diff --git a/CHANGELOG.md b/CHANGELOG.md
index f668209..125d4f9 100644
--- a/CHANGELOG.md
+++ b/CHANGELOG.md
@@ -5,6 +5,13 @@ All notable changes to this project will be documented in this file.
 The format is based on [Keep a Changelog](https://keepachangelog.com/en/1.0.0/),
 and this project adheres to [Semantic Versioning](https://semver.org/spec/v2.0.0.html).
 
+## [Unreleased]
+
+### Added
+- Fast path in the detector sampler for components whose output is deterministically given by a single error variable. These components now skip the JAX compilation and autoregressive sampling pipeline, significantly speeding up detector sampling for surface-code circuits at low physical error rates.
+
+
+
 ## [0.1.4] - 2026-04-28
 
 ### Fixed
diff --git a/src/tsim/circuit.py b/src/tsim/circuit.py
index 77eb160..0921056 100644
--- a/src/tsim/circuit.py
+++ b/src/tsim/circuit.py
@@ -740,6 +740,11 @@ def compile_detector_sampler(
     ) -> CompiledDetectorSampler:
         """Compile circuit into a detector sampler.
 
+        Connected components whose single output is deterministically given by
+        one f-variable are handled via a fast direct path (no compilation or
+        autoregressive sampling).  Remaining components go through the full
+        compilation pipeline.
+
         Args:
             strategy: Stabilizer rank decomposition strategy.
                 Must be one of "cat5", "bss", "cutting".
diff --git a/src/tsim/compile/pipeline.py b/src/tsim/compile/pipeline.py
index 8668c21..4789c78 100644
--- a/src/tsim/compile/pipeline.py
+++ b/src/tsim/compile/pipeline.py
@@ -5,13 +5,19 @@
 from typing import Literal
 
 import jax.numpy as jnp
+import numpy as np
 import pyzx_param as zx
 from pyzx_param.graph.base import BaseGraph
 from pyzx_param.simulate import DecompositionStrategy
 
 from tsim.compile.compile import CompiledScalarGraphs, compile_scalar_graphs
 from tsim.compile.stabrank import find_stab
-from tsim.core.graph import ConnectedComponent, connected_components, get_params
+from tsim.core.graph import (
+    ConnectedComponent,
+    classify_direct,
+    connected_components,
+    get_params,
+)
 from tsim.core.types import CompiledComponent, CompiledProgram, SamplingGraph
 
 DecompositionMode = Literal["sequential", "joint"]
@@ -52,24 +58,45 @@ def compile_program(
     f_indices_global = _get_f_indices(prepared.graph)
     num_outputs = prepared.num_outputs
 
+    direct_entries: list[tuple[int, int, bool]] = []  # (output_idx, f_idx, flip)
     compiled_components: list[CompiledComponent] = []
-    output_order: list[int] = []
+    compiled_output_order: list[int] = []
 
     sorted_components = sorted(components, key=lambda c: len(c.output_indices))
 
     for component in sorted_components:
-        compiled = _compile_component(
-            component=component,
-            f_indices_global=f_indices_global,
-            mode=mode,
-            strategy=strategy,
-        )
-        compiled_components.append(compiled)
-        output_order.extend(component.output_indices)
+        direct = classify_direct(component)
+        if direct is not None:
+            f_idx, flip = direct
+            direct_entries.append((component.output_indices[0], f_idx, flip))
+        else:
+            compiled = _compile_component(
+                component=component,
+                f_indices_global=f_indices_global,
+                mode=mode,
+                strategy=strategy,
+            )
+            compiled_components.append(compiled)
+            compiled_output_order.extend(component.output_indices)
+
+    # Sort direct entries by output index so that — together with the output
+    # prioritisation in transform_error_basis — the concatenated layout often
+    # matches the original output order, sparing a reindex at sample time.
+    direct_entries.sort()
+    direct_output_order = [e[0] for e in direct_entries]
+    direct_f_indices = [e[1] for e in direct_entries]
+    direct_flips = [e[2] for e in direct_entries]
+
+    output_order = np.array(direct_output_order + compiled_output_order, dtype=np.int32)
+    reindex = np.argsort(output_order)
+    is_identity = np.array_equal(reindex, np.arange(len(output_order)))
 
     return CompiledProgram(
         components=tuple(compiled_components),
-        output_order=jnp.array(output_order, dtype=jnp.int32),
+        direct_f_indices=jnp.array(direct_f_indices, dtype=jnp.int32),
+        direct_flips=jnp.array(direct_flips, dtype=jnp.bool_),
+        output_order=jnp.asarray(output_order),
+        output_reindex=None if is_identity else jnp.asarray(reindex),
         num_outputs=num_outputs,
         num_detectors=prepared.num_detectors,
     )
diff --git a/src/tsim/core/graph.py b/src/tsim/core/graph.py
index 0cc2491..66db35b 100644
--- a/src/tsim/core/graph.py
+++ b/src/tsim/core/graph.py
@@ -13,7 +13,7 @@
 from pyzx_param.graph.graph import Graph
 from pyzx_param.graph.graph_s import GraphS
 from pyzx_param.graph.scalar import Scalar
-from pyzx_param.utils import VertexType
+from pyzx_param.utils import EdgeType, VertexType
 
 from tsim.core.instructions import GraphRepresentation
 from tsim.core.parse import parse_stim_circuit
@@ -65,6 +65,65 @@ def connected_components(g: BaseGraph) -> list[ConnectedComponent]:
     return components
 
 
+def classify_direct(
+    component: ConnectedComponent,
+) -> tuple[int, bool] | None:
+    """Check if a component is directly determined by a single f-variable.
+
+    A component qualifies when its graph consists of exactly two vertices — one
+    boundary output and one Z-spider — connected by a Hadamard edge, where the
+    Z-spider carries a single ``f`` parameter and a constant phase of either 0
+    (no flip) or π (flip).
+
+    Args:
+        component: A connected component to classify.
+
+    Returns:
+        ``(f_index, flip)`` if the fast path applies, otherwise ``None``.
+
+    """
+    graph = component.graph
+    outputs = list(graph.outputs())
+    if len(outputs) != 1:
+        return None
+
+    vertices = list(graph.vertices())
+    if len(vertices) != 2:
+        return None
+
+    v_out = outputs[0]
+    neighbors = list(graph.neighbors(v_out))
+    if len(neighbors) != 1:
+        return None
+
+    v_det = neighbors[0]
+    if graph.type(v_det) != VertexType.Z:
+        return None
+    if graph.edge_type(graph.edge(v_out, v_det)) != EdgeType.HADAMARD:
+        return None
+
+    params = graph.get_params(v_det)
+    if len(params) != 1:
+        return None
+    f_param = next(iter(params))
+    if not f_param.startswith("f"):
+        return None
+
+    all_graph_params = get_params(graph)
+    if all_graph_params != {f_param}:
+        return None
+
+    phase = graph.phase(v_det)
+    if phase == 0:
+        flip = False
+    elif phase == Fraction(1, 1):
+        flip = True
+    else:
+        return None
+
+    return int(f_param[1:]), flip
+
+
 def _collect_vertices(
     g: BaseGraph,
     start: Any,
@@ -274,7 +333,21 @@ def transform_error_basis(
               then f0 = e1 XOR e3.
 
     """
-    parametrized_vertices = [v for v in g.vertices() if g._phaseVars.get(v)]
+    # Prioritize output-connected detector vertices so that f0, f1, ...
+    # are assigned in output order.  This maximises the chance that the
+    # direct-component fast path produces an identity permutation, avoiding
+    # a column reindex at sample time.
+    output_detectors = []
+    for v_out in g.outputs():
+        neighbors = list(g.neighbors(v_out))
+        if len(neighbors) == 1 and g._phaseVars.get(neighbors[0]):
+            output_detectors.append(neighbors[0])
+
+    output_det_set = set(output_detectors)
+    other_param_vertices = [
+        v for v in g.vertices() if v not in output_det_set and g._phaseVars.get(v)
+    ]
+    parametrized_vertices = output_detectors + other_param_vertices
 
     if not parametrized_vertices:
         g.scalar = Scalar()
diff --git a/src/tsim/core/types.py b/src/tsim/core/types.py
index 6757eac..4691b56 100644
--- a/src/tsim/core/types.py
+++ b/src/tsim/core/types.py
@@ -86,14 +86,22 @@ class CompiledProgram:
 
     Attributes:
         components: The compiled components, sorted by number of outputs.
-        output_order: Array for reordering component outputs to final order.
-            final_samples = combined[:, np.argsort(output_order)]
+        direct_f_indices: Precomputed f-parameter indices for direct components.
+        direct_flips: Precomputed flip flags for direct components.
+        output_order: Maps concatenated position to original output index.
+            The first ``len(direct_f_indices)`` entries correspond to direct
+            components; the remainder to compiled components.
+        output_reindex: Precomputed ``argsort(output_order)`` permutation,
+            or ``None`` when the outputs are already in order.
         num_outputs: Total number of outputs across all components.
         num_detectors: Number of detector outputs (for detector sampling).
 
     """
 
     components: tuple[CompiledComponent, ...]
+    direct_f_indices: Array
+    direct_flips: Array
     output_order: Array
+    output_reindex: Array | None
     num_outputs: int
     num_detectors: int
diff --git a/src/tsim/sampler.py b/src/tsim/sampler.py
index af94d1e..bfe4e74 100644
--- a/src/tsim/sampler.py
+++ b/src/tsim/sampler.py
@@ -130,11 +130,18 @@ def sample_program(
         match the original output indices.
 
     """
-    if len(program.components) == 0:
+    results: list[jax.Array] = []
+
+    if program.num_outputs == 0:
         batch_size = f_params.shape[0]
-        return jnp.empty((batch_size, 0), dtype=jnp.bool_)
+        return jnp.zeros((batch_size, 0), dtype=jnp.bool_)
 
-    results: list[jax.Array] = []
+    if len(program.direct_f_indices) > 0:
+        direct_bits = (
+            f_params[:, program.direct_f_indices].astype(jnp.bool_)
+            ^ program.direct_flips
+        )
+        results.append(direct_bits)
 
     for component in program.components:
         samples, key, max_norm_deviation = sample_component(component, f_params, key)
@@ -154,7 +161,9 @@ def sample_program(
         results.append(samples)
 
     combined = jnp.concatenate(results, axis=1)
-    return combined[:, jnp.argsort(program.output_order)]
+    if program.output_reindex is not None:
+        combined = combined[:, program.output_reindex]
+    return combined
 
 
 class _CompiledSamplerBase:
@@ -200,6 +209,22 @@ def __init__(
         self.circuit = circuit
         self._num_detectors = prepared.num_detectors
 
+        prog = self._program
+        self._direct_f_indices = np.asarray(prog.direct_f_indices)
+        self._direct_flips = np.asarray(prog.direct_flips, dtype=np.bool_)
+        self._direct_reindex = (
+            np.asarray(prog.output_reindex) if prog.output_reindex is not None else None
+        )
+        # Zero-copy fast path: f-indices are 0..n-1, no flips, no reindex.
+        # Hit by typical surface-code detector circuits at low noise.
+        n_direct = len(self._direct_f_indices)
+        self._direct_zero_copy = (
+            n_direct > 0
+            and self._direct_reindex is None
+            and not self._direct_flips.any()
+            and np.array_equal(self._direct_f_indices, np.arange(n_direct))
+        )
+
     def _peak_bytes_per_sample(self) -> int:
         """Estimate peak device memory per sample from compiled program structure."""
         peak = 0
@@ -276,6 +301,9 @@ def _sample_batches(
                 return empty, np.zeros(self._program.num_outputs, dtype=np.bool_)
             return empty
 
+        if not self._program.components and not compute_reference:
+            return self._sample_direct(shots)
+
         if batch_size is None:
             max_batch_size = self._estimate_batch_size()
             num_batches = max(1, ceil(shots / max_batch_size))
@@ -314,8 +342,20 @@ def _sample_batches(
             return result, reference
         return result
 
+    def _sample_direct(self, shots: int) -> np.ndarray:
+        """Fast path when all components are direct (pure numpy, no JAX)."""
+        f_params = self._channel_sampler.sample(shots)
+        if self._direct_zero_copy:
+            return f_params[:, : len(self._direct_f_indices)].view(np.bool_)
+        result = f_params[:, self._direct_f_indices] ^ self._direct_flips
+        if self._direct_reindex is not None:
+            result = result[:, self._direct_reindex]
+        return result.view(np.bool_)
+
     def __repr__(self) -> str:
         """Return a string representation with compilation statistics."""
+        n_direct = len(self._program.direct_f_indices)
+
         c_graphs = []
         c_params = []
         c_a_terms = []
@@ -356,7 +396,8 @@ def _format_bytes(n: int) -> str:
         )
 
         return (
-            f"{type(self).__name__}({np.sum(c_graphs)} graphs, "
+            f"{type(self).__name__}({n_direct} direct, "
+            f"{np.sum(c_graphs)} graphs, "
             f"{error_channel_bits} error channel bits, "
             f"{np.max(num_outputs) if num_outputs else 0} outputs for largest cc, "
             f"≤ {np.max(c_params) if c_params else 0} parameters, {np.sum(c_a_terms)} A terms, "
@@ -637,6 +678,15 @@ def probability_of(self, state: np.ndarray, *, batch_size: int) -> np.ndarray:
         p_norm = jnp.ones(batch_size)
         p_joint = jnp.ones(batch_size)
 
+        if len(self._program.direct_f_indices) > 0:
+            direct_bits = (
+                f_samples[:, self._program.direct_f_indices].astype(jnp.bool_)
+                ^ self._program.direct_flips
+            )
+            n_direct = len(self._program.direct_f_indices)
+            targets = state[self._program.output_order[:n_direct]]
+            p_joint = p_joint * (direct_bits == targets).all(axis=1)
+
         for component in self._program.components:
             assert len(component.compiled_scalar_graphs) == 2
 
diff --git a/test/integration/test_sampler.py b/test/integration/test_sampler.py
index d3780a4..e68579e 100644
--- a/test/integration/test_sampler.py
+++ b/test/integration/test_sampler.py
@@ -120,7 +120,10 @@ def test_sample_program_raises_on_component_norm_deviation(monkeypatch):
     )
     program = CompiledProgram(
         components=components,
+        direct_f_indices=jnp.array([], dtype=jnp.int32),
+        direct_flips=jnp.array([], dtype=jnp.bool_),
         output_order=jnp.array([0, 1]),
+        output_reindex=None,
         num_outputs=2,
         num_detectors=0,
     )
diff --git a/test/unit/test_sampler.py b/test/unit/test_sampler.py
index 7b40a5a..1562eb1 100644
--- a/test/unit/test_sampler.py
+++ b/test/unit/test_sampler.py
@@ -168,6 +168,15 @@ def test_detector_sampler_no_detectors_bit_packed():
     assert result.shape == (5, 0)
 
 
+def test_detector_sampler_no_detectors_with_reference_sample():
+    """Detector sampler with use_detector_reference_sample=True and no detectors returns (shots, 0)."""
+    c = Circuit("H 0\nM 0")
+    sampler = c.compile_detector_sampler()
+    result = sampler.sample(5, use_detector_reference_sample=True)
+    assert result.dtype == np.bool_
+    assert result.shape == (5, 0)
+
+
 def test_sampler_negative_shots_raises():
     sampler = Circuit("H 0\nM 0").compile_sampler(seed=0)
     with pytest.raises(ValueError, match="shots must be non-negative"):