type uses Im(Φ). For |0⟩ (real stabilizer state), Φ values
+    // should be real, so Im = 0, giving zero A-type correction.
+    eprintln!(
+        "A-type: p0_corr={:.8} p1_corr={:.8}",
+        p0.s_correction + p0.h_correction,
+        p1.s_correction + p1.h_correction
+    );
+    // The ca_correction is part of total but not separately exposed.
+    // Just check total is unchanged from noiseless.
+    assert!(
+        (p0.total - 1.0).abs() < 1e-6,
+        "A on |0⟩ should not change p(0)"
+    );
+    assert!(p1.total.abs() < 1e-6, "A on |0⟩ should not change p(1)");
+}
diff --git a/exp/pecos-eeg/tests/surface_code.rs b/exp/pecos-eeg/tests/surface_code.rs
new file mode 100644
index 000000000..cfb30fc0b
--- /dev/null
+++ b/exp/pecos-eeg/tests/surface_code.rs
@@ -0,0 +1,190 @@
+// Copyright 2026 The PECOS Developers
+//
+// Licensed under the Apache License, Version 2.0
+
+//! Integration test: EEG analysis on a repetition code circuit.
+
+use pecos_core::Gate;
+use pecos_eeg::Bm;
+use pecos_eeg::circuit::{NoiseModel, analyze_expanded};
+use pecos_eeg::dem_mapping::*;
+use pecos_eeg::eeg::EegType;
+use pecos_eeg::expand;
+use pecos_quantum::TickCircuit;
+
+/// Build a 3-qubit repetition code with 2 syndrome rounds.
+///
+/// Layout: data qubits 0,1,2; ancilla qubits 3,4
+/// Stabilizers: Z0Z1 (measured by ancilla 3), Z1Z2 (measured by ancilla 4)
+fn build_repetition_code() -> (Vec<Gate>, Vec<Detector>, Vec<Observable>) {
+    let mut tc = TickCircuit::new();
+
+    // Initialize all qubits
+    tc.tick().pz(&[0, 1, 2, 3, 4]);
+
+    // Two syndrome extraction rounds
+    for _round in 0..2 {
+        tc.tick().pz(&[3, 4]);
+        tc.tick().cx(&[(0, 3), (1, 4)]);
+        tc.tick().cx(&[(1, 3), (2, 4)]);
+        tc.tick().mz(&[3, 4]);
+    }
+
+    // Final data readout
+    tc.tick().mz(&[0, 1, 2]);
+
+    let gates: Vec<Gate> = tc
+        .iter_gate_batches()
+        .map(|batch| batch.as_gate().clone())
+        .collect();
+
+    // Detector stabilizers: X on ancilla qubit (anticommutes with Z errors
+    // that propagate through CX from data qubits).
+    let detectors = vec![
+        Detector {
+            id: 0,
+            stabilizer: Bm::x(3),
+        },
+        Detector {
+            id: 1,
+            stabilizer: Bm::x(4),
+        },
+    ];
+
+    let observables = vec![Observable {
+        id: 0,
+        pauli: Bm::x(0).multiply(&Bm::x(1)).multiply(&Bm::x(2)),
+    }];
+
+    (gates, detectors, observables)
+}
+
+#[test]
+fn test_repetition_code_no_noise() {
+    let (gates, _, _) = build_repetition_code();
+    let expanded = expand::expand_circuit(&gates);
+    let noise = NoiseModel::coherent_only(0.0);
+    let result = analyze_expanded(&expanded.gates, &noise);
+
+    assert!(result.generators.is_empty());
+}
+
+#[test]
+fn test_repetition_code_coherent_noise() {
+    let (gates, detectors, observables) = build_repetition_code();
+    let expanded = expand::expand_circuit(&gates);
+    let noise = NoiseModel::coherent_only(0.1);
+    let result = analyze_expanded(&expanded.gates, &noise);
+
+    let h_count = result
+        .generators
+        .iter()
+        .filter(|g| g.eeg_type == EegType::H)
+        .count();
+    assert!(h_count > 0, "Should have H generators from RZ noise");
+
+    let dem_entries = build_dem(&result.generators, &detectors, &observables);
+
+    assert!(
+        !dem_entries.is_empty(),
+        "Coherent noise should produce detection events"
+    );
+
+    let dem_str = format_dem(&dem_entries);
+    eprintln!("Coherent DEM:\n{dem_str}");
+
+    for entry in &dem_entries {
+        assert!(entry.probability > 0.0, "Probability must be positive");
+        assert!(
+            entry.probability < 1.0,
+            "Probability {:.6} too large",
+            entry.probability
+        );
+    }
+}
+
+#[test]
+fn test_repetition_code_depolarizing_noise() {
+    let (gates, detectors, observables) = build_repetition_code();
+    let expanded = expand::expand_circuit(&gates);
+    let noise = NoiseModel::depolarizing(0.003);
+    let result = analyze_expanded(&expanded.gates, &noise);
+
+    let s_count = result
+        .generators
+        .iter()
+        .filter(|g| g.eeg_type == EegType::S)
+        .count();
+    assert!(s_count > 0);
+
+    let dem_entries = build_dem(&result.generators, &detectors, &observables);
+
+    let dem_str = format_dem(&dem_entries);
+    eprintln!("Stochastic DEM:\n{dem_str}");
+
+    assert!(!dem_entries.is_empty());
+    for entry in &dem_entries {
+        assert!(entry.probability > 0.0);
+        assert!(entry.probability < 0.5);
+    }
+}
+
+#[test]
+fn test_repetition_code_combined_noise() {
+    let (gates, detectors, observables) = build_repetition_code();
+    let expanded = expand::expand_circuit(&gates);
+    let noise = NoiseModel::depolarizing(0.003).with_idle_rz(0.1);
+    let result = analyze_expanded(&expanded.gates, &noise);
+
+    let h_count = result
+        .generators
+        .iter()
+        .filter(|g| g.eeg_type == EegType::H)
+        .count();
+    let s_count = result
+        .generators
+        .iter()
+        .filter(|g| g.eeg_type == EegType::S)
+        .count();
+    assert!(h_count > 0);
+    assert!(s_count > 0);
+
+    let dem_entries = build_dem(&result.generators, &detectors, &observables);
+
+    let dem_str = format_dem(&dem_entries);
+    eprintln!("Combined DEM:\n{dem_str}");
+
+    assert!(!dem_entries.is_empty());
+}
+
+#[test]
+fn test_eeg_generator_count_scales_linearly() {
+    for num_rounds in [1, 2, 4, 8] {
+        let mut tc = TickCircuit::new();
+        tc.tick().pz(&[0, 1, 2, 3, 4]);
+
+        for _ in 0..num_rounds {
+            tc.tick().pz(&[3, 4]);
+            tc.tick().cx(&[(0, 3), (1, 4)]);
+            tc.tick().cx(&[(1, 3), (2, 4)]);
+            tc.tick().mz(&[3, 4]);
+        }
+        tc.tick().mz(&[0, 1, 2]);
+
+        let gates: Vec<Gate> = tc
+            .iter_gate_batches()
+            .map(|batch| batch.as_gate().clone())
+            .collect();
+        let expanded = expand::expand_circuit(&gates);
+        let noise = NoiseModel::coherent_only(0.1);
+        let result = analyze_expanded(&expanded.gates, &noise);
+
+        let h_count = result
+            .generators
+            .iter()
+            .filter(|g| g.eeg_type == EegType::H)
+            .count();
+        eprintln!("Rounds={num_rounds}: {h_count} H generators");
+        assert!(h_count < 1000, "Generator count should be polynomial");
+    }
+}
diff --git a/exp/pecos-experimental/src/hugr_executor.rs b/exp/pecos-experimental/src/hugr_executor.rs
index b5a792faf..c514664df 100644
--- a/exp/pecos-experimental/src/hugr_executor.rs
+++ b/exp/pecos-experimental/src/hugr_executor.rs
@@ -213,7 +213,8 @@ where
             | GateType::QFree
             | GateType::Idle
             | GateType::MeasCrosstalkGlobalPayload
-            | GateType::MeasCrosstalkLocalPayload => {}
+            | GateType::MeasCrosstalkLocalPayload
+            | GateType::TrackedPauliMeta => {}
 
             // Single-qubit Clifford gates
             GateType::X => {
@@ -317,6 +318,7 @@ where
             | GateType::CRZ
             | GateType::CH
             | GateType::CCX
+            | GateType::Channel
             | GateType::Custom => {
                 return Err(HugrExecutionError::UnsupportedGate {
                     gate_type: gate.gate_type,
diff --git a/exp/pecos-lindblad/Cargo.toml b/exp/pecos-lindblad/Cargo.toml
new file mode 100644
index 000000000..b91b7c1ad
--- /dev/null
+++ b/exp/pecos-lindblad/Cargo.toml
@@ -0,0 +1,33 @@
+[package]
+name = "pecos-lindblad"
+version.workspace = true
+edition.workspace = true
+authors.workspace = true
+homepage.workspace = true
+repository.workspace = true
+license.workspace = true
+keywords.workspace = true
+categories.workspace = true
+description = "Lindblad-to-Pauli-Lindblad noise synthesis for PECOS"
+readme = "README.md"
+
+[lib]
+crate-type = ["rlib"]
+
+[features]
+default = []
+serde = ["dep:serde"]
+
+[dependencies]
+num-complex.workspace = true
+pecos-quantum.workspace = true
+thiserror.workspace = true
+rand.workspace = true
+serde = { workspace = true, optional = true }
+
+[dev-dependencies]
+approx.workspace = true
+pecos-qec.workspace = true
+proptest.workspace = true
+rand.workspace = true
+serde_json.workspace = true
diff --git a/exp/pecos-lindblad/README.md b/exp/pecos-lindblad/README.md
new file mode 100644
index 000000000..6f8965f35
--- /dev/null
+++ b/exp/pecos-lindblad/README.md
@@ -0,0 +1,16 @@
+# pecos-lindblad
+
+Lindblad-to-Pauli-Lindblad noise synthesis for PECOS.
+
+Given a per-gate Lindbladian `{H_ideal, H_err, c_ops, tau_g}`, compute the
+effective Pauli-Lindblad rates `lambda_k` that feed into
+`pecos-qec::DemStabSim` or any Pauli-level noise channel.
+
+**Status:** experimental, Phase 1 (numerical baseline + 1Q identity test).
+
+**Design docs:**
+- `design/lindblad_sim_skeleton.md` -- crate layout, API surface, test plan
+- `design/lindblad_magnus_algorithm.md` -- math spec, closed forms, references
+
+**Primary reference:** Malekakhlagh et al., *Efficient Lindblad synthesis for
+noise model construction*, npj QI 2025, arXiv:2502.03462.
diff --git a/exp/pecos-lindblad/src/basis.rs b/exp/pecos-lindblad/src/basis.rs
new file mode 100644
index 000000000..7a6f94458
--- /dev/null
+++ b/exp/pecos-lindblad/src/basis.rs
@@ -0,0 +1,248 @@
+// Copyright 2026 The PECOS Developers
+//
+// Licensed under the Apache License, Version 2.0 (the "License"); you may not use this file except
+// in compliance with the License. You may obtain a copy of the License at
+//
+//     https://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software distributed under the License
+// is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express
+// or implied. See the License for the specific language governing permissions and limitations under
+// the License.
+
+//! Pauli basis types for Lindblad -> Pauli-Lindblad synthesis.
+
+use std::fmt;
+use std::str::FromStr;
+
+/// Single-qubit Pauli operator.
+#[derive(Clone, Copy, Debug, PartialEq, Eq, Hash)]
+#[cfg_attr(feature = "serde", derive(serde::Serialize, serde::Deserialize))]
+#[repr(u8)]
+pub enum Pauli1 {
+    I = 0,
+    X = 1,
+    Y = 2,
+    Z = 3,
+}
+
+impl Pauli1 {
+    pub fn from_char(c: char) -> Option<Self> {
+        match c {
+            'I' | 'i' => Some(Pauli1::I),
+            'X' | 'x' => Some(Pauli1::X),
+            'Y' | 'y' => Some(Pauli1::Y),
+            'Z' | 'z' => Some(Pauli1::Z),
+            _ => None,
+        }
+    }
+
+    pub fn to_char(self) -> char {
+        match self {
+            Pauli1::I => 'I',
+            Pauli1::X => 'X',
+            Pauli1::Y => 'Y',
+            Pauli1::Z => 'Z',
+        }
+    }
+
+    /// Pauli multiplication ignoring global phase. Returns the Hermitian
+    /// Pauli factor: XY -> Z (phase `i` dropped), etc. Safe for our use in
+    /// `PauliLindbladModel::sample`, where rates are carried by commuting
+    /// structure and phases cancel in `P rho P^dag` style actions.
+    pub fn multiply(self, other: Pauli1) -> Pauli1 {
+        use Pauli1::*;
+        match (self, other) {
+            (I, x) | (x, I) => x,
+            (X, X) | (Y, Y) | (Z, Z) => I,
+            (X, Y) | (Y, X) => Z,
+            (Y, Z) | (Z, Y) => X,
+            (X, Z) | (Z, X) => Y,
+        }
+    }
+
+    /// 1 if two single-qubit Paulis anticommute, 0 if they commute.
+    pub fn anticommutes_with(self, other: Pauli1) -> u8 {
+        use Pauli1::*;
+        match (self, other) {
+            (I, _) | (_, I) => 0,
+            (a, b) if a == b => 0,
+            _ => 1,
+        }
+    }
+}
+
+/// Multi-qubit Pauli string. Index 0 = leftmost factor.
+#[derive(Clone, Debug, PartialEq, Eq, Hash)]
+#[cfg_attr(feature = "serde", derive(serde::Serialize, serde::Deserialize))]
+pub struct PauliString(pub Vec<Pauli1>);
+
+#[derive(Clone, Copy, Debug, PartialEq, Eq)]
+pub struct ParsePauliStringError {
+    invalid_char: char,
+}
+
+impl fmt::Display for ParsePauliStringError {
+    fn fmt(&self, f: &mut fmt::Formatter<'_>) -> fmt::Result {
+        write!(f, "invalid Pauli character {:?}", self.invalid_char)
+    }
+}
+
+impl std::error::Error for ParsePauliStringError {}
+
+impl PauliString {
+    pub fn single(p: Pauli1) -> Self {
+        PauliString(vec![p])
+    }
+
+    pub fn from_label(s: &str) -> Option<Self> {
+        s.chars()
+            .map(Pauli1::from_char)
+            .collect::<Option<Vec<_>>>()
+            .map(PauliString)
+    }
+
+    pub fn num_qubits(&self) -> usize {
+        self.0.len()
+    }
+
+    /// Weight (number of non-identity factors).
+    pub fn weight(&self) -> usize {
+        self.0.iter().filter(|&&p| p != Pauli1::I).count()
+    }
+
+    /// Is this the identity string?
+    pub fn is_identity(&self) -> bool {
+        self.weight() == 0
+    }
+
+    /// Elementwise product with global phase dropped. See
+    /// [`Pauli1::multiply`].
+    pub fn multiply(&self, other: &PauliString) -> PauliString {
+        assert_eq!(self.num_qubits(), other.num_qubits(), "ragged multiply");
+        PauliString(
+            self.0
+                .iter()
+                .zip(&other.0)
+                .map(|(a, b)| a.multiply(*b))
+                .collect(),
+        )
+    }
+
+    /// Symplectic product `<self, other>_sp`: 1 if the two strings
+    /// anticommute, 0 if they commute. Equal to (sum of pairwise
+    /// anticommutes) mod 2.
+    pub fn symplectic_product(&self, other: &PauliString) -> u8 {
+        assert_eq!(self.num_qubits(), other.num_qubits(), "ragged symplectic");
+        self.0
+            .iter()
+            .zip(&other.0)
+            .map(|(a, b)| a.anticommutes_with(*b))
+            .sum::<u8>()
+            & 1
+    }
+
+    /// Enumerate all non-identity Pauli strings on `n` qubits. Length
+    /// 4^n - 1 = 3, 15, 63, ...
+    pub fn enumerate_nonidentity(n: usize) -> Vec<PauliString> {
+        let total = 1usize << (2 * n);
+        (1..total)
+            .map(|idx| {
+                // idx in base 4: two bits per qubit, low bits = rightmost factor
+                let mut qs = Vec::with_capacity(n);
+                for q in 0..n {
+                    let shift = 2 * (n - 1 - q);
+                    let bits = (idx >> shift) & 0b11;
+                    let p = match bits {
+                        0 => Pauli1::I,
+                        1 => Pauli1::X,
+                        2 => Pauli1::Y,
+                        3 => Pauli1::Z,
+                        _ => unreachable!(),
+                    };
+                    qs.push(p);
+                }
+                PauliString(qs)
+            })
+            .collect()
+    }
+}
+
+impl FromStr for PauliString {
+    type Err = ParsePauliStringError;
+
+    fn from_str(s: &str) -> Result<Self, Self::Err> {
+        let mut paulis = Vec::with_capacity(s.len());
+        for c in s.chars() {
+            let Some(pauli) = Pauli1::from_char(c) else {
+                return Err(ParsePauliStringError { invalid_char: c });
+            };
+            paulis.push(pauli);
+        }
+        Ok(PauliString(paulis))
+    }
+}
+
+impl fmt::Display for PauliString {
+    fn fmt(&self, f: &mut fmt::Formatter<'_>) -> fmt::Result {
+        for p in &self.0 {
+            write!(f, "{}", p.to_char())?;
+        }
+        Ok(())
+    }
+}
+
+#[cfg(test)]
+mod tests {
+    use super::*;
+
+    #[test]
+    fn roundtrip_string() {
+        let s = PauliString::from_label("XYZ").unwrap();
+        assert_eq!(s.num_qubits(), 3);
+        assert_eq!(s.weight(), 3);
+        assert_eq!(format!("{}", s), "XYZ");
+    }
+
+    #[test]
+    fn identity_weight() {
+        let s = PauliString::from_label("III").unwrap();
+        assert_eq!(s.weight(), 0);
+    }
+
+    #[test]
+    fn mixed_weight() {
+        let s = PauliString::from_label("IXI").unwrap();
+        assert_eq!(s.weight(), 1);
+    }
+
+    #[test]
+    fn symplectic_product_2q() {
+        let ix = PauliString::from_label("IX").unwrap();
+        let iz = PauliString::from_label("IZ").unwrap();
+        let zx = PauliString::from_label("ZX").unwrap();
+        assert_eq!(ix.symplectic_product(&iz), 1); // X,Z anticommute on right
+        assert_eq!(ix.symplectic_product(&ix), 0);
+        assert_eq!(zx.symplectic_product(&iz), 1); // X,Z on right anticommute
+        assert_eq!(zx.symplectic_product(&zx), 0);
+    }
+
+    #[test]
+    fn enumerate_1q_gives_xyz() {
+        let all = PauliString::enumerate_nonidentity(1);
+        assert_eq!(all.len(), 3);
+        assert_eq!(all[0], PauliString::from_label("X").unwrap());
+        assert_eq!(all[1], PauliString::from_label("Y").unwrap());
+        assert_eq!(all[2], PauliString::from_label("Z").unwrap());
+    }
+
+    #[test]
+    fn enumerate_2q_gives_15() {
+        let all = PauliString::enumerate_nonidentity(2);
+        assert_eq!(all.len(), 15);
+        // First should be IX (idx 1 = 0b01 = 0|X).
+        assert_eq!(all[0], PauliString::from_label("IX").unwrap());
+        // Last should be ZZ (idx 15 = 0b1111 = Z|Z).
+        assert_eq!(all[14], PauliString::from_label("ZZ").unwrap());
+    }
+}
diff --git a/exp/pecos-lindblad/src/gate.rs b/exp/pecos-lindblad/src/gate.rs
new file mode 100644
index 000000000..81c19cbb1
--- /dev/null
+++ b/exp/pecos-lindblad/src/gate.rs
@@ -0,0 +1,191 @@
+// Copyright 2026 The PECOS Developers
+//
+// Licensed under the Apache License, Version 2.0 (the "License"); you may not use this file except
+// in compliance with the License. You may obtain a copy of the License at
+//
+//     https://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software distributed under the License
+// is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express
+// or implied. See the License for the specific language governing permissions and limitations under
+// the License.
+
+//! Gate type: ideal Hamiltonian + noise Lindbladian + duration.
+
+use num_complex::Complex64;
+
+use crate::lindbladian::Lindbladian;
+use crate::matrix::{self, Matrix};
+
+/// A physical gate with its ideal rotation, noise model, and duration.
+#[derive(Clone, Debug)]
+pub struct Gate {
+    pub label: String,
+    pub num_qubits: usize,
+    /// Noise-free part of the dynamics. Sets the interaction frame.
+    pub ideal: Lindbladian,
+    /// Noise (coherent + incoherent) applied during the gate.
+    pub noise: Lindbladian,
+    /// Gate duration in the same time units as `gamma_j` of the noise.
+    pub tau_g: f64,
+}
+
+impl Gate {
+    /// Construct a gate from an arbitrary ideal Hamiltonian `H_g`, a noise
+    /// [`Lindbladian`], and a duration `tau_g`. Provides a general escape
+    /// hatch for gate types beyond the named constructors (e.g. iSWAP,
+    /// XX_theta, arbitrary SU(4)).
+    ///
+    /// The ideal Hamiltonian is passed as a `d x d` matrix where
+    /// `d = 2^num_qubits`. It must be Hermitian (caller's responsibility;
+    /// [`matrix::expm`] assumes this for unitarity).
+    pub fn from_hamiltonian(
+        label: impl Into<String>,
+        num_qubits: usize,
+        ideal_hamiltonian: Matrix,
+        noise: Lindbladian,
+        tau_g: f64,
+    ) -> Self {
+        let d = 1usize << num_qubits;
+        assert_eq!(ideal_hamiltonian.len(), d * d, "ideal H wrong shape");
+        assert_eq!(noise.d, d, "noise dim mismatch");
+        assert!(tau_g >= 0.0, "tau_g must be non-negative, got {}", tau_g);
+        // Lindbladian::new checks Hermiticity of its Hamiltonian input.
+        let ideal = Lindbladian::new(d, ideal_hamiltonian, Vec::new());
+        Self {
+            label: label.into(),
+            num_qubits,
+            ideal,
+            noise,
+            tau_g,
+        }
+    }
+
+    /// Identity gate (no ideal Hamiltonian) with a given noise Lindbladian
+    /// and duration.
+    pub fn identity(num_qubits: usize, noise: Lindbladian, tau_g: f64) -> Self {
+        let d = 1 << num_qubits;
+        assert_eq!(noise.d, d, "noise dim mismatch");
+        Self {
+            label: "I".to_string(),
+            num_qubits,
+            ideal: Lindbladian::zero(d),
+            noise,
+            tau_g,
+        }
+    }
+
+    /// 1-qubit arbitrary-angle X rotation: `X_theta = exp(-i theta/2 X)`.
+    /// Parameterized by drive frequency `omega_x` and rotation angle
+    /// `theta`; gate duration is `theta / omega_x`.
+    pub fn x_theta(omega_x: f64, theta: f64, noise: Lindbladian) -> Self {
+        assert!(omega_x > 0.0, "omega_x must be positive");
+        assert_eq!(noise.d, 2, "x_theta is 1-qubit");
+        let d = 2;
+        // H_g = (omega_x / 2) * X
+        let h_g: Matrix = matrix::scale(
+            &matrix::pauli_1q(crate::basis::Pauli1::X),
+            Complex64::new(omega_x / 2.0, 0.0),
+        );
+        let ideal = Lindbladian::new(d, h_g, Vec::new());
+        let tau_g = theta / omega_x;
+        Self {
+            label: format!("X_{{{:.4}}}", theta),
+            num_qubits: 1,
+            ideal,
+            noise,
+            tau_g,
+        }
+    }
+
+    /// 3-qubit `CX_theta ⊗ I` gate with coherent IZZ crosstalk between
+    /// target (qubit 1) and spectator (qubit 2). `H_g = (omega/2)(IXI - ZXI)`,
+    /// `H_delta = (delta/2) IZZ`, `tau_g = theta/omega`.
+    ///
+    /// The spectator qubit (q2) is untouched by the ideal gate but
+    /// experiences a `ZZ` interaction with the target. This is the 3Q
+    /// crosstalk case from arXiv:2502.03462 eqs. 1007-1011, the only
+    /// non-trivial 3Q case in the paper.
+    ///
+    /// Noise on this gate is **purely coherent** (zero c_ops) -- use
+    /// [`crate::synthesize_exact_unitary`] to synthesize Pauli-Lindblad
+    /// rates (the Omega_1 dissipative-noise path gives zero for coherent
+    /// noise).
+    pub fn cx_theta_with_izz_crosstalk(omega: f64, theta: f64, delta: f64) -> Self {
+        use crate::basis::Pauli1;
+        assert!(omega > 0.0, "omega must be positive");
+        let d = 8;
+        let i2 = matrix::identity(2);
+        let x = matrix::pauli_1q(Pauli1::X);
+        let z = matrix::pauli_1q(Pauli1::Z);
+        // H_g = (omega / 2) * (IXI - ZXI)
+        let ixi = matrix::kron(&matrix::kron(&i2, &x, 2, 2), &i2, 4, 2);
+        let zxi = matrix::kron(&matrix::kron(&z, &x, 2, 2), &i2, 4, 2);
+        let diff = matrix::sub(&ixi, &zxi);
+        let h_g = matrix::scale(&diff, Complex64::new(omega / 2.0, 0.0));
+        let ideal = Lindbladian::new(d, h_g, Vec::new());
+        // H_delta = (delta / 2) * IZZ
+        let izz = matrix::kron(&matrix::kron(&i2, &z, 2, 2), &z, 4, 2);
+        let h_delta = matrix::scale(&izz, Complex64::new(delta / 2.0, 0.0));
+        let noise = Lindbladian::new(d, h_delta, Vec::new());
+        let tau_g = theta / omega;
+        Self {
+            label: format!("CX_{{{:.4}}}⊗I+IZZ({:.4})", theta, delta),
+            num_qubits: 3,
+            ideal,
+            noise,
+            tau_g,
+        }
+    }
+
+    /// 2-qubit arbitrary-angle CX rotation:
+    /// `CX_theta = exp(-i (theta/2) (IX - ZX))`. Block-diagonal in the
+    /// computational basis with the top 2x2 block zero (identity action on
+    /// `|0l>`) and the bottom block = `omega_cx * X` (X rotation on the
+    /// target when control = `|1>`).
+    /// Reference: arXiv:2502.03462 lines 913-924.
+    pub fn cx_theta(omega_cx: f64, theta: f64, noise: Lindbladian) -> Self {
+        use crate::basis::Pauli1;
+        assert!(omega_cx > 0.0, "omega_cx must be positive");
+        assert_eq!(noise.d, 4, "cx_theta is 2-qubit");
+        let d = 4;
+        let i2 = matrix::identity(2);
+        let x = matrix::pauli_1q(Pauli1::X);
+        let z = matrix::pauli_1q(Pauli1::Z);
+        let ix = matrix::kron(&i2, &x, 2, 2);
+        let zx = matrix::kron(&z, &x, 2, 2);
+        // H_g = (omega_cx / 2) * (IX - ZX)
+        let diff = matrix::sub(&ix, &zx);
+        let h_g = matrix::scale(&diff, Complex64::new(omega_cx / 2.0, 0.0));
+        let ideal = Lindbladian::new(d, h_g, Vec::new());
+        let tau_g = theta / omega_cx;
+        Self {
+            label: format!("CX_{{{:.4}}}", theta),
+            num_qubits: 2,
+            ideal,
+            noise,
+            tau_g,
+        }
+    }
+
+    /// 2-qubit arbitrary-angle CZ rotation:
+    /// `CZ_theta = exp(-i (theta/2) (II - IZ - ZI + ZZ))`.
+    /// In computational basis `H_g = diag(0, 0, 0, 2 * omega_cz)`.
+    /// Reference: arXiv:2502.03462 lines 885-891.
+    pub fn cz_theta(omega_cz: f64, theta: f64, noise: Lindbladian) -> Self {
+        assert!(omega_cz > 0.0, "omega_cz must be positive");
+        assert_eq!(noise.d, 4, "cz_theta is 2-qubit");
+        let d = 4;
+        let mut h_g = matrix::zeros(d);
+        h_g[3 * d + 3] = Complex64::new(2.0 * omega_cz, 0.0);
+        let ideal = Lindbladian::new(d, h_g, Vec::new());
+        let tau_g = theta / omega_cz;
+        Self {
+            label: format!("CZ_{{{:.4}}}", theta),
+            num_qubits: 2,
+            ideal,
+            noise,
+            tau_g,
+        }
+    }
+}
diff --git a/exp/pecos-lindblad/src/lib.rs b/exp/pecos-lindblad/src/lib.rs
new file mode 100644
index 000000000..4f21a533c
--- /dev/null
+++ b/exp/pecos-lindblad/src/lib.rs
@@ -0,0 +1,104 @@
+// Copyright 2026 The PECOS Developers
+//
+// Licensed under the Apache License, Version 2.0 (the "License"); you may not use this file except
+// in compliance with the License. You may obtain a copy of the License at
+//
+//     https://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software distributed under the License
+// is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express
+// or implied. See the License for the specific language governing permissions and limitations under
+// the License.
+
+//! # pecos-lindblad
+//!
+//! Lindblad-to-Pauli-Lindblad noise synthesis for PECOS. Given a per-gate
+//! Lindbladian `{H_ideal, noise, tau_g}`, produces the effective
+//! Pauli-Lindblad rates `{lambda_k}` that feed
+//! [`pecos_qec::dem_stab::DemStabSim`] via
+//! [`pecos_qec::fault_tolerance::dem_builder::PerGateTypeNoise`].
+//!
+//! # Golden path
+//!
+//! ```
+//! use pecos_lindblad::{
+//!     noise_models::ad_pd_1q, synthesize_identity_1q, Gate, Pauli1, PauliString,
+//! };
+//!
+//! // Device parameters in physical (T_1, T_2) terms.
+//! let t1 = 100e-6;
+//! let t2 = 80e-6;
+//! let tau_g = 1e-6;
+//!
+//! let noise = ad_pd_1q(t1, t2);
+//! let gate = Gate::identity(1, noise, tau_g);
+//! let pl = synthesize_identity_1q(&gate);
+//!
+//! let lambda_x = pl.rate(&PauliString::single(Pauli1::X));
+//! assert!(lambda_x > 0.0);
+//! ```
+//!
+//! # Picking a synthesis path
+//!
+//! - [`synthesize_identity_1q`] -- fastest for 1-qubit identity gates
+//!   (closed-form, machine-precision).
+//! - [`synthesize_numerical`] -- any gate with purely dissipative noise
+//!   (AD, PD, depolarizing). Simpson's rule on the interaction-frame
+//!   Lindbladian.
+//! - [`synthesize_superop`] -- general: any gate, any mix of coherent
+//!   and dissipative noise, all orders of Magnus. Slower but correct
+//!   in all regimes.
+//!
+//! # Feature flags
+//!
+//! - `serde` -- (de)serialize [`PauliLindbladModel`] for caching.
+//!
+//! # Modules by audience
+//!
+//! - **Core forward synthesis**: [`Gate`], [`synthesize_identity_1q`],
+//!   [`synthesize_numerical`], [`synthesize_superop`].
+//! - **Noise-model verification** (diff helpers + analytic `(T_1, T_2)`
+//!   recovery + Monte Carlo UQ): see [`noise_models`] and
+//!   [`PauliLindbladModel::diff`], [`PauliLindbladModel::diagnose_gap`].
+//! - **Non-Markovian (TCL)**: see [`time_dep`] for 1/f dephasing,
+//!   Gaussian decay, coloured coherent noise.
+//!
+//! # Verified gate families (arXiv:2502.03462)
+//!
+//! | Gate | Paper eqs. | Constructor |
+//! |---|---|---|
+//! | 1Q identity + AD+PD (exact) | line 812 | [`Gate::identity`] |
+//! | 1Q `X_theta` + AD+PD | 869-874 | [`Gate::x_theta`] |
+//! | 2Q `CZ_theta` + AD+PD | 896-906 | [`Gate::cz_theta`] |
+//! | 2Q `CX_theta` + AD+PD | 929-956 | [`Gate::cx_theta`] |
+//! | 2Q coherent IZ/ZI/ZZ phase | 981, 986-990 | any `Gate` + `coherent_phase_2q` |
+//! | 3Q `CX ⊗ I` + IZZ crosstalk | 1009-1011 | [`Gate::cx_theta_with_izz_crosstalk`] |
+//!
+//! See `design/lindblad_magnus_algorithm.md` for the math spec.
+
+pub mod basis;
+pub mod gate;
+pub mod lindbladian;
+pub mod matrix;
+pub mod noise_models;
+pub mod pauli_lindblad;
+pub mod synthesis;
+pub mod time_dep;
+
+// Core API -- the golden path.
+pub use basis::{Pauli1, PauliString};
+pub use gate::Gate;
+pub use lindbladian::Lindbladian;
+pub use pauli_lindblad::PauliLindbladModel;
+pub use synthesis::{
+    DEFAULT_N_SLICES, DEFAULT_N_STEPS, synthesize_identity_1q, synthesize_numerical,
+    synthesize_superop,
+};
+
+// Advanced synthesis paths -- specialized cases of `synthesize_superop`.
+// Exposed for users who know they need the specific behavior.
+pub use synthesis::{
+    synthesize_exact_unitary, synthesize_numerical_1q, synthesize_superop_identity,
+};
+
+pub use time_dep::{HermitianFn, RateFn, TimeDepLindbladian, synthesize_superop_time_dep};
diff --git a/exp/pecos-lindblad/src/lindbladian.rs b/exp/pecos-lindblad/src/lindbladian.rs
new file mode 100644
index 000000000..5093158cc
--- /dev/null
+++ b/exp/pecos-lindblad/src/lindbladian.rs
@@ -0,0 +1,127 @@
+// Copyright 2026 The PECOS Developers
+//
+// Licensed under the Apache License, Version 2.0 (the "License"); you may not use this file except
+// in compliance with the License. You may obtain a copy of the License at
+//
+//     https://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software distributed under the License
+// is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express
+// or implied. See the License for the specific language governing permissions and limitations under
+// the License.
+
+//! Lindbladian type: Hermitian Hamiltonian plus rate-weighted collapse operators.
+
+use num_complex::Complex64;
+
+use crate::matrix::{self, Matrix};
+
+/// Time-independent Lindbladian of form
+/// `drho/dt = -i[H, rho] + sum_j gamma_j * D[c_j] rho`
+/// where `D[c] rho = c rho c^dag - 1/2 {c^dag c, rho}`.
+#[derive(Clone, Debug)]
+pub struct Lindbladian {
+    pub d: usize,
+    pub hamiltonian: Matrix,
+    pub collapse: Vec<(Matrix, f64)>,
+}
+
+impl Lindbladian {
+    pub fn new(d: usize, hamiltonian: Matrix, collapse: Vec<(Matrix, f64)>) -> Self {
+        assert_eq!(hamiltonian.len(), d * d, "hamiltonian wrong shape");
+        assert!(
+            matrix::is_hermitian(&hamiltonian, d, 1e-10),
+            "Lindbladian Hamiltonian must be Hermitian",
+        );
+        for (c, gamma) in &collapse {
+            assert_eq!(c.len(), d * d, "collapse op wrong shape");
+            assert!(
+                *gamma >= 0.0,
+                "collapse rate must be non-negative, got {}",
+                gamma
+            );
+        }
+        Self {
+            d,
+            hamiltonian,
+            collapse,
+        }
+    }
+
+    /// Zero Hamiltonian with no collapse ops (no-op).
+    pub fn zero(d: usize) -> Self {
+        Self {
+            d,
+            hamiltonian: matrix::zeros(d),
+            collapse: Vec::new(),
+        }
+    }
+
+    /// Build the `d^2 x d^2` Liouville-superoperator matrix representation
+    /// of `L`. Column-stacking convention: `vec(L(rho)) = L_super * vec(rho)`.
+    ///
+    /// `L(rho) = -i[H, rho] + sum_j gamma_j * ( c_j rho c_j^dag
+    ///                                         - 1/2 {c_j^dag c_j, rho} )`
+    /// translates to:
+    ///
+    /// `L_super = -i (I ⊗ H - H^T ⊗ I)
+    ///            + sum_j gamma_j * ( conj(c_j) ⊗ c_j
+    ///                               - 1/2 I ⊗ c_j^dag c_j
+    ///                               - 1/2 (c_j^dag c_j)^T ⊗ I )`
+    ///
+    /// (Note `(c^dag)^T = conj(c)`.)
+    pub fn superoperator(&self) -> Matrix {
+        let d = self.d;
+        let d2 = d * d;
+        let id = matrix::identity(d);
+        let neg_i = Complex64::new(0.0, -1.0);
+
+        // Hamiltonian part: -i (I ⊗ H - H^T ⊗ I).
+        let h_t = matrix::transpose(&self.hamiltonian, d);
+        let coh = matrix::sub(
+            &matrix::kron(&id, &self.hamiltonian, d, d),
+            &matrix::kron(&h_t, &id, d, d),
+        );
+        let mut l_super = matrix::scale(&coh, neg_i);
+
+        for (c, gamma) in &self.collapse {
+            let c_bar = matrix::conj(c);
+            let c_dag = matrix::dag(c, d);
+            let cdag_c = matrix::matmul(&c_dag, c, d);
+            let cdag_c_t = matrix::transpose(&cdag_c, d);
+
+            // gamma * ( c_bar ⊗ c - 1/2 I ⊗ c^dag c - 1/2 (c^dag c)^T ⊗ I )
+            let term_a = matrix::kron(&c_bar, c, d, d);
+            let term_b = matrix::kron(&id, &cdag_c, d, d);
+            let term_c = matrix::kron(&cdag_c_t, &id, d, d);
+            let inner = matrix::sub(
+                &term_a,
+                &matrix::add(
+                    &matrix::scale(&term_b, Complex64::new(0.5, 0.0)),
+                    &matrix::scale(&term_c, Complex64::new(0.5, 0.0)),
+                ),
+            );
+            let scaled = matrix::scale(&inner, Complex64::new(*gamma, 0.0));
+            l_super = matrix::add(&l_super, &scaled);
+        }
+
+        assert_eq!(l_super.len(), d2 * d2);
+        l_super
+    }
+
+    /// Apply `L` to a matrix `rho`. Returns `L(rho)`.
+    pub fn apply(&self, rho: &Matrix) -> Matrix {
+        let d = self.d;
+        let neg_i = Complex64::new(0.0, -1.0);
+        let mut out = matrix::scale(&matrix::commutator(&self.hamiltonian, rho, d), neg_i);
+        for (c, gamma) in &self.collapse {
+            let cdag = matrix::dag(c, d);
+            let c_rho_cdag = matrix::matmul(&matrix::matmul(c, rho, d), &cdag, d);
+            let cdag_c = matrix::matmul(&cdag, c, d);
+            let acom = matrix::anticommutator(&cdag_c, rho, d);
+            let diss = matrix::sub(&c_rho_cdag, &matrix::scale(&acom, Complex64::new(0.5, 0.0)));
+            out = matrix::add(&out, &matrix::scale(&diss, Complex64::new(*gamma, 0.0)));
+        }
+        out
+    }
+}
diff --git a/exp/pecos-lindblad/src/matrix.rs b/exp/pecos-lindblad/src/matrix.rs
new file mode 100644
index 000000000..fb1773949
--- /dev/null
+++ b/exp/pecos-lindblad/src/matrix.rs
@@ -0,0 +1,383 @@
+// Copyright 2026 The PECOS Developers
+//
+// Licensed under the Apache License, Version 2.0 (the "License"); you may not use this file except
+// in compliance with the License. You may obtain a copy of the License at
+//
+//     https://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software distributed under the License
+// is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express
+// or implied. See the License for the specific language governing permissions and limitations under
+// the License.
+
+//! Minimal dense complex-matrix helpers for Phase 1.
+//!
+//! Matrices are stored row-major as `Vec<Complex64>` of length `d*d`. Caller
+//! tracks `d`. This is intentionally primitive -- swap to faer / ndarray once
+//! Phase 1 numbers prove out.
+
+use num_complex::Complex64;
+
+use crate::basis::{Pauli1, PauliString};
+
+pub type Matrix = Vec<Complex64>;
+
+pub fn zeros(d: usize) -> Matrix {
+    vec![Complex64::new(0.0, 0.0); d * d]
+}
+
+pub fn identity(d: usize) -> Matrix {
+    let mut m = zeros(d);
+    for i in 0..d {
+        m[i * d + i] = Complex64::new(1.0, 0.0);
+    }
+    m
+}
+
+pub fn matmul(a: &Matrix, b: &Matrix, d: usize) -> Matrix {
+    let mut c = zeros(d);
+    for i in 0..d {
+        for k in 0..d {
+            let aik = a[i * d + k];
+            if aik == Complex64::new(0.0, 0.0) {
+                continue;
+            }
+            for j in 0..d {
+                c[i * d + j] += aik * b[k * d + j];
+            }
+        }
+    }
+    c
+}
+
+/// Conjugate transpose.
+pub fn dag(a: &Matrix, d: usize) -> Matrix {
+    let mut b = zeros(d);
+    for i in 0..d {
+        for j in 0..d {
+            b[j * d + i] = a[i * d + j].conj();
+        }
+    }
+    b
+}
+
+/// Plain transpose (no complex conjugation).
+pub fn transpose(a: &Matrix, d: usize) -> Matrix {
+    let mut b = zeros(d);
+    for i in 0..d {
+        for j in 0..d {
+            b[j * d + i] = a[i * d + j];
+        }
+    }
+    b
+}
+
+/// Element-wise complex conjugate.
+pub fn conj(a: &Matrix) -> Matrix {
+    a.iter().map(|c| c.conj()).collect()
+}
+
+pub fn trace(a: &Matrix, d: usize) -> Complex64 {
+    (0..d).map(|i| a[i * d + i]).sum()
+}
+
+pub fn scale(a: &Matrix, s: Complex64) -> Matrix {
+    a.iter().map(|x| x * s).collect()
+}
+
+pub fn add(a: &Matrix, b: &Matrix) -> Matrix {
+    a.iter().zip(b.iter()).map(|(x, y)| x + y).collect()
+}
+
+pub fn sub(a: &Matrix, b: &Matrix) -> Matrix {
+    a.iter().zip(b.iter()).map(|(x, y)| x - y).collect()
+}
+
+/// `A*B - B*A`.
+pub fn commutator(a: &Matrix, b: &Matrix, d: usize) -> Matrix {
+    sub(&matmul(a, b, d), &matmul(b, a, d))
+}
+
+/// `A*B + B*A`.
+pub fn anticommutator(a: &Matrix, b: &Matrix, d: usize) -> Matrix {
+    add(&matmul(a, b, d), &matmul(b, a, d))
+}
+
+/// 2x2 Pauli matrix for a single-qubit Pauli operator.
+pub fn pauli_1q(p: Pauli1) -> Matrix {
+    let z = Complex64::new(0.0, 0.0);
+    let o = Complex64::new(1.0, 0.0);
+    let i = Complex64::new(0.0, 1.0);
+    match p {
+        Pauli1::I => vec![o, z, z, o],
+        Pauli1::X => vec![z, o, o, z],
+        Pauli1::Y => vec![z, -i, i, z],
+        Pauli1::Z => vec![o, z, z, -o],
+    }
+}
+
+/// Lowering operator sigma_- = |1><0| = [[0,0],[1,0]].
+pub fn sigma_minus() -> Matrix {
+    let z = Complex64::new(0.0, 0.0);
+    let o = Complex64::new(1.0, 0.0);
+    vec![z, z, o, z]
+}
+
+/// Kronecker product of `a` (da x da) and `b` (db x db). Result is
+/// `(da * db) x (da * db)`.
+pub fn kron(a: &Matrix, b: &Matrix, da: usize, db: usize) -> Matrix {
+    let d = da * db;
+    let mut out = zeros(d);
+    for i in 0..da {
+        for j in 0..da {
+            let aij = a[i * da + j];
+            if aij == Complex64::new(0.0, 0.0) {
+                continue;
+            }
+            for k in 0..db {
+                for l in 0..db {
+                    let bkl = b[k * db + l];
+                    let row = i * db + k;
+                    let col = j * db + l;
+                    out[row * d + col] = aij * bkl;
+                }
+            }
+        }
+    }
+    out
+}
+
+/// Matrix representation of a multi-qubit Pauli string (tensor-product
+/// of 2x2 Pauli matrices, left-to-right).
+pub fn pauli_string_mat(ps: &PauliString) -> Matrix {
+    assert!(!ps.0.is_empty(), "empty PauliString");
+    let mut acc = pauli_1q(ps.0[0]);
+    let mut d = 2;
+    for p in ps.0.iter().skip(1) {
+        acc = kron(&acc, &pauli_1q(*p), d, 2);
+        d *= 2;
+    }
+    acc
+}
+
+/// Check whether a d x d matrix is (numerically) Hermitian: `M = M^dag`.
+/// Returns true if all `|M_ij - conj(M_ji)| < tol`.
+pub fn is_hermitian(m: &Matrix, d: usize, tol: f64) -> bool {
+    assert_eq!(m.len(), d * d, "is_hermitian: wrong shape");
+    for i in 0..d {
+        for j in 0..d {
+            if (m[i * d + j] - m[j * d + i].conj()).norm() > tol {
+                return false;
+            }
+        }
+    }
+    true
+}
+
+/// Check whether a d x d matrix is (numerically) diagonal.
+pub fn is_diagonal(m: &Matrix, d: usize, tol: f64) -> bool {
+    for i in 0..d {
+        for j in 0..d {
+            if i == j {
+                continue;
+            }
+            if m[i * d + j].norm() > tol {
+                return false;
+            }
+        }
+    }
+    true
+}
+
+/// Is a 4x4 matrix 2x2-block-diagonal? I.e. off-diagonal 2x2 blocks zero.
+pub fn is_2x2_block_diagonal(m: &Matrix, tol: f64) -> bool {
+    assert_eq!(m.len(), 16, "is_2x2_block_diagonal requires 4x4 input");
+    for r in 0..2 {
+        for c in 2..4 {
+            if m[r * 4 + c].norm() > tol {
+                return false;
+            }
+            if m[c * 4 + r].norm() > tol {
+                return false;
+            }
+        }
+    }
+    true
+}
+
+/// `exp(-i * H * t)` for a 4x4 2x2-block-diagonal Hermitian `H`, assuming
+/// each 2x2 block is traceless (true for CX_theta: blocks are `0_2` and
+/// `omega * X`).
+pub fn exp_minus_i_h_t_2x2_block_diag(h: &Matrix, t: f64) -> Matrix {
+    let d = 4;
+    assert_eq!(h.len(), d * d);
+    let mut ul = zeros(2);
+    let mut lr = zeros(2);
+    for r in 0..2 {
+        for c in 0..2 {
+            ul[r * 2 + c] = h[r * 4 + c];
+            lr[r * 2 + c] = h[(r + 2) * 4 + (c + 2)];
+        }
+    }
+    let ul_exp = exp_minus_i_h_t_1q_traceless(&ul, t);
+    let lr_exp = exp_minus_i_h_t_1q_traceless(&lr, t);
+    let mut out = zeros(d);
+    for r in 0..2 {
+        for c in 0..2 {
+            out[r * 4 + c] = ul_exp[r * 2 + c];
+            out[(r + 2) * 4 + (c + 2)] = lr_exp[r * 2 + c];
+        }
+    }
+    out
+}
+
+/// `exp(-i * H * t)` for a Hermitian `H`. Dispatches:
+/// - `H` diagonal -> elementwise exp (any `d`).
+/// - `d == 2`, non-diagonal, traceless -> Bloch form.
+/// - `d == 4`, 2x2-block-diagonal with traceless blocks -> block-wise
+///   Bloch form (covers CX_theta).
+/// - else falls through to general [`expm`] scaling-squaring.
+pub fn exp_minus_i_h_t(h: &Matrix, d: usize, t: f64) -> Matrix {
+    if is_diagonal(h, d, 1e-14) {
+        let mut u = zeros(d);
+        for i in 0..d {
+            let arg = Complex64::new(0.0, -h[i * d + i].re * t);
+            u[i * d + i] = arg.exp();
+        }
+        return u;
+    }
+    if d == 2 {
+        return exp_minus_i_h_t_1q_traceless(h, t);
+    }
+    if d == 4 && is_2x2_block_diagonal(h, 1e-14) {
+        return exp_minus_i_h_t_2x2_block_diag(h, t);
+    }
+    let arg = scale(h, Complex64::new(0.0, -t));
+    expm(&arg, d)
+}
+
+/// General matrix exponential via Taylor series + scaling + squaring.
+///
+/// - Scale: find `s` such that `||A/2^s|| < 0.5` (so Taylor converges quickly).
+/// - Taylor: `exp(A/2^s) ≈ sum_{k=0..=N} (A/2^s)^k / k!` with `N=20`.
+/// - Squaring: `exp(A) = (exp(A/2^s))^(2^s)` via `s` matrix squarings.
+///
+/// Accuracy ~machine-precision for Hermitian `A` with arbitrary norm;
+/// validated in module tests against Bloch-form and diagonal paths.
+pub fn expm(a: &Matrix, d: usize) -> Matrix {
+    let norm = inf_norm(a, d);
+    if norm < 1e-14 {
+        return identity(d);
+    }
+    // Choose s so that ||A / 2^s|| < 0.5.
+    let s_float = (norm / 0.5).log2().max(0.0).ceil();
+    let s: u32 = s_float as u32;
+    let factor = Complex64::new(2f64.powi(-(s as i32)), 0.0);
+    let scaled = scale(a, factor);
+    let mut result = taylor_exp(&scaled, d, 20);
+    for _ in 0..s {
+        result = matmul(&result, &result, d);
+    }
+    result
+}
+
+/// Taylor series of `exp(A)` truncated at degree `n`. Assumes `||A||`
+/// is already small (typically `< 0.5`).
+fn taylor_exp(a: &Matrix, d: usize, n: usize) -> Matrix {
+    let mut term = identity(d);
+    let mut sum = identity(d);
+    for k in 1..=n {
+        term = scale(&matmul(&term, a, d), Complex64::new(1.0 / k as f64, 0.0));
+        sum = add(&sum, &term);
+    }
+    sum
+}
+
+/// Infinity norm: max over rows of `sum_j |A_ij|`.
+pub fn inf_norm(a: &Matrix, d: usize) -> f64 {
+    (0..d)
+        .map(|i| (0..d).map(|j| a[i * d + j].norm()).sum::<f64>())
+        .fold(0.0, f64::max)
+}
+
+/// Column-stack vectorization `vec(M)` of a `d x d` matrix (length `d^2`).
+/// Convention: `vec(A rho B) = (B^T ⊗ A) vec(rho)`.
+pub fn vec_of(m: &Matrix, d: usize) -> Vec<Complex64> {
+    assert_eq!(m.len(), d * d);
+    let mut out = vec![Complex64::new(0.0, 0.0); d * d];
+    // Column-major layout: vec(M)[i + d*j] = M[i, j] = m[i*d + j].
+    for i in 0..d {
+        for j in 0..d {
+            out[i + d * j] = m[i * d + j];
+        }
+    }
+    out
+}
+
+/// Inverse of [`vec_of`]: reshape a `d^2` vector back to a `d x d`
+/// matrix (row-major storage).
+pub fn unvec(v: &[Complex64], d: usize) -> Matrix {
+    assert_eq!(v.len(), d * d);
+    let mut m = vec![Complex64::new(0.0, 0.0); d * d];
+    for i in 0..d {
+        for j in 0..d {
+            m[i * d + j] = v[i + d * j];
+        }
+    }
+    m
+}
+
+/// Matrix-vector product `A * v` for a `n x n` matrix `A` and length-`n`
+/// vector `v`.
+pub fn matvec(a: &Matrix, v: &[Complex64], n: usize) -> Vec<Complex64> {
+    assert_eq!(a.len(), n * n);
+    assert_eq!(v.len(), n);
+    let mut out = vec![Complex64::new(0.0, 0.0); n];
+    for i in 0..n {
+        let mut s = Complex64::new(0.0, 0.0);
+        for j in 0..n {
+            s += a[i * n + j] * v[j];
+        }
+        out[i] = s;
+    }
+    out
+}
+
+/// Matrix exponential `exp(-i * H * t)` for a 2x2 traceless Hermitian H.
+/// Uses the Bloch form: `exp(-i H t) = cos(r t) I - i sin(r t) H / r`
+/// where `r = sqrt(c_x^2 + c_y^2 + c_z^2)` is the Pauli-decomposition norm.
+/// Panics if `H` has nonzero trace.
+pub fn exp_minus_i_h_t_1q_traceless(h: &Matrix, t: f64) -> Matrix {
+    assert_eq!(h.len(), 4, "requires a 2x2 matrix");
+    // Check Hermitian (tolerant).
+    let h00 = h[0];
+    let h01 = h[1];
+    let h10 = h[2];
+    let h11 = h[3];
+    assert!(
+        h00.im.abs() < 1e-12 && h11.im.abs() < 1e-12,
+        "H not Hermitian (diagonal)"
+    );
+    assert!(
+        (h10 - h01.conj()).norm() < 1e-12,
+        "H not Hermitian (off-diagonal)"
+    );
+    let tr = (h00 + h11).re;
+    assert!(tr.abs() < 1e-12, "H must be traceless; got trace = {}", tr);
+
+    // Pauli decomposition: H = c_x X + c_y Y + c_z Z.
+    let c_x = h01.re;
+    let c_y = -h01.im; // since H_{01} = c_x - i c_y
+    let c_z = (h00.re - h11.re) * 0.5;
+
+    let r = (c_x * c_x + c_y * c_y + c_z * c_z).sqrt();
+    if r < 1e-15 {
+        return identity(2);
+    }
+    let c = (r * t).cos();
+    let s = (r * t).sin() / r;
+    let minus_i_s = Complex64::new(0.0, -s);
+    // result = c * I - i s * H
+    let i2 = identity(2);
+    add(&scale(&i2, Complex64::new(c, 0.0)), &scale(h, minus_i_s))
+}
diff --git a/exp/pecos-lindblad/src/noise_models.rs b/exp/pecos-lindblad/src/noise_models.rs
new file mode 100644
index 000000000..33202bade
--- /dev/null
+++ b/exp/pecos-lindblad/src/noise_models.rs
@@ -0,0 +1,434 @@
+// Copyright 2026 The PECOS Developers
+//
+// Licensed under the Apache License, Version 2.0 (the "License"); you may not use this file except
+// in compliance with the License. You may obtain a copy of the License at
+//
+//     https://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software distributed under the License
+// is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express
+// or implied. See the License for the specific language governing permissions and limitations under
+// the License.
+
+//! Device-parameter convenience constructors for noise [`Lindbladian`]s.
+//!
+//! Real QEC experiments are typically specified in terms of coherence
+//! times `(T_1, T_2)`, not raw Lindblad rates. This module converts
+//! between them and builds the tensor-product Lindbladians that the
+//! paper-fixture tests would otherwise hand-roll.
+//!
+//! # T1/T2 convention
+//!
+//! Standard textbook relation:
+//!
+//! ```text
+//! beta_down = 1 / T_1
+//! 1 / T_2   = 1 / (2 T_1) + 1 / T_phi
+//! beta_phi  = 1 / T_phi = 1/T_2 - 1/(2 T_1)
+//! ```
+//!
+//! `T_2 >= 2 T_1 / (1 + 2 T_1 / T_phi)`; pure-dephasing-free limit is
+//! `T_2 = 2 T_1` with `beta_phi = 0`.
+
+use num_complex::Complex64;
+
+use crate::basis::Pauli1;
+use crate::lindbladian::Lindbladian;
+use crate::matrix::{self, Matrix};
+
+/// Convert `(T_1, T_2)` to `(beta_down, beta_phi)`. Panics if `T_2 > 2 T_1`
+/// (unphysical -- dephasing would be negative).
+pub fn t1_t2_to_rates(t1: f64, t2: f64) -> (f64, f64) {
+    assert!(t1 > 0.0, "T_1 must be positive");
+    assert!(t2 > 0.0, "T_2 must be positive");
+    let beta_down = 1.0 / t1;
+    let inv_tphi = 1.0 / t2 - 1.0 / (2.0 * t1);
+    assert!(
+        inv_tphi >= -1e-15,
+        "T_2 ({}) > 2 T_1 ({}) violates 1/T_phi = 1/T_2 - 1/(2 T_1) >= 0",
+        t2,
+        2.0 * t1,
+    );
+    (beta_down, inv_tphi.max(0.0))
+}
+
+/// 1-qubit amplitude-damping + pure-dephasing Lindbladian from `(T_1, T_2)`.
+///
+/// Collapse operators: `sigma_- with rate 1/T_1`, `Z with rate beta_phi/2`
+/// where `beta_phi = 1/T_2 - 1/(2 T_1)`.
+pub fn ad_pd_1q(t1: f64, t2: f64) -> Lindbladian {
+    let (beta_down, beta_phi) = t1_t2_to_rates(t1, t2);
+    let d = 2;
+    let hamiltonian = matrix::zeros(d);
+    let collapse: Vec<(Matrix, f64)> = vec![
+        (matrix::sigma_minus(), beta_down),
+        (matrix::pauli_1q(Pauli1::Z), beta_phi / 2.0),
+    ];
+    Lindbladian::new(d, hamiltonian, collapse)
+}
+
+/// 2-qubit amplitude-damping + pure-dephasing, independently parameterised
+/// on left (`l`) and right (`r`) qubits.
+pub fn ad_pd_2q(t1_l: f64, t1_r: f64, t2_l: f64, t2_r: f64) -> Lindbladian {
+    let (bd_l, bp_l) = t1_t2_to_rates(t1_l, t2_l);
+    let (bd_r, bp_r) = t1_t2_to_rates(t1_r, t2_r);
+    let d = 4;
+    let i2 = matrix::identity(2);
+    let sm = matrix::sigma_minus();
+    let z = matrix::pauli_1q(Pauli1::Z);
+    let sm_l = matrix::kron(&sm, &i2, 2, 2);
+    let sm_r = matrix::kron(&i2, &sm, 2, 2);
+    let z_l = matrix::kron(&z, &i2, 2, 2);
+    let z_r = matrix::kron(&i2, &z, 2, 2);
+    let collapse: Vec<(Matrix, f64)> = vec![
+        (sm_l, bd_l),
+        (sm_r, bd_r),
+        (z_l, bp_l / 2.0),
+        (z_r, bp_r / 2.0),
+    ];
+    Lindbladian::new(d, matrix::zeros(d), collapse)
+}
+
+/// 2-qubit coherent phase noise:
+/// `H_delta = (delta_iz/2) IZ + (delta_zi/2) ZI + (delta_zz/2) ZZ`,
+/// no collapse operators (use [`crate::synthesize_exact_unitary`]).
+pub fn coherent_phase_2q(delta_iz: f64, delta_zi: f64, delta_zz: f64) -> Lindbladian {
+    let d = 4;
+    let i2 = matrix::identity(2);
+    let z = matrix::pauli_1q(Pauli1::Z);
+    let iz = matrix::kron(&i2, &z, 2, 2);
+    let zi = matrix::kron(&z, &i2, 2, 2);
+    let zz = matrix::kron(&z, &z, 2, 2);
+    let half = Complex64::new(0.5, 0.0);
+    let h_delta = matrix::add(
+        &matrix::add(
+            &matrix::scale(&iz, Complex64::new(delta_iz, 0.0) * half),
+            &matrix::scale(&zi, Complex64::new(delta_zi, 0.0) * half),
+        ),
+        &matrix::scale(&zz, Complex64::new(delta_zz, 0.0) * half),
+    );
+    Lindbladian::new(d, h_delta, Vec::new())
+}
+
+/// Analytic back-solve: given measured PL rates from a 1Q identity gate
+/// with AD+PD noise, recover `(T_1, T_2)`.
+///
+/// Inverse of [`ad_pd_1q`] applied to [`crate::synthesize_identity_1q`]
+/// using the paper's closed form (line 812):
+///
+/// ```text
+/// lambda_x = lambda_y = beta_down * tau_g / 4  =>  T_1   = tau_g / (4 lambda_x)
+/// lambda_z = beta_phi  * tau_g / 2             =>  T_phi = tau_g / (2 lambda_z)
+/// 1/T_2 = 1/(2 T_1) + 1/T_phi                  =>  T_2   = 1 / (1/(2 T_1) + 1/T_phi)
+/// ```
+///
+/// Returns `None` if rates are inconsistent (e.g. negative or would imply
+/// `T_2 > 2 T_1`). Averages `lambda_x` and `lambda_y` for robustness
+/// against small measurement noise.
+pub fn recover_t1_t2_from_identity_1q(
+    model: &crate::PauliLindbladModel,
+    tau_g: f64,
+) -> Option<(f64, f64)> {
+    use crate::{Pauli1, PauliString};
+    if tau_g <= 0.0 {
+        return None;
+    }
+    let lam_x = model.rate(&PauliString::single(Pauli1::X));
+    let lam_y = model.rate(&PauliString::single(Pauli1::Y));
+    let lam_z = model.rate(&PauliString::single(Pauli1::Z));
+    // AD gives equal lambda_x and lambda_y; average for noise robustness.
+    let lam_avg_xy = 0.5 * (lam_x + lam_y);
+    if lam_avg_xy <= 0.0 || lam_z < 0.0 {
+        return None;
+    }
+    let t1 = tau_g / (4.0 * lam_avg_xy);
+    if t1 <= 0.0 {
+        return None;
+    }
+    // lambda_z = 0 is allowed (pure-T1 limit => T_2 = 2 T_1).
+    let t2 = if lam_z < 1e-30 {
+        2.0 * t1
+    } else {
+        let t_phi = tau_g / (2.0 * lam_z);
+        let inv_t2 = 1.0 / (2.0 * t1) + 1.0 / t_phi;
+        if inv_t2 <= 0.0 {
+            return None;
+        }
+        1.0 / inv_t2
+    };
+    Some((t1, t2))
+}
+
+/// Recovered 2-qubit coherence-time parameters for the (left, right)
+/// qubits of a 2Q gate.
+#[derive(Clone, Copy, Debug, PartialEq)]
+pub struct RecoveredParams2Q {
+    pub t1_l: f64,
+    pub t2_l: f64,
+    pub t1_r: f64,
+    pub t2_r: f64,
+}
+
+/// Analytic 2Q recovery: given a measured `CZ_theta + AD+PD` PL model,
+/// back-solve `(T_1, T_2)` on each qubit.
+///
+/// Uses paper arXiv:2502.03462 eqs. 896-906:
+///
+/// ```text
+/// lambda_zi = (theta/2) * (beta_phi_l / omega_cz)
+/// lambda_iz = (theta/2) * (beta_phi_r / omega_cz)
+/// lambda_xi = lambda_yi = (2*theta + sin(2*theta))/16 * beta_down_l / omega_cz
+/// lambda_ix = lambda_iy = (2*theta + sin(2*theta))/16 * beta_down_r / omega_cz
+/// ```
+///
+/// Averages the degenerate-in-paper pairs (`lambda_xi` ≈ `lambda_yi`)
+/// for robustness against noisy measurements. Returns `None` if rates
+/// are inconsistent (e.g. negative) or would imply `T_2 > 2 T_1`.
+pub fn recover_ad_pd_2q_from_cz_theta(
+    model: &crate::PauliLindbladModel,
+    omega_cz: f64,
+    theta: f64,
+) -> Option<RecoveredParams2Q> {
+    use crate::PauliString;
+    if omega_cz <= 0.0 || theta <= 0.0 {
+        return None;
+    }
+    let r = |s: &str| model.rate(&PauliString::from_label(s).unwrap());
+    let factor_weight1_amp = (2.0 * theta + (2.0 * theta).sin()) / 16.0;
+
+    // Amplitude damping: average the two equal rates (paper's 2-fold degeneracy).
+    let beta_down_r = 0.5 * (r("IX") + r("IY")) * omega_cz / factor_weight1_amp;
+    let beta_down_l = 0.5 * (r("XI") + r("YI")) * omega_cz / factor_weight1_amp;
+
+    // Dephasing: single-rate back-solve.
+    let beta_phi_r = r("IZ") * 2.0 * omega_cz / theta;
+    let beta_phi_l = r("ZI") * 2.0 * omega_cz / theta;
+
+    if beta_down_l < 0.0 || beta_down_r < 0.0 || beta_phi_l < 0.0 || beta_phi_r < 0.0 {
+        return None;
+    }
+    if beta_down_l < 1e-300 || beta_down_r < 1e-300 {
+        return None;
+    }
+
+    let t1_l = 1.0 / beta_down_l;
+    let t1_r = 1.0 / beta_down_r;
+    // 1/T_2 = 1/(2 T_1) + 1/T_phi and 1/T_phi = beta_phi.
+    let inv_t2_l = 1.0 / (2.0 * t1_l) + beta_phi_l;
+    let inv_t2_r = 1.0 / (2.0 * t1_r) + beta_phi_r;
+    if inv_t2_l <= 0.0 || inv_t2_r <= 0.0 {
+        return None;
+    }
+    Some(RecoveredParams2Q {
+        t1_l,
+        t2_l: 1.0 / inv_t2_l,
+        t1_r,
+        t2_r: 1.0 / inv_t2_r,
+    })
+}
+
+/// Analytic 2Q recovery: given a measured `CX_theta + AD+PD` PL model,
+/// back-solve `(T_1, T_2)` on each qubit.
+///
+/// Uses paper arXiv:2502.03462 eqs. 929-956. `beta_down_r` and
+/// `beta_phi_r` mix in `lambda_iz` / `lambda_zz`; we exploit the
+/// identity
+///
+/// ```text
+/// lambda_iz - lambda_zz = sin(2*theta)/4 * beta_phi_r / omega
+/// ```
+///
+/// to decouple the right-qubit dephasing. Requires `sin(2 theta) != 0`
+/// -- at `theta = 0, pi/2, pi` the formula is degenerate and only
+/// `beta_down_r + 6 beta_phi_r` is recoverable; we return `None`.
+/// `beta_down_l` and `beta_phi_l` come from clean single-unknown rates
+/// (`lambda_xi`, `lambda_zi`).
+pub fn recover_ad_pd_2q_from_cx_theta(
+    model: &crate::PauliLindbladModel,
+    omega_cx: f64,
+    theta: f64,
+) -> Option<RecoveredParams2Q> {
+    use crate::PauliString;
+    if omega_cx <= 0.0 || theta <= 0.0 {
+        return None;
+    }
+    let s2 = (2.0 * theta).sin();
+    if s2.abs() < 1e-10 {
+        // Degenerate: can't separate beta_down_r from beta_phi_r.
+        return None;
+    }
+    let r = |s: &str| model.rate(&PauliString::from_label(s).unwrap());
+
+    // Left qubit: clean single-parameter back-solves.
+    let factor_weight1_amp_l = (2.0 * theta + s2) / 16.0;
+    let beta_down_l = 0.5 * (r("XI") + r("YI")) * omega_cx / factor_weight1_amp_l;
+    let beta_phi_l = r("ZI") * 2.0 * omega_cx / theta;
+
+    // Right qubit: beta_down_r from clean lambda_ix; beta_phi_r via the
+    // (lambda_iz - lambda_zz) decoupling.
+    let beta_down_r = r("IX") * 4.0 * omega_cx / theta;
+    let beta_phi_r = (r("IZ") - r("ZZ")) * 4.0 * omega_cx / s2;
+
+    if beta_down_l < 0.0 || beta_down_r < 0.0 || beta_phi_l < 0.0 || beta_phi_r < 0.0 {
+        return None;
+    }
+    if beta_down_l < 1e-300 || beta_down_r < 1e-300 {
+        return None;
+    }
+    let t1_l = 1.0 / beta_down_l;
+    let t1_r = 1.0 / beta_down_r;
+    let inv_t2_l = 1.0 / (2.0 * t1_l) + beta_phi_l;
+    let inv_t2_r = 1.0 / (2.0 * t1_r) + beta_phi_r;
+    if inv_t2_l <= 0.0 || inv_t2_r <= 0.0 {
+        return None;
+    }
+    Some(RecoveredParams2Q {
+        t1_l,
+        t2_l: 1.0 / inv_t2_l,
+        t1_r,
+        t2_r: 1.0 / inv_t2_r,
+    })
+}
+
+/// Consistency residual for a `CZ_theta + AD+PD` recovery: for the
+/// recovered parameters, compute the L2 residual between observed
+/// degenerate-pair rates (`lambda_xi` vs `lambda_yi`, etc.). Large
+/// residuals flag model mismatch (noise source beyond AD+PD).
+pub fn cz_recovery_residual(model: &crate::PauliLindbladModel) -> f64 {
+    use crate::PauliString;
+    let r = |s: &str| model.rate(&PauliString::from_label(s).unwrap());
+    let pairs = [
+        (r("IX"), r("IY")),
+        (r("XI"), r("YI")),
+        (r("ZX"), r("ZY")),
+        (r("XZ"), r("YZ")),
+    ];
+    pairs
+        .iter()
+        .map(|(a, b)| (a - b).powi(2))
+        .sum::<f64>()
+        .sqrt()
+}
+
+/// Per-Pauli mean + standard-deviation statistics from a Monte-Carlo
+/// uncertainty propagation.
+#[derive(Clone, Debug, Default)]
+pub struct RateUncertainty {
+    pub paulis: Vec<crate::PauliString>,
+    /// `means[i]` = mean of `rates[i]` across MC samples.
+    pub means: Vec<f64>,
+    /// `stds[i]` = sample standard deviation of `rates[i]`.
+    pub stds: Vec<f64>,
+    /// Number of samples drawn.
+    pub n_samples: usize,
+}
+
+/// Propagate parameter uncertainty into the Pauli-Lindblad rates by
+/// Monte-Carlo sampling.
+///
+/// `synthesize_sample` is called once per MC draw. The user builds the
+/// `Gate` from the (possibly jittered) parameters and returns the
+/// synthesized [`PauliLindbladModel`]. This routine aggregates across
+/// draws: per-Pauli sample mean + sample standard deviation.
+///
+/// The first sample determines the support enumeration; later samples
+/// are matched by support equality, so stochastic supports (same Pauli
+/// but generated in a different order) are fine.
+pub fn propagate_uncertainty(
+    n_samples: usize,
+    mut synthesize_sample: impl FnMut(usize) -> crate::PauliLindbladModel,
+) -> RateUncertainty {
+    assert!(n_samples >= 2, "need >=2 samples to compute std");
+
+    // Use the first sample to fix the Pauli set.
+    let first = synthesize_sample(0);
+    let n_p = first.supports.len();
+    let mut sum = first.rates.clone();
+    let mut sum_sq: Vec<f64> = first.rates.iter().map(|r| r * r).collect();
+
+    for k in 1..n_samples {
+        let model = synthesize_sample(k);
+        assert_eq!(
+            model.supports.len(),
+            n_p,
+            "MC draw {}: support size {} != expected {}",
+            k,
+            model.supports.len(),
+            n_p,
+        );
+        for (i, p) in first.supports.iter().enumerate() {
+            let r = model.rate(p);
+            sum[i] += r;
+            sum_sq[i] += r * r;
+        }
+    }
+
+    let n = n_samples as f64;
+    let means: Vec<f64> = sum.iter().map(|s| s / n).collect();
+    let stds: Vec<f64> = sum_sq
+        .iter()
+        .zip(means.iter())
+        .map(|(ss, m)| {
+            let var = (ss / n - m * m).max(0.0);
+            var.sqrt()
+        })
+        .collect();
+
+    RateUncertainty {
+        paulis: first.supports,
+        means,
+        stds,
+        n_samples,
+    }
+}
+
+impl RateUncertainty {
+    /// Look up mean rate for a given Pauli; returns 0 if not in support.
+    pub fn mean(&self, p: &crate::PauliString) -> f64 {
+        self.paulis
+            .iter()
+            .zip(&self.means)
+            .find(|(s, _)| *s == p)
+            .map(|(_, v)| *v)
+            .unwrap_or(0.0)
+    }
+
+    /// Look up standard deviation for a given Pauli; returns 0 if not in support.
+    pub fn std(&self, p: &crate::PauliString) -> f64 {
+        self.paulis
+            .iter()
+            .zip(&self.stds)
+            .find(|(s, _)| *s == p)
+            .map(|(_, v)| *v)
+            .unwrap_or(0.0)
+    }
+}
+
+#[cfg(test)]
+mod tests {
+    use super::*;
+
+    #[test]
+    fn t1_t2_round_trip() {
+        let t1 = 100e-6;
+        let t2 = 80e-6; // < 2 T_1 so physical
+        let (bd, bp) = t1_t2_to_rates(t1, t2);
+        assert!((bd - 1.0 / t1).abs() < 1e-15);
+        assert!((bp - (1.0 / t2 - 1.0 / (2.0 * t1))).abs() < 1e-15);
+    }
+
+    #[test]
+    fn t2_equals_2_t1_gives_zero_dephasing() {
+        // Dephasing-free limit.
+        let t1 = 100e-6;
+        let (bd, bp) = t1_t2_to_rates(t1, 2.0 * t1);
+        assert!((bd - 1.0 / t1).abs() < 1e-15);
+        assert!(bp < 1e-15, "bp should be ~0, got {}", bp);
+    }
+
+    #[test]
+    #[should_panic(expected = "T_2")]
+    fn unphysical_t2_panics() {
+        let _ = t1_t2_to_rates(100e-6, 300e-6); // T_2 > 2 T_1
+    }
+}
diff --git a/exp/pecos-lindblad/src/pauli_lindblad.rs b/exp/pecos-lindblad/src/pauli_lindblad.rs
new file mode 100644
index 000000000..f103a1c37
--- /dev/null
+++ b/exp/pecos-lindblad/src/pauli_lindblad.rs
@@ -0,0 +1,447 @@
+// Copyright 2026 The PECOS Developers
+//
+// Licensed under the Apache License, Version 2.0 (the "License"); you may not use this file except
+// in compliance with the License. You may obtain a copy of the License at
+//
+//     https://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software distributed under the License
+// is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express
+// or implied. See the License for the specific language governing permissions and limitations under
+// the License.
+
+//! Sparse Pauli-Lindblad noise model (arXiv:2201.09866 generator form).
+
+use std::collections::BTreeMap;
+
+use pecos_quantum::{ChannelError, DiagonalPtm, basis_bitmask, basis_label};
+use rand::{Rng, RngExt};
+
+use crate::basis::{Pauli1, PauliString};
+
+/// Sparse Pauli-Lindblad generator:
+/// `N(rho) = exp( sum_k lambda_k * (P_k rho P_k^dag - rho) )`.
+/// `rates[i]` is the integrated rate `lambda_k` (dimensionless) for
+/// `supports[i]`. All rates are non-negative for forward simulation.
+#[derive(Clone, Debug, Default)]
+#[cfg_attr(feature = "serde", derive(serde::Serialize, serde::Deserialize))]
+pub struct PauliLindbladModel {
+    pub supports: Vec<PauliString>,
+    pub rates: Vec<f64>,
+}
+
+impl PauliLindbladModel {
+    pub fn new(supports: Vec<PauliString>, rates: Vec<f64>) -> Self {
+        assert_eq!(
+            supports.len(),
+            rates.len(),
+            "supports/rates length mismatch"
+        );
+        for &r in &rates {
+            assert!(r >= 0.0, "negative PL rate: {}", r);
+        }
+        Self { supports, rates }
+    }
+
+    /// Look up the rate for a given Pauli support. Returns 0 if not present.
+    pub fn rate(&self, p: &PauliString) -> f64 {
+        self.supports
+            .iter()
+            .zip(&self.rates)
+            .find(|(s, _)| *s == p)
+            .map(|(_, r)| *r)
+            .unwrap_or(0.0)
+    }
+
+    /// Sum of all rates. To leading order this is the total probability of
+    /// *any* Pauli error firing during the gate.
+    pub fn total_rate(&self) -> f64 {
+        self.rates.iter().sum()
+    }
+
+    /// Number of qubits spanned by this model.
+    #[must_use]
+    pub fn num_qubits(&self) -> usize {
+        self.supports
+            .iter()
+            .map(PauliString::num_qubits)
+            .max()
+            .unwrap_or(0)
+    }
+
+    /// Converts the Pauli-Lindblad model to diagonal PTM fidelities.
+    ///
+    /// For `N(rho) = exp(sum_k lambda_k (P_k rho P_k - rho))`, a Pauli basis
+    /// element `B` has diagonal PTM entry
+    /// `exp(-2 * sum_{k: {P_k, B}=0} lambda_k)`.
+    ///
+    /// # Errors
+    ///
+    /// Returns an error when supports have inconsistent qubit counts or the
+    /// PECOS Pauli-basis dimension cannot be represented.
+    pub fn to_diagonal_ptm(&self) -> Result<DiagonalPtm, ChannelError> {
+        let n = self.num_qubits();
+        for support in &self.supports {
+            if support.num_qubits() != n {
+                return Err(ChannelError::UnsupportedChannelExpr {
+                    reason: format!(
+                        "PauliLindbladModel support {} has {} qubits in a {}-qubit model",
+                        support,
+                        support.num_qubits(),
+                        n
+                    ),
+                });
+            }
+        }
+
+        let basis_len = pecos_quantum::pauli_basis_len(n)?;
+        let mut fidelities = BTreeMap::new();
+        for basis_idx in 0..basis_len {
+            let label = basis_label(n, basis_idx)?;
+            let basis_pauli = PauliString::from_label(&label).ok_or_else(|| {
+                ChannelError::UnsupportedChannelExpr {
+                    reason: format!("internal basis label {label} was not a Lindblad Pauli string"),
+                }
+            })?;
+            let anticommuting_rate: f64 = self
+                .supports
+                .iter()
+                .zip(&self.rates)
+                .filter(|(support, _)| support.symplectic_product(&basis_pauli) == 1)
+                .map(|(_, rate)| *rate)
+                .sum();
+            fidelities.insert(
+                basis_bitmask(n, basis_idx)?,
+                (-2.0 * anticommuting_rate).exp(),
+            );
+        }
+        DiagonalPtm::try_new(n, fidelities)
+    }
+
+    /// Sum of rates restricted to a given Pauli weight (number of
+    /// non-identity factors).
+    pub fn rate_at_weight(&self, weight: usize) -> f64 {
+        self.supports
+            .iter()
+            .zip(&self.rates)
+            .filter(|(s, _)| s.weight() == weight)
+            .map(|(_, r)| *r)
+            .sum()
+    }
+
+    /// Largest single rate in the model.
+    pub fn max_rate(&self) -> f64 {
+        self.rates.iter().copied().fold(0.0, f64::max)
+    }
+
+    /// Adapter: export 1-qubit rates as `[lambda_X, lambda_Y, lambda_Z]`.
+    /// Panics if the model is not 1-qubit.
+    ///
+    /// Intended consumer: `pecos-qec::PerGateTypeNoise::with_1q_rates`.
+    pub fn to_noise_array_1q(&self) -> [f64; 3] {
+        assert!(
+            self.supports.iter().all(|s| s.num_qubits() == 1),
+            "to_noise_array_1q requires a 1-qubit model"
+        );
+        [
+            self.rate(&PauliString::single(Pauli1::X)),
+            self.rate(&PauliString::single(Pauli1::Y)),
+            self.rate(&PauliString::single(Pauli1::Z)),
+        ]
+    }
+
+    /// Adapter: export 2-qubit rates in `PAULI_2Q_ORDER` ordering
+    /// (IX, IY, IZ, XI, XX, XY, XZ, YI, YX, YY, YZ, ZI, ZX, ZY, ZZ).
+    /// Panics if the model is not 2-qubit.
+    ///
+    /// Intended consumer: `pecos-qec::PerGateTypeNoise::with_2q_rates`.
+    pub fn to_noise_array_2q(&self) -> [f64; 15] {
+        assert!(
+            self.supports.iter().all(|s| s.num_qubits() == 2),
+            "to_noise_array_2q requires a 2-qubit model"
+        );
+        const ORDER: [&str; 15] = [
+            "IX", "IY", "IZ", "XI", "XX", "XY", "XZ", "YI", "YX", "YY", "YZ", "ZI", "ZX", "ZY",
+            "ZZ",
+        ];
+        let mut out = [0.0; 15];
+        for (i, label) in ORDER.iter().enumerate() {
+            out[i] = self.rate(&PauliString::from_label(label).unwrap());
+        }
+        out
+    }
+
+    /// Per-Pauli residual `self - other`. Returns a vector of
+    /// `(pauli, self_rate, other_rate, residual)` for every Pauli in the
+    /// union of the two models' supports.
+    pub fn diff(&self, other: &Self) -> Vec<(PauliString, f64, f64, f64)> {
+        use std::collections::HashSet;
+        let mut all: HashSet<PauliString> = HashSet::new();
+        for p in self.supports.iter().chain(other.supports.iter()) {
+            all.insert(p.clone());
+        }
+        let mut out: Vec<_> = all
+            .into_iter()
+            .map(|p| {
+                let a = self.rate(&p);
+                let b = other.rate(&p);
+                (p, a, b, a - b)
+            })
+            .collect();
+        out.sort_by(|(_, _, _, x), (_, _, _, y)| {
+            y.abs()
+                .partial_cmp(&x.abs())
+                .unwrap_or(std::cmp::Ordering::Equal)
+        });
+        out
+    }
+
+    /// `L2` norm of the rate-residual vector between `self` and `other`.
+    pub fn residual_l2(&self, other: &Self) -> f64 {
+        self.diff(other)
+            .iter()
+            .map(|(_, _, _, r)| r * r)
+            .sum::<f64>()
+            .sqrt()
+    }
+
+    /// Pauli with the largest absolute residual against `other`. Returns
+    /// `None` if both models are empty.
+    pub fn max_residual(&self, other: &Self) -> Option<(PauliString, f64)> {
+        self.diff(other)
+            .into_iter()
+            .next()
+            .map(|(p, _, _, r)| (p, r))
+    }
+
+    /// Leading-order composition of two independent noise sources: rates
+    /// add per Pauli. Exact for small rates where `(1 - (1-p_A)(1-p_B)) ≈
+    /// p_A + p_B`. For larger rates, prefer [`synthesize_superop`] on the
+    /// combined physical Lindbladian directly (all-orders).
+    ///
+    /// Use case: combine a predicted physical-model PL with an
+    /// experimentally-observed residual-noise PL to get an effective
+    /// model for circuit-level noise.
+    pub fn compose_independent(&self, other: &Self) -> Self {
+        use std::collections::HashMap;
+        let mut combined: HashMap<PauliString, f64> = HashMap::new();
+        for (p, r) in self.supports.iter().zip(&self.rates) {
+            combined.insert(p.clone(), *r);
+        }
+        for (p, r) in other.supports.iter().zip(&other.rates) {
+            *combined.entry(p.clone()).or_insert(0.0) += *r;
+        }
+        let mut entries: Vec<_> = combined.into_iter().collect();
+        entries.sort_by(|(a, _), (b, _)| {
+            a.0.iter()
+                .map(|p| *p as u8)
+                .cmp(b.0.iter().map(|p| *p as u8))
+        });
+        let (supports, rates): (Vec<_>, Vec<_>) = entries.into_iter().unzip();
+        Self::new(supports, rates)
+    }
+
+    /// Aggregate absolute residual by Pauli weight. Returns `weight -> sum
+    /// of |residual|`. Useful for diagnosing which weight class of physics
+    /// is missing from the model (e.g. weight-2 residual large =>
+    /// correlated two-qubit noise missing).
+    pub fn residual_by_weight(&self, other: &Self) -> Vec<(usize, f64)> {
+        use std::collections::BTreeMap;
+        let mut agg: BTreeMap<usize, f64> = BTreeMap::new();
+        for (p, _, _, r) in self.diff(other) {
+            *agg.entry(p.weight()).or_insert(0.0) += r.abs();
+        }
+        agg.into_iter().collect()
+    }
+
+    /// Return the top `n` Pauli terms sorted by rate (descending).
+    /// Ties broken by lexicographic order on the Pauli string.
+    pub fn top_contributors(&self, n: usize) -> Vec<(PauliString, f64)> {
+        let mut pairs: Vec<_> = self
+            .supports
+            .iter()
+            .cloned()
+            .zip(self.rates.iter().copied())
+            .collect();
+        pairs.sort_by(|a, b| {
+            b.1.partial_cmp(&a.1)
+                .unwrap_or(std::cmp::Ordering::Equal)
+                .then_with(|| {
+                    a.0.0
+                        .iter()
+                        .map(|p| *p as u8)
+                        .cmp(b.0.0.iter().map(|p| *p as u8))
+                })
+        });
+        pairs.truncate(n);
+        pairs
+    }
+
+    /// Human-readable noise-budget table: total rate, per-weight-class
+    /// breakdown, and top contributors. Useful for answering "where
+    /// is my logical error budget going?"
+    ///
+    /// Format is stable for eyeballing; not an interchange format
+    /// (use `serde` for that).
+    pub fn explain(&self) -> String {
+        let total = self.total_rate();
+        let n_terms = self.supports.len();
+
+        let mut by_weight: std::collections::BTreeMap<usize, f64> =
+            std::collections::BTreeMap::new();
+        for (p, r) in self.supports.iter().zip(&self.rates) {
+            *by_weight.entry(p.weight()).or_insert(0.0) += *r;
+        }
+
+        let mut out = String::new();
+        out.push_str(&format!(
+            "Pauli-Lindblad noise budget ({} terms, total rate = {:.3e})\n",
+            n_terms, total,
+        ));
+        out.push_str(&"=".repeat(60));
+        out.push('\n');
+        out.push_str("By weight:\n");
+        for (w, r) in &by_weight {
+            let pct = if total > 0.0 { 100.0 * r / total } else { 0.0 };
+            out.push_str(&format!("  weight-{}: {:>11.3e}  {:5.1}%\n", w, r, pct));
+        }
+        out.push('\n');
+
+        let top_n = 10;
+        out.push_str(&format!("Top {} contributors:\n", top_n.min(n_terms)));
+        for (p, r) in self.top_contributors(top_n) {
+            let pct = if total > 0.0 { 100.0 * r / total } else { 0.0 };
+            out.push_str(&format!(
+                "  {:<12} {:>11.3e}  {:5.1}%\n",
+                p.to_string(),
+                r,
+                pct
+            ));
+        }
+        out
+    }
+
+    /// Heuristic diagnostic: given a predicted model (`self`) and a
+    /// measured model (`other`), suggest physical sources likely missing
+    /// from the prediction. Returns human-readable strings ordered by
+    /// residual magnitude. Thresholds are intentionally coarse; use as a
+    /// starting point, not a final verdict.
+    pub fn diagnose_gap(&self, other: &Self, tol: f64) -> Vec<String> {
+        let mut msgs = Vec::new();
+        let by_weight = self.residual_by_weight(other);
+
+        for (weight, total_abs) in &by_weight {
+            if *total_abs < tol {
+                continue;
+            }
+            match weight {
+                1 => msgs.push(format!(
+                    "weight-1 residual {:.3e}: suggests missing incoherent single-qubit noise \
+                     (T_1, T_phi mischaracterized, or extra dephasing/relaxation channels)",
+                    total_abs
+                )),
+                2 => msgs.push(format!(
+                    "weight-2 residual {:.3e}: suggests correlated 2-qubit noise not in model \
+                     (coherent ZZ crosstalk, leakage-induced correlations, or gate miscalibration)",
+                    total_abs
+                )),
+                w if *w >= 3 => msgs.push(format!(
+                    "weight-{} residual {:.3e}: high-weight residual; suggests multi-qubit \
+                     crosstalk or higher-order Magnus corrections needed",
+                    w, total_abs
+                )),
+                _ => {}
+            }
+        }
+        // Highlight the single worst Pauli as a concrete pointer.
+        if let Some((p, r)) = self.max_residual(other)
+            && r.abs() >= tol
+        {
+            msgs.push(format!(
+                "largest per-Pauli residual: |lambda_{{{}}}^pred - lambda_{{{}}}^meas| = {:.3e}",
+                p, p, r
+            ));
+        }
+        msgs
+    }
+
+    /// Sample an error realization over integrated duration `t_scale`:
+    /// each Pauli term independently fires with probability
+    /// `p_k = (1 - exp(-2 * lambda_k * t_scale)) / 2`. Returns the
+    /// product Pauli string (may be identity).
+    pub fn sample(&self, t_scale: f64, rng: &mut impl Rng) -> PauliString {
+        assert!(!self.supports.is_empty(), "cannot sample empty model");
+        let n = self.supports[0].num_qubits();
+        let mut acc = PauliString(vec![Pauli1::I; n]);
+        for (support, &lambda) in self.supports.iter().zip(&self.rates) {
+            assert_eq!(support.num_qubits(), n, "ragged supports");
+            let p_flip = 0.5 * (1.0 - (-2.0 * lambda * t_scale).exp());
+            if rng.random_range(0.0..1.0) < p_flip {
+                acc = acc.multiply(support);
+            }
+        }
+        acc
+    }
+}
+
+#[cfg(test)]
+mod tests {
+    use super::*;
+
+    #[test]
+    fn summary_helpers() {
+        let supports = vec![
+            PauliString::from_label("IX").unwrap(),
+            PauliString::from_label("IZ").unwrap(),
+            PauliString::from_label("XX").unwrap(),
+        ];
+        let rates = vec![0.001, 0.003, 0.002];
+        let model = PauliLindbladModel::new(supports, rates);
+        assert!((model.total_rate() - 0.006).abs() < 1e-12);
+        assert!((model.rate_at_weight(1) - 0.004).abs() < 1e-12); // IX + IZ
+        assert!((model.rate_at_weight(2) - 0.002).abs() < 1e-12); // XX
+        assert!((model.max_rate() - 0.003).abs() < 1e-12);
+    }
+
+    #[test]
+    fn sample_zero_rates_is_identity() {
+        use rand::SeedableRng;
+        use rand::rngs::StdRng;
+        let supports = vec![
+            PauliString::single(Pauli1::X),
+            PauliString::single(Pauli1::Y),
+            PauliString::single(Pauli1::Z),
+        ];
+        let model = PauliLindbladModel::new(supports, vec![0.0; 3]);
+        let mut rng = StdRng::seed_from_u64(42);
+        for _ in 0..100 {
+            let s = model.sample(1.0, &mut rng);
+            assert_eq!(s, PauliString::single(Pauli1::I));
+        }
+    }
+
+    #[test]
+    fn diagonal_ptm_matches_pauli_lindblad_rates() {
+        let model = PauliLindbladModel::new(
+            vec![
+                PauliString::single(Pauli1::X),
+                PauliString::single(Pauli1::Z),
+            ],
+            vec![0.2, 0.3],
+        );
+
+        let diagonal = model.to_diagonal_ptm().unwrap();
+        let label = |s: &str| {
+            let idx = ["I", "X", "Y", "Z"]
+                .iter()
+                .position(|label| *label == s)
+                .unwrap();
+            pecos_quantum::basis_bitmask(1, idx).unwrap()
+        };
+
+        assert!((diagonal.fidelity(&label("I")) - 1.0).abs() < 1e-12);
+        assert!((diagonal.fidelity(&label("X")) - (-0.6_f64).exp()).abs() < 1e-12);
+        assert!((diagonal.fidelity(&label("Y")) - (-1.0_f64).exp()).abs() < 1e-12);
+        assert!((diagonal.fidelity(&label("Z")) - (-0.4_f64).exp()).abs() < 1e-12);
+    }
+}
diff --git a/exp/pecos-lindblad/src/synthesis.rs b/exp/pecos-lindblad/src/synthesis.rs
new file mode 100644
index 000000000..e0f0cdb03
--- /dev/null
+++ b/exp/pecos-lindblad/src/synthesis.rs
@@ -0,0 +1,391 @@
+// Copyright 2026 The PECOS Developers
+//
+// Licensed under the Apache License, Version 2.0 (the "License"); you may not use this file except
+// in compliance with the License. You may obtain a copy of the License at
+//
+//     https://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software distributed under the License
+// is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express
+// or implied. See the License for the specific language governing permissions and limitations under
+// the License.
+
+//! Phases 1-3: numerical Pauli-Lindblad synthesis for arbitrary-qubit
+//! gates via interaction-frame transform + Simpson's rule + Walsh-Hadamard
+//! inversion.
+//!
+//! Entry points:
+//! - [`synthesize_identity_1q`]: fast path for 1Q `H_g = 0` (Phase 1;
+//!   exact + non-perturbative under AD + PD).
+//! - [`synthesize_numerical_1q`]: 1Q, general `H_g`, Simpson integrand.
+//! - [`synthesize_numerical`]: n-qubit, general `H_g`, Simpson integrand,
+//!   Walsh-Hadamard rate recovery.
+//!
+//! See `design/lindblad_magnus_algorithm.md` for the math spec and paper
+//! arXiv:2502.03462 for closed-form fixtures.
+
+use num_complex::Complex64;
+
+use crate::basis::{Pauli1, PauliString};
+use crate::gate::Gate;
+use crate::lindbladian::Lindbladian;
+use crate::matrix::{self, Matrix};
+use crate::pauli_lindblad::PauliLindbladModel;
+
+const PHASE1_PAULIS: [Pauli1; 3] = [Pauli1::X, Pauli1::Y, Pauli1::Z];
+
+/// Default number of Simpson intervals for time integration. Composite
+/// Simpson's 1/3 rule, order-4 accurate. 1024 gives ~1e-12 for smooth
+/// integrands on a bounded interval (sinusoidal at gate frequency up to a
+/// few cycles).
+pub const DEFAULT_N_STEPS: usize = 1024;
+
+/// Synthesize a 1-qubit Pauli-Lindblad model from an identity gate. Fast
+/// path: identity gate (`H_g = 0`) => interaction-frame Lindbladian is
+/// constant and `Omega_1 = L * tau_g`, so no time integration needed.
+pub fn synthesize_identity_1q(gate: &Gate) -> PauliLindbladModel {
+    assert_eq!(
+        gate.num_qubits, 1,
+        "synthesize_identity_1q requires 1 qubit"
+    );
+    assert!(
+        is_zero_matrix(&gate.ideal.hamiltonian),
+        "synthesize_identity_1q requires H_g = 0",
+    );
+    let tau = gate.tau_g;
+    let paulis: Vec<PauliString> = PHASE1_PAULIS
+        .iter()
+        .map(|&p| PauliString::single(p))
+        .collect();
+    let alphas: Vec<f64> = PHASE1_PAULIS
+        .iter()
+        .map(|&p| constant_alpha(&gate.noise, p) * tau)
+        .collect();
+    model_from_alphas_walsh(paulis, alphas, 1)
+}
+
+/// Synthesize a 1-qubit Pauli-Lindblad model from an arbitrary 1-qubit
+/// gate via Simpson's rule on `Omega_1 = int_0^{tau_g} L_I(t) dt`. Works
+/// for identity (reduces to the Phase 1 result) and for gates like
+/// `X_theta`, `Y_theta`, `Z_theta`.
+pub fn synthesize_numerical_1q(gate: &Gate, n_steps: usize) -> PauliLindbladModel {
+    assert_eq!(
+        gate.num_qubits, 1,
+        "synthesize_numerical_1q requires 1 qubit"
+    );
+    synthesize_numerical(gate, n_steps)
+}
+
+/// Default number of time slices for `synthesize_superop`. Midpoint-rule
+/// propagator per slice is second-order accurate; `N=128` gives ~`1e-10`
+/// precision for single-oscillation gates.
+pub const DEFAULT_N_SLICES: usize = 128;
+
+/// **General** synthesis for any gate with any combination of coherent
+/// and dissipative noise via time-slicing of the interaction-frame
+/// Lindblad superoperator.
+///
+/// For each midpoint `t_k`, builds `L_I(t_k) = U_g^dag(t_k) L_noise
+/// U_g(t_k)`, exponentiates to get a per-slice propagator
+/// `exp(L_I(t_k) * dt)` and multiplies them left-to-right to form
+/// `U_total`. Applies to each `vec(P_b)`, extracts Pauli fidelity, inverts
+/// via Walsh-Hadamard.
+///
+/// This is the only path that handles **gates with `H_g != 0` AND
+/// simultaneous coherent + dissipative noise** -- the general case that
+/// `synthesize_numerical` (dissipative leading-order only) and
+/// `synthesize_exact_unitary` (coherent, asserts no c_ops) don't cover.
+///
+/// Cost: `n_slices` per-slice superoperator builds + exps at size
+/// `d^2 x d^2`. For 2Q gates `d^2=16`, comfortably sub-second at
+/// `n_slices=128`.
+pub fn synthesize_superop(gate: &Gate, n_slices: usize) -> PauliLindbladModel {
+    assert!(n_slices >= 1, "n_slices must be >= 1");
+    let n = gate.num_qubits;
+    let d = 1usize << n;
+    let d2 = d * d;
+    let tau = gate.tau_g;
+    let dt = tau / n_slices as f64;
+
+    let h_g = &gate.ideal.hamiltonian;
+    let h_delta = &gate.noise.hamiltonian;
+
+    // U_total = prod_k exp(L_I(t_k) * dt), built left-to-right (newest leftmost).
+    let mut u_total = matrix::identity(d2);
+    for k in 0..n_slices {
+        let t_mid = (k as f64 + 0.5) * dt;
+        let u_g = matrix::exp_minus_i_h_t(h_g, d, t_mid);
+        let u_g_dag = matrix::dag(&u_g, d);
+
+        // Transform noise operators to the interaction frame at t_mid.
+        let h_i = matrix::matmul(&matrix::matmul(&u_g_dag, h_delta, d), &u_g, d);
+        let collapse_i: Vec<(Matrix, f64)> = gate
+            .noise
+            .collapse
+            .iter()
+            .map(|(c, g)| (matrix::matmul(&matrix::matmul(&u_g_dag, c, d), &u_g, d), *g))
+            .collect();
+
+        // L_I(t_mid) superop.
+        let lind_i = Lindbladian::new(d, h_i, collapse_i);
+        let l_super = lind_i.superoperator();
+
+        // Per-slice propagator and accumulate.
+        let u_slice = matrix::expm(&matrix::scale(&l_super, Complex64::new(dt, 0.0)), d2);
+        u_total = matrix::matmul(&u_slice, &u_total, d2);
+    }
+
+    // Apply to each Pauli, extract fidelities, invert.
+    let paulis = PauliString::enumerate_nonidentity(n);
+    let alphas: Vec<f64> = paulis
+        .iter()
+        .map(|p| {
+            let p_mat = matrix::pauli_string_mat(p);
+            let vec_p = matrix::vec_of(&p_mat, d);
+            let vec_applied = matrix::matvec(&u_total, &vec_p, d2);
+            let applied = matrix::unvec(&vec_applied, d);
+            let inner = matrix::trace(&matrix::matmul(&p_mat, &applied, d), d);
+            let f_b = inner.re / d as f64;
+            assert!(
+                f_b > 0.1,
+                "Pauli fidelity {} too low for {:?}; noise outside weak regime",
+                f_b,
+                p,
+            );
+            -f_b.ln()
+        })
+        .collect();
+    model_from_alphas_walsh(paulis, alphas, n)
+}
+
+/// Synthesize a Pauli-Lindblad model from **mixed coherent + dissipative
+/// noise** on a time-independent ideal Hamiltonian (currently: identity
+/// gate, `H_g = 0`) via the full Lindblad superoperator path.
+///
+/// Builds `L_super` (`d^2 x d^2`), exponentiates to get the channel
+/// `exp(L_super * tau_g)`, applies to each `vec(P_b)`, extracts Pauli
+/// fidelity `f_b = (1/d) tr(P_b * Lambda(P_b))`, then inverts via
+/// Walsh-Hadamard. Unifies the coherent and dissipative paths for the
+/// identity case: matches [`synthesize_identity_1q`] for pure AD+PD,
+/// matches [`synthesize_exact_unitary`] for pure coherent noise on
+/// identity, and handles **both at once** (the case the other paths
+/// reject).
+///
+/// Requires `gate.ideal.hamiltonian` to be (numerically) zero -- for
+/// non-trivial `H_g` the interaction-frame Lindbladian is time-dependent
+/// and requires either Magnus order >= 1 time-ordering (existing
+/// `synthesize_numerical` path for linear-order dissipative) or
+/// time-slicing (future work).
+pub fn synthesize_superop_identity(gate: &Gate) -> PauliLindbladModel {
+    let n = gate.num_qubits;
+    let d = 1usize << n;
+    assert!(
+        is_zero_matrix(&gate.ideal.hamiltonian),
+        "synthesize_superop_identity requires H_g = 0 (time-independent L_I)"
+    );
+    let tau = gate.tau_g;
+    let l_super = gate.noise.superoperator();
+    // channel = exp(L_super * tau_g)
+    let channel = matrix::expm(&matrix::scale(&l_super, Complex64::new(tau, 0.0)), d * d);
+
+    let paulis = PauliString::enumerate_nonidentity(n);
+    let alphas: Vec<f64> = paulis
+        .iter()
+        .map(|p| {
+            let p_mat = matrix::pauli_string_mat(p);
+            let vec_p = matrix::vec_of(&p_mat, d);
+            let vec_applied = matrix::matvec(&channel, &vec_p, d * d);
+            let applied = matrix::unvec(&vec_applied, d);
+            let inner = matrix::trace(&matrix::matmul(&p_mat, &applied, d), d);
+            let f_b = inner.re / d as f64;
+            assert!(
+                f_b > 0.1,
+                "Pauli fidelity {} too low for {:?}; noise outside weak-coupling regime",
+                f_b,
+                p,
+            );
+            -f_b.ln()
+        })
+        .collect();
+    model_from_alphas_walsh(paulis, alphas, n)
+}
+
+/// Synthesize a Pauli-Lindblad model for a gate with **purely coherent
+/// noise** (no collapse operators) via the exact error-unitary path.
+///
+/// For coherent noise the Pauli rates are quadratic in the perturbation
+/// strength (see `design/lindblad_magnus_algorithm.md` section 4.5). The
+/// linear-order [`synthesize_numerical`] path gives `alpha_b = 0` for
+/// coherent noise because `Tr(P_b L(P_b)) = 0` when `L` is a single
+/// commutator. This function computes the exact error unitary
+/// `U_err = U_ideal^dag * U_full` and extracts Pauli fidelities directly.
+///
+/// Requires `gate.noise.collapse` to be empty. Use
+/// [`synthesize_numerical`] for dissipative noise (AD, PD).
+pub fn synthesize_exact_unitary(gate: &Gate) -> PauliLindbladModel {
+    assert!(
+        gate.noise.collapse.is_empty(),
+        "synthesize_exact_unitary requires purely coherent noise (no c_ops)"
+    );
+    let n = gate.num_qubits;
+    let d = 1usize << n;
+    let tau = gate.tau_g;
+
+    let h_g = &gate.ideal.hamiltonian;
+    let h_delta = &gate.noise.hamiltonian;
+    let h_full = matrix::add(h_g, h_delta);
+
+    let u_full = matrix::expm(&matrix::scale(&h_full, Complex64::new(0.0, -tau)), d);
+    let u_ideal = matrix::expm(&matrix::scale(h_g, Complex64::new(0.0, -tau)), d);
+    let u_ideal_dag = matrix::dag(&u_ideal, d);
+    let u_err = matrix::matmul(&u_ideal_dag, &u_full, d);
+    let u_err_dag = matrix::dag(&u_err, d);
+
+    let paulis = PauliString::enumerate_nonidentity(n);
+    let alphas: Vec<f64> = paulis
+        .iter()
+        .map(|p| {
+            let p_mat = matrix::pauli_string_mat(p);
+            let up = matrix::matmul(&u_err, &p_mat, d);
+            let upudag = matrix::matmul(&up, &u_err_dag, d);
+            let inner = matrix::trace(&matrix::matmul(&p_mat, &upudag, d), d);
+            let f_b = inner.re / d as f64;
+            // For weak noise f_b ~ 1. Use alpha_b = -ln(f_b); equal to
+            // (1 - f_b) at leading order. Panic if f_b drifts out of the
+            // weak-noise regime (< 0.1 means you are outside the Magnus
+            // convergence radius and the PL model is not a good fit).
+            assert!(
+                f_b > 0.1,
+                "Pauli fidelity {} for {:?} below weak-noise threshold; noise too strong for PL model",
+                f_b,
+                p,
+            );
+            -f_b.ln()
+        })
+        .collect();
+
+    model_from_alphas_walsh(paulis, alphas, n)
+}
+
+/// Synthesize a Pauli-Lindblad model from an arbitrary gate. Enumerates all
+/// non-identity Paulis on `gate.num_qubits`, integrates `alpha_b * tau_g`
+/// for each via Simpson's rule on the interaction-frame Lindbladian, and
+/// inverts via Walsh-Hadamard.
+pub fn synthesize_numerical(gate: &Gate, n_steps: usize) -> PauliLindbladModel {
+    assert!(
+        n_steps >= 2 && n_steps.is_multiple_of(2),
+        "n_steps must be even and >= 2, got {}",
+        n_steps
+    );
+    let n = gate.num_qubits;
+    let paulis = PauliString::enumerate_nonidentity(n);
+    if is_zero_matrix(&gate.ideal.hamiltonian) {
+        let tau = gate.tau_g;
+        let alphas: Vec<f64> = paulis
+            .iter()
+            .map(|p| constant_alpha_pauli_string(&gate.noise, p) * tau)
+            .collect();
+        return model_from_alphas_walsh(paulis, alphas, n);
+    }
+
+    let alphas: Vec<f64> = paulis
+        .iter()
+        .map(|p| integrated_alpha(gate, p, n_steps))
+        .collect();
+    model_from_alphas_walsh(paulis, alphas, n)
+}
+
+/// `alpha_b = -Tr(P_b L(P_b)) / d` for time-independent L. Units: 1/time.
+fn constant_alpha(noise: &Lindbladian, p: Pauli1) -> f64 {
+    let d = noise.d;
+    let p_mat = matrix::pauli_1q(p);
+    let l_p = noise.apply(&p_mat);
+    let inner = matrix::trace(&matrix::matmul(&p_mat, &l_p, d), d);
+    -inner.re / d as f64
+}
+
+/// `alpha_b = -Tr(P_b L(P_b)) / d` for a time-independent Lindbladian and
+/// arbitrary-qubit Pauli string. Units: 1/time.
+fn constant_alpha_pauli_string(noise: &Lindbladian, p: &PauliString) -> f64 {
+    let d = noise.d;
+    let p_mat = matrix::pauli_string_mat(p);
+    let l_p = noise.apply(&p_mat);
+    let inner = matrix::trace(&matrix::matmul(&p_mat, &l_p, d), d);
+    -inner.re / d as f64
+}
+
+/// Integrated `alpha_b * tau_g = -Tr(P_b * Omega_1(P_b)) / d` via Simpson's
+/// rule on `[0, tau_g]`. Works for any `n_qubits`.
+fn integrated_alpha(gate: &Gate, p: &PauliString, n_steps: usize) -> f64 {
+    let n = gate.num_qubits;
+    assert_eq!(p.num_qubits(), n);
+    let d = 1usize << n;
+    let p_mat = matrix::pauli_string_mat(p);
+    let h_g = &gate.ideal.hamiltonian;
+    let tau = gate.tau_g;
+    let h_step = tau / n_steps as f64;
+
+    // integrand(t) = -Tr(P_b * L_I(t)(P_b)).re / d
+    //              = -Tr(P_b * U_g^†(t) L(U_g(t) P_b U_g^†(t)) U_g(t)) / d
+    let integrand = |t: f64| -> f64 {
+        let u = matrix::exp_minus_i_h_t(h_g, d, t);
+        let u_dag = matrix::dag(&u, d);
+        let rotated = matrix::matmul(&matrix::matmul(&u, &p_mat, d), &u_dag, d);
+        let l_rotated = gate.noise.apply(&rotated);
+        let l_i_pb = matrix::matmul(&matrix::matmul(&u_dag, &l_rotated, d), &u, d);
+        let inner = matrix::trace(&matrix::matmul(&p_mat, &l_i_pb, d), d);
+        -inner.re / d as f64
+    };
+
+    // Composite Simpson's 1/3 rule. Weights: 1, 4, 2, 4, 2, ..., 4, 1.
+    let mut s = integrand(0.0) + integrand(tau);
+    for k in 1..n_steps {
+        let t = k as f64 * h_step;
+        let w = if k % 2 == 1 { 4.0 } else { 2.0 };
+        s += w * integrand(t);
+    }
+    s * h_step / 3.0
+}
+
+/// Walsh-Hadamard inversion:
+///   `lambda_k = -(1/4^n) * sum_{b non-identity} (-1)^{<k,b>_sp} alpha_b`
+/// (see `design/lindblad_magnus_algorithm.md` step 4). alpha_I = 0 is
+/// implicit.
+fn model_from_alphas_walsh(
+    paulis: Vec<PauliString>,
+    alphas: Vec<f64>,
+    n_qubits: usize,
+) -> PauliLindbladModel {
+    assert_eq!(paulis.len(), alphas.len());
+    let norm = 1.0 / (1usize << (2 * n_qubits)) as f64;
+    let rates: Vec<f64> = paulis
+        .iter()
+        .map(|k| {
+            let mut s = 0.0;
+            for (b, &alpha_b) in paulis.iter().zip(alphas.iter()) {
+                let sign = if k.symplectic_product(b) == 0 {
+                    1.0
+                } else {
+                    -1.0
+                };
+                s += sign * alpha_b;
+            }
+            clip_negative(-norm * s)
+        })
+        .collect();
+    PauliLindbladModel::new(paulis, rates)
+}
+
+fn is_zero_matrix(m: &Matrix) -> bool {
+    m.iter()
+        .all(|c: &Complex64| c.re.abs() < 1e-14 && c.im.abs() < 1e-14)
+}
+
+/// Phase 1 positivity policy: clip tiny negatives to zero; panic on large
+/// negatives so bugs surface. Revisit in Phase 3 with per-user policy.
+fn clip_negative(lambda: f64) -> f64 {
+    if lambda < -1e-8 {
+        panic!("PauliLindbladModel rate unexpectedly negative: {}", lambda);
+    }
+    lambda.max(0.0)
+}
diff --git a/exp/pecos-lindblad/src/time_dep.rs b/exp/pecos-lindblad/src/time_dep.rs
new file mode 100644
index 000000000..aff773d04
--- /dev/null
+++ b/exp/pecos-lindblad/src/time_dep.rs
@@ -0,0 +1,216 @@
+// Copyright 2026 The PECOS Developers
+//
+// Licensed under the Apache License, Version 2.0 (the "License"); you may not use this file except
+// in compliance with the License. You may obtain a copy of the License at
+//
+//     https://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software distributed under the License
+// is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express
+// or implied. See the License for the specific language governing permissions and limitations under
+// the License.
+
+//! Time-dependent (time-convolutionless, TCL) Lindbladian support for
+//! non-Markovian dynamics.
+//!
+//! # Scope
+//!
+//! This module supports **time-local** non-Markovian master equations of
+//! the form
+//!
+//! ```text
+//! drho/dt = -i [H_delta(t), rho] + sum_j gamma_j(t) * D[c_j] rho
+//! ```
+//!
+//! where rates `gamma_j(t)` and coherent noise `H_delta(t)` can vary
+//! arbitrarily with time. This covers:
+//!
+//! - **1/f dephasing**: `gamma_phi(t) = gamma_0 * A / (A + t/t_c)` (leads to
+//!   non-exponential T_2 decay).
+//! - **Gaussian coherence decay**: `gamma_phi(t) ∝ t` gives `exp(-(t/T_2)^2)`.
+//! - **Pulse-shape-dependent dephasing**: `gamma_phi(t) ∝ |pulse(t)|^2`.
+//! - **Coloured coherent noise**: `H_delta(t) = (delta_0 cos(omega_d t) / 2) Z`.
+//!
+//! # Out of scope
+//!
+//! Time-nonlocal (true memory-kernel) master equations like
+//! Nakajima-Zwanzig `drho/dt = int_0^t K(t-s) rho(s) ds` require
+//! convolution integrals over the history of rho and are not supported.
+//! This is a genuine structural limit of the TCL framework.
+
+use std::sync::Arc;
+
+use num_complex::Complex64;
+
+use crate::lindbladian::Lindbladian;
+use crate::matrix::Matrix;
+
+/// Closure type for time-dependent scalar rates.
+pub type RateFn = Arc<dyn Fn(f64) -> f64 + Send + Sync>;
+
+/// Closure type for time-dependent Hermitian operators (d x d matrix).
+pub type HermitianFn = Arc<dyn Fn(f64) -> Matrix + Send + Sync>;
+
+/// Time-convolutionless (TCL) non-Markovian Lindbladian.
+///
+/// Stores a Hilbert-space dimension, a time-dependent coherent noise
+/// Hamiltonian (which may be constant zero), and a list of collapse
+/// operators with time-dependent rates. Evaluation at time `t` returns a
+/// standard [`Lindbladian`] snapshot.
+#[derive(Clone)]
+pub struct TimeDepLindbladian {
+    pub d: usize,
+    pub hamiltonian_fn: HermitianFn,
+    pub collapse_fns: Vec<(Matrix, RateFn)>,
+}
+
+impl TimeDepLindbladian {
+    /// Construct with a constant Hamiltonian and per-operator time-dep rates.
+    pub fn with_static_hamiltonian(
+        d: usize,
+        hamiltonian: Matrix,
+        collapse_fns: Vec<(Matrix, RateFn)>,
+    ) -> Self {
+        assert_eq!(hamiltonian.len(), d * d, "hamiltonian wrong shape");
+        let h_clone = hamiltonian.clone();
+        let hamiltonian_fn: HermitianFn = Arc::new(move |_t| h_clone.clone());
+        Self {
+            d,
+            hamiltonian_fn,
+            collapse_fns,
+        }
+    }
+
+    /// Construct with fully time-dependent Hamiltonian and rates.
+    pub fn new(d: usize, hamiltonian_fn: HermitianFn, collapse_fns: Vec<(Matrix, RateFn)>) -> Self {
+        Self {
+            d,
+            hamiltonian_fn,
+            collapse_fns,
+        }
+    }
+
+    /// Evaluate at time `t`, producing a static [`Lindbladian`] snapshot.
+    pub fn at(&self, t: f64) -> Lindbladian {
+        let h = (self.hamiltonian_fn)(t);
+        let collapse: Vec<(Matrix, f64)> = self
+            .collapse_fns
+            .iter()
+            .map(|(op, rate_fn)| (op.clone(), rate_fn(t)))
+            .collect();
+        Lindbladian::new(self.d, h, collapse)
+    }
+}
+
+impl std::fmt::Debug for TimeDepLindbladian {
+    fn fmt(&self, f: &mut std::fmt::Formatter<'_>) -> std::fmt::Result {
+        f.debug_struct("TimeDepLindbladian")
+            .field("d", &self.d)
+            .field("num_collapse", &self.collapse_fns.len())
+            .finish()
+    }
+}
+
+// ============================================================================
+// Synthesis entry point
+// ============================================================================
+
+use crate::basis::PauliString;
+use crate::matrix;
+use crate::pauli_lindblad::PauliLindbladModel;
+
+/// Synthesize a Pauli-Lindblad model from a time-dependent noise
+/// Lindbladian via time-slicing. Each slice's superoperator is the
+/// interaction-frame-transformed L(t_mid) snapshot.
+///
+/// `num_qubits` gives the Pauli enumeration dimension; `ideal_h` is the
+/// (time-independent) ideal gate Hamiltonian used for the interaction
+/// frame; `noise_td` is the time-dependent noise.
+pub fn synthesize_superop_time_dep(
+    num_qubits: usize,
+    ideal_h: &Matrix,
+    noise_td: &TimeDepLindbladian,
+    tau_g: f64,
+    n_slices: usize,
+) -> PauliLindbladModel {
+    assert!(n_slices >= 1);
+    let d = 1usize << num_qubits;
+    assert_eq!(ideal_h.len(), d * d);
+    assert_eq!(noise_td.d, d);
+    let d2 = d * d;
+    let dt = tau_g / n_slices as f64;
+
+    // Product of per-slice propagators, newest on left.
+    let mut u_total = matrix::identity(d2);
+    for k in 0..n_slices {
+        let t_mid = (k as f64 + 0.5) * dt;
+
+        // Evaluate time-dependent noise at this slice.
+        let lind_snap = noise_td.at(t_mid);
+
+        // Interaction-frame transform.
+        let u_g = matrix::exp_minus_i_h_t(ideal_h, d, t_mid);
+        let u_g_dag = matrix::dag(&u_g, d);
+        let h_i = matrix::matmul(
+            &matrix::matmul(&u_g_dag, &lind_snap.hamiltonian, d),
+            &u_g,
+            d,
+        );
+        let collapse_i: Vec<(Matrix, f64)> = lind_snap
+            .collapse
+            .iter()
+            .map(|(c, g)| (matrix::matmul(&matrix::matmul(&u_g_dag, c, d), &u_g, d), *g))
+            .collect();
+
+        let lind_i = Lindbladian::new(d, h_i, collapse_i);
+        let l_super = lind_i.superoperator();
+        let u_slice = matrix::expm(&matrix::scale(&l_super, Complex64::new(dt, 0.0)), d2);
+        u_total = matrix::matmul(&u_slice, &u_total, d2);
+    }
+
+    // Apply to each Pauli, extract fidelities, Walsh-Hadamard inversion.
+    let paulis = PauliString::enumerate_nonidentity(num_qubits);
+    let alphas: Vec<f64> = paulis
+        .iter()
+        .map(|p| {
+            let p_mat = matrix::pauli_string_mat(p);
+            let vec_p = matrix::vec_of(&p_mat, d);
+            let vec_applied = matrix::matvec(&u_total, &vec_p, d2);
+            let applied = matrix::unvec(&vec_applied, d);
+            let inner = matrix::trace(&matrix::matmul(&p_mat, &applied, d), d);
+            let f_b = inner.re / d as f64;
+            assert!(
+                f_b > 0.1,
+                "Pauli fidelity {} too low for {:?}; noise outside weak regime",
+                f_b,
+                p,
+            );
+            -f_b.ln()
+        })
+        .collect();
+    walsh_hadamard_invert(paulis, alphas, num_qubits)
+}
+
+fn walsh_hadamard_invert(
+    paulis: Vec<PauliString>,
+    alphas: Vec<f64>,
+    n_qubits: usize,
+) -> PauliLindbladModel {
+    let norm = 1.0 / (1usize << (2 * n_qubits)) as f64;
+    let rates: Vec<f64> = paulis
+        .iter()
+        .map(|k| {
+            let mut s = 0.0;
+            for (b, &a) in paulis.iter().zip(alphas.iter()) {
+                let sign = if k.symplectic_product(b) == 0 {
+                    1.0
+                } else {
+                    -1.0
+                };
+                s += sign * a;
+            }
+            (-norm * s).max(0.0)
+        })
+        .collect();
+    PauliLindbladModel::new(paulis, rates)
+}
diff --git a/exp/pecos-lindblad/tests/convergence.rs b/exp/pecos-lindblad/tests/convergence.rs
new file mode 100644
index 000000000..b2a88b575
--- /dev/null
+++ b/exp/pecos-lindblad/tests/convergence.rs
@@ -0,0 +1,69 @@
+// Copyright 2026 The PECOS Developers
+//
+// Licensed under the Apache License, Version 2.0 (the "License"); you may not use this file except
+// in compliance with the License. You may obtain a copy of the License at
+//
+//     https://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software distributed under the License
+// is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express
+// or implied. See the License for the specific language governing permissions and limitations under
+// the License.
+
+//! Simpson's-rule convergence test for `synthesize_numerical`.
+//!
+//! We sweep `N_STEPS` on a `CX_theta + AD+PD` fixture and verify that each
+//! step count converges (within tol) to `DEFAULT_N_STEPS = 1024`. Ensures
+//! that the default is neither needlessly large nor too small, and that
+//! users tweaking `N_STEPS` know what to expect.
+//!
+//! For the current test parameters, convergence is already at `1e-12`
+//! between `N = 64` and `N = 1024`, so `DEFAULT_N_STEPS = 1024` is
+//! comfortably safe (~16x over-sampled).
+
+use approx::assert_abs_diff_eq;
+
+use pecos_lindblad::noise_models::ad_pd_2q;
+use pecos_lindblad::{DEFAULT_N_STEPS, Gate, PauliString, synthesize_numerical};
+
+fn cx_rates(n_steps: usize) -> Vec<f64> {
+    let omega = 1.0;
+    let theta = std::f64::consts::FRAC_PI_4;
+    let noise = ad_pd_2q(100.0, 80.0, 120.0, 90.0);
+    let gate = Gate::cx_theta(omega, theta, noise);
+    let pl = synthesize_numerical(&gate, n_steps);
+    PauliString::enumerate_nonidentity(2)
+        .iter()
+        .map(|p| pl.rate(p))
+        .collect()
+}
+
+#[test]
+fn simpson_converges_for_cx_theta() {
+    let reference = cx_rates(DEFAULT_N_STEPS);
+    // Simpson's 1/3 rule has error O(h^4). At N=64 over a single-oscillation
+    // interval we expect ~1e-10; at N=128, ~1e-12; at N>=256, machine eps.
+    let tolerances = [
+        (16usize, 1e-6),
+        (32, 1e-8),
+        (64, 1e-10),
+        (128, 1e-12),
+        (256, 1e-13),
+    ];
+    for (n, tol) in tolerances {
+        let result = cx_rates(n);
+        for (a, b) in result.iter().zip(reference.iter()) {
+            assert_abs_diff_eq!(a, b, epsilon = tol);
+        }
+    }
+}
+
+#[test]
+fn default_n_steps_matches_fine_grid() {
+    // DEFAULT_N_STEPS = 1024 should match N = 2048 to ~machine precision.
+    let a = cx_rates(DEFAULT_N_STEPS);
+    let b = cx_rates(2048);
+    for (x, y) in a.iter().zip(b.iter()) {
+        assert_abs_diff_eq!(x, y, epsilon = 1e-14);
+    }
+}
diff --git a/exp/pecos-lindblad/tests/cross_path.rs b/exp/pecos-lindblad/tests/cross_path.rs
new file mode 100644
index 000000000..16ae23186
--- /dev/null
+++ b/exp/pecos-lindblad/tests/cross_path.rs
@@ -0,0 +1,78 @@
+// Copyright 2026 The PECOS Developers
+//
+// Licensed under the Apache License, Version 2.0 (the "License"); you may not use this file except
+// in compliance with the License. You may obtain a copy of the License at
+//
+//     https://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software distributed under the License
+// is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express
+// or implied. See the License for the specific language governing permissions and limitations under
+// the License.
+
+//! Cross-path consistency: different entry points must agree on inputs
+//! they both handle.
+//!
+//! - [`synthesize_identity_1q`] (fast) vs [`synthesize_numerical`] (Simpson)
+//!   for 1Q identity gate: should be bit-close (Simpson on constant
+//!   integrand is exact up to quadrature).
+//! - [`synthesize_numerical`] for 2Q identity vs manual 1Q decomposition:
+//!   for independent qubits, rates should be consistent with the
+//!   single-qubit theory.
+
+use approx::assert_abs_diff_eq;
+
+use pecos_lindblad::noise_models::{ad_pd_1q, ad_pd_2q};
+use pecos_lindblad::{
+    DEFAULT_N_STEPS, Gate, Pauli1, PauliString, synthesize_identity_1q, synthesize_numerical,
+};
+
+#[test]
+fn fast_identity_matches_simpson_1q() {
+    let noise = ad_pd_1q(150.0, 120.0);
+    let tau_g = 2.0;
+    let gate = Gate::identity(1, noise, tau_g);
+    let fast = synthesize_identity_1q(&gate);
+    let simpson = synthesize_numerical(&gate, DEFAULT_N_STEPS);
+    for p in [Pauli1::X, Pauli1::Y, Pauli1::Z] {
+        let key = PauliString::single(p);
+        assert_abs_diff_eq!(fast.rate(&key), simpson.rate(&key), epsilon = 1e-14);
+    }
+}
+
+#[test]
+fn identity_2q_rates_agree_with_1q_independent_qubits() {
+    // For identity + AD+PD acting independently on two qubits, we expect
+    // weight-1 rates {lambda_ix, lambda_iy, lambda_iz, lambda_xi, lambda_yi,
+    // lambda_zi} to match the single-qubit predictions (paper line 812):
+    //   lambda_{i·x} = lambda_{i·y} = beta_down_r * tau_g / 4
+    //   lambda_{i·z} = beta_phi_r * tau_g / 2
+    //   (mirror for the l qubit)
+    // Weight-2 rates should all be zero (no interaction between qubits).
+    let t1_l = 100.0;
+    let t2_l = 80.0;
+    let t1_r = 150.0;
+    let t2_r = 120.0;
+    let tau_g = 2.0;
+    let noise = ad_pd_2q(t1_l, t1_r, t2_l, t2_r);
+    let gate = Gate::identity(2, noise, tau_g);
+    let pl = synthesize_numerical(&gate, DEFAULT_N_STEPS);
+
+    let bd_l = 1.0 / t1_l;
+    let bd_r = 1.0 / t1_r;
+    let bp_l = 1.0 / t2_l - 1.0 / (2.0 * t1_l);
+    let bp_r = 1.0 / t2_r - 1.0 / (2.0 * t1_r);
+
+    let rate = |s: &str| pl.rate(&PauliString::from_label(s).unwrap());
+    assert_abs_diff_eq!(rate("IX"), bd_r * tau_g / 4.0, epsilon = 1e-12);
+    assert_abs_diff_eq!(rate("IY"), bd_r * tau_g / 4.0, epsilon = 1e-12);
+    assert_abs_diff_eq!(rate("IZ"), bp_r * tau_g / 2.0, epsilon = 1e-12);
+    assert_abs_diff_eq!(rate("XI"), bd_l * tau_g / 4.0, epsilon = 1e-12);
+    assert_abs_diff_eq!(rate("YI"), bd_l * tau_g / 4.0, epsilon = 1e-12);
+    assert_abs_diff_eq!(rate("ZI"), bp_l * tau_g / 2.0, epsilon = 1e-12);
+
+    // All weight-2 rates must be zero (no coupling).
+    for label in ["XX", "XY", "XZ", "YX", "YY", "YZ", "ZX", "ZY", "ZZ"] {
+        assert_abs_diff_eq!(rate(label), 0.0, epsilon = 1e-12);
+    }
+}
diff --git a/exp/pecos-lindblad/tests/custom_gate.rs b/exp/pecos-lindblad/tests/custom_gate.rs
new file mode 100644
index 000000000..5563b78e1
--- /dev/null
+++ b/exp/pecos-lindblad/tests/custom_gate.rs
@@ -0,0 +1,101 @@
+// Copyright 2026 The PECOS Developers
+//
+// Licensed under the Apache License, Version 2.0 (the "License"); you may not use this file except
+// in compliance with the License. You may obtain a copy of the License at
+//
+//     https://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software distributed under the License
+// is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express
+// or implied. See the License for the specific language governing permissions and limitations under
+// the License.
+
+//! Smoke test for `Gate::from_hamiltonian` — the general escape hatch
+//! that lets users build gates not in the named catalog. Exercises the
+//! `matrix::expm` fallback for a non-structured 4x4 Hamiltonian.
+
+use approx::assert_abs_diff_eq;
+use num_complex::Complex64;
+
+use pecos_lindblad::matrix::{self, Matrix};
+use pecos_lindblad::{
+    DEFAULT_N_STEPS, Gate, Lindbladian, Pauli1, PauliString, synthesize_exact_unitary,
+    synthesize_numerical,
+};
+
+/// iSWAP_theta generator: `H_g = (omega/2)(XX + YY)` (4x4 Hermitian,
+/// non-diagonal, non-block-diagonal in computational basis -- hits
+/// the `expm` fallback path).
+fn iswap_hamiltonian(omega: f64) -> Matrix {
+    let x = matrix::pauli_1q(Pauli1::X);
+    let y = matrix::pauli_1q(Pauli1::Y);
+    let xx = matrix::kron(&x, &x, 2, 2);
+    let yy = matrix::kron(&y, &y, 2, 2);
+    matrix::scale(&matrix::add(&xx, &yy), Complex64::new(omega / 2.0, 0.0))
+}
+
+#[test]
+fn iswap_theta_reduces_to_identity_at_zero_theta() {
+    // At theta=0 (or tau_g=0), the gate Hamiltonian has no time to act,
+    // so the result should match identity+AD+PD rates exactly.
+    let d = 2;
+    let i2 = matrix::identity(2);
+    let sm = matrix::sigma_minus();
+    let z1 = matrix::pauli_1q(Pauli1::Z);
+    let sm_l = matrix::kron(&sm, &i2, 2, 2);
+    let sm_r = matrix::kron(&i2, &sm, 2, 2);
+    let z_l = matrix::kron(&z1, &i2, 2, 2);
+    let z_r = matrix::kron(&i2, &z1, 2, 2);
+    let beta_down = 1e-4;
+    let beta_phi = 2e-4;
+    let _ = d;
+
+    let collapse: Vec<(Matrix, f64)> = vec![
+        (sm_l, beta_down),
+        (sm_r, beta_down),
+        (z_l, beta_phi / 2.0),
+        (z_r, beta_phi / 2.0),
+    ];
+    let noise = Lindbladian::new(4, matrix::zeros(4), collapse);
+    let tau_g = 0.0; // Degenerate duration.
+    let h_iswap = iswap_hamiltonian(1.0);
+    let gate = Gate::from_hamiltonian("iswap_0", 2, h_iswap, noise, tau_g);
+
+    let pl = synthesize_numerical(&gate, DEFAULT_N_STEPS);
+    // At tau_g=0 everything should vanish.
+    for ps in PauliString::enumerate_nonidentity(2) {
+        assert_abs_diff_eq!(pl.rate(&ps), 0.0, epsilon = 1e-14);
+    }
+}
+
+#[test]
+fn custom_hamiltonian_coherent_noise_produces_nonzero_rates() {
+    // Construct a non-structured 2Q Hamiltonian H_g = XX + YY (iSWAP
+    // generator) with coherent IZ phase noise. Verify synthesis runs
+    // and produces some non-zero rate (exercises expm fallback).
+    let omega = 1.0;
+    let theta = std::f64::consts::FRAC_PI_4;
+    let tau_g = theta / omega;
+    let h_g = iswap_hamiltonian(omega);
+
+    let i2 = matrix::identity(2);
+    let z1 = matrix::pauli_1q(Pauli1::Z);
+    let iz = matrix::kron(&i2, &z1, 2, 2);
+    let delta = 1e-4;
+    let h_delta = matrix::scale(&iz, Complex64::new(delta / 2.0, 0.0));
+    let noise = Lindbladian::new(4, h_delta, Vec::new());
+
+    let gate = Gate::from_hamiltonian("iswap_xy", 2, h_g, noise, tau_g);
+    let pl = synthesize_exact_unitary(&gate);
+
+    // Some rate should be non-zero; total rate in correct order of magnitude.
+    let total = pl.total_rate();
+    let expected_scale = (delta / omega).powi(2);
+    assert!(total > 0.0, "expected non-zero rates, got total={}", total);
+    assert!(
+        total < 10.0 * expected_scale,
+        "total rate {} exceeds scale {} by >10x -- higher-order term leak?",
+        total,
+        expected_scale,
+    );
+}
diff --git a/exp/pecos-lindblad/tests/cx_theta_2q.rs b/exp/pecos-lindblad/tests/cx_theta_2q.rs
new file mode 100644
index 000000000..30ce651b5
--- /dev/null
+++ b/exp/pecos-lindblad/tests/cx_theta_2q.rs
@@ -0,0 +1,173 @@
+// Copyright 2026 The PECOS Developers
+//
+// Licensed under the Apache License, Version 2.0 (the "License"); you may not use this file except
+// in compliance with the License. You may obtain a copy of the License at
+//
+//     https://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software distributed under the License
+// is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express
+// or implied. See the License for the specific language governing permissions and limitations under
+// the License.
+
+//! Parity test: 2-qubit CX_theta gate under independent AD + PD on each
+//! qubit vs closed-form leading-order results from arXiv:2502.03462
+//! eqs. 929-956 (appendix SubApp:CX_th+AD+PD).
+//!
+//! CX_theta is the showcase gate of the paper. Unlike CZ_theta, AD and PD
+//! contributions *mix* on `lambda_{iy, iz, zy, zz}` (each has both a
+//! `beta_down_r/omega` and `beta_phi_r/omega` term).
+//!
+//! Paper closed forms (10 non-zero rates):
+//!   lambda_ix = (theta/4)(beta_down_r/omega)
+//!   lambda_iy = [(12t+8s2+s4)/128] beta_down_r/omega
+//!             + [(4t-s4)/64] beta_phi_r/omega
+//!   lambda_iz = [(4t-s4)/128] beta_down_r/omega
+//!             + [(12t+8s2+s4)/64] beta_phi_r/omega
+//!   lambda_xi = lambda_yi = [(2t+s2)/16] beta_down_l/omega
+//!   lambda_xx = lambda_yx = [(2t-s2)/16] beta_down_l/omega
+//!   lambda_zi = (theta/2)(beta_phi_l/omega)
+//!   lambda_zy = [(12t-8s2+s4)/128] beta_down_r/omega
+//!             + [(4t-s4)/64] beta_phi_r/omega
+//!   lambda_zz = [(4t-s4)/128] beta_down_r/omega
+//!             + [(12t-8s2+s4)/64] beta_phi_r/omega
+//!
+//! where s2 = sin(2 theta), s4 = sin(4 theta).
+//!
+//! 5 rates are zero to leading order: XY, XZ, YY, YZ, ZX.
+
+use approx::assert_abs_diff_eq;
+use num_complex::Complex64;
+
+use pecos_lindblad::matrix::{self, Matrix};
+use pecos_lindblad::{
+    DEFAULT_N_STEPS, Gate, Lindbladian, Pauli1, PauliString, synthesize_numerical,
+};
+
+fn two_qubit_ad_plus_pd(
+    beta_down_l: f64,
+    beta_down_r: f64,
+    beta_phi_l: f64,
+    beta_phi_r: f64,
+) -> Lindbladian {
+    let d = 4;
+    let i2 = matrix::identity(2);
+    let sm = matrix::sigma_minus();
+    let z = matrix::pauli_1q(Pauli1::Z);
+    let sm_l = matrix::kron(&sm, &i2, 2, 2);
+    let sm_r = matrix::kron(&i2, &sm, 2, 2);
+    let z_l = matrix::kron(&z, &i2, 2, 2);
+    let z_r = matrix::kron(&i2, &z, 2, 2);
+
+    let collapse: Vec<(Matrix, f64)> = vec![
+        (sm_l, beta_down_l),
+        (sm_r, beta_down_r),
+        (z_l, beta_phi_l / 2.0),
+        (z_r, beta_phi_r / 2.0),
+    ];
+    let zero_ham: Matrix = vec![Complex64::new(0.0, 0.0); d * d];
+    Lindbladian::new(d, zero_ham, collapse)
+}
+
+#[allow(clippy::too_many_arguments)]
+fn paper_cx_rate(
+    label: &str,
+    theta: f64,
+    omega: f64,
+    bd_l: f64,
+    bd_r: f64,
+    bp_l: f64,
+    bp_r: f64,
+) -> f64 {
+    let s2 = (2.0 * theta).sin();
+    let s4 = (4.0 * theta).sin();
+    let f_amp_plus = (2.0 * theta + s2) / 16.0;
+    let f_amp_minus = (2.0 * theta - s2) / 16.0;
+    let f_dbl_plus = (12.0 * theta + 8.0 * s2 + s4) / 128.0;
+    let f_dbl_minus = (12.0 * theta - 8.0 * s2 + s4) / 128.0;
+    let f_anti_4 = (4.0 * theta - s4) / 64.0;
+    let f_anti_128 = (4.0 * theta - s4) / 128.0;
+    match label {
+        "IX" => (theta / 4.0) * (bd_r / omega),
+        "IY" => f_dbl_plus * (bd_r / omega) + f_anti_4 * (bp_r / omega),
+        "IZ" => {
+            f_anti_128 * (bd_r / omega) + (12.0 * theta + 8.0 * s2 + s4) / 64.0 * (bp_r / omega)
+        }
+        "XI" | "YI" => f_amp_plus * (bd_l / omega),
+        "XX" | "YX" => f_amp_minus * (bd_l / omega),
+        "ZI" => (theta / 2.0) * (bp_l / omega),
+        "ZY" => f_dbl_minus * (bd_r / omega) + f_anti_4 * (bp_r / omega),
+        "ZZ" => {
+            f_anti_128 * (bd_r / omega) + (12.0 * theta - 8.0 * s2 + s4) / 64.0 * (bp_r / omega)
+        }
+        "XY" | "XZ" | "YY" | "YZ" | "ZX" => 0.0,
+        _ => panic!("unknown label {}", label),
+    }
+}
+
+fn run_cx(theta: f64, omega: f64, bd_l: f64, bd_r: f64, bp_l: f64, bp_r: f64, tol: f64) {
+    let noise = two_qubit_ad_plus_pd(bd_l, bd_r, bp_l, bp_r);
+    let gate = Gate::cx_theta(omega, theta, noise);
+    let pl = synthesize_numerical(&gate, DEFAULT_N_STEPS);
+
+    let all_labels = [
+        "IX", "IY", "IZ", "XI", "XX", "XY", "XZ", "YI", "YX", "YY", "YZ", "ZI", "ZX", "ZY", "ZZ",
+    ];
+    for label in all_labels {
+        let got = pl.rate(&PauliString::from_label(label).unwrap());
+        let expected = paper_cx_rate(label, theta, omega, bd_l, bd_r, bp_l, bp_r);
+        assert_abs_diff_eq!(got, expected, epsilon = tol);
+    }
+}
+
+#[test]
+fn cx_theta_ad_plus_pd_pi_over_4() {
+    // Paper's showcase angle (sqrt(CX) = CX_{pi/4}).
+    run_cx(
+        std::f64::consts::FRAC_PI_4,
+        1.0,
+        1e-4, // AD l
+        2e-4, // AD r
+        5e-5, // PD l
+        7e-5, // PD r
+        1e-8,
+    );
+}
+
+#[test]
+fn cx_theta_ad_plus_pd_pi_over_2() {
+    // Clifford: full CNOT. Exercises sin(4 theta) = sin(2pi) = 0 terms.
+    run_cx(
+        std::f64::consts::FRAC_PI_2,
+        1.0,
+        1e-4,
+        1.5e-4,
+        3e-5,
+        4e-5,
+        1e-8,
+    );
+}
+
+#[test]
+fn cx_theta_ad_only() {
+    run_cx(std::f64::consts::FRAC_PI_3, 1.5, 3e-4, 1e-4, 0.0, 0.0, 1e-8);
+}
+
+#[test]
+fn cx_theta_pd_only() {
+    run_cx(std::f64::consts::FRAC_PI_4, 1.0, 0.0, 0.0, 2e-4, 3e-4, 1e-8);
+}
+
+#[test]
+fn cx_theta_symmetric_beta_down_symmetric_pd() {
+    // Exercise all non-zero rates simultaneously, symmetric noise case.
+    run_cx(
+        std::f64::consts::FRAC_PI_4,
+        1.0,
+        2e-4,
+        2e-4,
+        1e-4,
+        1e-4,
+        1e-8,
+    );
+}
diff --git a/exp/pecos-lindblad/tests/cz_theta_2q.rs b/exp/pecos-lindblad/tests/cz_theta_2q.rs
new file mode 100644
index 000000000..892b87a7f
--- /dev/null
+++ b/exp/pecos-lindblad/tests/cz_theta_2q.rs
@@ -0,0 +1,173 @@
+// Copyright 2026 The PECOS Developers
+//
+// Licensed under the Apache License, Version 2.0 (the "License"); you may not use this file except
+// in compliance with the License. You may obtain a copy of the License at
+//
+//     https://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software distributed under the License
+// is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express
+// or implied. See the License for the specific language governing permissions and limitations under
+// the License.
+
+//! Parity test: 2-qubit CZ_theta gate under independent AD + PD on each
+//! qubit vs closed-form leading-order results from arXiv:2502.03462
+//! eqs. 896-906 (appendix SubApp:CZ_th+AD+PD).
+//!
+//! String index convention: leftmost factor is the "l" (left) qubit.
+//!   "iz" == I (x) Z
+//!   "zx" == Z (x) X
+//!
+//! Paper closed forms (all others vanish to leading order):
+//!   lambda_iz = (theta/2) * beta_phi_r / omega_cz
+//!   lambda_zi = (theta/2) * beta_phi_l / omega_cz
+//!   lambda_ix = lambda_iy = (2t+sin2t)/16 * beta_down_r / omega_cz
+//!   lambda_xi = lambda_yi = (2t+sin2t)/16 * beta_down_l / omega_cz
+//!   lambda_zx = lambda_zy = (2t-sin2t)/16 * beta_down_r / omega_cz
+//!   lambda_xz = lambda_yz = (2t-sin2t)/16 * beta_down_l / omega_cz
+
+use approx::assert_abs_diff_eq;
+use num_complex::Complex64;
+
+use pecos_lindblad::matrix::{self, Matrix};
+use pecos_lindblad::{
+    DEFAULT_N_STEPS, Gate, Lindbladian, Pauli1, PauliString, synthesize_numerical,
+};
+
+fn two_qubit_ad_plus_pd(
+    beta_down_l: f64,
+    beta_down_r: f64,
+    beta_phi_l: f64,
+    beta_phi_r: f64,
+) -> Lindbladian {
+    let d = 4;
+    let i2 = matrix::identity(2);
+    let sm = matrix::sigma_minus();
+    let z = matrix::pauli_1q(Pauli1::Z);
+    // Kronecker: (l) ⊗ (r) with l = left qubit = index 0.
+    let sm_l = matrix::kron(&sm, &i2, 2, 2);
+    let sm_r = matrix::kron(&i2, &sm, 2, 2);
+    let z_l = matrix::kron(&z, &i2, 2, 2);
+    let z_r = matrix::kron(&i2, &z, 2, 2);
+
+    let collapse: Vec<(Matrix, f64)> = vec![
+        (sm_l, beta_down_l),
+        (sm_r, beta_down_r),
+        (z_l, beta_phi_l / 2.0),
+        (z_r, beta_phi_r / 2.0),
+    ];
+    let zero_ham: Matrix = vec![Complex64::new(0.0, 0.0); d * d];
+    Lindbladian::new(d, zero_ham, collapse)
+}
+
+#[derive(Debug, Clone, Copy)]
+struct CzExpected {
+    iz: f64,
+    zi: f64,
+    ix: f64,
+    iy: f64,
+    xi: f64,
+    yi: f64,
+    zx: f64,
+    zy: f64,
+    xz: f64,
+    yz: f64,
+}
+
+fn paper_closed_form(
+    theta: f64,
+    omega_cz: f64,
+    beta_down_l: f64,
+    beta_down_r: f64,
+    beta_phi_l: f64,
+    beta_phi_r: f64,
+) -> CzExpected {
+    let two_t = 2.0 * theta;
+    let sin_2t = two_t.sin();
+    let amp_r = (two_t + sin_2t) / 16.0 * (beta_down_r / omega_cz);
+    let amp_l = (two_t + sin_2t) / 16.0 * (beta_down_l / omega_cz);
+    let anti_r = (two_t - sin_2t) / 16.0 * (beta_down_r / omega_cz);
+    let anti_l = (two_t - sin_2t) / 16.0 * (beta_down_l / omega_cz);
+    CzExpected {
+        iz: (theta / 2.0) * (beta_phi_r / omega_cz),
+        zi: (theta / 2.0) * (beta_phi_l / omega_cz),
+        ix: amp_r,
+        iy: amp_r,
+        xi: amp_l,
+        yi: amp_l,
+        zx: anti_r,
+        zy: anti_r,
+        xz: anti_l,
+        yz: anti_l,
+    }
+}
+
+fn run_cz(
+    theta: f64,
+    omega_cz: f64,
+    beta_down_l: f64,
+    beta_down_r: f64,
+    beta_phi_l: f64,
+    beta_phi_r: f64,
+    tol: f64,
+) {
+    let noise = two_qubit_ad_plus_pd(beta_down_l, beta_down_r, beta_phi_l, beta_phi_r);
+    let gate = Gate::cz_theta(omega_cz, theta, noise);
+    let pl = synthesize_numerical(&gate, DEFAULT_N_STEPS);
+
+    let exp = paper_closed_form(
+        theta,
+        omega_cz,
+        beta_down_l,
+        beta_down_r,
+        beta_phi_l,
+        beta_phi_r,
+    );
+    let rate = |s: &str| pl.rate(&PauliString::from_label(s).unwrap());
+
+    assert_abs_diff_eq!(rate("IZ"), exp.iz, epsilon = tol);
+    assert_abs_diff_eq!(rate("ZI"), exp.zi, epsilon = tol);
+    assert_abs_diff_eq!(rate("IX"), exp.ix, epsilon = tol);
+    assert_abs_diff_eq!(rate("IY"), exp.iy, epsilon = tol);
+    assert_abs_diff_eq!(rate("XI"), exp.xi, epsilon = tol);
+    assert_abs_diff_eq!(rate("YI"), exp.yi, epsilon = tol);
+    assert_abs_diff_eq!(rate("ZX"), exp.zx, epsilon = tol);
+    assert_abs_diff_eq!(rate("ZY"), exp.zy, epsilon = tol);
+    assert_abs_diff_eq!(rate("XZ"), exp.xz, epsilon = tol);
+    assert_abs_diff_eq!(rate("YZ"), exp.yz, epsilon = tol);
+
+    // All remaining 5 Paulis should be (numerically) zero at leading order.
+    for label in ["XX", "XY", "YX", "YY", "ZZ"] {
+        assert_abs_diff_eq!(rate(label), 0.0, epsilon = tol);
+    }
+}
+
+#[test]
+fn cz_theta_ad_plus_pd_pi_over_4() {
+    // Weak noise beta/omega ~ 1e-4 => leading-order match to ~1e-8.
+    run_cz(
+        std::f64::consts::FRAC_PI_4,
+        1.0,
+        1e-4, // AD l
+        2e-4, // AD r
+        5e-5, // PD l
+        7e-5, // PD r
+        1e-8,
+    );
+}
+
+#[test]
+fn cz_theta_ad_plus_pd_pi_over_2() {
+    // theta=pi/2 is Clifford: paper predicts 4-fold degeneracies.
+    run_cz(std::f64::consts::FRAC_PI_2, 1.0, 1e-4, 1e-4, 0.0, 0.0, 1e-8);
+}
+
+#[test]
+fn cz_theta_ad_only() {
+    run_cz(std::f64::consts::FRAC_PI_3, 1.5, 3e-4, 1e-4, 0.0, 0.0, 1e-8);
+}
+
+#[test]
+fn cz_theta_pd_only() {
+    run_cz(std::f64::consts::FRAC_PI_4, 1.0, 0.0, 0.0, 2e-4, 3e-4, 1e-8);
+}
diff --git a/exp/pecos-lindblad/tests/dem_stab_integration.rs b/exp/pecos-lindblad/tests/dem_stab_integration.rs
new file mode 100644
index 000000000..1e2337edf
--- /dev/null
+++ b/exp/pecos-lindblad/tests/dem_stab_integration.rs
@@ -0,0 +1,152 @@
+// Copyright 2026 The PECOS Developers
+//
+// Licensed under the Apache License, Version 2.0 (the "License"); you may not use this file except
+// in compliance with the License. You may obtain a copy of the License at
+//
+//     https://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software distributed under the License
+// is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express
+// or implied. See the License for the specific language governing permissions and limitations under
+// the License.
+
+//! Scaffolded integration: synthesize a Pauli-Lindblad model from a
+//! physical Lindbladian, collapse to scalar p1/p2 (lossy), and feed the
+//! scalars to the existing uniform-depolarizing `DemStabSim`.
+//!
+//! **This is a scaffold, not the full bridge.** The paper's real payoff is
+//! per-location per-Pauli rates, but `pecos-qec::fault_tolerance::dem_builder`
+//! currently accepts only uniform-depolarizing `NoiseConfig { p1, p2,
+//! p_meas, p_prep }` (4 scalar probabilities). A proper integration requires
+//! generalizing `NoiseConfig` to accept a `PauliLindbladModel` per gate
+//! type; that change is out of scope for the `pecos-lindblad` crate and is
+//! tracked in `design/lindblad_sim_skeleton.md`.
+//!
+//! What this test proves *today*:
+//! - Lindbladian + duration -> PauliLindbladModel works end-to-end.
+//! - Summary helpers (`total_rate`, `rate_at_weight`) produce sensible numbers.
+//! - Output scalars are in a range that `DemStabSim` will accept.
+//! - DemStabSim runs with those scalars and returns shot batches.
+
+use num_complex::Complex64;
+use rand::SeedableRng;
+use rand::rngs::SmallRng;
+
+use pecos_lindblad::matrix::{self, Matrix};
+use pecos_lindblad::{
+    DEFAULT_N_STEPS, Gate, Lindbladian, Pauli1, synthesize_identity_1q, synthesize_numerical,
+};
+use pecos_qec::dem_stab::DemStabSim;
+use pecos_qec::fault_tolerance::dem_builder::{DetectorDef, NoiseConfig};
+use pecos_quantum::DagCircuit;
+
+fn ad_plus_pd_1q(beta_down: f64, beta_phi: f64) -> Lindbladian {
+    let d = 2;
+    let hamiltonian = matrix::zeros(d);
+    let collapse: Vec<(Matrix, f64)> = vec![
+        (matrix::sigma_minus(), beta_down),
+        (matrix::pauli_1q(Pauli1::Z), beta_phi / 2.0),
+    ];
+    Lindbladian::new(d, hamiltonian, collapse)
+}
+
+fn ad_plus_pd_2q(beta_down: f64, beta_phi: f64) -> Lindbladian {
+    let d = 4;
+    let i2 = matrix::identity(2);
+    let sm = matrix::sigma_minus();
+    let z = matrix::pauli_1q(Pauli1::Z);
+    let sm_l = matrix::kron(&sm, &i2, 2, 2);
+    let sm_r = matrix::kron(&i2, &sm, 2, 2);
+    let z_l = matrix::kron(&z, &i2, 2, 2);
+    let z_r = matrix::kron(&i2, &z, 2, 2);
+    let collapse: Vec<(Matrix, f64)> = vec![
+        (sm_l, beta_down),
+        (sm_r, beta_down),
+        (z_l, beta_phi / 2.0),
+        (z_r, beta_phi / 2.0),
+    ];
+    let zero_ham: Matrix = vec![Complex64::new(0.0, 0.0); d * d];
+    Lindbladian::new(d, zero_ham, collapse)
+}
+
+#[test]
+fn lindblad_derived_noise_config_feeds_dem_stab_sim() {
+    // Step 1: physical noise parameters from a hypothetical device.
+    let beta_down = 1e-4; // per time unit, e.g. inverse of T1
+    let beta_phi = 2e-4; // dephasing
+    let tau_1q = 40.0; // 1Q gate duration
+    let omega_cx = 1.0;
+    let theta = std::f64::consts::FRAC_PI_2; // full CNOT
+
+    // Step 2: synthesize Pauli-Lindblad models for each gate family.
+    let pl_1q = synthesize_identity_1q(&Gate::identity(
+        1,
+        ad_plus_pd_1q(beta_down, beta_phi),
+        tau_1q,
+    ));
+    let pl_cx = synthesize_numerical(
+        &Gate::cx_theta(omega_cx, theta, ad_plus_pd_2q(beta_down, beta_phi)),
+        DEFAULT_N_STEPS,
+    );
+
+    // Sanity-check the summaries.
+    let total_1q = pl_1q.total_rate();
+    let total_2q = pl_cx.total_rate();
+    assert!(
+        total_1q > 0.0 && total_1q < 0.1,
+        "1Q total rate out of range: {}",
+        total_1q
+    );
+    assert!(
+        total_2q > 0.0 && total_2q < 0.1,
+        "2Q total rate out of range: {}",
+        total_2q
+    );
+    // For the 1Q identity with AD+PD, only weight-1 rates should be non-zero.
+    assert!((pl_1q.rate_at_weight(1) - total_1q).abs() < 1e-12);
+    // For CX_theta, both weight-1 and weight-2 rates exist.
+    assert!(pl_cx.rate_at_weight(1) > 0.0);
+    assert!(pl_cx.rate_at_weight(2) > 0.0);
+
+    // Step 3: lossy collapse to scalar p1, p2 for DemStabSim.
+    // Caveat: DemStabSim treats p1 as uniform depolarizing (X/Y/Z equal).
+    // For asymmetric AD+PD the numbers here are order-of-magnitude correct
+    // but lose per-Pauli structure. This is the gap that motivates the
+    // proper integration (generalize NoiseConfig to carry a PL model).
+    let p1 = pl_1q.total_rate();
+    let p2 = pl_cx.total_rate();
+    let noise = NoiseConfig::new(p1, p2, 0.0, 0.0);
+
+    // Step 4: build a tiny repetition-code-style circuit and sample.
+    let mut dag = DagCircuit::new();
+    dag.pz(&[2]);
+    dag.cx(&[(0, 2)]);
+    dag.cx(&[(1, 2)]);
+    dag.mz(&[2]);
+
+    let sim = DemStabSim::builder()
+        .circuit(dag)
+        .noise(noise)
+        .detectors(vec![DetectorDef::new(0).with_records([-1])])
+        .build()
+        .expect("DemStabSim build");
+
+    // Step 5: shots flow through.
+    let mut rng = SmallRng::seed_from_u64(42);
+    let batch = sim.sample_batch(500, &mut rng);
+    assert_eq!(batch.detector_flips.len(), 500);
+    assert_eq!(batch.detector_flips[0].len(), 1);
+}
+
+#[test]
+fn lindblad_scalar_collapse_is_order_of_magnitude_sane() {
+    // For 1Q identity under AD only (no PD), paper closed form:
+    //   lambda_x = lambda_y = beta_down * tau / 4, lambda_z = 0
+    //   total = beta_down * tau / 2.
+    // The lossy scalar collapse should report the same total.
+    let beta_down = 3e-4;
+    let tau = 100.0;
+    let pl = synthesize_identity_1q(&Gate::identity(1, ad_plus_pd_1q(beta_down, 0.0), tau));
+    let expected = beta_down * tau / 2.0;
+    assert!((pl.total_rate() - expected).abs() < 1e-12);
+}
diff --git a/exp/pecos-lindblad/tests/diff_helpers.rs b/exp/pecos-lindblad/tests/diff_helpers.rs
new file mode 100644
index 000000000..2490840cb
--- /dev/null
+++ b/exp/pecos-lindblad/tests/diff_helpers.rs
@@ -0,0 +1,103 @@
+// Copyright 2026 The PECOS Developers
+//
+// Licensed under the Apache License, Version 2.0 (the "License"); you may not use this file except
+// in compliance with the License. You may obtain a copy of the License at
+//
+//     https://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software distributed under the License
+// is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express
+// or implied. See the License for the specific language governing permissions and limitations under
+// the License.
+
+//! Tests for validation-oriented diff helpers on `PauliLindbladModel`.
+
+use approx::assert_abs_diff_eq;
+
+use pecos_lindblad::{PauliLindbladModel, PauliString};
+
+fn model(entries: &[(&str, f64)]) -> PauliLindbladModel {
+    let supports: Vec<_> = entries
+        .iter()
+        .map(|(s, _)| PauliString::from_label(s).unwrap())
+        .collect();
+    let rates: Vec<_> = entries.iter().map(|(_, r)| *r).collect();
+    PauliLindbladModel::new(supports, rates)
+}
+
+#[test]
+fn diff_is_sorted_by_absolute_residual() {
+    let pred = model(&[("IX", 0.001), ("IZ", 0.005), ("XI", 0.002)]);
+    let meas = model(&[("IX", 0.0012), ("IZ", 0.008), ("XI", 0.002)]);
+    let d = pred.diff(&meas);
+    // IZ has largest absolute residual (0.003), IX next (0.0002), XI last (0).
+    assert_eq!(format!("{}", d[0].0), "IZ");
+    assert_eq!(format!("{}", d[1].0), "IX");
+    assert_eq!(format!("{}", d[2].0), "XI");
+    assert_abs_diff_eq!(d[0].3, -0.003, epsilon = 1e-12);
+}
+
+#[test]
+fn residual_l2_and_max() {
+    let a = model(&[("X", 0.01), ("Y", 0.02), ("Z", 0.03)]);
+    let b = model(&[("X", 0.02), ("Y", 0.00), ("Z", 0.03)]);
+    // Differences: X=-0.01, Y=+0.02, Z=0. L2 = sqrt(0.0001 + 0.0004) = sqrt(5)*0.01.
+    assert_abs_diff_eq!(a.residual_l2(&b), (5.0_f64).sqrt() * 0.01, epsilon = 1e-12);
+    let (worst_p, worst_r) = a.max_residual(&b).unwrap();
+    assert_eq!(format!("{}", worst_p), "Y");
+    assert_abs_diff_eq!(worst_r, 0.02, epsilon = 1e-12);
+}
+
+#[test]
+fn residual_by_weight_classifies_correctly() {
+    let a = model(&[("IX", 0.001), ("IY", 0.001), ("ZZ", 0.005), ("IZZ", 0.002)]);
+    let b = model(&[("IX", 0.002), ("IY", 0.001), ("ZZ", 0.009), ("IZZ", 0.0025)]);
+    let by_w = a.residual_by_weight(&b);
+    // Differences: IX=-0.001 (wt 1), IY=0 (wt 1), ZZ=-0.004 (wt 2), IZZ=-0.0005 (wt 2).
+    let w1 = by_w.iter().find(|(w, _)| *w == 1).unwrap().1;
+    let w2 = by_w.iter().find(|(w, _)| *w == 2).unwrap().1;
+    assert_abs_diff_eq!(w1, 0.001, epsilon = 1e-12);
+    assert_abs_diff_eq!(w2, 0.0045, epsilon = 1e-12);
+}
+
+#[test]
+fn diagnose_flags_large_weight_2_residual() {
+    let pred = model(&[("IX", 0.001), ("IZ", 0.005)]);
+    let meas = model(&[("IX", 0.001), ("IZ", 0.005), ("ZZ", 0.01)]);
+    // Predicted model missing ZZ -- diagnose should flag weight-2 residual.
+    let diagnoses = pred.diagnose_gap(&meas, 1e-5);
+    assert!(
+        diagnoses.iter().any(|m| m.contains("weight-2")),
+        "expected weight-2 diagnosis in {:?}",
+        diagnoses
+    );
+    assert!(
+        diagnoses.iter().any(|m| m.contains("ZZ")),
+        "expected ZZ mention in {:?}",
+        diagnoses
+    );
+}
+
+#[test]
+fn diagnose_quiet_when_models_agree() {
+    let pred = model(&[("X", 0.001), ("Z", 0.002)]);
+    let meas = model(&[("X", 0.001), ("Z", 0.002)]);
+    let diagnoses = pred.diagnose_gap(&meas, 1e-10);
+    assert!(
+        diagnoses.is_empty(),
+        "expected no diagnoses, got {:?}",
+        diagnoses
+    );
+}
+
+#[test]
+fn union_of_supports_considered() {
+    // a has X, b has Z; diff should include both with appropriate zero.
+    let a = model(&[("X", 0.003)]);
+    let b = model(&[("Z", 0.005)]);
+    let d = a.diff(&b);
+    assert_eq!(d.len(), 2);
+    // Largest |residual| is Z = 0 - 0.005 = -0.005.
+    assert_eq!(format!("{}", d[0].0), "Z");
+    assert_abs_diff_eq!(d[0].3, -0.005, epsilon = 1e-12);
+}
diff --git a/exp/pecos-lindblad/tests/expm_smoke.rs b/exp/pecos-lindblad/tests/expm_smoke.rs
new file mode 100644
index 000000000..2c1b3919a
--- /dev/null
+++ b/exp/pecos-lindblad/tests/expm_smoke.rs
@@ -0,0 +1,121 @@
+// Copyright 2026 The PECOS Developers
+//
+// Licensed under the Apache License, Version 2.0 (the "License"); you may not use this file except
+// in compliance with the License. You may obtain a copy of the License at
+//
+//     https://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software distributed under the License
+// is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express
+// or implied. See the License for the specific language governing permissions and limitations under
+// the License.
+
+//! Smoke tests for `matrix::expm` (general Taylor + scaling + squaring).
+
+use num_complex::Complex64;
+
+use pecos_lindblad::Pauli1;
+use pecos_lindblad::matrix::{self, Matrix};
+
+fn assert_close(a: &Matrix, b: &Matrix, tol: f64) {
+    assert_eq!(a.len(), b.len(), "matrix size mismatch");
+    for i in 0..a.len() {
+        let delta = (a[i] - b[i]).norm();
+        assert!(
+            delta < tol,
+            "entry {}: |{:?} - {:?}| = {} > {}",
+            i,
+            a[i],
+            b[i],
+            delta,
+            tol
+        );
+    }
+}
+
+#[test]
+fn expm_of_zero_is_identity() {
+    for d in [2, 3, 4, 8] {
+        let z = matrix::zeros(d);
+        let result = matrix::expm(&z, d);
+        assert_close(&result, &matrix::identity(d), 1e-14);
+    }
+}
+
+#[test]
+fn expm_of_diagonal_is_elementwise_exp() {
+    let d = 4;
+    let mut m = matrix::zeros(d);
+    m[0] = Complex64::new(0.5, 0.0);
+    m[d + 1] = Complex64::new(-0.3, 0.0);
+    m[2 * d + 2] = Complex64::new(0.0, 1.2);
+    m[3 * d + 3] = Complex64::new(-0.1, -0.4);
+    let result = matrix::expm(&m, d);
+    let mut expected = matrix::zeros(d);
+    for i in 0..d {
+        expected[i * d + i] = m[i * d + i].exp();
+    }
+    assert_close(&result, &expected, 1e-12);
+}
+
+#[test]
+fn expm_agrees_with_1q_bloch_on_traceless() {
+    // H = 1.3 * X + 0.7 * Y - 0.4 * Z (traceless Hermitian 2x2).
+    // Compare expm(-i * H * t) against exp_minus_i_h_t_1q_traceless.
+    let d = 2;
+    let x = matrix::pauli_1q(Pauli1::X);
+    let y = matrix::pauli_1q(Pauli1::Y);
+    let z = matrix::pauli_1q(Pauli1::Z);
+    let h = matrix::add(
+        &matrix::add(
+            &matrix::scale(&x, Complex64::new(1.3, 0.0)),
+            &matrix::scale(&y, Complex64::new(0.7, 0.0)),
+        ),
+        &matrix::scale(&z, Complex64::new(-0.4, 0.0)),
+    );
+    for t in [0.1, 0.7, 1.5] {
+        let bloch = matrix::exp_minus_i_h_t_1q_traceless(&h, t);
+        let via_expm = matrix::expm(&matrix::scale(&h, Complex64::new(0.0, -t)), d);
+        assert_close(&bloch, &via_expm, 1e-11);
+    }
+}
+
+#[test]
+fn expm_preserves_unitarity_for_hermitian_input() {
+    // For any Hermitian H, U = exp(-i H t) should satisfy U U^dag = I.
+    let d = 4;
+    let i2 = matrix::identity(2);
+    let x = matrix::pauli_1q(Pauli1::X);
+    let z = matrix::pauli_1q(Pauli1::Z);
+    let ix = matrix::kron(&i2, &x, 2, 2);
+    let zx = matrix::kron(&z, &x, 2, 2);
+    let h = matrix::sub(&ix, &zx); // CX-style Hermitian
+    let t = 0.47;
+    let u = matrix::expm(&matrix::scale(&h, Complex64::new(0.0, -t)), d);
+    let u_udag = matrix::matmul(&u, &matrix::dag(&u, d), d);
+    assert_close(&u_udag, &matrix::identity(d), 1e-11);
+}
+
+#[test]
+fn expm_fallback_used_for_non_structured_4x4() {
+    // Construct a 4x4 Hermitian that is NOT diagonal and NOT 2x2-block-diag.
+    // H = IX + XI + YZ (mixes all quadrants).
+    let d = 4;
+    let i2 = matrix::identity(2);
+    let x = matrix::pauli_1q(Pauli1::X);
+    let y = matrix::pauli_1q(Pauli1::Y);
+    let z = matrix::pauli_1q(Pauli1::Z);
+    let ix = matrix::kron(&i2, &x, 2, 2);
+    let xi = matrix::kron(&x, &i2, 2, 2);
+    let yz = matrix::kron(&y, &z, 2, 2);
+    let h = matrix::add(&matrix::add(&ix, &xi), &yz);
+
+    assert!(!matrix::is_diagonal(&h, d, 1e-14));
+    assert!(!matrix::is_2x2_block_diagonal(&h, 1e-14));
+
+    // Should not panic (falls through to general expm).
+    let u = matrix::exp_minus_i_h_t(&h, d, 0.3);
+    // Unitarity check.
+    let u_udag = matrix::matmul(&u, &matrix::dag(&u, d), d);
+    assert_close(&u_udag, &matrix::identity(d), 1e-11);
+}
diff --git a/exp/pecos-lindblad/tests/four_qubit_smoke.rs b/exp/pecos-lindblad/tests/four_qubit_smoke.rs
new file mode 100644
index 000000000..823508476
--- /dev/null
+++ b/exp/pecos-lindblad/tests/four_qubit_smoke.rs
@@ -0,0 +1,185 @@
+// Copyright 2026 The PECOS Developers
+//
+// Licensed under the Apache License, Version 2.0 (the "License"); you may not use this file except
+// in compliance with the License. You may obtain a copy of the License at
+//
+//     https://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software distributed under the License
+// is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express
+// or implied. See the License for the specific language governing permissions and limitations under
+// the License.
+
+//! 4-qubit smoke test: exercises the `d=16` matrix-exp path and 255-Pauli
+//! enumeration in the synthesis pipeline.
+//!
+//! Case: 4Q identity gate with AD+PD noise on a single qubit. Expected
+//! result (by independence): only the 3 weight-1 rates on that qubit are
+//! non-zero, all other 252 rates vanish.
+
+use approx::assert_abs_diff_eq;
+use num_complex::Complex64;
+
+use pecos_lindblad::matrix::{self, Matrix};
+use pecos_lindblad::{
+    DEFAULT_N_STEPS, Gate, Lindbladian, Pauli1, PauliString, synthesize_exact_unitary,
+    synthesize_numerical,
+};
+
+fn kron_all(ops: &[&Matrix]) -> Matrix {
+    // Left-associative Kronecker fold over a non-empty slice.
+    let mut acc = ops[0].clone();
+    let mut d = (ops[0].len() as f64).sqrt() as usize;
+    for op in &ops[1..] {
+        let d2 = (op.len() as f64).sqrt() as usize;
+        acc = matrix::kron(&acc, op, d, d2);
+        d *= d2;
+    }
+    acc
+}
+
+#[test]
+fn three_qubit_identity_ad_on_one_qubit_fast_smoke() {
+    let d = 8;
+    let i2 = matrix::identity(2);
+    let sm = matrix::sigma_minus();
+    let z = matrix::pauli_1q(Pauli1::Z);
+
+    let beta_down = 1e-3;
+    let beta_phi = 2e-3;
+    let tau_g = 5.0;
+
+    let sm_q1 = kron_all(&[&i2, &sm, &i2]);
+    let z_q1 = kron_all(&[&i2, &z, &i2]);
+
+    let collapse: Vec<(Matrix, f64)> = vec![(sm_q1, beta_down), (z_q1, beta_phi / 2.0)];
+    let hamiltonian: Matrix = vec![Complex64::new(0.0, 0.0); d * d];
+    let noise = Lindbladian::new(d, hamiltonian, collapse);
+
+    let gate = Gate::identity(3, noise, tau_g);
+    let pl = synthesize_numerical(&gate, DEFAULT_N_STEPS);
+    let pl_coarse = synthesize_numerical(&gate, 2);
+
+    let rate = |s: &str| pl.rate(&PauliString::from_label(s).unwrap());
+    assert_abs_diff_eq!(rate("IXI"), beta_down * tau_g / 4.0, epsilon = 1e-10);
+    assert_abs_diff_eq!(rate("IYI"), beta_down * tau_g / 4.0, epsilon = 1e-10);
+    assert_abs_diff_eq!(rate("IZI"), beta_phi * tau_g / 2.0, epsilon = 1e-10);
+    for ps in PauliString::enumerate_nonidentity(3) {
+        assert_abs_diff_eq!(pl.rate(&ps), pl_coarse.rate(&ps), epsilon = 1e-14);
+    }
+
+    for ps in PauliString::enumerate_nonidentity(3) {
+        let label = format!("{}", ps);
+        if label == "IXI" || label == "IYI" || label == "IZI" {
+            continue;
+        }
+        assert_abs_diff_eq!(pl.rate(&ps), 0.0, epsilon = 1e-10);
+    }
+}
+
+#[test]
+fn three_qubit_identity_coherent_zzz_fast_smoke() {
+    let d = 8;
+    let tau_g = 5.0;
+    let delta = 1e-4;
+
+    let z = matrix::pauli_1q(Pauli1::Z);
+    let zzz = kron_all(&[&z, &z, &z]);
+    let h_delta = matrix::scale(&zzz, Complex64::new(delta / 2.0, 0.0));
+    let noise = Lindbladian::new(d, h_delta, Vec::new());
+    let gate = Gate::identity(3, noise, tau_g);
+    let pl = synthesize_exact_unitary(&gate);
+
+    let expected = (delta * tau_g).powi(2) / 4.0;
+    assert_abs_diff_eq!(
+        pl.rate(&PauliString::from_label("ZZZ").unwrap()),
+        expected,
+        epsilon = 1e-10
+    );
+
+    for ps in PauliString::enumerate_nonidentity(3) {
+        if format!("{}", ps) == "ZZZ" {
+            continue;
+        }
+        assert_abs_diff_eq!(pl.rate(&ps), 0.0, epsilon = 1e-10);
+    }
+}
+
+#[test]
+#[ignore = "Slow 4Q validation; run explicitly with: cargo test -p pecos-lindblad --test four_qubit_smoke -- --ignored"]
+fn four_qubit_identity_ad_on_one_qubit() {
+    let d = 16;
+    let i2 = matrix::identity(2);
+    let sm = matrix::sigma_minus();
+    let z = matrix::pauli_1q(Pauli1::Z);
+
+    // AD + PD on qubit 1 only (0-indexed).
+    let beta_down = 1e-3;
+    let beta_phi = 2e-3;
+    let tau_g = 5.0;
+
+    let sm_q1 = kron_all(&[&i2, &sm, &i2, &i2]);
+    let z_q1 = kron_all(&[&i2, &z, &i2, &i2]);
+
+    let collapse: Vec<(Matrix, f64)> = vec![(sm_q1, beta_down), (z_q1, beta_phi / 2.0)];
+    let hamiltonian: Matrix = vec![Complex64::new(0.0, 0.0); d * d];
+    let noise = Lindbladian::new(d, hamiltonian, collapse);
+
+    let gate = Gate::identity(4, noise, tau_g);
+    let pl = synthesize_numerical(&gate, DEFAULT_N_STEPS);
+    let pl_coarse = synthesize_numerical(&gate, 2);
+
+    // Expected non-zero rates: lambda_{q1=X}, lambda_{q1=Y}, lambda_{q1=Z}
+    // on qubit 1 (index 1 from left in "qqqq" string).
+    //   lambda_IXII = lambda_IYII = beta_down * tau_g / 4
+    //   lambda_IZII = beta_phi * tau_g / 2
+    let rate = |s: &str| pl.rate(&PauliString::from_label(s).unwrap());
+    assert_abs_diff_eq!(rate("IXII"), beta_down * tau_g / 4.0, epsilon = 1e-10);
+    assert_abs_diff_eq!(rate("IYII"), beta_down * tau_g / 4.0, epsilon = 1e-10);
+    assert_abs_diff_eq!(rate("IZII"), beta_phi * tau_g / 2.0, epsilon = 1e-10);
+    for ps in PauliString::enumerate_nonidentity(4) {
+        assert_abs_diff_eq!(pl.rate(&ps), pl_coarse.rate(&ps), epsilon = 1e-14);
+    }
+
+    // All other 252 non-identity 4Q Paulis should be zero.
+    for ps in PauliString::enumerate_nonidentity(4) {
+        let label = format!("{}", ps);
+        if label == "IXII" || label == "IYII" || label == "IZII" {
+            continue;
+        }
+        assert_abs_diff_eq!(pl.rate(&ps), 0.0, epsilon = 1e-10);
+    }
+}
+
+#[test]
+#[ignore = "Slow 4Q validation; run explicitly with: cargo test -p pecos-lindblad --test four_qubit_smoke -- --ignored"]
+fn four_qubit_identity_coherent_zzzz_smoke() {
+    // 4Q identity with coherent ZZZZ noise -- since all Zs commute, each
+    // lambda_{all-Z} should be non-zero, everything else zero.
+    let d = 16;
+    let tau_g = 5.0;
+    let delta = 1e-4;
+
+    let z = matrix::pauli_1q(Pauli1::Z);
+    let zzzz = kron_all(&[&z, &z, &z, &z]);
+    let h_delta = matrix::scale(&zzzz, Complex64::new(delta / 2.0, 0.0));
+    let noise = Lindbladian::new(d, h_delta, Vec::new());
+    let gate = Gate::identity(4, noise, tau_g);
+    let pl = synthesize_exact_unitary(&gate);
+
+    // lambda_ZZZZ = (delta * tau_g)^2 / 4  (by analogy with 1Q phase noise).
+    let expected = (delta * tau_g).powi(2) / 4.0;
+    assert_abs_diff_eq!(
+        pl.rate(&PauliString::from_label("ZZZZ").unwrap()),
+        expected,
+        epsilon = 1e-10
+    );
+
+    // All other 254 non-identity 4Q Paulis zero.
+    for ps in PauliString::enumerate_nonidentity(4) {
+        if format!("{}", ps) == "ZZZZ" {
+            continue;
+        }
+        assert_abs_diff_eq!(pl.rate(&ps), 0.0, epsilon = 1e-10);
+    }
+}
diff --git a/exp/pecos-lindblad/tests/identity_1q.rs b/exp/pecos-lindblad/tests/identity_1q.rs
new file mode 100644
index 000000000..687e19aa8
--- /dev/null
+++ b/exp/pecos-lindblad/tests/identity_1q.rs
@@ -0,0 +1,129 @@
+// Copyright 2026 The PECOS Developers
+//
+// Licensed under the Apache License, Version 2.0 (the "License"); you may not use this file except
+// in compliance with the License. You may obtain a copy of the License at
+//
+//     https://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software distributed under the License
+// is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express
+// or implied. See the License for the specific language governing permissions and limitations under
+// the License.
+
+//! Golden-fixture test for 1-qubit identity gate under amplitude damping
+//! plus pure dephasing (arXiv:2502.03462 line 812, exact non-perturbative):
+//!
+//!   lambda_x = lambda_y = (beta_down * tau_g) / 4
+//!   lambda_z = (beta_phi * tau_g) / 2
+
+use approx::assert_abs_diff_eq;
+
+use pecos_lindblad::matrix::{self, Matrix};
+use pecos_lindblad::{Gate, Lindbladian, Pauli1, PauliString, synthesize_identity_1q};
+
+fn amplitude_damping_plus_dephasing(beta_down: f64, beta_phi: f64) -> Lindbladian {
+    let d = 2;
+    let hamiltonian = matrix::zeros(d);
+    let collapse: Vec<(Matrix, f64)> = vec![
+        (matrix::sigma_minus(), beta_down),
+        (matrix::pauli_1q(Pauli1::Z), beta_phi / 2.0),
+    ];
+    Lindbladian::new(d, hamiltonian, collapse)
+}
+
+#[test]
+fn identity_ad_plus_pd_matches_paper() {
+    let beta_down = 2e-4;
+    let beta_phi = 5e-4;
+    let tau_g = 50.0;
+    let noise = amplitude_damping_plus_dephasing(beta_down, beta_phi);
+    let gate = Gate::identity(1, noise, tau_g);
+
+    let pl = synthesize_identity_1q(&gate);
+
+    let expected_x = beta_down * tau_g / 4.0;
+    let expected_y = beta_down * tau_g / 4.0;
+    let expected_z = beta_phi * tau_g / 2.0;
+
+    assert_abs_diff_eq!(
+        pl.rate(&PauliString::single(Pauli1::X)),
+        expected_x,
+        epsilon = 1e-12
+    );
+    assert_abs_diff_eq!(
+        pl.rate(&PauliString::single(Pauli1::Y)),
+        expected_y,
+        epsilon = 1e-12
+    );
+    assert_abs_diff_eq!(
+        pl.rate(&PauliString::single(Pauli1::Z)),
+        expected_z,
+        epsilon = 1e-12
+    );
+}
+
+#[test]
+fn identity_ad_only() {
+    let beta_down = 1e-3;
+    let tau_g = 100.0;
+    let noise = amplitude_damping_plus_dephasing(beta_down, 0.0);
+    let gate = Gate::identity(1, noise, tau_g);
+
+    let pl = synthesize_identity_1q(&gate);
+
+    let expected_xy = beta_down * tau_g / 4.0;
+    assert_abs_diff_eq!(
+        pl.rate(&PauliString::single(Pauli1::X)),
+        expected_xy,
+        epsilon = 1e-12
+    );
+    assert_abs_diff_eq!(
+        pl.rate(&PauliString::single(Pauli1::Y)),
+        expected_xy,
+        epsilon = 1e-12
+    );
+    assert_abs_diff_eq!(
+        pl.rate(&PauliString::single(Pauli1::Z)),
+        0.0,
+        epsilon = 1e-12
+    );
+}
+
+#[test]
+fn identity_pd_only() {
+    let beta_phi = 7e-4;
+    let tau_g = 40.0;
+    let noise = amplitude_damping_plus_dephasing(0.0, beta_phi);
+    let gate = Gate::identity(1, noise, tau_g);
+
+    let pl = synthesize_identity_1q(&gate);
+
+    let expected_z = beta_phi * tau_g / 2.0;
+    assert_abs_diff_eq!(
+        pl.rate(&PauliString::single(Pauli1::X)),
+        0.0,
+        epsilon = 1e-12
+    );
+    assert_abs_diff_eq!(
+        pl.rate(&PauliString::single(Pauli1::Y)),
+        0.0,
+        epsilon = 1e-12
+    );
+    assert_abs_diff_eq!(
+        pl.rate(&PauliString::single(Pauli1::Z)),
+        expected_z,
+        epsilon = 1e-12
+    );
+}
+
+#[test]
+fn identity_zero_noise_gives_zero_rates() {
+    let noise = amplitude_damping_plus_dephasing(0.0, 0.0);
+    let gate = Gate::identity(1, noise, 1.0);
+
+    let pl = synthesize_identity_1q(&gate);
+
+    for p in [Pauli1::X, Pauli1::Y, Pauli1::Z] {
+        assert_abs_diff_eq!(pl.rate(&PauliString::single(p)), 0.0, epsilon = 1e-14);
+    }
+}
diff --git a/exp/pecos-lindblad/tests/input_validation.rs b/exp/pecos-lindblad/tests/input_validation.rs
new file mode 100644
index 000000000..8282a5572
--- /dev/null
+++ b/exp/pecos-lindblad/tests/input_validation.rs
@@ -0,0 +1,82 @@
+// Copyright 2026 The PECOS Developers
+//
+// Licensed under the Apache License, Version 2.0 (the "License"); you may not use this file except
+// in compliance with the License. You may obtain a copy of the License at
+//
+//     https://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software distributed under the License
+// is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express
+// or implied. See the License for the specific language governing permissions and limitations under
+// the License.
+
+//! Input-validation tests. Bad inputs must produce immediate panics at
+//! construction time rather than silently returning wrong results.
+
+use num_complex::Complex64;
+
+use pecos_lindblad::matrix::{self, Matrix};
+use pecos_lindblad::{Gate, Lindbladian};
+
+#[test]
+#[should_panic(expected = "Hermitian")]
+fn non_hermitian_hamiltonian_in_lindbladian_panics() {
+    let d = 2;
+    let mut h: Matrix = vec![Complex64::new(0.0, 0.0); d * d];
+    // Asymmetric imaginary entry makes this non-Hermitian.
+    h[1] = Complex64::new(1.0, 0.0);
+    h[2] = Complex64::new(2.0, 0.0); // Should be 1.0 for Hermitian.
+    let _ = Lindbladian::new(d, h, Vec::new());
+}
+
+#[test]
+#[should_panic(expected = "Hermitian")]
+fn non_hermitian_ideal_hamiltonian_in_gate_panics() {
+    let d = 2;
+    let mut h: Matrix = vec![Complex64::new(0.0, 0.0); d * d];
+    h[1] = Complex64::new(0.0, 1.0); // pure imaginary, not Hermitian paired with h[2]=0
+    let noise = Lindbladian::zero(d);
+    let _ = Gate::from_hamiltonian("bad", 1, h, noise, 1.0);
+}
+
+#[test]
+#[should_panic(expected = "non-negative")]
+fn negative_collapse_rate_panics() {
+    let d = 2;
+    let _ = Lindbladian::new(d, matrix::zeros(d), vec![(matrix::sigma_minus(), -1e-3)]);
+}
+
+#[test]
+#[should_panic(expected = "tau_g")]
+fn negative_tau_g_panics() {
+    let h = matrix::zeros(2);
+    let noise = Lindbladian::zero(2);
+    let _ = Gate::from_hamiltonian("bad", 1, h, noise, -1.0);
+}
+
+#[test]
+#[should_panic(expected = "wrong shape")]
+fn wrong_matrix_size_panics() {
+    // 3-element matrix is neither 1x1 nor any d*d.
+    let h: Matrix = vec![Complex64::new(0.0, 0.0); 3];
+    let _ = Lindbladian::new(2, h, Vec::new());
+}
+
+#[test]
+fn hermitian_traceless_is_accepted() {
+    // Pauli X is Hermitian, traceless.
+    let x = matrix::pauli_1q(pecos_lindblad::Pauli1::X);
+    let _ = Lindbladian::new(2, x, Vec::new());
+}
+
+#[test]
+fn hermitian_with_real_diagonal_is_accepted() {
+    // diag(1, -1, 0.5, -0.5) is Hermitian.
+    let d = 4;
+    let mut h: Matrix = vec![Complex64::new(0.0, 0.0); d * d];
+    h[0] = Complex64::new(1.0, 0.0);
+    h[d + 1] = Complex64::new(-1.0, 0.0);
+    h[2 * d + 2] = Complex64::new(0.5, 0.0);
+    h[3 * d + 3] = Complex64::new(-0.5, 0.0);
+    let _ = Lindbladian::new(d, h, Vec::new());
+}
diff --git a/exp/pecos-lindblad/tests/inverse_fit.rs b/exp/pecos-lindblad/tests/inverse_fit.rs
new file mode 100644
index 000000000..6193f6456
--- /dev/null
+++ b/exp/pecos-lindblad/tests/inverse_fit.rs
@@ -0,0 +1,138 @@
+// Copyright 2026 The PECOS Developers
+//
+// Licensed under the Apache License, Version 2.0 (the "License"); you may not use this file except
+// in compliance with the License. You may obtain a copy of the License at
+//
+//     https://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software distributed under the License
+// is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express
+// or implied. See the License for the specific language governing permissions and limitations under
+// the License.
+
+//! Inverse fit / parameter recovery tests. Closes the "validation loop":
+//! forward synthesis produces rates; inverse recovery back-solves physical
+//! parameters from rates. At the 1Q identity level, the recovery is
+//! analytic and must be a bit-exact round-trip of
+//! [`noise_models::ad_pd_1q`] -> [`synthesize_identity_1q`].
+
+use approx::assert_abs_diff_eq;
+
+use pecos_lindblad::noise_models::{ad_pd_1q, recover_t1_t2_from_identity_1q};
+use pecos_lindblad::{Gate, Pauli1, PauliLindbladModel, PauliString, synthesize_identity_1q};
+
+fn synth_1q(t1: f64, t2: f64, tau_g: f64) -> PauliLindbladModel {
+    synthesize_identity_1q(&Gate::identity(1, ad_pd_1q(t1, t2), tau_g))
+}
+
+#[test]
+fn round_trip_recovery_1q_ad_pd() {
+    for (t1, t2, tau) in [
+        (100.0, 80.0, 1.0),
+        (300.0, 200.0, 0.5),
+        (50.0, 50.0, 2.0), // T_2 = T_1 case
+    ] {
+        let pl = synth_1q(t1, t2, tau);
+        let (t1_rec, t2_rec) = recover_t1_t2_from_identity_1q(&pl, tau).unwrap();
+        assert_abs_diff_eq!(t1_rec, t1, epsilon = 1e-10);
+        assert_abs_diff_eq!(t2_rec, t2, epsilon = 1e-10);
+    }
+}
+
+#[test]
+fn recovery_handles_t2_equals_2_t1_limit() {
+    // Pure-T1 limit (no dephasing): T_2 = 2 T_1, so lambda_z = 0 exactly.
+    let t1 = 150.0;
+    let t2 = 2.0 * t1;
+    let tau = 1.0;
+    let pl = synth_1q(t1, t2, tau);
+    let (t1_rec, t2_rec) = recover_t1_t2_from_identity_1q(&pl, tau).unwrap();
+    assert_abs_diff_eq!(t1_rec, t1, epsilon = 1e-10);
+    assert_abs_diff_eq!(t2_rec, t2, epsilon = 1e-10);
+}
+
+#[test]
+fn recovery_returns_none_on_inconsistent_rates() {
+    // lambda_x=0 => cannot determine T_1.
+    let pl = PauliLindbladModel::new(
+        vec![
+            PauliString::single(Pauli1::X),
+            PauliString::single(Pauli1::Z),
+        ],
+        vec![0.0, 0.01],
+    );
+    assert!(recover_t1_t2_from_identity_1q(&pl, 1.0).is_none());
+}
+
+#[test]
+fn recovery_returns_none_on_zero_tau() {
+    let pl = synth_1q(100.0, 80.0, 1.0);
+    assert!(recover_t1_t2_from_identity_1q(&pl, 0.0).is_none());
+}
+
+#[test]
+fn compose_independent_sums_rates() {
+    let a = PauliLindbladModel::new(
+        vec![
+            PauliString::from_label("IX").unwrap(),
+            PauliString::from_label("ZZ").unwrap(),
+        ],
+        vec![0.001, 0.005],
+    );
+    let b = PauliLindbladModel::new(
+        vec![
+            PauliString::from_label("IX").unwrap(),
+            PauliString::from_label("XI").unwrap(),
+        ],
+        vec![0.002, 0.003],
+    );
+    let ab = a.compose_independent(&b);
+    // Expected support: IX (merged), XI, ZZ. Rates: IX=0.003, XI=0.003, ZZ=0.005.
+    assert_abs_diff_eq!(
+        ab.rate(&PauliString::from_label("IX").unwrap()),
+        0.003,
+        epsilon = 1e-14
+    );
+    assert_abs_diff_eq!(
+        ab.rate(&PauliString::from_label("XI").unwrap()),
+        0.003,
+        epsilon = 1e-14
+    );
+    assert_abs_diff_eq!(
+        ab.rate(&PauliString::from_label("ZZ").unwrap()),
+        0.005,
+        epsilon = 1e-14
+    );
+    assert_eq!(ab.supports.len(), 3);
+}
+
+#[test]
+fn compose_commutes() {
+    let a = PauliLindbladModel::new(vec![PauliString::single(Pauli1::X)], vec![0.01]);
+    let b = PauliLindbladModel::new(vec![PauliString::single(Pauli1::Z)], vec![0.02]);
+    let ab = a.compose_independent(&b);
+    let ba = b.compose_independent(&a);
+    for p in [Pauli1::X, Pauli1::Y, Pauli1::Z] {
+        let k = PauliString::single(p);
+        assert_abs_diff_eq!(ab.rate(&k), ba.rate(&k), epsilon = 1e-14);
+    }
+}
+
+#[test]
+fn round_trip_validation_workflow() {
+    // End-to-end: predict rates from (T1, T2), then recover T1/T2 from
+    // those rates, verify the loop closes.
+    let t1_nominal = 250.0;
+    let t2_nominal = 180.0;
+    let tau = 0.5;
+
+    // 1. Forward: physics -> rates.
+    let predicted = synth_1q(t1_nominal, t2_nominal, tau);
+
+    // 2. Inverse: rates -> physics.
+    let (t1_back, t2_back) = recover_t1_t2_from_identity_1q(&predicted, tau).unwrap();
+
+    // 3. Closure.
+    assert_abs_diff_eq!(t1_back, t1_nominal, epsilon = 1e-10);
+    assert_abs_diff_eq!(t2_back, t2_nominal, epsilon = 1e-10);
+}
diff --git a/exp/pecos-lindblad/tests/inverse_fit_2q.rs b/exp/pecos-lindblad/tests/inverse_fit_2q.rs
new file mode 100644
index 000000000..7fde76826
--- /dev/null
+++ b/exp/pecos-lindblad/tests/inverse_fit_2q.rs
@@ -0,0 +1,141 @@
+// Copyright 2026 The PECOS Developers
+//
+// Licensed under the Apache License, Version 2.0 (the "License"); you may not use this file except
+// in compliance with the License. You may obtain a copy of the License at
+//
+//     https://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software distributed under the License
+// is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express
+// or implied. See the License for the specific language governing permissions and limitations under
+// the License.
+
+//! 2-qubit inverse-fit tests for `CZ_theta + AD+PD`. Round-trip:
+//!   (T_1, T_2)_{l,r} -> synthesize -> PL rates -> recover -> (T_1, T_2)_{l,r}.
+//! Must be bit-close on clean (noiseless) synthetic data.
+
+use approx::assert_abs_diff_eq;
+
+use pecos_lindblad::noise_models::{
+    ad_pd_2q, cz_recovery_residual, recover_ad_pd_2q_from_cz_theta,
+};
+use pecos_lindblad::{
+    DEFAULT_N_STEPS, Gate, PauliLindbladModel, PauliString, synthesize_numerical,
+};
+
+fn synth_cz(
+    t1_l: f64,
+    t1_r: f64,
+    t2_l: f64,
+    t2_r: f64,
+    omega: f64,
+    theta: f64,
+) -> PauliLindbladModel {
+    let noise = ad_pd_2q(t1_l, t1_r, t2_l, t2_r);
+    let gate = Gate::cz_theta(omega, theta, noise);
+    synthesize_numerical(&gate, DEFAULT_N_STEPS)
+}
+
+#[test]
+fn round_trip_2q_asymmetric_params() {
+    // Four independent parameters; recovery should find all four.
+    let t1_l = 120.0;
+    let t1_r = 80.0;
+    let t2_l = 90.0;
+    let t2_r = 60.0;
+    let omega = 1.0;
+    let theta = std::f64::consts::FRAC_PI_4;
+
+    let pl = synth_cz(t1_l, t1_r, t2_l, t2_r, omega, theta);
+    let rec = recover_ad_pd_2q_from_cz_theta(&pl, omega, theta).unwrap();
+
+    assert_abs_diff_eq!(rec.t1_l, t1_l, epsilon = 1e-10);
+    assert_abs_diff_eq!(rec.t1_r, t1_r, epsilon = 1e-10);
+    assert_abs_diff_eq!(rec.t2_l, t2_l, epsilon = 1e-10);
+    assert_abs_diff_eq!(rec.t2_r, t2_r, epsilon = 1e-10);
+}
+
+#[test]
+fn round_trip_2q_at_pi_over_3() {
+    let pl = synth_cz(200.0, 200.0, 150.0, 150.0, 1.5, std::f64::consts::FRAC_PI_3);
+    let rec = recover_ad_pd_2q_from_cz_theta(&pl, 1.5, std::f64::consts::FRAC_PI_3).unwrap();
+    assert_abs_diff_eq!(rec.t1_l, 200.0, epsilon = 1e-10);
+    assert_abs_diff_eq!(rec.t1_r, 200.0, epsilon = 1e-10);
+    assert_abs_diff_eq!(rec.t2_l, 150.0, epsilon = 1e-10);
+    assert_abs_diff_eq!(rec.t2_r, 150.0, epsilon = 1e-10);
+}
+
+#[test]
+fn recovery_residual_small_for_pure_ad_pd() {
+    // On clean AD+PD synthesis, the degenerate rate pairs should
+    // coincide to machine precision -> residual ~ 0.
+    let pl = synth_cz(100.0, 80.0, 80.0, 60.0, 1.0, std::f64::consts::FRAC_PI_4);
+    let residual = cz_recovery_residual(&pl);
+    assert!(
+        residual < 1e-10,
+        "residual for clean AD+PD should be near zero: {}",
+        residual
+    );
+}
+
+#[test]
+fn recovery_residual_nonzero_under_model_mismatch() {
+    // Build a model where the degenerate pairs explicitly *differ* --
+    // simulating measured rates that don't fit the pure-AD+PD form.
+    let supports: Vec<_> = ["IX", "IY", "XI", "YI"]
+        .iter()
+        .map(|s| PauliString::from_label(s).unwrap())
+        .collect();
+    // IX, IY differ by 20% (not allowed under pure AD+PD for CZ).
+    let rates = vec![0.003, 0.0036, 0.002, 0.002];
+    let pl = PauliLindbladModel::new(supports, rates);
+    let residual = cz_recovery_residual(&pl);
+    assert!(
+        residual > 1e-4,
+        "expected residual to flag the mismatch, got {}",
+        residual
+    );
+}
+
+#[test]
+fn recovery_returns_none_on_negative_rates() {
+    let supports = vec![
+        PauliString::from_label("IX").unwrap(),
+        PauliString::from_label("IY").unwrap(),
+        PauliString::from_label("XI").unwrap(),
+        PauliString::from_label("YI").unwrap(),
+        PauliString::from_label("IZ").unwrap(),
+        PauliString::from_label("ZI").unwrap(),
+    ];
+    // lambda_ix is zero -> recovery can't infer beta_down_r.
+    let rates = vec![0.0, 0.0, 0.001, 0.001, 0.002, 0.002];
+    let pl = PauliLindbladModel::new(supports, rates);
+    assert!(recover_ad_pd_2q_from_cz_theta(&pl, 1.0, std::f64::consts::FRAC_PI_4).is_none());
+}
+
+#[test]
+fn round_trip_2q_validation_workflow() {
+    // End-to-end validation story: 4 device params -> 15 PL rates ->
+    // recover 4 params -> compare.
+    let t1_l = 250.0;
+    let t2_l = 180.0;
+    let t1_r = 300.0;
+    let t2_r = 220.0;
+    let omega = 1.0;
+    let theta = std::f64::consts::FRAC_PI_4;
+
+    // 1. Forward: physics -> rates.
+    let pl = synth_cz(t1_l, t1_r, t2_l, t2_r, omega, theta);
+
+    // 2. Consistency check: on clean data the 2-fold pair residual = 0.
+    assert!(cz_recovery_residual(&pl) < 1e-10);
+
+    // 3. Inverse.
+    let rec = recover_ad_pd_2q_from_cz_theta(&pl, omega, theta).unwrap();
+
+    // 4. Closure.
+    assert_abs_diff_eq!(rec.t1_l, t1_l, epsilon = 1e-10);
+    assert_abs_diff_eq!(rec.t2_l, t2_l, epsilon = 1e-10);
+    assert_abs_diff_eq!(rec.t1_r, t1_r, epsilon = 1e-10);
+    assert_abs_diff_eq!(rec.t2_r, t2_r, epsilon = 1e-10);
+}
diff --git a/exp/pecos-lindblad/tests/inverse_fit_2q_cx.rs b/exp/pecos-lindblad/tests/inverse_fit_2q_cx.rs
new file mode 100644
index 000000000..292d29a6c
--- /dev/null
+++ b/exp/pecos-lindblad/tests/inverse_fit_2q_cx.rs
@@ -0,0 +1,110 @@
+// Copyright 2026 The PECOS Developers
+//
+// Licensed under the Apache License, Version 2.0 (the "License"); you may not use this file except
+// in compliance with the License. You may obtain a copy of the License at
+//
+//     https://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software distributed under the License
+// is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express
+// or implied. See the License for the specific language governing permissions and limitations under
+// the License.
+
+//! 2-qubit inverse-fit tests for `CX_theta + AD+PD`. Trickier than the CZ
+//! case because `beta_down_r` and `beta_phi_r` mix in `lambda_iz` /
+//! `lambda_zz`. We use the `lambda_iz - lambda_zz` identity to decouple.
+
+use approx::assert_abs_diff_eq;
+
+use pecos_lindblad::noise_models::{ad_pd_2q, recover_ad_pd_2q_from_cx_theta};
+use pecos_lindblad::{DEFAULT_N_STEPS, Gate, PauliLindbladModel, synthesize_numerical};
+
+fn synth_cx(
+    t1_l: f64,
+    t1_r: f64,
+    t2_l: f64,
+    t2_r: f64,
+    omega: f64,
+    theta: f64,
+) -> PauliLindbladModel {
+    let noise = ad_pd_2q(t1_l, t1_r, t2_l, t2_r);
+    let gate = Gate::cx_theta(omega, theta, noise);
+    synthesize_numerical(&gate, DEFAULT_N_STEPS)
+}
+
+#[test]
+fn round_trip_cx_pi_over_4() {
+    let t1_l = 150.0;
+    let t1_r = 100.0;
+    let t2_l = 100.0;
+    let t2_r = 70.0;
+    let omega = 1.0;
+    let theta = std::f64::consts::FRAC_PI_4;
+
+    let pl = synth_cx(t1_l, t1_r, t2_l, t2_r, omega, theta);
+    let rec = recover_ad_pd_2q_from_cx_theta(&pl, omega, theta).unwrap();
+    // At beta/omega ~ 1e-2, next-order corrections ~ 1e-4 * 1e-2 = 1e-6.
+    // Use 1e-5 tolerance.
+    assert_abs_diff_eq!(rec.t1_l, t1_l, epsilon = 1e-5);
+    assert_abs_diff_eq!(rec.t1_r, t1_r, epsilon = 1e-5);
+    assert_abs_diff_eq!(rec.t2_l, t2_l, epsilon = 1e-5);
+    assert_abs_diff_eq!(rec.t2_r, t2_r, epsilon = 1e-5);
+}
+
+#[test]
+fn round_trip_cx_pi_over_3() {
+    let pl = synth_cx(200.0, 300.0, 150.0, 200.0, 1.5, std::f64::consts::FRAC_PI_3);
+    let rec = recover_ad_pd_2q_from_cx_theta(&pl, 1.5, std::f64::consts::FRAC_PI_3).unwrap();
+    assert_abs_diff_eq!(rec.t1_l, 200.0, epsilon = 1e-5);
+    assert_abs_diff_eq!(rec.t1_r, 300.0, epsilon = 1e-5);
+    assert_abs_diff_eq!(rec.t2_l, 150.0, epsilon = 1e-5);
+    assert_abs_diff_eq!(rec.t2_r, 200.0, epsilon = 1e-5);
+}
+
+#[test]
+fn recovery_returns_none_at_degenerate_angle_pi_over_2() {
+    // At theta = pi/2, sin(2 theta) = 0 -> beta_down_r and beta_phi_r
+    // are not independently recoverable.
+    let pl = synth_cx(100.0, 100.0, 80.0, 80.0, 1.0, std::f64::consts::FRAC_PI_2);
+    assert!(recover_ad_pd_2q_from_cx_theta(&pl, 1.0, std::f64::consts::FRAC_PI_2).is_none());
+}
+
+#[test]
+fn recovery_returns_none_at_zero_theta() {
+    // At theta = 0, the gate is trivial and rates vanish. Also degenerate.
+    let pl = synth_cx(100.0, 100.0, 80.0, 80.0, 1.0, 0.0);
+    assert!(recover_ad_pd_2q_from_cx_theta(&pl, 1.0, 0.0).is_none());
+}
+
+#[test]
+fn cx_round_trip_end_to_end() {
+    // Device-style story: dev data (T1, T2) per qubit -> rates ->
+    // recover -> compare.
+    let t1_l = 300.0;
+    let t2_l = 200.0;
+    let t1_r = 280.0;
+    let t2_r = 190.0;
+    let omega = 1.0;
+    let theta = std::f64::consts::FRAC_PI_4;
+
+    let pl = synth_cx(t1_l, t1_r, t2_l, t2_r, omega, theta);
+    let rec = recover_ad_pd_2q_from_cx_theta(&pl, omega, theta).unwrap();
+
+    // Print-style check: all 4 params recovered with ~5 decimal digits accuracy.
+    for (got, want, name) in [
+        (rec.t1_l, t1_l, "T1_l"),
+        (rec.t2_l, t2_l, "T2_l"),
+        (rec.t1_r, t1_r, "T1_r"),
+        (rec.t2_r, t2_r, "T2_r"),
+    ] {
+        let rel_err = (got - want).abs() / want;
+        assert!(
+            rel_err < 1e-4,
+            "{}: recovered {} vs true {} (rel_err={})",
+            name,
+            got,
+            want,
+            rel_err,
+        );
+    }
+}
diff --git a/exp/pecos-lindblad/tests/izz_crosstalk_3q.rs b/exp/pecos-lindblad/tests/izz_crosstalk_3q.rs
new file mode 100644
index 000000000..51e3ae982
--- /dev/null
+++ b/exp/pecos-lindblad/tests/izz_crosstalk_3q.rs
@@ -0,0 +1,106 @@
+// Copyright 2026 The PECOS Developers
+//
+// Licensed under the Apache License, Version 2.0 (the "License"); you may not use this file except
+// in compliance with the License. You may obtain a copy of the License at
+//
+//     https://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software distributed under the License
+// is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express
+// or implied. See the License for the specific language governing permissions and limitations under
+// the License.
+
+//! Parity test: 3-qubit `CX_theta ⊗ I` gate with coherent IZZ crosstalk
+//! between target (q1) and spectator (q2), vs closed-form results from
+//! arXiv:2502.03462 eqs. 1009-1011 (`SubApp:3QXtalk`).
+//!
+//! String index convention: leftmost factor = qubit 0 (control).
+//!   "IYZ" = I on q0, Y on q1, Z on q2.
+//!
+//! Paper closed forms (quadratic in delta, weight-3 rates):
+//!   lambda_iyz = lambda_zyz = sin^4(theta) / 16     * (delta / omega)^2
+//!   lambda_izz = [2 theta + sin 2 theta]^2 / 64     * (delta / omega)^2
+//!   lambda_zzz = [2 theta - sin 2 theta]^2 / 64     * (delta / omega)^2
+//!
+//! All other non-identity 3Q Paulis (there are 63 - 4 = 59 of them) are
+//! **zero** to leading order in delta/omega.
+//!
+//! **Weight-3 rates** break the standard sparse-PL weight-2 assumption --
+//! this test also exercises `PauliLindbladModel::supports` over the full
+//! 3Q basis.
+
+use approx::assert_abs_diff_eq;
+
+use pecos_lindblad::{Gate, PauliString, synthesize_exact_unitary};
+
+fn paper_rate(label: &str, theta: f64, omega: f64, delta: f64) -> f64 {
+    let dratio_sq = (delta / omega).powi(2);
+    let s = theta.sin();
+    let s2 = (2.0 * theta).sin();
+    match label {
+        "IYZ" | "ZYZ" => s.powi(4) / 16.0 * dratio_sq,
+        "IZZ" => (2.0 * theta + s2).powi(2) / 64.0 * dratio_sq,
+        "ZZZ" => (2.0 * theta - s2).powi(2) / 64.0 * dratio_sq,
+        _ => 0.0,
+    }
+}
+
+fn run_izz(theta: f64, omega: f64, delta: f64, tol: f64) {
+    let gate = Gate::cx_theta_with_izz_crosstalk(omega, theta, delta);
+    let pl = synthesize_exact_unitary(&gate);
+
+    // All 63 non-identity 3Q Paulis.
+    for ps in PauliString::enumerate_nonidentity(3) {
+        let label = format!("{}", ps);
+        let got = pl.rate(&ps);
+        let expected = paper_rate(&label, theta, omega, delta);
+        assert_abs_diff_eq!(got, expected, epsilon = tol);
+    }
+}
+
+#[test]
+fn izz_crosstalk_pi_over_4_weak() {
+    // delta/omega = 1e-3 => rates ~ 1e-6 at most; tol ~1e-10.
+    run_izz(std::f64::consts::FRAC_PI_4, 1.0, 1e-3, 1e-10);
+}
+
+#[test]
+fn izz_crosstalk_pi_over_2_weak() {
+    // theta = pi/2 (Clifford): sin(2 theta) = 0, so lambda_izz = lambda_zzz.
+    run_izz(std::f64::consts::FRAC_PI_2, 1.0, 1e-3, 1e-10);
+}
+
+#[test]
+fn izz_crosstalk_pi_over_3_weak() {
+    run_izz(std::f64::consts::FRAC_PI_3, 1.5, 5e-4, 1e-10);
+}
+
+#[test]
+fn izz_crosstalk_zero_delta_gives_zero_rates() {
+    // delta = 0 => no crosstalk => all rates zero.
+    let gate = Gate::cx_theta_with_izz_crosstalk(1.0, std::f64::consts::FRAC_PI_4, 0.0);
+    let pl = synthesize_exact_unitary(&gate);
+    for ps in PauliString::enumerate_nonidentity(3) {
+        assert_abs_diff_eq!(pl.rate(&ps), 0.0, epsilon = 1e-14);
+    }
+}
+
+#[test]
+fn izz_crosstalk_produces_only_weight_3_and_no_weight_2() {
+    // The paper's claim: this gate produces weight-2 (IZZ) AND weight-3
+    // (IYZ, ZYZ, ZZZ) rates but NO weight-1 rates. Verify the weight
+    // distribution in our output matches that claim.
+    let gate = Gate::cx_theta_with_izz_crosstalk(1.0, std::f64::consts::FRAC_PI_4, 1e-3);
+    let pl = synthesize_exact_unitary(&gate);
+
+    // Weight-1 rates should all be (numerically) zero.
+    for ps in PauliString::enumerate_nonidentity(3) {
+        if ps.weight() == 1 {
+            assert_abs_diff_eq!(pl.rate(&ps), 0.0, epsilon = 1e-10);
+        }
+    }
+
+    // At least one weight-3 rate (e.g. lambda_iyz) should be non-zero.
+    let iyz = PauliString::from_label("IYZ").unwrap();
+    assert!(pl.rate(&iyz) > 1e-12);
+}
diff --git a/exp/pecos-lindblad/tests/noise_budget.rs b/exp/pecos-lindblad/tests/noise_budget.rs
new file mode 100644
index 000000000..26f1ac1e7
--- /dev/null
+++ b/exp/pecos-lindblad/tests/noise_budget.rs
@@ -0,0 +1,93 @@
+// Copyright 2026 The PECOS Developers
+//
+// Licensed under the Apache License, Version 2.0 (the "License"); you may not use this file except
+// in compliance with the License. You may obtain a copy of the License at
+//
+//     https://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software distributed under the License
+// is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express
+// or implied. See the License for the specific language governing permissions and limitations under
+// the License.
+
+//! Tests for `PauliLindbladModel::top_contributors` / `explain`.
+
+use approx::assert_abs_diff_eq;
+
+use pecos_lindblad::{PauliLindbladModel, PauliString};
+
+fn model(entries: &[(&str, f64)]) -> PauliLindbladModel {
+    let supports: Vec<_> = entries
+        .iter()
+        .map(|(s, _)| PauliString::from_label(s).unwrap())
+        .collect();
+    let rates: Vec<_> = entries.iter().map(|(_, r)| *r).collect();
+    PauliLindbladModel::new(supports, rates)
+}
+
+#[test]
+fn top_contributors_sorted_by_rate_descending() {
+    let m = model(&[("IX", 0.001), ("ZI", 0.005), ("IY", 0.003), ("IZ", 0.002)]);
+    let top = m.top_contributors(4);
+    assert_eq!(format!("{}", top[0].0), "ZI"); // 0.005
+    assert_eq!(format!("{}", top[1].0), "IY"); // 0.003
+    assert_eq!(format!("{}", top[2].0), "IZ"); // 0.002
+    assert_eq!(format!("{}", top[3].0), "IX"); // 0.001
+}
+
+#[test]
+fn top_contributors_truncates_to_n() {
+    let m = model(&[("X", 0.01), ("Y", 0.02), ("Z", 0.03)]);
+    let top2 = m.top_contributors(2);
+    assert_eq!(top2.len(), 2);
+    assert_eq!(format!("{}", top2[0].0), "Z");
+    assert_eq!(format!("{}", top2[1].0), "Y");
+}
+
+#[test]
+fn top_contributors_ties_broken_lexicographically() {
+    let m = model(&[("X", 0.01), ("Y", 0.01), ("Z", 0.01)]);
+    let top = m.top_contributors(3);
+    // Tie on rate -> lexicographic on Pauli1 (I<X<Y<Z).
+    assert_eq!(format!("{}", top[0].0), "X");
+    assert_eq!(format!("{}", top[1].0), "Y");
+    assert_eq!(format!("{}", top[2].0), "Z");
+}
+
+#[test]
+fn explain_contains_expected_sections() {
+    let m = model(&[("IX", 0.001), ("ZZ", 0.005), ("XYZ", 0.0002)]);
+    let out = m.explain();
+    assert!(out.contains("Pauli-Lindblad noise budget"));
+    assert!(out.contains("By weight:"));
+    assert!(out.contains("Top"));
+    assert!(out.contains("weight-1"));
+    assert!(out.contains("weight-2"));
+    assert!(out.contains("weight-3"));
+    assert!(out.contains("ZZ"));
+    assert!(out.contains("XYZ"));
+}
+
+#[test]
+fn explain_weight_sums_match_rate_at_weight() {
+    // Sanity: per-weight row in explain() should align with
+    // rate_at_weight(w). Grug verify by parsing the weight sums out of
+    // the formatted output.
+    let m = model(&[("IX", 0.001), ("IY", 0.001), ("ZZ", 0.005), ("XYZ", 0.0002)]);
+    let w1 = m.rate_at_weight(1);
+    let w2 = m.rate_at_weight(2);
+    let w3 = m.rate_at_weight(3);
+    assert_abs_diff_eq!(w1, 0.002, epsilon = 1e-14);
+    assert_abs_diff_eq!(w2, 0.005, epsilon = 1e-14);
+    assert_abs_diff_eq!(w3, 0.0002, epsilon = 1e-14);
+    let total = m.total_rate();
+    assert_abs_diff_eq!(total, w1 + w2 + w3, epsilon = 1e-14);
+}
+
+#[test]
+fn explain_empty_model_handles_gracefully() {
+    let m = PauliLindbladModel::default();
+    let out = m.explain();
+    // Empty model: 0 terms, 0 total rate. Shouldn't panic.
+    assert!(out.contains("0 terms"));
+}
diff --git a/exp/pecos-lindblad/tests/noise_models_api.rs b/exp/pecos-lindblad/tests/noise_models_api.rs
new file mode 100644
index 000000000..f9ee9b57f
--- /dev/null
+++ b/exp/pecos-lindblad/tests/noise_models_api.rs
@@ -0,0 +1,87 @@
+// Copyright 2026 The PECOS Developers
+//
+// Licensed under the Apache License, Version 2.0 (the "License"); you may not use this file except
+// in compliance with the License. You may obtain a copy of the License at
+//
+//     https://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software distributed under the License
+// is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express
+// or implied. See the License for the specific language governing permissions and limitations under
+// the License.
+
+//! End-to-end sanity tests for the device-parameter convenience API in
+//! `noise_models`. Exercises the same paper fixtures as the hand-rolled
+//! tests but through the ergonomic `(T_1, T_2)` interface.
+
+use approx::assert_abs_diff_eq;
+
+use pecos_lindblad::noise_models::{ad_pd_1q, ad_pd_2q, coherent_phase_2q, t1_t2_to_rates};
+use pecos_lindblad::{
+    DEFAULT_N_STEPS, Gate, Pauli1, PauliString, synthesize_exact_unitary, synthesize_identity_1q,
+    synthesize_numerical,
+};
+
+#[test]
+fn identity_1q_via_device_params() {
+    // T1 = 100 us, T2 = 80 us => beta_down = 1e4, beta_phi = 7500.
+    let t1 = 100e-6;
+    let t2 = 80e-6;
+    let tau_g = 1e-6;
+    let (bd, bp) = t1_t2_to_rates(t1, t2);
+
+    let noise = ad_pd_1q(t1, t2);
+    let gate = Gate::identity(1, noise, tau_g);
+    let pl = synthesize_identity_1q(&gate);
+
+    let rate = |p: Pauli1| pl.rate(&PauliString::single(p));
+    assert_abs_diff_eq!(rate(Pauli1::X), bd * tau_g / 4.0, epsilon = 1e-14);
+    assert_abs_diff_eq!(rate(Pauli1::Y), bd * tau_g / 4.0, epsilon = 1e-14);
+    assert_abs_diff_eq!(rate(Pauli1::Z), bp * tau_g / 2.0, epsilon = 1e-14);
+}
+
+#[test]
+fn cx_theta_via_device_params_matches_hand_rolled() {
+    // Build the same gate both ways and confirm rates agree.
+    let omega = 1.0;
+    let theta = std::f64::consts::FRAC_PI_4;
+    let t1_l = 100.0;
+    let t1_r = 80.0;
+    let t2_l = 120.0;
+    let t2_r = 90.0;
+
+    let noise = ad_pd_2q(t1_l, t1_r, t2_l, t2_r);
+    let gate = Gate::cx_theta(omega, theta, noise);
+    let pl = synthesize_numerical(&gate, DEFAULT_N_STEPS);
+
+    // Paper eq 941 sanity: lambda_xi = (2 theta + sin 2 theta) / 16 * beta_down_l / omega.
+    let (bd_l, _) = t1_t2_to_rates(t1_l, t2_l);
+    let s2 = (2.0 * theta).sin();
+    let expected = (2.0 * theta + s2) / 16.0 * bd_l / omega;
+    assert_abs_diff_eq!(
+        pl.rate(&PauliString::from_label("XI").unwrap()),
+        expected,
+        epsilon = 1e-8
+    );
+}
+
+#[test]
+fn coherent_phase_2q_via_api() {
+    // Check that coherent_phase_2q + synthesize_exact_unitary reproduces
+    // paper eq 981 for CZ_theta.
+    let omega_cz = 1.0;
+    let theta = std::f64::consts::FRAC_PI_3;
+    let delta_iz = 1e-6;
+    let delta_zi = 2e-6;
+    let delta_zz = 5e-7;
+
+    let noise = coherent_phase_2q(delta_iz, delta_zi, delta_zz);
+    let gate = Gate::cz_theta(omega_cz, theta, noise);
+    let pl = synthesize_exact_unitary(&gate);
+
+    let rate = |s: &str| pl.rate(&PauliString::from_label(s).unwrap());
+    let factor = theta.powi(2) / 4.0 / omega_cz.powi(2);
+    assert_abs_diff_eq!(rate("IZ"), factor * delta_iz.powi(2), epsilon = 1e-14);
+    assert_abs_diff_eq!(rate("ZI"), factor * delta_zi.powi(2), epsilon = 1e-14);
+    assert_abs_diff_eq!(rate("ZZ"), factor * delta_zz.powi(2), epsilon = 1e-14);
+}
diff --git a/exp/pecos-lindblad/tests/non_markovian.rs b/exp/pecos-lindblad/tests/non_markovian.rs
new file mode 100644
index 000000000..1eb60aa13
--- /dev/null
+++ b/exp/pecos-lindblad/tests/non_markovian.rs
@@ -0,0 +1,208 @@
+// Copyright 2026 The PECOS Developers
+//
+// Licensed under the Apache License, Version 2.0 (the "License"); you may not use this file except
+// in compliance with the License. You may obtain a copy of the License at
+//
+//     https://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software distributed under the License
+// is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express
+// or implied. See the License for the specific language governing permissions and limitations under
+// the License.
+
+//! Non-Markovian dynamics tests. Two case studies:
+//!
+//! 1. **TCL sanity**: a constant-rate time-dependent Lindbladian must
+//!    reproduce the Markovian result for identity + PD to machine
+//!    precision.
+//! 2. **1/f-style rate**: `gamma_phi(t) = gamma_0 A / (A + t/t_c)` with
+//!    `A >> tau_g/t_c` reproduces Markov to leading order; as `tau_g/t_c`
+//!    grows, rates should DIFFER from Markov prediction, demonstrating
+//!    we actually capture the non-Markovian correction.
+
+use std::sync::Arc;
+
+use approx::assert_abs_diff_eq;
+use num_complex::Complex64;
+
+use pecos_lindblad::matrix::{self, Matrix};
+use pecos_lindblad::noise_models::ad_pd_1q;
+use pecos_lindblad::{
+    DEFAULT_N_SLICES, Gate, Pauli1, PauliString, RateFn, TimeDepLindbladian,
+    synthesize_identity_1q, synthesize_superop_time_dep,
+};
+
+/// 1-qubit Z operator for PD.
+fn z1q() -> Matrix {
+    matrix::pauli_1q(Pauli1::Z)
+}
+
+#[test]
+fn constant_rate_time_dep_matches_markovian() {
+    // Build a time-dependent Lindbladian whose rates happen to be constant.
+    // Synthesis should match the Markovian synthesize_identity_1q to
+    // high precision.
+    let beta_phi: f64 = 2e-3;
+    let tau_g: f64 = 1.0;
+    let d = 2;
+    let rate_fn: RateFn = Arc::new(move |_t| beta_phi / 2.0);
+    let noise_td =
+        TimeDepLindbladian::with_static_hamiltonian(d, matrix::zeros(d), vec![(z1q(), rate_fn)]);
+
+    // For identity gate, T1 = infinity effectively: use just PD.
+    let h_ideal = matrix::zeros(d);
+    let pl_td = synthesize_superop_time_dep(1, &h_ideal, &noise_td, tau_g, DEFAULT_N_SLICES);
+
+    // Markovian baseline: identity + PD only (no AD).
+    // For pure PD at rate beta_phi/2 on Z: paper eq 801 says
+    //   lambda_z = (beta_phi * tau_g) / 2.
+    // Our T1/T2 API requires beta_down > 0; emulate "AD off" via T2 = 2 T1
+    // at huge T1 so beta_down -> 0.
+    let t1 = 1e18;
+    let t2 = 1.0 / beta_phi; // 1/T_2 = 1/(2T_1) + beta_phi -> beta_phi
+    let noise_mk = ad_pd_1q(t1, t2);
+    let pl_mk = synthesize_identity_1q(&Gate::identity(1, noise_mk, tau_g));
+
+    for p in [Pauli1::X, Pauli1::Y, Pauli1::Z] {
+        let k = PauliString::single(p);
+        assert_abs_diff_eq!(pl_td.rate(&k), pl_mk.rate(&k), epsilon = 1e-9);
+    }
+}
+
+#[test]
+fn one_over_f_weak_non_markov_reduces_to_markov() {
+    // 1/f-ish rate: gamma_phi(t) = gamma_0 * A / (A + t/t_c) with A=1, t_c
+    // large compared to tau_g -> rate ~ gamma_0 constant -> should match
+    // Markov to high precision.
+    let gamma_0: f64 = 1e-3;
+    let t_c: f64 = 1e6; // very slow variation
+    let a: f64 = 1.0;
+    let tau_g: f64 = 1.0;
+    let d = 2;
+
+    let rate_fn: RateFn = Arc::new(move |t: f64| gamma_0 * a / (a + t / t_c) / 2.0);
+    let noise_td =
+        TimeDepLindbladian::with_static_hamiltonian(d, matrix::zeros(d), vec![(z1q(), rate_fn)]);
+    let h_ideal = matrix::zeros(d);
+    let pl_nm = synthesize_superop_time_dep(1, &h_ideal, &noise_td, tau_g, 256);
+
+    // Corresponding Markov (constant rate = gamma_0): lambda_z = gamma_0 * tau_g / 2.
+    let expected_z = gamma_0 * tau_g / 2.0;
+    assert_abs_diff_eq!(
+        pl_nm.rate(&PauliString::single(Pauli1::Z)),
+        expected_z,
+        epsilon = 1e-8
+    );
+}
+
+#[test]
+fn one_over_f_strong_non_markov_differs_from_markov() {
+    // Now use t_c comparable to tau_g -> gamma_phi(t) varies substantially
+    // over the gate. Predicted PL rate must DIFFER from the constant-rate
+    // Markov prediction, proving the non-Markovian correction is captured.
+    let gamma_0: f64 = 1e-3;
+    let a: f64 = 1.0;
+    let tau_g: f64 = 1.0;
+    let t_c: f64 = tau_g / 2.0; // rate drops substantially over the gate
+    let d = 2;
+
+    let rate_fn: RateFn = Arc::new(move |t: f64| gamma_0 * a / (a + t / t_c) / 2.0);
+    let noise_td =
+        TimeDepLindbladian::with_static_hamiltonian(d, matrix::zeros(d), vec![(z1q(), rate_fn)]);
+    let h_ideal = matrix::zeros(d);
+    let pl_nm = synthesize_superop_time_dep(1, &h_ideal, &noise_td, tau_g, 512);
+
+    // Analytic: integrated rate = int_0^tau_g gamma(t) dt
+    //   = int_0^tau_g gamma_0 / (1 + 2 t/tau_g) dt
+    //   = gamma_0 * (tau_g/2) * ln(1 + 2)
+    //   = gamma_0 * tau_g * ln(3) / 2
+    // lambda_z = (integrated rate) / 2 (paper convention: lambda_z = beta_phi * tau_g / 2).
+    // Wait: with our factor-of-1/2 in rate_fn (beta_phi/2), integrated is
+    // gamma_0 * tau_g * ln(3) / 2 / 2. Let me work this out again.
+    //
+    // Effective PD: D[Z] rho = Z rho Z - rho, rate = gamma_phi(t)/2.
+    // Integrated rate per paper: lambda_z = int (gamma_phi(t)/2) dt * 2 = int gamma_phi(t) dt.
+    // Hmm -- actually the paper's identity closed form is lambda_z = beta_phi * tau_g / 2
+    // where beta_phi is the RATE coefficient attached to (beta_phi/2) D[Z]
+    // (i.e. the "1/T_phi"). So:
+    //   lambda_z(const) = beta_phi * tau_g / 2.
+    // For time-dep: lambda_z(t-dep) = (1/2) * int_0^tau_g gamma_0/(1 + 2t/tau_g) dt
+    //                              = (1/2) * gamma_0 * (tau_g/2) * ln(1 + 2)
+    //                              = gamma_0 * tau_g * ln(3) / 4.
+    let expected_nm = gamma_0 * tau_g * (3.0_f64).ln() / 4.0;
+    let got = pl_nm.rate(&PauliString::single(Pauli1::Z));
+
+    // Same prediction via constant-rate Markov model:
+    let lambda_z_mk = gamma_0 * tau_g / 2.0;
+
+    // Markov and non-Markov disagree substantially.
+    assert!(
+        (got - lambda_z_mk).abs() > 0.1 * lambda_z_mk,
+        "non-Markov should differ substantially from Markov: got {}, markov {}",
+        got,
+        lambda_z_mk
+    );
+    // And our non-Markov result matches the analytic integrated-rate formula.
+    assert_abs_diff_eq!(got, expected_nm, epsilon = 1e-7);
+}
+
+#[test]
+fn time_dependent_coherent_noise_gaussian_pulse() {
+    // H_delta(t) = (delta * exp(-((t - tau_g/2)/sigma)^2) / 2) * Z
+    // (Gaussian envelope of coherent Z over the gate). Verify rates
+    // scale with the envelope's time integral.
+    let delta: f64 = 1e-4;
+    let tau_g: f64 = 1.0;
+    let sigma: f64 = tau_g / 4.0;
+    let d = 2;
+
+    let h_fn: pecos_lindblad::time_dep::HermitianFn = Arc::new(move |t: f64| {
+        let arg = ((t - tau_g / 2.0) / sigma).powi(2);
+        let amp = delta * (-arg).exp() / 2.0;
+        matrix::scale(&z1q(), Complex64::new(amp, 0.0))
+    });
+    let noise_td = TimeDepLindbladian::new(d, h_fn, vec![]);
+    let h_ideal = matrix::zeros(d);
+    let pl_nm = synthesize_superop_time_dep(1, &h_ideal, &noise_td, tau_g, 256);
+
+    // For purely coherent Z noise on identity:
+    //   effective unitary phase phi = int_0^tau_g (H(t) component of Z) dt
+    //   = delta * int_0^tau_g exp(-((t-tau/2)/sigma)^2) / 2 dt
+    //   = delta/2 * sigma * sqrt(pi) * erf(tau_g/(2 sigma)) ...
+    // for sigma = tau_g/4 and tau_g = 1: integral approx = sqrt(pi) * tau_g/4 * erf(2)
+    // erf(2) ~ 0.9953
+    let integral_gaussian = sigma * std::f64::consts::PI.sqrt() * erf(tau_g / (2.0 * sigma));
+    let phi = delta * integral_gaussian / 2.0;
+    // For coherent Z on identity: lambda_z = phi^2 / 2 (from -ln(cos(phi)) ~ phi^2/2).
+    // Walsh-Hadamard gives lambda_z = alpha_z * tau_g / 4 * 2 = ... actually the
+    // 1Q identity-coherent-Z result: lambda_z = phi^2 / 2 where phi is total phase.
+    //
+    // Actually from our previous phase-noise test: for constant (delta/2) Z,
+    //   lambda_z = (delta * tau_g / 2)^2 / 2 / 2 = phi^2 / 4 where phi = delta * tau_g / 2.
+    // Hmm let's just check order of magnitude.
+    let got = pl_nm.rate(&PauliString::single(Pauli1::Z));
+    assert!(got > 0.0, "Gaussian pulse should produce nonzero lambda_z");
+    // For coherent Z-on-identity, lambda_z ~ phi^2 at leading order.
+    // Allow factor-of-2 margin either side.
+    assert!(
+        got > 0.5 * phi * phi && got < 2.0 * phi * phi,
+        "got {}, phi^2 {} -- expected leading-order ~phi^2",
+        got,
+        phi * phi,
+    );
+}
+
+/// Abramowitz-Stegun approximation of erf. Accuracy ~7 digits.
+fn erf(x: f64) -> f64 {
+    let a1 = 0.254829592;
+    let a2 = -0.284496736;
+    let a3 = 1.421413741;
+    let a4 = -1.453152027;
+    let a5 = 1.061405429;
+    let p = 0.3275911;
+    let sign = if x < 0.0 { -1.0 } else { 1.0 };
+    let x = x.abs();
+    let t = 1.0 / (1.0 + p * x);
+    let y = 1.0 - (((((a5 * t + a4) * t) + a3) * t + a2) * t + a1) * t * (-x * x).exp();
+    sign * y
+}
diff --git a/exp/pecos-lindblad/tests/per_gate_bridge.rs b/exp/pecos-lindblad/tests/per_gate_bridge.rs
new file mode 100644
index 000000000..f6fc4e9be
--- /dev/null
+++ b/exp/pecos-lindblad/tests/per_gate_bridge.rs
@@ -0,0 +1,117 @@
+// Copyright 2026 The PECOS Developers
+//
+// Licensed under the Apache License, Version 2.0 (the "License"); you may not use this file except
+// in compliance with the License. You may obtain a copy of the License at
+//
+//     https://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software distributed under the License
+// is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express
+// or implied. See the License for the specific language governing permissions and limitations under
+// the License.
+
+//! End-to-end bridge: pecos-lindblad synthesis -> PauliLindbladModel
+//! adapter arrays -> pecos-qec PerGateTypeNoise -> DemStabSim.
+//!
+//! This is the **honest integration** the `Phase 5 scaffold` flagged as
+//! missing. Closes the loop: device params -> per-gate per-Pauli rates
+//! -> DEM mechanisms -> sampling -> shot batches.
+
+use rand::SeedableRng;
+use rand::rngs::SmallRng;
+
+use pecos_lindblad::noise_models::{ad_pd_1q, ad_pd_2q};
+use pecos_lindblad::{DEFAULT_N_STEPS, Gate, synthesize_identity_1q, synthesize_numerical};
+use pecos_qec::dem_stab::DemStabSim;
+use pecos_qec::fault_tolerance::dem_builder::{DetectorDef, NoiseConfig, PerGateTypeNoise};
+use pecos_quantum::{DagCircuit, GateType};
+
+#[test]
+fn lindblad_rates_flow_through_per_gate_noise_spec() {
+    // 1Q identity rates (for idle locations) and 2Q CX rates.
+    let t1 = 100.0;
+    let t2 = 80.0;
+    let tau_1q = 0.5;
+    let tau_cx = std::f64::consts::FRAC_PI_2;
+
+    let pl_1q = synthesize_identity_1q(&Gate::identity(1, ad_pd_1q(t1, t2), tau_1q));
+    let pl_cx = synthesize_numerical(
+        &Gate::cx_theta(1.0, tau_cx, ad_pd_2q(t1, t1, t2, t2)),
+        DEFAULT_N_STEPS,
+    );
+
+    // Bundle into a PerGateTypeNoise. The base noise model gives uncovered gate
+    // types (e.g. PZ prep, MZ measure) a small uniform rate.
+    let cfg = PerGateTypeNoise::from_base_noise(NoiseConfig::new(0.0, 0.0, 1e-3, 1e-3))
+        .with_1q_rates(GateType::H, pl_1q.to_noise_array_1q())
+        .with_2q_rates(GateType::CX, pl_cx.to_noise_array_2q());
+
+    // Small syndrome-extraction circuit.
+    let mut dag = DagCircuit::new();
+    dag.pz(&[2]);
+    dag.cx(&[(0, 2)]);
+    dag.cx(&[(1, 2)]);
+    dag.mz(&[2]);
+
+    let sim = DemStabSim::builder()
+        .circuit(dag)
+        .per_gate_noise(cfg) // overrides .noise() when both set
+        .detectors(vec![DetectorDef::new(0).with_records([-1])])
+        .build()
+        .expect("DemStabSim build");
+
+    // Sample shots; sanity-check detector flips length matches detector count.
+    let mut rng = SmallRng::seed_from_u64(42);
+    let batch = sim.sample_batch(500, &mut rng);
+    assert_eq!(batch.detector_flips.len(), 500);
+    assert_eq!(batch.detector_flips[0].len(), 1);
+}
+
+#[test]
+fn to_noise_array_1q_round_trip() {
+    let pl = synthesize_identity_1q(&Gate::identity(1, ad_pd_1q(100.0, 80.0), 1.0));
+    let arr = pl.to_noise_array_1q();
+    // Paper: lambda_x = lambda_y, lambda_z different.
+    assert!((arr[0] - arr[1]).abs() < 1e-14);
+    assert!(arr[2] > 0.0);
+    // Sum of rates matches total_rate.
+    assert!((arr.iter().sum::<f64>() - pl.total_rate()).abs() < 1e-14);
+}
+
+#[test]
+fn to_noise_array_2q_preserves_paper_structure() {
+    // CX + AD+PD produces specific non-zero rates per paper eq 929-956.
+    // Check the array matches the rate lookups.
+    let pl = synthesize_numerical(
+        &Gate::cx_theta(
+            1.0,
+            std::f64::consts::FRAC_PI_4,
+            ad_pd_2q(100.0, 80.0, 100.0, 80.0),
+        ),
+        DEFAULT_N_STEPS,
+    );
+    let arr = pl.to_noise_array_2q();
+    // Sum across the array matches total rate.
+    assert!((arr.iter().sum::<f64>() - pl.total_rate()).abs() < 1e-14);
+    // Several entries must be non-zero (IX, XI, IZ, ZI, ZZ and more).
+    let non_zero = arr.iter().filter(|r| r.abs() > 1e-12).count();
+    assert!(
+        non_zero >= 6,
+        "expected at least 6 non-zero rates in CX+AD+PD array, got {}",
+        non_zero
+    );
+}
+
+#[test]
+#[should_panic(expected = "1-qubit")]
+fn to_noise_array_1q_panics_on_2q_model() {
+    let pl = synthesize_numerical(
+        &Gate::cx_theta(
+            1.0,
+            std::f64::consts::FRAC_PI_4,
+            ad_pd_2q(100.0, 100.0, 80.0, 80.0),
+        ),
+        DEFAULT_N_STEPS,
+    );
+    let _ = pl.to_noise_array_1q();
+}
diff --git a/exp/pecos-lindblad/tests/phase_noise_2q.rs b/exp/pecos-lindblad/tests/phase_noise_2q.rs
new file mode 100644
index 000000000..9319adc87
--- /dev/null
+++ b/exp/pecos-lindblad/tests/phase_noise_2q.rs
@@ -0,0 +1,182 @@
+// Copyright 2026 The PECOS Developers
+//
+// Licensed under the Apache License, Version 2.0 (the "License"); you may not use this file except
+// in compliance with the License. You may obtain a copy of the License at
+//
+//     https://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software distributed under the License
+// is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express
+// or implied. See the License for the specific language governing permissions and limitations under
+// the License.
+
+//! Parity tests: 2-qubit gates under coherent phase noise from
+//! arXiv:2502.03462 SubApp:2QPhNoise (lines 962-1001).
+//!
+//! Noise Hamiltonian:
+//!   H_delta = (delta_iz/2) IZ + (delta_zi/2) ZI + (delta_zz/2) ZZ
+//!
+//! Cases tested:
+//! - (i)   Identity (H_g = 0): all three delta components commute with H_g,
+//!   so rates are quadratic-in-delta and decoupled (eq. 981).
+//! - (iii) CX_theta: phase noise doesn't commute with X_target, producing
+//!   mixing between delta_iz and delta_zz into lambda_iy, lambda_zy,
+//!   lambda_iz, lambda_zz (eqs. 986-990).
+//!
+//! Synthesis path: `synthesize_exact_unitary` (coherent noise, no c_ops).
+
+use approx::assert_abs_diff_eq;
+use num_complex::Complex64;
+
+use pecos_lindblad::matrix::{self, Matrix};
+use pecos_lindblad::{Gate, Lindbladian, Pauli1, PauliString, synthesize_exact_unitary};
+
+fn phase_noise_2q(delta_iz: f64, delta_zi: f64, delta_zz: f64) -> Lindbladian {
+    let d = 4;
+    let i2 = matrix::identity(2);
+    let z = matrix::pauli_1q(Pauli1::Z);
+    let iz = matrix::kron(&i2, &z, 2, 2);
+    let zi = matrix::kron(&z, &i2, 2, 2);
+    let zz = matrix::kron(&z, &z, 2, 2);
+    let half = Complex64::new(0.5, 0.0);
+    let h_delta: Matrix = matrix::add(
+        &matrix::add(
+            &matrix::scale(&iz, Complex64::new(delta_iz, 0.0) * half),
+            &matrix::scale(&zi, Complex64::new(delta_zi, 0.0) * half),
+        ),
+        &matrix::scale(&zz, Complex64::new(delta_zz, 0.0) * half),
+    );
+    Lindbladian::new(d, h_delta, Vec::new())
+}
+
+#[test]
+fn identity_2q_phase_noise_commuting_case() {
+    // Paper eq. 981: lambda_iz = (tau_g * delta_iz)^2 / 4, etc.
+    // (obtained by setting theta_cz = omega_cz * tau_g and dividing).
+    // Use weak noise so O(g^4) corrections stay below the 1e-10 tolerance.
+    // At g = delta * tau ~ 1e-5 the next-order correction ~g^4/24 ~ 4e-22.
+    let tau_g = 10.0;
+    let delta_iz = 1e-6;
+    let delta_zi = 2e-6;
+    let delta_zz = 5e-7;
+    let noise = phase_noise_2q(delta_iz, delta_zi, delta_zz);
+    let gate = Gate::identity(2, noise, tau_g);
+    let pl = synthesize_exact_unitary(&gate);
+
+    let rate = |s: &str| pl.rate(&PauliString::from_label(s).unwrap());
+    assert_abs_diff_eq!(
+        rate("IZ"),
+        (delta_iz * tau_g).powi(2) / 4.0,
+        epsilon = 1e-10
+    );
+    assert_abs_diff_eq!(
+        rate("ZI"),
+        (delta_zi * tau_g).powi(2) / 4.0,
+        epsilon = 1e-10
+    );
+    assert_abs_diff_eq!(
+        rate("ZZ"),
+        (delta_zz * tau_g).powi(2) / 4.0,
+        epsilon = 1e-10
+    );
+
+    // All others should be zero (phase noise commutes, so only Z-basis
+    // rates appear).
+    for label in [
+        "IX", "IY", "XI", "XX", "XY", "XZ", "YI", "YX", "YY", "YZ", "ZX", "ZY",
+    ] {
+        assert_abs_diff_eq!(rate(label), 0.0, epsilon = 1e-10);
+    }
+}
+
+#[test]
+fn cx_theta_phase_noise_mixing_case() {
+    // Paper eqs. 986-990: CX_theta with H_delta = IZ, ZI, ZZ phase noise.
+    //   lambda_zi = theta^2 / 4 * (delta_zi / omega)^2
+    //   lambda_iy = lambda_zy = sin^4(theta) / 16 * ((delta_iz - delta_zz) / omega)^2
+    //   lambda_iz = [2 theta (delta_iz + delta_zz)
+    //               + sin(2 theta)(delta_iz - delta_zz)]^2 / (64 omega^2)
+    //   lambda_zz = [2 theta (delta_iz + delta_zz)
+    //               + sin(2 theta)(delta_zz - delta_iz)]^2 / (64 omega^2)
+    let omega = 1.0;
+    let theta = std::f64::consts::FRAC_PI_4;
+    let delta_iz = 1e-3;
+    let delta_zi = 2e-3;
+    let delta_zz = 5e-4;
+
+    let noise = phase_noise_2q(delta_iz, delta_zi, delta_zz);
+    let gate = Gate::cx_theta(omega, theta, noise);
+    let pl = synthesize_exact_unitary(&gate);
+
+    let rate = |s: &str| pl.rate(&PauliString::from_label(s).unwrap());
+
+    let s2t = (2.0 * theta).sin();
+    let sin4 = theta.sin().powi(4);
+    let sum = delta_iz + delta_zz;
+    let diff_iz_zz = delta_iz - delta_zz;
+
+    let expected_zi = theta.powi(2) / 4.0 * (delta_zi / omega).powi(2);
+    let expected_iy_zy = sin4 / 16.0 * (diff_iz_zz / omega).powi(2);
+    let expected_iz = (2.0 * theta * sum + s2t * diff_iz_zz).powi(2) / (64.0 * omega.powi(2));
+    let expected_zz = (2.0 * theta * sum + s2t * (-diff_iz_zz)).powi(2) / (64.0 * omega.powi(2));
+
+    assert_abs_diff_eq!(rate("ZI"), expected_zi, epsilon = 1e-9);
+    assert_abs_diff_eq!(rate("IY"), expected_iy_zy, epsilon = 1e-9);
+    assert_abs_diff_eq!(rate("ZY"), expected_iy_zy, epsilon = 1e-9);
+    assert_abs_diff_eq!(rate("IZ"), expected_iz, epsilon = 1e-9);
+    assert_abs_diff_eq!(rate("ZZ"), expected_zz, epsilon = 1e-9);
+
+    // Other 10 rates should be zero to leading order.
+    for label in ["IX", "XI", "XX", "XY", "XZ", "YI", "YX", "YY", "YZ", "ZX"] {
+        assert_abs_diff_eq!(rate(label), 0.0, epsilon = 1e-9);
+    }
+}
+
+#[test]
+fn cz_theta_phase_noise_commuting_case() {
+    // Paper eq. 981 case (ii): CZ_theta with phase noise.
+    // Since H_g = (omega_cz/2)(II-IZ-ZI+ZZ) is diagonal and phase noise is
+    // also diagonal, the Hamiltonians commute. Leading-order rates:
+    //   lambda_iz = theta_cz^2 / 4 * (delta_iz / omega_cz)^2
+    //   lambda_zi = same with delta_zi
+    //   lambda_zz = same with delta_zz
+    let omega_cz = 1.0;
+    let theta = std::f64::consts::FRAC_PI_3;
+    let delta_iz = 1e-6;
+    let delta_zi = 2e-6;
+    let delta_zz = 5e-7;
+    let noise = phase_noise_2q(delta_iz, delta_zi, delta_zz);
+    let gate = Gate::cz_theta(omega_cz, theta, noise);
+    let pl = synthesize_exact_unitary(&gate);
+
+    let rate = |s: &str| pl.rate(&PauliString::from_label(s).unwrap());
+    let factor = theta.powi(2) / 4.0 / omega_cz.powi(2);
+    assert_abs_diff_eq!(rate("IZ"), factor * delta_iz.powi(2), epsilon = 1e-14);
+    assert_abs_diff_eq!(rate("ZI"), factor * delta_zi.powi(2), epsilon = 1e-14);
+    assert_abs_diff_eq!(rate("ZZ"), factor * delta_zz.powi(2), epsilon = 1e-14);
+
+    // All non-Z-basis rates should be zero (commuting case, no mixing).
+    for label in [
+        "IX", "IY", "XI", "XX", "XY", "XZ", "YI", "YX", "YY", "YZ", "ZX", "ZY",
+    ] {
+        assert_abs_diff_eq!(rate(label), 0.0, epsilon = 1e-14);
+    }
+}
+
+#[test]
+fn cx_theta_phase_noise_pi_over_2() {
+    // theta = pi/2 => sin(2 theta) = 0; the mixing term vanishes and
+    // lambda_iz = lambda_zz.
+    let omega = 1.0;
+    let theta = std::f64::consts::FRAC_PI_2;
+    let delta_iz = 1e-3;
+    let delta_zz = 2e-3;
+    let noise = phase_noise_2q(delta_iz, 0.0, delta_zz);
+    let gate = Gate::cx_theta(omega, theta, noise);
+    let pl = synthesize_exact_unitary(&gate);
+
+    let rate = |s: &str| pl.rate(&PauliString::from_label(s).unwrap());
+    let expected = (2.0 * theta * (delta_iz + delta_zz)).powi(2) / (64.0 * omega.powi(2));
+    assert_abs_diff_eq!(rate("IZ"), expected, epsilon = 1e-9);
+    assert_abs_diff_eq!(rate("ZZ"), expected, epsilon = 1e-9);
+}
diff --git a/exp/pecos-lindblad/tests/positivity_sweep.rs b/exp/pecos-lindblad/tests/positivity_sweep.rs
new file mode 100644
index 000000000..6d2fab378
--- /dev/null
+++ b/exp/pecos-lindblad/tests/positivity_sweep.rs
@@ -0,0 +1,91 @@
+// Copyright 2026 The PECOS Developers
+//
+// Licensed under the Apache License, Version 2.0 (the "License"); you may not use this file except
+// in compliance with the License. You may obtain a copy of the License at
+//
+//     https://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software distributed under the License
+// is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express
+// or implied. See the License for the specific language governing permissions and limitations under
+// the License.
+
+//! Positivity stress test: scan noise strength `beta/omega` across a range
+//! and verify `synthesize_numerical` never panics and produces only
+//! non-negative rates. Documents the regime where the first-order PL model
+//! stays self-consistent (leading order of Magnus assumes weak coupling).
+
+use pecos_lindblad::noise_models::ad_pd_2q;
+use pecos_lindblad::{DEFAULT_N_STEPS, Gate, PauliString, synthesize_numerical};
+
+fn max_negative_rate(rates: &[f64]) -> f64 {
+    rates
+        .iter()
+        .copied()
+        .filter(|&r| r < 0.0)
+        .map(|r| -r)
+        .fold(0.0, f64::max)
+}
+
+#[test]
+fn cx_theta_rates_non_negative_across_weak_regime() {
+    // beta/omega from 1e-5 to 1e-1 (a factor of 10^4 sweep). This brackets
+    // realistic device regimes: T1/tau_g >> 1 on IBM-like hardware maps to
+    // beta/omega ~ 1e-4 or smaller.
+    let omega = 1.0;
+    let theta = std::f64::consts::FRAC_PI_4;
+    let tau_g = theta / omega;
+
+    // Run the sweep by holding T2 = 2*T1 (pure-dephasing-free) and varying T1.
+    // Ratio beta_down * tau_g tracks inverse T1. Values: 0.1/tau_g ... 1e-5/tau_g.
+    let ratios = [1e-5, 1e-4, 1e-3, 1e-2, 5e-2, 1e-1];
+    for &r in &ratios {
+        let t1 = tau_g / r;
+        let t2 = 2.0 * t1;
+        let noise = ad_pd_2q(t1, t1, t2, t2);
+        let gate = Gate::cx_theta(omega, theta, noise);
+        let pl = synthesize_numerical(&gate, DEFAULT_N_STEPS);
+        let rates: Vec<f64> = PauliString::enumerate_nonidentity(2)
+            .iter()
+            .map(|p| pl.rate(p))
+            .collect();
+        assert!(
+            max_negative_rate(&rates) < 1e-12,
+            "negative rate at beta/omega={}: max negative = {}",
+            r,
+            max_negative_rate(&rates),
+        );
+        // Sanity: highest rate should scale linearly with r to leading order.
+        let total: f64 = rates.iter().sum();
+        assert!(
+            total > 0.0 && total < 2.0,
+            "total rate out of range at beta/omega={}: total={}",
+            r,
+            total,
+        );
+    }
+}
+
+#[test]
+fn identity_2q_rates_non_negative_across_weak_regime() {
+    // Same sweep on identity + AD+PD (Phase 1 exact-fixture regime).
+    let tau_g = 10.0;
+    let ratios = [1e-6, 1e-4, 1e-2, 1e-1];
+    for &r in &ratios {
+        let t1 = tau_g / r;
+        let t2 = 2.0 * t1;
+        let noise = ad_pd_2q(t1, t1, t2, t2);
+        let gate = Gate::identity(2, noise, tau_g);
+        let pl = synthesize_numerical(&gate, DEFAULT_N_STEPS);
+        let rates: Vec<f64> = PauliString::enumerate_nonidentity(2)
+            .iter()
+            .map(|p| pl.rate(p))
+            .collect();
+        assert!(
+            max_negative_rate(&rates) < 1e-12,
+            "negative rate at beta/omega={}: max negative = {}",
+            r,
+            max_negative_rate(&rates),
+        );
+    }
+}
diff --git a/exp/pecos-lindblad/tests/proptest_invariants.rs b/exp/pecos-lindblad/tests/proptest_invariants.rs
new file mode 100644
index 000000000..4ca5acccb
--- /dev/null
+++ b/exp/pecos-lindblad/tests/proptest_invariants.rs
@@ -0,0 +1,107 @@
+// Copyright 2026 The PECOS Developers
+//
+// Licensed under the Apache License, Version 2.0 (the "License"); you may not use this file except
+// in compliance with the License. You may obtain a copy of the License at
+//
+//     https://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software distributed under the License
+// is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express
+// or implied. See the License for the specific language governing permissions and limitations under
+// the License.
+
+//! Property-based invariants via proptest. Generates random Lindbladians
+//! and verifies:
+//!
+//! 1. All synthesized PL rates are non-negative (positivity).
+//! 2. At τ_g → 0, all rates vanish (no-time, no-error).
+//! 3. Rates scale linearly with τ_g at leading order in weak noise.
+//! 4. Walsh-Hadamard forward/inverse is a bijection on rate vectors.
+
+use proptest::prelude::*;
+
+use pecos_lindblad::noise_models::ad_pd_1q;
+use pecos_lindblad::{Gate, Pauli1, PauliLindbladModel, PauliString, synthesize_identity_1q};
+
+/// Generate physical `(T_1, T_2)` with `T_2 <= 2 T_1` (GKS-positive regime).
+fn t1_t2_strategy() -> impl Strategy<Value = (f64, f64)> {
+    (10.0f64..1000.0, 0.01f64..1.0).prop_map(|(t1, t2_ratio)| (t1, t2_ratio * 2.0 * t1))
+}
+
+proptest! {
+    #![proptest_config(ProptestConfig { cases: 64, ..ProptestConfig::default() })]
+
+    #[test]
+    fn identity_1q_rates_non_negative((t1, t2) in t1_t2_strategy(), tau_g in 0.01f64..50.0) {
+        let noise = ad_pd_1q(t1, t2);
+        let gate = Gate::identity(1, noise, tau_g);
+        let pl = synthesize_identity_1q(&gate);
+        for p in [Pauli1::X, Pauli1::Y, Pauli1::Z] {
+            let r = pl.rate(&PauliString::single(p));
+            prop_assert!(r >= 0.0, "rate for {:?} was negative: {}", p, r);
+        }
+    }
+
+    #[test]
+    fn identity_1q_rates_linear_in_tau(
+        (t1, t2) in t1_t2_strategy(),
+        tau_a in 0.01f64..5.0,
+    ) {
+        let tau_b = tau_a * 2.0;
+        let noise_a = ad_pd_1q(t1, t2);
+        let noise_b = ad_pd_1q(t1, t2);
+        let pl_a = synthesize_identity_1q(&Gate::identity(1, noise_a, tau_a));
+        let pl_b = synthesize_identity_1q(&Gate::identity(1, noise_b, tau_b));
+        for p in [Pauli1::X, Pauli1::Y, Pauli1::Z] {
+            let ra = pl_a.rate(&PauliString::single(p));
+            let rb = pl_b.rate(&PauliString::single(p));
+            // Identity+AD+PD is exact closed form with lambda_k ∝ tau_g.
+            prop_assert!(
+                (rb - 2.0 * ra).abs() < 1e-12,
+                "rate for {:?} not linear in tau: ra={}, rb={}",
+                p, ra, rb,
+            );
+        }
+    }
+}
+
+proptest! {
+    #![proptest_config(ProptestConfig { cases: 32, ..ProptestConfig::default() })]
+
+    /// Generate a random non-negative rate vector and verify the forward
+    /// Walsh-Hadamard map reproduces alpha_b = 2 Σ λ_k ⟨b,k⟩_sp.
+    #[test]
+    fn walsh_hadamard_forward_is_linear_in_rates(
+        lam_x in 0.0f64..0.1,
+        lam_y in 0.0f64..0.1,
+        lam_z in 0.0f64..0.1,
+    ) {
+        // Forward relation alpha_b = 2 Σ_k λ_k ⟨b,k⟩_sp for n=1.
+        //   alpha_X = 2(lam_y + lam_z)
+        //   alpha_Y = 2(lam_x + lam_z)
+        //   alpha_Z = 2(lam_x + lam_y)
+        let supports = vec![
+            PauliString::single(Pauli1::X),
+            PauliString::single(Pauli1::Y),
+            PauliString::single(Pauli1::Z),
+        ];
+        let rates = vec![lam_x, lam_y, lam_z];
+        let model = PauliLindbladModel::new(supports, rates);
+
+        let alpha = |b: &PauliString| -> f64 {
+            model
+                .supports
+                .iter()
+                .zip(&model.rates)
+                .map(|(k, lam)| 2.0 * lam * f64::from(b.symplectic_product(k)))
+                .sum()
+        };
+
+        let x = PauliString::single(Pauli1::X);
+        let y = PauliString::single(Pauli1::Y);
+        let z = PauliString::single(Pauli1::Z);
+        prop_assert!((alpha(&x) - 2.0 * (lam_y + lam_z)).abs() < 1e-14);
+        prop_assert!((alpha(&y) - 2.0 * (lam_x + lam_z)).abs() < 1e-14);
+        prop_assert!((alpha(&z) - 2.0 * (lam_x + lam_y)).abs() < 1e-14);
+    }
+}
diff --git a/exp/pecos-lindblad/tests/sample_statistics.rs b/exp/pecos-lindblad/tests/sample_statistics.rs
new file mode 100644
index 000000000..d8736b5b6
--- /dev/null
+++ b/exp/pecos-lindblad/tests/sample_statistics.rs
@@ -0,0 +1,131 @@
+// Copyright 2026 The PECOS Developers
+//
+// Licensed under the Apache License, Version 2.0 (the "License"); you may not use this file except
+// in compliance with the License. You may obtain a copy of the License at
+//
+//     https://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software distributed under the License
+// is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express
+// or implied. See the License for the specific language governing permissions and limitations under
+// the License.
+
+//! Statistical validation of [`PauliLindbladModel::sample`]. Build a
+//! known PL model and verify empirical flip probabilities match the
+//! analytical per-term formula `p_k = (1 - exp(-2 lambda_k t)) / 2`.
+//!
+//! Uses a binomial-CI tolerance of `5 sigma = 5 * sqrt(p(1-p)/N)` to keep
+//! flakiness very low.
+
+use rand::SeedableRng;
+use rand::rngs::StdRng;
+
+use pecos_lindblad::{Pauli1, PauliLindbladModel, PauliString};
+
+#[test]
+fn single_term_flip_probability_matches_formula() {
+    // 1Q PL with only lambda_x non-zero.
+    let lambda_x = 0.05;
+    let t_scale = 1.0;
+    let expected_p: f64 = 0.5 * (1.0 - f64::exp(-2.0 * lambda_x * t_scale));
+    let model = PauliLindbladModel::new(
+        vec![
+            PauliString::single(Pauli1::X),
+            PauliString::single(Pauli1::Y),
+            PauliString::single(Pauli1::Z),
+        ],
+        vec![lambda_x, 0.0, 0.0],
+    );
+
+    let n_samples: usize = 100_000;
+    let mut rng = StdRng::seed_from_u64(12345);
+    let mut x_hits = 0usize;
+    let mut y_hits = 0usize;
+    let mut z_hits = 0usize;
+    for _ in 0..n_samples {
+        let s = model.sample(t_scale, &mut rng);
+        let ch = s.0[0];
+        match ch {
+            Pauli1::X => x_hits += 1,
+            Pauli1::Y => y_hits += 1,
+            Pauli1::Z => z_hits += 1,
+            Pauli1::I => {}
+        }
+    }
+
+    let p_hat_x = x_hits as f64 / n_samples as f64;
+    let sigma = (expected_p * (1.0 - expected_p) / n_samples as f64).sqrt();
+    let tol = 5.0 * sigma;
+    assert!(
+        (p_hat_x - expected_p).abs() < tol,
+        "X flip rate: got {}, expected {}, diff {} > 5 sigma {}",
+        p_hat_x,
+        expected_p,
+        (p_hat_x - expected_p).abs(),
+        tol,
+    );
+    // Y/Z rates are 0; allow a small count due to X*X*X*X etc. not firing.
+    assert_eq!(y_hits, 0, "Y should never fire (lambda_y = 0)");
+    assert_eq!(z_hits, 0, "Z should never fire (lambda_z = 0)");
+}
+
+#[test]
+fn multi_term_sample_respects_independent_bernoullis() {
+    // Two independent Pauli terms. Empirical joint distribution over
+    // {I, X, Z, XZ=Y} should match the 2x2 independent Bernoulli table.
+    let lambda_x = 0.02;
+    let lambda_z = 0.03;
+    let t_scale = 1.0;
+    let p_x: f64 = 0.5 * (1.0 - f64::exp(-2.0 * lambda_x * t_scale));
+    let p_z: f64 = 0.5 * (1.0 - f64::exp(-2.0 * lambda_z * t_scale));
+
+    let model = PauliLindbladModel::new(
+        vec![
+            PauliString::single(Pauli1::X),
+            PauliString::single(Pauli1::Z),
+        ],
+        vec![lambda_x, lambda_z],
+    );
+
+    let n_samples: usize = 200_000;
+    let mut rng = StdRng::seed_from_u64(7);
+    // Bucket counts: [I, X, Y, Z]. Note X*Z (unordered) = Y in our
+    // sign-dropped multiplication table.
+    let mut counts = [0usize; 4];
+    for _ in 0..n_samples {
+        let s = model.sample(t_scale, &mut rng);
+        let idx = match s.0[0] {
+            Pauli1::I => 0,
+            Pauli1::X => 1,
+            Pauli1::Y => 2,
+            Pauli1::Z => 3,
+        };
+        counts[idx] += 1;
+    }
+    let emp = |k: usize| counts[k] as f64 / n_samples as f64;
+
+    // Analytical:
+    //   P(I) = (1-p_x)(1-p_z)
+    //   P(X) = p_x (1 - p_z)
+    //   P(Z) = (1 - p_x) p_z
+    //   P(Y) = p_x p_z
+    let e_i = (1.0 - p_x) * (1.0 - p_z);
+    let e_x = p_x * (1.0 - p_z);
+    let e_z = (1.0 - p_x) * p_z;
+    let e_y = p_x * p_z;
+
+    for (idx, expected) in [(0, e_i), (1, e_x), (2, e_y), (3, e_z)] {
+        let got = emp(idx);
+        let sigma = (expected * (1.0 - expected) / n_samples as f64).sqrt();
+        let tol = 5.0 * sigma;
+        assert!(
+            (got - expected).abs() < tol,
+            "bucket {}: got {}, expected {}, diff {} > 5 sigma {}",
+            idx,
+            got,
+            expected,
+            (got - expected).abs(),
+            tol,
+        );
+    }
+}
diff --git a/exp/pecos-lindblad/tests/serde_roundtrip.rs b/exp/pecos-lindblad/tests/serde_roundtrip.rs
new file mode 100644
index 000000000..8d9f99834
--- /dev/null
+++ b/exp/pecos-lindblad/tests/serde_roundtrip.rs
@@ -0,0 +1,82 @@
+// Copyright 2026 The PECOS Developers
+//
+// Licensed under the Apache License, Version 2.0 (the "License"); you may not use this file except
+// in compliance with the License. You may obtain a copy of the License at
+//
+//     https://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software distributed under the License
+// is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express
+// or implied. See the License for the specific language governing permissions and limitations under
+// the License.
+
+//! Serde round-trip tests (gated on the `serde` feature). Users can cache
+//! expensive synthesis results and reload them later.
+
+#![cfg(feature = "serde")]
+
+use pecos_lindblad::noise_models::ad_pd_2q;
+use pecos_lindblad::{
+    DEFAULT_N_STEPS, Gate, Pauli1, PauliLindbladModel, PauliString, synthesize_numerical,
+};
+
+#[test]
+fn pauli1_round_trip() {
+    for p in [Pauli1::I, Pauli1::X, Pauli1::Y, Pauli1::Z] {
+        let json = serde_json::to_string(&p).unwrap();
+        let restored: Pauli1 = serde_json::from_str(&json).unwrap();
+        assert_eq!(p, restored);
+    }
+}
+
+#[test]
+fn pauli_string_round_trip() {
+    for s in ["I", "X", "Y", "Z", "IX", "XYZI", "ZZZZZ"] {
+        let ps = PauliString::from_label(s).unwrap();
+        let json = serde_json::to_string(&ps).unwrap();
+        let restored: PauliString = serde_json::from_str(&json).unwrap();
+        assert_eq!(ps, restored);
+    }
+}
+
+#[test]
+fn pauli_lindblad_model_round_trip_via_cx_theta() {
+    // Synthesize a non-trivial 2Q CX_theta model, serialize, and verify
+    // round-trip is bit-exact.
+    let t1 = 100.0;
+    let t2 = 80.0;
+    let omega = 1.0;
+    let theta = std::f64::consts::FRAC_PI_4;
+    let noise = ad_pd_2q(t1, t1, t2, t2);
+    let gate = Gate::cx_theta(omega, theta, noise);
+    let pl = synthesize_numerical(&gate, DEFAULT_N_STEPS);
+
+    let json = serde_json::to_string(&pl).unwrap();
+    let restored: PauliLindbladModel = serde_json::from_str(&json).unwrap();
+
+    assert_eq!(pl.supports.len(), restored.supports.len());
+    for (a, b) in pl.supports.iter().zip(&restored.supports) {
+        assert_eq!(a, b);
+    }
+    for (a, b) in pl.rates.iter().zip(&restored.rates) {
+        assert_eq!(a.to_bits(), b.to_bits(), "rate mismatch {} vs {}", a, b);
+    }
+}
+
+#[test]
+fn pauli_lindblad_model_json_is_human_readable() {
+    // Sanity: verify the JSON shape is predictable enough for users to
+    // inspect / hand-edit.
+    let pl = PauliLindbladModel::new(
+        vec![
+            PauliString::from_label("X").unwrap(),
+            PauliString::from_label("Z").unwrap(),
+        ],
+        vec![0.001, 0.002],
+    );
+    let json = serde_json::to_string(&pl).unwrap();
+    // Expect something like: {"supports":[...],"rates":[0.001,0.002]}
+    assert!(json.contains("\"rates\""));
+    assert!(json.contains("\"supports\""));
+    assert!(json.contains("0.001") || json.contains("1e-3"));
+}
diff --git a/exp/pecos-lindblad/tests/superop_synthesis.rs b/exp/pecos-lindblad/tests/superop_synthesis.rs
new file mode 100644
index 000000000..4bdbe4bc4
--- /dev/null
+++ b/exp/pecos-lindblad/tests/superop_synthesis.rs
@@ -0,0 +1,129 @@
+// Copyright 2026 The PECOS Developers
+//
+// Licensed under the Apache License, Version 2.0 (the "License"); you may not use this file except
+// in compliance with the License. You may obtain a copy of the License at
+//
+//     https://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software distributed under the License
+// is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express
+// or implied. See the License for the specific language governing permissions and limitations under
+// the License.
+
+//! Tests for `synthesize_superop_identity` -- the unified path for
+//! identity gates with mixed coherent + dissipative noise. Validates
+//! consistency with:
+//!
+//! - `synthesize_identity_1q` (pure dissipative AD+PD)
+//! - `synthesize_exact_unitary` (pure coherent)
+//!
+//! and exercises the **new** mixed case (both at once) that the other two
+//! entry points reject or under-model.
+
+use approx::assert_abs_diff_eq;
+use num_complex::Complex64;
+
+use pecos_lindblad::matrix::{self, Matrix};
+use pecos_lindblad::noise_models::{ad_pd_1q, coherent_phase_2q};
+use pecos_lindblad::{
+    Gate, Lindbladian, Pauli1, PauliString, synthesize_exact_unitary, synthesize_identity_1q,
+    synthesize_superop_identity,
+};
+
+#[test]
+fn superop_identity_matches_fast_ad_pd_1q() {
+    // Pure AD+PD, 1Q identity. Superop path should match fast closed-form
+    // path to machine precision.
+    let t1 = 100.0;
+    let t2 = 80.0;
+    let tau_g = 5.0;
+    let noise = ad_pd_1q(t1, t2);
+    let gate = Gate::identity(1, noise, tau_g);
+
+    let fast = synthesize_identity_1q(&gate);
+    let superop = synthesize_superop_identity(&gate);
+
+    for p in [Pauli1::X, Pauli1::Y, Pauli1::Z] {
+        let key = PauliString::single(p);
+        assert_abs_diff_eq!(fast.rate(&key), superop.rate(&key), epsilon = 1e-10);
+    }
+}
+
+#[test]
+fn superop_identity_matches_exact_unitary_for_pure_coherent() {
+    // 2Q identity with pure coherent phase noise: both exact_unitary and
+    // superop paths should agree.
+    let tau_g = 10.0;
+    let delta_iz = 1e-5;
+    let delta_zi = 2e-5;
+    let delta_zz = 5e-6;
+    let noise = coherent_phase_2q(delta_iz, delta_zi, delta_zz);
+    let gate = Gate::identity(2, noise, tau_g);
+
+    let exact = synthesize_exact_unitary(&gate);
+    let superop = synthesize_superop_identity(&gate);
+
+    for ps in PauliString::enumerate_nonidentity(2) {
+        assert_abs_diff_eq!(exact.rate(&ps), superop.rate(&ps), epsilon = 1e-10);
+    }
+}
+
+#[test]
+fn superop_identity_handles_mixed_coherent_and_dissipative_2q() {
+    // THE new capability: simultaneous AD+PD AND coherent crosstalk on
+    // an identity gate. Neither `synthesize_identity_1q` (1Q only) nor
+    // `synthesize_exact_unitary` (coherent only) can handle this;
+    // `synthesize_numerical` catches only the Omega_1 dissipative part.
+    // Only `synthesize_superop_identity` gives the full answer.
+    let d = 4;
+    let tau_g = 1.0;
+    let beta_down = 1e-4;
+    let beta_phi = 2e-4;
+    let delta_zz = 1e-3;
+
+    // Hamiltonian part: (delta_zz / 2) ZZ coherent
+    let i2 = matrix::identity(2);
+    let z = matrix::pauli_1q(Pauli1::Z);
+    let zz = matrix::kron(&z, &z, 2, 2);
+    let h_delta = matrix::scale(&zz, Complex64::new(delta_zz / 2.0, 0.0));
+
+    // Dissipator part: AD+PD on both qubits
+    let sm = matrix::sigma_minus();
+    let sm_l = matrix::kron(&sm, &i2, 2, 2);
+    let sm_r = matrix::kron(&i2, &sm, 2, 2);
+    let z_l = matrix::kron(&z, &i2, 2, 2);
+    let z_r = matrix::kron(&i2, &z, 2, 2);
+    let collapse: Vec<(Matrix, f64)> = vec![
+        (sm_l, beta_down),
+        (sm_r, beta_down),
+        (z_l, beta_phi / 2.0),
+        (z_r, beta_phi / 2.0),
+    ];
+    let mixed = Lindbladian::new(d, h_delta, collapse);
+    let gate = Gate::identity(2, mixed, tau_g);
+    let pl = synthesize_superop_identity(&gate);
+
+    let rate = |s: &str| pl.rate(&PauliString::from_label(s).unwrap());
+
+    // Expected (leading-order superposition of independent contributions):
+    //   Dissipative (AD+PD) on each qubit contributes single-qubit rates
+    //   (paper line 812): lambda_{i·x,y} = beta_down * tau / 4,
+    //                     lambda_{i·z} = beta_phi * tau / 2 (mirror for l).
+    //   Coherent ZZ contributes lambda_ZZ = (delta_zz * tau)^2 / 4
+    //   (paper eq. 981 identity case).
+    // Cross terms between dissipative and coherent are O(beta * delta * tau^2)
+    // and small for these parameter values.
+    let expected_ix_iy = beta_down * tau_g / 4.0;
+    let expected_iz = beta_phi * tau_g / 2.0;
+    let expected_zz = (delta_zz * tau_g).powi(2) / 4.0;
+    let tol_dissipative = 1e-10;
+    let tol_coherent = 1e-10;
+
+    assert_abs_diff_eq!(rate("IX"), expected_ix_iy, epsilon = tol_dissipative);
+    assert_abs_diff_eq!(rate("IY"), expected_ix_iy, epsilon = tol_dissipative);
+    assert_abs_diff_eq!(rate("XI"), expected_ix_iy, epsilon = tol_dissipative);
+    assert_abs_diff_eq!(rate("YI"), expected_ix_iy, epsilon = tol_dissipative);
+    assert_abs_diff_eq!(rate("IZ"), expected_iz, epsilon = tol_dissipative);
+    assert_abs_diff_eq!(rate("ZI"), expected_iz, epsilon = tol_dissipative);
+    assert_abs_diff_eq!(rate("ZZ"), expected_zz, epsilon = tol_coherent);
+}
diff --git a/exp/pecos-lindblad/tests/synthesize_superop_full.rs b/exp/pecos-lindblad/tests/synthesize_superop_full.rs
new file mode 100644
index 000000000..628b66010
--- /dev/null
+++ b/exp/pecos-lindblad/tests/synthesize_superop_full.rs
@@ -0,0 +1,133 @@
+// Copyright 2026 The PECOS Developers
+//
+// Licensed under the Apache License, Version 2.0 (the "License"); you may not use this file except
+// in compliance with the License. You may obtain a copy of the License at
+//
+//     https://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software distributed under the License
+// is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express
+// or implied. See the License for the specific language governing permissions and limitations under
+// the License.
+
+//! Tests for `synthesize_superop` -- the fully-general time-sliced path
+//! that handles `H_g != 0` AND simultaneous coherent + dissipative noise.
+//!
+//! Three validation modes:
+//! 1. Matches `synthesize_numerical` on pure dissipative inputs (CX+AD+PD).
+//! 2. Matches `synthesize_exact_unitary` on pure coherent inputs (CX+phase).
+//! 3. NEW: handles mixed input that neither of the above covers
+//!    (CX_theta + AD+PD + coherent ZZ phase, all at once).
+
+use approx::assert_abs_diff_eq;
+use num_complex::Complex64;
+
+use pecos_lindblad::matrix::{self, Matrix};
+use pecos_lindblad::noise_models::{ad_pd_2q, coherent_phase_2q};
+use pecos_lindblad::{
+    DEFAULT_N_SLICES, DEFAULT_N_STEPS, Gate, Lindbladian, Pauli1, PauliString,
+    synthesize_exact_unitary, synthesize_numerical, synthesize_superop,
+};
+
+#[test]
+fn superop_matches_synthesize_numerical_cx_ad_pd() {
+    // Weak dissipative noise on CX_theta: superop (all orders) and
+    // synthesize_numerical (leading order) should agree to high precision.
+    let omega = 1.0;
+    let theta = std::f64::consts::FRAC_PI_4;
+    let noise = ad_pd_2q(1e5, 1e5, 8e4, 8e4); // very weak
+    let gate = Gate::cx_theta(omega, theta, noise);
+
+    let simpson = synthesize_numerical(&gate, DEFAULT_N_STEPS);
+    let superop = synthesize_superop(&gate, DEFAULT_N_SLICES);
+
+    for ps in PauliString::enumerate_nonidentity(2) {
+        // At this noise level (~1e-5), O(beta^2) corrections are ~1e-10
+        // and negligible. Expect agreement to ~1e-9.
+        assert_abs_diff_eq!(simpson.rate(&ps), superop.rate(&ps), epsilon = 1e-9);
+    }
+}
+
+#[test]
+fn superop_matches_synthesize_exact_unitary_cx_coherent() {
+    let omega = 1.0;
+    let theta = std::f64::consts::FRAC_PI_4;
+    let noise = coherent_phase_2q(1e-5, 2e-5, 5e-6);
+    let gate = Gate::cx_theta(omega, theta, noise);
+
+    let exact = synthesize_exact_unitary(&gate);
+    let superop = synthesize_superop(&gate, DEFAULT_N_SLICES);
+
+    for ps in PauliString::enumerate_nonidentity(2) {
+        assert_abs_diff_eq!(exact.rate(&ps), superop.rate(&ps), epsilon = 1e-10);
+    }
+}
+
+#[test]
+fn superop_handles_cx_mixed_ad_pd_plus_coherent_zz() {
+    // THE new capability: CX_theta with simultaneous AD+PD dissipators
+    // AND coherent ZZ phase noise. No other synthesis path can do this:
+    // - synthesize_numerical: dissipative leading-order, loses coherent
+    //   quadratic contribution.
+    // - synthesize_exact_unitary: asserts no c_ops, refuses mixed input.
+    // - synthesize_superop_identity: requires H_g = 0.
+    let d = 4;
+    let omega = 1.0;
+    let theta = std::f64::consts::FRAC_PI_4;
+    let t1 = 1e5; // very weak AD
+    let t2 = 8e4; // weak PD
+    let delta_zz = 1e-4; // weak coherent ZZ
+
+    let i2 = matrix::identity(2);
+    let sm = matrix::sigma_minus();
+    let z = matrix::pauli_1q(Pauli1::Z);
+    let sm_l = matrix::kron(&sm, &i2, 2, 2);
+    let sm_r = matrix::kron(&i2, &sm, 2, 2);
+    let z_l = matrix::kron(&z, &i2, 2, 2);
+    let z_r = matrix::kron(&i2, &z, 2, 2);
+    let zz = matrix::kron(&z, &z, 2, 2);
+
+    let beta_down = 1.0 / t1;
+    let beta_phi = 1.0 / t2 - 1.0 / (2.0 * t1);
+    let h_delta = matrix::scale(&zz, Complex64::new(delta_zz / 2.0, 0.0));
+    let collapse: Vec<(Matrix, f64)> = vec![
+        (sm_l, beta_down),
+        (sm_r, beta_down),
+        (z_l, beta_phi / 2.0),
+        (z_r, beta_phi / 2.0),
+    ];
+    let mixed = Lindbladian::new(d, h_delta, collapse);
+    let mixed_gate = Gate::cx_theta(omega, theta, mixed);
+
+    // Also build pure-dissipative and pure-coherent variants for
+    // superposition comparison.
+    let pure_diss = ad_pd_2q(t1, t1, t2, t2);
+    let diss_gate = Gate::cx_theta(omega, theta, pure_diss);
+    let pure_coh = coherent_phase_2q(0.0, 0.0, delta_zz);
+    let coh_gate = Gate::cx_theta(omega, theta, pure_coh);
+
+    let pl_mixed = synthesize_superop(&mixed_gate, DEFAULT_N_SLICES);
+    let pl_diss = synthesize_superop(&diss_gate, DEFAULT_N_SLICES);
+    let pl_coh = synthesize_superop(&coh_gate, DEFAULT_N_SLICES);
+
+    // At weak coupling, the mixed rates should equal the superposition of
+    // the two individual-noise rates (cross-terms are second-order small).
+    for ps in PauliString::enumerate_nonidentity(2) {
+        let expected = pl_diss.rate(&ps) + pl_coh.rate(&ps);
+        let got = pl_mixed.rate(&ps);
+        // Cross-term O(beta * delta * tau^2) ~ 1e-5 * 1e-4 * 1 = 1e-9.
+        // Use tolerance slightly above that to account for MC/numerical noise.
+        assert_abs_diff_eq!(got, expected, epsilon = 1e-8);
+    }
+
+    // Additional sanity: mixed has non-trivial rates from both sources.
+    let rate_mixed = |s: &str| pl_mixed.rate(&PauliString::from_label(s).unwrap());
+    assert!(
+        rate_mixed("IX") > 1e-8,
+        "dissipative contribution should be present"
+    );
+    assert!(
+        rate_mixed("ZZ") > 1e-10,
+        "coherent ZZ contribution should be present"
+    );
+}
diff --git a/exp/pecos-lindblad/tests/uncertainty_propagation.rs b/exp/pecos-lindblad/tests/uncertainty_propagation.rs
new file mode 100644
index 000000000..960c5b9db
--- /dev/null
+++ b/exp/pecos-lindblad/tests/uncertainty_propagation.rs
@@ -0,0 +1,127 @@
+// Copyright 2026 The PECOS Developers
+//
+// Licensed under the Apache License, Version 2.0 (the "License"); you may not use this file except
+// in compliance with the License. You may obtain a copy of the License at
+//
+//     https://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software distributed under the License
+// is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express
+// or implied. See the License for the specific language governing permissions and limitations under
+// the License.
+
+//! Monte-Carlo uncertainty propagation tests. For 1Q identity + AD+PD the
+//! rates are exactly `lambda_x = lambda_y = beta_down tau/4` and
+//! `lambda_z = beta_phi tau/2`, so uncertainty propagation is analytic:
+//!
+//!   d lambda_x / d T_1 = -tau / (4 T_1^2)
+//!   d lambda_z / d T_1 = -tau / (2 * 2 T_1^2) = -tau / (4 T_1^2) (from 1/(2T_1))
+//!   d lambda_z / d T_2 = -tau / (2 T_2^2)
+//!
+//! For small Gaussian jitter, first-order MC std should match these
+//! derivatives times the input sigma, to within Monte-Carlo error.
+
+use rand::rngs::StdRng;
+use rand::{RngExt, SeedableRng};
+
+use pecos_lindblad::noise_models::{ad_pd_1q, propagate_uncertainty};
+use pecos_lindblad::{Gate, Pauli1, PauliString, synthesize_identity_1q};
+
+fn gaussian(rng: &mut StdRng, mean: f64, sigma: f64) -> f64 {
+    // Box-Muller.
+    let u1: f64 = rng.random_range(1e-15f64..1.0f64);
+    let u2: f64 = rng.random_range(0.0f64..1.0f64);
+    mean + sigma * f64::sqrt(-2.0 * f64::ln(u1)) * f64::cos(2.0 * std::f64::consts::PI * u2)
+}
+
+#[test]
+fn uncertainty_propagation_gives_expected_std_scale() {
+    let t1_mean = 100.0;
+    let t2_mean = 80.0;
+    let t1_sigma = 5.0; // 5% relative
+    let t2_sigma = 4.0; // 5% relative
+    let tau_g = 1.0;
+    let n_samples = 2000;
+
+    let mut rng = StdRng::seed_from_u64(42);
+    let unc = propagate_uncertainty(n_samples, |_k| {
+        let t1 = gaussian(&mut rng, t1_mean, t1_sigma).max(t2_mean / 2.0 + 1e-3);
+        let t2 = gaussian(&mut rng, t2_mean, t2_sigma)
+            .min(2.0 * t1)
+            .max(1e-3);
+        let noise = ad_pd_1q(t1, t2);
+        let gate = Gate::identity(1, noise, tau_g);
+        synthesize_identity_1q(&gate)
+    });
+
+    // Sanity: means should be close to central-parameter prediction.
+    let beta_down = 1.0 / t1_mean;
+    let beta_phi = 1.0 / t2_mean - 1.0 / (2.0 * t1_mean);
+    let expected_mean_x = beta_down * tau_g / 4.0;
+    let expected_mean_z = beta_phi * tau_g / 2.0;
+
+    let got_mean_x = unc.mean(&PauliString::single(Pauli1::X));
+    let got_mean_z = unc.mean(&PauliString::single(Pauli1::Z));
+    // Monte-Carlo sample-mean error ~ std / sqrt(N); allow 5 sigma.
+    let got_std_x = unc.std(&PauliString::single(Pauli1::X));
+    let got_std_z = unc.std(&PauliString::single(Pauli1::Z));
+    let mean_err_tol_x = 5.0 * got_std_x / (n_samples as f64).sqrt();
+    let mean_err_tol_z = 5.0 * got_std_z / (n_samples as f64).sqrt();
+    // Add small bias tolerance for the boundary clamping above.
+    assert!(
+        (got_mean_x - expected_mean_x).abs() < 5.0 * mean_err_tol_x + 0.05 * expected_mean_x,
+        "mean_x: got {}, expected {}, diff {}",
+        got_mean_x,
+        expected_mean_x,
+        (got_mean_x - expected_mean_x).abs(),
+    );
+    assert!(
+        (got_mean_z - expected_mean_z).abs() < 5.0 * mean_err_tol_z + 0.05 * expected_mean_z,
+        "mean_z: got {}, expected {}, diff {}",
+        got_mean_z,
+        expected_mean_z,
+        (got_mean_z - expected_mean_z).abs(),
+    );
+
+    // Std should be non-trivial (not collapsed to zero) and in the right ballpark
+    // via first-order propagation: sigma_lambda_x ~ tau/(4 T_1^2) * sigma_T1.
+    let predicted_sigma_x = tau_g / (4.0 * t1_mean.powi(2)) * t1_sigma;
+    assert!(
+        got_std_x > 0.3 * predicted_sigma_x && got_std_x < 3.0 * predicted_sigma_x,
+        "sigma_x: got {}, predicted (1st-order) {}, out of factor-3 range",
+        got_std_x,
+        predicted_sigma_x,
+    );
+}
+
+#[test]
+fn uncertainty_std_scales_linearly_with_input_sigma() {
+    // Double the input sigma -> output sigma should roughly double
+    // (first-order Taylor expansion).
+    let t1_mean = 100.0;
+    let t2_mean = 80.0;
+    let tau_g = 1.0;
+
+    let run = |sigma_t1: f64, seed: u64| -> f64 {
+        let mut rng = StdRng::seed_from_u64(seed);
+        let unc = propagate_uncertainty(1000, |_k| {
+            let t1 = gaussian(&mut rng, t1_mean, sigma_t1).max(t2_mean / 2.0 + 1e-3);
+            let noise = ad_pd_1q(t1, t2_mean);
+            let gate = Gate::identity(1, noise, tau_g);
+            synthesize_identity_1q(&gate)
+        });
+        unc.std(&PauliString::single(Pauli1::X))
+    };
+
+    let s1 = run(2.0, 11);
+    let s2 = run(4.0, 11);
+    // Ratio should be ~2, allow 25% slack for MC noise.
+    let ratio = s2 / s1;
+    assert!(
+        (ratio - 2.0).abs() < 0.5,
+        "std did not scale linearly: s1={}, s2={}, ratio={}",
+        s1,
+        s2,
+        ratio
+    );
+}
diff --git a/exp/pecos-lindblad/tests/walsh_hadamard_roundtrip.rs b/exp/pecos-lindblad/tests/walsh_hadamard_roundtrip.rs
new file mode 100644
index 000000000..55ad8a78a
--- /dev/null
+++ b/exp/pecos-lindblad/tests/walsh_hadamard_roundtrip.rs
@@ -0,0 +1,114 @@
+// Copyright 2026 The PECOS Developers
+//
+// Licensed under the Apache License, Version 2.0 (the "License"); you may not use this file except
+// in compliance with the License. You may obtain a copy of the License at
+//
+//     https://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software distributed under the License
+// is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express
+// or implied. See the License for the specific language governing permissions and limitations under
+// the License.
+
+//! Walsh-Hadamard forward/inverse consistency. Starting from arbitrary
+//! non-negative rates `{lambda_k}`:
+//!
+//!   1. Forward map: `alpha_b = 2 * sum_k lambda_k * <b,k>_sp`.
+//!   2. Invert via Walsh-Hadamard: `lambda'_k = -(1/4^n) * sum_b (-1)^{<k,b>_sp} * alpha_b`.
+//!   3. Verify `lambda'_k == lambda_k` (self-consistency of the algorithm).
+//!
+//! This closes a gap in the existing coverage: paper-fixture tests verify
+//! the round-trip end-to-end but not the Walsh-Hadamard step in isolation,
+//! so a bug there could cancel against a parallel bug in synthesis.
+
+use approx::assert_abs_diff_eq;
+
+use pecos_lindblad::{Pauli1, PauliLindbladModel, PauliString};
+
+fn forward_alpha(model: &PauliLindbladModel, b: &PauliString) -> f64 {
+    // alpha_b = 2 * sum_k lambda_k * <b,k>_sp.
+    model
+        .supports
+        .iter()
+        .zip(&model.rates)
+        .map(|(k, lam)| 2.0 * lam * f64::from(b.symplectic_product(k)))
+        .sum()
+}
+
+fn inverse_walsh_hadamard(paulis: &[PauliString], alphas: &[f64], n_qubits: usize) -> Vec<f64> {
+    // lambda_k = -(1/4^n) * sum_b (-1)^{<k,b>_sp} * alpha_b (paper App B).
+    let norm = 1.0 / (1usize << (2 * n_qubits)) as f64;
+    paulis
+        .iter()
+        .map(|k| {
+            let s: f64 = paulis
+                .iter()
+                .zip(alphas.iter())
+                .map(|(b, &ab)| {
+                    let sign = if k.symplectic_product(b) == 0 {
+                        1.0
+                    } else {
+                        -1.0
+                    };
+                    sign * ab
+                })
+                .sum();
+            -norm * s
+        })
+        .collect()
+}
+
+fn round_trip(n_qubits: usize, seed_rates: &[(&str, f64)]) {
+    let supports: Vec<PauliString> = seed_rates
+        .iter()
+        .map(|(s, _)| PauliString::from_label(s).unwrap())
+        .collect();
+    let rates: Vec<f64> = seed_rates.iter().map(|(_, r)| *r).collect();
+    let model = PauliLindbladModel::new(supports.clone(), rates.clone());
+
+    // Enumerate all non-identity paulis to get alpha_b for each.
+    let all = PauliString::enumerate_nonidentity(n_qubits);
+    let alphas: Vec<f64> = all.iter().map(|b| forward_alpha(&model, b)).collect();
+    let recovered = inverse_walsh_hadamard(&all, &alphas, n_qubits);
+
+    // Build the "true" rates aligned to `all` order (0 for unseeded supports).
+    let mut expected = vec![0.0; all.len()];
+    for (s, r) in &rates
+        .iter()
+        .zip(&supports)
+        .map(|(r, s)| (s.clone(), *r))
+        .collect::<Vec<_>>()
+    {
+        if let Some(idx) = all.iter().position(|p| p == s) {
+            expected[idx] = *r;
+        }
+    }
+    for (got, want) in recovered.iter().zip(expected.iter()) {
+        assert_abs_diff_eq!(got, want, epsilon = 1e-12);
+    }
+}
+
+#[test]
+fn walsh_hadamard_round_trip_1q() {
+    round_trip(1, &[("X", 0.001), ("Y", 0.002), ("Z", 0.003)]);
+}
+
+#[test]
+fn walsh_hadamard_round_trip_2q_sparse() {
+    round_trip(2, &[("IX", 1e-3), ("IZ", 2e-3), ("XI", 3e-3), ("ZZ", 4e-4)]);
+}
+
+#[test]
+fn walsh_hadamard_round_trip_3q_with_weight_3() {
+    round_trip(
+        3,
+        &[("IYZ", 1e-4), ("IZZ", 2e-4), ("ZZZ", 5e-5), ("XII", 1e-3)],
+    );
+}
+
+#[test]
+fn walsh_hadamard_round_trip_dense_1q() {
+    // Dense 1Q (all 3 non-identity rates set) to exercise every row.
+    let _ = Pauli1::X; // re-export reachable
+    round_trip(1, &[("X", 0.1), ("Y", 0.2), ("Z", 0.3)]);
+}
diff --git a/exp/pecos-lindblad/tests/x_theta_1q.rs b/exp/pecos-lindblad/tests/x_theta_1q.rs
new file mode 100644
index 000000000..ae5705c72
--- /dev/null
+++ b/exp/pecos-lindblad/tests/x_theta_1q.rs
@@ -0,0 +1,134 @@
+// Copyright 2026 The PECOS Developers
+//
+// Licensed under the Apache License, Version 2.0 (the "License"); you may not use this file except
+// in compliance with the License. You may obtain a copy of the License at
+//
+//     https://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software distributed under the License
+// is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express
+// or implied. See the License for the specific language governing permissions and limitations under
+// the License.
+
+//! Parity test: 1-qubit X_theta gate under amplitude damping + pure
+//! dephasing vs closed-form leading-order results from arXiv:2502.03462
+//! eqs. 869-874 (appendix SubApp:X_th+AD+PD).
+//!
+//! Paper closed forms (lambda_k are dimensionless, integrated over the gate):
+//!   lambda_x = (theta / 4) * (beta_down / omega_x)
+//!   lambda_y = ((2 theta + sin 2 theta) / 16) * (beta_down / omega_x)
+//!            + ((2 theta - sin 2 theta) / 8)  * (beta_phi  / omega_x)
+//!   lambda_z = ((2 theta - sin 2 theta) / 16) * (beta_down / omega_x)
+//!            + ((2 theta + sin 2 theta) / 8)  * (beta_phi  / omega_x)
+//!
+//! The paper's approximation is "leading order in beta/omega"; at
+//! `beta/omega ~ 1e-2` deviation should be ~`O(1e-5)` per
+//! Appendix `App:LindPertPrecision` (line 1078).
+
+use approx::assert_abs_diff_eq;
+
+use pecos_lindblad::matrix::{self, Matrix};
+use pecos_lindblad::{
+    DEFAULT_N_STEPS, Gate, Lindbladian, Pauli1, PauliString, synthesize_numerical_1q,
+};
+
+fn ad_plus_pd_noise(beta_down: f64, beta_phi: f64) -> Lindbladian {
+    let d = 2;
+    let hamiltonian = matrix::zeros(d);
+    let collapse: Vec<(Matrix, f64)> = vec![
+        (matrix::sigma_minus(), beta_down),
+        (matrix::pauli_1q(Pauli1::Z), beta_phi / 2.0),
+    ];
+    Lindbladian::new(d, hamiltonian, collapse)
+}
+
+fn paper_closed_form(theta: f64, omega_x: f64, beta_down: f64, beta_phi: f64) -> (f64, f64, f64) {
+    let two_t = 2.0 * theta;
+    let sin_2t = two_t.sin();
+    let lambda_x = (theta / 4.0) * (beta_down / omega_x);
+    let lambda_y = ((two_t + sin_2t) / 16.0) * (beta_down / omega_x)
+        + ((two_t - sin_2t) / 8.0) * (beta_phi / omega_x);
+    let lambda_z = ((two_t - sin_2t) / 16.0) * (beta_down / omega_x)
+        + ((two_t + sin_2t) / 8.0) * (beta_phi / omega_x);
+    (lambda_x, lambda_y, lambda_z)
+}
+
+fn run_and_compare(theta: f64, omega_x: f64, beta_down: f64, beta_phi: f64, tol: f64) {
+    let noise = ad_plus_pd_noise(beta_down, beta_phi);
+    let gate = Gate::x_theta(omega_x, theta, noise);
+    let pl = synthesize_numerical_1q(&gate, DEFAULT_N_STEPS);
+
+    let (expected_x, expected_y, expected_z) =
+        paper_closed_form(theta, omega_x, beta_down, beta_phi);
+
+    let got_x = pl.rate(&PauliString::single(Pauli1::X));
+    let got_y = pl.rate(&PauliString::single(Pauli1::Y));
+    let got_z = pl.rate(&PauliString::single(Pauli1::Z));
+
+    assert_abs_diff_eq!(got_x, expected_x, epsilon = tol);
+    assert_abs_diff_eq!(got_y, expected_y, epsilon = tol);
+    assert_abs_diff_eq!(got_z, expected_z, epsilon = tol);
+}
+
+#[test]
+fn x_theta_ad_plus_pd_pi_over_4() {
+    // Weak noise => numerical integrand matches leading-order closed form
+    // to within ~O(beta^2 / omega^2). Use beta/omega = 1e-4 => tol ~1e-8.
+    let omega_x = 1.0;
+    let beta_down = 1e-4;
+    let beta_phi = 2e-4;
+    let theta = std::f64::consts::FRAC_PI_4;
+    run_and_compare(theta, omega_x, beta_down, beta_phi, 1e-8);
+}
+
+#[test]
+fn x_theta_ad_plus_pd_pi_over_2() {
+    let omega_x = 1.0;
+    let beta_down = 1e-4;
+    let beta_phi = 5e-5;
+    let theta = std::f64::consts::FRAC_PI_2;
+    run_and_compare(theta, omega_x, beta_down, beta_phi, 1e-8);
+}
+
+#[test]
+fn x_theta_ad_only_pi_over_3() {
+    // lambda_x = (theta/4)(beta_down/omega_x), lambda_y and lambda_z from
+    // beta_down only.
+    let omega_x = 2.0;
+    let beta_down = 3e-4;
+    let beta_phi = 0.0;
+    let theta = std::f64::consts::FRAC_PI_3;
+    run_and_compare(theta, omega_x, beta_down, beta_phi, 1e-8);
+}
+
+#[test]
+fn x_theta_pd_only_pi_over_2() {
+    // lambda_x = 0 (no AD).
+    let omega_x = 1.0;
+    let beta_down = 0.0;
+    let beta_phi = 4e-4;
+    let theta = std::f64::consts::FRAC_PI_2;
+    run_and_compare(theta, omega_x, beta_down, beta_phi, 1e-8);
+}
+
+#[test]
+fn numerical_1q_reduces_to_identity() {
+    // synthesize_numerical_1q on an identity gate (H_g = 0) should match
+    // the fast-path identity synthesis to high precision. Exercises the
+    // time-integral path on a constant integrand.
+    use pecos_lindblad::synthesize_identity_1q;
+
+    let beta_down = 1e-4;
+    let beta_phi = 3e-4;
+    let tau_g = 50.0;
+    let noise = ad_plus_pd_noise(beta_down, beta_phi);
+    let gate = Gate::identity(1, noise, tau_g);
+
+    let fast = synthesize_identity_1q(&gate);
+    let numerical = synthesize_numerical_1q(&gate, DEFAULT_N_STEPS);
+
+    for p in [Pauli1::X, Pauli1::Y, Pauli1::Z] {
+        let key = PauliString::single(p);
+        assert_abs_diff_eq!(fast.rate(&key), numerical.rate(&key), epsilon = 1e-12);
+    }
+}
diff --git a/exp/pecos-neo/Cargo.toml b/exp/pecos-neo/Cargo.toml
index 115fa6e10..69786fbac 100644
--- a/exp/pecos-neo/Cargo.toml
+++ b/exp/pecos-neo/Cargo.toml
@@ -28,6 +28,7 @@ num_cpus = "1.16"
 
 # Optional: for adapter to wrap classical engines
 pecos-engines = { workspace = true, optional = true }
+
 # Optional: for program types (Qasm, Program enum, etc.)
 pecos-programs = { workspace = true, optional = true }
 # Optional: for QASM support
@@ -37,6 +38,7 @@ pecos-hugr = { workspace = true, optional = true }
 
 [dev-dependencies]
 rand.workspace = true
+num-complex.workspace = true
 pecos-engines.workspace = true
 pecos-qasm.workspace = true
 pecos-hugr.workspace = true
diff --git a/exp/pecos-neo/src/adapter.rs b/exp/pecos-neo/src/adapter.rs
index 1d9c2f9d2..51d7a3cee 100644
--- a/exp/pecos-neo/src/adapter.rs
+++ b/exp/pecos-neo/src/adapter.rs
@@ -29,8 +29,9 @@
 //!
 //! ## Example
 //!
-#![cfg_attr(feature = "engines-adapter", doc = "```no_run")]
-#![cfg_attr(not(feature = "engines-adapter"), doc = "```ignore")]
+//! ```rust,no_run
+//! #[cfg(feature = "engines-adapter")]
+//! fn example() {
 //! use std::str::FromStr;
 //! use pecos_neo::adapter::ClassicalEngineAdapter;
 //! use pecos_neo::prelude::*;
@@ -61,6 +62,7 @@
 //!     .with_noise(noise);
 //!
 //! let result = runner.run_shot(&mut program);
+//! }
 //! ```
 
 use crate::command::{CommandQueue, GateCommand, GateType as NeoGateType};
@@ -85,6 +87,8 @@ fn convert_gate_type(core_type: CoreGateType) -> Option<NeoGateType> {
 
         // Single-qubit Cliffords
         CoreGateType::H => NeoGateType::H,
+        CoreGateType::F => NeoGateType::F,
+        CoreGateType::Fdg => NeoGateType::Fdg,
         CoreGateType::SX => NeoGateType::SX,
         CoreGateType::SXdg => NeoGateType::SXdg,
         CoreGateType::SY => NeoGateType::SY,
@@ -107,6 +111,10 @@ fn convert_gate_type(core_type: CoreGateType) -> Option<NeoGateType> {
         CoreGateType::CZ => NeoGateType::CZ,
         CoreGateType::SZZ => NeoGateType::SZZ,
         CoreGateType::SZZdg => NeoGateType::SZZdg,
+        CoreGateType::SXX => NeoGateType::SXX,
+        CoreGateType::SXXdg => NeoGateType::SXXdg,
+        CoreGateType::SYY => NeoGateType::SYY,
+        CoreGateType::SYYdg => NeoGateType::SYYdg,
         CoreGateType::SWAP => NeoGateType::SWAP,
         CoreGateType::CRZ => NeoGateType::CRZ,
         CoreGateType::RXX => NeoGateType::RXX,
@@ -133,15 +141,18 @@ fn convert_gate_type(core_type: CoreGateType) -> Option<NeoGateType> {
 }
 
 /// Convert a pecos-core `Gate` to a pecos-neo `GateCommand`.
-///
-/// Returns `None` if the gate type is not supported.
-fn convert_gate(gate: &Gate) -> Option<GateCommand> {
-    let neo_type = convert_gate_type(gate.gate_type)?;
+fn convert_gate(gate: &Gate) -> Result<GateCommand, pecos_core::errors::PecosError> {
+    let neo_type = convert_gate_type(gate.gate_type).ok_or_else(|| {
+        pecos_core::errors::PecosError::Input(format!(
+            "pecos-neo adapter does not support gate type {:?}",
+            gate.gate_type
+        ))
+    })?;
 
     let qubits = gate.qubits.iter().copied().collect();
     let angles = gate.angles.iter().copied().collect();
 
-    Some(GateCommand {
+    Ok(GateCommand {
         gate_type: neo_type,
         qubits,
         angles,
@@ -150,10 +161,9 @@ fn convert_gate(gate: &Gate) -> Option<GateCommand> {
 
 /// Convert a `ByteMessage` containing quantum operations to a `CommandQueue`.
 ///
-/// Skips any gates that can't be converted (with a warning in debug mode).
-///
 /// # Errors
-/// Returns `PecosError` if the byte message cannot be decoded.
+/// Returns `PecosError` if the byte message cannot be decoded or contains a
+/// gate unsupported by the pecos-neo command representation.
 #[cfg(feature = "engines-adapter")]
 pub fn byte_message_to_command_queue(
     message: &pecos_engines::ByteMessage,
@@ -163,9 +173,7 @@ pub fn byte_message_to_command_queue(
     let mut queue = CommandQueue::with_capacity(gates.len());
 
     for gate in &gates {
-        if let Some(cmd) = convert_gate(gate) {
-            queue.push(cmd);
-        }
+        queue.push(convert_gate(gate)?);
     }
 
     Ok(queue)
@@ -356,21 +364,27 @@ where
 ///
 /// This is useful when you have raw Gate objects and want to convert them
 /// to the pecos-neo format.
-#[must_use]
-pub fn gate_to_command(gate: &Gate) -> Option<GateCommand> {
+///
+/// # Errors
+///
+/// Returns `PecosError` if the gate has no pecos-neo command representation.
+pub fn gate_to_command(gate: &Gate) -> Result<GateCommand, pecos_core::errors::PecosError> {
     convert_gate(gate)
 }
 
 /// Convert a slice of pecos-core Gates to a `CommandQueue`.
-#[must_use]
-pub fn gates_to_command_queue(gates: &[Gate]) -> CommandQueue {
+///
+/// # Errors
+///
+/// Returns `PecosError` if any gate has no pecos-neo command representation.
+pub fn gates_to_command_queue(
+    gates: &[Gate],
+) -> Result<CommandQueue, pecos_core::errors::PecosError> {
     let mut queue = CommandQueue::with_capacity(gates.len());
     for gate in gates {
-        if let Some(cmd) = convert_gate(gate) {
-            queue.push(cmd);
-        }
+        queue.push(convert_gate(gate)?);
     }
-    queue
+    Ok(queue)
 }
 
 /// Convert a `CommandQueue` back to a Vec of pecos-core Gates.
@@ -398,6 +412,8 @@ fn convert_neo_to_core_gate_type(neo_type: NeoGateType) -> CoreGateType {
         NeoGateType::Y => CoreGateType::Y,
         NeoGateType::Z => CoreGateType::Z,
         NeoGateType::H => CoreGateType::H,
+        NeoGateType::F => CoreGateType::F,
+        NeoGateType::Fdg => CoreGateType::Fdg,
         NeoGateType::SX => CoreGateType::SX,
         NeoGateType::SXdg => CoreGateType::SXdg,
         NeoGateType::SY => CoreGateType::SY,
@@ -416,6 +432,10 @@ fn convert_neo_to_core_gate_type(neo_type: NeoGateType) -> CoreGateType {
         NeoGateType::CZ => CoreGateType::CZ,
         NeoGateType::SZZ => CoreGateType::SZZ,
         NeoGateType::SZZdg => CoreGateType::SZZdg,
+        NeoGateType::SXX => CoreGateType::SXX,
+        NeoGateType::SXXdg => CoreGateType::SXXdg,
+        NeoGateType::SYY => CoreGateType::SYY,
+        NeoGateType::SYYdg => CoreGateType::SYYdg,
         NeoGateType::SWAP => CoreGateType::SWAP,
         NeoGateType::CRZ => CoreGateType::CRZ,
         NeoGateType::RXX => CoreGateType::RXX,
@@ -493,7 +513,7 @@ mod tests {
             Gate::new(CoreGateType::MZ, vec![], vec![], vec![QubitId(0)]),
         ];
 
-        let queue = gates_to_command_queue(&gates);
+        let queue = gates_to_command_queue(&gates).expect("should convert");
         assert_eq!(queue.len(), 3);
     }
 
@@ -509,11 +529,23 @@ mod tests {
             ),
         ];
 
-        let queue = gates_to_command_queue(&original_gates);
+        let queue = gates_to_command_queue(&original_gates).expect("should convert");
         let back = command_queue_to_gates(&queue);
 
         assert_eq!(back.len(), 2);
         assert_eq!(back[0].gate_type, CoreGateType::H);
         assert_eq!(back[1].gate_type, CoreGateType::CX);
     }
+
+    #[test]
+    fn test_gate_to_command_rejects_channel_gate() {
+        let gate = Gate::channel(pecos_core::channel::Depolarizing(0.01, 0));
+
+        let err = gate_to_command(&gate).expect_err("channel gates need typed channel handling");
+
+        assert!(
+            err.to_string()
+                .contains("does not support gate type Channel")
+        );
+    }
 }
diff --git a/exp/pecos-neo/src/circuit.rs b/exp/pecos-neo/src/circuit.rs
index a445bd23e..d2911b78c 100644
--- a/exp/pecos-neo/src/circuit.rs
+++ b/exp/pecos-neo/src/circuit.rs
@@ -46,7 +46,6 @@ use smallvec::SmallVec;
 // ============================================================================
 
 impl From<pecos_core::gate_type::GateType> for GateType {
-    #[allow(clippy::match_same_arms)] // Unknown gate types explicitly map to I
     fn from(gt: pecos_core::gate_type::GateType) -> Self {
         use pecos_core::gate_type::GateType as CoreGT;
         match gt {
@@ -55,6 +54,8 @@ impl From<pecos_core::gate_type::GateType> for GateType {
             CoreGT::Y => Self::Y,
             CoreGT::Z => Self::Z,
             CoreGT::H => Self::H,
+            CoreGT::F => Self::F,
+            CoreGT::Fdg => Self::Fdg,
             CoreGT::SX => Self::SX,
             CoreGT::SXdg => Self::SXdg,
             CoreGT::SY => Self::SY,
@@ -71,6 +72,10 @@ impl From<pecos_core::gate_type::GateType> for GateType {
             CoreGT::CX => Self::CX,
             CoreGT::CY => Self::CY,
             CoreGT::CZ => Self::CZ,
+            CoreGT::SXX => Self::SXX,
+            CoreGT::SXXdg => Self::SXXdg,
+            CoreGT::SYY => Self::SYY,
+            CoreGT::SYYdg => Self::SYYdg,
             CoreGT::SZZ => Self::SZZ,
             CoreGT::SZZdg => Self::SZZdg,
             CoreGT::SWAP => Self::SWAP,
@@ -86,8 +91,7 @@ impl From<pecos_core::gate_type::GateType> for GateType {
             CoreGT::QAlloc => Self::QAlloc,
             CoreGT::QFree => Self::QFree,
             CoreGT::Idle => Self::Idle,
-            // Any unknown gate types default to identity
-            _ => Self::I,
+            other => panic!("unsupported pecos-core gate type for pecos-neo conversion: {other:?}"),
         }
     }
 }
@@ -101,6 +105,8 @@ impl From<GateType> for pecos_core::gate_type::GateType {
             GateType::Y => CoreGT::Y,
             GateType::Z => CoreGT::Z,
             GateType::H => CoreGT::H,
+            GateType::F => CoreGT::F,
+            GateType::Fdg => CoreGT::Fdg,
             GateType::SX => CoreGT::SX,
             GateType::SXdg => CoreGT::SXdg,
             GateType::SY => CoreGT::SY,
@@ -119,6 +125,10 @@ impl From<GateType> for pecos_core::gate_type::GateType {
             GateType::CZ => CoreGT::CZ,
             GateType::SZZ => CoreGT::SZZ,
             GateType::SZZdg => CoreGT::SZZdg,
+            GateType::SXX => CoreGT::SXX,
+            GateType::SXXdg => CoreGT::SXXdg,
+            GateType::SYY => CoreGT::SYY,
+            GateType::SYYdg => CoreGT::SYYdg,
             GateType::SWAP => CoreGT::SWAP,
             GateType::CRZ => CoreGT::CRZ,
             GateType::RXX => CoreGT::RXX,
@@ -178,14 +188,14 @@ impl From<Gate> for GateCommand {
 impl From<&TickCircuit> for CommandQueue {
     /// Convert a `TickCircuit` to a `CommandQueue`.
     ///
-    /// Gates are added in tick order - all gates from tick 0, then tick 1, etc.
-    /// Within each tick, gates are added in the order they appear.
+    /// Gate batches are added in tick order - all commands from tick 0, then tick 1, etc.
+    /// Within each tick, commands are added in the order they appear.
     fn from(circuit: &TickCircuit) -> Self {
         let mut queue = CommandQueue::new();
 
         for tick in circuit.ticks() {
-            for gate in tick.gates() {
-                queue.push(gate.into());
+            for gate in tick.iter_gate_batches() {
+                queue.push(gate.as_gate().into());
             }
         }
 
@@ -288,9 +298,11 @@ impl From<&CommandQueue> for TickCircuit {
                         angles,
                         params: SmallVec::new(),
                         qubits: qubit_ids,
+                        meas_ids: SmallVec::new(),
+                        channel: None,
                     };
-                    // Use try_add_gate and ignore errors (shouldn't happen with one gate per tick)
-                    let _ = tick.try_add_gate(gate);
+                    tick.try_add_gate(gate)
+                        .expect("one gate per tick should not have qubit conflicts");
                 }
             }
         }
@@ -419,6 +431,8 @@ mod tests {
             angles: smallvec::smallvec![Angle64::QUARTER_TURN],
             params: SmallVec::new(),
             qubits: smallvec::smallvec![QubitId(0)],
+            meas_ids: SmallVec::new(),
+            channel: None,
         };
 
         let cmd: GateCommand = (&gate).into();
diff --git a/exp/pecos-neo/src/command.rs b/exp/pecos-neo/src/command.rs
index b42bae781..a26c8b3a4 100644
--- a/exp/pecos-neo/src/command.rs
+++ b/exp/pecos-neo/src/command.rs
@@ -37,6 +37,8 @@ pub enum GateType {
 
     // Single-qubit Cliffords
     H,
+    F,
+    Fdg,
     SX,
     SXdg,
     SY,
@@ -59,6 +61,10 @@ pub enum GateType {
     CZ,
     SZZ,
     SZZdg,
+    SXX,
+    SXXdg,
+    SYY,
+    SYYdg,
     SWAP,
     CRZ,
     RXX,
@@ -90,6 +96,8 @@ impl GateType {
             | Self::Y
             | Self::Z
             | Self::H
+            | Self::F
+            | Self::Fdg
             | Self::SX
             | Self::SXdg
             | Self::SY
@@ -116,6 +124,10 @@ impl GateType {
             | Self::CZ
             | Self::SZZ
             | Self::SZZdg
+            | Self::SXX
+            | Self::SXXdg
+            | Self::SYY
+            | Self::SYYdg
             | Self::SWAP
             | Self::CRZ
             | Self::RXX
@@ -160,6 +172,31 @@ impl GateType {
     pub const fn is_preparation(self) -> bool {
         matches!(self, Self::PZ | Self::QAlloc)
     }
+
+    /// Returns true if this is an idle operation.
+    #[must_use]
+    pub const fn is_idle(self) -> bool {
+        matches!(self, Self::Idle)
+    }
+
+    /// Returns true if this is a resource management operation.
+    #[must_use]
+    pub const fn is_resource_management(self) -> bool {
+        matches!(self, Self::QAlloc | Self::QFree)
+    }
+
+    /// Returns true if this is a unitary gate (not preparation, measurement,
+    /// idle, or resource management).
+    ///
+    /// These are the gates that should receive gate depolarizing noise
+    /// (p1 for single-qubit, p2 for two-qubit).
+    #[must_use]
+    pub const fn is_unitary_gate(self) -> bool {
+        !self.is_measurement()
+            && !self.is_preparation()
+            && !self.is_idle()
+            && !self.is_resource_management()
+    }
 }
 
 /// A single quantum gate command.
diff --git a/exp/pecos-neo/src/command/builder.rs b/exp/pecos-neo/src/command/builder.rs
index 4a4ece180..aafe37175 100644
--- a/exp/pecos-neo/src/command/builder.rs
+++ b/exp/pecos-neo/src/command/builder.rs
@@ -136,6 +136,28 @@ impl CommandBuilder {
         self
     }
 
+    /// Add face gates.
+    #[must_use]
+    pub fn f(mut self, qubits: &[impl Into<QubitId> + Copy]) -> Self {
+        for &q in qubits {
+            self.queue
+                .push(GateCommand::new(GateType::F, smallvec::smallvec![q.into()]));
+        }
+        self
+    }
+
+    /// Add face-dagger gates.
+    #[must_use]
+    pub fn fdg(mut self, qubits: &[impl Into<QubitId> + Copy]) -> Self {
+        for &q in qubits {
+            self.queue.push(GateCommand::new(
+                GateType::Fdg,
+                smallvec::smallvec![q.into()],
+            ));
+        }
+        self
+    }
+
     /// Add SX (sqrt-X) gates.
     #[must_use]
     pub fn sx(mut self, qubits: &[impl Into<QubitId> + Copy]) -> Self {
@@ -276,6 +298,24 @@ impl CommandBuilder {
         self
     }
 
+    /// Add R1XY rotation gates with two angles (theta, phi).
+    #[must_use]
+    pub fn r1xy(
+        mut self,
+        qubits: &[impl Into<QubitId> + Copy],
+        theta: impl Into<Angle64> + Copy,
+        phi: impl Into<Angle64> + Copy,
+    ) -> Self {
+        for &q in qubits {
+            self.queue.push(GateCommand::with_angles(
+                GateType::R1XY,
+                smallvec::smallvec![q.into()],
+                smallvec::smallvec![theta.into(), phi.into()],
+            ));
+        }
+        self
+    }
+
     // Two-qubit gates
 
     /// Add CNOT (CX) gates.
@@ -321,6 +361,75 @@ impl CommandBuilder {
         self
     }
 
+    /// Add SXX gates.
+    #[must_use]
+    pub fn sxx(mut self, pairs: &[(impl Into<QubitId> + Copy, impl Into<QubitId> + Copy)]) -> Self {
+        for &(q0, q1) in pairs {
+            self.queue.push(GateCommand::new(
+                GateType::SXX,
+                smallvec::smallvec![q0.into(), q1.into()],
+            ));
+        }
+        self
+    }
+
+    /// Add `SXXdg` gates.
+    #[must_use]
+    pub fn sxxdg(
+        mut self,
+        pairs: &[(impl Into<QubitId> + Copy, impl Into<QubitId> + Copy)],
+    ) -> Self {
+        for &(q0, q1) in pairs {
+            self.queue.push(GateCommand::new(
+                GateType::SXXdg,
+                smallvec::smallvec![q0.into(), q1.into()],
+            ));
+        }
+        self
+    }
+
+    /// Add SYY gates.
+    #[must_use]
+    pub fn syy(mut self, pairs: &[(impl Into<QubitId> + Copy, impl Into<QubitId> + Copy)]) -> Self {
+        for &(q0, q1) in pairs {
+            self.queue.push(GateCommand::new(
+                GateType::SYY,
+                smallvec::smallvec![q0.into(), q1.into()],
+            ));
+        }
+        self
+    }
+
+    /// Add `SYYdg` gates.
+    #[must_use]
+    pub fn syydg(
+        mut self,
+        pairs: &[(impl Into<QubitId> + Copy, impl Into<QubitId> + Copy)],
+    ) -> Self {
+        for &(q0, q1) in pairs {
+            self.queue.push(GateCommand::new(
+                GateType::SYYdg,
+                smallvec::smallvec![q0.into(), q1.into()],
+            ));
+        }
+        self
+    }
+
+    /// Add `SZZdg` gates (inverse of `SZZ`).
+    #[must_use]
+    pub fn szzdg(
+        mut self,
+        pairs: &[(impl Into<QubitId> + Copy, impl Into<QubitId> + Copy)],
+    ) -> Self {
+        for &(q0, q1) in pairs {
+            self.queue.push(GateCommand::new(
+                GateType::SZZdg,
+                smallvec::smallvec![q0.into(), q1.into()],
+            ));
+        }
+        self
+    }
+
     /// Add SWAP gates.
     #[must_use]
     pub fn swap(
diff --git a/exp/pecos-neo/src/engines.rs b/exp/pecos-neo/src/engines.rs
index 5bff6aa35..4c482a07b 100644
--- a/exp/pecos-neo/src/engines.rs
+++ b/exp/pecos-neo/src/engines.rs
@@ -138,8 +138,8 @@ impl CommandSource for TickCircuitEngine {
         self.current_tick += 1;
 
         let mut queue = CommandQueue::new();
-        for gate in tick.gates() {
-            queue.push(gate.into());
+        for gate in tick.iter_gate_batches() {
+            queue.push(gate.as_gate().into());
         }
 
         Some(queue)
diff --git a/exp/pecos-neo/src/extensible/bridge.rs b/exp/pecos-neo/src/extensible/bridge.rs
index 0e9549674..ca367a006 100644
--- a/exp/pecos-neo/src/extensible/bridge.rs
+++ b/exp/pecos-neo/src/extensible/bridge.rs
@@ -21,6 +21,8 @@ impl GateType {
 
             // Single-qubit Cliffords
             Self::H => gates::H,
+            Self::F => gates::F,
+            Self::Fdg => gates::Fdg,
             Self::SX => gates::SX,
             Self::SXdg => gates::SXdg,
             Self::SY => gates::SY,
@@ -43,6 +45,10 @@ impl GateType {
             Self::CZ => gates::CZ,
             Self::SZZ => gates::SZZ,
             Self::SZZdg => gates::SZZdg,
+            Self::SXX => gates::SXX,
+            Self::SXXdg => gates::SXXdg,
+            Self::SYY => gates::SYY,
+            Self::SYYdg => gates::SYYdg,
             Self::SWAP => gates::SWAP,
             Self::CRZ => gates::CRZ,
             Self::RXX => gates::RXX,
@@ -94,6 +100,8 @@ impl GateId {
             14 => GateType::SYdg,
             15 => GateType::SZ,
             16 => GateType::SZdg,
+            17 => GateType::F,
+            18 => GateType::Fdg,
 
             // T gates
             20 => GateType::T,
@@ -113,6 +121,10 @@ impl GateId {
             53 => GateType::SWAP,
 
             // Two-qubit Clifford rotations
+            60 => GateType::SXX,
+            61 => GateType::SXXdg,
+            62 => GateType::SYY,
+            63 => GateType::SYYdg,
             64 => GateType::SZZ,
             65 => GateType::SZZdg,
 
@@ -202,6 +214,8 @@ mod tests {
             GateType::Y,
             GateType::Z,
             GateType::H,
+            GateType::F,
+            GateType::Fdg,
             GateType::SX,
             GateType::SXdg,
             GateType::SY,
@@ -220,6 +234,10 @@ mod tests {
             GateType::CZ,
             GateType::SZZ,
             GateType::SZZdg,
+            GateType::SXX,
+            GateType::SXXdg,
+            GateType::SYY,
+            GateType::SYYdg,
             GateType::SWAP,
             GateType::CRZ,
             GateType::RXX,
@@ -286,6 +304,8 @@ mod tests {
         assert_eq!(GateType::I.to_gate_id(), gates::I);
         assert_eq!(GateType::X.to_gate_id(), gates::X);
         assert_eq!(GateType::H.to_gate_id(), gates::H);
+        assert_eq!(GateType::F.to_gate_id(), gates::F);
+        assert_eq!(GateType::Fdg.to_gate_id(), gates::Fdg);
         assert_eq!(GateType::RZ.to_gate_id(), gates::RZ);
         assert_eq!(GateType::CX.to_gate_id(), gates::CX);
         assert_eq!(GateType::CCX.to_gate_id(), gates::CCX);
diff --git a/exp/pecos-neo/src/extensible/definitions.rs b/exp/pecos-neo/src/extensible/definitions.rs
index c1ed5cd6d..ef36b882b 100644
--- a/exp/pecos-neo/src/extensible/definitions.rs
+++ b/exp/pecos-neo/src/extensible/definitions.rs
@@ -325,6 +325,14 @@ impl GateDefinitions {
             gates::H,
             GateSpec::new("H").with_category(GateCategory::SingleQubitUnitary),
         );
+        self.set_core_spec(
+            gates::F,
+            GateSpec::new("F").with_category(GateCategory::SingleQubitUnitary),
+        );
+        self.set_core_spec(
+            gates::Fdg,
+            GateSpec::new("Fdg").with_category(GateCategory::SingleQubitUnitary),
+        );
         self.set_core_spec(
             gates::SX,
             GateSpec::new("SX").with_category(GateCategory::SingleQubitUnitary),
@@ -417,6 +425,42 @@ impl GateDefinitions {
                 .with_quantum_arity(2)
                 .with_category(GateCategory::TwoQubitUnitary),
         );
+        self.set_core_spec(
+            gates::SXX,
+            GateSpec::new("SXX")
+                .with_quantum_arity(2)
+                .with_category(GateCategory::TwoQubitUnitary),
+        );
+        self.set_core_spec(
+            gates::SXXdg,
+            GateSpec::new("SXXdg")
+                .with_quantum_arity(2)
+                .with_category(GateCategory::TwoQubitUnitary),
+        );
+        self.set_core_spec(
+            gates::SYY,
+            GateSpec::new("SYY")
+                .with_quantum_arity(2)
+                .with_category(GateCategory::TwoQubitUnitary),
+        );
+        self.set_core_spec(
+            gates::SYYdg,
+            GateSpec::new("SYYdg")
+                .with_quantum_arity(2)
+                .with_category(GateCategory::TwoQubitUnitary),
+        );
+        self.set_core_spec(
+            gates::SZZ,
+            GateSpec::new("SZZ")
+                .with_quantum_arity(2)
+                .with_category(GateCategory::TwoQubitUnitary),
+        );
+        self.set_core_spec(
+            gates::SZZdg,
+            GateSpec::new("SZZdg")
+                .with_quantum_arity(2)
+                .with_category(GateCategory::TwoQubitUnitary),
+        );
 
         // Two-qubit parameterized
         self.set_core_spec(
diff --git a/exp/pecos-neo/src/extensible/gate_id.rs b/exp/pecos-neo/src/extensible/gate_id.rs
index 73d9eed31..d6472d3c0 100644
--- a/exp/pecos-neo/src/extensible/gate_id.rs
+++ b/exp/pecos-neo/src/extensible/gate_id.rs
@@ -67,6 +67,8 @@ pub mod gates {
     pub const SYdg: GateId = GateId(14);
     pub const SZ: GateId = GateId(15);
     pub const SZdg: GateId = GateId(16);
+    pub const F: GateId = GateId(17);
+    pub const Fdg: GateId = GateId(18);
 
     // T gates
     pub const T: GateId = GateId(20);
diff --git a/exp/pecos-neo/src/extensible/queue_validation.rs b/exp/pecos-neo/src/extensible/queue_validation.rs
index a0c8737a3..daf559bee 100644
--- a/exp/pecos-neo/src/extensible/queue_validation.rs
+++ b/exp/pecos-neo/src/extensible/queue_validation.rs
@@ -149,6 +149,8 @@ pub fn is_clifford_gate_type(gate_type: GateType) -> bool {
             | GateType::Y
             | GateType::Z
             | GateType::H
+            | GateType::F
+            | GateType::Fdg
             | GateType::SX
             | GateType::SXdg
             | GateType::SY
@@ -160,6 +162,10 @@ pub fn is_clifford_gate_type(gate_type: GateType) -> bool {
             | GateType::CZ
             | GateType::SZZ
             | GateType::SZZdg
+            | GateType::SXX
+            | GateType::SXXdg
+            | GateType::SYY
+            | GateType::SYYdg
             | GateType::SWAP
             | GateType::MZ
             | GateType::MeasureLeaked
diff --git a/exp/pecos-neo/src/extensible/registry.rs b/exp/pecos-neo/src/extensible/registry.rs
index 946b6a916..d47d52f95 100644
--- a/exp/pecos-neo/src/extensible/registry.rs
+++ b/exp/pecos-neo/src/extensible/registry.rs
@@ -62,6 +62,14 @@ impl GateRegistry {
             gates::H,
             &GateSpec::new("H").with_category(GateCategory::SingleQubitUnitary),
         );
+        self.set_core(
+            gates::F,
+            &GateSpec::new("F").with_category(GateCategory::SingleQubitUnitary),
+        );
+        self.set_core(
+            gates::Fdg,
+            &GateSpec::new("Fdg").with_category(GateCategory::SingleQubitUnitary),
+        );
         self.set_core(
             gates::SX,
             &GateSpec::new("SX").with_category(GateCategory::SingleQubitUnitary),
diff --git a/exp/pecos-neo/src/extensible/tests.rs b/exp/pecos-neo/src/extensible/tests.rs
index 1728ffa1d..5ba2e2bb5 100644
--- a/exp/pecos-neo/src/extensible/tests.rs
+++ b/exp/pecos-neo/src/extensible/tests.rs
@@ -3,8 +3,225 @@
 
 use super::validator::GateForValidation;
 use super::*;
+use crate::command::{CommandBuilder, GateType as CommandGateType};
 use pecos_core::{Angle64, QubitId};
 
+#[derive(Debug, Clone, Copy)]
+struct StandardCliffordCase {
+    gate_type: CommandGateType,
+    gate_id: GateId,
+    name: &'static str,
+    arity: u8,
+    inverse: CommandGateType,
+}
+
+fn standard_clifford_cases() -> &'static [StandardCliffordCase] {
+    use CommandGateType::{
+        CX, CY, CZ, F, Fdg, H, I, SWAP, SX, SXX, SXXdg, SXdg, SY, SYY, SYYdg, SYdg, SZ, SZZ, SZZdg,
+        SZdg, X, Y, Z,
+    };
+
+    &[
+        StandardCliffordCase {
+            gate_type: I,
+            gate_id: gates::I,
+            name: "I",
+            arity: 1,
+            inverse: I,
+        },
+        StandardCliffordCase {
+            gate_type: X,
+            gate_id: gates::X,
+            name: "X",
+            arity: 1,
+            inverse: X,
+        },
+        StandardCliffordCase {
+            gate_type: Y,
+            gate_id: gates::Y,
+            name: "Y",
+            arity: 1,
+            inverse: Y,
+        },
+        StandardCliffordCase {
+            gate_type: Z,
+            gate_id: gates::Z,
+            name: "Z",
+            arity: 1,
+            inverse: Z,
+        },
+        StandardCliffordCase {
+            gate_type: H,
+            gate_id: gates::H,
+            name: "H",
+            arity: 1,
+            inverse: H,
+        },
+        StandardCliffordCase {
+            gate_type: F,
+            gate_id: gates::F,
+            name: "F",
+            arity: 1,
+            inverse: Fdg,
+        },
+        StandardCliffordCase {
+            gate_type: Fdg,
+            gate_id: gates::Fdg,
+            name: "Fdg",
+            arity: 1,
+            inverse: F,
+        },
+        StandardCliffordCase {
+            gate_type: SX,
+            gate_id: gates::SX,
+            name: "SX",
+            arity: 1,
+            inverse: SXdg,
+        },
+        StandardCliffordCase {
+            gate_type: SXdg,
+            gate_id: gates::SXdg,
+            name: "SXdg",
+            arity: 1,
+            inverse: SX,
+        },
+        StandardCliffordCase {
+            gate_type: SY,
+            gate_id: gates::SY,
+            name: "SY",
+            arity: 1,
+            inverse: SYdg,
+        },
+        StandardCliffordCase {
+            gate_type: SYdg,
+            gate_id: gates::SYdg,
+            name: "SYdg",
+            arity: 1,
+            inverse: SY,
+        },
+        StandardCliffordCase {
+            gate_type: SZ,
+            gate_id: gates::SZ,
+            name: "SZ",
+            arity: 1,
+            inverse: SZdg,
+        },
+        StandardCliffordCase {
+            gate_type: SZdg,
+            gate_id: gates::SZdg,
+            name: "SZdg",
+            arity: 1,
+            inverse: SZ,
+        },
+        StandardCliffordCase {
+            gate_type: CX,
+            gate_id: gates::CX,
+            name: "CX",
+            arity: 2,
+            inverse: CX,
+        },
+        StandardCliffordCase {
+            gate_type: CY,
+            gate_id: gates::CY,
+            name: "CY",
+            arity: 2,
+            inverse: CY,
+        },
+        StandardCliffordCase {
+            gate_type: CZ,
+            gate_id: gates::CZ,
+            name: "CZ",
+            arity: 2,
+            inverse: CZ,
+        },
+        StandardCliffordCase {
+            gate_type: SXX,
+            gate_id: gates::SXX,
+            name: "SXX",
+            arity: 2,
+            inverse: SXXdg,
+        },
+        StandardCliffordCase {
+            gate_type: SXXdg,
+            gate_id: gates::SXXdg,
+            name: "SXXdg",
+            arity: 2,
+            inverse: SXX,
+        },
+        StandardCliffordCase {
+            gate_type: SYY,
+            gate_id: gates::SYY,
+            name: "SYY",
+            arity: 2,
+            inverse: SYYdg,
+        },
+        StandardCliffordCase {
+            gate_type: SYYdg,
+            gate_id: gates::SYYdg,
+            name: "SYYdg",
+            arity: 2,
+            inverse: SYY,
+        },
+        StandardCliffordCase {
+            gate_type: SZZ,
+            gate_id: gates::SZZ,
+            name: "SZZ",
+            arity: 2,
+            inverse: SZZdg,
+        },
+        StandardCliffordCase {
+            gate_type: SZZdg,
+            gate_id: gates::SZZdg,
+            name: "SZZdg",
+            arity: 2,
+            inverse: SZZ,
+        },
+        StandardCliffordCase {
+            gate_type: SWAP,
+            gate_id: gates::SWAP,
+            name: "SWAP",
+            arity: 2,
+            inverse: SWAP,
+        },
+    ]
+}
+
+fn command_from_builder(gate_type: CommandGateType) -> crate::command::GateCommand {
+    let queue = match gate_type {
+        CommandGateType::I => CommandBuilder::new().identity(&[0]).build(),
+        CommandGateType::X => CommandBuilder::new().x(&[0]).build(),
+        CommandGateType::Y => CommandBuilder::new().y(&[0]).build(),
+        CommandGateType::Z => CommandBuilder::new().z(&[0]).build(),
+        CommandGateType::H => CommandBuilder::new().h(&[0]).build(),
+        CommandGateType::F => CommandBuilder::new().f(&[0]).build(),
+        CommandGateType::Fdg => CommandBuilder::new().fdg(&[0]).build(),
+        CommandGateType::SX => CommandBuilder::new().sx(&[0]).build(),
+        CommandGateType::SXdg => CommandBuilder::new().sxdg(&[0]).build(),
+        CommandGateType::SY => CommandBuilder::new().sy(&[0]).build(),
+        CommandGateType::SYdg => CommandBuilder::new().sydg(&[0]).build(),
+        CommandGateType::SZ => CommandBuilder::new().sz(&[0]).build(),
+        CommandGateType::SZdg => CommandBuilder::new().szdg(&[0]).build(),
+        CommandGateType::CX => CommandBuilder::new().cx(&[(0, 1)]).build(),
+        CommandGateType::CY => CommandBuilder::new().cy(&[(0, 1)]).build(),
+        CommandGateType::CZ => CommandBuilder::new().cz(&[(0, 1)]).build(),
+        CommandGateType::SXX => CommandBuilder::new().sxx(&[(0, 1)]).build(),
+        CommandGateType::SXXdg => CommandBuilder::new().sxxdg(&[(0, 1)]).build(),
+        CommandGateType::SYY => CommandBuilder::new().syy(&[(0, 1)]).build(),
+        CommandGateType::SYYdg => CommandBuilder::new().syydg(&[(0, 1)]).build(),
+        CommandGateType::SZZ => CommandBuilder::new().szz(&[(0, 1)]).build(),
+        CommandGateType::SZZdg => CommandBuilder::new().szzdg(&[(0, 1)]).build(),
+        CommandGateType::SWAP => CommandBuilder::new().swap(&[(0, 1)]).build(),
+        other => panic!("not a standard Clifford conformance gate: {other:?}"),
+    };
+
+    assert_eq!(
+        queue.len(),
+        1,
+        "{gate_type:?} builder should emit one command"
+    );
+    queue.iter().next().unwrap().clone()
+}
+
 // ============================================================================
 // GateId Tests
 // ============================================================================
@@ -1266,6 +1483,78 @@ fn test_validator_is_gate_allowed() {
     assert!(!validator.is_gate_allowed(gates::RZ, &[Angle64::from_turns(0.1)], &registry));
 }
 
+#[test]
+fn test_standard_cliffords_are_registered_defined_and_allowed() {
+    let registry = GateRegistry::new();
+    let definitions = GateDefinitions::new();
+    let validator = CliffordValidator::new();
+
+    for case in standard_clifford_cases() {
+        assert!(
+            registry.get(case.gate_id).is_some(),
+            "missing registry spec for {}",
+            case.name
+        );
+        assert!(
+            definitions.spec(case.gate_id).is_some(),
+            "missing gate definition for {}",
+            case.name
+        );
+        assert!(
+            validator.is_gate_allowed(case.gate_id, &[], &registry),
+            "Clifford validator should allow {}",
+            case.name
+        );
+    }
+}
+
+#[test]
+fn test_standard_clifford_gate_surface_is_consistent() {
+    let registry = GateRegistry::new();
+    let definitions = GateDefinitions::new();
+
+    for case in standard_clifford_cases() {
+        let registry_spec = registry.get(case.gate_id).unwrap();
+        let definition_spec = definitions.spec(case.gate_id).unwrap();
+        assert_eq!(registry_spec.name, case.name, "{case:?}");
+        assert_eq!(definition_spec.name, case.name, "{case:?}");
+        assert_eq!(registry_spec.quantum_arity, case.arity, "{case:?}");
+        assert_eq!(definition_spec.quantum_arity, case.arity, "{case:?}");
+        assert_eq!(
+            case.gate_type.quantum_arity(),
+            case.arity as usize,
+            "{case:?}"
+        );
+        assert_eq!(case.gate_type.angle_arity(), 0, "{case:?}");
+        assert_eq!(case.gate_type.to_gate_id(), case.gate_id, "{case:?}");
+        assert_eq!(
+            case.gate_id.try_to_gate_type(),
+            Some(case.gate_type),
+            "{case:?}"
+        );
+
+        let command = command_from_builder(case.gate_type);
+        assert_eq!(command.gate_type, case.gate_type, "{case:?}");
+        assert_eq!(command.qubits.len(), case.arity as usize, "{case:?}");
+        assert!(command.angles.is_empty(), "{case:?}");
+    }
+}
+
+#[test]
+fn test_standard_clifford_inverse_table_is_symmetric() {
+    for case in standard_clifford_cases() {
+        let inverse = standard_clifford_cases()
+            .iter()
+            .find(|candidate| candidate.gate_type == case.inverse)
+            .unwrap_or_else(|| panic!("missing inverse {:?} for {}", case.inverse, case.name));
+        assert_eq!(
+            inverse.inverse, case.gate_type,
+            "inverse table should be symmetric for {}",
+            case.name
+        );
+    }
+}
+
 #[test]
 fn test_validation_error_display() {
     let err = ValidationError::ForbiddenGate {
diff --git a/exp/pecos-neo/src/extensible/validator.rs b/exp/pecos-neo/src/extensible/validator.rs
index 7635f4673..758982989 100644
--- a/exp/pecos-neo/src/extensible/validator.rs
+++ b/exp/pecos-neo/src/extensible/validator.rs
@@ -141,6 +141,8 @@ impl CliffordValidator {
 
         // Cliffords
         allowed_gates.insert(gates::H);
+        allowed_gates.insert(gates::F);
+        allowed_gates.insert(gates::Fdg);
         allowed_gates.insert(gates::SX);
         allowed_gates.insert(gates::SXdg);
         allowed_gates.insert(gates::SY);
@@ -154,6 +156,10 @@ impl CliffordValidator {
         allowed_gates.insert(gates::CZ);
         allowed_gates.insert(gates::SWAP);
         allowed_gates.insert(gates::ISWAP);
+        allowed_gates.insert(gates::SXX);
+        allowed_gates.insert(gates::SXXdg);
+        allowed_gates.insert(gates::SYY);
+        allowed_gates.insert(gates::SYYdg);
         allowed_gates.insert(gates::SZZ);
         allowed_gates.insert(gates::SZZdg);
 
diff --git a/exp/pecos-neo/src/inline_channel.rs b/exp/pecos-neo/src/inline_channel.rs
new file mode 100644
index 000000000..e9f9830d9
--- /dev/null
+++ b/exp/pecos-neo/src/inline_channel.rs
@@ -0,0 +1,583 @@
+// Copyright 2026 The PECOS Developers
+//
+// Licensed under the Apache License, Version 2.0 (the "License"); you may not use this file except
+// in compliance with the License. You may obtain a copy of the License at
+//
+//     https://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software distributed under the License
+// is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express
+// or implied. See the License for the specific language governing permissions and limitations under
+// the License.
+
+//! Execution helpers for `TickCircuit`s containing inline channel gates.
+//!
+//! These routines consume the concrete channel operations inserted into a
+//! `TickCircuit`, rather than adding a separate event-driven noise model at
+//! execution time.
+
+use pecos_core::gate_type::GateType;
+use pecos_core::{Angle64, ChannelExpr, Gate, Pauli, PauliOperator, PauliString, QubitId};
+use pecos_quantum::TickCircuit;
+use pecos_random::{PecosRng, RngExt};
+use pecos_simulators::{ArbitraryRotationGateable, CliffordGateable, DensityMatrix, SparseStab};
+use thiserror::Error;
+
+const PROBABILITY_SUM_TOLERANCE: f64 = 1e-9;
+
+/// Error returned while executing a circuit with inline channel gates.
+#[derive(Debug, Error)]
+pub enum InlineChannelError {
+    /// A `Channel` gate had no channel payload.
+    #[error("Channel gate missing channel payload")]
+    MissingChannelPayload,
+
+    /// A two-qubit gate was given an odd number of qubits.
+    #[error("{gate_type:?} requires an even number of qubits, got {qubit_count}")]
+    InvalidPairArity {
+        gate_type: GateType,
+        qubit_count: usize,
+    },
+
+    /// A parameterized gate was missing one of its angle parameters.
+    #[error("{gate_type:?} is missing angle parameter {index}")]
+    MissingAngle { gate_type: GateType, index: usize },
+
+    /// Density-matrix execution does not support this gate on the inline path.
+    #[error("DensityMatrix inline-channel path does not support gate {gate_type:?}")]
+    UnsupportedDensityMatrixGate { gate_type: GateType },
+
+    /// Stabilizer execution does not support this gate on the inline path.
+    #[error("stabilizer inline-channel path does not support non-Clifford gate {gate_type:?}")]
+    UnsupportedStabilizerGate { gate_type: GateType },
+
+    /// The stabilizer backend was asked to sample a non-Pauli channel.
+    #[error("stabilizer backend can only sample inline Pauli channels")]
+    NonPauliChannel,
+
+    /// The stabilizer backend was asked to sample a channel that is not a Pauli mixed-unitary.
+    #[error("stabilizer backend can only sample inline Pauli mixed-unitary channels")]
+    NonPauliMixedUnitaryChannel,
+
+    /// A mixed-unitary channel had invalid probabilities.
+    #[error("channel probabilities must be non-negative and sum to 1")]
+    InvalidProbabilities,
+
+    /// Probability validation passed, but random sampling still missed every term.
+    #[error("Pauli channel sampling failed after probability validation")]
+    SamplingMiss,
+
+    /// `DensityMatrix` rejected a channel expression.
+    #[error("channel application failed: {0}")]
+    ChannelApplication(String),
+}
+
+/// Return the number of qubits needed to simulate the circuit.
+#[must_use]
+pub fn tick_circuit_num_qubits(circuit: &TickCircuit) -> usize {
+    circuit
+        .all_qubits()
+        .into_iter()
+        .map(|q| q.index() + 1)
+        .max()
+        .unwrap_or(0)
+}
+
+/// Execute an inline-channel `TickCircuit` using a density matrix simulator.
+///
+/// This path supports arbitrary channel expressions accepted by
+/// [`DensityMatrix::apply_channel_expr`], and also supports the standard
+/// unitary gates implemented by the density matrix simulator.
+///
+/// # Errors
+///
+/// Returns [`InlineChannelError`] when a channel payload is malformed, when a
+/// gate has invalid arity or missing parameters, or when the density matrix
+/// backend does not support a gate/channel.
+pub fn run_inline_channels_density_matrix(
+    circuit: &TickCircuit,
+    shots: usize,
+    seed: u64,
+) -> Result<Vec<Vec<u8>>, InlineChannelError> {
+    let num_qubits = tick_circuit_num_qubits(circuit);
+    let mut rows = Vec::with_capacity(shots);
+
+    for shot in 0..shots {
+        let shot_seed = seed.wrapping_add(shot as u64);
+        let mut sim = DensityMatrix::with_seed(num_qubits, shot_seed);
+        let mut row = Vec::new();
+
+        for tick in circuit.ticks() {
+            for gate in tick.iter_gate_batches() {
+                row.extend(apply_gate_to_density_matrix(&mut sim, gate.as_gate())?);
+            }
+        }
+
+        rows.push(row);
+    }
+
+    Ok(rows)
+}
+
+/// Execute an inline-channel `TickCircuit` using a stabilizer simulator.
+///
+/// This path supports Clifford gates plus channel gates whose payloads are
+/// Pauli or Pauli mixed-unitary channels. Non-Pauli channels are rejected
+/// explicitly.
+///
+/// # Errors
+///
+/// Returns [`InlineChannelError`] for unsupported gates, malformed channel
+/// probabilities, non-Pauli channels, invalid arity, or missing gate
+/// parameters.
+pub fn run_inline_pauli_channels_stabilizer(
+    circuit: &TickCircuit,
+    shots: usize,
+    seed: u64,
+) -> Result<Vec<Vec<u8>>, InlineChannelError> {
+    let num_qubits = tick_circuit_num_qubits(circuit);
+    let mut rows = Vec::with_capacity(shots);
+
+    for shot in 0..shots {
+        let shot_seed = seed.wrapping_add(shot as u64);
+        let mut sim = SparseStab::with_seed(num_qubits, shot_seed);
+        let mut rng = PecosRng::seed_from_u64(shot_seed ^ 0x5eed_5eed_5eed_5eed);
+        let mut row = Vec::new();
+
+        for tick in circuit.ticks() {
+            for gate in tick.iter_gate_batches() {
+                row.extend(apply_gate_to_stabilizer_with_pauli_channels(
+                    &mut sim,
+                    gate.as_gate(),
+                    &mut rng,
+                )?);
+            }
+        }
+
+        rows.push(row);
+    }
+
+    Ok(rows)
+}
+
+fn qubit_pairs(
+    qubits: &[QubitId],
+    gate_type: GateType,
+) -> Result<Vec<(QubitId, QubitId)>, InlineChannelError> {
+    if !qubits.len().is_multiple_of(2) {
+        return Err(InlineChannelError::InvalidPairArity {
+            gate_type,
+            qubit_count: qubits.len(),
+        });
+    }
+    Ok(qubits
+        .chunks_exact(2)
+        .map(|pair| (pair[0], pair[1]))
+        .collect())
+}
+
+fn gate_angle(gate: &Gate, index: usize) -> Result<Angle64, InlineChannelError> {
+    gate.angles
+        .get(index)
+        .copied()
+        .ok_or(InlineChannelError::MissingAngle {
+            gate_type: gate.gate_type,
+            index,
+        })
+}
+
+fn apply_gate_to_density_matrix(
+    sim: &mut DensityMatrix,
+    gate: &Gate,
+) -> Result<Vec<u8>, InlineChannelError> {
+    let qubits = gate.qubits.as_slice();
+    match gate.gate_type {
+        GateType::Channel => {
+            let channel = gate
+                .channel_expr()
+                .ok_or(InlineChannelError::MissingChannelPayload)?;
+            sim.apply_channel_expr(channel)
+                .map_err(|e| InlineChannelError::ChannelApplication(e.to_string()))?;
+            Ok(Vec::new())
+        }
+        GateType::PZ | GateType::QAlloc => {
+            sim.pz(qubits);
+            Ok(Vec::new())
+        }
+        GateType::MZ | GateType::MeasureFree | GateType::MeasureLeaked => Ok(sim
+            .mz(qubits)
+            .into_iter()
+            .map(|r| u8::from(r.outcome))
+            .collect()),
+        GateType::I | GateType::Idle => Ok(Vec::new()),
+        GateType::X => {
+            sim.x(qubits);
+            Ok(Vec::new())
+        }
+        GateType::Y => {
+            sim.y(qubits);
+            Ok(Vec::new())
+        }
+        GateType::Z => {
+            sim.z(qubits);
+            Ok(Vec::new())
+        }
+        GateType::H => {
+            sim.h(qubits);
+            Ok(Vec::new())
+        }
+        GateType::F => {
+            sim.f(qubits);
+            Ok(Vec::new())
+        }
+        GateType::Fdg => {
+            sim.fdg(qubits);
+            Ok(Vec::new())
+        }
+        GateType::SX => {
+            sim.sx(qubits);
+            Ok(Vec::new())
+        }
+        GateType::SXdg => {
+            sim.sxdg(qubits);
+            Ok(Vec::new())
+        }
+        GateType::SY => {
+            sim.sy(qubits);
+            Ok(Vec::new())
+        }
+        GateType::SYdg => {
+            sim.sydg(qubits);
+            Ok(Vec::new())
+        }
+        GateType::SZ => {
+            sim.sz(qubits);
+            Ok(Vec::new())
+        }
+        GateType::SZdg => {
+            sim.szdg(qubits);
+            Ok(Vec::new())
+        }
+        GateType::CX => {
+            sim.cx(&qubit_pairs(qubits, gate.gate_type)?);
+            Ok(Vec::new())
+        }
+        GateType::CY => {
+            sim.cy(&qubit_pairs(qubits, gate.gate_type)?);
+            Ok(Vec::new())
+        }
+        GateType::CZ => {
+            sim.cz(&qubit_pairs(qubits, gate.gate_type)?);
+            Ok(Vec::new())
+        }
+        GateType::SXX => {
+            sim.sxx(&qubit_pairs(qubits, gate.gate_type)?);
+            Ok(Vec::new())
+        }
+        GateType::SXXdg => {
+            sim.sxxdg(&qubit_pairs(qubits, gate.gate_type)?);
+            Ok(Vec::new())
+        }
+        GateType::SYY => {
+            sim.syy(&qubit_pairs(qubits, gate.gate_type)?);
+            Ok(Vec::new())
+        }
+        GateType::SYYdg => {
+            sim.syydg(&qubit_pairs(qubits, gate.gate_type)?);
+            Ok(Vec::new())
+        }
+        GateType::SZZ => {
+            sim.szz(&qubit_pairs(qubits, gate.gate_type)?);
+            Ok(Vec::new())
+        }
+        GateType::SZZdg => {
+            sim.szzdg(&qubit_pairs(qubits, gate.gate_type)?);
+            Ok(Vec::new())
+        }
+        GateType::SWAP => {
+            sim.swap(&qubit_pairs(qubits, gate.gate_type)?);
+            Ok(Vec::new())
+        }
+        GateType::T => {
+            sim.t(qubits);
+            Ok(Vec::new())
+        }
+        GateType::Tdg => {
+            sim.tdg(qubits);
+            Ok(Vec::new())
+        }
+        GateType::RX => {
+            sim.rx(gate_angle(gate, 0)?, qubits);
+            Ok(Vec::new())
+        }
+        GateType::RY => {
+            sim.ry(gate_angle(gate, 0)?, qubits);
+            Ok(Vec::new())
+        }
+        GateType::RZ => {
+            sim.rz(gate_angle(gate, 0)?, qubits);
+            Ok(Vec::new())
+        }
+        GateType::U => {
+            sim.u(
+                gate_angle(gate, 0)?,
+                gate_angle(gate, 1)?,
+                gate_angle(gate, 2)?,
+                qubits,
+            );
+            Ok(Vec::new())
+        }
+        GateType::R1XY => {
+            sim.r1xy(gate_angle(gate, 0)?, gate_angle(gate, 1)?, qubits);
+            Ok(Vec::new())
+        }
+        GateType::RXX => {
+            sim.rxx(gate_angle(gate, 0)?, &qubit_pairs(qubits, gate.gate_type)?);
+            Ok(Vec::new())
+        }
+        GateType::RYY => {
+            sim.ryy(gate_angle(gate, 0)?, &qubit_pairs(qubits, gate.gate_type)?);
+            Ok(Vec::new())
+        }
+        GateType::RZZ => {
+            sim.rzz(gate_angle(gate, 0)?, &qubit_pairs(qubits, gate.gate_type)?);
+            Ok(Vec::new())
+        }
+        gate_type => Err(InlineChannelError::UnsupportedDensityMatrixGate { gate_type }),
+    }
+}
+
+fn apply_pauli_string_to_stabilizer(sim: &mut SparseStab, pauli: &PauliString) {
+    for (p, q) in pauli.paulis() {
+        match p {
+            Pauli::I => {}
+            Pauli::X => {
+                sim.x(&[*q]);
+            }
+            Pauli::Y => {
+                sim.y(&[*q]);
+            }
+            Pauli::Z => {
+                sim.z(&[*q]);
+            }
+        }
+    }
+}
+
+fn sample_pauli_channel(
+    channel: &ChannelExpr,
+    rng: &mut PecosRng,
+) -> Result<Option<PauliString>, InlineChannelError> {
+    let ops = match channel {
+        ChannelExpr::Unitary(unitary) => {
+            let pauli = unitary
+                .clone()
+                .try_to_pauli_string()
+                .ok_or(InlineChannelError::NonPauliChannel)?;
+            return Ok((pauli.weight() > 0).then_some(pauli));
+        }
+        ChannelExpr::MixedUnitary(ops) => ops,
+        _ => return Err(InlineChannelError::NonPauliMixedUnitaryChannel),
+    };
+
+    let total: f64 = ops.iter().map(|(p, _)| *p).sum();
+    if (total - 1.0).abs() > PROBABILITY_SUM_TOLERANCE || ops.iter().any(|(p, _)| *p < 0.0) {
+        return Err(InlineChannelError::InvalidProbabilities);
+    }
+
+    let mut threshold = rng.random::<f64>() * total;
+    for (prob, unitary) in ops {
+        if threshold < *prob {
+            let pauli = unitary
+                .clone()
+                .try_to_pauli_string()
+                .ok_or(InlineChannelError::NonPauliChannel)?;
+            return Ok((pauli.weight() > 0).then_some(pauli));
+        }
+        threshold -= *prob;
+    }
+
+    Err(InlineChannelError::SamplingMiss)
+}
+
+fn apply_gate_to_stabilizer_with_pauli_channels(
+    sim: &mut SparseStab,
+    gate: &Gate,
+    rng: &mut PecosRng,
+) -> Result<Vec<u8>, InlineChannelError> {
+    let qubits = gate.qubits.as_slice();
+    match gate.gate_type {
+        GateType::Channel => {
+            let channel = gate
+                .channel_expr()
+                .ok_or(InlineChannelError::MissingChannelPayload)?;
+            if let Some(pauli) = sample_pauli_channel(channel, rng)? {
+                apply_pauli_string_to_stabilizer(sim, &pauli);
+            }
+            Ok(Vec::new())
+        }
+        GateType::PZ | GateType::QAlloc => {
+            sim.pz(qubits);
+            Ok(Vec::new())
+        }
+        GateType::MZ | GateType::MeasureFree | GateType::MeasureLeaked => Ok(sim
+            .mz(qubits)
+            .into_iter()
+            .map(|r| u8::from(r.outcome))
+            .collect()),
+        GateType::I | GateType::Idle => Ok(Vec::new()),
+        GateType::X => {
+            sim.x(qubits);
+            Ok(Vec::new())
+        }
+        GateType::Y => {
+            sim.y(qubits);
+            Ok(Vec::new())
+        }
+        GateType::Z => {
+            sim.z(qubits);
+            Ok(Vec::new())
+        }
+        GateType::H => {
+            sim.h(qubits);
+            Ok(Vec::new())
+        }
+        GateType::F => {
+            sim.f(qubits);
+            Ok(Vec::new())
+        }
+        GateType::Fdg => {
+            sim.fdg(qubits);
+            Ok(Vec::new())
+        }
+        GateType::SX => {
+            sim.sx(qubits);
+            Ok(Vec::new())
+        }
+        GateType::SXdg => {
+            sim.sxdg(qubits);
+            Ok(Vec::new())
+        }
+        GateType::SY => {
+            sim.sy(qubits);
+            Ok(Vec::new())
+        }
+        GateType::SYdg => {
+            sim.sydg(qubits);
+            Ok(Vec::new())
+        }
+        GateType::SZ => {
+            sim.sz(qubits);
+            Ok(Vec::new())
+        }
+        GateType::SZdg => {
+            sim.szdg(qubits);
+            Ok(Vec::new())
+        }
+        GateType::CX => {
+            sim.cx(&qubit_pairs(qubits, gate.gate_type)?);
+            Ok(Vec::new())
+        }
+        GateType::CY => {
+            sim.cy(&qubit_pairs(qubits, gate.gate_type)?);
+            Ok(Vec::new())
+        }
+        GateType::CZ => {
+            sim.cz(&qubit_pairs(qubits, gate.gate_type)?);
+            Ok(Vec::new())
+        }
+        GateType::SXX => {
+            sim.sxx(&qubit_pairs(qubits, gate.gate_type)?);
+            Ok(Vec::new())
+        }
+        GateType::SXXdg => {
+            sim.sxxdg(&qubit_pairs(qubits, gate.gate_type)?);
+            Ok(Vec::new())
+        }
+        GateType::SYY => {
+            sim.syy(&qubit_pairs(qubits, gate.gate_type)?);
+            Ok(Vec::new())
+        }
+        GateType::SYYdg => {
+            sim.syydg(&qubit_pairs(qubits, gate.gate_type)?);
+            Ok(Vec::new())
+        }
+        GateType::SZZ => {
+            sim.szz(&qubit_pairs(qubits, gate.gate_type)?);
+            Ok(Vec::new())
+        }
+        GateType::SZZdg => {
+            sim.szzdg(&qubit_pairs(qubits, gate.gate_type)?);
+            Ok(Vec::new())
+        }
+        GateType::SWAP => {
+            sim.swap(&qubit_pairs(qubits, gate.gate_type)?);
+            Ok(Vec::new())
+        }
+        gate_type => Err(InlineChannelError::UnsupportedStabilizerGate { gate_type }),
+    }
+}
+
+#[cfg(test)]
+mod tests {
+    use super::*;
+
+    #[test]
+    fn density_matrix_inline_bit_flip_channel_flips_measurement() {
+        let mut circuit = TickCircuit::new();
+        circuit.tick().pz(&[0]);
+        circuit.tick().channel(pecos_core::channel::BitFlip(1.0, 0));
+        circuit.tick().mz(&[0]);
+
+        let rows = run_inline_channels_density_matrix(&circuit, 3, 123).unwrap();
+
+        assert_eq!(rows, vec![vec![1], vec![1], vec![1]]);
+    }
+
+    #[test]
+    fn stabilizer_inline_pauli_channel_flips_measurement() {
+        let mut circuit = TickCircuit::new();
+        circuit.tick().pz(&[0]);
+        circuit.tick().channel(pecos_core::channel::BitFlip(1.0, 0));
+        circuit.tick().mz(&[0]);
+
+        let rows = run_inline_pauli_channels_stabilizer(&circuit, 3, 123).unwrap();
+
+        assert_eq!(rows, vec![vec![1], vec![1], vec![1]]);
+    }
+
+    #[test]
+    fn stabilizer_inline_channel_rejects_non_clifford_gate() {
+        let mut circuit = TickCircuit::new();
+        circuit.tick().pz(&[0]);
+        circuit.tick().t(&[0]);
+        circuit.tick().channel(pecos_core::channel::BitFlip(0.5, 0));
+        circuit.tick().mz(&[0]);
+
+        let err = run_inline_pauli_channels_stabilizer(&circuit, 1, 123).unwrap_err();
+
+        assert!(matches!(
+            err,
+            InlineChannelError::UnsupportedStabilizerGate {
+                gate_type: GateType::T
+            }
+        ));
+    }
+
+    #[test]
+    fn stabilizer_inline_channel_rejects_non_pauli_channel() {
+        let mut circuit = TickCircuit::new();
+        circuit.tick().pz(&[0]);
+        circuit
+            .tick()
+            .channel(pecos_core::channel::AmplitudeDamping(0.5, 0));
+        circuit.tick().mz(&[0]);
+
+        let err = run_inline_pauli_channels_stabilizer(&circuit, 1, 123).unwrap_err();
+
+        assert!(matches!(
+            err,
+            InlineChannelError::NonPauliMixedUnitaryChannel
+        ));
+    }
+}
diff --git a/exp/pecos-neo/src/lib.rs b/exp/pecos-neo/src/lib.rs
index 7c309e8d4..e9296bdb9 100644
--- a/exp/pecos-neo/src/lib.rs
+++ b/exp/pecos-neo/src/lib.rs
@@ -149,6 +149,7 @@ pub mod command;
 pub mod ecs;
 pub mod engines;
 pub mod extensible;
+pub mod inline_channel;
 pub mod noise;
 pub mod outcome;
 pub mod program;
diff --git a/exp/pecos-neo/src/noise/single_qubit.rs b/exp/pecos-neo/src/noise/single_qubit.rs
index 109cb8a58..1cfa6342c 100644
--- a/exp/pecos-neo/src/noise/single_qubit.rs
+++ b/exp/pecos-neo/src/noise/single_qubit.rs
@@ -217,10 +217,12 @@ impl NoiseChannel for SingleQubitChannel {
         if self.error_probability <= 0.0 {
             return false;
         }
-        // Respond to BeforeGate for leaked qubit handling and AfterGate for noise
+        // Respond only to unitary single-qubit gates.
+        // Preparations (PZ, QAlloc) and measurements (MZ) have their own
+        // noise channels and should not get gate depolarizing noise.
         match event {
             NoiseEvent::BeforeGate { gate_type, .. } | NoiseEvent::AfterGate { gate_type, .. } => {
-                gate_type.is_single_qubit()
+                gate_type.is_single_qubit() && gate_type.is_unitary_gate()
             }
             _ => false,
         }
@@ -272,7 +274,7 @@ impl NoiseChannel for SingleQubitChannel {
             NoiseEvent::BeforeGate {
                 gate_type, qubits, ..
             } => {
-                if !gate_type.is_single_qubit() {
+                if !gate_type.is_single_qubit() || !gate_type.is_unitary_gate() {
                     return None;
                 }
                 // Skip noise for noiseless gates (but still check leakage)
@@ -284,7 +286,7 @@ impl NoiseChannel for SingleQubitChannel {
             NoiseEvent::AfterGate {
                 gate_type, qubits, ..
             } => {
-                if !gate_type.is_single_qubit() {
+                if !gate_type.is_single_qubit() || !gate_type.is_unitary_gate() {
                     return None;
                 }
                 // Skip noise for noiseless gates
diff --git a/exp/pecos-neo/src/noise/two_qubit.rs b/exp/pecos-neo/src/noise/two_qubit.rs
index bbfdeec0e..c5770993c 100644
--- a/exp/pecos-neo/src/noise/two_qubit.rs
+++ b/exp/pecos-neo/src/noise/two_qubit.rs
@@ -436,9 +436,12 @@ impl NoiseChannel for TwoQubitChannel {
         if self.error_probability <= 0.0 {
             return false;
         }
+        // Only respond to unitary two-qubit gates.
+        // Non-unitary two-qubit operations (if any) should not get
+        // gate depolarizing noise.
         match event {
             NoiseEvent::BeforeGate { gate_type, .. } | NoiseEvent::AfterGate { gate_type, .. } => {
-                gate_type.is_two_qubit()
+                gate_type.is_two_qubit() && gate_type.is_unitary_gate()
             }
             _ => false,
         }
@@ -493,7 +496,7 @@ impl NoiseChannel for TwoQubitChannel {
             NoiseEvent::BeforeGate {
                 gate_type, qubits, ..
             } => {
-                if !gate_type.is_two_qubit() {
+                if !gate_type.is_two_qubit() || !gate_type.is_unitary_gate() {
                     return None;
                 }
                 if ctx.is_noiseless(*gate_type) {
@@ -507,7 +510,7 @@ impl NoiseChannel for TwoQubitChannel {
                 angles,
                 ..
             } => {
-                if !gate_type.is_two_qubit() {
+                if !gate_type.is_two_qubit() || !gate_type.is_unitary_gate() {
                     return None;
                 }
                 if ctx.is_noiseless(*gate_type) {
diff --git a/exp/pecos-neo/src/runner.rs b/exp/pecos-neo/src/runner.rs
index 25d679e07..08094abfe 100644
--- a/exp/pecos-neo/src/runner.rs
+++ b/exp/pecos-neo/src/runner.rs
@@ -1443,6 +1443,14 @@ impl<S: CliffordGateable> CircuitRunner<S> {
                 sim.h(qubits);
                 true
             }
+            GateType::F => {
+                sim.f(qubits);
+                true
+            }
+            GateType::Fdg => {
+                sim.fdg(qubits);
+                true
+            }
             GateType::SX => {
                 sim.sx(qubits);
                 true
@@ -1492,6 +1500,26 @@ impl<S: CliffordGateable> CircuitRunner<S> {
                 sim.szzdg(&pairs);
                 true
             }
+            GateType::SXX => {
+                let pairs = flat_to_pairs(qubits);
+                sim.sxx(&pairs);
+                true
+            }
+            GateType::SXXdg => {
+                let pairs = flat_to_pairs(qubits);
+                sim.sxxdg(&pairs);
+                true
+            }
+            GateType::SYY => {
+                let pairs = flat_to_pairs(qubits);
+                sim.syy(&pairs);
+                true
+            }
+            GateType::SYYdg => {
+                let pairs = flat_to_pairs(qubits);
+                sim.syydg(&pairs);
+                true
+            }
             GateType::SWAP => {
                 let pairs = flat_to_pairs(qubits);
                 sim.swap(&pairs);
@@ -1566,9 +1594,9 @@ impl<S: CliffordGateable> CircuitRunner<S> {
 
         // Perform measurement
         let results = sim.mz(&[qubit]);
-        let meas_result = results.first();
-        let outcome = meas_result.is_some_and(|r| r.outcome);
-        let is_deterministic = meas_result.is_none_or(|r| r.is_deterministic);
+        let meas_id = results.first();
+        let outcome = meas_id.is_some_and(|r| r.outcome);
+        let is_deterministic = meas_id.is_none_or(|r| r.is_deterministic);
 
         // Store result for conditionals
         if let Some(slot) = self.results.get_mut(result_id.0 as usize) {
@@ -2062,7 +2090,7 @@ impl<S: CliffordGateable> CircuitRunner<S> {
 
             NoiseResponse::InjectGates(gates) => {
                 for gate in gates.iter() {
-                    Self::execute_noise_gate(sim, gate);
+                    self.execute_noise_gate(sim, gate);
                 }
             }
 
@@ -2092,8 +2120,11 @@ impl<S: CliffordGateable> CircuitRunner<S> {
         }
     }
 
-    /// Execute a noise gate (injected Pauli error).
-    fn execute_noise_gate(sim: &mut S, gate: &GateCommand) {
+    /// Execute a noise gate (injected error).
+    ///
+    /// Handles Pauli gates directly. For non-Pauli gates (rotations, Cliffords),
+    /// delegates to the rotation executor if available, otherwise skips.
+    fn execute_noise_gate(&self, sim: &mut S, gate: &GateCommand) {
         let qubits = gate.qubits.as_slice();
         match gate.gate_type {
             GateType::X => {
@@ -2105,7 +2136,81 @@ impl<S: CliffordGateable> CircuitRunner<S> {
             GateType::Z => {
                 sim.z(qubits);
             }
-            _ => {}
+            GateType::H => {
+                sim.h(qubits);
+            }
+            GateType::F => {
+                sim.f(qubits);
+            }
+            GateType::Fdg => {
+                sim.fdg(qubits);
+            }
+            GateType::SX => {
+                sim.sx(qubits);
+            }
+            GateType::SXdg => {
+                sim.sxdg(qubits);
+            }
+            GateType::SY => {
+                sim.sy(qubits);
+            }
+            GateType::SYdg => {
+                sim.sydg(qubits);
+            }
+            GateType::SZ => {
+                sim.sz(qubits);
+            }
+            GateType::SZdg => {
+                sim.szdg(qubits);
+            }
+            GateType::CX => {
+                let pairs: Vec<_> = qubits.chunks(2).map(|c| (c[0], c[1])).collect();
+                sim.cx(&pairs);
+            }
+            GateType::CY => {
+                let pairs: Vec<_> = qubits.chunks(2).map(|c| (c[0], c[1])).collect();
+                sim.cy(&pairs);
+            }
+            GateType::CZ => {
+                let pairs: Vec<_> = qubits.chunks(2).map(|c| (c[0], c[1])).collect();
+                sim.cz(&pairs);
+            }
+            GateType::SXX => {
+                let pairs: Vec<_> = qubits.chunks(2).map(|c| (c[0], c[1])).collect();
+                sim.sxx(&pairs);
+            }
+            GateType::SXXdg => {
+                let pairs: Vec<_> = qubits.chunks(2).map(|c| (c[0], c[1])).collect();
+                sim.sxxdg(&pairs);
+            }
+            GateType::SYY => {
+                let pairs: Vec<_> = qubits.chunks(2).map(|c| (c[0], c[1])).collect();
+                sim.syy(&pairs);
+            }
+            GateType::SYYdg => {
+                let pairs: Vec<_> = qubits.chunks(2).map(|c| (c[0], c[1])).collect();
+                sim.syydg(&pairs);
+            }
+            GateType::SZZ => {
+                let pairs: Vec<_> = qubits.chunks(2).map(|c| (c[0], c[1])).collect();
+                sim.szz(&pairs);
+            }
+            GateType::SZZdg => {
+                let pairs: Vec<_> = qubits.chunks(2).map(|c| (c[0], c[1])).collect();
+                sim.szzdg(&pairs);
+            }
+            GateType::SWAP => {
+                let pairs: Vec<_> = qubits.chunks(2).map(|c| (c[0], c[1])).collect();
+                sim.swap(&pairs);
+            }
+            // Non-Clifford gates: delegate to rotation executor
+            other => {
+                if let Some(executor) = self.rotation_executor {
+                    executor(sim, GateId::from(other), gate.angles.as_slice(), qubits);
+                }
+                // If no rotation executor, silently skip (noise channel injected
+                // a gate the simulator can't handle).
+            }
         }
     }
 }
@@ -2292,6 +2397,9 @@ mod tests {
     use crate::command::CommandBuilder;
     use crate::extensible::{GateCategory, GateSpec, OpBuilder, gates};
     use crate::noise::single_qubit::SingleQubitChannel;
+    use num_complex::Complex64;
+    use pecos_core::clifford::Clifford;
+    use pecos_quantum::unitary_matrix::{ToMatrix, UnitaryMatrix};
     use pecos_simulators::{SparseStab, StateVec};
 
     // --- Basic execution tests ---
@@ -2934,4 +3042,223 @@ mod tests {
         let outcomes = runner.take_outcomes();
         assert_eq!(outcomes.len(), 1);
     }
+
+    #[test]
+    fn test_apply_gate_standard_clifford_inverse_sequences() {
+        let mut state = SparseStab::new(2);
+        let mut runner = CircuitRunner::<SparseStab>::new().with_seed(42);
+
+        runner
+            .apply_gate(&mut state, GateType::PZ, &[QubitId(0), QubitId(1)], &[])
+            .unwrap();
+        runner
+            .apply_gate(&mut state, GateType::F, &[QubitId(0)], &[])
+            .unwrap();
+        runner
+            .apply_gate(&mut state, GateType::Fdg, &[QubitId(0)], &[])
+            .unwrap();
+        runner
+            .apply_gate(&mut state, GateType::SXX, &[QubitId(0), QubitId(1)], &[])
+            .unwrap();
+        runner
+            .apply_gate(&mut state, GateType::SXXdg, &[QubitId(0), QubitId(1)], &[])
+            .unwrap();
+        runner
+            .apply_gate(&mut state, GateType::MZ, &[QubitId(0), QubitId(1)], &[])
+            .unwrap();
+
+        let outcomes = runner.take_outcomes();
+        assert_eq!(outcomes.len(), 2);
+        for outcome in outcomes.iter() {
+            assert!(
+                !outcome.outcome,
+                "inverse Clifford sequence should preserve |0>"
+            );
+            assert!(outcome.is_deterministic);
+        }
+    }
+
+    #[test]
+    fn test_apply_gate_standard_clifford_inverse_table() {
+        let cases = [
+            (GateType::I, GateType::I, vec![QubitId(0)]),
+            (GateType::X, GateType::X, vec![QubitId(0)]),
+            (GateType::Y, GateType::Y, vec![QubitId(0)]),
+            (GateType::Z, GateType::Z, vec![QubitId(0)]),
+            (GateType::H, GateType::H, vec![QubitId(0)]),
+            (GateType::F, GateType::Fdg, vec![QubitId(0)]),
+            (GateType::Fdg, GateType::F, vec![QubitId(0)]),
+            (GateType::SX, GateType::SXdg, vec![QubitId(0)]),
+            (GateType::SXdg, GateType::SX, vec![QubitId(0)]),
+            (GateType::SY, GateType::SYdg, vec![QubitId(0)]),
+            (GateType::SYdg, GateType::SY, vec![QubitId(0)]),
+            (GateType::SZ, GateType::SZdg, vec![QubitId(0)]),
+            (GateType::SZdg, GateType::SZ, vec![QubitId(0)]),
+            (GateType::CX, GateType::CX, vec![QubitId(0), QubitId(1)]),
+            (GateType::CY, GateType::CY, vec![QubitId(0), QubitId(1)]),
+            (GateType::CZ, GateType::CZ, vec![QubitId(0), QubitId(1)]),
+            (GateType::SXX, GateType::SXXdg, vec![QubitId(0), QubitId(1)]),
+            (GateType::SXXdg, GateType::SXX, vec![QubitId(0), QubitId(1)]),
+            (GateType::SYY, GateType::SYYdg, vec![QubitId(0), QubitId(1)]),
+            (GateType::SYYdg, GateType::SYY, vec![QubitId(0), QubitId(1)]),
+            (GateType::SZZ, GateType::SZZdg, vec![QubitId(0), QubitId(1)]),
+            (GateType::SZZdg, GateType::SZZ, vec![QubitId(0), QubitId(1)]),
+            (GateType::SWAP, GateType::SWAP, vec![QubitId(0), QubitId(1)]),
+        ];
+
+        for (gate, inverse, qubits) in cases {
+            let mut state = SparseStab::new(2);
+            let mut runner = CircuitRunner::<SparseStab>::new().with_seed(42);
+
+            runner
+                .apply_gate(&mut state, GateType::PZ, &[QubitId(0), QubitId(1)], &[])
+                .unwrap();
+            runner.apply_gate(&mut state, gate, &qubits, &[]).unwrap();
+            runner
+                .apply_gate(&mut state, inverse, &qubits, &[])
+                .unwrap();
+            runner
+                .apply_gate(&mut state, GateType::MZ, &[QubitId(0), QubitId(1)], &[])
+                .unwrap();
+
+            let outcomes = runner.take_outcomes();
+            assert_eq!(outcomes.len(), 2, "{gate:?} then {inverse:?}");
+            for outcome in outcomes.iter() {
+                assert!(
+                    !outcome.outcome,
+                    "{gate:?} then {inverse:?} should preserve |00>"
+                );
+                assert!(outcome.is_deterministic);
+            }
+        }
+    }
+
+    fn matrix_times_state(matrix: &UnitaryMatrix, state: &[Complex64]) -> Vec<Complex64> {
+        (0..matrix.nrows())
+            .map(|row| {
+                let mut value = Complex64::new(0.0, 0.0);
+                for col in 0..matrix.ncols() {
+                    value += matrix[(row, col)] * state[col];
+                }
+                value
+            })
+            .collect()
+    }
+
+    fn assert_states_close(actual: &[Complex64], expected: &[Complex64], label: &str) {
+        const TOLERANCE: f64 = 1e-10;
+        assert_eq!(actual.len(), expected.len(), "{label}");
+
+        let phase = actual
+            .iter()
+            .zip(expected.iter())
+            .find(|(a, e)| a.norm() > TOLERANCE || e.norm() > TOLERANCE)
+            .map_or(Complex64::new(1.0, 0.0), |(a, e)| {
+                assert!(
+                    a.norm() > TOLERANCE && e.norm() > TOLERANCE,
+                    "{label}: support differs, actual={a:?}, expected={e:?}"
+                );
+                *a / *e
+            });
+
+        for (idx, (a, e)) in actual.iter().zip(expected.iter()).enumerate() {
+            let diff = (*a - phase * *e).norm();
+            assert!(
+                diff < TOLERANCE,
+                "{label}: amplitude {idx} differs up to global phase {phase:?}, actual={a:?}, expected={e:?}, diff={diff}"
+            );
+        }
+    }
+
+    fn prepare_matrix_test_state(prep_index: usize) -> StateVec {
+        let mut state = StateVec::new(2);
+        match prep_index {
+            0 => {}
+            1 => {
+                state.x(&[QubitId(0)]);
+            }
+            2 => {
+                state.x(&[QubitId(1)]);
+            }
+            3 => {
+                state.h(&[QubitId(0)]);
+                state.cx(&[(QubitId(0), QubitId(1))]);
+            }
+            4 => {
+                state.sx(&[QubitId(0)]);
+                state.h(&[QubitId(1)]);
+            }
+            _ => unreachable!(),
+        }
+        state
+    }
+
+    #[test]
+    fn test_apply_gate_standard_cliffords_match_unitary_matrices() {
+        let one_qubit_cases = [
+            (GateType::I, Clifford::I),
+            (GateType::X, Clifford::X),
+            (GateType::Y, Clifford::Y),
+            (GateType::Z, Clifford::Z),
+            (GateType::H, Clifford::H),
+            (GateType::F, Clifford::F),
+            (GateType::Fdg, Clifford::Fdg),
+            (GateType::SX, Clifford::SX),
+            (GateType::SXdg, Clifford::SXdg),
+            (GateType::SY, Clifford::SY),
+            (GateType::SYdg, Clifford::SYdg),
+            (GateType::SZ, Clifford::SZ),
+            (GateType::SZdg, Clifford::SZdg),
+        ];
+        let two_qubit_cases = [
+            (GateType::CX, Clifford::CX),
+            (GateType::CY, Clifford::CY),
+            (GateType::CZ, Clifford::CZ),
+            (GateType::SXX, Clifford::SXX),
+            (GateType::SXXdg, Clifford::SXXdg),
+            (GateType::SYY, Clifford::SYY),
+            (GateType::SYYdg, Clifford::SYYdg),
+            (GateType::SZZ, Clifford::SZZ),
+            (GateType::SZZdg, Clifford::SZZdg),
+            (GateType::SWAP, Clifford::SWAP),
+        ];
+
+        for prep_index in 0..5 {
+            for (gate_type, clifford) in one_qubit_cases {
+                let mut state = prepare_matrix_test_state(prep_index);
+                let input = state.state();
+                let expected = matrix_times_state(&clifford.on_qubit(1).to_matrix(), &input);
+
+                let mut runner = CircuitRunner::<StateVec>::new().with_seed(42);
+                runner
+                    .apply_gate(&mut state, gate_type, &[QubitId(1)], &[])
+                    .unwrap();
+                let actual = state.state();
+
+                assert_states_close(
+                    &actual,
+                    &expected,
+                    &format!("{gate_type:?} on prep {prep_index}"),
+                );
+            }
+
+            for (gate_type, clifford) in two_qubit_cases {
+                let mut state = prepare_matrix_test_state(prep_index);
+                let input = state.state();
+                let expected = matrix_times_state(&clifford.on_qubits(0, 1).to_matrix(), &input);
+
+                let mut runner = CircuitRunner::<StateVec>::new().with_seed(42);
+                runner
+                    .apply_gate(&mut state, gate_type, &[QubitId(0), QubitId(1)], &[])
+                    .unwrap();
+                let actual = state.state();
+
+                assert_states_close(
+                    &actual,
+                    &expected,
+                    &format!("{gate_type:?} on prep {prep_index}"),
+                );
+            }
+        }
+    }
 }
diff --git a/exp/pecos-neo/src/sampling/importance_runner.rs b/exp/pecos-neo/src/sampling/importance_runner.rs
index 22f189e6d..bcf1bf036 100644
--- a/exp/pecos-neo/src/sampling/importance_runner.rs
+++ b/exp/pecos-neo/src/sampling/importance_runner.rs
@@ -630,6 +630,12 @@ impl<S: CliffordGateable> ImportanceSamplingRunner<S> {
             GateType::H => {
                 self.simulator.h(&qubits);
             }
+            GateType::F => {
+                self.simulator.f(&qubits);
+            }
+            GateType::Fdg => {
+                self.simulator.fdg(&qubits);
+            }
             GateType::SX => {
                 self.simulator.sx(&qubits);
             }
@@ -675,6 +681,26 @@ impl<S: CliffordGateable> ImportanceSamplingRunner<S> {
                     qubits.chunks_exact(2).map(|c| (c[0], c[1])).collect();
                 self.simulator.szzdg(&pairs);
             }
+            GateType::SXX => {
+                let pairs: Vec<(QubitId, QubitId)> =
+                    qubits.chunks_exact(2).map(|c| (c[0], c[1])).collect();
+                self.simulator.sxx(&pairs);
+            }
+            GateType::SXXdg => {
+                let pairs: Vec<(QubitId, QubitId)> =
+                    qubits.chunks_exact(2).map(|c| (c[0], c[1])).collect();
+                self.simulator.sxxdg(&pairs);
+            }
+            GateType::SYY => {
+                let pairs: Vec<(QubitId, QubitId)> =
+                    qubits.chunks_exact(2).map(|c| (c[0], c[1])).collect();
+                self.simulator.syy(&pairs);
+            }
+            GateType::SYYdg => {
+                let pairs: Vec<(QubitId, QubitId)> =
+                    qubits.chunks_exact(2).map(|c| (c[0], c[1])).collect();
+                self.simulator.syydg(&pairs);
+            }
             GateType::SWAP => {
                 let pairs: Vec<(QubitId, QubitId)> =
                     qubits.chunks_exact(2).map(|c| (c[0], c[1])).collect();
@@ -892,6 +918,25 @@ mod tests {
         // (unless by chance the proposal probability matched the decision)
     }
 
+    #[test]
+    fn test_importance_runner_handles_face_inverse_deterministically() {
+        let commands = CommandBuilder::new()
+            .pz(&[0])
+            .f(&[0])
+            .fdg(&[0])
+            .mz(&[0])
+            .build();
+
+        let mut runner = ImportanceSamplingRunner::new(SparseStab::new(1)).with_seed(42);
+        let result = runner.run_shot(&commands);
+
+        assert_eq!(result.outcomes.len(), 1);
+        let outcome = result.outcomes.get(QubitId(0)).unwrap();
+        assert!(!outcome.outcome);
+        assert!(outcome.is_deterministic);
+        assert!((result.weight.weight() - 1.0).abs() < 1e-10);
+    }
+
     #[test]
     fn test_importance_sampling_estimates_correct_rate() {
         // This test verifies that importance sampling produces
diff --git a/exp/pecos-neo/src/sampling/path.rs b/exp/pecos-neo/src/sampling/path.rs
index 2fe42db37..d6f3cc705 100644
--- a/exp/pecos-neo/src/sampling/path.rs
+++ b/exp/pecos-neo/src/sampling/path.rs
@@ -535,6 +535,12 @@ impl<S: CliffordGateable + ForcedMeasurement> PathExplorer<S> {
             GateType::H => {
                 self.simulator.h(&qubits);
             }
+            GateType::F => {
+                self.simulator.f(&qubits);
+            }
+            GateType::Fdg => {
+                self.simulator.fdg(&qubits);
+            }
             GateType::SX => {
                 self.simulator.sx(&qubits);
             }
@@ -578,6 +584,26 @@ impl<S: CliffordGateable + ForcedMeasurement> PathExplorer<S> {
                     qubits.chunks_exact(2).map(|c| (c[0], c[1])).collect();
                 self.simulator.szzdg(&pairs);
             }
+            GateType::SXX => {
+                let pairs: Vec<(QubitId, QubitId)> =
+                    qubits.chunks_exact(2).map(|c| (c[0], c[1])).collect();
+                self.simulator.sxx(&pairs);
+            }
+            GateType::SXXdg => {
+                let pairs: Vec<(QubitId, QubitId)> =
+                    qubits.chunks_exact(2).map(|c| (c[0], c[1])).collect();
+                self.simulator.sxxdg(&pairs);
+            }
+            GateType::SYY => {
+                let pairs: Vec<(QubitId, QubitId)> =
+                    qubits.chunks_exact(2).map(|c| (c[0], c[1])).collect();
+                self.simulator.syy(&pairs);
+            }
+            GateType::SYYdg => {
+                let pairs: Vec<(QubitId, QubitId)> =
+                    qubits.chunks_exact(2).map(|c| (c[0], c[1])).collect();
+                self.simulator.syydg(&pairs);
+            }
             GateType::SWAP => {
                 let pairs: Vec<(QubitId, QubitId)> =
                     qubits.chunks_exact(2).map(|c| (c[0], c[1])).collect();
@@ -759,6 +785,42 @@ mod tests {
         assert!(result1.outcomes.get_bit(QubitId(0)).unwrap());
     }
 
+    #[test]
+    fn test_path_explorer_records_face_inverse_as_deterministic() {
+        let commands = CommandBuilder::new()
+            .pz(&[0])
+            .f(&[0])
+            .fdg(&[0])
+            .mz(&[0])
+            .build();
+
+        let mut explorer = PathExplorer::new(SparseStab::new(1)).with_seed(42);
+        let result = explorer.run_and_record(&commands);
+
+        assert!(!result.outcomes.get_bit(QubitId(0)).unwrap());
+        assert_eq!(result.path.len(), 1);
+        let path_outcome = result.path.get(0).unwrap();
+        assert!(!path_outcome.outcome);
+        assert!(path_outcome.is_deterministic);
+    }
+
+    #[test]
+    fn test_path_explorer_replays_face_inverse_as_deterministic() {
+        let commands = CommandBuilder::new()
+            .pz(&[0])
+            .f(&[0])
+            .fdg(&[0])
+            .mz(&[0])
+            .build();
+        let mut explorer = PathExplorer::new(SparseStab::new(1));
+        let forced_one = EnumeratedPath { bits: 1, len: 1 };
+
+        let result = explorer.run_with_path(&commands, &forced_one);
+
+        assert!(!result.outcomes.get_bit(QubitId(0)).unwrap());
+        assert!(result.path.get(0).unwrap().is_deterministic);
+    }
+
     #[test]
     fn test_path_enumeration_statistics() {
         // Simple circuit: H then measure
diff --git a/exp/pecos-neo/src/tool.rs b/exp/pecos-neo/src/tool.rs
index 478c23224..6803f8937 100644
--- a/exp/pecos-neo/src/tool.rs
+++ b/exp/pecos-neo/src/tool.rs
@@ -96,11 +96,11 @@ pub use importance::{
 pub use plugin::{Plugin, PluginGroup};
 pub use resource::{Resource, Resources};
 pub use simulation::{
-    Circuit, CustomBackendBuilder, ImportanceSamplingBuilder, NoiseResource, Orchestrator,
-    QuantumBackend, SimConfig, SimNeoBuilder, SimNeoInput, Simulation, SimulationResults,
+    Circuit, CustomBackendBuilder, ImportanceSamplingBuilder, NoiseResource, QuantumBackend,
+    Sampling, SimConfig, SimNeoBuilder, SimNeoInput, Simulation, SimulationResults,
     SimulatorFactory, SparseStabBuilder, StateVecBuilder, StoredOverrides, custom_backend,
-    custom_backend_with_rotations, importance_sampling, sim_neo, sim_neo_builder, sparse_stab,
-    state_vector,
+    custom_backend_from_factory, custom_backend_with_rotations, importance_sampling, sim_neo,
+    sim_neo_builder, sparse_stab, state_vector,
 };
 #[cfg(feature = "engines-adapter")]
 pub use simulation::{PendingEngineBuilder, TypedProgram};
diff --git a/exp/pecos-neo/src/tool/simulation.rs b/exp/pecos-neo/src/tool/simulation.rs
index 5a4ca5736..d218dc1cd 100644
--- a/exp/pecos-neo/src/tool/simulation.rs
+++ b/exp/pecos-neo/src/tool/simulation.rs
@@ -363,6 +363,20 @@ where
     }
 }
 
+/// Create a custom backend from a `SimulatorFactory` implementation.
+///
+/// Unlike [`custom_backend()`] which takes a closure, this accepts any type
+/// implementing `SimulatorFactory` directly. Use this when the factory needs
+/// configuration state (e.g., `StabMpsBackend` with bond dimension settings).
+#[must_use]
+pub fn custom_backend_from_factory(
+    factory: impl SimulatorFactory + 'static,
+) -> CustomBackendBuilder {
+    CustomBackendBuilder {
+        factory: Box::new(factory),
+    }
+}
+
 /// Create a custom backend with rotation support from a factory closure.
 ///
 /// Like [`custom_backend()`], but enables rotation gates (T, RZ, etc.) for
@@ -646,7 +660,7 @@ impl Default for SimConfig {
 ///
 /// let circuit = CommandBuilder::new().pz(&[0]).h(&[0]).mz(&[0]).build();
 /// let results = sim_neo(circuit)
-///     .orchestrator(importance_sampling()
+///     .sampling(importance_sampling()
 ///         .with_p1(0.001)
 ///         .with_p2(0.01)
 ///         .with_p_meas(0.001)
@@ -721,10 +735,10 @@ impl ImportanceSamplingBuilder {
         self
     }
 
-    /// Build the orchestrator.
+    /// Build the sampling.
     #[must_use]
-    pub fn build(self) -> Orchestrator {
-        Orchestrator::ImportanceSampling { config: self }
+    pub fn build(self) -> Sampling {
+        Sampling::ImportanceSampling { config: self }
     }
 
     /// Get the single-qubit error rate.
@@ -758,13 +772,13 @@ impl Default for ImportanceSamplingBuilder {
     }
 }
 
-impl From<ImportanceSamplingBuilder> for Orchestrator {
+impl From<ImportanceSamplingBuilder> for Sampling {
     fn from(builder: ImportanceSamplingBuilder) -> Self {
         builder.build()
     }
 }
 
-/// Create an importance sampling orchestrator builder.
+/// Create an importance sampling sampling builder.
 ///
 /// Importance sampling biases noise toward higher error rates to observe
 /// rare events more frequently, then reweights results for unbiased estimates.
@@ -777,7 +791,7 @@ impl From<ImportanceSamplingBuilder> for Orchestrator {
 ///
 /// let circuit = CommandBuilder::new().pz(&[0]).h(&[0]).mz(&[0]).build();
 /// let results = sim_neo(circuit)
-///     .orchestrator(importance_sampling()
+///     .sampling(importance_sampling()
 ///         .with_p1(0.001)
 ///         .with_p2(0.01)
 ///         .with_boost(10.0))
@@ -809,7 +823,7 @@ pub fn importance_sampling() -> ImportanceSamplingBuilder {
 /// using the Tool/Schedule/Plugin system. Use `.workers(n)` or `.auto_workers()`
 /// for parallel execution.
 #[derive(Debug, Clone)]
-pub enum Orchestrator {
+pub enum Sampling {
     /// Monte Carlo execution (sequential with 1 worker, parallel with >1).
     ///
     /// Each worker runs a batch of shots independently with deterministic seeding.
@@ -832,20 +846,20 @@ pub enum Orchestrator {
     },
 }
 
-impl Default for Orchestrator {
+impl Default for Sampling {
     fn default() -> Self {
         Self::MonteCarlo { workers: 1 }
     }
 }
 
-impl Orchestrator {
-    /// Create a Monte Carlo orchestrator with specified workers.
+impl Sampling {
+    /// Create a Monte Carlo sampling with specified workers.
     #[must_use]
     pub fn monte_carlo(workers: usize) -> Self {
         Self::MonteCarlo { workers }
     }
 
-    /// Create a Monte Carlo orchestrator with auto-detected worker count.
+    /// Create a Monte Carlo sampling with auto-detected worker count.
     #[must_use]
     pub fn monte_carlo_auto() -> Self {
         let workers = std::thread::available_parallelism().map_or(1, std::num::NonZero::get);
@@ -1285,7 +1299,7 @@ pub struct SimNeoBuilder {
     /// Simulation configuration (data).
     config: SimConfig,
     /// Orchestration strategy (data).
-    orchestrator: Orchestrator,
+    sampling: Sampling,
     /// Quantum backend configuration (data).
     quantum_backend: QuantumBackend,
     /// Explicit qubit count override (data).
@@ -1309,7 +1323,7 @@ impl SimNeoBuilder {
             noise: None,
             definitions: None,
             config: SimConfig::default(),
-            orchestrator: Orchestrator::default(),
+            sampling: Sampling::default(),
             quantum_backend: QuantumBackend::default(),
             explicit_num_qubits: None,
             max_decomp_depth: None,
@@ -1330,7 +1344,7 @@ impl SimNeoBuilder {
             noise: None,
             definitions: None,
             config: SimConfig::default(),
-            orchestrator: Orchestrator::default(),
+            sampling: Sampling::default(),
             quantum_backend: QuantumBackend::default(),
             explicit_num_qubits: None,
             max_decomp_depth: None,
@@ -1352,7 +1366,7 @@ impl SimNeoBuilder {
             noise: None,
             definitions: None,
             config: SimConfig::default(),
-            orchestrator: Orchestrator::default(),
+            sampling: Sampling::default(),
             quantum_backend: QuantumBackend::default(),
             explicit_num_qubits: None,
             max_decomp_depth: None,
@@ -1379,7 +1393,7 @@ impl SimNeoBuilder {
             noise: None,
             definitions: None,
             config: SimConfig::default(),
-            orchestrator: Orchestrator::default(),
+            sampling: Sampling::default(),
             quantum_backend: QuantumBackend::default(),
             explicit_num_qubits: None,
             max_decomp_depth: None,
@@ -1616,9 +1630,9 @@ impl SimNeoBuilder {
         // Classical engines are stateful and cannot be parallelized across workers.
         // Static circuits can run in parallel since each worker gets its own simulator.
         if is_classical {
-            self.orchestrator = Orchestrator::MonteCarlo { workers: 1 };
+            self.sampling = Sampling::MonteCarlo { workers: 1 };
         } else {
-            self.orchestrator = Orchestrator::monte_carlo_auto();
+            self.sampling = Sampling::monte_carlo_auto();
         }
         self
     }
@@ -1652,28 +1666,28 @@ impl SimNeoBuilder {
     /// # Example
     ///
     /// ```no_run
-    /// use pecos_neo::tool::{sim_neo, Orchestrator};
+    /// use pecos_neo::tool::{sim_neo, Sampling};
     /// use pecos_neo::prelude::*;
     ///
     /// let circuit = CommandBuilder::new().pz(&[0]).h(&[0]).mz(&[0]).build();
     ///
     /// // Parallel Monte Carlo with 4 workers
     /// let results = sim_neo(circuit.clone())
-    ///     .orchestrator(Orchestrator::monte_carlo(4))
+    ///     .sampling(Sampling::monte_carlo(4))
     ///     .shots(1000)
     ///     .build()
     ///     .run();
     ///
     /// // Auto-detect worker count
     /// let results = sim_neo(circuit)
-    ///     .orchestrator(Orchestrator::monte_carlo_auto())
+    ///     .sampling(Sampling::monte_carlo_auto())
     ///     .shots(1000)
     ///     .build()
     ///     .run();
     /// ```
     #[must_use]
-    pub fn orchestrator(mut self, orchestrator: impl Into<Orchestrator>) -> Self {
-        self.orchestrator = orchestrator.into();
+    pub fn sampling(mut self, sampling: impl Into<Sampling>) -> Self {
+        self.sampling = sampling.into();
         self
     }
 
@@ -1691,7 +1705,7 @@ impl SimNeoBuilder {
     /// backends are not supported.
     #[must_use]
     pub fn workers(mut self, workers: usize) -> Self {
-        self.orchestrator = Orchestrator::monte_carlo(workers);
+        self.sampling = Sampling::monte_carlo(workers);
         self
     }
 
@@ -1700,7 +1714,7 @@ impl SimNeoBuilder {
     /// See [`workers()`](Self::workers) for requirements and panics.
     #[must_use]
     pub fn auto_workers(mut self) -> Self {
-        self.orchestrator = Orchestrator::monte_carlo_auto();
+        self.sampling = Sampling::monte_carlo_auto();
         self
     }
 
@@ -2035,14 +2049,14 @@ impl SimNeoBuilder {
             .insert_resource(self.config)
             .insert_resource(QuantumBackendResource(self.quantum_backend));
 
-        match &self.orchestrator {
-            Orchestrator::ImportanceSampling { config: is_config } => {
+        match &self.sampling {
+            Sampling::ImportanceSampling { config: is_config } => {
                 tool = tool.add_plugin(&ImportanceSamplingSimPlugin {
                     is_config: is_config.clone(),
                     explicit_num_qubits: self.explicit_num_qubits,
                 });
             }
-            Orchestrator::MonteCarlo { .. } => {
+            Sampling::MonteCarlo { .. } => {
                 tool = tool.add_plugin(&UnifiedSimulationPlugin {
                     explicit_num_qubits: self.explicit_num_qubits,
                 });
@@ -2076,7 +2090,7 @@ impl SimNeoBuilder {
 
         Simulation {
             tool,
-            orchestrator: self.orchestrator,
+            sampling: self.sampling,
             parallel_data,
         }
     }
@@ -2385,7 +2399,7 @@ fn unified_simulation_post_shot(resources: &mut Resources) {
 
 /// Plugin for importance-sampling simulation.
 ///
-/// Replaces [`UnifiedSimulationPlugin`] when the IS orchestrator is selected.
+/// Replaces [`UnifiedSimulationPlugin`] when the IS sampling is selected.
 /// Uses [`ImportanceSamplingRunner`] for biased noise with weight tracking.
 struct ImportanceSamplingSimPlugin {
     is_config: ImportanceSamplingBuilder,
@@ -2556,7 +2570,7 @@ fn is_sim_post_shot(resources: &mut Resources) {
 pub struct Simulation {
     tool: Tool,
     /// Orchestration strategy (stored as data).
-    orchestrator: Orchestrator,
+    sampling: Sampling,
     /// Data for parallel execution (if applicable).
     /// Stored separately from Tool to allow cloning for workers.
     parallel_data: Option<ParallelExecutionData>,
@@ -2610,7 +2624,7 @@ impl Simulation {
     /// Returns the simulation results. The simulation can be run again
     /// after reconfiguring with [`shots()`](Self::shots) or [`seed()`](Self::seed).
     ///
-    /// Execution strategy depends on the orchestrator:
+    /// Execution strategy depends on the sampling:
     /// - `MonteCarlo { workers: 1 }`: Runs shots via the Tool (default)
     /// - `MonteCarlo { workers: n }`: Parallelizes shots across n workers
     /// - `ImportanceSampling`: Runs via the Tool with `ImportanceSamplingSimPlugin`
@@ -2621,8 +2635,8 @@ impl Simulation {
         let config = self.tool.resource::<SimConfig>().clone();
 
         // Dispatch based on orchestration strategy
-        match &self.orchestrator {
-            Orchestrator::MonteCarlo { workers } if *workers > 1 => {
+        match &self.sampling {
+            Sampling::MonteCarlo { workers } if *workers > 1 => {
                 let data = self.parallel_data.as_ref().unwrap_or_else(|| {
                     panic!(
                         "Parallel Monte Carlo requires a static circuit \
@@ -3316,14 +3330,14 @@ mod tests {
 
     #[test]
     fn test_sim_neo_orchestrator_explicit() {
-        // Test explicit orchestrator configuration
-        use super::Orchestrator;
+        // Test explicit sampling configuration
+        use super::Sampling;
 
         let circuit = CommandBuilder::new().pz(&[0]).x(&[0]).mz(&[0]).build();
 
-        // Use explicit Orchestrator enum
+        // Use explicit Sampling enum
         let results = sim_neo(circuit)
-            .orchestrator(Orchestrator::monte_carlo(2))
+            .sampling(Sampling::monte_carlo(2))
             .shots(20)
             .seed(42)
             .run();
@@ -3351,7 +3365,7 @@ mod tests {
         // Run with default (1 worker)
         let single_results = sim_neo(circuit.clone()).shots(50).seed(42).run();
 
-        // Run with parallel Monte Carlo orchestrator (4 workers)
+        // Run with parallel Monte Carlo sampling (4 workers)
         let parallel_results = sim_neo(circuit).workers(4).shots(50).seed(42).run();
 
         // Results should be identical
@@ -3396,7 +3410,7 @@ mod tests {
             .seed(42)
             .run();
 
-        // Run with parallel Monte Carlo orchestrator
+        // Run with parallel Monte Carlo sampling
         let parallel_results = sim_neo(circuit)
             .noise(noise_par)
             .workers(4)
@@ -3585,7 +3599,7 @@ mod tests {
         }
     }
 
-    // --- Importance Sampling Orchestrator Tests ---
+    // --- Importance Sampling Sampling Tests ---
 
     #[test]
     fn test_sim_neo_importance_sampling_basic() {
@@ -3599,7 +3613,7 @@ mod tests {
             .build();
 
         let results = sim_neo(circuit)
-            .orchestrator(
+            .sampling(
                 importance_sampling()
                     .with_p1(0.01)
                     .with_p2(0.02)
@@ -3628,7 +3642,7 @@ mod tests {
         let circuit = CommandBuilder::new().pz(&[0]).h(&[0]).mz(&[0]).build();
 
         let results = sim_neo(circuit)
-            .orchestrator(
+            .sampling(
                 importance_sampling()
                     .with_uniform_error(0.01)
                     .with_boost(10.0),
@@ -3655,7 +3669,7 @@ mod tests {
 
         // Run with importance sampling (boosting noise that doesn't affect this test)
         let results = sim_neo(circuit)
-            .orchestrator(
+            .sampling(
                 importance_sampling()
                     .with_uniform_error(0.001)
                     .with_boost(100.0),
@@ -3694,13 +3708,13 @@ mod tests {
             .with_boost(10.0);
 
         let results1 = sim_neo(circuit.clone())
-            .orchestrator(is_builder.clone())
+            .sampling(is_builder.clone())
             .shots(20)
             .seed(42)
             .run();
 
         let results2 = sim_neo(circuit)
-            .orchestrator(is_builder)
+            .sampling(is_builder)
             .shots(20)
             .seed(42)
             .run();
@@ -3745,7 +3759,7 @@ mod tests {
             .build();
 
         let results = sim_neo(circuit)
-            .orchestrator(
+            .sampling(
                 importance_sampling()
                     .with_p1(0.001)
                     .with_p2(0.01)
@@ -3768,7 +3782,7 @@ mod tests {
         let circuit = CommandBuilder::new().pz(&[0]).h(&[0]).mz(&[0]).build();
 
         let results = sim_neo(circuit)
-            .orchestrator(
+            .sampling(
                 importance_sampling()
                     .with_uniform_error(0.01)
                     .with_boost(10.0),
diff --git a/exp/pecos-stab-tn/src/stab_mps.rs b/exp/pecos-stab-tn/src/stab_mps.rs
index 888c2b6f6..4a115d751 100644
--- a/exp/pecos-stab-tn/src/stab_mps.rs
+++ b/exp/pecos-stab-tn/src/stab_mps.rs
@@ -338,8 +338,11 @@ impl StabMpsBuilder {
     ///   for adversarial T-heavy subcircuits before truncation hits the cap.
     ///
     /// Override any of these with subsequent builder calls:
-    /// ```ignore
-    /// StabMps::builder(n).for_qec().max_bond_dim(64).build()
+    /// ```
+    /// use pecos_stab_tn::stab_mps::StabMps;
+    ///
+    /// let sim = StabMps::builder(4).for_qec().max_bond_dim(64).build();
+    /// assert_eq!(sim.num_qubits(), 4);
     /// ```
     #[must_use]
     pub fn for_qec(self) -> Self {
@@ -1880,6 +1883,22 @@ impl QuantumSimulator for StabMps {
     }
 }
 
+impl pecos_random::RngManageable for StabMps {
+    type Rng = PecosRng;
+
+    fn set_rng(&mut self, rng: Self::Rng) {
+        self.rng = rng;
+    }
+
+    fn rng(&self) -> &Self::Rng {
+        &self.rng
+    }
+
+    fn rng_mut(&mut self) -> &mut Self::Rng {
+        &mut self.rng
+    }
+}
+
 impl CliffordGateable for StabMps {
     fn sz(&mut self, qubits: &[QubitId]) -> &mut Self {
         // SZ commutes with RZ: skip `flush_pending_rz`. The pending RZ
@@ -5880,39 +5899,28 @@ mod tests {
     }
 
     #[test]
-    fn test_pauli_frame_faster_than_eager_for_many_noise_injects() {
-        // Timing sanity check: many Pauli injections into frame should
-        // be far faster than applying each to tableau.
-        use std::time::Instant;
-        let n = 32;
-        let num_injects = 10_000;
+    fn test_pauli_frame_matches_eager_for_many_noise_injects() {
+        let n = 6;
+        let num_injects = 1_000;
 
         let mut stn_frame = StabMps::builder(n)
             .seed(1)
             .pauli_frame_tracking(true)
             .build();
-        let start = Instant::now();
-        for _ in 0..num_injects {
-            stn_frame.apply_depolarizing(QubitId(0), 1.0);
-        }
-        let t_frame = start.elapsed().as_secs_f64();
-
         let mut stn_eager = StabMps::builder(n).seed(1).build();
-        let start = Instant::now();
-        for _ in 0..num_injects {
-            stn_eager.apply_depolarizing(QubitId(0), 1.0);
+
+        for k in 0..num_injects {
+            let q = QubitId(k % n);
+            let frame_pauli = stn_frame.apply_depolarizing(q, 1.0);
+            let eager_pauli = stn_eager.apply_depolarizing(q, 1.0);
+            assert_eq!(frame_pauli, eager_pauli);
         }
-        let t_eager = start.elapsed().as_secs_f64();
 
-        // Frame tracking should be at least 2x faster.
-        eprintln!(
-            "Pauli frame: {t_frame:.4}s; eager: {t_eager:.4}s  → {:.1}x",
-            t_eager / t_frame
-        );
-        assert!(
-            t_frame * 2.0 < t_eager,
-            "frame tracking should be >2x faster: frame={t_frame:.4}s eager={t_eager:.4}s"
-        );
+        stn_frame.flush_pauli_frame_to_state();
+        let frame_sv = stn_frame.state_vector();
+        let eager_sv = stn_eager.state_vector();
+
+        assert_state_vectors_match(&frame_sv, &eager_sv, "frame vs eager Pauli injections");
     }
 
     #[test]
diff --git a/exp/pecos-zx/src/viz/circuit_layout.rs b/exp/pecos-zx/src/viz/circuit_layout.rs
index f44100f97..f5334f2d8 100644
--- a/exp/pecos-zx/src/viz/circuit_layout.rs
+++ b/exp/pecos-zx/src/viz/circuit_layout.rs
@@ -285,7 +285,7 @@ pub fn layout_from_tick_circuit(tc: &TickCircuit) -> CircuitLayout {
         if tick_idx >= num_steps {
             break;
         }
-        for gate in tick.gates().iter() {
+        for gate in tick.gate_batches().iter() {
             let qubit_indices: Vec<usize> = gate.qubits.iter().map(|q| q.index()).collect();
 
             // TODO: TickCircuit classical bit/condition support
diff --git a/mkdocs.yml b/mkdocs.yml
index 21e546ce9..d1f4dca87 100644
--- a/mkdocs.yml
+++ b/mkdocs.yml
@@ -50,15 +50,24 @@ nav:
 - Home: README.md
 - User Guide:
   - Getting Started: user-guide/getting-started.md
+  - PECOS Concepts: user-guide/pecos-concepts.md
   - Command Line Interface: user-guide/cli.md
   - QASM Simulation: user-guide/qasm-simulation.md
   - WASM Foreign Objects: user-guide/wasm-foreign-objects.md
   - HUGR & Guppy Simulation: user-guide/hugr-simulation.md
   - Simulators: user-guide/simulators.md
+  - Engine Selection: user-guide/engine-selection.md
   - Gate Reference: user-guide/gates.md
   - Gate Naming Conventions: user-guide/gate-naming-conventions.md
   - Gate Naming (Future): user-guide/gate-naming-speculation.md
+  - Gate and Angle Types: user-guide/gate-angle-types.md
   - Noise Model Builders: user-guide/noise-model-builders.md
+  - Quantum Operator Algebra: user-guide/quantum-operator-algebra.md
+  - Quantum Information Primitives: user-guide/quantum-info.md
+  - Stabilizer Codes: user-guide/stabilizer-codes.md
+  - Pauli Algebra and QEC in Python: user-guide/python-pauli-qec.md
+  - Fault Tolerance Analysis: user-guide/fault-tolerance.md
+  - Fault Catalog Tutorial: user-guide/fault-catalog.md
   - QEC Geometry: user-guide/qec-geometry.md
   - QEC with Guppy: user-guide/qec-guppy.md
   - Decoders: user-guide/decoders.md
@@ -77,9 +86,14 @@ nav:
   - Developer Tools CLI: development/dev-tools.md
   - Documentation Testing: development/doc-testing.md
   - SLR and QECLib: development/slr-qeclib.md
-  - Circuit Representations: development/circuit-representations.md
+  - AST Infrastructure: development/ast-infrastructure.md
+  - Foreign Language Plugins: development/foreign-plugins.md
   - Parallel Blocks: development/parallel-blocks-and-optimization.md
-  - development/QIS_ARCHITECTURE.md
+- Experimental:
+  - experimental/index.md
+  - Composable Noise (pecos-neo): experimental/composable-noise.md
+- Proposals:
+  - proposals/README.md
 - Releases:
   - releases/changelog.md
 markdown_extensions:
@@ -126,4 +140,4 @@ extra:
     link: https://pypi.org/project/quantum-pecos/
   - icon: fontawesome/solid/book
     link: https://quantum-pecos.readthedocs.io/
-copyright: Copyright &copy; 2018-2025 The PECOS Developers
+copyright: Copyright &copy; 2018-2026 The PECOS Developers
diff --git a/pyproject.toml b/pyproject.toml
index 6228d25b1..3bde0ac88 100644
--- a/pyproject.toml
+++ b/pyproject.toml
@@ -1,12 +1,15 @@
 [project]
 name = "pecos-workspace"
-version = "0.8.0.dev5"
+version = "0.8.0.dev8"
+requires-python = ">=3.10"
 # Meta-package; runtime deps live in the member packages. Test/example/dev
 # tooling is declared in [dependency-groups] below.
 dependencies = []
 
 [project.optional-dependencies]
-cuda = ["quantum-pecos[cuda]"]
+# Keep this in sync with the cuda dependency group below. The extra supports
+# `uv sync --extra cuda`; the group supports `uv run --group cuda ...`.
+cuda = ["quantum-pecos[cuda]==0.8.0.dev8"]
 
 [tool.uv.workspace]
 members = [
@@ -35,6 +38,7 @@ dev = [
   "pre-commit",                             # Git hooks
   "black",                                  # Code formatting
   "ruff",                                   # Fast Python linting
+  "tomli>=1.1.0; python_version < '3.11'",  # TOML parsing (stdlib in 3.11+)
   "mkdocs",                                 # Documentation framework
   "mkdocs-material",                        # Material theme for MkDocs
   "mkdocstrings[python]",                   # Code documentation extraction
@@ -52,7 +56,6 @@ test = [ # exact pins so workspace tests run against a reproducible environment
   "pytest-timeout==2.4.0",
   "hypothesis==6.152.1",
   "stim==1.15.0",        # Stim-comparison and decomposition-invariant tests
-  "wasmtime==43.0.0",    # WebAssembly runtime exercised by integration tests
   "matplotlib>=2.2.0",   # Surface-patch render tests import matplotlib directly
 ]
 examples = [ # extras used by the examples/ tree and notebook walkthroughs
@@ -64,15 +67,20 @@ numpy-compat = [ # NumPy/SciPy compatibility tests - verify compatibility with s
   "scipy>=1.1.0",
 ]
 cuda = [ # CUDA Python packages for GPU-accelerated simulations (requires CUDA toolkit)
-  "quantum-pecos[cuda]",
+  "quantum-pecos[cuda]==0.8.0.dev8",
 ]
 
 [tool.uv]
 default-groups = ["dev", "test"]
-# Prevent uv from caching pecos-rslib wheels - always use freshly built version
-# This fixes stale code issues when uv sync/run reinstalls cached old wheels
+# Prevent uv from caching native workspace wheels - always use freshly built versions.
+# This fixes stale code issues when uv sync/run reinstalls cached old wheels.
 # See: https://github.com/astral-sh/uv/issues/11390
-reinstall-package = ["pecos-rslib", "pecos-rslib-cuda", "pecos-rslib-llvm"]
+reinstall-package = [
+  "pecos-rslib",
+  "pecos-rslib-cuda",
+  "pecos-rslib-exp",
+  "pecos-rslib-llvm",
+]
 
 [tool.black]
 line-length = 120
diff --git a/python/pecos-rslib-cuda/pyproject.toml b/python/pecos-rslib-cuda/pyproject.toml
index 3e96e850b..7d48eccb5 100644
--- a/python/pecos-rslib-cuda/pyproject.toml
+++ b/python/pecos-rslib-cuda/pyproject.toml
@@ -43,9 +43,6 @@ test = [
     "pytest>=9.0",
 ]
 
-[tool.uv.sources]
-pecos-rslib-cuda = { workspace = true }
-
 [tool.pytest.ini_options]
 markers = [
     "cuda: marks tests that require CUDA and cuQuantum (deselect with '-m \"not cuda\"')",
diff --git a/python/pecos-rslib-cuda/src/lib.rs b/python/pecos-rslib-cuda/src/lib.rs
index 1f3b61047..e68c01c60 100644
--- a/python/pecos-rslib-cuda/src/lib.rs
+++ b/python/pecos-rslib-cuda/src/lib.rs
@@ -19,7 +19,9 @@
 use pecos_core::{Angle64, QubitId};
 use pecos_cuquantum::{
     ArbitraryRotationGateable, CliffordGateable, CuDensityMat, CuStabilizer, CuStateVec,
-    CuTensorNet, QuantumSimulator, is_cuquantum_available as cuquantum_available,
+    CuTensorNet, QuantumSimulator, is_cudensitymat_usable as cudensitymat_usable,
+    is_cuquantum_available as cuquantum_available, is_custabilizer_usable as custabilizer_usable,
+    is_custatevec_usable as custatevec_usable, is_cutensornet_usable as cutensornet_usable,
 };
 use pyo3::exceptions::PyRuntimeError;
 use pyo3::prelude::*;
@@ -32,6 +34,30 @@ fn is_cuquantum_available() -> bool {
     cuquantum_available()
 }
 
+/// Check if the cuStateVec backend can create a simulator on this system.
+#[pyfunction]
+fn is_custatevec_usable() -> bool {
+    custatevec_usable()
+}
+
+/// Check if the cuStabilizer backend can create a frame simulator on this system.
+#[pyfunction]
+fn is_custabilizer_usable() -> bool {
+    custabilizer_usable()
+}
+
+/// Check if the cuTensorNet backend can create a handle on this system.
+#[pyfunction]
+fn is_cutensornet_usable() -> bool {
+    cutensornet_usable()
+}
+
+/// Check if the cuDensityMat backend can create a simulator on this system.
+#[pyfunction]
+fn is_cudensitymat_usable() -> bool {
+    cudensitymat_usable()
+}
+
 /// GPU-accelerated state vector quantum simulator using cuQuantum.
 ///
 /// This simulator can handle up to approximately 30 qubits (limited by GPU memory).
@@ -851,8 +877,12 @@ impl PyCuDensityMat {
 fn pecos_rslib_cuda(_py: Python<'_>, m: &Bound<'_, PyModule>) -> PyResult<()> {
     log::debug!("pecos_rslib_cuda module initializing...");
 
-    // Add availability check function
+    // Add availability check functions
     m.add_function(wrap_pyfunction!(is_cuquantum_available, m)?)?;
+    m.add_function(wrap_pyfunction!(is_custatevec_usable, m)?)?;
+    m.add_function(wrap_pyfunction!(is_custabilizer_usable, m)?)?;
+    m.add_function(wrap_pyfunction!(is_cutensornet_usable, m)?)?;
+    m.add_function(wrap_pyfunction!(is_cudensitymat_usable, m)?)?;
 
     // Add simulator classes
     m.add_class::<PyCuStateVec>()?;
diff --git a/python/pecos-rslib-exp/Cargo.toml b/python/pecos-rslib-exp/Cargo.toml
index 8180f9829..82b8162cd 100644
--- a/python/pecos-rslib-exp/Cargo.toml
+++ b/python/pecos-rslib-exp/Cargo.toml
@@ -18,10 +18,19 @@ doctest = false
 
 [dependencies]
 pecos-core.workspace = true
+pecos-eeg.workspace = true
+pecos-neo.workspace = true
+pecos-qec.workspace = true
+pecos-quantum.workspace = true
+pecos-random.workspace = true
 pecos-simulators.workspace = true
-pecos-stab-tn = { path = "../../exp/pecos-stab-tn" }
+serde = { workspace = true, features = ["derive"] }
+serde_json.workspace = true
+rayon.workspace = true
+pecos-stab-tn.workspace = true
 pyo3 = { workspace = true, features = ["extension-module", "abi3-py310", "generate-import-lib", "num-complex"] }
 num-complex.workspace = true
+smallvec.workspace = true
 
 [lints]
 workspace = true
diff --git a/python/pecos-rslib-exp/src/coherent_idle_channel.rs b/python/pecos-rslib-exp/src/coherent_idle_channel.rs
new file mode 100644
index 000000000..5b384666f
--- /dev/null
+++ b/python/pecos-rslib-exp/src/coherent_idle_channel.rs
@@ -0,0 +1,75 @@
+// Copyright 2026 The PECOS Developers
+//
+// Licensed under the Apache License, Version 2.0 (the "License"); you may not use this file
+// except in compliance with the License. You may obtain a copy of the License at
+//
+//     https://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software distributed under the
+// License is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either
+// express or implied. See the License for the specific language governing permissions and
+// limitations under the License.
+
+//! Coherent idle noise channel: RZ(angle) on both qubits after each CX gate.
+
+use pecos_core::Angle64;
+use pecos_neo::command::{GateCommand, GateType};
+use pecos_neo::noise::{NoiseChannel, NoiseContext, NoiseEvent, NoiseResponse};
+use pecos_random::PecosRng;
+use smallvec::SmallVec;
+
+/// Applies coherent RZ rotation after each two-qubit gate on both qubits.
+///
+/// Models uncompensated phase accumulation during idle time between gates.
+/// The rotation angle represents the coherent Z-phase acquired per gate
+/// application.
+#[derive(Clone)]
+pub struct CoherentIdleChannel {
+    angle: Angle64,
+}
+
+impl CoherentIdleChannel {
+    /// Create a coherent idle channel with the given RZ angle (radians).
+    pub fn new(angle_radians: f64) -> Self {
+        Self {
+            angle: Angle64::from_radians(angle_radians),
+        }
+    }
+}
+
+impl NoiseChannel for CoherentIdleChannel {
+    fn responds_to(&self, event: &NoiseEvent<'_>) -> bool {
+        matches!(
+            event,
+            NoiseEvent::AfterGate {
+                gate_type: GateType::CX | GateType::CZ | GateType::CY,
+                ..
+            }
+        )
+    }
+
+    fn apply(
+        &self,
+        event: &NoiseEvent<'_>,
+        _ctx: &mut NoiseContext,
+        _rng: &mut PecosRng,
+    ) -> NoiseResponse {
+        if let NoiseEvent::AfterGate { qubits, .. } = event {
+            let mut gates = SmallVec::new();
+            for &q in *qubits {
+                gates.push(GateCommand::rz(q, self.angle));
+            }
+            NoiseResponse::inject_gates(gates)
+        } else {
+            NoiseResponse::None
+        }
+    }
+
+    fn name(&self) -> &'static str {
+        "CoherentIdleRZ"
+    }
+
+    fn clone_box(&self) -> Box<dyn NoiseChannel> {
+        Box::new(self.clone())
+    }
+}
diff --git a/python/pecos-rslib-exp/src/eeg_bindings.rs b/python/pecos-rslib-exp/src/eeg_bindings.rs
new file mode 100644
index 000000000..c47445fc5
--- /dev/null
+++ b/python/pecos-rslib-exp/src/eeg_bindings.rs
@@ -0,0 +1,1412 @@
+// Copyright 2026 The PECOS Developers
+//
+// Licensed under the Apache License, Version 2.0
+
+//! Python bindings for EEG DEM builder.
+
+use pecos_core::pauli::pauli_bitmask::BitmaskStorage;
+use pecos_core::{Angle64, Gate, GateAngles, GateMeasIds, GateParams, QubitId};
+use pecos_eeg::Bm;
+use pecos_eeg::circuit::{self, NoiseModel};
+use pecos_eeg::correlation_table::CorrelationTableInput;
+use pecos_eeg::dem_mapping::{DemEntry, Detector, Observable};
+use pecos_eeg::noise_characterization::NoiseCharacterizationInput;
+use pyo3::prelude::*;
+use rayon::iter::{IntoParallelRefIterator, ParallelIterator};
+use std::collections::BTreeMap;
+
+type PyDemEvent = (f64, Vec<usize>, Vec<usize>);
+type PyEegEventDiagnostic = (Vec<usize>, usize, usize, Vec<f64>, f64);
+type MeasurementRecordDefinition = (usize, Vec<usize>, Vec<i32>);
+
+/// Build a DEM using forward EEG analysis (perturbative, fast).
+///
+/// Returns (raw_dem, decomposed_dem) where the decomposed version uses
+/// X/Z Pauli-aware decomposition for MWPM decoders.
+///
+/// Fast (milliseconds) but approximate (~50% error for coherent noise).
+/// For exact probabilities, use `coherent_dem_decomposed`.
+///
+/// h_formula: "taylor" (default), "sin_squared", "exact_commuting", or "exact_subset"
+#[pyfunction]
+#[pyo3(signature = (tick_circuit, idle_rz=0.0, p1=0.0, p2=0.0, p_meas=0.0, p_prep=0.0, h_formula="taylor", bch_order=1))]
+pub fn perturbative_dem(
+    tick_circuit: &Bound<'_, PyAny>,
+    idle_rz: f64,
+    p1: f64,
+    p2: f64,
+    p_meas: f64,
+    p_prep: f64,
+    h_formula: &str,
+    bch_order: u32,
+) -> PyResult<(String, String)> {
+    let (raw, decomposable) = run_eeg_decomposable(
+        tick_circuit,
+        idle_rz,
+        p1,
+        p2,
+        p_meas,
+        p_prep,
+        h_formula,
+        bch_order,
+    )?;
+    Ok((
+        pecos_eeg::dem_mapping::format_dem(&raw),
+        pecos_eeg::dem_mapping::format_dem_decomposed(&decomposable),
+    ))
+}
+
+/// Build perturbative DEM and return structured events: list of (prob, [det_ids], [obs_ids]).
+#[pyfunction]
+#[pyo3(signature = (tick_circuit, idle_rz=0.0, p1=0.0, p2=0.0, p_meas=0.0, p_prep=0.0, h_formula="taylor", bch_order=1))]
+pub fn perturbative_dem_events(
+    tick_circuit: &Bound<'_, PyAny>,
+    idle_rz: f64,
+    p1: f64,
+    p2: f64,
+    p_meas: f64,
+    p_prep: f64,
+    h_formula: &str,
+    bch_order: u32,
+) -> PyResult<Vec<PyDemEvent>> {
+    let entries = run_eeg(
+        tick_circuit,
+        idle_rz,
+        p1,
+        p2,
+        p_meas,
+        p_prep,
+        h_formula,
+        bch_order,
+    )?;
+    Ok(entries
+        .into_iter()
+        .map(|e| {
+            (
+                e.probability,
+                e.event.detectors.to_vec(),
+                e.event.observables.to_vec(),
+            )
+        })
+        .collect())
+}
+
+/// Return (num_h_generators, num_s_generators, num_detectors, numobservables).
+#[pyfunction]
+#[pyo3(signature = (tick_circuit, idle_rz=0.0, p1=0.0, p2=0.0, p_meas=0.0, p_prep=0.0))]
+pub fn eeg_summary(
+    tick_circuit: &Bound<'_, PyAny>,
+    idle_rz: f64,
+    p1: f64,
+    p2: f64,
+    p_meas: f64,
+    p_prep: f64,
+) -> PyResult<(usize, usize, usize, usize)> {
+    let noise = NoiseModel {
+        idle_rz,
+        p1,
+        p2,
+        p_meas,
+        p_prep,
+    };
+    let gates = extract_gates(tick_circuit)?;
+    let expanded = pecos_eeg::expand::expand_circuit(&gates);
+    let result = circuit::analyze_expanded(&expanded.gates, &noise);
+    let (detectors, observables) = extract_detectors_expanded(tick_circuit, &expanded)?;
+    let h = result
+        .generators
+        .iter()
+        .filter(|g| g.eeg_type == pecos_eeg::eeg::EegType::H)
+        .count();
+    let s = result
+        .generators
+        .iter()
+        .filter(|g| g.eeg_type == pecos_eeg::eeg::EegType::S)
+        .count();
+    Ok((h, s, detectors.len(), observables.len()))
+}
+
+/// Diagnostic: for each DEM event, return generator details.
+///
+/// Returns list of (det_ids, num_labels, num_same_label_groups, rates_by_label, max_combined_rate)
+/// This helps understand why perturbative formulas are inaccurate.
+#[pyfunction]
+#[pyo3(signature = (tick_circuit, idle_rz=0.0, p1=0.0, p2=0.0, p_meas=0.0, p_prep=0.0))]
+pub fn eeg_event_diagnostics(
+    tick_circuit: &Bound<'_, PyAny>,
+    idle_rz: f64,
+    p1: f64,
+    p2: f64,
+    p_meas: f64,
+    p_prep: f64,
+) -> PyResult<Vec<PyEegEventDiagnostic>> {
+    let noise = NoiseModel {
+        idle_rz,
+        p1,
+        p2,
+        p_meas,
+        p_prep,
+    };
+    let gates = extract_gates(tick_circuit)?;
+    let expanded = pecos_eeg::expand::expand_circuit(&gates);
+    let result = circuit::analyze_expanded(&expanded.gates, &noise);
+    let (detectors, _observables) = extract_detectors_expanded(tick_circuit, &expanded)?;
+
+    // Group H generators by DEM event, tracking labels
+    let mut h_events: BTreeMap<Vec<usize>, BTreeMap<Bm, f64>> = BTreeMap::new();
+
+    for g in &result.generators {
+        if g.eeg_type != pecos_eeg::eeg::EegType::H {
+            continue;
+        }
+        // Classify manually
+        let mut dets = Vec::new();
+        for det in &detectors {
+            if !g.label.commutes_with(&det.stabilizer) {
+                dets.push(det.id);
+            }
+        }
+        if dets.is_empty() {
+            continue;
+        }
+        *h_events
+            .entry(dets)
+            .or_default()
+            .entry(g.label.clone())
+            .or_insert(0.0) += g.coeff;
+    }
+
+    let mut out = Vec::new();
+    for (det_ids, labels) in &h_events {
+        let num_labels = labels.len();
+        let rates: Vec<f64> = labels.values().copied().collect();
+        let num_groups = rates.iter().filter(|&&r| r.abs() > 1e-15).count();
+        let max_combined = rates.iter().map(|r| r.abs()).fold(0.0_f64, f64::max);
+        out.push((det_ids.clone(), num_labels, num_groups, rates, max_combined));
+    }
+    Ok(out)
+}
+
+/// Compute per-detector marginals using ALL generators that flip each detector.
+///
+/// Unlike the DEM-based approach (which groups by event then sums), this pools
+/// all H generators for each detector into a single quadratic form with beta
+/// cross-terms. This captures cross-event interference that the per-event
+/// computation misses.
+///
+/// Returns list of (detector_id, probability).
+#[pyfunction]
+#[pyo3(signature = (tick_circuit, idle_rz=0.0, p1=0.0, p2=0.0, p_meas=0.0, p_prep=0.0, h_formula="taylor"))]
+pub fn eeg_per_detector(
+    tick_circuit: &Bound<'_, PyAny>,
+    idle_rz: f64,
+    p1: f64,
+    p2: f64,
+    p_meas: f64,
+    p_prep: f64,
+    h_formula: &str,
+) -> PyResult<Vec<(usize, f64)>> {
+    let noise = NoiseModel {
+        idle_rz,
+        p1,
+        p2,
+        p_meas,
+        p_prep,
+    };
+    let gates = extract_gates(tick_circuit)?;
+    let expanded = pecos_eeg::expand::expand_circuit(&gates);
+    let result = circuit::analyze_expanded(&expanded.gates, &noise);
+    let (detectors, _observables) = extract_detectors_expanded(tick_circuit, &expanded)?;
+
+    let expanded_pre_readout = exclude_final_mz(&expanded.gates);
+    let stab_group = pecos_eeg::stabilizer::StabilizerGroup::from_circuit(
+        &expanded_pre_readout,
+        expanded.num_qubits,
+    );
+
+    let formula = parse_h_formula(h_formula)?;
+
+    // Collect all H generators with their BCH-combined rates per label
+    let mut h_by_label: std::collections::BTreeMap<Bm, f64> = std::collections::BTreeMap::new();
+    for g in &result.generators {
+        if g.eeg_type == pecos_eeg::eeg::EegType::H {
+            *h_by_label.entry(g.label.clone()).or_insert(0.0) += g.coeff;
+        }
+    }
+    let h_labels: Vec<(Bm, f64)> = h_by_label
+        .into_iter()
+        .filter(|(_, c)| c.abs() > 1e-20)
+        .collect();
+
+    // Also collect S generators
+    let mut s_by_label: std::collections::BTreeMap<Bm, f64> = std::collections::BTreeMap::new();
+    for g in &result.generators {
+        if g.eeg_type == pecos_eeg::eeg::EegType::S {
+            *s_by_label.entry(g.label.clone()).or_insert(0.0) += g.coeff;
+        }
+    }
+
+    let mut results = Vec::new();
+
+    for det in &detectors {
+        // Find all H generators that anticommute with this detector
+        let det_h: Vec<(usize, f64)> = h_labels
+            .iter()
+            .enumerate()
+            .filter(|(_, (label, _))| !label.commutes_with(&det.stabilizer))
+            .map(|(i, (_, c))| (i, *c))
+            .collect();
+
+        // Find S generators that anticommute
+        let s_sum: f64 = s_by_label
+            .iter()
+            .filter(|(label, _)| !label.commutes_with(&det.stabilizer))
+            .map(|(_, c)| c)
+            .sum();
+
+        // S contribution
+        let p_s = if s_sum.abs() > 1e-20 {
+            (1.0 - (2.0 * s_sum).exp()) / 2.0
+        } else {
+            0.0
+        };
+
+        // H contribution: quadratic form with beta
+        let h_prob = match formula {
+            pecos_eeg::dem_mapping::HFormula::Taylor
+            | pecos_eeg::dem_mapping::HFormula::SinSquared
+            | pecos_eeg::dem_mapping::HFormula::ExactSubset => {
+                let mut total = 0.0_f64;
+                for (j, &(idx_j, h_j)) in det_h.iter().enumerate() {
+                    // Diagonal
+                    total += h_j * h_j;
+                    // Off-diagonal with beta
+                    for &(idx_k, h_k) in det_h.iter().skip(j + 1) {
+                        let q_j = &h_labels[idx_j].0;
+                        let q_k = &h_labels[idx_k].0;
+
+                        if !q_j.commutes_with(q_k) {
+                            continue;
+                        }
+                        let product = q_j.multiply(q_k);
+                        if product.is_identity() {
+                            total += 2.0 * h_j * h_k;
+                            continue;
+                        }
+                        match stab_group.is_stabilizer(&product) {
+                            Some(true) => {
+                                total += 2.0 * h_j * h_k;
+                            }
+                            Some(false) => {
+                                total -= 2.0 * h_j * h_k;
+                            }
+                            None => {}
+                        }
+                    }
+                }
+                let total = total.max(0.0);
+                match formula {
+                    pecos_eeg::dem_mapping::HFormula::SinSquared => total.sqrt().sin().powi(2),
+                    _ => total,
+                }
+            }
+            pecos_eeg::dem_mapping::HFormula::ExactCommuting => {
+                // Product formula over all generators for this detector
+                let mut prod_re = 1.0_f64;
+                let mut prod_im = 0.0_f64;
+                for &(idx_j, h_j) in &det_h {
+                    let label = &h_labels[idx_j].0;
+                    let p_stab = if label.is_identity() {
+                        Some(true)
+                    } else {
+                        stab_group.is_stabilizer(label)
+                    };
+
+                    let (f_re, f_im) = if let Some(sign) = p_stab {
+                        let s = if sign { 1.0 } else { -1.0 };
+                        let angle = 2.0 * s * h_j;
+                        (angle.cos(), angle.sin())
+                    } else {
+                        let dp = det.stabilizer.multiply(label);
+                        let dp_stab = if dp.is_identity() {
+                            Some(true)
+                        } else {
+                            stab_group.is_stabilizer(&dp)
+                        };
+                        if let Some(sign) = dp_stab {
+                            let s = if sign { 1.0 } else { -1.0 };
+                            let angle = -2.0 * s * h_j;
+                            (angle.cos(), angle.sin())
+                        } else {
+                            ((2.0 * h_j).cos(), 0.0)
+                        }
+                    };
+                    let new_re = prod_re * f_re - prod_im * f_im;
+                    let new_im = prod_re * f_im + prod_im * f_re;
+                    prod_re = new_re;
+                    prod_im = new_im;
+                }
+                (0.5 * (1.0 - prod_re)).max(0.0)
+            }
+        };
+
+        // Combine S and H (independent)
+        let p = if p_s.abs() > 1e-15 && h_prob > 1e-15 {
+            p_s + h_prob - 2.0 * p_s * h_prob
+        } else {
+            p_s.abs() + h_prob
+        };
+        results.push((det.id, p));
+    }
+
+    Ok(results)
+}
+
+/// Compute exact per-detector detection probabilities.
+///
+/// Uses backward Heisenberg propagation: walks the detector observable
+/// backward through the circuit, splitting at each noise source. Exact
+/// for both coherent (idle_rz) and stochastic (depolarizing) noise.
+///
+/// This is the most accurate DEM generation method in PECOS. Use it when:
+/// - You need exact detection rates under coherent noise
+/// - You want to validate the non-EEG DEM builder
+/// - You need per-detector probabilities (not a full DEM)
+///
+/// For a full DEM (event structure + probabilities), use `eeg_heisenberg_dem`.
+/// For fast approximate rates under coherent noise, use `eeg_dem_events`.
+/// For depolarizing-only noise, `DemSampler.from_circuit` is faster and exact.
+///
+/// Returns: list of (detector_id, probability) for each detector.
+///
+/// Example:
+///     probs = exact_detection_rates(tc, idle_rz=0.05)
+///     probs = exact_detection_rates(tc, idle_rz=0.05, p2=0.01)
+#[pyfunction]
+#[pyo3(signature = (tick_circuit, idle_rz=0.0, p1=0.0, p2=0.0, p_meas=0.0, p_prep=0.0, prune=1e-12, window=None))]
+pub fn exact_detection_rates(
+    tick_circuit: &Bound<'_, PyAny>,
+    idle_rz: f64,
+    p1: f64,
+    p2: f64,
+    p_meas: f64,
+    p_prep: f64,
+    prune: f64,
+    #[allow(unused_variables)] window: Option<usize>,
+) -> PyResult<Vec<(usize, f64)>> {
+    let noise = pecos_eeg::noise::UniformNoise {
+        idle_rz,
+        p1,
+        p2,
+        p_meas,
+        p_prep,
+    };
+    let gates = extract_gates(tick_circuit)?;
+    let expanded = pecos_eeg::expand::expand_circuit(&gates);
+    let (detectors, _observables) = extract_detectors_expanded(tick_circuit, &expanded)?;
+
+    // Build initial stabilizer group: Z on each original qubit
+    let init_gates: Vec<Gate> = (0..expanded.num_original_qubits)
+        .map(|q| pecos_eeg::expand::make_gate(pecos_core::gate_type::GateType::PZ, &[q]))
+        .collect();
+    let stab =
+        pecos_eeg::stabilizer::StabilizerGroup::from_circuit(&init_gates, expanded.num_qubits);
+
+    // Build qubit-to-gate index once, shared across all detector walks.
+    let gate_index = pecos_eeg::expand::GateIndex::build(&expanded.gates, expanded.num_qubits);
+
+    // Use noise map (with batched S-type) when stochastic noise is present.
+    // For coherent-only (idle_rz), the bitmap-enhanced linear scan is faster.
+    let has_stochastic = p1 > 0.0 || p2 > 0.0 || p_meas > 0.0 || p_prep > 0.0;
+
+    let noise_map = if has_stochastic {
+        Some(pecos_eeg::heisenberg::build_noise_map(
+            &expanded.gates,
+            &noise,
+            &gate_index.expansion_gates,
+        ))
+    } else {
+        None
+    };
+
+    // Parallelize across detectors — each walk is independent.
+    // Uses sparse traversal (heap + gate index) for O(active_gates) instead of O(all_gates).
+    let results: Vec<(usize, f64)> = detectors
+        .par_iter()
+        .map(|det| {
+            let p = pecos_eeg::heisenberg::heisenberg_sparse(
+                &expanded.gates,
+                &det.stabilizer,
+                &noise,
+                &stab,
+                prune,
+                &gate_index,
+                noise_map.as_deref(),
+            );
+            (det.id, p)
+        })
+        .collect();
+
+    Ok(results)
+}
+
+/// Compute exact pairwise detection rates via backward Heisenberg walk.
+///
+/// For each pair of detectors (i, j), computes P(Di AND Dj both fire)
+/// using the identity:
+///   P(Di=1, Dj=1) = (P(Di) + P(Dj) - P_walk(Si*Sj)) / 2
+/// where P_walk(Si*Sj) is a Heisenberg walk with the product stabilizer.
+///
+/// Returns a list of ((det_i, det_j), joint_probability) tuples.
+#[pyfunction]
+#[pyo3(signature = (tick_circuit, idle_rz=0.0, p1=0.0, p2=0.0, p_meas=0.0, p_prep=0.0, prune=1e-12))]
+pub fn exact_pairwise_rates(
+    tick_circuit: &Bound<'_, PyAny>,
+    idle_rz: f64,
+    p1: f64,
+    p2: f64,
+    p_meas: f64,
+    p_prep: f64,
+    prune: f64,
+) -> PyResult<Vec<((usize, usize), f64)>> {
+    let noise = pecos_eeg::noise::UniformNoise {
+        idle_rz,
+        p1,
+        p2,
+        p_meas,
+        p_prep,
+    };
+    let gates = extract_gates(tick_circuit)?;
+    let expanded = pecos_eeg::expand::expand_circuit(&gates);
+    let (detectors, _observables) = extract_detectors_expanded(tick_circuit, &expanded)?;
+
+    let init_gates: Vec<Gate> = (0..expanded.num_original_qubits)
+        .map(|q| pecos_eeg::expand::make_gate(pecos_core::gate_type::GateType::PZ, &[q]))
+        .collect();
+    let stab =
+        pecos_eeg::stabilizer::StabilizerGroup::from_circuit(&init_gates, expanded.num_qubits);
+
+    let gate_index = pecos_eeg::expand::GateIndex::build(&expanded.gates, expanded.num_qubits);
+    let has_stochastic = p1 > 0.0 || p2 > 0.0 || p_meas > 0.0 || p_prep > 0.0;
+    let noise_map = if has_stochastic {
+        Some(pecos_eeg::heisenberg::build_noise_map(
+            &expanded.gates,
+            &noise,
+            &gate_index.expansion_gates,
+        ))
+    } else {
+        None
+    };
+
+    let walk = |stab_bm: &Bm| -> f64 {
+        pecos_eeg::heisenberg::heisenberg_sparse(
+            &expanded.gates,
+            stab_bm,
+            &noise,
+            &stab,
+            prune,
+            &gate_index,
+            noise_map.as_deref(),
+        )
+    };
+
+    // Marginals
+    let marginals: Vec<f64> = detectors.iter().map(|d| walk(&d.stabilizer)).collect();
+
+    // Pairwise: P(Di AND Dj) = (P(Di) + P(Dj) - P_walk(Si*Sj)) / 2
+    let pairs: Vec<(usize, usize)> = (0..detectors.len())
+        .flat_map(|i| ((i + 1)..detectors.len()).map(move |j| (i, j)))
+        .collect();
+
+    let results: Vec<((usize, usize), f64)> = pairs
+        .par_iter()
+        .map(|&(i, j)| {
+            let product = detectors[i].stabilizer.multiply(&detectors[j].stabilizer);
+            let p_product = walk(&product);
+            let p_joint = (marginals[i] + marginals[j] - p_product) / 2.0;
+            ((detectors[i].id, detectors[j].id), p_joint.max(0.0))
+        })
+        .collect();
+
+    Ok(results)
+}
+
+/// Build a coherent DEM with exact Heisenberg marginals.
+///
+/// Combines backward mechanism extraction (correct structure) with
+/// Heisenberg-exact per-detector rates (correct probabilities).
+/// Fits mechanism probabilities to match the exact marginals.
+///
+/// Returns the DEM as a Stim-format string.
+#[pyfunction]
+#[pyo3(signature = (tick_circuit, idle_rz=0.0, p1=0.0, p2=0.0, p_meas=0.0, p_prep=0.0, prune=1e-12))]
+pub fn coherent_dem_exact(
+    tick_circuit: &Bound<'_, PyAny>,
+    idle_rz: f64,
+    p1: f64,
+    p2: f64,
+    p_meas: f64,
+    p_prep: f64,
+    prune: f64,
+) -> PyResult<String> {
+    let noise = pecos_eeg::noise::UniformNoise {
+        idle_rz,
+        p1,
+        p2,
+        p_meas,
+        p_prep,
+    };
+    let gates = extract_gates(tick_circuit)?;
+    let expanded = pecos_eeg::expand::expand_circuit(&gates);
+    let (detectors, observables) = extract_detectors_expanded(tick_circuit, &expanded)?;
+    let gate_index = pecos_eeg::expand::GateIndex::build(&expanded.gates, expanded.num_qubits);
+
+    // Compute Heisenberg exact marginals
+    let init_gates: Vec<Gate> = (0..expanded.num_original_qubits)
+        .map(|q| pecos_eeg::expand::make_gate(pecos_core::gate_type::GateType::PZ, &[q]))
+        .collect();
+    let stab =
+        pecos_eeg::stabilizer::StabilizerGroup::from_circuit(&init_gates, expanded.num_qubits);
+    let has_stochastic = p1 > 0.0 || p2 > 0.0 || p_meas > 0.0 || p_prep > 0.0;
+    let noise_map = if has_stochastic {
+        Some(pecos_eeg::heisenberg::build_noise_map(
+            &expanded.gates,
+            &noise,
+            &gate_index.expansion_gates,
+        ))
+    } else {
+        None
+    };
+
+    let walk = |stab_bm: &Bm| -> f64 {
+        pecos_eeg::heisenberg::heisenberg_sparse(
+            &expanded.gates,
+            stab_bm,
+            &noise,
+            &stab,
+            prune,
+            &gate_index,
+            noise_map.as_deref(),
+        )
+    };
+
+    let mut marginals = vec![0.0_f64; detectors.iter().map(|d| d.id + 1).max().unwrap_or(0)];
+    for det in &detectors {
+        let p = walk(&det.stabilizer);
+        if det.id < marginals.len() {
+            marginals[det.id] = p;
+        }
+    }
+
+    // Compute pairwise rates via product stabilizer walks
+    let mut pairwise: Vec<((usize, usize), f64)> = Vec::new();
+    for i in 0..detectors.len() {
+        for j in (i + 1)..detectors.len() {
+            let product = detectors[i].stabilizer.multiply(&detectors[j].stabilizer);
+            let p_product = walk(&product);
+            let p_joint =
+                (marginals[detectors[i].id] + marginals[detectors[j].id] - p_product) / 2.0;
+            if p_joint > 1e-10 {
+                pairwise.push(((detectors[i].id, detectors[j].id), p_joint.max(0.0)));
+            }
+        }
+    }
+
+    // Build DEM with exact marginals + pairwise
+    let entries = pecos_eeg::coherent_dem::build_coherent_dem_exact(
+        &expanded.gates,
+        &noise,
+        &detectors,
+        &observables,
+        &gate_index.expansion_gates,
+        &marginals,
+        Some(&pairwise),
+    );
+
+    Ok(pecos_eeg::dem_mapping::format_dem(&entries))
+}
+
+/// Build coherent DEM with proper X/Z decomposition for MWPM decoders.
+///
+/// Returns (raw_dem, decomposed_dem) where the decomposed version uses
+/// Pauli provenance to split hyperedges into X ^ Z components.
+/// Probabilities are fitted to Heisenberg-exact marginals via L-BFGS.
+#[pyfunction]
+#[pyo3(signature = (tick_circuit, idle_rz=0.0, p1=0.0, p2=0.0, p_meas=0.0, p_prep=0.0, prune=1e-12))]
+pub fn coherent_dem_decomposed(
+    tick_circuit: &Bound<'_, PyAny>,
+    idle_rz: f64,
+    p1: f64,
+    p2: f64,
+    p_meas: f64,
+    p_prep: f64,
+    prune: f64,
+) -> PyResult<(String, String)> {
+    let noise = pecos_eeg::noise::UniformNoise {
+        idle_rz,
+        p1,
+        p2,
+        p_meas,
+        p_prep,
+    };
+    let gates = extract_gates(tick_circuit)?;
+    let expanded = pecos_eeg::expand::expand_circuit(&gates);
+    let (detectors, observables) = extract_detectors_expanded(tick_circuit, &expanded)?;
+    let gate_index = pecos_eeg::expand::GateIndex::build(&expanded.gates, expanded.num_qubits);
+
+    // Compute Heisenberg-exact marginals for probability fitting
+    let init_gates: Vec<Gate> = (0..expanded.num_original_qubits)
+        .map(|q| pecos_eeg::expand::make_gate(pecos_core::gate_type::GateType::PZ, &[q]))
+        .collect();
+    let stab =
+        pecos_eeg::stabilizer::StabilizerGroup::from_circuit(&init_gates, expanded.num_qubits);
+    let has_stochastic = p1 > 0.0 || p2 > 0.0 || p_meas > 0.0 || p_prep > 0.0;
+    let noise_map = if has_stochastic {
+        Some(pecos_eeg::heisenberg::build_noise_map(
+            &expanded.gates,
+            &noise,
+            &gate_index.expansion_gates,
+        ))
+    } else {
+        None
+    };
+
+    let walk = |stab_bm: &Bm| -> f64 {
+        pecos_eeg::heisenberg::heisenberg_sparse(
+            &expanded.gates,
+            stab_bm,
+            &noise,
+            &stab,
+            prune,
+            &gate_index,
+            noise_map.as_deref(),
+        )
+    };
+
+    let mut marginals = vec![0.0_f64; detectors.iter().map(|d| d.id + 1).max().unwrap_or(0)];
+    for det in &detectors {
+        let p = walk(&det.stabilizer);
+        if det.id < marginals.len() {
+            marginals[det.id] = p;
+        }
+    }
+
+    // Pairwise rates for better fitting
+    let mut pairwise: Vec<((usize, usize), f64)> = Vec::new();
+    for i in 0..detectors.len() {
+        for j in (i + 1)..detectors.len() {
+            let product = detectors[i].stabilizer.multiply(&detectors[j].stabilizer);
+            let p_product = walk(&product);
+            let p_joint =
+                (marginals[detectors[i].id] + marginals[detectors[j].id] - p_product) / 2.0;
+            if p_joint > 1e-10 {
+                pairwise.push(((detectors[i].id, detectors[j].id), p_joint.max(0.0)));
+            }
+        }
+    }
+
+    // Build decomposable entries with exact-fitted probabilities
+    let entries = pecos_eeg::coherent_dem::build_coherent_dem_exact_decomposable(
+        &expanded.gates,
+        &noise,
+        &detectors,
+        &observables,
+        &gate_index.expansion_gates,
+        &marginals,
+        Some(&pairwise),
+    );
+
+    let raw = pecos_eeg::dem_mapping::format_dem(
+        &entries
+            .iter()
+            .map(|e| pecos_eeg::dem_mapping::DemEntry {
+                event: e.event.clone(),
+                probability: e.probability,
+            })
+            .collect::<Vec<_>>(),
+    );
+    let decomposed = pecos_eeg::dem_mapping::format_dem_decomposed(&entries);
+
+    Ok((raw, decomposed))
+}
+
+/// Compute exact k-body detector correlation table from Heisenberg walks.
+///
+/// Returns exact joint detection probabilities for all detector subsets
+/// up to `max_order`. No DEM approximation — captures all coherent
+/// interference. Useful for decoders that can consume raw correlation data.
+///
+/// Returns a list of (detector_indices, probability) pairs.
+#[pyfunction]
+#[pyo3(signature = (tick_circuit, idle_rz=0.0, p1=0.0, p2=0.0, p_meas=0.0, p_prep=0.0, max_order=2, prune=1e-12))]
+pub fn exact_correlation_table(
+    tick_circuit: &Bound<'_, PyAny>,
+    idle_rz: f64,
+    p1: f64,
+    p2: f64,
+    p_meas: f64,
+    p_prep: f64,
+    max_order: usize,
+    prune: f64,
+) -> PyResult<Vec<(Vec<String>, f64)>> {
+    let noise = pecos_eeg::noise::UniformNoise {
+        idle_rz,
+        p1,
+        p2,
+        p_meas,
+        p_prep,
+    };
+    let gates = extract_gates(tick_circuit)?;
+    let expanded = pecos_eeg::expand::expand_circuit(&gates);
+    let (detectors, observables) = extract_detectors_expanded(tick_circuit, &expanded)?;
+
+    let init_gates: Vec<Gate> = (0..expanded.num_original_qubits)
+        .map(|q| pecos_eeg::expand::make_gate(pecos_core::gate_type::GateType::PZ, &[q]))
+        .collect();
+    let stab =
+        pecos_eeg::stabilizer::StabilizerGroup::from_circuit(&init_gates, expanded.num_qubits);
+
+    let table = pecos_eeg::correlation_table::compute_correlation_table(CorrelationTableInput {
+        gates: &expanded.gates,
+        noise: &noise,
+        detectors: &detectors,
+        observables: &observables,
+        initial_stab: &stab,
+        num_qubits: expanded.num_qubits,
+        max_order,
+        prune_threshold: prune,
+    });
+
+    // String labels: "D0", "D1", "L0" — consistent with Stim DEM format.
+    let mut result: Vec<(Vec<String>, f64)> = table
+        .rates
+        .into_iter()
+        .map(|(k, v)| (k.into_iter().map(|d| format!("D{d}")).collect(), v))
+        .collect();
+
+    // Observable correlations with string labels
+    for ((det_ids, obs_id), prob) in table.observable_rates {
+        let mut labels: Vec<String> = det_ids.into_iter().map(|d| format!("D{d}")).collect();
+        labels.push(format!("L{obs_id}"));
+        result.push((labels, prob));
+    }
+
+    Ok(result)
+}
+
+/// Build a graphlike DEM from exact Heisenberg correlation tables.
+///
+/// Bypasses the DEM independent error model entirely. Edge weights come
+/// directly from exact pairwise correlations (including all coherent
+/// interference effects). For MWPM decoders.
+///
+/// Returns a DEM string suitable for pymatching/fusion_blossom.
+#[pyfunction]
+#[pyo3(signature = (tick_circuit, idle_rz=0.0, p1=0.0, p2=0.0, p_meas=0.0, p_prep=0.0, max_order=2, prune=1e-12))]
+pub fn correlation_matching_dem(
+    tick_circuit: &Bound<'_, PyAny>,
+    idle_rz: f64,
+    p1: f64,
+    p2: f64,
+    p_meas: f64,
+    p_prep: f64,
+    max_order: usize,
+    prune: f64,
+) -> PyResult<String> {
+    let noise = pecos_eeg::noise::UniformNoise {
+        idle_rz,
+        p1,
+        p2,
+        p_meas,
+        p_prep,
+    };
+    let gates = extract_gates(tick_circuit)?;
+    let expanded = pecos_eeg::expand::expand_circuit(&gates);
+    let (detectors, observables) = extract_detectors_expanded(tick_circuit, &expanded)?;
+
+    let init_gates: Vec<Gate> = (0..expanded.num_original_qubits)
+        .map(|q| pecos_eeg::expand::make_gate(pecos_core::gate_type::GateType::PZ, &[q]))
+        .collect();
+    let stab =
+        pecos_eeg::stabilizer::StabilizerGroup::from_circuit(&init_gates, expanded.num_qubits);
+
+    let table = pecos_eeg::correlation_table::compute_correlation_table(CorrelationTableInput {
+        gates: &expanded.gates,
+        noise: &noise,
+        detectors: &detectors,
+        observables: &observables,
+        initial_stab: &stab,
+        num_qubits: expanded.num_qubits,
+        max_order,
+        prune_threshold: prune,
+    });
+
+    Ok(table.to_matching_dem())
+}
+
+/// Compress mid-round noise to round boundaries (optional optimization).
+///
+/// Propagates gate noise forward to round boundaries, accumulating
+/// faults with the same effective Pauli label. Measurement and prep
+/// noise kept at original positions. Returns compression statistics.
+///
+/// For stochastic Pauli noise: exact. For coherent: within-round exact.
+///
+/// Returns (original_count, compressed_count, boundary_noise_labels).
+#[pyfunction]
+#[pyo3(signature = (tick_circuit, idle_rz=0.0, p1=0.0, p2=0.0, p_meas=0.0, p_prep=0.0))]
+pub fn compress_noise(
+    tick_circuit: &Bound<'_, PyAny>,
+    idle_rz: f64,
+    p1: f64,
+    p2: f64,
+    p_meas: f64,
+    p_prep: f64,
+) -> PyResult<(usize, usize)> {
+    let noise = pecos_eeg::noise::UniformNoise {
+        idle_rz,
+        p1,
+        p2,
+        p_meas,
+        p_prep,
+    };
+    let gates = extract_gates(tick_circuit)?;
+    let expanded = pecos_eeg::expand::expand_circuit(&gates);
+    let gate_index = pecos_eeg::expand::GateIndex::build(&expanded.gates, expanded.num_qubits);
+
+    let result = pecos_eeg::noise_compression::compress_noise_to_boundaries(
+        &expanded.gates,
+        &noise,
+        &gate_index.expansion_gates,
+    );
+
+    Ok((result.original_count, result.compressed_count))
+}
+
+/// Complete noise characterization: correlations + mechanisms + DEM.
+///
+/// Returns a JSON string containing:
+/// - Exact k-body detector correlations (from Heisenberg walks)
+/// - Detector-observable cross-correlations
+/// - Mechanism catalog with fitted probabilities
+/// - DEM string for standard decoders
+///
+/// This is the unified output that captures everything a decoder needs.
+#[pyfunction]
+#[pyo3(signature = (tick_circuit, idle_rz=0.0, p1=0.0, p2=0.0, p_meas=0.0, p_prep=0.0, max_order=2, prune=1e-12, compress=false))]
+pub fn noise_characterization(
+    tick_circuit: &Bound<'_, PyAny>,
+    idle_rz: f64,
+    p1: f64,
+    p2: f64,
+    p_meas: f64,
+    p_prep: f64,
+    max_order: usize,
+    prune: f64,
+    compress: bool,
+) -> PyResult<(String, String, String)> {
+    let base_noise = pecos_eeg::noise::UniformNoise {
+        idle_rz,
+        p1,
+        p2,
+        p_meas,
+        p_prep,
+    };
+    let gates = extract_gates(tick_circuit)?;
+    let expanded = pecos_eeg::expand::expand_circuit(&gates);
+    let (detectors, observables) = extract_detectors_expanded(tick_circuit, &expanded)?;
+
+    let init_gates: Vec<Gate> = (0..expanded.num_original_qubits)
+        .map(|q| pecos_eeg::expand::make_gate(pecos_core::gate_type::GateType::PZ, &[q]))
+        .collect();
+    let stab =
+        pecos_eeg::stabilizer::StabilizerGroup::from_circuit(&init_gates, expanded.num_qubits);
+
+    // For compressed mode: use original noise for Heisenberg targets (exact),
+    // compressed noise for mechanism structure (fast).
+    let structure_noise: Option<Box<dyn pecos_eeg::noise::NoiseSpec>> = if compress {
+        let gate_index = pecos_eeg::expand::GateIndex::build(&expanded.gates, expanded.num_qubits);
+        let compressed = pecos_eeg::noise_compression::compress_noise_to_boundaries(
+            &expanded.gates,
+            &base_noise,
+            &gate_index.expansion_gates,
+        );
+        Some(Box::new(
+            pecos_eeg::noise_compression::CompressedNoiseSpec::from_compressed(&compressed),
+        ))
+    } else {
+        None
+    };
+
+    let det_meas_ids = extract_meas_id_defs(tick_circuit, "detectors")?;
+    let obs_meas_ids = extract_meas_id_defs(tick_circuit, "observables")?;
+
+    let nc = pecos_eeg::noise_characterization::NoiseCharacterization::build(
+        NoiseCharacterizationInput {
+            gates: &expanded.gates,
+            noise: &base_noise,
+            structure_noise: structure_noise.as_deref(),
+            detectors: &detectors,
+            observables: &observables,
+            initial_stab: &stab,
+            num_qubits: expanded.num_qubits,
+            max_order,
+            prune_threshold: prune,
+            detector_meas_ids: &det_meas_ids,
+            observable_meas_ids: &obs_meas_ids,
+        },
+    );
+
+    Ok((
+        nc.to_json(),
+        nc.to_dem_string(),
+        nc.to_dem_string_decomposed(),
+    ))
+}
+
+// -- Internal --
+
+fn parse_h_formula(s: &str) -> PyResult<pecos_eeg::dem_mapping::HFormula> {
+    match s {
+        "taylor" => Ok(pecos_eeg::dem_mapping::HFormula::Taylor),
+        "sin_squared" => Ok(pecos_eeg::dem_mapping::HFormula::SinSquared),
+        "exact_commuting" => Ok(pecos_eeg::dem_mapping::HFormula::ExactCommuting),
+        "exact_subset" => Ok(pecos_eeg::dem_mapping::HFormula::ExactSubset),
+        _ => Err(pyo3::exceptions::PyValueError::new_err(format!(
+            "Unknown h_formula '{s}'. Use 'taylor', 'sin_squared', 'exact_commuting', or 'exact_subset'."
+        ))),
+    }
+}
+
+fn run_eeg(
+    py_tc: &Bound<'_, PyAny>,
+    idle_rz: f64,
+    p1: f64,
+    p2: f64,
+    p_meas: f64,
+    p_prep: f64,
+    h_formula: &str,
+    bch_order: u32,
+) -> PyResult<Vec<DemEntry>> {
+    let noise = NoiseModel {
+        idle_rz,
+        p1,
+        p2,
+        p_meas,
+        p_prep,
+    };
+    let gates = extract_gates(py_tc)?;
+
+    // Step 1: Expand circuit (defer measurements)
+    let expanded = pecos_eeg::expand::expand_circuit(&gates);
+
+    // Step 2: Propagate through expanded circuit
+    let result = pecos_eeg::circuit::analyze_expanded(&expanded.gates, &noise);
+
+    // Step 3: Build detectors using expanded circuit mapping
+    let (detectors, observables) = extract_detectors_expanded(py_tc, &expanded)?;
+
+    // Step 4: Compute stabilizer group from EXPANDED circuit (pre-readout).
+    // Use expanded frame directly — no lossy original-frame mapping.
+    // Strip trailing deferred MZ(aux) from the expanded circuit.
+    let expanded_pre_readout = exclude_final_mz(&expanded.gates);
+    let stab_group = pecos_eeg::stabilizer::StabilizerGroup::from_circuit(
+        &expanded_pre_readout,
+        expanded.num_qubits,
+    );
+
+    // Step 5: Build DEM (stabilizer check in expanded frame)
+    let config = pecos_eeg::dem_mapping::EegConfig {
+        h_formula: parse_h_formula(h_formula)?,
+        bch_order: if bch_order >= 2 {
+            pecos_eeg::dem_mapping::BchOrder::Second
+        } else {
+            pecos_eeg::dem_mapping::BchOrder::First
+        },
+    };
+    Ok(pecos_eeg::dem_mapping::build_dem_configured(
+        &result.generators,
+        &detectors,
+        &observables,
+        Some(&stab_group),
+        &config,
+    ))
+}
+
+fn run_eeg_decomposable(
+    py_tc: &Bound<'_, PyAny>,
+    idle_rz: f64,
+    p1: f64,
+    p2: f64,
+    p_meas: f64,
+    p_prep: f64,
+    h_formula: &str,
+    bch_order: u32,
+) -> PyResult<(
+    Vec<DemEntry>,
+    Vec<pecos_eeg::dem_mapping::DecomposableDemEntry>,
+)> {
+    let noise = NoiseModel {
+        idle_rz,
+        p1,
+        p2,
+        p_meas,
+        p_prep,
+    };
+    let gates = extract_gates(py_tc)?;
+    let expanded = pecos_eeg::expand::expand_circuit(&gates);
+    let result = pecos_eeg::circuit::analyze_expanded(&expanded.gates, &noise);
+    let (detectors, observables) = extract_detectors_expanded(py_tc, &expanded)?;
+    let expanded_pre_readout = exclude_final_mz(&expanded.gates);
+    let stab_group = pecos_eeg::stabilizer::StabilizerGroup::from_circuit(
+        &expanded_pre_readout,
+        expanded.num_qubits,
+    );
+    let config = pecos_eeg::dem_mapping::EegConfig {
+        h_formula: parse_h_formula(h_formula)?,
+        bch_order: if bch_order >= 2 {
+            pecos_eeg::dem_mapping::BchOrder::Second
+        } else {
+            pecos_eeg::dem_mapping::BchOrder::First
+        },
+    };
+    let raw = pecos_eeg::dem_mapping::build_dem_configured(
+        &result.generators,
+        &detectors,
+        &observables,
+        Some(&stab_group),
+        &config,
+    );
+    let decomposable = pecos_eeg::dem_mapping::build_dem_decomposable(
+        &result.generators,
+        &detectors,
+        &observables,
+        Some(&stab_group),
+        &config,
+    );
+    Ok((raw, decomposable))
+}
+
+/// Strip all trailing MZ from expanded circuit (deferred measurements).
+fn exclude_final_mz(gates: &[Gate]) -> Vec<Gate> {
+    let last_non_mz = gates
+        .iter()
+        .rposition(|g| g.gate_type != pecos_core::gate_type::GateType::MZ);
+    match last_non_mz {
+        Some(idx) => gates[..=idx].to_vec(),
+        None => Vec::new(),
+    }
+}
+
+fn extract_gates(py_tc: &Bound<'_, PyAny>) -> PyResult<Vec<Gate>> {
+    let num_ticks: usize = py_tc.call_method0("num_ticks")?.extract()?;
+    let mut gates = Vec::new();
+
+    for tick_idx in 0..num_ticks {
+        let py_tick = py_tc.call_method1("get_tick", (tick_idx,))?;
+        let py_gates = py_tick.call_method0("gate_batches")?;
+        let gate_list: Vec<Bound<'_, PyAny>> = py_gates.extract()?;
+
+        // Collect all gates in this tick first, then emit them.
+        // This preserves the simultaneity of gates within a tick:
+        // all Clifford gates in the tick execute "at once", and noise
+        // is injected after the entire tick (not between gates).
+        let mut tick_gates = Vec::new();
+
+        for gate in &gate_list {
+            let name: String = gate.getattr("gate_type")?.getattr("name")?.extract()?;
+            let qubits: Vec<usize> = gate.getattr("qubits")?.extract()?;
+
+            match name.as_str() {
+                "CX" | "CY" | "CZ" | "SWAP" | "SZZ" | "SZZdg" | "SXX" | "SXXdg" | "SYY"
+                | "SYYdg" => {
+                    // Split multi-pair 2q gates into individual pairs
+                    let gt = match name.as_str() {
+                        "CX" => pecos_core::gate_type::GateType::CX,
+                        "CY" => pecos_core::gate_type::GateType::CY,
+                        "CZ" => pecos_core::gate_type::GateType::CZ,
+                        "SWAP" => pecos_core::gate_type::GateType::SWAP,
+                        "SZZ" => pecos_core::gate_type::GateType::SZZ,
+                        "SZZdg" => pecos_core::gate_type::GateType::SZZdg,
+                        "SXX" => pecos_core::gate_type::GateType::SXX,
+                        "SXXdg" => pecos_core::gate_type::GateType::SXXdg,
+                        "SYY" => pecos_core::gate_type::GateType::SYY,
+                        _ => pecos_core::gate_type::GateType::SYYdg,
+                    };
+                    for pair in qubits.chunks(2) {
+                        if pair.len() == 2 {
+                            tick_gates.push(Gate {
+                                gate_type: gt,
+                                qubits: pair.iter().map(|&q| QubitId(q)).collect(),
+                                angles: GateAngles::new(),
+                                params: GateParams::new(),
+                                meas_ids: GateMeasIds::new(),
+                                channel: None,
+                            });
+                        }
+                    }
+                }
+                // Single-qubit gates: split multi-qubit into individual per-qubit gates
+                "H" | "X" | "Y" | "Z" | "SZ" | "SZdg" | "SX" | "SXdg" | "SY" | "SYdg" | "F"
+                | "Fdg" => {
+                    let gt = match name.as_str() {
+                        "H" => pecos_core::gate_type::GateType::H,
+                        "X" => pecos_core::gate_type::GateType::X,
+                        "Y" => pecos_core::gate_type::GateType::Y,
+                        "Z" => pecos_core::gate_type::GateType::Z,
+                        "SZ" => pecos_core::gate_type::GateType::SZ,
+                        "SZdg" => pecos_core::gate_type::GateType::SZdg,
+                        "SX" => pecos_core::gate_type::GateType::SX,
+                        "SXdg" => pecos_core::gate_type::GateType::SXdg,
+                        "SY" => pecos_core::gate_type::GateType::SY,
+                        "F" => pecos_core::gate_type::GateType::F,
+                        "Fdg" => pecos_core::gate_type::GateType::Fdg,
+                        _ => pecos_core::gate_type::GateType::SYdg,
+                    };
+                    for &q in &qubits {
+                        tick_gates.push(Gate {
+                            gate_type: gt,
+                            qubits: std::iter::once(QubitId(q)).collect(),
+                            angles: GateAngles::new(),
+                            params: GateParams::new(),
+                            meas_ids: GateMeasIds::new(),
+                            channel: None,
+                        });
+                    }
+                }
+                // PZ/QAlloc: split multi-qubit into per-qubit
+                "QAlloc" | "PZ" => {
+                    for &q in &qubits {
+                        tick_gates.push(Gate {
+                            gate_type: pecos_core::gate_type::GateType::PZ,
+                            qubits: std::iter::once(QubitId(q)).collect(),
+                            angles: GateAngles::new(),
+                            params: GateParams::new(),
+                            meas_ids: GateMeasIds::new(),
+                            channel: None,
+                        });
+                    }
+                }
+                // MZ: keep multi-qubit (expansion handles per-qubit)
+                _ => {
+                    let gt = match name.as_str() {
+                        "MZ" | "MeasureFree" => pecos_core::gate_type::GateType::MZ,
+                        "RZ" => pecos_core::gate_type::GateType::RZ,
+                        "Idle" | "I" => pecos_core::gate_type::GateType::Idle,
+                        other => {
+                            return Err(pyo3::exceptions::PyValueError::new_err(format!(
+                                "EEG extract_gates: unsupported gate type {other:?}"
+                            )));
+                        }
+                    };
+                    let mut g = Gate {
+                        gate_type: gt,
+                        qubits: qubits.iter().map(|&q| QubitId(q)).collect(),
+                        angles: GateAngles::new(),
+                        params: GateParams::new(),
+                        meas_ids: GateMeasIds::new(),
+                        channel: None,
+                    };
+                    if gt == pecos_core::gate_type::GateType::RZ
+                        && let Ok(angles) = gate.getattr("angles")?.extract::<Vec<f64>>()
+                        && let Some(&a) = angles.first()
+                    {
+                        g.angles.push(Angle64::from_radians(a));
+                    }
+                    tick_gates.push(g);
+                }
+            }
+        }
+
+        // Emit all gates from this tick. Gates within a tick are simultaneous,
+        // so noise injected after the last gate correctly sees all tick gates
+        // as already applied.
+        gates.extend(tick_gates);
+    }
+
+    Ok(gates)
+}
+
+fn measurement_record_index(record: i32, num_measurements: usize) -> Option<usize> {
+    let idx = if record < 0 {
+        i32::try_from(num_measurements).ok()?.checked_add(record)?
+    } else {
+        record
+    };
+    usize::try_from(idx)
+        .ok()
+        .filter(|&idx| idx < num_measurements)
+}
+
+fn extract_detectors_expanded(
+    py_tc: &Bound<'_, PyAny>,
+    expanded: &pecos_eeg::expand::ExpandedCircuit,
+) -> PyResult<(Vec<Detector>, Vec<Observable>)> {
+    // In the expanded circuit, each measurement record k maps to a
+    // Z-measurement on auxiliary qubit expanded.measurement_qubit[k].
+    //
+    // A detector defined by records {r1, r2, ...} has stabilizer
+    // Z_{aux_r1} * Z_{aux_r2} * ... in the expanded circuit.
+    let num_meas = expanded.measurement_qubit.len();
+
+    let mut detectors = Vec::new();
+    let mut observables = Vec::new();
+
+    // Parse detector JSON from metadata
+    if let Ok(det_json_str) = py_tc.call_method1("get_meta", ("detectors",))
+        && let Ok(det_json) = det_json_str.extract::<String>()
+        && let Ok(det_list) = serde_json_parse_detectors(&det_json)
+    {
+        for (id, records) in det_list {
+            let mut bm = Bm::default();
+            for &rec in &records {
+                if let Some(abs_idx) = measurement_record_index(rec, num_meas) {
+                    // Map to AUXILIARY qubit in expanded circuit
+                    let aux_qubit = expanded.measurement_qubit[abs_idx];
+                    bm.z_bits.xor_bit(aux_qubit);
+                }
+            }
+            detectors.push(Detector { id, stabilizer: bm });
+        }
+    }
+
+    // Parse observable JSON from metadata
+    if let Ok(obs_json_str) = py_tc.call_method1("get_meta", ("observables",))
+        && let Ok(obs_json) = obs_json_str.extract::<String>()
+        && let Ok(obs_list) = serde_json_parseobservables(&obs_json)
+    {
+        for (id, records) in obs_list {
+            let mut bm = Bm::default();
+            for &rec in &records {
+                if let Some(abs_idx) = measurement_record_index(rec, num_meas) {
+                    let aux_qubit = expanded.measurement_qubit[abs_idx];
+                    bm.z_bits.xor_bit(aux_qubit);
+                }
+            }
+            observables.push(Observable { id, pauli: bm });
+        }
+    }
+
+    Ok((detectors, observables))
+}
+
+/// Minimal JSON parser for detector definitions (avoids serde dependency).
+/// Parses [{"id": N, "records": [R1, R2, ...], ...}, ...]
+fn serde_json_parse_detectors(json: &str) -> Result<Vec<(usize, Vec<i32>)>, String> {
+    // Simple approach: find "id" and "records" fields via string scanning
+    let mut result = Vec::new();
+    let mut pos = 0;
+    while let Some(start) = json[pos..].find('{') {
+        let start = pos + start;
+        let end = json[start..]
+            .find('}')
+            .map(|e| start + e + 1)
+            .ok_or_else(|| "Unmatched brace".to_string())?;
+        let entry = &json[start..end];
+
+        let id = extract_json_int(entry, "\"id\"")
+            .and_then(|value| usize::try_from(value).ok())
+            .unwrap_or(result.len());
+        let records = extract_json_int_array(entry, "\"records\"").unwrap_or_default();
+
+        result.push((id, records));
+        pos = end;
+    }
+    Ok(result)
+}
+
+fn serde_json_parseobservables(json: &str) -> Result<Vec<(usize, Vec<i32>)>, String> {
+    serde_json_parse_detectors(json) // Same format
+}
+
+/// Extract MeasId definitions from circuit metadata JSON.
+fn extract_meas_id_defs(
+    py_tc: &Bound<'_, pyo3::PyAny>,
+    key: &str, // "detectors" or "observables"
+) -> PyResult<Vec<MeasurementRecordDefinition>> {
+    let mut result = Vec::new();
+    if let Ok(json_str) = py_tc.call_method1("get_meta", (key,))
+        && let Ok(s) = json_str.extract::<String>()
+    {
+        // Parse JSON: each item has id, meas_ids (optional), records
+        let items = parse_json_items(&s);
+        for (idx, (records, meas_ids)) in items.iter().enumerate() {
+            result.push((idx, meas_ids.clone(), records.clone()));
+        }
+    }
+    Ok(result)
+}
+
+/// Parse JSON array items, extracting records and meas_ids fields.
+fn parse_json_items(json: &str) -> Vec<(Vec<i32>, Vec<usize>)> {
+    let mut result = Vec::new();
+    // Split by "records" occurrences
+    let trimmed = json.trim();
+    if !trimmed.starts_with('[') {
+        return result;
+    }
+
+    // Simple state machine: find each {...} block and extract fields
+    let mut depth = 0;
+    let mut block_start = None;
+    for (i, ch) in trimmed.char_indices() {
+        match ch {
+            '{' => {
+                if depth == 1 {
+                    block_start = Some(i);
+                }
+                depth += 1;
+            }
+            '}' => {
+                depth -= 1;
+                if depth == 1
+                    && let Some(start) = block_start
+                {
+                    let block = &trimmed[start..=i];
+                    let records = extract_json_int_array(block, "records").unwrap_or_default();
+                    let meas_ids = extract_json_int_array(block, "meas_ids")
+                        .map(|v| {
+                            v.into_iter()
+                                .filter_map(|x| usize::try_from(x).ok())
+                                .collect()
+                        })
+                        .unwrap_or_default();
+                    result.push((records, meas_ids));
+                }
+            }
+            '[' if depth == 0 => {
+                depth = 1;
+            }
+            ']' if depth == 1 => {
+                break;
+            }
+            _ => {}
+        }
+    }
+    result
+}
+
+fn extract_json_int(s: &str, key: &str) -> Option<i64> {
+    let key_pos = s.find(key)?;
+    let after_key = &s[key_pos + key.len()..];
+    let colon = after_key.find(':')?;
+    let value_str = after_key[colon + 1..].trim();
+    // Read digits (possibly with minus)
+    let end = value_str
+        .find(|c: char| !c.is_ascii_digit() && c != '-')
+        .unwrap_or(value_str.len());
+    value_str[..end].trim().parse().ok()
+}
+
+fn extract_json_int_array(s: &str, key: &str) -> Option<Vec<i32>> {
+    let key_pos = s.find(key)?;
+    let after_key = &s[key_pos + key.len()..];
+    let bracket_start = after_key.find('[')?;
+    let bracket_end = after_key[bracket_start..].find(']')? + bracket_start;
+    let array_str = &after_key[bracket_start + 1..bracket_end];
+    let values: Vec<i32> = array_str
+        .split(',')
+        .filter_map(|v| v.trim().parse().ok())
+        .collect();
+    Some(values)
+}
diff --git a/python/pecos-rslib-exp/src/lib.rs b/python/pecos-rslib-exp/src/lib.rs
index 382b2f4d3..bf1a8fe67 100644
--- a/python/pecos-rslib-exp/src/lib.rs
+++ b/python/pecos-rslib-exp/src/lib.rs
@@ -10,13 +10,31 @@
 // express or implied. See the License for the specific language governing permissions and
 // limitations under the License.
 
+// Experimental PyO3 binding signatures are constrained by Python-callable APIs
+// and generated method wrappers. Python docstrings also contain Python snippets
+// that Clippy's Rust-doc Markdown lint misclassifies. Keep this list limited to
+// binding/docs shape lints.
+#![allow(
+    clippy::doc_markdown,
+    clippy::missing_errors_doc,
+    clippy::missing_panics_doc,
+    clippy::needless_pass_by_value,
+    clippy::too_many_arguments,
+    clippy::unnecessary_wraps,
+    clippy::unused_self
+)]
+
 //! Python bindings for experimental PECOS simulators.
 //!
 //! Exposes `StabMps` (stabilizer + MPS hybrid) and `Mast` (magic state
 //! injection) from `pecos-stab-tn` via `PyO3`.
 
+mod coherent_idle_channel;
+mod eeg_bindings;
 mod mast_bindings;
+mod sim_neo_bindings;
 mod stab_mps_bindings;
+pub mod stabmps_builder;
 
 use pecos_core::Angle64;
 use pyo3::prelude::*;
@@ -48,5 +66,38 @@ pub(crate) fn extract_angle(
 fn pecos_rslib_exp(m: &Bound<'_, PyModule>) -> PyResult<()> {
     m.add_class::<stab_mps_bindings::PyStabMps>()?;
     m.add_class::<mast_bindings::PyMast>()?;
+    m.add_class::<sim_neo_bindings::PySimNeoBuilder>()?;
+    m.add_class::<sim_neo_bindings::PyStabMpsBuilder>()?;
+    m.add_class::<sim_neo_bindings::PyNoiseModelBuilder>()?;
+    m.add_function(wrap_pyfunction!(sim_neo_bindings::py_sim_neo, m)?)?;
+    m.add_function(wrap_pyfunction!(sim_neo_bindings::stab_mps, m)?)?;
+    m.add_function(wrap_pyfunction!(sim_neo_bindings::depolarizing, m)?)?;
+    m.add_class::<sim_neo_bindings::PyStateVecBuilder>()?;
+    m.add_class::<sim_neo_bindings::PyStabilizerBuilder>()?;
+    m.add_function(wrap_pyfunction!(sim_neo_bindings::statevec, m)?)?;
+    m.add_function(wrap_pyfunction!(sim_neo_bindings::stabilizer, m)?)?;
+    m.add_class::<sim_neo_bindings::PyMeasSamplingBuilder>()?;
+    m.add_class::<sim_neo_bindings::PyRawMeasurementResult>()?;
+    m.add_function(wrap_pyfunction!(sim_neo_bindings::meas_sampling, m)?)?;
+    m.add_class::<sim_neo_bindings::PyFaultCatalog>()?;
+    m.add_class::<sim_neo_bindings::PyFaultLocation>()?;
+    m.add_class::<sim_neo_bindings::PyFaultAlternative>()?;
+    m.add_class::<sim_neo_bindings::PyFaultConfiguration>()?;
+    m.add_class::<sim_neo_bindings::PyFaultConfigurationIter>()?;
+    m.add_function(wrap_pyfunction!(sim_neo_bindings::fault_catalog, m)?)?;
+    // DEM generation functions
+    m.add_function(wrap_pyfunction!(eeg_bindings::exact_detection_rates, m)?)?;
+    m.add_function(wrap_pyfunction!(eeg_bindings::exact_pairwise_rates, m)?)?;
+    m.add_function(wrap_pyfunction!(eeg_bindings::coherent_dem_exact, m)?)?;
+    m.add_function(wrap_pyfunction!(eeg_bindings::coherent_dem_decomposed, m)?)?;
+    m.add_function(wrap_pyfunction!(eeg_bindings::exact_correlation_table, m)?)?;
+    m.add_function(wrap_pyfunction!(eeg_bindings::correlation_matching_dem, m)?)?;
+    m.add_function(wrap_pyfunction!(eeg_bindings::noise_characterization, m)?)?;
+    m.add_function(wrap_pyfunction!(eeg_bindings::compress_noise, m)?)?;
+    m.add_function(wrap_pyfunction!(eeg_bindings::perturbative_dem, m)?)?;
+    m.add_function(wrap_pyfunction!(eeg_bindings::perturbative_dem_events, m)?)?;
+    m.add_function(wrap_pyfunction!(eeg_bindings::eeg_summary, m)?)?;
+    m.add_function(wrap_pyfunction!(eeg_bindings::eeg_event_diagnostics, m)?)?;
+    m.add_function(wrap_pyfunction!(eeg_bindings::eeg_per_detector, m)?)?;
     Ok(())
 }
diff --git a/python/pecos-rslib-exp/src/mast_bindings.rs b/python/pecos-rslib-exp/src/mast_bindings.rs
index 5e4ec8f1e..6f8c32e54 100644
--- a/python/pecos-rslib-exp/src/mast_bindings.rs
+++ b/python/pecos-rslib-exp/src/mast_bindings.rs
@@ -120,11 +120,35 @@ impl PyMast {
                 self.inner.h(q);
                 Ok(None)
             }
+            "F" | "F1" => {
+                self.inner.f(q);
+                Ok(None)
+            }
+            "Fdg" | "F1d" | "F1dg" => {
+                self.inner.fdg(q);
+                Ok(None)
+            }
+            "SX" | "SqrtX" | "Q" => {
+                self.inner.sx(q);
+                Ok(None)
+            }
+            "SXdg" | "SqrtXdg" | "SqrtXd" | "Qd" => {
+                self.inner.sxdg(q);
+                Ok(None)
+            }
+            "SY" | "SqrtY" | "R" => {
+                self.inner.sy(q);
+                Ok(None)
+            }
+            "SYdg" | "SqrtYdg" | "SqrtYd" | "Rd" => {
+                self.inner.sydg(q);
+                Ok(None)
+            }
             "S" | "SZ" | "SqrtZ" => {
                 self.inner.sz(q);
                 Ok(None)
             }
-            "Sd" | "SZdg" | "SqrtZdg" => {
+            "Sd" | "SZdg" | "SqrtZdg" | "SqrtZd" => {
                 self.inner.szdg(q);
                 Ok(None)
             }
@@ -211,6 +235,34 @@ impl PyMast {
                 self.inner.cz(pair);
                 Ok(None)
             }
+            "SXX" => {
+                self.inner.sxx(pair);
+                Ok(None)
+            }
+            "SXXdg" => {
+                self.inner.sxxdg(pair);
+                Ok(None)
+            }
+            "SYY" => {
+                self.inner.syy(pair);
+                Ok(None)
+            }
+            "SYYdg" => {
+                self.inner.syydg(pair);
+                Ok(None)
+            }
+            "SZZ" => {
+                self.inner.szz(pair);
+                Ok(None)
+            }
+            "SZZdg" => {
+                self.inner.szzdg(pair);
+                Ok(None)
+            }
+            "SWAP" => {
+                self.inner.swap(pair);
+                Ok(None)
+            }
             "RZZ" => {
                 let angle = crate::extract_angle(params, "RZZ")?;
                 self.inner.rzz(angle, pair);
diff --git a/python/pecos-rslib-exp/src/sim_neo_bindings.rs b/python/pecos-rslib-exp/src/sim_neo_bindings.rs
new file mode 100644
index 000000000..57fd31c7f
--- /dev/null
+++ b/python/pecos-rslib-exp/src/sim_neo_bindings.rs
@@ -0,0 +1,1817 @@
+// Copyright 2026 The PECOS Developers
+//
+// Licensed under the Apache License, Version 2.0 (the "License"); you may not use this file
+// except in compliance with the License. You may obtain a copy of the License at
+//
+//     https://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software distributed under the
+// License is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either
+// express or implied. See the License for the specific language governing permissions and
+// limitations under the License.
+
+//! Python bindings for `sim_neo` with builder pattern.
+//!
+//! Mirrors the Rust-side API:
+//! ```python
+//! results = (sim_neo(tc)
+//!     .quantum(stab_mps().lazy_measure().max_bond_dim(128))
+//!     .noise(depolarizing().p1(0.003).p2(0.003).p_meas(0.003).p_prep(0.003).idle_rz(0.05))
+//!     .shots(5000)
+//!     .seed(42)
+//!     .run())
+//! ```
+
+use pecos_core::{Angle64, ChannelExpr, Gate, Pauli, PauliString, QuarterPhase, QubitId};
+use pecos_neo::command::CommandBuilder;
+use pecos_neo::noise::{
+    ComposableNoiseModel, MeasurementChannel, PreparationChannel, SingleQubitChannel,
+    TwoQubitChannel,
+};
+use pecos_neo::tool::sim_neo;
+use pecos_simulators::measurement_sampler::SampleResult;
+use pyo3::prelude::*;
+
+#[derive(serde::Deserialize)]
+struct RecDef {
+    records: Vec<i32>,
+}
+
+fn measurement_record_index(record: i32, num_measurements: usize) -> Option<usize> {
+    let idx = if record < 0 {
+        i32::try_from(num_measurements).ok()?.checked_add(record)?
+    } else {
+        record
+    };
+    usize::try_from(idx)
+        .ok()
+        .filter(|&idx| idx < num_measurements)
+}
+
+// ============================================================================
+// Columnar raw measurement result (stays in Rust memory)
+// ============================================================================
+
+/// Raw measurement batch — common result type for all sim_neo backends.
+///
+/// Stores either columnar bit-packed data (meas_sampling) or row-major
+/// data (stabilizer/statevec). The Python API is identical regardless of
+/// storage: `result[shot]`, `result.get(shot, meas)`, iteration, `len()`.
+#[pyclass(name = "RawMeasurementResult", module = "pecos_rslib_exp")]
+pub struct PyRawMeasurementResult {
+    storage: RawMeasurementStorage,
+}
+
+enum RawMeasurementStorage {
+    /// Columnar bit-packed (from meas_sampling geometric sampler).
+    Columnar(SampleResult),
+    /// Row-major (from gate-by-gate stabilizer/statevec simulation).
+    RowMajor {
+        rows: Vec<Vec<u8>>,
+        num_measurements: usize,
+    },
+}
+
+impl RawMeasurementStorage {
+    fn num_shots(&self) -> usize {
+        match self {
+            Self::Columnar(s) => s.shots(),
+            Self::RowMajor { rows, .. } => rows.len(),
+        }
+    }
+
+    fn num_measurements(&self) -> usize {
+        match self {
+            Self::Columnar(s) => s.num_measurements(),
+            Self::RowMajor {
+                num_measurements, ..
+            } => *num_measurements,
+        }
+    }
+
+    fn get(&self, shot: usize, measurement: usize) -> u8 {
+        match self {
+            Self::Columnar(s) => u8::from(s.get(shot, measurement).0),
+            Self::RowMajor { rows, .. } => rows[shot][measurement],
+        }
+    }
+
+    fn get_shot(&self, shot: usize) -> Vec<u8> {
+        match self {
+            Self::Columnar(s) => {
+                let n = s.num_measurements();
+                let mut row = Vec::with_capacity(n);
+                for meas in 0..n {
+                    row.push(u8::from(s.get(shot, meas).0));
+                }
+                row
+            }
+            Self::RowMajor { rows, .. } => rows[shot].clone(),
+        }
+    }
+}
+
+impl PyRawMeasurementResult {
+    /// Convert a signed Python index to a checked usize.
+    /// Negative indices raise IndexError (no Python-list-style wrapping).
+    fn check_index(idx: isize, len: usize, name: &str) -> PyResult<usize> {
+        if idx < 0 {
+            return Err(pyo3::exceptions::PyIndexError::new_err(format!(
+                "negative {name} index {idx}"
+            )));
+        }
+        let u = usize::try_from(idx).map_err(|_| {
+            pyo3::exceptions::PyIndexError::new_err(format!("invalid {name} index {idx}"))
+        })?;
+        if u >= len {
+            return Err(pyo3::exceptions::PyIndexError::new_err(format!(
+                "{name} {u} out of range ({len})"
+            )));
+        }
+        Ok(u)
+    }
+
+    /// Construct from columnar SampleResult (meas_sampling path).
+    pub fn from_columnar(result: SampleResult) -> Self {
+        Self {
+            storage: RawMeasurementStorage::Columnar(result),
+        }
+    }
+
+    /// Construct from row-major data (stabilizer/statevec path).
+    pub fn from_rows(rows: Vec<Vec<u8>>) -> Self {
+        let num_measurements = rows.first().map_or(0, Vec::len);
+        Self {
+            storage: RawMeasurementStorage::RowMajor {
+                rows,
+                num_measurements,
+            },
+        }
+    }
+}
+
+#[pymethods]
+impl PyRawMeasurementResult {
+    /// Number of shots.
+    #[getter]
+    fn num_shots(&self) -> usize {
+        self.storage.num_shots()
+    }
+
+    /// Number of measurements per shot.
+    #[getter]
+    fn num_measurements(&self) -> usize {
+        self.storage.num_measurements()
+    }
+
+    /// Get a single measurement bit (0 or 1).
+    fn get(&self, shot: isize, measurement: isize) -> PyResult<u8> {
+        let s = Self::check_index(shot, self.storage.num_shots(), "shot")?;
+        let m = Self::check_index(measurement, self.storage.num_measurements(), "measurement")?;
+        Ok(self.storage.get(s, m))
+    }
+
+    /// Get one full shot as a list of u8.
+    fn get_shot(&self, shot: isize) -> PyResult<Vec<u8>> {
+        let s = Self::check_index(shot, self.storage.num_shots(), "shot")?;
+        Ok(self.storage.get_shot(s))
+    }
+
+    /// Materialize all shots as list[list[int]].
+    fn to_list(&self) -> Vec<Vec<u8>> {
+        let n = self.storage.num_shots();
+        (0..n).map(|i| self.storage.get_shot(i)).collect()
+    }
+
+    fn __len__(&self) -> usize {
+        self.storage.num_shots()
+    }
+
+    fn __getitem__(&self, shot: isize) -> PyResult<Vec<u8>> {
+        let s = Self::check_index(shot, self.storage.num_shots(), "index")?;
+        Ok(self.storage.get_shot(s))
+    }
+}
+
+// ============================================================================
+// Noise model builder
+// ============================================================================
+
+/// Builder for composable noise models.
+///
+/// Example:
+///     depolarizing().p1(0.003).p2(0.003).p_meas(0.003).p_prep(0.003).idle_rz(0.05)
+#[pyclass(
+    name = "NoiseModelBuilder",
+    skip_from_py_object,
+    module = "pecos_rslib_exp"
+)]
+#[derive(Clone, Default)]
+pub struct PyNoiseModelBuilder {
+    p1: f64,
+    p2: f64,
+    p_meas: f64,
+    p_prep: f64,
+    idle_rz_angle: f64,
+}
+
+#[pymethods]
+impl PyNoiseModelBuilder {
+    #[new]
+    fn new() -> Self {
+        Self::default()
+    }
+
+    /// Single-qubit depolarizing rate (X/Y/Z each with p/3 after unitary 1q gates).
+    fn p1(&self, p: f64) -> Self {
+        Self {
+            p1: p,
+            ..self.clone()
+        }
+    }
+
+    /// Two-qubit depolarizing rate (15 Paulis each with p/15 after unitary 2q gates).
+    fn p2(&self, p: f64) -> Self {
+        Self {
+            p2: p,
+            ..self.clone()
+        }
+    }
+
+    /// Measurement bit-flip rate (symmetric, after MZ).
+    fn p_meas(&self, p: f64) -> Self {
+        Self {
+            p_meas: p,
+            ..self.clone()
+        }
+    }
+
+    /// Preparation error rate (X flip after PZ/QAlloc).
+    fn p_prep(&self, p: f64) -> Self {
+        Self {
+            p_prep: p,
+            ..self.clone()
+        }
+    }
+
+    /// Coherent idle RZ angle (radians) applied to both qubits after each CX.
+    fn idle_rz(&self, angle: f64) -> Self {
+        Self {
+            idle_rz_angle: angle,
+            ..self.clone()
+        }
+    }
+}
+
+impl PyNoiseModelBuilder {
+    fn build_noise(&self) -> Option<ComposableNoiseModel> {
+        let has_noise = self.p1 > 0.0
+            || self.p2 > 0.0
+            || self.p_meas > 0.0
+            || self.p_prep > 0.0
+            || self.idle_rz_angle > 0.0;
+
+        if !has_noise {
+            return None;
+        }
+
+        let mut noise = ComposableNoiseModel::new();
+        if self.p1 > 0.0 {
+            noise = noise.add_channel(SingleQubitChannel::depolarizing(self.p1));
+        }
+        if self.p2 > 0.0 {
+            noise = noise.add_channel(TwoQubitChannel::depolarizing(self.p2));
+        }
+        if self.p_meas > 0.0 {
+            noise = noise.add_channel(MeasurementChannel::symmetric(self.p_meas));
+        }
+        if self.p_prep > 0.0 {
+            noise = noise.add_channel(PreparationChannel::new(self.p_prep));
+        }
+        if self.idle_rz_angle > 0.0 {
+            noise = noise.add_channel(crate::coherent_idle_channel::CoherentIdleChannel::new(
+                self.idle_rz_angle,
+            ));
+        }
+        Some(noise)
+    }
+}
+
+/// Create a noise model builder.
+#[pyfunction]
+pub fn depolarizing() -> PyNoiseModelBuilder {
+    PyNoiseModelBuilder::new()
+}
+
+/// Marker type for the stabilizer (SparseStab) backend.
+///
+/// Pass to `.quantum()` to select the stabilizer simulator.
+///
+/// Example:
+///     sim_neo(tc).quantum(stabilizer()).noise(depolarizing().p2(0.01)).shots(10000).run()
+#[pyclass(
+    name = "StabilizerBuilder",
+    skip_from_py_object,
+    module = "pecos_rslib_exp"
+)]
+#[derive(Clone)]
+pub struct PyStabilizerBuilder;
+
+#[pymethods]
+impl PyStabilizerBuilder {
+    #[new]
+    fn new() -> Self {
+        Self
+    }
+}
+
+/// Marker type for the state vector backend.
+///
+/// Pass to `.quantum()` to select the state vector simulator.
+/// Supports arbitrary gates including non-Clifford (T, RZ, etc.).
+///
+/// Example:
+///     sim_neo(tc).quantum(statevec()).noise(depolarizing().idle_rz(0.05)).shots(10000).run()
+#[pyclass(
+    name = "StateVecBuilder",
+    skip_from_py_object,
+    module = "pecos_rslib_exp"
+)]
+#[derive(Clone)]
+pub struct PyStateVecBuilder;
+
+#[pymethods]
+impl PyStateVecBuilder {
+    #[new]
+    fn new() -> Self {
+        Self
+    }
+}
+
+/// Create a state vector backend builder.
+///
+/// Example:
+///     sim_neo(tc).quantum(statevec()).noise(...).shots(10000).run()
+#[pyfunction]
+pub fn statevec() -> PyStateVecBuilder {
+    PyStateVecBuilder
+}
+
+/// Create a stabilizer (SparseStab) backend builder.
+///
+/// Example:
+///     sim_neo(tc).quantum(stabilizer()).noise(...).shots(10000).run()
+#[pyfunction]
+pub fn stabilizer() -> PyStabilizerBuilder {
+    PyStabilizerBuilder
+}
+
+// ============================================================================
+// StabMps backend builder
+// ============================================================================
+
+/// Builder for StabMps backend configuration.
+///
+/// Example:
+///     stab_mps().lazy_measure().max_bond_dim(128)
+#[pyclass(
+    name = "StabMpsBuilder",
+    skip_from_py_object,
+    module = "pecos_rslib_exp"
+)]
+#[derive(Clone)]
+pub struct PyStabMpsBuilder {
+    pub(crate) inner: crate::stabmps_builder::StabMpsBuilder,
+}
+
+#[pymethods]
+impl PyStabMpsBuilder {
+    #[new]
+    fn new() -> Self {
+        Self {
+            inner: crate::stabmps_builder::StabMpsBuilder::new(),
+        }
+    }
+
+    fn lazy_measure(mut slf: PyRefMut<'_, Self>) -> PyRefMut<'_, Self> {
+        slf.inner.lazy_measure = true;
+        slf
+    }
+
+    fn max_bond_dim(mut slf: PyRefMut<'_, Self>, bd: usize) -> PyRefMut<'_, Self> {
+        slf.inner.max_bond_dim = bd;
+        slf
+    }
+
+    fn max_truncation_error(mut slf: PyRefMut<'_, Self>, err: f64) -> PyRefMut<'_, Self> {
+        slf.inner.max_truncation_error = Some(err);
+        slf
+    }
+
+    fn merge_rz(mut slf: PyRefMut<'_, Self>) -> PyRefMut<'_, Self> {
+        slf.inner.merge_rz = true;
+        slf
+    }
+}
+
+/// Create a StabMps backend builder.
+#[pyfunction]
+pub fn stab_mps() -> PyStabMpsBuilder {
+    PyStabMpsBuilder::new()
+}
+
+// ============================================================================
+// sim_neo builder
+// ============================================================================
+
+/// Measurement sampling backend builder.
+#[pyclass(
+    name = "MeasSamplingBuilder",
+    skip_from_py_object,
+    module = "pecos_rslib_exp"
+)]
+#[derive(Clone)]
+pub struct PyMeasSamplingBuilder {
+    method: String,
+}
+
+#[pymethods]
+impl PyMeasSamplingBuilder {
+    #[new]
+    #[pyo3(signature = (method="auto"))]
+    fn new(method: &str) -> Self {
+        Self {
+            method: method.to_string(),
+        }
+    }
+}
+
+/// Create a measurement sampling backend builder.
+///
+/// Samples raw measurement rows from a whole-circuit measurement model. Fast, handles coherent noise at any distance.
+///
+/// Methods:
+///   - "auto": uses coherent_dem if idle_rz > 0, else stochastic (default)
+///   - "stochastic": DEM from backward Pauli propagation
+///   - "coherent": DEM from EEG backward Heisenberg walk
+#[pyfunction]
+#[pyo3(signature = (method="auto"))]
+pub fn meas_sampling(method: &str) -> PyMeasSamplingBuilder {
+    PyMeasSamplingBuilder::new(method)
+}
+
+/// Builder for sim_neo simulations. Mirrors the Rust-side `SimNeoBuilder`.
+#[pyclass(
+    name = "SimNeoBuilder",
+    skip_from_py_object,
+    module = "pecos_rslib_exp"
+)]
+#[derive(Clone)]
+pub struct PySimNeoBuilder {
+    commands: pecos_neo::command::CommandQueue,
+    /// Original Rust TickCircuit for meas_sampling (avoids reconstruction).
+    /// Wrapped in Arc for Clone compatibility with pyo3.
+    tick_circuit: std::sync::Arc<pecos_quantum::TickCircuit>,
+    shots: usize,
+    seed: u64,
+    noise_config: Option<PyNoiseModelBuilder>,
+    backend: String,
+    stabmps_config: Option<crate::stabmps_builder::StabMpsBuilder>,
+    meas_sampling_method: Option<String>,
+}
+
+#[pymethods]
+impl PySimNeoBuilder {
+    /// Set the quantum backend.
+    ///
+    /// Accepts:
+    ///   - `state_vec()` — state vector (exact, supports non-Clifford gates)
+    ///   - `stabilizer()` — SparseStab (fast Clifford-only)
+    ///   - `stab_mps()` — hybrid stabilizer-MPS (Clifford + T gates)
+    ///
+    /// Example:
+    ///     sim_neo(tc).quantum(state_vec()).noise(...).run()
+    ///     sim_neo(tc).quantum(stabilizer()).noise(...).run()
+    ///     sim_neo(tc).quantum(stab_mps().lazy_measure()).noise(...).run()
+    fn quantum(&self, builder: &Bound<'_, PyAny>) -> PyResult<Self> {
+        let mut c = self.clone();
+        if builder.is_instance_of::<PyMeasSamplingBuilder>() {
+            let b: PyRef<'_, PyMeasSamplingBuilder> = builder.extract()?;
+            c.backend = "meas_sampling".to_string();
+            c.meas_sampling_method = Some(b.method.clone());
+            c.stabmps_config = None;
+        } else if builder.is_instance_of::<PyStabMpsBuilder>() {
+            let b: PyRef<'_, PyStabMpsBuilder> = builder.extract()?;
+            c.backend = "stabmps".to_string();
+            c.stabmps_config = Some(b.inner.clone());
+            c.meas_sampling_method = None;
+        } else if builder.is_instance_of::<PyStabilizerBuilder>() {
+            c.backend = "stabilizer".to_string();
+            c.stabmps_config = None;
+            c.meas_sampling_method = None;
+        } else if builder.is_instance_of::<PyStateVecBuilder>() {
+            c.backend = "statevec".to_string();
+            c.stabmps_config = None;
+            c.meas_sampling_method = None;
+        } else {
+            return Err(pyo3::exceptions::PyTypeError::new_err(
+                "quantum() expects statevec(), stabilizer(), stab_mps(), or meas_sampling()",
+            ));
+        }
+        Ok(c)
+    }
+
+    /// Set the noise model.
+    fn noise(&self, noise_builder: &PyNoiseModelBuilder) -> Self {
+        let mut c = self.clone();
+        c.noise_config = Some(noise_builder.clone());
+        c
+    }
+
+    /// Set number of shots.
+    fn shots(&self, n: usize) -> Self {
+        let mut c = self.clone();
+        c.shots = n;
+        c
+    }
+
+    /// Set random seed.
+    fn seed(&self, s: u64) -> Self {
+        let mut c = self.clone();
+        c.seed = s;
+        c
+    }
+
+    /// Run the simulation and return per-shot measurement outcomes.
+    ///
+    /// All backends return `RawMeasurementResult` which supports:
+    /// `result[shot]`, `result.get(shot, meas)`, `len(result)`, iteration.
+    fn run(&self) -> PyResult<PyRawMeasurementResult> {
+        if self.tick_circuit.has_channel_operations() {
+            return self.run_inline_channel_circuit();
+        }
+
+        if self.backend == "meas_sampling" {
+            return self.run_meas_sampling();
+        }
+
+        let noise = self
+            .noise_config
+            .as_ref()
+            .and_then(PyNoiseModelBuilder::build_noise);
+
+        let mut builder = sim_neo(self.commands.clone())
+            .shots(self.shots)
+            .seed(self.seed);
+
+        if let Some(n) = noise {
+            builder = builder.noise(n);
+        }
+
+        match self.backend.as_str() {
+            "stabmps" => {
+                let config = self.stabmps_config.clone().unwrap_or_default();
+                builder = builder.quantum(pecos_neo::tool::custom_backend_from_factory(config));
+            }
+            "statevec" => {
+                builder = builder.quantum(pecos_neo::tool::state_vector());
+            }
+            "stabilizer" => {
+                builder = builder.quantum(pecos_neo::tool::sparse_stab());
+            }
+            _ => {
+                return Err(PyErr::new::<pyo3::exceptions::PyValueError, _>(format!(
+                    "Unknown backend: {}",
+                    self.backend
+                )));
+            }
+        }
+
+        let mut sim = builder.build();
+        let results = sim.run();
+
+        let mut all_shots = Vec::with_capacity(self.shots);
+        for shot_outcomes in &results.outcomes {
+            let meas: Vec<u8> = shot_outcomes.iter().map(|o| u8::from(o.outcome)).collect();
+            all_shots.push(meas);
+        }
+
+        Ok(PyRawMeasurementResult::from_rows(all_shots))
+    }
+}
+
+impl PySimNeoBuilder {
+    fn run_inline_channel_circuit(&self) -> PyResult<PyRawMeasurementResult> {
+        if self.noise_config.is_some() {
+            return Err(pyo3::exceptions::PyValueError::new_err(
+                "sim_neo received a TickCircuit with inline channel operations; do not also pass .noise()",
+            ));
+        }
+
+        match self.backend.as_str() {
+            "statevec" => self.run_inline_channel_density_matrix(),
+            "stabilizer" => self.run_inline_pauli_channel_stabilizer(),
+            "stabmps" => Err(pyo3::exceptions::PyValueError::new_err(
+                "stab_mps backend does not support inline channel operations; use statevec()/default for density-matrix execution",
+            )),
+            "meas_sampling" => Err(pyo3::exceptions::PyValueError::new_err(
+                "meas_sampling backend builds its own measurement model and does not consume inline channel operations",
+            )),
+            other => Err(pyo3::exceptions::PyValueError::new_err(format!(
+                "Unknown backend: {other}"
+            ))),
+        }
+    }
+
+    fn run_inline_channel_density_matrix(&self) -> PyResult<PyRawMeasurementResult> {
+        let rows = pecos_neo::inline_channel::run_inline_channels_density_matrix(
+            &self.tick_circuit,
+            self.shots,
+            self.seed,
+        )
+        .map_err(|e| pyo3::exceptions::PyValueError::new_err(e.to_string()))?;
+        Ok(PyRawMeasurementResult::from_rows(rows))
+    }
+
+    fn run_inline_pauli_channel_stabilizer(&self) -> PyResult<PyRawMeasurementResult> {
+        let rows = pecos_neo::inline_channel::run_inline_pauli_channels_stabilizer(
+            &self.tick_circuit,
+            self.shots,
+            self.seed,
+        )
+        .map_err(|e| pyo3::exceptions::PyValueError::new_err(e.to_string()))?;
+        Ok(PyRawMeasurementResult::from_rows(rows))
+    }
+
+    /// DEM sampling backend: dispatches to stochastic or coherent path based on method.
+    fn run_meas_sampling(&self) -> PyResult<PyRawMeasurementResult> {
+        let noise_config = self.noise_config.as_ref().ok_or_else(|| {
+            pyo3::exceptions::PyValueError::new_err("DEM sampling requires .noise() to be set")
+        })?;
+
+        let method = self.meas_sampling_method.as_deref().unwrap_or("auto");
+
+        let has_coherent = noise_config.idle_rz_angle.abs() > 1e-15;
+
+        match method {
+            "stochastic" => {
+                if has_coherent {
+                    return Err(pyo3::exceptions::PyValueError::new_err(
+                        "DEM sampling method='stochastic' cannot handle idle_rz noise. \
+                         Use method='coherent' or method='auto'.",
+                    ));
+                }
+                self.run_stochastic_meas_columnar()
+            }
+            "coherent" | "coherent_approx" | "coherent_exact" => {
+                let rows = self.run_coherent_meas_sampling(noise_config, method)?;
+                Ok(PyRawMeasurementResult::from_rows(rows))
+            }
+            "auto" => {
+                if has_coherent {
+                    let rows = self.run_coherent_meas_sampling(noise_config, "coherent_approx")?;
+                    Ok(PyRawMeasurementResult::from_rows(rows))
+                } else {
+                    self.run_stochastic_meas_columnar()
+                }
+            }
+            other => Err(pyo3::exceptions::PyValueError::new_err(format!(
+                "Unknown DEM sampling method: {other:?}. \
+                     Use 'auto', 'stochastic', 'coherent', 'coherent_approx', or 'coherent_exact'."
+            ))),
+        }
+    }
+
+    /// Stochastic path: columnar raw-measurement sampling.
+    fn run_stochastic_meas_columnar(&self) -> PyResult<PyRawMeasurementResult> {
+        use pecos_qec::fault_tolerance::fault_sampler::{
+            self, RawMeasurementPlan, StochasticNoiseParams,
+        };
+
+        let noise_config = self.noise_config.as_ref().ok_or_else(|| {
+            pyo3::exceptions::PyRuntimeError::new_err("DEM sampling requires .noise() to be set")
+        })?;
+
+        let history = run_symbolic_sim_with_pz(&self.tick_circuit)?;
+
+        let noise = StochasticNoiseParams {
+            p1: noise_config.p1,
+            p2: noise_config.p2,
+            p_meas: noise_config.p_meas,
+            p_prep: noise_config.p_prep,
+        };
+        let mechanisms = fault_sampler::build_fault_table(&self.tick_circuit, &noise)
+            .map_err(|e| pyo3::exceptions::PyRuntimeError::new_err(e.to_string()))?;
+
+        let plan = RawMeasurementPlan::new(&history, mechanisms);
+        let result = plan.sample(self.shots, self.seed);
+
+        Ok(PyRawMeasurementResult::from_columnar(result))
+    }
+
+    /// Coherent path: EEG DemGenerator with measurement synthesis.
+    fn run_coherent_meas_sampling(
+        &self,
+        noise_config: &PyNoiseModelBuilder,
+        method: &str,
+    ) -> PyResult<Vec<Vec<u8>>> {
+        use pecos_eeg::dem_generator::select_generator;
+        use pecos_eeg::dem_simulator::{CircuitMeasurementMeta, run_dem_simulation};
+
+        // Extract metadata from stored TickCircuit
+        let num_meas_attr = self
+            .tick_circuit
+            .get_meta("num_measurements")
+            .and_then(|a| {
+                if let pecos_quantum::Attribute::String(s) = a {
+                    s.parse::<usize>().ok()
+                } else {
+                    None
+                }
+            })
+            .ok_or_else(|| {
+                pyo3::exceptions::PyValueError::new_err(
+                    "TickCircuit missing num_measurements metadata",
+                )
+            })?;
+        let det_json = self
+            .tick_circuit
+            .get_meta("detectors")
+            .and_then(|a| {
+                if let pecos_quantum::Attribute::String(s) = a {
+                    Some(s.clone())
+                } else {
+                    None
+                }
+            })
+            .unwrap_or_else(|| "[]".to_string());
+        let obs_json = self
+            .tick_circuit
+            .get_meta("observables")
+            .and_then(|a| {
+                if let pecos_quantum::Attribute::String(s) = a {
+                    Some(s.clone())
+                } else {
+                    None
+                }
+            })
+            .unwrap_or_else(|| "[]".to_string());
+
+        let det_records: Vec<Vec<i32>> = serde_json::from_str::<Vec<RecDef>>(&det_json)
+            .map(|defs| defs.iter().map(|d| d.records.clone()).collect())
+            .unwrap_or_default();
+        let obs_records: Vec<Vec<i32>> = serde_json::from_str::<Vec<RecDef>>(&obs_json)
+            .map(|defs| defs.iter().map(|d| d.records.clone()).collect())
+            .unwrap_or_default();
+
+        let meta = CircuitMeasurementMeta {
+            num_measurements: num_meas_attr,
+            detector_records: det_records,
+            observable_records: obs_records,
+        };
+
+        let noise = pecos_eeg::noise::UniformNoise {
+            idle_rz: noise_config.idle_rz_angle,
+            p1: noise_config.p1,
+            p2: noise_config.p2,
+            p_meas: noise_config.p_meas,
+            p_prep: noise_config.p_prep,
+        };
+
+        let gates = commands_to_gates(&self.commands);
+        let generator = select_generator(method, noise_config.idle_rz_angle);
+
+        let result = run_dem_simulation(
+            &gates,
+            &noise,
+            &meta,
+            generator.as_ref(),
+            self.shots,
+            self.seed,
+        );
+        Ok(result.measurements)
+    }
+}
+
+/// Convert CommandQueue to Vec<Gate> for EEG analysis.
+fn commands_to_gates(commands: &pecos_neo::command::CommandQueue) -> Vec<pecos_core::Gate> {
+    use pecos_core::{GateAngles, GateMeasIds, GateParams};
+
+    commands
+        .iter()
+        .map(|cmd| {
+            let qubits = cmd.qubits.iter().copied().collect();
+            let mut angles = GateAngles::new();
+            for &a in &cmd.angles {
+                angles.push(a);
+            }
+            // Convert pecos_neo::GateType to pecos_core::GateType
+            let gate_type: pecos_core::gate_type::GateType = cmd.gate_type.into();
+            Gate {
+                gate_type,
+                qubits,
+                angles,
+                params: GateParams::new(),
+                meas_ids: GateMeasIds::new(),
+                channel: None,
+            }
+        })
+        .collect()
+}
+
+// ============================================================================
+// Entry point
+// ============================================================================
+
+/// Create a sim_neo simulation builder from a TickCircuit.
+///
+/// Example:
+///     results = (sim_neo(tc)
+///         .quantum(stab_mps().lazy_measure().max_bond_dim(128))
+///         .noise(depolarizing().p1(0.003).p2(0.003).p_meas(0.003).idle_rz(0.05))
+///         .shots(5000)
+///         .seed(42)
+///         .run())
+#[pyfunction]
+#[pyo3(name = "sim_neo")]
+pub fn py_sim_neo(tick_circuit: &Bound<'_, PyAny>) -> PyResult<PySimNeoBuilder> {
+    // Build a Rust TickCircuit from the Python object.
+    // This is the canonical circuit representation used by DemSampler.
+    let tc = build_rust_tick_circuit(tick_circuit)?;
+    let commands = if tc.has_channel_operations() {
+        pecos_neo::command::CommandQueue::new()
+    } else {
+        extract_commands(tick_circuit)?
+    };
+
+    Ok(PySimNeoBuilder {
+        commands,
+        tick_circuit: std::sync::Arc::new(tc),
+        shots: 1,
+        seed: 42,
+        noise_config: None,
+        backend: "statevec".to_string(),
+        stabmps_config: None,
+        meas_sampling_method: None,
+    })
+}
+
+/// Build a proper Rust TickCircuit from a Python TickCircuit object.
+///
+/// First tries to extract the inner Rust TickCircuit directly (fast path).
+/// Falls back to rebuilding from Python gate iteration (slow path).
+fn build_rust_tick_circuit(py_tc: &Bound<'_, PyAny>) -> PyResult<pecos_quantum::TickCircuit> {
+    // Fast path: try to access the inner TickCircuit directly.
+    // The Python TickCircuit wraps `pub inner: TickCircuit` — access via
+    // the `_inner_tick_circuit()` method if available, or via serialization.
+    if let Ok(tc_bytes) = py_tc.call_method0("_serialize_inner")
+        && let Ok(bytes) = tc_bytes.extract::<Vec<u8>>()
+    {
+        // Deserialize — but TickCircuit doesn't impl serde. Skip.
+        let _ = bytes;
+    }
+
+    // The only reliable fast path: call `to_dag_circuit()` on the Python TC,
+    // then use DemSampler::from_circuit on that DagCircuit. But we can't get
+    // the DagCircuit across crate boundaries easily.
+    //
+    // For now: reconstruct via gate iteration (matches original structure if
+    // we respect tick boundaries from the Python object).
+    build_rust_tick_circuit_from_gates(py_tc)
+}
+
+/// Reconstruct TickCircuit from Python gate iteration, preserving tick structure.
+///
+/// Respects the original tick boundaries: all gates from the same Python tick
+/// go into the same Rust tick. Uses typed .mz() for measurements and .pz() for
+/// prep within each tick (these consume the TickHandle, so we process them after
+/// other gates in the tick).
+fn build_rust_tick_circuit_from_gates(
+    py_tc: &Bound<'_, PyAny>,
+) -> PyResult<pecos_quantum::TickCircuit> {
+    use pecos_quantum::{Attribute, TickMeasRef};
+
+    let num_ticks: usize = py_tc.call_method0("num_ticks")?.extract()?;
+    let mut tc = pecos_quantum::TickCircuit::default();
+    let mut all_meas_refs: Vec<TickMeasRef> = Vec::new();
+
+    for tick_idx in 0..num_ticks {
+        let py_tick = py_tc.call_method1("get_tick", (tick_idx,))?;
+        let py_gates = py_tick.call_method0("gate_batches")?;
+        let gates: Vec<Bound<'_, PyAny>> = py_gates.extract()?;
+
+        // Separate gates by type: MZ, PZ, and other
+        let mut mz_qubits: Vec<pecos_core::QubitId> = Vec::new();
+        let mut pz_qubits: Vec<pecos_core::QubitId> = Vec::new();
+        let mut other_gates: Vec<pecos_core::Gate> = Vec::new();
+
+        for gate in &gates {
+            let gate_type_obj = gate.getattr("gate_type")?;
+            let gate_name: String = format!("{gate_type_obj:?}");
+            let gate_name = gate_name
+                .split('.')
+                .next_back()
+                .unwrap_or(&gate_name)
+                .to_string();
+            let py_qubits = gate.getattr("qubits")?;
+            let qubits: Vec<usize> = py_qubits.extract()?;
+            let qubit_ids: Vec<pecos_core::QubitId> =
+                qubits.iter().map(|&q| pecos_core::QubitId(q)).collect();
+
+            match gate_name.as_str() {
+                "MZ" | "Measure" | "MeasureFree" => {
+                    mz_qubits.extend(qubit_ids);
+                }
+                "QAlloc" | "PZ" | "Prep" => {
+                    pz_qubits.extend(qubit_ids);
+                }
+                _ => {
+                    let core_gate = build_gate_from_python(gate, &gate_name, &qubit_ids)?;
+                    other_gates.push(core_gate);
+                }
+            }
+        }
+
+        // Add PZ first (prep before other gates)
+        if !pz_qubits.is_empty() {
+            tc.tick().pz(&pz_qubits);
+        }
+
+        // Add other gates in one tick (error on qubit conflicts)
+        if !other_gates.is_empty() {
+            let mut tick_handle = tc.tick();
+            for g in &other_gates {
+                if let Err(e) = tick_handle.try_add_gate(g.clone()) {
+                    return Err(pyo3::exceptions::PyRuntimeError::new_err(format!(
+                        "Gate conflict in tick {tick_idx}: {e}"
+                    )));
+                }
+            }
+        }
+
+        // Add MZ last (measure after other gates)
+        if !mz_qubits.is_empty() {
+            let refs = tc.tick().mz(&mz_qubits);
+            all_meas_refs.extend(refs);
+        }
+    }
+
+    // Copy metadata from Python TickCircuit
+    if let Ok(num_meas) = py_tc.call_method1("get_meta", ("num_measurements",))
+        && let Ok(s) = num_meas.extract::<String>()
+    {
+        tc.set_meta("num_measurements", Attribute::String(s));
+    }
+    if let Ok(det_json) = py_tc.call_method1("get_meta", ("detectors",))
+        && let Ok(s) = det_json.extract::<String>()
+    {
+        // Create structured annotations from JSON
+        create_annotations_from_json(&mut tc, &s, &all_meas_refs, true);
+        tc.set_meta("detectors", Attribute::String(s));
+    }
+    if let Ok(obs_json) = py_tc.call_method1("get_meta", ("observables",))
+        && let Ok(s) = obs_json.extract::<String>()
+    {
+        create_annotations_from_json(&mut tc, &s, &all_meas_refs, false);
+        tc.set_meta("observables", Attribute::String(s));
+    }
+    copy_tracked_pauli_annotations_from_python(py_tc, &mut tc)?;
+
+    // Compact for performance
+    tc.compact_ticks();
+
+    Ok(tc)
+}
+
+fn copy_tracked_pauli_annotations_from_python(
+    py_tc: &pyo3::Bound<'_, pyo3::PyAny>,
+    tc: &mut pecos_quantum::TickCircuit,
+) -> PyResult<()> {
+    let Ok(annotations) = py_tc.call_method0("annotations") else {
+        return Ok(());
+    };
+
+    for ann in annotations.try_iter()? {
+        let ann = ann?;
+        let kind: String = ann.get_item("kind")?.extract()?;
+        if kind != "tracked_pauli" {
+            continue;
+        }
+        let pauli_obj = ann.get_item("pauli")?;
+        let pauli_text = pauli_obj.str()?.to_string();
+        let pauli = parse_python_pauli_string(&pauli_text).ok_or_else(|| {
+            pyo3::exceptions::PyValueError::new_err(format!(
+                "Could not parse tracked Pauli annotation: {pauli_text}"
+            ))
+        })?;
+        let label: Option<String> = ann.get_item("label")?.extract()?;
+        if let Some(label) = label {
+            tc.tracked_pauli_labeled(&label, pauli);
+        } else {
+            tc.tracked_pauli(pauli);
+        }
+    }
+
+    Ok(())
+}
+
+fn parse_python_pauli_string(text: &str) -> Option<PauliString> {
+    let text = text.trim();
+    let text = text
+        .strip_prefix("+i*")
+        .or_else(|| text.strip_prefix("-i*"))
+        .or_else(|| text.strip_prefix('-'))
+        .unwrap_or(text)
+        .trim();
+    if text.is_empty() || text == "I" {
+        return Some(PauliString::new());
+    }
+
+    let mut paulis = Vec::new();
+    for token in text.split_whitespace() {
+        let mut chars = token.chars();
+        let p = match chars.next()? {
+            'X' | 'x' => pecos_core::Pauli::X,
+            'Y' | 'y' => pecos_core::Pauli::Y,
+            'Z' | 'z' => pecos_core::Pauli::Z,
+            'I' | 'i' => continue,
+            _ => return None,
+        };
+        let rest = chars.as_str().strip_prefix('_').unwrap_or(chars.as_str());
+        let qubit = rest.parse::<usize>().ok()?;
+        paulis.push((p, pecos_core::QubitId(qubit)));
+    }
+
+    Some(PauliString::with_phase_and_paulis(
+        pecos_core::QuarterPhase::PlusOne,
+        paulis,
+    ))
+}
+
+fn channel_expr_from_python_gate(gate: &Bound<'_, PyAny>) -> PyResult<ChannelExpr> {
+    let terms: Vec<(f64, Vec<(String, usize)>)> =
+        gate.call_method0("channel_mixed_pauli_terms")?.extract()?;
+    let mut ops = Vec::with_capacity(terms.len());
+    for (probability, terms) in terms {
+        let mut paulis = Vec::with_capacity(terms.len());
+        for (label, qubit) in terms {
+            let pauli = match label.as_str() {
+                "I" => continue,
+                "X" => Pauli::X,
+                "Y" => Pauli::Y,
+                "Z" => Pauli::Z,
+                other => {
+                    return Err(pyo3::exceptions::PyValueError::new_err(format!(
+                        "unsupported channel Pauli label {other:?}"
+                    )));
+                }
+            };
+            paulis.push((pauli, QubitId(qubit)));
+        }
+        let pauli_string = PauliString::with_phase_and_paulis(QuarterPhase::PlusOne, paulis);
+        ops.push((probability, pecos_core::UnitaryRep::from(pauli_string)));
+    }
+    Ok(ChannelExpr::MixedUnitary(ops))
+}
+
+/// Create detector or observable annotations from JSON metadata.
+fn create_annotations_from_json(
+    tc: &mut pecos_quantum::TickCircuit,
+    json_str: &str,
+    all_meas_refs: &[pecos_quantum::TickMeasRef],
+    is_detector: bool,
+) {
+    let num_meas = all_meas_refs.len();
+    if let Ok(defs) = serde_json::from_str::<Vec<RecDef>>(json_str) {
+        for def in &defs {
+            let refs: Vec<pecos_quantum::TickMeasRef> = def
+                .records
+                .iter()
+                .filter_map(|&rec| {
+                    let abs_idx = measurement_record_index(rec, num_meas)?;
+                    all_meas_refs.get(abs_idx).copied()
+                })
+                .collect();
+            if !refs.is_empty() {
+                if is_detector {
+                    tc.detector(&refs);
+                } else {
+                    tc.observable(&refs);
+                }
+            }
+        }
+    }
+}
+
+/// Build a pecos_core::Gate from a Python gate object.
+fn build_gate_from_python(
+    gate: &Bound<'_, PyAny>,
+    gate_name: &str,
+    qubit_ids: &[pecos_core::QubitId],
+) -> PyResult<pecos_core::Gate> {
+    use pecos_core::gate_type::GateType;
+    use pecos_core::{Gate, GateAngles, GateMeasIds, GateParams};
+
+    if gate_name == "Channel" {
+        return Ok(Gate::channel(channel_expr_from_python_gate(gate)?));
+    }
+
+    let gate_type = match gate_name {
+        "H" => GateType::H,
+        "X" => GateType::X,
+        "Y" => GateType::Y,
+        "Z" => GateType::Z,
+        "F" => GateType::F,
+        "Fdg" => GateType::Fdg,
+        "CX" | "CNOT" => GateType::CX,
+        "CY" => GateType::CY,
+        "CZ" => GateType::CZ,
+        "SZ" | "S" => GateType::SZ,
+        "SZdg" | "Sdg" => GateType::SZdg,
+        "SX" => GateType::SX,
+        "SXdg" => GateType::SXdg,
+        "SY" => GateType::SY,
+        "SYdg" => GateType::SYdg,
+        "T" => GateType::T,
+        "Tdg" => GateType::Tdg,
+        "SWAP" => GateType::SWAP,
+        "RZ" => GateType::RZ,
+        "RX" => GateType::RX,
+        "RY" => GateType::RY,
+        "RZZ" => GateType::RZZ,
+        "RXX" => GateType::RXX,
+        "RYY" => GateType::RYY,
+        "SZZ" => GateType::SZZ,
+        "SZZdg" => GateType::SZZdg,
+        "SXX" => GateType::SXX,
+        "SXXdg" => GateType::SXXdg,
+        "SYY" => GateType::SYY,
+        "SYYdg" => GateType::SYYdg,
+        "R1XY" => GateType::R1XY,
+        "I" | "Idle" => GateType::I,
+        other => {
+            return Err(pyo3::exceptions::PyValueError::new_err(format!(
+                "Unsupported gate type for meas_sampling simulation: {other}"
+            )));
+        }
+    };
+
+    let mut angles = GateAngles::new();
+    if let Ok(py_angle) = gate.getattr("angle")
+        && let Ok(a) = py_angle.extract::<f64>()
+    {
+        angles.push(pecos_core::Angle64::from_radians(a));
+    }
+    if let Ok(py_angles) = gate.getattr("angles")
+        && let Ok(a_list) = py_angles.extract::<Vec<f64>>()
+    {
+        for a in a_list {
+            angles.push(pecos_core::Angle64::from_radians(a));
+        }
+    }
+
+    Ok(Gate {
+        gate_type,
+        qubits: qubit_ids.iter().copied().collect(),
+        angles,
+        params: GateParams::new(),
+        meas_ids: GateMeasIds::new(),
+        channel: None,
+    })
+}
+
+// ============================================================================
+// Circuit extraction
+// ============================================================================
+
+/// Extract a CommandQueue from a Python TickCircuit by iterating its stored gate batches.
+fn extract_commands(py_tc: &Bound<'_, PyAny>) -> PyResult<pecos_neo::command::CommandQueue> {
+    let num_ticks: usize = py_tc.call_method0("num_ticks")?.extract()?;
+    let mut cb = CommandBuilder::new();
+
+    for tick_idx in 0..num_ticks {
+        let py_tick = py_tc.call_method1("get_tick", (tick_idx,))?;
+        let py_gates = py_tick.call_method0("gate_batches")?;
+        let gates: Vec<Bound<'_, PyAny>> = py_gates.extract()?;
+
+        for gate in &gates {
+            let gate_type_obj = gate.getattr("gate_type")?;
+            let name: String = gate_type_obj.getattr("name")?.extract()?;
+            let qubits: Vec<usize> = gate.getattr("qubits")?.extract()?;
+
+            match name.as_str() {
+                "QAlloc" | "PZ" => {
+                    cb = cb.pz(&qubits);
+                }
+                "H" => {
+                    cb = cb.h(&qubits);
+                }
+                "F" => {
+                    cb = cb.f(&qubits);
+                }
+                "Fdg" => {
+                    cb = cb.fdg(&qubits);
+                }
+                "X" => {
+                    cb = cb.x(&qubits);
+                }
+                "Y" => {
+                    cb = cb.y(&qubits);
+                }
+                "Z" => {
+                    cb = cb.z(&qubits);
+                }
+                "SZ" => {
+                    cb = cb.sz(&qubits);
+                }
+                "SZdg" => {
+                    cb = cb.szdg(&qubits);
+                }
+                "SX" => {
+                    cb = cb.sx(&qubits);
+                }
+                "SXdg" => {
+                    cb = cb.sxdg(&qubits);
+                }
+                "SY" => {
+                    cb = cb.sy(&qubits);
+                }
+                "SYdg" => {
+                    cb = cb.sydg(&qubits);
+                }
+                "CX" => {
+                    let pairs: Vec<(usize, usize)> =
+                        qubits.chunks(2).map(|c| (c[0], c[1])).collect();
+                    cb = cb.cx(&pairs);
+                }
+                "CY" => {
+                    let pairs: Vec<(usize, usize)> =
+                        qubits.chunks(2).map(|c| (c[0], c[1])).collect();
+                    cb = cb.cy(&pairs);
+                }
+                "CZ" => {
+                    let pairs: Vec<(usize, usize)> =
+                        qubits.chunks(2).map(|c| (c[0], c[1])).collect();
+                    cb = cb.cz(&pairs);
+                }
+                "SZZ" => {
+                    let pairs: Vec<(usize, usize)> =
+                        qubits.chunks(2).map(|c| (c[0], c[1])).collect();
+                    cb = cb.szz(&pairs);
+                }
+                "SZZdg" => {
+                    let pairs: Vec<(usize, usize)> =
+                        qubits.chunks(2).map(|c| (c[0], c[1])).collect();
+                    cb = cb.szzdg(&pairs);
+                }
+                "SXX" => {
+                    let pairs: Vec<(usize, usize)> =
+                        qubits.chunks(2).map(|c| (c[0], c[1])).collect();
+                    cb = cb.sxx(&pairs);
+                }
+                "SXXdg" => {
+                    let pairs: Vec<(usize, usize)> =
+                        qubits.chunks(2).map(|c| (c[0], c[1])).collect();
+                    cb = cb.sxxdg(&pairs);
+                }
+                "SYY" => {
+                    let pairs: Vec<(usize, usize)> =
+                        qubits.chunks(2).map(|c| (c[0], c[1])).collect();
+                    cb = cb.syy(&pairs);
+                }
+                "SYYdg" => {
+                    let pairs: Vec<(usize, usize)> =
+                        qubits.chunks(2).map(|c| (c[0], c[1])).collect();
+                    cb = cb.syydg(&pairs);
+                }
+                "SWAP" => {
+                    let pairs: Vec<(usize, usize)> =
+                        qubits.chunks(2).map(|c| (c[0], c[1])).collect();
+                    cb = cb.swap(&pairs);
+                }
+                "T" => {
+                    cb = cb.t(&qubits);
+                }
+                "Tdg" => {
+                    cb = cb.tdg(&qubits);
+                }
+                "MZ" => {
+                    cb = cb.mz(&qubits);
+                }
+                "RX" => {
+                    let angles: Vec<f64> = gate.getattr("angles")?.extract().unwrap_or_default();
+                    if let Some(&angle) = angles.first() {
+                        cb = cb.rx(&qubits, Angle64::from_radians(angle));
+                    }
+                }
+                "RY" => {
+                    let angles: Vec<f64> = gate.getattr("angles")?.extract().unwrap_or_default();
+                    if let Some(&angle) = angles.first() {
+                        cb = cb.ry(&qubits, Angle64::from_radians(angle));
+                    }
+                }
+                "RZ" => {
+                    let angles: Vec<f64> = gate.getattr("angles")?.extract().unwrap_or_default();
+                    if let Some(&angle) = angles.first() {
+                        cb = cb.rz(&qubits, Angle64::from_radians(angle));
+                    }
+                }
+                "R1XY" => {
+                    let angles: Vec<f64> = gate.getattr("angles")?.extract().unwrap_or_default();
+                    if angles.len() >= 2 {
+                        cb = cb.r1xy(
+                            &qubits,
+                            Angle64::from_radians(angles[0]),
+                            Angle64::from_radians(angles[1]),
+                        );
+                    }
+                }
+                "RZZ" => {
+                    let angles: Vec<f64> = gate.getattr("angles")?.extract().unwrap_or_default();
+                    if let Some(&angle) = angles.first() {
+                        let pairs: Vec<(usize, usize)> =
+                            qubits.chunks(2).map(|c| (c[0], c[1])).collect();
+                        cb = cb.rzz(&pairs, Angle64::from_radians(angle));
+                    }
+                }
+                "RXX" => {
+                    let angles: Vec<f64> = gate.getattr("angles")?.extract().unwrap_or_default();
+                    if let Some(&angle) = angles.first() {
+                        let pairs: Vec<(usize, usize)> =
+                            qubits.chunks(2).map(|c| (c[0], c[1])).collect();
+                        cb = cb.rxx(&pairs, Angle64::from_radians(angle));
+                    }
+                }
+                "RYY" => {
+                    let angles: Vec<f64> = gate.getattr("angles")?.extract().unwrap_or_default();
+                    if let Some(&angle) = angles.first() {
+                        let pairs: Vec<(usize, usize)> =
+                            qubits.chunks(2).map(|c| (c[0], c[1])).collect();
+                        cb = cb.ryy(&pairs, Angle64::from_radians(angle));
+                    }
+                }
+                "I" | "Idle" => {
+                    // Identity/Idle gates: skip (no-op for simulation)
+                }
+                _ => {
+                    return Err(PyErr::new::<pyo3::exceptions::PyValueError, _>(format!(
+                        "Unsupported gate type '{name}' in extract_commands. \
+                         Add support in sim_neo_bindings.rs or lower to supported gates \
+                         with tc.lower_clifford_rotations()."
+                    )));
+                }
+            }
+        }
+    }
+
+    Ok(cb.build())
+}
+
+/// Run SymbolicSparseStab through a TickCircuit with proper PZ (reset) semantics.
+///
+/// Iterates tick-by-tick to match the TickCircuit's measurement numbering,
+/// which is what detector and observable definitions reference.
+fn run_symbolic_sim_with_pz(
+    tc: &pecos_quantum::TickCircuit,
+) -> PyResult<pecos_simulators::symbolic_sparse_stab::MeasurementHistory> {
+    pecos_qec::fault_tolerance::fault_sampler::symbolic_measurement_history(tc)
+        .map_err(|e| pyo3::exceptions::PyRuntimeError::new_err(e.to_string()))
+}
+
+// ============================================================================
+// Fault Catalog Python API
+// ============================================================================
+
+/// One fault alternative at a physical location.
+#[pyclass(name = "FaultAlternative", module = "pecos_rslib_exp")]
+pub struct PyFaultAlternative {
+    /// "pauli", "measurement_flip", or "prep_flip"
+    #[pyo3(get)]
+    kind: String,
+    /// PauliString object (from pecos.quantum) for Pauli faults, None otherwise
+    pauli_obj: Py<PyAny>,
+    /// Measurement indices flipped
+    #[pyo3(get)]
+    measurements: Vec<usize>,
+    /// Detector indices flipped
+    #[pyo3(get)]
+    detectors: Vec<usize>,
+    /// Observable indices flipped
+    #[pyo3(get)]
+    observables: Vec<usize>,
+    /// Tracked-Pauli indices flipped
+    #[pyo3(get)]
+    tracked_paulis: Vec<usize>,
+    /// Probability of this alternative given the mechanism fires (1/k)
+    #[pyo3(get)]
+    conditional_probability: f64,
+    /// Marginal per-location alternative probability: p_i / k_i.
+    /// This is NOT "probability of this fault and no others." Full configuration
+    /// probabilities require multiplying by no_fault_probability for all other locations.
+    #[pyo3(get)]
+    absolute_probability: f64,
+    /// Total channel probability (same as parent location)
+    #[pyo3(get)]
+    channel_probability: f64,
+}
+
+#[pymethods]
+impl PyFaultAlternative {
+    #[getter]
+    fn pauli(&self, py: Python<'_>) -> Py<PyAny> {
+        self.pauli_obj.clone_ref(py)
+    }
+}
+
+/// A physical fault location in the circuit.
+#[pyclass(name = "FaultLocation", module = "pecos_rslib_exp")]
+pub struct PyFaultLocation {
+    #[pyo3(get)]
+    tick: usize,
+    #[pyo3(get)]
+    gate_index: usize,
+    #[pyo3(get)]
+    gate_type: String,
+    #[pyo3(get)]
+    qubits: Vec<usize>,
+    /// "p1", "p2", "p_meas", or "p_prep"
+    #[pyo3(get)]
+    channel: String,
+    #[pyo3(get)]
+    channel_probability: f64,
+    /// 1 - channel_probability
+    #[pyo3(get)]
+    no_fault_probability: f64,
+    #[pyo3(get)]
+    num_alternatives: usize,
+    #[pyo3(get)]
+    faults: Vec<Py<PyFaultAlternative>>,
+}
+
+/// A k-fault configuration yielded by `catalog.fault_configurations(k)`.
+#[pyclass(name = "FaultConfiguration", module = "pecos_rslib_exp")]
+pub struct PyFaultConfiguration {
+    #[pyo3(get)]
+    location_indices: Vec<usize>,
+    #[pyo3(get)]
+    alternative_indices: Vec<usize>,
+    /// The FaultLocation objects for selected locations.
+    #[pyo3(get)]
+    locations: Vec<Py<PyFaultLocation>>,
+    /// The FaultAlternative objects for selected alternatives.
+    #[pyo3(get)]
+    faults: Vec<Py<PyFaultAlternative>>,
+    #[pyo3(get)]
+    measurements: Vec<usize>,
+    #[pyo3(get)]
+    detectors: Vec<usize>,
+    #[pyo3(get)]
+    observables: Vec<usize>,
+    #[pyo3(get)]
+    tracked_paulis: Vec<usize>,
+    #[pyo3(get)]
+    selected_probability: f64,
+    #[pyo3(get)]
+    configuration_probability: f64,
+}
+
+/// Lazy Python iterator over k-fault configurations.
+#[pyclass(name = "FaultConfigurationIter", module = "pecos_rslib_exp")]
+pub struct PyFaultConfigurationIter {
+    /// Owned Rust iterator (self-contained, no borrows).
+    inner: pecos_qec::fault_tolerance::fault_sampler::OwnedFaultConfigIter,
+    /// Python-side location objects for building yielded configs.
+    py_locations: Vec<Py<PyFaultLocation>>,
+}
+
+#[pymethods]
+impl PyFaultConfigurationIter {
+    fn __iter__(slf: PyRef<'_, Self>) -> PyRef<'_, Self> {
+        slf
+    }
+
+    fn __next__(&mut self, py: Python<'_>) -> Option<PyFaultConfiguration> {
+        let config = self.inner.next()?;
+
+        // Build .locations and .faults references
+        let locations: Vec<Py<PyFaultLocation>> = config
+            .location_indices
+            .iter()
+            .map(|&i| self.py_locations[i].clone_ref(py))
+            .collect();
+        let faults: Vec<Py<PyFaultAlternative>> = config
+            .location_indices
+            .iter()
+            .zip(config.alternative_indices.iter())
+            .map(|(&loc_i, &alt_i)| {
+                let loc = self.py_locations[loc_i].borrow(py);
+                loc.faults[alt_i].clone_ref(py)
+            })
+            .collect();
+
+        Some(PyFaultConfiguration {
+            location_indices: config.location_indices,
+            alternative_indices: config.alternative_indices,
+            locations,
+            faults,
+            measurements: config.affected_measurements,
+            detectors: config.affected_detectors,
+            observables: config.affected_observables,
+            tracked_paulis: config.affected_tracked_paulis,
+            selected_probability: config.selected_probability,
+            configuration_probability: config.configuration_probability,
+        })
+    }
+}
+
+/// Complete fault catalog for a circuit and noise model.
+#[pyclass(name = "FaultCatalog", module = "pecos_rslib_exp")]
+pub struct PyFaultCatalog {
+    /// Physical fault locations in the structural catalog.
+    #[pyo3(get)]
+    locations: Vec<Py<PyFaultLocation>>,
+    /// Rust-side catalog for iterator support.
+    rust_catalog: pecos_qec::fault_tolerance::fault_sampler::FaultCatalog,
+}
+
+fn stochastic_params_from_inputs(
+    noise: Option<&PyNoiseModelBuilder>,
+    p1: Option<f64>,
+    p2: Option<f64>,
+    p_meas: Option<f64>,
+    p_prep: Option<f64>,
+) -> pecos_qec::fault_tolerance::fault_sampler::StochasticNoiseParams {
+    let mut params = noise.map_or(
+        pecos_qec::fault_tolerance::fault_sampler::StochasticNoiseParams {
+            p1: 0.0,
+            p2: 0.0,
+            p_meas: 0.0,
+            p_prep: 0.0,
+        },
+        |noise| pecos_qec::fault_tolerance::fault_sampler::StochasticNoiseParams {
+            p1: noise.p1,
+            p2: noise.p2,
+            p_meas: noise.p_meas,
+            p_prep: noise.p_prep,
+        },
+    );
+    if let Some(p) = p1 {
+        params.p1 = p;
+    }
+    if let Some(p) = p2 {
+        params.p2 = p;
+    }
+    if let Some(p) = p_meas {
+        params.p_meas = p;
+    }
+    if let Some(p) = p_prep {
+        params.p_prep = p;
+    }
+    params
+}
+
+fn py_locations_from_catalog(
+    py: Python<'_>,
+    catalog: &pecos_qec::fault_tolerance::fault_sampler::FaultCatalog,
+) -> PyResult<Vec<Py<PyFaultLocation>>> {
+    use pecos_qec::fault_tolerance::fault_sampler::{FaultChannel, FaultKind};
+
+    let quantum_mod = py.import("pecos.quantum")?;
+    let ps_class = quantum_mod.getattr("PauliString")?;
+    let pauli_enum = quantum_mod.getattr("Pauli")?;
+    let pauli_x = pauli_enum.getattr("X")?;
+    let pauli_y = pauli_enum.getattr("Y")?;
+    let pauli_z = pauli_enum.getattr("Z")?;
+
+    let mut locations = Vec::with_capacity(catalog.locations.len());
+    for loc in &catalog.locations {
+        let mut faults = Vec::with_capacity(loc.faults.len());
+        for fault in &loc.faults {
+            let pauli_obj: Py<PyAny> = if let Some(ps) = &fault.pauli {
+                let mut pair_list = Vec::new();
+                for (p, q) in ps.iter_pairs() {
+                    let py_pauli = match p {
+                        pecos_core::Pauli::X => &pauli_x,
+                        pecos_core::Pauli::Y => &pauli_y,
+                        pecos_core::Pauli::Z => &pauli_z,
+                        pecos_core::Pauli::I => continue,
+                    };
+                    let pair = pyo3::types::PyTuple::new(
+                        py,
+                        [py_pauli.as_any(), &q.index().into_pyobject(py)?.into_any()],
+                    )?;
+                    pair_list.push(pair.unbind());
+                }
+                let py_list = pyo3::types::PyList::new(py, pair_list.iter().map(|p| p.bind(py)))?;
+                ps_class.call1((py_list,))?.unbind()
+            } else {
+                py.None()
+            };
+
+            faults.push(Py::new(
+                py,
+                PyFaultAlternative {
+                    kind: match fault.kind {
+                        FaultKind::Pauli => "pauli".to_string(),
+                        FaultKind::MeasurementFlip => "measurement_flip".to_string(),
+                        FaultKind::PrepFlip => "prep_flip".to_string(),
+                    },
+                    pauli_obj,
+                    measurements: fault.affected_measurements.clone(),
+                    detectors: fault.affected_detectors.clone(),
+                    observables: fault.affected_observables.clone(),
+                    tracked_paulis: fault.affected_tracked_paulis.clone(),
+                    conditional_probability: fault.conditional_probability,
+                    absolute_probability: fault.absolute_probability,
+                    channel_probability: loc.channel_probability,
+                },
+            )?);
+        }
+
+        locations.push(Py::new(
+            py,
+            PyFaultLocation {
+                tick: loc.tick,
+                gate_index: loc.gate_index,
+                gate_type: format!("{:?}", loc.gate_type),
+                qubits: loc.qubits.clone(),
+                channel: match loc.channel {
+                    FaultChannel::P1 => "p1",
+                    FaultChannel::P2 => "p2",
+                    FaultChannel::PMeas => "p_meas",
+                    FaultChannel::PPrep => "p_prep",
+                }
+                .to_string(),
+                channel_probability: loc.channel_probability,
+                no_fault_probability: loc.no_fault_probability,
+                num_alternatives: loc.num_alternatives,
+                faults,
+            },
+        )?);
+    }
+    Ok(locations)
+}
+
+fn sync_py_catalog_probabilities(py: Python<'_>, catalog: &mut PyFaultCatalog) -> PyResult<()> {
+    if catalog.locations.len() != catalog.rust_catalog.locations.len() {
+        catalog.locations = py_locations_from_catalog(py, &catalog.rust_catalog)?;
+        return Ok(());
+    }
+
+    let fault_lengths_match = catalog
+        .locations
+        .iter()
+        .zip(&catalog.rust_catalog.locations)
+        .all(|(py_loc, rust_loc)| py_loc.borrow(py).faults.len() == rust_loc.faults.len());
+    if !fault_lengths_match {
+        catalog.locations = py_locations_from_catalog(py, &catalog.rust_catalog)?;
+        return Ok(());
+    }
+
+    for (py_loc, rust_loc) in catalog
+        .locations
+        .iter()
+        .zip(&catalog.rust_catalog.locations)
+    {
+        let mut loc = py_loc.borrow_mut(py);
+        loc.channel_probability = rust_loc.channel_probability;
+        loc.no_fault_probability = rust_loc.no_fault_probability;
+        loc.num_alternatives = rust_loc.num_alternatives;
+        for (py_fault, rust_fault) in loc.faults.iter().zip(&rust_loc.faults) {
+            let mut fault = py_fault.borrow_mut(py);
+            fault.conditional_probability = rust_fault.conditional_probability;
+            fault.absolute_probability = rust_fault.absolute_probability;
+            fault.channel_probability = rust_loc.channel_probability;
+        }
+    }
+    Ok(())
+}
+
+fn py_fault_catalog_from_rust(
+    py: Python<'_>,
+    catalog: pecos_qec::fault_tolerance::fault_sampler::FaultCatalog,
+) -> PyResult<PyFaultCatalog> {
+    let locations = py_locations_from_catalog(py, &catalog)?;
+    Ok(PyFaultCatalog {
+        locations,
+        rust_catalog: catalog,
+    })
+}
+
+#[pymethods]
+impl PyFaultCatalog {
+    fn __len__(&self) -> usize {
+        self.locations.len()
+    }
+
+    fn __getitem__(&self, py: Python<'_>, index: isize) -> PyResult<Py<PyFaultLocation>> {
+        let len = isize::try_from(self.locations.len()).map_err(|_| {
+            pyo3::exceptions::PyIndexError::new_err("fault catalog is too large to index")
+        })?;
+        let index = if index < 0 { len + index } else { index };
+        if index < 0 || index >= len {
+            return Err(pyo3::exceptions::PyIndexError::new_err(
+                "fault catalog index out of range",
+            ));
+        }
+        let index = usize::try_from(index).map_err(|_| {
+            pyo3::exceptions::PyIndexError::new_err("fault catalog index out of range")
+        })?;
+        Ok(self.locations[index].clone_ref(py))
+    }
+
+    fn __iter__(slf: PyRef<'_, Self>, py: Python<'_>) -> PyResult<Py<PyAny>> {
+        let locations = pyo3::types::PyList::new(py, slf.locations.iter().map(|loc| loc.bind(py)))?;
+        Ok(locations.call_method0("__iter__")?.unbind())
+    }
+
+    /// Recompute catalog probabilities for a new stochastic noise point.
+    #[pyo3(signature = (noise=None, *, p1=None, p2=None, p_meas=None, p_prep=None))]
+    fn with_noise(
+        &mut self,
+        py: Python<'_>,
+        noise: Option<&PyNoiseModelBuilder>,
+        p1: Option<f64>,
+        p2: Option<f64>,
+        p_meas: Option<f64>,
+        p_prep: Option<f64>,
+    ) -> PyResult<()> {
+        let params = stochastic_params_from_inputs(noise, p1, p2, p_meas, p_prep);
+        self.rust_catalog.with_noise(&params);
+        sync_py_catalog_probabilities(py, self)
+    }
+
+    /// Return a cloned catalog parameterized at a new stochastic noise point.
+    #[pyo3(signature = (noise=None, *, p1=None, p2=None, p_meas=None, p_prep=None))]
+    fn parameterized(
+        &self,
+        py: Python<'_>,
+        noise: Option<&PyNoiseModelBuilder>,
+        p1: Option<f64>,
+        p2: Option<f64>,
+        p_meas: Option<f64>,
+        p_prep: Option<f64>,
+    ) -> PyResult<PyFaultCatalog> {
+        let params = stochastic_params_from_inputs(noise, p1, p2, p_meas, p_prep);
+        py_fault_catalog_from_rust(py, self.rust_catalog.parameterized(&params))
+    }
+
+    /// Lazily iterate all k-fault configurations.
+    ///
+    /// Returns an iterator yielding `FaultConfiguration` objects one at a time.
+    fn fault_configurations(
+        &self,
+        py: Python<'_>,
+        k: usize,
+    ) -> PyResult<Py<PyFaultConfigurationIter>> {
+        use pecos_qec::fault_tolerance::fault_sampler::OwnedFaultConfigIter;
+        let inner = OwnedFaultConfigIter::new(self.rust_catalog.clone(), k);
+        let py_locations: Vec<Py<PyFaultLocation>> =
+            self.locations.iter().map(|l| l.clone_ref(py)).collect();
+        Py::new(
+            py,
+            PyFaultConfigurationIter {
+                inner,
+                py_locations,
+            },
+        )
+    }
+}
+
+/// Build a fault catalog for a circuit, optionally parameterized by a noise model.
+///
+/// Returns a ``FaultCatalog`` object with ``catalog.locations``. The catalog
+/// also supports direct iteration, indexing, and ``len(catalog)``.
+///
+/// Each location has attribute access: ``loc.tick``, ``loc.gate_type``,
+/// ``loc.qubits``, ``loc.faults``.
+///
+/// Each ``FaultAlternative`` has: ``fault.kind``, ``fault.pauli`` (a real
+/// PECOS ``PauliString`` or ``None``), ``fault.detectors``, ``fault.observables``,
+/// ``fault.tracked_paulis``, ``fault.measurements``, ``fault.conditional_probability``,
+/// ``fault.absolute_probability``, ``fault.channel_probability``.
+///
+/// When noise is omitted, returns a structural catalog with zero probabilities.
+/// The catalog includes all structurally supported physical fault locations.
+#[pyfunction]
+#[pyo3(signature = (tick_circuit, noise=None, *, p1=None, p2=None, p_meas=None, p_prep=None))]
+pub fn fault_catalog(
+    tick_circuit: &Bound<'_, PyAny>,
+    noise: Option<&PyNoiseModelBuilder>,
+    py: Python<'_>,
+    p1: Option<f64>,
+    p2: Option<f64>,
+    p_meas: Option<f64>,
+    p_prep: Option<f64>,
+) -> PyResult<PyFaultCatalog> {
+    use pecos_qec::fault_tolerance::fault_sampler::FaultCatalog;
+
+    let tc = build_rust_tick_circuit(tick_circuit)?;
+    let mut catalog = FaultCatalog::from_circuit(&tc)
+        .map_err(|e| pyo3::exceptions::PyRuntimeError::new_err(e.to_string()))?;
+    if noise.is_some() || p1.is_some() || p2.is_some() || p_meas.is_some() || p_prep.is_some() {
+        let noise_params = stochastic_params_from_inputs(noise, p1, p2, p_meas, p_prep);
+        catalog.with_noise(&noise_params);
+    }
+    py_fault_catalog_from_rust(py, catalog)
+}
diff --git a/python/pecos-rslib-exp/src/stab_mps_bindings.rs b/python/pecos-rslib-exp/src/stab_mps_bindings.rs
index abf19d293..feeb75fea 100644
--- a/python/pecos-rslib-exp/src/stab_mps_bindings.rs
+++ b/python/pecos-rslib-exp/src/stab_mps_bindings.rs
@@ -324,11 +324,35 @@ impl PyStabMps {
                 self.inner.h(q);
                 Ok(None)
             }
+            "F" | "F1" => {
+                self.inner.f(q);
+                Ok(None)
+            }
+            "Fdg" | "F1d" | "F1dg" => {
+                self.inner.fdg(q);
+                Ok(None)
+            }
+            "SX" | "SqrtX" | "Q" => {
+                self.inner.sx(q);
+                Ok(None)
+            }
+            "SXdg" | "SqrtXdg" | "SqrtXd" | "Qd" => {
+                self.inner.sxdg(q);
+                Ok(None)
+            }
+            "SY" | "SqrtY" | "R" => {
+                self.inner.sy(q);
+                Ok(None)
+            }
+            "SYdg" | "SqrtYdg" | "SqrtYd" | "Rd" => {
+                self.inner.sydg(q);
+                Ok(None)
+            }
             "S" | "SZ" | "SqrtZ" => {
                 self.inner.sz(q);
                 Ok(None)
             }
-            "Sd" | "SZdg" | "SqrtZdg" => {
+            "Sd" | "SZdg" | "SqrtZdg" | "SqrtZd" => {
                 self.inner.szdg(q);
                 Ok(None)
             }
@@ -408,6 +432,34 @@ impl PyStabMps {
                 self.inner.cz(pair);
                 Ok(None)
             }
+            "SXX" => {
+                self.inner.sxx(pair);
+                Ok(None)
+            }
+            "SXXdg" => {
+                self.inner.sxxdg(pair);
+                Ok(None)
+            }
+            "SYY" => {
+                self.inner.syy(pair);
+                Ok(None)
+            }
+            "SYYdg" => {
+                self.inner.syydg(pair);
+                Ok(None)
+            }
+            "SZZ" => {
+                self.inner.szz(pair);
+                Ok(None)
+            }
+            "SZZdg" => {
+                self.inner.szzdg(pair);
+                Ok(None)
+            }
+            "SWAP" => {
+                self.inner.swap(pair);
+                Ok(None)
+            }
             "RZZ" => {
                 let angle = crate::extract_angle(params, "RZZ")?;
                 self.inner.rzz(angle, pair);
diff --git a/python/pecos-rslib-exp/src/stabmps_builder.rs b/python/pecos-rslib-exp/src/stabmps_builder.rs
new file mode 100644
index 000000000..b4cf0a044
--- /dev/null
+++ b/python/pecos-rslib-exp/src/stabmps_builder.rs
@@ -0,0 +1,119 @@
+// Copyright 2026 The PECOS Developers
+//
+// Licensed under the Apache License, Version 2.0 (the "License"); you may not use this file
+// except in compliance with the License. You may obtain a copy of the License at
+//
+//     https://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software distributed under the
+// License is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either
+// express or implied. See the License for the specific language governing permissions and
+// limitations under the License.
+
+//! `StabMps` backend for `sim_neo`.
+//!
+//! Provides a `SimulatorFactory` implementation that creates `StabMps` simulators
+//! with configurable parameters (`lazy_measure`, `max_bond_dim`, etc.).
+
+use pecos_neo::noise::ComposableNoiseModel;
+use pecos_neo::program::{DynProgramRunner, ProgramRunner};
+use pecos_neo::tool::SimulatorFactory;
+use pecos_stab_tn::stab_mps::StabMps;
+
+/// Configuration for the `StabMps` backend.
+///
+/// Carries simulator parameters through the builder-of-builders pattern.
+/// Implements `SimulatorFactory` so it can be used with `custom_backend()`.
+#[derive(Debug, Clone)]
+pub struct StabMpsBuilder {
+    /// Use lazy measurement (correct for non-Clifford, slower).
+    pub lazy_measure: bool,
+    /// Maximum MPS bond dimension.
+    pub max_bond_dim: usize,
+    /// Maximum truncation error for MPS compression.
+    /// None = disabled (library default, use fixed bond dim cap only).
+    pub max_truncation_error: Option<f64>,
+    /// Merge consecutive RZ on same qubit before decomposition.
+    pub merge_rz: bool,
+}
+
+impl Default for StabMpsBuilder {
+    fn default() -> Self {
+        Self {
+            lazy_measure: false,
+            max_bond_dim: 64,
+            max_truncation_error: None,
+            merge_rz: false,
+        }
+    }
+}
+
+impl StabMpsBuilder {
+    /// Create with default settings.
+    #[must_use]
+    pub fn new() -> Self {
+        Self::default()
+    }
+
+    /// Enable lazy measurement (correct for non-Clifford states).
+    #[must_use]
+    pub fn with_lazy_measure(mut self, lazy: bool) -> Self {
+        self.lazy_measure = lazy;
+        self
+    }
+
+    /// Set maximum bond dimension.
+    #[must_use]
+    pub fn with_max_bond_dim(mut self, bd: usize) -> Self {
+        self.max_bond_dim = bd;
+        self
+    }
+
+    /// Set maximum truncation error.
+    #[must_use]
+    pub fn with_max_truncation_error(mut self, err: f64) -> Self {
+        self.max_truncation_error = Some(err);
+        self
+    }
+
+    /// Enable RZ merging.
+    #[must_use]
+    pub fn with_merge_rz(mut self, merge: bool) -> Self {
+        self.merge_rz = merge;
+        self
+    }
+}
+
+impl SimulatorFactory for StabMpsBuilder {
+    fn create_runner(
+        &self,
+        num_qubits: usize,
+        noise: Option<ComposableNoiseModel>,
+        seed: Option<u64>,
+    ) -> Box<dyn DynProgramRunner> {
+        let mut builder = StabMps::builder(num_qubits);
+        if self.lazy_measure {
+            builder = builder.lazy_measure(true);
+        }
+        builder = builder.max_bond_dim(self.max_bond_dim);
+        if let Some(err) = self.max_truncation_error {
+            builder = builder.max_truncation_error(err);
+        }
+        if self.merge_rz {
+            builder = builder.merge_rz(true);
+        }
+        if let Some(s) = seed {
+            builder = builder.seed(s);
+        }
+        let sim = builder.build();
+
+        let mut runner = ProgramRunner::rotations(sim);
+        if let Some(n) = noise {
+            runner = runner.with_noise(n);
+        }
+        if let Some(s) = seed {
+            runner = runner.with_seed(s);
+        }
+        Box::new(runner)
+    }
+}
diff --git a/python/pecos-rslib-llvm/pyproject.toml b/python/pecos-rslib-llvm/pyproject.toml
index de6566bad..553757192 100644
--- a/python/pecos-rslib-llvm/pyproject.toml
+++ b/python/pecos-rslib-llvm/pyproject.toml
@@ -42,9 +42,6 @@ test = [
     "pytest>=9.0",
 ]
 
-[tool.uv.sources]
-pecos-rslib-llvm = { workspace = true }
-
 [tool.ruff]
 lint.extend-select = ["S", "B", "PT"]
 lint.ignore = ["S101"]
diff --git a/python/pecos-rslib/Cargo.toml b/python/pecos-rslib/Cargo.toml
index fe1c44197..965296fe0 100644
--- a/python/pecos-rslib/Cargo.toml
+++ b/python/pecos-rslib/Cargo.toml
@@ -62,8 +62,10 @@ pecos-experimental.workspace = true
 
 # Third-party
 pyo3 = { workspace = true, features = ["extension-module", "abi3-py310", "generate-import-lib", "num-complex"] }
+rayon.workspace = true
 rand.workspace = true
 ndarray.workspace = true
+nalgebra.workspace = true
 num-complex.workspace = true
 parking_lot.workspace = true
 serde_json.workspace = true
diff --git a/python/pecos-rslib/pecos_rslib.pyi b/python/pecos-rslib/pecos_rslib.pyi
index f949198c5..afab181c1 100644
--- a/python/pecos-rslib/pecos_rslib.pyi
+++ b/python/pecos-rslib/pecos_rslib.pyi
@@ -18,9 +18,11 @@ from __future__ import annotations
 
 import os
 from typing import (
+    Any,
     Callable,
     Generic,
     Iterator,
+    Mapping,
     Sequence,
     TypeVar,
     overload,
@@ -1024,7 +1026,42 @@ class Pauli:
 class PauliString:
     """String of Pauli operators."""
 
-    ...
+    def __init__(
+        self,
+        paulis: list[tuple[Pauli, int]] | list[Pauli] | None = None,
+        phase: int = 0,
+    ) -> None: ...
+    @staticmethod
+    def from_str(s: str) -> PauliString: ...
+    @staticmethod
+    def from_dense_str(s: str) -> PauliString: ...
+    @staticmethod
+    def from_sparse_str(s: str) -> PauliString: ...
+    @staticmethod
+    def X(qubit: int) -> PauliString: ...
+    @staticmethod
+    def Y(qubit: int) -> PauliString: ...
+    @staticmethod
+    def Z(qubit: int) -> PauliString: ...
+    @staticmethod
+    def I() -> PauliString: ...  # noqa: E743
+    def to_dense_str(self, num_qubits: int | None = None) -> str: ...
+    def to_sparse_str(self) -> str: ...
+    def get_phase(self) -> int: ...
+    def get_paulis(self) -> list[tuple[Pauli, int]]: ...
+    def to_matrix(self, num_qubits: int | None = None) -> list[list[tuple[float, float]]]: ...
+    def commutes_with(self, other: PauliString) -> bool: ...
+    def anticommutes_with(self, other: PauliString) -> bool: ...
+    def weight(self) -> int: ...
+    def qubits(self) -> list[int]: ...
+    def __and__(self, other: PauliString) -> PauliString: ...
+    def __mul__(self, other: PauliString) -> PauliString: ...
+    def __neg__(self) -> PauliString: ...
+    def __eq__(self, other: object) -> bool: ...
+
+def X(qubit: int) -> PauliString: ...
+def Y(qubit: int) -> PauliString: ...
+def Z(qubit: int) -> PauliString: ...
 
 class PauliStabilizerGroup:
     """A group of commuting Pauli operators with real phases."""
@@ -1034,7 +1071,7 @@ class PauliStabilizerGroup:
 class PauliSequence:
     """Ordered sequence of Pauli operators with symplectic analysis."""
 
-    ...
+    def group_commuting(self) -> list[PauliSequence]: ...
 
 class CliffordRep:
     """Clifford gate in the Heisenberg picture."""
@@ -1152,6 +1189,134 @@ class PauliPropRs:
 
     ...
 
+ComplexMatrix = Sequence[Sequence[complex]]
+RealMatrix = Sequence[Sequence[float]]
+PauliProbabilityMap = Mapping[str | PauliString, float] | Sequence[tuple[str | PauliString, float]]
+
+class PauliChannel:
+    """Sparse Pauli error channel represented by probabilities."""
+
+    @staticmethod
+    def one_qubit(px: float, py: float, pz: float) -> PauliChannel: ...
+    @staticmethod
+    def from_probabilities(
+        num_qubits: int,
+        probabilities: PauliProbabilityMap,
+    ) -> PauliChannel: ...
+    def num_qubits(self) -> int: ...
+    def probabilities(self) -> dict[str, float]: ...
+    def total_error_rate(self) -> float: ...
+    def to_ptm(self) -> Ptm: ...
+
+class Ptm:
+    """Dense Pauli transfer matrix."""
+
+    def __init__(self, num_qubits: int, matrix: RealMatrix) -> None: ...
+    @staticmethod
+    def identity(num_qubits: int) -> Ptm: ...
+    def num_qubits(self) -> int: ...
+    def matrix(self) -> list[list[float]]: ...
+    def entry(self, output: int, input: int) -> float: ...
+    def to_choi(self) -> ChoiMatrix: ...
+    def to_kraus(self) -> KrausOps: ...
+    def to_superop(self) -> SuperOp: ...
+    def to_chi(self) -> ChiMatrix: ...
+
+class KrausOps:
+    """Kraus-operator channel representation."""
+
+    def __init__(self, num_qubits: int, operators: Sequence[ComplexMatrix]) -> None: ...
+    def num_qubits(self) -> int: ...
+    def operators(self) -> list[list[list[complex]]]: ...
+    def is_trace_preserving(self) -> bool: ...
+    def to_ptm(self) -> Ptm: ...
+    def to_choi(self) -> ChoiMatrix: ...
+    def to_superop(self) -> SuperOp: ...
+    def to_chi(self) -> ChiMatrix: ...
+    def to_stinespring(self) -> Stinespring: ...
+
+class ChoiMatrix:
+    """Choi-matrix channel representation."""
+
+    def __init__(self, num_qubits: int, matrix: ComplexMatrix) -> None: ...
+    def num_qubits(self) -> int: ...
+    def matrix(self) -> list[list[complex]]: ...
+    def apply_to_operator(self, operator: ComplexMatrix) -> list[list[complex]]: ...
+    def partial_trace_output(self) -> list[list[complex]]: ...
+    def partial_trace_input(self) -> list[list[complex]]: ...
+    def is_completely_positive(self) -> bool: ...
+    def is_trace_preserving(self) -> bool: ...
+    def is_cptp(self) -> bool: ...
+    def is_unital(self) -> bool: ...
+    def to_ptm(self) -> Ptm: ...
+    def to_kraus(self) -> KrausOps: ...
+    def to_superop(self) -> SuperOp: ...
+    def to_chi(self) -> ChiMatrix: ...
+
+class SuperOp:
+    """Column-stacked superoperator channel representation."""
+
+    def __init__(self, num_qubits: int, matrix: ComplexMatrix) -> None: ...
+    def num_qubits(self) -> int: ...
+    def matrix(self) -> list[list[complex]]: ...
+    def to_choi(self) -> ChoiMatrix: ...
+    def to_ptm(self) -> Ptm: ...
+    def to_kraus(self) -> KrausOps: ...
+    def compose(self, other: SuperOp) -> SuperOp: ...
+    def tensor(self, other: SuperOp) -> SuperOp: ...
+
+class ChiMatrix:
+    """Pauli-basis process matrix."""
+
+    def __init__(self, num_qubits: int, matrix: ComplexMatrix) -> None: ...
+    def num_qubits(self) -> int: ...
+    def matrix(self) -> list[list[complex]]: ...
+    def to_choi(self) -> ChoiMatrix: ...
+    def to_ptm(self) -> Ptm: ...
+
+class Stinespring:
+    """Stinespring isometry channel representation."""
+
+    def __init__(self, num_qubits: int, isometry: ComplexMatrix) -> None: ...
+    def num_qubits(self) -> int: ...
+    def environment_dim(self) -> int: ...
+    def isometry(self) -> list[list[complex]]: ...
+    def to_kraus(self) -> KrausOps: ...
+    def to_choi(self) -> ChoiMatrix: ...
+    def to_superop(self) -> SuperOp: ...
+
+def state_fidelity(left: Sequence[complex], right: Sequence[complex]) -> float: ...
+def state_fidelity_with_density_matrix(rho: ComplexMatrix, psi: Sequence[complex]) -> float: ...
+def purity(rho: ComplexMatrix) -> float: ...
+def entropy(rho: ComplexMatrix) -> float: ...
+def shannon_entropy(probabilities: Sequence[float], base: float) -> float: ...
+def negativity(rho: ComplexMatrix, dims: Sequence[int], subsystem: int) -> float: ...
+def logarithmic_negativity(rho: ComplexMatrix, dims: Sequence[int], subsystem: int) -> float: ...
+def schmidt_decomposition(
+    state: Sequence[complex],
+    dims: Sequence[int],
+    left_subsystems: Sequence[int],
+) -> list[tuple[float, list[complex], list[complex]]]: ...
+def partial_trace_subsystems(
+    rho: ComplexMatrix,
+    dims: Sequence[int],
+    traced_subsystems: Sequence[int],
+) -> list[list[complex]]: ...
+def partial_trace_qubits(
+    rho: ComplexMatrix,
+    num_qubits: int,
+    traced_qubits: Sequence[int],
+) -> list[list[complex]]: ...
+def hellinger_distance(left: Sequence[float], right: Sequence[float]) -> float: ...
+def hellinger_fidelity(left: Sequence[float], right: Sequence[float]) -> float: ...
+def process_fidelity(left: Ptm, right: Ptm) -> float: ...
+def average_gate_fidelity(left: Ptm, right: Ptm) -> float: ...
+def gate_error(left: Ptm, right: Ptm) -> float: ...
+def pauli_channel_diamond_norm(left: PauliChannel, right: PauliChannel) -> float: ...
+def pauli_channel_diamond_distance(left: PauliChannel, right: PauliChannel) -> float: ...
+def random_density_matrix(num_qubits: int, seed: int) -> list[list[complex]]: ...
+def random_quantum_channel(num_qubits: int, num_kraus: int, seed: int) -> KrausOps: ...
+
 # =============================================================================
 # Clifford Gate Constructors
 # =============================================================================
@@ -1228,6 +1393,288 @@ class llvm:
 
     ...
 
+# =============================================================================
+# Tick Circuit
+# =============================================================================
+
+class GateType:
+    """Gate type marker."""
+
+    H: GateType
+    X: GateType
+    Y: GateType
+    Z: GateType
+    S: GateType
+    Sdg: GateType
+    SX: GateType
+    SXdg: GateType
+    SY: GateType
+    SYdg: GateType
+    T: GateType
+    Tdg: GateType
+    I: GateType
+    CX: GateType
+    CY: GateType
+    CZ: GateType
+    RX: GateType
+    RY: GateType
+    RZ: GateType
+    RXX: GateType
+    RYY: GateType
+    RZZ: GateType
+    R1XY: GateType
+    U: GateType
+    F: GateType
+    Fdg: GateType
+    SXX: GateType
+    SXXdg: GateType
+    SYY: GateType
+    SYYdg: GateType
+    SZZ: GateType
+    SZZdg: GateType
+    SWAP: GateType
+    CH: GateType
+    CRZ: GateType
+    CCX: GateType
+    Measure: GateType
+    MeasureFree: GateType
+    Prep: GateType
+    QAlloc: GateType
+    QFree: GateType
+    TrackedPauliMeta: GateType
+    Custom: GateType
+
+    @property
+    def name(self) -> str: ...
+
+class Gate:
+    """Quantum gate or stored TickCircuit gate batch."""
+
+    def __init__(
+        self,
+        gate_type: GateType,
+        params: Sequence[float] | None = None,
+        qubits: Sequence[int] | None = None,
+    ) -> None: ...
+    @property
+    def gate_type(self) -> GateType: ...
+    @property
+    def qubits(self) -> list[int]: ...
+    @property
+    def params(self) -> list[float]: ...
+    @property
+    def angles(self) -> list[float]: ...
+    @property
+    def meas_ids(self) -> list[int]: ...
+    def is_single_qubit(self) -> bool: ...
+    def is_two_qubit(self) -> bool: ...
+    def is_channel(self) -> bool: ...
+    def channel_mixed_pauli_terms(self) -> list[Any]: ...
+    @staticmethod
+    def h(qubits: Sequence[int]) -> Gate: ...
+    @staticmethod
+    def x(qubits: Sequence[int]) -> Gate: ...
+    @staticmethod
+    def y(qubits: Sequence[int]) -> Gate: ...
+    @staticmethod
+    def z(qubits: Sequence[int]) -> Gate: ...
+    @staticmethod
+    def cx(pairs: Sequence[tuple[int, int]]) -> Gate: ...
+    @staticmethod
+    def cy(pairs: Sequence[tuple[int, int]]) -> Gate: ...
+    @staticmethod
+    def cz(pairs: Sequence[tuple[int, int]]) -> Gate: ...
+    @staticmethod
+    def mz(qubits: Sequence[int]) -> Gate: ...
+    @staticmethod
+    def pz(qubits: Sequence[int]) -> Gate: ...
+
+class DagCircuit:
+    """Directed acyclic graph circuit representation."""
+
+    def __init__(self) -> None: ...
+    def gate_count(self) -> int: ...
+    def gate(self, node: int) -> Gate | None: ...
+    def nodes(self) -> list[int]: ...
+    def to_tick_circuit(self) -> TickCircuit: ...
+
+class Tick:
+    """A single time slice of a tick-based quantum circuit."""
+
+    def __len__(self) -> int: ...
+    def gate_count(self) -> int:
+        """Number of individual gate applications in this tick."""
+        ...
+
+    def gate_batch_count(self) -> int:
+        """Number of stored compatible gate batches in this tick."""
+        ...
+
+    def is_empty(self) -> bool: ...
+    def gate_batches(self) -> list[Gate]: ...
+    def get_gate_attr(self, gate_idx: int, key: str) -> Any | None: ...
+    def set_gate_attr(self, gate_idx: int, key: str, value: Any) -> None: ...
+    def set_gate_attrs(self, gate_idx: int, attrs: Mapping[str, Any]) -> None: ...
+    def get_attr(self, key: str) -> Any | None: ...
+    def meta(self, key: str, value: Any) -> None: ...
+    def metas(self, attrs: Mapping[str, Any]) -> None: ...
+    def active_qubits(self) -> list[int]: ...
+    def uses_qubit(self, qubit: int) -> bool: ...
+    def find_conflicts(self, qubits: Sequence[int]) -> list[Any]: ...
+    def add_gate(self, gate: Gate) -> int: ...
+    def try_add_gate(self, gate: Gate) -> int: ...
+    def discard(self, qubits: Sequence[int]) -> int: ...
+    def remove_gate(self, idx: int) -> Gate | None: ...
+
+class TickHandle:
+    """Handle for adding gates to a tick."""
+
+    def index(self) -> int: ...
+    def meta(self, key: str, value: Any) -> TickHandle: ...
+    def metas(self, attrs: Mapping[str, Any]) -> TickHandle: ...
+    def h(self, qubits: Sequence[int]) -> TickHandle: ...
+    def x(self, qubits: Sequence[int]) -> TickHandle: ...
+    def y(self, qubits: Sequence[int]) -> TickHandle: ...
+    def z(self, qubits: Sequence[int]) -> TickHandle: ...
+    def i(self, qubits: Sequence[int]) -> TickHandle: ...
+    def sx(self, qubits: Sequence[int]) -> TickHandle: ...
+    def sxdg(self, qubits: Sequence[int]) -> TickHandle: ...
+    def sy(self, qubits: Sequence[int]) -> TickHandle: ...
+    def sydg(self, qubits: Sequence[int]) -> TickHandle: ...
+    def sz(self, qubits: Sequence[int]) -> TickHandle: ...
+    def szdg(self, qubits: Sequence[int]) -> TickHandle: ...
+    def t(self, qubits: Sequence[int]) -> TickHandle: ...
+    def tdg(self, qubits: Sequence[int]) -> TickHandle: ...
+    def rx(self, theta: Any, qubits: Sequence[int]) -> TickHandle: ...
+    def ry(self, theta: Any, qubits: Sequence[int]) -> TickHandle: ...
+    def rz(self, theta: Any, qubits: Sequence[int]) -> TickHandle: ...
+    def r1xy(self, theta: Any, phi: Any, qubits: Sequence[int]) -> TickHandle: ...
+    def u(self, theta: Any, phi: Any, lam: Any, qubits: Sequence[int]) -> TickHandle: ...
+    def cx(self, pairs: Sequence[tuple[int, int]]) -> TickHandle: ...
+    def cy(self, pairs: Sequence[tuple[int, int]]) -> TickHandle: ...
+    def cz(self, pairs: Sequence[tuple[int, int]]) -> TickHandle: ...
+    def szz(self, pairs: Sequence[tuple[int, int]]) -> TickHandle: ...
+    def szzdg(self, pairs: Sequence[tuple[int, int]]) -> TickHandle: ...
+    def f(self, qubits: Sequence[int]) -> TickHandle: ...
+    def fdg(self, qubits: Sequence[int]) -> TickHandle: ...
+    def sxx(self, pairs: Sequence[tuple[int, int]]) -> TickHandle: ...
+    def sxxdg(self, pairs: Sequence[tuple[int, int]]) -> TickHandle: ...
+    def syy(self, pairs: Sequence[tuple[int, int]]) -> TickHandle: ...
+    def syydg(self, pairs: Sequence[tuple[int, int]]) -> TickHandle: ...
+    def swap(self, pairs: Sequence[tuple[int, int]]) -> TickHandle: ...
+    def ch(self, pairs: Sequence[tuple[int, int]]) -> TickHandle: ...
+    def crz(self, theta: Any, pairs: Sequence[tuple[int, int]]) -> TickHandle: ...
+    def ccx(self, triples: Sequence[tuple[int, int, int]]) -> TickHandle: ...
+    def rxx(self, theta: Any, pairs: Sequence[tuple[int, int]]) -> TickHandle: ...
+    def ryy(self, theta: Any, pairs: Sequence[tuple[int, int]]) -> TickHandle: ...
+    def rzz(self, theta: Any, pairs: Sequence[tuple[int, int]]) -> TickHandle: ...
+    def add_gate(
+        self,
+        name: str,
+        qubits: Sequence[int],
+        angles: Sequence[float] | None = None,
+    ) -> TickHandle: ...
+    def custom(self, qubits: Sequence[int]) -> TickHandle: ...
+    def custom_gate(
+        self,
+        name: str,
+        qubits: Sequence[int],
+        angles: Sequence[float] | None = None,
+    ) -> TickHandle: ...
+    def pz(self, qubits: Sequence[int]) -> TickPrepHandle: ...
+    def mz(self, qubits: Sequence[int]) -> list[tuple[int, int, int]]: ...
+    def mz_with_ids(
+        self,
+        qubits: Sequence[int],
+        meas_ids: Sequence[int],
+    ) -> list[tuple[int, int, int]]: ...
+    def mz_free(self, qubits: Sequence[int]) -> list[tuple[int, int, int]]: ...
+    def qalloc(self, qubits: Sequence[int]) -> TickHandle: ...
+    def qfree(self, qubits: Sequence[int]) -> TickHandle: ...
+    def idle(self, duration: Any, qubits: Sequence[int]) -> TickHandle: ...
+
+class TickPrepHandle:
+    """Handle returned by preparation gates for attaching metadata."""
+
+    def meta(self, key: str, value: Any) -> None: ...
+    def metas(self, attrs: Mapping[str, Any]) -> None: ...
+
+class TickMeasureHandle:
+    """Handle returned by measurement gates for attaching metadata."""
+
+    def meta(self, key: str, value: Any) -> None: ...
+    def metas(self, attrs: Mapping[str, Any]) -> None: ...
+
+class TickCircuit:
+    """Tick-based quantum circuit representation."""
+
+    def __init__(self) -> None: ...
+    def tick(self) -> TickHandle:
+        """Add a new tick and return a handle for adding gates."""
+        ...
+
+    def num_ticks(self) -> int: ...
+    def gate_count(self) -> int:
+        """Total number of individual gate applications."""
+        ...
+
+    def gate_batch_count(self) -> int:
+        """Total number of stored compatible gate batches."""
+        ...
+
+    def num_measurements(self) -> int: ...
+    def next_tick_index(self) -> int: ...
+    def get_tick(self, idx: int) -> Tick | None: ...
+    def tick_at(self, idx: int) -> TickHandle: ...
+    def insert_tick(self, idx: int) -> TickHandle: ...
+    def gate_batches(self) -> list[tuple[int, Gate]]: ...
+    def all_qubits(self) -> list[int]: ...
+    def gate_counts_by_type(self) -> dict[str, int]: ...
+    def set_meta(self, key: str, value: Any) -> None: ...
+    def metas(self, attrs: Mapping[str, Any]) -> None: ...
+    def get_meta(self, key: str) -> Any | None: ...
+    def add_detector(
+        self,
+        records: Sequence[int],
+        coords: Sequence[float] | None = None,
+        label: str | None = None,
+        detector_id: int | None = None,
+    ) -> int: ...
+    def add_observable(
+        self,
+        records: Sequence[int],
+        observable_id: int | None = None,
+        label: str | None = None,
+    ) -> int: ...
+    def annotations(self) -> list[Any]: ...
+    def detector(self, measurements: Any, label: str | None = None) -> int: ...
+    def observable(self, measurements: Any, label: str | None = None) -> int: ...
+    def tracked_pauli(self, pauli: PauliString, label: str | None = None) -> int: ...
+    def clear(self) -> None: ...
+    def reset(self) -> None: ...
+    def reserve_ticks(self, n: int) -> None: ...
+    def discard(self, qubits: Sequence[int], tick_idx: int) -> int | None: ...
+    def set_tick_meta(self, tick_idx: int, key: str, value: Any) -> None: ...
+    def get_tick_meta(self, tick_idx: int, key: str) -> Any | None: ...
+    def set_gate_meta(self, tick_idx: int, gate_idx: int, key: str, value: Any) -> None: ...
+    def get_gate_meta(self, tick_idx: int, gate_idx: int, key: str) -> Any | None: ...
+    def lower_clifford_rotations(self) -> None: ...
+    def assign_missing_meas_ids(self) -> None: ...
+    def insert_idle_after_two_qubit_gates(self, duration: float = 1.0) -> None: ...
+    def fill_idle_gates(self) -> None: ...
+    def with_noise(
+        self,
+        p1: float = 0.0,
+        p2: float = 0.0,
+        p_meas: float = 0.0,
+        p_prep: float = 0.0,
+    ) -> TickCircuit: ...
+    def compact_ticks(self) -> None: ...
+    def import_gate_signatures(self, sigs: Mapping[str, tuple[int, int]]) -> None: ...
+    def gate_signatures(self) -> dict[str, tuple[int, int]]: ...
+    def import_registry(self, registry: Any) -> None: ...
+    def to_dag_circuit(self) -> DagCircuit: ...
+
 # =============================================================================
 # Namespace Modules
 # =============================================================================
@@ -1247,6 +1694,45 @@ class quantum:
     DensityMatrixEngineBuilder: type[DensityMatrixEngineBuilder]
     CoinTossEngineBuilder: type[CoinTossEngineBuilder]
 
+class quantum_info:
+    """Quantum-information channel and measure namespace."""
+
+    PauliChannel: type[PauliChannel]
+    Ptm: type[Ptm]
+    KrausOps: type[KrausOps]
+    ChoiMatrix: type[ChoiMatrix]
+    SuperOp: type[SuperOp]
+    ChiMatrix: type[ChiMatrix]
+    Stinespring: type[Stinespring]
+    state_fidelity: Callable[[Sequence[complex], Sequence[complex]], float]
+    state_fidelity_with_density_matrix: Callable[[ComplexMatrix, Sequence[complex]], float]
+    purity: Callable[[ComplexMatrix], float]
+    entropy: Callable[[ComplexMatrix], float]
+    shannon_entropy: Callable[[Sequence[float], float], float]
+    negativity: Callable[[ComplexMatrix, Sequence[int], int], float]
+    logarithmic_negativity: Callable[[ComplexMatrix, Sequence[int], int], float]
+    schmidt_decomposition: Callable[
+        [Sequence[complex], Sequence[int], Sequence[int]],
+        list[tuple[float, list[complex], list[complex]]],
+    ]
+    partial_trace_subsystems: Callable[
+        [ComplexMatrix, Sequence[int], Sequence[int]],
+        list[list[complex]],
+    ]
+    partial_trace_qubits: Callable[
+        [ComplexMatrix, int, Sequence[int]],
+        list[list[complex]],
+    ]
+    hellinger_distance: Callable[[Sequence[float], Sequence[float]], float]
+    hellinger_fidelity: Callable[[Sequence[float], Sequence[float]], float]
+    process_fidelity: Callable[[Ptm, Ptm], float]
+    average_gate_fidelity: Callable[[Ptm, Ptm], float]
+    gate_error: Callable[[Ptm, Ptm], float]
+    pauli_channel_diamond_norm: Callable[[PauliChannel, PauliChannel], float]
+    pauli_channel_diamond_distance: Callable[[PauliChannel, PauliChannel], float]
+    random_density_matrix: Callable[[int, int], list[list[complex]]]
+    random_quantum_channel: Callable[[int, int, int], KrausOps]
+
 class noise:
     """Noise model namespace."""
 
diff --git a/python/pecos-rslib/src/dag_circuit_bindings.rs b/python/pecos-rslib/src/dag_circuit_bindings.rs
index 02ea7062b..31bd12985 100644
--- a/python/pecos-rslib/src/dag_circuit_bindings.rs
+++ b/python/pecos-rslib/src/dag_circuit_bindings.rs
@@ -24,11 +24,87 @@
 
 use crate::dtypes::AngleParam;
 use crate::gate_registry_bindings::PyGateRegistry;
-use pecos_core::{Angle64, GateQubits, GateSignature, TimeUnits};
-use pecos_quantum::{Attribute, DagCircuit, Gate, GateType, QubitId, Tick, TickCircuit};
+use pecos_core::{Angle64, ChannelExpr, GateQubits, GateSignature, Pauli, TimeUnits};
+use pecos_quantum::{
+    Attribute, DagCircuit, Gate, GateType, QubitId, Tick, TickCircuit, TickGateError,
+};
 use pyo3::prelude::*;
 use pyo3::types::{PyBytes, PyDict, PyList};
-use std::collections::HashMap;
+
+type PyMixedPauliTerm = (f64, Vec<(String, usize)>);
+
+fn pauli_string_terms(pauli: &pecos_core::PauliString) -> Vec<(String, usize)> {
+    pauli
+        .paulis()
+        .iter()
+        .map(|(p, q)| {
+            let label = match p {
+                Pauli::I => "I",
+                Pauli::X => "X",
+                Pauli::Y => "Y",
+                Pauli::Z => "Z",
+            };
+            (label.to_string(), q.index())
+        })
+        .collect()
+}
+
+fn mixed_pauli_terms(channel: &ChannelExpr) -> PyResult<Vec<PyMixedPauliTerm>> {
+    match channel {
+        ChannelExpr::Unitary(unitary) => {
+            let pauli = unitary.clone().try_to_pauli_string().ok_or_else(|| {
+                pyo3::exceptions::PyValueError::new_err(
+                    "channel unitary is not representable as a Pauli operator",
+                )
+            })?;
+            Ok(vec![(1.0, pauli_string_terms(&pauli))])
+        }
+        ChannelExpr::MixedUnitary(ops) => ops
+            .iter()
+            .map(|(prob, unitary)| {
+                let pauli = unitary.clone().try_to_pauli_string().ok_or_else(|| {
+                    pyo3::exceptions::PyValueError::new_err(
+                        "mixed-unitary channel contains a non-Pauli unitary",
+                    )
+                })?;
+                Ok((*prob, pauli_string_terms(&pauli)))
+            })
+            .collect(),
+        _ => Err(pyo3::exceptions::PyValueError::new_err(
+            "channel is not a Pauli mixed-unitary channel",
+        )),
+    }
+}
+
+fn validate_probability(name: &str, p: f64) -> PyResult<()> {
+    if (0.0..=1.0).contains(&p) {
+        Ok(())
+    } else {
+        Err(pyo3::exceptions::PyValueError::new_err(format!(
+            "{name} must be in [0, 1], got {p}"
+        )))
+    }
+}
+
+fn receives_two_qubit_noise(gate_type: GateType) -> bool {
+    matches!(
+        gate_type,
+        GateType::CX
+            | GateType::CY
+            | GateType::CZ
+            | GateType::SZZ
+            | GateType::SZZdg
+            | GateType::SXX
+            | GateType::SXXdg
+            | GateType::SYY
+            | GateType::SYYdg
+            | GateType::SWAP
+            | GateType::CRZ
+            | GateType::RXX
+            | GateType::RYY
+            | GateType::RZZ
+    )
+}
 
 /// Convert a Rust Attribute to a Python object.
 fn attribute_to_py(py: Python<'_>, attr: &Attribute) -> Py<PyAny> {
@@ -529,6 +605,14 @@ impl PyGateType {
         }
     }
 
+    #[classattr]
+    #[pyo3(name = "TrackedPauliMeta")]
+    fn tracked_pauli_meta() -> Self {
+        Self {
+            inner: GateType::TrackedPauliMeta,
+        }
+    }
+
     #[classattr]
     #[pyo3(name = "Custom")]
     fn custom() -> Self {
@@ -619,6 +703,12 @@ impl PyGate {
         self.inner.qubits.iter().map(|q| usize::from(*q)).collect()
     }
 
+    /// Measurement result identities (one per qubit for measurement gates, empty otherwise).
+    #[getter]
+    fn meas_ids(&self) -> Vec<usize> {
+        self.inner.meas_ids.iter().map(|mr| mr.0).collect()
+    }
+
     /// Check if this is a single-qubit gate.
     fn is_single_qubit(&self) -> bool {
         self.inner.is_single_qubit()
@@ -629,6 +719,22 @@ impl PyGate {
         self.inner.is_two_qubit()
     }
 
+    /// Check if this gate carries a channel payload.
+    fn is_channel(&self) -> bool {
+        self.inner.is_channel()
+    }
+
+    /// Return a Pauli mixed-unitary channel payload as `(probability, terms)`.
+    ///
+    /// Each term is a list of `(pauli, qubit)` pairs. Identity terms are
+    /// represented by an empty list. Non-Pauli channels raise `ValueError`.
+    fn channel_mixed_pauli_terms(&self) -> PyResult<Vec<PyMixedPauliTerm>> {
+        let channel = self.inner.channel_expr().ok_or_else(|| {
+            pyo3::exceptions::PyValueError::new_err("gate does not carry a channel payload")
+        })?;
+        mixed_pauli_terms(channel)
+    }
+
     // Factory methods for common gates
 
     /// Create a Hadamard gate.
@@ -866,6 +972,27 @@ pyo3::create_exception!(
     pyo3::exceptions::PyException
 );
 
+/// Extract node indices from a list of either `int` or `(int, int)` tuples.
+/// This allows `detector()` / `observable()` to accept both raw node indices
+/// and measurement refs from `mz()`.
+fn extract_measurement_nodes(list: &Bound<'_, pyo3::types::PyList>) -> PyResult<Vec<usize>> {
+    list.iter()
+        .map(|item| {
+            // Try (node, qubit) tuple first
+            if let Ok((node, _qubit)) = item.extract::<(usize, usize)>() {
+                Ok(node)
+            } else {
+                // Fall back to plain int
+                item.extract::<usize>().map_err(|_| {
+                    pyo3::exceptions::PyTypeError::new_err(
+                        "measurements must be a list of ints or (node, qubit) tuples from mz()",
+                    )
+                })
+            }
+        })
+        .collect()
+}
+
 /// Python wrapper for `DagCircuit`.
 ///
 /// A directed acyclic graph representation of a quantum circuit where nodes are gates
@@ -897,8 +1024,10 @@ impl PyDagCircuit {
     /// Add a gate to the circuit.
     ///
     /// Returns the node index of the newly added gate.
-    fn add_gate(&mut self, gate: PyGate) -> usize {
-        self.inner.add_gate(gate.inner)
+    fn add_gate(&mut self, gate: PyGate) -> PyResult<usize> {
+        self.inner
+            .try_add_gate(gate.inner)
+            .map_err(pyo3::exceptions::PyValueError::new_err)
     }
 
     /// Remove a gate from the circuit.
@@ -1246,11 +1375,16 @@ impl PyDagCircuit {
 
     /// Measure qubits in the Z basis.
     ///
-    /// Note: Unlike gates, measurements break the chain in simulators.
-    /// This method still returns self for convenience in Python.
-    fn mz(slf: Py<Self>, py: Python<'_>, qubits: Vec<usize>) -> Py<Self> {
-        slf.borrow_mut(py).inner.mz(&qubits);
-        slf
+    /// Returns a list of `(node, qubit)` tuples that can be passed to
+    /// `detector()` and `observable()`.
+    ///
+    /// Example:
+    ///     >>> dag = `DagCircuit()`
+    ///     >>> ms = dag.mz([0, 1])
+    ///     >>> dag.detector(ms)
+    fn mz(slf: &Bound<'_, Self>, qubits: Vec<usize>) -> Vec<(usize, usize)> {
+        let refs = slf.borrow_mut().inner.mz(&qubits);
+        refs.iter().map(|r| (r.node, r.qubit.index())).collect()
     }
 
     /// Measure and free qubits (destructive measurement).
@@ -1277,6 +1411,113 @@ impl PyDagCircuit {
         slf
     }
 
+    // ==================== Annotations ====================
+
+    /// Annotate a detector: measurements whose XOR should be deterministic.
+    ///
+    /// Args:
+    ///     measurements: List of measurement refs from `mz()` (tuples of
+    ///         `(node, qubit)`), or plain node indices.
+    ///     label: Optional label string.
+    ///
+    /// Returns:
+    ///     The annotation index.
+    ///
+    /// Example:
+    ///     >>> ms = dag.mz([0, 1])
+    ///     >>> dag.detector(ms, `label="Z_0` `Z_1`")
+    #[pyo3(signature = (measurements, label=None))]
+    fn detector(
+        &mut self,
+        measurements: &Bound<'_, pyo3::types::PyList>,
+        label: Option<String>,
+    ) -> PyResult<usize> {
+        let nodes = extract_measurement_nodes(measurements)?;
+        Ok(if let Some(l) = label {
+            self.inner.detector_labeled(&l, &nodes)
+        } else {
+            self.inner.detector(&nodes)
+        })
+    }
+
+    /// Annotate a logical observable: measurements whose XOR gives a logical outcome.
+    ///
+    /// Args:
+    ///     measurements: List of measurement refs from `mz()` (tuples of
+    ///         `(node, qubit)`), or plain node indices.
+    ///     label: Optional label string.
+    ///
+    /// Returns:
+    ///     The annotation index.
+    #[pyo3(signature = (measurements, label=None))]
+    fn observable(
+        &mut self,
+        measurements: &Bound<'_, pyo3::types::PyList>,
+        label: Option<String>,
+    ) -> PyResult<usize> {
+        let nodes = extract_measurement_nodes(measurements)?;
+        Ok(if let Some(l) = label {
+            self.inner.observable_labeled(&l, &nodes)
+        } else {
+            self.inner.observable(&nodes)
+        })
+    }
+
+    /// Place a tracked-Pauli annotation at this point in the circuit.
+    ///
+    /// Only faults BEFORE this annotation can flip the operator.
+    /// Accepts a `PauliString`, which supports `PauliString.X(0) & PauliString.Z(1)`.
+    ///
+    /// Args:
+    ///     pauli: A `PauliString` to track.
+    ///     label: Optional label string.
+    ///
+    /// Returns:
+    ///     The annotation index.
+    ///
+    /// Example:
+    ///     >>> from pecos import PauliString
+    ///     >>> dag.tracked_pauli(PauliString.Z(0) & PauliString.Z(1))
+    #[pyo3(signature = (pauli, label=None))]
+    fn tracked_pauli(
+        &mut self,
+        pauli: &crate::pauli_bindings::PauliString,
+        label: Option<String>,
+    ) -> usize {
+        if let Some(l) = label {
+            self.inner.tracked_pauli_labeled(&l, pauli.inner.clone())
+        } else {
+            self.inner.tracked_pauli(pauli.inner.clone())
+        }
+    }
+
+    /// Get all annotations as a list of dicts.
+    ///
+    /// Each dict has keys: "pauli" (`PauliString`), "kind" (str), "label" (str or None).
+    fn annotations(&self, py: Python<'_>) -> PyResult<Py<pyo3::types::PyList>> {
+        let list = pyo3::types::PyList::empty(py);
+
+        for ann in self.inner.annotations() {
+            let dict = pyo3::types::PyDict::new(py);
+            let ps = crate::pauli_bindings::PauliString {
+                inner: ann.pauli.clone(),
+            };
+            dict.set_item("pauli", ps.into_pyobject(py)?)?;
+            let kind_str = match &ann.kind {
+                pecos_quantum::AnnotationKind::Detector { .. } => "detector",
+                pecos_quantum::AnnotationKind::Observable { .. } => "observable",
+                pecos_quantum::AnnotationKind::TrackedPauli => "tracked_pauli",
+            };
+            dict.set_item("kind", kind_str)?;
+            dict.set_item("label", &ann.label)?;
+            list.append(dict)?;
+        }
+
+        Ok(list.unbind())
+    }
+
+    // ==================== Metadata ====================
+
     /// Add metadata to the last added gate.
     ///
     /// Args:
@@ -1495,6 +1736,28 @@ pyo3::create_exception!(
     pyo3::exceptions::PyValueError
 );
 
+fn tick_gate_error_to_pyerr(err: TickGateError, tick_idx: Option<usize>) -> PyErr {
+    match err {
+        TickGateError::QubitConflict(mut err) => {
+            if let Some(tick_idx) = tick_idx {
+                err.tick_idx = Some(tick_idx);
+            }
+            PyErr::new::<QubitConflictError, _>(err.to_string())
+        }
+        TickGateError::InvalidGate {
+            message,
+            tick_idx: err_tick_idx,
+        } => {
+            let tick_idx = tick_idx.or(err_tick_idx);
+            let msg = match tick_idx {
+                Some(tick_idx) => format!("Invalid gate in tick {tick_idx}: {message}"),
+                None => format!("Invalid gate: {message}"),
+            };
+            PyErr::new::<pyo3::exceptions::PyValueError, _>(msg)
+        }
+    }
+}
+
 /// Convert HUGR bytes to a `DagCircuit`.
 ///
 /// This function takes serialized HUGR data (JSON or binary envelope format)
@@ -1800,20 +2063,30 @@ pub struct PyTick {
 
 #[pymethods]
 impl PyTick {
-    /// Get the number of gates in this tick.
+    /// Get the number of stored gate batches in this tick.
     fn __len__(&self) -> usize {
         self.inner.len()
     }
 
+    /// Get the number of individual gate applications in this tick.
+    fn gate_count(&self) -> usize {
+        self.inner.gate_count()
+    }
+
+    /// Get the number of compatible gate batches in this tick.
+    fn gate_batch_count(&self) -> usize {
+        self.inner.gate_batch_count()
+    }
+
     /// Check if the tick is empty.
     fn is_empty(&self) -> bool {
         self.inner.is_empty()
     }
 
-    /// Get the gates in this tick as a list.
-    fn gates(&self) -> Vec<PyGate> {
+    /// Get the stored gate batches in this tick as a list.
+    fn gate_batches(&self) -> Vec<PyGate> {
         self.inner
-            .gates()
+            .gate_batches()
             .iter()
             .map(|g: &Gate| PyGate { inner: g.clone() })
             .collect()
@@ -1903,8 +2176,10 @@ impl PyTick {
     /// Add a gate to this tick.
     ///
     /// Returns the index of the added gate within this tick.
-    fn add_gate(&mut self, gate: &PyGate) -> usize {
-        self.inner.add_gate(gate.inner.clone())
+    fn add_gate(&mut self, gate: &PyGate) -> PyResult<usize> {
+        self.inner
+            .try_add_gate(gate.inner.clone())
+            .map_err(|e| tick_gate_error_to_pyerr(e, None))
     }
 
     /// Try to add a gate to this tick, returning an error if any qubit is already in use.
@@ -1916,7 +2191,7 @@ impl PyTick {
     fn try_add_gate(&mut self, gate: &PyGate) -> PyResult<usize> {
         self.inner
             .try_add_gate(gate.inner.clone())
-            .map_err(|e| PyErr::new::<pyo3::exceptions::PyValueError, _>(e.to_string()))
+            .map_err(|e| tick_gate_error_to_pyerr(e, None))
     }
 
     /// Remove all gates that use any of the specified qubits.
@@ -1947,7 +2222,8 @@ impl PyTick {
 /// Use `tick()` to create a new tick and get a handle for adding gates.
 #[pyclass(name = "TickCircuit", module = "pecos_rslib.quantum")]
 pub struct PyTickCircuit {
-    inner: TickCircuit,
+    /// The underlying Rust TickCircuit.
+    pub inner: TickCircuit,
 }
 
 #[pymethods]
@@ -1970,6 +2246,16 @@ impl PyTickCircuit {
         self.inner.gate_count()
     }
 
+    /// Get the total number of compatible gate batches across all ticks.
+    fn gate_batch_count(&self) -> usize {
+        self.inner.gate_batch_count()
+    }
+
+    /// Get the total number of measurement results produced so far.
+    fn num_measurements(&self) -> usize {
+        self.inner.num_measurements()
+    }
+
     /// Get the next tick index that will be allocated.
     fn next_tick_index(&self) -> usize {
         self.inner.next_tick_index()
@@ -2015,6 +2301,41 @@ impl PyTickCircuit {
             .map(|attr| attribute_to_py(py, attr))
     }
 
+    /// Add detector metadata using measurement-record offsets.
+    ///
+    /// This is the typed equivalent of appending to the circuit-level
+    /// ``"detectors"`` JSON metadata list. Use ``detector(...)`` when you
+    /// already have explicit measurement handles from this TickCircuit.
+    #[pyo3(signature = (records, coords=None, label=None, detector_id=None))]
+    fn add_detector(
+        &mut self,
+        records: Vec<i64>,
+        coords: Option<Vec<f64>>,
+        label: Option<String>,
+        detector_id: Option<usize>,
+    ) -> PyResult<usize> {
+        self.inner
+            .add_detector_metadata(&records, coords.as_deref(), label.as_deref(), detector_id)
+            .map_err(pyo3::exceptions::PyValueError::new_err)
+    }
+
+    /// Add observable metadata using measurement-record offsets.
+    ///
+    /// Standard observables live in the ``L<n>`` decoder ID space. A label of
+    /// ``"L3"`` therefore selects observable id 3 unless ``observable_id`` is
+    /// provided, in which case the two must agree.
+    #[pyo3(signature = (records, observable_id=None, label=None))]
+    fn add_observable(
+        &mut self,
+        records: Vec<i64>,
+        observable_id: Option<usize>,
+        label: Option<String>,
+    ) -> PyResult<usize> {
+        self.inner
+            .add_observable_metadata(&records, observable_id, label.as_deref())
+            .map_err(pyo3::exceptions::PyValueError::new_err)
+    }
+
     // --- Circuit manipulation ---
 
     /// Clear the circuit and start fresh.
@@ -2123,18 +2444,18 @@ impl PyTickCircuit {
         Ok(dict.into())
     }
 
-    /// Get all gates in the circuit as a list.
+    /// Get all stored gate batches in the circuit as a list.
     ///
     /// Returns:
     ///     A list of (`tick_index`, gate) tuples.
-    fn gates(&self) -> Vec<(usize, PyGate)> {
+    fn gate_batches(&self) -> Vec<(usize, PyGate)> {
         self.inner
-            .iter_gates_with_tick()
+            .iter_gate_batches_with_tick()
             .map(|(tick_idx, gate)| {
                 (
                     tick_idx,
                     PyGate {
-                        inner: gate.clone(),
+                        inner: gate.as_gate().clone(),
                     },
                 )
             })
@@ -2274,6 +2595,160 @@ impl PyTickCircuit {
         }
     }
 
+    /// Lower Clifford-angle rotations to named Clifford gates.
+    ///
+    /// Replaces parameterized rotations at Clifford angles with their named
+    /// equivalents: RZ(pi/2) -> SZ, RZ(pi) -> Z, RX(pi/2) -> SX, etc.
+    ///
+    /// Use this on circuits from QIS trace (Guppy/Selene) that use
+    /// parameterized gates even for Clifford operations. Without this,
+    /// stabilizer simulators may reject the circuit.
+    ///
+    /// Modifies the circuit in place.
+    fn lower_clifford_rotations(&mut self) {
+        use pecos_quantum::pass::{CircuitPass, SimplifyRotations};
+        SimplifyRotations.apply_tick(&mut self.inner);
+    }
+
+    /// Assign MeasId to measurement gates that don't have them.
+    ///
+    /// Use on circuits from external sources (QIS trace, Stim import)
+    /// that don't assign MeasId during construction.
+    fn assign_missing_meas_ids(&mut self) {
+        use pecos_quantum::pass::{AssignMissingMeasIds, CircuitPass};
+        AssignMissingMeasIds.apply_tick(&mut self.inner);
+    }
+
+    /// Insert Idle gates after each two-qubit gate on both of its qubits.
+    ///
+    /// Models idle noise during two-qubit gate execution. The noise model
+    /// applies RZ(p_idle * duration) when it encounters an Idle gate.
+    ///
+    /// Args:
+    ///     duration: Idle time in abstract time units (default: 1.0).
+    #[pyo3(signature = (duration=1.0))]
+    fn insert_idle_after_two_qubit_gates(&mut self, duration: f64) {
+        self.inner.insert_idle_after_two_qubit_gates(duration);
+    }
+
+    /// Insert identity gates for qubits not operated on during each tick.
+    ///
+    /// For each tick, qubits not involved in any gate get an identity (I)
+    /// gate that receives `p1` noise. This matches Stim's convention of
+    /// `DEPOLARIZE1` on idle qubits between ticks.
+    fn fill_idle_gates(&mut self) {
+        self.inner.fill_idle_gates();
+    }
+
+    /// Return a new circuit with explicit Pauli channel operations inserted.
+    ///
+    /// This compiles gate-triggered quantum noise into inline channel gates.
+    /// Measurement readout noise is intentionally not represented here because
+    /// it is classical outcome noise, not a quantum channel after measurement.
+    #[pyo3(signature = (p1=0.0, p2=0.0, p_meas=0.0, p_prep=0.0))]
+    fn with_noise(&self, p1: f64, p2: f64, p_meas: f64, p_prep: f64) -> PyResult<Self> {
+        validate_probability("p1", p1)?;
+        validate_probability("p2", p2)?;
+        validate_probability("p_meas", p_meas)?;
+        validate_probability("p_prep", p_prep)?;
+
+        if p_meas > 0.0 {
+            return Err(pyo3::exceptions::PyValueError::new_err(
+                "TickCircuit.with_noise inserts quantum channel operations and cannot represent classical measurement readout noise; use sim_neo(...).noise(...) for p_meas",
+            ));
+        }
+
+        if p2 > 0.0 {
+            for (tick_idx, gate) in self.inner.iter_gate_batches_with_tick() {
+                if receives_two_qubit_noise(gate.gate_type) && !gate.qubits.len().is_multiple_of(2)
+                {
+                    return Err(pyo3::exceptions::PyValueError::new_err(format!(
+                        "{:?} at tick {tick_idx} has {} qubits; expected pairs",
+                        gate.gate_type,
+                        gate.qubits.len()
+                    )));
+                }
+            }
+        }
+
+        let noisy = self
+            .inner
+            .try_with_noise(&|gate: &Gate| -> Vec<ChannelExpr> {
+                let mut channels = Vec::new();
+                match gate.gate_type {
+                    GateType::PZ | GateType::QAlloc if p_prep > 0.0 => {
+                        channels.extend(
+                            gate.qubits
+                                .iter()
+                                .map(|q| pecos_core::channel::BitFlip(p_prep, q.index())),
+                        );
+                    }
+                    GateType::I
+                    | GateType::X
+                    | GateType::Y
+                    | GateType::Z
+                    | GateType::H
+                    | GateType::F
+                    | GateType::Fdg
+                    | GateType::SX
+                    | GateType::SXdg
+                    | GateType::SY
+                    | GateType::SYdg
+                    | GateType::SZ
+                    | GateType::SZdg
+                    | GateType::T
+                    | GateType::Tdg
+                    | GateType::RX
+                    | GateType::RY
+                    | GateType::RZ
+                    | GateType::U
+                    | GateType::R1XY
+                    | GateType::Idle
+                        if p1 > 0.0 =>
+                    {
+                        channels.extend(
+                            gate.qubits
+                                .iter()
+                                .map(|q| pecos_core::channel::Depolarizing(p1, q.index())),
+                        );
+                    }
+                    GateType::CX
+                    | GateType::CY
+                    | GateType::CZ
+                    | GateType::SZZ
+                    | GateType::SZZdg
+                    | GateType::SXX
+                    | GateType::SXXdg
+                    | GateType::SYY
+                    | GateType::SYYdg
+                    | GateType::SWAP
+                    | GateType::CRZ
+                    | GateType::RXX
+                    | GateType::RYY
+                    | GateType::RZZ
+                        if p2 > 0.0 =>
+                    {
+                        channels.extend(gate.qubits.chunks_exact(2).map(|pair| {
+                            pecos_core::channel::Depolarizing2(p2, pair[0].index(), pair[1].index())
+                        }));
+                    }
+                    _ => {}
+                }
+                channels
+            })
+            .map_err(pyo3::exceptions::PyValueError::new_err)?;
+        Ok(Self { inner: noisy })
+    }
+
+    /// Compact ticks by merging gates into earlier ticks when possible.
+    ///
+    /// ASAP scheduling: gates that don't share qubits are merged into the
+    /// same tick. Useful after replaying a serialized trace where each
+    /// gate got its own tick.
+    fn compact_ticks(&mut self) {
+        self.inner.compact_ticks();
+    }
+
     // --- Gate signature validation ---
 
     /// Import gate signatures for validation.
@@ -2281,7 +2756,7 @@ impl PyTickCircuit {
     /// Args:
     ///     sigs: A dictionary mapping gate names to (`quantum_arity`, `angle_arity`) tuples.
     fn import_gate_signatures(&mut self, sigs: &Bound<'_, PyDict>) -> PyResult<()> {
-        let mut sig_map = HashMap::new();
+        let mut sig_map = std::collections::BTreeMap::new();
         for (key, value) in sigs.iter() {
             let name: String = key.extract()?;
             let (quantum_arity, angle_arity): (usize, usize) = value.extract()?;
@@ -2314,7 +2789,8 @@ impl PyTickCircuit {
     /// Extracts signatures from all registered gates and imports them
     /// for validation when adding custom gates.
     fn import_registry(&mut self, registry: &PyGateRegistry) {
-        let sigs = registry.inner.signatures();
+        let sigs: std::collections::BTreeMap<_, _> =
+            registry.inner.signatures().into_iter().collect();
         self.inner.import_signatures(&sigs);
     }
 
@@ -2325,6 +2801,97 @@ impl PyTickCircuit {
             self.inner.gate_count()
         )
     }
+
+    // ==================== Annotations ====================
+
+    /// Annotate a detector: measurements whose XOR should be deterministic.
+    #[pyo3(signature = (measurements, label=None))]
+    fn detector(
+        &mut self,
+        measurements: &Bound<'_, pyo3::types::PyList>,
+        label: Option<String>,
+    ) -> PyResult<usize> {
+        let refs = extract_tick_meas_refs(measurements)?;
+        let idx = if let Some(l) = label {
+            self.inner.detector_labeled(&l, &refs)
+        } else {
+            self.inner.detector(&refs)
+        };
+        Ok(idx)
+    }
+
+    /// Annotate a logical observable.
+    #[pyo3(signature = (measurements, label=None))]
+    fn observable(
+        &mut self,
+        measurements: &Bound<'_, pyo3::types::PyList>,
+        label: Option<String>,
+    ) -> PyResult<usize> {
+        let refs = extract_tick_meas_refs(measurements)?;
+        let idx = if let Some(l) = label {
+            self.inner.observable_labeled(&l, &refs)
+        } else {
+            self.inner.observable(&refs)
+        };
+        Ok(idx)
+    }
+
+    /// Place a tracked-Pauli annotation.
+    #[pyo3(signature = (pauli, label=None))]
+    fn tracked_pauli(
+        &mut self,
+        pauli: &crate::pauli_bindings::PauliString,
+        label: Option<String>,
+    ) -> usize {
+        if let Some(l) = label {
+            self.inner.tracked_pauli_labeled(&l, pauli.inner.clone())
+        } else {
+            self.inner.tracked_pauli(pauli.inner.clone())
+        }
+    }
+
+    /// Get all annotations.
+    fn annotations(&self, py: Python<'_>) -> PyResult<Py<pyo3::types::PyList>> {
+        let list = pyo3::types::PyList::empty(py);
+        for ann in self.inner.annotations() {
+            let dict = pyo3::types::PyDict::new(py);
+            let ps = crate::pauli_bindings::PauliString {
+                inner: ann.pauli.clone(),
+            };
+            dict.set_item("pauli", ps.into_pyobject(py)?)?;
+            let kind_str = match &ann.kind {
+                pecos_quantum::AnnotationKind::Detector { .. } => "detector",
+                pecos_quantum::AnnotationKind::Observable { .. } => "observable",
+                pecos_quantum::AnnotationKind::TrackedPauli => "tracked_pauli",
+            };
+            dict.set_item("kind", kind_str)?;
+            dict.set_item("label", &ann.label)?;
+            list.append(dict)?;
+        }
+        Ok(list.unbind())
+    }
+}
+
+/// Extract `TickMeasRef` from Python list of `(tick, gate_idx, qubit)` tuples.
+fn extract_tick_meas_refs(
+    list: &Bound<'_, pyo3::types::PyList>,
+) -> PyResult<Vec<pecos_quantum::TickMeasRef>> {
+    list.iter()
+        .map(|item| {
+            let (tick, gate_idx, qubit): (usize, usize, usize) = item.extract().map_err(|_| {
+                pyo3::exceptions::PyTypeError::new_err(
+                    "measurements must be (tick, gate_idx, qubit) tuples from mz()",
+                )
+            })?;
+            Ok(pecos_quantum::TickMeasRef {
+                tick,
+                gate_idx,
+                qubit: pecos_core::QubitId::from(qubit),
+                record_idx: 0, // Populated by TickCircuit; placeholder for external construction
+                meas_id: pecos_core::MeasId(0), // Placeholder
+            })
+        })
+        .collect()
 }
 
 /// Handle to a specific tick for adding gates.
@@ -2361,17 +2928,7 @@ impl PyTickHandle {
                     self.last_gate_idx = Some(idx);
                     Ok(())
                 }
-                Err(err) => {
-                    let msg = format!(
-                        "Qubit(s) {:?} already in use in tick {}",
-                        err.conflicting_qubits
-                            .iter()
-                            .map(std::string::ToString::to_string)
-                            .collect::<Vec<_>>(),
-                        self.tick_idx
-                    );
-                    Err(PyErr::new::<QubitConflictError, _>(msg))
-                }
+                Err(err) => Err(tick_gate_error_to_pyerr(err, Some(self.tick_idx))),
             }
         } else {
             Ok(())
@@ -2386,17 +2943,7 @@ impl PyTickHandle {
                     self.last_gate_idx = Some(idx);
                     Ok(idx)
                 }
-                Err(err) => {
-                    let msg = format!(
-                        "Qubit(s) {:?} already in use in tick {}",
-                        err.conflicting_qubits
-                            .iter()
-                            .map(std::string::ToString::to_string)
-                            .collect::<Vec<_>>(),
-                        self.tick_idx
-                    );
-                    Err(PyErr::new::<QubitConflictError, _>(msg))
-                }
+                Err(err) => Err(tick_gate_error_to_pyerr(err, Some(self.tick_idx))),
             }
         } else {
             Ok(0)
@@ -2927,17 +3474,7 @@ impl PyTickHandle {
                                 );
                                 last_idx = Some(idx);
                             }
-                            Err(err) => {
-                                let msg = format!(
-                                    "Qubit(s) {:?} already in use in tick {}",
-                                    err.conflicting_qubits
-                                        .iter()
-                                        .map(std::string::ToString::to_string)
-                                        .collect::<Vec<_>>(),
-                                    tick_idx
-                                );
-                                return Err(PyErr::new::<QubitConflictError, _>(msg));
-                            }
+                            Err(err) => return Err(tick_gate_error_to_pyerr(err, Some(tick_idx))),
                         }
                     }
                     drop(circuit);
@@ -2956,17 +3493,7 @@ impl PyTickHandle {
                             slf.borrow_mut(py).last_gate_idx = Some(idx);
                             Ok(slf)
                         }
-                        Err(err) => {
-                            let msg = format!(
-                                "Qubit(s) {:?} already in use in tick {}",
-                                err.conflicting_qubits
-                                    .iter()
-                                    .map(std::string::ToString::to_string)
-                                    .collect::<Vec<_>>(),
-                                tick_idx
-                            );
-                            Err(PyErr::new::<QubitConflictError, _>(msg))
-                        }
+                        Err(err) => Err(tick_gate_error_to_pyerr(err, Some(tick_idx))),
                     }
                 }
             }
@@ -3043,17 +3570,7 @@ impl PyTickHandle {
                     slf.borrow_mut(py).last_gate_idx = Some(idx);
                     Ok(slf)
                 }
-                Err(err) => {
-                    let msg = format!(
-                        "Qubit(s) {:?} already in use in tick {}",
-                        err.conflicting_qubits
-                            .iter()
-                            .map(std::string::ToString::to_string)
-                            .collect::<Vec<_>>(),
-                        tick_idx
-                    );
-                    Err(PyErr::new::<QubitConflictError, _>(msg))
-                }
+                Err(err) => Err(tick_gate_error_to_pyerr(err, Some(tick_idx))),
             }
         } else {
             drop(circuit);
@@ -3083,35 +3600,91 @@ impl PyTickHandle {
 
     /// Measure qubits in the Z basis.
     ///
-    /// Returns a `TickMeasureHandle` that allows attaching metadata via `.meta()`.
-    /// This breaks the chain - only `.meta()` can be called on the result.
-    fn mz(slf: Py<Self>, py: Python<'_>, qubits: Vec<usize>) -> PyResult<PyTickMeasureHandle> {
-        let (circuit, tick_idx, gate_idx) = {
-            let mut handle = slf.borrow_mut(py);
-            let gate_idx = handle.add_gate_get_idx(py, Gate::mz(&qubits))?;
-            (handle.circuit.clone_ref(py), handle.tick_idx, gate_idx)
-        };
-        Ok(PyTickMeasureHandle {
-            circuit,
-            tick_idx,
-            gate_idx,
-        })
+    /// Returns a list of `(tick, gate_idx, qubit)` measurement refs
+    /// for use in `detector()` and `observable()` annotations.
+    fn mz(
+        slf: Py<Self>,
+        py: Python<'_>,
+        qubits: Vec<usize>,
+    ) -> PyResult<Vec<(usize, usize, usize)>> {
+        let mut handle = slf.borrow_mut(py);
+        let mut gate = Gate::mz(&qubits);
+        // Assign MeasId values (SSA identity for each measurement)
+        {
+            let mut circuit = handle.circuit.borrow_mut(py);
+            let base = circuit.inner.num_measurements();
+            for (i, _) in qubits.iter().enumerate() {
+                gate.meas_ids.push(pecos_core::MeasId(base + i));
+            }
+            // Increment the measurement counter
+            circuit.inner.advance_meas_counter(qubits.len());
+        }
+        let gate_idx = handle.add_gate_get_idx(py, gate)?;
+        let tick_idx = handle.tick_idx;
+        Ok(qubits.iter().map(|&q| (tick_idx, gate_idx, q)).collect())
+    }
+
+    /// Measure qubits with explicit MeasIds.
+    ///
+    /// Like ``mz()`` but assigns the given MeasIds instead of auto-assigning.
+    /// Used when MeasIds flow from an external source (e.g., Guppy result() IDs).
+    ///
+    /// The ``meas_ids`` list must have the same length as ``qubits``.
+    fn mz_with_ids(
+        slf: Py<Self>,
+        py: Python<'_>,
+        qubits: Vec<usize>,
+        meas_ids: Vec<usize>,
+    ) -> PyResult<Vec<(usize, usize, usize)>> {
+        if meas_ids.len() != qubits.len() {
+            return Err(pyo3::exceptions::PyValueError::new_err(format!(
+                "meas_ids length {} != qubits length {}",
+                meas_ids.len(),
+                qubits.len()
+            )));
+        }
+        let mut handle = slf.borrow_mut(py);
+        let mut gate = Gate::mz(&qubits);
+        for &mid in &meas_ids {
+            gate.meas_ids.push(pecos_core::MeasId(mid));
+        }
+        {
+            let mut circuit = handle.circuit.borrow_mut(py);
+            // Advance counter to at least past the highest ID we're assigning
+            let max_id = meas_ids.iter().copied().max().unwrap_or(0);
+            let current = circuit.inner.num_measurements();
+            if max_id >= current {
+                circuit.inner.advance_meas_counter(max_id + 1 - current);
+            }
+        }
+        let gate_idx = handle.add_gate_get_idx(py, gate)?;
+        let tick_idx = handle.tick_idx;
+        Ok(qubits.iter().map(|&q| (tick_idx, gate_idx, q)).collect())
     }
 
     /// Measure and free qubits (destructive measurement).
     ///
-    /// Returns a `TickMeasureHandle` that allows attaching metadata via `.meta()`.
-    fn mz_free(slf: Py<Self>, py: Python<'_>, qubits: Vec<usize>) -> PyResult<PyTickMeasureHandle> {
-        let (circuit, tick_idx, gate_idx) = {
-            let mut handle = slf.borrow_mut(py);
-            let gate_idx = handle.add_gate_get_idx(py, Gate::mz_free(&qubits))?;
-            (handle.circuit.clone_ref(py), handle.tick_idx, gate_idx)
-        };
-        Ok(PyTickMeasureHandle {
-            circuit,
-            tick_idx,
-            gate_idx,
-        })
+    /// Measure and free qubits (destructive measurement).
+    ///
+    /// Returns measurement refs for annotations.
+    fn mz_free(
+        slf: Py<Self>,
+        py: Python<'_>,
+        qubits: Vec<usize>,
+    ) -> PyResult<Vec<(usize, usize, usize)>> {
+        let mut handle = slf.borrow_mut(py);
+        let mut gate = Gate::mz_free(&qubits);
+        {
+            let mut circuit = handle.circuit.borrow_mut(py);
+            let base = circuit.inner.num_measurements();
+            for (i, _) in qubits.iter().enumerate() {
+                gate.meas_ids.push(pecos_core::MeasId(base + i));
+            }
+            circuit.inner.advance_meas_counter(qubits.len());
+        }
+        let gate_idx = handle.add_gate_get_idx(py, gate)?;
+        let tick_idx = handle.tick_idx;
+        Ok(qubits.iter().map(|&q| (tick_idx, gate_idx, q)).collect())
     }
 
     // --- Resource management ---
diff --git a/python/pecos-rslib/src/decoder_bindings.rs b/python/pecos-rslib/src/decoder_bindings.rs
index 8bee00356..bf9d27879 100644
--- a/python/pecos-rslib/src/decoder_bindings.rs
+++ b/python/pecos-rslib/src/decoder_bindings.rs
@@ -519,6 +519,50 @@ impl PyPyMatchingDecoder {
             .map_err(|e| PyErr::new::<pyo3::exceptions::PyRuntimeError, _>(e.to_string()))
     }
 
+    /// Decode a batch of syndromes at once.
+    ///
+    /// Much faster than calling `decode()` in a Python loop -- the entire batch
+    /// is processed in Rust with no per-shot Python overhead.
+    ///
+    /// # Arguments
+    ///
+    /// * `detection_events` - Flattened detection events array (`num_shots` * `num_detectors` bytes)
+    /// * `num_shots` - Number of shots in the batch
+    ///
+    /// # Returns
+    ///
+    /// List of observable predictions (one per shot), where each prediction
+    /// is a list of 0/1 values (one per observable). Use `observables_mask`
+    /// property on each element or just check index 0 for single-observable codes.
+    ///
+    /// # Example
+    ///
+    /// ```python
+    /// # detection_events is shape (num_shots, num_detectors), flattened
+    /// flat = detection_events.flatten().tolist()
+    /// predictions = decoder.decode_batch(flat, num_shots=len(detection_events))
+    /// num_errors = sum(p[0] != t for p, t in zip(predictions, true_flips))
+    /// ```
+    fn decode_batch(
+        &mut self,
+        detection_events: Vec<u8>,
+        num_shots: usize,
+    ) -> PyResult<Vec<Vec<u8>>> {
+        use pecos_decoders::BatchConfig as RustBatchConfig;
+
+        let num_detectors = self.inner.num_detectors();
+        let config = RustBatchConfig {
+            bit_packed_input: false,
+            bit_packed_output: false,
+            return_weights: false,
+        };
+
+        self.inner
+            .decode_batch_with_config(&detection_events, num_shots, num_detectors, config)
+            .map(|result| result.predictions)
+            .map_err(|e| PyErr::new::<pyo3::exceptions::PyRuntimeError, _>(e.to_string()))
+    }
+
     /// Number of detector nodes in the matching graph.
     #[getter]
     fn num_detectors(&self) -> usize {
@@ -1452,6 +1496,8 @@ impl PyTesseractResult {
 #[pyclass(name = "TesseractDecoder", module = "pecos_rslib.decoders", unsendable)]
 pub struct PyTesseractDecoder {
     inner: RustTesseractDecoder,
+    dem_string: String,
+    config: RustTesseractConfig,
 }
 
 #[pymethods]
@@ -1498,8 +1544,13 @@ impl PyTesseractDecoder {
         }
         config.verbose = verbose;
 
-        RustTesseractDecoder::new(dem, config)
-            .map(|inner| Self { inner })
+        let dem_string = dem.to_string();
+        RustTesseractDecoder::new(dem, config.clone())
+            .map(|inner| Self {
+                inner,
+                dem_string,
+                config,
+            })
             .map_err(|e| PyErr::new::<pyo3::exceptions::PyRuntimeError, _>(e.to_string()))
     }
 
@@ -1553,6 +1604,82 @@ impl PyTesseractDecoder {
         self.decode(detections)
     }
 
+    /// Decode a batch of syndromes in parallel using multiple decoder instances.
+    ///
+    /// Creates worker decoders on background threads and distributes shots
+    /// across them. Much faster than sequential decoding for large batches.
+    ///
+    /// # Arguments
+    ///
+    /// * `syndromes` - List of dense syndrome vectors
+    /// * `num_workers` - Number of parallel workers (default: number of CPUs)
+    ///
+    /// # Returns
+    ///
+    /// List of `TesseractResult` in the same order as inputs.
+    #[pyo3(signature = (syndromes, num_workers=None))]
+    fn decode_batch(
+        &self,
+        syndromes: Vec<Vec<u8>>,
+        num_workers: Option<usize>,
+    ) -> PyResult<Vec<PyTesseractResult>> {
+        use rayon::prelude::*;
+
+        let n_workers = num_workers.unwrap_or_else(rayon::current_num_threads);
+
+        // Build a thread pool with the requested size
+        let pool = rayon::ThreadPoolBuilder::new()
+            .num_threads(n_workers)
+            .build()
+            .map_err(|e| PyErr::new::<pyo3::exceptions::PyRuntimeError, _>(e.to_string()))?;
+
+        let dem_str = &self.dem_string;
+        let config = &self.config;
+
+        let results: Result<Vec<_>, _> = pool.install(|| {
+            syndromes
+                .par_iter()
+                .map(|syndrome| {
+                    // Each rayon task gets its own thread-local decoder
+                    thread_local! {
+                        static DECODER: std::cell::RefCell<Option<RustTesseractDecoder>> =
+                            const { std::cell::RefCell::new(None) };
+                    }
+
+                    DECODER.with(|cell| {
+                        let mut decoder_ref = cell.borrow_mut();
+                        if decoder_ref.is_none() {
+                            *decoder_ref = Some(
+                                RustTesseractDecoder::new(dem_str, config.clone())
+                                    .map_err(|e| e.to_string())?,
+                            );
+                        }
+                        let decoder = decoder_ref.as_mut().unwrap();
+
+                        // Convert dense to sparse
+                        let detections: Vec<u64> = syndrome
+                            .iter()
+                            .enumerate()
+                            .filter_map(|(i, &val)| if val != 0 { Some(i as u64) } else { None })
+                            .collect();
+
+                        let detections_arr = ndarray::Array1::from_vec(detections);
+                        decoder
+                            .decode_detections(&detections_arr.view())
+                            .map(|r| PyTesseractResult {
+                                observables_mask: r.observables_mask,
+                                cost: r.cost,
+                                low_confidence: r.low_confidence,
+                            })
+                            .map_err(|e| e.to_string())
+                    })
+                })
+                .collect()
+        });
+
+        results.map_err(PyErr::new::<pyo3::exceptions::PyRuntimeError, _>)
+    }
+
     /// Number of detectors in the error model.
     #[getter]
     fn num_detectors(&self) -> usize {
@@ -2036,6 +2163,292 @@ impl PyMinSumBpDecoder {
     }
 }
 
+// =============================================================================
+// DEM-Aware Decoder (wraps check-matrix decoders for DEM-level decoding)
+// =============================================================================
+
+use pecos_decoder_core::DemCheckMatrix;
+
+/// Decoder type for the DEM-aware wrapper.
+enum InnerDecoder {
+    BpOsd(RustBpOsdDecoder),
+    BpLsd(RustBpLsdDecoder),
+    UnionFind(RustUnionFindDecoder),
+    RelayBp(Box<RustRelayBpDecoder>),
+    MinSumBp(Box<RustMinSumBpDecoder>),
+}
+
+/// DEM-aware decoder that wraps a check-matrix decoder.
+///
+/// Parses a DEM string, extracts the check matrix and observable matrix,
+/// creates the inner decoder, and provides `decode_syndrome()` that returns
+/// an `observables_mask` -- the same interface as `PyMatching` and Tesseract.
+///
+/// # Example
+///
+/// ```python
+/// from pecos_rslib.decoders import DemAwareDecoder
+///
+/// decoder = DemAwareDecoder.from_dem(dem_string, decoder_type="bp_osd")
+/// result = decoder.decode_syndrome([0, 1, 1, 0])
+/// print(f"Observable prediction: {result.observables_mask}")
+/// ```
+#[pyclass(name = "DemAwareDecoder", module = "pecos_rslib.decoders", unsendable)]
+pub struct PyDemAwareDecoder {
+    inner: InnerDecoder,
+    dem_check_matrix: DemCheckMatrix,
+}
+
+/// Result from a DEM-aware decoder.
+#[pyclass(
+    name = "DemAwareResult",
+    module = "pecos_rslib.decoders",
+    skip_from_py_object
+)]
+#[derive(Clone)]
+pub struct PyDemAwareResult {
+    /// Bitmask of predicted observable flips.
+    #[pyo3(get)]
+    pub observables_mask: u64,
+    /// Whether the BP decoder converged.
+    #[pyo3(get)]
+    pub converged: bool,
+    /// Number of BP iterations used.
+    #[pyo3(get)]
+    pub iterations: usize,
+}
+
+#[pymethods]
+impl PyDemAwareResult {
+    fn __repr__(&self) -> String {
+        format!(
+            "DemAwareResult(observables_mask={}, converged={}, iterations={})",
+            self.observables_mask, self.converged, self.iterations
+        )
+    }
+}
+
+#[pymethods]
+impl PyDemAwareDecoder {
+    /// Create a DEM-aware decoder from a DEM string.
+    ///
+    /// # Arguments
+    ///
+    /// * `dem` - DEM string in Stim format
+    /// * `decoder_type` - One of "`bp_osd`", "`bp_lsd`", "`union_find`", "`relay_bp`", "`min_sum_bp`"
+    /// * `error_rate` - Override error rate for BP priors (default: use DEM probabilities)
+    /// * `max_iter` - Maximum BP iterations (default: 100)
+    ///
+    /// # Example
+    ///
+    /// ```python
+    /// decoder = DemAwareDecoder.from_dem(dem, decoder_type="bp_osd")
+    /// ```
+    #[staticmethod]
+    #[pyo3(signature = (dem, decoder_type="bp_osd", error_rate=None, max_iter=100))]
+    fn from_dem(
+        dem: &str,
+        decoder_type: &str,
+        error_rate: Option<f64>,
+        max_iter: usize,
+    ) -> PyResult<Self> {
+        let dcm = DemCheckMatrix::from_dem_str(dem)
+            .map_err(|e| PyErr::new::<pyo3::exceptions::PyValueError, _>(e.to_string()))?;
+
+        if dcm.num_mechanisms == 0 {
+            return Err(PyErr::new::<pyo3::exceptions::PyValueError, _>(
+                "DEM contains no error mechanisms",
+            ));
+        }
+
+        // Error priors: use per-mechanism probabilities from DEM, or uniform override
+        let priors: Vec<f64> = if let Some(p) = error_rate {
+            vec![p; dcm.num_mechanisms]
+        } else {
+            dcm.error_priors.clone()
+        };
+
+        // Build the check matrix in the two formats decoders need:
+        // SparseMatrix for LDPC decoders, Array2 view for Relay/MinSum.
+        let sparse_h = RustSparseMatrix::from_dense(&dcm.check_matrix.view());
+
+        let inner = match decoder_type {
+            "bp_osd" => {
+                let decoder = RustBpOsdDecoder::new(
+                    &sparse_h,
+                    None,          // error_rate
+                    Some(&priors), // error_channel
+                    max_iter,
+                    RustBpMethod::ProductSum,
+                    RustBpSchedule::Parallel,
+                    1.0, // ms_scaling_factor
+                    RustOsdMethod::Osd0,
+                    0, // osd_order
+                    RustInputVectorType::Syndrome,
+                    None,
+                    None,
+                    None,
+                )
+                .map_err(|e| PyErr::new::<pyo3::exceptions::PyRuntimeError, _>(e.to_string()))?;
+                InnerDecoder::BpOsd(decoder)
+            }
+            "bp_lsd" => {
+                let decoder = RustBpLsdDecoder::new(
+                    &sparse_h,
+                    None,          // error_rate
+                    Some(&priors), // error_channel
+                    max_iter,
+                    RustBpMethod::ProductSum,
+                    RustBpSchedule::Parallel,
+                    1.0,                // ms_scaling_factor
+                    RustOsdMethod::Off, // lsd_method (LSD-0)
+                    0,                  // lsd_order
+                    0,                  // bits_per_step
+                    RustInputVectorType::Syndrome,
+                    None,
+                    None,
+                    None,
+                )
+                .map_err(|e| PyErr::new::<pyo3::exceptions::PyRuntimeError, _>(e.to_string()))?;
+                InnerDecoder::BpLsd(decoder)
+            }
+            "union_find" => {
+                let decoder = RustUnionFindDecoder::new(&sparse_h, RustUfMethod::Inversion)
+                    .map_err(|e| {
+                        PyErr::new::<pyo3::exceptions::PyRuntimeError, _>(e.to_string())
+                    })?;
+                InnerDecoder::UnionFind(decoder)
+            }
+            "relay_bp" => {
+                use pecos_decoders::RelayBpBuilder as RustRelayBpBuilderT;
+                let h_view = dcm.check_matrix.view();
+                let decoder = RustRelayBpBuilderT::new(&h_view)
+                    .error_priors(&priors)
+                    .max_iter(max_iter)
+                    .build()
+                    .map_err(|e| {
+                        PyErr::new::<pyo3::exceptions::PyRuntimeError, _>(e.to_string())
+                    })?;
+                InnerDecoder::RelayBp(Box::new(decoder))
+            }
+            "min_sum_bp" => {
+                use pecos_decoders::MinSumBpBuilder as RustMinSumBpBuilderT;
+                let h_view = dcm.check_matrix.view();
+                let decoder = RustMinSumBpBuilderT::new(&h_view)
+                    .error_priors(&priors)
+                    .max_iter(max_iter)
+                    .build()
+                    .map_err(|e| {
+                        PyErr::new::<pyo3::exceptions::PyRuntimeError, _>(e.to_string())
+                    })?;
+                InnerDecoder::MinSumBp(Box::new(decoder))
+            }
+            _ => {
+                return Err(PyErr::new::<pyo3::exceptions::PyValueError, _>(format!(
+                    "Unknown decoder type: {decoder_type}. \
+                     Supported: bp_osd, bp_lsd, union_find, relay_bp, min_sum_bp"
+                )));
+            }
+        };
+
+        Ok(Self {
+            inner,
+            dem_check_matrix: dcm,
+        })
+    }
+
+    /// Decode a dense syndrome vector.
+    ///
+    /// # Arguments
+    ///
+    /// * `syndrome` - Dense syndrome vector (0 or 1 for each detector)
+    ///
+    /// # Returns
+    ///
+    /// `DemAwareResult` with `observables_mask`, `converged`, and `iterations`.
+    fn decode_syndrome(&mut self, syndrome: Vec<u8>) -> PyResult<PyDemAwareResult> {
+        let arr = Array1::from_vec(syndrome);
+        let (decoding, converged, iterations) = match &mut self.inner {
+            InnerDecoder::BpOsd(d) => {
+                let r = d.decode(&arr.view()).map_err(|e| {
+                    PyErr::new::<pyo3::exceptions::PyRuntimeError, _>(e.to_string())
+                })?;
+                (r.decoding.to_vec(), r.converged, r.iterations)
+            }
+            InnerDecoder::BpLsd(d) => {
+                let r = d.decode(&arr.view()).map_err(|e| {
+                    PyErr::new::<pyo3::exceptions::PyRuntimeError, _>(e.to_string())
+                })?;
+                (r.decoding.to_vec(), r.converged, r.iterations)
+            }
+            InnerDecoder::UnionFind(d) => {
+                let r = d.decode(&arr.view(), &[], 0).map_err(|e| {
+                    PyErr::new::<pyo3::exceptions::PyRuntimeError, _>(e.to_string())
+                })?;
+                (r.decoding.to_vec(), r.converged, r.iterations)
+            }
+            InnerDecoder::RelayBp(d) => {
+                let r = d.decode(&arr.view()).map_err(|e| {
+                    PyErr::new::<pyo3::exceptions::PyRuntimeError, _>(e.to_string())
+                })?;
+                (r.decoding.to_vec(), r.converged, r.iterations)
+            }
+            InnerDecoder::MinSumBp(d) => {
+                let r = d.decode(&arr.view()).map_err(|e| {
+                    PyErr::new::<pyo3::exceptions::PyRuntimeError, _>(e.to_string())
+                })?;
+                (r.decoding.to_vec(), r.converged, r.iterations)
+            }
+        };
+
+        let correction: Vec<u8> = decoding.iter().map(|&v| v & 1).collect();
+        let observables_mask = self
+            .dem_check_matrix
+            .observables_mask_from_correction(&correction);
+
+        Ok(PyDemAwareResult {
+            observables_mask,
+            converged,
+            iterations,
+        })
+    }
+
+    /// Number of detectors in the model.
+    #[getter]
+    fn num_detectors(&self) -> usize {
+        self.dem_check_matrix.num_detectors
+    }
+
+    /// Number of observables in the model.
+    #[getter]
+    fn num_observables(&self) -> usize {
+        self.dem_check_matrix.num_observables
+    }
+
+    /// Number of error mechanisms in the model.
+    #[getter]
+    fn num_mechanisms(&self) -> usize {
+        self.dem_check_matrix.num_mechanisms
+    }
+
+    fn __repr__(&self) -> String {
+        let decoder_name = match &self.inner {
+            InnerDecoder::BpOsd(_) => "bp_osd",
+            InnerDecoder::BpLsd(_) => "bp_lsd",
+            InnerDecoder::UnionFind(_) => "union_find",
+            InnerDecoder::RelayBp(_) => "relay_bp",
+            InnerDecoder::MinSumBp(_) => "min_sum_bp",
+        };
+        format!(
+            "DemAwareDecoder(type={}, detectors={}, mechanisms={}, observables={})",
+            decoder_name,
+            self.dem_check_matrix.num_detectors,
+            self.dem_check_matrix.num_mechanisms,
+            self.dem_check_matrix.num_observables,
+        )
+    }
+}
+
 // =============================================================================
 // Module Registration
 // =============================================================================
@@ -2075,6 +2488,10 @@ pub fn register_decoders_module(parent_module: &Bound<'_, PyModule>) -> PyResult
     decoders_module.add_class::<PyMinSumBpBuilder>()?;
     decoders_module.add_class::<PyMinSumBpDecoder>()?;
 
+    // DEM-aware decoder wrapper
+    decoders_module.add_class::<PyDemAwareResult>()?;
+    decoders_module.add_class::<PyDemAwareDecoder>()?;
+
     // Add submodule to parent
     parent_module.add_submodule(&decoders_module)?;
 
diff --git a/python/pecos-rslib/src/fault_tolerance_bindings.rs b/python/pecos-rslib/src/fault_tolerance_bindings.rs
index ec593b879..4d2e459e6 100644
--- a/python/pecos-rslib/src/fault_tolerance_bindings.rs
+++ b/python/pecos-rslib/src/fault_tolerance_bindings.rs
@@ -48,13 +48,13 @@ use pecos_qec::fault_tolerance::dem_builder::{
     ContributionRenderRecord as RustContributionRenderRecord,
     ContributionRenderStrategy as RustContributionRenderStrategy,
     ContributionRenderSummary as RustContributionRenderSummary, DemBuilder as RustDemBuilder,
+    DemSampler as RustNewDemSampler, DemSamplerBuilder as RustNewDemSamplerBuilder,
     DetectorErrorModel as RustDetectorErrorModel, DirectSourceFamily as RustDirectSourceFamily,
     EquivalenceResult as RustEquivalenceResult, FaultContribution as RustFaultContribution,
-    FaultSourceType as RustFaultSourceType, MeasurementNoiseModel as RustMeasurementNoiseModel,
-    MemBuilder as RustMemBuilder, ParsedDem as RustParsedDem,
+    FaultSourceType as RustFaultSourceType, NoiseConfig, ParsedDem as RustParsedDem,
     TwoDetectorDirectRenderPolicy as RustTwoDetectorDirectRenderPolicy,
     compare_dems_exact as rust_compare_dems_exact,
-    compare_dems_statistical as rust_compare_dems_statistical, record_offset_to_absolute_index,
+    compare_dems_statistical as rust_compare_dems_statistical,
     verify_dem_equivalence as rust_verify_dem_equivalence,
 };
 use pecos_qec::fault_tolerance::influence_builder::InfluenceBuilder as RustInfluenceBuilder;
@@ -67,16 +67,21 @@ use pecos_quantum::QubitId;
 use pyo3::Py;
 use pyo3::prelude::*;
 
-/// Type alias for batch sampling results: (`detection_events_per_shot`, `observable_flips_per_shot`)
-type BatchSampleResult = (Vec<Vec<bool>>, Vec<Vec<bool>>);
+type PyDemMechanismTuple = (f64, Vec<u32>, Vec<u32>);
+type PyDemFitResult = (Vec<PyDemMechanismTuple>, Vec<f64>);
 
-fn json_record_offset(value: &serde_json::Value) -> PyResult<i32> {
-    let raw = value
-        .as_i64()
-        .ok_or_else(|| pyo3::exceptions::PyValueError::new_err("Record offset must be integer"))?;
-    i32::try_from(raw).map_err(|_| {
-        pyo3::exceptions::PyValueError::new_err("Record offset must fit into signed 32-bit range")
-    })
+// Adapter for decoder factories that require `Send + Sync` trait objects.
+// Decoder implementations own their state; Python access remains GIL-mediated.
+struct SendWrapper(Box<dyn pecos_decoders::ObservableDecoder>);
+unsafe impl Send for SendWrapper {}
+unsafe impl Sync for SendWrapper {}
+impl pecos_decoders::ObservableDecoder for SendWrapper {
+    fn decode_to_observables(
+        &mut self,
+        syndrome: &[u8],
+    ) -> Result<u64, pecos_decoders::DecoderError> {
+        self.0.decode_to_observables(syndrome)
+    }
 }
 
 // =============================================================================
@@ -159,7 +164,7 @@ impl From<&DagSpacetimeLocation> for PyFaultLocation {
 
 /// A fault influence map built from a DAG circuit.
 ///
-/// Maps fault locations to their effects on detectors and logical observables.
+/// Maps fault locations to their effects on detectors and DEM outputs.
 /// Uses CSR (Compressed Sparse Row) layout for cache-efficient storage.
 ///
 /// This is functionally equivalent to a Detector Error Model (DEM) but stored
@@ -172,7 +177,7 @@ impl From<&DagSpacetimeLocation> for PyFaultLocation {
 /// influence_map = analyzer.build_influence_map()
 ///
 /// # Query fault influence
-/// has_syndrome, causes_logical = influence_map.classify_fault(loc_idx=0, pauli=1)
+/// has_syndrome, flips_dem_output = influence_map.classify_fault(loc_idx=0, pauli=1)
 ///
 /// # Get detector indices flipped by this fault
 /// detector_indices = influence_map.get_detector_indices(loc_idx=0, pauli=1)
@@ -196,13 +201,22 @@ impl PyDagFaultInfluenceMap {
         self.inner.detectors.len()
     }
 
-    /// Number of logical observables tracked.
+    /// Total number of outputs in the DEM `L<n>` namespace.
     #[getter]
-    fn num_logicals(&self) -> usize {
-        self.inner
-            .influences
-            .max_logical_index()
-            .map_or(0, |i| i + 1)
+    fn num_dem_outputs(&self) -> usize {
+        self.inner.num_dem_outputs()
+    }
+
+    /// Number of observable DEM outputs.
+    #[getter]
+    fn num_observables(&self) -> usize {
+        self.inner.num_observables()
+    }
+
+    /// Number of tracked Paulis.
+    #[getter]
+    fn num_tracked_paulis(&self) -> usize {
+        self.inner.num_tracked_paulis()
     }
 
     /// Get all fault locations.
@@ -235,11 +249,16 @@ impl PyDagFaultInfluenceMap {
     ///     pauli: Pauli type (1=X, 2=Y, 3=Z).
     ///
     /// Returns:
-    ///     Tuple (`has_syndrome`, `causes_logical_error`).
+    ///     Tuple (`has_syndrome`, `flips_dem_output`).
     ///     - `has_syndrome`: True if the fault flips at least one detector.
-    ///     - `causes_logical_error`: True if the fault flips the logical observable.
+    ///     - `flips_dem_output`: True if the fault flips at least one standard observable DEM output.
     fn classify_fault(&self, loc_idx: usize, pauli: u8) -> (bool, bool) {
-        self.inner.classify_fault(loc_idx, pauli)
+        (
+            self.inner
+                .influences
+                .has_detector_flips(loc_idx, Pauli::from_u8(pauli)),
+            self.inner.has_observable_flips(loc_idx, pauli),
+        )
     }
 
     /// Get detector indices flipped by a fault.
@@ -254,16 +273,36 @@ impl PyDagFaultInfluenceMap {
         self.inner.get_detector_indices(loc_idx, pauli).to_vec()
     }
 
-    /// Get logical indices flipped by a fault.
+    /// Get standard DEM `L<n>` observable indices flipped by a fault.
+    fn get_dem_output_indices(&self, loc_idx: usize, pauli: u8) -> Vec<u32> {
+        self.inner.get_observable_indices(loc_idx, pauli)
+    }
+
+    /// Get raw internal non-detector influence indices flipped by a fault.
+    ///
+    /// These are implementation indices used to propagate both observables and
+    /// tracked Paulis. Prefer `get_dem_output_indices`,
+    /// `get_observable_indices`, or `get_tracked_pauli_indices` for public DEM
+    /// semantics.
+    fn get_internal_dem_output_indices(&self, loc_idx: usize, pauli: u8) -> Vec<u32> {
+        self.inner.get_dem_output_indices(loc_idx, pauli).to_vec()
+    }
+
+    /// Get tracked-Pauli indices flipped by a fault.
     ///
     /// Args:
     ///     `loc_idx`: Location index.
     ///     pauli: Pauli type (1=X, 2=Y, 3=Z).
     ///
     /// Returns:
-    ///     List of logical indices that are flipped by this fault.
-    fn get_logical_indices(&self, loc_idx: usize, pauli: u8) -> Vec<u32> {
-        self.inner.get_logical_indices(loc_idx, pauli).to_vec()
+    ///     List of tracked-Pauli indices that are flipped by this fault.
+    fn get_tracked_pauli_indices(&self, loc_idx: usize, pauli: u8) -> Vec<u32> {
+        self.inner.get_tracked_pauli_indices(loc_idx, pauli)
+    }
+
+    /// Get observable indices flipped by a fault.
+    fn get_observable_indices(&self, loc_idx: usize, pauli: u8) -> Vec<u32> {
+        self.inner.get_observable_indices(loc_idx, pauli)
     }
 
     /// Check if a fault at the given location flips any detector.
@@ -280,18 +319,26 @@ impl PyDagFaultInfluenceMap {
             .has_detector_flips(loc_idx, Pauli::from_u8(pauli))
     }
 
-    /// Check if a fault at the given location flips a logical observable.
+    /// Check if a fault at the given location flips any standard DEM output.
+    fn has_dem_output_flips(&self, loc_idx: usize, pauli: u8) -> bool {
+        self.inner.has_observable_flips(loc_idx, pauli)
+    }
+
+    /// Check if a fault at the given location flips any observable.
+    fn has_observable_flips(&self, loc_idx: usize, pauli: u8) -> bool {
+        self.inner.has_observable_flips(loc_idx, pauli)
+    }
+
+    /// Check if a fault at the given location flips any tracked Pauli.
     ///
     /// Args:
     ///     `loc_idx`: Location index.
     ///     pauli: Pauli type (1=X, 2=Y, 3=Z).
     ///
     /// Returns:
-    ///     True if the fault flips the logical observable.
-    fn has_logical_flips(&self, loc_idx: usize, pauli: u8) -> bool {
-        self.inner
-            .influences
-            .has_logical_flips(loc_idx, Pauli::from_u8(pauli))
+    ///     True if the fault flips at least one tracked Pauli.
+    fn has_tracked_pauli_flips(&self, loc_idx: usize, pauli: u8) -> bool {
+        self.inner.has_tracked_pauli_flips(loc_idx, pauli)
     }
 
     /// Get memory statistics for this influence map.
@@ -303,7 +350,7 @@ impl PyDagFaultInfluenceMap {
         let dict = pyo3::types::PyDict::new(py);
         dict.set_item("num_locations", stats.num_locations)?;
         dict.set_item("total_detector_entries", stats.total_detector_entries)?;
-        dict.set_item("total_logical_entries", stats.total_logical_entries)?;
+        dict.set_item("total_dem_output_entries", stats.total_dem_output_entries)?;
         dict.set_item("offset_bytes", stats.offset_bytes)?;
         dict.set_item("data_bytes", stats.data_bytes)?;
         dict.set_item("total_bytes", stats.total_bytes)?;
@@ -314,48 +361,57 @@ impl PyDagFaultInfluenceMap {
     ///
     /// Returns:
     ///     Dictionary containing all CSR arrays:
-    ///     - `num_locations`, `num_detectors`, `num_logicals`
+    ///     - `num_locations`, `num_detectors`, `num_dem_outputs`
+    ///     - `num_internal_dem_outputs` for the raw CSR bit-plane width
     ///     - `detector_offsets_x`, `detector_data_x`
     ///     - `detector_offsets_y`, `detector_data_y`
     ///     - `detector_offsets_z`, `detector_data_z`
-    ///     - `logical_offsets_x`, `logical_data_x`
-    ///     - `logical_offsets_y`, `logical_data_y`
-    ///     - `logical_offsets_z`, `logical_data_z`
+    ///     - `dem_output_offsets_x`, `dem_output_data_x`
+    ///     - `dem_output_offsets_y`, `dem_output_data_y`
+    ///     - `dem_output_offsets_z`, `dem_output_data_z`
     fn export_csr(&self, py: Python<'_>) -> PyResult<Py<pyo3::types::PyDict>> {
+        let num_internal_dem_outputs = self
+            .inner
+            .influences
+            .max_dem_output_index()
+            .map_or(0, |idx| idx + 1);
         let (
             num_locations,
             num_detectors,
-            num_logicals,
+            num_dem_outputs,
             det_off_x,
             det_data_x,
             det_off_y,
             det_data_y,
             det_off_z,
             det_data_z,
-            log_off_x,
-            log_data_x,
-            log_off_y,
-            log_data_y,
-            log_off_z,
-            log_data_z,
+            dem_output_offsets_x,
+            dem_output_data_x,
+            dem_output_offsets_y,
+            dem_output_data_y,
+            dem_output_offsets_z,
+            dem_output_data_z,
         ) = self.inner.export_csr();
 
         let dict = pyo3::types::PyDict::new(py);
         dict.set_item("num_locations", num_locations)?;
         dict.set_item("num_detectors", num_detectors)?;
-        dict.set_item("num_logicals", num_logicals)?;
+        dict.set_item("num_dem_outputs", num_dem_outputs)?;
+        dict.set_item("num_internal_dem_outputs", num_internal_dem_outputs)?;
+        dict.set_item("num_observables", self.num_observables())?;
+        dict.set_item("num_tracked_paulis", self.num_tracked_paulis())?;
         dict.set_item("detector_offsets_x", det_off_x)?;
         dict.set_item("detector_data_x", det_data_x)?;
         dict.set_item("detector_offsets_y", det_off_y)?;
         dict.set_item("detector_data_y", det_data_y)?;
         dict.set_item("detector_offsets_z", det_off_z)?;
         dict.set_item("detector_data_z", det_data_z)?;
-        dict.set_item("logical_offsets_x", log_off_x)?;
-        dict.set_item("logical_data_x", log_data_x)?;
-        dict.set_item("logical_offsets_y", log_off_y)?;
-        dict.set_item("logical_data_y", log_data_y)?;
-        dict.set_item("logical_offsets_z", log_off_z)?;
-        dict.set_item("logical_data_z", log_data_z)?;
+        dict.set_item("dem_output_offsets_x", &dem_output_offsets_x)?;
+        dict.set_item("dem_output_data_x", &dem_output_data_x)?;
+        dict.set_item("dem_output_offsets_y", &dem_output_offsets_y)?;
+        dict.set_item("dem_output_data_y", &dem_output_data_y)?;
+        dict.set_item("dem_output_offsets_z", &dem_output_offsets_z)?;
+        dict.set_item("dem_output_data_z", &dem_output_data_z)?;
         Ok(dict.unbind())
     }
 
@@ -374,10 +430,10 @@ impl PyDagFaultInfluenceMap {
 
     fn __repr__(&self) -> String {
         format!(
-            "DagFaultInfluenceMap(locations={}, detectors={}, logicals={})",
+            "DagFaultInfluenceMap(locations={}, detectors={}, tracked_paulis={})",
             self.num_locations(),
             self.num_detectors(),
-            self.num_logicals()
+            self.num_tracked_paulis()
         )
     }
 
@@ -498,16 +554,18 @@ impl PyDagFaultAnalyzer {
 /// dag = DagCircuit()
 /// # ... build circuit ...
 ///
-/// # Build influence map with logical operator tracking
+/// # Build influence map with tracked Paulis
 /// builder = InfluenceBuilder(dag)
-/// builder.with_logical_z([0, 1, 2])  # Top row qubits for d=3 surface code
+/// builder.with_tracked_z([0, 1, 2])  # Track a Z string on these qubits
 /// influence_map = builder.build()
 /// ```
 #[pyclass(name = "InfluenceBuilder", module = "pecos_rslib.qec")]
 pub struct PyInfluenceBuilder {
     dag: DagCircuit,
-    logical_x_qubits: Vec<usize>,
-    logical_z_qubits: Vec<usize>,
+    tracked_x_qubits: Vec<usize>,
+    tracked_z_qubits: Vec<usize>,
+    tracked_paulis: Vec<pecos_core::PauliString>,
+    use_circuit_tracked_paulis: bool,
 }
 
 #[pymethods]
@@ -520,38 +578,86 @@ impl PyInfluenceBuilder {
     fn new(dag: &crate::dag_circuit_bindings::PyDagCircuit) -> Self {
         Self {
             dag: dag.inner.clone(),
-            logical_x_qubits: Vec::new(),
-            logical_z_qubits: Vec::new(),
+            tracked_x_qubits: Vec::new(),
+            tracked_z_qubits: Vec::new(),
+            tracked_paulis: Vec::new(),
+            use_circuit_tracked_paulis: false,
         }
     }
 
-    /// Add a logical X operator to track.
+    /// Add an X-string tracked Pauli.
+    ///
+    /// The tracked Pauli is X on all specified qubits and is sensitive to Z errors.
+    ///
+    /// Args:
+    ///     qubits: List of qubit indices for the tracked X Pauli.
+    ///
+    /// Returns:
+    ///     Self for method chaining.
+    fn with_tracked_x(mut slf: PyRefMut<'_, Self>, qubits: Vec<usize>) -> PyRefMut<'_, Self> {
+        slf.tracked_x_qubits = qubits;
+        slf
+    }
+
+    /// Add a Z-string tracked Pauli.
     ///
-    /// The logical X is defined as X on all specified qubits.
-    /// This logical is sensitive to Z errors.
+    /// The tracked Pauli is Z on all specified qubits and is sensitive to X errors.
     ///
     /// Args:
-    ///     qubits: List of qubit indices for the logical X operator.
+    ///     qubits: List of qubit indices for the tracked Z Pauli.
     ///
     /// Returns:
     ///     Self for method chaining.
-    fn with_logical_x(mut slf: PyRefMut<'_, Self>, qubits: Vec<usize>) -> PyRefMut<'_, Self> {
-        slf.logical_x_qubits = qubits;
+    fn with_tracked_z(mut slf: PyRefMut<'_, Self>, qubits: Vec<usize>) -> PyRefMut<'_, Self> {
+        slf.tracked_z_qubits = qubits;
         slf
     }
 
-    /// Add a logical Z operator to track.
+    /// Add a tracked Pauli.
     ///
-    /// The logical Z is defined as Z on all specified qubits.
-    /// This logical is sensitive to X errors.
+    /// Each entry is a `(qubit, pauli)` tuple where pauli is "X", "Y", or "Z".
     ///
     /// Args:
-    ///     qubits: List of qubit indices for the logical Z operator.
+    ///     entries: List of (`qubit_index`, `pauli_str`) tuples.
+    ///
+    /// Returns:
+    ///     Self for method chaining.
+    fn with_tracked_pauli(
+        mut slf: PyRefMut<'_, Self>,
+        entries: Vec<(usize, String)>,
+    ) -> PyResult<PyRefMut<'_, Self>> {
+        let paulis: Vec<(pecos_core::Pauli, pecos_core::QubitId)> = entries
+            .iter()
+            .map(|(qubit, p)| {
+                let pauli = match p.to_uppercase().as_str() {
+                    "X" => Ok(pecos_core::Pauli::X),
+                    "Y" => Ok(pecos_core::Pauli::Y),
+                    "Z" => Ok(pecos_core::Pauli::Z),
+                    _ => Err(pyo3::exceptions::PyValueError::new_err(format!(
+                        "Invalid Pauli type: {p}. Expected 'X', 'Y', or 'Z'."
+                    ))),
+                }?;
+                Ok((pauli, pecos_core::QubitId::from(*qubit)))
+            })
+            .collect::<PyResult<_>>()?;
+        slf.tracked_paulis
+            .push(pecos_core::PauliString::with_phase_and_paulis(
+                pecos_core::QuarterPhase::PlusOne,
+                paulis,
+            ));
+        Ok(slf)
+    }
+
+    /// Use annotations from the circuit (observables and tracked Paulis).
+    ///
+    /// Extracts observable and `tracked_pauli()` annotations from the
+    /// circuit. Tracked Paulis are propagated with positional awareness
+    /// (only faults before each annotation's position affect it).
     ///
     /// Returns:
     ///     Self for method chaining.
-    fn with_logical_z(mut slf: PyRefMut<'_, Self>, qubits: Vec<usize>) -> PyRefMut<'_, Self> {
-        slf.logical_z_qubits = qubits;
+    fn with_circuit_annotations(mut slf: PyRefMut<'_, Self>) -> PyRefMut<'_, Self> {
+        slf.use_circuit_tracked_paulis = true;
         slf
     }
 
@@ -563,11 +669,23 @@ impl PyInfluenceBuilder {
     /// 3. Backward propagation to build the influence map
     ///
     /// Returns:
-    ///     `DagFaultInfluenceMap` with proper detector definitions and logical tracking.
+    ///     `DagFaultInfluenceMap` with proper detector definitions and tracked Paulis.
     fn build(&self) -> PyDagFaultInfluenceMap {
-        let builder = RustInfluenceBuilder::new(&self.dag)
-            .with_logical_x(self.logical_x_qubits.clone())
-            .with_logical_z(self.logical_z_qubits.clone());
+        let mut builder = RustInfluenceBuilder::new(&self.dag);
+
+        if !self.tracked_x_qubits.is_empty() {
+            builder = builder.with_x(&self.tracked_x_qubits);
+        }
+        if !self.tracked_z_qubits.is_empty() {
+            builder = builder.with_z(&self.tracked_z_qubits);
+        }
+
+        if self.use_circuit_tracked_paulis {
+            builder = builder.with_circuit_annotations(&self.dag);
+        }
+        for pauli in &self.tracked_paulis {
+            builder = builder.with_tracked_pauli(pauli.clone());
+        }
 
         let inner = builder.build();
         PyDagFaultInfluenceMap { inner }
@@ -575,8 +693,11 @@ impl PyInfluenceBuilder {
 
     fn __repr__(&self) -> String {
         format!(
-            "InfluenceBuilder(logical_x={:?}, logical_z={:?})",
-            self.logical_x_qubits, self.logical_z_qubits
+            "InfluenceBuilder(tracked_x={:?}, tracked_z={:?}, tracked_paulis={}, circuit_annotations={})",
+            self.tracked_x_qubits,
+            self.tracked_z_qubits,
+            self.tracked_paulis.len(),
+            self.use_circuit_tracked_paulis,
         )
     }
 }
@@ -585,11 +706,11 @@ impl PyInfluenceBuilder {
 // Detector Error Model
 // =============================================================================
 
-/// A Detector Error Model (DEM) in Stim-compatible format.
+/// A Detector Error Model (DEM) in standard DEM text format.
 ///
 /// This represents the error model of a quantum circuit, mapping error
-/// mechanisms to their probabilities. It can be converted to Stim format
-/// for use with Stim-based decoders.
+/// mechanisms to their probabilities. It can be exported as DEM text for use
+/// with compatible decoders.
 ///
 /// # Example
 ///
@@ -610,13 +731,45 @@ pub struct PyDetectorErrorModel {
     inner: RustDetectorErrorModel,
 }
 
+fn split_dem_outputs_for_dem(
+    dem_outputs: &[u32],
+    dem: &RustDetectorErrorModel,
+) -> (Vec<u32>, Vec<u32>) {
+    if dem
+        .dem_outputs()
+        .iter()
+        .all(|output| output.kind.is_none() && output.records.is_empty() && output.pauli.is_none())
+    {
+        return (dem_outputs.to_vec(), Vec::new());
+    }
+
+    let mut observables = Vec::new();
+    let mut tracked_paulis = Vec::new();
+    for &output_id in dem_outputs {
+        if let Some(output) = dem.dem_outputs().get(output_id as usize) {
+            if output.is_observable() {
+                observables.push(output_id);
+            }
+            if output.is_tracked_pauli() {
+                tracked_paulis.push(output_id);
+            }
+        }
+    }
+    (observables, tracked_paulis)
+}
+
 fn contribution_summary_to_pydict(
     py: Python<'_>,
     summary: RustContributionEffectSummary,
+    dem: &RustDetectorErrorModel,
 ) -> PyResult<Py<pyo3::types::PyDict>> {
     let dict = pyo3::types::PyDict::new(py);
     dict.set_item("detectors", summary.effect.detectors.to_vec())?;
-    dict.set_item("logicals", summary.effect.logicals.to_vec())?;
+    let dem_outputs = summary.effect.dem_outputs.to_vec();
+    let (observables, tracked_paulis) = split_dem_outputs_for_dem(&dem_outputs, dem);
+    dict.set_item("dem_outputs", &dem_outputs)?;
+    dict.set_item("observables", observables)?;
+    dict.set_item("tracked_paulis", tracked_paulis)?;
     dict.set_item("num_contributions", summary.num_contributions)?;
     dict.set_item("total_probability", summary.total_probability)?;
     dict.set_item("direct_count", summary.direct_count)?;
@@ -633,10 +786,15 @@ fn contribution_summary_to_pydict(
 fn contribution_render_summary_to_pydict(
     py: Python<'_>,
     summary: RustContributionRenderSummary,
+    dem: &RustDetectorErrorModel,
 ) -> PyResult<Py<pyo3::types::PyDict>> {
     let dict = pyo3::types::PyDict::new(py);
     dict.set_item("detectors", summary.effect.detectors.to_vec())?;
-    dict.set_item("logicals", summary.effect.logicals.to_vec())?;
+    let dem_outputs = summary.effect.dem_outputs.to_vec();
+    let (observables, tracked_paulis) = split_dem_outputs_for_dem(&dem_outputs, dem);
+    dict.set_item("dem_outputs", &dem_outputs)?;
+    dict.set_item("observables", observables)?;
+    dict.set_item("tracked_paulis", tracked_paulis)?;
     dict.set_item("rendered_targets", summary.rendered_targets)?;
     dict.set_item("num_contributions", summary.num_contributions)?;
     dict.set_item("total_probability", summary.total_probability)?;
@@ -660,8 +818,9 @@ fn contribution_render_summary_to_pydict(
 fn contribution_render_record_to_pydict(
     py: Python<'_>,
     record: RustContributionRenderRecord,
+    dem: &RustDetectorErrorModel,
 ) -> PyResult<Py<pyo3::types::PyDict>> {
-    let dict = contribution_record_to_pydict(py, record.contribution)?;
+    let dict = contribution_record_to_pydict(py, record.contribution, dem)?;
     let render_strategy = match record.render_strategy {
         RustContributionRenderStrategy::SourceComponents => "SourceComponents",
         RustContributionRenderStrategy::RecordedComponents => "RecordedComponents",
@@ -696,6 +855,7 @@ fn parse_two_detector_direct_render_policy(
 fn contribution_record_to_pydict(
     py: Python<'_>,
     contribution: RustFaultContribution,
+    dem: &RustDetectorErrorModel,
 ) -> PyResult<Py<pyo3::types::PyDict>> {
     fn pauli_label(pauli: Pauli) -> &'static str {
         match pauli {
@@ -708,7 +868,11 @@ fn contribution_record_to_pydict(
 
     let dict = pyo3::types::PyDict::new(py);
     dict.set_item("detectors", contribution.effect.detectors.to_vec())?;
-    dict.set_item("logicals", contribution.effect.logicals.to_vec())?;
+    let dem_outputs = contribution.effect.dem_outputs.to_vec();
+    let (observables, tracked_paulis) = split_dem_outputs_for_dem(&dem_outputs, dem);
+    dict.set_item("dem_outputs", &dem_outputs)?;
+    dict.set_item("observables", observables)?;
+    dict.set_item("tracked_paulis", tracked_paulis)?;
     dict.set_item("probability", contribution.probability)?;
     dict.set_item("location_indices", contribution.location_indices.to_vec())?;
     dict.set_item(
@@ -745,31 +909,31 @@ fn contribution_record_to_pydict(
             dict.set_item("source_type", "Direct")?;
             if let Some((first, second)) = contribution.direct_component_effects {
                 dict.set_item("component_1_detectors", first.detectors.to_vec())?;
-                dict.set_item("component_1_logicals", first.logicals.to_vec())?;
+                dict.set_item("component_1_dem_outputs", first.dem_outputs.to_vec())?;
                 dict.set_item("component_2_detectors", second.detectors.to_vec())?;
-                dict.set_item("component_2_logicals", second.logicals.to_vec())?;
+                dict.set_item("component_2_dem_outputs", second.dem_outputs.to_vec())?;
             }
         }
         RustFaultSourceType::DirectOneSidedComponent => {
             dict.set_item("source_type", "DirectOneSidedComponent")?;
             if let Some((first, second)) = contribution.direct_component_effects {
                 dict.set_item("component_1_detectors", first.detectors.to_vec())?;
-                dict.set_item("component_1_logicals", first.logicals.to_vec())?;
+                dict.set_item("component_1_dem_outputs", first.dem_outputs.to_vec())?;
                 dict.set_item("component_2_detectors", second.detectors.to_vec())?;
-                dict.set_item("component_2_logicals", second.logicals.to_vec())?;
+                dict.set_item("component_2_dem_outputs", second.dem_outputs.to_vec())?;
             }
         }
         RustFaultSourceType::YDecomposed {
             x_detectors,
-            x_logicals,
+            x_dem_outputs,
             z_detectors,
-            z_logicals,
+            z_dem_outputs,
         } => {
             dict.set_item("source_type", "YDecomposed")?;
             dict.set_item("x_detectors", x_detectors.to_vec())?;
-            dict.set_item("x_logicals", x_logicals.to_vec())?;
+            dict.set_item("x_dem_outputs", x_dem_outputs.to_vec())?;
             dict.set_item("z_detectors", z_detectors.to_vec())?;
-            dict.set_item("z_logicals", z_logicals.to_vec())?;
+            dict.set_item("z_dem_outputs", z_dem_outputs.to_vec())?;
         }
     }
 
@@ -778,23 +942,88 @@ fn contribution_record_to_pydict(
 
 #[pymethods]
 impl PyDetectorErrorModel {
+    /// Build a DetectorErrorModel directly from a circuit and noise.
+    ///
+    /// Accepts both `TickCircuit` and `DagCircuit`. Reads detector/tracked-Pauli
+    /// definitions from circuit metadata.
+    ///
+    /// Example:
+    ///     >>> dem = DetectorErrorModel.from_circuit(tc, p2=0.01)
+    ///     >>> print(dem.to_string())
+    ///     >>> sampler = dem.to_sampler()
+    #[staticmethod]
+    #[pyo3(signature = (circuit, p1=0.001, p2=0.01, p_meas=0.001, p_prep=0.001))]
+    fn from_circuit(
+        circuit: &pyo3::Bound<'_, pyo3::PyAny>,
+        p1: f64,
+        p2: f64,
+        p_meas: f64,
+        p_prep: f64,
+    ) -> PyResult<Self> {
+        use pecos_qec::fault_tolerance::dem_builder::DemBuilder;
+
+        if let Ok(dag) =
+            circuit.extract::<pyo3::PyRef<'_, crate::dag_circuit_bindings::PyDagCircuit>>()
+        {
+            Ok(Self {
+                inner: DemBuilder::from_circuit(&dag.inner, p1, p2, p_meas, p_prep),
+            })
+        } else if let Ok(tc) =
+            circuit.extract::<pyo3::PyRef<'_, crate::dag_circuit_bindings::PyTickCircuit>>()
+        {
+            Ok(Self {
+                inner: DemBuilder::from_tick_circuit(&tc.inner, p1, p2, p_meas, p_prep),
+            })
+        } else {
+            Err(pyo3::exceptions::PyTypeError::new_err(
+                "from_circuit() expects a DagCircuit or TickCircuit",
+            ))
+        }
+    }
+
+    /// Build a DetectorErrorModel from PECOS DEM metadata JSON.
+    ///
+    /// This imports observable and tracked-Pauli metadata only; mechanism
+    /// errors must be provided through DEM text or built from a circuit.
+    ///
+    /// Raises:
+    ///     `ValueError`: If the metadata JSON is malformed or uses unsupported fields.
+    #[staticmethod]
+    fn from_pecos_metadata_json(json: &str) -> PyResult<Self> {
+        let inner = RustDetectorErrorModel::new()
+            .with_pecos_metadata_json(json)
+            .map_err(|err| pyo3::exceptions::PyValueError::new_err(err.to_string()))?;
+        Ok(Self { inner })
+    }
+
     /// Number of detectors in the model.
     #[getter]
     fn num_detectors(&self) -> usize {
         self.inner.num_detectors()
     }
 
-    /// Number of logical observables in the model.
+    /// Number of observables in the model.
     #[getter]
     fn num_observables(&self) -> usize {
         self.inner.num_observables()
     }
 
+    /// Total number of outputs in the DEM `L<n>` namespace.
+    #[getter]
+    fn num_dem_outputs(&self) -> usize {
+        self.inner.num_dem_outputs()
+    }
+
+    /// Number of tracked Paulis in the model.
+    #[getter]
+    fn num_tracked_paulis(&self) -> usize {
+        self.inner.num_tracked_paulis()
+    }
+
     /// Convert the DEM to a string in standard DEM format.
     ///
     /// Each error mechanism is output with its total probability, with no
-    /// splitting into decomposed forms. This matches Stim's
-    /// `detector_error_model(decompose_errors=False)` output.
+    /// splitting into decomposed forms.
     ///
     /// Returns:
     ///     A string in DEM format with one entry per mechanism.
@@ -809,8 +1038,6 @@ impl PyDetectorErrorModel {
     /// including L0 cancellation forms where available. Hyperedge errors
     /// (affecting 3+ detectors) are decomposed into graphlike components.
     ///
-    /// This matches Stim's `detector_error_model(decompose_errors=True)` output.
-    ///
     /// Returns:
     ///     A string in DEM format with decomposed representations.
     fn to_string_decomposed(&self) -> String {
@@ -855,12 +1082,20 @@ impl PyDetectorErrorModel {
 
     /// Returns debug info about all unique contribution effects.
     ///
-    /// Shows each unique detector/logical pattern and how many contributions
+    /// Shows each unique detector/DEM-output pattern and how many contributions
     /// target it with their total probability.
     fn all_contribution_effects(&self) -> String {
         self.inner.all_contribution_effects()
     }
 
+    /// Build a `DemSampler` directly from this DEM — no string round-trip.
+    fn to_sampler(&self) -> PyResult<PyDemSampler> {
+        use pecos_qec::fault_tolerance::dem_builder::DemSampler;
+
+        let inner = DemSampler::from_detector_error_model(&self.inner);
+        Ok(PyDemSampler { inner })
+    }
+
     /// Returns structured summaries for all unique contribution effects.
     fn contribution_effect_summaries(
         &self,
@@ -869,7 +1104,7 @@ impl PyDetectorErrorModel {
         self.inner
             .contribution_effect_summaries()
             .into_iter()
-            .map(|summary| contribution_summary_to_pydict(py, summary))
+            .map(|summary| contribution_summary_to_pydict(py, summary, &self.inner))
             .collect()
     }
 
@@ -881,7 +1116,7 @@ impl PyDetectorErrorModel {
         self.inner
             .contribution_render_summaries()
             .into_iter()
-            .map(|summary| contribution_render_summary_to_pydict(py, summary))
+            .map(|summary| contribution_render_summary_to_pydict(py, summary, &self.inner))
             .collect()
     }
 
@@ -896,7 +1131,7 @@ impl PyDetectorErrorModel {
         self.inner
             .contribution_render_summaries_with_two_detector_direct_policy(policy)
             .into_iter()
-            .map(|summary| contribution_render_summary_to_pydict(py, summary))
+            .map(|summary| contribution_render_summary_to_pydict(py, summary, &self.inner))
             .collect()
     }
 
@@ -908,7 +1143,7 @@ impl PyDetectorErrorModel {
         self.inner
             .contribution_render_records()
             .into_iter()
-            .map(|record| contribution_render_record_to_pydict(py, record))
+            .map(|record| contribution_render_record_to_pydict(py, record, &self.inner))
             .collect()
     }
 
@@ -923,29 +1158,31 @@ impl PyDetectorErrorModel {
         self.inner
             .contribution_render_records_with_two_detector_direct_policy(policy)
             .into_iter()
-            .map(|record| contribution_render_record_to_pydict(py, record))
+            .map(|record| contribution_render_record_to_pydict(py, record, &self.inner))
             .collect()
     }
 
-    /// Returns source-tracked contributions for a full detector/logical effect.
+    /// Returns source-tracked contributions for a full detector/DEM-output effect.
     fn contributions_for_effect(
         &self,
         py: Python<'_>,
         detectors: Vec<u32>,
-        logicals: Vec<u32>,
+        dem_outputs: Vec<u32>,
     ) -> PyResult<Vec<Py<pyo3::types::PyDict>>> {
         self.inner
-            .contributions_for_effect(&detectors, &logicals)
+            .contributions_for_effect(&detectors, &dem_outputs)
             .into_iter()
-            .map(|contribution| contribution_record_to_pydict(py, contribution))
+            .map(|contribution| contribution_record_to_pydict(py, contribution, &self.inner))
             .collect()
     }
 
     fn __repr__(&self) -> String {
         format!(
-            "DetectorErrorModel(detectors={}, observables={}, contributions={})",
+            "DetectorErrorModel(detectors={}, dem_outputs={}, observables={}, tracked_paulis={}, contributions={})",
             self.num_detectors(),
+            self.num_dem_outputs(),
             self.num_observables(),
+            self.num_tracked_paulis(),
             self.num_contributions()
         )
     }
@@ -959,12 +1196,17 @@ impl PyDetectorErrorModel {
 // DEM Builder
 // =============================================================================
 
-/// Builder for Detector Error Models (DEMs).
+/// Advanced builder for Detector Error Models (DEMs).
 ///
-/// Constructs a DEM from a fault influence map and detector/observable metadata.
-/// Uses the per-qubit fault model for accurate depolarizing noise analysis.
+/// For most use cases, prefer `DetectorErrorModel.from_circuit()` or
+/// `DemSampler.from_circuit()` which handle everything automatically.
 ///
-/// # Example
+/// Use `DemBuilder` directly when you need:
+/// - A custom fault influence map
+/// - Non-standard noise configuration
+/// - Manual detector and observable definitions
+///
+/// # Example (advanced)
 ///
 /// ```python
 /// from pecos_rslib.qec import DagFaultAnalyzer, DemBuilder
@@ -990,15 +1232,10 @@ impl PyDetectorErrorModel {
 #[pyclass(name = "DemBuilder", module = "pecos_rslib.qec")]
 pub struct PyDemBuilder {
     influence_map: RustDagFaultInfluenceMap,
-    p1: f64,
-    p2: f64,
-    p_meas: f64,
-    p_init: f64,
+    noise: NoiseConfig,
     detectors_json: Option<String>,
     observables_json: Option<String>,
     num_measurements: Option<usize>,
-    /// Measurement order: list of qubits in `TickCircuit` measurement execution order.
-    /// This allows proper mapping between record offsets and influence map indices.
     measurement_order: Option<Vec<usize>>,
 }
 
@@ -1012,10 +1249,7 @@ impl PyDemBuilder {
     fn new(influence_map: &PyDagFaultInfluenceMap) -> Self {
         Self {
             influence_map: influence_map.inner.clone(),
-            p1: 0.01,
-            p2: 0.01,
-            p_meas: 0.01,
-            p_init: 0.01,
+            noise: NoiseConfig::default(),
             detectors_json: None,
             observables_json: None,
             num_measurements: None,
@@ -1029,21 +1263,35 @@ impl PyDemBuilder {
     ///     p1: Single-qubit depolarizing error rate.
     ///     p2: Two-qubit depolarizing error rate.
     ///     `p_meas`: Measurement error rate.
-    ///     `p_init`: Initialization (prep) error rate.
+    ///     `p_prep`: Initialization (prep) error rate.
+    ///     `p_idle`: Optional idle noise rate per time unit.
+    ///     t1: Optional T1 relaxation time.
+    ///     t2: Optional T2 dephasing time.
     ///
     /// Returns:
     ///     Self for method chaining.
+    #[pyo3(signature = (p1, p2, p_meas, p_prep, p_idle=None, t1=None, t2=None, idle_rz=None))]
+    #[allow(clippy::too_many_arguments)]
     fn with_noise(
         mut slf: PyRefMut<'_, Self>,
         p1: f64,
         p2: f64,
         p_meas: f64,
-        p_init: f64,
+        p_prep: f64,
+        p_idle: Option<f64>,
+        t1: Option<f64>,
+        t2: Option<f64>,
+        idle_rz: Option<f64>,
     ) -> PyRefMut<'_, Self> {
-        slf.p1 = p1;
-        slf.p2 = p2;
-        slf.p_meas = p_meas;
-        slf.p_init = p_init;
+        let mut noise = NoiseConfig::new(p1, p2, p_meas, p_prep);
+        noise.p_idle = p_idle.unwrap_or(0.0);
+        if let (Some(t1_val), Some(t2_val)) = (t1, t2) {
+            noise = noise.set_t1_t2(t1_val, t2_val);
+        }
+        if let Some(rz) = idle_rz {
+            noise = noise.set_idle_rz(rz);
+        }
+        slf.noise = noise;
         slf
     }
 
@@ -1063,13 +1311,8 @@ impl PyDemBuilder {
 
     /// Set the observable definitions from JSON.
     ///
-    /// Args:
-    ///     json: JSON string with observable definitions.
-    ///           Format: [{"id": 0, "records": [-1, -3, -5]}, ...]
-    ///           Public surface descriptors using "`observable_id`" are also accepted.
-    ///
-    /// Returns:
-    ///     Self for method chaining.
+    /// Tracked Paulis are carried by the influence map; this helper is for
+    /// observable metadata.
     fn with_observables_json(mut slf: PyRefMut<'_, Self>, json: String) -> PyRefMut<'_, Self> {
         slf.observables_json = Some(json);
         slf
@@ -1116,12 +1359,8 @@ impl PyDemBuilder {
     /// Raises:
     ///     `ValueError`: If the detector or observable JSON is malformed.
     fn build(&self) -> PyResult<PyDetectorErrorModel> {
-        let mut builder = RustDemBuilder::new(&self.influence_map).with_noise(
-            self.p1,
-            self.p2,
-            self.p_meas,
-            self.p_init,
-        );
+        let mut builder =
+            RustDemBuilder::new(&self.influence_map).with_noise_config(self.noise.clone());
 
         if let Some(num) = self.num_measurements {
             builder = builder.with_num_measurements(num);
@@ -1154,8 +1393,8 @@ impl PyDemBuilder {
 
     fn __repr__(&self) -> String {
         format!(
-            "DemBuilder(p1={}, p2={}, p_meas={}, p_init={})",
-            self.p1, self.p2, self.p_meas, self.p_init
+            "DemBuilder(p1={}, p2={}, p_meas={}, p_prep={}, p_idle={:?})",
+            self.noise.p1, self.noise.p2, self.noise.p_meas, self.noise.p_prep, self.noise.p_idle
         )
     }
 }
@@ -1164,984 +1403,1950 @@ impl PyDemBuilder {
 // Helper Functions
 // =============================================================================
 
-/// Parse detector records from JSON string.
+/// `UnionFind` decoder that passes LLRs (from DEM error priors) for weighted decoding.
 ///
-/// Extracts the "records" arrays from detector definitions.
-fn parse_detector_records(detectors_json: &str) -> PyResult<Vec<Vec<i32>>> {
-    if detectors_json.is_empty() {
-        return Ok(Vec::new());
-    }
-
-    let detectors: Vec<serde_json::Value> = serde_json::from_str(detectors_json)
-        .map_err(|e| pyo3::exceptions::PyValueError::new_err(format!("Invalid JSON: {e}")))?;
-
-    let mut detector_records = Vec::with_capacity(detectors.len());
+/// The generic `CheckMatrixObservableDecoder` calls `Decoder::decode` which
+/// passes empty LLRs. This wrapper stores the LLRs and passes them through
+/// to the C++ UF decoder each shot, giving it edge-weight information.
+struct WeightedUfObservableDecoder {
+    decoder: pecos_decoders::UnionFindDecoder,
+    dcm: pecos_decoder_core::dem::DemCheckMatrix,
+    llrs: Vec<f64>,
+}
 
-    for det in &detectors {
-        let records = det
-            .get("records")
-            .and_then(|r| r.as_array())
-            .ok_or_else(|| {
-                pyo3::exceptions::PyValueError::new_err("Detector missing 'records' array")
-            })?;
+impl pecos_decoders::ObservableDecoder for WeightedUfObservableDecoder {
+    fn decode_to_observables(
+        &mut self,
+        syndrome: &[u8],
+    ) -> Result<u64, pecos_decoder_core::DecoderError> {
+        let arr = ndarray::Array1::from_vec(syndrome.to_vec());
+        // bits_per_step=1: grow one bit at a time, sorted by LLR weight.
+        // bits_per_step=0 with non-empty LLRs causes the C++ UF decoder to
+        // add zero bits per step, looping forever.
+        let result = self
+            .decoder
+            .decode(&arr.view(), &self.llrs, 1)
+            .map_err(|e| pecos_decoder_core::DecoderError::DecodingFailed(e.to_string()))?;
+        Ok(self
+            .dcm
+            .observables_mask_from_correction(result.decoding.as_slice().unwrap_or(&[])))
+    }
+}
 
-        let offsets: Vec<i32> = records
-            .iter()
-            .map(json_record_offset)
-            .collect::<PyResult<Vec<_>>>()?;
+/// Wrapper that relabels syndromes before passing to an inner decoder.
+///
+/// Used for Fusion Blossom parallel where detector IDs need to be
+/// round-contiguous for partitioning.
+struct RelabeledObservableDecoder {
+    decoder: pecos_decoders::FusionBlossomDecoder,
+    old_to_new: Vec<usize>,
+}
 
-        detector_records.push(offsets);
+impl pecos_decoders::ObservableDecoder for RelabeledObservableDecoder {
+    fn decode_to_observables(
+        &mut self,
+        syndrome: &[u8],
+    ) -> Result<u64, pecos_decoder_core::DecoderError> {
+        // Relabel syndrome into the expanded vertex space (detectors + virtual + gap)
+        let expected = self.decoder.num_nodes();
+        let mut relabeled = vec![0u8; expected];
+        for (old_id, &val) in syndrome.iter().enumerate() {
+            if old_id < self.old_to_new.len() {
+                let new_id = self.old_to_new[old_id];
+                if new_id < expected {
+                    relabeled[new_id] = val;
+                }
+            }
+        }
+        let arr = ndarray::Array1::from_vec(relabeled);
+        let result = self
+            .decoder
+            .decode(&arr.view())
+            .map_err(|e| pecos_decoder_core::DecoderError::DecodingFailed(e.to_string()))?;
+        let mut mask = 0u64;
+        for (i, &v) in result.observable.iter().enumerate() {
+            if v != 0 {
+                mask |= 1 << i;
+            }
+        }
+        Ok(mask)
     }
+}
 
-    Ok(detector_records)
+/// Convert a `DemMatchingGraph` to a DEM string for inner decoder construction.
+fn subgraph_to_dem_string(graph: &pecos_decoder_core::DemMatchingGraph) -> String {
+    let mut lines = Vec::new();
+    for edge in &graph.edges {
+        let p = edge.probability;
+        let mut targets = Vec::new();
+        targets.push(format!("D{}", edge.node1));
+        if let Some(n2) = edge.node2 {
+            targets.push(format!("D{n2}"));
+        }
+        for &obs in &edge.observables {
+            targets.push(format!("L{obs}"));
+        }
+        lines.push(format!("error({p}) {}", targets.join(" ")));
+    }
+    lines.join("\n")
 }
 
-/// Parse observable records from JSON string.
+/// Create an `ObservableDecoder` from a DEM string and decoder type name.
 ///
-/// Extracts the "records" arrays from observable definitions.
-fn parse_observable_records(observables_json: &str) -> PyResult<Vec<Vec<i32>>> {
-    if observables_json.is_empty() {
-        return Ok(Vec::new());
-    }
+/// This is the shared factory used by `SampleBatch.decode_count`,
+/// `DemSampler.sample_decode_count`, and the parallel variants.
+fn create_observable_decoder(
+    dem: &str,
+    decoder_type: &str,
+) -> PyResult<Box<dyn pecos_decoders::ObservableDecoder>> {
+    use pecos_decoder_core::{CheckMatrixObservableDecoder, DemCheckMatrix};
+    use pecos_decoders::{
+        BeliefFindDecoder, BpLsdDecoder, BpMethod, BpOsdDecoder, BpSchedule, InputVectorType,
+        MinSumBpBuilder, OsdMethod, PyMatchingDecoder, RelayBpBuilder, SparseMatrix,
+        TesseractConfig, TesseractDecoder, UfMethod, UnionFindDecoder,
+    };
 
-    let observables: Vec<serde_json::Value> = serde_json::from_str(observables_json)
-        .map_err(|e| pyo3::exceptions::PyValueError::new_err(format!("Invalid JSON: {e}")))?;
+    match decoder_type {
+        "pymatching" => {
+            // Default: correlated matching enabled (exploits X-Z correlations
+            // from depolarizing noise for ~20% fewer errors at d>=5).
+            let d = PyMatchingDecoder::from_dem_with_correlations(dem, true)
+                .map_err(|e| PyErr::new::<pyo3::exceptions::PyRuntimeError, _>(e.to_string()))?;
+            Ok(Box::new(d))
+        }
+        "pymatching_uncorrelated" => {
+            let d = PyMatchingDecoder::from_dem(dem)
+                .map_err(|e| PyErr::new::<pyo3::exceptions::PyRuntimeError, _>(e.to_string()))?;
+            Ok(Box::new(d))
+        }
+        "tesseract" => {
+            let d = TesseractDecoder::new(dem, TesseractConfig::fast())
+                .map_err(|e| PyErr::new::<pyo3::exceptions::PyRuntimeError, _>(e.to_string()))?;
+            Ok(Box::new(d))
+        }
+        s if s.starts_with("k_mwpm") => {
+            // K-MWPM: enumerate K matchings via decoding tree, majority vote.
+            // Uses UF as the inner MWPM solver (supports decode_with_weights).
+            use pecos_decoder_core::k_mwpm::{KMwpmConfig, KMwpmDecoder};
+            let mut k: usize = 10;
+            if let Some(params) = s.strip_prefix("k_mwpm:") {
+                for kv in params.split(',') {
+                    let parts: Vec<&str> = kv.splitn(2, '=').collect();
+                    if parts.len() == 2 && (parts[0] == "K" || parts[0] == "k") {
+                        k = parts[1].parse().unwrap_or(10);
+                    }
+                }
+            }
+            // Use FB (standard, non-correlated) as the inner MWPM.
+            // K-MWPM captures correlation benefit by exploring multiple matchings.
+            let fb = pecos_decoders::FusionBlossomDecoder::from_dem(dem)
+                .map_err(|e| PyErr::new::<pyo3::exceptions::PyRuntimeError, _>(e.to_string()))?;
+            Ok(Box::new(KMwpmDecoder::new(fb, KMwpmConfig { k })))
+        }
+        "astar" => {
+            let d =
+                pecos_decoders::AStarDecoder::from_dem(dem, pecos_decoders::AStarConfig::default())
+                    .map_err(|e| {
+                        PyErr::new::<pyo3::exceptions::PyRuntimeError, _>(e.to_string())
+                    })?;
+            Ok(Box::new(d))
+        }
+        "astar_full" => {
+            // A* on non-decomposed DEM (preserves hyperedges for Y-error correlations).
+            let d = pecos_decoders::AStarDecoder::from_dem_full(
+                dem,
+                pecos_decoders::AStarConfig::default(),
+            )
+            .map_err(|e| PyErr::new::<pyo3::exceptions::PyRuntimeError, _>(e.to_string()))?;
+            Ok(Box::new(d))
+        }
+        "fusion_blossom" => {
+            // Auto: use parallel for large problems (500+ detectors), serial otherwise
+            let graph = pecos_decoder_core::DemMatchingGraph::from_dem_str(dem)
+                .map_err(|e| PyErr::new::<pyo3::exceptions::PyRuntimeError, _>(e.to_string()))?;
+            let has_coords = graph
+                .detector_coords
+                .iter()
+                .any(std::option::Option::is_some);
+            if graph.num_detectors >= 500 && has_coords {
+                return create_observable_decoder(dem, "fusion_blossom_parallel");
+            }
+            create_observable_decoder(dem, "fusion_blossom_serial")
+        }
+        "fusion_blossom_serial" => {
+            use pecos_decoder_core::DemMatchingGraph;
+            use pecos_decoders::{FusionBlossomConfig, FusionBlossomDecoder};
+            let graph = DemMatchingGraph::from_dem_str(dem)
+                .map_err(|e| PyErr::new::<pyo3::exceptions::PyRuntimeError, _>(e.to_string()))?;
+
+            // Use absolute weight scaling. Fusion Blossom uses integer weights;
+            // we multiply by 1000 for precision (matching the internal 1000x
+            // scaling in add_edge). The upstream tutorial uses relative scaling
+            // but that loses weight ordering when the range is narrow.
+
+            let config = FusionBlossomConfig {
+                num_nodes: Some(graph.num_detectors),
+                num_observables: graph.num_observables,
+                ..Default::default()
+            };
+            let mut decoder = FusionBlossomDecoder::new(config)
+                .map_err(|e| PyErr::new::<pyo3::exceptions::PyRuntimeError, _>(e.to_string()))?;
+            for edge in &graph.edges {
+                let obs: Vec<usize> = edge.observables.iter().map(|&o| o as usize).collect();
+                let scaled_weight = edge.weight;
+                match edge.node2 {
+                    Some(n2) => {
+                        decoder
+                            .add_edge(edge.node1 as usize, n2 as usize, &obs, Some(scaled_weight))
+                            .map_err(|e| {
+                                PyErr::new::<pyo3::exceptions::PyRuntimeError, _>(e.to_string())
+                            })?;
+                    }
+                    None => {
+                        decoder
+                            .add_boundary_edge(edge.node1 as usize, &obs, Some(scaled_weight))
+                            .map_err(|e| {
+                                PyErr::new::<pyo3::exceptions::PyRuntimeError, _>(e.to_string())
+                            })?;
+                    }
+                }
+            }
+            Ok(Box::new(decoder))
+        }
+        "fusion_blossom_correlated" => {
+            use pecos_decoder_core::DemMatchingGraph;
+            use pecos_decoder_core::correlation_table::CorrelationTable;
+            use pecos_decoder_core::two_pass_decoder::TwoPassDecoder;
+            use pecos_decoders::{FusionBlossomConfig, FusionBlossomDecoder};
+
+            let graph = DemMatchingGraph::from_dem_str(dem)
+                .map_err(|e| PyErr::new::<pyo3::exceptions::PyRuntimeError, _>(e.to_string()))?;
+
+            let config = FusionBlossomConfig {
+                num_nodes: Some(graph.num_detectors),
+                num_observables: graph.num_observables,
+                ..Default::default()
+            };
+            let mut decoder = FusionBlossomDecoder::new(config)
+                .map_err(|e| PyErr::new::<pyo3::exceptions::PyRuntimeError, _>(e.to_string()))?;
+
+            // Build edge index map and weights
+            let mut edge_index_map = std::collections::BTreeMap::new();
+            let mut base_weights = Vec::new();
+            for (idx, edge) in graph.edges.iter().enumerate() {
+                let obs: Vec<usize> = edge.observables.iter().map(|&o| o as usize).collect();
+                base_weights.push(edge.weight);
+                let key = if let Some(n2) = edge.node2 {
+                    decoder
+                        .add_edge(edge.node1 as usize, n2 as usize, &obs, Some(edge.weight))
+                        .map_err(|e| {
+                            PyErr::new::<pyo3::exceptions::PyRuntimeError, _>(e.to_string())
+                        })?;
+                    if edge.node1 <= n2 {
+                        (edge.node1, n2)
+                    } else {
+                        (n2, edge.node1)
+                    }
+                } else {
+                    decoder
+                        .add_boundary_edge(edge.node1 as usize, &obs, Some(edge.weight))
+                        .map_err(|e| {
+                            PyErr::new::<pyo3::exceptions::PyRuntimeError, _>(e.to_string())
+                        })?;
+                    (edge.node1, u32::MAX)
+                };
+                edge_index_map.insert(key, idx);
+            }
 
-    let mut observable_records = Vec::with_capacity(observables.len());
+            // Build correlation table from DEM decomposition
+            let corr_table =
+                CorrelationTable::from_dem_str(dem, &edge_index_map, graph.edges.len()).map_err(
+                    |e| PyErr::new::<pyo3::exceptions::PyRuntimeError, _>(e.to_string()),
+                )?;
 
-    for obs in &observables {
-        let records = obs
-            .get("records")
-            .and_then(|r| r.as_array())
-            .ok_or_else(|| {
-                pyo3::exceptions::PyValueError::new_err("Observable missing 'records' array")
-            })?;
+            let two_pass = TwoPassDecoder::new(decoder, base_weights, corr_table);
+            Ok(Box::new(two_pass))
+        }
+        s if s.starts_with("perturbed_fb_corr") => {
+            // Fast perturbed correlated FB ensemble.
+            // Parses DemCheckMatrix once, builds K members with perturbed weights
+            // via from_check_matrix_correlated (skips DEM text re-parsing).
+
+            use pecos_decoder_core::ensemble::EnsembleDecoder;
+            use pecos_decoders::FusionBlossomDecoder;
+
+            let mut k: usize = 5;
+            let mut sigma: f64 = 0.5;
+            let mut seed: u64 = 42;
+            if let Some(params) = s.strip_prefix("perturbed_fb_corr:") {
+                for kv in params.split(',') {
+                    let parts: Vec<&str> = kv.splitn(2, '=').collect();
+                    if parts.len() == 2 {
+                        match parts[0] {
+                            "K" | "k" => k = parts[1].parse().unwrap_or(5),
+                            "sigma" | "s" => sigma = parts[1].parse().unwrap_or(0.5),
+                            "seed" => seed = parts[1].parse().unwrap_or(42),
+                            _ => {}
+                        }
+                    }
+                }
+            }
 
-        let offsets: Vec<i32> = records
-            .iter()
-            .map(json_record_offset)
-            .collect::<PyResult<Vec<_>>>()?;
+            // Build K members using from_dem_correlated on perturbed DEM text.
+            // This is faster than the generic perturbed: path because it reuses
+            // the same DEM parsing approach that FB_corr uses (which handles
+            // duplicate edges correctly).
+            let mut members: Vec<Box<dyn pecos_decoders::ObservableDecoder>> =
+                Vec::with_capacity(k);
+
+            // Unperturbed anchor.
+            members.push(Box::new(
+                FusionBlossomDecoder::from_dem_correlated(dem).map_err(|e| {
+                    PyErr::new::<pyo3::exceptions::PyRuntimeError, _>(e.to_string())
+                })?,
+            ));
 
-        observable_records.push(offsets);
-    }
+            // K-1 perturbed members.
+            let mut rng = pecos_random::PecosRng::seed_from_u64(seed);
+            let mut next_f64 = || rng.next_f64();
+            for _ in 1..k {
+                let perturbed =
+                    pecos_decoder_core::perturbed::perturb_dem(dem, sigma, &mut next_f64);
+                if let Ok(dec) = FusionBlossomDecoder::from_dem_correlated(&perturbed) {
+                    members.push(Box::new(dec));
+                }
+            }
 
-    Ok(observable_records)
-}
+            Ok(Box::new(EnsembleDecoder::new(members)))
+        }
+        "fusion_blossom_parallel" => {
+            use pecos_decoder_core::DemMatchingGraph;
+            use pecos_decoders::{FusionBlossomConfig, FusionBlossomDecoder, PartitionConfig};
+
+            let graph = DemMatchingGraph::from_dem_str(dem)
+                .map_err(|e| PyErr::new::<pyo3::exceptions::PyRuntimeError, _>(e.to_string()))?;
+
+            // Group detectors by time coordinate for round-contiguous relabeling.
+            let mut round_groups: std::collections::BTreeMap<i64, Vec<u32>> =
+                std::collections::BTreeMap::new();
+            #[allow(clippy::cast_possible_truncation)] // time coords and detector IDs are small
+            for (id, coord) in graph.detector_coords.iter().enumerate() {
+                let t = coord
+                    .as_ref()
+                    .and_then(|c| c.get(2))
+                    .copied()
+                    .unwrap_or(0.0);
+                round_groups
+                    .entry((t * 1000.0) as i64)
+                    .or_default()
+                    .push(id as u32);
+            }
+            let num_rounds = round_groups.len();
+            if num_rounds < 2 {
+                // Not enough rounds to partition -- fall back to serial
+                return create_observable_decoder(dem, "fusion_blossom");
+            }
 
-// =============================================================================
-// Measurement Noise Model
-// =============================================================================
+            // Relabel: each round gets [detectors] [boundary_virtual] contiguously.
+            // This ensures boundary edges stay within the same vertex range as
+            // the round's detectors.
+            let num_dets = graph.num_detectors;
+            let mut old_to_new = vec![0usize; num_dets];
+            let mut det_to_round = vec![0usize; num_dets];
+            let mut new_id = 0usize;
+            let mut round_starts = Vec::new();
+            let mut round_ends = Vec::new(); // end of each round (after boundary vertex)
+            let mut partition_boundary = Vec::new();
+            for (round_idx, (_round, ids)) in round_groups.iter().enumerate() {
+                round_starts.push(new_id);
+                for &old_id in ids {
+                    old_to_new[old_id as usize] = new_id;
+                    det_to_round[old_id as usize] = round_idx;
+                    new_id += 1;
+                }
+                // Virtual boundary vertex for this round, right after detectors
+                partition_boundary.push(new_id);
+                new_id += 1;
+                round_ends.push(new_id);
+            }
+            let total_vertex_num = new_id;
+
+            let config = FusionBlossomConfig {
+                num_nodes: Some(total_vertex_num),
+                num_observables: graph.num_observables,
+                ..Default::default()
+            };
+            let mut decoder = FusionBlossomDecoder::new(config)
+                .map_err(|e| PyErr::new::<pyo3::exceptions::PyRuntimeError, _>(e.to_string()))?;
+            // Mark per-partition boundary vertices as virtual
+            for &bnd in &partition_boundary {
+                decoder.virtual_vertices.push(bnd);
+            }
 
-/// A Measurement Noise Model (MNM) for fast approximate sampling.
-///
-/// Unlike a DEM which maps error mechanisms to detector effects, the MNM maps
-/// directly to measurement effects. This allows sampling raw measurement outcomes
-/// without needing detector definitions.
-///
-/// # Sampling Modes
-///
-/// - **Per-fault-location** (accurate): Sample each (location, Pauli) independently
-/// - **Per-mechanism** (fast, approximate): Sample each unique measurement effect once
-///
-/// The MNM enables the fast per-mechanism mode while still producing raw measurement
-/// outcomes that can be converted to detection events using any detector definition.
-///
-/// # Example
-///
-/// ```python
-/// from pecos_rslib.qec import MemBuilder
-///
-/// # Build MNM from influence map
-/// mnm = MemBuilder(influence_map).with_noise(0.01, 0.01, 0.01, 0.01).build()
-///
-/// # Sample measurement outcomes
-/// outcomes = mnm.sample()
-/// ```
-#[pyclass(name = "MeasurementNoiseModel", module = "pecos_rslib.qec")]
-pub struct PyMeasurementNoiseModel {
-    inner: RustMeasurementNoiseModel,
-}
+            for edge in &graph.edges {
+                let obs: Vec<usize> = edge.observables.iter().map(|&o| o as usize).collect();
+                let n1 = old_to_new[edge.node1 as usize];
+                if let Some(n2) = edge.node2 {
+                    let n2 = old_to_new[n2 as usize];
+                    decoder
+                        .add_edge(n1, n2, &obs, Some(edge.weight))
+                        .map_err(|e| {
+                            PyErr::new::<pyo3::exceptions::PyRuntimeError, _>(e.to_string())
+                        })?;
+                } else {
+                    // Route boundary edge to this detector's round boundary vertex
+                    let round_idx = det_to_round[edge.node1 as usize];
+                    let bnd = partition_boundary[round_idx];
+                    decoder
+                        .add_edge(n1, bnd, &obs, Some(edge.weight))
+                        .map_err(|e| {
+                            PyErr::new::<pyo3::exceptions::PyRuntimeError, _>(e.to_string())
+                        })?;
+                }
+            }
 
-#[pymethods]
-impl PyMeasurementNoiseModel {
-    /// Number of distinct mechanisms in the model.
-    #[getter]
-    fn num_mechanisms(&self) -> usize {
-        self.inner.num_mechanisms()
-    }
+            // Build partition config matching the upstream time-partition pattern.
+            // Each partition covers multiple rounds. The interface between
+            // adjacent partitions is the first round of the later partition's
+            // rounds (which is skipped from its range, creating the gap).
+
+            // Partition ranges: each partition covers multiple rounds of detectors
+            // plus that partition's boundary vertices.
+            // Boundary vertices are at indices [num_dets, num_dets + num_rounds).
+            // We assign boundary vertex for round R to the partition that contains round R.
+            let partition_num = num_rounds.clamp(2, 4);
+
+            // Build partition config. Each partition covers multiple rounds.
+            // Partition boundaries fall between rounds. The first round of
+            // each non-first partition is the interface gap (its vertices
+            // are excluded from the partition range).
+            let mut part_config = PartitionConfig::new(total_vertex_num);
+            part_config.partitions.clear();
+
+            for p_idx in 0..partition_num {
+                let start_round = p_idx * num_rounds / partition_num;
+                let end_round = (p_idx + 1) * num_rounds / partition_num;
+                // First partition starts at its first round.
+                // Subsequent partitions skip their first round (interface gap).
+                let start_vertex = if p_idx == 0 {
+                    round_starts[start_round]
+                } else {
+                    round_starts[(start_round + 1).min(num_rounds - 1)]
+                };
+                let end_vertex = round_ends[end_round - 1];
+                if start_vertex < end_vertex {
+                    part_config
+                        .partitions
+                        .push(pecos_decoders::VertexRange::new(start_vertex, end_vertex));
+                }
+            }
 
-    /// Number of measurements in the circuit.
-    #[getter]
-    fn num_measurements(&self) -> usize {
-        self.inner.num_measurements
-    }
+            // Linear fusion chain: merge adjacent partitions left to right
+            let n_parts = part_config.partitions.len();
+            part_config.fusions.clear();
+            if n_parts > 1 {
+                let mut active: Vec<usize> = (0..n_parts).collect();
+                while active.len() > 1 {
+                    let mut next_active = Vec::new();
+                    let mut i = 0;
+                    while i + 1 < active.len() {
+                        part_config.fusions.push((active[i], active[i + 1]));
+                        next_active.push(n_parts + part_config.fusions.len() - 1);
+                        i += 2;
+                    }
+                    if i < active.len() {
+                        next_active.push(active[i]);
+                    }
+                    active = next_active;
+                }
+            }
 
-    /// Sample measurement outcomes.
-    ///
-    /// Each noise mechanism is sampled once according to its probability.
-    /// When a mechanism fires, its measurements are XOR'd into the outcomes.
-    ///
-    /// Args:
-    ///     seed: Optional random seed for reproducibility.
-    ///
-    /// Returns:
-    ///     List of boolean measurement outcomes.
-    #[pyo3(signature = (seed=None))]
-    fn sample(&self, seed: Option<u64>) -> Vec<bool> {
-        use pecos_random::PecosRng;
-        use rand::RngExt;
+            decoder.set_partition_config(part_config);
 
-        let mut rng = match seed {
-            Some(s) => PecosRng::seed_from_u64(s),
-            None => PecosRng::seed_from_u64(rand::rng().random()),
-        };
+            Ok(Box::new(RelabeledObservableDecoder {
+                decoder,
+                old_to_new,
+            }))
+        }
+        "bp_osd" | "bp_lsd" | "belief_find" | "union_find" | "relay_bp" | "min_sum_bp" => {
+            let dcm = DemCheckMatrix::from_dem_str(dem)
+                .map_err(|e| PyErr::new::<pyo3::exceptions::PyRuntimeError, _>(e.to_string()))?;
+            let sparse_h = SparseMatrix::from_dense(&dcm.check_matrix.view());
+            match decoder_type {
+                "bp_osd" => {
+                    let d = BpOsdDecoder::new(
+                        &sparse_h,
+                        None,
+                        Some(&dcm.error_priors),
+                        100,
+                        BpMethod::ProductSum,
+                        BpSchedule::Parallel,
+                        1.0,
+                        OsdMethod::Osd0,
+                        0,
+                        InputVectorType::Syndrome,
+                        None,
+                        None,
+                        None,
+                    )
+                    .map_err(|e| {
+                        PyErr::new::<pyo3::exceptions::PyRuntimeError, _>(e.to_string())
+                    })?;
+                    Ok(Box::new(CheckMatrixObservableDecoder::new(d, dcm)))
+                }
+                "bp_lsd" => {
+                    let d = BpLsdDecoder::new(
+                        &sparse_h,
+                        None,
+                        Some(&dcm.error_priors),
+                        100,
+                        BpMethod::ProductSum,
+                        BpSchedule::Parallel,
+                        1.0,
+                        OsdMethod::Off,
+                        0,
+                        0,
+                        InputVectorType::Syndrome,
+                        None,
+                        None,
+                        None,
+                    )
+                    .map_err(|e| {
+                        PyErr::new::<pyo3::exceptions::PyRuntimeError, _>(e.to_string())
+                    })?;
+                    Ok(Box::new(CheckMatrixObservableDecoder::new(d, dcm)))
+                }
+                "belief_find" => {
+                    let d = BeliefFindDecoder::new(
+                        &sparse_h,
+                        None,
+                        Some(&dcm.error_priors),
+                        100,
+                        BpMethod::ProductSum,
+                        1.0,
+                        BpSchedule::Parallel,
+                        None,
+                        None,
+                        None,
+                        UfMethod::Inversion,
+                        0,
+                    )
+                    .map_err(|e| {
+                        PyErr::new::<pyo3::exceptions::PyRuntimeError, _>(e.to_string())
+                    })?;
+                    Ok(Box::new(CheckMatrixObservableDecoder::new(d, dcm)))
+                }
+                "union_find" => {
+                    let d = UnionFindDecoder::new(&sparse_h, UfMethod::Inversion).map_err(|e| {
+                        PyErr::new::<pyo3::exceptions::PyRuntimeError, _>(e.to_string())
+                    })?;
+                    let llrs: Vec<f64> = dcm
+                        .error_priors
+                        .iter()
+                        .map(|&p| {
+                            if p > 0.0 && p < 1.0 {
+                                ((1.0 - p) / p).ln()
+                            } else {
+                                0.0
+                            }
+                        })
+                        .collect();
+                    Ok(Box::new(WeightedUfObservableDecoder {
+                        decoder: d,
+                        dcm,
+                        llrs,
+                    }))
+                }
+                "relay_bp" => {
+                    let h_view = dcm.check_matrix.view();
+                    let d = RelayBpBuilder::new(&h_view)
+                        .error_priors(&dcm.error_priors)
+                        .build()
+                        .map_err(|e| {
+                            PyErr::new::<pyo3::exceptions::PyRuntimeError, _>(e.to_string())
+                        })?;
+                    Ok(Box::new(CheckMatrixObservableDecoder::new(d, dcm)))
+                }
+                "min_sum_bp" => {
+                    let h_view = dcm.check_matrix.view();
+                    let d = MinSumBpBuilder::new(&h_view)
+                        .error_priors(&dcm.error_priors)
+                        .build()
+                        .map_err(|e| {
+                            PyErr::new::<pyo3::exceptions::PyRuntimeError, _>(e.to_string())
+                        })?;
+                    Ok(Box::new(CheckMatrixObservableDecoder::new(d, dcm)))
+                }
+                _ => unreachable!(),
+            }
+        }
+        // UF decoder: "pecos_uf" (fast), "pecos_uf:balanced", "pecos_uf:accurate"
+        // Also accepts legacy "pecos_uf_correlated" as alias for balanced.
+        "pecos_uf" | "pecos_uf:fast" => {
+            let d =
+                pecos_decoders::UfDecoder::from_dem(dem, pecos_decoders::UfDecoderConfig::fast())
+                    .map_err(|e| PyErr::new::<pyo3::exceptions::PyRuntimeError, _>(e.to_string()))?;
+            Ok(Box::new(d))
+        }
+        "pecos_uf:balanced" | "pecos_uf_correlated" => {
+            // Two-pass correlated UF: first pass identifies matched edges,
+            // correlation table adjusts weights, second pass re-decodes.
+            use pecos_decoder_core::DemMatchingGraph;
+            use pecos_decoder_core::correlation_table::CorrelationTable;
+            use pecos_decoder_core::two_pass_decoder::TwoPassDecoder;
+
+            let graph = DemMatchingGraph::from_dem_str(dem)
+                .map_err(|e| PyErr::new::<pyo3::exceptions::PyRuntimeError, _>(e.to_string()))?;
+
+            let mut edge_index_map = std::collections::BTreeMap::new();
+            let mut base_weights = Vec::with_capacity(graph.edges.len());
+            for (idx, edge) in graph.edges.iter().enumerate() {
+                base_weights.push(edge.weight);
+                let key = match edge.node2 {
+                    Some(n2) => {
+                        if edge.node1 <= n2 {
+                            (edge.node1, n2)
+                        } else {
+                            (n2, edge.node1)
+                        }
+                    }
+                    None => (edge.node1, u32::MAX),
+                };
+                edge_index_map.insert(key, idx);
+            }
 
-        self.inner.sample(&mut rng)
-    }
+            let corr_table =
+                CorrelationTable::from_dem_str(dem, &edge_index_map, graph.edges.len()).map_err(
+                    |e| PyErr::new::<pyo3::exceptions::PyRuntimeError, _>(e.to_string()),
+                )?;
+
+            let uf = pecos_decoders::UfDecoder::from_matching_graph(
+                &graph,
+                pecos_decoders::UfDecoderConfig::balanced(),
+            );
+            let two_pass = TwoPassDecoder::new(uf, base_weights, corr_table);
+            Ok(Box::new(two_pass))
+        }
+        "pecos_uf:bp" => {
+            // BP+UF hybrid: flooding BP (fast, good for d<=7).
+            let d =
+                pecos_decoders::BpUfDecoder::from_dem(dem, pecos_decoders::BpUfConfig::balanced())
+                    .map_err(|e| {
+                        PyErr::new::<pyo3::exceptions::PyRuntimeError, _>(e.to_string())
+                    })?;
+            Ok(Box::new(d))
+        }
+        "belief_matching_mgbp" => {
+            // Belief-matching with matching-graph BP (Hack et al. 2026 style).
+            // BP runs on the matching graph (simpler, better convergence)
+            // instead of the Tanner graph.
+            use pecos_decoder_core::DemMatchingGraph;
+            use pecos_decoder_core::bp_matching::BpMatchingDecoder;
+            use pecos_decoder_core::correlation_table::CorrelationTable;
+            use pecos_decoders::{FusionBlossomConfig, FusionBlossomDecoder};
+
+            let bp = pecos_decoders::BpUfDecoder::from_dem(
+                dem,
+                pecos_decoders::BpUfConfig::matching_bp(),
+            )
+            .map_err(|e| PyErr::new::<pyo3::exceptions::PyRuntimeError, _>(e.to_string()))?;
+
+            let graph = DemMatchingGraph::from_dem_str(dem)
+                .map_err(|e| PyErr::new::<pyo3::exceptions::PyRuntimeError, _>(e.to_string()))?;
+            let config = FusionBlossomConfig {
+                num_nodes: Some(graph.num_detectors),
+                num_observables: graph.num_observables,
+                ..Default::default()
+            };
+            let mut fb = FusionBlossomDecoder::new(config)
+                .map_err(|e| PyErr::new::<pyo3::exceptions::PyRuntimeError, _>(e.to_string()))?;
+            let mut edge_index_map = std::collections::BTreeMap::new();
+            for (idx, edge) in graph.edges.iter().enumerate() {
+                let obs: Vec<usize> = edge.observables.iter().map(|&o| o as usize).collect();
+                let key = if let Some(n2) = edge.node2 {
+                    fb.add_edge(edge.node1 as usize, n2 as usize, &obs, Some(edge.weight))
+                        .map_err(|e| {
+                            PyErr::new::<pyo3::exceptions::PyRuntimeError, _>(e.to_string())
+                        })?;
+                    if edge.node1 <= n2 {
+                        (edge.node1, n2)
+                    } else {
+                        (n2, edge.node1)
+                    }
+                } else {
+                    fb.add_boundary_edge(edge.node1 as usize, &obs, Some(edge.weight))
+                        .map_err(|e| {
+                            PyErr::new::<pyo3::exceptions::PyRuntimeError, _>(e.to_string())
+                        })?;
+                    (edge.node1, u32::MAX)
+                };
+                edge_index_map.insert(key, idx);
+            }
+            let corr_table =
+                CorrelationTable::from_dem_str(dem, &edge_index_map, graph.edges.len()).map_err(
+                    |e| PyErr::new::<pyo3::exceptions::PyRuntimeError, _>(e.to_string()),
+                )?;
+            Ok(Box::new(BpMatchingDecoder::with_correlations(
+                fb, bp, corr_table,
+            )))
+        }
+        "pecos_uf:bp_serial" => {
+            // BP+UF hybrid: serial BP (slower, maintains threshold at d=7-11+).
+            let d =
+                pecos_decoders::BpUfDecoder::from_dem(dem, pecos_decoders::BpUfConfig::accurate())
+                    .map_err(|e| {
+                        PyErr::new::<pyo3::exceptions::PyRuntimeError, _>(e.to_string())
+                    })?;
+            Ok(Box::new(d))
+        }
+        "belief_matching" => {
+            // Belief-matching: BP soft info → Fusion Blossom MWPM with dynamic weights.
+            // Achieves ~0.94% circuit-level threshold (Higgott 2022).
+            use pecos_decoder_core::DemMatchingGraph;
+            use pecos_decoder_core::bp_matching::BpMatchingDecoder;
+            use pecos_decoders::{FusionBlossomConfig, FusionBlossomDecoder};
+
+            // Build BP weight provider.
+            let bp =
+                pecos_decoders::BpUfDecoder::from_dem(dem, pecos_decoders::BpUfConfig::balanced())
+                    .map_err(|e| {
+                        PyErr::new::<pyo3::exceptions::PyRuntimeError, _>(e.to_string())
+                    })?;
+
+            // Build Fusion Blossom as the matching backend.
+            let graph = DemMatchingGraph::from_dem_str(dem)
+                .map_err(|e| PyErr::new::<pyo3::exceptions::PyRuntimeError, _>(e.to_string()))?;
+            let config = FusionBlossomConfig {
+                num_nodes: Some(graph.num_detectors),
+                num_observables: graph.num_observables,
+                ..Default::default()
+            };
+            let mut fb = FusionBlossomDecoder::new(config)
+                .map_err(|e| PyErr::new::<pyo3::exceptions::PyRuntimeError, _>(e.to_string()))?;
+            for edge in &graph.edges {
+                let obs: Vec<usize> = edge.observables.iter().map(|&o| o as usize).collect();
+                match edge.node2 {
+                    Some(n2) => {
+                        fb.add_edge(edge.node1 as usize, n2 as usize, &obs, Some(edge.weight))
+                            .map_err(|e| {
+                                PyErr::new::<pyo3::exceptions::PyRuntimeError, _>(e.to_string())
+                            })?;
+                    }
+                    None => {
+                        fb.add_boundary_edge(edge.node1 as usize, &obs, Some(edge.weight))
+                            .map_err(|e| {
+                                PyErr::new::<pyo3::exceptions::PyRuntimeError, _>(e.to_string())
+                            })?;
+                    }
+                }
+            }
 
-    /// Sample multiple shots of measurement outcomes.
-    ///
-    /// Args:
-    ///     `num_shots`: Number of shots to sample.
-    ///     seed: Optional random seed for reproducibility.
-    ///
-    /// Returns:
-    ///     List of lists, where each inner list contains boolean measurement outcomes.
-    #[pyo3(signature = (num_shots, seed=None))]
-    fn sample_batch(&self, num_shots: usize, seed: Option<u64>) -> Vec<Vec<bool>> {
-        use pecos_random::PecosRng;
-        use rand::RngExt;
+            Ok(Box::new(BpMatchingDecoder::new(fb, bp)))
+        }
+        "belief_matching_correlated" => {
+            // Correlated belief-matching: BP + correlation table + Fusion Blossom MWPM.
+            // Two-pass: BP weights → MWPM → correlation adjustment → MWPM.
+            // Combines BP soft info with X-Z cross-lattice correlations.
+            use pecos_decoder_core::DemMatchingGraph;
+            use pecos_decoder_core::bp_matching::BpMatchingDecoder;
+            use pecos_decoder_core::correlation_table::CorrelationTable;
+            use pecos_decoders::{FusionBlossomConfig, FusionBlossomDecoder};
+
+            let bp =
+                pecos_decoders::BpUfDecoder::from_dem(dem, pecos_decoders::BpUfConfig::balanced())
+                    .map_err(|e| {
+                        PyErr::new::<pyo3::exceptions::PyRuntimeError, _>(e.to_string())
+                    })?;
+
+            let graph = DemMatchingGraph::from_dem_str(dem)
+                .map_err(|e| PyErr::new::<pyo3::exceptions::PyRuntimeError, _>(e.to_string()))?;
+
+            // Build Fusion Blossom.
+            let config = FusionBlossomConfig {
+                num_nodes: Some(graph.num_detectors),
+                num_observables: graph.num_observables,
+                ..Default::default()
+            };
+            let mut fb = FusionBlossomDecoder::new(config)
+                .map_err(|e| PyErr::new::<pyo3::exceptions::PyRuntimeError, _>(e.to_string()))?;
+
+            let mut edge_index_map = std::collections::BTreeMap::new();
+            for (idx, edge) in graph.edges.iter().enumerate() {
+                let obs: Vec<usize> = edge.observables.iter().map(|&o| o as usize).collect();
+                let key = if let Some(n2) = edge.node2 {
+                    fb.add_edge(edge.node1 as usize, n2 as usize, &obs, Some(edge.weight))
+                        .map_err(|e| {
+                            PyErr::new::<pyo3::exceptions::PyRuntimeError, _>(e.to_string())
+                        })?;
+                    if edge.node1 <= n2 {
+                        (edge.node1, n2)
+                    } else {
+                        (n2, edge.node1)
+                    }
+                } else {
+                    fb.add_boundary_edge(edge.node1 as usize, &obs, Some(edge.weight))
+                        .map_err(|e| {
+                            PyErr::new::<pyo3::exceptions::PyRuntimeError, _>(e.to_string())
+                        })?;
+                    (edge.node1, u32::MAX)
+                };
+                edge_index_map.insert(key, idx);
+            }
 
-        let mut rng = match seed {
-            Some(s) => PecosRng::seed_from_u64(s),
-            None => PecosRng::seed_from_u64(rand::rng().random()),
-        };
+            // Build correlation table from decomposed DEM.
+            let corr_table =
+                CorrelationTable::from_dem_str(dem, &edge_index_map, graph.edges.len()).map_err(
+                    |e| PyErr::new::<pyo3::exceptions::PyRuntimeError, _>(e.to_string()),
+                )?;
 
-        (0..num_shots)
-            .map(|_| self.inner.sample(&mut rng))
-            .collect()
-    }
+            Ok(Box::new(BpMatchingDecoder::with_correlations(
+                fb, bp, corr_table,
+            )))
+        }
+        s if s.starts_with("belief_matching_hybrid:") => {
+            // Hybrid correlated belief-matching: non-decomposed DEM for BP,
+            // decomposed DEM for matching graph + correlations.
+            // Format: "belief_matching_hybrid:<full_dem_string>"
+            // The main `dem` param is the decomposed DEM.
+            use pecos_decoder_core::DemMatchingGraph;
+            use pecos_decoder_core::bp_matching::BpMatchingDecoder;
+            use pecos_decoder_core::correlation_table::CorrelationTable;
+            use pecos_decoders::{FusionBlossomConfig, FusionBlossomDecoder};
+
+            let full_dem = &s["belief_matching_hybrid:".len()..];
+
+            // BP uses non-decomposed DEM, matching uses decomposed.
+            let bp = pecos_decoders::BpUfDecoder::from_dual_dem(
+                full_dem,
+                dem,
+                pecos_decoders::BpUfConfig::balanced(),
+            )
+            .map_err(|e| PyErr::new::<pyo3::exceptions::PyRuntimeError, _>(e.to_string()))?;
+
+            // Build Fusion Blossom from decomposed DEM.
+            let graph = DemMatchingGraph::from_dem_str(dem)
+                .map_err(|e| PyErr::new::<pyo3::exceptions::PyRuntimeError, _>(e.to_string()))?;
+            let config = FusionBlossomConfig {
+                num_nodes: Some(graph.num_detectors),
+                num_observables: graph.num_observables,
+                ..Default::default()
+            };
+            let mut fb = FusionBlossomDecoder::new(config)
+                .map_err(|e| PyErr::new::<pyo3::exceptions::PyRuntimeError, _>(e.to_string()))?;
+            let mut edge_index_map = std::collections::BTreeMap::new();
+            for (idx, edge) in graph.edges.iter().enumerate() {
+                let obs: Vec<usize> = edge.observables.iter().map(|&o| o as usize).collect();
+                let key = if let Some(n2) = edge.node2 {
+                    fb.add_edge(edge.node1 as usize, n2 as usize, &obs, Some(edge.weight))
+                        .map_err(|e| {
+                            PyErr::new::<pyo3::exceptions::PyRuntimeError, _>(e.to_string())
+                        })?;
+                    if edge.node1 <= n2 {
+                        (edge.node1, n2)
+                    } else {
+                        (n2, edge.node1)
+                    }
+                } else {
+                    fb.add_boundary_edge(edge.node1 as usize, &obs, Some(edge.weight))
+                        .map_err(|e| {
+                            PyErr::new::<pyo3::exceptions::PyRuntimeError, _>(e.to_string())
+                        })?;
+                    (edge.node1, u32::MAX)
+                };
+                edge_index_map.insert(key, idx);
+            }
+            let corr_table =
+                CorrelationTable::from_dem_str(dem, &edge_index_map, graph.edges.len()).map_err(
+                    |e| PyErr::new::<pyo3::exceptions::PyRuntimeError, _>(e.to_string()),
+                )?;
+
+            Ok(Box::new(BpMatchingDecoder::with_correlations(
+                fb, bp, corr_table,
+            )))
+        }
+        s if s.starts_with("windowed") => {
+            // Windowed decoder: "windowed" or "windowed:step=N,buf=M,inner=TYPE,mode=MODE"
+            // inner= takes the REST of the string (supports nested specs with commas).
+            let mut config = pecos_decoders::WindowedConfig::default();
+            let mut inner_type = "pecos_uf".to_string();
+            let mut mode = String::new();
+            if let Some(params) = s.strip_prefix("windowed:") {
+                // Split inner= from the rest: "step=5,buf=5,inner=perturbed:K=7,sigma=0.5"
+                // → params before inner, inner spec
+                let (own_params, inner_spec) = if let Some(idx) = params.find(",inner=") {
+                    (&params[..idx], Some(&params[idx + 7..]))
+                } else if let Some(idx) = params.find("inner=") {
+                    (&params[..idx.saturating_sub(1)], Some(&params[idx + 6..]))
+                } else {
+                    (params, None)
+                };
+                if let Some(spec) = inner_spec {
+                    inner_type = spec.to_string();
+                }
+                for kv in own_params.split(',') {
+                    let parts: Vec<&str> = kv.splitn(2, '=').collect();
+                    if parts.len() == 2 {
+                        match parts[0] {
+                            "step" => config.step_size = parts[1].parse().unwrap_or(0),
+                            "buf" | "buffer" => config.buffer_size = parts[1].parse().unwrap_or(0),
+                            "mode" => mode = parts[1].to_string(),
+                            "seam" => config.seam_half_width = parts[1].parse().unwrap_or(0),
+                            "ext" | "core_extend" => {
+                                config.core_extend = parts[1].parse().unwrap_or(0);
+                            }
+                            "wmax" | "commit_weight_max" => {
+                                config.commit_weight_max = parts[1].parse().unwrap_or(0.0);
+                            }
+                            _ => {}
+                        }
+                    }
+                }
+            }
 
-    /// Get all mechanisms and their probabilities.
-    ///
-    /// Returns:
-    ///     List of (measurements, probability) tuples.
-    fn get_mechanisms(&self) -> Vec<(Vec<u32>, f64)> {
-        self.inner
+            if mode == "sandwich" || (mode.is_empty() && config.buffer_size > 0) {
+                // Sandwich decoder (two-phase): best accuracy with buf > 0.
+                // Default: buf=step, wmax=2.5, PM residual decoder.
+                if config.buffer_size == 0 {
+                    config.buffer_size = config.step_size;
+                }
+                if config.commit_weight_max == 0.0 {
+                    config.commit_weight_max = 2.5;
+                }
+                let phase2_type = if inner_type == "pecos_uf" {
+                    "pymatching".to_string()
+                } else {
+                    inner_type.clone()
+                };
+                let phase1_factory = |sub_dem: &str| -> Result<
+                    pecos_decoders::UfDecoder,
+                    pecos_decoders::DecoderError,
+                > {
+                    pecos_decoders::UfDecoder::from_dem(
+                        sub_dem,
+                        pecos_decoders::UfDecoderConfig::windowed(),
+                    )
+                };
+                let phase2_factory = |sub_dem: &str| -> Result<
+                    Box<dyn pecos_decoders::ObservableDecoder>,
+                    pecos_decoders::DecoderError,
+                > {
+                    create_observable_decoder(sub_dem, &phase2_type)
+                        .map_err(|e| pecos_decoders::DecoderError::InternalError(e.to_string()))
+                };
+                let dec = pecos_decoders::SandwichWindowedDecoder::from_dem(
+                    dem,
+                    config,
+                    phase1_factory,
+                    phase2_factory,
+                )
+                .map_err(|e| PyErr::new::<pyo3::exceptions::PyRuntimeError, _>(e.to_string()))?;
+                Ok(Box::new(dec))
+            } else if mode == "overlap" {
+                // Single-phase overlapping (UF by default).
+                let factory = |sub_dem: &str| -> Result<
+                    pecos_decoders::UfDecoder,
+                    pecos_decoders::DecoderError,
+                > {
+                    pecos_decoders::UfDecoder::from_dem(
+                        sub_dem,
+                        pecos_decoders::UfDecoderConfig::windowed(),
+                    )
+                };
+                let dec =
+                    pecos_decoders::OverlappingWindowedDecoder::from_dem(dem, config, factory)
+                        .map_err(|e| {
+                            PyErr::new::<pyo3::exceptions::PyRuntimeError, _>(e.to_string())
+                        })?;
+                Ok(Box::new(dec))
+            } else {
+                // Non-overlapping with pluggable inner decoder.
+                let factory = |sub_dem: &str| -> Result<
+                    Box<dyn pecos_decoders::ObservableDecoder>,
+                    pecos_decoders::DecoderError,
+                > {
+                    create_observable_decoder(sub_dem, &inner_type)
+                        .map_err(|e| pecos_decoders::DecoderError::InternalError(e.to_string()))
+                };
+                let dec = pecos_decoders::WindowedDecoder::from_dem(dem, config, factory).map_err(
+                    |e| PyErr::new::<pyo3::exceptions::PyRuntimeError, _>(e.to_string()),
+                )?;
+                Ok(Box::new(dec))
+            }
+        }
+        "pecos_uf:accurate" => {
+            // UIUF CSS-aware mode. Single-DEM path falls back to balanced.
+            // For proper UIUF, use CssUfDecoder directly with separate X/Z DEMs
+            // via the PyCssUfDecoder Python class.
+            create_observable_decoder(dem, "pecos_uf:balanced")
+        }
+        "mwpf" => {
+            let d =
+                pecos_decoders::MwpfDecoder::from_dem(dem, pecos_decoders::MwpfConfig::default())
+                    .map_err(|e| PyErr::new::<pyo3::exceptions::PyRuntimeError, _>(e.to_string()))?;
+            Ok(Box::new(d))
+        }
+        s if s.starts_with("mwpf:") => {
+            // Parse "mwpf:key=val,key=val" config overrides.
+            // Keys: c/cluster_node_limit, t/timeout, once/only_solve_primal_once, solver
+            let mut config = pecos_decoders::MwpfConfig::default();
+            for kv in s[5..].split(',') {
+                let parts: Vec<&str> = kv.splitn(2, '=').collect();
+                if parts.len() != 2 {
+                    continue;
+                }
+                match parts[0] {
+                    "c" | "cluster_node_limit" => {
+                        config.cluster_node_limit = parts[1].parse().unwrap_or(50);
+                    }
+                    "t" | "timeout" => {
+                        config.timeout = parts[1].parse().ok();
+                    }
+                    "once" | "only_solve_primal_once" => {
+                        config.only_solve_primal_once = parts[1] == "true" || parts[1] == "1";
+                    }
+                    "solver" => {
+                        config.solver_type = match parts[1] {
+                            "uf" | "union_find" => pecos_decoders::MwpfSolverType::UnionFind,
+                            "sh" | "single_hair" => pecos_decoders::MwpfSolverType::SingleHair,
+                            "bp" | "bp_hybrid" => pecos_decoders::MwpfSolverType::BpHybrid,
+                            _ => pecos_decoders::MwpfSolverType::JointSingleHair,
+                        };
+                    }
+                    _ => {}
+                }
+            }
+            let d = pecos_decoders::MwpfDecoder::from_dem(dem, config)
+                .map_err(|e| PyErr::new::<pyo3::exceptions::PyRuntimeError, _>(e.to_string()))?;
+            Ok(Box::new(d))
+        }
+        s if s.starts_with("perturbed") => {
+            // Perturbed-weight ensemble: "perturbed" or "perturbed:K=15,sigma=0.7,inner=TYPE"
+            // inner= takes the REST of the string (supports nested decoder specs).
+            use pecos_decoder_core::perturbed::{PerturbedConfig, build_perturbed_ensemble};
+
+            let mut config = PerturbedConfig::default();
+            let mut inner_type = "pymatching".to_string();
+            if let Some(params) = s.strip_prefix("perturbed:") {
+                // Extract inner= (takes rest of string for nesting support)
+                let (own_params, inner_spec) = if let Some(idx) = params.find(",inner=") {
+                    (&params[..idx], Some(&params[idx + 7..]))
+                } else if let Some(idx) = params.find("inner=") {
+                    (&params[..idx.saturating_sub(1)], Some(&params[idx + 6..]))
+                } else {
+                    (params, None)
+                };
+                if let Some(spec) = inner_spec {
+                    inner_type = spec.to_string();
+                }
+                for kv in own_params.split(',') {
+                    let parts: Vec<&str> = kv.splitn(2, '=').collect();
+                    if parts.len() == 2 {
+                        match parts[0] {
+                            "K" | "k" => config.k = parts[1].parse().unwrap_or(15),
+                            "sigma" | "s" => config.sigma = parts[1].parse().unwrap_or(0.7),
+                            "seed" => config.seed = parts[1].parse().unwrap_or(42),
+                            _ => {}
+                        }
+                    }
+                }
+            }
+
+            let ensemble = build_perturbed_ensemble(dem, &config, |sub_dem| {
+                create_observable_decoder(sub_dem, &inner_type)
+                    .map_err(|e| pecos_decoders::DecoderError::InternalError(e.to_string()))
+            })
+            .map_err(|e| PyErr::new::<pyo3::exceptions::PyRuntimeError, _>(e.to_string()))?;
+
+            Ok(Box::new(ensemble))
+        }
+        s if s.starts_with("beamsearch") => {
+            // Beam search windowed decoder: "beamsearch" or "beamsearch:K=5,sigma=0.5,buf=5"
+            let mut config = pecos_decoders::BeamSearchConfig::default();
+            if let Some(params) = s.strip_prefix("beamsearch:") {
+                for kv in params.split(',') {
+                    let parts: Vec<&str> = kv.splitn(2, '=').collect();
+                    if parts.len() == 2 {
+                        match parts[0] {
+                            "K" | "k" => config.beam_width = parts[1].parse().unwrap_or(5),
+                            "sigma" | "s" => {
+                                config.perturbation_sigma = parts[1].parse().unwrap_or(0.5);
+                            }
+                            "seed" => config.seed = parts[1].parse().unwrap_or(42),
+                            "step" => config.window.step_size = parts[1].parse().unwrap_or(0),
+                            "buf" | "buffer" => {
+                                config.window.buffer_size = parts[1].parse().unwrap_or(0);
+                            }
+                            "wmax" => {
+                                config.window.commit_weight_max = parts[1].parse().unwrap_or(0.0);
+                            }
+                            _ => {}
+                        }
+                    }
+                }
+            }
+            // Match sandwich defaults: buf=step, wmax=2.5.
+            // When step=0 (auto), buf also needs to be auto. Set buf=5 as a
+            // reasonable default (will be auto-tuned by parse_dem_params).
+            if config.window.buffer_size == 0 {
+                if config.window.step_size > 0 {
+                    config.window.buffer_size = config.window.step_size;
+                } else {
+                    config.window.buffer_size = 5; // auto: will be refined by d_est
+                }
+            }
+            if config.window.commit_weight_max == 0.0 {
+                config.window.commit_weight_max = 2.5;
+            }
+
+            let phase1_factory = |sub_dem: &str| -> Result<
+                pecos_decoders::UfDecoder,
+                pecos_decoders::DecoderError,
+            > {
+                pecos_decoders::UfDecoder::from_dem(
+                    sub_dem,
+                    pecos_decoders::UfDecoderConfig::windowed(),
+                )
+            };
+            let phase2_factory = |sub_dem: &str| -> Result<
+                Box<dyn pecos_decoders::ObservableDecoder>,
+                pecos_decoders::DecoderError,
+            > {
+                create_observable_decoder(sub_dem, "pymatching")
+                    .map_err(|e| pecos_decoders::DecoderError::InternalError(e.to_string()))
+            };
+            let dec = pecos_decoders::BeamSearchWindowedDecoder::from_dem(
+                dem,
+                config,
+                phase1_factory,
+                Some(phase2_factory),
+            )
+            .map_err(|e| PyErr::new::<pyo3::exceptions::PyRuntimeError, _>(e.to_string()))?;
+            Ok(Box::new(dec))
+        }
+        s if s.starts_with("ensemble:") => {
+            // Parse "ensemble:dec1,dec2,dec3" -- create multiple decoders and vote.
+            use pecos_decoder_core::ensemble::EnsembleDecoder;
+            let members_str = &s[9..];
+            let mut members: Vec<Box<dyn pecos_decoders::ObservableDecoder>> = Vec::new();
+            for spec in members_str.split(',') {
+                let spec = spec.trim();
+                if spec.is_empty() {
+                    continue;
+                }
+                members.push(create_observable_decoder(dem, spec)?);
+            }
+            if members.is_empty() {
+                return Err(PyErr::new::<pyo3::exceptions::PyValueError, _>(
+                    "ensemble: needs at least one decoder",
+                ));
+            }
+            Ok(Box::new(EnsembleDecoder::new(members)))
+        }
+        // Per-observable subgraph decoder: requires stab_coords from Python.
+        // This is NOT callable from the string-based create_observable_decoder API.
+        // Use the Python ObservableSubgraphDecoder class directly instead.
+        s if s == "observable_subgraph" || s.starts_with("observable_subgraph:") => {
+            Err(PyErr::new::<pyo3::exceptions::PyValueError, _>(
+                "observable_subgraph decoder requires stab_coords. \
+                 Use pecos_rslib.qec.ObservableSubgraphDecoder class directly.",
+            ))
+        }
+        _ => Err(PyErr::new::<pyo3::exceptions::PyValueError, _>(format!(
+            "Unsupported decoder_type: {decoder_type}. \
+             Supported: pymatching, tesseract, mwpf, pecos_uf (or pecos_uf:fast/balanced/accurate), \
+             observable_subgraph, ensemble:d1,d2,..., bp_osd, bp_lsd, union_find, relay_bp, min_sum_bp."
+        ))),
+    }
+}
+
+/// Pre-generated sample batch held in Rust memory.
+///
+/// Created by `DemSampler.generate_samples()`. Can be decoded by multiple
+/// decoders without re-sampling, and without crossing the Rust/Python boundary
+/// per shot.
+///
+/// # Example
+///
+/// ```python
+/// samples = sampler.generate_samples(10000, seed=42)
+/// pm_errors = samples.decode_count(dem, "pymatching")
+/// ts_errors = samples.decode_count(dem, "tesseract")
+/// # Both decoders ran on the exact same samples.
+/// ```
+#[pyclass(name = "SampleBatch", module = "pecos_rslib.qec")]
+pub struct PySampleBatch {
+    /// Columnar bit-packed detector columns: det_columns[det_idx][word_idx]
+    det_columns: Vec<Vec<u64>>,
+    /// Columnar bit-packed observable columns: obs_columns[obs_idx][word_idx]
+    obs_columns: Vec<Vec<u64>>,
+    num_detectors: usize,
+    num_shots: usize,
+}
+
+impl PySampleBatch {
+    /// Extract syndrome for one shot into a pre-allocated buffer.
+    fn extract_syndrome(&self, shot: usize, buf: &mut [u8]) {
+        buf.fill(0);
+        let word_idx = shot / 64;
+        let bit_mask = 1u64 << (shot % 64);
+        for (det_idx, col) in self.det_columns.iter().enumerate() {
+            if col[word_idx] & bit_mask != 0 {
+                buf[det_idx] = 1;
+            }
+        }
+    }
+
+    /// Extract observable mask for one shot.
+    fn extract_obs_mask(&self, shot: usize) -> u64 {
+        let word_idx = shot / 64;
+        let bit_mask = 1u64 << (shot % 64);
+        let mut mask = 0u64;
+        for (obs_idx, col) in self.obs_columns.iter().enumerate() {
+            if col[word_idx] & bit_mask != 0 {
+                mask |= 1u64 << obs_idx;
+            }
+        }
+        mask
+    }
+
+    /// Build from columnar data (from generate_samples).
+    fn from_columnar(
+        det_columns: Vec<Vec<u64>>,
+        obs_columns: Vec<Vec<u64>>,
+        num_shots: usize,
+    ) -> Self {
+        let num_detectors = det_columns.len();
+        Self {
+            det_columns,
+            obs_columns,
+            num_detectors,
+            num_shots,
+        }
+    }
+
+    /// Build from row-major data (from Python constructor).
+    fn from_row_major(detection_events: Vec<Vec<u8>>, observable_masks: Vec<u64>) -> Self {
+        let num_shots = detection_events.len();
+        let num_detectors = detection_events.first().map_or(0, Vec::len);
+        let num_words = num_shots.div_ceil(64);
+
+        // Convert row-major → columnar
+        let mut det_columns = vec![vec![0u64; num_words]; num_detectors];
+        for (shot, row) in detection_events.iter().enumerate() {
+            let word_idx = shot / 64;
+            let bit_mask = 1u64 << (shot % 64);
+            for (det_idx, &val) in row.iter().enumerate() {
+                if val != 0 {
+                    det_columns[det_idx][word_idx] |= bit_mask;
+                }
+            }
+        }
+
+        // Find max observable index
+        let max_obs = observable_masks
             .iter()
-            .map(|(m, &p)| (m.measurements.to_vec(), p))
-            .collect()
+            .map(|m| 64 - m.leading_zeros() as usize)
+            .max()
+            .unwrap_or(0);
+        let mut obs_columns = vec![vec![0u64; num_words]; max_obs];
+        for (shot, &mask) in observable_masks.iter().enumerate() {
+            let word_idx = shot / 64;
+            let bit_mask = 1u64 << (shot % 64);
+            for (obs_idx, obs_column) in obs_columns.iter_mut().enumerate().take(max_obs) {
+                if mask & (1u64 << obs_idx) != 0 {
+                    obs_column[word_idx] |= bit_mask;
+                }
+            }
+        }
+
+        Self {
+            det_columns,
+            obs_columns,
+            num_detectors,
+            num_shots,
+        }
     }
+}
 
-    /// Convert measurement outcomes to detection events.
+#[pymethods]
+impl PySampleBatch {
+    /// Build a SampleBatch from detection event arrays and observable masks.
     ///
-    /// Given raw measurement outcomes and detector definitions, computes which
-    /// detectors fire by XOR'ing the specified measurement records for each detector.
+    /// Args:
+    ///     detection_events: List of syndromes, each a list of u8 (0/1).
+    ///     observable_masks: List of u64 true observable flip masks.
+    #[new]
+    #[pyo3(signature = (detection_events, observable_masks))]
+    fn new(detection_events: Vec<Vec<u8>>, observable_masks: Vec<u64>) -> PyResult<Self> {
+        if detection_events.len() != observable_masks.len() {
+            return Err(pyo3::exceptions::PyValueError::new_err(format!(
+                "detection_events ({}) and observable_masks ({}) must have same length",
+                detection_events.len(),
+                observable_masks.len(),
+            )));
+        }
+        let expected_len = detection_events.first().map_or(0, Vec::len);
+        for (i, row) in detection_events.iter().enumerate() {
+            if row.len() != expected_len {
+                return Err(pyo3::exceptions::PyValueError::new_err(format!(
+                    "detection_events row {i} has length {} but expected {expected_len} \
+                     (matching row 0)",
+                    row.len()
+                )));
+            }
+        }
+        Ok(Self::from_row_major(detection_events, observable_masks))
+    }
+
+    /// Number of shots in this batch.
+    #[getter]
+    fn num_shots(&self) -> usize {
+        self.num_shots
+    }
+
+    /// Get the syndrome for shot `i` as a list of u8 values.
+    fn get_syndrome(&self, i: usize) -> PyResult<Vec<u8>> {
+        if i >= self.num_shots {
+            return Err(PyErr::new::<pyo3::exceptions::PyIndexError, _>(format!(
+                "Shot index {i} out of range (num_shots={})",
+                self.num_shots
+            )));
+        }
+        let mut buf = vec![0u8; self.num_detectors];
+        self.extract_syndrome(i, &mut buf);
+        Ok(buf)
+    }
+
+    /// Get the expected observable mask for shot `i`.
+    fn get_observable_mask(&self, i: usize) -> PyResult<u64> {
+        if i >= self.num_shots {
+            return Err(PyErr::new::<pyo3::exceptions::PyIndexError, _>(format!(
+                "Shot index {i} out of range (num_shots={})",
+                self.num_shots
+            )));
+        }
+        Ok(self.extract_obs_mask(i))
+    }
+
+    /// Decode all samples with the given decoder type and return the error count.
     ///
-    /// If measurement order was provided when building the MNM, outcomes are first
-    /// reordered from influence map order to `TickCircuit` order before applying
-    /// detector records.
+    /// This runs entirely in Rust -- no per-shot Python crossing.
     ///
     /// Args:
-    ///     outcomes: List of boolean measurement outcomes (from `sample()`).
-    ///     `detectors_json`: JSON string with detector definitions.
-    ///         Format: [{"id": 0, "records": [-1, -5]}, ...]
-    ///         Public surface descriptors using "`detector_id`" are also accepted.
-    ///         Records are negative offsets from end of measurement list.
+    ///     dem: DEM string in standard DEM text format for the decoder.
+    ///     `decoder_type`: "pymatching", "tesseract", "`bp_osd`", "`bp_lsd`", "`union_find`",
+    ///                   "`relay_bp`", or "`min_sum_bp`".
     ///
     /// Returns:
-    ///     List of boolean detection events (True = detector fired).
-    ///
-    /// Example:
-    ///     >>> outcomes = `mnm.sample()`
-    ///     >>> `detection_events` = `mnm.to_detection_events(outcomes`, `detectors_json`)
-    fn to_detection_events(
-        &self,
-        outcomes: Vec<bool>,
-        detectors_json: &str,
-    ) -> PyResult<Vec<bool>> {
-        let detector_records = parse_detector_records(detectors_json)?;
-        // Use instance method which applies im_to_tc reordering if set
-        Ok(self
-            .inner
-            .compute_detection_events(&outcomes, &detector_records))
+    ///     Number of logical errors.
+    #[pyo3(signature = (dem, decoder_type="pymatching"))]
+    fn decode_count(&self, dem: &str, decoder_type: &str) -> PyResult<usize> {
+        let mut decoder = create_observable_decoder(dem, decoder_type)?;
+        let mut errors = 0usize;
+        let mut syndrome = vec![0u8; self.num_detectors];
+        for i in 0..self.num_shots {
+            self.extract_syndrome(i, &mut syndrome);
+            let predicted = decoder.decode_to_observables(&syndrome).unwrap_or(u64::MAX);
+            if predicted != self.extract_obs_mask(i) {
+                errors += 1;
+            }
+        }
+        Ok(errors)
     }
 
-    /// Sample and convert to detection events in one step.
+    /// Parallel decode: distributes samples across rayon workers.
     ///
-    /// This is a convenience method that combines `sample()` and `to_detection_events()`.
+    /// Each worker creates its own decoder instance. Faster for slow decoders.
     ///
     /// Args:
-    ///     `detectors_json`: JSON string with detector definitions.
-    ///     seed: Optional random seed for reproducibility.
+    ///     dem: DEM string for the decoder.
+    ///     `decoder_type`: Decoder type string.
+    ///     `num_workers`: Number of parallel workers (default: number of CPUs).
     ///
     /// Returns:
-    ///     Tuple of (`measurement_outcomes`, `detection_events`).
-    #[pyo3(signature = (detectors_json, seed=None))]
-    fn sample_with_detectors(
+    ///     Number of logical errors.
+    #[pyo3(signature = (dem, decoder_type="pymatching", num_workers=None))]
+    fn decode_count_parallel(
         &self,
-        detectors_json: &str,
-        seed: Option<u64>,
-    ) -> PyResult<(Vec<bool>, Vec<bool>)> {
-        use pecos_random::PecosRng;
-        use rand::RngExt;
-
-        let detector_records = parse_detector_records(detectors_json)?;
-
-        let mut rng = match seed {
-            Some(s) => PecosRng::seed_from_u64(s),
-            None => PecosRng::seed_from_u64(rand::rng().random()),
-        };
+        dem: &str,
+        decoder_type: &str,
+        num_workers: Option<usize>,
+    ) -> PyResult<usize> {
+        use rayon::prelude::*;
+
+        let n_workers = num_workers.unwrap_or_else(rayon::current_num_threads);
+        let pool = rayon::ThreadPoolBuilder::new()
+            .num_threads(n_workers)
+            .build()
+            .map_err(|e| PyErr::new::<pyo3::exceptions::PyRuntimeError, _>(e.to_string()))?;
+
+        let dem_str = dem.to_string();
+        let dt = decoder_type.to_string();
+        let n = self.num_shots;
+        let num_dets = self.num_detectors;
+
+        // Materialize row-major data for parallel decode.
+        let detection_events: Vec<Vec<u8>> = (0..n)
+            .map(|i| {
+                let mut s = vec![0u8; num_dets];
+                self.extract_syndrome(i, &mut s);
+                s
+            })
+            .collect();
+        let observable_masks: Vec<u64> = (0..n).map(|i| self.extract_obs_mask(i)).collect();
+
+        let total_errors: usize = pool.install(|| {
+            (0..n)
+                .into_par_iter()
+                .map_init(
+                    || create_observable_decoder(&dem_str, &dt).unwrap(),
+                    |decoder, i| {
+                        let predicted = decoder
+                            .decode_to_observables(&detection_events[i])
+                            .unwrap_or(u64::MAX);
+                        usize::from(predicted != observable_masks[i])
+                    },
+                )
+                .sum()
+        });
 
-        let (outcomes, detection_events) = self
-            .inner
-            .sample_with_detectors(&detector_records, &mut rng);
-        Ok((outcomes, detection_events))
+        Ok(total_errors)
     }
 
-    /// Sample multiple shots and convert to detection events.
+    /// Batch decode all samples at once using `PyMatching`'s batch API.
     ///
-    /// Args:
-    ///     `num_shots`: Number of shots to sample.
-    ///     `detectors_json`: JSON string with detector definitions.
-    ///     seed: Optional random seed for reproducibility.
+    /// Sends all detection events in a single flat array to the decoder,
+    /// which can vectorize across shots. Faster than per-shot decode for
+    /// `PyMatching`. Only supports pymatching decoder.
     ///
     /// Returns:
-    ///     List of (`measurement_outcomes`, `detection_events`) tuples.
-    #[pyo3(signature = (num_shots, detectors_json, seed=None))]
-    fn sample_batch_with_detectors(
-        &self,
-        num_shots: usize,
-        detectors_json: &str,
-        seed: Option<u64>,
-    ) -> PyResult<Vec<(Vec<bool>, Vec<bool>)>> {
-        use pecos_random::PecosRng;
-        use rand::RngExt;
-
-        let detector_records = parse_detector_records(detectors_json)?;
+    ///     Number of logical errors.
+    #[pyo3(signature = (dem))]
+    fn decode_count_batch(&self, dem: &str) -> PyResult<usize> {
+        use pecos_decoders::{BatchConfig, PyMatchingDecoder};
+
+        let mut decoder = PyMatchingDecoder::from_dem(dem)
+            .map_err(|e| PyErr::new::<pyo3::exceptions::PyRuntimeError, _>(e.to_string()))?;
+
+        let num_detectors = decoder.num_detectors();
+
+        // Flatten all detection events into a single contiguous array
+        let mut flat = Vec::with_capacity(self.num_shots * num_detectors);
+        let mut syndrome = vec![0u8; self.num_detectors];
+        for i in 0..self.num_shots {
+            self.extract_syndrome(i, &mut syndrome);
+            // Pad or truncate to decoder's num_detectors
+            let take = syndrome.len().min(num_detectors);
+            flat.extend_from_slice(&syndrome[..take]);
+            flat.extend(std::iter::repeat_n(0, num_detectors - take));
+        }
 
-        let mut rng = match seed {
-            Some(s) => PecosRng::seed_from_u64(s),
-            None => PecosRng::seed_from_u64(rand::rng().random()),
+        let config = BatchConfig {
+            bit_packed_input: false,
+            bit_packed_output: false,
+            return_weights: false,
         };
 
-        let results: Vec<_> = (0..num_shots)
-            .map(|_| {
-                self.inner
-                    .sample_with_detectors(&detector_records, &mut rng)
-            })
-            .collect();
+        let result = decoder
+            .decode_batch_with_config(&flat, self.num_shots, num_detectors, config)
+            .map_err(|e| PyErr::new::<pyo3::exceptions::PyRuntimeError, _>(e.to_string()))?;
+
+        // Count errors by comparing predictions to true observable masks
+        let num_observables = decoder.num_observables();
+        let mut num_errors = 0usize;
+        for (i, prediction) in result.predictions.iter().enumerate() {
+            let mut predicted_mask = 0u64;
+            for (j, &v) in prediction.iter().enumerate() {
+                if v != 0 && j < num_observables {
+                    predicted_mask |= 1 << j;
+                }
+            }
+            if predicted_mask != self.extract_obs_mask(i) {
+                num_errors += 1;
+            }
+        }
 
-        Ok(results)
+        Ok(num_errors)
     }
 
-    /// Sample for threshold estimation with both detection events and observable flips.
+    /// Decode all samples and collect per-shot timing statistics.
     ///
-    /// This matches Stim's DEM sampler output format, returning the information
-    /// needed for decoding and logical error rate computation.
+    /// Returns a `DecodeStats` with error count, total time, median, and
+    /// percentile per-shot decode times. Useful for understanding decoder
+    /// performance characteristics (heavy tails, etc.).
     ///
     /// Args:
-    ///     `detectors_json`: JSON string with detector definitions.
-    ///     `observables_json`: JSON string with observable definitions.
-    ///     seed: Optional random seed for reproducibility.
+    ///     dem: DEM string for the decoder.
+    ///     `decoder_type`: Decoder type string.
     ///
     /// Returns:
-    ///     Tuple of (`detection_events`, `observable_flips`).
-    #[pyo3(signature = (detectors_json, observables_json, seed=None))]
-    fn sample_for_decoding(
-        &self,
-        detectors_json: &str,
-        observables_json: &str,
-        seed: Option<u64>,
-    ) -> PyResult<(Vec<bool>, Vec<bool>)> {
-        use pecos_random::PecosRng;
-        use rand::RngExt;
-
-        let detector_records = parse_detector_records(detectors_json)?;
-        let observable_records = parse_observable_records(observables_json)?;
-
-        let mut rng = match seed {
-            Some(s) => PecosRng::seed_from_u64(s),
-            None => PecosRng::seed_from_u64(rand::rng().random()),
-        };
+    ///     `DecodeStats` with timing breakdown.
+    #[pyo3(signature = (dem, decoder_type="pymatching"))]
+    fn decode_stats(&self, dem: &str, decoder_type: &str) -> PyResult<PyDecodeStats> {
+        use std::time::Instant;
+
+        let mut decoder = create_observable_decoder(dem, decoder_type)?;
+        let mut num_errors = 0usize;
+        let mut per_shot_seconds: Vec<f64> = Vec::with_capacity(self.num_shots);
+        let mut syndrome = vec![0u8; self.num_detectors];
+
+        for i in 0..self.num_shots {
+            self.extract_syndrome(i, &mut syndrome);
+            let t0 = Instant::now();
+            let predicted = decoder.decode_to_observables(&syndrome).unwrap_or(u64::MAX);
+            let elapsed = t0.elapsed().as_secs_f64();
+            per_shot_seconds.push(elapsed);
+            if predicted != self.extract_obs_mask(i) {
+                num_errors += 1;
+            }
+        }
 
-        let (detection_events, observable_flips) =
-            self.inner
-                .sample_for_decoding(&detector_records, &observable_records, &mut rng);
-        Ok((detection_events, observable_flips))
+        Ok(PyDecodeStats::from_times(
+            self.num_shots,
+            num_errors,
+            per_shot_seconds,
+        ))
     }
 
-    /// Batch sample for threshold estimation.
+    /// Decode all shots with per-shot timing, using parallel workers.
     ///
-    /// Efficiently samples multiple shots, returning detection events and observable
-    /// flips for each shot. This is the PECOS native alternative to Stim's DEM sampler.
+    /// Like `decode_stats` but distributes shots across rayon threads.
+    /// Useful for slow decoders (MWPF, Tesseract, BP+OSD) where a single
+    /// shot can take seconds.
     ///
-    /// Args:
-    ///     `num_shots`: Number of shots to sample.
-    ///     `detectors_json`: JSON string with detector definitions.
-    ///     `observables_json`: JSON string with observable definitions.
-    ///     seed: Optional random seed for reproducibility.
+    /// Per-shot timing is still collected (each worker times its own shots).
+    /// The total wall-clock time is approximately `serial_total / num_workers`.
     ///
-    /// Returns:
-    ///     Tuple of (`detection_events_per_shot`, `observable_flips_per_shot`) as numpy-compatible lists.
-    #[pyo3(signature = (num_shots, detectors_json, observables_json, seed=None))]
-    fn sample_batch_for_decoding(
+    /// Args:
+    ///     dem: DEM string for the decoder.
+    ///     `decoder_type`: Decoder type string.
+    ///     `num_workers`: Number of parallel workers (default: number of CPUs).
+    #[pyo3(signature = (dem, decoder_type="mwpf", num_workers=None))]
+    fn decode_stats_parallel(
         &self,
-        num_shots: usize,
-        detectors_json: &str,
-        observables_json: &str,
-        seed: Option<u64>,
-    ) -> PyResult<BatchSampleResult> {
-        use pecos_random::PecosRng;
-        use rand::RngExt;
+        dem: &str,
+        decoder_type: &str,
+        num_workers: Option<usize>,
+    ) -> PyResult<PyDecodeStats> {
+        use rayon::prelude::*;
+
+        let n_workers = num_workers.unwrap_or_else(rayon::current_num_threads);
+
+        // Validate decoder type early.
+        create_observable_decoder(dem, decoder_type)?;
+
+        let pool = rayon::ThreadPoolBuilder::new()
+            .num_threads(n_workers)
+            .build()
+            .map_err(|e| PyErr::new::<pyo3::exceptions::PyRuntimeError, _>(e.to_string()))?;
+
+        let dem_str = dem.to_string();
+        let dt = decoder_type.to_string();
+        let num_dets = self.num_detectors;
+
+        // Materialize row-major data for parallel decode.
+        let detection_events: Vec<Vec<u8>> = (0..self.num_shots)
+            .map(|i| {
+                let mut s = vec![0u8; num_dets];
+                self.extract_syndrome(i, &mut s);
+                s
+            })
+            .collect();
+        let observable_masks: Vec<u64> = (0..self.num_shots)
+            .map(|i| self.extract_obs_mask(i))
+            .collect();
 
-        let detector_records = parse_detector_records(detectors_json)?;
-        let observable_records = parse_observable_records(observables_json)?;
+        // Each worker decodes a slice of shots and returns (errors, per_shot_times).
+        let results: Vec<(usize, Vec<f64>)> = pool.install(|| {
+            let chunk_size = self.num_shots.div_ceil(n_workers);
+            (0..n_workers)
+                .into_par_iter()
+                .map(|worker_id| {
+                    let start = worker_id * chunk_size;
+                    let end = (start + chunk_size).min(self.num_shots);
+                    if start >= end {
+                        return (0, Vec::new());
+                    }
 
-        let mut rng = match seed {
-            Some(s) => PecosRng::seed_from_u64(s),
-            None => PecosRng::seed_from_u64(rand::rng().random()),
-        };
+                    let mut decoder = create_observable_decoder(&dem_str, &dt).unwrap();
+                    let mut errors = 0usize;
+                    let mut times = Vec::with_capacity(end - start);
+
+                    for i in start..end {
+                        let t0 = std::time::Instant::now();
+                        let predicted = decoder
+                            .decode_to_observables(&detection_events[i])
+                            .unwrap_or(u64::MAX);
+                        times.push(t0.elapsed().as_secs_f64());
+                        if predicted != observable_masks[i] {
+                            errors += 1;
+                        }
+                    }
+                    (errors, times)
+                })
+                .collect()
+        });
 
-        let (all_detection_events, all_observable_flips) = self.inner.sample_batch_for_decoding(
-            num_shots,
-            &detector_records,
-            &observable_records,
-            &mut rng,
-        );
+        let mut total_errors = 0usize;
+        let mut all_times = Vec::with_capacity(self.num_shots);
+        for (errs, times) in results {
+            total_errors += errs;
+            all_times.extend(times);
+        }
 
-        Ok((all_detection_events, all_observable_flips))
+        Ok(PyDecodeStats::from_times(
+            self.num_shots,
+            total_errors,
+            all_times,
+        ))
     }
 
     fn __repr__(&self) -> String {
-        format!(
-            "MeasurementNoiseModel(mechanisms={}, measurements={})",
-            self.num_mechanisms(),
-            self.num_measurements()
-        )
+        format!("SampleBatch(num_shots={})", self.num_shots)
     }
 }
 
-// =============================================================================
-// Noisy Sampler (DEM-style sampling)
-// =============================================================================
-
-/// Fast noisy sampler for threshold estimation.
-///
-/// This is essentially a DEM sampler - it samples fault locations and uses
-/// the influence map to determine detector and logical effects. This is the
-/// recommended approach for threshold estimation as it directly samples
-/// detector flips and observable flips without intermediate steps.
-///
-/// Two modes are supported:
-/// - Uniform noise: Same error probability at all locations (fast)
-/// - Circuit-level noise: Per-gate-type probabilities (p1, p2, `p_meas`, `p_init`)
-///
-/// # Example
-///
-/// ```python
-/// from pecos_rslib.qec import DagFaultAnalyzer, NoisySampler
-///
-/// # Build influence map
-/// analyzer = DagFaultAnalyzer(dag)
-/// influence_map = analyzer.build_influence_map()
-///
-/// # Uniform noise (simple)
-/// sampler = NoisySampler(influence_map, p_error=0.01, seed=42)
-///
-/// # Circuit-level noise (accurate)
-/// sampler = NoisySampler.with_circuit_noise(
-///     influence_map, p1=0.001, p2=0.01, p_meas=0.01, p_init=0.001, seed=42
-/// )
-///
-/// # Sample for threshold estimation
-/// det_events, obs_flips = sampler.sample_batch(num_shots=10000)
-/// ```
-#[pyclass(name = "NoisySampler", module = "pecos_rslib.qec")]
-pub struct PyNoisySampler {
-    /// Owned influence map (cloned from input).
-    influence_map: RustDagFaultInfluenceMap,
-    /// Per-location error probabilities (for circuit-level noise).
-    per_location_probs: Vec<f64>,
-    /// RNG seed.
-    seed: u64,
+/// Per-shot decode timing statistics.
+#[pyclass(name = "DecodeStats", module = "pecos_rslib.qec", skip_from_py_object)]
+#[derive(Clone)]
+pub struct PyDecodeStats {
+    #[pyo3(get)]
+    pub num_shots: usize,
+    #[pyo3(get)]
+    pub num_errors: usize,
+    #[pyo3(get)]
+    pub logical_error_rate: f64,
+    #[pyo3(get)]
+    pub total_seconds: f64,
+    #[pyo3(get)]
+    pub per_shot_mean: f64,
+    #[pyo3(get)]
+    pub per_shot_median: f64,
+    #[pyo3(get)]
+    pub per_shot_p99: f64,
+    #[pyo3(get)]
+    pub per_shot_min: f64,
+    #[pyo3(get)]
+    pub per_shot_max: f64,
+    /// Quantile summary for distribution visualization (violin plots).
+    /// 21 values at percentiles [0, 5, 10, 15, ..., 90, 95, 100].
+    #[pyo3(get)]
+    pub quantiles: Vec<f64>,
 }
 
-#[pymethods]
-impl PyNoisySampler {
-    /// Create a new noisy sampler with uniform error probability.
-    ///
-    /// Args:
-    ///     `influence_map`: A `DagFaultInfluenceMap` from `DagFaultAnalyzer` or `InfluenceBuilder`.
-    ///     `p_error`: Uniform depolarizing error probability per fault location.
-    ///     seed: Random seed for reproducibility.
-    #[new]
-    #[pyo3(signature = (influence_map, p_error, seed=None))]
-    fn new(influence_map: &PyDagFaultInfluenceMap, p_error: f64, seed: Option<u64>) -> Self {
-        use rand::RngExt;
-        let actual_seed = seed.unwrap_or_else(|| rand::rng().random());
-        let num_locations = influence_map.inner.locations.len();
-        Self {
-            influence_map: influence_map.inner.clone(),
-            per_location_probs: vec![p_error; num_locations],
-            seed: actual_seed,
-        }
-    }
+impl PyDecodeStats {
+    // Shot counts and error counts are well within f64 mantissa range (2^52).
+    // Percentile index computation is bounded by array length.
+    #[allow(
+        clippy::cast_precision_loss,
+        clippy::cast_possible_truncation,
+        clippy::cast_sign_loss
+    )]
+    fn from_times(num_shots: usize, num_errors: usize, mut times: Vec<f64>) -> Self {
+        let total_seconds: f64 = times.iter().sum();
+        let per_shot_mean = if num_shots > 0 {
+            total_seconds / num_shots as f64
+        } else {
+            0.0
+        };
 
-    /// Create a sampler with circuit-level noise (different rates per gate type).
-    ///
-    /// This matches the noise model used by `DemBuilder` and Stim, with different
-    /// error probabilities for different gate types.
-    ///
-    /// Args:
-    ///     `influence_map`: A `DagFaultInfluenceMap` from `DagFaultAnalyzer` or `InfluenceBuilder`.
-    ///     p1: Single-qubit gate error probability.
-    ///     p2: Two-qubit gate error probability.
-    ///     `p_meas`: Measurement error probability.
-    ///     `p_init`: Initialization/prep error probability.
-    ///     seed: Random seed for reproducibility.
-    #[staticmethod]
-    #[pyo3(signature = (influence_map, p1, p2, p_meas, p_init, seed=None))]
-    fn with_circuit_noise(
-        influence_map: &PyDagFaultInfluenceMap,
-        p1: f64,
-        p2: f64,
-        p_meas: f64,
-        p_init: f64,
-        seed: Option<u64>,
-    ) -> Self {
-        use pecos_core::gate_type::GateType;
-        use rand::RngExt;
+        times.sort_by(|a, b| a.partial_cmp(b).unwrap_or(std::cmp::Ordering::Equal));
 
-        let actual_seed = seed.unwrap_or_else(|| rand::rng().random());
+        let percentile = |p: f64| -> f64 {
+            if times.is_empty() {
+                return 0.0;
+            }
+            let idx = (p / 100.0 * (times.len() - 1) as f64).round() as usize;
+            times[idx.min(times.len() - 1)]
+        };
 
-        // Build per-location probabilities based on gate type
-        let per_location_probs: Vec<f64> = influence_map
-            .inner
-            .locations
-            .iter()
-            .map(|loc| {
-                #[allow(clippy::match_same_arms)] // Explicitly list known single-qubit gates
-                match loc.gate_type {
-                    GateType::PZ | GateType::QAlloc => p_init,
-                    GateType::MZ | GateType::MeasureFree => p_meas,
-                    GateType::CX | GateType::CZ | GateType::CY | GateType::SWAP => p2,
-                    GateType::H
-                    | GateType::SZ
-                    | GateType::SZdg
-                    | GateType::SX
-                    | GateType::SXdg
-                    | GateType::SY
-                    | GateType::SYdg
-                    | GateType::X
-                    | GateType::Y
-                    | GateType::Z
-                    | GateType::T
-                    | GateType::Tdg => p1,
-                    _ => p1, // Default to p1 for unknown gates
-                }
-            })
-            .collect();
+        // 21 quantiles at [0, 5, 10, ..., 95, 100] for violin plots
+        let quantiles: Vec<f64> = (0..=20).map(|i| percentile(f64::from(i) * 5.0)).collect();
 
         Self {
-            influence_map: influence_map.inner.clone(),
-            per_location_probs,
-            seed: actual_seed,
+            num_shots,
+            num_errors,
+            logical_error_rate: if num_shots > 0 {
+                num_errors as f64 / num_shots as f64
+            } else {
+                0.0
+            },
+            total_seconds,
+            per_shot_mean,
+            per_shot_median: percentile(50.0),
+            per_shot_p99: percentile(99.0),
+            per_shot_min: times.first().copied().unwrap_or(0.0),
+            per_shot_max: times.last().copied().unwrap_or(0.0),
+            quantiles,
         }
     }
+}
 
-    /// Sample a single shot.
-    ///
-    /// Returns:
-    ///     Tuple of (`detector_flips`, `logical_flips`) where each is a list of
-    ///     indices that flipped.
-    fn sample_one(&mut self) -> (Vec<u32>, Vec<u32>) {
-        use pecos_qec::fault_tolerance::noisy_sampler::{NoisySampler, PerLocationNoiseModel};
-
-        let noise_model = PerLocationNoiseModel::new(self.per_location_probs.clone());
-        let mut sampler = NoisySampler::new(&self.influence_map, noise_model, self.seed);
-        let result = sampler.sample_one();
-        // Update seed for next call
-        self.seed = self.seed.wrapping_add(1);
-        (result.detector_flips, result.logical_flips)
+#[pymethods]
+impl PyDecodeStats {
+    fn __repr__(&self) -> String {
+        format!(
+            "DecodeStats(shots={}, errors={}, LER={:.4}, median={:.2e}s, p99={:.2e}s, max={:.2e}s)",
+            self.num_shots,
+            self.num_errors,
+            self.logical_error_rate,
+            self.per_shot_median,
+            self.per_shot_p99,
+            self.per_shot_max,
+        )
     }
+}
+
+#[pyclass(name = "DemSampler", module = "pecos_rslib.qec")]
+pub struct PyDemSampler {
+    inner: RustNewDemSampler,
+}
 
-    /// Sample multiple shots and return as arrays suitable for decoding.
+#[pymethods]
+impl PyDemSampler {
+    /// Build a sampler directly from a circuit and noise parameters.
     ///
-    /// This is the main method for threshold estimation. Returns detection
-    /// events and observable flips in the same format as Stim's DEM sampler.
+    /// This is the simplest path: builds the influence map, extracts
+    /// annotations, and configures the sampler in one step.
     ///
     /// Args:
-    ///     `num_shots`: Number of shots to sample.
+    ///     circuit: A `DagCircuit` with gates and annotations.
+    ///     p1: Single-qubit depolarizing error rate.
+    ///     p2: Two-qubit depolarizing error rate.
+    ///     `p_meas`: Measurement error rate.
+    ///     `p_prep`: Initialization error rate.
+    ///     `p_idle`: Optional idle noise rate per time unit.
     ///
-    /// Returns:
-    ///     Tuple of (`detection_events`, `observable_flips`) where:
-    ///     - `detection_events`: List of lists, each inner list contains bool per detector
-    ///     - `observable_flips`: List of lists, each inner list contains bool per observable
-    fn sample_batch(&mut self, num_shots: usize) -> (Vec<Vec<bool>>, Vec<Vec<bool>>) {
-        use pecos_qec::fault_tolerance::noisy_sampler::{NoisySampler, PerLocationNoiseModel};
-
-        let noise_model = PerLocationNoiseModel::new(self.per_location_probs.clone());
-        let mut sampler = NoisySampler::new(&self.influence_map, noise_model, self.seed);
-        let num_detectors = self.influence_map.detectors.len();
-        let num_logicals = self
-            .influence_map
-            .influences
-            .max_logical_index()
-            .map_or(1, |i| i + 1);
-
-        let mut all_det_events = Vec::with_capacity(num_shots);
-        let mut all_obs_flips = Vec::with_capacity(num_shots);
-
-        for _ in 0..num_shots {
-            let result = sampler.sample_one();
-
-            // Convert sparse detector flips to dense bool array
-            let mut det_events = vec![false; num_detectors];
-            for &idx in &result.detector_flips {
-                if (idx as usize) < num_detectors {
-                    det_events[idx as usize] = true;
-                }
-            }
-
-            // Convert sparse logical flips to dense bool array
-            let mut obs_flips = vec![false; num_logicals];
-            for &idx in &result.logical_flips {
-                if (idx as usize) < num_logicals {
-                    obs_flips[idx as usize] = true;
-                }
-            }
-
-            all_det_events.push(det_events);
-            all_obs_flips.push(obs_flips);
+    /// Example:
+    ///     >>> sampler = DemSampler.from_circuit(dag, p1=0.001, p2=0.01)
+    ///     >>> sampler = DemSampler.from_circuit(tc, p2=0.01)  # TickCircuit also works
+    #[staticmethod]
+    #[pyo3(signature = (circuit, p1=0.001, p2=0.01, p_meas=0.001, p_prep=0.001, p_idle=None, idle_rz=None))]
+    fn from_circuit(
+        circuit: &Bound<'_, pyo3::PyAny>,
+        p1: f64,
+        p2: f64,
+        p_meas: f64,
+        p_prep: f64,
+        p_idle: Option<f64>,
+        idle_rz: Option<f64>,
+    ) -> PyResult<Self> {
+        let mut noise = NoiseConfig::new(p1, p2, p_meas, p_prep);
+        noise.p_idle = p_idle.unwrap_or(0.0);
+        if let Some(rz) = idle_rz {
+            noise = noise.set_idle_rz(rz);
         }
 
-        // Update seed for reproducibility of subsequent calls
-        self.seed = self.seed.wrapping_add(num_shots as u64);
-
-        (all_det_events, all_obs_flips)
-    }
-
-    /// Sample and compute statistics directly in Rust.
-    ///
-    /// This is more efficient than sampling and processing in Python
-    /// when you only need aggregate statistics.
-    ///
-    /// Args:
-    ///     `num_shots`: Number of shots to sample.
-    ///
-    /// Returns:
-    ///     Dictionary with statistics:
-    ///     - `total_shots`: Number of shots
-    ///     - `logical_error_count`: Shots with logical errors
-    ///     - `syndrome_count`: Shots with non-trivial syndrome
-    ///     - `undetectable_count`: Shots with undetectable logical errors
-    ///     - `logical_error_rate`: Fraction with logical errors
-    ///     - `syndrome_rate`: Fraction with syndromes
-    fn sample_statistics(
-        &mut self,
-        num_shots: usize,
-        py: Python<'_>,
-    ) -> PyResult<Py<pyo3::types::PyDict>> {
-        use pecos_qec::fault_tolerance::noisy_sampler::{NoisySampler, PerLocationNoiseModel};
-
-        let noise_model = PerLocationNoiseModel::new(self.per_location_probs.clone());
-        let mut sampler = NoisySampler::new(&self.influence_map, noise_model, self.seed);
-        let stats = sampler.sample_statistics(num_shots);
-
-        // Update seed
-        self.seed = self.seed.wrapping_add(num_shots as u64);
-
-        let dict = pyo3::types::PyDict::new(py);
-        dict.set_item("total_shots", stats.total_shots)?;
-        dict.set_item("logical_error_count", stats.logical_error_count)?;
-        dict.set_item("syndrome_count", stats.syndrome_count)?;
-        dict.set_item("undetectable_count", stats.undetectable_count)?;
-        dict.set_item("logical_error_rate", stats.logical_error_rate())?;
-        dict.set_item("syndrome_rate", stats.syndrome_rate())?;
-        dict.set_item("undetectable_rate", stats.undetectable_rate())?;
-        dict.set_item("average_faults", stats.average_faults())?;
-        Ok(dict.unbind())
-    }
-
-    /// Number of fault locations.
-    #[getter]
-    fn num_locations(&self) -> usize {
-        self.influence_map.locations.len()
-    }
-
-    /// Number of detectors.
-    #[getter]
-    fn num_detectors(&self) -> usize {
-        self.influence_map.detectors.len()
-    }
-
-    /// Number of logical observables.
-    #[getter]
-    fn num_logicals(&self) -> usize {
-        self.influence_map
-            .influences
-            .max_logical_index()
-            .map_or(1, |i| i + 1)
+        // Accept both DagCircuit and TickCircuit
+        if let Ok(dag) =
+            circuit.extract::<pyo3::PyRef<'_, crate::dag_circuit_bindings::PyDagCircuit>>()
+        {
+            let inner = RustNewDemSampler::from_circuit(&dag.inner, &noise)
+                .map_err(|e| pyo3::exceptions::PyValueError::new_err(e.to_string()))?;
+            Ok(Self { inner })
+        } else if let Ok(tc) =
+            circuit.extract::<pyo3::PyRef<'_, crate::dag_circuit_bindings::PyTickCircuit>>()
+        {
+            let inner = RustNewDemSampler::from_tick_circuit(&tc.inner, &noise)
+                .map_err(|e| pyo3::exceptions::PyValueError::new_err(e.to_string()))?;
+            Ok(Self { inner })
+        } else {
+            Err(pyo3::exceptions::PyTypeError::new_err(
+                "from_circuit() expects a DagCircuit or TickCircuit",
+            ))
+        }
     }
 
-    /// Sample with explicit detector and observable definitions.
-    ///
-    /// This combines `NoisySampler`'s fast per-location sampling with explicit
-    /// detector/observable definitions (like MNM uses). This gives the best of
-    /// both worlds: fast Rust-side sampling with Stim-compatible output.
+    /// Create a sampler from a standard DEM-format string.
     ///
-    /// Args:
-    ///     `num_shots`: Number of shots to sample.
-    ///     `detectors_json`: JSON string with detector definitions.
-    ///     `observables_json`: JSON string with observable definitions.
-    ///     `measurement_order`: Optional list of qubit indices in `TickCircuit` measurement
-    ///         execution order. Required when detector definitions use `TickCircuit`
-    ///         measurement indices but the influence map uses a different ordering.
-    ///         measurement_order[i] is the qubit measured at `TickCircuit` index i.
+    /// Parses `error(p) D0 D3 L0` lines and builds a sampling engine.
+    /// Useful for sampling from DEMs produced by EEG analysis.
     ///
-    /// Returns:
-    ///     Tuple of (`detection_events`, `observable_flips`) matching Stim's format.
-    #[pyo3(signature = (num_shots, detectors_json, observables_json, measurement_order=None))]
-    fn sample_with_definitions(
-        &mut self,
-        num_shots: usize,
-        detectors_json: &str,
-        observables_json: &str,
-        measurement_order: Option<Vec<usize>>,
-    ) -> PyResult<BatchSampleResult> {
-        use pecos_qec::fault_tolerance::noisy_sampler::{NoisySampler, PerLocationNoiseModel};
-        use std::collections::HashMap;
-
-        let detector_records = parse_detector_records(detectors_json)?;
-        let observable_records = parse_observable_records(observables_json)?;
-
-        let noise_model = PerLocationNoiseModel::new(self.per_location_probs.clone());
-        let mut sampler = NoisySampler::new(&self.influence_map, noise_model, self.seed);
-        let num_im_measurements = self.influence_map.detectors.len();
-
-        // Build mapping from influence map indices to TickCircuit indices if measurement_order provided
-        let im_to_tc: Option<Vec<usize>> = measurement_order.as_ref().map(|tc_order| {
-            // Build (qubit, occurrence) -> TC index mapping
-            let mut qubit_occurrences: HashMap<usize, Vec<usize>> = HashMap::new();
-            for (tc_idx, &qubit) in tc_order.iter().enumerate() {
-                qubit_occurrences.entry(qubit).or_default().push(tc_idx);
+    /// Example:
+    ///     >>> from pecos_rslib_exp import eeg_heisenberg_dem
+    ///     >>> dem_str = eeg_heisenberg_dem(tc, idle_rz=0.05)
+    ///     >>> sampler = DemSampler.from_dem_string(dem_str)
+    ///     >>> results = sampler.sample_batch(shots=1000000)
+    #[staticmethod]
+    #[pyo3(signature = (dem_string))]
+    fn from_dem_string(dem_string: &str) -> PyResult<Self> {
+        use pecos_qec::fault_tolerance::dem_builder::SamplingEngine;
+
+        let mut mechanisms = Vec::new();
+        let mut max_det = 0u32;
+        let mut max_obs = 0u32;
+
+        for line in dem_string.lines() {
+            let line = line.trim();
+            if line.is_empty() || line.starts_with('#') {
+                continue;
             }
 
-            // Track how many times we've seen each qubit in the IM
-            let mut qubit_seen_count: HashMap<usize, usize> = HashMap::new();
-
-            // For each IM measurement, find corresponding TC index
-            self.influence_map
-                .measurements
-                .iter()
-                .map(|&(_node, qubit, _basis)| {
-                    let occurrence = *qubit_seen_count.entry(qubit).or_insert(0);
-                    qubit_seen_count.insert(qubit, occurrence + 1);
-
-                    // Get the TC index for this qubit's nth occurrence
-                    qubit_occurrences
-                        .get(&qubit)
-                        .and_then(|indices| indices.get(occurrence).copied())
-                        .unwrap_or(usize::MAX)
-                })
-                .collect()
-        });
-
-        let num_tc_measurements = measurement_order
-            .as_ref()
-            .map_or(num_im_measurements, std::vec::Vec::len);
-
-        let mut all_det_events = Vec::with_capacity(num_shots);
-        let mut all_obs_flips = Vec::with_capacity(num_shots);
-
-        for _ in 0..num_shots {
-            let result = sampler.sample_one();
-
-            // Convert sparse IM measurement flips to dense TC measurement array
-            let mut meas_outcomes = vec![false; num_tc_measurements];
-
-            if let Some(ref mapping) = im_to_tc {
-                // Reorder from IM order to TC order
-                for &im_idx in &result.detector_flips {
-                    let im_idx = im_idx as usize;
-                    if im_idx < mapping.len() {
-                        let tc_idx = mapping[im_idx];
-                        if tc_idx < num_tc_measurements {
-                            meas_outcomes[tc_idx] = !meas_outcomes[tc_idx];
-                        }
-                    }
-                }
-            } else {
-                // No reordering needed
-                for &idx in &result.detector_flips {
-                    if (idx as usize) < num_tc_measurements {
-                        meas_outcomes[idx as usize] = true;
-                    }
+            // Parse: error(prob) D0 D3 L0
+            let Some(rest) = line.strip_prefix("error(") else {
+                continue;
+            };
+            let Some(paren_end) = rest.find(')') else {
+                continue;
+            };
+            let prob: f64 = rest[..paren_end].parse().map_err(|e| {
+                pyo3::exceptions::PyValueError::new_err(format!("bad probability: {e}"))
+            })?;
+            let tokens = rest[paren_end + 1..].split_whitespace();
+            let mut dets = Vec::new();
+            let mut obs = Vec::new();
+            for tok in tokens {
+                if let Some(d) = tok.strip_prefix('D') {
+                    let id: u32 = d.parse().map_err(|e| {
+                        pyo3::exceptions::PyValueError::new_err(format!("bad detector: {e}"))
+                    })?;
+                    dets.push(id);
+                    max_det = max_det.max(id + 1);
+                } else if let Some(l) = tok.strip_prefix('L') {
+                    let id: u32 = l.parse().map_err(|e| {
+                        pyo3::exceptions::PyValueError::new_err(format!("bad observable: {e}"))
+                    })?;
+                    obs.push(id);
+                    max_obs = max_obs.max(id + 1);
                 }
             }
-
-            // Apply detector definitions (XOR of measurement outcomes)
-            let det_events: Vec<bool> = detector_records
-                .iter()
-                .map(|records| {
-                    let mut fired = false;
-                    for &offset in records {
-                        if let Some(abs_idx) =
-                            record_offset_to_absolute_index(num_tc_measurements, offset)
-                            && abs_idx < num_tc_measurements
-                            && meas_outcomes[abs_idx]
-                        {
-                            fired = !fired;
-                        }
-                    }
-                    fired
-                })
-                .collect();
-
-            // Apply observable definitions
-            let obs_flips: Vec<bool> = observable_records
-                .iter()
-                .map(|records| {
-                    let mut flipped = false;
-                    for &offset in records {
-                        if let Some(abs_idx) =
-                            record_offset_to_absolute_index(num_tc_measurements, offset)
-                            && abs_idx < num_tc_measurements
-                            && meas_outcomes[abs_idx]
-                        {
-                            flipped = !flipped;
-                        }
-                    }
-                    flipped
-                })
-                .collect();
-
-            all_det_events.push(det_events);
-            all_obs_flips.push(obs_flips);
+            if prob > 0.0 {
+                mechanisms.push((prob, dets, obs));
+            }
         }
 
-        self.seed = self.seed.wrapping_add(num_shots as u64);
-        Ok((all_det_events, all_obs_flips))
+        let engine =
+            SamplingEngine::from_mechanisms(mechanisms, max_det as usize, max_obs as usize);
+        let inner = RustNewDemSampler::from_engine(engine);
+        Ok(Self { inner })
     }
 
-    fn __repr__(&self) -> String {
-        format!(
-            "NoisySampler(locations={}, detectors={}, logicals={})",
-            self.num_locations(),
-            self.num_detectors(),
-            self.num_logicals(),
-        )
+    /// Create a sampler in raw measurement mode with uniform noise.
+    #[staticmethod]
+    #[pyo3(signature = (influence_map, p_error))]
+    fn raw_uniform(influence_map: &PyDagFaultInfluenceMap, p_error: f64) -> PyResult<Self> {
+        Self::from_influence_map(influence_map, p_error)
     }
-}
-
-// =============================================================================
-// MNM Builder
-// =============================================================================
-
-/// Builder for Measurement Noise Models (MNMs).
-///
-/// Constructs a MNM from a fault influence map. The MNM aggregates fault locations
-/// by their measurement effects (which measurements flip), enabling fast approximate
-/// sampling.
-///
-/// # Comparison with DEM
-///
-/// | Aspect | DEM | MNM |
-/// |--------|-----|-----|
-/// | Maps to | Detectors | Measurements |
-/// | Use case | Decoding | Sampling |
-/// | Aggregates by | Detector signature | Measurement signature |
-/// | Output | Stim-compatible DEM | Raw measurement outcomes |
-///
-/// # Example
-///
-/// ```python
-/// from pecos_rslib.qec import DagFaultAnalyzer, MemBuilder
-///
-/// # Build influence map
-/// analyzer = DagFaultAnalyzer(dag)
-/// influence_map = analyzer.build_influence_map()
-///
-/// # Build MNM for fast sampling
-/// mnm = MemBuilder(influence_map).with_noise(0.01, 0.01, 0.01, 0.01).build()
-///
-/// # Sample many shots quickly
-/// for _ in range(10000):
-///     outcomes = mnm.sample()
-/// ```
-#[pyclass(name = "MemBuilder", module = "pecos_rslib.qec")]
-pub struct PyMemBuilder {
-    influence_map: RustDagFaultInfluenceMap,
-    p1: f64,
-    p2: f64,
-    p_meas: f64,
-    p_init: f64,
-    /// Measurement order from original circuit (list of qubits in measurement order).
-    measurement_order: Option<Vec<usize>>,
-}
 
-#[pymethods]
-impl PyMemBuilder {
-    /// Create a new MNM builder from a fault influence map.
-    ///
-    /// Args:
-    ///     `influence_map`: A `DagFaultInfluenceMap` from `DagFaultAnalyzer`.
-    #[new]
-    fn new(influence_map: &PyDagFaultInfluenceMap) -> Self {
-        Self {
-            influence_map: influence_map.inner.clone(),
-            p1: 0.01,
-            p2: 0.01,
-            p_meas: 0.01,
-            p_init: 0.01,
-            measurement_order: None,
-        }
+    /// Create a sampler in raw measurement mode with circuit-level noise.
+    #[staticmethod]
+    #[pyo3(signature = (influence_map, p1, p2, p_meas, p_prep))]
+    fn raw(
+        influence_map: &PyDagFaultInfluenceMap,
+        p1: f64,
+        p2: f64,
+        p_meas: f64,
+        p_prep: f64,
+    ) -> PyResult<Self> {
+        Self::from_influence_map_circuit_noise(influence_map, p1, p2, p_meas, p_prep)
     }
 
-    /// Set the noise parameters.
-    ///
-    /// Args:
-    ///     p1: Single-qubit depolarizing error rate.
-    ///     p2: Two-qubit depolarizing error rate.
-    ///     `p_meas`: Measurement error rate.
-    ///     `p_init`: Initialization (prep) error rate.
+    /// Create a sampler in detector-event mode.
     ///
-    /// Returns:
-    ///     Self for method chaining.
-    fn with_noise(
-        mut slf: PyRefMut<'_, Self>,
+    /// The `observables` argument defines observables.
+    #[staticmethod]
+    #[pyo3(signature = (influence_map, detectors, observables, p1, p2, p_meas, p_prep, p_idle=None, t1=None, t2=None))]
+    #[allow(clippy::too_many_arguments)]
+    fn with_detectors(
+        influence_map: &PyDagFaultInfluenceMap,
+        detectors: Vec<Vec<i32>>,
+        observables: Vec<Vec<i32>>,
         p1: f64,
         p2: f64,
         p_meas: f64,
-        p_init: f64,
-    ) -> PyRefMut<'_, Self> {
-        slf.p1 = p1;
-        slf.p2 = p2;
-        slf.p_meas = p_meas;
-        slf.p_init = p_init;
-        slf
+        p_prep: f64,
+        p_idle: Option<f64>,
+        t1: Option<f64>,
+        t2: Option<f64>,
+    ) -> PyResult<Self> {
+        let mut noise = NoiseConfig::new(p1, p2, p_meas, p_prep);
+        noise.p_idle = p_idle.unwrap_or(0.0);
+        if let (Some(t1_val), Some(t2_val)) = (t1, t2) {
+            noise = noise.set_t1_t2(t1_val, t2_val);
+        }
+        let inner = RustNewDemSamplerBuilder::new(&influence_map.inner)
+            .with_noise_config(noise)
+            .with_detectors(detectors, observables)
+            .build()
+            .map_err(|e| pyo3::exceptions::PyValueError::new_err(e.to_string()))?;
+        Ok(Self { inner })
     }
 
-    /// Set the measurement order from the original circuit (e.g., `TickCircuit`).
-    ///
-    /// This is needed when detector definitions use `TickCircuit` measurement indices
-    /// but the influence map uses a different ordering based on DAG topology.
+    /// Create a sampler directly from an influence map with uniform noise.
     ///
     /// Args:
-    ///     order: List of qubit indices in measurement execution order.
-    ///            order[i] is the qubit measured at `TickCircuit` measurement index i.
-    ///
-    /// Returns:
-    ///     Self for method chaining.
-    fn with_measurement_order(
-        mut slf: PyRefMut<'_, Self>,
-        order: Vec<usize>,
-    ) -> PyRefMut<'_, Self> {
-        slf.measurement_order = Some(order);
-        slf
-    }
-
-    /// Build the Measurement Noise Model.
-    ///
-    /// This aggregates all fault locations by their measurement effects.
-    /// Locations that produce the same measurement signature have their
-    /// probabilities combined using the independent error formula.
-    ///
-    /// Returns:
-    ///     A `MeasurementNoiseModel` for fast approximate sampling.
-    fn build(&self) -> PyMeasurementNoiseModel {
-        let mut builder = RustMemBuilder::new(&self.influence_map).with_noise(
-            self.p1,
-            self.p2,
-            self.p_meas,
-            self.p_init,
-        );
-
-        if let Some(ref order) = self.measurement_order {
-            builder = builder.with_measurement_order(order.clone());
-        }
-
-        let inner = builder.build();
-        PyMeasurementNoiseModel { inner }
+    ///     `influence_map`: A `DagFaultInfluenceMap` from `DagFaultAnalyzer` or `InfluenceBuilder`.
+    ///     `p_error`: Uniform depolarizing error probability per fault location.
+    #[staticmethod]
+    fn from_influence_map(influence_map: &PyDagFaultInfluenceMap, p_error: f64) -> PyResult<Self> {
+        let inner = RustNewDemSamplerBuilder::new(&influence_map.inner)
+            .with_uniform_noise(p_error)
+            .raw_measurements()
+            .build()
+            .map_err(|e| pyo3::exceptions::PyValueError::new_err(e.to_string()))?;
+        Ok(Self { inner })
     }
 
-    fn __repr__(&self) -> String {
-        format!(
-            "MemBuilder(p1={}, p2={}, p_meas={}, p_init={})",
-            self.p1, self.p2, self.p_meas, self.p_init
-        )
+    /// Create a sampler from an influence map with circuit-level noise.
+    #[staticmethod]
+    fn from_influence_map_circuit_noise(
+        influence_map: &PyDagFaultInfluenceMap,
+        p1: f64,
+        p2: f64,
+        p_meas: f64,
+        p_prep: f64,
+    ) -> PyResult<Self> {
+        let inner = RustNewDemSamplerBuilder::new(&influence_map.inner)
+            .with_noise(p1, p2, p_meas, p_prep)
+            .raw_measurements()
+            .build()
+            .map_err(|e| pyo3::exceptions::PyValueError::new_err(e.to_string()))?;
+        Ok(Self { inner })
     }
-}
-
-// =============================================================================
-// DEM Sampler (Fast DEM-style sampling)
-// =============================================================================
-
-/// Fast DEM-style sampler for threshold estimation.
-///
-/// This sampler aggregates fault effects directly into detector/observable signatures,
-/// matching Stim's DEM sampler semantics. It uses data-oriented design for optimal
-/// cache performance:
-///
-/// - Precomputed u64 thresholds (no f64 comparison during sampling)
-/// - CSR layout for detector/observable indices
-/// - Bit-packed outcomes for compact storage and fast XOR
-///
-/// # Example
-///
-/// ```python
-/// from pecos_rslib.qec import DagFaultAnalyzer, DemSamplerBuilder
-///
-/// # Build influence map
-/// analyzer = DagFaultAnalyzer(dag)
-/// influence_map = analyzer.build_influence_map()
-///
-/// # Build sampler with explicit detector/observable definitions
-/// # `detectors_json` may use either `id` or `detector_id`.
-/// # `observables_json` may use either `id` or `observable_id`.
-/// sampler = DemSamplerBuilder(influence_map) \
-///     .with_noise(0.01, 0.01, 0.01, 0.01) \
-///     .with_detectors_json(detectors_json) \
-///     .with_observables_json(observables_json) \
-///     .with_measurement_order(measurement_order) \
-///     .build()
-///
-/// # Fast batch sampling for threshold estimation
-/// det_events, obs_flips = sampler.sample_batch(10000)
-/// ```
-#[pyclass(name = "DemSampler", module = "pecos_rslib.qec")]
-pub struct PyDemSampler {
-    inner: pecos_qec::fault_tolerance::dem_builder::DemSampler,
-}
 
-#[pymethods]
-impl PyDemSampler {
     /// Number of mechanisms in the sampler.
     #[getter]
     fn num_mechanisms(&self) -> usize {
         self.inner.num_mechanisms()
     }
 
-    /// Number of detectors.
+    /// Number of output channels (detectors or measurements).
+    #[getter]
+    fn num_outputs(&self) -> usize {
+        self.inner.num_outputs()
+    }
+
+    /// Number of detectors (alias for `num_outputs`).
     #[getter]
     fn num_detectors(&self) -> usize {
-        self.inner.num_detectors()
+        self.inner.num_outputs()
     }
 
-    /// Number of observables.
+    /// Number of observables when sampler metadata is known.
     #[getter]
     fn num_observables(&self) -> usize {
         self.inner.num_observables()
     }
 
+    /// Total number of outputs in the DEM `L<n>` namespace.
+    #[getter]
+    fn num_dem_outputs(&self) -> usize {
+        self.inner.num_dem_outputs()
+    }
+
+    /// Number of tracked Paulis.
+    #[getter]
+    fn num_tracked_paulis(&self) -> usize {
+        self.inner.num_tracked_paulis()
+    }
+
     /// Sample a single shot.
     ///
     /// Args:
     ///     seed: Optional random seed for reproducibility.
     ///
     /// Returns:
-    ///     Tuple of (`detection_events`, `observable_flips`) as boolean lists.
+    ///     Tuple of (`detection_events`, `dem_output_flips`) as boolean lists.
     #[pyo3(signature = (seed=None))]
     fn sample(&self, seed: Option<u64>) -> (Vec<bool>, Vec<bool>) {
         use pecos_random::PecosRng;
@@ -2162,7 +3367,7 @@ impl PyDemSampler {
     ///     seed: Optional random seed for reproducibility.
     ///
     /// Returns:
-    ///     Tuple of (`all_detection_events`, `all_observable_flips`).
+    ///     Tuple of (`all_detection_events`, `all_dem_output_flips`).
     #[pyo3(signature = (num_shots, seed=None))]
     fn sample_batch(
         &self,
@@ -2180,22 +3385,93 @@ impl PyDemSampler {
         self.inner.sample_batch(num_shots, &mut rng)
     }
 
-    /// Compute statistics without storing individual shots.
-    ///
-    /// This is the most efficient method for threshold estimation when you
-    /// only need aggregate statistics (logical error rate, syndrome rate).
+    /// Sample direct tracked-Pauli flips.
     ///
-    /// Args:
-    ///     `num_shots`: Number of shots to sample.
-    ///     seed: Optional random seed for reproducibility.
+    /// Raises:
+    ///     RuntimeError: If this sampler carries tracked Paulis but the
+    ///         backend cannot evaluate tracked-Pauli flips directly.
+    #[pyo3(signature = (seed=None))]
+    fn sample_tracked_paulis(&self, seed: Option<u64>) -> PyResult<Vec<bool>> {
+        use pecos_random::PecosRng;
+        use rand::RngExt;
+
+        let mut rng = match seed {
+            Some(s) => PecosRng::seed_from_u64(s),
+            None => PecosRng::seed_from_u64(rand::rng().random()),
+        };
+
+        self.inner
+            .sample_tracked_pauli_flips(&mut rng)
+            .map_err(|e| PyErr::new::<pyo3::exceptions::PyRuntimeError, _>(e.to_string()))
+    }
+
+    /// Sample direct tracked-Pauli flips for multiple shots.
     ///
-    /// Returns:
-    ///     Dictionary with statistics:
-    ///     - `total_shots`: Number of shots
-    ///     - `logical_error_count`: Shots with logical errors
+    /// Raises:
+    ///     RuntimeError: If this sampler carries tracked Paulis but the
+    ///         backend cannot evaluate tracked-Pauli flips directly.
+    #[pyo3(signature = (num_shots, seed=None))]
+    fn sample_tracked_pauli_batch(
+        &self,
+        num_shots: usize,
+        seed: Option<u64>,
+    ) -> PyResult<Vec<Vec<bool>>> {
+        use pecos_random::PecosRng;
+        use rand::RngExt;
+
+        let mut rng = match seed {
+            Some(s) => PecosRng::seed_from_u64(s),
+            None => PecosRng::seed_from_u64(rand::rng().random()),
+        };
+
+        self.inner
+            .sample_tracked_pauli_batch(num_shots, &mut rng)
+            .map_err(|e| PyErr::new::<pyo3::exceptions::PyRuntimeError, _>(e.to_string()))
+    }
+
+    /// Generate samples and store them in Rust memory as a `SampleBatch`.
+    ///
+    /// The batch can then be decoded by multiple decoders without re-sampling.
+    /// This is the proper way to compare decoders: same samples, different decoders.
+    ///
+    /// Args:
+    ///     `num_shots`: Number of shots to sample.
+    ///     seed: Optional random seed for reproducibility.
+    ///
+    /// Returns:
+    ///     `SampleBatch` object with samples held in Rust memory.
+    #[pyo3(signature = (num_shots, seed=None))]
+    fn generate_samples(&self, num_shots: usize, seed: Option<u64>) -> PySampleBatch {
+        use pecos_random::PecosRng;
+        use rand::RngExt;
+
+        let mut rng = match seed {
+            Some(s) => PecosRng::seed_from_u64(s),
+            None => PecosRng::seed_from_u64(rand::rng().random()),
+        };
+
+        // Use geometric columnar sampler via DemSampler.
+        let (det_columns, obs_columns) = self.inner.sample_batch_geometric(num_shots, &mut rng);
+
+        PySampleBatch::from_columnar(det_columns, obs_columns, num_shots)
+    }
+
+    /// Compute statistics without storing individual shots.
+    ///
+    /// This is the most efficient method for threshold estimation when you
+    /// only need aggregate statistics (logical error rate, syndrome rate).
+    ///
+    /// Args:
+    ///     `num_shots`: Number of shots to sample.
+    ///     seed: Optional random seed for reproducibility.
+    ///
+    /// Returns:
+    ///     Dictionary with statistics:
+    ///     - `total_shots`: Number of shots
+    ///     - `logical_error_count`: Shots with selected observable flips
     ///     - `syndrome_count`: Shots with non-trivial syndrome
-    ///     - `undetectable_count`: Shots with undetectable logical errors
-    ///     - `logical_error_rate`: Fraction with logical errors
+    ///     - `undetectable_count`: Shots with observable flips and no syndrome
+    ///     - `logical_error_rate`: Fraction with selected observable flips
     ///     - `syndrome_rate`: Fraction with syndromes
     ///     - `undetectable_rate`: Fraction with undetectable errors
     #[pyo3(signature = (num_shots, seed=None))]
@@ -2209,6 +3485,24 @@ impl PyDemSampler {
 
         let actual_seed = seed.unwrap_or_else(|| rand::rng().random());
         let stats = self.inner.sample_statistics(num_shots, actual_seed);
+        let observable_indices = self.inner.observable_ids();
+        let tracked_pauli_result = self.inner.tracked_pauli_ids();
+        let tracked_pauli_statistics_error =
+            tracked_pauli_result.as_ref().err().map(ToString::to_string);
+        let tracked_pauli_indices = tracked_pauli_result.unwrap_or_default();
+        let per_observable = stats.observable_counts(&observable_indices);
+        let per_tracked_pauli: Vec<usize> = tracked_pauli_indices
+            .iter()
+            .filter_map(|&idx| stats.dem_output_counts().get(idx).copied())
+            .collect();
+        let logical_rates = stats.logical_rates(&observable_indices);
+        #[allow(clippy::cast_precision_loss)] // Counts are converted to rates for Python reporting.
+        let n = stats.total_shots as f64;
+        #[allow(clippy::cast_precision_loss)] // Counts are converted to rates for Python reporting.
+        let tracked_pauli_rates: Vec<f64> = per_tracked_pauli
+            .iter()
+            .map(|&count| count as f64 / n)
+            .collect();
 
         let dict = pyo3::types::PyDict::new(py);
         dict.set_item("total_shots", stats.total_shots)?;
@@ -2218,15 +3512,178 @@ impl PyDemSampler {
         dict.set_item("logical_error_rate", stats.logical_error_rate())?;
         dict.set_item("syndrome_rate", stats.syndrome_rate())?;
         dict.set_item("undetectable_rate", stats.undetectable_rate())?;
+        dict.set_item("per_detector", &stats.per_detector)?;
+        dict.set_item("per_observable", per_observable)?;
+        dict.set_item("per_tracked_pauli", per_tracked_pauli)?;
+        dict.set_item("per_dem_output", stats.dem_output_counts())?;
+        dict.set_item("detector_rates", stats.detector_rates())?;
+        dict.set_item("logical_rates", logical_rates)?;
+        dict.set_item("tracked_pauli_rates", tracked_pauli_rates)?;
+        dict.set_item("dem_output_rates", stats.dem_output_rates())?;
+        dict.set_item(
+            "tracked_pauli_statistics_supported",
+            tracked_pauli_statistics_error.is_none(),
+        )?;
+        if let Some(error) = tracked_pauli_statistics_error {
+            dict.set_item("tracked_pauli_statistics_error", error)?;
+        }
+        Ok(dict.unbind())
+    }
+
+    /// Get labels for the sampler's output channels.
+    ///
+    /// Returns a dict with:
+    ///     - `outputs`: labels for output channels (raw measurements or detectors)
+    ///     - `dem_outputs`: labels for all DEM `L<n>` targets
+    ///     - `observables`: labels for observables
+    ///     - `tracked_paulis`: labels for tracked Paulis
+    ///     - `dual_detectors`: labels for dual-output detector channels
+    fn labels(&self, py: Python<'_>) -> PyResult<Py<pyo3::types::PyDict>> {
+        let labels = self.inner.labels();
+        let dict = pyo3::types::PyDict::new(py);
+        dict.set_item("outputs", &labels.outputs)?;
+        dict.set_item("dem_outputs", &labels.dem_output_labels)?;
+        dict.set_item("observables", &labels.dem_output_labels)?;
+        dict.set_item("tracked_paulis", &labels.tracked_pauli_labels)?;
+        dict.set_item("dual_detectors", &labels.dual_detectors)?;
         Ok(dict.unbind())
     }
 
+    /// Sample and decode in a tight Rust loop, returning only the error count.
+    ///
+    /// This is the fastest path for threshold estimation -- no per-shot data
+    /// crosses the Rust/Python boundary. The sampler produces detection events,
+    /// the decoder decodes them via the `ObservableDecoder` trait, and errors
+    /// are counted, all in Rust.
+    ///
+    /// Args:
+    ///     dem: DEM string in standard DEM text format for the decoder.
+    ///     `num_shots`: Number of shots to sample and decode.
+    ///     `decoder_type`: "pymatching" or "tesseract".
+    ///     seed: Optional random seed for reproducibility.
+    ///
+    /// Returns:
+    ///     Number of logical errors (mismatches between decoder prediction and true flip).
+    #[pyo3(signature = (dem, num_shots, decoder_type="pymatching", seed=None))]
+    fn sample_decode_count(
+        &self,
+        dem: &str,
+        num_shots: usize,
+        decoder_type: &str,
+        seed: Option<u64>,
+    ) -> PyResult<usize> {
+        use pecos_random::PecosRng;
+        use rand::RngExt;
+
+        let actual_seed = seed.unwrap_or_else(|| rand::rng().random());
+        let mut rng = PecosRng::seed_from_u64(actual_seed);
+
+        let mut decoder = create_observable_decoder(dem, decoder_type)?;
+        let observable_mask = self.inner.observable_dem_output_mask();
+
+        // Tight sample+decode loop -- no Python involvement.
+        // Single-threaded: sample and decode sequentially.
+        let mut errors = 0usize;
+        for _ in 0..num_shots {
+            let (det_events, obs_flips) = self.inner.sample(&mut rng);
+            let syndrome: Vec<u8> = det_events.iter().map(|&b| u8::from(b)).collect();
+            let predicted_mask = decoder.decode_to_observables(&syndrome).unwrap_or(u64::MAX);
+            let true_mask = self.inner.observable_mask_from_dem_output_flips(&obs_flips);
+            if (predicted_mask & observable_mask) != true_mask {
+                errors += 1;
+            }
+        }
+        Ok(errors)
+    }
+
+    /// Parallel sample+decode: distributes shots across threads.
+    ///
+    /// Each thread gets its own sampler clone and decoder instance.
+    /// Much faster for slow decoders (Tesseract) where decode time dominates.
+    ///
+    /// Args:
+    ///     dem: DEM string in standard DEM text format for the decoder.
+    ///     `num_shots`: Number of shots to sample and decode.
+    ///     `decoder_type`: "pymatching", "tesseract", "`bp_osd`", "`bp_lsd`", or "`union_find`".
+    ///     seed: Optional base random seed. Each thread gets seed + `thread_id`.
+    ///     `num_workers`: Number of parallel workers (default: number of CPUs).
+    ///
+    /// Returns:
+    ///     Number of logical errors.
+    #[pyo3(signature = (dem, num_shots, decoder_type="pymatching", seed=None, num_workers=None))]
+    fn sample_decode_count_parallel(
+        &self,
+        dem: &str,
+        num_shots: usize,
+        decoder_type: &str,
+        seed: Option<u64>,
+        num_workers: Option<usize>,
+    ) -> PyResult<usize> {
+        use rayon::prelude::*;
+
+        let actual_seed = seed.unwrap_or(0);
+        let n_workers = num_workers.unwrap_or_else(rayon::current_num_threads);
+
+        // Validate decoder type early
+        create_observable_decoder(dem, decoder_type)?;
+
+        let pool = rayon::ThreadPoolBuilder::new()
+            .num_threads(n_workers)
+            .build()
+            .map_err(|e| PyErr::new::<pyo3::exceptions::PyRuntimeError, _>(e.to_string()))?;
+
+        let shots_per_worker = num_shots / n_workers;
+        let remainder = num_shots % n_workers;
+
+        let sampler = &self.inner;
+        let observable_mask = sampler.observable_dem_output_mask();
+        let dem_str = dem.to_string();
+        let dt = decoder_type.to_string();
+
+        let total_errors: usize = pool.install(|| {
+            (0..n_workers)
+                .into_par_iter()
+                .map(|worker_id| {
+                    use pecos_random::PecosRng;
+
+                    let my_shots = shots_per_worker + usize::from(worker_id < remainder);
+                    if my_shots == 0 {
+                        return 0;
+                    }
+
+                    let my_sampler = sampler.clone();
+                    let mut my_rng =
+                        PecosRng::seed_from_u64(actual_seed.wrapping_add(worker_id as u64));
+                    // unwrap is safe: we validated above
+                    let mut decoder = create_observable_decoder(&dem_str, &dt).unwrap();
+
+                    let mut errors = 0usize;
+                    for _ in 0..my_shots {
+                        let (det_events, obs_flips) = my_sampler.sample(&mut my_rng);
+                        let syndrome: Vec<u8> = det_events.iter().map(|&b| u8::from(b)).collect();
+                        let predicted =
+                            decoder.decode_to_observables(&syndrome).unwrap_or(u64::MAX);
+                        let truth = my_sampler.observable_mask_from_dem_output_flips(&obs_flips);
+                        if (predicted & observable_mask) != truth {
+                            errors += 1;
+                        }
+                    }
+                    errors
+                })
+                .sum()
+        });
+
+        Ok(total_errors)
+    }
+
     fn __repr__(&self) -> String {
         format!(
-            "DemSampler(mechanisms={}, detectors={}, observables={})",
+            "DemSampler(mechanisms={}, outputs={}, dem_outputs={}, observables={}, tracked_paulis={})",
             self.num_mechanisms(),
-            self.num_detectors(),
+            self.num_outputs(),
+            self.num_dem_outputs(),
             self.num_observables(),
+            self.num_tracked_paulis(),
         )
     }
 }
@@ -2234,14 +3691,11 @@ impl PyDemSampler {
 /// Builder for `DemSampler`.
 ///
 /// Constructs a `DemSampler` from a fault influence map, noise parameters,
-/// and explicit detector/observable definitions.
+/// and explicit detector / observable definitions.
 #[pyclass(name = "DemSamplerBuilder", module = "pecos_rslib.qec")]
 pub struct PyDemSamplerBuilder {
     influence_map: RustDagFaultInfluenceMap,
-    p1: f64,
-    p2: f64,
-    p_meas: f64,
-    p_init: f64,
+    noise: NoiseConfig,
     detectors_json: Option<String>,
     observables_json: Option<String>,
     measurement_order: Option<Vec<usize>>,
@@ -2254,10 +3708,7 @@ impl PyDemSamplerBuilder {
     fn new(influence_map: &PyDagFaultInfluenceMap) -> Self {
         Self {
             influence_map: influence_map.inner.clone(),
-            p1: 0.01,
-            p2: 0.01,
-            p_meas: 0.01,
-            p_init: 0.01,
+            noise: NoiseConfig::default(),
             detectors_json: None,
             observables_json: None,
             measurement_order: None,
@@ -2265,17 +3716,28 @@ impl PyDemSamplerBuilder {
     }
 
     /// Set noise parameters.
+    #[pyo3(signature = (p1, p2, p_meas, p_prep, p_idle=None, t1=None, t2=None, idle_rz=None))]
+    #[allow(clippy::too_many_arguments)]
     fn with_noise(
         mut slf: PyRefMut<'_, Self>,
         p1: f64,
         p2: f64,
         p_meas: f64,
-        p_init: f64,
+        p_prep: f64,
+        p_idle: Option<f64>,
+        t1: Option<f64>,
+        t2: Option<f64>,
+        idle_rz: Option<f64>,
     ) -> PyRefMut<'_, Self> {
-        slf.p1 = p1;
-        slf.p2 = p2;
-        slf.p_meas = p_meas;
-        slf.p_init = p_init;
+        let mut noise = NoiseConfig::new(p1, p2, p_meas, p_prep);
+        noise.p_idle = p_idle.unwrap_or(0.0);
+        if let (Some(t1_val), Some(t2_val)) = (t1, t2) {
+            noise = noise.set_t1_t2(t1_val, t2_val);
+        }
+        if let Some(rz) = idle_rz {
+            noise = noise.set_idle_rz(rz);
+        }
+        slf.noise = noise;
         slf
     }
 
@@ -2290,8 +3752,8 @@ impl PyDemSamplerBuilder {
 
     /// Set observable definitions from JSON.
     ///
-    /// Accepts either legacy observable rows with an `"id"` key or public surface
-    /// descriptor rows with an `"observable_id"` key.
+    /// Tracked Paulis are carried by the influence map; this helper is for
+    /// observable metadata.
     fn with_observables_json(mut slf: PyRefMut<'_, Self>, json: String) -> PyRefMut<'_, Self> {
         slf.observables_json = Some(json);
         slf
@@ -2308,14 +3770,8 @@ impl PyDemSamplerBuilder {
 
     /// Build the `DemSampler`.
     fn build(&self) -> PyResult<PyDemSampler> {
-        use pecos_qec::fault_tolerance::dem_builder::DemSamplerBuilder;
-
-        let mut builder = DemSamplerBuilder::new(&self.influence_map).with_noise(
-            self.p1,
-            self.p2,
-            self.p_meas,
-            self.p_init,
-        );
+        let mut builder = RustNewDemSamplerBuilder::new(&self.influence_map)
+            .with_noise_config(self.noise.clone());
 
         if let Some(ref json) = self.detectors_json {
             builder = builder
@@ -2333,14 +3789,16 @@ impl PyDemSamplerBuilder {
             builder = builder.with_measurement_order(order.clone());
         }
 
-        let inner = builder.build();
+        let inner = builder
+            .build()
+            .map_err(|e| pyo3::exceptions::PyValueError::new_err(e.to_string()))?;
         Ok(PyDemSampler { inner })
     }
 
     fn __repr__(&self) -> String {
         format!(
-            "DemSamplerBuilder(p1={}, p2={}, p_meas={}, p_init={})",
-            self.p1, self.p2, self.p_meas, self.p_init
+            "DemSamplerBuilder(p1={}, p2={}, p_meas={}, p_prep={}, p_idle={:?})",
+            self.noise.p1, self.noise.p2, self.noise.p_meas, self.noise.p_prep, self.noise.p_idle
         )
     }
 }
@@ -2476,7 +3934,7 @@ impl PyEquivalenceResult {
 
 /// A parsed Detector Error Model.
 ///
-/// Parses DEM strings in Stim/PECOS format and provides methods for
+/// Parses standard and PECOS DEM strings and provides methods for
 /// aggregation and sampling.
 ///
 /// # Example
@@ -2498,7 +3956,7 @@ impl PyParsedDem {
     /// Parse a DEM from a string.
     ///
     /// Args:
-    ///     `dem_str`: DEM string in Stim/PECOS format.
+    ///     `dem_str`: DEM string in standard or PECOS DEM text format.
     ///
     /// Returns:
     ///     `ParsedDem` object.
@@ -2525,10 +3983,36 @@ impl PyParsedDem {
         self.inner.num_detectors
     }
 
-    /// Number of observables (max ID + 1).
+    /// Number of observables.
     #[getter]
     fn num_observables(&self) -> u32 {
-        self.inner.num_observables
+        self.inner.num_observables()
+    }
+
+    /// Total number of outputs in the DEM `L<n>` namespace.
+    #[getter]
+    fn num_dem_outputs(&self) -> u32 {
+        self.inner.num_dem_outputs()
+    }
+
+    /// Number of tracked Paulis.
+    #[getter]
+    fn num_tracked_paulis(&self) -> u32 {
+        self.inner.num_tracked_paulis()
+    }
+
+    /// Convert to a decomposed (graphlike) DEM string.
+    ///
+    /// Mechanisms with <= 2 detectors pass through unchanged.
+    /// Hyperedges (3+ detectors) cannot be decomposed without Pauli
+    /// provenance and will raise an error.
+    ///
+    /// For proper decomposition, use ``coherent_dem_decomposed()``
+    /// or ``noise_characterization()`` which track X/Z components.
+    fn to_string_decomposed(&self) -> PyResult<String> {
+        self.inner
+            .to_string_decomposed()
+            .map_err(pyo3::exceptions::PyValueError::new_err)
     }
 
     /// Aggregate mechanisms by their effect.
@@ -2551,260 +4035,1499 @@ impl PyParsedDem {
             dict.set_item(key_tuple, prob)?;
         }
 
-        Ok(dict.unbind())
-    }
+        Ok(dict.unbind())
+    }
+
+    /// Sample from this DEM.
+    ///
+    /// Args:
+    ///     seed: Optional random seed for reproducibility.
+    ///
+    /// Returns:
+    ///     Tuple of (`detector_events`, `dem_output_flips`) as boolean lists.
+    #[pyo3(signature = (seed=None))]
+    fn sample(&self, seed: Option<u64>) -> (Vec<bool>, Vec<bool>) {
+        use pecos_random::PecosRng;
+        use rand::RngExt;
+
+        let mut rng = match seed {
+            Some(s) => PecosRng::seed_from_u64(s),
+            None => PecosRng::seed_from_u64(rand::rng().random()),
+        };
+
+        self.inner.sample(&mut rng)
+    }
+
+    /// Sample multiple shots from this DEM.
+    ///
+    /// Args:
+    ///     `num_shots`: Number of shots to sample.
+    ///     seed: Optional random seed for reproducibility.
+    ///
+    /// Returns:
+    ///     Tuple of (`all_detector_events`, `all_dem_output_flips`).
+    #[pyo3(signature = (num_shots, seed=None))]
+    fn sample_batch(
+        &self,
+        num_shots: usize,
+        seed: Option<u64>,
+    ) -> (Vec<Vec<bool>>, Vec<Vec<bool>>) {
+        use pecos_random::PecosRng;
+        use rand::RngExt;
+
+        let mut rng = match seed {
+            Some(s) => PecosRng::seed_from_u64(s),
+            None => PecosRng::seed_from_u64(rand::rng().random()),
+        };
+
+        self.inner.sample_batch(num_shots, &mut rng)
+    }
+
+    /// Convert to an optimized `DemSampler` for fast batch sampling.
+    ///
+    /// The `DemSampler` uses geometric skip sampling and parallel chunked
+    /// processing, which is significantly faster than `sample_batch` for
+    /// large shot counts and low error rates.
+    ///
+    /// Returns:
+    ///     `DemSampler`: Optimized sampler for this DEM.
+    ///
+    /// Example:
+    ///     >>> dem = `ParsedDem.from_string("error(0.01)` D0 D1")
+    ///     >>> sampler = `dem.to_dem_sampler()`
+    ///     >>> stats = `sampler.sample_statistics(100000`, seed=42)
+    fn to_dem_sampler(&self) -> PyDemSampler {
+        PyDemSampler {
+            inner: self.inner.to_dem_sampler(),
+        }
+    }
+
+    fn __repr__(&self) -> String {
+        format!(
+            "ParsedDem(mechanisms={}, detectors={}, dem_outputs={}, observables={}, tracked_paulis={})",
+            self.inner.mechanisms.len(),
+            self.inner.num_detectors,
+            self.inner.num_dem_outputs(),
+            self.inner.num_observables(),
+            self.inner.num_tracked_paulis()
+        )
+    }
+}
+
+/// Compare two DEMs for exact mechanism match.
+///
+/// This comparison aggregates mechanisms by effect and compares probabilities.
+/// Appropriate for non-decomposed DEMs or when exact match is required.
+///
+/// Args:
+///     dem1: First DEM string or `ParsedDem`.
+///     dem2: Second DEM string or `ParsedDem`.
+///     `prob_tolerance`: Relative tolerance for probability comparison (default 1e-6).
+///
+/// Returns:
+///     `EquivalenceResult` with comparison statistics.
+///
+/// Example:
+///     >>> result = `compare_dems_exact(dem1_str`, `dem2_str`, `prob_tolerance=0.001`)
+///     >>> if result.equivalent:
+///     ...     print("DEMs are equivalent")
+#[pyfunction]
+#[pyo3(signature = (dem1, dem2, prob_tolerance=1e-6))]
+fn compare_dems_exact(
+    dem1: &str,
+    dem2: &str,
+    prob_tolerance: f64,
+) -> PyResult<PyEquivalenceResult> {
+    let parsed1 = dem1
+        .parse::<RustParsedDem>()
+        .map_err(|e| pyo3::exceptions::PyValueError::new_err(format!("DEM1 parse error: {e}")))?;
+    let parsed2 = dem2
+        .parse::<RustParsedDem>()
+        .map_err(|e| pyo3::exceptions::PyValueError::new_err(format!("DEM2 parse error: {e}")))?;
+
+    let inner = rust_compare_dems_exact(&parsed1, &parsed2, prob_tolerance);
+    Ok(PyEquivalenceResult { inner })
+}
+
+/// Compare two DEMs statistically by sampling.
+///
+/// This is the most robust comparison method as it accounts for all
+/// decomposition strategies and probability combinations. It compares
+/// the joint distribution of syndrome patterns, not just marginal rates.
+///
+/// Args:
+///     dem1: First DEM string or `ParsedDem`.
+///     dem2: Second DEM string or `ParsedDem`.
+///     `num_shots`: Number of shots for sampling (default 100,000).
+///     seed: Random seed (default 42).
+///     tolerance: Maximum relative difference to consider equivalent (default 0.05).
+///
+/// Returns:
+///     `EquivalenceResult` with comparison statistics.
+///
+/// Example:
+///     >>> result = `compare_dems_statistical(dem1_str`, `dem2_str`, `num_shots=50000`)
+///     >>> print(f"Correlation: {result.correlation}")
+#[pyfunction]
+#[pyo3(signature = (dem1, dem2, num_shots=100_000, seed=42, tolerance=0.05))]
+fn compare_dems_statistical(
+    dem1: &str,
+    dem2: &str,
+    num_shots: usize,
+    seed: u64,
+    tolerance: f64,
+) -> PyResult<PyEquivalenceResult> {
+    let parsed1 = dem1
+        .parse::<RustParsedDem>()
+        .map_err(|e| pyo3::exceptions::PyValueError::new_err(format!("DEM1 parse error: {e}")))?;
+    let parsed2 = dem2
+        .parse::<RustParsedDem>()
+        .map_err(|e| pyo3::exceptions::PyValueError::new_err(format!("DEM2 parse error: {e}")))?;
+
+    let inner = rust_compare_dems_statistical(&parsed1, &parsed2, num_shots, seed, tolerance);
+    Ok(PyEquivalenceResult { inner })
+}
+
+/// Convenience function to verify DEM equivalence.
+///
+/// Args:
+///     dem1: First DEM string.
+///     dem2: Second DEM string.
+///     method: Comparison method - "exact" or "statistical" (default "exact").
+///     `prob_tolerance`: For exact: probability tolerance (default 1e-6).
+///     `num_shots`: For statistical: number of shots (default 100,000).
+///     tolerance: For statistical: rate tolerance (default 0.05).
+///     seed: For statistical: random seed (default 42).
+///
+/// Returns:
+///     True if DEMs are equivalent within tolerance.
+///
+/// Example:
+///     >>> if `verify_dem_equivalence(dem1`, dem2, method="exact"):
+///     ...     print("DEMs match exactly")
+#[pyfunction]
+#[pyo3(signature = (dem1, dem2, method="exact", prob_tolerance=1e-6, num_shots=100_000, tolerance=0.05, seed=42))]
+fn verify_dem_equivalence(
+    dem1: &str,
+    dem2: &str,
+    method: &str,
+    prob_tolerance: f64,
+    num_shots: usize,
+    tolerance: f64,
+    seed: u64,
+) -> PyResult<bool> {
+    let comparison_method = match method {
+        "exact" => RustComparisonMethod::Exact { prob_tolerance },
+        "statistical" => RustComparisonMethod::Statistical {
+            num_shots,
+            seed,
+            tolerance,
+        },
+        _ => {
+            return Err(pyo3::exceptions::PyValueError::new_err(
+                "method must be 'exact' or 'statistical'",
+            ));
+        }
+    };
+
+    rust_verify_dem_equivalence(dem1, dem2, &comparison_method)
+        .map_err(|e| pyo3::exceptions::PyValueError::new_err(e.to_string()))
+}
+
+/// Assert that two DEMs are equivalent, raising an error if not.
+///
+/// This is a convenience function for testing that raises `AssertionError`
+/// if the DEMs are not equivalent.
+///
+/// Args:
+///     dem1: First DEM string.
+///     dem2: Second DEM string.
+///     method: Comparison method - "exact" or "statistical" (default "exact").
+///     `prob_tolerance`: For exact: probability tolerance (default 1e-6).
+///     `num_shots`: For statistical: number of shots (default 100,000).
+///     tolerance: For statistical: rate tolerance (default 0.05).
+///     seed: For statistical: random seed (default 42).
+///
+/// Raises:
+///     `AssertionError`: If DEMs are not equivalent.
+///
+/// Example:
+///     >>> `assert_dems_equivalent(dem1`, dem2, method="exact")  # Raises if not equivalent
+#[pyfunction]
+#[pyo3(signature = (dem1, dem2, method="exact", prob_tolerance=1e-6, num_shots=100_000, tolerance=0.05, seed=42))]
+fn assert_dems_equivalent(
+    dem1: &str,
+    dem2: &str,
+    method: &str,
+    prob_tolerance: f64,
+    num_shots: usize,
+    tolerance: f64,
+    seed: u64,
+) -> PyResult<()> {
+    let parsed1 = dem1
+        .parse::<RustParsedDem>()
+        .map_err(|e| pyo3::exceptions::PyValueError::new_err(format!("DEM1 parse error: {e}")))?;
+    let parsed2 = dem2
+        .parse::<RustParsedDem>()
+        .map_err(|e| pyo3::exceptions::PyValueError::new_err(format!("DEM2 parse error: {e}")))?;
+
+    let result = match method {
+        "exact" => rust_compare_dems_exact(&parsed1, &parsed2, prob_tolerance),
+        "statistical" => {
+            rust_compare_dems_statistical(&parsed1, &parsed2, num_shots, seed, tolerance)
+        }
+        _ => {
+            return Err(pyo3::exceptions::PyValueError::new_err(
+                "method must be 'exact' or 'statistical'",
+            ));
+        }
+    };
+
+    if result.equivalent {
+        Ok(())
+    } else {
+        let msg = format!(
+            "DEMs are not equivalent: max_rate_diff={:.6}, only_in_dem1={:?}, only_in_dem2={:?}",
+            result.max_rate_difference, result.details.only_in_dem1, result.details.only_in_dem2
+        );
+        Err(pyo3::exceptions::PyAssertionError::new_err(msg))
+    }
+}
+
+// =============================================================================
+// CSS UF Decoder (UIUF)
+// =============================================================================
+
+/// CSS-aware Union-Find decoder using the UIUF algorithm.
+///
+/// Takes separate X and Z DEM strings and decodes them jointly, exploiting
+/// Y-error identification through cluster intersection.
+///
+/// `Example::`
+///
+///     decoder = CssUfDecoder(x_dem_str, z_dem_str)
+///     x_obs, z_obs = decoder.decode_css(x_syndrome, z_syndrome)
+///
+#[pyclass(name = "CssUfDecoder", module = "pecos_rslib.qec")]
+pub struct PyCssUfDecoder {
+    inner: pecos_decoders::CssUfDecoder,
+}
+
+#[pymethods]
+impl PyCssUfDecoder {
+    /// Create a CSS UF decoder from X and Z DEM strings.
+    ///
+    /// The qubit-edge mapping is auto-detected from detector coordinates.
+    /// If coordinates are missing, falls back to independent X/Z decoding.
+    #[new]
+    fn new(x_dem: &str, z_dem: &str) -> PyResult<Self> {
+        let inner = pecos_decoders::CssUfDecoder::from_dems(
+            x_dem,
+            z_dem,
+            pecos_decoders::UfDecoderConfig::accurate(),
+        )
+        .map_err(|e| PyErr::new::<pyo3::exceptions::PyRuntimeError, _>(e.to_string()))?;
+        Ok(Self { inner })
+    }
+
+    /// Decode X and Z syndromes jointly using UIUF.
+    ///
+    /// Args:
+    ///     `x_syndrome`: X-basis detection events (bytes).
+    ///     `z_syndrome`: Z-basis detection events (bytes).
+    ///
+    /// Returns:
+    ///     Tuple of (`x_observable_mask`, `z_observable_mask`).
+    fn decode_css(&mut self, x_syndrome: &[u8], z_syndrome: &[u8]) -> PyResult<(u64, u64)> {
+        self.inner
+            .decode_css(x_syndrome, z_syndrome)
+            .map_err(|e| PyErr::new::<pyo3::exceptions::PyRuntimeError, _>(e.to_string()))
+    }
+
+    /// Number of matched qubit pairs between X and Z graphs.
+    /// 0 means no mapping was found (falls back to independent decode).
+    #[getter]
+    fn num_qubit_pairs(&self) -> usize {
+        self.inner.num_qubit_pairs()
+    }
+
+    /// Count erasures the intersection would produce for given syndromes.
+    fn count_erasures(&mut self, x_syndrome: &[u8], z_syndrome: &[u8]) -> usize {
+        self.inner
+            .count_intersection_erasures(x_syndrome, z_syndrome)
+    }
+
+    /// Decode a batch of syndromes and return the error count.
+    ///
+    /// Each shot has concatenated `[x_syndrome | z_syndrome]`.
+    /// The `x_syndrome` length is specified by `x_num_detectors`.
+    ///
+    /// Args:
+    ///     syndromes: List of concatenated syndrome byte arrays.
+    ///     `true_obs_masks`: True observable masks for each shot.
+    ///     `x_num_detectors`: Length of the X syndrome prefix.
+    ///
+    /// Returns:
+    ///     Number of logical errors.
+    fn decode_count_batch(
+        &mut self,
+        syndromes: Vec<Vec<u8>>,
+        true_obs_masks: Vec<u64>,
+        x_num_detectors: usize,
+    ) -> PyResult<usize> {
+        let mut errors = 0;
+        for (syn, &true_obs) in syndromes.iter().zip(true_obs_masks.iter()) {
+            let x_syn = &syn[..x_num_detectors.min(syn.len())];
+            let z_syn = &syn[x_num_detectors.min(syn.len())..];
+            let (x_obs, z_obs) = self
+                .inner
+                .decode_css(x_syn, z_syn)
+                .map_err(|e| PyErr::new::<pyo3::exceptions::PyRuntimeError, _>(e.to_string()))?;
+            let predicted = x_obs ^ z_obs;
+            if predicted != true_obs {
+                errors += 1;
+            }
+        }
+        Ok(errors)
+    }
+}
+
+// =============================================================================
+// Observable Subgraph Decoder (Python class)
+// =============================================================================
+
+/// Per-observable subgraph decoder for transversal gates.
+///
+/// Partitions a DEM into per-observable graphlike subgraphs using
+/// stabilizer coordinate information, then decodes each independently.
+///
+/// Args:
+///     dem: DEM string with detector coordinate declarations.
+///     `stab_coords`: List of dicts, one per logical qubit. Each dict has
+///         keys "X" and "Z" mapping to lists of (x, y) ancilla coordinates.
+///     `inner_decoder`: Inner decoder type string (default "`pecos_uf:fast`").
+///
+/// Example:
+///     >>> decoder = `ObservableSubgraphDecoder`(
+///     ...     `dem_str`,
+///     ...     [{"X": [(1,0), (3,1)], "Z": [(0,3), (1,1)]}],
+///     ...     "`pecos_uf:fast`",
+///     ... )
+///     >>> obs = decoder.decode(syndrome)
+#[pyclass(name = "ObservableSubgraphDecoder", module = "pecos_rslib.qec")]
+pub struct PyObservableSubgraphDecoder {
+    inner: pecos_decoder_core::observable_subgraph::ObservableSubgraphDecoder,
+}
+
+#[pymethods]
+impl PyObservableSubgraphDecoder {
+    #[new]
+    #[pyo3(signature = (dem, stab_coords, inner_decoder="pecos_uf:fast", max_time_radius=None))]
+    fn new(
+        dem: &str,
+        stab_coords: Vec<pyo3::Bound<'_, pyo3::types::PyDict>>,
+        inner_decoder: &str,
+        max_time_radius: Option<i64>,
+    ) -> PyResult<Self> {
+        use pecos_decoder_core::observable_subgraph::{ObservableSubgraphDecoder, QubitStabCoords};
+
+        // Parse stab_coords from Python dicts
+        let mut rust_stab_coords = Vec::with_capacity(stab_coords.len());
+        for dict in &stab_coords {
+            let x_list: Vec<(f64, f64)> = dict
+                .get_item("X")?
+                .ok_or_else(|| PyErr::new::<pyo3::exceptions::PyKeyError, _>("Missing 'X' key"))?
+                .extract()?;
+            let z_list: Vec<(f64, f64)> = dict
+                .get_item("Z")?
+                .ok_or_else(|| PyErr::new::<pyo3::exceptions::PyKeyError, _>("Missing 'Z' key"))?
+                .extract()?;
+            rust_stab_coords.push(QubitStabCoords {
+                x_positions: x_list,
+                z_positions: z_list,
+            });
+        }
+
+        let inner = ObservableSubgraphDecoder::from_dem_windowed(
+            dem,
+            &rust_stab_coords,
+            max_time_radius,
+            |subgraph| {
+                let sub_dem = subgraph_to_dem_string(subgraph);
+                let decoder = create_observable_decoder(&sub_dem, inner_decoder)
+                    .map_err(|e| pecos_decoders::DecoderError::InternalError(e.to_string()))?;
+                Ok(Box::new(SendWrapper(decoder))
+                    as Box<dyn pecos_decoders::ObservableDecoder + Send + Sync>)
+            },
+        )
+        .map_err(|e| PyErr::new::<pyo3::exceptions::PyRuntimeError, _>(e.to_string()))?;
+
+        Ok(Self { inner })
+    }
+
+    /// Decode a syndrome and return observable flip predictions.
+    fn decode(&mut self, syndrome: Vec<u8>) -> PyResult<u64> {
+        use pecos_decoder_core::ObservableDecoder;
+        self.inner
+            .decode_to_observables(&syndrome)
+            .map_err(|e| PyErr::new::<pyo3::exceptions::PyRuntimeError, _>(e.to_string()))
+    }
+
+    /// Number of observables this decoder handles.
+    fn num_observables(&self) -> usize {
+        self.inner.num_observables()
+    }
+
+    /// Decode a batch of syndromes and return observable predictions.
+    ///
+    /// Args:
+    ///     syndromes: 2D numpy array of shape (`num_shots`, `num_detectors`).
+    ///
+    /// Returns:
+    ///     List of observable flip masks (one per shot).
+    fn decode_batch(&mut self, syndromes: Vec<Vec<u8>>) -> PyResult<Vec<u64>> {
+        use pecos_decoder_core::ObservableDecoder;
+        let mut results = Vec::with_capacity(syndromes.len());
+        for syn in &syndromes {
+            let obs = self
+                .inner
+                .decode_to_observables(syn)
+                .map_err(|e| PyErr::new::<pyo3::exceptions::PyRuntimeError, _>(e.to_string()))?;
+            results.push(obs);
+        }
+        Ok(results)
+    }
+
+    /// Decode a `SampleBatch` and return the number of logical errors.
+    ///
+    /// This runs entirely in Rust — no Python per-shot overhead.
+    ///
+    /// Args:
+    ///     batch: A `SampleBatch` from `DemSampler.generate_samples()`.
+    ///
+    /// Returns:
+    ///     Number of logical errors.
+    fn decode_count(&mut self, batch: &PySampleBatch) -> PyResult<usize> {
+        let detection_events: Vec<Vec<u8>> = (0..batch.num_shots)
+            .map(|i| {
+                let mut s = vec![0u8; batch.num_detectors];
+                batch.extract_syndrome(i, &mut s);
+                s
+            })
+            .collect();
+        let observable_masks: Vec<u64> = (0..batch.num_shots)
+            .map(|i| batch.extract_obs_mask(i))
+            .collect();
+        self.inner
+            .decode_count_batched(&detection_events, &observable_masks)
+            .map_err(|e| PyErr::new::<pyo3::exceptions::PyRuntimeError, _>(e.to_string()))
+    }
+
+    /// Decode a `SampleBatch` in parallel using rayon.
+    ///
+    /// Creates per-worker decoder instances to avoid lock contention.
+    /// Requires the DEM string and inner decoder type for reconstruction.
+    #[pyo3(signature = (batch, dem, stab_coords, inner_decoder="pymatching", num_workers=None, max_time_radius=None))]
+    fn decode_count_parallel(
+        &self,
+        batch: &PySampleBatch,
+        dem: &str,
+        stab_coords: Vec<pyo3::Bound<'_, pyo3::types::PyDict>>,
+        inner_decoder: &str,
+        num_workers: Option<usize>,
+        max_time_radius: Option<i64>,
+    ) -> PyResult<usize> {
+        use pecos_decoder_core::observable_subgraph::{ObservableSubgraphDecoder, QubitStabCoords};
+        use rayon::prelude::*;
+
+        // Parse stab_coords
+        let mut sc = Vec::with_capacity(stab_coords.len());
+        for dict in &stab_coords {
+            let x: Vec<(f64, f64)> = dict
+                .get_item("X")?
+                .ok_or_else(|| PyErr::new::<pyo3::exceptions::PyKeyError, _>("X"))?
+                .extract()?;
+            let z: Vec<(f64, f64)> = dict
+                .get_item("Z")?
+                .ok_or_else(|| PyErr::new::<pyo3::exceptions::PyKeyError, _>("Z"))?
+                .extract()?;
+            sc.push(QubitStabCoords {
+                x_positions: x,
+                z_positions: z,
+            });
+        }
+
+        let dem_str = dem.to_string();
+        let inner_str = inner_decoder.to_string();
+        let n = batch.num_shots;
+
+        // Materialize row-major data for parallel decode.
+        let events: Vec<Vec<u8>> = (0..n)
+            .map(|i| {
+                let mut s = vec![0u8; batch.num_detectors];
+                batch.extract_syndrome(i, &mut s);
+                s
+            })
+            .collect();
+        let masks: Vec<u64> = (0..n).map(|i| batch.extract_obs_mask(i)).collect();
+
+        let pool = rayon::ThreadPoolBuilder::new()
+            .num_threads(num_workers.unwrap_or(0))
+            .build()
+            .map_err(|e| PyErr::new::<pyo3::exceptions::PyRuntimeError, _>(e.to_string()))?;
+
+        let errors: usize = pool.install(|| {
+            // Split into chunks, each chunk gets its own decoder + batch decode
+            let chunk_size = n.div_ceil(rayon::current_num_threads());
+            (0..n)
+                .collect::<Vec<_>>()
+                .par_chunks(chunk_size.max(1))
+                .map(|chunk| {
+                    // Build a fresh decoder for this worker
+                    let mut dec = ObservableSubgraphDecoder::from_dem_windowed(
+                        &dem_str,
+                        &sc,
+                        max_time_radius,
+                        |subgraph| {
+                            let sub_dem = subgraph_to_dem_string(subgraph);
+                            let d =
+                                create_observable_decoder(&sub_dem, &inner_str).map_err(|e| {
+                                    pecos_decoders::DecoderError::InternalError(e.to_string())
+                                })?;
+                            Ok(Box::new(SendWrapper(d))
+                                as Box<dyn pecos_decoders::ObservableDecoder + Send + Sync>)
+                        },
+                    )
+                    .unwrap();
+
+                    // Collect chunk syndromes and masks for batch decode
+                    let chunk_syns: Vec<Vec<u8>> =
+                        chunk.iter().map(|&i| events[i].clone()).collect();
+                    let chunk_masks: Vec<u64> = chunk.iter().map(|&i| masks[i]).collect();
+                    dec.decode_count_batched(&chunk_syns, &chunk_masks)
+                        .unwrap_or(chunk.len())
+                })
+                .sum()
+        });
+
+        Ok(errors)
+    }
+
+    /// Number of detectors in each subgraph.
+    fn subgraph_sizes(&self) -> Vec<usize> {
+        (0..self.inner.num_observables())
+            .map(|i| self.inner.subgraph(i).map_or(0, |sg| sg.detector_map.len()))
+            .collect()
+    }
+
+    /// Diagnostics: (`num_edges`, `skipped_hyperedges`) for each subgraph.
+    fn subgraph_diagnostics(&self) -> Vec<(usize, usize)> {
+        (0..self.inner.num_observables())
+            .map(|i| {
+                self.inner.subgraph(i).map_or((0, 0), |sg| {
+                    (sg.graph.edges.len(), sg.graph.skipped_hyperedges)
+                })
+            })
+            .collect()
+    }
+
+    /// Count ghost edges (3-detector cross-qubit hyperedges) in the DEM.
+    ///
+    /// These are the hyperedges that the ghost protocol decomposes for
+    /// modular per-qubit decoding. Returns (`total_ghost_edges`, `num_qubits`).
+    #[staticmethod]
+    fn count_ghost_edges(
+        dem: &str,
+        stab_coords: Vec<pyo3::Bound<'_, pyo3::types::PyDict>>,
+    ) -> PyResult<(usize, usize)> {
+        use pecos_decoder_core::ghost_protocol::extract_ghost_edges_from_dem;
+        use pecos_decoder_core::observable_subgraph::QubitStabCoords;
+
+        let mut sc = Vec::with_capacity(stab_coords.len());
+        for dict in &stab_coords {
+            let x: Vec<(f64, f64)> = dict
+                .get_item("X")?
+                .ok_or_else(|| PyErr::new::<pyo3::exceptions::PyKeyError, _>("X"))?
+                .extract()?;
+            let z: Vec<(f64, f64)> = dict
+                .get_item("Z")?
+                .ok_or_else(|| PyErr::new::<pyo3::exceptions::PyKeyError, _>("Z"))?
+                .extract()?;
+            sc.push(QubitStabCoords {
+                x_positions: x,
+                z_positions: z,
+            });
+        }
+
+        let edges = extract_ghost_edges_from_dem(dem, &sc);
+        let num_qubits = sc.len();
+        Ok((edges.len(), num_qubits))
+    }
+
+    /// Get the per-subgraph DEM strings (graphlike, suitable for windowed decoding).
+    ///
+    /// Each string is a DEM with local detector IDs (0..N) that can be
+    /// passed to windowed or sandwich decoders.
+    fn subgraph_dems(&self) -> Vec<String> {
+        (0..self.inner.num_observables())
+            .map(|i| {
+                self.inner
+                    .subgraph(i)
+                    .map_or(String::new(), |sg| subgraph_to_dem_string(&sg.graph))
+            })
+            .collect()
+    }
+
+    /// Get the detector map for each subgraph (local → global index mapping).
+    fn subgraph_detector_maps(&self) -> Vec<Vec<usize>> {
+        (0..self.inner.num_observables())
+            .map(|i| {
+                self.inner
+                    .subgraph(i)
+                    .map_or(Vec::new(), |sg| sg.detector_map.clone())
+            })
+            .collect()
+    }
+}
+
+// =============================================================================
+// Windowed OSD Decoder (Python class)
+// =============================================================================
+
+/// Windowed observable subgraph decoder for deep circuits.
+///
+/// Splits the DEM into time windows, runs OSD within each window.
+/// Prevents the observing region from spanning the full circuit.
+///
+/// Args:
+///     dem: DEM string.
+///     `stab_coords`: Stabilizer coordinates per logical qubit.
+///     `inner_decoder`: Inner MWPM decoder type.
+///     step: Core window size in time steps.
+///     buffer: Buffer size on each side (0 = non-overlapping).
+#[pyclass(name = "WindowedOsdDecoder", module = "pecos_rslib.qec")]
+pub struct PyWindowedOsdDecoder {
+    inner: pecos_decoder_core::windowed_osd::WindowedOsdDecoder,
+}
+
+#[pymethods]
+impl PyWindowedOsdDecoder {
+    #[new]
+    #[pyo3(signature = (dem, stab_coords, inner_decoder="pymatching", step=8, buffer=4))]
+    fn new(
+        dem: &str,
+        stab_coords: Vec<pyo3::Bound<'_, pyo3::types::PyDict>>,
+        inner_decoder: &str,
+        step: usize,
+        buffer: usize,
+    ) -> PyResult<Self> {
+        use pecos_decoder_core::observable_subgraph::QubitStabCoords;
+        use pecos_decoder_core::windowed_osd::{WindowedOsdConfig, WindowedOsdDecoder};
+
+        let mut sc = Vec::with_capacity(stab_coords.len());
+        for dict in &stab_coords {
+            let x: Vec<(f64, f64)> = dict
+                .get_item("X")?
+                .ok_or_else(|| PyErr::new::<pyo3::exceptions::PyKeyError, _>("X"))?
+                .extract()?;
+            let z: Vec<(f64, f64)> = dict
+                .get_item("Z")?
+                .ok_or_else(|| PyErr::new::<pyo3::exceptions::PyKeyError, _>("Z"))?
+                .extract()?;
+            sc.push(QubitStabCoords {
+                x_positions: x,
+                z_positions: z,
+            });
+        }
+
+        let config = WindowedOsdConfig { step, buffer };
+
+        let inner = WindowedOsdDecoder::from_dem(dem, &sc, &config, |subgraph| {
+            let sub_dem = subgraph_to_dem_string(subgraph);
+            let d = create_observable_decoder(&sub_dem, inner_decoder)
+                .map_err(|e| pecos_decoders::DecoderError::InternalError(e.to_string()))?;
+            Ok(Box::new(SendWrapper(d))
+                as Box<dyn pecos_decoders::ObservableDecoder + Send + Sync>)
+        })
+        .map_err(|e| PyErr::new::<pyo3::exceptions::PyRuntimeError, _>(e.to_string()))?;
+
+        Ok(Self { inner })
+    }
+
+    fn decode(&mut self, syndrome: Vec<u8>) -> PyResult<u64> {
+        use pecos_decoder_core::ObservableDecoder;
+        self.inner
+            .decode_to_observables(&syndrome)
+            .map_err(|e| PyErr::new::<pyo3::exceptions::PyRuntimeError, _>(e.to_string()))
+    }
+
+    fn decode_count(&mut self, batch: &PySampleBatch) -> PyResult<usize> {
+        use pecos_decoder_core::ObservableDecoder;
+        let mut errors = 0usize;
+        let mut syndrome = vec![0u8; batch.num_detectors];
+        for i in 0..batch.num_shots {
+            batch.extract_syndrome(i, &mut syndrome);
+            let predicted = self
+                .inner
+                .decode_to_observables(&syndrome)
+                .map_err(|e| PyErr::new::<pyo3::exceptions::PyRuntimeError, _>(e.to_string()))?;
+            if predicted != batch.extract_obs_mask(i) {
+                errors += 1;
+            }
+        }
+        Ok(errors)
+    }
+
+    fn num_windows(&self) -> usize {
+        self.inner.windows.len()
+    }
+}
+
+// =============================================================================
+// Logical Algorithm Decoder (Python class)
+// =============================================================================
+
+/// Decoder for logical quantum algorithms with per-segment OSD and
+/// Pauli frame propagation at transversal gate boundaries.
+///
+/// Built from a descriptor dict produced by
+/// ``LogicalCircuitBuilder.build_algorithm_descriptor()``.
+///
+/// Supports both batch mode (``decode``, ``decode_count``) and
+/// streaming mode (``feed_sparse``, ``flush``, ``reset``).
+#[pyclass(name = "LogicalAlgorithmDecoder", module = "pecos_rslib.qec")]
+pub struct PyLogicalAlgorithmDecoder {
+    inner: pecos_decoder_core::logical_algorithm::StreamingLogicalDecoder,
+}
+
+#[pymethods]
+impl PyLogicalAlgorithmDecoder {
+    /// Build from a descriptor dict and inner decoder type.
+    ///
+    /// Args:
+    ///     descriptor: Dict from ``LogicalCircuitBuilder.build_algorithm_descriptor()``.
+    ///     `inner_decoder`: Decoder type string for each segment's OSD inner decoder.
+    #[new]
+    #[pyo3(signature = (descriptor, inner_decoder="pymatching"))]
+    fn new(
+        descriptor: &pyo3::Bound<'_, pyo3::types::PyDict>,
+        inner_decoder: &str,
+    ) -> PyResult<Self> {
+        use pecos_decoder_core::logical_algorithm::{
+            AlgorithmDescriptor, BoundaryGate, LogicalAlgorithmDecoder, SegmentDescriptor,
+        };
+        use pecos_decoder_core::observable_subgraph::{ObservableSubgraphDecoder, QubitStabCoords};
+
+        // Parse full DEM and stab_coords for full-circuit OSD
+        let full_dem: String = descriptor
+            .get_item("full_dem")?
+            .ok_or_else(|| PyErr::new::<pyo3::exceptions::PyKeyError, _>("full_dem"))?
+            .extract()?;
+
+        // Use first segment's stab_coords as the base (they have the
+        // original X/Z assignment; the full-circuit DEM uses original coords).
+        let seg_list: Vec<pyo3::Bound<'_, pyo3::types::PyDict>> = descriptor
+            .get_item("segments")?
+            .ok_or_else(|| PyErr::new::<pyo3::exceptions::PyKeyError, _>("segments"))?
+            .extract()?;
+
+        let num_obs: usize = descriptor
+            .get_item("num_observables")?
+            .ok_or_else(|| PyErr::new::<pyo3::exceptions::PyKeyError, _>("num_observables"))?
+            .extract()?;
+
+        // Parse stab_coords from the first segment (original orientation)
+        let first_seg = &seg_list[0];
+        let sc_list: Vec<pyo3::Bound<'_, pyo3::types::PyDict>> = first_seg
+            .get_item("stab_coords")?
+            .ok_or_else(|| PyErr::new::<pyo3::exceptions::PyKeyError, _>("stab_coords"))?
+            .extract()?;
+        let mut rust_sc = Vec::with_capacity(sc_list.len());
+        for sc_dict in &sc_list {
+            let x: Vec<(f64, f64)> = sc_dict
+                .get_item("X")?
+                .ok_or_else(|| PyErr::new::<pyo3::exceptions::PyKeyError, _>("X"))?
+                .extract()?;
+            let z: Vec<(f64, f64)> = sc_dict
+                .get_item("Z")?
+                .ok_or_else(|| PyErr::new::<pyo3::exceptions::PyKeyError, _>("Z"))?
+                .extract()?;
+            rust_sc.push(QubitStabCoords {
+                x_positions: x,
+                z_positions: z,
+            });
+        }
+
+        let inner_str = inner_decoder.to_string();
+
+        // Build full-circuit OSD from the full DEM
+        let full_osd = ObservableSubgraphDecoder::from_dem(&full_dem, &rust_sc, |subgraph| {
+            let sub_dem = subgraph_to_dem_string(subgraph);
+            let d = create_observable_decoder(&sub_dem, &inner_str)
+                .map_err(|e| pecos_decoders::DecoderError::InternalError(e.to_string()))?;
+            Ok(Box::new(SendWrapper(d))
+                as Box<dyn pecos_decoders::ObservableDecoder + Send + Sync>)
+        })
+        .map_err(|e| PyErr::new::<pyo3::exceptions::PyRuntimeError, _>(e.to_string()))?;
+
+        // Parse segment descriptors (for metadata)
+        let mut seg_descs = Vec::with_capacity(seg_list.len());
+        for seg_dict in &seg_list {
+            let n_det: usize = seg_dict
+                .get_item("num_detectors")?
+                .ok_or_else(|| PyErr::new::<pyo3::exceptions::PyKeyError, _>("num_detectors"))?
+                .extract()?;
+            seg_descs.push(SegmentDescriptor {
+                num_detectors: n_det,
+                num_observables: num_obs,
+            });
+        }
+
+        // Parse boundary gates
+        let bg_list: Vec<Vec<pyo3::Bound<'_, pyo3::types::PyDict>>> = descriptor
+            .get_item("boundary_gates")?
+            .ok_or_else(|| PyErr::new::<pyo3::exceptions::PyKeyError, _>("boundary_gates"))?
+            .extract()?;
+
+        let mut boundary_gates = Vec::with_capacity(bg_list.len());
+        for gates in &bg_list {
+            let mut bg_vec = Vec::new();
+            for gate_dict in gates {
+                let gate_type: String = gate_dict
+                    .get_item("type")?
+                    .ok_or_else(|| PyErr::new::<pyo3::exceptions::PyKeyError, _>("type"))?
+                    .extract()?;
+                match gate_type.as_str() {
+                    "Hadamard" => {
+                        let x: u32 = gate_dict.get_item("x_obs_bit")?.unwrap().extract()?;
+                        let z: u32 = gate_dict.get_item("z_obs_bit")?.unwrap().extract()?;
+                        bg_vec.push(BoundaryGate::Hadamard {
+                            x_obs_bit: x,
+                            z_obs_bit: z,
+                        });
+                    }
+                    "Cnot" => {
+                        bg_vec.push(BoundaryGate::Cnot {
+                            ctrl_x_bit: gate_dict.get_item("ctrl_x_bit")?.unwrap().extract()?,
+                            ctrl_z_bit: gate_dict.get_item("ctrl_z_bit")?.unwrap().extract()?,
+                            tgt_x_bit: gate_dict.get_item("tgt_x_bit")?.unwrap().extract()?,
+                            tgt_z_bit: gate_dict.get_item("tgt_z_bit")?.unwrap().extract()?,
+                        });
+                    }
+                    "SGate" => {
+                        let x: u32 = gate_dict.get_item("x_obs_bit")?.unwrap().extract()?;
+                        let z: u32 = gate_dict.get_item("z_obs_bit")?.unwrap().extract()?;
+                        bg_vec.push(BoundaryGate::SGate {
+                            x_obs_bit: x,
+                            z_obs_bit: z,
+                        });
+                    }
+                    "TGateInjection" => {
+                        let z: u32 = gate_dict.get_item("z_obs_bit")?.unwrap().extract()?;
+                        let a: u32 = gate_dict.get_item("ancilla_z_bit")?.unwrap().extract()?;
+                        bg_vec.push(BoundaryGate::TGateInjection {
+                            z_obs_bit: z,
+                            ancilla_z_bit: a,
+                        });
+                    }
+                    _ => {
+                        return Err(PyErr::new::<pyo3::exceptions::PyValueError, _>(format!(
+                            "Unknown gate type: {gate_type}"
+                        )));
+                    }
+                }
+            }
+            boundary_gates.push(bg_vec);
+        }
+
+        let algo_desc = AlgorithmDescriptor {
+            segments: seg_descs,
+            boundary_gates,
+            num_observables: num_obs,
+        };
+
+        let algo_dec = LogicalAlgorithmDecoder::new(Box::new(full_osd), algo_desc);
+        let inner = pecos_decoder_core::logical_algorithm::StreamingLogicalDecoder::new(algo_dec);
+        Ok(Self { inner })
+    }
+
+    // -- Batch mode --
+
+    /// Decode a single syndrome and return observable flip mask.
+    fn decode(&mut self, syndrome: Vec<u8>) -> PyResult<u64> {
+        self.inner.reset();
+        self.inner
+            .decode_shot(&syndrome)
+            .map_err(|e| PyErr::new::<pyo3::exceptions::PyRuntimeError, _>(e.to_string()))
+    }
+
+    /// Decode a batch of samples and count logical errors.
+    fn decode_count(&mut self, batch: &PySampleBatch) -> PyResult<usize> {
+        let detection_events: Vec<Vec<u8>> = (0..batch.num_shots)
+            .map(|i| {
+                let mut s = vec![0u8; batch.num_detectors];
+                batch.extract_syndrome(i, &mut s);
+                s
+            })
+            .collect();
+        let observable_masks: Vec<u64> = (0..batch.num_shots)
+            .map(|i| batch.extract_obs_mask(i))
+            .collect();
+        pecos_decoder_core::logical_algorithm::streaming_decode_count(
+            &mut self.inner,
+            &detection_events,
+            &observable_masks,
+        )
+        .map_err(|e| PyErr::new::<pyo3::exceptions::PyRuntimeError, _>(e.to_string()))
+    }
+
+    // -- Streaming mode --
+
+    /// Feed sparse detection events: list of (`detector_index`, value) pairs.
+    fn feed_sparse(&mut self, detectors: Vec<(u32, u8)>) {
+        self.inner.feed_sparse(&detectors);
+    }
+
+    /// Feed a dense syndrome (all detectors in order).
+    fn feed_dense(&mut self, syndrome: Vec<u8>) {
+        self.inner.feed_dense(&syndrome);
+    }
+
+    /// Decode the accumulated syndrome. Call at segment boundaries or end.
+    fn flush(&mut self) -> PyResult<u64> {
+        self.inner
+            .flush()
+            .map_err(|e| PyErr::new::<pyo3::exceptions::PyRuntimeError, _>(e.to_string()))
+    }
+
+    /// Reset syndrome buffer for the next shot.
+    fn reset(&mut self) {
+        self.inner.reset();
+    }
+
+    /// Current accumulated observable correction.
+    fn accumulated_obs(&self) -> u64 {
+        self.inner.accumulated_obs()
+    }
+
+    // -- Metadata --
+
+    /// Number of segments.
+    fn num_segments(&self) -> usize {
+        self.inner.num_segments()
+    }
+
+    /// Rounds fed so far.
+    fn rounds_fed(&self) -> usize {
+        self.inner.rounds_fed()
+    }
+}
+
+// =============================================================================
+// Logical Circuit Decoder with Budget (Python class)
+// =============================================================================
+
+/// Budget-aware decoder for logical quantum circuits.
+///
+/// Selects decode strategy based on available reaction time:
+/// - ``"unlimited"``: full-circuit OSD (Clifford circuits, offline)
+/// - ``"windowed"``: default windowed OSD (~1ms reaction time)
+/// - ``"10ms"``, ``"1000us"``, etc.: explicit reaction time budget
+///
+/// The reaction time is the time available at feed-forward decision
+/// points (T gates, magic state injection). For Clifford-only circuits,
+/// use ``"unlimited"`` since there are no mid-circuit decisions.
+///
+/// `Example::`
+///
+///     desc = builder.build_algorithm_descriptor(p1=0.001, p2=0.001)
+///     decoder = LogicalCircuitDecoder(desc, budget="unlimited")
+///     errors = decoder.decode_count(batch)
+#[pyclass(name = "LogicalCircuitDecoder", module = "pecos_rslib.qec")]
+pub struct PyLogicalCircuitDecoder {
+    inner: pecos_decoder_core::logical_algorithm::LogicalCircuitDecoder,
+}
+
+#[pymethods]
+impl PyLogicalCircuitDecoder {
+    #[new]
+    #[pyo3(signature = (descriptor, budget="unlimited", inner_decoder="pymatching"))]
+    fn new(
+        descriptor: &pyo3::Bound<'_, pyo3::types::PyDict>,
+        budget: &str,
+        inner_decoder: &str,
+    ) -> PyResult<Self> {
+        use pecos_decoder_core::decode_budget::DecodeBudget;
+        use pecos_decoder_core::logical_algorithm::{
+            AlgorithmDescriptor, BoundaryGate, FullCircuitStrategy, LogicalCircuitDecoder,
+            SegmentDescriptor,
+        };
+        use pecos_decoder_core::observable_subgraph::{ObservableSubgraphDecoder, QubitStabCoords};
+
+        // Parse full DEM
+        let full_dem: String = descriptor
+            .get_item("full_dem")?
+            .ok_or_else(|| PyErr::new::<pyo3::exceptions::PyKeyError, _>("full_dem"))?
+            .extract()?;
+
+        let seg_list: Vec<pyo3::Bound<'_, pyo3::types::PyDict>> = descriptor
+            .get_item("segments")?
+            .ok_or_else(|| PyErr::new::<pyo3::exceptions::PyKeyError, _>("segments"))?
+            .extract()?;
+
+        let num_obs: usize = descriptor
+            .get_item("num_observables")?
+            .ok_or_else(|| PyErr::new::<pyo3::exceptions::PyKeyError, _>("num_observables"))?
+            .extract()?;
+
+        // Parse stab_coords from first segment
+        let first_seg = &seg_list[0];
+        let sc_list: Vec<pyo3::Bound<'_, pyo3::types::PyDict>> = first_seg
+            .get_item("stab_coords")?
+            .ok_or_else(|| PyErr::new::<pyo3::exceptions::PyKeyError, _>("stab_coords"))?
+            .extract()?;
+        let mut rust_sc = Vec::with_capacity(sc_list.len());
+        for sc_dict in &sc_list {
+            let x: Vec<(f64, f64)> = sc_dict
+                .get_item("X")?
+                .ok_or_else(|| PyErr::new::<pyo3::exceptions::PyKeyError, _>("X"))?
+                .extract()?;
+            let z: Vec<(f64, f64)> = sc_dict
+                .get_item("Z")?
+                .ok_or_else(|| PyErr::new::<pyo3::exceptions::PyKeyError, _>("Z"))?
+                .extract()?;
+            rust_sc.push(QubitStabCoords {
+                x_positions: x,
+                z_positions: z,
+            });
+        }
+        let num_qubits = rust_sc.len();
+
+        let inner_str = inner_decoder.to_string();
+        let full_osd = ObservableSubgraphDecoder::from_dem(&full_dem, &rust_sc, |subgraph| {
+            let sub_dem = subgraph_to_dem_string(subgraph);
+            let d = create_observable_decoder(&sub_dem, &inner_str)
+                .map_err(|e| pecos_decoders::DecoderError::InternalError(e.to_string()))?;
+            Ok(Box::new(SendWrapper(d))
+                as Box<dyn pecos_decoders::ObservableDecoder + Send + Sync>)
+        })
+        .map_err(|e| PyErr::new::<pyo3::exceptions::PyRuntimeError, _>(e.to_string()))?;
+
+        // Parse segments
+        let mut seg_descs = Vec::with_capacity(seg_list.len());
+        for seg_dict in &seg_list {
+            let n_det: usize = seg_dict
+                .get_item("num_detectors")?
+                .ok_or_else(|| PyErr::new::<pyo3::exceptions::PyKeyError, _>("num_detectors"))?
+                .extract()?;
+            seg_descs.push(SegmentDescriptor {
+                num_detectors: n_det,
+                num_observables: num_obs,
+            });
+        }
+
+        // Parse boundary gates
+        let bg_list: Vec<Vec<pyo3::Bound<'_, pyo3::types::PyDict>>> = descriptor
+            .get_item("boundary_gates")?
+            .ok_or_else(|| PyErr::new::<pyo3::exceptions::PyKeyError, _>("boundary_gates"))?
+            .extract()?;
+
+        let mut boundary_gates = Vec::with_capacity(bg_list.len());
+        for gates in &bg_list {
+            let mut bg_vec = Vec::new();
+            for gate_dict in gates {
+                let gate_type: String = gate_dict
+                    .get_item("type")?
+                    .ok_or_else(|| PyErr::new::<pyo3::exceptions::PyKeyError, _>("type"))?
+                    .extract()?;
+                match gate_type.as_str() {
+                    "Hadamard" => {
+                        bg_vec.push(BoundaryGate::Hadamard {
+                            x_obs_bit: gate_dict.get_item("x_obs_bit")?.unwrap().extract()?,
+                            z_obs_bit: gate_dict.get_item("z_obs_bit")?.unwrap().extract()?,
+                        });
+                    }
+                    "Cnot" => {
+                        bg_vec.push(BoundaryGate::Cnot {
+                            ctrl_x_bit: gate_dict.get_item("ctrl_x_bit")?.unwrap().extract()?,
+                            ctrl_z_bit: gate_dict.get_item("ctrl_z_bit")?.unwrap().extract()?,
+                            tgt_x_bit: gate_dict.get_item("tgt_x_bit")?.unwrap().extract()?,
+                            tgt_z_bit: gate_dict.get_item("tgt_z_bit")?.unwrap().extract()?,
+                        });
+                    }
+                    "SGate" => {
+                        bg_vec.push(BoundaryGate::SGate {
+                            x_obs_bit: gate_dict.get_item("x_obs_bit")?.unwrap().extract()?,
+                            z_obs_bit: gate_dict.get_item("z_obs_bit")?.unwrap().extract()?,
+                        });
+                    }
+                    "TGateInjection" => {
+                        let z: u32 = gate_dict.get_item("z_obs_bit")?.unwrap().extract()?;
+                        let a: u32 = gate_dict.get_item("ancilla_z_bit")?.unwrap().extract()?;
+                        bg_vec.push(BoundaryGate::TGateInjection {
+                            z_obs_bit: z,
+                            ancilla_z_bit: a,
+                        });
+                    }
+                    _ => {
+                        return Err(PyErr::new::<pyo3::exceptions::PyValueError, _>(format!(
+                            "Unknown gate type: {gate_type}"
+                        )));
+                    }
+                }
+            }
+            boundary_gates.push(bg_vec);
+        }
+
+        let algo_desc = AlgorithmDescriptor {
+            segments: seg_descs,
+            boundary_gates,
+            num_observables: num_obs,
+        };
+
+        // Select budget: "unlimited" for full-circuit, "windowed" for
+        // bounded-latency, or a cycle time in microseconds like "1000us".
+        let mut distance = 0usize;
+        while distance.saturating_mul(distance) < num_qubits {
+            distance += 1;
+        }
+        let decode_budget = match budget {
+            "unlimited" | "offline" => DecodeBudget::unlimited(),
+            "windowed" => {
+                DecodeBudget::from_reaction_time(std::time::Duration::from_millis(1), distance)
+            }
+            s if s.ends_with("us") => {
+                let us: u64 = s[..s.len() - 2].parse().map_err(|_| {
+                    PyErr::new::<pyo3::exceptions::PyValueError, _>(format!(
+                        "Invalid cycle time: {s}"
+                    ))
+                })?;
+                DecodeBudget::from_reaction_time(std::time::Duration::from_micros(us), distance)
+            }
+            s if s.ends_with("ms") => {
+                let ms: u64 = s[..s.len() - 2].parse().map_err(|_| {
+                    PyErr::new::<pyo3::exceptions::PyValueError, _>(format!(
+                        "Invalid cycle time: {s}"
+                    ))
+                })?;
+                DecodeBudget::from_reaction_time(std::time::Duration::from_millis(ms), distance)
+            }
+            _ => {
+                return Err(PyErr::new::<pyo3::exceptions::PyValueError, _>(format!(
+                    "Unknown budget: {budget}. Use: unlimited, windowed, or a cycle time like 1000us, 10ms"
+                )));
+            }
+        };
+
+        // Select strategy based on budget.
+        let strategy: Box<dyn pecos_decoder_core::decode_budget::DecodeStrategy + Send + Sync> =
+            if decode_budget.is_unlimited() {
+                // Unlimited: full-circuit OSD (maximum accuracy)
+                Box::new(FullCircuitStrategy::new(Box::new(full_osd)))
+            } else {
+                // Windowed: per-subgraph sandwich decoding.
+                // Extract per-subgraph DEMs and detector maps from the full OSD.
+                use pecos_decoder_core::logical_algorithm::WindowedOsdStrategy;
+
+                let mut sub_dems = Vec::new();
+                let mut det_maps = Vec::new();
+                for i in 0..full_osd.num_observables() {
+                    if let Some(sg) = full_osd.subgraph(i) {
+                        sub_dems.push(subgraph_to_dem_string(&sg.graph));
+                        det_maps.push(sg.detector_map.clone());
+                    }
+                }
 
-    /// Sample from this DEM.
-    ///
-    /// Args:
-    ///     seed: Optional random seed for reproducibility.
-    ///
-    /// Returns:
-    ///     Tuple of (`detector_events`, `observable_flips`) as boolean lists.
-    #[pyo3(signature = (seed=None))]
-    fn sample(&self, seed: Option<u64>) -> (Vec<bool>, Vec<bool>) {
-        use pecos_random::PecosRng;
-        use rand::RngExt;
+                let d = decode_budget.code_distance;
+                let buf = decode_budget.overlap_rounds.min(d * 2); // cap at 2d
+                let windowed_str = if buf > 0 {
+                    format!("windowed:step={d},buf={buf},wmax=2.5")
+                } else {
+                    // No overlap: use plain PM (faster, but accuracy limited
+                    // to non-overlapping windowed matching)
+                    format!("windowed:step={d},buf=0")
+                };
+
+                let wosd = WindowedOsdStrategy::new(sub_dems, det_maps, |dem_str| {
+                    let dec = create_observable_decoder(dem_str, &windowed_str)
+                        .map_err(|e| pecos_decoders::DecoderError::InternalError(e.to_string()))?;
+                    Ok(Box::new(SendWrapper(dec))
+                        as Box<dyn pecos_decoders::ObservableDecoder + Send + Sync>)
+                })
+                .map_err(|e| PyErr::new::<pyo3::exceptions::PyRuntimeError, _>(e.to_string()))?;
 
-        let mut rng = match seed {
-            Some(s) => PecosRng::seed_from_u64(s),
-            None => PecosRng::seed_from_u64(rand::rng().random()),
-        };
+                Box::new(wosd)
+            };
 
-        self.inner.sample(&mut rng)
+        let inner = LogicalCircuitDecoder::new(algo_desc, strategy, decode_budget, num_qubits);
+        Ok(Self { inner })
     }
 
-    /// Sample multiple shots from this DEM.
-    ///
-    /// Args:
-    ///     `num_shots`: Number of shots to sample.
-    ///     seed: Optional random seed for reproducibility.
-    ///
-    /// Returns:
-    ///     Tuple of (`all_detector_events`, `all_observable_flips`).
-    #[pyo3(signature = (num_shots, seed=None))]
-    fn sample_batch(
-        &self,
-        num_shots: usize,
-        seed: Option<u64>,
-    ) -> (Vec<Vec<bool>>, Vec<Vec<bool>>) {
-        use pecos_random::PecosRng;
-        use rand::RngExt;
+    /// Decode a single syndrome.
+    fn decode(&mut self, syndrome: Vec<u8>) -> PyResult<u64> {
+        use pecos_decoder_core::ObservableDecoder;
+        self.inner
+            .decode_to_observables(&syndrome)
+            .map_err(|e| PyErr::new::<pyo3::exceptions::PyRuntimeError, _>(e.to_string()))
+    }
 
-        let mut rng = match seed {
-            Some(s) => PecosRng::seed_from_u64(s),
-            None => PecosRng::seed_from_u64(rand::rng().random()),
-        };
+    /// Decode a batch and count errors.
+    fn decode_count(&mut self, batch: &PySampleBatch) -> PyResult<usize> {
+        let detection_events: Vec<Vec<u8>> = (0..batch.num_shots)
+            .map(|i| {
+                let mut s = vec![0u8; batch.num_detectors];
+                batch.extract_syndrome(i, &mut s);
+                s
+            })
+            .collect();
+        let observable_masks: Vec<u64> = (0..batch.num_shots)
+            .map(|i| batch.extract_obs_mask(i))
+            .collect();
+        self.inner
+            .decode_count(&detection_events, &observable_masks)
+            .map_err(|e| PyErr::new::<pyo3::exceptions::PyRuntimeError, _>(e.to_string()))
+    }
 
-        self.inner.sample_batch(num_shots, &mut rng)
+    /// Number of segments.
+    fn num_segments(&self) -> usize {
+        self.inner.num_segments()
     }
 
-    /// Convert to an optimized `DemSampler` for fast batch sampling.
-    ///
-    /// The `DemSampler` uses geometric skip sampling and parallel chunked
-    /// processing, which is significantly faster than `sample_batch` for
-    /// large shot counts and low error rates.
-    ///
-    /// Returns:
-    ///     `DemSampler`: Optimized sampler for this DEM.
-    ///
-    /// Example:
-    ///     >>> dem = `ParsedDem.from_string("error(0.01)` D0 D1")
-    ///     >>> sampler = `dem.to_dem_sampler()`
-    ///     >>> stats = `sampler.sample_statistics(100000`, seed=42)
-    fn to_dem_sampler(&self) -> PyDemSampler {
-        PyDemSampler {
-            inner: self.inner.to_dem_sampler(),
-        }
+    /// Total detectors.
+    fn total_detectors(&self) -> usize {
+        self.inner.total_detectors()
     }
 
-    fn __repr__(&self) -> String {
-        format!(
-            "ParsedDem(mechanisms={}, detectors={}, observables={})",
-            self.inner.mechanisms.len(),
-            self.inner.num_detectors,
-            self.inner.num_observables
-        )
+    /// Whether the circuit has feed-forward decision points (T gates).
+    /// If False, the reaction time budget doesn't matter — Clifford only.
+    fn has_decision_points(&self) -> bool {
+        self.inner.has_decision_points()
+    }
+
+    /// Number of decision points.
+    fn num_decision_points(&self) -> usize {
+        self.inner.num_decision_points()
+    }
+
+    /// Reset for next shot.
+    fn reset(&mut self) {
+        self.inner.reset();
     }
 }
 
-/// Compare two DEMs for exact mechanism match.
-///
-/// This comparison aggregates mechanisms by effect and compares probabilities.
-/// Appropriate for non-decomposed DEMs or when exact match is required.
+// =============================================================================
+// Correlation Analysis Functions
+// =============================================================================
+
+/// Compute a detector flip frequency matrix from fired-detector lists.
 ///
 /// Args:
-///     dem1: First DEM string or `ParsedDem`.
-///     dem2: Second DEM string or `ParsedDem`.
-///     `prob_tolerance`: Relative tolerance for probability comparison (default 1e-6).
+///     fired_per_shot: List of lists, each inner list contains the detector
+///         indices that fired in that shot (sorted ascending).
+///     num_detectors: Total number of detectors.
 ///
 /// Returns:
-///     `EquivalenceResult` with comparison statistics.
-///
-/// Example:
-///     >>> result = `compare_dems_exact(dem1_str`, `dem2_str`, `prob_tolerance=0.001`)
-///     >>> if result.equivalent:
-///     ...     print("DEMs are equivalent")
+///     Flat list of length ``num_detectors^2`` (row-major). Diagonal entries
+///     are marginal rates; off-diagonal ``M[i*n+j]`` = 0.5 * P(i AND j fire).
 #[pyfunction]
-#[pyo3(signature = (dem1, dem2, prob_tolerance=1e-6))]
-fn compare_dems_exact(
-    dem1: &str,
-    dem2: &str,
-    prob_tolerance: f64,
-) -> PyResult<PyEquivalenceResult> {
-    let parsed1 = dem1
-        .parse::<RustParsedDem>()
-        .map_err(|e| pyo3::exceptions::PyValueError::new_err(format!("DEM1 parse error: {e}")))?;
-    let parsed2 = dem2
-        .parse::<RustParsedDem>()
-        .map_err(|e| pyo3::exceptions::PyValueError::new_err(format!("DEM2 parse error: {e}")))?;
-
-    let inner = rust_compare_dems_exact(&parsed1, &parsed2, prob_tolerance);
-    Ok(PyEquivalenceResult { inner })
+#[pyo3(signature = (fired_per_shot, num_detectors))]
+fn detector_flip_matrix(fired_per_shot: Vec<Vec<u32>>, num_detectors: usize) -> Vec<f64> {
+    pecos_qec::fault_tolerance::correlation::flip_matrix_from_fired(&fired_per_shot, num_detectors)
 }
 
-/// Compare two DEMs statistically by sampling.
+/// Compute per-round detector flip frequency matrices.
 ///
-/// This is the most robust comparison method as it accounts for all
-/// decomposition strategies and probability combinations. It compares
-/// the joint distribution of syndrome patterns, not just marginal rates.
-///
-/// Args:
-///     dem1: First DEM string or `ParsedDem`.
-///     dem2: Second DEM string or `ParsedDem`.
-///     `num_shots`: Number of shots for sampling (default 100,000).
-///     seed: Random seed (default 42).
-///     tolerance: Maximum relative difference to consider equivalent (default 0.05).
+/// Returns a list of flat matrices, one per round.
+#[pyfunction]
+#[pyo3(signature = (fired_per_shot, num_detectors, dets_per_round))]
+fn detector_flip_matrices_by_round(
+    fired_per_shot: Vec<Vec<u32>>,
+    num_detectors: usize,
+    dets_per_round: usize,
+) -> Vec<Vec<f64>> {
+    pecos_qec::fault_tolerance::correlation::flip_matrices_by_round(
+        &fired_per_shot,
+        num_detectors,
+        dets_per_round,
+    )
+}
+
+/// Compute k-body detector firing rates up to a given order.
 ///
-/// Returns:
-///     `EquivalenceResult` with comparison statistics.
+/// Returns a list of ``(detector_indices, rate)`` pairs where
+/// ``detector_indices`` is a tuple of sorted detector indices.
+#[pyfunction]
+#[pyo3(signature = (fired_per_shot, num_detectors, max_order=3))]
+fn detector_k_body_rates(
+    fired_per_shot: Vec<Vec<u32>>,
+    num_detectors: usize,
+    max_order: usize,
+) -> Vec<(Vec<u32>, f64)> {
+    pecos_qec::fault_tolerance::correlation::k_body_rates(&fired_per_shot, num_detectors, max_order)
+        .into_iter()
+        .collect()
+}
+
+/// Compute per-round k-body detector firing rates.
 ///
-/// Example:
-///     >>> result = `compare_dems_statistical(dem1_str`, `dem2_str`, `num_shots=50000`)
-///     >>> print(f"Correlation: {result.correlation}")
+/// Returns a list (one per round) of lists of ``(local_indices, rate)`` pairs.
 #[pyfunction]
-#[pyo3(signature = (dem1, dem2, num_shots=100_000, seed=42, tolerance=0.05))]
-fn compare_dems_statistical(
-    dem1: &str,
-    dem2: &str,
-    num_shots: usize,
-    seed: u64,
-    tolerance: f64,
-) -> PyResult<PyEquivalenceResult> {
-    let parsed1 = dem1
-        .parse::<RustParsedDem>()
-        .map_err(|e| pyo3::exceptions::PyValueError::new_err(format!("DEM1 parse error: {e}")))?;
-    let parsed2 = dem2
-        .parse::<RustParsedDem>()
-        .map_err(|e| pyo3::exceptions::PyValueError::new_err(format!("DEM2 parse error: {e}")))?;
+#[pyo3(signature = (fired_per_shot, num_detectors, dets_per_round, max_order=3))]
+fn detector_k_body_rates_by_round(
+    fired_per_shot: Vec<Vec<u32>>,
+    num_detectors: usize,
+    dets_per_round: usize,
+    max_order: usize,
+) -> Vec<Vec<(Vec<u32>, f64)>> {
+    pecos_qec::fault_tolerance::correlation::k_body_rates_by_round(
+        &fired_per_shot,
+        num_detectors,
+        dets_per_round,
+        max_order,
+    )
+    .into_iter()
+    .map(|m| m.into_iter().collect())
+    .collect()
+}
 
-    let inner = rust_compare_dems_statistical(&parsed1, &parsed2, num_shots, seed, tolerance);
-    Ok(PyEquivalenceResult { inner })
+/// Compare two flat flip matrices. Returns (max_rel_err, frob_rel_err, worst_i, worst_j).
+#[pyfunction]
+#[pyo3(signature = (sim, dem, num_detectors, min_rate=0.0005))]
+fn compare_flip_matrices_rs(
+    sim: Vec<f64>,
+    dem: Vec<f64>,
+    num_detectors: usize,
+    min_rate: f64,
+) -> (f64, f64, usize, usize) {
+    pecos_qec::fault_tolerance::correlation::compare_flip_matrices(
+        &sim,
+        &dem,
+        num_detectors,
+        min_rate,
+    )
 }
 
-/// Convenience function to verify DEM equivalence.
+/// Compare k-body rates grouped by order.
 ///
 /// Args:
-///     dem1: First DEM string.
-///     dem2: Second DEM string.
-///     method: Comparison method - "exact" or "statistical" (default "exact").
-///     `prob_tolerance`: For exact: probability tolerance (default 1e-6).
-///     `num_shots`: For statistical: number of shots (default 100,000).
-///     tolerance: For statistical: rate tolerance (default 0.05).
-///     seed: For statistical: random seed (default 42).
+///     sim: List of ``(detector_indices, rate)`` from simulation.
+///     dem: List of ``(detector_indices, rate)`` from DEM.
+///     min_rate: Minimum rate to consider.
 ///
 /// Returns:
-///     True if DEMs are equivalent within tolerance.
-///
-/// Example:
-///     >>> if `verify_dem_equivalence(dem1`, dem2, method="exact"):
-///     ...     print("DEMs match exactly")
+///     List of ``(order, max_rel_err, rms_rel_err, worst_event)`` tuples.
 #[pyfunction]
-#[pyo3(signature = (dem1, dem2, method="exact", prob_tolerance=1e-6, num_shots=100_000, tolerance=0.05, seed=42))]
-fn verify_dem_equivalence(
-    dem1: &str,
-    dem2: &str,
-    method: &str,
-    prob_tolerance: f64,
-    num_shots: usize,
-    tolerance: f64,
-    seed: u64,
-) -> PyResult<bool> {
-    let comparison_method = match method {
-        "exact" => RustComparisonMethod::Exact { prob_tolerance },
-        "statistical" => RustComparisonMethod::Statistical {
-            num_shots,
-            seed,
-            tolerance,
-        },
-        _ => {
-            return Err(pyo3::exceptions::PyValueError::new_err(
-                "method must be 'exact' or 'statistical'",
-            ));
-        }
-    };
-
-    rust_verify_dem_equivalence(dem1, dem2, &comparison_method)
-        .map_err(|e| pyo3::exceptions::PyValueError::new_err(e.to_string()))
+#[pyo3(signature = (sim, dem, min_rate=0.0005))]
+fn compare_k_body_rates_rs(
+    sim: Vec<(Vec<u32>, f64)>,
+    dem: Vec<(Vec<u32>, f64)>,
+    min_rate: f64,
+) -> Vec<(usize, f64, f64, Vec<u32>)> {
+    let sim_map: std::collections::BTreeMap<Vec<u32>, f64> = sim.into_iter().collect();
+    let dem_map: std::collections::BTreeMap<Vec<u32>, f64> = dem.into_iter().collect();
+    pecos_qec::fault_tolerance::correlation::compare_k_body(&sim_map, &dem_map, min_rate)
+        .into_iter()
+        .map(|(order, (me, rms, worst))| (order, me, rms, worst))
+        .collect()
 }
 
-/// Assert that two DEMs are equivalent, raising an error if not.
+/// Fit DEM mechanism probabilities to match target detector marginals.
 ///
-/// This is a convenience function for testing that raises `AssertionError`
-/// if the DEMs are not equivalent.
+/// Takes the mechanism structure (from a stochastic DEM) and exact
+/// per-detector marginals (from Heisenberg EEG), and adjusts mechanism
+/// probabilities so the DEM reproduces those marginals.
 ///
 /// Args:
-///     dem1: First DEM string.
-///     dem2: Second DEM string.
-///     method: Comparison method - "exact" or "statistical" (default "exact").
-///     `prob_tolerance`: For exact: probability tolerance (default 1e-6).
-///     `num_shots`: For statistical: number of shots (default 100,000).
-///     tolerance: For statistical: rate tolerance (default 0.05).
-///     seed: For statistical: random seed (default 42).
+///     mechanisms: List of ``(probability, detector_indices, observable_indices)``
+///         from the stochastic DEM.
+///     target_marginals: Exact per-detector rates from Heisenberg EEG.
+///     max_iterations: Maximum fitting iterations (default 200).
+///     tolerance: Convergence threshold (default 1e-12).
 ///
-/// Raises:
-///     `AssertionError`: If DEMs are not equivalent.
-///
-/// Example:
-///     >>> `assert_dems_equivalent(dem1`, dem2, method="exact")  # Raises if not equivalent
+/// Returns:
+///     Tuple of ``(fitted_mechanisms, residuals)`` where
+///     ``fitted_mechanisms`` has the same format as input but with
+///     adjusted probabilities, and ``residuals`` is the per-detector
+///     absolute error after fitting.
 #[pyfunction]
-#[pyo3(signature = (dem1, dem2, method="exact", prob_tolerance=1e-6, num_shots=100_000, tolerance=0.05, seed=42))]
-fn assert_dems_equivalent(
-    dem1: &str,
-    dem2: &str,
-    method: &str,
-    prob_tolerance: f64,
-    num_shots: usize,
+#[pyo3(signature = (mechanisms, target_marginals, max_iterations=200, tolerance=1e-12))]
+fn fit_dem_to_marginals(
+    mechanisms: Vec<PyDemMechanismTuple>,
+    target_marginals: Vec<f64>,
+    max_iterations: usize,
     tolerance: f64,
-    seed: u64,
-) -> PyResult<()> {
-    let parsed1 = dem1
-        .parse::<RustParsedDem>()
-        .map_err(|e| pyo3::exceptions::PyValueError::new_err(format!("DEM1 parse error: {e}")))?;
-    let parsed2 = dem2
-        .parse::<RustParsedDem>()
-        .map_err(|e| pyo3::exceptions::PyValueError::new_err(format!("DEM2 parse error: {e}")))?;
+) -> PyDemFitResult {
+    use pecos_qec::fault_tolerance::correlation::{
+        DemMechanism, fit_dem_to_marginals as fit_inner,
+    };
 
-    let result = match method {
-        "exact" => rust_compare_dems_exact(&parsed1, &parsed2, prob_tolerance),
-        "statistical" => {
-            rust_compare_dems_statistical(&parsed1, &parsed2, num_shots, seed, tolerance)
-        }
-        _ => {
-            return Err(pyo3::exceptions::PyValueError::new_err(
-                "method must be 'exact' or 'statistical'",
-            ));
-        }
+    let mechs: Vec<DemMechanism> = mechanisms
+        .iter()
+        .map(|(p, d, o)| DemMechanism {
+            probability: *p,
+            detectors: d.clone(),
+            observables: o.clone(),
+        })
+        .collect();
+
+    let (fitted, residuals) = fit_inner(&mechs, &target_marginals, max_iterations, tolerance);
+
+    let result: Vec<(f64, Vec<u32>, Vec<u32>)> = fitted
+        .iter()
+        .map(|m| (m.probability, m.detectors.clone(), m.observables.clone()))
+        .collect();
+
+    (result, residuals)
+}
+
+/// Format DEM mechanisms as a standard DEM string.
+#[pyfunction]
+fn mechanisms_to_dem_string(mechanisms: Vec<(f64, Vec<u32>, Vec<u32>)>) -> String {
+    use pecos_qec::fault_tolerance::correlation::{
+        DemMechanism, mechanisms_to_dem_string as fmt_inner,
     };
 
-    if result.equivalent {
-        Ok(())
-    } else {
-        let msg = format!(
-            "DEMs are not equivalent: max_rate_diff={:.6}, only_in_dem1={:?}, only_in_dem2={:?}",
-            result.max_rate_difference, result.details.only_in_dem1, result.details.only_in_dem2
-        );
-        Err(pyo3::exceptions::PyAssertionError::new_err(msg))
+    let mechs: Vec<DemMechanism> = mechanisms
+        .iter()
+        .map(|(p, d, o)| DemMechanism {
+            probability: *p,
+            detectors: d.clone(),
+            observables: o.clone(),
+        })
+        .collect();
+
+    fmt_inner(&mechs)
+}
+
+/// Query whether a decoder type requires decomposed (graphlike) DEMs.
+///
+/// Returns ``"graphlike"`` for MWPM decoders that need decomposed DEMs
+/// (hyperedges cause errors), ``"any"`` for decoders that handle both
+/// raw and decomposed DEMs.
+///
+/// Raises ``ValueError`` for unknown decoder types.
+#[pyfunction]
+fn decoder_dem_requirement(decoder_type: &str) -> PyResult<String> {
+    let base = decoder_type.split(':').next().unwrap_or(decoder_type);
+    match base {
+        "pymatching"
+        | "pymatching_uncorrelated"
+        | "fusion_blossom"
+        | "fusion_blossom_serial"
+        | "fusion_blossom_parallel"
+        | "fusion_blossom_correlated"
+        | "pecos_uf"
+        | "pecos_uf_correlated"
+        | "windowed"
+        | "k_mwpm"
+        | "perturbed_fb_corr"
+        | "perturbed_fb"
+        | "ensemble" => Ok("graphlike".to_string()),
+        "tesseract" | "astar" | "astar_full" | "bp_osd" | "bp_lsd" | "union_find"
+        | "min_sum_bp" | "relay_bp" | "mwpf" | "chromobius" => Ok("any".to_string()),
+        _ => Err(pyo3::exceptions::PyValueError::new_err(format!(
+            "Unknown decoder type: {decoder_type:?}",
+        ))),
     }
 }
 
@@ -2822,9 +5545,13 @@ pub fn register_qec_module(m: &Bound<'_, PyModule>) -> PyResult<()> {
     qec.add_class::<PyInfluenceBuilder>()?;
     qec.add_class::<PyDetectorErrorModel>()?;
     qec.add_class::<PyDemBuilder>()?;
-    qec.add_class::<PyMeasurementNoiseModel>()?;
-    qec.add_class::<PyMemBuilder>()?;
-    qec.add_class::<PyNoisySampler>()?;
+    qec.add_class::<PySampleBatch>()?;
+    qec.add_class::<PyCssUfDecoder>()?;
+    qec.add_class::<PyObservableSubgraphDecoder>()?;
+    qec.add_class::<PyWindowedOsdDecoder>()?;
+    qec.add_class::<PyLogicalAlgorithmDecoder>()?;
+    qec.add_class::<PyLogicalCircuitDecoder>()?;
+    qec.add_class::<PyDecodeStats>()?;
     qec.add_class::<PyDemSampler>()?;
     qec.add_class::<PyDemSamplerBuilder>()?;
     qec.add_class::<PyEquivalenceResult>()?;
@@ -2836,6 +5563,17 @@ pub fn register_qec_module(m: &Bound<'_, PyModule>) -> PyResult<()> {
     qec.add_function(wrap_pyfunction!(verify_dem_equivalence, &qec)?)?;
     qec.add_function(wrap_pyfunction!(assert_dems_equivalent, &qec)?)?;
 
+    // Correlation analysis
+    qec.add_function(wrap_pyfunction!(detector_flip_matrix, &qec)?)?;
+    qec.add_function(wrap_pyfunction!(detector_flip_matrices_by_round, &qec)?)?;
+    qec.add_function(wrap_pyfunction!(detector_k_body_rates, &qec)?)?;
+    qec.add_function(wrap_pyfunction!(detector_k_body_rates_by_round, &qec)?)?;
+    qec.add_function(wrap_pyfunction!(compare_flip_matrices_rs, &qec)?)?;
+    qec.add_function(wrap_pyfunction!(compare_k_body_rates_rs, &qec)?)?;
+    qec.add_function(wrap_pyfunction!(fit_dem_to_marginals, &qec)?)?;
+    qec.add_function(wrap_pyfunction!(mechanisms_to_dem_string, &qec)?)?;
+    qec.add_function(wrap_pyfunction!(decoder_dem_requirement, &qec)?)?;
+
     // Add Pauli constants
     qec.add("PAULI_I", 0u8)?;
     qec.add("PAULI_X", 1u8)?;
@@ -2844,6 +5582,10 @@ pub fn register_qec_module(m: &Bound<'_, PyModule>) -> PyResult<()> {
 
     m.add_submodule(&qec)?;
 
+    // Keep the common DEM sampler import available at the package root for
+    // scripts that use `from pecos_rslib import DemSampler`.
+    m.add("DemSampler", qec.getattr("DemSampler")?)?;
+
     // Register in sys.modules so 'from pecos_rslib.qec import ...' works
     let sys = m.py().import("sys")?;
     let modules = sys.getattr("modules")?;
diff --git a/python/pecos-rslib/src/gate_registry_bindings.rs b/python/pecos-rslib/src/gate_registry_bindings.rs
index b0d718111..5bb237c93 100644
--- a/python/pecos-rslib/src/gate_registry_bindings.rs
+++ b/python/pecos-rslib/src/gate_registry_bindings.rs
@@ -59,6 +59,7 @@ fn parse_gate_type(name: &str) -> PyResult<GateType> {
         "QAlloc" => Ok(GateType::QAlloc),
         "QFree" => Ok(GateType::QFree),
         "Idle" => Ok(GateType::Idle),
+        "TrackedPauli" | "TrackedPauliMeta" | "TP" => Ok(GateType::TrackedPauliMeta),
         _ => Err(pyo3::exceptions::PyValueError::new_err(format!(
             "Unknown gate type: '{name}'"
         ))),
diff --git a/python/pecos-rslib/src/lib.rs b/python/pecos-rslib/src/lib.rs
index d2c529a08..f22d4f96d 100644
--- a/python/pecos-rslib/src/lib.rs
+++ b/python/pecos-rslib/src/lib.rs
@@ -1,4 +1,16 @@
-#![allow(clippy::needless_pass_by_value)] // PyO3 requires owned values from Python
+// PyO3 binding signatures are constrained by the Python ABI and generated
+// method wrappers. Python docstrings also contain Python snippets that Clippy's
+// Rust-doc Markdown lint misclassifies. Keep this list limited to binding/docs
+// shape lints.
+#![allow(
+    clippy::doc_markdown,
+    clippy::missing_errors_doc,
+    clippy::missing_panics_doc,
+    clippy::needless_pass_by_value,
+    clippy::too_many_arguments,
+    clippy::unnecessary_wraps,
+    clippy::unused_self
+)]
 #![doc(html_root_url = "https://docs.rs/pecos-rslib")]
 // Disable doctests since they don't work with our workspace setup
 #![cfg_attr(docsrs, feature(doc_cfg))]
@@ -49,6 +61,7 @@ mod phir_json_bridge;
 mod programs_module;
 mod py_foreign_decoder;
 mod py_foreign_simulator;
+mod quantum_info_bindings;
 mod shot_results_bindings;
 mod sim;
 mod simulator_utils;
@@ -303,6 +316,9 @@ fn pecos_rslib(_py: Python<'_>, m: &Bound<'_, PyModule>) -> PyResult<()> {
     // Register quantum circuit types (DagCircuit, Gate, GateType, QubitId)
     dag_circuit_bindings::register_quantum_circuit_types(m)?;
 
+    // Register quantum-information channel and measure types
+    quantum_info_bindings::register_quantum_info_module(m)?;
+
     // Register gate registry types (GateRegistry, GateDefBuilder, AngleSource)
     gate_registry_bindings::register_gate_registry_types(m)?;
 
diff --git a/python/pecos-rslib/src/pauli_bindings.rs b/python/pecos-rslib/src/pauli_bindings.rs
index bd5e22a93..07a685d4c 100644
--- a/python/pecos-rslib/src/pauli_bindings.rs
+++ b/python/pecos-rslib/src/pauli_bindings.rs
@@ -16,6 +16,11 @@
 //! to Python, allowing quantum error models to use native Pauli representations
 //! instead of string-based arrays.
 
+// pyfunction generates internal modules named after the function (X, Y, Z)
+#![allow(non_snake_case)]
+
+use std::hash::{Hash, Hasher};
+
 use crate::prelude::{
     Pauli as RustPauli, PauliOperator, PauliString as RustPauliString, QuarterPhase, QubitId,
 };
@@ -201,7 +206,7 @@ impl PauliString {
         };
 
         // Build PauliString from input
-        let rust_paulis = if let Some(pauli_input) = paulis {
+        let mut rust_paulis = if let Some(pauli_input) = paulis {
             use pyo3::types::PyList;
 
             // Try to extract as a list - using cast() per PyO3 0.27 API
@@ -247,50 +252,63 @@ impl PauliString {
             Vec::new()
         };
 
+        rust_paulis.retain(|(pauli, _)| *pauli != RustPauli::I);
+        rust_paulis.sort_by_key(|(_, qubit)| *qubit);
+        for window in rust_paulis.windows(2) {
+            if window[0].1 == window[1].1 {
+                return Err(pyo3::exceptions::PyValueError::new_err(format!(
+                    "multiple non-identity Pauli operators were specified for qubit {}; \
+                     use multiplication (*) if you intend to compose Paulis on the same qubit",
+                    window[0].1.index()
+                )));
+            }
+        }
+
         // Construct RustPauliString using the new constructor
         let inner = RustPauliString::with_phase_and_paulis(rust_phase, rust_paulis);
 
         Ok(PauliString { inner })
     }
 
-    /// Create `PauliString` from a string like "XYZ" or "IXZI"
+    /// Create `PauliString` from dense or sparse string notation.
     ///
     /// Args:
-    ///     s: String of Pauli operators (I, X, Y, Z)
+    ///     s: Dense notation like "XIZ" or sparse notation like "X0 Z2".
     ///
     /// Returns:
-    ///     `PauliString` with operators on sequential qubits starting at 0
+    ///     `PauliString` parsed with the same auto-detection as Rust.
     ///
     /// Examples:
-    ///     >>> ps = `PauliString.from_str("XYZ`")
+    ///     >>> ps = PauliString.from_str("XYZ")
     ///     >>> # X on qubit 0, Y on qubit 1, Z on qubit 2
+    ///     >>> ps = PauliString.from_str("X0 Z2")
+    ///     >>> # X on qubit 0, Z on qubit 2
     #[staticmethod]
     fn from_str(s: &str) -> PyResult<Self> {
-        // Parse string character by character
-        let mut paulis = Vec::new();
-
-        for (i, c) in s.chars().enumerate() {
-            let pauli = match c {
-                'I' | 'i' => RustPauli::I,
-                'X' | 'x' => RustPauli::X,
-                'Y' | 'y' => RustPauli::Y,
-                'Z' | 'z' => RustPauli::Z,
-                _ => {
-                    return Err(pyo3::exceptions::PyValueError::new_err(format!(
-                        "Invalid Pauli character '{c}' at position {i}. Must be 'I', 'X', 'Y', or 'Z'"
-                    )));
-                }
-            };
-
-            // Only store non-identity operators (sparse representation)
-            if pauli != RustPauli::I {
-                paulis.push((pauli, QubitId::new(i)));
-            }
-        }
+        s.parse::<RustPauliString>()
+            .map(|inner| PauliString { inner })
+            .map_err(|err| pyo3::exceptions::PyValueError::new_err(err.to_string()))
+    }
 
-        let inner = RustPauliString::with_phase_and_paulis(QuarterPhase::PlusOne, paulis);
+    /// Create `PauliString` from dense string notation.
+    ///
+    /// Dense notation uses one Pauli character per qubit index, e.g. "XIZ"
+    /// means X on qubit 0 and Z on qubit 2.
+    #[staticmethod]
+    fn from_dense_str(s: &str) -> PyResult<Self> {
+        RustPauliString::from_dense_str(s)
+            .map(|inner| PauliString { inner })
+            .map_err(|err| pyo3::exceptions::PyValueError::new_err(err.to_string()))
+    }
 
-        Ok(PauliString { inner })
+    /// Create `PauliString` from sparse string notation.
+    ///
+    /// Sparse notation uses Pauli/qubit tokens, e.g. "X0 Z2".
+    #[staticmethod]
+    fn from_sparse_str(s: &str) -> PyResult<Self> {
+        RustPauliString::from_sparse_str(s)
+            .map(|inner| PauliString { inner })
+            .map_err(|err| pyo3::exceptions::PyValueError::new_err(err.to_string()))
     }
 
     /// String representation
@@ -326,6 +344,21 @@ impl PauliString {
         format!("{phase_str}{pauli_str}")
     }
 
+    /// Dense string representation with an explicit phase prefix.
+    ///
+    /// Example: `+XIZ` for X on qubit 0 and Z on qubit 2.
+    #[pyo3(signature = (num_qubits=None))]
+    fn to_dense_str(&self, num_qubits: Option<usize>) -> String {
+        self.inner.to_dense_str(num_qubits)
+    }
+
+    /// Sparse string representation with an explicit phase prefix.
+    ///
+    /// Example: `+X0 Z2` for X on qubit 0 and Z on qubit 2.
+    fn to_sparse_str(&self) -> String {
+        self.inner.to_sparse_str()
+    }
+
     /// Repr for debugging
     fn __repr__(&self) -> String {
         let phase = self.get_phase();
@@ -419,11 +452,155 @@ impl PauliString {
     fn anticommutes_with(&self, other: &PauliString) -> bool {
         !self.inner.commutes_with(&other.inner)
     }
+
+    // ---- Single-qubit constructors ----
+
+    /// Create X on a single qubit: `PauliString.X(3)`
+    #[staticmethod]
+    #[allow(non_snake_case)]
+    fn X(qubit: usize) -> Self {
+        PauliString {
+            inner: RustPauliString::x(qubit),
+        }
+    }
+
+    /// Create Y on a single qubit: `PauliString.Y(3)`
+    #[staticmethod]
+    #[allow(non_snake_case)]
+    fn Y(qubit: usize) -> Self {
+        PauliString {
+            inner: RustPauliString::y(qubit),
+        }
+    }
+
+    /// Create Z on a single qubit: `PauliString.Z(3)`
+    #[staticmethod]
+    #[allow(non_snake_case)]
+    fn Z(qubit: usize) -> Self {
+        PauliString {
+            inner: RustPauliString::z(qubit),
+        }
+    }
+
+    /// Create identity: `PauliString.I()`
+    #[staticmethod]
+    #[allow(non_snake_case)]
+    fn I() -> Self {
+        PauliString {
+            inner: RustPauliString::identity(),
+        }
+    }
+
+    // ---- Tensor product operator (&) ----
+
+    /// Tensor product: `PauliString.X(0) & PauliString.Z(1)`
+    fn __and__(&self, other: &PauliString) -> PyResult<Self> {
+        let mut lhs_qubits = self.inner.qubits();
+        lhs_qubits.sort_unstable();
+        lhs_qubits.dedup();
+
+        let mut rhs_qubits = other.inner.qubits();
+        rhs_qubits.sort_unstable();
+        rhs_qubits.dedup();
+
+        let mut overlap = Vec::new();
+        let mut lhs_idx = 0;
+        let mut rhs_idx = 0;
+        while lhs_idx < lhs_qubits.len() && rhs_idx < rhs_qubits.len() {
+            match lhs_qubits[lhs_idx].cmp(&rhs_qubits[rhs_idx]) {
+                std::cmp::Ordering::Less => lhs_idx += 1,
+                std::cmp::Ordering::Greater => rhs_idx += 1,
+                std::cmp::Ordering::Equal => {
+                    overlap.push(lhs_qubits[lhs_idx]);
+                    lhs_idx += 1;
+                    rhs_idx += 1;
+                }
+            }
+        }
+
+        if !overlap.is_empty() {
+            return Err(pyo3::exceptions::PyValueError::new_err(format!(
+                "tensor product requires disjoint Pauli support; overlapping qubits: {overlap:?}"
+            )));
+        }
+
+        Ok(PauliString {
+            inner: self.inner.clone() & other.inner.clone(),
+        })
+    }
+
+    /// Pauli multiplication: `PauliString.X(0) * PauliString.Y(0)`
+    fn __mul__(&self, other: &PauliString) -> Self {
+        PauliString {
+            inner: self.inner.clone() * other.inner.clone(),
+        }
+    }
+
+    /// Negation: `-PauliString.X(0)`
+    fn __neg__(&self) -> Self {
+        PauliString {
+            inner: -self.inner.clone(),
+        }
+    }
+
+    /// Equality check.
+    fn __eq__(&self, other: &PauliString) -> bool {
+        self.inner == other.inner
+    }
+
+    /// Hash for use in dictionaries and sets.
+    fn __hash__(&self) -> u64 {
+        let mut hasher = std::collections::hash_map::DefaultHasher::new();
+        self.inner.hash(&mut hasher);
+        hasher.finish()
+    }
+
+    /// Number of non-identity Pauli operators.
+    fn weight(&self) -> usize {
+        self.inner.weight()
+    }
+
+    /// List of qubit indices with non-identity operators.
+    fn qubits(&self) -> Vec<usize> {
+        self.inner.qubits()
+    }
+}
+
+// Module-level constructor functions for `from pecos import X, Y, Z`
+
+/// Create a single-qubit X `PauliString`: `X(3)`
+#[pyfunction]
+#[allow(non_snake_case)]
+pub fn X(qubit: usize) -> PauliString {
+    PauliString {
+        inner: RustPauliString::x(qubit),
+    }
+}
+
+/// Create a single-qubit Y `PauliString`: `Y(3)`
+#[pyfunction]
+#[allow(non_snake_case)]
+pub fn Y(qubit: usize) -> PauliString {
+    PauliString {
+        inner: RustPauliString::y(qubit),
+    }
+}
+
+/// Create a single-qubit Z `PauliString`: `Z(3)`
+#[pyfunction]
+#[allow(non_snake_case)]
+pub fn Z(qubit: usize) -> PauliString {
+    PauliString {
+        inner: RustPauliString::z(qubit),
+    }
 }
 
 /// Register Pauli types with Python module
 pub fn register_pauli_types(m: &Bound<'_, PyModule>) -> PyResult<()> {
     m.add_class::<Pauli>()?;
     m.add_class::<PauliString>()?;
+    m.add_function(pyo3::wrap_pyfunction!(X, m)?)?;
+    m.add_function(pyo3::wrap_pyfunction!(Y, m)?)?;
+    m.add_function(pyo3::wrap_pyfunction!(Z, m)?)?;
     Ok(())
 }
diff --git a/python/pecos-rslib/src/pauli_sequence_bindings.rs b/python/pecos-rslib/src/pauli_sequence_bindings.rs
index 4fad77cee..f6cf9cf3d 100644
--- a/python/pecos-rslib/src/pauli_sequence_bindings.rs
+++ b/python/pecos-rslib/src/pauli_sequence_bindings.rs
@@ -126,9 +126,18 @@ impl PyPauliSequence {
         self.inner.is_abelian()
     }
 
-    /// Commutation matrix: result[i][j] is True if i and j commute.
-    fn commutation_matrix(&self) -> Vec<Vec<bool>> {
-        self.inner.commutation_matrix()
+    /// Anticommutation matrix: result[i][j] is 1 if i and j anticommute.
+    fn commutation_matrix(&self) -> Vec<Vec<u8>> {
+        self.inner.commutation_matrix().rows()
+    }
+
+    /// Greedily partition Pauli strings into mutually commuting groups.
+    fn group_commuting(&self) -> Vec<Self> {
+        self.inner
+            .group_commuting()
+            .into_iter()
+            .map(|inner| Self { inner })
+            .collect()
     }
 
     /// Row-reduced form: independent Pauli strings in echelon form.
diff --git a/python/pecos-rslib/src/quantum_info_bindings.rs b/python/pecos-rslib/src/quantum_info_bindings.rs
new file mode 100644
index 000000000..a4ffc5958
--- /dev/null
+++ b/python/pecos-rslib/src/quantum_info_bindings.rs
@@ -0,0 +1,943 @@
+// Copyright 2026 The PECOS Developers
+//
+// Licensed under the Apache License, Version 2.0 (the "License"); you may not use this file except
+// in compliance with the License. You may obtain a copy of the License at
+//
+//     https://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software distributed under the License
+// is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express
+// or implied. See the License for the specific language governing permissions and limitations under
+// the License.
+
+//! Thin Python bindings for PECOS quantum-information primitives.
+
+use std::collections::BTreeMap;
+
+use crate::pauli_bindings::PauliString as PyPauliString;
+use nalgebra::{DMatrix, DVector};
+use num_complex::Complex64;
+use pecos_core::{Pauli as RustPauli, PauliBitmaskSmall, QuarterPhase};
+use pecos_quantum::{
+    ChiMatrix as RustChiMatrix, ChoiMatrix as RustChoiMatrix, KrausOps as RustKrausOps,
+    PauliChannel as RustPauliChannel, ProcessTomographyDesign as RustProcessTomographyDesign,
+    Ptm as RustPtm, Stinespring as RustStinespring, SuperOp as RustSuperOp,
+    average_gate_fidelity as rust_average_gate_fidelity, entropy as rust_entropy,
+    gate_error as rust_gate_error, hellinger_distance as rust_hellinger_distance,
+    hellinger_fidelity as rust_hellinger_fidelity,
+    logarithmic_negativity as rust_logarithmic_negativity, negativity as rust_negativity,
+    partial_trace_qubits as rust_partial_trace_qubits,
+    partial_trace_subsystems as rust_partial_trace_subsystems, pauli_basis_len,
+    process_fidelity as rust_process_fidelity, purity as rust_purity,
+    random_density_matrix as rust_random_density_matrix,
+    random_quantum_channel as rust_random_quantum_channel, state_fidelity as rust_state_fidelity,
+    state_fidelity_with_density_matrix as rust_state_fidelity_with_density_matrix,
+};
+use pecos_random::PecosRng;
+use pyo3::prelude::*;
+use pyo3::types::{PyDict, PyModule, PyTuple};
+
+type PySchmidtTerm = (f64, Vec<Complex64>, Vec<Complex64>);
+
+fn py_value_err(err: impl std::fmt::Display) -> PyErr {
+    pyo3::exceptions::PyValueError::new_err(err.to_string())
+}
+
+fn real_matrix_from_rows(rows: Vec<Vec<f64>>) -> PyResult<DMatrix<f64>> {
+    let row_count = rows.len();
+    let col_count = rows.first().map_or(0, Vec::len);
+    if rows.iter().any(|row| row.len() != col_count) {
+        return Err(pyo3::exceptions::PyValueError::new_err(
+            "matrix rows must all have the same length",
+        ));
+    }
+    let data: Vec<f64> = rows.into_iter().flatten().collect();
+    Ok(DMatrix::from_row_slice(row_count, col_count, &data))
+}
+
+fn complex_matrix_from_rows(rows: Vec<Vec<Complex64>>) -> PyResult<DMatrix<Complex64>> {
+    let row_count = rows.len();
+    let col_count = rows.first().map_or(0, Vec::len);
+    if rows.iter().any(|row| row.len() != col_count) {
+        return Err(pyo3::exceptions::PyValueError::new_err(
+            "matrix rows must all have the same length",
+        ));
+    }
+    let data: Vec<Complex64> = rows.into_iter().flatten().collect();
+    Ok(DMatrix::from_row_slice(row_count, col_count, &data))
+}
+
+fn complex_matrices_from_rows(
+    matrices: Vec<Vec<Vec<Complex64>>>,
+) -> PyResult<Vec<DMatrix<Complex64>>> {
+    matrices.into_iter().map(complex_matrix_from_rows).collect()
+}
+
+fn real_matrix_to_rows(matrix: &DMatrix<f64>) -> Vec<Vec<f64>> {
+    (0..matrix.nrows())
+        .map(|row| (0..matrix.ncols()).map(|col| matrix[(row, col)]).collect())
+        .collect()
+}
+
+fn complex_matrix_to_rows(matrix: &DMatrix<Complex64>) -> Vec<Vec<Complex64>> {
+    (0..matrix.nrows())
+        .map(|row| (0..matrix.ncols()).map(|col| matrix[(row, col)]).collect())
+        .collect()
+}
+
+fn complex_matrices_to_rows(matrices: &[DMatrix<Complex64>]) -> Vec<Vec<Vec<Complex64>>> {
+    matrices.iter().map(complex_matrix_to_rows).collect()
+}
+
+fn parse_pauli_label(num_qubits: usize, label: &str) -> PyResult<PauliBitmaskSmall> {
+    let label = label.trim();
+    if label.len() != num_qubits {
+        return Err(pyo3::exceptions::PyValueError::new_err(format!(
+            "Pauli label '{label}' has length {}, expected {num_qubits}",
+            label.len()
+        )));
+    }
+    let mut index = 0usize;
+    for (qubit, ch) in label.chars().rev().enumerate() {
+        let digit = match ch {
+            'I' => 0,
+            'X' => 1,
+            'Y' => 2,
+            'Z' => 3,
+            _ => {
+                return Err(pyo3::exceptions::PyValueError::new_err(format!(
+                    "invalid Pauli label '{label}'; expected only I, X, Y, Z"
+                )));
+            }
+        };
+        index |= digit << (2 * qubit);
+    }
+    pecos_quantum::basis_bitmask(num_qubits, index).map_err(py_value_err)
+}
+
+fn parse_pauli_string_key(
+    num_qubits: usize,
+    pauli_string: &PyPauliString,
+) -> PyResult<PauliBitmaskSmall> {
+    if pauli_string.inner.get_phase() != QuarterPhase::PlusOne {
+        return Err(pyo3::exceptions::PyValueError::new_err(
+            "PauliChannel probabilities require unphased PauliString keys",
+        ));
+    }
+
+    let mut out = PauliBitmaskSmall::identity();
+    for (pauli, qubit) in pauli_string.inner.get_paulis() {
+        let qubit = qubit.index();
+        if qubit >= num_qubits {
+            return Err(pyo3::exceptions::PyValueError::new_err(format!(
+                "PauliString key acts on qubit {qubit}, outside num_qubits={num_qubits}"
+            )));
+        }
+        let single = match pauli {
+            RustPauli::I => PauliBitmaskSmall::identity(),
+            RustPauli::X => PauliBitmaskSmall::x(qubit),
+            RustPauli::Y => PauliBitmaskSmall::y(qubit),
+            RustPauli::Z => PauliBitmaskSmall::z(qubit),
+        };
+        out = out.multiply(&single);
+    }
+    Ok(out)
+}
+
+fn parse_pauli_probability_key(
+    num_qubits: usize,
+    key: &Bound<'_, PyAny>,
+) -> PyResult<PauliBitmaskSmall> {
+    if let Ok(label) = key.extract::<String>() {
+        return parse_pauli_label(num_qubits, &label);
+    }
+    if let Ok(pauli_string) = key.extract::<PyRef<'_, PyPauliString>>() {
+        return parse_pauli_string_key(num_qubits, &pauli_string);
+    }
+    Err(pyo3::exceptions::PyTypeError::new_err(
+        "PauliChannel probability keys must be dense Pauli labels or PauliString objects",
+    ))
+}
+
+fn insert_probability(
+    probabilities: &mut BTreeMap<PauliBitmaskSmall, f64>,
+    pauli: PauliBitmaskSmall,
+    probability: f64,
+) -> PyResult<()> {
+    if probabilities.insert(pauli, probability).is_some() {
+        return Err(pyo3::exceptions::PyValueError::new_err(
+            "duplicate PauliChannel probability key",
+        ));
+    }
+    Ok(())
+}
+
+fn pauli_probabilities_from_py(
+    num_qubits: usize,
+    probabilities: &Bound<'_, PyAny>,
+) -> PyResult<BTreeMap<PauliBitmaskSmall, f64>> {
+    let mut out = BTreeMap::new();
+    if let Ok(dict) = probabilities.cast::<PyDict>() {
+        for (key, value) in dict.iter() {
+            let pauli = parse_pauli_probability_key(num_qubits, &key)?;
+            insert_probability(&mut out, pauli, value.extract()?)?;
+        }
+    } else {
+        for item in probabilities.try_iter()? {
+            let tuple: Bound<'_, PyTuple> = item?.cast_into()?;
+            if tuple.len() != 2 {
+                return Err(pyo3::exceptions::PyValueError::new_err(
+                    "PauliChannel probability sequences must contain (pauli, probability) pairs",
+                ));
+            }
+            let pauli = parse_pauli_probability_key(num_qubits, &tuple.get_item(0)?)?;
+            insert_probability(&mut out, pauli, tuple.get_item(1)?.extract()?)?;
+        }
+    }
+    Ok(out)
+}
+
+#[pyclass(name = "PauliChannel", module = "pecos_rslib.quantum_info")]
+pub struct PyPauliChannel {
+    inner: RustPauliChannel,
+}
+
+#[pymethods]
+impl PyPauliChannel {
+    #[staticmethod]
+    fn one_qubit(px: f64, py: f64, pz: f64) -> PyResult<Self> {
+        Ok(Self {
+            inner: RustPauliChannel::one_qubit(px, py, pz).map_err(py_value_err)?,
+        })
+    }
+
+    #[staticmethod]
+    fn from_probabilities(num_qubits: usize, probabilities: &Bound<'_, PyAny>) -> PyResult<Self> {
+        Ok(Self {
+            inner: RustPauliChannel::try_new(
+                num_qubits,
+                pauli_probabilities_from_py(num_qubits, probabilities)?,
+            )
+            .map_err(py_value_err)?,
+        })
+    }
+
+    fn num_qubits(&self) -> usize {
+        self.inner.num_qubits()
+    }
+
+    fn probabilities(&self) -> PyResult<BTreeMap<String, f64>> {
+        let mut out = BTreeMap::new();
+        let basis_len = pauli_basis_len(self.inner.num_qubits()).map_err(py_value_err)?;
+        for basis_index in 0..basis_len {
+            let pauli = pecos_quantum::basis_bitmask(self.inner.num_qubits(), basis_index)
+                .map_err(py_value_err)?;
+            let probability = self.inner.probability(&pauli);
+            if probability > 0.0 {
+                out.insert(
+                    pecos_quantum::basis_label(self.inner.num_qubits(), basis_index)
+                        .map_err(py_value_err)?,
+                    probability,
+                );
+            }
+        }
+        Ok(out)
+    }
+
+    fn total_error_rate(&self) -> f64 {
+        self.inner.total_error_rate()
+    }
+
+    fn to_ptm(&self) -> PyResult<PyPtm> {
+        Ok(PyPtm {
+            inner: self.inner.to_ptm().map_err(py_value_err)?,
+        })
+    }
+
+    fn __repr__(&self) -> String {
+        format!("PauliChannel(num_qubits={})", self.inner.num_qubits())
+    }
+}
+
+#[pyclass(name = "Ptm", module = "pecos_rslib.quantum_info")]
+pub struct PyPtm {
+    inner: RustPtm,
+}
+
+#[pymethods]
+impl PyPtm {
+    #[new]
+    fn new(num_qubits: usize, matrix: Vec<Vec<f64>>) -> PyResult<Self> {
+        Ok(Self {
+            inner: RustPtm::try_new(num_qubits, real_matrix_from_rows(matrix)?)
+                .map_err(py_value_err)?,
+        })
+    }
+
+    #[staticmethod]
+    fn identity(num_qubits: usize) -> PyResult<Self> {
+        Ok(Self {
+            inner: RustPtm::identity(num_qubits).map_err(py_value_err)?,
+        })
+    }
+
+    fn num_qubits(&self) -> usize {
+        self.inner.num_qubits()
+    }
+
+    fn matrix(&self) -> Vec<Vec<f64>> {
+        real_matrix_to_rows(self.inner.matrix())
+    }
+
+    fn entry(&self, output: usize, input: usize) -> f64 {
+        self.inner.entry(output, input)
+    }
+
+    fn to_choi(&self) -> PyResult<PyChoiMatrix> {
+        Ok(PyChoiMatrix {
+            inner: self.inner.to_choi().map_err(py_value_err)?,
+        })
+    }
+
+    fn to_kraus(&self) -> PyResult<PyKrausOps> {
+        Ok(PyKrausOps {
+            inner: self.inner.to_kraus().map_err(py_value_err)?,
+        })
+    }
+
+    fn to_superop(&self) -> PyResult<PySuperOp> {
+        Ok(PySuperOp {
+            inner: self.inner.to_superop().map_err(py_value_err)?,
+        })
+    }
+
+    fn to_chi(&self) -> PyResult<PyChiMatrix> {
+        Ok(PyChiMatrix {
+            inner: self.inner.to_chi().map_err(py_value_err)?,
+        })
+    }
+
+    fn __repr__(&self) -> String {
+        format!("Ptm(num_qubits={})", self.inner.num_qubits())
+    }
+}
+
+#[pyclass(name = "KrausOps", module = "pecos_rslib.quantum_info")]
+pub struct PyKrausOps {
+    inner: RustKrausOps,
+}
+
+#[pymethods]
+impl PyKrausOps {
+    #[new]
+    fn new(num_qubits: usize, operators: Vec<Vec<Vec<Complex64>>>) -> PyResult<Self> {
+        let operators = operators
+            .into_iter()
+            .map(complex_matrix_from_rows)
+            .collect::<PyResult<Vec<_>>>()?;
+        Ok(Self {
+            inner: RustKrausOps::try_new(num_qubits, operators).map_err(py_value_err)?,
+        })
+    }
+
+    fn num_qubits(&self) -> usize {
+        self.inner.num_qubits()
+    }
+
+    fn operators(&self) -> Vec<Vec<Vec<Complex64>>> {
+        self.inner
+            .operators()
+            .iter()
+            .map(complex_matrix_to_rows)
+            .collect()
+    }
+
+    fn is_trace_preserving(&self) -> bool {
+        self.inner.is_trace_preserving()
+    }
+
+    fn to_ptm(&self) -> PyResult<PyPtm> {
+        Ok(PyPtm {
+            inner: self.inner.to_ptm().map_err(py_value_err)?,
+        })
+    }
+
+    fn to_choi(&self) -> PyResult<PyChoiMatrix> {
+        Ok(PyChoiMatrix {
+            inner: self.inner.to_choi().map_err(py_value_err)?,
+        })
+    }
+
+    fn to_superop(&self) -> PyResult<PySuperOp> {
+        Ok(PySuperOp {
+            inner: self.inner.to_superop().map_err(py_value_err)?,
+        })
+    }
+
+    fn to_chi(&self) -> PyResult<PyChiMatrix> {
+        Ok(PyChiMatrix {
+            inner: self.inner.to_chi().map_err(py_value_err)?,
+        })
+    }
+
+    fn to_stinespring(&self) -> PyResult<PyStinespring> {
+        Ok(PyStinespring {
+            inner: self.inner.to_stinespring().map_err(py_value_err)?,
+        })
+    }
+
+    fn __repr__(&self) -> String {
+        format!("KrausOps(num_qubits={})", self.inner.num_qubits())
+    }
+}
+
+#[pyclass(name = "ChoiMatrix", module = "pecos_rslib.quantum_info")]
+pub struct PyChoiMatrix {
+    inner: RustChoiMatrix,
+}
+
+#[pymethods]
+impl PyChoiMatrix {
+    #[new]
+    fn new(num_qubits: usize, matrix: Vec<Vec<Complex64>>) -> PyResult<Self> {
+        Ok(Self {
+            inner: RustChoiMatrix::try_new(num_qubits, complex_matrix_from_rows(matrix)?)
+                .map_err(py_value_err)?,
+        })
+    }
+
+    #[staticmethod]
+    fn from_matrix_unit_outputs(
+        num_qubits: usize,
+        outputs: Vec<Vec<Vec<Complex64>>>,
+    ) -> PyResult<Self> {
+        Ok(Self {
+            inner: RustChoiMatrix::from_matrix_unit_outputs(
+                num_qubits,
+                &complex_matrices_from_rows(outputs)?,
+            )
+            .map_err(py_value_err)?,
+        })
+    }
+
+    fn num_qubits(&self) -> usize {
+        self.inner.num_qubits()
+    }
+
+    fn matrix(&self) -> Vec<Vec<Complex64>> {
+        complex_matrix_to_rows(self.inner.matrix())
+    }
+
+    fn apply_to_operator(&self, operator: Vec<Vec<Complex64>>) -> PyResult<Vec<Vec<Complex64>>> {
+        Ok(complex_matrix_to_rows(
+            &self
+                .inner
+                .apply_to_operator(&complex_matrix_from_rows(operator)?)
+                .map_err(py_value_err)?,
+        ))
+    }
+
+    fn partial_trace_output(&self) -> PyResult<Vec<Vec<Complex64>>> {
+        Ok(complex_matrix_to_rows(
+            &self.inner.partial_trace_output().map_err(py_value_err)?,
+        ))
+    }
+
+    fn partial_trace_input(&self) -> PyResult<Vec<Vec<Complex64>>> {
+        Ok(complex_matrix_to_rows(
+            &self.inner.partial_trace_input().map_err(py_value_err)?,
+        ))
+    }
+
+    fn is_completely_positive(&self) -> bool {
+        self.inner.is_completely_positive()
+    }
+
+    fn is_trace_preserving(&self) -> bool {
+        self.inner.is_trace_preserving()
+    }
+
+    fn is_cptp(&self) -> bool {
+        self.inner.is_cptp()
+    }
+
+    fn is_unital(&self) -> bool {
+        self.inner.is_unital()
+    }
+
+    fn to_ptm(&self) -> PyResult<PyPtm> {
+        Ok(PyPtm {
+            inner: self.inner.to_ptm().map_err(py_value_err)?,
+        })
+    }
+
+    fn to_kraus(&self) -> PyResult<PyKrausOps> {
+        Ok(PyKrausOps {
+            inner: self.inner.to_kraus().map_err(py_value_err)?,
+        })
+    }
+
+    fn to_superop(&self) -> PyResult<PySuperOp> {
+        Ok(PySuperOp {
+            inner: self.inner.to_superop().map_err(py_value_err)?,
+        })
+    }
+
+    fn to_chi(&self) -> PyResult<PyChiMatrix> {
+        Ok(PyChiMatrix {
+            inner: self.inner.to_chi().map_err(py_value_err)?,
+        })
+    }
+
+    fn __repr__(&self) -> String {
+        format!("ChoiMatrix(num_qubits={})", self.inner.num_qubits())
+    }
+}
+
+#[pyclass(name = "ProcessTomographyDesign", module = "pecos_rslib.quantum_info")]
+pub struct PyProcessTomographyDesign {
+    inner: RustProcessTomographyDesign,
+}
+
+#[pymethods]
+impl PyProcessTomographyDesign {
+    #[staticmethod]
+    fn matrix_unit(num_qubits: usize) -> PyResult<Self> {
+        Ok(Self {
+            inner: RustProcessTomographyDesign::matrix_unit(num_qubits).map_err(py_value_err)?,
+        })
+    }
+
+    fn num_qubits(&self) -> usize {
+        self.inner.num_qubits()
+    }
+
+    fn dim(&self) -> usize {
+        self.inner.dim()
+    }
+
+    fn num_inputs(&self) -> usize {
+        self.inner.num_inputs()
+    }
+
+    fn input_index(&self, row: usize, col: usize) -> PyResult<usize> {
+        self.inner.input_index(row, col).map_err(py_value_err)
+    }
+
+    fn input_metadata(&self, index: usize) -> PyResult<(usize, usize, usize)> {
+        let input = self.inner.input_metadata(index).map_err(py_value_err)?;
+        Ok((input.index, input.row, input.col))
+    }
+
+    fn input_metadata_all(&self) -> Vec<(usize, usize, usize)> {
+        self.inner
+            .input_metadata_all()
+            .into_iter()
+            .map(|input| (input.index, input.row, input.col))
+            .collect()
+    }
+
+    fn input_operator(&self, index: usize) -> PyResult<Vec<Vec<Complex64>>> {
+        Ok(complex_matrix_to_rows(
+            &self.inner.input_operator(index).map_err(py_value_err)?,
+        ))
+    }
+
+    fn input_operators(&self) -> Vec<Vec<Vec<Complex64>>> {
+        complex_matrices_to_rows(&self.inner.input_operators())
+    }
+
+    fn simulate_outputs(&self, channel: &PyChoiMatrix) -> PyResult<Vec<Vec<Vec<Complex64>>>> {
+        Ok(complex_matrices_to_rows(
+            &self
+                .inner
+                .simulate_outputs(&channel.inner)
+                .map_err(py_value_err)?,
+        ))
+    }
+
+    fn reconstruct_choi(&self, outputs: Vec<Vec<Vec<Complex64>>>) -> PyResult<PyChoiMatrix> {
+        Ok(PyChoiMatrix {
+            inner: self
+                .inner
+                .reconstruct_choi(&complex_matrices_from_rows(outputs)?)
+                .map_err(py_value_err)?,
+        })
+    }
+
+    fn __repr__(&self) -> String {
+        format!(
+            "ProcessTomographyDesign(num_qubits={}, num_inputs={})",
+            self.inner.num_qubits(),
+            self.inner.num_inputs()
+        )
+    }
+}
+
+#[pyclass(name = "SuperOp", module = "pecos_rslib.quantum_info")]
+pub struct PySuperOp {
+    inner: RustSuperOp,
+}
+
+#[pymethods]
+impl PySuperOp {
+    #[new]
+    fn new(num_qubits: usize, matrix: Vec<Vec<Complex64>>) -> PyResult<Self> {
+        Ok(Self {
+            inner: RustSuperOp::try_new(num_qubits, complex_matrix_from_rows(matrix)?)
+                .map_err(py_value_err)?,
+        })
+    }
+
+    fn num_qubits(&self) -> usize {
+        self.inner.num_qubits()
+    }
+
+    fn matrix(&self) -> Vec<Vec<Complex64>> {
+        complex_matrix_to_rows(self.inner.matrix())
+    }
+
+    fn to_choi(&self) -> PyResult<PyChoiMatrix> {
+        Ok(PyChoiMatrix {
+            inner: self.inner.to_choi().map_err(py_value_err)?,
+        })
+    }
+
+    fn to_ptm(&self) -> PyResult<PyPtm> {
+        Ok(PyPtm {
+            inner: self.inner.to_ptm().map_err(py_value_err)?,
+        })
+    }
+
+    fn to_kraus(&self) -> PyResult<PyKrausOps> {
+        Ok(PyKrausOps {
+            inner: self.inner.to_kraus().map_err(py_value_err)?,
+        })
+    }
+
+    fn compose(&self, other: &PySuperOp) -> PyResult<PySuperOp> {
+        Ok(PySuperOp {
+            inner: self.inner.compose(&other.inner).map_err(py_value_err)?,
+        })
+    }
+
+    fn tensor(&self, other: &PySuperOp) -> PyResult<PySuperOp> {
+        Ok(PySuperOp {
+            inner: self.inner.tensor(&other.inner).map_err(py_value_err)?,
+        })
+    }
+
+    fn __repr__(&self) -> String {
+        format!("SuperOp(num_qubits={})", self.inner.num_qubits())
+    }
+}
+
+#[pyclass(name = "ChiMatrix", module = "pecos_rslib.quantum_info")]
+pub struct PyChiMatrix {
+    inner: RustChiMatrix,
+}
+
+#[pymethods]
+impl PyChiMatrix {
+    #[new]
+    fn new(num_qubits: usize, matrix: Vec<Vec<Complex64>>) -> PyResult<Self> {
+        Ok(Self {
+            inner: RustChiMatrix::try_new(num_qubits, complex_matrix_from_rows(matrix)?)
+                .map_err(py_value_err)?,
+        })
+    }
+
+    fn num_qubits(&self) -> usize {
+        self.inner.num_qubits()
+    }
+
+    fn matrix(&self) -> Vec<Vec<Complex64>> {
+        complex_matrix_to_rows(self.inner.matrix())
+    }
+
+    fn to_choi(&self) -> PyResult<PyChoiMatrix> {
+        Ok(PyChoiMatrix {
+            inner: self.inner.to_choi().map_err(py_value_err)?,
+        })
+    }
+
+    fn to_ptm(&self) -> PyResult<PyPtm> {
+        Ok(PyPtm {
+            inner: self.inner.to_ptm().map_err(py_value_err)?,
+        })
+    }
+
+    fn __repr__(&self) -> String {
+        format!("ChiMatrix(num_qubits={})", self.inner.num_qubits())
+    }
+}
+
+#[pyclass(name = "Stinespring", module = "pecos_rslib.quantum_info")]
+pub struct PyStinespring {
+    inner: RustStinespring,
+}
+
+#[pymethods]
+impl PyStinespring {
+    #[new]
+    fn new(num_qubits: usize, isometry: Vec<Vec<Complex64>>) -> PyResult<Self> {
+        Ok(Self {
+            inner: RustStinespring::try_new(num_qubits, complex_matrix_from_rows(isometry)?)
+                .map_err(py_value_err)?,
+        })
+    }
+
+    fn num_qubits(&self) -> usize {
+        self.inner.num_qubits()
+    }
+
+    fn environment_dim(&self) -> usize {
+        self.inner.environment_dim()
+    }
+
+    fn isometry(&self) -> Vec<Vec<Complex64>> {
+        complex_matrix_to_rows(self.inner.isometry())
+    }
+
+    fn to_kraus(&self) -> PyResult<PyKrausOps> {
+        Ok(PyKrausOps {
+            inner: self.inner.to_kraus().map_err(py_value_err)?,
+        })
+    }
+
+    fn to_choi(&self) -> PyResult<PyChoiMatrix> {
+        Ok(PyChoiMatrix {
+            inner: self.inner.to_choi().map_err(py_value_err)?,
+        })
+    }
+
+    fn to_superop(&self) -> PyResult<PySuperOp> {
+        Ok(PySuperOp {
+            inner: self.inner.to_superop().map_err(py_value_err)?,
+        })
+    }
+
+    fn __repr__(&self) -> String {
+        format!(
+            "Stinespring(num_qubits={}, environment_dim={})",
+            self.inner.num_qubits(),
+            self.inner.environment_dim()
+        )
+    }
+}
+
+#[pyfunction]
+fn state_fidelity(left: Vec<Complex64>, right: Vec<Complex64>) -> PyResult<f64> {
+    rust_state_fidelity(&DVector::from_vec(left), &DVector::from_vec(right)).map_err(py_value_err)
+}
+
+#[pyfunction]
+fn state_fidelity_with_density_matrix(
+    rho: Vec<Vec<Complex64>>,
+    psi: Vec<Complex64>,
+) -> PyResult<f64> {
+    rust_state_fidelity_with_density_matrix(
+        &complex_matrix_from_rows(rho)?,
+        &DVector::from_vec(psi),
+    )
+    .map_err(py_value_err)
+}
+
+#[pyfunction]
+fn purity(rho: Vec<Vec<Complex64>>) -> PyResult<f64> {
+    rust_purity(&complex_matrix_from_rows(rho)?).map_err(py_value_err)
+}
+
+#[pyfunction]
+fn entropy(rho: Vec<Vec<Complex64>>) -> PyResult<f64> {
+    rust_entropy(&complex_matrix_from_rows(rho)?).map_err(py_value_err)
+}
+
+#[pyfunction]
+fn shannon_entropy(probabilities: Vec<f64>, base: f64) -> PyResult<f64> {
+    pecos_quantum::shannon_entropy(&probabilities, base).map_err(py_value_err)
+}
+
+#[pyfunction]
+fn negativity(rho: Vec<Vec<Complex64>>, dims: Vec<usize>, subsystem: usize) -> PyResult<f64> {
+    rust_negativity(&complex_matrix_from_rows(rho)?, &dims, subsystem).map_err(py_value_err)
+}
+
+#[pyfunction]
+fn logarithmic_negativity(
+    rho: Vec<Vec<Complex64>>,
+    dims: Vec<usize>,
+    subsystem: usize,
+) -> PyResult<f64> {
+    rust_logarithmic_negativity(&complex_matrix_from_rows(rho)?, &dims, subsystem)
+        .map_err(py_value_err)
+}
+
+#[pyfunction]
+fn schmidt_decomposition(
+    state: Vec<Complex64>,
+    dims: Vec<usize>,
+    left_subsystems: Vec<usize>,
+) -> PyResult<Vec<PySchmidtTerm>> {
+    pecos_quantum::schmidt_decomposition(&DVector::from_vec(state), &dims, &left_subsystems)
+        .map_err(py_value_err)
+}
+
+#[pyfunction]
+fn partial_trace_subsystems(
+    rho: Vec<Vec<Complex64>>,
+    dims: Vec<usize>,
+    traced_subsystems: Vec<usize>,
+) -> PyResult<Vec<Vec<Complex64>>> {
+    Ok(complex_matrix_to_rows(
+        &rust_partial_trace_subsystems(&complex_matrix_from_rows(rho)?, &dims, &traced_subsystems)
+            .map_err(py_value_err)?,
+    ))
+}
+
+#[pyfunction]
+fn partial_trace_qubits(
+    rho: Vec<Vec<Complex64>>,
+    num_qubits: usize,
+    traced_qubits: Vec<usize>,
+) -> PyResult<Vec<Vec<Complex64>>> {
+    Ok(complex_matrix_to_rows(
+        &rust_partial_trace_qubits(&complex_matrix_from_rows(rho)?, num_qubits, &traced_qubits)
+            .map_err(py_value_err)?,
+    ))
+}
+
+#[pyfunction]
+fn hellinger_distance(left: Vec<f64>, right: Vec<f64>) -> PyResult<f64> {
+    rust_hellinger_distance(&left, &right).map_err(py_value_err)
+}
+
+#[pyfunction]
+fn hellinger_fidelity(left: Vec<f64>, right: Vec<f64>) -> PyResult<f64> {
+    rust_hellinger_fidelity(&left, &right).map_err(py_value_err)
+}
+
+#[pyfunction]
+fn process_fidelity(left: &PyPtm, right: &PyPtm) -> PyResult<f64> {
+    rust_process_fidelity(&left.inner, &right.inner).map_err(py_value_err)
+}
+
+#[pyfunction]
+fn average_gate_fidelity(left: &PyPtm, right: &PyPtm) -> PyResult<f64> {
+    rust_average_gate_fidelity(&left.inner, &right.inner).map_err(py_value_err)
+}
+
+#[pyfunction]
+fn gate_error(left: &PyPtm, right: &PyPtm) -> PyResult<f64> {
+    rust_gate_error(&left.inner, &right.inner).map_err(py_value_err)
+}
+
+#[pyfunction]
+fn pauli_channel_diamond_norm(left: &PyPauliChannel, right: &PyPauliChannel) -> PyResult<f64> {
+    pecos_quantum::pauli_channel_diamond_norm(&left.inner, &right.inner).map_err(py_value_err)
+}
+
+#[pyfunction]
+fn pauli_channel_diamond_distance(left: &PyPauliChannel, right: &PyPauliChannel) -> PyResult<f64> {
+    pecos_quantum::pauli_channel_diamond_distance(&left.inner, &right.inner).map_err(py_value_err)
+}
+
+#[pyfunction]
+fn matrix_unit_basis(num_qubits: usize) -> PyResult<Vec<Vec<Vec<Complex64>>>> {
+    Ok(complex_matrices_to_rows(
+        &pecos_quantum::matrix_unit_basis(num_qubits).map_err(py_value_err)?,
+    ))
+}
+
+#[pyfunction]
+fn random_density_matrix(num_qubits: usize, seed: u64) -> PyResult<Vec<Vec<Complex64>>> {
+    let mut rng = PecosRng::seed_from_u64(seed);
+    Ok(complex_matrix_to_rows(
+        &rust_random_density_matrix(&mut rng, num_qubits).map_err(py_value_err)?,
+    ))
+}
+
+#[pyfunction]
+fn random_quantum_channel(num_qubits: usize, num_kraus: usize, seed: u64) -> PyResult<PyKrausOps> {
+    let mut rng = PecosRng::seed_from_u64(seed);
+    Ok(PyKrausOps {
+        inner: rust_random_quantum_channel(&mut rng, num_qubits, num_kraus)
+            .map_err(py_value_err)?,
+    })
+}
+
+pub fn register_quantum_info_module(parent: &Bound<'_, PyModule>) -> PyResult<()> {
+    parent.add_class::<PyPauliChannel>()?;
+    parent.add_class::<PyPtm>()?;
+    parent.add_class::<PyKrausOps>()?;
+    parent.add_class::<PyChoiMatrix>()?;
+    parent.add_class::<PyProcessTomographyDesign>()?;
+    parent.add_class::<PySuperOp>()?;
+    parent.add_class::<PyChiMatrix>()?;
+    parent.add_class::<PyStinespring>()?;
+
+    parent.add_function(wrap_pyfunction!(state_fidelity, parent)?)?;
+    parent.add_function(wrap_pyfunction!(
+        state_fidelity_with_density_matrix,
+        parent
+    )?)?;
+    parent.add_function(wrap_pyfunction!(purity, parent)?)?;
+    parent.add_function(wrap_pyfunction!(entropy, parent)?)?;
+    parent.add_function(wrap_pyfunction!(shannon_entropy, parent)?)?;
+    parent.add_function(wrap_pyfunction!(negativity, parent)?)?;
+    parent.add_function(wrap_pyfunction!(logarithmic_negativity, parent)?)?;
+    parent.add_function(wrap_pyfunction!(schmidt_decomposition, parent)?)?;
+    parent.add_function(wrap_pyfunction!(partial_trace_subsystems, parent)?)?;
+    parent.add_function(wrap_pyfunction!(partial_trace_qubits, parent)?)?;
+    parent.add_function(wrap_pyfunction!(hellinger_distance, parent)?)?;
+    parent.add_function(wrap_pyfunction!(hellinger_fidelity, parent)?)?;
+    parent.add_function(wrap_pyfunction!(process_fidelity, parent)?)?;
+    parent.add_function(wrap_pyfunction!(average_gate_fidelity, parent)?)?;
+    parent.add_function(wrap_pyfunction!(gate_error, parent)?)?;
+    parent.add_function(wrap_pyfunction!(pauli_channel_diamond_norm, parent)?)?;
+    parent.add_function(wrap_pyfunction!(pauli_channel_diamond_distance, parent)?)?;
+    parent.add_function(wrap_pyfunction!(matrix_unit_basis, parent)?)?;
+    parent.add_function(wrap_pyfunction!(random_density_matrix, parent)?)?;
+    parent.add_function(wrap_pyfunction!(random_quantum_channel, parent)?)?;
+
+    let py = parent.py();
+    let module = PyModule::new(py, "quantum_info")?;
+    for name in [
+        "PauliChannel",
+        "Ptm",
+        "KrausOps",
+        "ChoiMatrix",
+        "ProcessTomographyDesign",
+        "SuperOp",
+        "ChiMatrix",
+        "Stinespring",
+        "state_fidelity",
+        "state_fidelity_with_density_matrix",
+        "purity",
+        "entropy",
+        "shannon_entropy",
+        "negativity",
+        "logarithmic_negativity",
+        "schmidt_decomposition",
+        "partial_trace_subsystems",
+        "partial_trace_qubits",
+        "hellinger_distance",
+        "hellinger_fidelity",
+        "process_fidelity",
+        "average_gate_fidelity",
+        "gate_error",
+        "pauli_channel_diamond_norm",
+        "pauli_channel_diamond_distance",
+        "matrix_unit_basis",
+        "random_density_matrix",
+        "random_quantum_channel",
+    ] {
+        module.add(name, parent.getattr(name)?)?;
+    }
+
+    let sys = py.import("sys")?;
+    let modules = sys.getattr("modules")?;
+    modules.set_item("pecos_rslib.quantum_info", &module)?;
+    parent.add_submodule(&module)?;
+    Ok(())
+}
diff --git a/python/quantum-pecos/src/pecos/__init__.py b/python/quantum-pecos/src/pecos/__init__.py
index e36ede4ed..c7c7f7af9 100644
--- a/python/quantum-pecos/src/pecos/__init__.py
+++ b/python/quantum-pecos/src/pecos/__init__.py
@@ -47,6 +47,9 @@
     ShotVec,  # Simulation result: vector of shots
     TimeUnits,  # Abstract time duration in arbitrary units
     WasmForeignObject,  # WASM foreign object for classical coprocessor
+    X,  # Single-qubit Pauli X constructor: X(qubit) -> PauliString
+    Y,  # Single-qubit Pauli Y constructor: Y(qubit) -> PauliString
+    Z,  # Single-qubit Pauli Z constructor: Z(qubit) -> PauliString
     abs,  # Absolute value
     acos,  # Inverse cosine
     acosh,  # Inverse hyperbolic cosine
@@ -281,8 +284,8 @@ def __getattr__(name: str):
 biased_depolarizing_noise = pecos_rslib.biased_depolarizing_noise
 general_noise = pecos_rslib.general_noise
 state_vector = pecos_rslib.state_vector
-sparse_stab = pecos_rslib.sparse_stab
 stabilizer = pecos_rslib.stabilizer
+sparse_stab = pecos_rslib.sparse_stab
 stab_vec = pecos_rslib.stab_vec
 density_matrix = pecos_rslib.density_matrix
 hugr_engine = pecos_rslib.hugr_engine
@@ -338,6 +341,9 @@ def __getattr__(name: str):
     "WasmError",
     "WasmForeignObject",
     "Wat",
+    "X",
+    "Y",
+    "Z",
     "__version__",
     "abs",
     "acos",
diff --git a/python/quantum-pecos/src/pecos/circuits/quantum_circuit.py b/python/quantum-pecos/src/pecos/circuits/quantum_circuit.py
index 19ef17633..ae03fb7bf 100644
--- a/python/quantum-pecos/src/pecos/circuits/quantum_circuit.py
+++ b/python/quantum-pecos/src/pecos/circuits/quantum_circuit.py
@@ -159,7 +159,7 @@ def active_qudits(self) -> list[set[int]]:
             if tick is not None:
                 # Get individual qubits from all gates in the tick
                 active: set[int] = set()
-                for gate in tick.gates():
+                for gate in tick.gate_batches():
                     for q in gate.qubits:
                         active.add(q)
                 result.append(active)
@@ -380,7 +380,7 @@ def _iter_tick(
         # Use a dict to preserve insertion order and group gates
         grouped: dict[tuple[str, str], tuple[set[Location], JSONDict]] = {}
 
-        for gate_idx, gate in enumerate(tick_obj.gates()):
+        for gate_idx, gate in enumerate(tick_obj.gate_batches()):
             # Check for stored original symbol in metadata
             stored_symbol = tick_obj.get_gate_attr(gate_idx, "_symbol")
 
@@ -769,7 +769,7 @@ def active_qudits(self) -> set[Location]:
             return set()
 
         active: set[Location] = set()
-        for gate in tick.gates():
+        for gate in tick.gate_batches():
             qubits = list(gate.qubits)
             if len(qubits) == 1:
                 active.add(qubits[0])
diff --git a/python/quantum-pecos/src/pecos/guppy/surface.py b/python/quantum-pecos/src/pecos/guppy/surface.py
index 7d11e01fc..66883176e 100644
--- a/python/quantum-pecos/src/pecos/guppy/surface.py
+++ b/python/quantum-pecos/src/pecos/guppy/surface.py
@@ -159,10 +159,25 @@ def generate_guppy_source(patch: "SurfacePatch") -> str:
     lines.extend(f"    h(ax{stab.index})" for stab in geom.x_stabilizers)
 
     # Measure ancillas (destructive)
+    # Each measurement gets a per-measurement result() call that ties the
+    # physical measurement to a MeasId. The result() names encode the
+    # stabilizer type and index. The AllocateResult IDs generated by
+    # these calls flow through the trace and become MeasIds on the TickCircuit.
     lines.append("")
+    # Measure ancillas with per-measurement result() identity.
+    # Tag format: "label:idx" where label is the stabilizer name and idx is the
+    # round-local measurement index. The global MeasId is assigned by the runtime
+    # via AllocateResult and flows through the trace automatically.
     lines.append("    # Measure ancillas")
-    lines.extend(f"    sx{stab.index} = measure(ax{stab.index})" for stab in geom.x_stabilizers)
-    lines.extend(f"    sz{stab.index} = measure(az{stab.index})" for stab in geom.z_stabilizers)
+    idx = 0
+    for stab in geom.x_stabilizers:
+        lines.append(f"    sx{stab.index} = measure(ax{stab.index})")
+        lines.append(f'    result("sx{stab.index}:meas:{idx}", sx{stab.index})')
+        idx += 1
+    for stab in geom.z_stabilizers:
+        lines.append(f"    sz{stab.index} = measure(az{stab.index})")
+        lines.append(f'    result("sz{stab.index}:meas:{idx}", sz{stab.index})')
+        idx += 1
 
     x_calls = ", ".join(f"sx{s.index}" for s in geom.x_stabilizers)
     z_calls = ", ".join(f"sz{s.index}" for s in geom.z_stabilizers)
diff --git a/python/quantum-pecos/src/pecos/noise/depolarizing_error_model.py b/python/quantum-pecos/src/pecos/noise/depolarizing_error_model.py
index 9e15a7cb0..9f1c21a0c 100644
--- a/python/quantum-pecos/src/pecos/noise/depolarizing_error_model.py
+++ b/python/quantum-pecos/src/pecos/noise/depolarizing_error_model.py
@@ -72,7 +72,7 @@ def __init__(self, error_params: dict) -> None:
                 - p1: Single-qubit gate error probability
                 - p2: Two-qubit gate error probability
                 - p_meas: Measurement error probability
-                - p_init: Initialization error probability
+                - p_prep: Preparation error probability
                 - scale: Optional scaling factor for all error rates
                 - p1_error_model: Optional custom single-qubit Pauli error distribution
                 - p2_error_model: Optional custom two-qubit Pauli error distribution
@@ -125,7 +125,7 @@ def _scale(self) -> None:
             self._eparams["p_meas"] = pc.mean(self._eparams["p_meas"])
 
         self._eparams["p_meas"] *= scale
-        self._eparams["p_init"] *= scale
+        self._eparams["p_prep"] *= scale
 
     def shot_reinit(self) -> None:
         """Run all code needed at the beginning of each shot, e.g., resetting state."""
@@ -159,7 +159,7 @@ def process(
             elif op.name in {"init |0>", "Init", "Init +Z"}:
                 qops_after = noise_initz_bitflip(
                     op,
-                    p=self._eparams["p_init"],
+                    p=self._eparams["p_prep"],
                 )
 
             # ########################################
diff --git a/python/quantum-pecos/src/pecos/noise/error_depolar.py b/python/quantum-pecos/src/pecos/noise/error_depolar.py
index 5d0683db7..b723b9649 100644
--- a/python/quantum-pecos/src/pecos/noise/error_depolar.py
+++ b/python/quantum-pecos/src/pecos/noise/error_depolar.py
@@ -72,7 +72,7 @@ def scaling(self) -> None:
             self.error_params["p_meas"] = pc.mean(self.error_params["p_meas"])
 
         self.error_params["p_meas"] *= scale
-        self.error_params["p_init"] *= scale
+        self.error_params["p_prep"] *= scale
 
     def start(
         self,
@@ -152,7 +152,7 @@ def generate_tick_errors(
             # INITS WITH X NOISE
             elif symbol == "init |0>":
                 noisy = set(locations) - self.error_params["noiseless_qubits"]
-                noise_init_bitflip(noisy, after, "X", p=self.error_params["p_init"])
+                noise_init_bitflip(noisy, after, "X", p=self.error_params["p_prep"])
 
             # ########################################
             # ONE QUBIT GATES
diff --git a/python/quantum-pecos/src/pecos/noise/generic_error_model.py b/python/quantum-pecos/src/pecos/noise/generic_error_model.py
index a2ebaaf77..0d892db99 100644
--- a/python/quantum-pecos/src/pecos/noise/generic_error_model.py
+++ b/python/quantum-pecos/src/pecos/noise/generic_error_model.py
@@ -80,7 +80,7 @@ def __init__(self, error_params: dict) -> None:
                 - p1: Single-qubit gate error probability
                 - p2: Two-qubit gate error probability
                 - p_meas: Measurement error probability
-                - p_init: Initialization error probability
+                - p_prep: Preparation error probability
                 - scale: Optional scaling factor for all error rates
                 - p1_error_model: Optional custom single-qubit Pauli error distribution
                 - p2_error_model: Optional custom two-qubit Pauli error distribution
@@ -134,7 +134,7 @@ def _scale(self) -> None:
             self._eparams["p_meas"] = pc.mean(self._eparams["p_meas"])
 
         self._eparams["p_meas"] *= scale
-        self._eparams["p_init"] *= scale
+        self._eparams["p_prep"] *= scale
 
     def shot_reinit(self) -> None:
         """Run all code needed at the beginning of each shot, e.g., resetting state."""
@@ -165,7 +165,7 @@ def process(
             if op.name in {"init |0>", "Init", "Init +Z"}:
                 qops_after = noise_initz_bitflip_leakage(
                     op,
-                    p=self._eparams["p_init"],
+                    p=self._eparams["p_prep"],
                     machine=self.machine,
                 )
 
diff --git a/python/quantum-pecos/src/pecos/noise/simple_depolarizing_error_model.py b/python/quantum-pecos/src/pecos/noise/simple_depolarizing_error_model.py
index a739f8822..4569c4677 100644
--- a/python/quantum-pecos/src/pecos/noise/simple_depolarizing_error_model.py
+++ b/python/quantum-pecos/src/pecos/noise/simple_depolarizing_error_model.py
@@ -62,7 +62,7 @@ def __init__(self, error_params: dict) -> None:
                 - p1: Single-qubit gate error probability
                 - p2: Two-qubit gate error probability
                 - p_meas: Measurement error probability
-                - p_init: Initialization error probability
+                - p_prep: Initialization error probability
         """
         self.error_params = dict(error_params)
         self.machine = None
@@ -127,7 +127,7 @@ def process(
                 # Use fused operation to check and get error indices in one pass
                 error_indices = pc.random.compare_indices(
                     len(op.args),
-                    self._eparams["p_init"],
+                    self._eparams["p_prep"],
                 )
 
                 for idx in error_indices:
diff --git a/python/quantum-pecos/src/pecos/qec/__init__.py b/python/quantum-pecos/src/pecos/qec/__init__.py
index 3288d2966..362efa148 100644
--- a/python/quantum-pecos/src/pecos/qec/__init__.py
+++ b/python/quantum-pecos/src/pecos/qec/__init__.py
@@ -38,9 +38,6 @@
     EquivalenceResult,
     FaultLocation,
     InfluenceBuilder,
-    MeasurementNoiseModel,
-    MemBuilder,
-    NoisySampler,
     ParsedDem,
     assert_dems_equivalent,
     compare_dems_exact,
@@ -50,6 +47,15 @@
 
 from pecos.qec import analysis, color, protocols, surface
 from pecos.qec.analysis import (
+    build_adaptive_dem,
+    compare_flip_matrices,
+    compare_k_body_rates,
+    detector_flip_matrices_by_round,
+    detector_flip_matrix,
+    detector_k_body_rates,
+    detector_k_body_rates_by_round,
+    empirical_correlation_table,
+    fit_dem_from_simulation,
     logical_error_rate,
     logical_fidelity,
     logical_from_data,
@@ -86,12 +92,14 @@
     StabilizerSupport,
     SurfacePatch,
     SurfacePatchBuilder,
+    build_memory_circuit,
     compute_x_stabilizer_supports,
     compute_z_stabilizer_supports,
     generate_nonrotated_surface_layout,
     generate_surface_layout,
     parity_matrix_x,
     parity_matrix_z,
+    surface_code_memory,
 )
 
 __all__ = [
@@ -110,9 +118,6 @@
     "EquivalenceResult",
     "FaultLocation",
     "InfluenceBuilder",
-    "MeasurementNoiseModel",
-    "MemBuilder",
-    "NoisySampler",
     "ParsedDem",
     "assert_dems_equivalent",
     "compare_dems_exact",
@@ -124,6 +129,15 @@
     "PAULI_Y",
     "PAULI_Z",
     # Analysis utilities
+    "build_adaptive_dem",
+    "compare_flip_matrices",
+    "compare_k_body_rates",
+    "detector_flip_matrices_by_round",
+    "detector_flip_matrix",
+    "detector_k_body_rates",
+    "detector_k_body_rates_by_round",
+    "empirical_correlation_table",
+    "fit_dem_from_simulation",
     "logical_error_rate",
     "logical_fidelity",
     "logical_from_data",
@@ -158,6 +172,8 @@
     "StabilizerSupport",
     "SurfacePatch",
     "SurfacePatchBuilder",
+    "build_memory_circuit",
+    "surface_code_memory",
     # Color code
     "ColorCode488",
     "ColorCode488Builder",
diff --git a/python/quantum-pecos/src/pecos/qec/analysis.py b/python/quantum-pecos/src/pecos/qec/analysis.py
index b2121afa6..2f22f1f8e 100644
--- a/python/quantum-pecos/src/pecos/qec/analysis.py
+++ b/python/quantum-pecos/src/pecos/qec/analysis.py
@@ -10,7 +10,9 @@
 
 from __future__ import annotations
 
+import json
 import math
+from itertools import combinations
 from typing import TYPE_CHECKING
 
 if TYPE_CHECKING:
@@ -216,3 +218,630 @@ def lower_bound_fidelity(f1: float, f2: float) -> float:
         Lower bound on true fidelity.
     """
     return (4 / 5) * (f1 + f2) - (3 / 5)
+
+
+# ---------------------------------------------------------------------------
+# Detector flip frequency matrices
+# ---------------------------------------------------------------------------
+
+
+def detector_flip_matrix(
+    detector_events: Sequence[Sequence[int]],
+    num_detectors: int,
+) -> list[list[float]]:
+    """Compute the detector flip frequency matrix from sampled detector events.
+
+    The matrix M has:
+      - M[i][i] = P(detector i fires)                    (marginal rate)
+      - M[i][j] = 0.5 * P(detector i AND j both fire)    (half joint rate)
+
+    The factor 0.5 on off-diagonal entries makes the matrix interpretable
+    as a covariance-like object: each correlated error mechanism contributes
+    equally to M[i][j] and M[j][i].
+
+    Args:
+        detector_events: Per-shot detector outcomes. Each entry is a sequence
+            of detector indices that fired in that shot. Alternatively, each
+            entry can be a full-length binary vector (0/1) of length
+            ``num_detectors``.
+        num_detectors: Total number of detectors.
+
+    Returns:
+        ``num_detectors x num_detectors`` matrix as nested lists.
+    """
+    n = num_detectors
+    shots = len(detector_events)
+    if shots == 0:
+        return [[0.0] * n for _ in range(n)]
+
+    inv_shots = 1.0 / shots
+    half_inv = 0.5 * inv_shots
+
+    # Accumulate as flat list for speed
+    m = [0.0] * (n * n)
+
+    for events in detector_events:
+        # Determine which detectors fired
+        fired = [i for i in range(n) if events[i]] if len(events) == n else list(events)
+
+        for a in fired:
+            m[a * n + a] += inv_shots  # diagonal
+            for b in fired:
+                if b > a:
+                    m[a * n + b] += half_inv
+                    m[b * n + a] += half_inv
+
+    return [m[i * n : (i + 1) * n] for i in range(n)]
+
+
+def detector_flip_matrices_by_round(
+    detector_events: Sequence[Sequence[int]],
+    num_detectors: int,
+    detectors_per_round: int,
+) -> list[list[list[float]]]:
+    """Compute per-round detector flip frequency matrices.
+
+    Groups detectors into rounds of ``detectors_per_round`` each and
+    computes a separate flip frequency matrix for each round.
+
+    Args:
+        detector_events: Per-shot detector outcomes (same format as
+            :func:`detector_flip_matrix`).
+        num_detectors: Total number of detectors.
+        detectors_per_round: Number of detectors in each syndrome
+            extraction round.
+
+    Returns:
+        List of matrices, one per round.
+    """
+    num_rounds = (num_detectors + detectors_per_round - 1) // detectors_per_round
+    shots = len(detector_events)
+    if shots == 0:
+        return [[[0.0] * detectors_per_round for _ in range(detectors_per_round)] for _ in range(num_rounds)]
+
+    inv_shots = 1.0 / shots
+    half_inv = 0.5 * inv_shots
+    k = detectors_per_round
+
+    # One flat matrix per round
+    matrices = [[0.0] * (k * k) for _ in range(num_rounds)]
+
+    for events in detector_events:
+        fired = [i for i in range(num_detectors) if events[i]] if len(events) == num_detectors else list(events)
+
+        # Bin by round
+        round_fired: dict[int, list[int]] = {}
+        for d in fired:
+            r = d // k
+            local = d % k
+            round_fired.setdefault(r, []).append(local)
+
+        for r, local_ids in round_fired.items():
+            if r >= num_rounds:
+                continue
+            mat = matrices[r]
+            for a in local_ids:
+                mat[a * k + a] += inv_shots
+                for b in local_ids:
+                    if b > a:
+                        mat[a * k + b] += half_inv
+                        mat[b * k + a] += half_inv
+
+    return [[matrices[r][i * k : (i + 1) * k] for i in range(k)] for r in range(num_rounds)]
+
+
+def compare_flip_matrices(
+    sim_matrix: Sequence[Sequence[float]],
+    dem_matrix: Sequence[Sequence[float]],
+    *,
+    min_rate: float = 0.0005,
+) -> tuple[float, float, tuple[int, int]]:
+    """Compare two detector flip frequency matrices.
+
+    Args:
+        sim_matrix: Ground truth matrix (from simulation).
+        dem_matrix: Test matrix (from DEM sampling).
+        min_rate: Minimum entry value to consider (avoids division by tiny
+            numbers from statistical noise).
+
+    Returns:
+        Tuple of ``(max_relative_error, frobenius_relative_error,
+        worst_element)`` where ``worst_element`` is the ``(i, j)`` index
+        of the largest relative error.
+    """
+    n = len(sim_matrix)
+    max_err = 0.0
+    worst = (0, 0)
+    sum_sq_diff = 0.0
+    sum_sq_sim = 0.0
+
+    for i in range(n):
+        for j in range(n):
+            s = sim_matrix[i][j]
+            d = dem_matrix[i][j]
+            diff = d - s
+            sum_sq_diff += diff * diff
+            sum_sq_sim += s * s
+            if s > min_rate:
+                rel = abs(diff / s)
+                if rel > max_err:
+                    max_err = rel
+                    worst = (i, j)
+
+    frob_rel = (sum_sq_diff**0.5) / max(sum_sq_sim**0.5, 1e-30)
+    return max_err, frob_rel, worst
+
+
+# ---------------------------------------------------------------------------
+# Higher-order detector correlation analysis
+# ---------------------------------------------------------------------------
+
+
+def detector_k_body_rates(
+    detector_events: Sequence[Sequence[int]],
+    num_detectors: int,
+    max_order: int = 3,
+) -> dict[tuple[int, ...], float]:
+    """Compute k-body detector firing rates up to a given order.
+
+    For each subset of detectors of size 1..max_order that fires together
+    in at least one shot, records the joint firing probability.
+
+    - 1-body: ``(i,)`` -> P(Di fires)
+    - 2-body: ``(i, j)`` -> P(Di AND Dj fire)
+    - 3-body: ``(i, j, k)`` -> P(Di AND Dj AND Dk fire)
+
+    Keys are sorted tuples of detector indices.
+
+    Args:
+        detector_events: Per-shot detector outcomes. Each entry is either
+            a list of fired detector indices or a full binary vector.
+        num_detectors: Total number of detectors.
+        max_order: Maximum correlation order (default 3).
+
+    Returns:
+        Dict mapping detector index tuples to joint firing rates.
+    """
+    shots = len(detector_events)
+    if shots == 0:
+        return {}
+
+    inv_shots = 1.0 / shots
+    rates: dict[tuple[int, ...], float] = {}
+
+    for events in detector_events:
+        fired = [i for i in range(num_detectors) if events[i]] if len(events) == num_detectors else sorted(events)
+
+        for k in range(1, min(max_order, len(fired)) + 1):
+            for combo in combinations(fired, k):
+                if combo in rates:
+                    rates[combo] += inv_shots
+                else:
+                    rates[combo] = inv_shots
+
+    return rates
+
+
+def detector_k_body_rates_by_round(
+    detector_events: Sequence[Sequence[int]],
+    num_detectors: int,
+    detectors_per_round: int,
+    max_order: int = 3,
+) -> list[dict[tuple[int, ...], float]]:
+    """Compute per-round k-body detector firing rates.
+
+    Groups detectors into rounds, then computes k-body rates within
+    each round. Detector indices in the returned dicts are round-local
+    (0..detectors_per_round-1).
+
+    Args:
+        detector_events: Per-shot detector outcomes.
+        num_detectors: Total number of detectors.
+        detectors_per_round: Number of detectors per round.
+        max_order: Maximum correlation order (default 3).
+
+    Returns:
+        List of dicts, one per round, mapping local detector index
+        tuples to joint firing rates.
+    """
+    k = detectors_per_round
+    num_rounds = (num_detectors + k - 1) // k
+    shots = len(detector_events)
+    if shots == 0:
+        return [{} for _ in range(num_rounds)]
+
+    inv_shots = 1.0 / shots
+    round_rates: list[dict[tuple[int, ...], float]] = [{} for _ in range(num_rounds)]
+
+    for events in detector_events:
+        fired = [i for i in range(num_detectors) if events[i]] if len(events) == num_detectors else sorted(events)
+
+        # Bin fired detectors by round
+        round_fired: dict[int, list[int]] = {}
+        for d in fired:
+            r = d // k
+            local = d % k
+            round_fired.setdefault(r, []).append(local)
+
+        for r, local_ids in round_fired.items():
+            if r >= num_rounds:
+                continue
+            rr = round_rates[r]
+            for order in range(1, min(max_order, len(local_ids)) + 1):
+                for combo in combinations(local_ids, order):
+                    if combo in rr:
+                        rr[combo] += inv_shots
+                    else:
+                        rr[combo] = inv_shots
+
+    return round_rates
+
+
+def compare_k_body_rates(
+    sim_rates: dict[tuple[int, ...], float],
+    dem_rates: dict[tuple[int, ...], float],
+    *,
+    min_rate: float = 0.0005,
+    max_order: int | None = None,
+) -> dict[int, tuple[float, float, tuple[int, ...]]]:
+    """Compare k-body rates between simulation and DEM, grouped by order.
+
+    Args:
+        sim_rates: Ground truth rates from simulation.
+        dem_rates: Rates from DEM sampling.
+        min_rate: Minimum rate to consider for relative error.
+        max_order: If set, only compare up to this order.
+
+    Returns:
+        Dict mapping order k to ``(max_relative_error,
+        rms_relative_error, worst_event)`` for that order.
+    """
+    # Collect all keys
+    all_keys = set(sim_rates.keys()) | set(dem_rates.keys())
+
+    # Group by order
+    by_order: dict[int, list[tuple[tuple[int, ...], float, float]]] = {}
+    for key in all_keys:
+        k = len(key)
+        if max_order is not None and k > max_order:
+            continue
+        s = sim_rates.get(key, 0.0)
+        d = dem_rates.get(key, 0.0)
+        by_order.setdefault(k, []).append((key, s, d))
+
+    result: dict[int, tuple[float, float, tuple[int, ...]]] = {}
+    for k in sorted(by_order.keys()):
+        entries = by_order[k]
+        max_err = 0.0
+        worst: tuple[int, ...] = ()
+        sum_sq_rel = 0.0
+        count = 0
+
+        for key, s, d in entries:
+            if s > min_rate:
+                rel = abs(d / s - 1)
+                if rel > max_err:
+                    max_err = rel
+                    worst = key
+                sum_sq_rel += rel * rel
+                count += 1
+
+        rms = (sum_sq_rel / max(count, 1)) ** 0.5
+        result[k] = (max_err, rms, worst)
+
+    return result
+
+
+# ---------------------------------------------------------------------------
+# Simulation-based correlation table
+# ---------------------------------------------------------------------------
+
+
+def empirical_correlation_table(
+    tick_circuit: object,
+    noise_builder: object,
+    shots: int,
+    max_order: int = 2,
+    *,
+    backend: str = "stabilizer",
+    seed: int = 42,
+) -> list[tuple[tuple[int, ...], float]]:
+    """Build an empirical correlation table from simulation.
+
+    Runs ``sim_neo`` with the given noise model, extracts detector events
+    per shot, and computes k-body joint detection rates. Same output format
+    as :func:`exact_correlation_table` from the Heisenberg walk.
+
+    Args:
+        tick_circuit: A ``TickCircuit`` with detector metadata.
+        noise_builder: A noise builder (e.g., ``depolarizing().p1(0.001).p2(0.01)``).
+        shots: Number of simulation shots.
+        max_order: Maximum correlation order (1 = marginals, 2 = pairwise, etc.).
+        backend: Simulator backend — ``"stabilizer"``, ``"statevec"``,
+            or ``"meas_sampling"``. The meas_sampling backend uses the fast
+            whole-circuit DEM-based sampler (geometric/O(fired)) instead of
+            gate-by-gate simulation.
+        seed: RNG seed.
+
+    Returns:
+        List of ``(detector_indices_tuple, probability)`` pairs, same format
+        as ``exact_correlation_table``.
+
+    Example::
+
+        from pecos_rslib_exp import depolarizing
+        from pecos.qec.analysis import empirical_correlation_table
+
+        table = empirical_correlation_table(
+            tc, depolarizing().p1(0.001).p2(0.01), shots=100000, max_order=3,
+        )
+        for indices, prob in table:
+            print(f"P({indices}) = {prob:.6f}")
+    """
+    from pecos_rslib_exp import (
+        meas_sampling,
+        sim_neo,
+        stabilizer,
+        statevec,
+    )
+
+    if backend == "meas_sampling":
+        results = sim_neo(tick_circuit).quantum(meas_sampling()).noise(noise_builder).shots(shots).seed(seed).run()
+    elif backend in ("stabilizer", "statevec"):
+        backend_obj = stabilizer() if backend == "stabilizer" else statevec()
+        results = sim_neo(tick_circuit).quantum(backend_obj).noise(noise_builder).shots(shots).seed(seed).run()
+    else:
+        supported = "'stabilizer', 'statevec', 'meas_sampling'"
+        msg = f"Unknown backend {backend!r}. Supported: {supported}."
+        raise ValueError(
+            msg,
+        )
+
+    det_json = json.loads(tick_circuit.get_meta("detectors"))
+    obs_json_str = tick_circuit.get_meta("observables")
+    obs_json = json.loads(obs_json_str) if obs_json_str else []
+    num_meas = int(tick_circuit.get_meta("num_measurements"))
+    len(det_json)
+
+    # Extract fired detectors and observables per shot
+    fired_per_shot: list[list[int]] = []
+    obs_per_shot: list[list[int]] = []
+    for r in results:
+        meas = list(r)
+        fired: list[int] = []
+        for i, det in enumerate(det_json):
+            val = 0
+            for rec in det["records"]:
+                idx = num_meas + rec
+                if 0 <= idx < len(meas):
+                    val ^= meas[idx]
+            if val:
+                fired.append(i)
+        fired_per_shot.append(fired)
+
+        obs_fired: list[int] = []
+        for i, obs in enumerate(obs_json):
+            val = 0
+            for rec in obs["records"]:
+                idx = num_meas + rec
+                if 0 <= idx < len(meas):
+                    val ^= meas[idx]
+            if val:
+                obs_fired.append(i)
+        obs_per_shot.append(obs_fired)
+
+    # Compute detector k-body rates with string labels
+    inv_shots = 1.0 / shots
+    rates: dict[tuple[str, ...], float] = {}
+
+    for fired in fired_per_shot:
+        labels = [f"D{d}" for d in fired]
+        for k in range(1, min(max_order, len(labels)) + 1):
+            for combo in combinations(labels, k):
+                rates[combo] = rates.get(combo, 0.0) + inv_shots
+
+    # Observable marginals: P(Lj)
+    for obs_fired in obs_per_shot:
+        for o in obs_fired:
+            key = (f"L{o}",)
+            rates[key] = rates.get(key, 0.0) + inv_shots
+
+    # Detector-observable pairwise: P(Di AND Lj)
+    for fired, obs_fired in zip(fired_per_shot, obs_per_shot, strict=False):
+        for d in fired:
+            for o in obs_fired:
+                key = (f"D{d}", f"L{o}")
+                rates[key] = rates.get(key, 0.0) + inv_shots
+
+    return sorted(rates.items())
+
+
+def fit_dem_from_simulation(
+    tick_circuit: object,
+    noise_builder: object,
+    shots: int,
+    *,
+    backend: str = "stabilizer",
+    seed: int = 42,
+    max_correlation_order: int = 2,
+) -> str:
+    """Build a DEM fitted to simulation data.
+
+    Runs simulation to get empirical detection rates, uses the circuit's
+    mechanism structure, and fits mechanism probabilities to match the
+    empirical marginals and pairwise rates. Returns a Stim DEM string.
+
+    This is the "hardware calibration" workflow: real noise statistics
+    (or accurate simulation) combined with circuit-derived structure.
+
+    Args:
+        tick_circuit: A ``TickCircuit`` with detector metadata.
+        noise_builder: A noise builder (e.g., ``depolarizing().p1(0.001)``).
+        shots: Number of simulation shots.
+        backend: Simulator backend — ``"stabilizer"``, ``"statevec"``,
+            or ``"meas_sampling"``. The meas_sampling backend uses the fast
+            whole-circuit DEM-based sampler instead of gate-by-gate simulation.
+        seed: RNG seed.
+        max_correlation_order: Max order for empirical rates (1 or 2).
+
+    Returns:
+        Stim-format DEM string with simulation-fitted probabilities.
+    """
+    if max_correlation_order < 1:
+        msg = "max_correlation_order must be at least 1"
+        raise ValueError(msg)
+
+    from pecos_rslib.qec import (
+        DagFaultAnalyzer,
+        DemBuilder,
+        fit_dem_to_marginals,
+        mechanisms_to_dem_string,
+    )
+    from pecos_rslib_exp import (
+        meas_sampling,
+        sim_neo,
+        stabilizer,
+        statevec,
+    )
+
+    # Step 1: Get mechanism structure from circuit
+    dag = tick_circuit.to_dag_circuit()
+    analyzer = DagFaultAnalyzer(dag)
+    influence = analyzer.build_influence_map()
+    # Use dummy noise to get mechanism structure (probabilities will be replaced)
+    builder = DemBuilder(influence)
+    builder = builder.with_noise(p1=0.01, p2=0.01, p_meas=0.01, p_prep=0.01)
+    builder = builder.with_detectors_json(tick_circuit.get_meta("detectors"))
+    builder = builder.with_observables_json(tick_circuit.get_meta("observables"))
+    builder = builder.with_num_measurements(
+        int(tick_circuit.get_meta("num_measurements")),
+    )
+    dem = builder.build()
+    dem_str = dem.to_string()
+
+    mechs: list[tuple[float, list[int], list[int]]] = []
+    for raw_line in dem_str.strip().split("\n"):
+        line = raw_line.strip()
+        if line.startswith("error("):
+            pe = line.index(")")
+            prob = float(line[6:pe])
+            toks = line[pe + 1 :].split()
+            ds = sorted(int(t[1:]) for t in toks if t.startswith("D"))
+            os = sorted(int(t[1:]) for t in toks if t.startswith("L"))
+            mechs.append((prob, ds, os))
+
+    # Step 2: Run simulation and extract empirical rates
+    det_json = json.loads(tick_circuit.get_meta("detectors"))
+    num_meas = int(tick_circuit.get_meta("num_measurements"))
+    num_dets = len(det_json)
+
+    if backend == "meas_sampling":
+        results = sim_neo(tick_circuit).quantum(meas_sampling()).noise(noise_builder).shots(shots).seed(seed).run()
+    elif backend in ("stabilizer", "statevec"):
+        backend_obj = stabilizer() if backend == "stabilizer" else statevec()
+        results = sim_neo(tick_circuit).quantum(backend_obj).noise(noise_builder).shots(shots).seed(seed).run()
+    else:
+        supported = "'stabilizer', 'statevec', 'meas_sampling'"
+        msg = f"Unknown backend {backend!r}. Supported: {supported}."
+        raise ValueError(msg)
+
+    inv_shots = 1.0 / shots
+    emp_marginals = [0.0] * num_dets
+    for r in results:
+        meas = list(r)
+        for i, det in enumerate(det_json):
+            val = 0
+            for rec in det["records"]:
+                idx = num_meas + rec
+                if 0 <= idx < len(meas):
+                    val ^= meas[idx]
+            if val:
+                emp_marginals[i] += inv_shots
+
+    # Step 3: Fit mechanism probabilities to empirical marginals
+    fitted, _residuals = fit_dem_to_marginals(mechs, emp_marginals)
+
+    return mechanisms_to_dem_string(fitted)
+
+
+def build_adaptive_dem(
+    tick_circuit: object,
+    noise_params: dict[str, float],
+    *,
+    max_order: int = 2,
+    prune: float = 1e-12,
+) -> tuple[str, str]:
+    """Build the best DEM using adaptive mechanism structure.
+
+    Uses influence map mechanisms for stochastic noise sources and EEG
+    backward extraction mechanisms for coherent (idle_rz) noise sources.
+    Fits all mechanism probabilities to Heisenberg exact marginals + pairwise.
+
+    Args:
+        tick_circuit: A ``TickCircuit`` with detector metadata.
+        noise_params: Dict with keys p1, p2, p_meas, p_prep, idle_rz.
+        max_order: Correlation order for Heisenberg targets (default 2).
+        prune: Pruning threshold for Heisenberg walks.
+
+    Returns:
+        Tuple of (json_str, dem_str) — noise characterization JSON and
+        Stim DEM string.
+    """
+    idle_rz = noise_params.get("idle_rz", 0.0)
+
+    if idle_rz == 0.0 or idle_rz < 1e-10:
+        # Pure stochastic: from_circuit is best
+        from pecos_rslib.qec import DemSampler
+
+        DemSampler.from_circuit(
+            tick_circuit,
+            p1=noise_params.get("p1", 0.0),
+            p2=noise_params.get("p2", 0.0),
+            p_meas=noise_params.get("p_meas", 0.0),
+            p_prep=noise_params.get("p_prep", 0.0),
+        )
+        # For consistency, also compute correlation table
+        from pecos_rslib_exp import exact_correlation_table
+
+        table = exact_correlation_table(tick_circuit, **noise_params, max_order=max_order)
+        # Return a minimal JSON with correlations
+        json_out = json.dumps(
+            {
+                "correlations": [{"nodes": list(labels), "probability": prob} for labels, prob in table],
+            },
+            indent=2,
+        )
+        # Get DEM string from the sampler's internal DEM
+        dem_str = ""  # from_circuit doesn't expose DEM string directly
+        # Rebuild via DemBuilder
+        from pecos_rslib.qec import DagFaultAnalyzer, DemBuilder
+
+        dag = tick_circuit.to_dag_circuit()
+        analyzer = DagFaultAnalyzer(dag)
+        influence = analyzer.build_influence_map()
+        builder = DemBuilder(influence)
+        builder = builder.with_noise(
+            p1=noise_params.get("p1", 0.0),
+            p2=noise_params.get("p2", 0.0),
+            p_meas=noise_params.get("p_meas", 0.0),
+            p_prep=noise_params.get("p_prep", 0.0),
+        )
+        builder = builder.with_detectors_json(tick_circuit.get_meta("detectors"))
+        builder = builder.with_observables_json(tick_circuit.get_meta("observables"))
+        builder = builder.with_num_measurements(
+            int(tick_circuit.get_meta("num_measurements")),
+        )
+        dem = builder.build()
+        dem_str = dem.to_string()
+
+        return json_out, dem_str
+
+    # Has coherent noise: use noise_characterization (EEG structure + L-BFGS fit)
+    from pecos_rslib_exp import noise_characterization
+
+    return noise_characterization(
+        tick_circuit,
+        **noise_params,
+        max_order=max_order,
+        prune=prune,
+    )
diff --git a/python/quantum-pecos/src/pecos/qec/surface/__init__.py b/python/quantum-pecos/src/pecos/qec/surface/__init__.py
index caf89931b..fb702c3f1 100644
--- a/python/quantum-pecos/src/pecos/qec/surface/__init__.py
+++ b/python/quantum-pecos/src/pecos/qec/surface/__init__.py
@@ -19,12 +19,12 @@
 
 # Circuit generation from geometry (unified abstraction)
 from pecos.qec.surface.circuit_builder import (
-    CircuitOp,
     DagCircuitRenderer,
     GuppyRenderer,
     OpType,
     QubitAllocation,
     StimRenderer,
+    SurfaceCircuitStep,
     TickCircuitRenderer,
     build_surface_code_circuit,
     classify_stabilizer_boundary,
@@ -56,6 +56,7 @@
     NoiseModel,
     SimulationResult,
     SurfaceDecoder,
+    build_memory_circuit,
     build_native_sampler,
     build_stim_circuit_from_patch,
     generate_circuit_level_dem,
@@ -63,6 +64,7 @@
     generate_repetition_code_dem,
     generate_surface_code_dem,
     run_noisy_memory_experiment,
+    surface_code_memory,
     syndromes_to_detection_events,
 )
 from pecos.qec.surface.layouts import (
@@ -76,6 +78,12 @@
     get_rotated_logical_x,
     get_rotated_logical_z,
 )
+from pecos.qec.surface.logical_circuit import (
+    LogicalCircuitBuilder,
+    LogicalGateType,
+    LogicalOp,
+    PatchState,
+)
 from pecos.qec.surface.parity import (
     parity_matrix_x,
     parity_matrix_z,
@@ -134,6 +142,7 @@
     "NoiseModel",
     "SimulationResult",
     "SurfaceDecoder",
+    "build_memory_circuit",
     "build_native_sampler",
     "build_stim_circuit_from_patch",
     "generate_circuit_level_dem",
@@ -141,12 +150,13 @@
     "generate_repetition_code_dem",
     "generate_surface_code_dem",
     "run_noisy_memory_experiment",
+    "surface_code_memory",
     "syndromes_to_detection_events",
     # Visualization
     "plot_patch",
     "plot_surface_code",
     # Circuit generation (unified abstraction)
-    "CircuitOp",
+    "SurfaceCircuitStep",
     "DagCircuitRenderer",
     "GuppyRenderer",
     "OpType",
@@ -171,5 +181,10 @@
     "get_stabilizer_schedule_entries",
     "get_stabilizer_schedule_metadata",
     "get_stabilizer_touch_label",
+    # Logical circuit builder (transversal gates)
+    "LogicalCircuitBuilder",
+    "LogicalGateType",
+    "LogicalOp",
+    "PatchState",
     "tick_circuit_to_stim",
 ]
diff --git a/python/quantum-pecos/src/pecos/qec/surface/circuit_builder.py b/python/quantum-pecos/src/pecos/qec/surface/circuit_builder.py
index 6f4ef4e67..14ce63767 100644
--- a/python/quantum-pecos/src/pecos/qec/surface/circuit_builder.py
+++ b/python/quantum-pecos/src/pecos/qec/surface/circuit_builder.py
@@ -107,8 +107,8 @@ class OpType(Enum):
 
 
 @dataclass
-class CircuitOp:
-    """A circuit operation."""
+class SurfaceCircuitStep:
+    """A surface-code circuit builder step."""
 
     op_type: OpType
     qubits: list[int] = field(default_factory=list)
@@ -167,7 +167,7 @@ def build_surface_code_circuit(
     num_rounds: int,
     basis: str = "Z",
     ancilla_budget: int | None = None,
-) -> tuple[list[CircuitOp], QubitAllocation]:
+) -> tuple[list[SurfaceCircuitStep], QubitAllocation]:
     """Build abstract circuit operations for a surface code memory experiment.
 
     This generates the circuit structure matching the Guppy implementation:
@@ -235,44 +235,44 @@ def z_anc_q(stab_idx: int) -> int:
     # Get CNOT schedule
     cnot_rounds = compute_cnot_schedule(patch)
 
-    ops: list[CircuitOp] = []
+    ops: list[SurfaceCircuitStep] = []
 
     # =========================================================================
     # prep_z_basis / prep_x_basis
     # =========================================================================
-    ops.append(CircuitOp(OpType.COMMENT, label=f"prep_{basis.lower()}_basis"))
+    ops.append(SurfaceCircuitStep(OpType.COMMENT, label=f"prep_{basis.lower()}_basis"))
 
     # Allocate and reset data qubits
-    ops.extend(CircuitOp(OpType.ALLOC, [data_q(i)], f"data[{i}]") for i in range(num_data))
+    ops.extend(SurfaceCircuitStep(OpType.ALLOC, [data_q(i)], f"data[{i}]") for i in range(num_data))
 
     # For X-basis: H on each data qubit
     if basis.upper() == "X":
-        ops.extend(CircuitOp(OpType.H, [data_q(i)]) for i in range(num_data))
+        ops.extend(SurfaceCircuitStep(OpType.H, [data_q(i)]) for i in range(num_data))
 
-    ops.append(CircuitOp(OpType.TICK))
+    ops.append(SurfaceCircuitStep(OpType.TICK))
 
     # =========================================================================
     # syndrome_extraction (called num_rounds times)
     # =========================================================================
     for rnd in range(num_rounds):
         ops.append(
-            CircuitOp(OpType.COMMENT, label=f"syndrome_extraction round {rnd + 1}"),
+            SurfaceCircuitStep(OpType.COMMENT, label=f"syndrome_extraction round {rnd + 1}"),
         )
         if effective_ancilla_budget == total_ancilla:
-            ops.extend(CircuitOp(OpType.ALLOC, [x_anc_q(s.index)], f"ax{s.index}") for s in geom.x_stabilizers)
-            ops.extend(CircuitOp(OpType.ALLOC, [z_anc_q(s.index)], f"az{s.index}") for s in geom.z_stabilizers)
+            ops.extend(SurfaceCircuitStep(OpType.ALLOC, [x_anc_q(s.index)], f"ax{s.index}") for s in geom.x_stabilizers)
+            ops.extend(SurfaceCircuitStep(OpType.ALLOC, [z_anc_q(s.index)], f"az{s.index}") for s in geom.z_stabilizers)
 
-            ops.append(CircuitOp(OpType.COMMENT, label="Hadamard on X ancillas"))
-            ops.extend(CircuitOp(OpType.H, [x_anc_q(s.index)], f"ax{s.index}") for s in geom.x_stabilizers)
+            ops.append(SurfaceCircuitStep(OpType.COMMENT, label="Hadamard on X ancillas"))
+            ops.extend(SurfaceCircuitStep(OpType.H, [x_anc_q(s.index)], f"ax{s.index}") for s in geom.x_stabilizers)
 
-            ops.append(CircuitOp(OpType.TICK))
+            ops.append(SurfaceCircuitStep(OpType.TICK))
 
             for rnd_idx, cx_round in enumerate(cnot_rounds):
-                ops.append(CircuitOp(OpType.COMMENT, label=f"CX round {rnd_idx + 1}"))
+                ops.append(SurfaceCircuitStep(OpType.COMMENT, label=f"CX round {rnd_idx + 1}"))
                 for stab_type, stab_idx, data_idx in cx_round:
                     if stab_type == "X":
                         ops.append(
-                            CircuitOp(
+                            SurfaceCircuitStep(
                                 OpType.CX,
                                 [x_anc_q(stab_idx), data_q(data_idx)],
                                 f"X{stab_idx}",
@@ -280,26 +280,30 @@ def z_anc_q(stab_idx: int) -> int:
                         )
                     else:
                         ops.append(
-                            CircuitOp(
+                            SurfaceCircuitStep(
                                 OpType.CX,
                                 [data_q(data_idx), z_anc_q(stab_idx)],
                                 f"Z{stab_idx}",
                             ),
                         )
-                ops.append(CircuitOp(OpType.TICK))
+                ops.append(SurfaceCircuitStep(OpType.TICK))
 
-            ops.append(CircuitOp(OpType.COMMENT, label="Hadamard on X ancillas"))
-            ops.extend(CircuitOp(OpType.H, [x_anc_q(s.index)], f"ax{s.index}") for s in geom.x_stabilizers)
+            ops.append(SurfaceCircuitStep(OpType.COMMENT, label="Hadamard on X ancillas"))
+            ops.extend(SurfaceCircuitStep(OpType.H, [x_anc_q(s.index)], f"ax{s.index}") for s in geom.x_stabilizers)
 
-            ops.append(CircuitOp(OpType.COMMENT, label="Measure ancillas"))
-            ops.extend(CircuitOp(OpType.MEASURE, [x_anc_q(s.index)], f"sx{s.index}") for s in geom.x_stabilizers)
-            ops.extend(CircuitOp(OpType.MEASURE, [z_anc_q(s.index)], f"sz{s.index}") for s in geom.z_stabilizers)
+            ops.append(SurfaceCircuitStep(OpType.COMMENT, label="Measure ancillas"))
+            ops.extend(
+                SurfaceCircuitStep(OpType.MEASURE, [x_anc_q(s.index)], f"sx{s.index}") for s in geom.x_stabilizers
+            )
+            ops.extend(
+                SurfaceCircuitStep(OpType.MEASURE, [z_anc_q(s.index)], f"sz{s.index}") for s in geom.z_stabilizers
+            )
 
-            ops.append(CircuitOp(OpType.TICK))
+            ops.append(SurfaceCircuitStep(OpType.TICK))
         else:
             stabilizer_batches = _batched_stabilizers(patch, effective_ancilla_budget)
             for batch in stabilizer_batches:
-                ops.append(CircuitOp(OpType.COMMENT, label="Prepare ancillas"))
+                ops.append(SurfaceCircuitStep(OpType.COMMENT, label="Prepare ancillas"))
                 batch_ancillas = {
                     (stab_type, stab_idx): x_anc_q(stab_idx) if stab_type == "X" else z_anc_q(stab_idx)
                     for stab_type, stab_idx in batch
@@ -307,7 +311,7 @@ def z_anc_q(stab_idx: int) -> int:
 
                 for stab_type, stab_idx in batch:
                     ops.append(
-                        CircuitOp(
+                        SurfaceCircuitStep(
                             OpType.ALLOC,
                             [batch_ancillas[(stab_type, stab_idx)]],
                             f"a{stab_type.lower()}{stab_idx}",
@@ -316,23 +320,23 @@ def z_anc_q(stab_idx: int) -> int:
 
                 x_stabilizers_in_batch = [stab_idx for stab_type, stab_idx in batch if stab_type == "X"]
                 if x_stabilizers_in_batch:
-                    ops.append(CircuitOp(OpType.COMMENT, label="Hadamard on X ancillas"))
+                    ops.append(SurfaceCircuitStep(OpType.COMMENT, label="Hadamard on X ancillas"))
                     ops.extend(
-                        CircuitOp(OpType.H, [batch_ancillas[("X", stab_idx)]], f"ax{stab_idx}")
+                        SurfaceCircuitStep(OpType.H, [batch_ancillas[("X", stab_idx)]], f"ax{stab_idx}")
                         for stab_idx in x_stabilizers_in_batch
                     )
 
-                ops.append(CircuitOp(OpType.TICK))
+                ops.append(SurfaceCircuitStep(OpType.TICK))
 
                 for rnd_idx, cx_round in enumerate(cnot_rounds):
-                    ops.append(CircuitOp(OpType.COMMENT, label=f"CX round {rnd_idx + 1}"))
+                    ops.append(SurfaceCircuitStep(OpType.COMMENT, label=f"CX round {rnd_idx + 1}"))
                     for stab_type, stab_idx, data_idx in cx_round:
                         ancilla_q = batch_ancillas.get((stab_type, stab_idx))
                         if ancilla_q is None:
                             continue
                         if stab_type == "X":
                             ops.append(
-                                CircuitOp(
+                                SurfaceCircuitStep(
                                     OpType.CX,
                                     [ancilla_q, data_q(data_idx)],
                                     f"X{stab_idx}",
@@ -340,54 +344,56 @@ def z_anc_q(stab_idx: int) -> int:
                             )
                         else:
                             ops.append(
-                                CircuitOp(
+                                SurfaceCircuitStep(
                                     OpType.CX,
                                     [data_q(data_idx), ancilla_q],
                                     f"Z{stab_idx}",
                                 ),
                             )
-                    ops.append(CircuitOp(OpType.TICK))
+                    ops.append(SurfaceCircuitStep(OpType.TICK))
 
                 if x_stabilizers_in_batch:
-                    ops.append(CircuitOp(OpType.COMMENT, label="Hadamard on X ancillas"))
+                    ops.append(SurfaceCircuitStep(OpType.COMMENT, label="Hadamard on X ancillas"))
                     ops.extend(
-                        CircuitOp(OpType.H, [batch_ancillas[("X", stab_idx)]], f"ax{stab_idx}")
+                        SurfaceCircuitStep(OpType.H, [batch_ancillas[("X", stab_idx)]], f"ax{stab_idx}")
                         for stab_idx in x_stabilizers_in_batch
                     )
 
-                ops.append(CircuitOp(OpType.COMMENT, label="Measure ancillas"))
+                ops.append(SurfaceCircuitStep(OpType.COMMENT, label="Measure ancillas"))
                 for stab_type, stab_idx in batch:
                     measure_label = f"sx{stab_idx}" if stab_type == "X" else f"sz{stab_idx}"
                     ops.append(
-                        CircuitOp(
+                        SurfaceCircuitStep(
                             OpType.MEASURE,
                             [batch_ancillas[(stab_type, stab_idx)]],
                             measure_label,
                         ),
                     )
 
-                ops.append(CircuitOp(OpType.TICK))
+                ops.append(SurfaceCircuitStep(OpType.TICK))
 
     # =========================================================================
     # measure_z_basis / measure_x_basis
     # =========================================================================
-    ops.append(CircuitOp(OpType.COMMENT, label=f"measure_{basis.lower()}_basis"))
+    ops.append(SurfaceCircuitStep(OpType.COMMENT, label=f"measure_{basis.lower()}_basis"))
 
     # For X-basis: H on each data qubit first
     if basis.upper() == "X":
-        ops.extend(CircuitOp(OpType.H, [data_q(i)]) for i in range(num_data))
+        ops.extend(SurfaceCircuitStep(OpType.H, [data_q(i)]) for i in range(num_data))
 
     # Measure all data qubits
-    ops.extend(CircuitOp(OpType.MEASURE, [data_q(i)], f"final[{i}]") for i in range(num_data))
+    ops.extend(SurfaceCircuitStep(OpType.MEASURE, [data_q(i)], f"final[{i}]") for i in range(num_data))
 
     return ops, allocation
 
 
-def classify_stabilizer_boundary(stab_type: str, data_qubits: tuple[int, ...], d: int) -> str:
+def classify_stabilizer_boundary(stab_type: str, data_qubits: tuple[int, ...], d: int, dz: int | None = None) -> str:
     """Public wrapper for classifying a boundary stabilizer."""
     from pecos.qec.surface.schedule import _classify_boundary
 
-    return _classify_boundary(stab_type, data_qubits, d)
+    if dz is None:
+        dz = d
+    return _classify_boundary(stab_type, data_qubits, d, dz)
 
 
 def get_stabilizer_region(stab: Stabilizer, patch: SurfacePatch) -> str:
@@ -427,7 +433,7 @@ def get_stabilizer_schedule_entries(stab: Stabilizer, patch: SurfacePatch) -> li
     """Return the per-round touch schedule for one stabilizer."""
     from pecos.qec.surface.schedule import get_stab_schedule
 
-    schedule = get_stab_schedule(stab.stab_type, stab.data_qubits, stab.is_boundary, patch.distance)
+    schedule = get_stab_schedule(stab.stab_type, stab.data_qubits, stab.is_boundary, patch.dx, patch.dz)
     return [
         {
             "round_0based": round_0based,
@@ -529,7 +535,7 @@ class CircuitRenderer(ABC):
     @abstractmethod
     def render(
         self,
-        ops: list[CircuitOp],
+        ops: list[SurfaceCircuitStep],
         allocation: QubitAllocation,
         patch: SurfacePatch,
         num_rounds: int,
@@ -547,7 +553,7 @@ def __init__(
         p1: float = 0.0,
         p2: float = 0.0,
         p_meas: float = 0.0,
-        p_init: float = 0.0,
+        p_prep: float = 0.0,
         add_detectors: bool = True,
     ) -> None:
         """Initialize Stim renderer.
@@ -556,18 +562,18 @@ def __init__(
             p1: Single-qubit depolarizing error rate
             p2: Two-qubit depolarizing error rate
             p_meas: Measurement error rate
-            p_init: Initialization error rate
+            p_prep: Initialization error rate
             add_detectors: Whether to add DETECTOR annotations
         """
         self.p1 = p1
         self.p2 = p2
         self.p_meas = p_meas
-        self.p_init = p_init
+        self.p_prep = p_prep
         self.add_detectors = add_detectors
 
     def render(
         self,
-        ops: list[CircuitOp],
+        ops: list[SurfaceCircuitStep],
         allocation: QubitAllocation,
         patch: SurfacePatch,
         num_rounds: int,
@@ -598,8 +604,8 @@ def render(
 
             elif op.op_type == OpType.ALLOC:
                 lines.append(f"R {op.qubits[0]}")
-                if self.p_init > 0:
-                    lines.append(f"X_ERROR({self.p_init}) {op.qubits[0]}")
+                if self.p_prep > 0:
+                    lines.append(f"X_ERROR({self.p_prep}) {op.qubits[0]}")
 
             elif op.op_type == OpType.H:
                 lines.append(f"H {op.qubits[0]}")
@@ -729,7 +735,7 @@ class GuppyRenderer(CircuitRenderer):
 
     def render(
         self,
-        _ops: list[CircuitOp],
+        _ops: list[SurfaceCircuitStep],
         _allocation: QubitAllocation,
         patch: SurfacePatch,
         _num_rounds: int,
@@ -756,7 +762,7 @@ class DagCircuitRenderer(CircuitRenderer):
 
     def render(
         self,
-        ops: list[CircuitOp],
+        ops: list[SurfaceCircuitStep],
         _allocation: QubitAllocation,
         _patch: SurfacePatch,
         _num_rounds: int,
@@ -829,7 +835,7 @@ def __init__(self, *, add_detectors: bool = True) -> None:
 
     def render(
         self,
-        ops: list[CircuitOp],
+        ops: list[SurfaceCircuitStep],
         allocation: QubitAllocation,
         patch: SurfacePatch,
         num_rounds: int,
@@ -874,14 +880,16 @@ def render(
         # Track measurements for detector annotations
         meas_count = 0
         stab_meas_record: dict[tuple[str, int, int], int] = {}
+        stab_meas_refs: dict[tuple[str, int, int], list] = {}
+        final_meas_refs_by_qubit: dict[int, list] = {}
         current_round = -1
         current_phase = "prep"
         current_cx_round = 0
         final_meas_start = 0
 
-        # Store all tick metadata to apply at the end (workaround for metadata
-        # being lost when new ticks are created)
-        # Format: {tick_idx: {'phase': str, 'round': int, 'cx_round': int, 'gates': [(label, role), ...]}}
+        # Store tick-level metadata to apply at the end by tick index. Gate
+        # metadata is attached immediately as each gate is emitted so it
+        # participates in TickCircuit's batching decisions.
         all_tick_metadata: dict[int, dict] = {}
 
         def get_stabilizer_from_label(label: str) -> str:
@@ -974,7 +982,6 @@ def new_tick() -> TickHandle:
                 "phase": current_phase,
                 "round": current_round,
                 "cx_round": current_cx_round,
-                "gates": [],
             }
             return current_tick_handle
 
@@ -993,24 +1000,34 @@ def mark_qubits_used(qubits: list[int]) -> None:
             """Mark qubits as used in current tick."""
             qubits_in_current_tick.update(qubits)
 
-        def queue_gate_metadata(meta: dict | None = None) -> None:
-            """Queue metadata for the current gate.
+        def gate_metadata(meta: dict | None = None) -> dict:
+            """Build metadata for the current gate context.
 
             Args:
                 meta: Optional dict with gate metadata (e.g., {"label": "data[0]"})
             """
-            if current_tick_idx >= 0:
-                context = {
-                    "phase": current_phase,
-                }
-                if current_round >= 0:
-                    context["syndrome_round"] = current_round
-                if current_cx_round > 0:
-                    context["cx_round"] = current_cx_round
-                merged_meta = context
-                if meta:
-                    merged_meta = {**context, **meta}
-                all_tick_metadata[current_tick_idx]["gates"].append(merged_meta)
+            context: dict[str, object] = {
+                "phase": current_phase,
+            }
+            if current_round >= 0:
+                context["syndrome_round"] = current_round
+            if current_cx_round > 0:
+                context["cx_round"] = current_cx_round
+            if meta:
+                return {**context, **meta}
+            return context
+
+        def apply_gate_metadata(handle: TickHandle, meta: dict | None = None) -> None:
+            """Attach metadata to the gate most recently added to a handle."""
+            handle.metas(gate_metadata(meta))
+
+        def apply_measurement_metadata(meas_refs: list, meta: dict | None = None) -> None:
+            """Attach metadata to the measurement gate just emitted."""
+            if not meas_refs:
+                return
+            tick_idx, gate_idx, _ = meas_refs[0]
+            for key, value in gate_metadata(meta).items():
+                circuit.set_gate_meta(tick_idx, gate_idx, key, value)
 
         for op in ops:
             if op.op_type == OpType.COMMENT:
@@ -1041,88 +1058,91 @@ def queue_gate_metadata(meta: dict | None = None) -> None:
                     tick.qalloc([q])
                     allocated.add(q)
                 else:
-                    tick.pz([q])
+                    tick = tick.pz([q])
                 mark_qubits_used([q])
                 # Label helps identify which qubit (e.g., "data[0]", "ax0")
                 meta = get_ancilla_gate_metadata(q, op.label)
                 if op.label:
                     meta["label"] = op.label
-                queue_gate_metadata(meta or None)
+                apply_gate_metadata(tick, meta or None)
 
             elif op.op_type == OpType.PREP:
                 q = op.qubits[0]
-                get_tick_for_qubits([q]).pz([q])
+                tick = get_tick_for_qubits([q]).pz([q])
                 mark_qubits_used([q])
                 meta = get_ancilla_gate_metadata(q, op.label)
                 if op.label:
                     meta["label"] = op.label
-                queue_gate_metadata(meta or None)
+                apply_gate_metadata(tick, meta or None)
 
             elif op.op_type == OpType.H:
                 q = op.qubits[0]
-                get_tick_for_qubits([q]).h([q])
+                tick = get_tick_for_qubits([q]).h([q])
                 mark_qubits_used([q])
                 meta = get_ancilla_gate_metadata(q, op.label)
                 if op.label:
                     meta["label"] = op.label
-                queue_gate_metadata(meta or None)
+                apply_gate_metadata(tick, meta or None)
 
             elif op.op_type == OpType.X:
                 q = op.qubits[0]
-                get_tick_for_qubits([q]).x([q])
+                tick = get_tick_for_qubits([q]).x([q])
                 mark_qubits_used([q])
                 meta = get_ancilla_gate_metadata(q, op.label)
                 if op.label:
                     meta["label"] = op.label
-                queue_gate_metadata(meta or None)
+                apply_gate_metadata(tick, meta or None)
 
             elif op.op_type == OpType.Z:
                 q = op.qubits[0]
-                get_tick_for_qubits([q]).z([q])
+                tick = get_tick_for_qubits([q]).z([q])
                 mark_qubits_used([q])
                 meta = get_ancilla_gate_metadata(q, op.label)
                 if op.label:
                     meta["label"] = op.label
-                queue_gate_metadata(meta or None)
+                apply_gate_metadata(tick, meta or None)
 
             elif op.op_type == OpType.CX:
                 qubits = op.qubits
-                get_tick_for_qubits(qubits).cx([(qubits[0], qubits[1])])
+                tick = get_tick_for_qubits(qubits).cx([(qubits[0], qubits[1])])
                 mark_qubits_used(qubits)
                 meta = get_cx_gate_metadata(qubits[0], qubits[1], op.label)
                 if op.label:
                     meta["label"] = op.label
-                queue_gate_metadata(meta or None)
+                apply_gate_metadata(tick, meta or None)
 
             elif op.op_type == OpType.MEASURE:
                 q = op.qubits[0]
-                get_tick_for_qubits([q]).mz([q])
+                meas_refs = get_tick_for_qubits([q]).mz([q])
                 mark_qubits_used([q])
                 # Label helps identify measurement (e.g., "sx0", "sz0", "final[0]")
                 meta = get_ancilla_gate_metadata(q, op.label)
                 if op.label:
                     meta["label"] = op.label
-                queue_gate_metadata(meta or None)
+                apply_measurement_metadata(meas_refs, meta or None)
 
-                # Track measurement index for detectors
+                # Track measurement index and refs for detectors
                 if op.label.startswith("sx"):
                     stab_idx = int(op.label[2:])
                     stab_meas_record[("X", stab_idx, current_round)] = meas_count
+                    stab_meas_refs[("X", stab_idx, current_round)] = meas_refs
                 elif op.label.startswith("sz"):
                     stab_idx = int(op.label[2:])
                     stab_meas_record[("Z", stab_idx, current_round)] = meas_count
+                    stab_meas_refs[("Z", stab_idx, current_round)] = meas_refs
                 elif op.label.startswith("final"):
                     if "final[0]" in op.label:
                         final_meas_start = meas_count
+                    # Track all final measurement refs by data qubit
+                    final_meas_refs_by_qubit[q] = meas_refs
                 meas_count += 1
 
             elif op.op_type == OpType.TICK:
                 current_tick_handle = None
                 qubits_in_current_tick = set()
 
-        # Apply tick-level and gate-level metadata
-        # We use the circuit's set_tick_meta and set_gate_meta methods
-        # which modify the ticks in place (unlike get_tick() which returns a copy)
+        # Apply tick-level metadata in place. Gate metadata is attached as each
+        # gate is emitted so batching decisions can account for it immediately.
         for tick_idx, tick_meta in all_tick_metadata.items():
             # Set tick-level metadata
             circuit.set_tick_meta(tick_idx, "phase", tick_meta["phase"])
@@ -1131,12 +1151,6 @@ def queue_gate_metadata(meta: dict | None = None) -> None:
             if tick_meta["cx_round"] > 0:
                 circuit.set_tick_meta(tick_idx, "cx_round", tick_meta["cx_round"])
 
-            # Set gate-level metadata (only for gates that have meaningful metadata)
-            for gate_idx, gate_meta in enumerate(tick_meta["gates"]):
-                if gate_meta:
-                    for key, value in gate_meta.items():
-                        circuit.set_gate_meta(tick_idx, gate_idx, key, value)
-
         # Add detector annotations as metadata
         if self.add_detectors:
             geom = patch.geometry
@@ -1241,16 +1255,103 @@ def queue_gate_metadata(meta: dict | None = None) -> None:
                 },
             ]
 
-            # Store as metadata
+            # Store as metadata (legacy path for DemBuilder/caching)
             circuit.set_meta("detectors", json.dumps(detectors))
             circuit.set_meta("observables", json.dumps(observables))
             circuit.set_meta("num_measurements", str(meas_count))
             circuit.set_meta("num_detectors", str(len(detectors)))
+
+            # Also add typed PauliAnnotation annotations (new path)
+            self._add_typed_annotations(
+                circuit,
+                geom,
+                num_rounds,
+                basis,
+                stab_meas_refs,
+                final_meas_refs_by_qubit,
+                deterministic_type_round0,
+            )
         circuit.set_meta("basis", basis.upper())
         circuit.set_meta("ancilla_budget", str(allocation.total - len(allocation.data_qubits)))
 
         return circuit
 
+    @staticmethod
+    def _add_typed_annotations(
+        circuit: TickCircuit,
+        geom: object,
+        num_rounds: int,
+        basis: str,
+        stab_meas_refs: dict,
+        final_meas_refs_by_qubit: dict,
+        deterministic_type_round0: str,
+    ) -> None:
+        """Add typed PauliAnnotation detectors and observables to the circuit.
+
+        This mirrors the JSON detector logic but uses the new annotation API
+        with TickMeasRef measurement references.
+        """
+        # Syndrome detectors for X stabilizers
+        for rnd in range(num_rounds):
+            for s in geom.x_stabilizers:
+                curr_refs = stab_meas_refs.get(("X", s.index, rnd))
+                if curr_refs is None:
+                    continue
+                if rnd == 0:
+                    if deterministic_type_round0 == "X":
+                        circuit.detector(curr_refs, label=f"Sx{s.index}_r{rnd}")
+                else:
+                    prev_refs = stab_meas_refs.get(("X", s.index, rnd - 1), [])
+                    circuit.detector(prev_refs + curr_refs, label=f"Sx{s.index}_r{rnd}")
+
+        # Syndrome detectors for Z stabilizers
+        for rnd in range(num_rounds):
+            for s in geom.z_stabilizers:
+                curr_refs = stab_meas_refs.get(("Z", s.index, rnd))
+                if curr_refs is None:
+                    continue
+                if rnd == 0:
+                    if deterministic_type_round0 == "Z":
+                        circuit.detector(curr_refs, label=f"Sz{s.index}_r{rnd}")
+                else:
+                    prev_refs = stab_meas_refs.get(("Z", s.index, rnd - 1), [])
+                    circuit.detector(prev_refs + curr_refs, label=f"Sz{s.index}_r{rnd}")
+
+        # Final detectors
+        if basis.upper() == "Z":
+            stabilizers = geom.z_stabilizers
+            stab_type = "Z"
+            logical_qubits = list(geom.logical_z.data_qubits) if geom.logical_z else []
+        else:
+            stabilizers = geom.x_stabilizers
+            stab_type = "X"
+            logical_qubits = list(geom.logical_x.data_qubits) if geom.logical_x else []
+
+        for s in stabilizers:
+            # Data qubit measurement refs for this stabilizer
+            data_refs = []
+            for dq in s.data_qubits:
+                if dq in final_meas_refs_by_qubit:
+                    data_refs.extend(final_meas_refs_by_qubit[dq])
+            # Last syndrome round ref
+            last_syn_refs = stab_meas_refs.get(
+                (stab_type, s.index, num_rounds - 1),
+                [],
+            )
+            label_prefix = "Sx" if stab_type == "X" else "Sz"
+            circuit.detector(
+                data_refs + last_syn_refs,
+                label=f"{label_prefix}{s.index}_final",
+            )
+
+        # Logical observable
+        obs_refs = []
+        for q in logical_qubits:
+            if q in final_meas_refs_by_qubit:
+                obs_refs.extend(final_meas_refs_by_qubit[q])
+        if obs_refs:
+            circuit.observable(obs_refs, label=f"logical_{basis.upper()}")
+
 
 # Convenience functions
 
@@ -1264,7 +1365,7 @@ def generate_stim_from_patch(
     p1: float = 0.0,
     p2: float = 0.0,
     p_meas: float = 0.0,
-    p_init: float = 0.0,
+    p_prep: float = 0.0,
 ) -> str:
     """Generate Stim circuit from SurfacePatch.
 
@@ -1276,13 +1377,13 @@ def generate_stim_from_patch(
         p1: Single-qubit error rate
         p2: Two-qubit error rate
         p_meas: Measurement error rate
-        p_init: Initialization error rate
+        p_prep: Initialization error rate
 
     Returns:
         Stim circuit string
     """
     ops, allocation = build_surface_code_circuit(patch, num_rounds, basis, ancilla_budget)
-    renderer = StimRenderer(p1=p1, p2=p2, p_meas=p_meas, p_init=p_init)
+    renderer = StimRenderer(p1=p1, p2=p2, p_meas=p_meas, p_prep=p_prep)
     return renderer.render(ops, allocation, patch, num_rounds, basis)
 
 
@@ -1485,7 +1586,7 @@ def tick_circuit_to_stim(
     p1: float = 0.0,
     p2: float = 0.0,
     p_meas: float = 0.0,
-    p_init: float = 0.0,
+    p_prep: float = 0.0,
 ) -> str:
     """Convert TickCircuit to Stim circuit string.
 
@@ -1497,7 +1598,7 @@ def tick_circuit_to_stim(
         p1: Single-qubit error rate
         p2: Two-qubit error rate
         p_meas: Measurement error rate
-        p_init: Initialization error rate
+        p_prep: Initialization error rate
 
     Returns:
         Stim circuit string
@@ -1605,7 +1706,7 @@ def _gate_to_stim(
 
     for tick_idx in range(tc.num_ticks()):
         tick = tc.get_tick(tick_idx)
-        for gate in tick.gates():
+        for gate in tick.gate_batches():
             instructions, noise_kind = _gate_to_stim(gate)
             if not instructions:
                 continue
@@ -1624,8 +1725,8 @@ def _gate_to_stim(
                 lines.append(f"DEPOLARIZE1({p1}) {qubit_str}")
             elif noise_kind == "two" and p2 > 0:
                 lines.append(f"DEPOLARIZE2({p2}) {qubit_str}")
-            elif noise_kind == "prep" and p_init > 0:
-                lines.append(f"X_ERROR({p_init}) {qubit_str}")
+            elif noise_kind == "prep" and p_prep > 0:
+                lines.append(f"X_ERROR({p_prep}) {qubit_str}")
 
         # Add TICK after each tick (except the last)
         if tick_idx < tc.num_ticks() - 1:
@@ -1689,7 +1790,7 @@ def generate_dem_from_patch(
         p1=p,
         p2=p,
         p_meas=p,
-        p_init=p,
+        p_prep=p,
     )
     circuit = stim.Circuit(circuit_str)
     return str(circuit.detector_error_model())
@@ -1701,7 +1802,7 @@ def generate_dem_from_tick_circuit_via_pauli_frame(
     p1: float = 0.01,
     p2: float = 0.01,
     p_meas: float = 0.01,
-    p_init: float = 0.01,
+    p_prep: float = 0.01,
 ) -> str:
     """Generate DEM from TickCircuit using pure Python Pauli frame simulation.
 
@@ -1717,7 +1818,7 @@ def generate_dem_from_tick_circuit_via_pauli_frame(
         p1: Single-qubit depolarizing error rate
         p2: Two-qubit depolarizing error rate
         p_meas: Measurement error rate
-        p_init: Initialization (prep) error rate
+        p_prep: Initialization (prep) error rate
 
     Returns:
         DEM string in Stim-compatible format
@@ -1760,7 +1861,7 @@ def generate_dem_from_tick_circuit_via_pauli_frame(
 
     for tick_idx in range(tc.num_ticks()):
         tick = tc.get_tick(tick_idx)
-        for gate in tick.gates():
+        for gate in tick.gate_batches():
             gate_name = gate.gate_type.name
             qubits = list(gate.qubits)
             meas_idx = None
@@ -1893,14 +1994,13 @@ def simulate_error(
 
     # Process each gate as a potential error location
     for op_idx, (_tick_idx, gate_name, qubits, meas_idx) in enumerate(circuit_ops):
-
-        if gate_name in ("QAlloc", "PZ") and p_init > 0:
+        if gate_name in ("QAlloc", "PZ") and p_prep > 0:
             # Initialization error: X error after prep
             q = qubits[0]
             dets, obs = simulate_error(op_idx + 1, {q: "X"})
             if dets or obs:
                 key = (frozenset(dets), frozenset(obs))
-                error_mechanisms[key] += p_init
+                error_mechanisms[key] += p_prep
 
         elif gate_name == "H" and p1 > 0:
             # Single-qubit gate error: depolarizing (each Pauli with prob p1/3)
@@ -1973,7 +2073,7 @@ def generate_dem_from_tick_circuit_via_stim(
     p1: float = 0.01,
     p2: float = 0.01,
     p_meas: float = 0.01,
-    p_init: float = 0.01,
+    p_prep: float = 0.01,
     decompose_errors: bool = True,
     maximal_decomposition: bool = False,
 ) -> str:
@@ -1988,7 +2088,7 @@ def generate_dem_from_tick_circuit_via_stim(
         p1: Single-qubit depolarizing error rate
         p2: Two-qubit depolarizing error rate
         p_meas: Measurement error rate
-        p_init: Initialization (prep) error rate
+        p_prep: Initialization (prep) error rate
         decompose_errors: If True (default), ask Stim to decompose hyperedge
             errors into graphlike components. Set to False to preserve raw
             hyperedges.
@@ -2005,7 +2105,7 @@ def generate_dem_from_tick_circuit_via_stim(
         msg = "Stim is required for this function. Install with: pip install stim"
         raise ImportError(msg) from e
 
-    stim_str = tick_circuit_to_stim(tc, p1=p1, p2=p2, p_meas=p_meas, p_init=p_init)
+    stim_str = tick_circuit_to_stim(tc, p1=p1, p2=p2, p_meas=p_meas, p_prep=p_prep)
     circuit = stim.Circuit(stim_str)
     dem = circuit.detector_error_model(decompose_errors=decompose_errors or maximal_decomposition)
     if maximal_decomposition:
@@ -2034,7 +2134,7 @@ def _extract_measurement_order(tc: TickCircuit) -> list[int]:
         tick = tc.get_tick(tick_idx)
         if tick is None:
             continue
-        gates = tick.gates()
+        gates = tick.gate_batches()
         for gate in gates:
             gate_type = str(gate.gate_type)
             if "MZ" in gate_type:
@@ -2116,7 +2216,10 @@ def generate_dem_from_tick_circuit(
     p1: float = 0.01,
     p2: float = 0.01,
     p_meas: float = 0.01,
-    p_init: float = 0.01,
+    p_prep: float = 0.01,
+    p_idle: float | None = None,
+    t1: float | None = None,
+    t2: float | None = None,
     decompose_errors: bool = True,
     maximal_decomposition: bool = False,
 ) -> str:
@@ -2143,7 +2246,11 @@ def generate_dem_from_tick_circuit(
         p1: Single-qubit depolarizing error rate
         p2: Two-qubit depolarizing error rate
         p_meas: Measurement error rate
-        p_init: Initialization (prep) error rate
+        p_prep: Initialization (prep) error rate
+        p_idle: Optional idle noise rate per explicit idle-gate time unit.
+            The caller is responsible for inserting idle gates where needed.
+        t1: Optional T1 relaxation time for explicit idle gates.
+        t2: Optional T2 dephasing time for explicit idle gates.
         decompose_errors: If True (default), decompose hyperedge errors into
             graphlike components using the `^` separator. Set to False to
             output raw hyperedges. Ignored if maximal_decomposition=True.
@@ -2178,7 +2285,7 @@ def generate_dem_from_tick_circuit(
 
     # Build DEM using Rust DemBuilder
     builder = DemBuilder(influence_map)
-    builder.with_noise(p1, p2, p_meas, p_init)
+    builder.with_noise(p1, p2, p_meas, p_prep, p_idle=p_idle, t1=t1, t2=t2)
     builder.with_num_measurements(num_measurements)
     builder.with_measurement_order(measurement_order)
     builder.with_detectors_json(detectors_json)
@@ -2197,12 +2304,12 @@ def generate_dem_from_tick_circuit(
 def generate_dem_from_tick_circuit_via_autodetection(
     tc: TickCircuit,
     *,
-    logical_z_qubits: list[int] | None = None,
-    logical_x_qubits: list[int] | None = None,
+    tracked_z_qubits: list[int] | None = None,
+    tracked_x_qubits: list[int] | None = None,
     p1: float = 0.01,
     p2: float = 0.01,
     p_meas: float = 0.01,
-    p_init: float = 0.01,
+    p_prep: float = 0.01,
 ) -> str:
     """Generate DEM from TickCircuit using auto-discovered detectors.
 
@@ -2216,16 +2323,19 @@ def generate_dem_from_tick_circuit_via_autodetection(
 
     Args:
         tc: TickCircuit (detector annotations not required)
-        logical_z_qubits: Qubit indices for logical Z operator (for X error tracking)
-        logical_x_qubits: Qubit indices for logical X operator (for Z error tracking)
+        tracked_z_qubits: Qubit indices for a tracked Z Pauli (for X error tracking)
+        tracked_x_qubits: Qubit indices for a tracked X Pauli (for Z error tracking)
         p1: Single-qubit depolarizing error rate
         p2: Two-qubit depolarizing error rate
         p_meas: Measurement error rate
-        p_init: Initialization (prep) error rate
+        p_prep: Initialization (prep) error rate
 
     Returns:
-        DEM string in Stim-compatible format
+        PECOS DEM string. With no tracked Paulis this is Stim-compatible;
+        tracked Paulis are represented with PECOS `pecos_tracked_pauli`
+        metadata lines.
     """
+    import json
     from collections import defaultdict
 
     from pecos.qec import PAULI_X, PAULI_Y, PAULI_Z, InfluenceBuilder
@@ -2235,18 +2345,17 @@ def generate_dem_from_tick_circuit_via_autodetection(
 
     # Build influence map with auto-discovered detectors
     builder = InfluenceBuilder(dag)
-    if logical_z_qubits:
-        builder.with_logical_z(logical_z_qubits)
-    if logical_x_qubits:
-        builder.with_logical_x(logical_x_qubits)
+    if tracked_x_qubits:
+        builder.with_tracked_x(tracked_x_qubits)
+    if tracked_z_qubits:
+        builder.with_tracked_z(tracked_z_qubits)
     influence_map = builder.build()
 
     # Get all fault locations and auto-discovered detectors
     locations = influence_map.get_locations()
     num_detectors = influence_map.num_detectors
-    num_logicals = influence_map.num_logicals
 
-    # Collect error mechanisms: (detectors, logicals) -> probability
+    # Collect error mechanisms: (detectors, DEM outputs) -> probability
     error_mechanisms: dict[tuple[frozenset[int], frozenset[int]], float] = defaultdict(
         float,
     )
@@ -2256,23 +2365,23 @@ def generate_dem_from_tick_circuit_via_autodetection(
         gate_type = loc.gate_type
 
         if "PZ" in gate_type or "QAlloc" in gate_type:
-            if p_init <= 0:
+            if p_prep <= 0:
                 continue
             for pauli in [PAULI_X]:
                 dets = set(influence_map.get_detector_indices(loc_idx, pauli))
-                logs = set(influence_map.get_logical_indices(loc_idx, pauli))
-                if dets or logs:
-                    key = (frozenset(dets), frozenset(logs))
-                    error_mechanisms[key] += p_init
+                dem_outputs = set(influence_map.get_observable_indices(loc_idx, pauli))
+                if dets or dem_outputs:
+                    key = (frozenset(dets), frozenset(dem_outputs))
+                    error_mechanisms[key] += p_prep
 
         elif "MZ" in gate_type:
             if p_meas <= 0:
                 continue
             for pauli in [PAULI_X]:
                 dets = set(influence_map.get_detector_indices(loc_idx, pauli))
-                logs = set(influence_map.get_logical_indices(loc_idx, pauli))
-                if dets or logs:
-                    key = (frozenset(dets), frozenset(logs))
+                dem_outputs = set(influence_map.get_observable_indices(loc_idx, pauli))
+                if dets or dem_outputs:
+                    key = (frozenset(dets), frozenset(dem_outputs))
                     error_mechanisms[key] += p_meas
 
         elif "CX" in gate_type:
@@ -2280,9 +2389,9 @@ def generate_dem_from_tick_circuit_via_autodetection(
                 continue
             for pauli in [PAULI_X, PAULI_Y, PAULI_Z]:
                 dets = set(influence_map.get_detector_indices(loc_idx, pauli))
-                logs = set(influence_map.get_logical_indices(loc_idx, pauli))
-                if dets or logs:
-                    key = (frozenset(dets), frozenset(logs))
+                dem_outputs = set(influence_map.get_observable_indices(loc_idx, pauli))
+                if dets or dem_outputs:
+                    key = (frozenset(dets), frozenset(dem_outputs))
                     error_mechanisms[key] += p2 / 3
 
         elif "H" in gate_type:
@@ -2290,27 +2399,52 @@ def generate_dem_from_tick_circuit_via_autodetection(
                 continue
             for pauli in [PAULI_X, PAULI_Y, PAULI_Z]:
                 dets = set(influence_map.get_detector_indices(loc_idx, pauli))
-                logs = set(influence_map.get_logical_indices(loc_idx, pauli))
-                if dets or logs:
-                    key = (frozenset(dets), frozenset(logs))
+                dem_outputs = set(influence_map.get_observable_indices(loc_idx, pauli))
+                if dets or dem_outputs:
+                    key = (frozenset(dets), frozenset(dem_outputs))
                     error_mechanisms[key] += p1 / 3
 
     # Generate DEM output
     # Add detector declarations (auto-discovered, no coordinates)
     lines = [f"detector D{det_idx}" for det_idx in range(num_detectors)]
 
-    # Add logical observables
-    lines.extend(f"logical_observable L{log_idx}" for log_idx in range(num_logicals))
+    def _pauli_string(pauli: str, qubits: list[int] | None) -> str:
+        if not qubits:
+            return "+I"
+        return "+" + " ".join(f"{pauli}{q}" for q in qubits)
+
+    tracked_pauli_metadata = []
+    if tracked_x_qubits:
+        tracked_pauli_metadata.append(
+            {
+                "id": len(tracked_pauli_metadata),
+                "kind": "tracked_pauli",
+                "label": "tracked_x",
+                "pauli": _pauli_string("X", tracked_x_qubits),
+            },
+        )
+    if tracked_z_qubits:
+        tracked_pauli_metadata.append(
+            {
+                "id": len(tracked_pauli_metadata),
+                "kind": "tracked_pauli",
+                "label": "tracked_z",
+                "pauli": _pauli_string("Z", tracked_z_qubits),
+            },
+        )
+    lines.extend(
+        f"pecos_tracked_pauli {json.dumps(metadata, separators=(',', ':'))}" for metadata in tracked_pauli_metadata
+    )
 
     # Add error mechanisms
-    for (dets, logs), prob in sorted(
+    for (dets, dem_outputs), prob in sorted(
         error_mechanisms.items(),
         key=lambda x: (sorted(x[0][0]), sorted(x[0][1])),
     ):
-        if prob > 0 and (dets or logs):
+        if prob > 0 and (dets or dem_outputs):
             det_str = " ".join(f"D{d}" for d in sorted(dets))
-            log_str = " ".join(f"L{log_idx}" for log_idx in sorted(logs))
-            targets = f"{det_str} {log_str}".strip()
+            dem_output_str = " ".join(f"L{idx}" for idx in sorted(dem_outputs))
+            targets = f"{det_str} {dem_output_str}".strip()
             lines.append(f"error({prob:.6g}) {targets}")
 
     return "\n".join(lines)
diff --git a/python/quantum-pecos/src/pecos/qec/surface/circuit_gen.py b/python/quantum-pecos/src/pecos/qec/surface/circuit_gen.py
index ff69a0ab6..0886f965e 100644
--- a/python/quantum-pecos/src/pecos/qec/surface/circuit_gen.py
+++ b/python/quantum-pecos/src/pecos/qec/surface/circuit_gen.py
@@ -33,7 +33,7 @@ def generate_stim_circuit(
     p1: float = 0.0,
     p2: float = 0.0,
     p_meas: float = 0.0,
-    p_init: float = 0.0,
+    p_prep: float = 0.0,
 ) -> str:
     """Generate a Stim circuit from SurfacePatch geometry.
 
@@ -53,7 +53,7 @@ def generate_stim_circuit(
         p1: Single-qubit gate depolarizing error rate
         p2: Two-qubit gate depolarizing error rate
         p_meas: Measurement error rate (X_ERROR before M)
-        p_init: Initialization error rate (X_ERROR after R)
+        p_prep: Initialization error rate (X_ERROR after R)
 
     Returns:
         Stim circuit string with noise and detector annotations
@@ -109,8 +109,8 @@ def z_anc_q(stab_idx: int) -> int:
     # Allocate data qubits (R = reset = qubit())
     for i in range(num_data):
         lines.append(f"R {data_q(i)}")
-        if p_init > 0:
-            lines.append(f"X_ERROR({p_init}) {data_q(i)}")
+        if p_prep > 0:
+            lines.append(f"X_ERROR({p_prep}) {data_q(i)}")
 
     # For X-basis: H on each data qubit
     if basis.upper() == "X":
@@ -140,14 +140,14 @@ def z_anc_q(stab_idx: int) -> int:
         # Guppy: ax{i} = qubit() for each X stabilizer
         for s in geom.x_stabilizers:
             lines.append(f"R {x_anc_q(s.index)}")
-            if p_init > 0:
-                lines.append(f"X_ERROR({p_init}) {x_anc_q(s.index)}")
+            if p_prep > 0:
+                lines.append(f"X_ERROR({p_prep}) {x_anc_q(s.index)}")
 
         # Guppy: az{i} = qubit() for each Z stabilizer
         for s in geom.z_stabilizers:
             lines.append(f"R {z_anc_q(s.index)}")
-            if p_init > 0:
-                lines.append(f"X_ERROR({p_init}) {z_anc_q(s.index)}")
+            if p_prep > 0:
+                lines.append(f"X_ERROR({p_prep}) {z_anc_q(s.index)}")
 
         lines.append("")
 
@@ -341,7 +341,7 @@ def generate_circuit_level_dem(
         p1=p,
         p2=p,
         p_meas=p,
-        p_init=p,
+        p_prep=p,
     )
 
     # Parse and generate DEM
@@ -474,7 +474,7 @@ def compare_dems(
     stim_dem = generate_circuit_level_dem(patch, num_rounds, basis, p=p)
 
     # Generate phenomenological DEM
-    noise = NoiseModel(p1=p, p2=p, p_meas=p, p_init=p)
+    noise = NoiseModel(p1=p, p2=p, p_meas=p, p_prep=p)
     stab_type = "X" if basis.upper() == "X" else "Z"
     phenom_dem = generate_surface_code_dem(patch, num_rounds, noise, stab_type)
 
diff --git a/python/quantum-pecos/src/pecos/qec/surface/decode.py b/python/quantum-pecos/src/pecos/qec/surface/decode.py
index 78844bf57..6ffb604b9 100644
--- a/python/quantum-pecos/src/pecos/qec/surface/decode.py
+++ b/python/quantum-pecos/src/pecos/qec/surface/decode.py
@@ -57,6 +57,15 @@
     from pecos.qec.surface.patch import Stabilizer, SurfacePatch
 
 
+def _validate_probability(name: str, value: float) -> float:
+    """Return ``value`` as a float after validating it is a probability."""
+    probability = float(value)
+    if not 0.0 <= probability <= 1.0:
+        msg = f"{name} must be a probability in [0, 1], got {value!r}"
+        raise ValueError(msg)
+    return probability
+
+
 class DecoderType(str, Enum):
     """Available decoder backends."""
 
@@ -70,32 +79,53 @@ class DecoderType(str, Enum):
 
 @dataclass
 class NoiseModel:
-    """Depolarizing noise parameters for surface code simulation.
+    """Circuit-level noise parameters for QEC simulation.
 
-    These parameters match the DepolarizingErrorModel in selene_sim.
+    Matches the Rust ``NoiseConfig`` type. All parameters are optional
+    beyond the four base rates.
 
     Attributes:
-        p1: Single-qubit gate error rate
-        p2: Two-qubit gate error rate
-        p_meas: Measurement error rate
-        p_init: Initialization error rate
+        p1: Single-qubit gate error rate.
+        p2: Two-qubit gate error rate.
+        p_meas: Measurement error rate.
+        p_prep: Initialization error rate.
+        p_idle: Idle noise rate per time unit (uniform depolarizing).
+        t1: T1 relaxation time for idle noise (same units as idle duration).
+        t2: T2 dephasing time (must satisfy t2 <= 2*t1).
     """
 
-    p1: float = 0.0  # Single-qubit gate error rate
-    p2: float = 0.0  # Two-qubit gate error rate
-    p_meas: float = 0.0  # Measurement error rate
-    p_init: float = 0.0  # Initialization error rate
+    p1: float = 0.0
+    p2: float = 0.0
+    p_meas: float = 0.0
+    p_prep: float = 0.0
+    p_idle: float | None = None
+    t1: float | None = None
+    t2: float | None = None
+
+    @staticmethod
+    def uniform(physical_error_rate: float) -> NoiseModel:
+        """Create a uniform circuit-level noise model from one physical error rate."""
+        p = _validate_probability("physical_error_rate", physical_error_rate)
+        return NoiseModel(p1=p, p2=p, p_meas=p, p_prep=p)
 
     @property
     def is_noiseless(self) -> bool:
         """True if all error rates are zero."""
-        return self.p1 == 0.0 and self.p2 == 0.0 and self.p_meas == 0.0 and self.p_init == 0.0
+        return (
+            self.p1 == 0.0
+            and self.p2 == 0.0
+            and self.p_meas == 0.0
+            and self.p_prep == 0.0
+            and (self.p_idle is None or self.p_idle == 0.0)
+        )
 
     @property
     def physical_error_rate(self) -> float:
-        """Approximate combined physical error rate (for DEM weights)."""
-        # Use maximum as a conservative estimate
-        return max(self.p1, self.p2, self.p_meas, self.p_init)
+        """Approximate combined physical error rate."""
+        rates = [self.p1, self.p2, self.p_meas, self.p_prep]
+        if self.p_idle is not None:
+            rates.append(self.p_idle)
+        return max(rates)
 
 
 @dataclass
@@ -518,6 +548,9 @@ def tuple_args(payload: Any, op_name: str, arity: int) -> tuple[Any, ...]:
             msg = f"Unsupported traced QIS quantum op {op_name!r}"
             raise ValueError(msg)
 
+    # Compact: ASAP-schedule gates into minimal ticks
+    tick_circuit.compact_ticks()
+
     return tick_circuit
 
 
@@ -538,12 +571,38 @@ def _gate_triples(qubits: list[int], gate_type: str) -> list[tuple[int, int, int
 
 
 def _replay_lowered_qis_trace_into_tick_circuit(chunks: list[dict[str, Any]]) -> Any:
-    """Replay lowered post-Selene ByteMessage gate batches into a TickCircuit."""
+    """Replay lowered post-Selene ByteMessage gate batches into a TickCircuit.
+
+    The lowered trace emits gates one at a time. We replay each into its own
+    tick, then compact (ASAP schedule) so that gates on disjoint qubits share
+    a tick --- matching the parallel structure of the abstract circuit.
+
+    MeasIds flow from Guppy result() objects: AllocateResult IDs from the
+    operations stream are stamped on MZ gates via mz_with_ids().
+    """
     from pecos_rslib.quantum import TickCircuit
 
     tick_circuit = TickCircuit()
 
     for chunk in chunks:
+        # Extract AllocateResult ID → MZ qubit mapping from the operations stream.
+        # Each AllocateResult(id=N) is followed by Quantum.Measure([qubit, slot]).
+        # This gives us the MeasId to stamp on each MZ gate.
+        meas_id_queue: list[tuple[int, int]] = []  # (qubit, meas_id) pairs
+        last_alloc_id: int | None = None
+        for op in chunk.get("operations") or []:
+            op_dict = dict(op)
+            if "AllocateResult" in op_dict:
+                last_alloc_id = int(op_dict["AllocateResult"]["id"])
+            elif "Quantum" in op_dict:
+                q_op = op_dict["Quantum"]
+                if "Measure" in q_op and last_alloc_id is not None:
+                    qubit = int(q_op["Measure"][0])
+                    meas_id_queue.append((qubit, last_alloc_id))
+                    last_alloc_id = None
+
+        meas_id_idx = 0  # next MeasId to assign
+
         for gate in chunk.get("lowered_quantum_ops") or []:
             gate_type = str(gate["gate_type"])
             qubits = [int(q) for q in gate.get("qubits", [])]
@@ -569,7 +628,26 @@ def _replay_lowered_qis_trace_into_tick_circuit(chunks: list[dict[str, Any]]) ->
             elif gate_type == "PZ":
                 tick.pz(qubits)
             elif gate_type == "MZ":
-                tick.mz(qubits)
+                # Stamp MeasIds from the AllocateResult stream
+                meas_ids = []
+                for q in qubits:
+                    if meas_id_idx < len(meas_id_queue):
+                        expected_q, mid = meas_id_queue[meas_id_idx]
+                        if expected_q == q:
+                            meas_ids.append(mid)
+                            meas_id_idx += 1
+                        else:
+                            # Qubit mismatch — fall back to auto-assign
+                            meas_ids = []
+                            break
+                    else:
+                        meas_ids = []
+                        break
+
+                if meas_ids:
+                    tick.mz_with_ids(qubits, meas_ids)
+                else:
+                    tick.mz(qubits)
             elif gate_type == "RX":
                 tick.rx(angles[0], qubits)
             elif gate_type == "RY":
@@ -590,6 +668,8 @@ def _replay_lowered_qis_trace_into_tick_circuit(chunks: list[dict[str, Any]]) ->
                 tick.crz(angles[0], _gate_pairs(qubits, gate_type))
             elif gate_type == "SZZ":
                 tick.szz(_gate_pairs(qubits, gate_type))
+            elif gate_type == "SZZdg":
+                tick.szzdg(_gate_pairs(qubits, gate_type))
             elif gate_type == "RZZ":
                 tick.rzz(angles[0], _gate_pairs(qubits, gate_type))
             elif gate_type == "CCX":
@@ -598,6 +678,9 @@ def _replay_lowered_qis_trace_into_tick_circuit(chunks: list[dict[str, Any]]) ->
                 msg = f"Unsupported lowered traced gate {gate_type!r}"
                 raise ValueError(msg)
 
+    # Compact: ASAP-schedule gates into minimal ticks
+    tick_circuit.compact_ticks()
+
     return tick_circuit
 
 
@@ -679,6 +762,63 @@ def _build_surface_tick_circuit_for_native_model(
     return traced_tc
 
 
+def build_memory_circuit(
+    *,
+    rounds: int,
+    distance: int | None = None,
+    patch: SurfacePatch | None = None,
+    basis: str = "Z",
+    ancilla_budget: int | None = None,
+    circuit_source: Literal["abstract", "traced_qis"] = "abstract",
+) -> Any:
+    """Build the standard surface-code memory ``TickCircuit``.
+
+    This is the public, friendly entry point for the circuit used by PECOS's
+    native DEM, sampler, and decoder helpers.
+
+    Args:
+        rounds: Number of syndrome-extraction rounds.
+        distance: Rotated surface-code distance. Provide either ``distance``
+            or ``patch``.
+        patch: Explicit surface-code patch. Provide either ``patch`` or
+            ``distance``.
+        basis: Memory basis, ``"Z"`` or ``"X"``.
+        ancilla_budget: Optional cap on simultaneously live ancillas.
+        circuit_source: ``"abstract"`` for the native surface builder or
+            ``"traced_qis"`` for the lowered traced QIS gate stream.
+
+    Returns:
+        A Rust-backed ``TickCircuit`` with detector and observable metadata.
+
+    Example:
+        >>> from pecos.qec.surface import build_memory_circuit
+        >>> tc = build_memory_circuit(distance=3, rounds=3, basis="Z")
+        >>> int(tc.get_meta("num_measurements")) > 0
+        True
+    """
+    from pecos.qec.surface.patch import SurfacePatch
+
+    if rounds < 1:
+        msg = f"rounds must be >= 1, got {rounds}"
+        raise ValueError(msg)
+    if patch is None:
+        if distance is None:
+            msg = "build_memory_circuit requires either distance=... or patch=..."
+            raise ValueError(msg)
+        patch = SurfacePatch.create(distance=distance)
+    elif distance is not None:
+        msg = "build_memory_circuit accepts either distance=... or patch=..., not both"
+        raise ValueError(msg)
+
+    return _build_surface_tick_circuit_for_native_model(
+        patch,
+        rounds,
+        basis,
+        ancilla_budget=ancilla_budget,
+        circuit_source=circuit_source,
+    )
+
+
 def _can_use_cached_surface_topology(
     *,
     ancilla_budget: int | None,
@@ -687,6 +827,21 @@ def _can_use_cached_surface_topology(
     return ancilla_budget is None
 
 
+def _uses_dedicated_idle_noise(
+    *,
+    p_idle: float | None,
+    t1: float | None,
+    t2: float | None,
+) -> bool:
+    """Return True when noise parameters require explicit idle locations."""
+    return (p_idle is not None and p_idle > 0.0) or (t1 is not None and t2 is not None)
+
+
+def _noise_uses_dedicated_idle_noise(noise: NoiseModel) -> bool:
+    """Return True when this noise model requires explicit idle locations."""
+    return _uses_dedicated_idle_noise(p_idle=noise.p_idle, t1=noise.t1, t2=noise.t2)
+
+
 @cache
 def _cached_surface_native_topology(
     patch_key: tuple[int, int, str, bool],
@@ -694,6 +849,7 @@ def _cached_surface_native_topology(
     basis: str,
     ancilla_budget: int | None,
     circuit_source: Literal["abstract", "traced_qis"],
+    include_idle_gates: bool,
 ) -> _CachedNativeSurfaceTopology:
     """Cache topology-only native analysis shared across noise parameters."""
     import json
@@ -709,6 +865,12 @@ def _cached_surface_native_topology(
         ancilla_budget=ancilla_budget,
         circuit_source=circuit_source,
     )
+    if include_idle_gates:
+        # Insert idle gates only when the requested noise model includes a
+        # dedicated idle channel. Otherwise inserted idle gates receive ordinary
+        # one-qubit gate noise and change the explicit circuit-level DEM.
+        tc.fill_idle_gates()
+
     dag = tc.to_dag_circuit()
     analyzer = DagFaultAnalyzer(dag)
     influence_map = analyzer.build_influence_map()
@@ -740,7 +902,7 @@ def _dem_string_from_cached_surface_topology(
 
     dem = (
         DemBuilder(topology.influence_map)
-        .with_noise(noise.p1, noise.p2, noise.p_meas, noise.p_init)
+        .with_noise(noise.p1, noise.p2, noise.p_meas, noise.p_prep, p_idle=noise.p_idle, t1=noise.t1, t2=noise.t2)
         .with_num_measurements(topology.num_measurements)
         .with_measurement_order(list(topology.measurement_order))
         .with_detectors_json(topology.detectors_json)
@@ -760,20 +922,25 @@ def _cached_surface_native_dem_string(
     p1: float,
     p2: float,
     p_meas: float,
-    p_init: float,
+    p_prep: float,
     decompose_errors: bool,
+    p_idle: float | None = None,
+    t1: float | None = None,
+    t2: float | None = None,
 ) -> str:
     """Cache native DEM strings across callers for one topology + noise tuple."""
+    include_idle_gates = _uses_dedicated_idle_noise(p_idle=p_idle, t1=t1, t2=t2)
     topology = _cached_surface_native_topology(
         patch_key,
         num_rounds,
         basis,
         ancilla_budget,
         circuit_source,
+        include_idle_gates,
     )
     return _dem_string_from_cached_surface_topology(
         topology,
-        NoiseModel(p1=p1, p2=p2, p_meas=p_meas, p_init=p_init),
+        NoiseModel(p1=p1, p2=p2, p_meas=p_meas, p_prep=p_prep, p_idle=p_idle, t1=t1, t2=t2),
         decompose_errors=decompose_errors,
     )
 
@@ -790,10 +957,14 @@ def _build_native_sampler_from_cached_surface_topology(
     topology: _CachedNativeSurfaceTopology,
     noise: NoiseModel,
     *,
-    sampling_model: Literal["dem", "influence_dem", "mnm"] = "dem",
+    sampling_model: Literal[
+        "dem",
+        "influence_dem",
+        "mnm",
+    ] = "dem",  # "mnm" accepted for compat, mapped to "influence_dem",
 ) -> NativeSampler:
     """Construct a native sampler from cached topology-only analysis."""
-    from pecos.qec import DemSamplerBuilder, MemBuilder, ParsedDem
+    from pecos.qec import DemSampler, ParsedDem
 
     if sampling_model == "dem":
         dem_str = _dem_string_from_cached_surface_topology(
@@ -802,20 +973,25 @@ def _build_native_sampler_from_cached_surface_topology(
             decompose_errors=True,
         )
         sampler = ParsedDem.from_string(dem_str).to_dem_sampler()
-    elif sampling_model == "influence_dem":
-        sampler = (
-            DemSamplerBuilder(topology.influence_map)
-            .with_noise(noise.p1, noise.p2, noise.p_meas, noise.p_init)
-            .with_detectors_json(topology.detectors_json)
-            .with_observables_json(topology.observables_json)
-            .with_measurement_order(list(topology.measurement_order))
-            .build()
+    elif sampling_model in ("influence_dem", "mnm"):
+        import json
+
+        det_records = [d["records"] for d in json.loads(topology.detectors_json)]
+        obs_records = [o["records"] for o in json.loads(topology.observables_json)] if topology.observables_json else []
+        sampler = DemSampler.with_detectors(
+            topology.influence_map,
+            det_records,
+            obs_records,
+            noise.p1,
+            noise.p2,
+            noise.p_meas,
+            noise.p_prep,
+            p_idle=noise.p_idle,
+            t1=noise.t1,
+            t2=noise.t2,
         )
-    elif sampling_model == "mnm":
-        builder = MemBuilder(topology.influence_map)
-        builder.with_noise(noise.p1, noise.p2, noise.p_meas, noise.p_init)
-        builder.with_measurement_order(list(topology.measurement_order))
-        sampler = builder.build()
+        # Remap sampling_model for NativeSampler dispatch
+        sampling_model = "influence_dem"
     else:
         msg = f"Unknown native sampling_model {sampling_model!r}"
         raise ValueError(msg)
@@ -834,13 +1010,20 @@ def _build_native_sampler_from_tick_circuit(
     tc: Any,
     noise: NoiseModel,
     *,
-    sampling_model: Literal["dem", "influence_dem", "mnm"] = "dem",
+    sampling_model: Literal[
+        "dem",
+        "influence_dem",
+        "mnm",
+    ] = "dem",  # "mnm" accepted for compat, mapped to "influence_dem",
 ) -> NativeSampler:
     """Construct a native sampler directly from a TickCircuit."""
     import json
 
-    from pecos.qec import DagFaultAnalyzer, DemSamplerBuilder, MemBuilder, ParsedDem
-    from pecos.qec.surface.circuit_builder import _extract_measurement_order, generate_dem_from_tick_circuit
+    from pecos.qec import DagFaultAnalyzer, DemSampler, ParsedDem
+    from pecos.qec.surface.circuit_builder import generate_dem_from_tick_circuit
+
+    if _noise_uses_dedicated_idle_noise(noise):
+        tc.fill_idle_gates()
 
     dag = tc.to_dag_circuit()
     analyzer = DagFaultAnalyzer(dag)
@@ -848,8 +1031,6 @@ def _build_native_sampler_from_tick_circuit(
 
     detectors_json = tc.get_meta("detectors") or "[]"
     observables_json = tc.get_meta("observables") or "[]"
-    measurement_order = _extract_measurement_order(tc)
-
     num_detectors = len(json.loads(detectors_json)) if detectors_json else 0
     num_observables = len(json.loads(observables_json)) if observables_json else 0
 
@@ -859,24 +1040,40 @@ def _build_native_sampler_from_tick_circuit(
             p1=noise.p1,
             p2=noise.p2,
             p_meas=noise.p_meas,
-            p_init=noise.p_init,
+            p_prep=noise.p_prep,
+            p_idle=noise.p_idle,
+            t1=noise.t1,
+            t2=noise.t2,
             decompose_errors=True,
         )
         sampler = ParsedDem.from_string(dem_str).to_dem_sampler()
-    elif sampling_model == "influence_dem":
-        sampler = (
-            DemSamplerBuilder(influence_map)
-            .with_noise(noise.p1, noise.p2, noise.p_meas, noise.p_init)
-            .with_detectors_json(detectors_json)
-            .with_observables_json(observables_json)
-            .with_measurement_order(measurement_order)
-            .build()
+    elif sampling_model in ("influence_dem", "mnm"):
+        det_records = [d["records"] for d in json.loads(detectors_json)]
+        obs_records = [o["records"] for o in json.loads(observables_json)] if observables_json else []
+        sampler = DemSampler.with_detectors(
+            influence_map,
+            det_records,
+            obs_records,
+            noise.p1,
+            noise.p2,
+            noise.p_meas,
+            noise.p_prep,
+            p_idle=noise.p_idle,
+            t1=noise.t1,
+            t2=noise.t2,
+        )
+        sampling_model = "influence_dem"
+    elif sampling_model == "from_circuit":
+        # Direct from_circuit path: uses DagCircuit annotations and any
+        # explicit idle locations inserted above for dedicated idle noise.
+        sampler = DemSampler.from_circuit(
+            dag,
+            p1=noise.p1,
+            p2=noise.p2,
+            p_meas=noise.p_meas,
+            p_prep=noise.p_prep,
+            p_idle=noise.p_idle,
         )
-    elif sampling_model == "mnm":
-        builder = MemBuilder(influence_map)
-        builder.with_noise(noise.p1, noise.p2, noise.p_meas, noise.p_init)
-        builder.with_measurement_order(measurement_order)
-        sampler = builder.build()
     else:
         msg = f"Unknown native sampling_model {sampling_model!r}"
         raise ValueError(msg)
@@ -952,8 +1149,11 @@ def generate_circuit_level_dem_from_builder(
             noise.p1,
             noise.p2,
             noise.p_meas,
-            noise.p_init,
+            noise.p_prep,
             decompose_errors=decompose_errors,
+            p_idle=noise.p_idle,
+            t1=noise.t1,
+            t2=noise.t2,
         )
 
     tc = _build_surface_tick_circuit_for_native_model(
@@ -963,12 +1163,17 @@ def generate_circuit_level_dem_from_builder(
         ancilla_budget=ancilla_budget,
         circuit_source=circuit_source,
     )
+    if _noise_uses_dedicated_idle_noise(noise):
+        tc.fill_idle_gates()
     return generate_dem_from_tick_circuit(
         tc,
         p1=noise.p1,
         p2=noise.p2,
         p_meas=noise.p_meas,
-        p_init=noise.p_init,
+        p_prep=noise.p_prep,
+        p_idle=noise.p_idle,
+        t1=noise.t1,
+        t2=noise.t2,
         decompose_errors=decompose_errors,
     )
 
@@ -1020,7 +1225,7 @@ def generate_circuit_level_dem(
         rounds=num_rounds,
         after_clifford_depolarization=noise.p2 if noise.p2 > 0 else 0.0,
         before_measure_flip_probability=noise.p_meas if noise.p_meas > 0 else 0.0,
-        after_reset_flip_probability=noise.p_init if noise.p_init > 0 else 0.0,
+        after_reset_flip_probability=noise.p_prep if noise.p_prep > 0 else 0.0,
     )
 
     # Generate DEM from circuit
@@ -2157,6 +2362,67 @@ def decode_memory_x(
 
         return is_logical_error, result
 
+    def _get_css_uf_decoder(self) -> Any:
+        """Get or create the UIUF CSS UF decoder."""
+        if not hasattr(self, "_css_uf_decoder") or self._css_uf_decoder is None:
+            from pecos_rslib.qec import CssUfDecoder
+
+            x_dem = self.get_dem("X", circuit_level=True)
+            z_dem = self.get_dem("Z", circuit_level=True)
+            # Strip logical_observable lines (not needed for matching graph).
+            x_dem = "\n".join(line for line in x_dem.split("\n") if not line.startswith("logical_observable"))
+            z_dem = "\n".join(line for line in z_dem.split("\n") if not line.startswith("logical_observable"))
+            self._css_uf_decoder = CssUfDecoder(x_dem, z_dem)
+        return self._css_uf_decoder
+
+    def decode_memory_z_uiuf(
+        self,
+        synx_list: list,
+        synz_list: list,
+        final: NDArray[np.uint8] | list[int],
+    ) -> tuple[bool, DecodingResult]:
+        """Decode Z-basis memory using UIUF (joint X/Z intersection).
+
+        Like ``decode_memory_z`` but uses both X and Z syndromes jointly
+        to identify Y errors and improve accuracy.
+
+        Args:
+            synx_list: List of X syndrome arrays, one per round
+            synz_list: List of Z syndrome arrays, one per round
+            final: Final data qubit measurements
+
+        Returns:
+            (is_logical_error, decoding_result)
+        """
+        import numpy as np
+
+        geom = self.patch.geometry
+        logical_z_qubits = geom.logical_z.data_qubits if geom.logical_z else ()
+        final_parity = sum(final[q] for q in logical_z_qubits) % 2
+
+        # Compute detection events for both bases.
+        x_events = self._compute_dem_detection_events_x(synx_list, synz_list, final)
+        z_events = self._compute_dem_detection_events_z(synx_list, synz_list, final)
+        x_flat = x_events.ravel().astype(np.uint8)
+        z_flat = z_events.ravel().astype(np.uint8)
+
+        # Joint decode via UIUF.
+        decoder = self._get_css_uf_decoder()
+        x_obs, z_obs = decoder.decode_css(bytes(x_flat), bytes(z_flat))
+
+        # For Z-basis memory, we care about the Z observable (L0).
+        predicted_obs = z_obs & 1
+        corrected_parity = (final_parity + predicted_obs) % 2
+        is_logical_error = corrected_parity != 0
+
+        return is_logical_error, DecodingResult(
+            x_correction=np.zeros(self.patch.num_data, dtype=np.uint8),
+            z_correction=np.zeros(self.patch.num_data, dtype=np.uint8),
+            logical_x_flip=bool(x_obs & 1),
+            logical_z_flip=bool(predicted_obs),
+            decoding_weight=0.0,
+        )
+
 
 @dataclass
 class SimulationResult:
@@ -2187,6 +2453,107 @@ class SimulationResult:
     decoder_type: str | None = None
 
 
+def _memory_noise_model(
+    physical_error_rate: float | None,
+    noise_model: NoiseModel | None,
+) -> NoiseModel:
+    """Resolve the surface-memory noise inputs into an explicit NoiseModel."""
+    if noise_model is not None:
+        if physical_error_rate is not None:
+            msg = "pass either physical_error_rate or noise_model, not both"
+            raise ValueError(msg)
+        return noise_model
+    p = 0.001 if physical_error_rate is None else physical_error_rate
+    return NoiseModel.uniform(p)
+
+
+def surface_code_memory(
+    *,
+    distance: int = 3,
+    physical_error_rate: float | None = None,
+    noise_model: NoiseModel | None = None,
+    shots: int = 1000,
+    rounds: int | None = None,
+    basis: str = "Z",
+    decoder_type: str = "pymatching",
+    seed: int | None = None,
+    decode: bool = True,
+    circuit_source: Literal["abstract", "traced_qis"] = "abstract",
+    ancilla_budget: int | None = None,
+) -> SimulationResult:
+    """Run the recommended native surface-code memory workflow.
+
+    This helper keeps the quick-start path short while using PECOS's Rust-backed
+    circuit-level DEM sampler and decoder machinery internally.
+
+    Args:
+        distance: Rotated surface-code distance.
+        physical_error_rate: Uniform physical error rate used for one-qubit
+            gates, two-qubit gates, measurements, and preparation. Defaults to
+            ``0.001`` when ``noise_model`` is not provided.
+        noise_model: Explicit circuit-level noise model. Mutually exclusive
+            with ``physical_error_rate``.
+        shots: Number of Monte Carlo shots.
+        rounds: Number of syndrome-extraction rounds. Defaults to ``distance``.
+        basis: Memory basis, ``"Z"`` or ``"X"``.
+        decoder_type: Decoder backend passed to ``SampleBatch.decode_count``.
+        seed: Optional sampler seed.
+        decode: If false, report the raw observable-flip rate.
+        circuit_source: ``"abstract"`` or ``"traced_qis"`` circuit source.
+        ancilla_budget: Optional cap on simultaneously live ancillas.
+
+    Returns:
+        ``SimulationResult`` with logical and raw error counts/rates.
+
+    Example:
+        >>> from pecos.qec.surface import surface_code_memory
+        >>> result = surface_code_memory(distance=3, physical_error_rate=0.0, shots=4, rounds=1)
+        >>> result.logical_error_rate
+        0.0
+    """
+    from pecos.qec import ParsedDem
+    from pecos.qec.surface.patch import SurfacePatch
+
+    if distance < 1:
+        msg = f"distance must be >= 1, got {distance}"
+        raise ValueError(msg)
+    if shots < 0:
+        msg = f"shots must be >= 0, got {shots}"
+        raise ValueError(msg)
+    num_rounds = distance if rounds is None else rounds
+    if num_rounds < 1:
+        msg = f"rounds must be >= 1, got {num_rounds}"
+        raise ValueError(msg)
+
+    noise_model = _memory_noise_model(physical_error_rate, noise_model)
+    patch = SurfacePatch.create(distance=distance)
+    dem = generate_circuit_level_dem_from_builder(
+        patch,
+        num_rounds=num_rounds,
+        noise=noise_model,
+        basis=basis,
+        decompose_errors=True,
+        ancilla_budget=ancilla_budget,
+        circuit_source=circuit_source,
+    )
+    batch = ParsedDem.from_string(dem).to_dem_sampler().generate_samples(shots, seed)
+    num_raw_errors = sum(1 for shot in range(shots) if batch.get_observable_mask(shot) != 0)
+    num_logical_errors = batch.decode_count(dem, decoder_type) if decode else num_raw_errors
+
+    return SimulationResult(
+        distance=distance,
+        num_shots=shots,
+        num_rounds=num_rounds,
+        basis=basis,
+        num_logical_errors=num_logical_errors,
+        num_raw_errors=num_raw_errors,
+        logical_error_rate=num_logical_errors / shots if shots else 0.0,
+        raw_error_rate=num_raw_errors / shots if shots else 0.0,
+        decoded=decode,
+        decoder_type=decoder_type if decode else None,
+    )
+
+
 def run_noisy_memory_experiment(
     distance: int,
     num_rounds: int,
@@ -2219,7 +2586,7 @@ def run_noisy_memory_experiment(
 
     Example:
         >>> from pecos.qec.surface import run_noisy_memory_experiment, NoiseModel
-        >>> noise = NoiseModel(p1=0.001, p2=0.01, p_meas=0.01, p_init=0.001)
+        >>> noise = NoiseModel(p1=0.001, p2=0.01, p_meas=0.01, p_prep=0.001)
         >>> result = run_noisy_memory_experiment(
         ...     distance=3,
         ...     num_rounds=3,
@@ -2249,11 +2616,13 @@ def run_noisy_memory_experiment(
     # Create decoder if needed
     decoder = None
     if decode:
+        # UIUF uses pymatching-type DEMs internally (decoded via CssUfDecoder).
+        dt = "pymatching" if decoder_type == "pecos_uf_uiuf" else decoder_type
         decoder = SurfaceDecoder(
             patch,
             num_rounds=num_rounds,
             noise=noise,
-            decoder_type=decoder_type,
+            decoder_type=dt,
         )
 
     # Build and compile circuit
@@ -2267,7 +2636,7 @@ def run_noisy_memory_experiment(
         p_1q=noise.p1,
         p_2q=noise.p2,
         p_meas=noise.p_meas,
-        p_init=noise.p_init,
+        p_init=noise.p_prep,
     )
 
     # Run shots
@@ -2308,7 +2677,9 @@ def run_noisy_memory_experiment(
             final_arr = np.array(final, dtype=np.uint8)
 
             # Decode based on basis
-            if basis.upper() == "Z":
+            if decoder_type == "pecos_uf_uiuf" and basis.upper() == "Z":
+                is_error, _ = decoder.decode_memory_z_uiuf(synx_list, synz_list, final_arr)
+            elif basis.upper() == "Z":
                 is_error, _ = decoder.decode_memory_z(synx_list, synz_list, final_arr)
             else:
                 is_error, _ = decoder.decode_memory_x(synx_list, synz_list, final_arr)
@@ -2350,8 +2721,7 @@ class NativeSampler:
 
     Two sampling backends are available:
     - `dem` (default): sample the generated decomposed DEM via `ParsedDem`
-    - `influence_dem`: sample directly from the influence-map detector mechanisms
-    - `mnm`: samples measurement outcomes first via `MeasurementNoiseModel`
+    - `influence_dem`: sample directly from the influence-map via `DemSampler`
 
     Attributes:
         sampler: The underlying Rust sampler object
@@ -2367,7 +2737,9 @@ class NativeSampler:
     observables_json: str
     num_detectors: int
     num_observables: int
-    sampling_model: Literal["dem", "influence_dem", "mnm"] = "dem"
+    sampling_model: Literal["dem", "influence_dem", "mnm"] = (
+        "dem"  # "mnm" accepted for compat, mapped to "influence_dem"
+    )
 
     def sample(
         self,
@@ -2387,18 +2759,7 @@ def sample(
             - detection_events: shape (num_shots, num_detectors)
             - observable_flips: shape (num_shots, num_observables)
         """
-        if self.sampling_model in ("dem", "influence_dem"):
-            det_events, obs_flips = self.sampler.sample_batch(num_shots, seed)
-        elif self.sampling_model == "mnm":
-            det_events, obs_flips = self.sampler.sample_batch_for_decoding(
-                num_shots,
-                self.detectors_json,
-                self.observables_json,
-                seed,
-            )
-        else:
-            msg = f"Unknown native sampling_model {self.sampling_model!r}"
-            raise ValueError(msg)
+        det_events, obs_flips = self.sampler.sample_batch(num_shots, seed)
         return np.array(det_events, dtype=bool), np.array(obs_flips, dtype=bool)
 
 
@@ -2409,7 +2770,11 @@ def build_native_sampler(
     basis: str = "Z",
     ancilla_budget: int | None = None,
     circuit_source: Literal["abstract", "traced_qis"] = "abstract",
-    sampling_model: Literal["dem", "influence_dem", "mnm"] = "dem",
+    sampling_model: Literal[
+        "dem",
+        "influence_dem",
+        "mnm",
+    ] = "dem",  # "mnm" accepted for compat, mapped to "influence_dem",
 ) -> NativeSampler:
     """Build a PECOS native sampler for threshold estimation.
 
@@ -2420,10 +2785,8 @@ def build_native_sampler(
     The pipeline is:
     - `sampling_model="dem"`:
       TickCircuit -> DemBuilder -> ParsedDem -> DemSampler
-    - `sampling_model="influence_dem"`:
-      TickCircuit -> DagCircuit -> DagFaultAnalyzer -> InfluenceMap -> direct mechanism sampler
-    - `sampling_model="mnm"`:
-      TickCircuit -> DagCircuit -> DagFaultAnalyzer -> InfluenceMap -> MeasurementNoiseModel -> Sampler
+    - `sampling_model="influence_dem"` (or `"mnm"` for compat):
+      TickCircuit -> DagCircuit -> DagFaultAnalyzer -> InfluenceMap -> DemSampler (with detector defs)
 
     Args:
         patch: Surface code patch with geometry
@@ -2438,9 +2801,9 @@ def build_native_sampler(
             before native PECOS fault analysis.
         sampling_model: Which native sampling backend to use. ``"dem"``
             samples the generated decomposed DEM and is the default.
-            ``"influence_dem"`` uses the older direct influence-map sampler for
-            debugging. ``"mnm"`` preserves the measurement-noise-model
-            approximation.
+            ``"influence_dem"`` uses the influence-map-based DemSampler with
+            detector definitions. ``"mnm"`` is accepted for compatibility
+            and maps to ``"influence_dem"``.
 
     Returns:
         NativeSampler that can generate samples for threshold estimation
@@ -2461,6 +2824,7 @@ def build_native_sampler(
             basis,
             ancilla_budget,
             circuit_source,
+            _noise_uses_dedicated_idle_noise(noise),
         )
         if sampling_model == "dem":
             dem_str = _cached_surface_native_dem_string(
@@ -2472,8 +2836,11 @@ def build_native_sampler(
                 noise.p1,
                 noise.p2,
                 noise.p_meas,
-                noise.p_init,
+                noise.p_prep,
                 decompose_errors=True,
+                p_idle=noise.p_idle,
+                t1=noise.t1,
+                t2=noise.t2,
             )
             sampler = _cached_parsed_dem(dem_str).to_dem_sampler()
             return NativeSampler(
diff --git a/python/quantum-pecos/src/pecos/qec/surface/layouts/rotated_lattice.py b/python/quantum-pecos/src/pecos/qec/surface/layouts/rotated_lattice.py
index 1d92b947c..e62938f88 100644
--- a/python/quantum-pecos/src/pecos/qec/surface/layouts/rotated_lattice.py
+++ b/python/quantum-pecos/src/pecos/qec/surface/layouts/rotated_lattice.py
@@ -32,22 +32,28 @@ class RotatedPosition:
     y: int
 
 
-def compute_rotated_x_stabilizers(d: int) -> list[StabilizerSupport]:
+def compute_rotated_x_stabilizers(dx: int, dz: int | None = None) -> list[StabilizerSupport]:
     """Compute X stabilizer supports for rotated surface code.
 
     X stabilizers are placed at dual lattice faces where (row + col) is odd.
     Boundary X stabilizers (weight 2) are on the top and bottom edges.
 
-    This convention matches the QASM reference and Rust implementations.
+    Degenerate cases:
+    - dx=1: no X stabilizers (single row, no top/bottom boundary)
+    - dz=1: no X stabilizers (single column, no X-type faces)
+    - dx=1, dz=1: single qubit, no stabilizers
 
     Args:
-        d: Code distance (must be odd >= 3)
+        dx: Number of rows (X distance). Must be >= 1.
+        dz: Number of columns (Z distance). Must be >= 1. Defaults to dx.
 
     Returns:
         List of StabilizerSupport for X stabilizers
     """
-    if d < 3 or d % 2 == 0:
-        msg = f"Distance must be odd >= 3, got {d}"
+    if dz is None:
+        dz = dx
+    if dx < 1 or dz < 1:
+        msg = f"Distances must be >= 1, got dx={dx}, dz={dz}"
         raise ValueError(msg)
 
     supports = []
@@ -55,7 +61,7 @@ def compute_rotated_x_stabilizers(d: int) -> list[StabilizerSupport]:
 
     # Top boundary X stabilizers (weight 2)
     # Virtual dual row r=-1: X-type when (-1+col)%2==1, i.e. col even
-    for col in range(0, d - 1, 2):
+    for col in range(0, dz - 1, 2):
         q1 = col
         q2 = col + 1
         supports.append(
@@ -68,13 +74,13 @@ def compute_rotated_x_stabilizers(d: int) -> list[StabilizerSupport]:
         stab_idx += 1
 
     # Bulk X stabilizers (weight 4)
-    for row in range(d - 1):
-        for col in range(d - 1):
+    for row in range(dx - 1):
+        for col in range(dz - 1):
             if (row + col) % 2 == 1:
-                q_tl = row * d + col
-                q_tr = row * d + col + 1
-                q_bl = (row + 1) * d + col
-                q_br = (row + 1) * d + col + 1
+                q_tl = row * dz + col
+                q_tr = row * dz + col + 1
+                q_bl = (row + 1) * dz + col
+                q_br = (row + 1) * dz + col + 1
 
                 supports.append(
                     StabilizerSupport(
@@ -86,10 +92,11 @@ def compute_rotated_x_stabilizers(d: int) -> list[StabilizerSupport]:
                 stab_idx += 1
 
     # Bottom boundary X stabilizers (weight 2)
-    # Virtual dual row r=d-1: for odd d, (d-1+col)%2==1 requires col odd
-    for col in range(1, d - 1, 2):
-        q1 = (d - 1) * d + col
-        q2 = (d - 1) * d + col + 1
+    # Virtual dual row r=dx-1: X-type when (dx-1+col)%2==1
+    bottom_start = 1 if dx % 2 == 1 else 0
+    for col in range(bottom_start, dz - 1, 2):
+        q1 = (dx - 1) * dz + col
+        q2 = (dx - 1) * dz + col + 1
         supports.append(
             StabilizerSupport(
                 index=stab_idx,
@@ -102,32 +109,39 @@ def compute_rotated_x_stabilizers(d: int) -> list[StabilizerSupport]:
     return supports
 
 
-def compute_rotated_z_stabilizers(d: int) -> list[StabilizerSupport]:
+def compute_rotated_z_stabilizers(dx: int, dz: int | None = None) -> list[StabilizerSupport]:
     """Compute Z stabilizer supports for rotated surface code.
 
     Z stabilizers are placed at dual lattice faces where (row + col) is even.
     Boundary Z stabilizers (weight 2) are on the left and right edges.
 
-    This convention matches the QASM reference and Rust implementations.
+    Degenerate cases:
+    - dz=1: no Z stabilizers (single column, no left/right boundary)
+    - dx=1: Z stabilizers become the repetition code parity checks
+    - dx=1, dz=1: single qubit, no stabilizers
 
     Args:
-        d: Code distance (must be odd >= 3)
+        dx: Number of rows (X distance). Must be >= 1.
+        dz: Number of columns (Z distance). Must be >= 1. Defaults to dx.
 
     Returns:
         List of StabilizerSupport for Z stabilizers
     """
-    if d < 3 or d % 2 == 0:
-        msg = f"Distance must be odd >= 3, got {d}"
+    if dz is None:
+        dz = dx
+    if dx < 1 or dz < 1:
+        msg = f"Distances must be >= 1, got dx={dx}, dz={dz}"
         raise ValueError(msg)
 
     supports = []
     stab_idx = 0
 
     # Right boundary Z stabilizers (weight 2)
-    # Virtual dual col c=d-1: Z-type when (row+d-1)%2==0, i.e. row even (for odd d)
-    for row in range(0, d - 1, 2):
-        q1 = row * d + (d - 1)
-        q2 = (row + 1) * d + (d - 1)
+    # Virtual dual col c=dz-1: Z-type when (row+dz-1)%2==0
+    right_start = 0 if dz % 2 == 1 else 1
+    for row in range(right_start, dx - 1, 2):
+        q1 = row * dz + (dz - 1)
+        q2 = (row + 1) * dz + (dz - 1)
         supports.append(
             StabilizerSupport(
                 index=stab_idx,
@@ -138,13 +152,13 @@ def compute_rotated_z_stabilizers(d: int) -> list[StabilizerSupport]:
         stab_idx += 1
 
     # Bulk Z stabilizers (weight 4)
-    for row in range(d - 1):
-        for col in range(d - 1):
+    for row in range(dx - 1):
+        for col in range(dz - 1):
             if (row + col) % 2 == 0:
-                q_tl = row * d + col
-                q_tr = row * d + col + 1
-                q_bl = (row + 1) * d + col
-                q_br = (row + 1) * d + col + 1
+                q_tl = row * dz + col
+                q_tr = row * dz + col + 1
+                q_bl = (row + 1) * dz + col
+                q_br = (row + 1) * dz + col + 1
 
                 supports.append(
                     StabilizerSupport(
@@ -156,10 +170,10 @@ def compute_rotated_z_stabilizers(d: int) -> list[StabilizerSupport]:
                 stab_idx += 1
 
     # Left boundary Z stabilizers (weight 2)
-    # Virtual dual col c=-1: Z-type when (row+(-1))%2==0, i.e. row odd
-    for row in range(1, d - 1, 2):
-        q1 = row * d
-        q2 = (row + 1) * d
+    # Virtual dual col c=-1: Z-type when (row-1)%2==0, i.e. row odd
+    for row in range(1, dx - 1, 2):
+        q1 = row * dz
+        q2 = (row + 1) * dz
         supports.append(
             StabilizerSupport(
                 index=stab_idx,
@@ -172,8 +186,8 @@ def compute_rotated_z_stabilizers(d: int) -> list[StabilizerSupport]:
     # Re-order: left-to-right (ascending column), bottom-to-top (descending row)
     supports.sort(
         key=lambda s: (
-            sum(q % d for q in s.data_qubits) / len(s.data_qubits),
-            -sum(q // d for q in s.data_qubits) / len(s.data_qubits),
+            sum(q % dz for q in s.data_qubits) / len(s.data_qubits),
+            -sum(q // dz for q in s.data_qubits) / len(s.data_qubits),
         ),
     )
     return [
@@ -181,14 +195,18 @@ def compute_rotated_z_stabilizers(d: int) -> list[StabilizerSupport]:
     ]
 
 
-def get_rotated_logical_x(d: int) -> tuple[int, ...]:
-    """Get logical X operator qubits (left edge)."""
-    return tuple(i * d for i in range(d))
+def get_rotated_logical_x(dx: int, dz: int | None = None) -> tuple[int, ...]:
+    """Get logical X operator qubits (left edge, weight dx)."""
+    if dz is None:
+        dz = dx
+    return tuple(i * dz for i in range(dx))
 
 
-def get_rotated_logical_z(d: int) -> tuple[int, ...]:
-    """Get logical Z operator qubits (top edge)."""
-    return tuple(range(d))
+def get_rotated_logical_z(dx: int, dz: int | None = None) -> tuple[int, ...]:
+    """Get logical Z operator qubits (top edge, weight dz)."""
+    if dz is None:
+        dz = dx
+    return tuple(range(dz))
 
 
 def rotated_id_to_position(qubit_id: int, d: int) -> tuple[int, int]:
diff --git a/python/quantum-pecos/src/pecos/qec/surface/logical_circuit.py b/python/quantum-pecos/src/pecos/qec/surface/logical_circuit.py
new file mode 100644
index 000000000..c5d10a619
--- /dev/null
+++ b/python/quantum-pecos/src/pecos/qec/surface/logical_circuit.py
@@ -0,0 +1,1587 @@
+# Copyright 2026 The PECOS Developers
+# Licensed under the Apache License, Version 2.0
+
+"""Logical circuit builder for surface codes with transversal gates.
+
+Generates PECOS TickCircuit circuits natively, with Stim circuit strings
+derived via ``tick_circuit_to_stim()``. Supports:
+
+- Memory experiments (syndrome extraction rounds)
+- Transversal Hadamard (H on all data qubits, swaps X<->Z stabilizers)
+- Transversal CNOT (CX between corresponding data qubits of two patches)
+- Transversal SZ via gate teleportation (CX + |+Y> ancilla consumption)
+
+Output formats:
+
+- ``to_tick_circuit()`` -- PECOS TickCircuit (source of truth)
+- ``to_dag_circuit()`` -- PECOS DagCircuit (for fault analysis)
+- ``to_stim()`` -- Stim circuit string (derived from TickCircuit)
+- ``build_dem()`` -- DEM via PECOS DagFaultAnalyzer (no Stim)
+- ``build_decoder()`` -- integrated decoder pipeline
+
+References:
+- Geher et al., "Error-corrected Hadamard gate" (arXiv:2312.11605)
+- Sahay et al., "Error correction of transversal CNOT" (arXiv:2408.01393)
+- Serra-Peralta et al., "Decoding across transversal Clifford gates" (arXiv:2505.13599)
+"""
+
+from __future__ import annotations
+
+import json
+from dataclasses import dataclass, field
+from enum import Enum, auto
+from typing import TYPE_CHECKING
+
+if TYPE_CHECKING:
+    from pecos.qec.surface.patch import Stabilizer, SurfacePatch
+
+PatchSnapshot = dict[str, tuple[bool, list[str], list[str], list[str], list[str]]]
+
+
+class LogicalGateType(Enum):
+    """Types of logical operations in a surface code circuit."""
+
+    MEMORY = auto()
+    TRANSVERSAL_H = auto()
+    TRANSVERSAL_SZ = auto()
+    TRANSVERSAL_SZdg = auto()
+    TRANSVERSAL_CX = auto()
+
+
+@dataclass
+class PatchState:
+    """Tracks the stabilizer assignment state of a patch.
+
+    After transversal H, X-stabilizers become Z-stabilizers and vice versa.
+    This state tracks which physical stabilizers are currently X-type vs Z-type,
+    so that detectors can be formed correctly across gate boundaries.
+    """
+
+    patch: SurfacePatch
+    label: str
+    qubit_offset: int = 0
+    coord_offset: tuple[float, float] = (0.0, 0.0)
+    x_z_swapped: bool = False
+    # Teleportation corrections: ancilla Z measurements to XOR into this
+    # patch's observable (from CX teleportation gates).
+    z_obs_includes: list[str] = field(default_factory=list)
+    x_obs_includes: list[str] = field(default_factory=list)
+    # After CX, some observables become non-reliable depending on the
+    # measurement basis. Track which bases are "entangled" and with whom.
+    # x_entangled_with: this patch's X observable is entangled with these
+    # patches (measuring X on this patch alone is non-deterministic).
+    x_entangled_with: list[str] = field(default_factory=list)
+    z_entangled_with: list[str] = field(default_factory=list)
+
+    @property
+    def current_x_stabilizers(self) -> list[Stabilizer]:
+        """Stabilizers currently measuring X-type checks."""
+        if self.x_z_swapped:
+            return self.patch.geometry.z_stabilizers
+        return self.patch.geometry.x_stabilizers
+
+    @property
+    def current_z_stabilizers(self) -> list[Stabilizer]:
+        """Stabilizers currently measuring Z-type checks."""
+        if self.x_z_swapped:
+            return self.patch.geometry.x_stabilizers
+        return self.patch.geometry.z_stabilizers
+
+
+@dataclass
+class LogicalOp:
+    """A logical operation in the circuit."""
+
+    gate_type: LogicalGateType
+    patches: list[str]
+    rounds: int = 0
+    basis: str = "Z"
+    per_patch_basis: dict[str, str] = field(default_factory=dict)
+    # For teleportation CX: the target's Z measurement should be included
+    # in the control's observable for the Pauli frame correction.
+    teleportation: bool = False
+    # Type of magic state injection: "T" for T-gate, "SZ" for SZ, or None.
+    # Used by build_algorithm_descriptor() to emit the correct boundary gate.
+    injection_type: str | None = None
+
+
+class LogicalCircuitBuilder:
+    """Builds surface code circuits with transversal gates.
+
+    Composes logical operations on one or more patches, generating Stim
+    circuits with correct detector annotations across gate boundaries.
+
+    Example::
+
+        patch = SurfacePatch.create(distance=3)
+        builder = LogicalCircuitBuilder()
+        builder.add_patch(patch, "A")
+        builder.add_memory("A", rounds=3, basis="Z")
+        builder.add_transversal_h("A")
+        builder.add_memory("A", rounds=3, basis="X")
+        stim_str = builder.to_stim(p1=0.001, p2=0.001)
+    """
+
+    def __init__(self) -> None:
+        """Initialize an empty logical circuit builder."""
+        self._patches: dict[str, PatchState] = {}
+        self._operations: list[LogicalOp] = []
+
+    def add_patch(
+        self,
+        patch: SurfacePatch,
+        label: str,
+        qubit_offset: int = 0,
+        coord_offset: tuple[float, float] | None = None,
+    ) -> None:
+        """Register a surface code patch.
+
+        Args:
+            patch: The surface code patch.
+            label: Unique label for this patch.
+            qubit_offset: Offset added to all qubit indices for this patch.
+                Use this when multiple patches share a qubit index space.
+            coord_offset: (dx, dy) spatial offset for this patch's
+                QUBIT_COORDS and DETECTOR coordinates. If None, computed
+                automatically based on patch index (patches are spaced
+                apart so coordinates don't overlap).
+        """
+        if label in self._patches:
+            msg = f"Patch '{label}' already registered"
+            raise ValueError(msg)
+        if coord_offset is None:
+            # Auto-space: shift each patch by (d*2 + 2) * patch_index in x
+            patch_idx = len(self._patches)
+            spacing = patch.geometry.dz * 2 + 2
+            coord_offset = (patch_idx * spacing, 0.0)
+        self._patches[label] = PatchState(
+            patch=patch,
+            label=label,
+            qubit_offset=qubit_offset,
+            coord_offset=coord_offset,
+        )
+
+    def add_memory(
+        self,
+        patch_labels: str | list[str],
+        rounds: int,
+        basis: str | dict[str, str] = "Z",
+    ) -> None:
+        """Add syndrome extraction rounds for one or more patches.
+
+        When multiple patches are given, their syndrome extraction runs
+        in parallel (same time window).
+
+        Args:
+            patch_labels: Label(s) of the patch(es). String for single
+                patch, list for parallel multi-patch.
+            rounds: Number of syndrome extraction rounds.
+            basis: Measurement basis. Either a single string ('X', 'Y', 'Z')
+                applied to all patches, or a dict mapping patch labels to
+                their individual basis (e.g., ``{"D": "Z", "Y": "Y"}``).
+                Only used for initialization and final measurement.
+        """
+        if isinstance(patch_labels, str):
+            patch_labels = [patch_labels]
+        for label in patch_labels:
+            if label not in self._patches:
+                msg = f"Unknown patch '{label}'"
+                raise ValueError(msg)
+
+        if isinstance(basis, str):
+            default_basis = basis.upper()
+            per_patch = {}
+        else:
+            default_basis = "Z"
+            per_patch = {k: v.upper() for k, v in basis.items()}
+
+        self._operations.append(
+            LogicalOp(
+                gate_type=LogicalGateType.MEMORY,
+                patches=list(patch_labels),
+                rounds=rounds,
+                basis=default_basis,
+                per_patch_basis=per_patch,
+            ),
+        )
+
+    def _require_square(self, patch_label: str, gate_name: str) -> None:
+        """Check that a patch is square (dx=dz), required for transversal gates."""
+        patch = self._patches[patch_label].patch
+        if patch.geometry.dx != patch.geometry.dz:
+            msg = f"{gate_name} requires a square patch (dx=dz), got dx={patch.geometry.dx}, dz={patch.geometry.dz}"
+            raise ValueError(msg)
+
+    def add_transversal_h(self, patch_label: str) -> None:
+        """Add a transversal Hadamard gate on a patch.
+
+        Applies H to every data qubit. After this:
+        - X-stabilizers become Z-stabilizers and vice versa
+        - Logical X and logical Z are exchanged
+        - Detectors at the boundary compare cross-type measurements
+
+        The patch must be square (dx=dz) for the code to remain valid.
+
+        Args:
+            patch_label: Label of the patch.
+        """
+        if patch_label not in self._patches:
+            msg = f"Unknown patch '{patch_label}'"
+            raise ValueError(msg)
+        self._require_square(patch_label, "Transversal H")
+        self._operations.append(
+            LogicalOp(
+                gate_type=LogicalGateType.TRANSVERSAL_H,
+                patches=[patch_label],
+            ),
+        )
+
+    def add_transversal_sz(self, patch_label: str) -> None:
+        """Add a fold-transversal SZ gate on a patch.
+
+        Implements the fold-transversal S gate using the Bravyi et al.
+        half-cycle trick (arXiv:2412.01391). The fold operation is
+        inserted at mid-cycle of a syndrome extraction round:
+        - On-diagonal data qubits (r + c = d-1): SZ gate
+        - On-diagonal X-ancilla qubits: SZdg gate
+        - Off-diagonal: CZ between each qubit and its mirror
+
+        After this gate:
+        - Z-stabilizers are unchanged
+        - X-stabilizers pick up Z-stabilizer partners:
+          X_stab -> X_stab * Z_stab_mirror
+
+        The patch must be square (dx=dz).
+
+        Args:
+            patch_label: Label of the patch.
+        """
+        if patch_label not in self._patches:
+            msg = f"Unknown patch '{patch_label}'"
+            raise ValueError(msg)
+        self._require_square(patch_label, "Transversal SZ")
+        self._operations.append(
+            LogicalOp(
+                gate_type=LogicalGateType.TRANSVERSAL_SZ,
+                patches=[patch_label],
+            ),
+        )
+
+    def add_transversal_szdg(self, patch_label: str) -> None:
+        """Add SZdg (S-dagger) on all data qubits of a patch.
+
+        Inverse of add_transversal_sz. Used for mirroring circuits
+        that contain SZ gates.
+        """
+        if patch_label not in self._patches:
+            msg = f"Unknown patch '{patch_label}'"
+            raise ValueError(msg)
+        self._require_square(patch_label, "Transversal SZdg")
+        self._operations.append(
+            LogicalOp(
+                gate_type=LogicalGateType.TRANSVERSAL_SZdg,
+                patches=[patch_label],
+            ),
+        )
+
+    def add_sz_via_teleportation(
+        self,
+        data_label: str,
+        ancilla_label: str,
+        rounds_before: int = 3,
+        rounds_after: int = 3,
+    ) -> None:
+        """Apply logical SZ via gate teleportation with |+Y> ancilla.
+
+        Complete protocol:
+        1. Prepare ancilla in |+Y> = S|+> (non-fault-tolerant injection)
+        2. Syndrome rounds to project ancilla into code space
+        3. Transversal CX(data=control, ancilla=target)
+        4. Syndrome rounds
+        5. Ancilla measured in Z-basis (final round)
+
+        After CX, data has S|psi> (up to Z correction from ancilla outcome).
+        The Z correction is a Pauli frame update tracked by the decoder.
+
+        Note: The |+Y> injection is non-fault-tolerant (distance-1).
+        For fault-tolerant SZ, use magic state distillation on the
+        injected state before consumption.
+
+        Args:
+            data_label: Label of the data patch (receives the SZ gate).
+            ancilla_label: Label of the ancilla patch (consumed).
+            rounds_before: Syndrome rounds before CX.
+            rounds_after: Syndrome rounds after CX.
+        """
+        # Step 1: Init both patches — data continues in Z, ancilla in |+Y>.
+        # Per-patch basis lets us do this in a single parallel segment.
+        self.add_memory(
+            [data_label, ancilla_label],
+            rounds=rounds_before,
+            basis={data_label: "Z", ancilla_label: "Y"},
+        )
+        # Step 2: CX(data=control, ancilla=target) — teleports S onto data.
+        # Marked as teleportation so observable propagation includes the
+        # ancilla's Z measurement as a Pauli frame correction.
+        self._operations.append(
+            LogicalOp(
+                gate_type=LogicalGateType.TRANSVERSAL_CX,
+                patches=[data_label, ancilla_label],
+                teleportation=True,
+            ),
+        )
+        # Step 3: Post-CX extraction. Ancilla measured in Z-basis at final round.
+        # If ancilla measures logical -1, apply Z correction (Pauli frame update).
+        self.add_memory([data_label, ancilla_label], rounds=rounds_after, basis="Z")
+
+    def add_t_via_injection(
+        self,
+        data_label: str,
+        ancilla_label: str,
+        rounds_before: int = 3,
+        rounds_after: int = 3,
+    ) -> None:
+        """Apply logical T gate via magic state injection.
+
+        Complete protocol:
+        1. Prepare ancilla in |T> = T|+> (non-fault-tolerant injection)
+        2. Syndrome rounds to project ancilla into code space
+        3. Transversal CX(data=control, ancilla=target)
+        4. Syndrome rounds
+        5. Ancilla measured in Z-basis (final round)
+
+        After CX, data has T|psi> (up to S correction from ancilla outcome).
+        The S correction is a conditional feed-forward operation — this is
+        a DECISION POINT where the decoder must provide the Pauli frame.
+
+        The corrected measurement outcome determines:
+          corrected = raw_measurement XOR frame[z_obs_bit]
+          if corrected == 1: apply S gate on data
+
+        Note: The |T> injection is non-fault-tolerant (distance-1).
+        For fault-tolerant T, use magic state distillation on the
+        injected state before consumption.
+
+        Args:
+            data_label: Label of the data patch (receives the T gate).
+            ancilla_label: Label of the ancilla patch (consumed).
+            rounds_before: Syndrome rounds before CX.
+            rounds_after: Syndrome rounds after CX.
+        """
+        # Step 1: Init both patches — data continues in Z, ancilla gets |+>.
+        # The real protocol prepares |T> = T|+> on the ancilla, but T is
+        # non-Clifford and invisible to the fault analyzer. We prepare
+        # |+> as a Clifford stand-in: same error structure (H gate noise
+        # via p1, prep noise via p_prep), just missing the non-Clifford
+        # phase which doesn't affect error correlations in the DEM.
+        self.add_memory(
+            [data_label, ancilla_label],
+            rounds=rounds_before,
+            basis={data_label: "Z", ancilla_label: "X"},
+        )
+        # Step 2: CX(data=control, ancilla=target) — teleports T onto data.
+        self._operations.append(
+            LogicalOp(
+                gate_type=LogicalGateType.TRANSVERSAL_CX,
+                patches=[data_label, ancilla_label],
+                teleportation=True,
+                injection_type="T",
+            ),
+        )
+        # Step 3: Post-CX extraction. Ancilla measured in Z-basis.
+        # If ancilla measures logical -1 (corrected by frame), apply S.
+        # This is the feed-forward decision point.
+        self.add_memory(
+            [data_label, ancilla_label],
+            rounds=rounds_after,
+            basis="Z",
+        )
+
+    def add_transversal_cx(self, control_label: str, target_label: str) -> None:
+        """Add a transversal CNOT between two patches.
+
+        Applies CX between corresponding data qubits. After this:
+        - X-errors on control propagate to target
+        - Z-errors on target propagate back to control
+        - Weight-3 hyperedges appear in the DEM at the gate boundary
+
+        Both patches must have the same geometry.
+
+        Args:
+            control_label: Label of the control patch.
+            target_label: Label of the target patch.
+        """
+        if control_label not in self._patches:
+            msg = f"Unknown patch '{control_label}'"
+            raise ValueError(msg)
+        if target_label not in self._patches:
+            msg = f"Unknown patch '{target_label}'"
+            raise ValueError(msg)
+        ctrl = self._patches[control_label]
+        tgt = self._patches[target_label]
+        if ctrl.patch.geometry.num_data != tgt.patch.geometry.num_data:
+            msg = (
+                f"Patches must have same geometry for transversal CX. "
+                f"'{control_label}' has {ctrl.patch.geometry.num_data} data qubits, "
+                f"'{target_label}' has {tgt.patch.geometry.num_data} data qubits."
+            )
+            raise ValueError(msg)
+        self._operations.append(
+            LogicalOp(
+                gate_type=LogicalGateType.TRANSVERSAL_CX,
+                patches=[control_label, target_label],
+            ),
+        )
+
+    def _snapshot_and_reset(self) -> PatchSnapshot:
+        """Snapshot patch states and reset for generation."""
+        saved = {
+            label: (
+                ps.x_z_swapped,
+                list(ps.z_obs_includes),
+                list(ps.x_obs_includes),
+                list(ps.x_entangled_with),
+                list(ps.z_entangled_with),
+            )
+            for label, ps in self._patches.items()
+        }
+        for ps in self._patches.values():
+            ps.x_z_swapped = False
+            ps.z_obs_includes = []
+            ps.x_obs_includes = []
+            ps.x_entangled_with = []
+            ps.z_entangled_with = []
+        return saved
+
+    def _restore(self, saved: PatchSnapshot) -> None:
+        """Restore patch states from snapshot."""
+        for label, (swapped, z_obs, x_obs, x_ent, z_ent) in saved.items():
+            ps = self._patches[label]
+            ps.x_z_swapped = swapped
+            ps.z_obs_includes = z_obs
+            ps.x_obs_includes = x_obs
+            ps.x_entangled_with = x_ent
+            ps.z_entangled_with = z_ent
+
+    def to_tick_circuit(self) -> object:
+        """Generate a PECOS TickCircuit with detector and observable annotations.
+
+        This is the primary output — the TickCircuit is the source of truth.
+        Use ``to_stim()`` for Stim format (derived from TickCircuit via
+        ``tick_circuit_to_stim``), or ``.to_dag_circuit()`` for fault analysis.
+
+        Returns:
+            TickCircuit with gates, detectors, and observables as metadata.
+        """
+        saved = self._snapshot_and_reset()
+        gen = _CircuitGenerator(
+            patches=self._patches,
+            operations=self._operations,
+        )
+        tc = gen.generate()
+        self._restore(saved)
+        return tc
+
+    def to_dag_circuit(self) -> object:
+        """Generate a PECOS DagCircuit for fault analysis.
+
+        Converts the TickCircuit to a DagCircuit, which can be used
+        with ``DagFaultAnalyzer`` for fault propagation analysis.
+
+        Returns:
+            DagCircuit instance.
+        """
+        return self.to_tick_circuit().to_dag_circuit()
+
+    def to_stim(
+        self,
+        *,
+        p1: float = 0.0,
+        p2: float = 0.0,
+        p_meas: float = 0.0,
+        p_prep: float = 0.0,
+    ) -> str:
+        """Generate a Stim circuit string with correct detectors.
+
+        Builds a TickCircuit (source of truth), then converts to Stim
+        format with noise injection via ``tick_circuit_to_stim()``.
+
+        Args:
+            p1: Single-qubit depolarizing error rate.
+            p2: Two-qubit depolarizing error rate.
+            p_meas: Measurement error rate.
+            p_prep: Preparation error rate.
+
+        Returns:
+            Stim circuit string.
+        """
+        from pecos.qec.surface.circuit_builder import tick_circuit_to_stim
+
+        tc = self.to_tick_circuit()
+        return tick_circuit_to_stim(tc, p1=p1, p2=p2, p_meas=p_meas, p_prep=p_prep)
+
+    def stab_coords(self) -> list[dict[str, list[tuple[float, float]]]]:
+        """Compute stabilizer coordinates for all patches.
+
+        Returns a list (one per patch, in registration order) of dicts
+        with keys "X" and "Z" mapping to ancilla (x, y) positions.
+        These coordinates match the detector annotations in the Stim circuit.
+
+        Used as input to ``ObservableSubgraphDecoder``.
+        """
+        result = []
+        for ps in self._patches.values():
+            geom = ps.patch.geometry
+            cx, cy = ps.coord_offset
+            x_coords = []
+            for s in geom.x_stabilizers:
+                positions = [geom.id_to_pos[q] for q in s.data_qubits]
+                avg_row = sum(r for r, c in positions) / len(positions)
+                avg_col = sum(c for r, c in positions) / len(positions)
+                x_coords.append((avg_col * 2 + cx, avg_row * 2 + cy))
+            z_coords = []
+            for s in geom.z_stabilizers:
+                positions = [geom.id_to_pos[q] for q in s.data_qubits]
+                avg_row = sum(r for r, c in positions) / len(positions)
+                avg_col = sum(c for r, c in positions) / len(positions)
+                z_coords.append((avg_col * 2 + cx, avg_row * 2 + cy))
+            result.append({"X": x_coords, "Z": z_coords})
+        return result
+
+    def build_dem(
+        self,
+        *,
+        p1: float = 0.001,
+        p2: float = 0.001,
+        p_meas: float = 0.001,
+        p_prep: float = 0.0,
+    ) -> str:
+        """Generate a DEM using the PECOS-native fault analysis pipeline.
+
+        TickCircuit -> DagCircuit -> DagFaultAnalyzer -> DemBuilder.
+        No Stim dependency.
+
+        Args:
+            p1: Single-qubit depolarizing error rate.
+            p2: Two-qubit depolarizing error rate.
+            p_meas: Measurement error rate.
+            p_prep: Preparation error rate.
+
+        Returns:
+            DEM string in Stim-compatible format.
+        """
+        from pecos_rslib.qec import DagFaultAnalyzer, DemBuilder
+
+        tc = self.to_tick_circuit()
+        dc = tc.to_dag_circuit()
+        analyzer = DagFaultAnalyzer(dc)
+        influence_map = analyzer.build_influence_map()
+
+        det_json = tc.get_meta("detectors")
+        obs_json = tc.get_meta("observables")
+        num_meas = int(tc.get_meta("num_measurements"))
+
+        meas_order = []
+        for tick_idx in range(tc.num_ticks()):
+            tick = tc.get_tick(tick_idx)
+            for gate in tick.gate_batches():
+                if gate.gate_type.name == "MZ":
+                    meas_order.extend(int(q) for q in gate.qubits)
+
+        dem_builder = DemBuilder(influence_map)
+        dem_builder = dem_builder.with_noise(p1, p2, p_meas, p_prep)
+        dem_builder = dem_builder.with_detectors_json(det_json)
+        dem_builder = dem_builder.with_observables_json(obs_json)
+        dem_builder = dem_builder.with_num_measurements(num_meas)
+        dem_builder = dem_builder.with_measurement_order(meas_order)
+
+        return str(dem_builder.build())
+
+    def build_sampler_and_decoder(
+        self,
+        *,
+        p1: float = 0.001,
+        p2: float = 0.001,
+        p_meas: float = 0.001,
+        p_prep: float = 0.0,
+        inner_decoder: str = "pymatching",
+    ) -> tuple[object, object, str]:
+        """Build a DemSampler and OSD decoder without any string round-trip.
+
+        Returns:
+            Tuple of (DemSampler, ObservableSubgraphDecoder, dem_str).
+            dem_str is also returned for compatibility with existing code.
+        """
+        from pecos_rslib.qec import DagFaultAnalyzer, DemBuilder, ObservableSubgraphDecoder
+
+        tc = self.to_tick_circuit()
+        dc = tc.to_dag_circuit()
+        analyzer = DagFaultAnalyzer(dc)
+        influence_map = analyzer.build_influence_map()
+
+        det_json = tc.get_meta("detectors")
+        obs_json = tc.get_meta("observables")
+        num_meas = int(tc.get_meta("num_measurements"))
+
+        meas_order = []
+        for tick_idx in range(tc.num_ticks()):
+            tick = tc.get_tick(tick_idx)
+            for gate in tick.gate_batches():
+                if gate.gate_type.name == "MZ":
+                    meas_order.extend(int(q) for q in gate.qubits)
+
+        dem_builder = DemBuilder(influence_map)
+        dem_builder = dem_builder.with_noise(p1, p2, p_meas, p_prep)
+        dem_builder = dem_builder.with_detectors_json(det_json)
+        dem_builder = dem_builder.with_observables_json(obs_json)
+        dem_builder = dem_builder.with_num_measurements(num_meas)
+        dem_builder = dem_builder.with_measurement_order(meas_order)
+
+        dem = dem_builder.build()
+        sampler = dem.to_sampler()
+        dem_str = str(dem)
+
+        sc = self.stab_coords()
+        decoder = ObservableSubgraphDecoder(dem_str, sc, inner_decoder)
+
+        return sampler, decoder, dem_str
+
+    def build_algorithm_descriptor(
+        self,
+        *,
+        p1: float = 0.001,
+        p2: float = 0.001,
+        p_meas: float = 0.001,
+        p_prep: float = 0.0,
+        buffer: int = 0,
+    ) -> dict:
+        """Extract per-segment DEMs and boundary gates for LogicalAlgorithmDecoder.
+
+        Splits the full circuit DEM at gate boundaries. Each memory operation
+        becomes a segment; each transversal gate becomes a boundary gate with
+        Pauli frame propagation rules.
+
+        Returns:
+            Dict with keys: segments, boundary_gates, num_observables, full_dem.
+        """
+        # Build the full DEM
+        full_dem = self.build_dem(p1=p1, p2=p2, p_meas=p_meas, p_prep=p_prep)
+        sc = self.stab_coords()
+
+        # Parse detector time coordinates from full DEM
+        det_times = {}
+        for raw_line in full_dem.split("\n"):
+            line = raw_line.strip()
+            if line.startswith("detector("):
+                paren = line.index(")")
+                coords = [float(x) for x in line[len("detector(") : paren].split(",")]
+                tokens = line[paren + 1 :].split()
+                for tok in tokens:
+                    if tok.startswith("D"):
+                        det_id = int(tok[1:])
+                        det_times[det_id] = coords[-1] if coords else 0.0
+
+        # Compute segment time boundaries from operations.
+        # Each MEMORY op has a number of rounds. Time coordinates are
+        # sequential round indices across all segments.
+        segments = []
+        boundary_gates = []
+        # Gates accumulate between consecutive MEMORY ops.
+        pending_gates = []
+        time_cursor = 0.0
+        patch_labels = list(self._patches.keys())
+        num_patches = len(patch_labels)
+
+        # Track X/Z swap state per patch for stab_coords.
+        # After transversal H, the X and Z stabilizer types swap.
+        x_z_swapped = dict.fromkeys(patch_labels, False)
+
+        for i, op in enumerate(self._operations):
+            if op.gate_type == LogicalGateType.MEMORY:
+                # If there are pending gates, they form the boundary
+                # between the previous segment and this one.
+                if segments and pending_gates:
+                    boundary_gates.append(pending_gates)
+                    pending_gates = []
+                elif segments:
+                    # No gate between segments — empty boundary
+                    boundary_gates.append([])
+                    pending_gates = []
+                seg_start = time_cursor
+                seg_end = time_cursor + op.rounds
+                time_cursor = seg_end
+
+                # Find detectors in this time range, extended by buffer.
+                # Buffer extends the window into adjacent segments for
+                # cross-boundary error correlation context.
+                buf_start = max(0, seg_start - buffer)
+                buf_end = seg_end + buffer
+
+                is_last = all(
+                    self._operations[j].gate_type != LogicalGateType.MEMORY for j in range(i + 1, len(self._operations))
+                )
+                if is_last:
+                    seg_det_ids = sorted(d for d, t in det_times.items() if t >= buf_start)
+                else:
+                    seg_det_ids = sorted(d for d, t in det_times.items() if buf_start <= t < buf_end)
+
+                # Build per-segment stab_coords respecting X/Z swap state
+                seg_sc = []
+                for label in patch_labels:
+                    base = sc[patch_labels.index(label)]
+                    if x_z_swapped[label]:
+                        # Swap X and Z positions
+                        seg_sc.append({"X": base["Z"], "Z": base["X"]})
+                    else:
+                        seg_sc.append({"X": base["X"], "Z": base["Z"]})
+
+                segments.append(
+                    {
+                        "det_ids": seg_det_ids,
+                        "num_detectors": len(seg_det_ids),
+                        "time_start": seg_start,
+                        "time_end": seg_end,
+                        "stab_coords": seg_sc,
+                    },
+                )
+
+            elif op.gate_type == LogicalGateType.TRANSVERSAL_H:
+                label = op.patches[0]
+                idx = patch_labels.index(label)
+                pending_gates.append(
+                    {
+                        "type": "Hadamard",
+                        "x_obs_bit": idx * 2,
+                        "z_obs_bit": idx * 2 + 1,
+                    },
+                )
+                x_z_swapped[label] = not x_z_swapped[label]
+
+            elif op.gate_type == LogicalGateType.TRANSVERSAL_CX:
+                ctrl_label, tgt_label = op.patches[0], op.patches[1]
+                ctrl_idx = patch_labels.index(ctrl_label)
+                tgt_idx = patch_labels.index(tgt_label)
+                if op.injection_type == "T":
+                    pending_gates.append(
+                        {
+                            "type": "TGateInjection",
+                            "z_obs_bit": ctrl_idx * 2 + 1,
+                            "ancilla_z_bit": tgt_idx * 2 + 1,
+                        },
+                    )
+                else:
+                    pending_gates.append(
+                        {
+                            "type": "Cnot",
+                            "ctrl_x_bit": ctrl_idx * 2,
+                            "ctrl_z_bit": ctrl_idx * 2 + 1,
+                            "tgt_x_bit": tgt_idx * 2,
+                            "tgt_z_bit": tgt_idx * 2 + 1,
+                        },
+                    )
+
+            elif op.gate_type in (LogicalGateType.TRANSVERSAL_SZ, LogicalGateType.TRANSVERSAL_SZdg):
+                label = op.patches[0]
+                idx = patch_labels.index(label)
+                pending_gates.append(
+                    {
+                        "type": "SGate",
+                        "x_obs_bit": idx * 2,
+                        "z_obs_bit": idx * 2 + 1,
+                    },
+                )
+
+        # Build per-segment sub-DEMs by filtering the full DEM.
+        # Each segment gets only the mechanisms involving its detectors.
+        seg_dems = []
+        for seg in segments:
+            set(seg["det_ids"])
+            # Build local detector index mapping
+            global_to_local = {g: local_id for local_id, g in enumerate(seg["det_ids"])}
+
+            lines = []
+            # Add detector coordinate declarations
+            for raw_line in full_dem.split("\n"):
+                line = raw_line.strip()
+                if line.startswith("detector("):
+                    paren = line.index(")")
+                    tokens = line[paren + 1 :].split()
+                    for tok in tokens:
+                        if tok.startswith("D"):
+                            d_id = int(tok[1:])
+                            if d_id in global_to_local:
+                                local = global_to_local[d_id]
+                                coords = line[len("detector(") : paren]
+                                lines.append(f"detector({coords}) D{local}")
+
+            # Add error mechanisms (remap detector IDs)
+            for raw_line in full_dem.split("\n"):
+                line = raw_line.strip()
+                if not line.startswith("error("):
+                    continue
+                tokens = line.split()
+                prob_tok = tokens[0]
+                new_tokens = [prob_tok]
+                has_local_det = False
+                for tok in tokens[1:]:
+                    if tok.startswith("D"):
+                        d_id = int(tok[1:])
+                        if d_id in global_to_local:
+                            new_tokens.append(f"D{global_to_local[d_id]}")
+                            has_local_det = True
+                    elif tok.startswith("L"):
+                        new_tokens.append(tok)
+                if has_local_det:
+                    lines.append(" ".join(new_tokens))
+
+            seg_dems.append("\n".join(lines))
+
+        return {
+            "segments": [
+                {
+                    "dem": seg_dems[i],
+                    "num_detectors": segments[i]["num_detectors"],
+                    "stab_coords": segments[i]["stab_coords"],
+                }
+                for i in range(len(segments))
+            ],
+            "boundary_gates": boundary_gates,
+            "num_observables": num_patches * 2,
+            "full_dem": full_dem,
+        }
+
+    def build_decoder(
+        self,
+        *,
+        p1: float = 0.001,
+        p2: float = 0.001,
+        p_meas: float = 0.001,
+        p_prep: float = 0.0,
+        inner_decoder: str = "fusion_blossom_serial",
+        use_stim_dem: bool = True,
+    ) -> tuple[object, object]:
+        """Build an ObservableSubgraphDecoder for this circuit.
+
+        Args:
+            p1: Single-qubit depolarizing error rate.
+            p2: Two-qubit depolarizing error rate.
+            p_meas: Measurement error rate.
+            p_prep: Preparation error rate.
+            inner_decoder: Decoder type for each subgraph.
+            use_stim_dem: If True, use Stim for DEM generation (more error
+                mechanisms). If False, use PECOS-native DEM pipeline.
+
+        Returns:
+            Tuple of (stim.Circuit, ObservableSubgraphDecoder).
+        """
+        import stim
+        from pecos_rslib.qec import ObservableSubgraphDecoder
+
+        stim_str = self.to_stim(p1=p1, p2=p2, p_meas=p_meas, p_prep=p_prep)
+        circuit = stim.Circuit(stim_str)
+
+        if use_stim_dem:
+            dem = circuit.detector_error_model(ignore_decomposition_failures=True)
+            dem_str = str(dem)
+        else:
+            dem_str = self.build_dem(p1=p1, p2=p2, p_meas=p_meas, p_prep=p_prep)
+
+        sc = self.stab_coords()
+        decoder = ObservableSubgraphDecoder(dem_str, sc, inner_decoder)
+        return circuit, decoder
+
+
+class _CircuitGenerator:
+    """Internal: generates a PECOS TickCircuit for logical circuits.
+
+    Builds a TickCircuit with detector and observable annotations as
+    JSON metadata. The TickCircuit is the source of truth; Stim circuit
+    strings are derived from it via tick_circuit_to_stim().
+    """
+
+    def __init__(
+        self,
+        patches: dict[str, PatchState],
+        operations: list[LogicalOp],
+    ) -> None:
+        from pecos_rslib.quantum import TickCircuit
+
+        self.patches = patches
+        self.operations = operations
+
+        self.tc = TickCircuit()
+        self._current_tick = None
+        self._allocated: set[int] = set()
+        self.meas_count = 0
+
+        self.stab_meas: dict[tuple[str, str, int, int, int], int] = {}
+        self.data_meas: dict[tuple[str, int], int] = {}
+
+        self.segment_idx = 0
+        self.next_observable_idx = 0
+        self.round_time = 0.0
+
+        self._det_json: list[dict] = []
+        self._obs_json: list[dict] = []
+
+    def _new_tick(self) -> object:
+        self._current_tick = self.tc.tick()
+        return self._current_tick
+
+    def _tick(self) -> object:
+        if self._current_tick is None:
+            return self._new_tick()
+        return self._current_tick
+
+    def _end_tick(self) -> None:
+        self._current_tick = None
+
+    def _emit_qalloc_or_reset(self, qubits: list[int]) -> None:
+        t = self._tick()
+        new_qs = [q for q in qubits if q not in self._allocated]
+        old_qs = [q for q in qubits if q in self._allocated]
+        if new_qs:
+            t.qalloc(new_qs)
+            self._allocated.update(new_qs)
+        if old_qs:
+            t.pz(old_qs)
+
+    def generate(self) -> object:
+        """Generate the TickCircuit with detector/observable metadata."""
+        is_first = True
+        # Per-patch last memory index: for each patch, the last MEMORY
+        # operation that includes it. This ensures each patch gets its
+        # final measurement emitted in the correct segment.
+        last_mem_for_patch: dict[str, int] = {}
+        for i, op in enumerate(self.operations):
+            if op.gate_type == LogicalGateType.MEMORY:
+                for label in op.patches:
+                    last_mem_for_patch[label] = i
+
+        for op_idx, op in enumerate(self.operations):
+            if op.gate_type == LogicalGateType.MEMORY:
+                # A patch is "last" in this segment if this is its last memory op.
+                last_patches = {label for label in op.patches if last_mem_for_patch.get(label) == op_idx}
+                self._emit_memory_segment(
+                    op,
+                    is_first=is_first,
+                    is_last=bool(last_patches),
+                    last_patches=last_patches,
+                )
+                is_first = False
+                self.segment_idx += 1
+
+            elif op.gate_type == LogicalGateType.TRANSVERSAL_H:
+                self._emit_transversal_h(op)
+
+            elif op.gate_type == LogicalGateType.TRANSVERSAL_SZ:
+                self._emit_transversal_sz(op)
+
+            elif op.gate_type == LogicalGateType.TRANSVERSAL_SZdg:
+                self._emit_transversal_szdg(op)
+
+            elif op.gate_type == LogicalGateType.TRANSVERSAL_CX:
+                self._emit_transversal_cx(op)
+
+        # Build detector/observable definitions with both formats:
+        # - "records": negative offsets (Stim compatibility, legacy)
+        # - "meas_ids": absolute MeasResult IDs (stable, preferred)
+        total = self.meas_count
+        det_out = [
+            {
+                "id": d["id"],
+                "coords": d["coords"],
+                "records": [idx - total for idx in d["abs_records"]],
+                "meas_ids": d["abs_records"],
+            }
+            for d in self._det_json
+        ]
+        obs_out = [
+            {
+                "id": o["id"],
+                "records": [idx - total for idx in o["abs_records"]],
+                "meas_ids": o["abs_records"],
+            }
+            for o in self._obs_json
+        ]
+
+        self.tc.set_meta("detectors", json.dumps(det_out))
+        self.tc.set_meta("observables", json.dumps(obs_out))
+        self.tc.set_meta("num_measurements", str(total))
+        return self.tc
+
+    def _first_memory_basis(self, patch_label: str | None = None) -> str:
+        """Basis of the first memory segment (prep basis)."""
+        for op in self.operations:
+            if op.gate_type == LogicalGateType.MEMORY:
+                if patch_label and patch_label in op.per_patch_basis:
+                    return op.per_patch_basis[patch_label]
+                return op.basis
+        return "Z"
+
+    def _last_memory_basis(self, patch_label: str | None = None) -> str:
+        """Basis of the last memory segment (measurement basis)."""
+        last = "Z"
+        for op in self.operations:
+            if op.gate_type == LogicalGateType.MEMORY:
+                if patch_label and patch_label in op.per_patch_basis:
+                    last = op.per_patch_basis[patch_label]
+                else:
+                    last = op.basis
+        return last
+
+    def _emit_meas(self, qubits: list[int]) -> list[int]:
+        self._tick().mz(qubits)
+        indices = list(range(self.meas_count, self.meas_count + len(qubits)))
+        self.meas_count += len(qubits)
+        return indices
+
+    def _emit_final_meas(self, qubits: list[int]) -> list[int]:
+        self._tick().mz(qubits)
+        indices = list(range(self.meas_count, self.meas_count + len(qubits)))
+        self.meas_count += len(qubits)
+        return indices
+
+    def _rec(self, abs_idx: int) -> int:
+        return abs_idx - self.meas_count
+
+    def _data_qubits(self, patch_label: str) -> list[int]:
+        ps = self.patches[patch_label]
+        return [ps.qubit_offset + i for i in range(ps.patch.geometry.num_data)]
+
+    def _emit_memory_segment(
+        self,
+        op: LogicalOp,
+        *,
+        is_first: bool,
+        is_last: bool,
+        last_patches: set[str] | None = None,
+    ) -> None:
+        """Emit syndrome extraction rounds for one or more patches."""
+        from pecos.qec.surface.schedule import compute_cnot_schedule
+
+        num_rounds = op.rounds
+
+        # Precompute per-patch data
+        patch_info = []
+        for patch_label in op.patches:
+            ps = self.patches[patch_label]
+            patch = ps.patch
+            geom = patch.geometry
+            offset = ps.qubit_offset
+            num_x = len(geom.x_stabilizers)
+            num_z = len(geom.z_stabilizers)
+            anc_base = offset + geom.num_data
+
+            if ps.x_z_swapped:
+                x_anc_qs = [anc_base + num_x + i for i in range(num_z)]
+                z_anc_qs = [anc_base + i for i in range(num_x)]
+                current_x_stabs = geom.z_stabilizers
+                current_z_stabs = geom.x_stabilizers
+            else:
+                x_anc_qs = [anc_base + i for i in range(num_x)]
+                z_anc_qs = [anc_base + num_x + i for i in range(num_z)]
+                current_x_stabs = geom.x_stabilizers
+                current_z_stabs = geom.z_stabilizers
+
+            patch_info.append(
+                {
+                    "label": patch_label,
+                    "ps": ps,
+                    "geom": geom,
+                    "offset": offset,
+                    "num_x": num_x,
+                    "anc_base": anc_base,
+                    "data_qs": [offset + i for i in range(geom.num_data)],
+                    "x_anc_qs": x_anc_qs,
+                    "z_anc_qs": z_anc_qs,
+                    "current_x_stabs": current_x_stabs,
+                    "current_z_stabs": current_z_stabs,
+                    "schedule": compute_cnot_schedule(patch),
+                },
+            )
+
+        # Initialization — per-patch basis
+        if is_first:
+            t = self._new_tick()
+            for pi in patch_info:
+                self._emit_qalloc_or_reset(pi["data_qs"])
+            self._end_tick()
+
+            need_h = []
+            need_hs = []
+            for pi in patch_info:
+                pb = op.per_patch_basis.get(pi["label"], op.basis)
+                if pb == "X":
+                    need_h.extend(pi["data_qs"])
+                elif pb == "Y":
+                    need_hs.extend(pi["data_qs"])
+
+            if need_h or need_hs:
+                t = self._new_tick()
+                if need_h:
+                    t.h(need_h)
+                if need_hs:
+                    t.h(need_hs)
+                self._end_tick()
+            if need_hs:
+                t = self._new_tick()
+                t.sz(need_hs)
+                self._end_tick()
+
+        # Syndrome extraction rounds
+        for rnd in range(num_rounds):
+            # Reset ancillas
+            t = self._new_tick()
+            for pi in patch_info:
+                self._emit_qalloc_or_reset(pi["x_anc_qs"] + pi["z_anc_qs"])
+            self._end_tick()
+
+            # H on X-type ancillas
+            all_x_anc = [q for pi in patch_info for q in pi["x_anc_qs"]]
+            t = self._new_tick()
+            t.h(all_x_anc)
+            self._end_tick()
+
+            # CX rounds
+            num_cx_rounds = max(len(pi["schedule"]) for pi in patch_info)
+            for cx_round_idx in range(num_cx_rounds):
+                all_pairs = []
+                for pi in patch_info:
+                    if cx_round_idx >= len(pi["schedule"]):
+                        continue
+                    for phys_type, stab_idx, data_idx in pi["schedule"][cx_round_idx]:
+                        data_q = pi["offset"] + data_idx
+                        if phys_type == "X":
+                            anc_q = pi["anc_base"] + stab_idx
+                        else:
+                            anc_q = pi["anc_base"] + pi["num_x"] + stab_idx
+                        currently_x = (phys_type == "X") != pi["ps"].x_z_swapped
+                        if currently_x:
+                            all_pairs.append((anc_q, data_q))
+                        else:
+                            all_pairs.append((data_q, anc_q))
+                t = self._new_tick()
+                if all_pairs:
+                    t.cx(all_pairs)
+                self._end_tick()
+
+            # H on X-type ancillas
+            t = self._new_tick()
+            t.h(all_x_anc)
+            self._end_tick()
+
+            # Measure ancillas
+            t = self._new_tick()
+            for pi in patch_info:
+                x_meas = self._emit_meas(pi["x_anc_qs"])
+                z_meas = self._emit_meas(pi["z_anc_qs"])
+                for i, s in enumerate(pi["current_x_stabs"]):
+                    self.stab_meas[(pi["label"], "X", s.index, self.segment_idx, rnd)] = x_meas[i]
+                for i, s in enumerate(pi["current_z_stabs"]):
+                    self.stab_meas[(pi["label"], "Z", s.index, self.segment_idx, rnd)] = z_meas[i]
+            # Invalidate _last_round_cache since stab_meas changed
+            if hasattr(self, "_last_round_cache"):
+                del self._last_round_cache
+            self._end_tick()
+
+            # Detectors
+            for pi in patch_info:
+                self._emit_round_detectors(pi["label"], rnd, is_first_segment=is_first)
+
+            self.round_time += 1.0
+
+        # Final measurement: two phases so cross-patch observable
+        # references work (all data measurements must exist before
+        # any observable is emitted).
+        if is_last and last_patches:
+            final_patches = [pi for pi in patch_info if pi["label"] in last_patches]
+            for pi in final_patches:
+                self._emit_final_data_measurements(pi["label"])
+            for pi in final_patches:
+                self._emit_final_detectors_and_observables(pi["label"])
+
+    def _emit_round_detectors(
+        self,
+        patch_label: str,
+        round_idx: int,
+        *,
+        is_first_segment: bool,
+    ) -> None:
+        """Emit detectors for one syndrome round.
+
+        Handles three cases:
+        1. First round of first segment: only basis-matching stabs are deterministic
+        2. First round after a gate boundary: cross-type comparison needed
+        3. Normal round: compare same-type measurements in consecutive rounds
+        """
+        ps = self.patches[patch_label]
+        geom = ps.patch.geometry
+        seg = self.segment_idx
+
+        for stab_type in ["X", "Z"]:
+            stabs = geom.x_stabilizers if stab_type == "X" else geom.z_stabilizers
+            for s in stabs:
+                curr_key = (patch_label, stab_type, s.index, seg, round_idx)
+                curr_idx = self.stab_meas.get(curr_key)
+                if curr_idx is None:
+                    continue
+
+                if round_idx == 0 and is_first_segment and seg == 0:
+                    # First round of very first segment:
+                    # Only stabilizers matching the prep basis are deterministic.
+                    # Find the prep basis from the first memory operation.
+                    init_basis = self._first_memory_basis(patch_label)
+                    det_type = "Z" if init_basis == "Z" else "X"
+                    # Account for X/Z swap
+                    effective_type = stab_type
+                    if ps.x_z_swapped:
+                        effective_type = "Z" if stab_type == "X" else "X"
+                    if effective_type == det_type:
+                        self._add_detector(
+                            patch_label,
+                            stab_type,
+                            s.index,
+                            [curr_idx],
+                        )
+
+                elif round_idx == 0 and seg > 0:
+                    # First round after a gate boundary.
+                    # Need to find the matching measurement from the previous segment.
+                    self._emit_boundary_detector(patch_label, stab_type, s.index, curr_idx)
+
+                elif round_idx > 0:
+                    # Normal: compare with previous round in same segment
+                    prev_key = (patch_label, stab_type, s.index, seg, round_idx - 1)
+                    prev_idx = self.stab_meas.get(prev_key)
+                    if prev_idx is not None:
+                        self._add_detector(
+                            patch_label,
+                            stab_type,
+                            s.index,
+                            [curr_idx, prev_idx],
+                        )
+
+    def _emit_boundary_detector(
+        self,
+        patch_label: str,
+        stab_type: str,
+        stab_index: int,
+        curr_meas_idx: int,
+    ) -> None:
+        """Emit a detector at a gate boundary.
+
+        After transversal H: an X-check in the new segment corresponds to what
+        was a Z-check in the previous segment (and vice versa). The detector
+        compares the current measurement with the last measurement of the
+        *conjugated* type from the previous segment.
+        """
+        self.patches[patch_label]
+        prev_seg = self.segment_idx - 1
+
+        # Find the gate that affects this specific patch at this boundary
+        gate_op = self._find_gate_before_segment(self.segment_idx, patch_label)
+
+        if (
+            gate_op is not None
+            and gate_op.gate_type == LogicalGateType.TRANSVERSAL_H
+            and patch_label in gate_op.patches
+        ):
+            # After H on THIS patch: X-stabs were Z-stabs, Z-stabs were X-stabs
+            conjugated_type = "Z" if stab_type == "X" else "X"
+            # Find the last round of the previous segment
+            prev_last_round = self._last_round_of_segment(patch_label, conjugated_type, prev_seg)
+            if prev_last_round is not None:
+                prev_key = (patch_label, conjugated_type, stab_index, prev_seg, prev_last_round)
+                prev_idx = self.stab_meas.get(prev_key)
+                if prev_idx is not None:
+                    self._add_detector(
+                        patch_label,
+                        stab_type,
+                        stab_index,
+                        [curr_meas_idx, prev_idx],
+                    )
+            # If no previous measurement found, this stabilizer wasn't measured before
+            # (e.g., it's the non-deterministic type). No detector.
+
+        elif (
+            gate_op is not None
+            and gate_op.gate_type == LogicalGateType.TRANSVERSAL_CX
+            and patch_label in gate_op.patches
+        ):
+            # After CX(control, target):
+            #   Control X-stabs: propagated to target → 3-body detector
+            #     post_ctrl_X XOR pre_ctrl_X XOR pre_tgt_X
+            #   Target Z-stabs: propagated back to control → 3-body detector
+            #     post_tgt_Z XOR pre_tgt_Z XOR pre_ctrl_Z
+            #   Control Z-stabs: unchanged → normal 2-body detector
+            #   Target X-stabs: unchanged → normal 2-body detector
+            ctrl_label = gate_op.patches[0]
+            tgt_label = gate_op.patches[1]
+            is_control = patch_label == ctrl_label
+
+            prev_last_round = self._last_round_of_segment(patch_label, stab_type, prev_seg)
+            if prev_last_round is None:
+                return  # No previous measurement
+
+            prev_key = (patch_label, stab_type, stab_index, prev_seg, prev_last_round)
+            prev_idx = self.stab_meas.get(prev_key)
+            if prev_idx is None:
+                return
+
+            needs_cross_patch = (is_control and stab_type == "X") or (not is_control and stab_type == "Z")
+
+            if needs_cross_patch:
+                # 3-body detector: also include the other patch's measurement
+                other_label = tgt_label if is_control else ctrl_label
+                other_last_round = self._last_round_of_segment(other_label, stab_type, prev_seg)
+                if other_last_round is not None:
+                    other_key = (other_label, stab_type, stab_index, prev_seg, other_last_round)
+                    other_idx = self.stab_meas.get(other_key)
+                    if other_idx is not None:
+                        self._add_detector(
+                            patch_label,
+                            stab_type,
+                            stab_index,
+                            [curr_meas_idx, prev_idx, other_idx],
+                        )
+                        return
+                # Fall through to 2-body if cross-patch measurement not found
+            self._add_detector(
+                patch_label,
+                stab_type,
+                stab_index,
+                [curr_meas_idx, prev_idx],
+            )
+
+        else:
+            # No gate boundary — normal comparison with previous segment
+            prev_last_round = self._last_round_of_segment(patch_label, stab_type, prev_seg)
+            if prev_last_round is not None:
+                prev_key = (patch_label, stab_type, stab_index, prev_seg, prev_last_round)
+                prev_idx = self.stab_meas.get(prev_key)
+                if prev_idx is not None:
+                    self._add_detector(
+                        patch_label,
+                        stab_type,
+                        stab_index,
+                        [curr_meas_idx, prev_idx],
+                    )
+
+    def _find_gate_before_segment(
+        self,
+        segment_idx: int,
+        patch_label: str | None = None,
+    ) -> LogicalOp | None:
+        """Find the gate operation that precedes a memory segment.
+
+        If patch_label is given, returns the gate that affects that specific
+        patch (checking gate_op.patches). This handles the case where multiple
+        gates are stacked between segments (e.g., H on A then H on B).
+        """
+        mem_count = 0
+        for i, op in enumerate(self.operations):
+            if op.gate_type == LogicalGateType.MEMORY:
+                if mem_count == segment_idx:
+                    # Look backwards for gates
+                    for j in range(i - 1, -1, -1):
+                        if self.operations[j].gate_type == LogicalGateType.MEMORY:
+                            break
+                        if patch_label is None:
+                            return self.operations[j]
+                        if patch_label in self.operations[j].patches:
+                            return self.operations[j]
+                    return None
+                mem_count += 1
+        return None
+
+    def _last_round_of_segment(self, patch_label: str, stab_type: str, seg_idx: int) -> int | None:
+        """Find the last round index for a stabilizer type in a segment.
+
+        Uses a cached index built on first call, then O(1) lookups.
+        """
+        if not hasattr(self, "_last_round_cache"):
+            # Build cache from stab_meas keys: (patch, type, seg) → max_round
+            cache: dict[tuple[str, str, int], int] = {}
+            for patch, stype, _sidx, seg, rnd in self.stab_meas:
+                key = (patch, stype, seg)
+                if key not in cache or rnd > cache[key]:
+                    cache[key] = rnd
+            self._last_round_cache = cache
+        return self._last_round_cache.get((patch_label, stab_type, seg_idx))
+
+    def _ancilla_spatial_coords(
+        self,
+        patch_label: str,
+        stab_type: str,
+        stab_index: int,
+    ) -> tuple[float, float]:
+        """Compute the spatial position of a stabilizer's ancilla.
+
+        Returns (x, y) including the patch's coord_offset, using the
+        average position of the stabilizer's data qubits.
+        """
+        ps = self.patches[patch_label]
+        geom = ps.patch.geometry
+        cx, cy = ps.coord_offset
+        stabs = geom.x_stabilizers if stab_type == "X" else geom.z_stabilizers
+        s = stabs[stab_index]
+        positions = [geom.id_to_pos[q] for q in s.data_qubits]
+        avg_row = sum(r for r, c in positions) / len(positions)
+        avg_col = sum(c for r, c in positions) / len(positions)
+        return (avg_col * 2 + cx, avg_row * 2 + cy)
+
+    def _add_detector(
+        self,
+        patch_label: str,
+        stab_type: str,
+        stab_index: int,
+        meas_indices: list[int],
+    ) -> None:
+        anc_x, anc_y = self._ancilla_spatial_coords(patch_label, stab_type, stab_index)
+        # Store absolute indices; convert to relative offsets in generate()
+        self._det_json.append(
+            {
+                "id": len(self._det_json),
+                "coords": [anc_x, anc_y, self.round_time],
+                "abs_records": list(meas_indices),
+            },
+        )
+
+    def _emit_transversal_h(self, op: LogicalOp) -> None:
+        ps = self.patches[op.patches[0]]
+        t = self._new_tick()
+        t.h(self._data_qubits(op.patches[0]))
+        self._end_tick()
+        ps.x_z_swapped = not ps.x_z_swapped
+
+    def _emit_transversal_sz(self, op: LogicalOp) -> None:
+        t = self._new_tick()
+        t.sz(self._data_qubits(op.patches[0]))
+        self._end_tick()
+
+    def _emit_transversal_szdg(self, op: LogicalOp) -> None:
+        t = self._new_tick()
+        t.szdg(self._data_qubits(op.patches[0]))
+        self._end_tick()
+
+    def _emit_transversal_cx(self, op: LogicalOp) -> None:
+        ctrl_label, tgt_label = op.patches[0], op.patches[1]
+        ctrl_ps = self.patches[ctrl_label]
+        tgt_ps = self.patches[tgt_label]
+
+        if ctrl_ps.x_z_swapped != tgt_ps.x_z_swapped:
+            msg = (
+                f"Transversal CX requires same stabilizer orientation. "
+                f"'{ctrl_label}' swapped={ctrl_ps.x_z_swapped}, "
+                f"'{tgt_label}' swapped={tgt_ps.x_z_swapped}."
+            )
+            raise ValueError(msg)
+
+        pairs = list(zip(self._data_qubits(ctrl_label), self._data_qubits(tgt_label), strict=False))
+        t = self._new_tick()
+        t.cx(pairs)
+        self._end_tick()
+
+        if op.teleportation:
+            ctrl_ps.z_obs_includes.append(tgt_label)
+
+        # Track entanglement: CX spreads X on control to target,
+        # and Z on target to control.
+        ctrl_ps.x_entangled_with.append(tgt_label)
+        tgt_ps.z_entangled_with.append(ctrl_label)
+
+    def _emit_final_data_measurements(self, patch_label: str) -> None:
+        ps = self.patches[patch_label]
+        geom = ps.patch.geometry
+        data_qs = self._data_qubits(patch_label)
+        meas_basis = self._last_memory_basis(patch_label)
+
+        if meas_basis == "X":
+            t = self._new_tick()
+            t.h(data_qs)
+            self._end_tick()
+
+        t = self._new_tick()
+        meas_indices = self._emit_final_meas(data_qs)
+        self._end_tick()
+        for i, q in enumerate(range(geom.num_data)):
+            self.data_meas[(patch_label, q)] = meas_indices[i]
+
+    def _emit_final_detectors_and_observables(self, patch_label: str) -> None:
+        ps = self.patches[patch_label]
+        geom = ps.patch.geometry
+        meas_basis = self._last_memory_basis(patch_label)
+
+        if meas_basis == "Z":
+            final_stabs = geom.x_stabilizers if ps.x_z_swapped else geom.z_stabilizers
+            lookup_type = "Z"
+        else:
+            final_stabs = geom.z_stabilizers if ps.x_z_swapped else geom.x_stabilizers
+            lookup_type = "X"
+
+        if ps.x_z_swapped:
+            logical_op = geom.logical_z if meas_basis == "X" else geom.logical_x
+        else:
+            logical_op = geom.logical_x if meas_basis == "X" else geom.logical_z
+
+        seg = self.segment_idx
+        last_rnd = self._last_round_of_segment(patch_label, lookup_type, seg)
+
+        if last_rnd is not None:
+            for s in final_stabs:
+                data_rec = [self.data_meas[(patch_label, dq)] for dq in s.data_qubits]
+                syn_key = (patch_label, lookup_type, s.index, seg, last_rnd)
+                syn_idx = self.stab_meas.get(syn_key)
+                if syn_idx is not None:
+                    all_idx = [*data_rec, syn_idx]
+                    anc_x, anc_y = self._ancilla_spatial_coords(patch_label, lookup_type, s.index)
+                    self._det_json.append(
+                        {
+                            "id": len(self._det_json),
+                            "coords": [anc_x, anc_y, self.round_time],
+                            "abs_records": list(all_idx),
+                        },
+                    )
+
+        if logical_op is not None:
+            # Check if this observable is reliable given entanglement.
+            # After CX(ctrl, tgt): ctrl's X is entangled with tgt,
+            # tgt's Z is entangled with ctrl.
+            # An observable is reliable if:
+            # - Not entangled, OR
+            # - The entangled partner is measured in the same basis
+            entangled_with = ps.x_entangled_with if meas_basis == "X" else ps.z_entangled_with
+            is_reliable = True
+            for other_label in entangled_with:
+                other_basis = self._last_memory_basis(other_label)
+                if other_basis != meas_basis:
+                    is_reliable = False
+                    break
+
+            if not is_reliable:
+                # Skip non-reliable observables — they're physically
+                # non-deterministic and would cause Stim DEM errors.
+                # The decoder handles these through the 3-body detectors.
+                self.next_observable_idx += 1
+                return
+
+            obs_idx = self.next_observable_idx
+            self.next_observable_idx += 1
+            obs_indices = [self.data_meas[(patch_label, q)] for q in logical_op.data_qubits]
+
+            # Teleportation corrections
+            for other_label in ps.z_obs_includes:
+                other_logical = self.patches[other_label].patch.geometry.logical_z
+                if other_logical is not None:
+                    for q in other_logical.data_qubits:
+                        key = (other_label, q)
+                        if key in self.data_meas:
+                            obs_indices.append(self.data_meas[key])
+
+            self._obs_json.append(
+                {
+                    "id": obs_idx,
+                    "abs_records": list(obs_indices),
+                },
+            )
diff --git a/python/quantum-pecos/src/pecos/qec/surface/patch.py b/python/quantum-pecos/src/pecos/qec/surface/patch.py
index 322c171f4..ef48dd28b 100644
--- a/python/quantum-pecos/src/pecos/qec/surface/patch.py
+++ b/python/quantum-pecos/src/pecos/qec/surface/patch.py
@@ -152,7 +152,8 @@ def _get_stabilizer_schedule_metadata(stab: Stabilizer, patch: SurfacePatch) ->
             stab.stab_type,
             stab.data_qubits,
             stab.is_boundary,
-            patch.distance,
+            patch.dx,
+            patch.dz,
         )
     ]
     rounds = [int(entry["round_0based"]) for entry in entries]
@@ -213,12 +214,11 @@ def _generate_layout(self) -> None:
                 self.id_to_pos[idx] = pos
 
     def _generate_stabilizers(self) -> None:
-        d = min(self.dx, self.dz)
-
         if self.rotated:
-            x_supports = compute_rotated_x_stabilizers(d)
-            z_supports = compute_rotated_z_stabilizers(d)
+            x_supports = compute_rotated_x_stabilizers(self.dx, self.dz)
+            z_supports = compute_rotated_z_stabilizers(self.dx, self.dz)
         else:
+            d = min(self.dx, self.dz)
             x_supports = compute_x_stabilizer_supports(d)
             z_supports = compute_z_stabilizer_supports(d)
 
@@ -246,11 +246,9 @@ def _generate_stabilizers(self) -> None:
         self.num_z_stab = len(self.z_stabilizers)
 
     def _generate_logical_operators(self) -> None:
-        d = min(self.dx, self.dz)
-
         if self.rotated:
-            logical_x_qubits = get_rotated_logical_x(d)
-            logical_z_qubits = get_rotated_logical_z(d)
+            logical_x_qubits = get_rotated_logical_x(self.dx, self.dz)
+            logical_z_qubits = get_rotated_logical_z(self.dx, self.dz)
         else:
             logical_x_qubits = tuple(i * self.dz for i in range(self.dx))
             logical_z_qubits = tuple(range(self.dz))
@@ -301,27 +299,34 @@ def create(
     ) -> SurfacePatch:
         """Create a surface code patch.
 
+        Supports any positive dimensions:
+        - dx=dz=d (odd >= 3): standard surface code [[d^2, 1, d]]
+        - dx != dz: asymmetric surface code
+        - dx=1, dz=N: Z-repetition code [[N, 1, 1]] (N-1 X stabilizers)
+        - dx=N, dz=1: X-repetition code [[N, 1, 1]] (N-1 Z stabilizers)
+        - dx=dz=1: single physical qubit, no stabilizers
+
         Args:
-            distance: Symmetric code distance (must be odd >= 3).
-            dx: X distance for asymmetric codes.
-            dz: Z distance for asymmetric codes.
+            distance: Symmetric code distance (>= 1).
+            dx: X distance (rows) for asymmetric codes (>= 1).
+            dz: Z distance (columns) for asymmetric codes (>= 1).
             orientation: Patch boundary orientation.
             rotated: If True (default), use the rotated layout which is more
                 common and uses fewer qubits. If False, use the standard
                 (non-rotated) layout.
         """
         if distance is not None:
-            if distance < 3 or distance % 2 == 0:
-                msg = f"Distance must be odd >= 3, got {distance}"
+            if distance < 1:
+                msg = f"Distance must be >= 1, got {distance}"
                 raise ValueError(msg)
             dx = dx or distance
             dz = dz or distance
         elif dx is not None and dz is not None:
-            if dx < 3 or dx % 2 == 0:
-                msg = f"dx must be odd >= 3, got {dx}"
+            if dx < 1:
+                msg = f"dx must be >= 1, got {dx}"
                 raise ValueError(msg)
-            if dz < 3 or dz % 2 == 0:
-                msg = f"dz must be odd >= 3, got {dz}"
+            if dz < 1:
+                msg = f"dz must be >= 1, got {dz}"
                 raise ValueError(msg)
         else:
             msg = "Must provide either distance or both dx and dz"
diff --git a/python/quantum-pecos/src/pecos/qec/surface/plot.py b/python/quantum-pecos/src/pecos/qec/surface/plot.py
index 2a30134f4..d02bf9345 100644
--- a/python/quantum-pecos/src/pecos/qec/surface/plot.py
+++ b/python/quantum-pecos/src/pecos/qec/surface/plot.py
@@ -136,6 +136,7 @@ def _annotate_cnot_order(ax: plt.Axes, stabilizers: list, d: int) -> None:
             stab.data_qubits,
             stab.is_boundary,
             d,
+            d,
         )
 
         # Compute centroid of the stabilizer
diff --git a/python/quantum-pecos/src/pecos/qec/surface/schedule.py b/python/quantum-pecos/src/pecos/qec/surface/schedule.py
index 410dd9ac6..8972fc934 100644
--- a/python/quantum-pecos/src/pecos/qec/surface/schedule.py
+++ b/python/quantum-pecos/src/pecos/qec/surface/schedule.py
@@ -31,28 +31,28 @@
     from pecos.qec.surface.patch import SurfacePatch
 
 
-def _classify_boundary(stab_type: str, data_qubits: tuple[int, ...], d: int) -> str:
+def _classify_boundary(stab_type: str, data_qubits: tuple[int, ...], dx: int, dz: int) -> str:
     """Classify which boundary a weight-2 stabilizer sits on.
 
     Returns one of: 'top', 'bottom', 'left', 'right'.
     """
-    rows = [q // d for q in data_qubits]
-    cols = [q % d for q in data_qubits]
+    rows = [q // dz for q in data_qubits]
+    cols = [q % dz for q in data_qubits]
 
     if stab_type == "X":
         # X boundaries are top and bottom
         if all(r == 0 for r in rows):
             return "top"
-        if all(r == d - 1 for r in rows):
+        if all(r == dx - 1 for r in rows):
             return "bottom"
     else:
         # Z boundaries are left and right
-        if all(c == d - 1 for c in cols):
+        if all(c == dz - 1 for c in cols):
             return "right"
         if all(c == 0 for c in cols):
             return "left"
 
-    msg = f"Cannot classify boundary for {stab_type} stab with qubits {data_qubits} (d={d})"
+    msg = f"Cannot classify boundary for {stab_type} stab with qubits {data_qubits} (dx={dx}, dz={dz})"
     raise ValueError(msg)
 
 
@@ -60,7 +60,8 @@ def get_stab_schedule(
     stab_type: str,
     data_qubits: tuple[int, ...],
     is_boundary: bool,
-    d: int,
+    dx: int,
+    dz: int,
 ) -> list[tuple[int, int]]:
     """Compute the per-stabilizer CNOT schedule.
 
@@ -69,7 +70,8 @@ def get_stab_schedule(
         data_qubits: Tuple of data qubit IDs. For bulk (weight 4):
             (TL, TR, BL, BR). For boundary (weight 2): two qubits.
         is_boundary: Whether this is a boundary stabilizer.
-        d: Code distance.
+        dx: Number of rows (X distance).
+        dz: Number of columns (Z distance).
 
     Returns:
         List of (round_0based, data_qubit) pairs, sorted by round.
@@ -82,7 +84,7 @@ def get_stab_schedule(
         return [(0, tr), (1, br), (2, tl), (3, bl)]
 
     # Boundary weight-2 stabilizer
-    boundary = _classify_boundary(stab_type, data_qubits, d)
+    boundary = _classify_boundary(stab_type, data_qubits, dx, dz)
 
     if boundary == "bottom":
         # Bottom X: rounds 0,1 -- right first then left
@@ -115,16 +117,17 @@ def compute_cnot_schedule(patch: SurfacePatch) -> list[list[tuple[str, int, int]
         List of 4 rounds, each a list of (stab_type, stab_index, data_qubit)
         tuples representing CX gates to execute in parallel.
     """
-    d = patch.distance
+    dx = patch.dx
+    dz = patch.dz
     rounds: list[list[tuple[str, int, int]]] = [[] for _ in range(4)]
 
     for stab in patch.x_stabilizers:
-        schedule = get_stab_schedule("X", stab.data_qubits, stab.is_boundary, d)
+        schedule = get_stab_schedule("X", stab.data_qubits, stab.is_boundary, dx, dz)
         for rnd, data_q in schedule:
             rounds[rnd].append(("X", stab.index, data_q))
 
     for stab in patch.z_stabilizers:
-        schedule = get_stab_schedule("Z", stab.data_qubits, stab.is_boundary, d)
+        schedule = get_stab_schedule("Z", stab.data_qubits, stab.is_boundary, dx, dz)
         for rnd, data_q in schedule:
             rounds[rnd].append(("Z", stab.index, data_q))
 
diff --git a/python/quantum-pecos/src/pecos/quantum/__init__.py b/python/quantum-pecos/src/pecos/quantum/__init__.py
index 96bc863b6..d9c190b84 100644
--- a/python/quantum-pecos/src/pecos/quantum/__init__.py
+++ b/python/quantum-pecos/src/pecos/quantum/__init__.py
@@ -56,19 +56,23 @@
     >>> errors = array([Pauli.X, Pauli.Y, Pauli.Z])
 
     >>> # Create Pauli strings with convenient syntax
-    >>> from pecos.quantum import pauli_string
-    >>> ps = pauli_string("XYZ", phase=-1)  # -X_0 Y_1 Z_2
+    >>> from pecos.quantum import X, Z, pauli_string
+    >>> ps = X(0) & Z(3)
+    >>> from_text = pauli_string("X0 Z3")
+    >>> assert ps == from_text
 """
 
 from __future__ import annotations
 
+from collections.abc import Mapping as MappingABC
+from collections.abc import Sequence as SequenceABC
 from typing import TYPE_CHECKING
 
 from pecos.quantum import commute, gate_groups
 from pecos.typing import INTEGER_TYPES
 
 if TYPE_CHECKING:
-    from collections.abc import Sequence
+    from collections.abc import Mapping, Sequence
 
     from pecos.typing import Integer
 
@@ -118,6 +122,9 @@
         SZdg,
         SZZdg,
         TableauWrapper,
+        X,
+        Y,
+        Z,
         adjust_tableau_string,
         sparse_stab,
     )
@@ -152,7 +159,7 @@
 
 
 def pauli_string(
-    operators: str | Sequence[tuple[Pauli, int]] | dict[int, Pauli],
+    operators: str | Sequence[tuple[Pauli, int]] | Sequence[Pauli] | Mapping[int, Pauli],
     phase: complex = 1,
 ) -> PauliString:
     """Create a PauliString from a convenient specification.
@@ -162,9 +169,10 @@ def pauli_string(
 
     Args:
         operators: One of the following:
-            - String like "XYZ" or "IXZI" (sequential qubits starting at 0)
-            - List of (Pauli, qubit_index) tuples
-            - Dict mapping qubit_index -> Pauli
+            - Sparse string like "X0 Z2" or dense string like "XIZ"
+            - Sequence of (Pauli, qubit_index) tuples
+            - Sequence of Pauli values for implicit qubits 0, 1, 2, ...
+            - Mapping from qubit_index -> Pauli
         phase: Phase factor, one of:
             - 1 or +1: Plus one (default)
             - -1: Minus one
@@ -175,11 +183,19 @@ def pauli_string(
         PauliString object
 
     Examples:
-        >>> from pecos.quantum import Pauli, pauli_string
+        >>> from pecos.quantum import Pauli, X, Z, pauli_string
 
-        >>> # From string (sequential qubits)
-        >>> ps = pauli_string("XYZ")
-        >>> print(ps)  # X_0 Y_1 Z_2
+        >>> # Constructor syntax is preferred for ordinary code
+        >>> ps = X(0) & Z(2)
+        >>> print(ps)  # X_0 Z_2
+
+        >>> # From sparse string (explicit qubit indices)
+        >>> ps = pauli_string("X0 Z2")
+        >>> print(ps)  # X_0 Z_2
+
+        >>> # From dense string (character position is qubit index)
+        >>> ps = pauli_string("XIZ")
+        >>> print(ps)  # X_0 Z_2
 
         >>> # From list of (Pauli, qubit) tuples
         >>> ps = pauli_string([(Pauli.X, 0), (Pauli.Z, 2)])
@@ -229,14 +245,14 @@ def pauli_string(
             paulis = ps.get_paulis()
             return PauliString(paulis, phase=phase_code)
         return ps
-    if isinstance(operators, dict):
-        # Dict format - convert to list
+    if isinstance(operators, MappingABC):
+        # Mapping format - convert to list
         paulis = [(pauli, qubit) for qubit, pauli in sorted(operators.items())]
         return PauliString(paulis, phase=phase_code)
-    if isinstance(operators, list):
-        # Already in list format
-        return PauliString(operators, phase=phase_code)
-    msg = f"Invalid operators type: {type(operators)}. Must be str, dict, or list"
+    if isinstance(operators, SequenceABC):
+        # PyO3 constructor accepts lists, so normalize all Python sequences.
+        return PauliString(list(operators), phase=phase_code)
+    msg = f"Invalid operators type: {type(operators)}. Must be str, mapping, or sequence"
     raise TypeError(msg)
 
 
@@ -295,6 +311,9 @@ def pauli_string(
     "TickHandle",
     "TickMeasureHandle",
     "TickPrepHandle",
+    "X",
+    "Y",
+    "Z",
     "adjust_tableau_string",
     "commute",
     "gate_groups",
diff --git a/python/quantum-pecos/src/pecos/quantum_info.py b/python/quantum-pecos/src/pecos/quantum_info.py
new file mode 100644
index 000000000..5cc313105
--- /dev/null
+++ b/python/quantum-pecos/src/pecos/quantum_info.py
@@ -0,0 +1,70 @@
+"""Quantum-information channel representations and measures.
+
+This module re-exports the Rust-backed implementations from
+``pecos_rslib.quantum_info``. Computation and validation happen in Rust; this
+file only provides the public Python import location.
+"""
+
+from __future__ import annotations
+
+from pecos_rslib.quantum_info import (
+    ChiMatrix,
+    ChoiMatrix,
+    KrausOps,
+    PauliChannel,
+    ProcessTomographyDesign,
+    Ptm,
+    Stinespring,
+    SuperOp,
+    average_gate_fidelity,
+    entropy,
+    gate_error,
+    hellinger_distance,
+    hellinger_fidelity,
+    logarithmic_negativity,
+    matrix_unit_basis,
+    negativity,
+    partial_trace_qubits,
+    partial_trace_subsystems,
+    pauli_channel_diamond_distance,
+    pauli_channel_diamond_norm,
+    process_fidelity,
+    purity,
+    random_density_matrix,
+    random_quantum_channel,
+    schmidt_decomposition,
+    shannon_entropy,
+    state_fidelity,
+    state_fidelity_with_density_matrix,
+)
+
+__all__ = [
+    "ChiMatrix",
+    "ChoiMatrix",
+    "KrausOps",
+    "PauliChannel",
+    "ProcessTomographyDesign",
+    "Ptm",
+    "Stinespring",
+    "SuperOp",
+    "average_gate_fidelity",
+    "entropy",
+    "gate_error",
+    "hellinger_distance",
+    "hellinger_fidelity",
+    "logarithmic_negativity",
+    "matrix_unit_basis",
+    "negativity",
+    "partial_trace_qubits",
+    "partial_trace_subsystems",
+    "pauli_channel_diamond_distance",
+    "pauli_channel_diamond_norm",
+    "process_fidelity",
+    "purity",
+    "random_density_matrix",
+    "random_quantum_channel",
+    "schmidt_decomposition",
+    "shannon_entropy",
+    "state_fidelity",
+    "state_fidelity_with_density_matrix",
+]
diff --git a/python/quantum-pecos/src/pecos/typing.py b/python/quantum-pecos/src/pecos/typing.py
index 6ac4e47fd..022297e17 100644
--- a/python/quantum-pecos/src/pecos/typing.py
+++ b/python/quantum-pecos/src/pecos/typing.py
@@ -23,12 +23,143 @@
 
 from __future__ import annotations
 
-from typing import TYPE_CHECKING, Generic, Protocol, TypeAlias, TypedDict, TypeVar
+from typing import TYPE_CHECKING, Generic, Literal, Protocol, TypeAlias, TypedDict, TypeVar
 
 import pecos_rslib as prs
+from phir.model import (
+    Barrier as _Barrier,
+)
+from phir.model import (
+    Comment as _Comment,
+)
+from phir.model import (
+    COp as _COp,
+)
+from phir.model import (
+    CVarDefine as _CVarDefine,
+)
+from phir.model import (
+    ExportVar as _ExportVar,
+)
+from phir.model import (
+    FFCall as _FFCall,
+)
+from phir.model import (
+    IfBlock as _IfBlock,
+)
+from phir.model import (
+    MOpType as _MOpType,
+)
+from phir.model import (
+    Op as _Op,
+)
+from phir.model import (
+    PHIRModel as _PHIRModel,
+)
+from phir.model import (
+    QOp as _QOp,
+)
+from phir.model import (
+    QParBlock as _QParBlock,
+)
+from phir.model import (
+    QVarDefine as _QVarDefine,
+)
+from phir.model import (
+    SeqBlock as _SeqBlock,
+)
+from pydantic import model_validator
+
+
+class _PecosCVarDefine(_CVarDefine):
+    """CVarDefine extended with 8-bit and 16-bit integer data types.
+
+    The upstream PHIR spec's ``CVarDefine`` only accepts ``i32``, ``i64``,
+    ``u32``, ``u64``. PECOS additionally supports ``i8``, ``u8``, ``i16``,
+    ``u16`` for classical registers. The parent class's ``check_size``
+    validator covers 32 and 64-bit cases; this subclass adds the matching
+    check for 8-bit and 16-bit sizes.
+    """
+
+    data_type: Literal["i8", "i16", "i32", "i64", "u8", "u16", "u32", "u64"]  # type: ignore[assignment]
+
+    @model_validator(mode="after")
+    def _check_size_small(self) -> _PecosCVarDefine:
+        """Check that ``size`` fits within 8-bit and 16-bit data types."""
+        msg = "`size` is greater than what `data_type` can handle"
+        if self.size:
+            match self.data_type:
+                case "i8" | "u8":
+                    if self.size > 8:
+                        raise ValueError(msg)
+                case "i16" | "u16":
+                    if self.size > 16:
+                        raise ValueError(msg)
+        return self
+
+
+_PecosDataMgmt: TypeAlias = _PecosCVarDefine | _QVarDefine | _ExportVar
+
+
+class ResultCOp(_Op):
+    """PECOS-specific ``Result`` classical operation.
+
+    Copies the value of internal classical registers to external result
+    variables, creating the destination variable if needed. Used by the
+    PECOS ``HybridEngine`` to transmit measurement bits between the inner
+    and outer classical interpreters.
+
+    Example:
+        ``{"cop": "Result", "args": ["m"], "returns": ["c"]}``
+
+    This operation is a PECOS extension, not part of the upstream PHIR
+    specification.
+    """
+
+    cop: Literal["Result"]
+    args: list[str]
+    returns: list[str]
+
+
+_PecosOpType: TypeAlias = _FFCall | _COp | ResultCOp | _QOp | _MOpType | _Barrier
+
+
+class _PecosSeqBlock(_SeqBlock):
+    """SeqBlock extended with PECOS-specific classical operations."""
+
+    ops: list[_PecosOpType | _PecosBlockType]  # type: ignore[assignment]
+
+
+class _PecosIfBlock(_IfBlock):
+    """IfBlock extended with PECOS-specific classical operations."""
+
+    true_branch: list[_PecosOpType | _PecosBlockType]  # type: ignore[assignment]
+    false_branch: list[_PecosOpType | _PecosBlockType] | None = None  # type: ignore[assignment]
+
+
+_PecosBlockType: TypeAlias = _PecosSeqBlock | _QParBlock | _PecosIfBlock
+_PecosCmd: TypeAlias = _PecosDataMgmt | _PecosOpType | _PecosBlockType | _Comment
+
+
+class PhirModel(_PHIRModel):
+    """PHIR model extended with PECOS-specific classical operations.
+
+    Adds support for the ``Result`` cop used by PECOS ``HybridEngine`` to
+    map internal measurement registers to external result variables. Fully
+    backwards-compatible with upstream PHIR programs.
+
+    The upstream ``phir.model.PHIRModel`` rejects programs containing
+    ``Result`` cops because ``Result`` is not in the PHIR specification.
+    Use this class (or ``pecos.typing.PhirModel``) when validating
+    programs that may contain PECOS extensions.
+    """
+
+    ops: list[_PecosCmd]  # type: ignore[assignment]
+
 
-# Import external PHIR model with consistent naming
-from phir.model import PHIRModel as PhirModel
+_PecosSeqBlock.model_rebuild()
+_PecosIfBlock.model_rebuild()
+PhirModel.model_rebuild()
 
 # Type variable for dtype (used with Array[DType])
 DType = TypeVar("DType")
@@ -139,7 +270,7 @@ class ErrorParams(TypedDict, total=False):
     p2: float
     p2_mem: float | None
     p_meas: float | tuple[float, ...]
-    p_init: float
+    p_prep: float
     scale: float
     noiseless_qubits: set[int]
 
diff --git a/python/quantum-pecos/tests/conftest.py b/python/quantum-pecos/tests/conftest.py
index ecfcd5563..7076b0d55 100644
--- a/python/quantum-pecos/tests/conftest.py
+++ b/python/quantum-pecos/tests/conftest.py
@@ -1,38 +1,7 @@
-# Copyright 2025 The PECOS Developers
-#
-# Licensed under the Apache License, Version 2.0 (the "License"); you may not use this file except in compliance with
-# the License.You may obtain a copy of the License at
-#
-#     https://www.apache.org/licenses/LICENSE-2.0
-#
-# Unless required by applicable law or agreed to in writing, software distributed under the License is distributed on an
-# "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. See the License for the
-# specific language governing permissions and limitations under the License.
+"""Shared pytest setup for the Python test suite."""
 
-"""Test configuration and shared fixtures."""
-
-import pytest
-
-# Configure matplotlib to use non-interactive backend for tests (if available)
-# This must be done before importing matplotlib.pyplot to avoid GUI backend issues on Windows
-try:
-    import matplotlib as mpl
-
-    mpl.use("Agg")
-except ImportError:
-    # matplotlib is optional - only needed for visualization tests
-    pass
-
-# Note: llvmlite functionality is now always available via Rust (pecos_rslib.ir and pecos_rslib.binding)
-# No need for conditional test skipping
-
-
-def pytest_configure(config: pytest.Config) -> None:
-    """Register test-tree-local markers used by direct pytest invocations."""
-    config.addinivalue_line(
-        "markers",
-        (
-            "slow: mark tests that provide extra integration coverage but are "
-            "excluded from the default fast Python test lane"
-        ),
-    )
+# The test tree contains ``tests/pecos``. Pytest can import tests from that
+# directory as a namespace package named ``pecos`` when an individual file is run
+# in isolation. Import the installed/source package first so later
+# ``import pecos`` statements resolve to the public PECOS package.
+import pecos
diff --git a/python/quantum-pecos/tests/docs/conftest.py b/python/quantum-pecos/tests/docs/conftest.py
index 354dada23..7a5ed3ca1 100644
--- a/python/quantum-pecos/tests/docs/conftest.py
+++ b/python/quantum-pecos/tests/docs/conftest.py
@@ -63,7 +63,7 @@ def cuda_check() -> bool:
 
 
 @pytest.fixture(autouse=True)
-def restore_cwd():  # noqa: ANN201
+def restore_cwd():
     """Restore the current working directory after each test.
 
     Some tests (e.g., WASM examples) change the working directory,
diff --git a/python/quantum-pecos/tests/docs/rust_crate/Cargo.lock b/python/quantum-pecos/tests/docs/rust_crate/Cargo.lock
index 04256d57e..9b4910bed 100644
--- a/python/quantum-pecos/tests/docs/rust_crate/Cargo.lock
+++ b/python/quantum-pecos/tests/docs/rust_crate/Cargo.lock
@@ -590,6 +590,15 @@ version = "0.8.7"
 source = "registry+https://github.com/rust-lang/crates.io-index"
 checksum = "773648b94d0e5d620f64f280777445740e61fe701025087ec8b57f45c791888b"
 
+[[package]]
+name = "cpp_demangle"
+version = "0.4.5"
+source = "registry+https://github.com/rust-lang/crates.io-index"
+checksum = "f2bb79cb74d735044c972aae58ed0aaa9a837e85b01106a54c39e42e97f62253"
+dependencies = [
+ "cfg-if",
+]
+
 [[package]]
 name = "cpufeatures"
 version = "0.2.17"
@@ -610,27 +619,27 @@ dependencies = [
 
 [[package]]
 name = "cranelift-assembler-x64"
-version = "0.130.1"
+version = "0.131.1"
 source = "registry+https://github.com/rust-lang/crates.io-index"
-checksum = "046d4b584c3bb9b5eb500c8f29549bec36be11000f1ba2a927cef3d1a9875691"
+checksum = "f8628cc4ba7f88a9205a7ee42327697abc61195a1e3d92cfae172d6a946e722e"
 dependencies = [
  "cranelift-assembler-x64-meta",
 ]
 
 [[package]]
 name = "cranelift-assembler-x64-meta"
-version = "0.130.1"
+version = "0.131.1"
 source = "registry+https://github.com/rust-lang/crates.io-index"
-checksum = "b9b194a7870becb1490366fc0ae392ccd188065ff35f8391e77ac659db6fb977"
+checksum = "d582754487e6c9a065a91c42ccf1bdd8d5977af33468dac5ae9bec0ce88acb3e"
 dependencies = [
  "cranelift-srcgen",
 ]
 
 [[package]]
 name = "cranelift-bforest"
-version = "0.130.1"
+version = "0.131.1"
 source = "registry+https://github.com/rust-lang/crates.io-index"
-checksum = "bb6a4ab44c6b371e661846b97dab687387a60ac4e2f864e2d4257284aad9e889"
+checksum = "fb59c81ace12ee7c33074db7903d4d75d1f40b28cd3e8e6f491de57b29129eb9"
 dependencies = [
  "cranelift-entity",
  "wasmtime-internal-core",
@@ -638,9 +647,9 @@ dependencies = [
 
 [[package]]
 name = "cranelift-bitset"
-version = "0.130.1"
+version = "0.131.1"
 source = "registry+https://github.com/rust-lang/crates.io-index"
-checksum = "b8b7a44150c2f471a94023482bda1902710746e4bed9f9973d60c5a94319b06d"
+checksum = "f25c06993a681be9cf3140798a3d4ac5bec955e7444416a2fdc87fda8567285d"
 dependencies = [
  "serde",
  "serde_derive",
@@ -649,9 +658,9 @@ dependencies = [
 
 [[package]]
 name = "cranelift-codegen"
-version = "0.130.1"
+version = "0.131.1"
 source = "registry+https://github.com/rust-lang/crates.io-index"
-checksum = "01b06598133b1dd76758b8b95f8d6747c124124aade50cea96a3d88b962da9fa"
+checksum = "27b61f95c5a211918f5d336254a61a488b36a5818de47a868e8c4658dce9cccc"
 dependencies = [
  "bumpalo",
  "cranelift-assembler-x64",
@@ -677,9 +686,9 @@ dependencies = [
 
 [[package]]
 name = "cranelift-codegen-meta"
-version = "0.130.1"
+version = "0.131.1"
 source = "registry+https://github.com/rust-lang/crates.io-index"
-checksum = "6190e2e7bcf0a678da2f715363d34ed530fedf7a2f0ab75edaefef72a70465ff"
+checksum = "0b85aa822fce72080d041d7c2cf7c3f5c6ecdea7afae68379ba4ef85269c4fa5"
 dependencies = [
  "cranelift-assembler-x64-meta",
  "cranelift-codegen-shared",
@@ -690,24 +699,24 @@ dependencies = [
 
 [[package]]
 name = "cranelift-codegen-shared"
-version = "0.130.1"
+version = "0.131.1"
 source = "registry+https://github.com/rust-lang/crates.io-index"
-checksum = "f583cf203d1aa8b79560e3b01f929bdacf9070b015eec4ea9c46e22a3f83e4a0"
+checksum = "833eb9fc89326cd072cc19e96892f09b5692c0dfe17cd4da2858ba30c2cd85c0"
 
 [[package]]
 name = "cranelift-control"
-version = "0.130.1"
+version = "0.131.1"
 source = "registry+https://github.com/rust-lang/crates.io-index"
-checksum = "803159df35cc398ae54473c150b16d6c77e92ab2948be638488de126a3328fbc"
+checksum = "9d005320f487e6e8a3edcc7f2fd4f43fcc9946d1013bf206ea649789ac1617fc"
 dependencies = [
  "arbitrary",
 ]
 
 [[package]]
 name = "cranelift-entity"
-version = "0.130.1"
+version = "0.131.1"
 source = "registry+https://github.com/rust-lang/crates.io-index"
-checksum = "3109e417257082d88087f5bcce677525bdaa8322b88dd7f175ed1a1fd41d546c"
+checksum = "5e62ef34c6e720f347a79ece043e8584e242d168911da640bac654a33a6aaaf5"
 dependencies = [
  "cranelift-bitset",
  "serde",
@@ -717,9 +726,9 @@ dependencies = [
 
 [[package]]
 name = "cranelift-frontend"
-version = "0.130.1"
+version = "0.131.1"
 source = "registry+https://github.com/rust-lang/crates.io-index"
-checksum = "14db6b0e0e4994c581092df78d837be2072578f7cb2528f96a6cf895e56dee63"
+checksum = "dfa2ad00399dd47e7e7e33cb1dc23b0e39ed9dcd01e8f026fc37af91655031b8"
 dependencies = [
  "cranelift-codegen",
  "log",
@@ -729,15 +738,15 @@ dependencies = [
 
 [[package]]
 name = "cranelift-isle"
-version = "0.130.1"
+version = "0.131.1"
 source = "registry+https://github.com/rust-lang/crates.io-index"
-checksum = "ec66ea5025c7317383699778282ac98741d68444f956e3b1d7b62f12b7216e67"
+checksum = "02c51975ed217b4e8e5a7fd11e9ec83a96104bdff311dddcb505d1d8a9fd7fc6"
 
 [[package]]
 name = "cranelift-native"
-version = "0.130.1"
+version = "0.131.1"
 source = "registry+https://github.com/rust-lang/crates.io-index"
-checksum = "373ade56438e6232619d85678477d0a88a31b3581936e0503e61e96b546b0800"
+checksum = "f9b1889e00da9729d8f8525f3c12998ded86ea709058ff844ebe00b97548de0e"
 dependencies = [
  "cranelift-codegen",
  "libc",
@@ -746,9 +755,9 @@ dependencies = [
 
 [[package]]
 name = "cranelift-srcgen"
-version = "0.130.1"
+version = "0.131.1"
 source = "registry+https://github.com/rust-lang/crates.io-index"
-checksum = "ef53619d3cd5c78fd998c6d9420547af26b72e6456f94c2a8a2334cb76b42baa"
+checksum = "d5a8f82fd5124f009f72167e60139245cd3b56cfd4b53050f22110c48c5f4da1"
 
 [[package]]
 name = "crc"
@@ -871,7 +880,7 @@ checksum = "b0f4697d190a142477b16aef7da8a99bfdc41e7e8b1687583c0d23a79c7afc1e"
 dependencies = [
  "cc",
  "codespan-reporting",
- "indexmap 2.13.0",
+ "indexmap 2.14.0",
  "proc-macro2",
  "quote",
  "scratch",
@@ -886,7 +895,7 @@ checksum = "d0956799fa8678d4c50eed028f2de1c0552ae183c76e976cf7ca8c4e36a7c328"
 dependencies = [
  "clap",
  "codespan-reporting",
- "indexmap 2.13.0",
+ "indexmap 2.14.0",
  "proc-macro2",
  "quote",
  "syn",
@@ -904,7 +913,7 @@ version = "1.0.194"
 source = "registry+https://github.com/rust-lang/crates.io-index"
 checksum = "e6acc6b5822b9526adfb4fc377b67128fdd60aac757cc4a741a6278603f763cf"
 dependencies = [
- "indexmap 2.13.0",
+ "indexmap 2.14.0",
  "proc-macro2",
  "quote",
  "syn",
@@ -1076,7 +1085,7 @@ dependencies = [
  "libc",
  "option-ext",
  "redox_users",
- "windows-sys 0.59.0",
+ "windows-sys 0.60.2",
 ]
 
 [[package]]
@@ -1436,7 +1445,7 @@ checksum = "0bf7f043f89559805f8c7cacc432749b2fa0d0a0a9ee46ce47164ed5ba7f126c"
 dependencies = [
  "fnv",
  "hashbrown 0.16.1",
- "indexmap 2.13.0",
+ "indexmap 2.14.0",
  "stable_deref_trait",
 ]
 
@@ -1579,6 +1588,15 @@ dependencies = [
  "serde_core",
 ]
 
+[[package]]
+name = "hashbrown"
+version = "0.17.1"
+source = "registry+https://github.com/rust-lang/crates.io-index"
+checksum = "ed5909b6e89a2db4456e54cd5f673791d7eca6732202bbf2a9cc504fe2f9b84a"
+dependencies = [
+ "foldhash 0.2.0",
+]
+
 [[package]]
 name = "heck"
 version = "0.4.1"
@@ -1677,7 +1695,7 @@ dependencies = [
  "enum_dispatch",
  "html-escape",
  "hugr-model",
- "indexmap 2.13.0",
+ "indexmap 2.14.0",
  "itertools 0.14.0",
  "ordered-float",
  "pastey",
@@ -1731,7 +1749,7 @@ dependencies = [
  "bumpalo",
  "capnp",
  "derive_more 2.1.1",
- "indexmap 2.13.0",
+ "indexmap 2.14.0",
  "itertools 0.14.0",
  "ordered-float",
  "pest",
@@ -1983,12 +2001,12 @@ dependencies = [
 
 [[package]]
 name = "indexmap"
-version = "2.13.0"
+version = "2.14.0"
 source = "registry+https://github.com/rust-lang/crates.io-index"
-checksum = "7714e70437a7dc3ac8eb7e6f8df75fd8eb422675fc7678aff7364301092b1017"
+checksum = "d466e9454f08e4a911e14806c24e16fba1b4c121d1ea474396f396069cf949d9"
 dependencies = [
  "equivalent",
- "hashbrown 0.16.1",
+ "hashbrown 0.17.1",
  "serde",
  "serde_core",
 ]
@@ -2537,13 +2555,13 @@ dependencies = [
 
 [[package]]
 name = "object"
-version = "0.38.1"
+version = "0.39.1"
 source = "registry+https://github.com/rust-lang/crates.io-index"
-checksum = "271638cd5fa9cca89c4c304675ca658efc4e64a66c716b7cfe1afb4b9611dbbc"
+checksum = "2e5a6c098c7a3b6547378093f5cc30bc54fd361ce711e05293a5cc589562739b"
 dependencies = [
  "crc32fast",
- "hashbrown 0.16.1",
- "indexmap 2.13.0",
+ "hashbrown 0.17.1",
+ "indexmap 2.14.0",
  "memchr",
 ]
 
@@ -2706,6 +2724,8 @@ version = "0.2.0-dev.0"
 dependencies = [
  "anyhow",
  "ndarray 0.17.2",
+ "pecos-random",
+ "rayon",
  "thiserror 2.0.18",
 ]
 
@@ -2727,6 +2747,7 @@ dependencies = [
  "pecos-decoder-core",
  "pecos-decoders",
  "pecos-engines",
+ "pecos-foreign",
  "pecos-hugr",
  "pecos-neo",
  "pecos-num",
@@ -2759,6 +2780,21 @@ dependencies = [
  "serde_json",
 ]
 
+[[package]]
+name = "pecos-foreign"
+version = "0.2.0-dev.0"
+dependencies = [
+ "dirs",
+ "libloading 0.9.0",
+ "log",
+ "ndarray 0.17.2",
+ "pecos-core",
+ "pecos-decoder-core",
+ "pecos-engines",
+ "pecos-random",
+ "pecos-simulators",
+]
+
 [[package]]
 name = "pecos-hugr"
 version = "0.2.0-dev.0"
@@ -2908,12 +2944,14 @@ dependencies = [
  "ndarray 0.17.2",
  "pecos-core",
  "pecos-decoder-core",
+ "pecos-num",
  "pecos-quantum",
  "pecos-random",
  "pecos-simulators",
  "rand 0.10.1",
  "rand_core 0.10.0",
  "rayon",
+ "serde_json",
  "smallvec",
  "thiserror 2.0.18",
  "wide 1.2.0",
@@ -2972,6 +3010,8 @@ dependencies = [
  "num-complex",
  "pecos-core",
  "pecos-num",
+ "pecos-random",
+ "serde_json",
  "smallvec",
  "tket",
 ]
@@ -2990,6 +3030,7 @@ dependencies = [
 name = "pecos-simulators"
 version = "0.2.0-dev.0"
 dependencies = [
+ "nalgebra",
  "num-complex",
  "pecos-core",
  "pecos-quantum",
@@ -3065,7 +3106,7 @@ source = "registry+https://github.com/rust-lang/crates.io-index"
 checksum = "b4c5cc86750666a3ed20bdaf5ca2a0344f9c67674cae0515bec2da16fbaa47db"
 dependencies = [
  "fixedbitset 0.4.2",
- "indexmap 2.13.0",
+ "indexmap 2.14.0",
 ]
 
 [[package]]
@@ -3076,7 +3117,7 @@ checksum = "8701b58ea97060d5e5b155d383a69952a60943f0e6dfe30b04c287beb0b27455"
 dependencies = [
  "fixedbitset 0.5.7",
  "hashbrown 0.15.5",
- "indexmap 2.13.0",
+ "indexmap 2.14.0",
  "serde",
 ]
 
@@ -3199,7 +3240,7 @@ source = "registry+https://github.com/rust-lang/crates.io-index"
 checksum = "93980406f12d9f8140ed5abe7155acb10bb1e69ea55c88960b9c2f117445ef96"
 dependencies = [
  "equivalent",
- "indexmap 2.13.0",
+ "indexmap 2.14.0",
  "serde",
 ]
 
@@ -3236,9 +3277,9 @@ dependencies = [
 
 [[package]]
 name = "pulley-interpreter"
-version = "43.0.1"
+version = "44.0.1"
 source = "registry+https://github.com/rust-lang/crates.io-index"
-checksum = "010dec3755eb61b2f1051ecb3611b718460b7a74c131e474de2af20a845938af"
+checksum = "b9326e3a0093d170582cf64ed9e4cf253b8aac155ec4a294ff62330450bbf094"
 dependencies = [
  "cranelift-bitset",
  "log",
@@ -3248,9 +3289,9 @@ dependencies = [
 
 [[package]]
 name = "pulley-macros"
-version = "43.0.1"
+version = "44.0.1"
 source = "registry+https://github.com/rust-lang/crates.io-index"
-checksum = "ad360c32e85ca4b083ac0e2b6856e8f11c3d5060dafa7d5dc57b370857fa3018"
+checksum = "00c6433917e3789605b1f4cd2a589f637ff17212344e7fa5ba99544625ba52c7"
 dependencies = [
  "proc-macro2",
  "quote",
@@ -3679,6 +3720,12 @@ dependencies = [
  "unicode-ident",
 ]
 
+[[package]]
+name = "rustc-demangle"
+version = "0.1.27"
+source = "registry+https://github.com/rust-lang/crates.io-index"
+checksum = "b50b8869d9fc858ce7266cce0194bd74df58b9d0e3f6df3a9fc8eb470d95c09d"
+
 [[package]]
 name = "rustc-hash"
 version = "2.1.1"
@@ -4037,7 +4084,7 @@ dependencies = [
  "chrono",
  "hex",
  "indexmap 1.9.3",
- "indexmap 2.13.0",
+ "indexmap 2.14.0",
  "schemars 0.9.0",
  "schemars 1.2.1",
  "serde_core",
@@ -4428,7 +4475,7 @@ dependencies = [
  "fxhash",
  "hugr",
  "hugr-core",
- "indexmap 2.13.0",
+ "indexmap 2.14.0",
  "itertools 0.14.0",
  "lazy_static",
  "num-rational",
@@ -4473,7 +4520,7 @@ dependencies = [
  "derive_more 2.1.1",
  "hugr",
  "hugr-core",
- "indexmap 2.13.0",
+ "indexmap 2.14.0",
  "itertools 0.14.0",
  "lazy_static",
  "serde",
@@ -4514,7 +4561,7 @@ version = "1.1.0+spec-1.1.0"
 source = "registry+https://github.com/rust-lang/crates.io-index"
 checksum = "f8195ca05e4eb728f4ba94f3e3291661320af739c4e43779cbdfae82ab239fcc"
 dependencies = [
- "indexmap 2.13.0",
+ "indexmap 2.14.0",
  "serde_core",
  "serde_spanned",
  "toml_datetime",
@@ -4538,7 +4585,7 @@ version = "0.25.8+spec-1.1.0"
 source = "registry+https://github.com/rust-lang/crates.io-index"
 checksum = "16bff38f1d86c47f9ff0647e6838d7bb362522bdf44006c7068c2b1e606f1f3c"
 dependencies = [
- "indexmap 2.13.0",
+ "indexmap 2.14.0",
  "toml_datetime",
  "toml_parser",
  "winnow",
@@ -4881,12 +4928,22 @@ dependencies = [
 
 [[package]]
 name = "wasm-encoder"
-version = "0.245.1"
+version = "0.246.2"
+source = "registry+https://github.com/rust-lang/crates.io-index"
+checksum = "61fb705ce81adde29d2a8e99d87995e39a6e927358c91398f374474746070ef7"
+dependencies = [
+ "leb128fmt",
+ "wasmparser 0.246.2",
+]
+
+[[package]]
+name = "wasm-encoder"
+version = "0.248.0"
 source = "registry+https://github.com/rust-lang/crates.io-index"
-checksum = "3f9dca005e69bf015e45577e415b9af8c67e8ee3c0e38b5b0add5aa92581ed5c"
+checksum = "ac92cf547bc18d27ecc521015c08c353b4f18b84ab388bb6d1b6b682c620d9b6"
 dependencies = [
  "leb128fmt",
- "wasmparser 0.245.1",
+ "wasmparser 0.248.0",
 ]
 
 [[package]]
@@ -4896,7 +4953,7 @@ source = "registry+https://github.com/rust-lang/crates.io-index"
 checksum = "bb0e353e6a2fbdc176932bbaab493762eb1255a7900fe0fea1a2f96c296cc909"
 dependencies = [
  "anyhow",
- "indexmap 2.13.0",
+ "indexmap 2.14.0",
  "wasm-encoder 0.244.0",
  "wasmparser 0.244.0",
 ]
@@ -4909,39 +4966,50 @@ checksum = "47b807c72e1bac69382b3a6fb3dbe8ea4c0ed87ff5629b8685ae6b9a611028fe"
 dependencies = [
  "bitflags",
  "hashbrown 0.15.5",
- "indexmap 2.13.0",
+ "indexmap 2.14.0",
  "semver",
 ]
 
 [[package]]
 name = "wasmparser"
-version = "0.245.1"
+version = "0.246.2"
 source = "registry+https://github.com/rust-lang/crates.io-index"
-checksum = "4f08c9adee0428b7bddf3890fc27e015ac4b761cc608c822667102b8bfd6995e"
+checksum = "71cde4757396defafd25417cfb36aa3161027d06d865b0c24baaae229aac005d"
 dependencies = [
  "bitflags",
  "hashbrown 0.16.1",
- "indexmap 2.13.0",
+ "indexmap 2.14.0",
  "semver",
  "serde",
 ]
 
+[[package]]
+name = "wasmparser"
+version = "0.248.0"
+source = "registry+https://github.com/rust-lang/crates.io-index"
+checksum = "aa4439c5eee9df71ee0c6efb37f63b1fcb1fec38f85f5142c54e7ed05d33091a"
+dependencies = [
+ "bitflags",
+ "indexmap 2.14.0",
+ "semver",
+]
+
 [[package]]
 name = "wasmprinter"
-version = "0.245.1"
+version = "0.246.2"
 source = "registry+https://github.com/rust-lang/crates.io-index"
-checksum = "5f41517a3716fbb8ccf46daa9c1325f760fcbff5168e75c7392288e410b91ac8"
+checksum = "6e41f7493ba994b8a779430a4c25ff550fd5a40d291693af43a6ef48688f00e3"
 dependencies = [
  "anyhow",
  "termcolor",
- "wasmparser 0.245.1",
+ "wasmparser 0.246.2",
 ]
 
 [[package]]
 name = "wasmtime"
-version = "43.0.1"
+version = "44.0.1"
 source = "registry+https://github.com/rust-lang/crates.io-index"
-checksum = "ce205cd643d661b5ba5ba4717e13730262e8cdbc8f2eacbc7b906d45c1a74026"
+checksum = "372db8bbad8ec962038101f75ab2c3ffcd18797d7d3ae877a58ab9873cd0c4bd"
 dependencies = [
  "addr2line",
  "async-trait",
@@ -4962,7 +5030,7 @@ dependencies = [
  "serde_derive",
  "smallvec",
  "target-lexicon",
- "wasmparser 0.245.1",
+ "wasmparser 0.246.2",
  "wasmtime-environ",
  "wasmtime-internal-core",
  "wasmtime-internal-cranelift",
@@ -4977,36 +5045,38 @@ dependencies = [
 
 [[package]]
 name = "wasmtime-environ"
-version = "43.0.1"
+version = "44.0.1"
 source = "registry+https://github.com/rust-lang/crates.io-index"
-checksum = "0b8b78abf3677d4a0a5db82e5015b4d085ff3a1b8b472cbb8c70d4b769f019ce"
+checksum = "1e15aa0d1545e48d9b25ca604e9e27b4cd6d5886d30ac5787b57b3a2daf85b57"
 dependencies = [
  "anyhow",
+ "cpp_demangle",
  "cranelift-bforest",
  "cranelift-bitset",
  "cranelift-entity",
  "gimli",
  "hashbrown 0.16.1",
- "indexmap 2.13.0",
+ "indexmap 2.14.0",
  "log",
  "object",
  "postcard",
+ "rustc-demangle",
  "serde",
  "serde_derive",
  "sha2 0.10.9",
  "smallvec",
  "target-lexicon",
- "wasm-encoder 0.245.1",
- "wasmparser 0.245.1",
+ "wasm-encoder 0.246.2",
+ "wasmparser 0.246.2",
  "wasmprinter",
  "wasmtime-internal-core",
 ]
 
 [[package]]
 name = "wasmtime-internal-core"
-version = "43.0.1"
+version = "44.0.1"
 source = "registry+https://github.com/rust-lang/crates.io-index"
-checksum = "22632b187e1b0716f1b9ac57ad29013bed33175fcb19e10bb6896126f82fac67"
+checksum = "8f2c7fa6523647262bfb4095dbdf4087accefe525813e783f81a0c682f418ce4"
 dependencies = [
  "hashbrown 0.16.1",
  "libm",
@@ -5015,9 +5085,9 @@ dependencies = [
 
 [[package]]
 name = "wasmtime-internal-cranelift"
-version = "43.0.1"
+version = "44.0.1"
 source = "registry+https://github.com/rust-lang/crates.io-index"
-checksum = "8b3ca07b3e0bb3429674b173b5800577719d600774dd81bff58f775c0aaa64ee"
+checksum = "98c032f422e39061dfc43f32190c0a3526b04161ec4867f362958f3fe9d1fe29"
 dependencies = [
  "cfg-if",
  "cranelift-codegen",
@@ -5033,7 +5103,7 @@ dependencies = [
  "smallvec",
  "target-lexicon",
  "thiserror 2.0.18",
- "wasmparser 0.245.1",
+ "wasmparser 0.246.2",
  "wasmtime-environ",
  "wasmtime-internal-core",
  "wasmtime-internal-unwinder",
@@ -5042,9 +5112,9 @@ dependencies = [
 
 [[package]]
 name = "wasmtime-internal-fiber"
-version = "43.0.1"
+version = "44.0.1"
 source = "registry+https://github.com/rust-lang/crates.io-index"
-checksum = "20c8b2c9704eb1f33ead025ec16038277ccb63d0a14c31e99d5b765d7c36da55"
+checksum = "d8dd76d80adf450cc260ba58f23c28030401930b19149695b1d121f7d621e791"
 dependencies = [
  "cc",
  "cfg-if",
@@ -5057,9 +5127,9 @@ dependencies = [
 
 [[package]]
 name = "wasmtime-internal-jit-debug"
-version = "43.0.1"
+version = "44.0.1"
 source = "registry+https://github.com/rust-lang/crates.io-index"
-checksum = "d950310d07391d34369f62c48336ebb14eacbd4d6f772bb5f349c24e838e0664"
+checksum = "ab453cc600b28ee5d3f9495aa6d4cb2c81eda40903e9287296b548fba8b2391d"
 dependencies = [
  "cc",
  "wasmtime-internal-versioned-export-macros",
@@ -5067,9 +5137,9 @@ dependencies = [
 
 [[package]]
 name = "wasmtime-internal-jit-icache-coherence"
-version = "43.0.1"
+version = "44.0.1"
 source = "registry+https://github.com/rust-lang/crates.io-index"
-checksum = "3606662c156962d096be3127b8b8ae8ee2f8be3f896dad29259ff01ddb64abfd"
+checksum = "6a1859e920871515d324fb9757c3e448d6ed1512ca6ccdff14b6e016505d6ada"
 dependencies = [
  "cfg-if",
  "libc",
@@ -5079,9 +5149,9 @@ dependencies = [
 
 [[package]]
 name = "wasmtime-internal-unwinder"
-version = "43.0.1"
+version = "44.0.1"
 source = "registry+https://github.com/rust-lang/crates.io-index"
-checksum = "75eef0747e52dc545b075f64fd0e0cc237ae738e641266b1970e07e2d744bc32"
+checksum = "f1dfe405bd6adb1386d935a30f16a236bd4ef0d3c383e7cbbab98d063c9d9b73"
 dependencies = [
  "cfg-if",
  "cranelift-codegen",
@@ -5092,9 +5162,9 @@ dependencies = [
 
 [[package]]
 name = "wasmtime-internal-versioned-export-macros"
-version = "43.0.1"
+version = "44.0.1"
 source = "registry+https://github.com/rust-lang/crates.io-index"
-checksum = "d8b0a5dab02a8fb527f547855ecc0e05f9fdc3d5bd57b8b080349408f9a6cece"
+checksum = "2a9b9165fc45d42c81edfe3e9cb458e58720594ad5db6553c4079ea041a4a581"
 dependencies = [
  "proc-macro2",
  "quote",
@@ -5103,22 +5173,22 @@ dependencies = [
 
 [[package]]
 name = "wast"
-version = "245.0.1"
+version = "248.0.0"
 source = "registry+https://github.com/rust-lang/crates.io-index"
-checksum = "28cf1149285569120b8ce39db8b465e8a2b55c34cbb586bd977e43e2bc7300bf"
+checksum = "acc54622ed5a5cddafcdf152043f9d4aed54d4a653d686b7dfe874809fca99d7"
 dependencies = [
  "bumpalo",
  "leb128fmt",
  "memchr",
  "unicode-width",
- "wasm-encoder 0.245.1",
+ "wasm-encoder 0.248.0",
 ]
 
 [[package]]
 name = "wat"
-version = "1.245.1"
+version = "1.248.0"
 source = "registry+https://github.com/rust-lang/crates.io-index"
-checksum = "cd48d1679b6858988cb96b154dda0ec5bbb09275b71db46057be37332d5477be"
+checksum = "d75cd9e510603909748e6ebab89f27cd04472c1d9d85a3c88a7a6fc51a1a7934"
 dependencies = [
  "wast",
 ]
@@ -5508,7 +5578,7 @@ checksum = "b7c566e0f4b284dd6561c786d9cb0142da491f46a9fbed79ea69cdad5db17f21"
 dependencies = [
  "anyhow",
  "heck 0.5.0",
- "indexmap 2.13.0",
+ "indexmap 2.14.0",
  "prettyplease",
  "syn",
  "wasm-metadata",
@@ -5539,7 +5609,7 @@ checksum = "9d66ea20e9553b30172b5e831994e35fbde2d165325bec84fc43dbf6f4eb9cb2"
 dependencies = [
  "anyhow",
  "bitflags",
- "indexmap 2.13.0",
+ "indexmap 2.14.0",
  "log",
  "serde",
  "serde_derive",
@@ -5558,7 +5628,7 @@ checksum = "ecc8ac4bc1dc3381b7f59c34f00b67e18f910c2c0f50015669dde7def656a736"
 dependencies = [
  "anyhow",
  "id-arena",
- "indexmap 2.13.0",
+ "indexmap 2.14.0",
  "log",
  "semver",
  "serde",
diff --git a/python/quantum-pecos/tests/docs/rust_crate/Cargo.toml b/python/quantum-pecos/tests/docs/rust_crate/Cargo.toml
index cd448a9ef..847ca2bb2 100644
--- a/python/quantum-pecos/tests/docs/rust_crate/Cargo.toml
+++ b/python/quantum-pecos/tests/docs/rust_crate/Cargo.toml
@@ -17,6 +17,7 @@ pecos-num = { path = "../../../../../crates/pecos-num" }
 pecos-qec = { path = "../../../../../crates/pecos-qec" }
 pecos-decoders = { path = "../../../../../crates/pecos-decoders", features = ["ldpc"] }
 pecos-decoder-core = { path = "../../../../../crates/pecos-decoder-core" }
+pecos-foreign = { path = "../../../../../crates/pecos-foreign" }
 pecos-random = { path = "../../../../../crates/pecos-random" }
 pecos-qasm = { path = "../../../../../crates/pecos-qasm" }
 pecos-programs = { path = "../../../../../crates/pecos-programs" }
diff --git a/python/quantum-pecos/tests/docs/rust_crate/tests/development_foreign_plugins.rs b/python/quantum-pecos/tests/docs/rust_crate/tests/development_foreign_plugins.rs
new file mode 100644
index 000000000..aa983bbc2
--- /dev/null
+++ b/python/quantum-pecos/tests/docs/rust_crate/tests/development_foreign_plugins.rs
@@ -0,0 +1,14 @@
+//! Auto-generated Rust tests from development/foreign-plugins.md
+//! DO NOT EDIT - Generated by scripts/docs/generate_doc_tests.py
+#![allow(unused_imports, unused_variables, unused_mut, unused_assignments, dead_code, non_snake_case)]
+
+
+#[test]
+fn test_development_foreign_plugins_rust_3() {
+    use pecos_foreign::discovery::discover_plugins;
+    let plugins = discover_plugins(); // scans ~/.pecos/plugins/
+    for plugin in &plugins {
+        println!("Loaded: {} (decoder: {}, simulator: {})",
+            plugin.name, plugin.decoder.is_some(), plugin.simulator.is_some());
+    }
+}
diff --git a/python/quantum-pecos/tests/docs/rust_crate/tests/user_guide_circuit_representation.rs b/python/quantum-pecos/tests/docs/rust_crate/tests/user_guide_circuit_representation.rs
index 050209522..4862d6ab2 100644
--- a/python/quantum-pecos/tests/docs/rust_crate/tests/user_guide_circuit_representation.rs
+++ b/python/quantum-pecos/tests/docs/rust_crate/tests/user_guide_circuit_representation.rs
@@ -8,7 +8,7 @@ fn test_user_guide_circuit_representation_rust_1() {
     use pecos::core::{Gate, QubitId};
     use pecos::dag::DAG;
     use pecos::digraph::DiGraph;
-    use pecos::quantum::{Attribute, DagCircuit, TickCircuit};
+    use pecos::quantum::{Attribute, DagCircuit, TickCircuit, TickGateError};
 
 // Fluent builder API
 let mut circuit = DagCircuit::new();
@@ -76,8 +76,9 @@ circuit.h(&[0]).meta("error_rate", Attribute::Float(0.001));
 // Multiple metadata entries
 circuit.cx(&[(0, 1)]).meta("duration_ns", Attribute::Int(50));
 
-// Measurements break the chain but still support metadata
-circuit.mz(&[0]).meta("basis", Attribute::String("Z".into()));
+// Measurements return refs (not &mut Self), so chain separately
+circuit.mz(&[0]);
+circuit.meta("basis", Attribute::String("Z".into()));
 
 }
 
@@ -162,6 +163,7 @@ circuit.tick().mz(&[0, 1]);
 
 println!("Number of ticks: {}", circuit.num_ticks());
 println!("Total gates: {}", circuit.gate_count());
+println!("Gate batches: {}", circuit.gate_batch_count());
 
 }
 
@@ -181,7 +183,9 @@ tick.h(&[0]);
 // tick.cx(&[(0, 1)]);
 
 // Use try_add_gate for fallible operations
-if let Err(e) = tick.try_add_gate(Gate::cx(&[(0, 1)])) {
+if let Err(pecos::quantum::TickGateError::QubitConflict(e)) =
+    tick.try_add_gate(Gate::cx(&[(0, 1)]))
+{
     println!("Conflict on qubits: {:?}", e.conflicting_qubits);
 }
 
diff --git a/python/quantum-pecos/tests/docs/rust_crate/tests/user_guide_fault_catalog.rs b/python/quantum-pecos/tests/docs/rust_crate/tests/user_guide_fault_catalog.rs
new file mode 100644
index 000000000..385fdc037
--- /dev/null
+++ b/python/quantum-pecos/tests/docs/rust_crate/tests/user_guide_fault_catalog.rs
@@ -0,0 +1,114 @@
+//! Auto-generated Rust tests from user-guide/fault-catalog.md
+//! DO NOT EDIT - Generated by scripts/docs/generate_doc_tests.py
+#![allow(unused_imports, unused_variables, unused_mut, unused_assignments, dead_code, non_snake_case)]
+
+
+
+#[test]
+fn test_user_guide_fault_catalog_rust_1() -> Result<(), Box<dyn std::error::Error>> {
+    use pecos_quantum::{Attribute, TickCircuit};
+    use pecos_qec::fault_tolerance::fault_sampler::{
+FaultCatalog, StochasticNoiseParams,
+};
+    let mut circuit = TickCircuit::new();
+    circuit.tick().h(&[0]);
+    circuit.tick().mz(&[0]);
+
+    circuit.set_meta("num_measurements", Attribute::String("1".into()));
+    circuit.set_meta(
+        "detectors",
+        Attribute::String(r#"[{"records":[-1]}]"#.into()),
+    );
+    circuit.set_meta(
+        "observables",
+        Attribute::String(r#"[{"records":[-1]}]"#.into()),
+    );
+
+    // Structural catalog (no noise):
+    let mut catalog = FaultCatalog::from_circuit(&circuit).unwrap();
+
+    // Parameterize:
+    let noise = StochasticNoiseParams {
+        p1: 0.03,
+        p2: 0.0,
+        p_meas: 0.01,
+        p_prep: 0.0,
+    };
+    catalog.with_noise(&noise);
+
+    // Or one-shot convenience:
+    // let catalog = build_fault_catalog(&circuit, &noise).unwrap();
+
+    for loc in &catalog.locations {
+        println!(
+            "tick={} gate={:?} channel={:?} p={} k={}",
+            loc.tick,
+            loc.gate_type,
+            loc.channel,
+            loc.channel_probability,
+            loc.num_alternatives
+        );
+
+        for fault in &loc.faults {
+            println!(
+                "  {:?} dets={:?} obs={:?} tracked={:?} p_alt={}",
+                fault.kind,
+                fault.affected_detectors,
+                fault.affected_observables,
+                fault.affected_tracked_paulis,
+                fault.absolute_probability
+            );
+        }
+    }
+    Ok(())
+}
+
+
+
+#[test]
+fn test_user_guide_fault_catalog_rust_2() -> Result<(), Box<dyn std::error::Error>> {
+    use pecos_quantum::{Attribute, TickCircuit};
+    use pecos_qec::fault_tolerance::fault_sampler::{
+FaultCatalog, StochasticNoiseParams,
+};
+    let mut circuit = TickCircuit::new();
+    circuit.tick().h(&[0]);
+    circuit.tick().mz(&[0]);
+
+    circuit.set_meta("num_measurements", Attribute::String("1".into()));
+    circuit.set_meta(
+        "detectors",
+        Attribute::String(r#"[{"records":[-1]}]"#.into()),
+    );
+    circuit.set_meta(
+        "observables",
+        Attribute::String(r#"[{"records":[-1]}]"#.into()),
+    );
+
+    // Structural catalog (no noise):
+    let mut catalog = FaultCatalog::from_circuit(&circuit).unwrap();
+
+    // Parameterize:
+    let noise = StochasticNoiseParams {
+        p1: 0.03,
+        p2: 0.0,
+        p_meas: 0.01,
+        p_prep: 0.0,
+    };
+    catalog.with_noise(&noise);
+
+    // Or one-shot convenience:
+    // let catalog = build_fault_catalog(&circuit, &noise).unwrap();
+
+    for event in catalog.fault_configurations(2) {
+        println!(
+            "locations={:?} alternatives={:?} dets={:?} obs={:?} p={}",
+            event.location_indices,
+            event.alternative_indices,
+            event.affected_detectors,
+            event.affected_observables,
+            event.configuration_probability
+        );
+    }
+    Ok(())
+}
diff --git a/python/quantum-pecos/tests/docs/rust_crate/tests/user_guide_fault_tolerance.rs b/python/quantum-pecos/tests/docs/rust_crate/tests/user_guide_fault_tolerance.rs
index 442214c2f..2de380d96 100644
--- a/python/quantum-pecos/tests/docs/rust_crate/tests/user_guide_fault_tolerance.rs
+++ b/python/quantum-pecos/tests/docs/rust_crate/tests/user_guide_fault_tolerance.rs
@@ -7,7 +7,8 @@
 
 #[test]
 fn test_user_guide_fault_tolerance_rust_1() {
-    use pecos_core::{PauliString, QuarterPhase, Xs, Zs};
+    use pecos_core::{PauliString, QuarterPhase};
+    use pecos_core::pauli::{Xs, Zs};
     use pecos_qec::{ErrorClass, StabilizerCodeSpec, StabilizerFlipChecker};
     let code = StabilizerCodeSpec::builder(3)
         .check(Zs([0, 1]))
@@ -24,8 +25,7 @@ fn test_user_guide_fault_tolerance_rust_1() {
 
 #[test]
 fn test_user_guide_fault_tolerance_rust_2() {
-    use pecos_core::pauli::constructors::*;
-    use pecos_core::{Xs, Zs};
+    use pecos_core::pauli::*;
     use pecos_qec::{ErrorClass, StabilizerCodeSpec, StabilizerFlipChecker};
     let code = StabilizerCodeSpec::builder(3)
         .check(Zs([0, 1]))
@@ -51,8 +51,7 @@ fn test_user_guide_fault_tolerance_rust_2() {
 
 #[test]
 fn test_user_guide_fault_tolerance_rust_3() -> Result<(), Box<dyn std::error::Error>> {
-    use pecos_core::pauli::constructors::*;
-    use pecos_core::{Xs, Zs};
+    use pecos_core::pauli::*;
     use pecos_qec::{StabilizerCodeSpec, StabilizerFlipChecker};
     let code = StabilizerCodeSpec::builder(3)
         .check(Zs([0, 1])).check(Zs([1, 2]))
@@ -72,7 +71,7 @@ fn test_user_guide_fault_tolerance_rust_3() -> Result<(), Box<dyn std::error::Er
 
 #[test]
 fn test_user_guide_fault_tolerance_rust_4() -> Result<(), Box<dyn std::error::Error>> {
-    use pecos_core::{Xs, Zs};
+    use pecos_core::pauli::{Xs, Zs};
     use pecos_qec::{StabilizerCodeSpec, StabilizerFlipChecker};
     let code = StabilizerCodeSpec::builder(3)
         .check(Zs([0, 1])).check(Zs([1, 2]))
@@ -98,7 +97,7 @@ fn test_user_guide_fault_tolerance_rust_4() -> Result<(), Box<dyn std::error::Er
 
 #[test]
 fn test_user_guide_fault_tolerance_rust_5() {
-    use pecos_core::{Xs, Zs};
+    use pecos_core::pauli::{Xs, Zs};
     use pecos_qec::{StabilizerCodeSpec, StabilizerFlipChecker};
     let code = StabilizerCodeSpec::builder(3)
         .check(Zs([0, 1])).check(Zs([1, 2]))
@@ -196,7 +195,7 @@ fn test_user_guide_fault_tolerance_rust_8() -> Result<(), Box<dyn std::error::Er
 
 // Build DEM from a fault influence map
 let dem = DemBuilder::new(&influence_map)
-    .with_noise(0.01, 0.01, 0.01, 0.01)  // p1, p2, p_meas, p_init
+    .with_noise(0.01, 0.01, 0.01, 0.01)  // p1, p2, p_meas, p_prep
     .with_detectors_json(detectors_json)?
     .with_observables_json(observables_json)?
     .build();
@@ -209,7 +208,7 @@ println!("DEM has {} detectors, {} contributions",
 
 #[test]
 fn test_user_guide_fault_tolerance_rust_9() -> Result<(), Box<dyn std::error::Error>> {
-    use pecos_core::{Xs, Zs};
+    use pecos_core::pauli::{Xs, Zs};
     use pecos_qec::{DemBuilder, DistanceSearchConfig, StabilizerCodeSpec, calculate_distance};
     use pecos_qec::fault_tolerance::propagator::DagFaultAnalyzer;
     use pecos_quantum::DagCircuit;
@@ -259,7 +258,7 @@ let result = calculate_distance(&code, &DistanceSearchConfig::with_max_weight(5)
 
 #[test]
 fn test_user_guide_fault_tolerance_rust_10() -> Result<(), Box<dyn std::error::Error>> {
-    use pecos_core::{Xs, Zs};
+    use pecos_core::pauli::{Xs, Zs};
     use pecos_qec::{DemBuilder, DistanceSearchConfig, StabilizerCodeSpec, find_min_weight_logicals_with_info};
     use pecos_qec::fault_tolerance::propagator::DagFaultAnalyzer;
     use pecos_quantum::DagCircuit;
@@ -302,7 +301,7 @@ for op in &logicals {
 
 #[test]
 fn test_user_guide_fault_tolerance_rust_11() -> Result<(), Box<dyn std::error::Error>> {
-    use pecos_core::pauli::constructors::Zs;
+    use pecos_core::pauli::Zs;
     use pecos_qec::{DemBuilder, discover_logical_operators};
     use pecos_qec::fault_tolerance::propagator::DagFaultAnalyzer;
     use pecos_quantum::DagCircuit;
diff --git a/python/quantum-pecos/tests/docs/rust_crate/tests/user_guide_gate_angle_types.rs b/python/quantum-pecos/tests/docs/rust_crate/tests/user_guide_gate_angle_types.rs
index 0014195f7..2d173e251 100644
--- a/python/quantum-pecos/tests/docs/rust_crate/tests/user_guide_gate_angle_types.rs
+++ b/python/quantum-pecos/tests/docs/rust_crate/tests/user_guide_gate_angle_types.rs
@@ -92,7 +92,7 @@ fn test_user_guide_gate_angle_types_rust_5() {
 #[test]
 fn test_user_guide_gate_angle_types_rust_6() {
     use pecos_core::{phase, phase_turn};
-    use pecos_core::unitary_rep::X;
+    use pecos_core::unitary::X;
     let op = phase!(pi / 4) * X(0);      // e^{i*pi/4} * X
     let op = phase_turn!(1 / 8) * X(0);  // same thing
 }
diff --git a/python/quantum-pecos/tests/docs/rust_crate/tests/user_guide_pecos_concepts.rs b/python/quantum-pecos/tests/docs/rust_crate/tests/user_guide_pecos_concepts.rs
new file mode 100644
index 000000000..1b1038856
--- /dev/null
+++ b/python/quantum-pecos/tests/docs/rust_crate/tests/user_guide_pecos_concepts.rs
@@ -0,0 +1,25 @@
+//! Auto-generated Rust tests from user-guide/pecos-concepts.md
+//! DO NOT EDIT - Generated by scripts/docs/generate_doc_tests.py
+#![allow(unused_imports, unused_variables, unused_mut, unused_assignments, dead_code, non_snake_case)]
+
+
+
+#[test]
+fn test_user_guide_pecos_concepts_rust_1() {
+    use pecos_core::pauli::*;
+    use pecos_core::PauliOperator;
+    let logical_x = X(0) & X(1) & X(2);
+    let z_probe = Z(3);
+
+    assert_eq!(logical_x.weight(), 3);
+    assert!(logical_x.commutes_with(&z_probe));
+}
+
+
+
+#[test]
+fn test_user_guide_pecos_concepts_rust_2() {
+    use pecos_core::{PauliOperator, PauliString};
+    let stabilizer: PauliString = "Z0 Z1 Z4 Z5".parse().unwrap();
+    assert_eq!(stabilizer.weight(), 4);
+}
diff --git a/python/quantum-pecos/tests/docs/rust_crate/tests/user_guide_quantum_operator_algebra.rs b/python/quantum-pecos/tests/docs/rust_crate/tests/user_guide_quantum_operator_algebra.rs
index 66fd6aa5b..ba16ea200 100644
--- a/python/quantum-pecos/tests/docs/rust_crate/tests/user_guide_quantum_operator_algebra.rs
+++ b/python/quantum-pecos/tests/docs/rust_crate/tests/user_guide_quantum_operator_algebra.rs
@@ -7,7 +7,7 @@
 
 #[test]
 fn test_user_guide_quantum_operator_algebra_rust_1() {
-    use pecos_core::pauli::constructors::*;
+    use pecos_core::pauli::*;
     use pecos_core::PauliOperator;
     let p = X(0);          // X on qubit 0
     let q = Z(3);          // Z on qubit 3
@@ -33,7 +33,7 @@ fn test_user_guide_quantum_operator_algebra_rust_1() {
 
 #[test]
 fn test_user_guide_quantum_operator_algebra_rust_2() {
-    use pecos_core::pauli::constructors::*;
+    use pecos_core::pauli::*;
     use pecos_core::pauli::algebra::i;
     let imag = i * X(0);          // iX
     let neg_imag = -i * Y(1);     // -iY
@@ -43,7 +43,7 @@ fn test_user_guide_quantum_operator_algebra_rust_2() {
 
 #[test]
 fn test_user_guide_quantum_operator_algebra_rust_3() {
-    use pecos_core::pauli::constructors::*;
+    use pecos_core::pauli::*;
     use pecos_core::{PauliOperator, QuarterPhase};
     let a = X(0) & Z(1);
     let b = Z(0) & X(1);
@@ -70,9 +70,16 @@ fn test_user_guide_quantum_operator_algebra_rust_3() {
 #[test]
 fn test_user_guide_quantum_operator_algebra_rust_4() {
     use pecos_core::PauliString;
-    let p: PauliString = "XZI".parse().unwrap();    // X(0) & Z(1)
-    let q: PauliString = "+XZZXI".parse().unwrap(); // with explicit phase
-    let r: PauliString = "-iYX".parse().unwrap();   // -i * Y(0) * X(1)
+    let sparse: PauliString = "X0 Z3".parse().unwrap();
+    let dense: PauliString = "XIIZ".parse().unwrap();
+    let explicit_sparse = PauliString::from_sparse_str("X0 Z3").unwrap();
+    let explicit_dense = PauliString::from_dense_str("XIIZ").unwrap();
+
+    assert_eq!(sparse, dense);
+    assert_eq!(sparse, explicit_sparse);
+    assert_eq!(dense, explicit_dense);
+    assert_eq!(sparse.to_sparse_str(), "+X0 Z3");
+    assert_eq!(sparse.to_dense_str(None), "+XIIZ");
 }
 
 
@@ -80,7 +87,7 @@ fn test_user_guide_quantum_operator_algebra_rust_4() {
 
 #[test]
 fn test_user_guide_quantum_operator_algebra_rust_5() {
-    use pecos_core::pauli::constructors::*;
+    use pecos_core::pauli::*;
     use pecos_core::clifford_rep::CliffordRep;
     let h = CliffordRep::h(0);
     assert_eq!(*h.x_image(0), Z(0));  // H X H^dag = Z
@@ -100,7 +107,7 @@ fn test_user_guide_quantum_operator_algebra_rust_5() {
 
 #[test]
 fn test_user_guide_quantum_operator_algebra_rust_6() {
-    use pecos_core::unitary_rep::*;
+    use pecos_core::unitary::*;
     use pecos_core::Angle64;
     let circuit = T(1) * CX(0, 1) * H(0);  // apply H, then CX, then T
 
@@ -123,7 +130,7 @@ fn test_user_guide_quantum_operator_algebra_rust_6() {
 }
 
 
-// Measurement and preparation
+// Measurement, preparation, and reset
 
 #[test]
 fn test_user_guide_quantum_operator_algebra_rust_7() {
@@ -131,25 +138,33 @@ fn test_user_guide_quantum_operator_algebra_rust_7() {
     let mz = MZ(0);           // Z-basis measurement on qubit 0
     let mx = MX(1);           // X-basis measurement on qubit 1
     let pz = PZ(0);           // Prepare |0> on qubit 0
+    let reset = Reset(0);     // Reset to |0>
+    assert!(mz.is_gate());
+}
+
+
+// Noise channels
 
-    // Noise channels
+#[test]
+fn test_user_guide_quantum_operator_algebra_rust_8() {
+    use pecos_core::op::*;
     let depol = Depolarizing(0.01, 0);            // 1% depolarizing on qubit 0
     let deph = Dephasing(0.02, 1);                // 2% dephasing on qubit 1
     let amp_damp = AmplitudeDamping(0.05, 0);     // T1 decay
     let phase_damp = PhaseDamping(0.03, 0);       // T2 dephasing
     let erasure = Erasure(0.01, 0);               // Erasure channel
-    let reset = Reset(0);                         // Reset to |0>
     let leak = Leakage(0.001, 0);                 // Leakage to non-computational state
 
     // Custom Pauli channel
     let pauli_ch = PauliChannel(0.01, 0.01, 0.01, 0);  // px, py, pz
+    assert!(depol.is_channel());
 }
 
 
 // Pauli & Pauli stays Pauli
 
 #[test]
-fn test_user_guide_quantum_operator_algebra_rust_8() {
+fn test_user_guide_quantum_operator_algebra_rust_9() {
     use pecos_core::op::*;
     let p = X(0) & Y(3);
     assert!(p.is_pauli());
@@ -162,15 +177,19 @@ fn test_user_guide_quantum_operator_algebra_rust_8() {
     let u = X(0) & H(3) & T(5);
     assert!(u.is_unitary());
 
-    // Adding a measurement promotes to Channel
-    let ch = H(0) & MZ(1);
+    // Adding a measurement promotes to Gate
+    let g = H(0) & MZ(1);
+    assert!(g.is_gate());
+
+    // Adding noise promotes to Channel
+    let ch = g & Depolarizing(0.01, 2);
     assert!(ch.is_channel());
 }
 
 
 
 #[test]
-fn test_user_guide_quantum_operator_algebra_rust_9() {
+fn test_user_guide_quantum_operator_algebra_rust_10() {
     use pecos_core::op::*;
     let p = X(0) & Z(1);
     let ps = p.as_pauli().unwrap();  // borrow the inner PauliString
@@ -188,7 +207,7 @@ fn test_user_guide_quantum_operator_algebra_rust_9() {
 
 
 #[test]
-fn test_user_guide_quantum_operator_algebra_rust_10() {
+fn test_user_guide_quantum_operator_algebra_rust_11() {
     use pecos_core::op::*;
     let circuit = T(1) * CX(0, 1) * H(0);
     let inverse = circuit.dg();  // works for Pauli, Clifford, Unitary
@@ -201,18 +220,18 @@ fn test_user_guide_quantum_operator_algebra_rust_10() {
 
 
 #[test]
-fn test_user_guide_quantum_operator_algebra_rust_11() {
+fn test_user_guide_quantum_operator_algebra_rust_12() {
     use pecos_core::op::*;
     let circuit = CX(0, 3) & H(5);
-    assert_eq!(circuit.num_qubits(), 6);     // spans qubits 0..5
-    assert_eq!(circuit.qubits(), vec![0, 1, 2, 3, 4, 5]);  // full range
+    assert_eq!(circuit.num_qubits(), 6);     // matrix span is qubits 0..5
+    assert_eq!(circuit.qubits(), vec![0, 3, 5]);  // actual support
 }
 
 
 
 #[test]
-fn test_user_guide_quantum_operator_algebra_rust_12() {
-    use pecos_core::pauli::constructors::*;
+fn test_user_guide_quantum_operator_algebra_rust_13() {
+    use pecos_core::pauli::*;
     use pecos_quantum::PauliSequence;
     let seq = PauliSequence::new(vec![
         Zs([0, 1]),
@@ -238,8 +257,8 @@ fn test_user_guide_quantum_operator_algebra_rust_12() {
 
 
 #[test]
-fn test_user_guide_quantum_operator_algebra_rust_13() {
-    use pecos_core::pauli::constructors::*;
+fn test_user_guide_quantum_operator_algebra_rust_14() {
+    use pecos_core::pauli::*;
     use pecos_quantum::PauliSet;
     let mut set = PauliSet::new();
     set.insert(&X(0));
@@ -259,8 +278,8 @@ fn test_user_guide_quantum_operator_algebra_rust_13() {
 // Generators with imaginary phase
 
 #[test]
-fn test_user_guide_quantum_operator_algebra_rust_14() {
-    use pecos_core::pauli::constructors::*;
+fn test_user_guide_quantum_operator_algebra_rust_15() {
+    use pecos_core::pauli::*;
     use pecos_core::pauli::algebra::i;
     use pecos_quantum::PauliGroup;
     let group = PauliGroup::new(vec![
@@ -280,8 +299,8 @@ fn test_user_guide_quantum_operator_algebra_rust_14() {
 // Repetition code stabilizers
 
 #[test]
-fn test_user_guide_quantum_operator_algebra_rust_15() -> Result<(), Box<dyn std::error::Error>> {
-    use pecos_core::pauli::constructors::*;
+fn test_user_guide_quantum_operator_algebra_rust_16() -> Result<(), Box<dyn std::error::Error>> {
+    use pecos_core::pauli::*;
     use pecos_core::clifford_rep::CliffordRep;
     use pecos_quantum::PauliStabilizerGroup;
     let stab = PauliStabilizerGroup::new(vec![
@@ -309,8 +328,8 @@ fn test_user_guide_quantum_operator_algebra_rust_15() -> Result<(), Box<dyn std:
 // Upward (widening) -- always succeeds
 
 #[test]
-fn test_user_guide_quantum_operator_algebra_rust_16() {
-    use pecos_core::pauli::constructors::*;
+fn test_user_guide_quantum_operator_algebra_rust_17() {
+    use pecos_core::pauli::*;
     use pecos_quantum::{PauliGroup, PauliSequence, PauliSet, PauliStabilizerGroup};
     let stab = PauliStabilizerGroup::new(vec![Zs([0, 1])]).unwrap();
     let group: PauliGroup = stab.clone().into();        // drop phase constraint
@@ -332,8 +351,8 @@ fn test_user_guide_quantum_operator_algebra_rust_16() {
 // Build a stabilizer group
 
 #[test]
-fn test_user_guide_quantum_operator_algebra_rust_17() {
-    use pecos_core::pauli::constructors::*;
+fn test_user_guide_quantum_operator_algebra_rust_18() {
+    use pecos_core::pauli::*;
     use pecos_qec::StabilizerCode;
     use pecos_quantum::PauliStabilizerGroup;
     let group = PauliStabilizerGroup::new(vec![
diff --git a/python/quantum-pecos/tests/docs/rust_crate/tests/user_guide_stabilizer_codes.rs b/python/quantum-pecos/tests/docs/rust_crate/tests/user_guide_stabilizer_codes.rs
index ace8e0fdb..4ff540231 100644
--- a/python/quantum-pecos/tests/docs/rust_crate/tests/user_guide_stabilizer_codes.rs
+++ b/python/quantum-pecos/tests/docs/rust_crate/tests/user_guide_stabilizer_codes.rs
@@ -5,7 +5,7 @@
 
 #[test]
 fn test_user_guide_stabilizer_codes_rust_1() {
-    use pecos_core::pauli::constructors::*;
+    use pecos_core::pauli::*;
     use pecos_core::PauliOperator;
 
 // Single-qubit Paulis
@@ -31,7 +31,7 @@ assert!(!X(0).commutes_with(&Z(0)));
 
 #[test]
 fn test_user_guide_stabilizer_codes_rust_2() {
-    use pecos_core::pauli::constructors::*;
+    use pecos_core::pauli::*;
     use pecos_core::PauliOperator;
     use pecos_qec::StabilizerCode;
 
@@ -51,7 +51,7 @@ let code = StabilizerCode::repetition(3);
 
 #[test]
 fn test_user_guide_stabilizer_codes_rust_3() {
-    use pecos_core::pauli::constructors::*;
+    use pecos_core::pauli::*;
     use pecos_core::PauliOperator;
     use pecos_qec::StabilizerCode;
 
@@ -66,7 +66,7 @@ println!("{}", code.code_parameters());           // [[7, 1]]
 
 #[test]
 fn test_user_guide_stabilizer_codes_rust_4() {
-    use pecos_core::pauli::constructors::*;
+    use pecos_core::pauli::*;
     use pecos_core::PauliOperator;
     use pecos_qec::StabilizerCode;
 
@@ -84,7 +84,7 @@ for (i, op) in logicals.iter().enumerate() {
 
 #[test]
 fn test_user_guide_stabilizer_codes_rust_5() {
-    use pecos_core::pauli::constructors::*;
+    use pecos_core::pauli::*;
     use pecos_core::PauliOperator;
     use pecos_qec::StabilizerCode;
 
@@ -103,7 +103,7 @@ assert_eq!(trivial.distance(), Some(1));
 
 #[test]
 fn test_user_guide_stabilizer_codes_rust_6() {
-    use pecos_core::pauli::constructors::*;
+    use pecos_core::pauli::*;
     use pecos_core::PauliOperator;
     use pecos_qec::StabilizerCode;
 
@@ -122,7 +122,7 @@ assert_eq!(code.syndrome(&Z(0)), vec![false, false]);
 
 #[test]
 fn test_user_guide_stabilizer_codes_rust_7() {
-    use pecos_core::pauli::constructors::*;
+    use pecos_core::pauli::*;
     use pecos_core::PauliOperator;
     use pecos_qec::StabilizerCode;
 
@@ -135,7 +135,7 @@ assert_eq!(toric.distance(), Some(2));
 
 #[test]
 fn test_user_guide_stabilizer_codes_rust_8() {
-    use pecos_core::pauli::constructors::*;
+    use pecos_core::pauli::*;
     use pecos_core::PauliOperator;
     use pecos_qec::StabilizerCode;
     use pecos_quantum::PauliStabilizerGroup;
@@ -154,8 +154,8 @@ assert_eq!(code.num_logical_qubits(), 3);
 
 #[test]
 fn test_user_guide_stabilizer_codes_rust_9() {
-    use pecos_core::pauli::constructors::*;
-    use pecos_core::{PauliOperator, Xs, Zs};
+    use pecos_core::pauli::*;
+    use pecos_core::PauliOperator;
     use pecos_qec::StabilizerCodeSpec;
 
 // Build a 3-qubit bit-flip code with explicit logicals
@@ -177,7 +177,7 @@ assert_eq!(code.num_logical_qubits(), 1);
 
 #[test]
 fn test_user_guide_stabilizer_codes_rust_10() {
-    use pecos_core::pauli::constructors::*;
+    use pecos_core::pauli::*;
     use pecos_core::PauliOperator;
     use pecos_qec::{StabilizerCode, StabilizerCodeSpec};
 
@@ -195,8 +195,8 @@ spec.verify().unwrap();
 
 #[test]
 fn test_user_guide_stabilizer_codes_rust_11() {
-    use pecos_core::pauli::constructors::*;
-    use pecos_core::{PauliOperator, Xs, Zs};
+    use pecos_core::pauli::*;
+    use pecos_core::PauliOperator;
     use pecos_qec::{StabilizerCodeSpec, StabilizerFlipChecker};
 
 let code = StabilizerCodeSpec::builder(7)
diff --git a/python/quantum-pecos/tests/pecos/integration/state_sim_tests/test_cuda_simulators.py b/python/quantum-pecos/tests/pecos/integration/state_sim_tests/test_cuda_simulators.py
index 3cf7a5c48..e5b118e4f 100644
--- a/python/quantum-pecos/tests/pecos/integration/state_sim_tests/test_cuda_simulators.py
+++ b/python/quantum-pecos/tests/pecos/integration/state_sim_tests/test_cuda_simulators.py
@@ -23,13 +23,28 @@
 
 import pytest
 
-# Check if CUDA simulators are available
+# Check if CUDA simulator libraries and runtime-backed simulators are available.
 try:
-    from pecos_rslib_cuda import is_cuquantum_available
+    from pecos_rslib_cuda import (
+        is_cudensitymat_usable,
+        is_cuquantum_available,
+        is_custabilizer_usable,
+        is_custatevec_usable,
+        is_cutensornet_usable,
+    )
 
     CUQUANTUM_AVAILABLE = is_cuquantum_available()
 except ImportError:
     CUQUANTUM_AVAILABLE = False
+    CUSTATEVEC_USABLE = False
+    CUSTABILIZER_USABLE = False
+    CUTENSORNET_USABLE = False
+    CUDENSITYMAT_USABLE = False
+else:
+    CUSTATEVEC_USABLE = is_custatevec_usable()
+    CUSTABILIZER_USABLE = is_custabilizer_usable()
+    CUTENSORNET_USABLE = is_cutensornet_usable()
+    CUDENSITYMAT_USABLE = is_cudensitymat_usable()
 
 # Skip all tests in this module if cuQuantum is not available
 pytestmark = pytest.mark.skipif(
@@ -41,6 +56,11 @@
 class TestCudaStateVec:
     """Tests for CudaStateVec (Rust cuQuantum state vector simulator)."""
 
+    pytestmark = pytest.mark.skipif(
+        not CUSTATEVEC_USABLE,
+        reason="CudaStateVec runtime is not usable on this machine",
+    )
+
     def test_import(self) -> None:
         """Test that CudaStateVec can be imported."""
         from pecos.simulators import CudaStateVec
@@ -172,6 +192,11 @@ def test_run_gate_interface(self) -> None:
 class TestCudaStabilizer:
     """Tests for CudaStabilizer (Rust cuQuantum stabilizer simulator)."""
 
+    pytestmark = pytest.mark.skipif(
+        not CUSTABILIZER_USABLE,
+        reason="CudaStabilizer runtime is not usable on this machine",
+    )
+
     def test_import(self) -> None:
         """Test that CudaStabilizer can be imported."""
         from pecos.simulators import CudaStabilizer
@@ -275,6 +300,11 @@ def test_surface_code_syndrome(self) -> None:
 class TestCuTensorNet:
     """Tests for CuTensorNet handle."""
 
+    pytestmark = pytest.mark.skipif(
+        not CUTENSORNET_USABLE,
+        reason="CuTensorNet runtime is not usable on this machine",
+    )
+
     def test_import(self) -> None:
         """Test that CuTensorNet can be imported from pecos_rslib_cuda."""
         from pecos_rslib_cuda import CuTensorNet
@@ -300,6 +330,11 @@ def test_version(self) -> None:
 class TestCuDensityMat:
     """Tests for CuDensityMat density matrix simulator."""
 
+    pytestmark = pytest.mark.skipif(
+        not CUDENSITYMAT_USABLE,
+        reason="CuDensityMat runtime is not usable on this machine",
+    )
+
     def test_import(self) -> None:
         """Test that CuDensityMat can be imported from pecos_rslib_cuda."""
         from pecos_rslib_cuda import CuDensityMat
@@ -337,6 +372,10 @@ def test_small_qubit_count(self) -> None:
 class TestQuantumSimulatorBackend:
     """Tests for QuantumSimulator with CUDA backends."""
 
+    @pytest.mark.skipif(
+        not CUSTATEVEC_USABLE,
+        reason="CudaStateVec runtime is not usable on this machine",
+    )
     def test_cuda_statevec_backend(self) -> None:
         """Test QuantumSimulator with CudaStateVec backend."""
         from pecos.simulators.quantum_simulator import QuantumSimulator
@@ -346,6 +385,10 @@ def test_cuda_statevec_backend(self) -> None:
 
         assert sim.num_qubits == 4
 
+    @pytest.mark.skipif(
+        not CUSTABILIZER_USABLE,
+        reason="CudaStabilizer runtime is not usable on this machine",
+    )
     def test_cuda_stabilizer_backend(self) -> None:
         """Test QuantumSimulator with CudaStabilizer backend."""
         from pecos.simulators.quantum_simulator import QuantumSimulator
diff --git a/python/quantum-pecos/tests/pecos/integration/state_sim_tests/test_statevec.py b/python/quantum-pecos/tests/pecos/integration/state_sim_tests/test_statevec.py
index e46385da5..fe2cb5641 100644
--- a/python/quantum-pecos/tests/pecos/integration/state_sim_tests/test_statevec.py
+++ b/python/quantum-pecos/tests/pecos/integration/state_sim_tests/test_statevec.py
@@ -430,7 +430,7 @@ def test_hybrid_engine_noisy(simulator: str) -> None:
             "p1": 2e-1,
             "p2": 2e-1,
             "p_meas": 2e-1,
-            "p_init": 1e-1,
+            "p_prep": 1e-1,
             "p1_error_model": {
                 "X": 0.25,
                 "Y": 0.25,
diff --git a/python/quantum-pecos/tests/pecos/integration/test_backend_seed_determinism.py b/python/quantum-pecos/tests/pecos/integration/test_backend_seed_determinism.py
index 0c1a2f5ec..7cb51baf2 100644
--- a/python/quantum-pecos/tests/pecos/integration/test_backend_seed_determinism.py
+++ b/python/quantum-pecos/tests/pecos/integration/test_backend_seed_determinism.py
@@ -108,7 +108,7 @@
         "p1": 2e-1,
         "p2": 2e-1,
         "p_meas": 2e-1,
-        "p_init": 1e-1,
+        "p_prep": 1e-1,
         "p1_error_model": {
             "X": 0.25,
             "Y": 0.25,
diff --git a/python/quantum-pecos/tests/pecos/integration/test_hybrid_engine_old_error_model.py b/python/quantum-pecos/tests/pecos/integration/test_hybrid_engine_old_error_model.py
index 942f5afc7..aa91761fb 100644
--- a/python/quantum-pecos/tests/pecos/integration/test_hybrid_engine_old_error_model.py
+++ b/python/quantum-pecos/tests/pecos/integration/test_hybrid_engine_old_error_model.py
@@ -18,7 +18,7 @@ def test_simple_conditional() -> None:
     error_params = {
         "p1": 0.01,
         "p2": 0.01,
-        "p_init": 0.01,
+        "p_prep": 0.01,
         "p_meas": 0.01,
         "p2_mem": 0.01,
     }
diff --git a/python/quantum-pecos/tests/pecos/integration/test_phir.py b/python/quantum-pecos/tests/pecos/integration/test_phir.py
index a3e21fb61..467872450 100644
--- a/python/quantum-pecos/tests/pecos/integration/test_phir.py
+++ b/python/quantum-pecos/tests/pecos/integration/test_phir.py
@@ -16,9 +16,6 @@
 
 import pytest
 from pecos import WasmForeignObject
-from pecos.classical_interpreters.phir_classical_interpreter import (
-    PhirClassicalInterpreter,
-)
 from pecos.engines.hybrid_engine import HybridEngine
 from pecos.noise.generic_error_model import GenericErrorModel
 from phir.model import PHIRModel
@@ -60,7 +57,7 @@ def test_spec_example_noisy_wasmtime() -> None:
             "p1": 2e-1,
             "p2": 2e-1,
             "p_meas": 2e-1,
-            "p_init": 1e-1,
+            "p_prep": 1e-1,
             "p1_error_model": {
                 "X": 0.25,
                 "Y": 0.25,
@@ -95,7 +92,7 @@ def test_example1_noisy_wasmtime() -> None:
             "p1": 2e-1,
             "p2": 2e-1,
             "p_meas": 2e-1,
-            "p_init": 1e-1,
+            "p_prep": 1e-1,
             "p1_error_model": {
                 "X": 0.25,
                 "Y": 0.25,
@@ -129,7 +126,7 @@ def test_example1_no_wasm_noisy() -> None:
             "p1": 2e-1,
             "p2": 2e-1,
             "p_meas": 2e-1,
-            "p_init": 1e-1,
+            "p_prep": 1e-1,
             "p1_error_model": {
                 "X": 0.25,
                 "Y": 0.25,
@@ -211,11 +208,7 @@ def test_bell_qparallel_cliff() -> None:
     Tests that a program creating and measuring a Bell state using qparallel blocks returns expected results
     with Clifford circuits and stabilizer simulator.
     """
-    # Create an interpreter with validation disabled for testing Result instruction
-    interp = PhirClassicalInterpreter()
-    interp.phir_validate = False
-
-    results = HybridEngine(qsim="stabilizer", cinterp=interp).run(
+    results = HybridEngine(qsim="stabilizer").run(
         program=json.load(
             Path.open(this_dir / "phir" / "bell_qparallel_cliff.phir.json"),
         ),
@@ -235,10 +228,7 @@ def test_bell_qparallel_cliff_barrier() -> None:
     Tests that a program creating and measuring a Bell state using qparallel blocks and barriers returns expected
     results with Clifford circuits and stabilizer simulator.
     """
-    interp = PhirClassicalInterpreter()
-    interp.phir_validate = False
-
-    results = HybridEngine(qsim="stabilizer", cinterp=interp).run(
+    results = HybridEngine(qsim="stabilizer").run(
         program=json.load(
             Path.open(this_dir / "phir" / "bell_qparallel_cliff_barrier.phir.json"),
         ),
@@ -258,10 +248,7 @@ def test_bell_qparallel_cliff_ifbarrier() -> None:
     Tests that a program creating and measuring a Bell state using qparallel blocks and conditional barriers
     returns expected results with Clifford circuits and stabilizer simulator.
     """
-    interp = PhirClassicalInterpreter()
-    interp.phir_validate = False
-
-    results = HybridEngine(qsim="stabilizer", cinterp=interp).run(
+    results = HybridEngine(qsim="stabilizer").run(
         program=json.load(
             Path.open(this_dir / "phir" / "bell_qparallel_cliff_ifbarrier.phir.json"),
         ),
diff --git a/python/quantum-pecos/tests/pecos/integration/test_phir_dep.py b/python/quantum-pecos/tests/pecos/integration/test_phir_dep.py
index 5ed34b167..f6412b1ed 100644
--- a/python/quantum-pecos/tests/pecos/integration/test_phir_dep.py
+++ b/python/quantum-pecos/tests/pecos/integration/test_phir_dep.py
@@ -14,6 +14,7 @@
 import json
 from pathlib import Path
 
+import pytest
 from pecos.typing import PhirModel
 
 this_dir = Path(__file__).parent
@@ -25,3 +26,97 @@ def test_spec_example() -> None:
     data = json.load(Path.open(this_dir / "phir/spec_example.phir.json"))
 
     PhirModel.model_validate(data)
+
+
+def test_pecos_result_cop_top_level() -> None:
+    """PECOS Result cop validates at the top level of a PHIR program.
+
+    The upstream ``phir.model.PHIRModel`` rejects Result because it is a
+    PECOS extension, not part of the spec. ``pecos.typing.PhirModel``
+    subclasses the upstream model to add Result support.
+    """
+    data = {
+        "format": "PHIR/JSON",
+        "version": "0.1.0",
+        "ops": [
+            {"data": "cvar_define", "data_type": "u32", "variable": "m", "size": 1},
+            {"data": "cvar_define", "data_type": "u32", "variable": "c", "size": 1},
+            {"cop": "Result", "args": ["m"], "returns": ["c"]},
+        ],
+    }
+
+    PhirModel.model_validate(data)
+
+
+def test_pecos_result_cop_inside_seqblock() -> None:
+    """Result cop validates when nested inside a SeqBlock."""
+    data = {
+        "format": "PHIR/JSON",
+        "version": "0.1.0",
+        "ops": [
+            {"data": "cvar_define", "data_type": "u32", "variable": "m", "size": 1},
+            {"data": "cvar_define", "data_type": "u32", "variable": "c", "size": 1},
+            {
+                "block": "sequence",
+                "ops": [{"cop": "Result", "args": ["m"], "returns": ["c"]}],
+            },
+        ],
+    }
+
+    PhirModel.model_validate(data)
+
+
+@pytest.mark.parametrize(
+    ("dtype", "size"),
+    [
+        ("i8", 8),
+        ("u8", 8),
+        ("i16", 16),
+        ("u16", 16),
+        ("i32", 32),
+        ("u32", 32),
+        ("i64", 64),
+        ("u64", 64),
+    ],
+)
+def test_pecos_cvar_define_small_dtypes(dtype: str, size: int) -> None:
+    """PECOS extends CVarDefine to support 8-bit and 16-bit integer dtypes.
+
+    The upstream ``phir.model.CVarDefine`` only permits ``i32``, ``i64``,
+    ``u32``, ``u64``. PECOS programs use 8/16-bit dtypes too.
+    """
+    data = {
+        "format": "PHIR/JSON",
+        "version": "0.1.0",
+        "ops": [{"data": "cvar_define", "data_type": dtype, "variable": "v", "size": size}],
+    }
+
+    PhirModel.model_validate(data)
+
+
+def test_cvar_define_size_exceeding_dtype_rejected() -> None:
+    """Extension remains strict: size must fit in the declared dtype."""
+    from pydantic import ValidationError
+
+    for dtype, bad_size in [("i8", 16), ("u8", 9), ("i16", 32), ("u16", 17)]:
+        data = {
+            "format": "PHIR/JSON",
+            "version": "0.1.0",
+            "ops": [{"data": "cvar_define", "data_type": dtype, "variable": "v", "size": bad_size}],
+        }
+        with pytest.raises(ValidationError):
+            PhirModel.model_validate(data)
+
+
+def test_malformed_result_cop_still_rejected() -> None:
+    """Extension remains strict: Result cop missing required fields is rejected."""
+    from pydantic import ValidationError
+
+    data = {
+        "format": "PHIR/JSON",
+        "version": "0.1.0",
+        "ops": [{"cop": "Result"}],  # missing args and returns
+    }
+
+    with pytest.raises(ValidationError):
+        PhirModel.model_validate(data)
diff --git a/python/quantum-pecos/tests/pecos/test_pauli_string_bindings.py b/python/quantum-pecos/tests/pecos/test_pauli_string_bindings.py
new file mode 100644
index 000000000..c0ba3beb5
--- /dev/null
+++ b/python/quantum-pecos/tests/pecos/test_pauli_string_bindings.py
@@ -0,0 +1,153 @@
+# Copyright 2026 The PECOS Developers
+#
+# Licensed under the Apache License, Version 2.0
+
+import pytest
+from pecos_rslib import H, Pauli, PauliString, X, Y, Z
+
+
+def test_pauli_string_from_str_accepts_dense_and_sparse_formats() -> None:
+    expected = X(0) & X(1) & Z(3)
+
+    assert PauliString.from_str("XXIZ") == expected
+    assert PauliString.from_str("X0 X1 Z3") == expected
+    assert PauliString.from_str("X 0 X 1 Z 3") == expected
+
+
+def test_pauli_string_common_representations_are_interchangeable_and_hash_equal() -> None:
+    from_constructors = X(0) & Y(2) & Z(5)
+    from_class_constructors = PauliString.X(0) & PauliString.Y(2) & PauliString.Z(5)
+    from_sparse = PauliString.from_str("X0 Y2 Z5")
+    from_explicit_sparse = PauliString.from_sparse_str("X0 Y2 Z5")
+    from_dense = PauliString.from_str("XIYIIZ")
+    from_explicit_dense = PauliString.from_dense_str("XIYIIZ")
+    from_tuples = PauliString([(Pauli.Z, 5), (Pauli.X, 0), (Pauli.Y, 2)])
+
+    forms = [
+        from_constructors,
+        from_class_constructors,
+        from_sparse,
+        from_explicit_sparse,
+        from_dense,
+        from_explicit_dense,
+        from_tuples,
+    ]
+    assert all(form == from_constructors for form in forms)
+    assert len({hash(form) for form in forms}) == 1
+    assert {form: idx for idx, form in enumerate(forms)} == {from_constructors: len(forms) - 1}
+
+
+def test_pauli_string_tensor_result_is_pauli_string() -> None:
+    tensor = X(0) & Y(3)
+
+    assert isinstance(tensor, PauliString)
+    assert tensor.get_paulis() == [(Pauli.X, 0), (Pauli.Y, 3)]
+
+
+def test_pauli_string_tensor_equality_hash_and_text_forms_match() -> None:
+    tensor = X(0) & Y(3)
+    same_sparse = PauliString.from_sparse_str("X0 Y3")
+    same_dense = PauliString.from_dense_str("XIIY")
+    same_from_tuples = PauliString([(Pauli.Y, 3), (Pauli.X, 0)])
+
+    assert tensor == same_sparse == same_dense == same_from_tuples
+    assert len({tensor, same_sparse, same_dense, same_from_tuples}) == 1
+    assert tensor.to_sparse_str() == "+X0 Y3"
+    assert tensor.to_dense_str() == "+XIIY"
+
+
+def test_pauli_string_explicit_from_dense_and_sparse_formats() -> None:
+    expected = X(0) & Z(3)
+
+    assert PauliString.from_dense_str("XIIZ") == expected
+    assert PauliString.from_sparse_str("X0 Z3") == expected
+
+
+def test_pauli_string_from_str_sparse_keeps_phase_and_high_qubits() -> None:
+    pauli = PauliString.from_str("-i X2 Z10000")
+
+    assert pauli.get_phase() == 3
+    assert pauli.get_paulis() == [(Pauli.X, 2), (Pauli.Z, 10000)]
+    assert pauli.weight() == 2
+
+
+def test_pauli_string_dense_and_sparse_round_trips() -> None:
+    pauli = PauliString.from_sparse_str("-i X2 Z4")
+
+    assert pauli.to_sparse_str() == "-iX2 Z4"
+    assert pauli.to_dense_str() == "-iIIXIZ"
+    assert pauli.to_dense_str(num_qubits=7) == "-iIIXIZII"
+    assert PauliString.from_sparse_str(pauli.to_sparse_str()) == pauli
+    assert PauliString.from_dense_str(pauli.to_dense_str()) == pauli
+
+
+def test_pauli_string_tuple_constructor_canonicalizes_for_hashing() -> None:
+    sorted_pauli = PauliString([(Pauli.X, 0), (Pauli.Y, 3)])
+    unsorted_pauli = PauliString([(Pauli.Y, 3), (Pauli.X, 0)])
+    constructed = X(0) & PauliString.Y(3)
+
+    assert sorted_pauli == unsorted_pauli == constructed
+    assert hash(sorted_pauli) == hash(unsorted_pauli) == hash(constructed)
+    assert {sorted_pauli: "first", unsorted_pauli: "second"} == {constructed: "second"}
+
+
+def test_pauli_string_tuple_constructor_rejects_duplicate_qubits() -> None:
+    with pytest.raises(ValueError, match="multiple non-identity"):
+        PauliString([(Pauli.X, 0), (Pauli.Z, 0)])
+
+    assert PauliString([(Pauli.I, 0), (Pauli.X, 0)]) == X(0)
+
+
+def test_pauli_string_tensor_rejects_overlapping_qubits() -> None:
+    with pytest.raises(ValueError, match=r"overlapping qubits: \[0\]"):
+        _ = X(0) & Y(0)
+
+    with pytest.raises(ValueError, match="tensor product requires disjoint Pauli support"):
+        _ = X(0) & Z(0)
+
+    with pytest.raises(ValueError, match=r"overlapping qubits: \[2\]"):
+        _ = (X(0) & Y(2)) & Z(2)
+
+
+def test_pauli_string_tensor_rejects_non_pauli_operands_explicitly() -> None:
+    with pytest.raises(TypeError):
+        _ = X(0) & H(1)
+
+    with pytest.raises(TypeError):
+        _ = H(0) & H(1)
+
+
+def test_pauli_string_composition_allows_same_qubit() -> None:
+    composed = X(0) * Z(0)
+
+    assert composed.get_paulis() == [(Pauli.Y, 0)]
+    assert composed.get_phase() == 3
+
+
+def test_pauli_string_tensor_result_is_hashable() -> None:
+    tensor = X(0) & Y(3)
+
+    assert {tensor: "xy"}[PauliString.from_sparse_str("X0 Y3")] == "xy"
+
+
+def test_pauli_string_tensor_preserves_phase_through_string_roundtrip() -> None:
+    tensor = -X(0) & Z(1)
+
+    assert tensor.get_phase() == 2
+    assert tensor.to_sparse_str() == "-X0 Z1"
+    assert tensor.to_dense_str() == "-XZ"
+    assert PauliString.from_sparse_str(tensor.to_sparse_str()) == tensor
+    assert PauliString.from_dense_str(tensor.to_dense_str()) == tensor
+
+
+def test_quantum_namespace_exports_pauli_constructors() -> None:
+    import pecos.quantum as quantum
+    from pecos.quantum import pauli_string
+
+    expected = X(0) & Z(3)
+
+    assert quantum.X(0) & quantum.Z(3) == expected
+    assert pauli_string("X0 Z3") == expected
+    assert pauli_string("XIIZ") == expected
+    assert pauli_string(((quantum.Pauli.X, 0), (quantum.Pauli.Z, 3))) == expected
+    assert pauli_string({0: quantum.Pauli.X, 3: quantum.Pauli.Z}) == expected
diff --git a/python/quantum-pecos/tests/pecos/test_quantum_info_bindings.py b/python/quantum-pecos/tests/pecos/test_quantum_info_bindings.py
new file mode 100644
index 000000000..1ef48572b
--- /dev/null
+++ b/python/quantum-pecos/tests/pecos/test_quantum_info_bindings.py
@@ -0,0 +1,318 @@
+from __future__ import annotations
+
+import pytest
+from pecos.quantum import X, Z
+from pecos.quantum_info import (
+    ChiMatrix,
+    ChoiMatrix,
+    PauliChannel,
+    ProcessTomographyDesign,
+    Ptm,
+    Stinespring,
+    SuperOp,
+    average_gate_fidelity,
+    entropy,
+    gate_error,
+    hellinger_distance,
+    hellinger_fidelity,
+    logarithmic_negativity,
+    matrix_unit_basis,
+    negativity,
+    partial_trace_qubits,
+    partial_trace_subsystems,
+    pauli_channel_diamond_distance,
+    pauli_channel_diamond_norm,
+    process_fidelity,
+    purity,
+    random_density_matrix,
+    random_quantum_channel,
+    schmidt_decomposition,
+    shannon_entropy,
+    state_fidelity,
+    state_fidelity_with_density_matrix,
+)
+from pecos_rslib import PauliString
+
+
+def assert_close(actual: float, expected: float, tol: float = 1e-12) -> None:
+    assert abs(actual - expected) < tol
+
+
+def assert_matrix_close(actual: list[list[complex]], expected: list[list[complex]]) -> None:
+    assert len(actual) == len(expected)
+    for actual_row, expected_row in zip(actual, expected, strict=True):
+        assert len(actual_row) == len(expected_row)
+        for actual_value, expected_value in zip(actual_row, expected_row, strict=True):
+            assert abs(actual_value - expected_value) < 1e-12
+
+
+def test_pauli_channel_exposes_probabilities_and_ptm() -> None:
+    channel = PauliChannel.one_qubit(0.1, 0.2, 0.0)
+
+    assert channel.num_qubits() == 1
+    assert_close(channel.total_error_rate(), 0.3)
+    assert channel.probabilities() == {"I": 0.7, "X": 0.1, "Y": 0.2}
+
+    ptm = channel.to_ptm()
+    assert ptm.num_qubits() == 1
+    assert_close(ptm.entry(0, 0), 1.0)
+
+    other = PauliChannel.one_qubit(0.0, 0.2, 0.3)
+    assert_close(pauli_channel_diamond_norm(channel, other), 0.6)
+    assert_close(pauli_channel_diamond_distance(channel, other), 0.3)
+
+
+def test_pauli_channel_accepts_pauli_string_probability_keys() -> None:
+    channel = PauliChannel.from_probabilities(
+        2,
+        {
+            PauliString.I(): 0.97,
+            X(0): 0.01,
+            Z(1): 0.02,
+        },
+    )
+
+    assert channel.probabilities() == {"II": 0.97, "IX": 0.01, "ZI": 0.02}
+    assert_close(channel.total_error_rate(), 0.03)
+
+    from_sequence = PauliChannel.from_probabilities(
+        2,
+        [
+            (PauliString.I(), 0.97),
+            (X(0), 0.01),
+            (Z(1), 0.02),
+        ],
+    )
+    assert from_sequence.probabilities() == channel.probabilities()
+
+
+def test_pauli_channel_rejects_ambiguous_pauli_string_keys() -> None:
+    with pytest.raises(ValueError, match="unphased"):
+        PauliChannel.from_probabilities(1, {-X(0): 1.0})
+
+    with pytest.raises(ValueError, match="outside num_qubits"):
+        PauliChannel.from_probabilities(1, {Z(1): 1.0})
+
+    with pytest.raises(ValueError, match="duplicate"):
+        PauliChannel.from_probabilities(1, [("X", 0.5), (X(0), 0.5)])
+
+
+def test_choi_and_kraus_wrappers_round_trip_identity_channel() -> None:
+    identity = Ptm.identity(1)
+    choi = identity.to_choi()
+
+    assert isinstance(choi, ChoiMatrix)
+    assert choi.is_completely_positive()
+    assert choi.is_trace_preserving()
+    assert choi.is_cptp()
+    assert choi.is_unital()
+    assert_matrix_close(
+        choi.partial_trace_output(),
+        [[1.0 + 0.0j, 0.0 + 0.0j], [0.0 + 0.0j, 1.0 + 0.0j]],
+    )
+
+    kraus = choi.to_kraus()
+    assert kraus.num_qubits() == 1
+    assert kraus.is_trace_preserving()
+    assert_close(process_fidelity(kraus.to_ptm(), identity), 1.0)
+    assert_close(average_gate_fidelity(kraus.to_ptm(), identity), 1.0)
+    assert_close(gate_error(kraus.to_ptm(), identity), 0.0)
+
+    superop = kraus.to_superop()
+    assert isinstance(superop, SuperOp)
+    assert_close(process_fidelity(superop.to_ptm(), identity), 1.0)
+
+    chi = kraus.to_chi()
+    assert isinstance(chi, ChiMatrix)
+    assert_close(process_fidelity(chi.to_ptm(), identity), 1.0)
+
+    stinespring = kraus.to_stinespring()
+    assert isinstance(stinespring, Stinespring)
+    assert stinespring.environment_dim() == 1
+    assert_close(process_fidelity(stinespring.to_kraus().to_ptm(), identity), 1.0)
+
+
+def test_superop_compose_and_tensor_wrappers() -> None:
+    identity = Ptm.identity(1).to_superop()
+    x_channel = PauliChannel.one_qubit(1.0, 0.0, 0.0).to_ptm().to_superop()
+
+    composed = x_channel.compose(x_channel)
+    assert isinstance(composed, SuperOp)
+    assert composed.num_qubits() == 1
+    assert_matrix_close(composed.matrix(), identity.matrix())
+
+    tensor = identity.tensor(identity)
+    assert tensor.num_qubits() == 2
+    assert_matrix_close(
+        tensor.matrix(),
+        [[1.0 + 0.0j if row == col else 0.0 + 0.0j for col in range(16)] for row in range(16)],
+    )
+
+    scalar_identity = Ptm.identity(0).to_superop()
+    assert scalar_identity.num_qubits() == 0
+    assert_matrix_close(scalar_identity.matrix(), [[1.0 + 0.0j]])
+
+    with pytest.raises(ValueError, match="channel qubit count mismatch"):
+        identity.compose(tensor)
+
+
+def test_zero_qubit_channel_wrappers_round_trip_scalar_identity() -> None:
+    identity = Ptm.identity(0)
+
+    assert identity.num_qubits() == 0
+    assert identity.matrix() == [[1.0]]
+
+    choi = identity.to_choi()
+    assert choi.num_qubits() == 0
+    assert_matrix_close(choi.matrix(), [[1.0 + 0.0j]])
+
+    kraus = identity.to_kraus()
+    assert kraus.num_qubits() == 0
+    assert kraus.operators() == [[[1.0 + 0.0j]]]
+
+    superop = identity.to_superop()
+    assert superop.num_qubits() == 0
+    assert_matrix_close(superop.matrix(), [[1.0 + 0.0j]])
+
+    chi = identity.to_chi()
+    assert chi.num_qubits() == 0
+    assert_matrix_close(chi.matrix(), [[1.0 + 0.0j]])
+
+    stinespring = kraus.to_stinespring()
+    assert stinespring.num_qubits() == 0
+    assert stinespring.environment_dim() == 1
+    assert_matrix_close(stinespring.isometry(), [[1.0 + 0.0j]])
+
+
+def test_process_tomography_design_reconstructs_identity_channel() -> None:
+    design = ProcessTomographyDesign.matrix_unit(1)
+
+    assert design.num_qubits() == 1
+    assert design.dim() == 2
+    assert design.num_inputs() == 4
+    assert design.input_metadata_all() == [(0, 0, 0), (1, 1, 0), (2, 0, 1), (3, 1, 1)]
+    assert design.input_index(1, 0) == 1
+    assert_matrix_close(
+        design.input_operator(2),
+        [[0.0 + 0.0j, 1.0 + 0.0j], [0.0 + 0.0j, 0.0 + 0.0j]],
+    )
+    assert design.input_operators() == matrix_unit_basis(1)
+
+    choi = Ptm.identity(1).to_choi()
+    outputs = design.simulate_outputs(choi)
+    reconstructed = design.reconstruct_choi(outputs)
+    assert_matrix_close(reconstructed.matrix(), choi.matrix())
+    assert reconstructed.is_cptp()
+    assert reconstructed.is_unital()
+
+
+def test_process_tomography_design_reconstructs_random_two_qubit_channel() -> None:
+    channel = random_quantum_channel(2, 2, 321)
+    choi = channel.to_choi()
+    design = ProcessTomographyDesign.matrix_unit(2)
+
+    assert design.dim() == 4
+    assert design.num_inputs() == 16
+
+    outputs = design.simulate_outputs(choi)
+    reconstructed = design.reconstruct_choi(outputs)
+
+    assert_matrix_close(reconstructed.matrix(), choi.matrix())
+    assert reconstructed.is_cptp()
+
+
+def test_choi_from_matrix_unit_outputs_static_constructor() -> None:
+    outputs = matrix_unit_basis(1)
+    reconstructed = ChoiMatrix.from_matrix_unit_outputs(1, outputs)
+    assert_matrix_close(reconstructed.matrix(), Ptm.identity(1).to_choi().matrix())
+
+
+def test_state_measure_wrappers() -> None:
+    zero = [1.0 + 0.0j, 0.0 + 0.0j]
+    plus = [2.0**-0.5 + 0.0j, 2.0**-0.5 + 0.0j]
+    zero_density = [[1.0 + 0.0j, 0.0 + 0.0j], [0.0 + 0.0j, 0.0 + 0.0j]]
+    bell = [2.0**-0.5 + 0.0j, 0.0 + 0.0j, 0.0 + 0.0j, 2.0**-0.5 + 0.0j]
+    bell_density = [
+        [0.5 + 0.0j, 0.0 + 0.0j, 0.0 + 0.0j, 0.5 + 0.0j],
+        [0.0 + 0.0j, 0.0 + 0.0j, 0.0 + 0.0j, 0.0 + 0.0j],
+        [0.0 + 0.0j, 0.0 + 0.0j, 0.0 + 0.0j, 0.0 + 0.0j],
+        [0.5 + 0.0j, 0.0 + 0.0j, 0.0 + 0.0j, 0.5 + 0.0j],
+    ]
+
+    assert_close(state_fidelity(zero, zero), 1.0)
+    assert_close(state_fidelity(zero, plus), 0.5)
+    assert_close(state_fidelity_with_density_matrix(zero_density, zero), 1.0)
+    assert_close(purity(zero_density), 1.0)
+    assert_close(entropy(zero_density), 0.0)
+    assert_close(shannon_entropy([0.5, 0.5], 2.0), 1.0)
+    assert_close(negativity(bell_density, [2, 2], 1), 0.5)
+    assert_close(logarithmic_negativity(bell_density, [2, 2], 1), 1.0)
+    expected_reduced = [[0.5 + 0.0j, 0.0 + 0.0j], [0.0 + 0.0j, 0.5 + 0.0j]]
+    assert_matrix_close(partial_trace_qubits(bell_density, 2, [1]), expected_reduced)
+    assert_matrix_close(partial_trace_subsystems(bell_density, [2, 2], [1]), expected_reduced)
+    assert_close(hellinger_distance([1.0, 0.0], [0.0, 1.0]), 1.0)
+    assert_close(hellinger_fidelity([0.25, 0.75], [0.25, 0.75]), 1.0)
+    schmidt = schmidt_decomposition(bell, [2, 2], [0])
+    assert len(schmidt) == 2
+    assert_close(schmidt[0][0], 2.0**-0.5)
+    assert_close(schmidt[1][0], 2.0**-0.5)
+
+
+def test_quantum_info_wrappers_raise_value_errors_for_invalid_inputs() -> None:
+    with pytest.raises(ValueError, match="vector length mismatch"):
+        state_fidelity([1.0 + 0.0j], [1.0 + 0.0j, 0.0 + 0.0j])
+
+    with pytest.raises(ValueError, match="state vector squared norm"):
+        state_fidelity([1.0 + 0.0j, 1.0 + 0.0j], [1.0 + 0.0j, 0.0 + 0.0j])
+
+    with pytest.raises(ValueError, match="matrix must be square"):
+        purity([[1.0 + 0.0j, 0.0 + 0.0j]])
+
+    with pytest.raises(ValueError, match="probability distribution must sum"):
+        shannon_entropy([0.25, 0.25], 2.0)
+
+    rho = [[1.0 + 0.0j, 0.0 + 0.0j], [0.0 + 0.0j, 0.0 + 0.0j]]
+    with pytest.raises(ValueError, match="duplicate subsystem"):
+        partial_trace_subsystems(rho, [2], [0, 0])
+
+    with pytest.raises(ValueError, match="outside"):
+        partial_trace_subsystems(rho, [2], [1])
+
+    with pytest.raises(ValueError, match="invalid subsystem dimensions"):
+        schmidt_decomposition([1.0 + 0.0j, 0.0 + 0.0j], [2, 2], [0])
+
+    with pytest.raises(ValueError, match="invalid matrix shape"):
+        SuperOp(1, [[1.0 + 0.0j]])
+
+    with pytest.raises(ValueError, match="not an isometry"):
+        Stinespring(1, [[2.0 + 0.0j, 0.0 + 0.0j], [0.0 + 0.0j, 2.0 + 0.0j]])
+
+    with pytest.raises(ValueError, match="qubit count mismatch"):
+        process_fidelity(Ptm.identity(1), Ptm.identity(2))
+
+    with pytest.raises(ValueError, match="qubit count mismatch"):
+        average_gate_fidelity(Ptm.identity(1), Ptm.identity(2))
+
+    with pytest.raises(ValueError, match="qubit count mismatch"):
+        gate_error(Ptm.identity(1), Ptm.identity(2))
+
+
+def test_random_generators_are_seed_reproducible_and_valid() -> None:
+    rho = random_density_matrix(1, 123)
+    same_rho = random_density_matrix(1, 123)
+    different_rho = random_density_matrix(1, 124)
+
+    assert rho == same_rho
+    assert rho != different_rho
+    assert_close((rho[0][0] + rho[1][1]).real, 1.0)
+
+    channel = random_quantum_channel(1, 2, 123)
+    same_channel = random_quantum_channel(1, 2, 123)
+    assert channel.operators() == same_channel.operators()
+    assert channel.is_trace_preserving()
+
+    two_qubit = random_quantum_channel(2, 2, 125)
+    assert two_qubit.num_qubits() == 2
+    assert two_qubit.is_trace_preserving()
+    assert two_qubit.to_superop().num_qubits() == 2
+    assert len(two_qubit.to_superop().matrix()) == 16
diff --git a/python/quantum-pecos/tests/pecos/test_selene_plugin_workspace.py b/python/quantum-pecos/tests/pecos/test_selene_plugin_workspace.py
index 822518776..60e5fcb12 100644
--- a/python/quantum-pecos/tests/pecos/test_selene_plugin_workspace.py
+++ b/python/quantum-pecos/tests/pecos/test_selene_plugin_workspace.py
@@ -7,7 +7,7 @@
 try:
     import tomllib
 except ModuleNotFoundError:  # pragma: no cover
-    import tomli as tomllib
+    import tomli as tomllib  # type: ignore[no-redef]
 
 
 def _repo_root() -> Path:
diff --git a/python/quantum-pecos/tests/pecos/test_selene_sim_parity.py b/python/quantum-pecos/tests/pecos/test_selene_sim_parity.py
index 405674c1d..1e7ec9cb4 100644
--- a/python/quantum-pecos/tests/pecos/test_selene_sim_parity.py
+++ b/python/quantum-pecos/tests/pecos/test_selene_sim_parity.py
@@ -18,6 +18,7 @@
 import os
 import tempfile
 from collections import Counter, defaultdict
+from collections.abc import Iterable
 from pathlib import Path
 
 import pytest
@@ -187,6 +188,13 @@ def _collect_selene_named_results(
 ) -> dict[str, list[int] | list[list[int]]]:
     from selene_sim import DepolarizingErrorModel, SimpleRuntime, Stim
 
+    def result_values(values: object) -> list[int]:
+        if isinstance(values, int):
+            return [int(values)]
+        if isinstance(values, Iterable):
+            return [int(v) for v in values]
+        return [int(values)]
+
     results: dict[str, list[int] | list[list[int]]] = defaultdict(list)
     try:
         for shot_results in instance.run_shots(
@@ -205,7 +213,7 @@ def _collect_selene_named_results(
         ):
             shot_rows: dict[str, list[int]] = defaultdict(list)
             for name, values in shot_results:
-                shot_rows[name].extend(int(v) for v in values)
+                shot_rows[name].extend(result_values(values))
             for name, values in shot_rows.items():
                 # Match ShotMap.to_dict(): one-bit registers become a flat list across
                 # shots, while vector-valued registers remain nested by shot.
@@ -230,7 +238,7 @@ def _collect_selene_named_results_with_custom_noise(
     p1: float,
     p2: float,
     p_meas: float,
-    p_init: float,
+    p_prep: float,
     seed: int,
 ) -> dict[str, list[int] | list[list[int]]]:
     from selene_sim import DepolarizingErrorModel, SimpleRuntime, Stim
@@ -245,7 +253,7 @@ def _collect_selene_named_results_with_custom_noise(
                 p_1q=p1,
                 p_2q=p2,
                 p_meas=p_meas,
-                p_init=p_init,
+                p_init=p_prep,
             ),
             runtime=SimpleRuntime(),
             random_seed=seed,
@@ -363,8 +371,9 @@ def test_surface_memory_selene_backends_return_same_register_shapes(basis: str)
         seed=123,
     )
 
-    assert set(sim_results) == {"final", "synx", "synz"}
-    assert set(selene_results) == {"final", "synx", "synz"}
+    expected_registers = {"final", "synx", "synz"}
+    assert expected_registers.issubset(sim_results)
+    assert expected_registers.issubset(selene_results)
 
     for key in ("final", "synx", "synz"):
         assert len(sim_results[key]) == 2
@@ -496,7 +505,7 @@ def test_tiny_syndrome_memory_p2_only_matches_between_selene_backends_statistica
         p1=0.0,
         p2=p2,
         p_meas=0.0,
-        p_init=0.0,
+        p_prep=0.0,
         seed=123,
     )
 
diff --git a/python/quantum-pecos/tests/pecos/unit/test_qasm_to_phir_json.py b/python/quantum-pecos/tests/pecos/unit/test_qasm_to_phir_json.py
index 7cb11c255..d4a07dcea 100644
--- a/python/quantum-pecos/tests/pecos/unit/test_qasm_to_phir_json.py
+++ b/python/quantum-pecos/tests/pecos/unit/test_qasm_to_phir_json.py
@@ -157,11 +157,9 @@ def _run_phir_json(phir: dict, *, shots: int = 1, seed: int = 42) -> dict:
     from pecos_rslib import RustPhirClassicalInterpreter
 
     py_i = PhirClassicalInterpreter()
-    py_i.phir_validate = False
     py_r = HybridEngine(cinterp=py_i).run(phir, shots=shots, seed=seed, return_int=True)
 
     rs_i = RustPhirClassicalInterpreter()
-    rs_i.phir_validate = False
     rs_r = HybridEngine(cinterp=rs_i).run(phir, shots=shots, seed=seed, return_int=True)
 
     py_vals = {k: int(v[0]) for k, v in py_r.items()}
diff --git a/python/quantum-pecos/tests/pecos/unit/test_rust_python_parity.py b/python/quantum-pecos/tests/pecos/unit/test_rust_python_parity.py
index eb49bc872..d6671a8b5 100644
--- a/python/quantum-pecos/tests/pecos/unit/test_rust_python_parity.py
+++ b/python/quantum-pecos/tests/pecos/unit/test_rust_python_parity.py
@@ -46,7 +46,6 @@ def run_both(
         kw["qsim"] = qsim
 
     py_i = PhirClassicalInterpreter()
-    py_i.phir_validate = False
     py_r = HybridEngine(cinterp=py_i, **kw).run(
         phir,
         foreign_object=foreign_object,
@@ -56,7 +55,6 @@ def run_both(
     )
 
     rs_i = RustPhirClassicalInterpreter()
-    rs_i.phir_validate = False
     rs_r = HybridEngine(cinterp=rs_i, **kw).run(
         phir,
         foreign_object=foreign_object,
@@ -106,7 +104,6 @@ def test_wasm_spec_example() -> None:
     math_wat = WAT_DIR / "math.wat"
 
     py_i = PhirClassicalInterpreter()
-    py_i.phir_validate = False
     py_r = HybridEngine(cinterp=py_i).run(
         phir,
         foreign_object=WasmForeignObject(math_wat),
@@ -115,7 +112,6 @@ def test_wasm_spec_example() -> None:
     )
 
     rs_i = RustPhirClassicalInterpreter()
-    rs_i.phir_validate = False
     rs_r = HybridEngine(cinterp=rs_i).run(
         phir,
         foreign_object=WasmForeignObject(math_wat),
diff --git a/python/quantum-pecos/tests/qec/surface/test_circuit_fuzz.py b/python/quantum-pecos/tests/qec/surface/test_circuit_fuzz.py
new file mode 100644
index 000000000..d368f82d9
--- /dev/null
+++ b/python/quantum-pecos/tests/qec/surface/test_circuit_fuzz.py
@@ -0,0 +1,1042 @@
+# Copyright 2026 The PECOS Developers
+# Licensed under the Apache License, Version 2.0
+
+"""Random circuit fuzzing comparing physical and logical PECOS simulations.
+
+Generates random stabilizer circuits, runs them at two levels:
+1. Physical: single-qubit PECOS SparseStab (ground truth)
+2. Logical: encoded in a surface code via LogicalCircuitBuilder,
+   TickCircuit replayed on SparseStab with detector/tracked-Pauli checking
+
+No Stim dependency. Pure PECOS end-to-end.
+"""
+
+from __future__ import annotations
+
+import json
+import random
+
+import pytest
+from pecos.qec.surface import LogicalCircuitBuilder, SurfacePatch
+from pecos_rslib import SparseStab
+from pecos_rslib.quantum import TickCircuit
+
+# ---------------------------------------------------------------------------
+# TickCircuit simulation on SparseStab
+# ---------------------------------------------------------------------------
+
+
+def simulate_tick_circuit(tc: TickCircuit, seed: int = 0) -> tuple[list[int], int, dict[int, int]]:
+    """Simulate a TickCircuit on PECOS SparseStab.
+
+    Returns (flat_measurements, det_fired, observable_values).
+    """
+    max_q = 0
+    for i in range(tc.num_ticks()):
+        for g in tc.get_tick(i).gate_batches():
+            for q in g.qubits:
+                max_q = max(max_q, int(q))
+
+    sim = SparseStab(max_q + 1)
+    sim.set_seed(seed)
+    flat = []
+
+    for i in range(tc.num_ticks()):
+        for g in tc.get_tick(i).gate_batches():
+            name = g.gate_type.name
+            qs = [int(q) for q in g.qubits]
+            if name == "QAlloc":
+                pass
+            elif name == "PZ":
+                sim.run_gate("PZ", set(qs))
+            elif name == "MZ":
+                for q in qs:
+                    r = sim.run_gate("MZ", {q})
+                    flat.append(r.get(q, 0))
+            elif name in ("CX", "CZ"):
+                pairs = {(qs[j], qs[j + 1]) for j in range(0, len(qs), 2)}
+                sim.run_gate(name, pairs)
+            else:
+                sim.run_gate(name, set(qs))
+
+    num_meas = int(tc.get_meta("num_measurements"))
+
+    # Check detectors
+    det_fired = 0
+    det_json = tc.get_meta("detectors")
+    if det_json:
+        for det in json.loads(det_json):
+            val = 0
+            for rec in det["records"]:
+                idx = num_meas + rec
+                if 0 <= idx < len(flat):
+                    val ^= flat[idx]
+            if val != 0:
+                det_fired += 1
+
+    # Extract observables
+    obs_vals = {}
+    obs_json = tc.get_meta("observables")
+    if obs_json:
+        for obs in json.loads(obs_json):
+            val = 0
+            for rec in obs["records"]:
+                idx = num_meas + rec
+                if 0 <= idx < len(flat):
+                    val ^= flat[idx]
+            obs_vals[obs["id"]] = val
+
+    return flat, det_fired, obs_vals
+
+
+def physical_sim_1q(gates: list[str], init_basis: str, meas_basis: str) -> int:
+    """Single-qubit ground truth on SparseStab."""
+    sim = SparseStab(1)
+    if init_basis == "X":
+        sim.run_gate("H", {0})
+    for g in gates:
+        sim.run_gate(g, {0})
+    if meas_basis == "X":
+        sim.run_gate("H", {0})
+    return sim.run_gate("MZ", {0}).get(0, 0)
+
+
+# ---------------------------------------------------------------------------
+# Fixtures
+# ---------------------------------------------------------------------------
+
+
+@pytest.fixture
+def patch():
+    return SurfacePatch.create(distance=3)
+
+
+@pytest.fixture
+def nq(patch):
+    return patch.geometry.num_data + patch.geometry.num_ancilla
+
+
+# ---------------------------------------------------------------------------
+# Deterministic gate correctness (observable values)
+# ---------------------------------------------------------------------------
+
+
+class TestGateCorrectness:
+    """Verify gate observables match physical ground truth (pure PECOS)."""
+
+    def test_memory_z(self, patch):
+        b = LogicalCircuitBuilder()
+        b.add_patch(patch, "A")
+        b.add_memory("A", 2, "Z")
+        _, det, obs = simulate_tick_circuit(b.to_tick_circuit())
+        assert det == 0
+        assert obs[0] == 0
+
+    def test_memory_x(self, patch):
+        b = LogicalCircuitBuilder()
+        b.add_patch(patch, "A")
+        b.add_memory("A", 2, "X")
+        _, det, obs = simulate_tick_circuit(b.to_tick_circuit())
+        assert det == 0
+        assert obs[0] == 0
+
+    def test_h_z_to_x(self, patch):
+        b = LogicalCircuitBuilder()
+        b.add_patch(patch, "A")
+        b.add_memory("A", 2, "Z")
+        b.add_transversal_h("A")
+        b.add_memory("A", 2, "X")
+        _, det, obs = simulate_tick_circuit(b.to_tick_circuit())
+        assert det == 0
+        assert obs[0] == 0
+
+    def test_h_x_to_z(self, patch):
+        b = LogicalCircuitBuilder()
+        b.add_patch(patch, "A")
+        b.add_memory("A", 2, "X")
+        b.add_transversal_h("A")
+        b.add_memory("A", 2, "Z")
+        _, det, obs = simulate_tick_circuit(b.to_tick_circuit())
+        assert det == 0
+        assert obs[0] == 0
+
+    def test_hh_identity(self, patch):
+        b = LogicalCircuitBuilder()
+        b.add_patch(patch, "A")
+        b.add_memory("A", 2, "Z")
+        b.add_transversal_h("A")
+        b.add_memory("A", 2, "X")
+        b.add_transversal_h("A")
+        b.add_memory("A", 2, "Z")
+        _, det, obs = simulate_tick_circuit(b.to_tick_circuit())
+        assert det == 0
+        assert obs[0] == 0
+
+    def test_cx_00_zz(self, patch, nq):
+        b = LogicalCircuitBuilder()
+        b.add_patch(patch, "C", qubit_offset=0)
+        b.add_patch(patch, "T", qubit_offset=nq)
+        b.add_memory(["C", "T"], 2, "Z")
+        b.add_transversal_cx("C", "T")
+        b.add_memory(["C", "T"], 2, "Z")
+        _, det, obs = simulate_tick_circuit(b.to_tick_circuit())
+        assert det == 0
+        assert obs[0] == 0
+        assert obs[1] == 0
+
+    def test_cx_pp_xx(self, patch, nq):
+        b = LogicalCircuitBuilder()
+        b.add_patch(patch, "C", qubit_offset=0)
+        b.add_patch(patch, "T", qubit_offset=nq)
+        b.add_memory(["C", "T"], 2, "X")
+        b.add_transversal_cx("C", "T")
+        b.add_memory(["C", "T"], 2, "X")
+        _, det, obs = simulate_tick_circuit(b.to_tick_circuit())
+        assert det == 0
+        assert obs[0] == 0
+        assert obs[1] == 0
+
+
+# ---------------------------------------------------------------------------
+# Noiseless detector validity (multiple seeds)
+# ---------------------------------------------------------------------------
+
+
+class TestNoiselessDetectors:
+    """Verify 0 detector fires across many seeds (PECOS-only)."""
+
+    @pytest.mark.parametrize("seed", range(20))
+    def test_memory_z(self, patch, seed):
+        b = LogicalCircuitBuilder()
+        b.add_patch(patch, "A")
+        b.add_memory("A", 3, "Z")
+        _, det, _ = simulate_tick_circuit(b.to_tick_circuit(), seed)
+        assert det == 0
+
+    @pytest.mark.parametrize("seed", range(20))
+    def test_h(self, patch, seed):
+        b = LogicalCircuitBuilder()
+        b.add_patch(patch, "A")
+        b.add_memory("A", 2, "Z")
+        b.add_transversal_h("A")
+        b.add_memory("A", 2, "X")
+        _, det, _ = simulate_tick_circuit(b.to_tick_circuit(), seed)
+        assert det == 0
+
+    @pytest.mark.parametrize("seed", range(20))
+    def test_cx(self, patch, nq, seed):
+        b = LogicalCircuitBuilder()
+        b.add_patch(patch, "C", qubit_offset=0)
+        b.add_patch(patch, "T", qubit_offset=nq)
+        b.add_memory(["C", "T"], 2, "Z")
+        b.add_transversal_cx("C", "T")
+        b.add_memory(["C", "T"], 2, "Z")
+        _, det, _ = simulate_tick_circuit(b.to_tick_circuit(), seed)
+        assert det == 0
+
+
+# ---------------------------------------------------------------------------
+# Fuzz: physical vs logical H sequences
+# ---------------------------------------------------------------------------
+
+
+class TestFuzzH:
+    @pytest.mark.parametrize("seed", range(50))
+    def test_random_h(self, patch, seed):
+        rng = random.Random(seed)
+        num_h = rng.randint(0, 8)
+        init_b = rng.choice(["Z", "X"])
+        eff_b = init_b
+        for _ in range(num_h):
+            eff_b = "X" if eff_b == "Z" else "Z"
+
+        expected = physical_sim_1q(["H"] * num_h, init_b, eff_b)
+
+        b = LogicalCircuitBuilder()
+        b.add_patch(patch, "A")
+        b.add_memory("A", 2, init_b)
+        cur = init_b
+        for _ in range(num_h):
+            b.add_transversal_h("A")
+            cur = "X" if cur == "Z" else "Z"
+            b.add_memory("A", 2, cur)
+
+        _, det, obs = simulate_tick_circuit(b.to_tick_circuit())
+        assert det == 0
+        assert obs[0] == expected
+
+
+# ---------------------------------------------------------------------------
+# Fuzz: H+CX composition
+# ---------------------------------------------------------------------------
+
+
+class TestFuzzCX:
+    """Fuzz CX with various init/meas bases against physical SparseStab."""
+
+    @pytest.mark.parametrize("seed", range(50))
+    def test_random_cx(self, patch, nq, seed):
+        rng = random.Random(seed)
+        ic = rng.choice(["Z", "X"])
+        it = rng.choice(["Z", "X"])
+        mc = rng.choice(["Z", "X"])
+        mt = rng.choice(["Z", "X"])
+
+        # Physical ground truth: detect deterministic outcomes
+        results = []
+        for _ in range(50):
+            sim = SparseStab(2)
+            if ic == "X":
+                sim.run_gate("H", {0})
+            if it == "X":
+                sim.run_gate("H", {1})
+            sim.run_gate("CX", {(0, 1)})
+            if mc == "X":
+                sim.run_gate("H", {0})
+            if mt == "X":
+                sim.run_gate("H", {1})
+            r = sim.run_gate("MZ", {0, 1})
+            results.append((r.get(0, 0), r.get(1, 0)))
+        r0s, r1s = [r[0] for r in results], [r[1] for r in results]
+        exp0 = r0s[0] if len(set(r0s)) == 1 else None
+        exp1 = r1s[0] if len(set(r1s)) == 1 else None
+
+        # Encoded
+        b = LogicalCircuitBuilder()
+        b.add_patch(patch, "C", qubit_offset=0)
+        b.add_patch(patch, "T", qubit_offset=nq)
+        b.add_memory(["C", "T"], 2, basis={"C": ic, "T": it})
+        b.add_transversal_cx("C", "T")
+        b.add_memory(["C", "T"], 2, basis={"C": mc, "T": mt})
+
+        _, det, obs = simulate_tick_circuit(b.to_tick_circuit())
+        assert det == 0, f"Noiseless det fired: {ic}{it}->{mc}{mt}"
+
+        if exp0 is not None and 0 in obs:
+            assert obs[0] == exp0, f"obs0: got {obs[0]} expected {exp0}"
+        if exp1 is not None and 1 in obs:
+            assert obs[1] == exp1, f"obs1: got {obs[1]} expected {exp1}"
+
+
+class TestFuzzComposition:
+    @pytest.mark.parametrize("seed", range(30))
+    def test_random_h_cx(self, patch, nq, seed):
+        rng = random.Random(seed)
+        num_ops = rng.randint(1, 6)
+
+        b = LogicalCircuitBuilder()
+        b.add_patch(patch, "A", qubit_offset=0)
+        b.add_patch(patch, "B", qubit_offset=nq)
+        b.add_memory(["A", "B"], 2, "Z")
+        eff = {"A": "Z", "B": "Z"}
+
+        for _ in range(num_ops):
+            op = rng.choice(["H_A", "H_B", "CX"])
+            if op == "H_A":
+                b.add_transversal_h("A")
+                eff["A"] = "X" if eff["A"] == "Z" else "Z"
+                b.add_memory(["A", "B"], 2, basis={"A": eff["A"], "B": eff["B"]})
+            elif op == "H_B":
+                b.add_transversal_h("B")
+                eff["B"] = "X" if eff["B"] == "Z" else "Z"
+                b.add_memory(["A", "B"], 2, basis={"A": eff["A"], "B": eff["B"]})
+            else:
+                if eff["A"] != eff["B"]:
+                    continue
+                b.add_transversal_cx("A", "B")
+                b.add_memory(["A", "B"], 2, basis={"A": eff["A"], "B": eff["B"]})
+
+        _, det, _ = simulate_tick_circuit(b.to_tick_circuit())
+        assert det == 0
+
+
+# ---------------------------------------------------------------------------
+# Distance scaling
+# ---------------------------------------------------------------------------
+
+
+class TestDistanceScaling:
+    @pytest.fixture
+    def patch5(self):
+        return SurfacePatch.create(distance=5)
+
+    @pytest.fixture
+    def nq5(self, patch5):
+        return patch5.geometry.num_data + patch5.geometry.num_ancilla
+
+    def test_d5_memory(self, patch5):
+        b = LogicalCircuitBuilder()
+        b.add_patch(patch5, "A")
+        b.add_memory("A", 3, "Z")
+        _, det, obs = simulate_tick_circuit(b.to_tick_circuit())
+        assert det == 0
+        assert obs[0] == 0
+
+    def test_d5_h(self, patch5):
+        b = LogicalCircuitBuilder()
+        b.add_patch(patch5, "A")
+        b.add_memory("A", 2, "Z")
+        b.add_transversal_h("A")
+        b.add_memory("A", 2, "X")
+        _, det, obs = simulate_tick_circuit(b.to_tick_circuit())
+        assert det == 0
+        assert obs[0] == 0
+
+    @pytest.mark.parametrize("seed", range(5))
+    def test_d5_cx(self, patch5, nq5, seed):
+        b = LogicalCircuitBuilder()
+        b.add_patch(patch5, "C", qubit_offset=0)
+        b.add_patch(patch5, "T", qubit_offset=nq5)
+        b.add_memory(["C", "T"], 2, "Z")
+        b.add_transversal_cx("C", "T")
+        b.add_memory(["C", "T"], 2, "Z")
+        _, det, obs = simulate_tick_circuit(b.to_tick_circuit(), seed)
+        assert det == 0
+        assert obs[0] == 0
+        assert obs[1] == 0
+
+    def test_d5_pecos_dem(self, patch5):
+        b = LogicalCircuitBuilder()
+        b.add_patch(patch5, "A")
+        b.add_memory("A", 2, "Z")
+        dem_str = b.build_dem(p1=0.001, p2=0.001, p_meas=0.001)
+        errors = [line for line in dem_str.split("\n") if line.startswith("error(")]
+        assert len(errors) > 0
+
+
+# ---------------------------------------------------------------------------
+# TickCircuit structural tests
+# ---------------------------------------------------------------------------
+
+# ---------------------------------------------------------------------------
+# SZ teleportation
+# ---------------------------------------------------------------------------
+
+
+class TestReliableObservables:
+    """Verify that non-reliable observables are correctly skipped."""
+
+    def test_cx_same_basis_both_reliable(self, patch, nq):
+        """CX with same-basis measurements: both observables emitted."""
+        b = LogicalCircuitBuilder()
+        b.add_patch(patch, "C", qubit_offset=0)
+        b.add_patch(patch, "T", qubit_offset=nq)
+        b.add_memory(["C", "T"], 2, "Z")
+        b.add_transversal_cx("C", "T")
+        b.add_memory(["C", "T"], 2, "Z")
+        tc = b.to_tick_circuit()
+        obs = json.loads(tc.get_meta("observables"))
+        assert len(obs) == 2, f"Expected 2 observables, got {len(obs)}"
+
+    def test_cx_cross_basis_skips_unreliable(self, patch, nq):
+        """CX with cross-basis: non-deterministic observables skipped."""
+        b = LogicalCircuitBuilder()
+        b.add_patch(patch, "C", qubit_offset=0)
+        b.add_patch(patch, "T", qubit_offset=nq)
+        b.add_memory(["C", "T"], 2, basis={"C": "X", "T": "Z"})
+        b.add_transversal_cx("C", "T")
+        b.add_memory(["C", "T"], 2, basis={"C": "X", "T": "Z"})
+        tc = b.to_tick_circuit()
+        obs = json.loads(tc.get_meta("observables"))
+        # Ctrl measured in X after CX: X_ctrl entangled with tgt (measured Z)
+        # → ctrl X observable is non-reliable → skipped
+        # Tgt measured in Z after CX: Z_tgt entangled with ctrl (measured X)
+        # → tgt Z observable is non-reliable → skipped
+        # Both should be skipped
+        assert len(obs) == 0, f"Expected 0 observables (both non-reliable), got {len(obs)}"
+
+    def test_cx_zx_one_reliable(self, patch, nq):
+        """CX|0>|+> with meas(Z,X): both should be reliable.
+
+        After CX: Z_ctrl unchanged, X_tgt unchanged.
+        Measuring ctrl in Z: reliable (Z not entangled).
+        Measuring tgt in X: reliable (X not entangled).
+        """
+        b = LogicalCircuitBuilder()
+        b.add_patch(patch, "C", qubit_offset=0)
+        b.add_patch(patch, "T", qubit_offset=nq)
+        b.add_memory(["C", "T"], 2, basis={"C": "Z", "T": "X"})
+        b.add_transversal_cx("C", "T")
+        b.add_memory(["C", "T"], 2, basis={"C": "Z", "T": "X"})
+        tc = b.to_tick_circuit()
+        obs = json.loads(tc.get_meta("observables"))
+        assert len(obs) == 2, f"Expected 2 observables, got {len(obs)}"
+
+        _, det, obs_vals = simulate_tick_circuit(tc)
+        assert det == 0
+        assert obs_vals[0] == 0
+        assert obs_vals[1] == 0
+
+
+class TestSZTeleportation:
+    def test_sz_preserves_z(self, patch, nq):
+        """SZ|0> = |0>: Z eigenvalue preserved."""
+        b = LogicalCircuitBuilder()
+        b.add_patch(patch, "D", qubit_offset=0)
+        b.add_patch(patch, "Y", qubit_offset=nq)
+        b.add_memory("D", 2, "Z")
+        b.add_sz_via_teleportation("D", "Y", 2, 2)
+        b.add_memory("D", 2, "Z")
+        _, det, obs = simulate_tick_circuit(b.to_tick_circuit())
+        assert det == 0
+        assert obs[0] == 0
+
+    def test_sz_phase_single_qubit(self):
+        """Verify SZ teleportation protocol at the single-qubit level.
+
+        The phase test (SZ^2|+> = Z|+> = |->) cannot be verified at the
+        logical level because the |+Y> injection is non-fault-tolerant
+        (distance-1 error). But we CAN verify the protocol works on a
+        single physical qubit, confirming the circuit structure is correct.
+        """
+        sim = SparseStab(3)
+        # Qubit 0: data (|+>), Qubit 1: ancilla 1 (|+Y>), Qubit 2: ancilla 2 (|+Y>)
+
+        # Prep |+>
+        sim.run_gate("H", {0})
+        # Prep |+Y> = S|+>
+        sim.run_gate("H", {1})
+        sim.run_gate("SZ", {1})
+        sim.run_gate("H", {2})
+        sim.run_gate("SZ", {2})
+
+        # First teleportation: CX(data, anc1), measure anc1 in Z
+        sim.run_gate("CX", {(0, 1)})
+        r1 = sim.run_gate("MZ", {1})
+        m1 = r1.get(1, 0)
+
+        # Second teleportation: CX(data, anc2), measure anc2 in Z
+        sim.run_gate("CX", {(0, 2)})
+        r2 = sim.run_gate("MZ", {2})
+        m2 = r2.get(2, 0)
+
+        # Measure data in X basis: SZ^2|+> = Z|+> = |->
+        sim.run_gate("H", {0})
+        r_data = sim.run_gate("MZ", {0})
+        data_val = r_data.get(0, 0)
+
+        # Corrected observable: data_X XOR m1 XOR m2
+        corrected = data_val ^ m1 ^ m2
+        assert (
+            corrected == 1
+        ), f"SZ^2|+> should give |-> (corrected=1), got data={data_val} m1={m1} m2={m2} corrected={corrected}"
+
+
+# ---------------------------------------------------------------------------
+# Gate composition
+# ---------------------------------------------------------------------------
+
+
+class TestGateComposition:
+    def test_h_cx_h(self, patch, nq):
+        """H -> CX -> H on both patches."""
+        b = LogicalCircuitBuilder()
+        b.add_patch(patch, "A", qubit_offset=0)
+        b.add_patch(patch, "B", qubit_offset=nq)
+        b.add_memory(["A", "B"], 2, "Z")
+        b.add_transversal_h("A")
+        b.add_transversal_h("B")
+        b.add_memory(["A", "B"], 2, "X")
+        b.add_transversal_cx("A", "B")
+        b.add_memory(["A", "B"], 2, "X")
+        b.add_transversal_h("A")
+        b.add_transversal_h("B")
+        b.add_memory(["A", "B"], 2, "Z")
+        _, det, obs = simulate_tick_circuit(b.to_tick_circuit())
+        assert det == 0
+        assert obs[0] == 0
+        assert obs[1] == 0
+
+    def test_triple_h(self, patch):
+        """HHH = H: |0> -> |+>."""
+        b = LogicalCircuitBuilder()
+        b.add_patch(patch, "A")
+        b.add_memory("A", 2, "Z")
+        for i in range(3):
+            b.add_transversal_h("A")
+            cur = "X" if i % 2 == 0 else "Z"
+            b.add_memory("A", 2, cur)
+        _, det, obs = simulate_tick_circuit(b.to_tick_circuit())
+        assert det == 0
+        assert obs[0] == 0
+
+
+# ---------------------------------------------------------------------------
+# Decoder pipeline (PECOS-native)
+# ---------------------------------------------------------------------------
+
+
+class TestDecoderPipeline:
+    """Test the full decode pipeline using PECOS DEM + PECOS sampler."""
+
+    def test_build_decoder_pecos_dem(self, patch):
+        """build_decoder with PECOS-native DEM produces a working decoder."""
+        b = LogicalCircuitBuilder()
+        b.add_patch(patch, "A")
+        b.add_memory("A", 3, "Z")
+        _, decoder = b.build_decoder(p1=0.001, p2=0.001, p_meas=0.001, use_stim_dem=False)
+        assert decoder.num_observables() == 1
+
+    def test_pecos_dem_decode_memory(self, patch):
+        """End-to-end: PECOS DEM → PECOS sample → decode → low error rate."""
+        from pecos_rslib.qec import ParsedDem
+
+        b = LogicalCircuitBuilder()
+        b.add_patch(patch, "A")
+        b.add_memory("A", 3, "Z")
+        dem_str = b.build_dem(p1=0.001, p2=0.001, p_meas=0.001)
+
+        parsed = ParsedDem.from_string(dem_str)
+        rust_sampler = parsed.to_dem_sampler()
+        batch = rust_sampler.generate_samples(5000, seed=42)
+        errors = batch.decode_count(dem_str, "pecos_uf:fast")
+        ler = errors / 5000
+        # At d=3 p=0.001, LER should be very low
+        assert ler < 0.05, f"LER too high: {ler}"
+
+    def test_observable_subgraph_decoder(self, patch, nq):
+        """OSD with PECOS DEM on CX circuit."""
+        from pecos_rslib.qec import ObservableSubgraphDecoder, ParsedDem
+
+        b = LogicalCircuitBuilder()
+        b.add_patch(patch, "C", qubit_offset=0)
+        b.add_patch(patch, "T", qubit_offset=nq)
+        b.add_memory(["C", "T"], 3, "Z")
+        b.add_transversal_cx("C", "T")
+        b.add_memory(["C", "T"], 3, "Z")
+
+        dem_str = b.build_dem(p1=0.001, p2=0.001, p_meas=0.001)
+        sc = b.stab_coords()
+        osd = ObservableSubgraphDecoder(dem_str, sc, "pecos_uf:fast")
+        assert osd.num_observables() == 2
+
+        sizes = osd.subgraph_sizes()
+        for s in sizes:
+            assert s > 0, "Empty subgraph"
+
+    def test_pecos_dem_cx_decode(self, patch, nq):
+        """End-to-end CX: PECOS DEM → sample → decode."""
+        from pecos_rslib.qec import ParsedDem
+
+        b = LogicalCircuitBuilder()
+        b.add_patch(patch, "C", qubit_offset=0)
+        b.add_patch(patch, "T", qubit_offset=nq)
+        b.add_memory(["C", "T"], 3, "Z")
+        b.add_transversal_cx("C", "T")
+        b.add_memory(["C", "T"], 3, "Z")
+
+        dem_str = b.build_dem(p1=0.001, p2=0.001, p_meas=0.001)
+        parsed = ParsedDem.from_string(dem_str)
+        rust_sampler = parsed.to_dem_sampler()
+        batch = rust_sampler.generate_samples(5000, seed=42)
+        errors = batch.decode_count(dem_str, "pecos_uf:fast")
+        ler = errors / 5000
+        assert ler < 0.1, f"CX LER too high: {ler}"
+
+
+# ---------------------------------------------------------------------------
+# TickCircuit structural tests
+# ---------------------------------------------------------------------------
+
+# ---------------------------------------------------------------------------
+# Threshold: error suppression with distance (d=3 vs d=5)
+# ---------------------------------------------------------------------------
+
+
+class TestThreshold:
+    """Verify error suppression increases with distance.
+
+    Uses Stim DEM for error mechanisms (more complete noise model)
+    and PECOS decoder for correction. Tests at p=0.001 where we should
+    be well below threshold.
+    """
+
+    def _run_threshold(self, builder, _d, decoder_type="pecos_uf:fast"):
+        import stim
+        from pecos_rslib.qec import ParsedDem
+
+        c = stim.Circuit(builder.to_stim(p1=0.001, p2=0.001, p_meas=0.001))
+        dem = c.detector_error_model(decompose_errors=True, ignore_decomposition_failures=True)
+        dem_str = str(dem)
+        parsed = ParsedDem.from_string(dem_str)
+        sampler = parsed.to_dem_sampler()
+        batch = sampler.generate_samples(20000, seed=42)
+        errors = batch.decode_count(dem_str, decoder_type)
+        return errors / 20000
+
+    def test_memory_suppression(self):
+        """Memory: d=5 should have lower LER than d=3."""
+        lers = {}
+        for d in [3, 5]:
+            patch = SurfacePatch.create(distance=d)
+            b = LogicalCircuitBuilder()
+            b.add_patch(patch, "A")
+            b.add_memory("A", rounds=d, basis="Z")
+            lers[d] = self._run_threshold(b, d, "pymatching")
+        assert lers[5] < lers[3], f"d=5 ({lers[5]}) not better than d=3 ({lers[3]})"
+
+    def test_h_suppression(self):
+        """H gate: d=5 should have lower LER than d=3."""
+        lers = {}
+        for d in [3, 5]:
+            patch = SurfacePatch.create(distance=d)
+            b = LogicalCircuitBuilder()
+            b.add_patch(patch, "A")
+            b.add_memory("A", rounds=d, basis="Z")
+            b.add_transversal_h("A")
+            b.add_memory("A", rounds=d, basis="X")
+            lers[d] = self._run_threshold(b, d, "pymatching")
+        assert lers[5] < lers[3], f"d=5 ({lers[5]}) not better than d=3 ({lers[3]})"
+
+
+# ---------------------------------------------------------------------------
+# TickCircuit structural tests
+# ---------------------------------------------------------------------------
+
+# ---------------------------------------------------------------------------
+# Noisy fuzz: random circuits decode with reasonable error rates
+# ---------------------------------------------------------------------------
+
+
+class TestNoisyFuzz:
+    """Verify that random circuits with noise decode with sub-50% error rate.
+
+    This is a basic sanity check: if the decoder is completely broken,
+    the LER would be ~50%. Any reasonable decoder should do much better.
+    """
+
+    @pytest.mark.parametrize("seed", range(5))
+    def test_noisy_h(self, patch, seed):
+        import stim
+        from pecos_rslib.qec import ParsedDem
+
+        rng = random.Random(seed)
+        num_h = rng.randint(1, 4)
+        init_b = "Z"
+        b = LogicalCircuitBuilder()
+        b.add_patch(patch, "A")
+        b.add_memory("A", 2, init_b)
+        cur = init_b
+        for _ in range(num_h):
+            b.add_transversal_h("A")
+            cur = "X" if cur == "Z" else "Z"
+            b.add_memory("A", 2, cur)
+
+        c = stim.Circuit(b.to_stim(p1=0.001, p2=0.001, p_meas=0.001))
+        dem = c.detector_error_model(decompose_errors=True)
+        dem_str = str(dem)
+        parsed = ParsedDem.from_string(dem_str)
+        batch = parsed.to_dem_sampler().generate_samples(5000, seed=seed)
+        errors = batch.decode_count(dem_str, "pecos_uf:fast")
+        ler = errors / 5000
+        assert ler < 0.1, f"LER too high: {ler}"
+
+
+# ---------------------------------------------------------------------------
+# TickCircuit structural tests
+# ---------------------------------------------------------------------------
+
+# ---------------------------------------------------------------------------
+# Composed noisy gate sequences
+# ---------------------------------------------------------------------------
+
+
+class TestNoisyComposition:
+    """Verify that multi-gate sequences with noise decode correctly."""
+
+    def test_noisy_h_cx_h(self, patch, nq):
+        """H -> CX -> H with noise: should decode with low LER."""
+        import stim
+        from pecos_rslib.qec import ParsedDem
+
+        b = LogicalCircuitBuilder()
+        b.add_patch(patch, "A", qubit_offset=0)
+        b.add_patch(patch, "B", qubit_offset=nq)
+        b.add_memory(["A", "B"], 2, "Z")
+        b.add_transversal_h("A")
+        b.add_transversal_h("B")
+        b.add_memory(["A", "B"], 2, "X")
+        b.add_transversal_cx("A", "B")
+        b.add_memory(["A", "B"], 2, "X")
+        b.add_transversal_h("A")
+        b.add_transversal_h("B")
+        b.add_memory(["A", "B"], 2, "Z")
+
+        # Use Stim DEM (more error mechanisms) for noisy test
+        c = stim.Circuit(b.to_stim(p1=0.001, p2=0.001, p_meas=0.001))
+        dem = c.detector_error_model(decompose_errors=True, ignore_decomposition_failures=True)
+        dem_str = str(dem)
+        parsed = ParsedDem.from_string(dem_str)
+        batch = parsed.to_dem_sampler().generate_samples(10000, seed=42)
+        errors = batch.decode_count(dem_str, "pecos_uf:fast")
+        ler = errors / 10000
+        assert ler < 0.1, f"H-CX-H LER too high: {ler}"
+
+    @pytest.mark.parametrize("seed", range(5))
+    def test_noisy_random_composition(self, patch, nq, seed):
+        """Random H+CX with noise: should decode with sub-50% LER."""
+        import stim
+        from pecos_rslib.qec import ParsedDem
+
+        rng = random.Random(seed)
+        b = LogicalCircuitBuilder()
+        b.add_patch(patch, "A", qubit_offset=0)
+        b.add_patch(patch, "B", qubit_offset=nq)
+        b.add_memory(["A", "B"], 2, "Z")
+        eff = {"A": "Z", "B": "Z"}
+
+        for _ in range(rng.randint(1, 4)):
+            op = rng.choice(["H_A", "H_B", "CX"])
+            if op == "H_A":
+                b.add_transversal_h("A")
+                eff["A"] = "X" if eff["A"] == "Z" else "Z"
+                b.add_memory(["A", "B"], 2, basis={"A": eff["A"], "B": eff["B"]})
+            elif op == "H_B":
+                b.add_transversal_h("B")
+                eff["B"] = "X" if eff["B"] == "Z" else "Z"
+                b.add_memory(["A", "B"], 2, basis={"A": eff["A"], "B": eff["B"]})
+            else:
+                if eff["A"] != eff["B"]:
+                    continue
+                b.add_transversal_cx("A", "B")
+                b.add_memory(["A", "B"], 2, basis={"A": eff["A"], "B": eff["B"]})
+
+        c = stim.Circuit(b.to_stim(p1=0.001, p2=0.001, p_meas=0.001))
+        dem = c.detector_error_model(decompose_errors=True, ignore_decomposition_failures=True)
+        dem_str = str(dem)
+        parsed = ParsedDem.from_string(dem_str)
+        batch = parsed.to_dem_sampler().generate_samples(5000, seed=42)
+        errors = batch.decode_count(dem_str, "pecos_uf:fast")
+        ler = errors / 5000
+        assert ler < 0.2, f"Random composition LER too high: {ler}"
+
+
+# ---------------------------------------------------------------------------
+# OSD accuracy comparison
+# ---------------------------------------------------------------------------
+
+
+class TestOSDAccuracy:
+    """Compare observable subgraph decoder accuracy against baseline."""
+
+    def test_osd_better_than_naive_on_cx(self, patch, nq):
+        """OSD should outperform naive decomposed MWPM on CX circuits."""
+        import stim
+        from pecos_rslib.qec import ObservableSubgraphDecoder, ParsedDem
+
+        b = LogicalCircuitBuilder()
+        b.add_patch(patch, "C", qubit_offset=0)
+        b.add_patch(patch, "T", qubit_offset=nq)
+        b.add_memory(["C", "T"], 3, "Z")
+        b.add_transversal_cx("C", "T")
+        b.add_memory(["C", "T"], 3, "Z")
+
+        c = stim.Circuit(b.to_stim(p1=0.001, p2=0.001, p_meas=0.001))
+        dem = c.detector_error_model(ignore_decomposition_failures=True)
+        dem_str = str(dem)
+
+        # Sample
+        sampler = dem.compile_sampler()
+        det_events, obs_flips, _ = sampler.sample(20000)
+
+        # Naive: decomposed MWPM via PECOS UF
+        dem_decomp = c.detector_error_model(decompose_errors=True, ignore_decomposition_failures=True)
+        parsed = ParsedDem.from_string(str(dem_decomp))
+        batch_naive = parsed.to_dem_sampler().generate_samples(20000, seed=42)
+        naive_errors = batch_naive.decode_count(str(dem_decomp), "pecos_uf:fast")
+        naive_ler = naive_errors / 20000
+
+        # OSD with FB
+        sc = b.stab_coords()
+        osd = ObservableSubgraphDecoder(dem_str, sc, "fusion_blossom_serial")
+        osd_errors = sum(
+            1
+            for i in range(20000)
+            if osd.decode(det_events[i].tolist()) != sum((1 << j) for j in range(obs_flips.shape[1]) if obs_flips[i, j])
+        )
+        osd_ler = osd_errors / 20000
+
+        # OSD should be at least as good (usually much better)
+        assert osd_ler <= naive_ler * 1.5 + 0.001, f"OSD ({osd_ler:.5f}) much worse than naive ({naive_ler:.5f})"
+
+
+# ---------------------------------------------------------------------------
+# PECOS-native DEM with OSD decoder on CX
+# ---------------------------------------------------------------------------
+
+
+class TestPecosDemWithOSD:
+    """Test PECOS-native DEM pipeline with observable subgraph decoder."""
+
+    def test_pecos_dem_osd_cx(self, patch, nq):
+        """PECOS DEM → OSD decoder on CX circuit."""
+        from pecos_rslib.qec import ObservableSubgraphDecoder, ParsedDem
+
+        b = LogicalCircuitBuilder()
+        b.add_patch(patch, "C", qubit_offset=0)
+        b.add_patch(patch, "T", qubit_offset=nq)
+        b.add_memory(["C", "T"], 3, "Z")
+        b.add_transversal_cx("C", "T")
+        b.add_memory(["C", "T"], 3, "Z")
+
+        dem_str = b.build_dem(p1=0.001, p2=0.001, p_meas=0.001)
+
+        # Verify DEM has content
+        errors = [line for line in dem_str.split("\n") if line.startswith("error(")]
+        assert len(errors) > 0
+
+        # Build OSD decoder from PECOS DEM
+        sc = b.stab_coords()
+        osd = ObservableSubgraphDecoder(dem_str, sc, "pecos_uf:fast")
+        assert osd.num_observables() == 2
+
+        # Sample and decode
+        parsed = ParsedDem.from_string(dem_str)
+        batch = parsed.to_dem_sampler().generate_samples(5000, seed=42)
+        errors = batch.decode_count(dem_str, "pecos_uf:fast")
+        ler = errors / 5000
+        assert ler < 0.1, f"PECOS DEM + OSD CX LER too high: {ler}"
+
+
+# ---------------------------------------------------------------------------
+# TickCircuit structural tests
+# ---------------------------------------------------------------------------
+
+# ---------------------------------------------------------------------------
+# Mirrored brickwork circuits
+# ---------------------------------------------------------------------------
+
+
+def _build_mirrored_brickwork(num_qubits, depth, seed, patch, rounds=2):
+    """Build a mirrored brickwork circuit (identity, output = |0...0>).
+
+    Forward: random H gates + CX brickwork layers.
+    Mirror: exact reverse (H and CX are self-inverse).
+    """
+    nq = patch.geometry.num_data + patch.geometry.num_ancilla
+
+    b = LogicalCircuitBuilder()
+    labels = [f"Q{i}" for i in range(num_qubits)]
+    for i, label in enumerate(labels):
+        b.add_patch(patch, label, qubit_offset=i * nq)
+
+    eff = dict.fromkeys(labels, "Z")
+    b.add_memory(labels, rounds, "Z")
+
+    rng = random.Random(seed)
+    ops_forward = []
+
+    for layer in range(depth):
+        layer_ops = []
+        for label in labels:
+            # H is the only single-qubit logical gate available.
+            # SZ requires teleportation (not a standalone gate on the surface code).
+            if rng.random() < 0.5:
+                b.add_transversal_h(label)
+                eff[label] = "X" if eff[label] == "Z" else "Z"
+                layer_ops.append(("H", label))
+        b.add_memory(labels, rounds, basis={label: eff[label] for label in labels})
+
+        offset = layer % 2
+        cx_applied = []
+        for i in range(offset, num_qubits - 1, 2):
+            ctrl, tgt = labels[i], labels[i + 1]
+            if eff[ctrl] == eff[tgt]:
+                b.add_transversal_cx(ctrl, tgt)
+                cx_applied.append((ctrl, tgt))
+        if cx_applied:
+            b.add_memory(labels, rounds, basis={label: eff[label] for label in labels})
+            layer_ops.append(("CX", cx_applied))
+        ops_forward.append(layer_ops)
+
+    for layer_ops in reversed(ops_forward):
+        for op_type, *args in reversed(layer_ops):
+            if op_type == "CX":
+                for ctrl, tgt in reversed(args[0]):
+                    if eff[ctrl] == eff[tgt]:
+                        b.add_transversal_cx(ctrl, tgt)
+                b.add_memory(labels, rounds, basis={label: eff[label] for label in labels})
+        for op_type, *args in reversed(layer_ops):
+            if op_type == "H":
+                label = args[0]
+                b.add_transversal_h(label)
+                eff[label] = "X" if eff[label] == "Z" else "Z"
+        b.add_memory(labels, rounds, basis={label: eff[label] for label in labels})
+
+    return b
+
+
+class TestMirroredBrickwork:
+    """Mirrored brickwork circuits: identity circuit, output always |0...0>.
+
+    Tests random H + CX brickwork layers at various widths and depths.
+    The mirror guarantees the output is |0...0> regardless of random choices.
+    """
+
+    @pytest.mark.parametrize("width", [2, 3, 4])
+    @pytest.mark.parametrize("depth", [1, 2, 3])
+    @pytest.mark.parametrize("seed", range(5))
+    def test_brickwork_d3(self, width, depth, seed):
+        patch = SurfacePatch.create(distance=3)
+        b = _build_mirrored_brickwork(width, depth, seed, patch)
+        tc = b.to_tick_circuit()
+        det_fired, obs_vals = simulate_tick_circuit(tc, seed)[-2:]
+        assert det_fired == 0, f"w={width} d={depth}: {det_fired} detectors fired"
+        for obs_id, val in obs_vals.items():
+            assert val == 0, f"w={width} d={depth}: obs{obs_id}={val}"
+
+    @pytest.mark.parametrize("width", [2, 3])
+    @pytest.mark.parametrize("seed", range(3))
+    def test_brickwork_d5(self, width, seed):
+        patch = SurfacePatch.create(distance=5)
+        b = _build_mirrored_brickwork(width, 2, seed, patch)
+        tc = b.to_tick_circuit()
+        det_fired, obs_vals = simulate_tick_circuit(tc, seed)[-2:]
+        assert det_fired == 0
+        for val in obs_vals.values():
+            assert val == 0
+
+
+# ---------------------------------------------------------------------------
+# TickCircuit structural tests
+# ---------------------------------------------------------------------------
+
+
+class TestTickCircuitStructure:
+    def test_gate_count_and_gate_batch_count_are_distinct(self):
+        tc = TickCircuit()
+        tc.tick().h([0]).h([1]).cx([(2, 3), (4, 5)])
+
+        tick = tc.get_tick(0)
+        assert tick.gate_count() == 4
+        assert tick.gate_batch_count() == 2
+        assert len(tick.gate_batches()) == 2
+        assert len(tick) == 2
+
+        assert tc.gate_count() == 4
+        assert tc.gate_batch_count() == 2
+        assert len(tc.gate_batches()) == 2
+
+    @pytest.mark.parametrize("num_qubits", [1, 2, 3, 5, 8])
+    @pytest.mark.parametrize("depth", [10, 30])
+    @pytest.mark.parametrize("seed", range(3))
+    def test_build_roundtrip(self, num_qubits, depth, seed):
+        gate_set = ["H", "SZ", "X", "Z"]
+        if num_qubits >= 2:
+            gate_set.extend(["CX", "CZ"])
+        rng = random.Random(seed)
+        tc = TickCircuit()
+        t = tc.tick()
+        t.qalloc(list(range(num_qubits)))
+        for _ in range(depth):
+            gate = rng.choice(gate_set)
+            t = tc.tick()
+            if gate in ("CX", "CZ"):
+                q1, q2 = rng.sample(range(num_qubits), 2)
+                getattr(t, gate.lower())([(q1, q2)])
+            else:
+                q = rng.randint(0, num_qubits - 1)
+                getattr(t, gate.lower())([q])
+        t = tc.tick()
+        t.mz(list(range(num_qubits)))
+        assert tc.num_ticks() >= 2
diff --git a/python/quantum-pecos/tests/qec/surface/test_surface_decoder.py b/python/quantum-pecos/tests/qec/surface/test_surface_decoder.py
index 18da22565..c89112f6b 100644
--- a/python/quantum-pecos/tests/qec/surface/test_surface_decoder.py
+++ b/python/quantum-pecos/tests/qec/surface/test_surface_decoder.py
@@ -59,7 +59,7 @@ def test_default_values(self) -> None:
         assert noise.p1 == 0.0
         assert noise.p2 == 0.0
         assert noise.p_meas == 0.0
-        assert noise.p_init == 0.0
+        assert noise.p_prep == 0.0
 
     def test_is_noiseless(self) -> None:
         """Test is_noiseless property."""
@@ -67,11 +67,11 @@ def test_is_noiseless(self) -> None:
         assert not NoiseModel(p1=0.01).is_noiseless
         assert not NoiseModel(p2=0.01).is_noiseless
         assert not NoiseModel(p_meas=0.01).is_noiseless
-        assert not NoiseModel(p_init=0.01).is_noiseless
+        assert not NoiseModel(p_prep=0.01).is_noiseless
 
     def test_physical_error_rate(self) -> None:
         """Test physical_error_rate property."""
-        noise = NoiseModel(p1=0.001, p2=0.01, p_meas=0.005, p_init=0.002)
+        noise = NoiseModel(p1=0.001, p2=0.01, p_meas=0.005, p_prep=0.002)
         assert noise.physical_error_rate == 0.01  # max of all rates
 
 
@@ -212,7 +212,7 @@ def test_get_dem_caches_circuit_level_dem(self, monkeypatch: pytest.MonkeyPatch)
         import pecos.qec.surface.decode as decode_module
 
         patch = SurfacePatch.create(distance=3)
-        noise = NoiseModel(p1=0.001, p2=0.01, p_meas=0.01, p_init=0.001)
+        noise = NoiseModel(p1=0.001, p2=0.01, p_meas=0.01, p_prep=0.001)
         decoder = SurfaceDecoder(
             patch,
             num_rounds=3,
@@ -304,7 +304,7 @@ def test_generate_dem_from_patch_can_skip_stim_decomposition(self) -> None:
         from pecos.qec.surface.decode import generate_dem_from_patch
 
         patch = SurfacePatch.create(distance=3)
-        noise = NoiseModel(p1=0.001, p2=0.01, p_meas=0.01, p_init=0.001)
+        noise = NoiseModel(p1=0.001, p2=0.01, p_meas=0.01, p_prep=0.001)
 
         full_dem = generate_dem_from_patch(patch, num_rounds=4, noise=noise, basis="X", decompose_errors=False)
         decomposed_dem = generate_dem_from_patch(patch, num_rounds=4, noise=noise, basis="X", decompose_errors=True)
@@ -316,7 +316,7 @@ def test_generate_dem_from_tick_circuit_supports_raw_and_decomposed_output(self)
         """Native TickCircuit DEM helper should preserve both public output forms."""
         patch = SurfacePatch.create(distance=3)
         tc = generate_tick_circuit_from_patch(patch, num_rounds=4, basis="X")
-        params = {"p1": 0.001, "p2": 0.01, "p_meas": 0.01, "p_init": 0.001}
+        params = {"p1": 0.001, "p2": 0.01, "p_meas": 0.01, "p_prep": 0.001}
 
         raw_dem = generate_dem_from_tick_circuit(tc, **params, decompose_errors=False)
         decomposed_dem = generate_dem_from_tick_circuit(tc, **params, decompose_errors=True)
@@ -330,8 +330,8 @@ def test_native_circuit_level_dem_threads_ancilla_budget(self) -> None:
         from pecos.qec.surface.decode import generate_circuit_level_dem_from_builder
 
         patch = SurfacePatch.create(distance=3)
-        noise = NoiseModel(p1=0.001, p2=0.01, p_meas=0.01, p_init=0.001)
-        params = {"p1": noise.p1, "p2": noise.p2, "p_meas": noise.p_meas, "p_init": noise.p_init}
+        noise = NoiseModel(p1=0.001, p2=0.01, p_meas=0.01, p_prep=0.001)
+        params = {"p1": noise.p1, "p2": noise.p2, "p_meas": noise.p_meas, "p_prep": noise.p_prep}
 
         full_tc = generate_tick_circuit_from_patch(patch, num_rounds=2, basis="X")
         batched_tc = generate_tick_circuit_from_patch(
@@ -369,8 +369,8 @@ def test_native_circuit_level_dem_cache_respects_patch_geometry(self) -> None:
         from pecos.qec.surface.decode import generate_circuit_level_dem_from_builder
 
         patch = SurfacePatch.create(dx=3, dz=5)
-        noise = NoiseModel(p1=0.001, p2=0.01, p_meas=0.01, p_init=0.001)
-        params = {"p1": noise.p1, "p2": noise.p2, "p_meas": noise.p_meas, "p_init": noise.p_init}
+        noise = NoiseModel(p1=0.001, p2=0.01, p_meas=0.01, p_prep=0.001)
+        params = {"p1": noise.p1, "p2": noise.p2, "p_meas": noise.p_meas, "p_prep": noise.p_prep}
 
         tc = generate_tick_circuit_from_patch(patch, num_rounds=2, basis="X")
         expected_dem = generate_dem_from_tick_circuit(tc, **params, decompose_errors=False)
@@ -383,6 +383,49 @@ def test_native_circuit_level_dem_cache_respects_patch_geometry(self) -> None:
 
         assert cached_dem == expected_dem
 
+    def test_native_circuit_level_dem_cache_inserts_idle_gates_only_for_idle_noise(self) -> None:
+        """Shared native DEM caching should make idle locations an explicit noise choice."""
+        from pecos.qec.surface.circuit_builder import generate_dem_from_tick_circuit, generate_tick_circuit_from_patch
+        from pecos.qec.surface.decode import generate_circuit_level_dem_from_builder
+
+        patch = SurfacePatch.create(distance=3)
+        base_noise = NoiseModel(p1=0.001, p2=0.01, p_meas=0.01, p_prep=0.001)
+        base_params = {
+            "p1": base_noise.p1,
+            "p2": base_noise.p2,
+            "p_meas": base_noise.p_meas,
+            "p_prep": base_noise.p_prep,
+            "decompose_errors": False,
+        }
+
+        tc = generate_tick_circuit_from_patch(patch, num_rounds=2, basis="X")
+        expected_base_dem = generate_dem_from_tick_circuit(tc, **base_params)
+        cached_base_dem = generate_circuit_level_dem_from_builder(
+            patch,
+            num_rounds=2,
+            noise=base_noise,
+            basis="X",
+        )
+
+        idle_noise = NoiseModel(p1=0.001, p2=0.01, p_meas=0.01, p_prep=0.001, p_idle=0.002)
+        idle_tc = generate_tick_circuit_from_patch(patch, num_rounds=2, basis="X")
+        idle_tc.fill_idle_gates()
+        expected_idle_dem = generate_dem_from_tick_circuit(
+            idle_tc,
+            **base_params,
+            p_idle=idle_noise.p_idle,
+        )
+        cached_idle_dem = generate_circuit_level_dem_from_builder(
+            patch,
+            num_rounds=2,
+            noise=idle_noise,
+            basis="X",
+        )
+
+        assert cached_base_dem == expected_base_dem
+        assert cached_idle_dem == expected_idle_dem
+        assert cached_idle_dem != cached_base_dem
+
     def test_traced_qis_native_dem_and_sampler_build(self) -> None:
         """The traced-QIS circuit source should build DEMs and samplers end-to-end."""
         from pecos.qec.surface import build_native_sampler
@@ -391,7 +434,7 @@ def test_traced_qis_native_dem_and_sampler_build(self) -> None:
         _require_selene_runtime()
 
         patch = SurfacePatch.create(distance=3)
-        noise = NoiseModel(p1=0.001, p2=0.001, p_meas=0.001, p_init=0.001)
+        noise = NoiseModel(p1=0.001, p2=0.001, p_meas=0.001, p_prep=0.001)
 
         dem = generate_circuit_level_dem_from_builder(
             patch,
@@ -426,7 +469,7 @@ def test_traced_qis_native_dem_and_sampler_build(self) -> None:
         mnm_det_events, mnm_obs_flips = mnm_sampler.sample(4, seed=7)
         assert mnm_det_events.shape == (4, mnm_sampler.num_detectors)
         assert mnm_obs_flips.shape == (4, mnm_sampler.num_observables)
-        assert mnm_sampler.sampling_model == "mnm"
+        assert mnm_sampler.sampling_model == "influence_dem"  # "mnm" remapped to unified sampler
 
         influence_sampler = build_native_sampler(
             patch,
@@ -476,7 +519,7 @@ def extract_errors(dem_str: str) -> dict[str, float]:
             return errors
 
         patch = SurfacePatch.create(distance=3)
-        noise = NoiseModel(p1=0.003, p2=0.003, p_meas=0.003, p_init=0.003)
+        noise = NoiseModel(p1=0.003, p2=0.003, p_meas=0.003, p_prep=0.003)
 
         for basis in ("X", "Z"):
             tc = _build_surface_tick_circuit_for_native_model(
@@ -490,7 +533,7 @@ def extract_errors(dem_str: str) -> dict[str, float]:
                 p1=noise.p1,
                 p2=noise.p2,
                 p_meas=noise.p_meas,
-                p_init=noise.p_init,
+                p_prep=noise.p_prep,
                 decompose_errors=False,
             )
             stim_dem = str(
@@ -500,7 +543,7 @@ def extract_errors(dem_str: str) -> dict[str, float]:
                         p1=noise.p1,
                         p2=noise.p2,
                         p_meas=noise.p_meas,
-                        p_init=noise.p_init,
+                        p_prep=noise.p_prep,
                     ),
                 ).detector_error_model(decompose_errors=False),
             )
@@ -531,8 +574,8 @@ def test_traced_qis_native_topology_cache_is_shared_across_public_apis(self) ->
         _require_selene_runtime()
 
         patch = SurfacePatch.create(distance=3)
-        noise_a = NoiseModel(p1=0.001, p2=0.001, p_meas=0.001, p_init=0.001)
-        noise_b = NoiseModel(p1=0.002, p2=0.002, p_meas=0.002, p_init=0.002)
+        noise_a = NoiseModel(p1=0.001, p2=0.001, p_meas=0.001, p_prep=0.001)
+        noise_b = NoiseModel(p1=0.002, p2=0.002, p_meas=0.002, p_prep=0.002)
 
         _cached_surface_native_topology.cache_clear()
         _cached_surface_native_dem_string.cache_clear()
@@ -582,7 +625,7 @@ def test_generate_dem_from_tick_circuit_maximal_decomposition_prefers_singletons
         """Maximal decomposition should no longer be a no-op."""
         patch = SurfacePatch.create(distance=3)
         tc = generate_tick_circuit_from_patch(patch, num_rounds=20, basis="X")
-        params = {"p1": 0.0, "p2": 0.00235, "p_meas": 0.01972626855445279, "p_init": 0.0010045162906914633}
+        params = {"p1": 0.0, "p2": 0.00235, "p_meas": 0.01972626855445279, "p_prep": 0.0010045162906914633}
 
         decomposed_dem = generate_dem_from_tick_circuit(tc, **params, decompose_errors=True)
         maximal_dem = generate_dem_from_tick_circuit(
diff --git a/python/quantum-pecos/tests/qec/surface/test_surface_geometry.py b/python/quantum-pecos/tests/qec/surface/test_surface_geometry.py
new file mode 100644
index 000000000..e0db9ab13
--- /dev/null
+++ b/python/quantum-pecos/tests/qec/surface/test_surface_geometry.py
@@ -0,0 +1,325 @@
+# Copyright 2026 The PECOS Developers
+# Licensed under the Apache License, Version 2.0
+
+"""Tests for surface code geometry across all dimensions.
+
+Verifies that the stabilizer generators, code parameters, CNOT scheduling,
+and circuit generation work correctly for:
+- Standard odd square codes (d=3,5,7)
+- Even square codes (d=2,4)
+- Asymmetric codes (dx != dz)
+- Repetition codes (dx=1 or dz=1)
+- Single qubit (dx=dz=1)
+"""
+
+import pytest
+from pecos.qec.surface import SurfacePatch
+from pecos.qec.surface.schedule import compute_cnot_schedule
+
+# ============================================================
+# Code parameters: n, k, d
+# ============================================================
+
+
+@pytest.mark.parametrize(
+    ("dx", "dz", "expected_n", "expected_k", "expected_d"),
+    [
+        # Single qubit
+        (1, 1, 1, 1, 1),
+        # Repetition codes (X checks)
+        (1, 3, 3, 1, 1),
+        (1, 5, 5, 1, 1),
+        (1, 7, 7, 1, 1),
+        # Repetition codes (Z checks)
+        (3, 1, 3, 1, 1),
+        (5, 1, 5, 1, 1),
+        # Even square
+        (2, 2, 4, 1, 2),
+        (4, 4, 16, 1, 4),
+        # Odd square (standard surface code)
+        (3, 3, 9, 1, 3),
+        (5, 5, 25, 1, 5),
+        (7, 7, 49, 1, 7),
+        # Asymmetric
+        (2, 3, 6, 1, 2),
+        (3, 2, 6, 1, 2),
+        (3, 5, 15, 1, 3),
+        (5, 3, 15, 1, 3),
+        (2, 5, 10, 1, 2),
+    ],
+)
+def test_code_parameters(dx, dz, expected_n, expected_k, expected_d):
+    """Code parameters [[n,k,d]] should be correct for all dimensions."""
+    patch = SurfacePatch.create(dx=dx, dz=dz)
+    n = patch.num_data
+    k = n - patch.geometry.num_x_stab - patch.geometry.num_z_stab
+    d = patch.distance
+
+    assert n == expected_n
+    assert k == expected_k
+    assert d == expected_d
+
+
+# ============================================================
+# Stabilizer structure
+# ============================================================
+
+
+@pytest.mark.parametrize(
+    ("dx", "dz", "expected_x", "expected_z"),
+    [
+        (1, 1, 0, 0),
+        (1, 3, 2, 0),
+        (3, 1, 0, 2),
+        (1, 5, 4, 0),
+        (5, 1, 0, 4),
+        (2, 2, 2, 1),
+        (3, 3, 4, 4),
+        (2, 3, 3, 2),
+        (3, 2, 2, 3),
+        (4, 4, 8, 7),
+        (5, 5, 12, 12),
+    ],
+)
+def test_stabilizer_counts(dx, dz, expected_x, expected_z):
+    """Number of X and Z stabilizers should match expected values."""
+    patch = SurfacePatch.create(dx=dx, dz=dz)
+    assert patch.geometry.num_x_stab == expected_x
+    assert patch.geometry.num_z_stab == expected_z
+
+
+def test_repetition_code_x_checks():
+    """dx=1 repetition code should have only X stabilizers (adjacent XX pairs)."""
+    patch = SurfacePatch.create(dx=1, dz=5)
+    assert patch.geometry.num_z_stab == 0
+    qubits = [s.data_qubits for s in patch.geometry.x_stabilizers]
+    # All should be adjacent pairs covering 0..4
+    for q1, q2 in qubits:
+        assert q2 == q1 + 1
+
+
+def test_repetition_code_z_checks():
+    """dz=1 repetition code should have only Z stabilizers (adjacent ZZ pairs)."""
+    patch = SurfacePatch.create(dx=5, dz=1)
+    assert patch.geometry.num_x_stab == 0
+    qubits = [s.data_qubits for s in patch.geometry.z_stabilizers]
+    for q1, q2 in qubits:
+        assert q2 == q1 + 1
+
+
+def test_all_data_qubits_in_stabilizer_support():
+    """Every data qubit (except logical operator edges) should appear in at least one stabilizer."""
+    for dx, dz in [(3, 3), (2, 3), (3, 2), (2, 2), (4, 4)]:
+        patch = SurfacePatch.create(dx=dx, dz=dz)
+        touched = set()
+        for s in patch.geometry.x_stabilizers:
+            touched.update(s.data_qubits)
+        for s in patch.geometry.z_stabilizers:
+            touched.update(s.data_qubits)
+        assert touched == set(range(patch.num_data)), f"Untouched qubits in {dx}x{dz}"
+
+
+def test_stabilizer_weights():
+    """Bulk stabilizers should be weight 4, boundary weight 2."""
+    for dx, dz in [(3, 3), (5, 5), (2, 3), (3, 5)]:
+        patch = SurfacePatch.create(dx=dx, dz=dz)
+        for s in list(patch.geometry.x_stabilizers) + list(patch.geometry.z_stabilizers):
+            if s.is_boundary:
+                assert len(s.data_qubits) == 2, f"Boundary stab has weight {len(s.data_qubits)}"
+            else:
+                assert len(s.data_qubits) == 4, f"Bulk stab has weight {len(s.data_qubits)}"
+
+
+# ============================================================
+# Logical operators
+# ============================================================
+
+
+def test_logical_x_weight_equals_dx():
+    """Logical X should have weight dx (left edge of the grid)."""
+    for dx, dz in [(3, 3), (3, 5), (5, 3), (2, 3), (1, 5)]:
+        patch = SurfacePatch.create(dx=dx, dz=dz)
+        assert len(patch.geometry.logical_x.data_qubits) == dx
+
+
+def test_logical_z_weight_equals_dz():
+    """Logical Z should have weight dz (top edge of the grid)."""
+    for dx, dz in [(3, 3), (3, 5), (5, 3), (2, 3), (1, 5)]:
+        patch = SurfacePatch.create(dx=dx, dz=dz)
+        assert len(patch.geometry.logical_z.data_qubits) == dz
+
+
+def test_logical_x_is_left_edge():
+    """Logical X qubits should be column 0 of the dx x dz grid."""
+    for dx, dz in [(3, 3), (3, 5), (2, 3)]:
+        patch = SurfacePatch.create(dx=dx, dz=dz)
+        expected = tuple(i * dz for i in range(dx))
+        assert patch.geometry.logical_x.data_qubits == expected
+
+
+def test_logical_z_is_top_edge():
+    """Logical Z qubits should be row 0 of the dx x dz grid."""
+    for dx, dz in [(3, 3), (3, 5), (2, 3)]:
+        patch = SurfacePatch.create(dx=dx, dz=dz)
+        expected = tuple(range(dz))
+        assert patch.geometry.logical_z.data_qubits == expected
+
+
+# ============================================================
+# CNOT schedule: no conflicts
+# ============================================================
+
+
+@pytest.mark.parametrize(
+    ("dx", "dz"),
+    [
+        (1, 3),
+        (3, 1),
+        (2, 2),
+        (2, 3),
+        (3, 2),
+        (3, 3),
+        (3, 5),
+        (5, 3),
+        (4, 4),
+        (5, 5),
+    ],
+)
+def test_cnot_schedule_no_conflicts(dx, dz):
+    """No data qubit should be touched twice in the same CNOT round."""
+    patch = SurfacePatch.create(dx=dx, dz=dz)
+    schedule = compute_cnot_schedule(patch)
+    for rnd_idx, rnd in enumerate(schedule):
+        data_qubits = [dq for _, _, dq in rnd]
+        assert len(data_qubits) == len(
+            set(data_qubits),
+        ), f"{dx}x{dz} round {rnd_idx}: data qubit collision {data_qubits}"
+
+
+# ============================================================
+# Backward compatibility: square odd codes unchanged
+# ============================================================
+
+
+def test_square_odd_codes_match_original():
+    """The generalized generators should produce identical results to the
+    original single-d generators for square odd codes.
+    """
+    from pecos.qec.surface.layouts.rotated_lattice import (
+        compute_rotated_x_stabilizers,
+        compute_rotated_z_stabilizers,
+        get_rotated_logical_x,
+        get_rotated_logical_z,
+    )
+
+    for d in [3, 5, 7]:
+        x_single = compute_rotated_x_stabilizers(d)
+        x_pair = compute_rotated_x_stabilizers(d, d)
+        z_single = compute_rotated_z_stabilizers(d)
+        z_pair = compute_rotated_z_stabilizers(d, d)
+
+        assert len(x_single) == len(x_pair)
+        assert len(z_single) == len(z_pair)
+
+        for a, b in zip(x_single, x_pair, strict=False):
+            assert a.data_qubits == b.data_qubits
+            assert a.is_boundary == b.is_boundary
+
+        for a, b in zip(z_single, z_pair, strict=False):
+            assert a.data_qubits == b.data_qubits
+            assert a.is_boundary == b.is_boundary
+
+        assert get_rotated_logical_x(d) == get_rotated_logical_x(d, d)
+        assert get_rotated_logical_z(d) == get_rotated_logical_z(d, d)
+
+
+# ============================================================
+# Transposition symmetry
+# ============================================================
+
+
+def test_transpose_swaps_x_and_z_counts():
+    """Swapping dx and dz should swap the number of X and Z stabilizers."""
+    for dx, dz in [(2, 3), (3, 5), (2, 5), (1, 3), (1, 5)]:
+        p1 = SurfacePatch.create(dx=dx, dz=dz)
+        p2 = SurfacePatch.create(dx=dz, dz=dx)
+        assert p1.geometry.num_x_stab == p2.geometry.num_z_stab
+        assert p1.geometry.num_z_stab == p2.geometry.num_x_stab
+
+
+# ============================================================
+# Circuit generation
+# ============================================================
+
+
+@pytest.mark.parametrize(
+    ("dx", "dz"),
+    [
+        (1, 1),
+        (1, 3),
+        (3, 1),
+        (2, 2),
+        (2, 3),
+        (3, 2),
+        (3, 3),
+    ],
+)
+def test_circuit_generation(dx, dz):
+    """LogicalCircuitBuilder should produce a valid TickCircuit for all dimensions."""
+    from pecos.qec.surface import LogicalCircuitBuilder
+
+    patch = SurfacePatch.create(dx=dx, dz=dz)
+    lcb = LogicalCircuitBuilder()
+    lcb.add_patch(patch, "A")
+    basis = "Z" if dx >= dz else "X"
+    lcb.add_memory("A", rounds=2, basis=basis)
+    tc = lcb.to_tick_circuit()
+
+    assert tc.num_ticks() > 0
+    assert tc.gate_count() > 0
+
+
+# ============================================================
+# Transversal gate square check
+# ============================================================
+
+
+def test_transversal_h_rejects_nonsquare():
+    """Transversal H should reject non-square patches."""
+    from pecos.qec.surface import LogicalCircuitBuilder
+
+    patch = SurfacePatch.create(dx=2, dz=3)
+    lcb = LogicalCircuitBuilder()
+    lcb.add_patch(patch, "A")
+    with pytest.raises(ValueError, match="square"):
+        lcb.add_transversal_h("A")
+
+
+def test_transversal_h_accepts_square():
+    """Transversal H should accept square patches of any distance."""
+    from pecos.qec.surface import LogicalCircuitBuilder
+
+    for d in [2, 3, 4, 5]:
+        patch = SurfacePatch.create(distance=d)
+        lcb = LogicalCircuitBuilder()
+        lcb.add_patch(patch, "A")
+        lcb.add_memory("A", rounds=1, basis="Z")
+        lcb.add_transversal_h("A")
+        lcb.add_memory("A", rounds=1, basis="X")
+
+
+# ============================================================
+# Validation
+# ============================================================
+
+
+def test_distance_zero_rejected():
+    """Distance 0 should raise ValueError."""
+    with pytest.raises(ValueError, match=r"Distance must be >= 1"):
+        SurfacePatch.create(distance=0)
+
+
+def test_negative_distance_rejected():
+    """Negative distance should raise ValueError."""
+    with pytest.raises(ValueError, match=r"dx must be >= 1"):
+        SurfacePatch.create(dx=-1, dz=3)
diff --git a/python/quantum-pecos/tests/qec/surface/test_surface_metadata.py b/python/quantum-pecos/tests/qec/surface/test_surface_metadata.py
index 2bc627c27..f5f7fa606 100644
--- a/python/quantum-pecos/tests/qec/surface/test_surface_metadata.py
+++ b/python/quantum-pecos/tests/qec/surface/test_surface_metadata.py
@@ -54,8 +54,8 @@ def test_surface_schedule_helpers_expose_region_and_touch_labels() -> None:
     assert get_stabilizer_touch_label(x_bulk, patch, 4) == "BL"
     assert get_stabilizer_touch_label(x_bulk, patch, 5) == "BR"
 
-    assert get_stab_schedule("X", x_top.data_qubits, x_top.is_boundary, patch.distance) == [(2, 1), (3, 0)]
-    assert get_stab_schedule("Z", z_left.data_qubits, z_left.is_boundary, patch.distance) == [(0, 3), (1, 6)]
+    assert get_stab_schedule("X", x_top.data_qubits, x_top.is_boundary, patch.dx, patch.dz) == [(2, 1), (3, 0)]
+    assert get_stab_schedule("Z", z_left.data_qubits, z_left.is_boundary, patch.dx, patch.dz) == [(0, 3), (1, 6)]
 
     assert get_stabilizer_schedule_entries(x_top, patch) == [
         {"round_0based": 2, "data_qubit": 1, "touch_label": "right"},
@@ -210,7 +210,7 @@ def test_tick_circuit_exposes_measurement_order() -> None:
         tick = tc.get_tick(tick_index)
         if tick is None:
             continue
-        for gate in tick.gates():
+        for gate in tick.gate_batches():
             if "MZ" not in str(gate.gate_type):
                 continue
             for qubit in gate.qubits:
diff --git a/python/quantum-pecos/tests/qec/test_analysis_meas_sampling.py b/python/quantum-pecos/tests/qec/test_analysis_meas_sampling.py
new file mode 100644
index 000000000..800c1f717
--- /dev/null
+++ b/python/quantum-pecos/tests/qec/test_analysis_meas_sampling.py
@@ -0,0 +1,127 @@
+# Copyright 2026 The PECOS Developers
+# Licensed under the Apache License, Version 2.0
+
+"""Tests for analysis helpers with DEM-backed sampling backends."""
+
+import pytest
+from pecos.qec.analysis import empirical_correlation_table, fit_dem_from_simulation
+from pecos.qec.surface import SurfacePatch
+from pecos.qec.surface.decode import _build_surface_tick_circuit_for_native_model
+from pecos_rslib_exp import depolarizing
+
+
+@pytest.fixture
+def d3_circuit_and_noise():
+    patch = SurfacePatch.create(distance=3)
+    tc = _build_surface_tick_circuit_for_native_model(patch, 6, "Z", circuit_source="abstract")
+    noise = depolarizing().p1(0.005).p2(0.005).p_meas(0.005).p_prep(0.005)
+    return tc, noise
+
+
+class TestEmpiricalCorrelationTable:
+    def test_meas_sampling_returns_nonempty(self, d3_circuit_and_noise):
+        tc, noise = d3_circuit_and_noise
+        table = empirical_correlation_table(
+            tc,
+            noise,
+            shots=5000,
+            max_order=1,
+            backend="meas_sampling",
+            seed=42,
+        )
+        assert len(table) > 0, "Should return at least one rate entry"
+
+    def test_meas_sampling_label_shape(self, d3_circuit_and_noise):
+        tc, noise = d3_circuit_and_noise
+        table = empirical_correlation_table(
+            tc,
+            noise,
+            shots=5000,
+            max_order=1,
+            backend="meas_sampling",
+            seed=42,
+        )
+        # Each entry is (detector_indices_tuple, probability)
+        for indices, prob in table:
+            assert isinstance(indices, tuple)
+            assert len(indices) >= 1
+            assert isinstance(prob, float)
+            assert 0.0 <= prob <= 1.0
+
+    def test_meas_sampling_rates_close_to_stabilizer(self, d3_circuit_and_noise):
+        tc, noise = d3_circuit_and_noise
+        shots = 20000
+
+        meas_table = empirical_correlation_table(
+            tc,
+            noise,
+            shots=shots,
+            max_order=1,
+            backend="meas_sampling",
+            seed=42,
+        )
+        stab_table = empirical_correlation_table(
+            tc,
+            noise,
+            shots=shots,
+            max_order=1,
+            backend="stabilizer",
+            seed=42,
+        )
+
+        # Both should have the same entries (same detectors)
+        meas_dict = dict(meas_table)
+        stab_dict = dict(stab_table)
+
+        assert set(meas_dict.keys()) == set(stab_dict.keys()), "Same detector indices should appear in both"
+
+        # Rates should be statistically close (within 20% relative for active detectors)
+        close_count = 0
+        active_count = 0
+        for key, d in meas_dict.items():
+            s = stab_dict[key]
+            if s > 0.005:
+                active_count += 1
+                if abs(d - s) / s < 0.20:
+                    close_count += 1
+
+        assert active_count > 0, "Should have active detectors"
+        assert close_count >= active_count * 0.8, f"Only {close_count}/{active_count} rates within 20% of stabilizer"
+
+
+class TestFitDemFromSimulation:
+    def test_meas_sampling_returns_dem_string(self, d3_circuit_and_noise):
+        tc, noise = d3_circuit_and_noise
+        dem_str = fit_dem_from_simulation(
+            tc,
+            noise,
+            shots=10000,
+            backend="meas_sampling",
+            seed=42,
+        )
+        assert isinstance(dem_str, str)
+        assert "error(" in dem_str, "DEM string should contain error(...) lines"
+
+    def test_meas_sampling_has_multiple_mechanisms(self, d3_circuit_and_noise):
+        tc, noise = d3_circuit_and_noise
+        dem_str = fit_dem_from_simulation(
+            tc,
+            noise,
+            shots=10000,
+            backend="meas_sampling",
+            seed=42,
+        )
+        error_lines = [line for line in dem_str.strip().split("\n") if line.strip().startswith("error(")]
+        assert len(error_lines) > 10, f"Expected many mechanisms, got {len(error_lines)}"
+
+
+class TestInvalidBackend:
+    def test_empirical_correlation_table_rejects_unknown(self, d3_circuit_and_noise):
+        tc, noise = d3_circuit_and_noise
+        with pytest.raises(ValueError, match=r"Unknown backend.*'bogus'"):
+            empirical_correlation_table(tc, noise, shots=10, backend="bogus")
+
+    def test_fit_dem_from_simulation_rejects_unknown(self, d3_circuit_and_noise):
+        tc, noise = d3_circuit_and_noise
+        with pytest.raises(ValueError, match=r"Unknown backend.*'nope'"):
+            fit_dem_from_simulation(tc, noise, shots=10, backend="nope")
diff --git a/python/quantum-pecos/tests/qec/test_decomposed_dem_invariants.py b/python/quantum-pecos/tests/qec/test_decomposed_dem_invariants.py
index 555249cf7..11f2e90ad 100644
--- a/python/quantum-pecos/tests/qec/test_decomposed_dem_invariants.py
+++ b/python/quantum-pecos/tests/qec/test_decomposed_dem_invariants.py
@@ -55,7 +55,7 @@ def parse_dem_with_decomposed(
 
 
 def xor_targets(parts: list[tuple[tuple[int, ...], tuple[int, ...]]]) -> tuple[tuple[int, ...], tuple[int, ...]]:
-    """XOR a decomposed list of detector/logical targets into one combined effect."""
+    """XOR a decomposed list of detector/DEM-output observables into one combined effect."""
     dets: set[int] = set()
     logs: set[int] = set()
     for part_dets, part_logs in parts:
@@ -97,10 +97,10 @@ def xor_lists(left: list[int], right: list[int]) -> list[int]:
 
 
 def xor_effect_rows(left: dict[str, list[int]], right: dict[str, list[int]]) -> tuple[list[int], list[int]]:
-    """XOR two structured detector/logical rows."""
+    """XOR two structured detector/DEM-output rows."""
     return (
         xor_lists(left["detectors"], right["detectors"]),
-        xor_lists(left["logicals"], right["logicals"]),
+        xor_lists(left["dem_outputs"], right["dem_outputs"]),
     )
 
 
@@ -144,10 +144,10 @@ def build_source_tracked_dem(distance: int, basis: str, rounds: int = 20) -> obj
     dag = tc.to_dag_circuit()
     analyzer = DagFaultAnalyzer(dag)
     influence_map = analyzer.build_influence_map()
-    noise = NoiseModel(p1=0.01, p2=0.01, p_meas=0.01, p_init=0.01)
+    noise = NoiseModel(p1=0.01, p2=0.01, p_meas=0.01, p_prep=0.01)
 
     builder = DemBuilder(influence_map)
-    builder.with_noise(noise.p1, noise.p2, noise.p_meas, noise.p_init)
+    builder.with_noise(noise.p1, noise.p2, noise.p_meas, noise.p_prep)
     builder.with_num_measurements(int(tc.get_meta("num_measurements") or "0"))
     builder.with_measurement_order(get_measurement_order_from_tick_circuit(tc))
     builder.with_detectors_json(tc.get_meta("detectors"))
@@ -173,12 +173,12 @@ def test_dem_builder_accepts_public_surface_descriptor_json() -> None:
     tc = generate_tick_circuit_from_patch(patch, num_rounds=4, basis="X")
     dag = tc.to_dag_circuit()
     influence_map = DagFaultAnalyzer(dag).build_influence_map()
-    noise = NoiseModel(p1=0.001, p2=0.01, p_meas=0.01, p_init=0.001)
+    noise = NoiseModel(p1=0.001, p2=0.01, p_meas=0.01, p_prep=0.001)
 
     def _build(detectors_json: str, observables_json: str | None) -> object:
         """Build one source-tracked DEM from serialized detector metadata."""
         builder = DemBuilder(influence_map)
-        builder.with_noise(noise.p1, noise.p2, noise.p_meas, noise.p_init)
+        builder.with_noise(noise.p1, noise.p2, noise.p_meas, noise.p_prep)
         builder.with_num_measurements(int(tc.get_meta("num_measurements") or "0"))
         builder.with_measurement_order(get_measurement_order_from_tick_circuit(tc))
         builder.with_detectors_json(detectors_json)
@@ -304,12 +304,12 @@ def test_native_decomposed_components_are_graphlike_and_map_back_to_full_dem(dis
 
     patch = SurfacePatch.create(distance=distance)
     tc = generate_tick_circuit_from_patch(patch, num_rounds=20, basis=basis)
-    params = {"p1": 0.01, "p2": 0.01, "p_meas": 0.01, "p_init": 0.01}
+    params = {"p1": 0.01, "p2": 0.01, "p_meas": 0.01, "p_prep": 0.01}
 
     full_dem = generate_dem_from_tick_circuit(tc, **params, decompose_errors=False)
     native_decomp_dem = generate_dem_from_tick_circuit(tc, **params, decompose_errors=True)
 
-    full_targets, _ = parse_dem_with_decomposed(full_dem)
+    fuldem_outputs, _ = parse_dem_with_decomposed(full_dem)
     _direct_targets, decomposed_targets = parse_dem_with_decomposed(native_decomp_dem)
 
     assert decomposed_targets, "expected representative circuit to contain decomposed terms"
@@ -322,7 +322,7 @@ def test_native_decomposed_components_are_graphlike_and_map_back_to_full_dem(dis
 
         combined = xor_targets(parts)
         msg = f"decomposed components must XOR back to an effect present in the full DEM: {parts!r} -> {combined!r}"
-        assert combined in full_targets, msg
+        assert combined in fuldem_outputs, msg
 
         if combined[1]:
             saw_l0_decomposition = True
@@ -341,7 +341,7 @@ def test_native_decomposed_matches_stim_singleton_l0_edges_for_representative_ci
 
     patch = SurfacePatch.create(distance=3)
     tc = generate_tick_circuit_from_patch(patch, num_rounds=20, basis=basis)
-    params = {"p1": 0.01, "p2": 0.01, "p_meas": 0.01, "p_init": 0.01}
+    params = {"p1": 0.01, "p2": 0.01, "p_meas": 0.01, "p_prep": 0.01}
 
     native_decomp_dem = generate_dem_from_tick_circuit(tc, **params, decompose_errors=True)
     stim_dem = generate_dem_from_tick_circuit_via_stim(tc, **params)
@@ -364,7 +364,7 @@ def test_native_decomposed_preserves_all_stim_direct_observable_targets(distance
 
     patch = SurfacePatch.create(distance=distance)
     tc = generate_tick_circuit_from_patch(patch, num_rounds=20, basis=basis)
-    params = {"p1": 0.01, "p2": 0.01, "p_meas": 0.01, "p_init": 0.01}
+    params = {"p1": 0.01, "p2": 0.01, "p_meas": 0.01, "p_prep": 0.01}
 
     native_decomp_dem = generate_dem_from_tick_circuit(tc, **params, decompose_errors=True)
     stim_dem = generate_dem_from_tick_circuit_via_stim(tc, **params)
@@ -392,7 +392,7 @@ def test_native_full_matches_stim_full_graph_summary_for_representative_circuit(
 
     patch = SurfacePatch.create(distance=distance)
     tc = generate_tick_circuit_from_patch(patch, num_rounds=20, basis=basis)
-    params = {"p1": 0.01, "p2": 0.01, "p_meas": 0.01, "p_init": 0.01}
+    params = {"p1": 0.01, "p2": 0.01, "p_meas": 0.01, "p_prep": 0.01}
 
     native_full_dem = generate_dem_from_tick_circuit(tc, **params, decompose_errors=False)
     stim_full_dem = generate_dem_from_tick_circuit_via_stim(tc, **params, decompose_errors=False)
@@ -418,7 +418,7 @@ def test_generate_dem_from_tick_circuit_via_stim_can_skip_decomposition() -> Non
         p1=0.01,
         p2=0.01,
         p_meas=0.01,
-        p_init=0.01,
+        p_prep=0.01,
         decompose_errors=False,
     )
 
@@ -434,7 +434,7 @@ def test_structured_source_tracking_summaries_include_graphlike_decomposable_cou
     summaries = dem.contribution_effect_summaries()
     assert summaries
 
-    pair_summaries = [summary for summary in summaries if len(summary["detectors"]) == 2 and not summary["logicals"]]
+    pair_summaries = [summary for summary in summaries if len(summary["detectors"]) == 2 and not summary["dem_outputs"]]
     assert pair_summaries
     assert all("graphlike_decomposable_count" in summary for summary in pair_summaries)
     assert all(summary["graphlike_decomposable_count"] >= 0 for summary in pair_summaries)
@@ -448,10 +448,10 @@ def test_structured_source_tracking_bindings_are_self_consistent(basis: str) ->
     summaries = dem.contribution_effect_summaries()
     assert summaries
 
-    observable_summary = next(row for row in summaries if row["logicals"])
+    observable_summary = next(row for row in summaries if row["dem_outputs"])
     contributions = dem.contributions_for_effect(
         observable_summary["detectors"],
-        observable_summary["logicals"],
+        observable_summary["dem_outputs"],
     )
 
     assert contributions
@@ -489,12 +489,12 @@ def test_structured_source_tracking_y_decomposed_rows_xor_back_to_effect(basis:
     assert summaries
 
     for summary in summaries[:20]:
-        contributions = dem.contributions_for_effect(summary["detectors"], summary["logicals"])
+        contributions = dem.contributions_for_effect(summary["detectors"], summary["dem_outputs"])
         y_rows = [row for row in contributions if row["source_type"] == "YDecomposed"]
         assert y_rows
         for row in y_rows:
             assert xor_lists(row["x_detectors"], row["z_detectors"]) == summary["detectors"]
-            assert xor_lists(row["x_logicals"], row["z_logicals"]) == summary["logicals"]
+            assert xor_lists(row["x_dem_outputs"], row["z_dem_outputs"]) == summary["dem_outputs"]
 
 
 @pytest.mark.parametrize("basis", ["X", "Z"])
@@ -504,7 +504,7 @@ def test_structured_direct_component_rows_xor_back_to_effect(basis: str) -> None
 
     rows = []
     for summary in dem.contribution_effect_summaries():
-        for row in dem.contributions_for_effect(summary["detectors"], summary["logicals"]):
+        for row in dem.contributions_for_effect(summary["detectors"], summary["dem_outputs"]):
             if row["source_type"] not in DIRECT_SOURCE_TYPES:
                 continue
             if "component_1_detectors" not in row or "component_2_detectors" not in row:
@@ -516,15 +516,15 @@ def test_structured_direct_component_rows_xor_back_to_effect(basis: str) -> None
     for summary, row in rows[:100]:
         left = {
             "detectors": row["component_1_detectors"],
-            "logicals": row["component_1_logicals"],
+            "dem_outputs": row["component_1_dem_outputs"],
         }
         right = {
             "detectors": row["component_2_detectors"],
-            "logicals": row["component_2_logicals"],
+            "dem_outputs": row["component_2_dem_outputs"],
         }
         dets, logs = xor_effect_rows(left, right)
         assert dets == summary["detectors"]
-        assert logs == summary["logicals"]
+        assert logs == summary["dem_outputs"]
 
 
 @pytest.mark.parametrize("basis", ["X", "Z"])
@@ -534,7 +534,7 @@ def test_structured_one_sided_direct_component_rows_are_exposed(basis: str) -> N
 
     rows = []
     for summary in dem.contribution_effect_summaries():
-        for row in dem.contributions_for_effect(summary["detectors"], summary["logicals"]):
+        for row in dem.contributions_for_effect(summary["detectors"], summary["dem_outputs"]):
             if row["source_type"] != "DirectOneSidedComponent":
                 continue
             rows.append((summary, row))
@@ -542,22 +542,22 @@ def test_structured_one_sided_direct_component_rows_are_exposed(basis: str) -> N
     assert rows
 
     for summary, row in rows[:100]:
-        left_non_empty = bool(row["component_1_detectors"] or row["component_1_logicals"])
-        right_non_empty = bool(row["component_2_detectors"] or row["component_2_logicals"])
+        left_non_empty = bool(row["component_1_detectors"] or row["component_1_dem_outputs"])
+        right_non_empty = bool(row["component_2_detectors"] or row["component_2_dem_outputs"])
         assert left_non_empty != right_non_empty
         assert row["direct_source_family"] == "TwoLocationOneSidedComponent"
         direct_dets, direct_logs = xor_effect_rows(
             {
                 "detectors": row["component_1_detectors"],
-                "logicals": row["component_1_logicals"],
+                "dem_outputs": row["component_1_dem_outputs"],
             },
             {
                 "detectors": row["component_2_detectors"],
-                "logicals": row["component_2_logicals"],
+                "dem_outputs": row["component_2_dem_outputs"],
             },
         )
         assert direct_dets == summary["detectors"]
-        assert direct_logs == summary["logicals"]
+        assert direct_logs == summary["dem_outputs"]
 
 
 @pytest.mark.parametrize("basis", ["X", "Z"])
@@ -569,7 +569,7 @@ def test_structured_direct_source_families_are_exposed_for_direct_rows(basis: st
     for summary in dem.contribution_effect_summaries():
         rows.extend(
             row
-            for row in dem.contributions_for_effect(summary["detectors"], summary["logicals"])
+            for row in dem.contributions_for_effect(summary["detectors"], summary["dem_outputs"])
             if row["source_type"] in DIRECT_SOURCE_TYPES
         )
 
@@ -587,17 +587,17 @@ def test_structured_source_tracking_summaries_partition_all_contributions(basis:
     summaries = dem.contribution_effect_summaries()
     assert summaries
 
-    effect_keys = {(tuple(summary["detectors"]), tuple(summary["logicals"])) for summary in summaries}
+    effect_keys = {(tuple(summary["detectors"]), tuple(summary["dem_outputs"])) for summary in summaries}
     assert len(effect_keys) == len(summaries)
 
     total_count = 0
     total_probability = 0.0
     for summary in summaries:
-        contributions = dem.contributions_for_effect(summary["detectors"], summary["logicals"])
+        contributions = dem.contributions_for_effect(summary["detectors"], summary["dem_outputs"])
         total_count += len(contributions)
         total_probability += sum(float(row["probability"]) for row in contributions)
         assert all(row["detectors"] == summary["detectors"] for row in contributions)
-        assert all(row["logicals"] == summary["logicals"] for row in contributions)
+        assert all(row["dem_outputs"] == summary["dem_outputs"] for row in contributions)
 
     assert total_count == dem.num_contributions
     assert total_count == sum(int(summary["num_contributions"]) for summary in summaries)
@@ -647,7 +647,7 @@ def test_structured_render_records_reproduce_render_summaries(basis: str) -> Non
     for row in render_records:
         key = (
             tuple(row["detectors"]),
-            tuple(row["logicals"]),
+            tuple(row["dem_outputs"]),
             str(row["rendered_targets"]),
         )
         bucket = regrouped.setdefault(
@@ -692,7 +692,7 @@ def test_structured_render_records_reproduce_render_summaries(basis: str) -> Non
     for summary in render_summaries:
         key = (
             tuple(summary["detectors"]),
-            tuple(summary["logicals"]),
+            tuple(summary["dem_outputs"]),
             str(summary["rendered_targets"]),
         )
         bucket = regrouped[key]
diff --git a/python/quantum-pecos/tests/qec/test_dem_equivalence.py b/python/quantum-pecos/tests/qec/test_dem_equivalence.py
index 4fd21b4f8..073470eff 100644
--- a/python/quantum-pecos/tests/qec/test_dem_equivalence.py
+++ b/python/quantum-pecos/tests/qec/test_dem_equivalence.py
@@ -25,15 +25,18 @@ def test_parse_simple_mechanism(self) -> None:
         assert dem.num_mechanisms == 1
         assert dem.num_detectors == 2
         assert dem.num_observables == 0
+        assert dem.num_tracked_paulis == 0
 
-    def test_parse_mechanism_with_observable(self) -> None:
-        """Parse mechanism with observable."""
+    def test_parse_mechanism_with_tracked_pauli(self) -> None:
+        """Parse mechanism with a Stim DEM output exposed as a tracked Pauli."""
         dem_str = "error(0.02) D0 L0"
         dem = ParsedDem.from_string(dem_str)
 
         assert dem.num_mechanisms == 1
         assert dem.num_detectors == 1
+        assert dem.num_dem_outputs == 1
         assert dem.num_observables == 1
+        assert dem.num_tracked_paulis == 0
 
     def test_parse_decomposed_mechanism(self) -> None:
         """Parse a decomposed mechanism (XOR chain)."""
@@ -55,7 +58,9 @@ def test_parse_multiple_mechanisms(self) -> None:
 
         assert dem.num_mechanisms == 3
         assert dem.num_detectors == 3
+        assert dem.num_dem_outputs == 1
         assert dem.num_observables == 1
+        assert dem.num_tracked_paulis == 0
 
     def test_parse_detector_declarations(self) -> None:
         """Parse detector declarations."""
@@ -337,7 +342,7 @@ def surface_code_dem(self) -> tuple[str, str]:
         patch = SurfacePatch.create(distance=3)
         tc = generate_tick_circuit_from_patch(patch, num_rounds=1, basis="Z")
 
-        noise = {"p1": 0.01, "p2": 0.01, "p_meas": 0.01, "p_init": 0.01}
+        noise = {"p1": 0.01, "p2": 0.01, "p_meas": 0.01, "p_prep": 0.01}
 
         pecos_dem = generate_dem_from_tick_circuit(tc, **noise, decompose_errors=False)
 
@@ -403,7 +408,7 @@ def surface_code_dem_pair(self) -> tuple[str, str]:
         patch = SurfacePatch.create(distance=3)
         tc = generate_tick_circuit_from_patch(patch, num_rounds=2, basis="Z")
 
-        noise = {"p1": 0.01, "p2": 0.01, "p_meas": 0.01, "p_init": 0.01}
+        noise = {"p1": 0.01, "p2": 0.01, "p_meas": 0.01, "p_prep": 0.01}
 
         raw_dem = generate_dem_from_tick_circuit(tc, **noise, decompose_errors=False)
         decomposed_dem = generate_dem_from_tick_circuit(
@@ -523,7 +528,7 @@ def test_decomposition_equivalence_various_sizes(
         patch = SurfacePatch.create(distance=distance)
         tc = generate_tick_circuit_from_patch(patch, num_rounds=num_rounds, basis="Z")
 
-        noise = {"p1": 0.01, "p2": 0.01, "p_meas": 0.01, "p_init": 0.01}
+        noise = {"p1": 0.01, "p2": 0.01, "p_meas": 0.01, "p_prep": 0.01}
 
         raw_dem_str = generate_dem_from_tick_circuit(
             tc,
diff --git a/python/quantum-pecos/tests/qec/test_dem_probability_analysis.py b/python/quantum-pecos/tests/qec/test_dem_probability_analysis.py
index b78296090..6be66cc3e 100644
--- a/python/quantum-pecos/tests/qec/test_dem_probability_analysis.py
+++ b/python/quantum-pecos/tests/qec/test_dem_probability_analysis.py
@@ -236,7 +236,7 @@ def test_dem_comparison_d3() -> None:
     p1 = 0.01
     p2 = 0.01
     p_meas = 0.01
-    p_init = 0.01
+    p_prep = 0.01
 
     # Generate DEMs
     pecos_dem = generate_dem_from_tick_circuit(
@@ -244,7 +244,7 @@ def test_dem_comparison_d3() -> None:
         p1=p1,
         p2=p2,
         p_meas=p_meas,
-        p_init=p_init,
+        p_prep=p_prep,
         decompose_errors=False,
     )
     stim_dem = generate_dem_from_tick_circuit_via_stim(
@@ -252,7 +252,7 @@ def test_dem_comparison_d3() -> None:
         p1=p1,
         p2=p2,
         p_meas=p_meas,
-        p_init=p_init,
+        p_prep=p_prep,
     )
 
     print("\n--- PECOS DEM (raw, no decomposition) ---")
@@ -417,14 +417,14 @@ def analyze_decomposition_pattern() -> None:
     patch = SurfacePatch.create(distance=3)
     tc = generate_tick_circuit_from_patch(patch, num_rounds=1, basis="Z")
 
-    p1, p2, p_meas, p_init = 0.01, 0.01, 0.01, 0.01
+    p1, p2, p_meas, p_prep = 0.01, 0.01, 0.01, 0.01
 
     stim_dem = generate_dem_from_tick_circuit_via_stim(
         tc,
         p1=p1,
         p2=p2,
         p_meas=p_meas,
-        p_init=p_init,
+        p_prep=p_prep,
     )
 
     errors, decomposed = parse_stim_dem_with_decomposed(stim_dem)
@@ -459,7 +459,7 @@ def analyze_decomposition_pattern() -> None:
         p1=p1,
         p2=p2,
         p_meas=p_meas,
-        p_init=p_init,
+        p_prep=p_prep,
         decompose_errors=False,
     )
     pecos_errors = parse_dem(pecos_dem)
diff --git a/python/quantum-pecos/tests/qec/test_dem_sampler.py b/python/quantum-pecos/tests/qec/test_dem_sampler.py
index 65825a815..5728e7e4e 100644
--- a/python/quantum-pecos/tests/qec/test_dem_sampler.py
+++ b/python/quantum-pecos/tests/qec/test_dem_sampler.py
@@ -60,6 +60,10 @@ def test_dem_sampler_sampling() -> None:
     builder.with_observables_json('[{"id": 0, "records": [-1]}]')
     sampler = builder.build()
 
+    assert sampler.num_dem_outputs == 1
+    assert sampler.num_observables == 1
+    assert sampler.num_tracked_paulis == 0
+
     # Single sample
     det_events, obs_flips = sampler.sample(seed=42)
     assert isinstance(det_events, list)
@@ -129,12 +133,239 @@ def test_dem_sampler_statistics() -> None:
     assert "logical_error_rate" in stats
     assert "syndrome_rate" in stats
     assert "undetectable_rate" in stats
+    assert "per_dem_output" in stats
+    assert "dem_output_rates" in stats
+    assert "observable_error_count" not in stats
+    assert "observable_error_rate" not in stats
+    assert "per_tracked_op" not in stats
+    assert "tracked_op_statistics_supported" not in stats
+    assert stats["per_dem_output"] == stats["per_observable"]
+    assert stats["dem_output_rates"] == stats["logical_rates"]
+    assert stats["tracked_pauli_statistics_supported"] is True
+    assert "tracked_pauli_statistics_error" not in stats
+    assert sampler.sample_tracked_paulis(seed=42) == []
+    assert sampler.sample_tracked_pauli_batch(2, seed=42) == [[], []]
 
     assert stats["total_shots"] == 10000
     assert 0.0 <= stats["logical_error_rate"] <= 1.0
     assert 0.0 <= stats["syndrome_rate"] <= 1.0
 
 
+def test_dem_sampler_tracked_pauli_labels() -> None:
+    """Test sampler labels expose PECOS tracked-Pauli terminology."""
+    from pecos_rslib import DagCircuit, PauliString
+    from pecos_rslib.qec import DemSampler
+
+    dag = DagCircuit()
+    dag.pz([0])
+    dag.h([0])
+    dag.tracked_pauli(PauliString.from_str("X"), label="x_check")
+
+    sampler = DemSampler.from_circuit(dag, p1=0.03, p2=0.0, p_meas=0.0, p_prep=0.0)
+
+    labels = sampler.labels()
+
+    assert sampler.num_tracked_paulis == 1
+    assert sampler.num_dem_outputs == 0
+    assert sampler.num_observables == 0
+    assert "dem_outputs" in labels
+    assert "tracked_paulis" in labels
+    assert labels["dem_outputs"] == []
+    assert labels["tracked_paulis"] == ["x_check"]
+
+    stats = sampler.sample_statistics(2000, seed=7)
+    assert stats["logical_error_count"] == 0
+    assert stats["per_observable"] == []
+    assert stats["per_tracked_pauli"] == []
+    assert stats["per_dem_output"] == []
+    assert stats["tracked_pauli_statistics_supported"] is False
+    assert "cannot directly sample tracked Pauli flips" in stats["tracked_pauli_statistics_error"]
+
+    with pytest.raises(RuntimeError, match="cannot directly sample tracked Pauli flips"):
+        sampler.sample_tracked_paulis(seed=7)
+    with pytest.raises(RuntimeError, match="cannot directly sample tracked Pauli flips"):
+        sampler.sample_tracked_pauli_batch(4, seed=7)
+
+
+def test_detector_error_model_rejects_legacy_tracked_metadata_json() -> None:
+    """Python metadata import should fail fast on legacy tracked-op fields."""
+    from pecos_rslib.qec import DetectorErrorModel
+
+    old_json = """
+    {
+      "format": "pecos.dem.metadata",
+      "version": 1,
+      "observables": [],
+      "tracked_paulis": [],
+      "tracked_ops": [
+        {
+          "id": 0,
+          "kind": "tracked_op",
+          "label": "old_name",
+          "pauli": "+X0",
+          "records": []
+        }
+      ]
+    }
+    """
+
+    with pytest.raises(ValueError, match="unsupported legacy metadata field: tracked_ops"):
+        DetectorErrorModel.from_pecos_metadata_json(old_json)
+
+
+def test_dem_events_split_observables_and_tracked_paulis() -> None:
+    """DEM summaries report detector, observable, and tracked-Pauli effects separately."""
+    from pecos_rslib import DagCircuit, PauliString
+    from pecos_rslib.qec import DetectorErrorModel
+
+    dag = DagCircuit()
+    dag.pz([0])
+    dag.h([0])
+    dag.tracked_pauli(PauliString.from_str("X"), label="x_check")
+    dag.mz([0])
+    dag.set_attr("num_measurements", "1")
+    dag.set_attr("observables", '[{"id": 0, "records": [-1]}]')
+
+    dem = DetectorErrorModel.from_circuit(
+        dag,
+        p1=0.03,
+        p2=0.0,
+        p_meas=0.02,
+        p_prep=0.0,
+    )
+    sampler = dem.to_sampler()
+
+    assert dem.num_dem_outputs == 1
+    assert dem.num_observables == 1
+    assert dem.num_tracked_paulis == 1
+    assert sampler.num_dem_outputs == 1
+    assert sampler.num_observables == 1
+    assert sampler.num_tracked_paulis == 1
+    assert sampler.labels()["tracked_paulis"] == ["x_check"]
+
+    summaries = dem.contribution_effect_summaries()
+    assert summaries
+    assert all("dem_outputs" in row for row in summaries)
+    assert all("observables" in row for row in summaries)
+    assert all("tracked_paulis" in row for row in summaries)
+
+    observable_hits = {idx for row in summaries for idx in row["observables"]}
+    tracked_hits = {idx for row in summaries for idx in row["tracked_paulis"]}
+    assert 0 in observable_hits
+    assert tracked_hits == set()
+
+
+def test_sample_decode_count_ignores_tracked_paulis() -> None:
+    """Decoder error counting uses observables, not tracked Paulis."""
+    from pecos_rslib import DagCircuit, PauliString
+    from pecos_rslib.qec import DemSampler, DetectorErrorModel
+
+    dag = DagCircuit()
+    dag.pz([0])
+    dag.pz([1])
+    dag.h([1])
+    dag.tracked_pauli(PauliString.from_str("IZ"), label="tracked_z")
+    dag.mz([0])
+    dag.set_attr("num_measurements", "1")
+    dag.set_attr("detectors", '[{"id": 0, "records": [-1]}]')
+    dag.set_attr("observables", '[{"id": 0, "records": [-1]}]')
+
+    sampler = DemSampler.from_circuit(
+        dag,
+        p1=0.4,
+        p2=0.0,
+        p_meas=0.15,
+        p_prep=0.0,
+    )
+    dem = DetectorErrorModel.from_circuit(
+        dag,
+        p1=0.4,
+        p2=0.0,
+        p_meas=0.15,
+        p_prep=0.0,
+    )
+
+    assert sampler.num_dem_outputs == 1
+    assert sampler.num_observables == 1
+    assert sampler.num_tracked_paulis == 1
+    assert "logical_observable L0" in dem.to_string()
+    assert "logical_observable L1" not in dem.to_string()
+
+    errors = sampler.sample_decode_count(dem.to_string(), 2000, seed=17)
+    assert errors == 0
+
+
+def test_influence_map_tracks_dem_outputs_and_tracked_paulis_separately() -> None:
+    """Test influence maps expose DEM outputs and filtered tracked Paulis."""
+    from pecos_rslib import DagCircuit
+    from pecos_rslib.qec import InfluenceBuilder
+
+    dag = DagCircuit()
+    dag.pz([0])
+    dag.h([0])
+
+    builder = InfluenceBuilder(dag)
+    builder.with_tracked_pauli([(0, "X")])
+    influence_map = builder.build()
+
+    assert influence_map.num_tracked_paulis > 0
+    assert influence_map.num_observables == 0
+    assert influence_map.num_dem_outputs == 0
+
+    csr = influence_map.export_csr()
+    assert csr["num_dem_outputs"] == influence_map.num_dem_outputs
+    assert csr["num_internal_dem_outputs"] == influence_map.num_tracked_paulis
+    assert csr["num_observables"] == 0
+    assert csr["num_tracked_paulis"] == influence_map.num_tracked_paulis
+    assert "dem_output_offsets_x" in csr
+    assert "dem_output_data_x" in csr
+
+    for loc_idx in range(influence_map.num_locations):
+        tracked = influence_map.get_tracked_pauli_indices(loc_idx, 1)
+        dem_outputs = influence_map.get_dem_output_indices(loc_idx, 1)
+        internal_dem_outputs = influence_map.get_internal_dem_output_indices(loc_idx, 1)
+        assert dem_outputs == []
+        assert tracked == internal_dem_outputs
+        assert not influence_map.has_dem_output_flips(loc_idx, 1)
+        assert influence_map.has_tracked_pauli_flips(loc_idx, 1) == bool(tracked)
+
+
+def test_influence_builder_does_not_add_empty_tracked_paulis() -> None:
+    """An unconfigured Python InfluenceBuilder should not create identity tracked Paulis."""
+    from pecos_rslib import DagCircuit
+    from pecos_rslib.qec import InfluenceBuilder
+
+    dag = DagCircuit()
+    dag.pz([0])
+    dag.h([0])
+    dag.mz([0])
+
+    influence_map = InfluenceBuilder(dag).build()
+
+    assert influence_map.num_dem_outputs == 0
+    assert influence_map.num_observables == 0
+    assert influence_map.num_tracked_paulis == 0
+
+
+def test_influence_builder_tracked_x_z_are_dem_outputs() -> None:
+    """Tracked X/Z helpers create tracked Paulis, not observables."""
+    from pecos_rslib import DagCircuit
+    from pecos_rslib.qec import InfluenceBuilder
+
+    dag = DagCircuit()
+    dag.pz([0])
+    dag.h([0])
+
+    builder = InfluenceBuilder(dag)
+    builder.with_tracked_x([0])
+    builder.with_tracked_z([0])
+    influence_map = builder.build()
+
+    assert influence_map.num_dem_outputs == 0
+    assert influence_map.num_observables == 0
+    assert influence_map.num_tracked_paulis == 2
+
+
 def test_dem_sampler_zero_noise() -> None:
     """Test that zero noise produces no errors."""
     from pecos_rslib import DagCircuit
@@ -181,7 +412,8 @@ def test_dem_sampler_repr() -> None:
     repr_str = repr(sampler)
     assert "DemSampler" in repr_str
     assert "mechanisms" in repr_str
-    assert "detectors" in repr_str
+    assert "dem_outputs" in repr_str
+    assert "tracked_paulis" in repr_str
 
 
 if __name__ == "__main__":
diff --git a/python/quantum-pecos/tests/qec/test_dem_sampler_modes.py b/python/quantum-pecos/tests/qec/test_dem_sampler_modes.py
new file mode 100644
index 000000000..24a113e61
--- /dev/null
+++ b/python/quantum-pecos/tests/qec/test_dem_sampler_modes.py
@@ -0,0 +1,246 @@
+# Copyright 2026 The PECOS Developers
+#
+# Licensed under the Apache License, Version 2.0 (the "License"); you may not use this file except
+# in compliance with the License. You may obtain a copy of the License at
+#
+#     https://www.apache.org/licenses/LICENSE-2.0
+#
+# Unless required by applicable law or agreed to in writing, software distributed under the License
+# is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express
+# or implied. See the License for the specific language governing permissions and limitations under
+# the License.
+
+"""Tests for DemSampler Python bindings."""
+
+from __future__ import annotations
+
+from typing import TYPE_CHECKING
+
+import pytest
+from pecos.qec import DagFaultAnalyzer, DemSampler, DemSamplerBuilder
+from pecos_rslib import DagCircuit
+
+if TYPE_CHECKING:
+    from pecos.qec import DagFaultInfluenceMap
+
+
+def _build_repetition_code_circuit(num_rounds: int = 3) -> DagCircuit:
+    """Build a simple repetition code circuit."""
+    dag = DagCircuit()
+    for _ in range(num_rounds):
+        dag.pz([3])
+        dag.pz([4])
+        dag.cx([(0, 3)])
+        dag.cx([(1, 3)])
+        dag.cx([(1, 4)])
+        dag.cx([(2, 4)])
+        dag.mz([3])
+        dag.mz([4])
+    return dag
+
+
+def _build_influence_map(dag: DagCircuit) -> DagFaultInfluenceMap:
+    """Build influence map with logical Z."""
+    analyzer = DagFaultAnalyzer(dag)
+    return analyzer.build_influence_map()
+
+
+class TestDemSamplerRawMode:
+    """Test raw measurement output mode."""
+
+    def test_raw_uniform_creates_sampler(self) -> None:
+        """Test that raw_uniform constructor creates a valid sampler."""
+        dag = _build_repetition_code_circuit(2)
+        im = _build_influence_map(dag)
+        sampler = DemSampler.raw_uniform(im, 0.01)
+        assert sampler.num_mechanisms > 0
+
+    def test_raw_circuit_noise_creates_sampler(self) -> None:
+        """Test that raw constructor with per-gate noise creates a valid sampler."""
+        dag = _build_repetition_code_circuit(2)
+        im = _build_influence_map(dag)
+        sampler = DemSampler.raw(im, 0.001, 0.01, 0.005, 0.001)
+        assert sampler.num_mechanisms > 0
+
+    def test_raw_sample_returns_correct_shape(self) -> None:
+        """Test that raw sample returns non-empty output and observable lists."""
+        dag = _build_repetition_code_circuit(2)
+        im = _build_influence_map(dag)
+        sampler = DemSampler.raw_uniform(im, 0.01)
+        outputs, obs = sampler.sample(seed=42)
+        assert isinstance(outputs, list)
+        assert isinstance(obs, list)
+        assert len(outputs) > 0
+
+    def test_raw_sample_batch(self) -> None:
+        """Test that sample_batch returns the requested number of shots."""
+        dag = _build_repetition_code_circuit(2)
+        im = _build_influence_map(dag)
+        sampler = DemSampler.raw_uniform(im, 0.01)
+        all_outputs, _all_obs = sampler.sample_batch(100, seed=42)
+        assert len(all_outputs) == 100
+
+    def test_raw_zero_noise_statistics(self) -> None:
+        """Test that zero noise produces no syndromes or logical errors."""
+        dag = _build_repetition_code_circuit(2)
+        im = _build_influence_map(dag)
+        sampler = DemSampler.raw_uniform(im, 0.0)
+        stats = sampler.sample_statistics(1000, seed=42)
+        assert stats["syndrome_count"] == 0
+        assert stats["logical_error_count"] == 0
+
+    def test_raw_high_noise_produces_syndromes(self) -> None:
+        """Test that high noise produces a non-trivial syndrome rate."""
+        dag = _build_repetition_code_circuit(2)
+        im = _build_influence_map(dag)
+        sampler = DemSampler.raw_uniform(im, 0.1)
+        stats = sampler.sample_statistics(5000, seed=42)
+        assert stats["syndrome_rate"] > 0.05
+
+
+class TestDemSamplerDetectorMode:
+    """Test detector-event output mode."""
+
+    def test_detector_mode_creates_sampler(self) -> None:
+        """Test that detector mode creates a sampler with correct output counts."""
+        dag = _build_repetition_code_circuit(2)
+        im = _build_influence_map(dag)
+        sampler = DemSampler.with_detectors(
+            im,
+            detectors=[[-1], [-2]],
+            observables=[],
+            p1=0.001,
+            p2=0.01,
+            p_meas=0.005,
+            p_prep=0.001,
+        )
+        assert sampler.num_outputs == 2
+        assert sampler.num_observables == 0
+
+    def test_detector_mode_sample_shape(self) -> None:
+        """Test detector mode sample returns detector and observable counts."""
+        dag = _build_repetition_code_circuit(2)
+        im = _build_influence_map(dag)
+        sampler = DemSampler.with_detectors(
+            im,
+            detectors=[[-1], [-2]],
+            observables=[[-1]],
+            p1=0.001,
+            p2=0.01,
+            p_meas=0.005,
+            p_prep=0.001,
+        )
+        det_events, obs_flips = sampler.sample(seed=42)
+        assert len(det_events) == 2
+        assert len(obs_flips) == 1
+        assert sampler.num_dem_outputs == 1
+        assert sampler.num_observables == 1
+        assert sampler.num_tracked_paulis == 0
+
+    def test_detector_mode_matches_dem_sampler_builder(self) -> None:
+        """DemSampler detector mode should match DemSamplerBuilder exactly."""
+        dag = _build_repetition_code_circuit(3)
+        im = _build_influence_map(dag)
+
+        p1, p2, p_meas, p_prep = 0.001, 0.01, 0.005, 0.001
+        det_records = [[-1], [-2]]
+        obs_records = []
+        num_shots = 20_000
+        seed = 42
+
+        # DemSamplerBuilder path
+        import json
+
+        det_json = json.dumps([{"id": i, "records": r} for i, r in enumerate(det_records)])
+        obs_json = json.dumps([{"id": i, "records": r} for i, r in enumerate(obs_records)])
+        dem_sampler = (
+            DemSamplerBuilder(im)
+            .with_noise(p1, p2, p_meas, p_prep)
+            .with_detectors_json(det_json)
+            .with_observables_json(obs_json)
+            .build()
+        )
+        dem_stats = dem_sampler.sample_statistics(num_shots, seed)
+
+        # DemSampler detector mode
+        unified_sampler = DemSampler.with_detectors(
+            im,
+            detectors=det_records,
+            observables=obs_records,
+            p1=p1,
+            p2=p2,
+            p_meas=p_meas,
+            p_prep=p_prep,
+        )
+        unified_stats = unified_sampler.sample_statistics(num_shots, seed)
+
+        # Should match exactly (same seed → same internal DemSamplerBuilder path)
+        assert dem_stats["syndrome_count"] == unified_stats["syndrome_count"]
+        assert dem_stats["logical_error_count"] == unified_stats["logical_error_count"]
+
+
+class TestDemSamplerValidation:
+    """Test detector definition validation."""
+
+    def test_linearly_dependent_detectors_rejected(self) -> None:
+        """Test that linearly dependent detector definitions are rejected."""
+        dag = _build_repetition_code_circuit(2)
+        im = _build_influence_map(dag)
+
+        # D2 = D0 XOR D1 → linearly dependent
+        with pytest.raises(ValueError, match="linearly independent"):
+            DemSampler.with_detectors(
+                im,
+                detectors=[[0], [1], [0, 1]],
+                observables=[],
+                p1=0.001,
+                p2=0.01,
+                p_meas=0.005,
+                p_prep=0.001,
+            )
+
+    def test_independent_detectors_accepted(self) -> None:
+        """Test that linearly independent detector definitions are accepted."""
+        dag = _build_repetition_code_circuit(2)
+        im = _build_influence_map(dag)
+
+        sampler = DemSampler.with_detectors(
+            im,
+            detectors=[[0], [1]],
+            observables=[],
+            p1=0.001,
+            p2=0.01,
+            p_meas=0.005,
+            p_prep=0.001,
+        )
+        assert sampler.num_outputs == 2
+
+
+class TestDemSamplerRepr:
+    """Test string representation."""
+
+    def test_repr_raw_mode(self) -> None:
+        """Test repr output for raw mode sampler."""
+        dag = _build_repetition_code_circuit(2)
+        im = _build_influence_map(dag)
+        sampler = DemSampler.raw_uniform(im, 0.01)
+        r = repr(sampler)
+        assert "DemSampler" in r
+        assert "DemSampler" in r
+
+    def test_repr_detector_mode(self) -> None:
+        """Test repr output for detector mode sampler."""
+        dag = _build_repetition_code_circuit(2)
+        im = _build_influence_map(dag)
+        sampler = DemSampler.with_detectors(
+            im,
+            detectors=[[-1]],
+            observables=[],
+            p1=0.01,
+            p2=0.01,
+            p_meas=0.01,
+            p_prep=0.01,
+        )
+        r = repr(sampler)
+        assert "DemSampler" in r
+        assert "DemSampler" in r
diff --git a/python/quantum-pecos/tests/qec/test_dem_sampler_vs_stim.py b/python/quantum-pecos/tests/qec/test_dem_sampler_vs_stim.py
index c99668f13..e21072a7f 100644
--- a/python/quantum-pecos/tests/qec/test_dem_sampler_vs_stim.py
+++ b/python/quantum-pecos/tests/qec/test_dem_sampler_vs_stim.py
@@ -39,7 +39,7 @@ def extract_measurement_order(tc: "TickCircuit") -> list[int]:
         tick = tc.get_tick(tick_idx)
         if tick is None:
             continue
-        for gate in tick.gates():
+        for gate in tick.gate_batches():
             gate_type = str(gate.gate_type)
             if "MZ" in gate_type:
                 for qubit in gate.qubits:
@@ -154,7 +154,7 @@ def surface_code_d3(self) -> tuple:
     @pytest.fixture
     def noise_params(self) -> dict[str, float]:
         """Standard noise parameters for testing."""
-        return {"p1": 0.01, "p2": 0.01, "p_meas": 0.01, "p_init": 0.01}
+        return {"p1": 0.01, "p2": 0.01, "p_meas": 0.01, "p_prep": 0.01}
 
     def test_dem_mechanism_counts_match(
         self,
@@ -278,19 +278,19 @@ def test_sampling_statistics_match_stim(
         # Stim sampling - returns (det_events, obs_flips, error_data)
         stim_det_events, stim_obs_flips, _ = stim_sampler.sample(num_shots)
         stim_syndrome_count = np.any(stim_det_events, axis=1).sum()
-        stim_logical_count = np.any(stim_obs_flips, axis=1).sum()
+        stim_observable_count = np.any(stim_obs_flips, axis=1).sum()
 
         # Compare rates
         pecos_syndrome_rate = pecos_stats["syndrome_rate"]
         stim_syndrome_rate = stim_syndrome_count / num_shots
 
         pecos_logical_rate = pecos_stats["logical_error_rate"]
-        stim_logical_rate = stim_logical_count / num_shots
+        stim_logical_rate = stim_observable_count / num_shots
 
         # Compare absolute differences - allow up to 10% relative difference
         # Known: PECOS and Stim have slightly different DEM generation
         syndrome_diff = abs(pecos_syndrome_rate - stim_syndrome_rate)
-        logical_diff = abs(pecos_logical_rate - stim_logical_rate)
+        observable_diff = abs(pecos_logical_rate - stim_logical_rate)
 
         # Syndrome rates should be within 20% relative
         max_rate = max(pecos_syndrome_rate, stim_syndrome_rate, 0.001)
@@ -301,11 +301,11 @@ def test_sampling_statistics_match_stim(
         )
 
         # Logical error rates should be within 30% relative (more variable)
-        max_logical = max(pecos_logical_rate, stim_logical_rate, 0.001)
-        logical_rel_diff = logical_diff / max_logical
-        assert logical_rel_diff < 0.5, (
+        max_observable = max(pecos_logical_rate, stim_logical_rate, 0.001)
+        observable_rel_diff = observable_diff / max_observable
+        assert observable_rel_diff < 0.5, (
             f"Logical error rate mismatch: PECOS={pecos_logical_rate:.4f}, "
-            f"Stim={stim_logical_rate:.4f}, rel_diff={logical_rel_diff:.1%}"
+            f"Stim={stim_logical_rate:.4f}, rel_diff={observable_rel_diff:.1%}"
         )
 
     def test_detector_firing_rates_correlate(
@@ -386,7 +386,7 @@ def test_multi_round_d3_r3(self) -> None:
         patch = SurfacePatch.create(distance=3)
         tc = generate_tick_circuit_from_patch(patch, num_rounds=3, basis="Z")
 
-        noise_params = {"p1": 0.01, "p2": 0.01, "p_meas": 0.01, "p_init": 0.01}
+        noise_params = {"p1": 0.01, "p2": 0.01, "p_meas": 0.01, "p_prep": 0.01}
 
         # Build PECOS sampler
         dag = tc.to_dag_circuit()
@@ -423,7 +423,7 @@ def test_multi_round_d3_r3(self) -> None:
         max_rate = max(pecos_stats["logical_error_rate"], stim_logical_rate, 0.001)
         rel_diff = abs(pecos_stats["logical_error_rate"] - stim_logical_rate) / max_rate
         assert rel_diff < 0.5, (
-            f"Logical rate mismatch for d=3, r=3: "
+            f"Observable rate mismatch for d=3, r=3: "
             f"PECOS={pecos_stats['logical_error_rate']:.4f}, Stim={stim_logical_rate:.4f}, "
             f"rel_diff={rel_diff:.1%}"
         )
@@ -441,7 +441,7 @@ def test_logical_error_rate_scales(self, distance: int) -> None:
         patch = SurfacePatch.create(distance=distance)
         tc = generate_tick_circuit_from_patch(patch, num_rounds=1, basis="Z")
 
-        noise_params = {"p1": 0.001, "p2": 0.001, "p_meas": 0.001, "p_init": 0.001}
+        noise_params = {"p1": 0.001, "p2": 0.001, "p_meas": 0.001, "p_prep": 0.001}
 
         # Build sampler
         dag = tc.to_dag_circuit()
@@ -482,7 +482,7 @@ def test_x_basis_dem_matches_stim(self) -> None:
         patch = SurfacePatch.create(distance=3)
         tc = generate_tick_circuit_from_patch(patch, num_rounds=1, basis="X")
 
-        noise = {"p1": 0.01, "p2": 0.01, "p_meas": 0.01, "p_init": 0.01}
+        noise = {"p1": 0.01, "p2": 0.01, "p_meas": 0.01, "p_prep": 0.01}
 
         # Generate DEMs (non-decomposed for exact comparison)
         pecos_dem = generate_dem_from_tick_circuit(tc, **noise, decompose_errors=False)
@@ -531,7 +531,7 @@ def test_x_basis_sampling_matches_stim(self) -> None:
         patch = SurfacePatch.create(distance=3)
         tc = generate_tick_circuit_from_patch(patch, num_rounds=2, basis="X")
 
-        noise = {"p1": 0.01, "p2": 0.01, "p_meas": 0.01, "p_init": 0.01}
+        noise = {"p1": 0.01, "p2": 0.01, "p_meas": 0.01, "p_prep": 0.01}
 
         # Build PECOS sampler
         dag = tc.to_dag_circuit()
@@ -541,7 +541,9 @@ def test_x_basis_sampling_matches_stim(self) -> None:
         builder = DemSamplerBuilder(influence_map)
         builder.with_noise(**noise)
         builder.with_detectors_json(tc.get_meta("detectors") or "[]")
-        builder.with_observables_json(tc.get_meta("observables") or "[]")
+        builder.with_observables_json(
+            tc.get_meta("observables") or "[]",
+        )
         builder.with_measurement_order(extract_measurement_order(tc))
         pecos_sampler = builder.build()
 
@@ -572,20 +574,20 @@ class TestAsymmetricNoise:
     @pytest.mark.parametrize(
         "noise_params",
         [
-            {"p1": 0.001, "p2": 0.01, "p_meas": 0.005, "p_init": 0.002},  # p2 dominant
-            {"p1": 0.02, "p2": 0.001, "p_meas": 0.001, "p_init": 0.001},  # p1 dominant
+            {"p1": 0.001, "p2": 0.01, "p_meas": 0.005, "p_prep": 0.002},  # p2 dominant
+            {"p1": 0.02, "p2": 0.001, "p_meas": 0.001, "p_prep": 0.001},  # p1 dominant
             {
                 "p1": 0.001,
                 "p2": 0.001,
                 "p_meas": 0.05,
-                "p_init": 0.001,
+                "p_prep": 0.001,
             },  # p_meas dominant
             {
                 "p1": 0.001,
                 "p2": 0.001,
                 "p_meas": 0.001,
-                "p_init": 0.05,
-            },  # p_init dominant
+                "p_prep": 0.05,
+            },  # p_prep dominant
         ],
     )
     def test_asymmetric_noise_dem_matches_stim(
@@ -740,8 +742,8 @@ def _add_noise_to_stim(
             if name == "R":
                 for t in targets:
                     noisy.append("R", [t.value])
-                    if noise["p_init"] > 0:
-                        noisy.append("X_ERROR", [t.value], noise["p_init"])
+                    if noise["p_prep"] > 0:
+                        noisy.append("X_ERROR", [t.value], noise["p_prep"])
             elif name in ("H", "S", "S_DAG"):
                 for t in targets:
                     noisy.append(name, [t.value])
@@ -823,7 +825,7 @@ def test_random_circuit_sampling_produces_valid_results(self, seed: int) -> None
         records = [-i for i in range(1, num_qubits + 1)]
         detectors_json = f'[{{"id": 0, "records": {records}}}]'
 
-        noise = {"p1": 0.01, "p2": 0.01, "p_meas": 0.01, "p_init": 0.01}
+        noise = {"p1": 0.01, "p2": 0.01, "p_meas": 0.01, "p_prep": 0.01}
 
         builder = DemSamplerBuilder(influence_map)
         builder.with_noise(**noise)
@@ -864,7 +866,7 @@ def test_dem_exact_match(self, distance: int, num_rounds: int, basis: str) -> No
         patch = SurfacePatch.create(distance=distance)
         tc = generate_tick_circuit_from_patch(patch, num_rounds=num_rounds, basis=basis)
 
-        noise = {"p1": 0.01, "p2": 0.01, "p_meas": 0.01, "p_init": 0.01}
+        noise = {"p1": 0.01, "p2": 0.01, "p_meas": 0.01, "p_prep": 0.01}
 
         # Generate non-decomposed DEMs
         pecos_dem = generate_dem_from_tick_circuit(tc, **noise, decompose_errors=False)
diff --git a/python/quantum-pecos/tests/qec/test_fault_catalog.py b/python/quantum-pecos/tests/qec/test_fault_catalog.py
new file mode 100644
index 000000000..bd2950276
--- /dev/null
+++ b/python/quantum-pecos/tests/qec/test_fault_catalog.py
@@ -0,0 +1,515 @@
+# Copyright 2026 The PECOS Developers
+# Licensed under the Apache License, Version 2.0
+
+"""Tests for the fault_catalog() public API."""
+
+import pytest
+from pecos.quantum import PauliString, TickCircuit
+from pecos_rslib_exp import (
+    FaultAlternative,
+    FaultCatalog,
+    FaultLocation,
+    depolarizing,
+    fault_catalog,
+)
+
+
+def build_h_mz():
+    """H(0) MZ(0): single-qubit depolarizing."""
+    tc = TickCircuit()
+    tc.tick().h([0])
+    tick = tc.tick()
+    tick.mz([0])
+    tc.set_meta("num_measurements", "1")
+    tc.set_meta("detectors", "[]")
+    tc.set_meta("observables", "[]")
+    return tc
+
+
+def build_cx_mz():
+    """CX(0,1) MZ(0) MZ(1): two-qubit depolarizing."""
+    tc = TickCircuit()
+    tc.tick().cx([(0, 1)])
+    tick = tc.tick()
+    tick.mz([0])
+    tick = tc.tick()
+    tick.mz([1])
+    tc.set_meta("num_measurements", "2")
+    tc.set_meta("detectors", "[]")
+    tc.set_meta("observables", "[]")
+    return tc
+
+
+def pauli_terms(pauli):
+    """Return a {qubit: label} map from a PECOS PauliString."""
+    return {q: str(p).split(".")[-1] for p, q in pauli.get_paulis()}
+
+
+class TestFaultCatalogStructure:
+    def test_returns_fault_catalog(self):
+        tc = build_h_mz()
+        noise = depolarizing().p1(0.03).p2(0).p_meas(0).p_prep(0)
+        catalog = fault_catalog(tc, noise)
+
+        assert isinstance(catalog, FaultCatalog)
+        assert isinstance(catalog.locations, list)
+        assert len(catalog) > 0
+        assert isinstance(catalog[0], FaultLocation)
+        assert catalog[0] is catalog.locations[0]
+
+    def test_fault_catalog_is_sequence_like(self):
+        tc = build_h_mz()
+        noise = depolarizing().p1(0.03).p2(0).p_meas(0).p_prep(0)
+        catalog = fault_catalog(tc, noise)
+
+        assert len(list(catalog)) == len(catalog.locations)
+        assert catalog[-1] is catalog.locations[-1]
+
+    def test_location_attributes(self):
+        tc = build_h_mz()
+        noise = depolarizing().p1(0.03).p2(0).p_meas(0).p_prep(0)
+        catalog = fault_catalog(tc, noise)
+
+        loc = catalog[0]
+        assert hasattr(loc, "tick")
+        assert hasattr(loc, "gate_index")
+        assert hasattr(loc, "gate_type")
+        assert hasattr(loc, "qubits")
+        assert hasattr(loc, "channel_probability")
+        assert hasattr(loc, "faults")
+
+    def test_fault_alternative_attributes(self):
+        tc = build_h_mz()
+        noise = depolarizing().p1(0.03).p2(0).p_meas(0).p_prep(0)
+        catalog = fault_catalog(tc, noise)
+
+        fault = catalog[0].faults[0]
+        assert isinstance(fault, FaultAlternative)
+        assert hasattr(fault, "kind")
+        assert hasattr(fault, "pauli")
+        assert hasattr(fault, "detectors")
+        assert hasattr(fault, "observables")
+        assert hasattr(fault, "tracked_paulis")
+        assert hasattr(fault, "measurements")
+        assert hasattr(fault, "conditional_probability")
+        assert hasattr(fault, "absolute_probability")
+        assert hasattr(fault, "channel_probability")
+
+
+class TestPauliStringOutput:
+    def test_pauli_alternatives_are_pauli_string(self):
+        tc = build_h_mz()
+        noise = depolarizing().p1(0.03).p2(0).p_meas(0).p_prep(0)
+        catalog = fault_catalog(tc, noise)
+
+        for loc in catalog:
+            for fault in loc.faults:
+                if fault.kind == "pauli":
+                    assert isinstance(fault.pauli, PauliString), f"Expected PauliString, got {type(fault.pauli)}"
+
+    def test_meas_prep_faults_have_none_pauli(self):
+        tc = TickCircuit()
+        tc.tick().pz([0])
+        tick = tc.tick()
+        tick.mz([0])
+        tc.set_meta("num_measurements", "1")
+        tc.set_meta("detectors", "[]")
+        tc.set_meta("observables", "[]")
+
+        noise = depolarizing().p1(0).p2(0).p_meas(0.01).p_prep(0.01)
+        catalog = fault_catalog(tc, noise)
+
+        for loc in catalog:
+            for fault in loc.faults:
+                if fault.kind in ("measurement_flip", "prep_flip"):
+                    assert fault.pauli is None
+
+    def test_two_qubit_pauli_has_two_terms(self):
+        tc = build_cx_mz()
+        noise = depolarizing().p1(0).p2(0.15).p_meas(0).p_prep(0)
+        catalog = fault_catalog(tc, noise)
+
+        cx_loc = next(loc for loc in catalog if loc.gate_type == "CX")
+        # At least some alternatives should have two Pauli terms (XX, XY, etc.)
+        two_term = [f for f in cx_loc.faults if len(f.pauli.get_paulis()) == 2]
+        assert len(two_term) == 9, f"Expected 9 two-qubit Paulis, got {len(two_term)}"
+
+    def test_new_gate_pauli_labels_and_measurement_effects(self):
+        tc = TickCircuit()
+        tc.tick().sx([0])
+        tc.tick().szz([(0, 1)])
+        tick = tc.tick()
+        tick.mz([0])
+        tick.mz([1])
+        tc.set_meta("num_measurements", "2")
+        tc.set_meta("detectors", "[]")
+        tc.set_meta("observables", "[]")
+
+        noise = depolarizing().p1(0.03).p2(0.15).p_meas(0).p_prep(0)
+        catalog = fault_catalog(tc, noise)
+
+        sx_loc = next(loc for loc in catalog if loc.gate_type == "SX")
+        assert [pauli_terms(f.pauli) for f in sx_loc.faults] == [
+            {0: "X"},
+            {0: "Y"},
+            {0: "Z"},
+        ]
+        assert any(f.measurements for f in sx_loc.faults)
+
+        szz_loc = next(loc for loc in catalog if loc.gate_type == "SZZ")
+        assert len(szz_loc.faults) == 15
+        observed = {(terms.get(0, "I"), terms.get(1, "I")) for terms in (pauli_terms(f.pauli) for f in szz_loc.faults)}
+        expected = {
+            ("X", "I"),
+            ("Y", "I"),
+            ("Z", "I"),
+            ("I", "X"),
+            ("I", "Y"),
+            ("I", "Z"),
+            ("X", "X"),
+            ("X", "Y"),
+            ("X", "Z"),
+            ("Y", "X"),
+            ("Y", "Y"),
+            ("Y", "Z"),
+            ("Z", "X"),
+            ("Z", "Y"),
+            ("Z", "Z"),
+        }
+        assert observed == expected
+        assert any(f.measurements for f in szz_loc.faults)
+
+
+class TestNoEffectLocationsIncluded:
+    def test_no_downstream_measurement_location_included(self):
+        """A gate with p1>0 but no MZ after it still appears in the catalog."""
+        tc = TickCircuit()
+        tc.tick().h([0])  # No MZ follows — no measurement effect
+        tc.set_meta("num_measurements", "0")
+        tc.set_meta("detectors", "[]")
+        tc.set_meta("observables", "[]")
+
+        noise = depolarizing().p1(0.01).p2(0).p_meas(0).p_prep(0)
+        catalog = fault_catalog(tc, noise)
+
+        h_locs = [loc for loc in catalog if loc.gate_type == "H"]
+        assert len(h_locs) == 1, "H with no downstream MZ should still appear"
+        assert len(h_locs[0].faults) == 3
+        # All alternatives should have empty effects
+        for fault in h_locs[0].faults:
+            assert fault.measurements == []
+            assert fault.detectors == []
+            assert fault.observables == []
+            assert abs(fault.absolute_probability - 0.01 / 3) < 1e-10
+
+    def test_prep_fault_with_no_effect_included(self):
+        """PZ followed by H then MZ: prep X → H → Z → no flip. Still in catalog."""
+        tc = TickCircuit()
+        tc.tick().pz([0])
+        tc.tick().h([0])
+        tick = tc.tick()
+        tick.mz([0])
+        tc.set_meta("num_measurements", "1")
+        tc.set_meta("detectors", "[]")
+        tc.set_meta("observables", "[]")
+
+        noise = depolarizing().p1(0).p2(0).p_meas(0).p_prep(0.005)
+        catalog = fault_catalog(tc, noise)
+
+        prep_locs = [loc for loc in catalog if any(f.kind == "prep_flip" for f in loc.faults)]
+        assert len(prep_locs) == 1
+        fault = prep_locs[0].faults[0]
+        assert fault.kind == "prep_flip"
+        assert fault.pauli is None
+        # Prep X through H becomes Z which doesn't flip MZ → empty
+        assert fault.measurements == []
+
+
+class TestProbabilities:
+    def test_structural_catalog_without_noise(self):
+        tc = build_h_mz()
+        catalog = fault_catalog(tc)
+
+        assert len(catalog.locations) == 2
+        assert {loc.channel for loc in catalog.locations} == {"p1", "p_meas"}
+        assert all(loc.channel_probability == 0.0 for loc in catalog.locations)
+        assert all(loc.no_fault_probability == 1.0 for loc in catalog.locations)
+        assert all(fault.absolute_probability == 0.0 for loc in catalog.locations for fault in loc.faults)
+
+    def test_with_noise_updates_existing_python_references(self):
+        tc = build_h_mz()
+        catalog = fault_catalog(tc)
+        h_loc = next(loc for loc in catalog if loc.channel == "p1")
+        h_fault = h_loc.faults[0]
+        mz_loc = next(loc for loc in catalog if loc.channel == "p_meas")
+
+        catalog.with_noise(p1=0.06, p_meas=0.02)
+
+        assert abs(h_loc.channel_probability - 0.06) < 1e-12
+        assert abs(h_loc.no_fault_probability - 0.94) < 1e-12
+        assert abs(h_fault.absolute_probability - 0.02) < 1e-12
+        assert abs(h_fault.channel_probability - 0.06) < 1e-12
+        assert abs(mz_loc.channel_probability - 0.02) < 1e-12
+        assert abs(mz_loc.faults[0].absolute_probability - 0.02) < 1e-12
+
+    def test_parameterized_returns_independent_catalog(self):
+        tc = build_h_mz()
+        catalog = fault_catalog(tc, p1=0.03, p_meas=0.01)
+        clone = catalog.parameterized(p1=0.09, p_meas=0.04)
+
+        original_h = next(loc for loc in catalog if loc.channel == "p1")
+        clone_h = next(loc for loc in clone if loc.channel == "p1")
+        assert abs(original_h.channel_probability - 0.03) < 1e-12
+        assert abs(clone_h.channel_probability - 0.09) < 1e-12
+        assert original_h is not clone_h
+
+    def test_sparse_channel_keeps_zero_probability_structure(self):
+        tc = build_h_mz()
+        catalog = fault_catalog(tc, p1=0.0, p_meas=0.02)
+
+        h_loc = next(loc for loc in catalog if loc.channel == "p1")
+        mz_loc = next(loc for loc in catalog if loc.channel == "p_meas")
+        assert h_loc.channel_probability == 0.0
+        assert all(f.absolute_probability == 0.0 for f in h_loc.faults)
+        assert abs(mz_loc.channel_probability - 0.02) < 1e-12
+        assert abs(mz_loc.faults[0].absolute_probability - 0.02) < 1e-12
+
+    def test_single_qubit_location_fields(self):
+        tc = build_h_mz()
+        noise = depolarizing().p1(0.03).p2(0).p_meas(0).p_prep(0)
+        catalog = fault_catalog(tc, noise)
+
+        h_loc = next(loc for loc in catalog if loc.gate_type == "H")
+        assert h_loc.channel == "p1"
+        assert abs(h_loc.channel_probability - 0.03) < 1e-10
+        assert abs(h_loc.no_fault_probability - 0.97) < 1e-10
+        assert h_loc.num_alternatives == 3
+        for fault in h_loc.faults:
+            assert abs(fault.conditional_probability - 1.0 / 3) < 1e-10
+            assert abs(fault.absolute_probability - 0.01) < 1e-10
+
+    def test_two_qubit_location_fields(self):
+        tc = build_cx_mz()
+        noise = depolarizing().p1(0).p2(0.15).p_meas(0).p_prep(0)
+        catalog = fault_catalog(tc, noise)
+
+        cx_loc = next(loc for loc in catalog if loc.gate_type == "CX")
+        assert cx_loc.channel == "p2"
+        assert abs(cx_loc.channel_probability - 0.15) < 1e-10
+        assert abs(cx_loc.no_fault_probability - 0.85) < 1e-10
+        assert cx_loc.num_alternatives == 15
+        for fault in cx_loc.faults:
+            assert abs(fault.conditional_probability - 1.0 / 15) < 1e-10
+            assert abs(fault.absolute_probability - 0.01) < 1e-10
+
+    def test_full_configuration_probability(self):
+        """Compute one full-circuit event probability from catalog fields."""
+        tc = build_h_mz()
+        noise = depolarizing().p1(0.03).p2(0).p_meas(0.01).p_prep(0)
+        catalog = fault_catalog(tc, noise)
+
+        # Pick first alternative at H location, no fault at MZ location
+        h_loc = next(loc for loc in catalog if loc.channel == "p1")
+        mz_loc = next(loc for loc in catalog if loc.channel == "p_meas")
+
+        # P(alt 0 at H, no fault at MZ) = (p1/3) * (1 - p_meas)
+        config_prob = h_loc.faults[0].absolute_probability * mz_loc.no_fault_probability
+        expected = (0.03 / 3) * (1 - 0.01)  # 0.01 * 0.99 = 0.0099
+        assert abs(config_prob - expected) < 1e-10
+
+
+class TestDetectorObservableMapping:
+    def test_detectors_are_lists(self):
+        tc = TickCircuit()
+        tc.tick().h([0])
+        tc.tick().cx([(0, 1)])
+        tc.tick().h([0])
+        tick = tc.tick()
+        tick.mz([0])
+        tick = tc.tick()
+        tick.mz([1])
+        tc.set_meta("num_measurements", "2")
+        tc.set_meta("detectors", '[{"records": [-2, -1]}]')
+        tc.set_meta("observables", "[]")
+
+        noise = depolarizing().p1(0.01).p2(0).p_meas(0).p_prep(0)
+        catalog = fault_catalog(tc, noise)
+
+        has_det = any(f.detectors for loc in catalog for f in loc.faults)
+        assert has_det, "Some faults should fire detectors"
+
+        for loc in catalog:
+            for fault in loc.faults:
+                assert isinstance(fault.detectors, list)
+                assert isinstance(fault.observables, list)
+
+
+class TestFaultConfigurations:
+    def test_k0_one_no_fault_event(self):
+        tc = build_h_mz()
+        noise = depolarizing().p1(0.03).p2(0).p_meas(0.01).p_prep(0)
+        catalog = fault_catalog(tc, noise)
+
+        configs = list(catalog.fault_configurations(0))
+        assert len(configs) == 1
+        c = configs[0]
+        assert c.location_indices == []
+        assert c.alternative_indices == []
+        assert c.measurements == []
+        assert c.detectors == []
+        assert c.observables == []
+        assert c.selected_probability == 1.0
+        # config_prob = product of all no_fault_probability
+        expected = 1.0
+        for loc in catalog.locations:
+            expected *= loc.no_fault_probability
+        assert abs(c.configuration_probability - expected) < 1e-12
+
+    def test_k1_exposes_single_fault(self):
+        tc = build_h_mz()
+        noise = depolarizing().p1(0.03).p2(0).p_meas(0.01).p_prep(0)
+        catalog = fault_catalog(tc, noise)
+
+        configs = list(catalog.fault_configurations(1))
+        # Total = sum of num_alternatives
+        expected_count = sum(loc.num_alternatives for loc in catalog.locations)
+        assert len(configs) == expected_count
+
+        # First config: location 0, alternative 0
+        c = configs[0]
+        assert c.location_indices == [0]
+        assert c.alternative_indices == [0]
+        assert c.selected_probability > 0
+
+    def test_k1_skips_zero_probability_structural_locations(self):
+        tc = build_h_mz()
+        catalog = fault_catalog(tc, p1=0.03, p_meas=0.0)
+
+        assert len(catalog.locations) == 2
+        h_idx = next(i for i, loc in enumerate(catalog) if loc.gate_type == "H")
+        mz_idx = next(i for i, loc in enumerate(catalog) if loc.gate_type == "MZ")
+        assert catalog.locations[mz_idx].channel_probability == 0.0
+
+        configs = list(catalog.fault_configurations(1))
+        assert len(configs) == 3
+        assert all(c.location_indices == [h_idx] for c in configs)
+        assert all(c.selected_probability > 0 for c in configs)
+        assert all(mz_idx not in c.location_indices for c in configs)
+        assert list(catalog.fault_configurations(2)) == []
+
+    def test_all_zero_noise_only_yields_k0(self):
+        tc = build_h_mz()
+        catalog = fault_catalog(tc, p1=0.0, p_meas=0.0)
+
+        k0 = list(catalog.fault_configurations(0))
+        assert len(k0) == 1
+        assert k0[0].configuration_probability == 1.0
+        assert list(catalog.fault_configurations(1)) == []
+
+    def test_nonzero_silent_faults_are_yielded(self):
+        tc = TickCircuit()
+        tc.tick().h([0])
+        tc.set_meta("num_measurements", "0")
+        tc.set_meta("detectors", "[]")
+        tc.set_meta("observables", "[]")
+
+        catalog = fault_catalog(tc, p1=0.03, p_meas=0.0)
+        configs = list(catalog.fault_configurations(1))
+
+        assert len(configs) == 3
+        assert all(c.measurements == [] for c in configs)
+        assert all(c.detectors == [] for c in configs)
+        assert all(c.observables == [] for c in configs)
+        assert all(c.selected_probability > 0 for c in configs)
+
+    def test_with_noise_zeroes_channel_for_new_iterators(self):
+        tc = build_h_mz()
+        catalog = fault_catalog(tc, p1=0.03, p_meas=0.01)
+
+        catalog.with_noise(p1=0.0, p_meas=0.02)
+
+        mz_idx = next(i for i, loc in enumerate(catalog) if loc.gate_type == "MZ")
+        configs = list(catalog.fault_configurations(1))
+        assert len(configs) == 1
+        assert configs[0].location_indices == [mz_idx]
+        assert configs[0].selected_probability == pytest.approx(0.02)
+
+    def test_k2_xor_cancels_effects(self):
+        """Two faults flipping the same detector XOR-cancel."""
+        tc = TickCircuit()
+        tc.tick().h([0])
+        tc.tick().h([0])
+        tick = tc.tick()
+        tick.mz([0])
+        tc.set_meta("num_measurements", "1")
+        tc.set_meta("detectors", '[{"records":[-1]}]')
+        tc.set_meta("observables", "[]")
+
+        noise = depolarizing().p1(0.03).p2(0).p_meas(0).p_prep(0)
+        catalog = fault_catalog(tc, noise)
+
+        configs = list(catalog.fault_configurations(2))
+        # Some configs should have empty detectors (XOR cancel)
+        cancelled = [c for c in configs if c.detectors == []]
+        assert len(cancelled) > 0
+
+    def test_k2_probability_hand_calc(self):
+        tc = build_h_mz()
+        noise = depolarizing().p1(0.03).p2(0).p_meas(0.01).p_prep(0)
+        catalog = fault_catalog(tc, noise)
+        # 2 locations: H(3 alts, p=0.03) and MZ(1 alt, p=0.01)
+        # k=2: both fire. selected = (0.03/3) * (0.01/1) = 0.0001
+        # config = 0.0001 (no unselected locations)
+
+        configs = list(catalog.fault_configurations(2))
+        assert len(configs) == 3  # 3 H alternatives x 1 MZ alternative
+        for c in configs:
+            assert abs(c.selected_probability - 0.0001) < 1e-12
+            assert abs(c.configuration_probability - 0.0001) < 1e-12
+
+    def test_returns_lazy_iterator_not_list(self):
+        tc = build_h_mz()
+        noise = depolarizing().p1(0.03).p2(0).p_meas(0.01).p_prep(0)
+        catalog = fault_catalog(tc, noise)
+
+        it = catalog.fault_configurations(1)
+        assert not isinstance(it, list), "Should be a lazy iterator, not a list"
+        assert hasattr(it, "__next__"), "Should have __next__"
+        first = next(it)
+        assert hasattr(first, "location_indices")
+        assert hasattr(first, "locations")
+        assert hasattr(first, "faults")
+        assert hasattr(first, "tracked_paulis")
+
+    def test_yielded_locations_and_faults(self):
+        tc = build_h_mz()
+        noise = depolarizing().p1(0.03).p2(0).p_meas(0.01).p_prep(0)
+        catalog = fault_catalog(tc, noise)
+
+        first = next(catalog.fault_configurations(1))
+        # .locations should be the FaultLocation objects for selected indices
+        assert len(first.locations) == 1
+        assert first.locations[0] is catalog.locations[first.location_indices[0]]
+        # .faults should be the FaultAlternative objects
+        assert len(first.faults) == 1
+        loc = catalog.locations[first.location_indices[0]]
+        assert first.faults[0] is loc.faults[first.alternative_indices[0]]
+
+    def test_tracked_paulis_are_distinct_from_observables(self):
+        tc = TickCircuit()
+        tc.tick().h([0])
+        tc.tracked_pauli(PauliString.from_str("Z"), label="tracked_z")
+        tc.set_meta("detectors", "[]")
+        tc.set_meta("observables", "[]")
+
+        noise = depolarizing().p1(0.03).p2(0).p_meas(0).p_prep(0)
+        catalog = fault_catalog(tc, noise)
+
+        h_loc = next(loc for loc in catalog if loc.gate_type == "H")
+        tracked = [fault.tracked_paulis for fault in h_loc.faults]
+        assert tracked.count([0]) == 2
+        assert tracked.count([]) == 1
+        assert all(fault.observables == [] for fault in h_loc.faults)
+
+        configs = list(catalog.fault_configurations(1))
+        assert any(c.tracked_paulis == [0] and c.observables == [] for c in configs)
diff --git a/python/quantum-pecos/tests/qec/test_inline_channel_sim_neo.py b/python/quantum-pecos/tests/qec/test_inline_channel_sim_neo.py
new file mode 100644
index 000000000..242cbdcbb
--- /dev/null
+++ b/python/quantum-pecos/tests/qec/test_inline_channel_sim_neo.py
@@ -0,0 +1,74 @@
+# Copyright 2026 The PECOS Developers
+# Licensed under the Apache License, Version 2.0
+
+"""Inline TickCircuit channel tests for sim_neo Python bindings."""
+
+import pytest
+from pecos_rslib.quantum import TickCircuit
+from pecos_rslib_exp import depolarizing, meas_sampling, sim_neo, stabilizer
+
+
+def prep_measure_circuit() -> TickCircuit:
+    tc = TickCircuit()
+    tc.tick().pz([0])
+    tc.tick().mz([0])
+    return tc
+
+
+def measurement_rows(result) -> list[list[int]]:
+    return [list(row) for row in result.to_list()]
+
+
+def test_tick_circuit_with_noise_inserts_channel_payload() -> None:
+    noisy = prep_measure_circuit().with_noise(p_prep=1.0)
+    channel_gates = [gate for _, gate in noisy.gate_batches() if gate.is_channel()]
+
+    assert len(channel_gates) == 1
+    assert channel_gates[0].channel_mixed_pauli_terms() == [
+        (0.0, []),
+        (1.0, [("X", 0)]),
+    ]
+
+
+def test_tick_circuit_with_noise_rejects_measurement_readout_noise() -> None:
+    with pytest.raises(ValueError, match="measurement readout noise"):
+        prep_measure_circuit().with_noise(p_meas=0.1)
+
+
+def test_tick_circuit_with_noise_rejects_invalid_probabilities() -> None:
+    with pytest.raises(ValueError, match="p1 must be in \\[0, 1\\]"):
+        prep_measure_circuit().with_noise(p1=-0.1)
+
+    with pytest.raises(ValueError, match="p2 must be in \\[0, 1\\]"):
+        prep_measure_circuit().with_noise(p2=1.1)
+
+
+def test_sim_neo_default_routes_inline_channels_through_density_matrix() -> None:
+    noisy = prep_measure_circuit().with_noise(p_prep=1.0)
+
+    result = sim_neo(noisy).shots(5).seed(123).run()
+
+    assert measurement_rows(result) == [[1], [1], [1], [1], [1]]
+
+
+def test_sim_neo_stabilizer_samples_inline_pauli_channels() -> None:
+    noisy = prep_measure_circuit().with_noise(p_prep=1.0)
+
+    result = sim_neo(noisy).quantum(stabilizer()).shots(5).seed(123).run()
+
+    assert measurement_rows(result) == [[1], [1], [1], [1], [1]]
+
+
+def test_sim_neo_rejects_noise_builder_with_inline_channels() -> None:
+    noisy = prep_measure_circuit().with_noise(p_prep=1.0)
+    noise = depolarizing().p1(0.1)
+
+    with pytest.raises(ValueError, match="do not also pass"):
+        sim_neo(noisy).noise(noise).run()
+
+
+def test_sim_neo_meas_sampling_rejects_inline_channels() -> None:
+    noisy = prep_measure_circuit().with_noise(p_prep=1.0)
+
+    with pytest.raises(ValueError, match="does not consume inline channel"):
+        sim_neo(noisy).quantum(meas_sampling()).run()
diff --git a/python/quantum-pecos/tests/qec/test_meas_sampling_backend.py b/python/quantum-pecos/tests/qec/test_meas_sampling_backend.py
new file mode 100644
index 000000000..a0564c682
--- /dev/null
+++ b/python/quantum-pecos/tests/qec/test_meas_sampling_backend.py
@@ -0,0 +1,177 @@
+# Copyright 2026 The PECOS Developers
+# Licensed under the Apache License, Version 2.0
+
+"""Integration tests for meas_sampling() sim_neo backend.
+
+Tests the d=3 surface code 57/48 regression and method dispatch.
+"""
+
+import json
+
+import pytest
+from pecos.qec.surface import SurfacePatch
+from pecos.qec.surface.decode import _build_surface_tick_circuit_for_native_model
+from pecos_rslib_exp import depolarizing, meas_sampling, sim_neo, stabilizer
+
+
+@pytest.fixture
+def d3_tc():
+    patch = SurfacePatch.create(distance=3)
+    return _build_surface_tick_circuit_for_native_model(patch, 6, "Z", circuit_source="abstract")
+
+
+@pytest.fixture
+def depol():
+    return depolarizing().p1(0.0005).p2(0.005).p_meas(0.005).p_prep(0.005)
+
+
+@pytest.fixture
+def coherent():
+    return depolarizing().p1(0.0005).p2(0.005).p_meas(0.005).p_prep(0.005).idle_rz(0.05)
+
+
+class TestD3SurfaceCode57vs48:
+    def test_raw_output_is_57_measurements(self, d3_tc, depol):
+        r = sim_neo(d3_tc).quantum(meas_sampling()).noise(depol).shots(10).seed(42).run()
+        assert len(r[0]) == 57
+
+    def test_nondet_measurement_mean_half(self, d3_tc, depol):
+        shots = 5000
+        r = sim_neo(d3_tc).quantum(meas_sampling()).noise(depol).shots(shots).seed(42).run()
+        mean_0 = sum(s[0] for s in r) / shots
+        assert abs(mean_0 - 0.5) < 0.05, f"meas[0]={mean_0:.3f}"
+
+    def test_det_measurement_mean_low(self, d3_tc, depol):
+        shots = 5000
+        r = sim_neo(d3_tc).quantum(meas_sampling()).noise(depol).shots(shots).seed(42).run()
+        mean_4 = sum(s[4] for s in r) / shots
+        assert mean_4 < 0.1, f"meas[4]={mean_4:.3f}"
+
+    def test_z_type_detection_rates_match_stabilizer(self, d3_tc, depol):
+        """Z-type detector rates match stabilizer (known-good subset)."""
+        shots = 10000
+        det_json = json.loads(d3_tc.get_meta("detectors"))
+        num_meas = int(d3_tc.get_meta("num_measurements"))
+        num_dets = len(det_json)
+
+        def rates(results):
+            r = [0.0] * num_dets
+            for shot in results:
+                for i, det in enumerate(det_json):
+                    val = 0
+                    for rec in det["records"]:
+                        idx = num_meas + rec
+                        if 0 <= idx < len(shot):
+                            val ^= shot[idx]
+                    if val:
+                        r[i] += 1.0 / len(results)
+            return r
+
+        meas_r = sim_neo(d3_tc).quantum(meas_sampling()).noise(depol).shots(shots).seed(42).run()
+        stab_r = sim_neo(d3_tc).quantum(stabilizer()).noise(depol).shots(shots).seed(42).run()
+
+        meas_rates = rates(meas_r)
+        stab_rates = rates(stab_r)
+
+        # Z-type detectors (deterministic measurements) should match.
+        close_count = sum(
+            1 for d, s in zip(meas_rates, stab_rates, strict=False) if s > 0.001 and abs(d - s) / s < 0.15
+        )
+        total_active = sum(1 for s in stab_rates if s > 0.001)
+
+        # At least half the detectors should match (Z-type ones)
+        assert (
+            close_count >= total_active // 2
+        ), f"Only {close_count}/{total_active} detectors within 15% of stabilizer."
+
+    def test_all_detection_rates_match_stabilizer(self, d3_tc, depol):
+        """ALL detector rates should match stabilizer (target correctness)."""
+        shots = 20000
+        det_json = json.loads(d3_tc.get_meta("detectors"))
+        num_meas = int(d3_tc.get_meta("num_measurements"))
+        num_dets = len(det_json)
+
+        def rates(results):
+            r = [0.0] * num_dets
+            for shot in results:
+                for i, det in enumerate(det_json):
+                    val = 0
+                    for rec in det["records"]:
+                        idx = num_meas + rec
+                        if 0 <= idx < len(shot):
+                            val ^= shot[idx]
+                    if val:
+                        r[i] += 1.0 / len(results)
+            return r
+
+        meas_r = sim_neo(d3_tc).quantum(meas_sampling()).noise(depol).shots(shots).seed(42).run()
+        stab_r = sim_neo(d3_tc).quantum(stabilizer()).noise(depol).shots(shots).seed(42).run()
+
+        meas_rates = rates(meas_r)
+        stab_rates = rates(stab_r)
+
+        max_diff = max(abs(d - s) / max(s, 1e-10) for d, s in zip(meas_rates, stab_rates, strict=False) if s > 0.001)
+        assert max_diff < 0.15, f"Max relative det rate diff: {max_diff:.1%}"
+
+    def test_observable_flip_rates_match_stabilizer(self, d3_tc):
+        """Observable record extraction should match the stabilizer backend."""
+        shots = 5000
+        noise = depolarizing().p1(0.001).p2(0.01).p_meas(0.01).p_prep(0.01)
+        obs_json = json.loads(d3_tc.get_meta("observables") or "[]")
+        num_meas = int(d3_tc.get_meta("num_measurements"))
+        assert obs_json, "surface-code memory circuit should define observables"
+
+        def rates(results):
+            r = [0.0] * len(obs_json)
+            for shot in results:
+                for i, obs in enumerate(obs_json):
+                    val = 0
+                    for rec in obs["records"]:
+                        idx = num_meas + rec
+                        if 0 <= idx < len(shot):
+                            val ^= shot[idx]
+                    if val:
+                        r[i] += 1.0 / len(results)
+            return r
+
+        meas_r = sim_neo(d3_tc).quantum(meas_sampling()).noise(noise).shots(shots).seed(42).run()
+        stab_r = sim_neo(d3_tc).quantum(stabilizer()).noise(noise).shots(shots).seed(43).run()
+
+        meas_rates = rates(meas_r)
+        stab_rates = rates(stab_r)
+        for i, (meas_rate, stab_rate) in enumerate(zip(meas_rates, stab_rates, strict=False)):
+            abs_diff = abs(meas_rate - stab_rate)
+            rel_diff = abs_diff / max(stab_rate, 1e-12)
+            assert (
+                abs_diff < 0.03 or rel_diff < 0.5
+            ), f"Observable L{i} rate mismatch: meas_sampling={meas_rate:.4f}, stabilizer={stab_rate:.4f}"
+
+
+class TestMethodDispatch:
+    def test_auto_no_idle_rz(self, d3_tc, depol):
+        r = sim_neo(d3_tc).quantum(meas_sampling("auto")).noise(depol).shots(10).seed(42).run()
+        assert len(r[0]) == 57
+
+    def test_auto_with_idle_rz(self, d3_tc, coherent):
+        r = sim_neo(d3_tc).quantum(meas_sampling("auto")).noise(coherent).shots(10).seed(42).run()
+        assert len(r[0]) == 57
+
+    def test_stochastic_rejects_idle_rz(self, d3_tc, coherent):
+        with pytest.raises(Exception, match="idle_rz"):
+            sim_neo(d3_tc).quantum(meas_sampling("stochastic")).noise(coherent).shots(10).seed(42).run()
+
+    def test_coherent_no_idle_rz(self, d3_tc, depol):
+        r = sim_neo(d3_tc).quantum(meas_sampling("coherent")).noise(depol).shots(10).seed(42).run()
+        assert len(r[0]) == 57
+
+    def test_coherent_with_idle_rz(self, d3_tc, coherent):
+        r = sim_neo(d3_tc).quantum(meas_sampling("coherent")).noise(coherent).shots(10).seed(42).run()
+        assert len(r[0]) == 57
+
+    def test_invalid_method(self, d3_tc, depol):
+        with pytest.raises(Exception, match="Unknown"):
+            sim_neo(d3_tc).quantum(meas_sampling("bogus")).noise(depol).shots(10).seed(42).run()
+
+    def test_no_noise_errors(self, d3_tc):
+        with pytest.raises(Exception, match="noise"):
+            sim_neo(d3_tc).quantum(meas_sampling()).shots(10).seed(42).run()
diff --git a/python/quantum-pecos/tests/qec/test_meas_sampling_generality.py b/python/quantum-pecos/tests/qec/test_meas_sampling_generality.py
new file mode 100644
index 000000000..f8315c5f5
--- /dev/null
+++ b/python/quantum-pecos/tests/qec/test_meas_sampling_generality.py
@@ -0,0 +1,283 @@
+# Copyright 2026 The PECOS Developers
+# Licensed under the Apache License, Version 2.0
+
+"""Generality tests for meas_sampling() stochastic raw measurement backend.
+
+These test the core fault propagation and measurement sampling logic
+on minimal hand-built circuits — not surface-code-specific.
+"""
+
+import json
+
+import pytest
+from pecos.quantum import TickCircuit
+from pecos_rslib_exp import depolarizing, meas_sampling, sim_neo, stabilizer, statevec
+
+
+def build_two_round_x_check():
+    """Minimal 2-round X-check: ancilla q0, data q1 q2."""
+    tc = TickCircuit()
+    # Round 1
+    tc.tick().h([0])
+    tc.tick().cx([(0, 1)])
+    tc.tick().cx([(0, 2)])
+    tc.tick().h([0])
+    tick = tc.tick()
+    tick.mz([0])
+    tc.tick().pz([0])
+    # Round 2
+    tc.tick().h([0])
+    tc.tick().cx([(0, 1)])
+    tc.tick().cx([(0, 2)])
+    tc.tick().h([0])
+    tick = tc.tick()
+    tick.mz([0])
+
+    # Detector: m0 XOR m1 should be 0 in noiseless case
+    tc.set_meta("num_measurements", "2")
+    tc.set_meta("detectors", json.dumps([{"records": [-1, -2]}]))
+    tc.set_meta("observables", "[]")
+    return tc
+
+
+def build_three_round_z_check():
+    """3-round Z-check on single data qubit: ancilla q0, data q1."""
+    tc = TickCircuit()
+    for _ in range(3):
+        tc.tick().pz([0])
+        tc.tick().cx([(1, 0)])  # data is control for Z-check
+        tick = tc.tick()
+        tick.mz([0])
+
+    tc.set_meta("num_measurements", "3")
+    tc.set_meta(
+        "detectors",
+        json.dumps(
+            [
+                {"records": [-2, -3]},  # m0 XOR m1
+                {"records": [-1, -2]},  # m1 XOR m2
+            ],
+        ),
+    )
+    tc.set_meta("observables", "[]")
+    return tc
+
+
+class TestMeasurementFaultIndependence:
+    """Measurement faults must not cancel through Copy chains."""
+
+    def test_two_round_meas_fault_both_fire(self):
+        """A detector comparing two Copy-linked measurements should see
+        faults from BOTH measurements independently.
+        """
+        tc = build_two_round_x_check()
+        # Measurement-only noise: each meas flips with p=0.01
+        depol = depolarizing().p1(0).p2(0).p_meas(0.01).p_prep(0)
+        shots = 50000
+
+        meas_r = sim_neo(tc).quantum(meas_sampling()).noise(depol).shots(shots).seed(42).run()
+        stab_r = sim_neo(tc).quantum(stabilizer()).noise(depol).shots(shots).seed(42).run()
+
+        # Extract detector rate
+        def det_rate(results):
+            return sum(s[0] ^ s[1] for s in results) / len(results)
+
+        meas_rate = det_rate(meas_r)
+        stab_rate = det_rate(stab_r)
+
+        # Expected: ~2*p_meas = 0.02 (two independent flips)
+        assert (
+            abs(meas_rate - stab_rate) / max(stab_rate, 1e-10) < 0.15
+        ), f"Meas fault rate mismatch: dem={meas_rate:.4f} stab={stab_rate:.4f}"
+
+
+class TestPrepFaultAbsorption:
+    """Prep faults propagate forward but get absorbed at PZ/MZ."""
+
+    def test_prep_fault_reaches_next_measurement(self):
+        """A prep fault on PZ(ancilla) should flip the next ancilla MZ."""
+        tc = build_two_round_x_check()
+        # Prep-only noise
+        depol = depolarizing().p1(0).p2(0).p_meas(0).p_prep(0.01)
+        shots = 50000
+
+        meas_r = sim_neo(tc).quantum(meas_sampling()).noise(depol).shots(shots).seed(42).run()
+        stab_r = sim_neo(tc).quantum(stabilizer()).noise(depol).shots(shots).seed(42).run()
+
+        def det_rate(results):
+            return sum(s[0] ^ s[1] for s in results) / len(results)
+
+        meas_rate = det_rate(meas_r)
+        stab_rate = det_rate(stab_r)
+
+        # Prep faults fire the detector (X error → detected at MZ)
+        assert stab_rate > 0.005, f"Stabilizer should see prep faults: {stab_rate}"
+        assert (
+            abs(meas_rate - stab_rate) / stab_rate < 0.15
+        ), f"Prep fault rate mismatch: dem={meas_rate:.4f} stab={stab_rate:.4f}"
+
+    def test_prep_fault_does_not_cross_reset(self):
+        """A prep fault should NOT propagate past a subsequent PZ on the same qubit."""
+        tc = build_three_round_z_check()
+        depol = depolarizing().p1(0).p2(0).p_meas(0).p_prep(0.01)
+        shots = 50000
+
+        meas_r = sim_neo(tc).quantum(meas_sampling()).noise(depol).shots(shots).seed(42).run()
+        stab_r = sim_neo(tc).quantum(stabilizer()).noise(depol).shots(shots).seed(42).run()
+
+        # Extract detector 0 (m0 XOR m1) rate
+        def det_rate(results, d):
+            num_meas = 3
+            recs = [{"records": [-2, -3]}, {"records": [-1, -2]}][d]["records"]
+            fired = sum(1 for s in results if sum(s[num_meas + r] for r in recs) % 2 == 1)
+            return fired / len(results)
+
+        for d in [0, 1]:
+            meas_rate = det_rate(meas_r, d)
+            stab_rate = det_rate(stab_r, d)
+            assert (
+                abs(meas_rate - stab_rate) / max(stab_rate, 1e-10) < 0.20
+            ), f"Det {d} prep fault mismatch: dem={meas_rate:.4f} stab={stab_rate:.4f}"
+
+
+class TestMultiRoundNonSurface:
+    """Multi-round circuits that are NOT surface codes."""
+
+    def test_three_round_z_check_all_noise(self):
+        """3-round Z-check with full depolarizing noise matches stabilizer."""
+        tc = build_three_round_z_check()
+        depol = depolarizing().p1(0.001).p2(0.005).p_meas(0.005).p_prep(0.005)
+        shots = 50000
+
+        meas_r = sim_neo(tc).quantum(meas_sampling()).noise(depol).shots(shots).seed(42).run()
+        stab_r = sim_neo(tc).quantum(stabilizer()).noise(depol).shots(shots).seed(42).run()
+
+        def det_rate(results, d):
+            num_meas = 3
+            recs = [{"records": [-2, -3]}, {"records": [-1, -2]}][d]["records"]
+            fired = sum(1 for s in results if sum(s[num_meas + r] for r in recs) % 2 == 1)
+            return fired / len(results)
+
+        for d in [0, 1]:
+            meas_rate = det_rate(meas_r, d)
+            stab_rate = det_rate(stab_r, d)
+            assert (
+                abs(meas_rate - stab_rate) / max(stab_rate, 1e-10) < 0.15
+            ), f"Det {d} mismatch: dem={meas_rate:.4f} stab={stab_rate:.4f}"
+
+
+class TestZeroNoise:
+    """With zero noise, all detectors must fire at rate 0."""
+
+    def test_two_round_x_check_zero_noise(self):
+        tc = build_two_round_x_check()
+        depol = depolarizing().p1(0).p2(0).p_meas(0).p_prep(0)
+        r = sim_neo(tc).quantum(meas_sampling()).noise(depol).shots(1000).seed(42).run()
+        det_fires = sum(s[0] ^ s[1] for s in r)
+        assert det_fires == 0, f"Zero-noise detector fired {det_fires}/1000 times"
+
+    def test_three_round_z_check_zero_noise(self):
+        tc = build_three_round_z_check()
+        depol = depolarizing().p1(0).p2(0).p_meas(0).p_prep(0)
+        r = sim_neo(tc).quantum(meas_sampling()).noise(depol).shots(1000).seed(42).run()
+        for d in [0, 1]:
+            num_meas = 3
+            recs = [{"records": [-2, -3]}, {"records": [-1, -2]}][d]["records"]
+            fired = sum(1 for s in r if sum(s[num_meas + r_] for r_ in recs) % 2 == 1)
+            assert fired == 0, f"Zero-noise det {d} fired {fired}/1000"
+
+    def test_new_clifford_gates_match_stabilizer_zero_noise(self):
+        """meas_sampling and stabilizer agree exactly on a noiseless new-gate circuit."""
+        tc = TickCircuit()
+        tc.tick().pz([0, 1, 2])
+        tc.tick().x([0])
+        tc.tick().cy([(0, 1)])
+        tc.tick().szz([(1, 2)])
+        tc.tick().swap([(1, 2)])
+        tc.tick().sx([2])
+        tc.tick().sxdg([2])
+        tick = tc.tick()
+        tick.mz([0])
+        tick.mz([1])
+        tick.mz([2])
+        tc.set_meta("num_measurements", "3")
+        tc.set_meta("detectors", "[]")
+        tc.set_meta("observables", "[]")
+
+        depol = depolarizing().p1(0).p2(0).p_meas(0).p_prep(0)
+        shots = 32
+        meas_r = sim_neo(tc).quantum(meas_sampling()).noise(depol).shots(shots).seed(11).run()
+        stab_r = sim_neo(tc).quantum(stabilizer()).noise(depol).shots(shots).seed(99).run()
+
+        assert len(meas_r) == len(stab_r) == shots
+        for shot in range(shots):
+            assert list(meas_r[shot]) == list(stab_r[shot]) == [1, 0, 1]
+
+
+class TestCYGateSupport:
+    """CY gate should work through the meas_sampling public path."""
+
+    def test_cy_sign_has_circuit_level_measurement_effect(self):
+        """CY maps XX to -YZ, so measuring YZ after CY gives odd parity."""
+        tc = TickCircuit()
+        tc.tick().pz([0, 1])
+        tc.tick().h([0])
+        tc.tick().h([1])
+        tc.tick().cy([(0, 1)])
+        tc.tick().f([0])
+        tick = tc.tick()
+        tick.mz([0])
+        tick.mz([1])
+        tc.set_meta("num_measurements", "2")
+        tc.set_meta("detectors", "[]")
+        tc.set_meta("observables", "[]")
+
+        depol = depolarizing().p1(0).p2(0).p_meas(0).p_prep(0)
+        for backend in (stabilizer(), statevec()):
+            result = sim_neo(tc).quantum(backend).noise(depol).shots(32).seed(123).run()
+            for shot in range(result.num_shots):
+                row = list(result[shot])
+                assert row[0] ^ row[1] == 1
+
+    def test_cy_circuit_shape_and_values(self):
+        """H(0) CY(0,1) MZ(0) MZ(1): 2 measurements, no unsupported-gate error."""
+        tc = TickCircuit()
+        tc.tick().h([0])
+        tc.tick().cy([(0, 1)])
+        tick = tc.tick()
+        tick.mz([0])
+        tick = tc.tick()
+        tick.mz([1])
+        tc.set_meta("num_measurements", "2")
+        tc.set_meta("detectors", "[]")
+        tc.set_meta("observables", "[]")
+
+        depol = depolarizing().p1(0.005).p2(0.005).p_meas(0.005).p_prep(0.005)
+        result = sim_neo(tc).quantum(meas_sampling()).noise(depol).shots(100).seed(42).run()
+
+        assert len(result) == 100
+        assert len(result[0]) == 2
+        for shot in range(100):
+            for meas in range(2):
+                assert result.get(shot, meas) in (0, 1)
+
+    def test_cy_matches_stabilizer_protocol(self):
+        """CY circuit: meas_sampling and stabilizer produce same output shape."""
+        tc = TickCircuit()
+        tc.tick().h([0])
+        tc.tick().cy([(0, 1)])
+        tick = tc.tick()
+        tick.mz([0])
+        tick = tc.tick()
+        tick.mz([1])
+        tc.set_meta("num_measurements", "2")
+        tc.set_meta("detectors", "[]")
+        tc.set_meta("observables", "[]")
+
+        depol = depolarizing().p1(0.005).p2(0.005).p_meas(0.005).p_prep(0.005)
+
+        meas_r = sim_neo(tc).quantum(meas_sampling()).noise(depol).shots(100).seed(42).run()
+        stab_r = sim_neo(tc).quantum(stabilizer()).noise(depol).shots(100).seed(42).run()
+
+        assert len(meas_r) == len(stab_r) == 100
+        assert meas_r.num_measurements == stab_r.num_measurements == 2
diff --git a/python/quantum-pecos/tests/qec/test_parsed_dem_sampler.py b/python/quantum-pecos/tests/qec/test_parsed_dem_sampler.py
index b21f4db0c..11537c084 100644
--- a/python/quantum-pecos/tests/qec/test_parsed_dem_sampler.py
+++ b/python/quantum-pecos/tests/qec/test_parsed_dem_sampler.py
@@ -146,6 +146,33 @@ def test_optimized_sampler_creation(self) -> None:
         assert sampler.num_mechanisms == 1
         assert sampler.num_detectors == 2
 
+    def test_optimized_sampler_projects_tracked_paulis_but_fails_direct_sampling(self) -> None:
+        """Parsed PECOS DEM samplers preserve tracked-Pauli IDs but do not sample them directly."""
+        from pecos_rslib.qec import ParsedDem
+
+        parsed = ParsedDem.from_string("error(0.1) D0 TP1")
+        sampler = parsed.to_dem_sampler()
+
+        assert parsed.num_tracked_paulis == 2
+        assert sampler.num_detectors == 1
+        assert sampler.num_dem_outputs == 0
+        assert sampler.num_tracked_paulis == 2
+
+        detectors, dem_outputs = sampler.sample(seed=11)
+        assert len(detectors) == 1
+        assert isinstance(detectors[0], bool)
+        assert dem_outputs == []
+
+        with pytest.raises(RuntimeError, match="cannot directly sample tracked Pauli flips"):
+            sampler.sample_tracked_paulis(seed=11)
+
+    def test_parser_rejects_legacy_tracked_metadata_extension(self) -> None:
+        """The PECOS DEM parser should not accept old tracked-op extension lines."""
+        from pecos_rslib.qec import ParsedDem
+
+        with pytest.raises(ValueError, match="unsupported PECOS DEM extension line"):
+            ParsedDem.from_string('pecos_tracked_op {"id":0,"pauli":"+X0"}')
+
     def test_optimized_matches_naive_sampler(self) -> None:
         """Optimized sampler should produce same statistics as naive sampler."""
         from pecos_rslib.qec import ParsedDem
diff --git a/python/quantum-pecos/tests/qec/test_qec_ux_entrypoints.py b/python/quantum-pecos/tests/qec/test_qec_ux_entrypoints.py
new file mode 100644
index 000000000..aceeb3050
--- /dev/null
+++ b/python/quantum-pecos/tests/qec/test_qec_ux_entrypoints.py
@@ -0,0 +1,146 @@
+"""User-facing QEC entry point and metadata ergonomics tests."""
+
+from __future__ import annotations
+
+import json
+from pathlib import Path
+
+import pytest
+
+
+def test_sim_neo_stack_runs_from_exp() -> None:
+    pecos_rslib_exp = pytest.importorskip("pecos_rslib_exp")
+    from pecos.quantum import TickCircuit
+
+    tc = TickCircuit()
+    tc.tick().mz([0])
+
+    result = (
+        pecos_rslib_exp.sim_neo(tc)
+        .quantum(pecos_rslib_exp.stabilizer())
+        .noise(pecos_rslib_exp.depolarizing())
+        .shots(2)
+        .seed(123)
+        .run()
+    )
+    assert result.num_shots == 2
+    assert pecos_rslib_exp.meas_sampling() is not None
+    assert callable(pecos_rslib_exp.fault_catalog)
+
+
+def test_build_memory_circuit_is_public_surface_helper() -> None:
+    from pecos.qec.surface import build_memory_circuit
+
+    tc = build_memory_circuit(distance=3, rounds=2, basis="Z")
+
+    assert int(tc.get_meta("num_measurements")) > 0
+    assert json.loads(tc.get_meta("detectors"))
+    assert json.loads(tc.get_meta("observables"))
+
+
+def test_surface_code_memory_runs_native_zero_noise_quick_start() -> None:
+    from pecos.qec.surface import surface_code_memory
+
+    result = surface_code_memory(
+        distance=3,
+        physical_error_rate=0.0,
+        shots=4,
+        rounds=1,
+        seed=123,
+    )
+
+    assert result.distance == 3
+    assert result.num_shots == 4
+    assert result.num_rounds == 1
+    assert result.logical_error_rate == 0.0
+    assert result.raw_error_rate == 0.0
+
+
+def test_surface_code_memory_rejects_ambiguous_noise_inputs() -> None:
+    from pecos.qec.surface import NoiseModel, surface_code_memory
+
+    with pytest.raises(ValueError, match="either physical_error_rate or noise_model"):
+        surface_code_memory(
+            physical_error_rate=0.0,
+            noise_model=NoiseModel.uniform(0.001),
+            shots=0,
+            rounds=1,
+        )
+
+
+def test_tick_circuit_metadata_helpers_build_detector_and_observable_json() -> None:
+    from pecos.quantum import TickCircuit
+
+    tc = TickCircuit()
+    det_id = tc.add_detector(records=[-1], coords=[0.0, 1.0, 2.0], label="d0")
+    obs_id = tc.add_observable(records=[-1, -2], label="L2")
+
+    detectors = json.loads(tc.get_meta("detectors"))
+    observables = json.loads(tc.get_meta("observables"))
+
+    assert det_id == 0
+    assert detectors == [{"id": 0, "records": [-1], "coords": [0.0, 1.0, 2.0], "label": "d0"}]
+    assert int(tc.get_meta("num_detectors")) == 1
+
+    assert obs_id == 2
+    assert observables == [{"id": 2, "records": [-1, -2], "label": "L2"}]
+    assert int(tc.get_meta("num_observables")) == 3
+
+
+def test_tracked_pauli_public_api_uses_current_names_only() -> None:
+    from pecos.quantum import DagCircuit, GateRegistry, GateType, TickCircuit, X
+
+    assert GateType.TrackedPauliMeta.name == "TrackedPauli"
+    assert repr(GateType.TrackedPauliMeta) == "GateType.TrackedPauli"
+
+    stub_text = (Path(__file__).parents[3] / "pecos-rslib" / "pecos_rslib.pyi").read_text()
+    assert "TrackedPauliMeta: GateType" in stub_text
+    assert "TrackedOperator" not in stub_text
+
+    for circuit in (DagCircuit(), TickCircuit()):
+        assert hasattr(circuit, "tracked_pauli")
+        assert not hasattr(circuit, "tracked_operator")
+        assert not hasattr(circuit, "tracked_op")
+
+        idx = circuit.tracked_pauli(X(0), label="x_probe")
+        assert idx == 0
+        assert circuit.annotations()[0]["kind"] == "tracked_pauli"
+        assert circuit.annotations()[0]["label"] == "x_probe"
+
+    for alias in ("TrackedPauli", "TrackedPauliMeta", "TP"):
+        registry = GateRegistry()
+        registry.define(f"Use{alias}", 1).step(alias, [0]).register_into(registry)
+        assert registry.decompose(f"Use{alias}", [7], []) == [
+            ("TrackedPauli", [7], [], {}),
+        ]
+
+    registry = GateRegistry()
+    with pytest.raises(ValueError, match="Unknown gate type"):
+        registry.define("Legacy", 1).step("TrackedOperator", [0])
+
+
+def test_tick_circuit_observable_helper_rejects_conflicting_label_id() -> None:
+    from pecos.quantum import TickCircuit
+
+    tc = TickCircuit()
+    with pytest.raises(ValueError, match="conflicts"):
+        tc.add_observable(records=[-1], observable_id=1, label="L2")
+
+
+def test_tick_circuit_reset_clears_annotations_and_measurement_records() -> None:
+    from pecos.quantum import TickCircuit, Z
+
+    tc = TickCircuit()
+    measurements = tc.tick().mz([0])
+    tc.detector(measurements)
+    tc.observable(measurements)
+    tc.tracked_pauli(Z(0))
+
+    assert tc.num_measurements() == 1
+    assert len(tc.annotations()) == 3
+
+    tc.reset()
+
+    assert tc.num_ticks() == 0
+    assert tc.num_measurements() == 0
+    assert tc.annotations() == []
diff --git a/python/quantum-pecos/tests/qec/test_raw_measurement_result.py b/python/quantum-pecos/tests/qec/test_raw_measurement_result.py
new file mode 100644
index 000000000..7bb169a1e
--- /dev/null
+++ b/python/quantum-pecos/tests/qec/test_raw_measurement_result.py
@@ -0,0 +1,190 @@
+# Copyright 2026 The PECOS Developers
+# Licensed under the Apache License, Version 2.0
+
+"""Tests proving RawMeasurementResult protocol compatibility across backends.
+
+All sim_neo backends now return RawMeasurementResult, a common Rust-backed
+type that supports indexing, iteration, len(), and get(). This test verifies
+the output contract is identical for stabilizer and meas_sampling.
+"""
+
+import pytest
+from pecos.qec.surface import SurfacePatch
+from pecos.qec.surface.decode import _build_surface_tick_circuit_for_native_model
+from pecos_rslib_exp import depolarizing, meas_sampling, sim_neo, stabilizer
+
+
+@pytest.fixture
+def d3_results():
+    """Run both backends on the same circuit and return their results."""
+    patch = SurfacePatch.create(distance=3)
+    tc = _build_surface_tick_circuit_for_native_model(patch, 6, "Z", circuit_source="abstract")
+    depol = depolarizing().p1(0.005).p2(0.005).p_meas(0.005).p_prep(0.005)
+
+    stab_r = sim_neo(tc).quantum(stabilizer()).noise(depol).shots(100).seed(42).run()
+    meas_r = sim_neo(tc).quantum(meas_sampling()).noise(depol).shots(100).seed(42).run()
+    return stab_r, meas_r
+
+
+class TestCommonProtocol:
+    """Both backends return objects with the same interface."""
+
+    def test_len(self, d3_results):
+        stab_r, meas_r = d3_results
+        assert len(stab_r) == 100
+        assert len(meas_r) == 100
+
+    def test_indexing(self, d3_results):
+        stab_r, meas_r = d3_results
+        # r[shot] returns a sequence of u8 values
+        s0 = stab_r[0]
+        d0 = meas_r[0]
+        assert len(s0) == len(d0) == 57  # d=3 surface code has 57 measurements
+
+    def test_item_values(self, d3_results):
+        stab_r, meas_r = d3_results
+        # Individual values are 0 or 1
+        for val in stab_r[0]:
+            assert val in (0, 1)
+        for val in meas_r[0]:
+            assert val in (0, 1)
+
+    def test_list_conversion(self, d3_results):
+        stab_r, meas_r = d3_results
+        s_row = list(stab_r[0])
+        d_row = list(meas_r[0])
+        assert all(isinstance(v, int) for v in s_row)
+        assert all(isinstance(v, int) for v in d_row)
+        assert len(s_row) == len(d_row) == 57
+
+    def test_iteration(self, d3_results):
+        stab_r, meas_r = d3_results
+        stab_count = 0
+        for row in stab_r:
+            stab_count += 1
+            assert len(row) == 57
+        assert stab_count == 100
+
+        dem_count = 0
+        for row in meas_r:
+            dem_count += 1
+            assert len(row) == 57
+        assert dem_count == 100
+
+    def test_out_of_range_raises_index_error(self, d3_results):
+        stab_r, meas_r = d3_results
+        with pytest.raises(IndexError):
+            stab_r[100]
+        with pytest.raises(IndexError):
+            meas_r[100]
+
+    def test_num_shots_property(self, d3_results):
+        stab_r, meas_r = d3_results
+        assert stab_r.num_shots == 100
+        assert meas_r.num_shots == 100
+
+    def test_num_measurements_property(self, d3_results):
+        stab_r, meas_r = d3_results
+        assert stab_r.num_measurements == 57
+        assert meas_r.num_measurements == 57
+
+    def test_get_method(self, d3_results):
+        stab_r, meas_r = d3_results
+        # get(shot, meas) returns 0 or 1
+        assert stab_r.get(0, 0) in (0, 1)
+        assert meas_r.get(0, 0) in (0, 1)
+
+    def test_get_out_of_range(self, d3_results):
+        stab_r, meas_r = d3_results
+        with pytest.raises(IndexError):
+            stab_r.get(100, 0)
+        with pytest.raises(IndexError):
+            meas_r.get(0, 57)
+
+    def test_get_shot_method(self, d3_results):
+        stab_r, meas_r = d3_results
+        s = stab_r.get_shot(0)
+        d = meas_r.get_shot(0)
+        assert len(s) == len(d) == 57
+
+    def test_to_list(self, d3_results):
+        stab_r, meas_r = d3_results
+        sl = stab_r.to_list()
+        dl = meas_r.to_list()
+        assert len(sl) == len(dl) == 100
+        assert len(sl[0]) == len(dl[0]) == 57
+
+    def test_negative_index_raises_index_error(self, d3_results):
+        """Negative indexing raises IndexError, never OverflowError."""
+        stab_r, meas_r = d3_results
+        with pytest.raises(IndexError):
+            stab_r[-1]
+        with pytest.raises(IndexError):
+            meas_r[-1]
+
+    def test_negative_get_raises_index_error(self, d3_results):
+        stab_r, meas_r = d3_results
+        # Negative shot
+        with pytest.raises(IndexError):
+            stab_r.get(-1, 0)
+        with pytest.raises(IndexError):
+            meas_r.get(-1, 0)
+        # Negative measurement
+        with pytest.raises(IndexError):
+            stab_r.get(0, -1)
+        with pytest.raises(IndexError):
+            meas_r.get(0, -1)
+
+    def test_get_shot_negative_raises_index_error(self, d3_results):
+        stab_r, meas_r = d3_results
+        with pytest.raises(IndexError):
+            stab_r.get_shot(-1)
+        with pytest.raises(IndexError):
+            meas_r.get_shot(-1)
+
+    def test_out_of_range_uses_len(self, d3_results):
+        """result[len(result)] raises IndexError."""
+        stab_r, meas_r = d3_results
+        with pytest.raises(IndexError):
+            stab_r[len(stab_r)]
+        with pytest.raises(IndexError):
+            meas_r[len(meas_r)]
+
+
+class TestGenericConsumer:
+    """A generic helper that works unchanged for any backend."""
+
+    def compute_measurement_means(self, result):
+        """Compute per-measurement mean across all shots — works for any backend."""
+        shots = len(result)
+        if shots == 0:
+            return []
+        n_meas = len(result[0])
+        means = [0.0] * n_meas
+        for row in result:
+            for i, val in enumerate(row):
+                means[i] += val
+        return [m / shots for m in means]
+
+    def test_generic_consumer_stabilizer(self):
+        patch = SurfacePatch.create(distance=3)
+        tc = _build_surface_tick_circuit_for_native_model(patch, 6, "Z", circuit_source="abstract")
+        depol = depolarizing().p1(0.005).p2(0.005).p_meas(0.005).p_prep(0.005)
+        result = sim_neo(tc).quantum(stabilizer()).noise(depol).shots(1000).seed(42).run()
+
+        means = self.compute_measurement_means(result)
+        assert len(means) == 57
+        # Non-det measurements should be ~0.5, det should be ~0
+        nondet = sum(1 for m in means if abs(m - 0.5) < 0.15)
+        assert nondet > 0
+
+    def test_generic_consumer_meas_sampling(self):
+        patch = SurfacePatch.create(distance=3)
+        tc = _build_surface_tick_circuit_for_native_model(patch, 6, "Z", circuit_source="abstract")
+        depol = depolarizing().p1(0.005).p2(0.005).p_meas(0.005).p_prep(0.005)
+        result = sim_neo(tc).quantum(meas_sampling()).noise(depol).shots(1000).seed(42).run()
+
+        means = self.compute_measurement_means(result)
+        assert len(means) == 57
+        nondet = sum(1 for m in means if abs(m - 0.5) < 0.15)
+        assert nondet > 0
diff --git a/python/quantum-pecos/tests/qec/test_sample_batch.py b/python/quantum-pecos/tests/qec/test_sample_batch.py
new file mode 100644
index 000000000..4170da0ac
--- /dev/null
+++ b/python/quantum-pecos/tests/qec/test_sample_batch.py
@@ -0,0 +1,95 @@
+# Copyright 2026 The PECOS Developers
+# Licensed under the Apache License, Version 2.0
+
+"""Tests for SampleBatch columnar storage and validation."""
+
+import pytest
+from pecos_rslib.qec import DemSampler, SampleBatch
+
+
+class TestSampleBatchConstruction:
+    def test_round_trip_get_syndrome(self):
+        batch = SampleBatch([[1, 0], [0, 1]], [1, 0])
+        assert list(batch.get_syndrome(0)) == [1, 0]
+        assert list(batch.get_syndrome(1)) == [0, 1]
+
+    def test_round_trip_get_observable_mask(self):
+        batch = SampleBatch([[1, 0], [0, 1]], [1, 0])
+        assert batch.get_observable_mask(0) == 1
+        assert batch.get_observable_mask(1) == 0
+
+    def test_num_shots(self):
+        batch = SampleBatch([[0, 0], [1, 1], [0, 1]], [0, 0, 0])
+        assert batch.num_shots == 3
+
+    def test_ragged_rows_longer_rejected(self):
+        with pytest.raises(ValueError, match=r"row 1.*length 3.*expected 2"):
+            SampleBatch([[1, 0], [0, 1, 1]], [0, 0])
+
+    def test_ragged_rows_shorter_rejected(self):
+        with pytest.raises(ValueError, match=r"row 2.*length 1.*expected 2"):
+            SampleBatch([[1, 0], [0, 1], [0]], [0, 0, 0])
+
+    def test_length_mismatch_rejected(self):
+        with pytest.raises(ValueError, match="must have same length"):
+            SampleBatch([[1, 0]], [0, 0])
+
+    def test_empty_batch(self):
+        batch = SampleBatch([], [])
+        assert batch.num_shots == 0
+
+
+class TestGeneratedSampleBatch:
+    @pytest.fixture
+    def d3_setup(self):
+        from pecos.qec.surface import SurfacePatch
+        from pecos.qec.surface.decode import _build_surface_tick_circuit_for_native_model
+
+        patch = SurfacePatch.create(distance=3)
+        tc = _build_surface_tick_circuit_for_native_model(
+            patch,
+            6,
+            "Z",
+            circuit_source="abstract",
+        )
+        sampler = DemSampler.from_circuit(
+            tc,
+            p1=0.005,
+            p2=0.005,
+            p_meas=0.005,
+            p_prep=0.005,
+        )
+        return sampler, tc
+
+    def test_num_shots(self, d3_setup):
+        sampler, _ = d3_setup
+        batch = sampler.generate_samples(100, seed=42)
+        assert batch.num_shots == 100
+
+    def test_get_syndrome_shape(self, d3_setup):
+        sampler, _ = d3_setup
+        batch = sampler.generate_samples(10, seed=42)
+        syn = batch.get_syndrome(0)
+        assert len(syn) == sampler.num_detectors
+
+    def test_get_observable_mask_type(self, d3_setup):
+        sampler, _ = d3_setup
+        batch = sampler.generate_samples(10, seed=42)
+        mask = batch.get_observable_mask(0)
+        assert isinstance(mask, int)
+
+    def test_decode_count(self, d3_setup):
+        import stim
+        from pecos.qec.surface.circuit_builder import tick_circuit_to_stim
+
+        sampler, tc = d3_setup
+        noise = {"p1": 0.005, "p2": 0.005, "p_meas": 0.005, "p_prep": 0.005}
+        stim_str = tick_circuit_to_stim(tc, **noise)
+        dem_str = str(
+            stim.Circuit(stim_str).detector_error_model(decompose_errors=True),
+        )
+
+        batch = sampler.generate_samples(1000, seed=42)
+        errors = batch.decode_count(dem_str, "pymatching")
+        assert isinstance(errors, int)
+        assert 0 <= errors <= 1000
diff --git a/python/quantum-pecos/tests/qec/test_traced_qis_clifford_pipeline.py b/python/quantum-pecos/tests/qec/test_traced_qis_clifford_pipeline.py
new file mode 100644
index 000000000..47b0ca312
--- /dev/null
+++ b/python/quantum-pecos/tests/qec/test_traced_qis_clifford_pipeline.py
@@ -0,0 +1,290 @@
+# Copyright 2026 The PECOS Developers
+# Licensed under the Apache License, Version 2.0
+
+"""Smoke tests for the traced-QIS surface-code route after Clifford lowering."""
+
+import random
+
+from pecos.qec.surface import SurfacePatch
+from pecos.qec.surface.decode import _build_surface_tick_circuit_for_native_model
+from pecos.quantum import TickCircuit
+from pecos_rslib_exp import (
+    Mast,
+    StabMps,
+    depolarizing,
+    fault_catalog,
+    meas_sampling,
+    sim_neo,
+    stabilizer,
+    statevec,
+)
+
+ONE_Q_INVERSES = {
+    "X": "X",
+    "Y": "Y",
+    "Z": "Z",
+    "H": "H",
+    "F": "Fdg",
+    "Fdg": "F",
+    "SX": "SXdg",
+    "SXdg": "SX",
+    "SY": "SYdg",
+    "SYdg": "SY",
+    "SZ": "SZdg",
+    "SZdg": "SZ",
+}
+
+TWO_Q_INVERSES = {
+    "CX": "CX",
+    "CY": "CY",
+    "CZ": "CZ",
+    "SXX": "SXXdg",
+    "SXXdg": "SXX",
+    "SYY": "SYYdg",
+    "SYYdg": "SYY",
+    "SZZ": "SZZdg",
+    "SZZdg": "SZZ",
+    "SWAP": "SWAP",
+}
+
+TICK_1Q_METHODS = {
+    "X": "x",
+    "Y": "y",
+    "Z": "z",
+    "H": "h",
+    "F": "f",
+    "Fdg": "fdg",
+    "SX": "sx",
+    "SXdg": "sxdg",
+    "SY": "sy",
+    "SYdg": "sydg",
+    "SZ": "sz",
+    "SZdg": "szdg",
+}
+
+TICK_2Q_METHODS = {
+    "CX": "cx",
+    "CY": "cy",
+    "CZ": "cz",
+    "SXX": "sxx",
+    "SXXdg": "sxxdg",
+    "SYY": "syy",
+    "SYYdg": "syydg",
+    "SZZ": "szz",
+    "SZZdg": "szzdg",
+    "SWAP": "swap",
+}
+
+
+def build_lowered_traced_qis_surface_code(rounds=3):
+    patch = SurfacePatch.create(distance=3)
+    tc = _build_surface_tick_circuit_for_native_model(patch, rounds, "Z", circuit_source="traced_qis")
+    tc.lower_clifford_rotations()
+    return tc
+
+
+def traced_qis_noise():
+    return depolarizing().p1(0.0003).p2(0.003).p_meas(0.0015).p_prep(0.0015)
+
+
+def zero_noise():
+    return depolarizing().p1(0).p2(0).p_meas(0).p_prep(0)
+
+
+def build_explicit_clifford_gate_circuit():
+    tc = TickCircuit()
+    tc.tick().szdg([0])
+    tc.tick().sx([0])
+    tc.tick().sxdg([1])
+    tc.tick().sy([0])
+    tc.tick().sydg([1])
+    tc.tick().f([0])
+    tc.tick().fdg([1])
+    tc.tick().cy([(0, 1)])
+    tc.tick().cz([(0, 1)])
+    tc.tick().sxx([(0, 1)])
+    tc.tick().sxxdg([(0, 1)])
+    tc.tick().syy([(0, 1)])
+    tc.tick().syydg([(0, 1)])
+    tc.tick().szz([(0, 1)])
+    tc.tick().szzdg([(0, 1)])
+    tc.tick().swap([(0, 1)])
+    tc.tick().mz([0, 1])
+    tc.set_meta("num_measurements", "2")
+    tc.set_meta("detectors", "[]")
+    tc.set_meta("observables", "[]")
+    return tc
+
+
+def random_standard_clifford_sequence(seed, depth=14, num_qubits=3):
+    rng = random.Random(seed)
+    sequence = []
+    for _ in range(depth):
+        if rng.random() < 0.55:
+            gate = rng.choice(tuple(ONE_Q_INVERSES))
+            qubits = (rng.randrange(num_qubits),)
+        else:
+            gate = rng.choice(tuple(TWO_Q_INVERSES))
+            q0, q1 = rng.sample(range(num_qubits), 2)
+            qubits = (q0, q1)
+        sequence.append((gate, qubits))
+    return sequence
+
+
+def inverse_standard_clifford_sequence(sequence):
+    inverse = []
+    for gate, qubits in reversed(sequence):
+        if len(qubits) == 1:
+            inverse.append((ONE_Q_INVERSES[gate], qubits))
+        else:
+            inverse.append((TWO_Q_INVERSES[gate], qubits))
+    return inverse
+
+
+def apply_tick_gate(tc, gate, qubits):
+    tick = tc.tick()
+    if len(qubits) == 1:
+        getattr(tick, TICK_1Q_METHODS[gate])([qubits[0]])
+    else:
+        getattr(tick, TICK_2Q_METHODS[gate])([(qubits[0], qubits[1])])
+
+
+def build_mirrored_random_clifford_circuit(seed, num_qubits=3):
+    sequence = random_standard_clifford_sequence(seed, num_qubits=num_qubits)
+    tc = TickCircuit()
+    tc.tick().pz(list(range(num_qubits)))
+    for gate, qubits in sequence + inverse_standard_clifford_sequence(sequence):
+        apply_tick_gate(tc, gate, qubits)
+    tc.tick().mz(list(range(num_qubits)))
+    tc.set_meta("num_measurements", str(num_qubits))
+    tc.set_meta("detectors", "[]")
+    tc.set_meta("observables", "[]")
+    return tc, sequence
+
+
+def run_direct_wrapper_mirrored_circuit(sim, sequence, num_qubits=3):
+    for q in range(num_qubits):
+        sim.run_1q_gate("PZ", q)
+
+    for gate, qubits in sequence + inverse_standard_clifford_sequence(sequence):
+        if len(qubits) == 1:
+            sim.run_1q_gate(gate, qubits[0])
+        else:
+            sim.run_2q_gate(gate, qubits)
+
+    return [sim.run_1q_gate("MZ", q) for q in range(num_qubits)]
+
+
+def test_meas_sampling_runs_on_lowered_traced_qis_surface_code():
+    tc = build_lowered_traced_qis_surface_code()
+    shots = 8
+
+    result = sim_neo(tc).quantum(meas_sampling()).noise(traced_qis_noise()).shots(shots).seed(123).run()
+
+    assert result.num_shots == shots
+    assert result.num_measurements == int(tc.get_meta("num_measurements"))
+    assert len(result[0]) == result.num_measurements
+
+
+def test_fault_catalog_builds_on_lowered_traced_qis_surface_code():
+    tc = build_lowered_traced_qis_surface_code()
+
+    catalog = fault_catalog(tc, traced_qis_noise())
+    first = next(catalog.fault_configurations(1))
+
+    assert len(catalog) > 0
+    assert len(first.locations) == 1
+    assert len(first.faults) == 1
+    assert first.locations[0] is catalog.locations[first.location_indices[0]]
+
+
+def test_lowered_traced_qis_pipeline_sampling_and_catalog_smoke():
+    tc = build_lowered_traced_qis_surface_code(rounds=2)
+    noise = traced_qis_noise()
+
+    result = sim_neo(tc).quantum(meas_sampling()).noise(noise).shots(3).seed(321).run()
+    catalog = fault_catalog(tc, noise)
+    first_fault = next(catalog.fault_configurations(1))
+
+    assert result.num_shots == 3
+    assert result.num_measurements == int(tc.get_meta("num_measurements"))
+    assert len(catalog) > 0
+    assert len(first_fault.locations) == 1
+    assert len(first_fault.faults) == 1
+
+
+def test_explicit_python_gate_names_map_to_rust_clifford_gates():
+    tc = build_explicit_clifford_gate_circuit()
+    noise = depolarizing().p1(0.03).p2(0.15).p_meas(0).p_prep(0)
+
+    result = sim_neo(tc).quantum(meas_sampling()).noise(noise).shots(3).seed(123).run()
+    assert result.num_shots == 3
+    assert result.num_measurements == 2
+
+    catalog = fault_catalog(tc, noise)
+    # Structural catalog includes all locations (including p_meas=0 and p_prep=0).
+    # Count only alternatives at locations with nonzero channel probability.
+    nonzero_alts = sum(len(loc.faults) for loc in catalog if loc.channel_probability > 0.0)
+    assert nonzero_alts == 156
+
+
+def test_sim_neo_native_backends_accept_face_gates():
+    tc = TickCircuit()
+    tc.tick().pz([0])
+    tc.tick().f([0])
+    tc.tick().fdg([0])
+    tc.tick().mz([0])
+    tc.set_meta("num_measurements", "1")
+    tc.set_meta("detectors", "[]")
+    tc.set_meta("observables", "[]")
+
+    for backend in (stabilizer(), statevec()):
+        result = sim_neo(tc).quantum(backend).noise(zero_noise()).shots(2).seed(123).run()
+        assert result.num_measurements == 1
+        assert all(result[shot][0] == 0 for shot in range(result.num_shots))
+
+
+def test_direct_exp_wrappers_accept_standard_clifford_names():
+    for sim in (StabMps(2, seed=123), Mast(2, 1, seed=123)):
+        for gate in ("I", "X", "Y", "Z", "H", "F", "Fdg", "SX", "SXdg", "SY", "SYdg", "SZ", "SZdg"):
+            sim.run_1q_gate(gate, 0)
+
+        for gate in (
+            "CX",
+            "CY",
+            "CZ",
+            "SXX",
+            "SXXdg",
+            "SYY",
+            "SYYdg",
+            "SZZ",
+            "SZZdg",
+            "SWAP",
+        ):
+            sim.run_2q_gate(gate, (0, 1))
+
+
+def test_direct_exp_wrappers_face_inverse_is_deterministic():
+    for sim in (StabMps(1, seed=123), Mast(1, 1, seed=123)):
+        sim.run_1q_gate("PZ", 0)
+        sim.run_1q_gate("F", 0)
+        sim.run_1q_gate("Fdg", 0)
+        assert sim.run_1q_gate("MZ", 0) == 0
+
+
+def test_random_mirrored_standard_clifford_circuits_match_across_backends():
+    expected = [0, 0, 0]
+
+    for seed in (7, 19, 41):
+        tc, sequence = build_mirrored_random_clifford_circuit(seed)
+
+        backend_results = {}
+        for name, backend in (("stabilizer", stabilizer()), ("statevec", statevec())):
+            result = sim_neo(tc).quantum(backend).noise(zero_noise()).shots(4).seed(seed).run()
+            backend_results[name] = [list(row) for row in result.to_list()]
+
+        backend_results["StabMps"] = [run_direct_wrapper_mirrored_circuit(StabMps(3, seed=seed), sequence)]
+        backend_results["Mast"] = [run_direct_wrapper_mirrored_circuit(Mast(3, 1, seed=seed), sequence)]
+
+        for name, rows in backend_results.items():
+            assert all(row == expected for row in rows), (seed, name, rows)
diff --git a/python/quantum-pecos/tests/qec/test_traced_qis_slow_integration.py b/python/quantum-pecos/tests/qec/test_traced_qis_slow_integration.py
new file mode 100644
index 000000000..3b194a7dd
--- /dev/null
+++ b/python/quantum-pecos/tests/qec/test_traced_qis_slow_integration.py
@@ -0,0 +1,182 @@
+# Copyright 2026 The PECOS Developers
+# Licensed under the Apache License, Version 2.0
+
+"""Slow traced-QIS integration tests for the raw-measurement pipeline."""
+
+import json
+import math
+
+import numpy as np
+import pytest
+from pecos.qec.surface import SurfacePatch
+from pecos.qec.surface.circuit_builder import tick_circuit_to_stim
+from pecos.qec.surface.decode import _build_surface_tick_circuit_for_native_model
+from pecos_rslib.qec import DemSampler
+from pecos_rslib_exp import depolarizing, fault_catalog, meas_sampling, sim_neo
+
+pymatching = pytest.importorskip("pymatching")
+stim = pytest.importorskip("stim")
+
+pytestmark = pytest.mark.slow
+
+
+def _noise_args(error_rate=0.003):
+    return {
+        "p1": error_rate * 0.1,
+        "p2": error_rate,
+        "p_meas": error_rate * 0.5,
+        "p_prep": error_rate * 0.5,
+    }
+
+
+def _depolarizing_noise(noise_args):
+    return (
+        depolarizing()
+        .p1(noise_args["p1"])
+        .p2(noise_args["p2"])
+        .p_meas(noise_args["p_meas"])
+        .p_prep(noise_args["p_prep"])
+    )
+
+
+def _build_lowered_traced_qis_surface_code(distance, rounds, basis="Z"):
+    patch = SurfacePatch.create(distance=distance)
+    circuit = _build_surface_tick_circuit_for_native_model(patch, rounds, basis, circuit_source="traced_qis")
+    circuit.lower_clifford_rotations()
+    return circuit
+
+
+def _pymatching_decoder(circuit, noise_args):
+    stim_str = tick_circuit_to_stim(circuit, **noise_args)
+    dem = stim.Circuit(stim_str).detector_error_model(decompose_errors=True)
+    return pymatching.Matching.from_detector_error_model(dem)
+
+
+def _extract_observable_mask(row, observables, num_measurements):
+    mask = 0
+    for obs_index, obs in enumerate(observables):
+        value = 0
+        for rec in obs["records"]:
+            idx = num_measurements + rec
+            if 0 <= idx < len(row):
+                value ^= int(row[idx])
+        if value:
+            mask |= 1 << obs_index
+    return mask
+
+
+def _decode_raw_measurements(result, circuit, matching, shots):
+    detectors = json.loads(circuit.get_meta("detectors"))
+    observables = json.loads(circuit.get_meta("observables") or "[]")
+    num_measurements = int(circuit.get_meta("num_measurements"))
+    syndrome = np.zeros(len(detectors), dtype=np.uint8)
+
+    errors = 0
+    for shot_index in range(shots):
+        row = result[shot_index]
+        syndrome.fill(0)
+
+        for det_index, det in enumerate(detectors):
+            value = 0
+            for rec in det["records"]:
+                idx = num_measurements + rec
+                if 0 <= idx < len(row):
+                    value ^= int(row[idx])
+            syndrome[det_index] = value
+
+        predicted = matching.decode(syndrome)
+        predicted_mask = sum(int(bit) << index for index, bit in enumerate(predicted))
+        actual_mask = _extract_observable_mask(row, observables, num_measurements)
+        errors += predicted_mask != actual_mask
+
+    return errors
+
+
+def _decode_native_dem_samples(circuit, noise_args, matching, shots, seed):
+    sampler = DemSampler.from_circuit(circuit, **noise_args)
+    batch = sampler.generate_samples(shots, seed=seed)
+    syndrome = np.zeros(sampler.num_detectors, dtype=np.uint8)
+
+    errors = 0
+    for shot_index in range(shots):
+        sampled_syndrome = batch.get_syndrome(shot_index)
+        for det_index in range(sampler.num_detectors):
+            syndrome[det_index] = sampled_syndrome[det_index]
+        predicted = matching.decode(syndrome)
+        predicted_mask = sum(int(bit) << index for index, bit in enumerate(predicted))
+        errors += predicted_mask != batch.get_observable_mask(shot_index)
+
+    return errors
+
+
+def _assert_statistically_consistent(meas_errors, native_errors, shots):
+    meas_ler = meas_errors / shots
+    native_ler = native_errors / shots
+    pooled = (meas_errors + native_errors) / (2 * shots)
+    variance = 2 * max(pooled * (1 - pooled), 1 / shots) / shots
+    tolerance = max(0.04, 7 * math.sqrt(variance))
+
+    assert abs(meas_ler - native_ler) <= tolerance, (
+        "meas_sampling and native DEM LERs differ more than stochastic tolerance: "
+        f"meas={meas_errors}/{shots} ({meas_ler:.4f}), "
+        f"native={native_errors}/{shots} ({native_ler:.4f}), "
+        f"tolerance={tolerance:.4f}"
+    )
+
+
+@pytest.mark.parametrize(
+    ("distance", "rounds", "shots"),
+    [
+        (3, 6, 2_500),
+        (5, 10, 2_500),
+    ],
+)
+def test_traced_qis_meas_sampling_ler_tracks_native_dem_pymatching(distance, rounds, shots):
+    noise_args = _noise_args()
+    circuit = _build_lowered_traced_qis_surface_code(distance, rounds)
+    matching = _pymatching_decoder(circuit, noise_args)
+
+    raw_result = (
+        sim_neo(circuit).quantum(meas_sampling()).noise(_depolarizing_noise(noise_args)).shots(shots).seed(1234).run()
+    )
+    meas_errors = _decode_raw_measurements(raw_result, circuit, matching, shots)
+    native_errors = _decode_native_dem_samples(circuit, noise_args, matching, shots, seed=5678)
+
+    assert 0 <= meas_errors <= shots
+    assert 0 <= native_errors <= shots
+    _assert_statistically_consistent(meas_errors, native_errors, shots)
+
+
+def test_d3_traced_qis_zero_noise_pymatching_pipeline_has_no_logical_errors():
+    noise_args = _noise_args(error_rate=0.0)
+    circuit = _build_lowered_traced_qis_surface_code(distance=3, rounds=3)
+    matching = _pymatching_decoder(circuit, noise_args)
+    shots = 64
+
+    raw_result = (
+        sim_neo(circuit).quantum(meas_sampling()).noise(_depolarizing_noise(noise_args)).shots(shots).seed(2468).run()
+    )
+    meas_errors = _decode_raw_measurements(raw_result, circuit, matching, shots)
+    native_errors = _decode_native_dem_samples(circuit, noise_args, matching, shots, seed=1357)
+
+    assert meas_errors == 0
+    assert native_errors == 0
+
+
+def test_d3_traced_qis_fault_catalog_builds_with_all_noise_channels_enabled():
+    noise_args = _noise_args()
+    circuit = _build_lowered_traced_qis_surface_code(distance=3, rounds=9)
+    catalog = fault_catalog(circuit, _depolarizing_noise(noise_args))
+
+    alternative_counts = [len(location.faults) for location in catalog]
+    assert len(catalog) > 100
+    assert 1 in alternative_counts
+    assert 3 in alternative_counts
+    assert 15 in alternative_counts
+    assert sum(alternative_counts) > 1_000
+
+    first_event = next(catalog.fault_configurations(1))
+    assert len(first_event.locations) == 1
+    assert len(first_event.faults) == 1
+    assert first_event.locations[0] is catalog.locations[first_event.location_indices[0]]
+    assert first_event.faults[0] is first_event.locations[0].faults[first_event.alternative_indices[0]]
diff --git a/ruff.toml b/ruff.toml
index 8855358c6..e012768bd 100644
--- a/ruff.toml
+++ b/ruff.toml
@@ -179,7 +179,13 @@ ignore = [
     "PLC0415",  # Import inside function - lazy loading of guppy, stim, json
     "SLF001",   # Private member access - accessing patch and circuit internals
 ]
+"python/quantum-pecos/src/pecos/qec/surface/logical_circuit.py" = [
+    "PLC0415",  # Lazy imports keep optional decoder/stim/Rust bindings out of import time
+]
 # QEC analysis modules
+"python/quantum-pecos/src/pecos/qec/analysis.py" = [
+    "PLC0415",  # Lazy imports keep optional Rust/Python analysis dependencies out of import time
+]
 "python/quantum-pecos/src/pecos/qec/analysis/dem_builder.py" = [
     "SLF001",   # Private member access - accessing internal circuit/tick data
 ]
@@ -197,6 +203,8 @@ ignore = [
 
 # Test files
 "python/*/tests/**/*.py" = [
+    "ANN",      # Test functions and fixtures are clearer without exhaustive type annotations
+    "D",        # Test names describe behavior; per-test docstrings add noise
     "F401",     # Imported but unused - OK in tests for import availability checks
     "INP001",   # File is part of an implicit namespace package - OK for test directories
     "S101",     # Use of `assert` detected - Assert is standard practice in test files
@@ -240,8 +248,24 @@ ignore = [
 ]
 
 # Scripts and examples - not packages
-"scripts/**/*.py" = ["INP001", "S603", "PLC0415", "S301", "BLE001"]  # Script files: no __init__.py, subprocess calls, lazy imports, pickle, broad except
-"examples/**/*.py" = ["INP001", "BLE001"]  # Example files don't need __init__.py and can use broad exception handling
+"scripts/**/*.py" = [
+    "ANN",      # Command-line scripts do not need library-level annotations
+    "D",        # Top-level module docstrings document scripts
+    "EXE001",   # Scripts are commonly invoked through `python path/to/script.py`
+    "INP001",   # Script files are not import packages
+    "S603",     # Scripts may call trusted local tools
+    "PLC0415",  # Lazy imports keep optional dependencies out of import time
+    "S301",     # Scripts may read trusted local data artifacts
+    "BLE001",   # CLI/report scripts often convert broad failures into user-facing output
+]
+"examples/**/*.py" = [
+    "ANN",      # Examples favor readable demonstration code over exhaustive annotations
+    "D",        # Module/function names and surrounding text document examples
+    "INP001",   # Example files are not packages
+    "BLE001",   # Examples may catch broad optional-dependency/runtime failures
+    "S108",     # Examples commonly default to /tmp output paths
+    "S311",     # Example sweeps use deterministic pseudo-random circuits, not crypto
+]
 
 
 # Jupyter notebooks - exploratory code, less strict than library code
diff --git a/scripts/bench_raw_meas_sampling.py b/scripts/bench_raw_meas_sampling.py
new file mode 100644
index 000000000..7622c1cfd
--- /dev/null
+++ b/scripts/bench_raw_meas_sampling.py
@@ -0,0 +1,122 @@
+#!/usr/bin/env python3
+# Copyright 2026 The PECOS Developers
+# Licensed under the Apache License, Version 2.0
+"""Benchmark: raw measurement sampling / detector DEM vs stabilizer simulation.
+
+Compares detector DEM (generate_samples), raw meas_sampling, and stabilizer.
+Quick smoke test by default (~10s). Use --full for stable headline numbers.
+
+Usage:
+    uv run python scripts/bench_raw_meas_sampling.py          # quick
+    .venv/bin/python scripts/bench_raw_meas_sampling.py --full # full (release)
+"""
+
+import sys
+import time
+
+from pecos.qec.surface import SurfacePatch
+from pecos.qec.surface.decode import _build_surface_tick_circuit_for_native_model
+from pecos_rslib.qec import DemSampler
+from pecos_rslib_exp import depolarizing, meas_sampling, sim_neo, stabilizer
+
+FULL = "--full" in sys.argv
+
+
+def build(d):
+    patch = SurfacePatch.create(distance=d)
+    return _build_surface_tick_circuit_for_native_model(patch, 6, "Z", circuit_source="abstract")
+
+
+def main():
+    noise_args = {"p1": 0.005, "p2": 0.005, "p_meas": 0.005, "p_prep": 0.005}
+    depol = depolarizing().p1(0.005).p2(0.005).p_meas(0.005).p_prep(0.005)
+    mode = "full" if FULL else "quick"
+
+    print(f"Raw measurement / detector DEM benchmark ({mode}): surface code, 6 rounds, p=0.005")
+    print("=" * 78)
+
+    # ---- Section 1: Generation only ----
+    gen_configs = (
+        [(3, [100_000, 1_000_000]), (5, [100_000, 1_000_000]), (7, [100_000, 1_000_000])]
+        if FULL
+        else [(3, [10_000, 100_000]), (5, [10_000, 100_000])]
+    )
+    stab_limit = 100_000 if FULL else 10_000
+
+    print()
+    print("1. Generation only (no decoding):")
+    print(f"{'d':>3} {'shots':>10} | {'Det DEM':>9} | {'Raw meas':>9} | {'Stab sim':>9} | {'stab/det':>9}")
+    print("-" * 72)
+
+    for d, shot_list in gen_configs:
+        tc = build(d)
+        sampler = DemSampler.from_circuit(tc, **noise_args)
+
+        for shots in shot_list:
+            t0 = time.perf_counter()
+            _ = sampler.generate_samples(shots, seed=42)
+            t_det = time.perf_counter() - t0
+
+            t0 = time.perf_counter()
+            _ = sim_neo(tc).quantum(meas_sampling()).noise(depol).shots(shots).seed(42).run()
+            t_raw = time.perf_counter() - t0
+
+            if shots <= stab_limit:
+                t0 = time.perf_counter()
+                _ = sim_neo(tc).quantum(stabilizer()).noise(depol).shots(shots).seed(42).run()
+                t_stab = time.perf_counter() - t0
+                stab_s = f"{t_stab * 1000:>8.0f}ms"
+                ratio_s = f"{t_stab / t_det:>8.0f}x"
+            else:
+                stab_s = ratio_s = f"{'--':>9}"
+
+            label = f"d={d}" if shots == shot_list[0] else ""
+            print(
+                f"{label:>3} {shots:>10,} | {t_det * 1000:>8.1f}ms | {t_raw * 1000:>8.1f}ms | {stab_s} | {ratio_s}",
+            )
+        print()
+
+    # ---- Section 2: Generate + decode end-to-end ----
+    dec_configs = [(3, [10_000, 100_000]), (5, [10_000, 100_000])] if FULL else [(3, [1_000, 10_000]), (5, [1_000])]
+
+    print("2. Detector DEM generate + pymatching decode:")
+    print(f"{'d':>3} {'shots':>10} | {'generate':>9} | {'decode':>9} | {'total':>9} | {'gen%':>6}")
+    print("-" * 62)
+
+    import stim
+    from pecos.qec.surface.circuit_builder import tick_circuit_to_stim
+
+    for d, shot_list in dec_configs:
+        tc = build(d)
+        sampler = DemSampler.from_circuit(tc, **noise_args)
+        stim_str = tick_circuit_to_stim(tc, **noise_args)
+        dem_str = str(stim.Circuit(stim_str).detector_error_model(decompose_errors=True))
+
+        for shots in shot_list:
+            t0 = time.perf_counter()
+            batch = sampler.generate_samples(shots, seed=42)
+            t_gen = time.perf_counter() - t0
+
+            t0 = time.perf_counter()
+            _ = batch.decode_count(dem_str, "pymatching")
+            t_dec = time.perf_counter() - t0
+
+            t_total = t_gen + t_dec
+            gen_pct = t_gen / t_total * 100
+
+            label = f"d={d}" if shots == shot_list[0] else ""
+            print(
+                f"{label:>3} {shots:>10,} | {t_gen * 1000:>8.1f}ms | "
+                f"{t_dec * 1000:>8.1f}ms | {t_total * 1000:>8.1f}ms | {gen_pct:>5.1f}%",
+            )
+        print()
+
+    print("Notes:")
+    print("  generate_samples is 3-6x faster after columnar SampleBatch.")
+    print("  End-to-end generate+decode is decode-dominated (<1% generation).")
+    if not FULL:
+        print("  Use --full for larger shot counts and stable headline numbers.")
+
+
+if __name__ == "__main__":
+    main()
diff --git a/scripts/check_python_workspace.py b/scripts/check_python_workspace.py
new file mode 100644
index 000000000..5d0259b09
--- /dev/null
+++ b/scripts/check_python_workspace.py
@@ -0,0 +1,241 @@
+#!/usr/bin/env python3
+# Copyright 2026 The PECOS Developers
+# Licensed under the Apache License, Version 2.0
+"""Validate PECOS Python workspace metadata.
+
+This check is intentionally narrower than a full packaging linter. It guards
+the invariants that tend to drift in this repository: package versions,
+workspace membership, internal dependency pins, and uv workspace sources.
+"""
+
+from __future__ import annotations
+
+import re
+import sys
+from dataclasses import dataclass
+from pathlib import Path
+from typing import Any
+
+try:
+    import tomllib
+except ModuleNotFoundError:  # pragma: no cover - Python 3.10 fallback
+    try:
+        import tomli as tomllib  # type: ignore[no-redef]
+    except ModuleNotFoundError:
+        print("error: Python 3.11+ or the 'tomli' package is required", file=sys.stderr)
+        sys.exit(2)
+
+
+REPO_ROOT = Path(__file__).resolve().parents[1]
+ROOT_PYPROJECT = REPO_ROOT / "pyproject.toml"
+DEPENDENCY_NAME_RE = re.compile(r"^\s*([A-Za-z0-9_.-]+)")
+
+
+@dataclass(frozen=True)
+class Package:
+    path: Path
+    rel_dir: str
+    name: str
+    normalized_name: str
+    version: str
+    data: dict[str, Any]
+
+
+def normalize_name(name: str) -> str:
+    return re.sub(r"[-_.]+", "-", name).lower()
+
+
+def load_toml(path: Path) -> dict[str, Any]:
+    with path.open("rb") as handle:
+        return tomllib.load(handle)
+
+
+def fail(errors: list[str], message: str) -> None:
+    errors.append(message)
+
+
+def rel(path: Path) -> str:
+    return path.relative_to(REPO_ROOT).as_posix()
+
+
+def load_package(path: Path, errors: list[str]) -> Package | None:
+    data = load_toml(path)
+    project = data.get("project")
+    if not isinstance(project, dict):
+        fail(errors, f"{rel(path)}: missing [project] table")
+        return None
+
+    name = project.get("name")
+    version = project.get("version")
+    if not isinstance(name, str) or not name:
+        fail(errors, f"{rel(path)}: missing [project].name")
+        return None
+    if not isinstance(version, str) or not version:
+        fail(errors, f"{rel(path)}: missing [project].version")
+        return None
+
+    return Package(
+        path=path,
+        rel_dir=rel(path.parent),
+        name=name,
+        normalized_name=normalize_name(name),
+        version=version,
+        data=data,
+    )
+
+
+def dependency_name(requirement: str) -> str | None:
+    match = DEPENDENCY_NAME_RE.match(requirement)
+    if match is None:
+        return None
+    return normalize_name(match.group(1))
+
+
+def has_exact_version_pin(requirement: str, version: str) -> bool:
+    return re.search(rf"(^|[^=!<>~])==\s*{re.escape(version)}(\s*(;|,|$))", requirement) is not None
+
+
+def iter_dependency_lists(data: dict[str, Any]) -> list[tuple[str, list[Any]]]:
+    lists: list[tuple[str, list[Any]]] = []
+    project = data.get("project", {})
+    if isinstance(project, dict):
+        dependencies = project.get("dependencies", [])
+        if isinstance(dependencies, list):
+            lists.append(("[project].dependencies", dependencies))
+
+        optional = project.get("optional-dependencies", {})
+        if isinstance(optional, dict):
+            for extra, deps in sorted(optional.items()):
+                if isinstance(deps, list):
+                    lists.append((f"[project.optional-dependencies].{extra}", deps))
+
+    dependency_groups = data.get("dependency-groups", {})
+    if isinstance(dependency_groups, dict):
+        for group, deps in sorted(dependency_groups.items()):
+            if isinstance(deps, list):
+                lists.append((f"[dependency-groups].{group}", deps))
+
+    return lists
+
+
+def internal_dependencies(package: Package, workspace_names: set[str], errors: list[str]) -> set[str]:
+    internal: set[str] = set()
+    for section, deps in iter_dependency_lists(package.data):
+        for dep in deps:
+            if not isinstance(dep, str):
+                fail(errors, f"{rel(package.path)}: {section} contains non-string dependency {dep!r}")
+                continue
+            dep_name = dependency_name(dep)
+            if dep_name is None or dep_name not in workspace_names or dep_name == package.normalized_name:
+                continue
+            internal.add(dep_name)
+            if not has_exact_version_pin(dep, package.version):
+                fail(
+                    errors,
+                    f"{rel(package.path)}: {section} dependency {dep!r} must pin "
+                    f"workspace package version =={package.version}",
+                )
+    return internal
+
+
+def workspace_sources(package: Package, errors: list[str]) -> set[str]:
+    tool = package.data.get("tool", {})
+    uv = tool.get("uv", {}) if isinstance(tool, dict) else {}
+    sources = uv.get("sources", {}) if isinstance(uv, dict) else {}
+    if not isinstance(sources, dict):
+        fail(errors, f"{rel(package.path)}: [tool.uv.sources] must be a table")
+        return set()
+
+    names: set[str] = set()
+    for name, source in sources.items():
+        normalized = normalize_name(name)
+        if not isinstance(source, dict) or source.get("workspace") is not True:
+            continue
+        names.add(normalized)
+    return names
+
+
+def check_cuda_extra_group(root_data: dict[str, Any], errors: list[str]) -> None:
+    project = root_data.get("project", {})
+    optional = project.get("optional-dependencies", {}) if isinstance(project, dict) else {}
+    dependency_groups = root_data.get("dependency-groups", {})
+    cuda_extra = optional.get("cuda") if isinstance(optional, dict) else None
+    cuda_group = dependency_groups.get("cuda") if isinstance(dependency_groups, dict) else None
+
+    if cuda_extra is None or cuda_group is None:
+        return
+    if cuda_extra != cuda_group:
+        fail(
+            errors,
+            "pyproject.toml: [project.optional-dependencies].cuda and [dependency-groups].cuda must stay identical",
+        )
+
+
+def main() -> int:
+    errors: list[str] = []
+
+    root = load_package(ROOT_PYPROJECT, errors)
+    package_paths = sorted((REPO_ROOT / "python").rglob("pyproject.toml"))
+    packages = [pkg for path in package_paths if (pkg := load_package(path, errors)) is not None]
+    if root is None:
+        for error in errors:
+            print(f"error: {error}", file=sys.stderr)
+        return 1
+
+    all_packages = [root, *packages]
+    workspace_names = {pkg.normalized_name for pkg in all_packages}
+
+    for pkg in all_packages:
+        if pkg.version != root.version:
+            fail(
+                errors,
+                f"{rel(pkg.path)}: version {pkg.version!r} does not match root version {root.version!r}",
+            )
+
+    root_tool = root.data.get("tool", {})
+    root_uv = root_tool.get("uv", {}) if isinstance(root_tool, dict) else {}
+    workspace = root_uv.get("workspace", {}) if isinstance(root_uv, dict) else {}
+    members = workspace.get("members") if isinstance(workspace, dict) else None
+    expected_members = sorted(pkg.rel_dir for pkg in packages)
+    if not isinstance(members, list) or any(not isinstance(member, str) for member in members):
+        fail(errors, "pyproject.toml: [tool.uv.workspace].members must be a string list")
+    elif sorted(members) != expected_members:
+        fail(
+            errors,
+            "pyproject.toml: [tool.uv.workspace].members does not match Python package directories\n"
+            f"  expected: {expected_members}\n"
+            f"  found:    {sorted(members)}",
+        )
+
+    check_cuda_extra_group(root.data, errors)
+
+    for pkg in all_packages:
+        internal = internal_dependencies(pkg, workspace_names, errors)
+        sources = workspace_sources(pkg, errors)
+        missing_sources = sorted(internal - sources)
+        extra_sources = sorted((sources & workspace_names) - internal)
+        if missing_sources:
+            fail(
+                errors,
+                f"{rel(pkg.path)}: missing [tool.uv.sources] workspace entries for {missing_sources}",
+            )
+        if extra_sources:
+            fail(
+                errors,
+                f"{rel(pkg.path)}: unused internal [tool.uv.sources] workspace entries {extra_sources}",
+            )
+
+    if errors:
+        for error in errors:
+            print(f"error: {error}", file=sys.stderr)
+        return 1
+
+    print(
+        f"Python workspace metadata OK: {len(packages)} packages, "
+        f"version {root.version}, {len(expected_members)} uv workspace members",
+    )
+    return 0
+
+
+if __name__ == "__main__":
+    raise SystemExit(main())
diff --git a/scripts/compare_meas_sampling_pipeline.py b/scripts/compare_meas_sampling_pipeline.py
new file mode 100644
index 000000000..5fc987a36
--- /dev/null
+++ b/scripts/compare_meas_sampling_pipeline.py
@@ -0,0 +1,223 @@
+#!/usr/bin/env python3
+# Copyright 2026 The PECOS Developers
+# Licensed under the Apache License, Version 2.0
+"""Compare meas_sampling pipeline against native DEM sampler on surface-code memory.
+
+Uses the Guppy → traced QIS → TickCircuit pipeline (lowered to Clifford gates).
+Decodes with PyMatching. Compares logical error rates and timing.
+
+Usage:
+    .venv/bin/python scripts/compare_meas_sampling_pipeline.py
+    .venv/bin/python scripts/compare_meas_sampling_pipeline.py --distances 3 5 7 --shots 10000
+"""
+
+from __future__ import annotations
+
+import argparse
+import json
+import time
+
+import numpy as np
+import pymatching
+import stim
+from pecos.qec.surface import SurfacePatch
+from pecos.qec.surface.circuit_builder import tick_circuit_to_stim
+from pecos.qec.surface.decode import _build_surface_tick_circuit_for_native_model
+from pecos_rslib.qec import DemSampler
+from pecos_rslib_exp import depolarizing, meas_sampling, sim_neo
+
+
+def build_circuit(distance, rounds, basis="Z"):
+    """Build a traced-QIS surface-code TickCircuit, lowered to Clifford gates."""
+    patch = SurfacePatch.create(distance=distance)
+    tc = _build_surface_tick_circuit_for_native_model(
+        patch,
+        rounds,
+        basis,
+        circuit_source="traced_qis",
+    )
+    # Lower R1XY/RZ rotations to standard Clifford gates (H, SZ, SZdg, etc.)
+    tc.lower_clifford_rotations()
+    return tc
+
+
+def get_pymatching_decoder(tc, noise_args):
+    """Build a PyMatching decoder from a circuit's Stim DEM."""
+    stim_str = tick_circuit_to_stim(tc, **noise_args)
+    dem = stim.Circuit(stim_str).detector_error_model(decompose_errors=True)
+    return pymatching.Matching.from_detector_error_model(dem)
+
+
+def run_meas_sampling(tc, noise_args, shots, seed):
+    """Sample raw measurements via meas_sampling."""
+    depol = (
+        depolarizing()
+        .p1(noise_args["p1"])
+        .p2(noise_args["p2"])
+        .p_meas(
+            noise_args["p_meas"],
+        )
+        .p_prep(noise_args["p_prep"])
+    )
+
+    t0 = time.perf_counter()
+    result = sim_neo(tc).quantum(meas_sampling()).noise(depol).shots(shots).seed(seed).run()
+    t_sample = time.perf_counter() - t0
+    return result, t_sample
+
+
+def extract_and_decode(result, tc, matching, shots):
+    """Extract detection events from raw measurements and decode with PyMatching."""
+    det_json = json.loads(tc.get_meta("detectors"))
+    obs_json_str = tc.get_meta("observables")
+    obs_json = json.loads(obs_json_str) if obs_json_str else []
+    num_meas = int(tc.get_meta("num_measurements"))
+    num_dets = len(det_json)
+
+    t0 = time.perf_counter()
+
+    errors = 0
+    syndrome = np.zeros(num_dets, dtype=np.uint8)
+
+    for shot_idx in range(shots):
+        row = result[shot_idx]
+
+        # Extract detector events
+        syndrome.fill(0)
+        for i, det in enumerate(det_json):
+            val = 0
+            for rec in det["records"]:
+                idx = num_meas + rec
+                if 0 <= idx < len(row):
+                    val ^= row[idx]
+            syndrome[i] = val
+
+        # Extract observable flips
+        actual_mask = 0
+        for i, obs in enumerate(obs_json):
+            val = 0
+            for rec in obs["records"]:
+                idx = num_meas + rec
+                if 0 <= idx < len(row):
+                    val ^= row[idx]
+            if val:
+                actual_mask |= 1 << i
+
+        # Decode
+        predicted = matching.decode(syndrome)
+        pred_mask = sum(int(v) << j for j, v in enumerate(predicted))
+        if pred_mask != actual_mask:
+            errors += 1
+
+    t_decode = time.perf_counter() - t0
+    return errors, t_decode
+
+
+def run_native_sampler(tc, noise_args, matching, shots, seed):
+    """Sample + decode via the native DEM sampler path."""
+    sampler = DemSampler.from_circuit(tc, **noise_args)
+    num_dets = sampler.num_detectors
+
+    t0 = time.perf_counter()
+    batch = sampler.generate_samples(shots, seed=seed)
+    t_sample = time.perf_counter() - t0
+
+    t0 = time.perf_counter()
+    errors = 0
+    syndrome = np.zeros(num_dets, dtype=np.uint8)
+
+    for i in range(shots):
+        syn = batch.get_syndrome(i)
+        for j in range(num_dets):
+            syndrome[j] = syn[j]
+
+        predicted = matching.decode(syndrome)
+        pred_mask = sum(int(v) << j for j, v in enumerate(predicted))
+        if pred_mask != batch.get_observable_mask(i):
+            errors += 1
+
+    t_decode = time.perf_counter() - t0
+    return errors, t_sample, t_decode
+
+
+def main():
+    parser = argparse.ArgumentParser(description=__doc__)
+    parser.add_argument("--distances", type=int, nargs="+", default=[3, 5])
+    parser.add_argument(
+        "--rounds-per-d",
+        type=int,
+        default=3,
+        help="Syndrome rounds = distance * rounds_per_d",
+    )
+    parser.add_argument("--shots", type=int, default=5000)
+    parser.add_argument("--error-rate", type=float, default=0.003)
+    parser.add_argument("--seed", type=int, default=42)
+    args = parser.parse_args()
+
+    p = args.error_rate
+    noise_args = {"p1": p * 0.1, "p2": p, "p_meas": p * 0.5, "p_prep": p * 0.5}
+
+    print("=" * 80)
+    print("meas_sampling vs native DEM sampler: traced-QIS surface-code memory + PyMatching")
+    print("=" * 80)
+    print(f"  shots={args.shots}, p={p}")
+    print(
+        f"  noise: p1={noise_args['p1']:.1e} p2={noise_args['p2']:.1e} "
+        f"p_meas={noise_args['p_meas']:.1e} p_prep={noise_args['p_prep']:.1e}",
+    )
+    print("  circuit: Guppy -> traced QIS -> lower_clifford_rotations()")
+    print()
+
+    header = (
+        f"{'d':>3} {'rounds':>6} | {'backend':>15} | {'sample':>8} | "
+        f"{'decode':>8} | {'total':>8} | {'LER':>8} | {'errors':>10}"
+    )
+    print(header)
+    print("-" * len(header))
+
+    for d in args.distances:
+        rounds = d * args.rounds_per_d
+        tc = build_circuit(d, rounds)
+
+        matching = get_pymatching_decoder(tc, noise_args)
+
+        # --- meas_sampling ---
+        result, t_sample_ms = run_meas_sampling(tc, noise_args, args.shots, args.seed)
+        errors_ms, t_decode_ms = extract_and_decode(result, tc, matching, args.shots)
+        ler_ms = errors_ms / args.shots
+        t_total_ms = t_sample_ms + t_decode_ms
+
+        print(
+            f"d={d:>1} {rounds:>6} | {'meas_sampling':>15} | {t_sample_ms*1000:>7.0f}ms | "
+            f"{t_decode_ms*1000:>7.0f}ms | {t_total_ms*1000:>7.0f}ms | "
+            f"{ler_ms:>7.4f} | {errors_ms:>5}/{args.shots}",
+        )
+
+        # --- native DEM sampler ---
+        errors_ns, t_sample_ns, t_decode_ns = run_native_sampler(
+            tc,
+            noise_args,
+            matching,
+            args.shots,
+            args.seed,
+        )
+        ler_ns = errors_ns / args.shots
+        t_total_ns = t_sample_ns + t_decode_ns
+
+        print(
+            f"    {' ':>6} | {'native_sampler':>15} | {t_sample_ns*1000:>7.0f}ms | "
+            f"{t_decode_ns*1000:>7.0f}ms | {t_total_ns*1000:>7.0f}ms | "
+            f"{ler_ns:>7.4f} | {errors_ns:>5}/{args.shots}",
+        )
+        print()
+
+    print("Notes:")
+    print("  Circuit: Guppy surface code -> traced QIS -> lower_clifford_rotations()")
+    print("  Decoder: PyMatching (stim DEM, decompose_errors=True)")
+    print("  meas_sampling: geometric raw measurement DEM sampler + Python extraction")
+    print("  native_sampler: DemSampler.generate_samples (detector events directly)")
+    print("  LER differences from different RNG streams, not systematic bias.")
+
+
+if __name__ == "__main__":
+    main()
diff --git a/scripts/docs/generate_doc_tests.py b/scripts/docs/generate_doc_tests.py
index 80c6d917b..d716c37af 100755
--- a/scripts/docs/generate_doc_tests.py
+++ b/scripts/docs/generate_doc_tests.py
@@ -21,9 +21,10 @@
 Supported markers in markdown:
     <!--skip--> or <!--skip: reason-->     - Skip this block
     <!--skip-if-no-cuda-->                 - Skip if CUDA+cupy not available
-    <!--skip-if-no-cuda-rust-->            - Skip if CUDA Rust bindings not available
+    <!--skip-if-no-cuda-rust-->            - Skip if CUDA Rust simulators cannot initialize
     <!--expect-error: pattern-->           - Expect error matching regex pattern
     <!--expect-output: text-->             - Expect stdout to contain text
+    <!--requires-module: package[, ...]--> - Skip if Python module is unavailable
     <!--test-name: my_test-->              - Name the test function
     <!--mark.slow-->                       - Add @pytest.mark.slow
     <!--continuation-->                    - Continue from previous block's state
@@ -69,6 +70,9 @@ class CodeBlock:
     skip_if_no_cuda_rust: bool = False
     expect_error: str | None = None
     expect_output: str | None = None
+    expect_output_block: str | None = None
+    expect_output_mode: str = "exact"  # "exact" or "ellipsis"
+    required_modules: list[str] = field(default_factory=list)
     test_name: str | None = None
     marks: list[str] = field(default_factory=list)
     is_continuation: bool = False
@@ -196,6 +200,9 @@ def _parse_marker_comment(comment: str) -> dict:
         "skip_if_no_cuda_rust": False,
         "expect_error": None,
         "expect_output": None,
+        "expect_output_block": False,
+        "expect_output_mode": "exact",
+        "required_modules": [],
         "test_name": None,
         "marks": [],
         "is_continuation": False,
@@ -239,12 +246,24 @@ def _parse_marker_comment(comment: str) -> dict:
             result["expect_error"] = match.group(1).strip()
             result["skip"] = False  # Don't skip, we want to test the error
 
-    # Check for expect-output
-    if "expect-output" in comment_lower:
+    # Check for expect-output-block (must check before expect-output substring match)
+    if "expect-output-block" in comment_lower:
+        result["expect_output_block"] = True
+        mode_match = re.search(r"expect-output-block:\s*(\w+)\s*-->", comment, re.IGNORECASE)
+        if mode_match:
+            result["expect_output_mode"] = mode_match.group(1).strip().lower()
+    # Check for expect-output (substring match)
+    elif "expect-output" in comment_lower:
         match = re.search(r"expect-output:\s*(.+?)\s*-->", comment, re.IGNORECASE)
         if match:
             result["expect_output"] = match.group(1).strip()
 
+    # Check for required Python modules
+    if "requires-module" in comment_lower:
+        match = re.search(r"requires-module:\s*(.+?)\s*-->", comment, re.IGNORECASE)
+        if match:
+            result["required_modules"] = [module.strip() for module in match.group(1).split(",") if module.strip()]
+
     # Check for test-name
     match = re.search(r"test-name:\s*(\w+)", comment, re.IGNORECASE)
     if match:
@@ -381,6 +400,21 @@ def extract_code_blocks(file_path: Path, language: str = "python") -> list[CodeB
         block_skip = attrs["skip"] or doc_skip
         block_skip_reason = attrs["skip_reason"] or doc_skip_reason
 
+        # If expect-output-block, look for a ```output fence after this code block
+        output_block_text = None
+        output_mode = attrs["expect_output_mode"]
+        if attrs["expect_output_block"]:
+            after_fence = content[match.end() :]
+            output_match = re.match(r"\s*```output\n(.*?)```", after_fence, re.DOTALL)
+            if output_match:
+                output_block_text = output_match.group(1).rstrip("\n")
+            else:
+                msg = (
+                    f"{file_path}:{line_number}: expect-output-block marker "
+                    f"but no ```output fence found after code block"
+                )
+                raise ValueError(msg)
+
         block = CodeBlock(
             code=full_code,
             language=language,
@@ -393,6 +427,9 @@ def extract_code_blocks(file_path: Path, language: str = "python") -> list[CodeB
             skip_if_no_cuda_rust=attrs["skip_if_no_cuda_rust"],
             expect_error=attrs["expect_error"],
             expect_output=attrs["expect_output"],
+            expect_output_block=output_block_text,
+            expect_output_mode=output_mode,
+            required_modules=attrs["required_modules"],
             test_name=attrs["test_name"],
             marks=attrs["marks"],
             is_continuation=attrs["is_continuation"],
@@ -431,7 +468,7 @@ def generate_test_function(block: CodeBlock, file_stem: str) -> str:
         )
     elif block.skip_if_no_cuda_rust:
         lines.append(
-            '@pytest.mark.skipif(not cuda_rust_available(), reason="CUDA Rust bindings not available")',
+            '@pytest.mark.skipif(not cuda_rust_available(), reason="CUDA Rust simulator runtime not available")',
         )
 
     lines.extend(f"@pytest.mark.{mark}" for mark in block.marks)
@@ -442,6 +479,8 @@ def generate_test_function(block: CodeBlock, file_stem: str) -> str:
     # Docstring with source file and line number for easy navigation
     lines.append(f'    """Test from {block.source_file}:{block.line_number}."""')
 
+    lines.extend(f'    pytest.importorskip("{module}")' for module in block.required_modules)
+
     # Generate function body based on test type and language
     if block.language == "rust":
         if block.expect_error:
@@ -450,6 +489,8 @@ def generate_test_function(block: CodeBlock, file_stem: str) -> str:
             lines.extend(_generate_rust_exec_body(block))
     elif block.expect_error:
         lines.extend(_generate_expect_error_body(block))
+    elif block.expect_output_block is not None:
+        lines.extend(_generate_expect_output_block_body(block))
     elif block.expect_output:
         lines.extend(_generate_expect_output_body(block))
     elif _uses_guppy_decorator(block.code):
@@ -493,7 +534,7 @@ def _generate_guppy_body(block: CodeBlock) -> list[str]:
         "    # Guppy needs file-based execution for inspect.getsourcelines()",
         "    # Run in temp directory to avoid polluting project root with generated files",
         "    with tempfile.TemporaryDirectory() as tmpdir:",
-        "        temp_path = Path(tmpdir) / 'test_code.py'",
+        '        temp_path = Path(tmpdir) / "test_code.py"',
         "        temp_path.write_text(code)",
         "",
         "        result = subprocess.run(",
@@ -519,10 +560,10 @@ def _generate_expect_error_body(block: CodeBlock) -> list[str]:
         # Guppy code needs subprocess execution
         # Run in temp directory to avoid polluting project root with generated files
         lines = [
+            "    import re",
             "    import subprocess",
             "    import sys",
             "    import tempfile",
-            "    import re",
             "    from pathlib import Path",
             "",
             '    code = """',
@@ -531,7 +572,7 @@ def _generate_expect_error_body(block: CodeBlock) -> list[str]:
             f'    expected_pattern = r"{escaped_pattern}"',
             "",
             "    with tempfile.TemporaryDirectory() as tmpdir:",
-            "        temp_path = Path(tmpdir) / 'test_code.py'",
+            '        temp_path = Path(tmpdir) / "test_code.py"',
             "        temp_path.write_text(code)",
             "",
             "        result = subprocess.run(",
@@ -542,16 +583,16 @@ def _generate_expect_error_body(block: CodeBlock) -> list[str]:
             "            check=False,",
             "            cwd=tmpdir,",
             "        )",
-            "        assert result.returncode != 0, 'Expected code to fail but it succeeded'",
+            '        assert result.returncode != 0, "Expected code to fail but it succeeded"',
             "        assert re.search(expected_pattern, result.stderr), \\",
             '            f"Error did not match pattern {expected_pattern!r}:\\n{result.stderr}"',
         ]
     else:
         # Regular code can use subprocess with -c
         lines = [
+            "    import re",
             "    import subprocess",
             "    import sys",
-            "    import re",
             "",
             '    code = """',
             *[line.rstrip() for line in escaped_code.split("\n")],
@@ -565,7 +606,7 @@ def _generate_expect_error_body(block: CodeBlock) -> list[str]:
             "        timeout=30,",
             "        check=False,",
             "    )",
-            "    assert result.returncode != 0, 'Expected code to fail but it succeeded'",
+            '    assert result.returncode != 0, "Expected code to fail but it succeeded"',
             "    assert re.search(expected_pattern, result.stderr), \\",
             '        f"Error did not match pattern {expected_pattern!r}:\\n{result.stderr}"',
         ]
@@ -590,9 +631,9 @@ def _generate_rust_rustc_body(block: CodeBlock) -> list[str]:
     has_main = "fn main()" in block.code
 
     lines = [
+        "    import os",
         "    import subprocess",
         "    import tempfile",
-        "    import os",
         "    from pathlib import Path",
         "",
         '    code = """',
@@ -659,9 +700,9 @@ def _generate_rust_expect_error_body(block: CodeBlock) -> list[str]:
     escaped_pattern = block.expect_error.replace('"', '\\"') if block.expect_error else ""
 
     return [
+        "    import re",
         "    import subprocess",
         "    import tempfile",
-        "    import re",
         "    from pathlib import Path",
         "",
         '    code = """',
@@ -709,7 +750,7 @@ def _generate_expect_output_body(block: CodeBlock) -> list[str]:
             f'    expected_output = "{escaped_output}"',
             "",
             "    with tempfile.TemporaryDirectory() as tmpdir:",
-            "        temp_path = Path(tmpdir) / 'test_code.py'",
+            '        temp_path = Path(tmpdir) / "test_code.py"',
             "        temp_path.write_text(code)",
             "",
             "        result = subprocess.run(",
@@ -751,6 +792,50 @@ def _generate_expect_output_body(block: CodeBlock) -> list[str]:
     return lines
 
 
+def _generate_expect_output_block_body(block: CodeBlock) -> list[str]:
+    """Generate test body that checks stdout matches expected output exactly.
+
+    Uses Python's doctest.OutputChecker for matching. Supports exact mode
+    (default) and ellipsis mode (``...`` skips variable parts).
+    """
+    escaped_code = block.code.replace("\\", "\\\\").replace('"""', '\\"\\"\\"')
+    escaped_expected = block.expect_output_block.replace("\\", "\\\\").replace('"""', '\\"\\"\\"')
+    use_ellipsis = block.expect_output_mode == "ellipsis"
+
+    return [
+        "    import doctest",
+        "    import subprocess",
+        "    import sys",
+        "",
+        '    code = """',
+        *[line.rstrip() for line in escaped_code.split("\n")],
+        '"""',
+        '    expected = """',
+        *[line.rstrip() for line in escaped_expected.split("\n")],
+        '"""',
+        "",
+        "    result = subprocess.run(",
+        '        [sys.executable, "-c", code],',
+        "        capture_output=True,",
+        "        text=True,",
+        "        timeout=30,",
+        "        check=False,",
+        "    )",
+        "    if result.returncode != 0:",
+        '        pytest.fail(f"Code failed:\\n{result.stderr}")',
+        "",
+        "    checker = doctest.OutputChecker()",
+        f"    flags = doctest.ELLIPSIS if {use_ellipsis} else 0",
+        "    if not checker.check_output(expected.strip(), result.stdout.strip(), flags):",
+        "        diff = checker.output_difference(",
+        '            doctest.Example("", expected.strip()),',
+        "            result.stdout.strip(),",
+        "            flags,",
+        "        )",
+        '        pytest.fail(f"Output mismatch:\\n{diff}")',
+    ]
+
+
 def generate_test_file(file_path: Path, blocks: list[CodeBlock]) -> str:
     """Generate a complete pytest test file for a markdown file."""
     file_stem = _sanitize_name(file_path.stem)
@@ -771,7 +856,6 @@ def generate_test_file(file_path: Path, blocks: list[CodeBlock]) -> str:
     if needs_cuda_check:
         lines.extend(
             [
-                "",
                 "",
                 "def _check_cuda() -> bool:",
                 '    """Return True if CUDA toolkit and cupy are available."""',
@@ -813,13 +897,12 @@ def generate_test_file(file_path: Path, blocks: list[CodeBlock]) -> str:
     if needs_cuda_rust_check:
         lines.extend(
             [
-                "",
                 "",
                 "def _check_cuda_rust() -> bool:",
-                '    """Return True if CUDA Rust bindings (pecos_rslib_cuda) are available."""',
+                '    """Return True if CUDA Rust simulators can initialize."""',
                 "    try:",
-                "        from pecos_rslib_cuda import is_cuquantum_available",
-                "        return is_cuquantum_available()",
+                "        from pecos_rslib_cuda import is_custabilizer_usable, is_custatevec_usable",
+                "        return is_custatevec_usable() and is_custabilizer_usable()",
                 "    except ImportError:",
                 "        return False",
                 "",
@@ -916,7 +999,7 @@ def cuda_check() -> bool:
 
 
 @pytest.fixture(autouse=True)
-def restore_cwd():  # noqa: ANN201
+def restore_cwd():
     """Restore the current working directory after each test.
 
     Some tests (e.g., WASM examples) change the working directory,
@@ -1252,6 +1335,13 @@ def main() -> None:
         if not pytest_blocks:
             continue
 
+        # Skip file entirely if every block has an unconditional skip marker
+        # (e.g. document-level <!--skip-->). No point generating a test file
+        # full of skipped tests — it just adds noise to pytest output.
+        if all(b.skip for b in pytest_blocks):
+            total_skipped += len(pytest_blocks)
+            continue
+
         # Count skipped blocks
         total_skipped += sum(
             1
diff --git a/scripts/docs/test_working_examples.py b/scripts/docs/test_working_examples.py
index f7b37f6e0..3f80e22d0 100755
--- a/scripts/docs/test_working_examples.py
+++ b/scripts/docs/test_working_examples.py
@@ -26,8 +26,8 @@
 import tempfile
 from pathlib import Path
 
-# Import shared extraction function from test_code_examples
-from test_code_examples import extract_code_blocks
+# Import shared functions from test_code_examples
+from test_code_examples import _uses_guppy_decorator, extract_code_blocks
 
 # Files to test (relative to the docs directory)
 TEST_FILES = [
@@ -52,15 +52,36 @@ def test_python_block(
     print(f"Testing Python block #{block_number} from {file_path}...")
 
     try:
-        # Execute the code block and capture output
-        result = subprocess.run(
-            [sys.executable, "-c", code_block],
-            capture_output=True,
-            text=True,
-            timeout=30,
-            check=False,
-            shell=False,
-        )
+        # Guppy code needs to be in a file for inspect.getsourcelines() to work
+        if _uses_guppy_decorator(code_block):
+            with tempfile.NamedTemporaryFile(
+                mode="w",
+                suffix=".py",
+                delete=False,
+                encoding="utf-8",
+            ) as f:
+                f.write(code_block)
+                temp_path = f.name
+            try:
+                result = subprocess.run(
+                    [sys.executable, temp_path],
+                    capture_output=True,
+                    text=True,
+                    timeout=60,
+                    check=False,
+                    shell=False,
+                )
+            finally:
+                Path(temp_path).unlink(missing_ok=True)
+        else:
+            result = subprocess.run(
+                [sys.executable, "-c", code_block],
+                capture_output=True,
+                text=True,
+                timeout=30,
+                check=False,
+                shell=False,
+            )
 
         if result.returncode != 0:
             print(f"FAIL: Error in Python block #{block_number} from {file_path}:")
diff --git a/scripts/native_bench/bench_pecos/Cargo.lock b/scripts/native_bench/bench_pecos/Cargo.lock
index 02bd8a052..23fa1c190 100644
--- a/scripts/native_bench/bench_pecos/Cargo.lock
+++ b/scripts/native_bench/bench_pecos/Cargo.lock
@@ -2081,6 +2081,8 @@ dependencies = [
  "num-complex",
  "pecos-core",
  "pecos-num",
+ "pecos-random",
+ "serde_json",
  "smallvec",
 ]
 
@@ -2098,6 +2100,7 @@ dependencies = [
 name = "pecos-simulators"
 version = "0.2.0-dev.0"
 dependencies = [
+ "nalgebra",
  "num-complex",
  "pecos-core",
  "pecos-quantum",
@@ -2664,9 +2667,9 @@ checksum = "f87165f0995f63a9fbeea62b64d10b4d9d8e78ec6d7d51fb2125fda7bb36788f"
 
 [[package]]
 name = "rustls-webpki"
-version = "0.103.11"
+version = "0.103.13"
 source = "registry+https://github.com/rust-lang/crates.io-index"
-checksum = "20a6af516fea4b20eccceaf166e8aa666ac996208e8a644ce3ef5aa783bc7cd4"
+checksum = "61c429a8649f110dddef65e2a5ad240f747e85f7758a6bccc7e5777bd33f756e"
 dependencies = [
  "aws-lc-rs",
  "ring",
diff --git a/uv.lock b/uv.lock
index 4ea9dd070..dac8bd4a5 100644
--- a/uv.lock
+++ b/uv.lock
@@ -3,11 +3,9 @@ revision = 3
 requires-python = ">=3.10"
 resolution-markers = [
     "python_full_version >= '3.14' and platform_machine == 'x86_64' and sys_platform == 'darwin'",
-    "python_full_version >= '3.12' and python_full_version < '3.14' and platform_machine == 'x86_64' and sys_platform == 'darwin'",
-    "python_full_version == '3.11.*' and platform_machine == 'x86_64' and sys_platform == 'darwin'",
+    "python_full_version >= '3.11' and python_full_version < '3.14' and platform_machine == 'x86_64' and sys_platform == 'darwin'",
     "(python_full_version >= '3.14' and platform_machine != 'x86_64') or (python_full_version >= '3.14' and sys_platform != 'darwin')",
-    "(python_full_version >= '3.12' and python_full_version < '3.14' and platform_machine != 'x86_64') or (python_full_version >= '3.12' and python_full_version < '3.14' and sys_platform != 'darwin')",
-    "(python_full_version == '3.11.*' and platform_machine != 'x86_64') or (python_full_version == '3.11.*' and sys_platform != 'darwin')",
+    "(python_full_version >= '3.11' and python_full_version < '3.14' and platform_machine != 'x86_64') or (python_full_version >= '3.11' and python_full_version < '3.14' and sys_platform != 'darwin')",
     "python_full_version < '3.11' and platform_machine == 'x86_64' and sys_platform == 'darwin'",
     "(python_full_version < '3.11' and platform_machine != 'x86_64') or (python_full_version < '3.11' and sys_platform != 'darwin')",
 ]
@@ -161,16 +159,15 @@ wheels = [
 
 [[package]]
 name = "backrefs"
-version = "6.2"
+version = "7.0"
 source = { registry = "https://pypi.org/simple" }
-sdist = { url = "https://files.pythonhosted.org/packages/4e/a6/e325ec73b638d3ede4421b5445d4a0b8b219481826cc079d510100af356c/backrefs-6.2.tar.gz", hash = "sha256:f44ff4d48808b243b6c0cdc6231e22195c32f77046018141556c66f8bab72a49", size = 7012303, upload-time = "2026-02-16T19:10:15.828Z" }
+sdist = { url = "https://files.pythonhosted.org/packages/5e/a7/a7dd63622beef68cc0d3c3c36d472e143dd95443d5ebf14cd1a5b4dfbf11/backrefs-7.0.tar.gz", hash = "sha256:4989bb9e1e99eb23647c7160ed51fb21d0b41b5d200f2d3017da41e023097e82", size = 7012453, upload-time = "2026-04-28T16:28:04.215Z" }
 wheels = [
-    { url = "https://files.pythonhosted.org/packages/1b/39/3765df263e08a4df37f4f43cb5aa3c6c17a4bdd42ecfe841e04c26037171/backrefs-6.2-py310-none-any.whl", hash = "sha256:0fdc7b012420b6b144410342caeb8adc54c6866cf12064abc9bb211302e496f8", size = 381075, upload-time = "2026-02-16T19:10:04.322Z" },
-    { url = "https://files.pythonhosted.org/packages/0f/f0/35240571e1b67ffb19dafb29ab34150b6f59f93f717b041082cdb1bfceb1/backrefs-6.2-py311-none-any.whl", hash = "sha256:08aa7fae530c6b2361d7bdcbda1a7c454e330cc9dbcd03f5c23205e430e5c3be", size = 392874, upload-time = "2026-02-16T19:10:06.314Z" },
-    { url = "https://files.pythonhosted.org/packages/e3/63/77e8c9745b4d227cce9f5e0a6f68041278c5f9b18588b35905f5f19c1beb/backrefs-6.2-py312-none-any.whl", hash = "sha256:c3f4b9cb2af8cda0d87ab4f57800b57b95428488477be164dd2b47be54db0c90", size = 398787, upload-time = "2026-02-16T19:10:08.274Z" },
-    { url = "https://files.pythonhosted.org/packages/c5/71/c754b1737ad99102e03fa3235acb6cb6d3ac9d6f596cbc3e5f236705abd8/backrefs-6.2-py313-none-any.whl", hash = "sha256:12df81596ab511f783b7d87c043ce26bc5b0288cf3bb03610fe76b8189282b2b", size = 400747, upload-time = "2026-02-16T19:10:09.791Z" },
-    { url = "https://files.pythonhosted.org/packages/af/75/be12ba31a6eb20dccef2320cd8ccb3f7d9013b68ba4c70156259fee9e409/backrefs-6.2-py314-none-any.whl", hash = "sha256:e5f805ae09819caa1aa0623b4a83790e7028604aa2b8c73ba602c4454e665de7", size = 412602, upload-time = "2026-02-16T19:10:12.317Z" },
-    { url = "https://files.pythonhosted.org/packages/21/f8/d02f650c47d05034dcd6f9c8cf94f39598b7a89c00ecda0ecb2911bc27e9/backrefs-6.2-py39-none-any.whl", hash = "sha256:664e33cd88c6840b7625b826ecf2555f32d491800900f5a541f772c485f7cda7", size = 381077, upload-time = "2026-02-16T19:10:13.74Z" },
+    { url = "https://files.pythonhosted.org/packages/d4/39/39a31d7eae729ea14ed10c3ccef79371197177b9355a86cb3525709e8502/backrefs-7.0-py310-none-any.whl", hash = "sha256:b57cd227ea556b0aed3dc9b8da4628db4eabc0402c6d7fcfc69283a93955f7e9", size = 380824, upload-time = "2026-04-28T16:27:55.647Z" },
+    { url = "https://files.pythonhosted.org/packages/c9/b5/9302644225ba7dfa934a2ff2b9c7bb85701313a90dddb3dfaf693fa5bae2/backrefs-7.0-py311-none-any.whl", hash = "sha256:a0fa7360c63509e9e077e174ef4e6d3c21c8db94189b9d957289ae6d794b9475", size = 392626, upload-time = "2026-04-28T16:27:57.42Z" },
+    { url = "https://files.pythonhosted.org/packages/36/da/87912ddec6e06feffbaa3d7aa18fc6352bee2e8f1fee185d7d1690f8f4e8/backrefs-7.0-py312-none-any.whl", hash = "sha256:ca42ce6a49ace3d75684dfa9937f3373902a63284ecb385ce36d15e5dcb41c12", size = 398537, upload-time = "2026-04-28T16:27:58.913Z" },
+    { url = "https://files.pythonhosted.org/packages/00/bb/90ba423612b6aa0adccc6b1874bcd4a9b44b660c0c16f346611e00f64ac3/backrefs-7.0-py313-none-any.whl", hash = "sha256:f2c52955d631b9e1ac4cd56209f0a3a946d592b98e7790e77699339ae01c102a", size = 400491, upload-time = "2026-04-28T16:28:00.928Z" },
+    { url = "https://files.pythonhosted.org/packages/3e/5c/fb93d3092640a24dfb7bd7727a24016d7c01774ca013e60efd3f683c8002/backrefs-7.0-py314-none-any.whl", hash = "sha256:a6448b28180e3ca01134c9cf09dcebafad8531072e09903c5451748a05f24bc9", size = 412349, upload-time = "2026-04-28T16:28:02.412Z" },
 ]
 
 [[package]]
@@ -249,11 +246,11 @@ css = [
 
 [[package]]
 name = "certifi"
-version = "2026.2.25"
+version = "2026.4.22"
 source = { registry = "https://pypi.org/simple" }
-sdist = { url = "https://files.pythonhosted.org/packages/af/2d/7bf41579a8986e348fa033a31cdd0e4121114f6bce2457e8876010b092dd/certifi-2026.2.25.tar.gz", hash = "sha256:e887ab5cee78ea814d3472169153c2d12cd43b14bd03329a39a9c6e2e80bfba7", size = 155029, upload-time = "2026-02-25T02:54:17.342Z" }
+sdist = { url = "https://files.pythonhosted.org/packages/25/ee/6caf7a40c36a1220410afe15a1cc64993a1f864871f698c0f93acb72842a/certifi-2026.4.22.tar.gz", hash = "sha256:8d455352a37b71bf76a79caa83a3d6c25afee4a385d632127b6afb3963f1c580", size = 137077, upload-time = "2026-04-22T11:26:11.191Z" }
 wheels = [
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+    { url = "https://files.pythonhosted.org/packages/22/30/7cd8fdcdfbc5b869528b079bfb76dcdf6056b1a2097a662e5e8c04f42965/certifi-2026.4.22-py3-none-any.whl", hash = "sha256:3cb2210c8f88ba2318d29b0388d1023c8492ff72ecdde4ebdaddbb13a31b1c4a", size = 135707, upload-time = "2026-04-22T11:26:09.372Z" },
 ]
 
 [[package]]
@@ -454,14 +451,14 @@ wheels = [
 
 [[package]]
 name = "click"
-version = "8.3.2"
+version = "8.3.3"
 source = { registry = "https://pypi.org/simple" }
 dependencies = [
     { name = "colorama", marker = "sys_platform == 'win32'" },
 ]
-sdist = { url = "https://files.pythonhosted.org/packages/57/75/31212c6bf2503fdf920d87fee5d7a86a2e3bcf444984126f13d8e4016804/click-8.3.2.tar.gz", hash = "sha256:14162b8b3b3550a7d479eafa77dfd3c38d9dc8951f6f69c78913a8f9a7540fd5", size = 302856, upload-time = "2026-04-03T19:14:45.118Z" }
+sdist = { url = "https://files.pythonhosted.org/packages/bb/63/f9e1ea081ce35720d8b92acde70daaedace594dc93b693c869e0d5910718/click-8.3.3.tar.gz", hash = "sha256:398329ad4837b2ff7cbe1dd166a4c0f8900c3ca3a218de04466f38f6497f18a2", size = 328061, upload-time = "2026-04-22T15:11:27.506Z" }
 wheels = [
-    { url = "https://files.pythonhosted.org/packages/e4/20/71885d8b97d4f3dde17b1fdb92dbd4908b00541c5a3379787137285f602e/click-8.3.2-py3-none-any.whl", hash = "sha256:1924d2c27c5653561cd2cae4548d1406039cb79b858b747cfea24924bbc1616d", size = 108379, upload-time = "2026-04-03T19:14:43.505Z" },
+    { url = "https://files.pythonhosted.org/packages/ae/44/c1221527f6a71a01ec6fbad7fa78f1d50dfa02217385cf0fa3eec7087d59/click-8.3.3-py3-none-any.whl", hash = "sha256:a2bf429bb3033c89fa4936ffb35d5cb471e3719e1f3c8a7c3fff0b8314305613", size = 110502, upload-time = "2026-04-22T15:11:25.044Z" },
 ]
 
 [[package]]
@@ -559,11 +556,9 @@ version = "1.3.3"
 source = { registry = "https://pypi.org/simple" }
 resolution-markers = [
     "python_full_version >= '3.14' and platform_machine == 'x86_64' and sys_platform == 'darwin'",
-    "python_full_version >= '3.12' and python_full_version < '3.14' and platform_machine == 'x86_64' and sys_platform == 'darwin'",
-    "python_full_version == '3.11.*' and platform_machine == 'x86_64' and sys_platform == 'darwin'",
+    "python_full_version >= '3.11' and python_full_version < '3.14' and platform_machine == 'x86_64' and sys_platform == 'darwin'",
     "(python_full_version >= '3.14' and platform_machine != 'x86_64') or (python_full_version >= '3.14' and sys_platform != 'darwin')",
-    "(python_full_version >= '3.12' and python_full_version < '3.14' and platform_machine != 'x86_64') or (python_full_version >= '3.12' and python_full_version < '3.14' and sys_platform != 'darwin')",
-    "(python_full_version == '3.11.*' and platform_machine != 'x86_64') or (python_full_version == '3.11.*' and sys_platform != 'darwin')",
+    "(python_full_version >= '3.11' and python_full_version < '3.14' and platform_machine != 'x86_64') or (python_full_version >= '3.11' and python_full_version < '3.14' and sys_platform != 'darwin')",
 ]
 dependencies = [
     { name = "numpy", version = "2.4.4", source = { registry = "https://pypi.org/simple" }, marker = "python_full_version >= '3.11'" },
@@ -645,115 +640,115 @@ wheels = [
 
 [[package]]
 name = "coverage"
-version = "7.13.5"
-source = { registry = "https://pypi.org/simple" }
-sdist = { url = "https://files.pythonhosted.org/packages/9d/e0/70553e3000e345daff267cec284ce4cbf3fc141b6da229ac52775b5428f1/coverage-7.13.5.tar.gz", hash = "sha256:c81f6515c4c40141f83f502b07bbfa5c240ba25bbe73da7b33f1e5b6120ff179", size = 915967, upload-time = "2026-03-17T10:33:18.341Z" }
-wheels = [
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