QUANTUM_SAMPLING.md

Quantum Stochastic Sampling (Pre-release)

Note: This is a pre-release version. While the theoretical foundations and algorithms are complete, the implementation is under active development. This document describes the mathematical framework and planned functionality.

Development Status

• Mathematical Framework: ✅ Complete
• Core Algorithms: ✅ Complete
• Implementation: 🚧 In Progress
• Hardware Integration: 🚧 In Progress
• Performance Validation: 🚧 In Progress

Overview

The library provides comprehensive quantum stochastic sampling capabilities:

1. Quantum Monte Carlo
2. Stochastic Optimization
3. Quantum Annealing
4. Error Mitigation

Quantum Monte Carlo

Configuration

// Configure Monte Carlo
monte_carlo_config_t config = {
    .sampling_type = SAMPLING_QUANTUM,
    .num_samples = 1000000,
    .burn_in = 1000,
    .use_quantum = true,
    .enable_gpu = true,
    .enable_distributed = true
};

// Initialize Monte Carlo
initialize_quantum_monte_carlo(&config);

Features

1. Sampling Types

   • Path integral
   • Variational
   • Diffusion
   • Hybrid
   • Custom sampling

2. Operations

   • State sampling
   • Path generation
   • Error estimation
   • Convergence analysis
   • Result validation

Stochastic Optimization

Configuration

// Configure optimization
stochastic_optimization_config_t config = {
    .optimization_type = OPT_QUANTUM,
    .learning_rate = 0.01,
    .momentum = 0.9,
    .num_iterations = 1000,
    .enable_adaptive = true,
    .use_quantum_noise = true
};

// Initialize optimization
initialize_stochastic_optimization(&config);

Features

1. Optimization Types

   • Quantum gradient descent
   • Stochastic annealing
   • Evolutionary algorithms
   • Hybrid methods
   • Custom optimization

2. Operations

   • Parameter updates
   • Gradient estimation
   • Noise injection
   • Convergence testing
   • Performance monitoring

Quantum Annealing

Configuration

// Configure annealing
quantum_annealing_config_t config = {
    .annealing_type = ANNEAL_QUANTUM,
    .schedule_type = SCHEDULE_ADAPTIVE,
    .initial_temperature = 1.0,
    .final_temperature = 0.01,
    .num_sweeps = 1000,
    .enable_quantum_tunneling = true
};

// Initialize annealing
initialize_quantum_annealing(&config);

Features

1. Annealing Types

   • Quantum annealing
   • Simulated annealing
   • Hybrid annealing
   • Parallel tempering
   • Custom annealing

2. Operations

   • Schedule optimization
   • State evolution
   • Energy calculation
   • Tunneling analysis
   • Result verification

Error Mitigation

Configuration

// Configure error mitigation
error_mitigation_config_t config = {
    .mitigation_type = MITIGATE_QUANTUM,
    .error_threshold = 0.01,
    .sampling_overhead = 2.0,
    .enable_extrapolation = true,
    .use_quantum_error_correction = true
};

// Initialize mitigation
initialize_error_mitigation(&config);

Features

1. Mitigation Types

   • Zero-noise extrapolation
   • Richardson extrapolation
   • Probabilistic error cancellation
   • Quantum error correction
   • Custom mitigation

2. Operations

   • Error estimation
   • Noise characterization
   • Result correction
   • Validation
   • Performance analysis

Performance Optimization

Hardware Acceleration

// Configure acceleration
sampling_acceleration_config_t config = {
    .use_gpu = true,
    .use_quantum = true,
    .enable_tensor_cores = true,
    .enable_distributed = true,
    .optimization_level = OPTIMIZE_AGGRESSIVE
};

// Initialize acceleration
initialize_sampling_acceleration(&config);

Memory Management

// Configure memory management
sampling_memory_config_t config = {
    .max_memory = 32 * 1024 * 1024 * 1024ull,  // 32GB
    .enable_swapping = true,
    .compression_level = COMPRESSION_AGGRESSIVE,
    .enable_checkpointing = true
};

// Initialize memory management
initialize_sampling_memory(&config);

Best Practices

1. Sampling Strategy

   • Choose appropriate method
   • Optimize parameters
   • Monitor convergence
   • Validate results

2. Error Control

   • Use error mitigation
   • Monitor error rates
   • Implement validation
   • Track performance

3. Resource Management

   • Monitor memory usage
   • Optimize sampling
   • Use distributed computing
   • Track efficiency

4. Performance

   • Profile operations
   • Optimize parameters
   • Balance resources
   • Monitor metrics

Advanced Features

Adaptive Sampling

// Configure adaptive sampling
adaptive_sampling_config_t config = {
    .adaptation_type = ADAPT_QUANTUM,
    .learning_rate = 0.01,
    .num_iterations = 1000,
    .enable_quantum = true,
    .use_gpu = true
};

// Initialize adaptive sampling
initialize_adaptive_sampling(&config);

Sampling Ensembles

// Configure ensemble sampling
ensemble_sampling_config_t config = {
    .num_samplers = 5,
    .aggregation_method = ENSEMBLE_WEIGHTED,
    .diversity_measure = DIVERSITY_QUANTUM,
    .enable_quantum = true
};

// Initialize ensemble
initialize_sampling_ensemble(&config);

Integration

System Integration

// Configure sampling system
sampling_system_config_t config = {
    .enable_all_features = true,
    .auto_optimization = true,
    .monitoring_level = MONITOR_DETAILED,
    .error_budget = 0.01
};

// Initialize sampling system
initialize_sampling_system(&config);

Cleanup

// Cleanup sampling system
void cleanup_sampling_system() {
    // Stop sampling
    stop_monte_carlo();
    stop_optimization();
    stop_annealing();
    stop_error_mitigation();
    
    // Clean resources
    cleanup_monte_carlo_resources();
    cleanup_optimization_resources();
    cleanup_annealing_resources();
    cleanup_mitigation_resources();
}

Error Handling

Sampling Errors

// Handle sampling errors
void handle_sampling_error(sampling_error_t error) {
    switch (error) {
        case SAMPLING_ERROR_CONVERGENCE:
            increase_num_samples();
            retry_sampling();
            break;
            
        case SAMPLING_ERROR_NOISE:
            enable_error_mitigation();
            retry_sampling();
            break;
            
        case SAMPLING_ERROR_HARDWARE:
            switch_to_classical_mode();
            break;
            
        default:
            log_sampling_error(error);
            abort_sampling();
    }
}

Recovery

// Configure sampling recovery
recovery_config_t config = {
    .max_retries = 3,
    .checkpoint_interval = 100,
    .enable_logging = true,
    .fallback_strategy = FALLBACK_CLASSICAL
};

// Initialize recovery
initialize_sampling_recovery(&config);