quantrs2_sim/

quantum_inspired_classical.rs

//! Quantum-Inspired Classical Algorithms Framework
//!
//! This module provides a comprehensive implementation of quantum-inspired classical algorithms
//! that leverage quantum mechanical principles, quantum physics concepts, and quantum computation
//! techniques while running on classical computers. These algorithms often provide advantages
//! over traditional classical algorithms by incorporating quantum-inspired heuristics.

use scirs2_core::ndarray::{Array1, Array2};
use scirs2_core::random::{thread_rng, Rng};
use scirs2_core::Complex64;
use serde::{Deserialize, Serialize};
use std::collections::HashMap;
use std::f64::consts::PI;
use std::sync::{Arc, Mutex};

use crate::error::{Result, SimulatorError};
use crate::scirs2_integration::SciRS2Backend;
use scirs2_core::random::prelude::*;

/// Quantum-inspired classical algorithms configuration
#[derive(Debug, Clone, Serialize, Deserialize)]
pub struct QuantumInspiredConfig {
    /// Number of classical variables/qubits to simulate
    pub num_variables: usize,
    /// Algorithm category to use
    pub algorithm_category: AlgorithmCategory,
    /// Specific algorithm configuration
    pub algorithm_config: AlgorithmConfig,
    /// Optimization settings
    pub optimization_config: OptimizationConfig,
    /// Machine learning settings (when applicable)
    pub ml_config: Option<MLConfig>,
    /// Sampling algorithm settings
    pub sampling_config: SamplingConfig,
    /// Linear algebra settings
    pub linalg_config: LinalgConfig,
    /// Graph algorithm settings
    pub graph_config: GraphConfig,
    /// Performance benchmarking settings
    pub benchmarking_config: BenchmarkingConfig,
    /// Enable quantum-inspired heuristics
    pub enable_quantum_heuristics: bool,
    /// Precision for calculations
    pub precision: f64,
    /// Random seed for reproducibility
    pub random_seed: Option<u64>,
}

impl Default for QuantumInspiredConfig {
    fn default() -> Self {
        Self {
            num_variables: 16,
            algorithm_category: AlgorithmCategory::Optimization,
            algorithm_config: AlgorithmConfig::default(),
            optimization_config: OptimizationConfig::default(),
            ml_config: Some(MLConfig::default()),
            sampling_config: SamplingConfig::default(),
            linalg_config: LinalgConfig::default(),
            graph_config: GraphConfig::default(),
            benchmarking_config: BenchmarkingConfig::default(),
            enable_quantum_heuristics: true,
            precision: 1e-8,
            random_seed: None,
        }
    }
}

/// Categories of quantum-inspired algorithms
#[derive(Debug, Clone, Copy, PartialEq, Eq, Serialize, Deserialize)]
pub enum AlgorithmCategory {
    /// Quantum-inspired optimization algorithms
    Optimization,
    /// Quantum-inspired machine learning algorithms
    MachineLearning,
    /// Quantum-inspired sampling algorithms
    Sampling,
    /// Quantum-inspired linear algebra algorithms
    LinearAlgebra,
    /// Quantum-inspired graph algorithms
    GraphAlgorithms,
    /// Hybrid quantum-classical algorithms
    HybridQuantumClassical,
}

/// Algorithm-specific configuration
#[derive(Debug, Clone, Serialize, Deserialize)]
pub struct AlgorithmConfig {
    /// Maximum number of iterations
    pub max_iterations: usize,
    /// Convergence tolerance
    pub tolerance: f64,
    /// Population size (for evolutionary algorithms)
    pub population_size: usize,
    /// Elite ratio (for genetic algorithms)
    pub elite_ratio: f64,
    /// Mutation rate
    pub mutation_rate: f64,
    /// Crossover rate
    pub crossover_rate: f64,
    /// Temperature schedule (for simulated annealing)
    pub temperature_schedule: TemperatureSchedule,
    /// Quantum-inspired parameters
    pub quantum_parameters: QuantumParameters,
}

impl Default for AlgorithmConfig {
    fn default() -> Self {
        Self {
            max_iterations: 1000,
            tolerance: 1e-6,
            population_size: 100,
            elite_ratio: 0.1,
            mutation_rate: 0.1,
            crossover_rate: 0.8,
            temperature_schedule: TemperatureSchedule::Exponential,
            quantum_parameters: QuantumParameters::default(),
        }
    }
}

/// Temperature schedule for simulated annealing-like algorithms
#[derive(Debug, Clone, Copy, PartialEq, Eq, Serialize, Deserialize)]
pub enum TemperatureSchedule {
    /// Exponential cooling
    Exponential,
    /// Linear cooling
    Linear,
    /// Logarithmic cooling
    Logarithmic,
    /// Quantum-inspired adiabatic schedule
    QuantumAdiabatic,
    /// Custom schedule
    Custom,
}

/// Quantum-inspired parameters
#[derive(Debug, Clone, Serialize, Deserialize)]
pub struct QuantumParameters {
    /// Superposition coefficient
    pub superposition_strength: f64,
    /// Entanglement strength
    pub entanglement_strength: f64,
    /// Interference strength
    pub interference_strength: f64,
    /// Quantum tunneling probability
    pub tunneling_probability: f64,
    /// Decoherence rate
    pub decoherence_rate: f64,
    /// Measurement probability
    pub measurement_probability: f64,
    /// Quantum walk parameters
    pub quantum_walk_params: QuantumWalkParams,
}

impl Default for QuantumParameters {
    fn default() -> Self {
        Self {
            superposition_strength: 0.5,
            entanglement_strength: 0.3,
            interference_strength: 0.2,
            tunneling_probability: 0.1,
            decoherence_rate: 0.01,
            measurement_probability: 0.1,
            quantum_walk_params: QuantumWalkParams::default(),
        }
    }
}

/// Quantum walk parameters
#[derive(Debug, Clone, Serialize, Deserialize)]
pub struct QuantumWalkParams {
    /// Coin bias
    pub coin_bias: f64,
    /// Step size
    pub step_size: f64,
    /// Number of steps
    pub num_steps: usize,
    /// Walk dimension
    pub dimension: usize,
}

impl Default for QuantumWalkParams {
    fn default() -> Self {
        Self {
            coin_bias: 0.5,
            step_size: 1.0,
            num_steps: 100,
            dimension: 1,
        }
    }
}

/// Optimization configuration
#[derive(Debug, Clone, Serialize, Deserialize)]
pub struct OptimizationConfig {
    /// Optimization algorithm type
    pub algorithm_type: OptimizationAlgorithm,
    /// Objective function type
    pub objective_function: ObjectiveFunction,
    /// Search space bounds
    pub bounds: Vec<(f64, f64)>,
    /// Constraint handling method
    pub constraint_method: ConstraintMethod,
    /// Multi-objective optimization settings
    pub multi_objective: bool,
    /// Parallel processing settings
    pub parallel_evaluation: bool,
}

impl Default for OptimizationConfig {
    fn default() -> Self {
        Self {
            algorithm_type: OptimizationAlgorithm::QuantumGeneticAlgorithm,
            objective_function: ObjectiveFunction::Quadratic,
            bounds: vec![(-10.0, 10.0); 16],
            constraint_method: ConstraintMethod::PenaltyFunction,
            multi_objective: false,
            parallel_evaluation: true,
        }
    }
}

/// Quantum-inspired optimization algorithms
#[derive(Debug, Clone, Copy, PartialEq, Eq, Serialize, Deserialize)]
pub enum OptimizationAlgorithm {
    /// Quantum-inspired genetic algorithm
    QuantumGeneticAlgorithm,
    /// Quantum-inspired particle swarm optimization
    QuantumParticleSwarm,
    /// Quantum-inspired simulated annealing
    QuantumSimulatedAnnealing,
    /// Quantum-inspired differential evolution
    QuantumDifferentialEvolution,
    /// Quantum approximate optimization algorithm (classical simulation)
    ClassicalQAOA,
    /// Variational quantum eigensolver (classical simulation)
    ClassicalVQE,
    /// Quantum-inspired ant colony optimization
    QuantumAntColony,
    /// Quantum-inspired harmony search
    QuantumHarmonySearch,
}

/// Objective function types
#[derive(Debug, Clone, Copy, PartialEq, Eq, Serialize, Deserialize)]
pub enum ObjectiveFunction {
    /// Quadratic function
    Quadratic,
    /// Rastrigin function
    Rastrigin,
    /// Rosenbrock function
    Rosenbrock,
    /// Ackley function
    Ackley,
    /// Sphere function
    Sphere,
    /// Griewank function
    Griewank,
    /// Custom function
    Custom,
}

/// Constraint handling methods
#[derive(Debug, Clone, Copy, PartialEq, Eq, Serialize, Deserialize)]
pub enum ConstraintMethod {
    /// Penalty function method
    PenaltyFunction,
    /// Barrier function method
    BarrierFunction,
    /// Lagrange multiplier method
    LagrangeMultiplier,
    /// Projection method
    Projection,
    /// Rejection method
    Rejection,
}

/// Machine learning configuration
#[derive(Debug, Clone, Serialize, Deserialize)]
pub struct MLConfig {
    /// ML algorithm type
    pub algorithm_type: MLAlgorithm,
    /// Network architecture
    pub architecture: NetworkArchitecture,
    /// Training configuration
    pub training_config: TrainingConfig,
    /// Tensor network configuration
    pub tensor_network_config: TensorNetworkConfig,
}

impl Default for MLConfig {
    fn default() -> Self {
        Self {
            algorithm_type: MLAlgorithm::QuantumInspiredNeuralNetwork,
            architecture: NetworkArchitecture::default(),
            training_config: TrainingConfig::default(),
            tensor_network_config: TensorNetworkConfig::default(),
        }
    }
}

/// Quantum-inspired machine learning algorithms
#[derive(Debug, Clone, Copy, PartialEq, Eq, Serialize, Deserialize)]
pub enum MLAlgorithm {
    /// Quantum-inspired neural network
    QuantumInspiredNeuralNetwork,
    /// Tensor network machine learning
    TensorNetworkML,
    /// Matrix product state neural network
    MPSNeuralNetwork,
    /// Quantum-inspired autoencoder
    QuantumInspiredAutoencoder,
    /// Quantum-inspired reinforcement learning
    QuantumInspiredRL,
    /// Quantum-inspired support vector machine
    QuantumInspiredSVM,
    /// Quantum-inspired clustering
    QuantumInspiredClustering,
    /// Quantum-inspired dimensionality reduction
    QuantumInspiredPCA,
}

/// Network architecture configuration
#[derive(Debug, Clone, Serialize, Deserialize)]
pub struct NetworkArchitecture {
    /// Input dimension
    pub input_dim: usize,
    /// Hidden layers
    pub hidden_layers: Vec<usize>,
    /// Output dimension
    pub output_dim: usize,
    /// Activation function
    pub activation: ActivationFunction,
    /// Quantum-inspired connections
    pub quantum_connections: bool,
}

impl Default for NetworkArchitecture {
    fn default() -> Self {
        Self {
            input_dim: 16,
            hidden_layers: vec![32, 16],
            output_dim: 8,
            activation: ActivationFunction::QuantumInspiredTanh,
            quantum_connections: true,
        }
    }
}

/// Activation functions
#[derive(Debug, Clone, Copy, PartialEq, Eq, Serialize, Deserialize)]
pub enum ActivationFunction {
    /// Quantum-inspired tanh
    QuantumInspiredTanh,
    /// Quantum-inspired sigmoid
    QuantumInspiredSigmoid,
    /// Quantum-inspired `ReLU`
    QuantumInspiredReLU,
    /// Quantum-inspired softmax
    QuantumInspiredSoftmax,
    /// Quantum phase activation
    QuantumPhase,
}

/// Training configuration
#[derive(Debug, Clone, Serialize, Deserialize)]
pub struct TrainingConfig {
    /// Learning rate
    pub learning_rate: f64,
    /// Number of epochs
    pub epochs: usize,
    /// Batch size
    pub batch_size: usize,
    /// Optimizer type
    pub optimizer: OptimizerType,
    /// Regularization strength
    pub regularization: f64,
}

impl Default for TrainingConfig {
    fn default() -> Self {
        Self {
            learning_rate: 0.01,
            epochs: 100,
            batch_size: 32,
            optimizer: OptimizerType::QuantumInspiredAdam,
            regularization: 0.001,
        }
    }
}

/// Optimizer types
#[derive(Debug, Clone, Copy, PartialEq, Eq, Serialize, Deserialize)]
pub enum OptimizerType {
    /// Quantum-inspired Adam
    QuantumInspiredAdam,
    /// Quantum-inspired SGD
    QuantumInspiredSGD,
    /// Quantum natural gradient
    QuantumNaturalGradient,
    /// Quantum-inspired `RMSprop`
    QuantumInspiredRMSprop,
}

/// Tensor network configuration
#[derive(Debug, Clone, Serialize, Deserialize)]
pub struct TensorNetworkConfig {
    /// Bond dimension
    pub bond_dimension: usize,
    /// Network topology
    pub topology: TensorTopology,
    /// Contraction method
    pub contraction_method: ContractionMethod,
    /// Truncation threshold
    pub truncation_threshold: f64,
}

impl Default for TensorNetworkConfig {
    fn default() -> Self {
        Self {
            bond_dimension: 64,
            topology: TensorTopology::MPS,
            contraction_method: ContractionMethod::OptimalContraction,
            truncation_threshold: 1e-12,
        }
    }
}

/// Tensor network topologies
#[derive(Debug, Clone, Copy, PartialEq, Eq, Serialize, Deserialize)]
pub enum TensorTopology {
    /// Matrix Product State
    MPS,
    /// Matrix Product Operator
    MPO,
    /// Tree Tensor Network
    TTN,
    /// Projected Entangled Pair State
    PEPS,
    /// Multi-scale Entanglement Renormalization Ansatz
    MERA,
}

/// Contraction methods
#[derive(Debug, Clone, Copy, PartialEq, Eq, Serialize, Deserialize)]
pub enum ContractionMethod {
    /// Optimal contraction ordering
    OptimalContraction,
    /// Greedy contraction
    GreedyContraction,
    /// Dynamic programming contraction
    DynamicProgramming,
    /// Branch and bound contraction
    BranchAndBound,
}

/// Sampling configuration
#[derive(Debug, Clone, Serialize, Deserialize)]
pub struct SamplingConfig {
    /// Sampling algorithm type
    pub algorithm_type: SamplingAlgorithm,
    /// Number of samples
    pub num_samples: usize,
    /// Burn-in period
    pub burn_in: usize,
    /// Thinning factor
    pub thinning: usize,
    /// Proposal distribution
    pub proposal_distribution: ProposalDistribution,
    /// Wave function configuration
    pub wave_function_config: WaveFunctionConfig,
}

impl Default for SamplingConfig {
    fn default() -> Self {
        Self {
            algorithm_type: SamplingAlgorithm::QuantumInspiredMCMC,
            num_samples: 10_000,
            burn_in: 1000,
            thinning: 10,
            proposal_distribution: ProposalDistribution::Gaussian,
            wave_function_config: WaveFunctionConfig::default(),
        }
    }
}

/// Quantum-inspired sampling algorithms
#[derive(Debug, Clone, Copy, PartialEq, Eq, Serialize, Deserialize)]
pub enum SamplingAlgorithm {
    /// Quantum-inspired Markov Chain Monte Carlo
    QuantumInspiredMCMC,
    /// Variational Monte Carlo with quantum-inspired wave functions
    QuantumInspiredVMC,
    /// Quantum-inspired importance sampling
    QuantumInspiredImportanceSampling,
    /// Path integral Monte Carlo (classical simulation)
    ClassicalPIMC,
    /// Quantum-inspired Gibbs sampling
    QuantumInspiredGibbs,
    /// Quantum-inspired Metropolis-Hastings
    QuantumInspiredMetropolis,
}

/// Proposal distributions
#[derive(Debug, Clone, Copy, PartialEq, Eq, Serialize, Deserialize)]
pub enum ProposalDistribution {
    /// Gaussian distribution
    Gaussian,
    /// Uniform distribution
    Uniform,
    /// Cauchy distribution
    Cauchy,
    /// Quantum-inspired distribution
    QuantumInspired,
}

/// Wave function configuration
#[derive(Debug, Clone, Serialize, Deserialize)]
pub struct WaveFunctionConfig {
    /// Wave function type
    pub wave_function_type: WaveFunctionType,
    /// Number of variational parameters
    pub num_parameters: usize,
    /// Jastrow factor strength
    pub jastrow_strength: f64,
    /// Backflow parameters
    pub backflow_enabled: bool,
}

impl Default for WaveFunctionConfig {
    fn default() -> Self {
        Self {
            wave_function_type: WaveFunctionType::SlaterJastrow,
            num_parameters: 32,
            jastrow_strength: 1.0,
            backflow_enabled: false,
        }
    }
}

/// Wave function types
#[derive(Debug, Clone, Copy, PartialEq, Eq, Serialize, Deserialize)]
pub enum WaveFunctionType {
    /// Slater-Jastrow wave function
    SlaterJastrow,
    /// Quantum-inspired neural network wave function
    QuantumNeuralNetwork,
    /// Matrix product state wave function
    MatrixProductState,
    /// Pfaffian wave function
    Pfaffian,
    /// BCS wave function
    BCS,
}

/// Linear algebra configuration
#[derive(Debug, Clone, Serialize, Deserialize)]
pub struct LinalgConfig {
    /// Linear algebra algorithm type
    pub algorithm_type: LinalgAlgorithm,
    /// Matrix dimension
    pub matrix_dimension: usize,
    /// Precision requirements
    pub precision: f64,
    /// Maximum number of iterations
    pub max_iterations: usize,
    /// Krylov subspace dimension
    pub krylov_dimension: usize,
}

impl Default for LinalgConfig {
    fn default() -> Self {
        Self {
            algorithm_type: LinalgAlgorithm::QuantumInspiredLinearSolver,
            matrix_dimension: 1024,
            precision: 1e-8,
            max_iterations: 1000,
            krylov_dimension: 50,
        }
    }
}

/// Quantum-inspired linear algebra algorithms
#[derive(Debug, Clone, Copy, PartialEq, Eq, Serialize, Deserialize)]
pub enum LinalgAlgorithm {
    /// Quantum-inspired linear system solver
    QuantumInspiredLinearSolver,
    /// Quantum-inspired SVD
    QuantumInspiredSVD,
    /// Quantum-inspired eigenvalue solver
    QuantumInspiredEigenSolver,
    /// Quantum-inspired matrix inversion
    QuantumInspiredInversion,
    /// Quantum-inspired PCA
    QuantumInspiredPCA,
    /// Quantum-inspired matrix exponentiation
    QuantumInspiredMatrixExp,
}

/// Graph algorithm configuration
#[derive(Debug, Clone, Serialize, Deserialize)]
pub struct GraphConfig {
    /// Graph algorithm type
    pub algorithm_type: GraphAlgorithm,
    /// Number of vertices
    pub num_vertices: usize,
    /// Graph connectivity
    pub connectivity: f64,
    /// Walk parameters
    pub walk_params: QuantumWalkParams,
    /// Community detection parameters
    pub community_params: CommunityDetectionParams,
}

impl Default for GraphConfig {
    fn default() -> Self {
        Self {
            algorithm_type: GraphAlgorithm::QuantumInspiredRandomWalk,
            num_vertices: 100,
            connectivity: 0.1,
            walk_params: QuantumWalkParams::default(),
            community_params: CommunityDetectionParams::default(),
        }
    }
}

/// Quantum-inspired graph algorithms
#[derive(Debug, Clone, Copy, PartialEq, Eq, Serialize, Deserialize)]
pub enum GraphAlgorithm {
    /// Quantum-inspired random walk
    QuantumInspiredRandomWalk,
    /// Quantum-inspired shortest path
    QuantumInspiredShortestPath,
    /// Quantum-inspired graph coloring
    QuantumInspiredGraphColoring,
    /// Quantum-inspired community detection
    QuantumInspiredCommunityDetection,
    /// Quantum-inspired maximum cut
    QuantumInspiredMaxCut,
    /// Quantum-inspired graph matching
    QuantumInspiredGraphMatching,
}

/// Community detection parameters
#[derive(Debug, Clone, Serialize, Deserialize)]
pub struct CommunityDetectionParams {
    /// Resolution parameter
    pub resolution: f64,
    /// Number of iterations
    pub num_iterations: usize,
    /// Modularity threshold
    pub modularity_threshold: f64,
}

impl Default for CommunityDetectionParams {
    fn default() -> Self {
        Self {
            resolution: 1.0,
            num_iterations: 100,
            modularity_threshold: 0.01,
        }
    }
}

/// Benchmarking configuration
#[derive(Debug, Clone, Serialize, Deserialize)]
pub struct BenchmarkingConfig {
    /// Enable benchmarking
    pub enabled: bool,
    /// Number of benchmark runs
    pub num_runs: usize,
    /// Benchmark classical algorithms for comparison
    pub compare_classical: bool,
    /// Record detailed metrics
    pub detailed_metrics: bool,
    /// Performance analysis settings
    pub performance_analysis: PerformanceAnalysisConfig,
}

impl Default for BenchmarkingConfig {
    fn default() -> Self {
        Self {
            enabled: true,
            num_runs: 10,
            compare_classical: true,
            detailed_metrics: true,
            performance_analysis: PerformanceAnalysisConfig::default(),
        }
    }
}

/// Performance analysis configuration
#[derive(Debug, Clone, Serialize, Deserialize)]
pub struct PerformanceAnalysisConfig {
    /// Analyze convergence behavior
    pub analyze_convergence: bool,
    /// Analyze scalability
    pub analyze_scalability: bool,
    /// Analyze quantum advantage
    pub analyze_quantum_advantage: bool,
    /// Record memory usage
    pub record_memory_usage: bool,
}

impl Default for PerformanceAnalysisConfig {
    fn default() -> Self {
        Self {
            analyze_convergence: true,
            analyze_scalability: true,
            analyze_quantum_advantage: true,
            record_memory_usage: true,
        }
    }
}

/// Main quantum-inspired classical algorithms framework
#[derive(Debug)]
pub struct QuantumInspiredFramework {
    /// Configuration
    config: QuantumInspiredConfig,
    /// Current state
    state: QuantumInspiredState,
    /// `SciRS2` backend for numerical operations
    backend: Option<SciRS2Backend>,
    /// Performance statistics
    stats: QuantumInspiredStats,
    /// Random number generator
    rng: Arc<Mutex<scirs2_core::random::CoreRandom>>,
}

/// Framework state
#[derive(Debug)]
pub struct QuantumInspiredState {
    /// Current variables/solution
    pub variables: Array1<f64>,
    /// Current objective value
    pub objective_value: f64,
    /// Current iteration
    pub iteration: usize,
    /// Best solution found
    pub best_solution: Array1<f64>,
    /// Best objective value
    pub best_objective: f64,
    /// Convergence history
    pub convergence_history: Vec<f64>,
    /// Runtime statistics
    pub runtime_stats: RuntimeStats,
}

/// Runtime statistics
#[derive(Debug, Clone)]
pub struct RuntimeStats {
    /// Total function evaluations
    pub function_evaluations: usize,
    /// Total gradient evaluations
    pub gradient_evaluations: usize,
    /// Total CPU time (seconds)
    pub cpu_time: f64,
    /// Memory usage (bytes)
    pub memory_usage: usize,
    /// Quantum-inspired operations count
    pub quantum_operations: usize,
}

impl Default for RuntimeStats {
    fn default() -> Self {
        Self {
            function_evaluations: 0,
            gradient_evaluations: 0,
            cpu_time: 0.0,
            memory_usage: 0,
            quantum_operations: 0,
        }
    }
}

/// Framework statistics
#[derive(Debug, Clone, Default)]
pub struct QuantumInspiredStats {
    /// Algorithm execution statistics
    pub execution_stats: ExecutionStats,
    /// Performance comparison statistics
    pub comparison_stats: ComparisonStats,
    /// Convergence analysis
    pub convergence_analysis: ConvergenceAnalysis,
    /// Quantum advantage metrics
    pub quantum_advantage_metrics: QuantumAdvantageMetrics,
}

/// Execution statistics
#[derive(Debug, Clone)]
pub struct ExecutionStats {
    /// Total runtime (seconds)
    pub total_runtime: f64,
    /// Average runtime per iteration (seconds)
    pub avg_runtime_per_iteration: f64,
    /// Peak memory usage (bytes)
    pub peak_memory_usage: usize,
    /// Successful runs
    pub successful_runs: usize,
    /// Failed runs
    pub failed_runs: usize,
}

impl Default for ExecutionStats {
    fn default() -> Self {
        Self {
            total_runtime: 0.0,
            avg_runtime_per_iteration: 0.0,
            peak_memory_usage: 0,
            successful_runs: 0,
            failed_runs: 0,
        }
    }
}

/// Performance comparison statistics
#[derive(Debug, Clone)]
pub struct ComparisonStats {
    /// Quantum-inspired algorithm performance
    pub quantum_inspired_performance: f64,
    /// Classical algorithm performance
    pub classical_performance: f64,
    /// Speedup factor
    pub speedup_factor: f64,
    /// Solution quality comparison
    pub solution_quality_ratio: f64,
    /// Convergence speed comparison
    pub convergence_speed_ratio: f64,
}

impl Default for ComparisonStats {
    fn default() -> Self {
        Self {
            quantum_inspired_performance: 0.0,
            classical_performance: 0.0,
            speedup_factor: 1.0,
            solution_quality_ratio: 1.0,
            convergence_speed_ratio: 1.0,
        }
    }
}

/// Convergence analysis
#[derive(Debug, Clone)]
pub struct ConvergenceAnalysis {
    /// Convergence rate
    pub convergence_rate: f64,
    /// Number of iterations to convergence
    pub iterations_to_convergence: usize,
    /// Final gradient norm
    pub final_gradient_norm: f64,
    /// Convergence achieved
    pub converged: bool,
    /// Convergence criterion
    pub convergence_criterion: String,
}

impl Default for ConvergenceAnalysis {
    fn default() -> Self {
        Self {
            convergence_rate: 0.0,
            iterations_to_convergence: 0,
            final_gradient_norm: f64::INFINITY,
            converged: false,
            convergence_criterion: "tolerance".to_string(),
        }
    }
}

/// Quantum advantage metrics
#[derive(Debug, Clone)]
pub struct QuantumAdvantageMetrics {
    /// Theoretical quantum speedup
    pub theoretical_speedup: f64,
    /// Practical quantum advantage
    pub practical_advantage: f64,
    /// Problem complexity class
    pub complexity_class: String,
    /// Quantum resource requirements
    pub quantum_resource_requirements: usize,
    /// Classical resource requirements
    pub classical_resource_requirements: usize,
}

impl Default for QuantumAdvantageMetrics {
    fn default() -> Self {
        Self {
            theoretical_speedup: 1.0,
            practical_advantage: 1.0,
            complexity_class: "NP".to_string(),
            quantum_resource_requirements: 0,
            classical_resource_requirements: 0,
        }
    }
}

/// Optimization result
#[derive(Debug, Clone)]
pub struct OptimizationResult {
    /// Optimal solution
    pub solution: Array1<f64>,
    /// Optimal objective value
    pub objective_value: f64,
    /// Number of iterations
    pub iterations: usize,
    /// Convergence achieved
    pub converged: bool,
    /// Runtime statistics
    pub runtime_stats: RuntimeStats,
    /// Algorithm-specific metadata
    pub metadata: HashMap<String, f64>,
}

/// Machine learning training result
#[derive(Debug, Clone)]
pub struct MLTrainingResult {
    /// Final model parameters
    pub parameters: Array1<f64>,
    /// Training loss history
    pub loss_history: Vec<f64>,
    /// Validation accuracy
    pub validation_accuracy: f64,
    /// Training time (seconds)
    pub training_time: f64,
    /// Model complexity metrics
    pub complexity_metrics: HashMap<String, f64>,
}

/// Sampling result
#[derive(Debug, Clone)]
pub struct SamplingResult {
    /// Generated samples
    pub samples: Array2<f64>,
    /// Sample statistics
    pub statistics: SampleStatistics,
    /// Acceptance rate
    pub acceptance_rate: f64,
    /// Effective sample size
    pub effective_sample_size: usize,
    /// Auto-correlation times
    pub autocorr_times: Array1<f64>,
}

/// Sample statistics
#[derive(Debug, Clone)]
pub struct SampleStatistics {
    /// Sample mean
    pub mean: Array1<f64>,
    /// Sample variance
    pub variance: Array1<f64>,
    /// Sample skewness
    pub skewness: Array1<f64>,
    /// Sample kurtosis
    pub kurtosis: Array1<f64>,
    /// Correlation matrix
    pub correlation_matrix: Array2<f64>,
}

/// Linear algebra result
#[derive(Debug, Clone)]
pub struct LinalgResult {
    /// Solution vector
    pub solution: Array1<Complex64>,
    /// Eigenvalues (if applicable)
    pub eigenvalues: Option<Array1<Complex64>>,
    /// Eigenvectors (if applicable)
    pub eigenvectors: Option<Array2<Complex64>>,
    /// Singular values (if applicable)
    pub singular_values: Option<Array1<f64>>,
    /// Residual norm
    pub residual_norm: f64,
    /// Number of iterations
    pub iterations: usize,
}

/// Graph algorithm result
#[derive(Debug, Clone)]
pub struct GraphResult {
    /// Solution (e.g., coloring, path, communities)
    pub solution: Vec<usize>,
    /// Objective value
    pub objective_value: f64,
    /// Graph metrics
    pub graph_metrics: GraphMetrics,
    /// Walk statistics (if applicable)
    pub walk_stats: Option<WalkStatistics>,
}

/// Graph metrics
#[derive(Debug, Clone)]
pub struct GraphMetrics {
    /// Modularity (for community detection)
    pub modularity: f64,
    /// Clustering coefficient
    pub clustering_coefficient: f64,
    /// Average path length
    pub average_path_length: f64,
    /// Graph diameter
    pub diameter: usize,
}

/// Walk statistics
#[derive(Debug, Clone)]
pub struct WalkStatistics {
    /// Visit frequency
    pub visit_frequency: Array1<f64>,
    /// Hitting times
    pub hitting_times: Array1<f64>,
    /// Return times
    pub return_times: Array1<f64>,
    /// Mixing time
    pub mixing_time: f64,
}

/// Benchmarking results
#[derive(Debug, Clone)]
pub struct BenchmarkingResults {
    /// Algorithm performance metrics
    pub performance_metrics: Vec<f64>,
    /// Execution times
    pub execution_times: Vec<f64>,
    /// Memory usage
    pub memory_usage: Vec<usize>,
    /// Solution qualities
    pub solution_qualities: Vec<f64>,
    /// Convergence rates
    pub convergence_rates: Vec<f64>,
    /// Statistical analysis
    pub statistical_analysis: StatisticalAnalysis,
}

/// Statistical analysis results
#[derive(Debug, Clone)]
pub struct StatisticalAnalysis {
    /// Mean performance
    pub mean_performance: f64,
    /// Standard deviation
    pub std_deviation: f64,
    /// Confidence intervals
    pub confidence_intervals: (f64, f64),
    /// Statistical significance
    pub p_value: f64,
    /// Effect size
    pub effect_size: f64,
}

impl QuantumInspiredFramework {
    /// Create a new quantum-inspired framework
    pub fn new(config: QuantumInspiredConfig) -> Result<Self> {
        let state = QuantumInspiredState {
            variables: Array1::zeros(config.num_variables),
            objective_value: f64::INFINITY,
            iteration: 0,
            best_solution: Array1::zeros(config.num_variables),
            best_objective: f64::INFINITY,
            convergence_history: Vec::new(),
            runtime_stats: RuntimeStats::default(),
        };

        // Note: For seeded RNG we would need to restructure to store the RNG
        // For now, just use thread_rng() and ignore the seed
        let rng = thread_rng();

        Ok(Self {
            config,
            state,
            backend: None,
            stats: QuantumInspiredStats::default(),
            rng: Arc::new(Mutex::new(rng)),
        })
    }

    /// Set `SciRS2` backend for numerical operations
    pub fn set_backend(&mut self, backend: SciRS2Backend) {
        self.backend = Some(backend);
    }

    /// Run optimization algorithm
    pub fn optimize(&mut self) -> Result<OptimizationResult> {
        let start_time = std::time::Instant::now();

        match self.config.optimization_config.algorithm_type {
            OptimizationAlgorithm::QuantumGeneticAlgorithm => self.quantum_genetic_algorithm(),
            OptimizationAlgorithm::QuantumParticleSwarm => {
                self.quantum_particle_swarm_optimization()
            }
            OptimizationAlgorithm::QuantumSimulatedAnnealing => self.quantum_simulated_annealing(),
            OptimizationAlgorithm::QuantumDifferentialEvolution => {
                self.quantum_differential_evolution()
            }
            OptimizationAlgorithm::ClassicalQAOA => self.classical_qaoa_simulation(),
            OptimizationAlgorithm::ClassicalVQE => self.classical_vqe_simulation(),
            OptimizationAlgorithm::QuantumAntColony => self.quantum_ant_colony_optimization(),
            OptimizationAlgorithm::QuantumHarmonySearch => self.quantum_harmony_search(),
        }
    }

    /// Quantum-inspired genetic algorithm
    fn quantum_genetic_algorithm(&mut self) -> Result<OptimizationResult> {
        let pop_size = self.config.algorithm_config.population_size;
        let num_vars = self.config.num_variables;
        let max_iterations = self.config.algorithm_config.max_iterations;

        // Initialize population with quantum-inspired superposition
        let mut population = self.initialize_quantum_population(pop_size, num_vars)?;
        let mut fitness_values = vec![0.0; pop_size];

        // Evaluate initial population
        for (i, individual) in population.iter().enumerate() {
            fitness_values[i] = self.evaluate_objective(individual)?;
            self.state.runtime_stats.function_evaluations += 1;
        }

        for generation in 0..max_iterations {
            self.state.iteration = generation;

            // Selection using quantum-inspired interference
            let parents = self.quantum_selection(&population, &fitness_values)?;

            // Quantum-inspired crossover
            let mut offspring = self.quantum_crossover(&parents)?;

            // Quantum-inspired mutation
            self.quantum_mutation(&mut offspring)?;

            // Evaluate offspring
            let mut offspring_fitness = vec![0.0; offspring.len()];
            for (i, individual) in offspring.iter().enumerate() {
                offspring_fitness[i] = self.evaluate_objective(individual)?;
                self.state.runtime_stats.function_evaluations += 1;
            }

            // Quantum-inspired replacement using entanglement
            self.quantum_replacement(
                &mut population,
                &mut fitness_values,
                offspring,
                offspring_fitness,
            )?;

            // Update best solution
            let best_idx = fitness_values
                .iter()
                .enumerate()
                .min_by(|(_, a), (_, b)| a.partial_cmp(b).unwrap_or(std::cmp::Ordering::Equal))
                .map(|(idx, _)| idx)
                .unwrap_or(0);

            if fitness_values[best_idx] < self.state.best_objective {
                self.state.best_objective = fitness_values[best_idx];
                self.state.best_solution = population[best_idx].clone();
            }

            self.state
                .convergence_history
                .push(self.state.best_objective);

            // Check convergence
            if self.check_convergence()? {
                break;
            }
        }

        Ok(OptimizationResult {
            solution: self.state.best_solution.clone(),
            objective_value: self.state.best_objective,
            iterations: self.state.iteration,
            converged: self.check_convergence()?,
            runtime_stats: self.state.runtime_stats.clone(),
            metadata: HashMap::new(),
        })
    }

    /// Initialize quantum-inspired population with superposition
    fn initialize_quantum_population(
        &self,
        pop_size: usize,
        num_vars: usize,
    ) -> Result<Vec<Array1<f64>>> {
        let mut population = Vec::with_capacity(pop_size);
        let bounds = &self.config.optimization_config.bounds;
        let quantum_params = &self.config.algorithm_config.quantum_parameters;

        for _ in 0..pop_size {
            let mut individual = Array1::zeros(num_vars);

            for j in 0..num_vars {
                let (min_bound, max_bound) = if j < bounds.len() {
                    bounds[j]
                } else {
                    (-1.0, 1.0)
                };

                // Quantum-inspired initialization with superposition
                let mut rng = self.rng.lock().expect("RNG lock poisoned");
                let base_value = rng.gen::<f64>().mul_add(max_bound - min_bound, min_bound);

                // Add quantum superposition effect
                let superposition_noise = (rng.gen::<f64>() - 0.5)
                    * quantum_params.superposition_strength
                    * (max_bound - min_bound);

                individual[j] = (base_value + superposition_noise).clamp(min_bound, max_bound);
            }

            population.push(individual);
        }

        Ok(population)
    }

    /// Quantum-inspired selection using interference
    fn quantum_selection(
        &self,
        population: &[Array1<f64>],
        fitness: &[f64],
    ) -> Result<Vec<Array1<f64>>> {
        let pop_size = population.len();
        let elite_size = (self.config.algorithm_config.elite_ratio * pop_size as f64) as usize;
        let quantum_params = &self.config.algorithm_config.quantum_parameters;

        // Elite selection
        let mut indexed_fitness: Vec<(usize, f64)> =
            fitness.iter().enumerate().map(|(i, &f)| (i, f)).collect();
        indexed_fitness.sort_by(|a, b| a.1.partial_cmp(&b.1).unwrap_or(std::cmp::Ordering::Equal));

        let mut parents = Vec::new();

        // Add elite individuals
        for i in 0..elite_size {
            parents.push(population[indexed_fitness[i].0].clone());
        }

        // Quantum-inspired tournament selection for remaining parents
        let mut rng = self.rng.lock().expect("RNG lock poisoned");
        while parents.len() < pop_size {
            let tournament_size = 3;
            let mut tournament_indices = Vec::new();

            for _ in 0..tournament_size {
                tournament_indices.push(rng.gen_range(0..pop_size));
            }

            // Quantum interference-based selection probability
            let mut selection_probabilities = vec![0.0; tournament_size];
            for (i, &idx) in tournament_indices.iter().enumerate() {
                let normalized_fitness = 1.0 / (1.0 + fitness[idx]);
                let interference_factor = (quantum_params.interference_strength
                    * (i as f64 * PI / tournament_size as f64))
                    .cos()
                    .abs();
                selection_probabilities[i] = normalized_fitness * (1.0 + interference_factor);
            }

            // Normalize probabilities
            let sum: f64 = selection_probabilities.iter().sum();
            for prob in &mut selection_probabilities {
                *prob /= sum;
            }

            // Select based on quantum probabilities
            let mut cumulative = 0.0;
            let random_val = rng.gen::<f64>();
            for (i, &prob) in selection_probabilities.iter().enumerate() {
                cumulative += prob;
                if random_val <= cumulative {
                    parents.push(population[tournament_indices[i]].clone());
                    break;
                }
            }
        }

        Ok(parents)
    }

    /// Quantum-inspired crossover with entanglement
    fn quantum_crossover(&self, parents: &[Array1<f64>]) -> Result<Vec<Array1<f64>>> {
        let mut offspring = Vec::new();
        let crossover_rate = self.config.algorithm_config.crossover_rate;
        let quantum_params = &self.config.algorithm_config.quantum_parameters;
        let mut rng = self.rng.lock().expect("RNG lock poisoned");

        for i in (0..parents.len()).step_by(2) {
            if i + 1 < parents.len() && rng.gen::<f64>() < crossover_rate {
                let parent1 = &parents[i];
                let parent2 = &parents[i + 1];

                let mut child1 = parent1.clone();
                let mut child2 = parent2.clone();

                // Quantum-inspired crossover with entanglement
                for j in 0..parent1.len() {
                    let entanglement_strength = quantum_params.entanglement_strength;
                    let alpha = rng.gen::<f64>();

                    // Quantum entanglement-based recombination
                    let entangled_val1 = alpha.mul_add(parent1[j], (1.0 - alpha) * parent2[j]);
                    let entangled_val2 = (1.0 - alpha).mul_add(parent1[j], alpha * parent2[j]);

                    // Add quantum entanglement correlation
                    let correlation = entanglement_strength
                        * (parent1[j] - parent2[j]).abs()
                        * (rng.gen::<f64>() - 0.5);

                    child1[j] = entangled_val1 + correlation;
                    child2[j] = entangled_val2 - correlation;
                }

                offspring.push(child1);
                offspring.push(child2);
            } else {
                offspring.push(parents[i].clone());
                if i + 1 < parents.len() {
                    offspring.push(parents[i + 1].clone());
                }
            }
        }

        Ok(offspring)
    }

    /// Quantum-inspired mutation with tunneling
    fn quantum_mutation(&mut self, population: &mut [Array1<f64>]) -> Result<()> {
        let mutation_rate = self.config.algorithm_config.mutation_rate;
        let quantum_params = &self.config.algorithm_config.quantum_parameters;
        let bounds = &self.config.optimization_config.bounds;
        let mut rng = self.rng.lock().expect("RNG lock poisoned");

        for individual in population.iter_mut() {
            for j in 0..individual.len() {
                if rng.gen::<f64>() < mutation_rate {
                    let (min_bound, max_bound) = if j < bounds.len() {
                        bounds[j]
                    } else {
                        (-1.0, 1.0)
                    };

                    // Quantum tunneling-inspired mutation
                    let current_val = individual[j];
                    let range = max_bound - min_bound;

                    // Standard mutation
                    let gaussian_mutation =
                        rng.gen::<f64>() * 0.1 * range * (rng.gen::<f64>() - 0.5);

                    // Quantum tunneling effect
                    let tunneling_prob = quantum_params.tunneling_probability;
                    let tunneling_mutation = if rng.gen::<f64>() < tunneling_prob {
                        // Large jump to explore distant regions
                        (rng.gen::<f64>() - 0.5) * range
                    } else {
                        0.0
                    };

                    individual[j] = (current_val + gaussian_mutation + tunneling_mutation)
                        .clamp(min_bound, max_bound);
                }
            }
        }

        self.state.runtime_stats.quantum_operations += population.len();
        Ok(())
    }

    /// Quantum-inspired replacement using quantum measurement
    fn quantum_replacement(
        &self,
        population: &mut Vec<Array1<f64>>,
        fitness: &mut Vec<f64>,
        offspring: Vec<Array1<f64>>,
        offspring_fitness: Vec<f64>,
    ) -> Result<()> {
        let quantum_params = &self.config.algorithm_config.quantum_parameters;
        let measurement_prob = quantum_params.measurement_probability;
        let mut rng = self.rng.lock().expect("RNG lock poisoned");

        // Combine populations
        let mut combined_population = population.clone();
        combined_population.extend(offspring);

        let mut combined_fitness = fitness.clone();
        combined_fitness.extend(offspring_fitness);

        // Quantum measurement-based selection
        let pop_size = population.len();
        let mut new_population = Vec::with_capacity(pop_size);
        let mut new_fitness = Vec::with_capacity(pop_size);

        // Sort combined population by fitness
        let mut indexed_combined: Vec<(usize, f64)> = combined_fitness
            .iter()
            .enumerate()
            .map(|(i, &f)| (i, f))
            .collect();
        indexed_combined.sort_by(|a, b| a.1.partial_cmp(&b.1).unwrap_or(std::cmp::Ordering::Equal));

        // Select top individuals with quantum measurement probability
        for i in 0..pop_size {
            if i < indexed_combined.len() {
                let idx = indexed_combined[i].0;

                // Quantum measurement-based acceptance
                let acceptance_prob = if rng.gen::<f64>() < measurement_prob {
                    // Quantum measurement collapses to definite state
                    1.0
                } else {
                    // Classical selection probability
                    1.0 / (1.0 + (i as f64 / pop_size as f64))
                };

                if rng.gen::<f64>() < acceptance_prob {
                    new_population.push(combined_population[idx].clone());
                    new_fitness.push(combined_fitness[idx]);
                }
            }
        }

        // Fill remaining slots with best individuals
        while new_population.len() < pop_size {
            for i in 0..indexed_combined.len() {
                if new_population.len() >= pop_size {
                    break;
                }
                let idx = indexed_combined[i].0;
                if !new_population.iter().any(|x| {
                    x.iter()
                        .zip(combined_population[idx].iter())
                        .all(|(a, b)| (a - b).abs() < 1e-10)
                }) {
                    new_population.push(combined_population[idx].clone());
                    new_fitness.push(combined_fitness[idx]);
                }
            }
        }

        // Truncate to exact population size
        new_population.truncate(pop_size);
        new_fitness.truncate(pop_size);

        *population = new_population;
        *fitness = new_fitness;

        Ok(())
    }

    /// Quantum particle swarm optimization
    fn quantum_particle_swarm_optimization(&mut self) -> Result<OptimizationResult> {
        let pop_size = self.config.algorithm_config.population_size;
        let num_vars = self.config.num_variables;
        let max_iterations = self.config.algorithm_config.max_iterations;
        let quantum_params = self.config.algorithm_config.quantum_parameters.clone();
        let bounds = self.config.optimization_config.bounds.clone();

        // Initialize particles
        let mut particles = self.initialize_quantum_population(pop_size, num_vars)?;
        let mut velocities: Vec<Array1<f64>> = vec![Array1::zeros(num_vars); pop_size];
        let mut personal_best = particles.clone();
        let mut personal_best_fitness = vec![f64::INFINITY; pop_size];
        let mut global_best = Array1::zeros(num_vars);
        let mut global_best_fitness = f64::INFINITY;

        // Evaluate initial particles
        for (i, particle) in particles.iter().enumerate() {
            let fitness = self.evaluate_objective(particle)?;
            personal_best_fitness[i] = fitness;

            if fitness < global_best_fitness {
                global_best_fitness = fitness;
                global_best = particle.clone();
            }

            self.state.runtime_stats.function_evaluations += 1;
        }

        // PSO parameters
        let w = 0.7; // Inertia weight
        let c1 = 2.0; // Cognitive parameter
        let c2 = 2.0; // Social parameter

        for iteration in 0..max_iterations {
            self.state.iteration = iteration;

            for i in 0..pop_size {
                let mut rng = self.rng.lock().expect("RNG lock poisoned");

                // Update velocity with quantum-inspired terms
                for j in 0..num_vars {
                    let r1 = rng.gen::<f64>();
                    let r2 = rng.gen::<f64>();

                    // Classical PSO velocity update
                    let cognitive_term = c1 * r1 * (personal_best[i][j] - particles[i][j]);
                    let social_term = c2 * r2 * (global_best[j] - particles[i][j]);

                    // Quantum-inspired terms
                    let quantum_fluctuation =
                        quantum_params.superposition_strength * (rng.gen::<f64>() - 0.5);
                    let quantum_tunneling =
                        if rng.gen::<f64>() < quantum_params.tunneling_probability {
                            (rng.gen::<f64>() - 0.5) * 2.0
                        } else {
                            0.0
                        };

                    velocities[i][j] = w * velocities[i][j]
                        + cognitive_term
                        + social_term
                        + quantum_fluctuation
                        + quantum_tunneling;
                }

                // Update position
                for j in 0..num_vars {
                    particles[i][j] += velocities[i][j];

                    // Apply bounds
                    let (min_bound, max_bound) = if j < bounds.len() {
                        bounds[j]
                    } else {
                        (-10.0, 10.0)
                    };
                    particles[i][j] = particles[i][j].clamp(min_bound, max_bound);
                }

                // Drop RNG lock before calling evaluate_objective
                drop(rng);

                // Evaluate new position
                let fitness = self.evaluate_objective(&particles[i])?;
                self.state.runtime_stats.function_evaluations += 1;

                // Update personal best
                if fitness < personal_best_fitness[i] {
                    personal_best_fitness[i] = fitness;
                    personal_best[i] = particles[i].clone();
                }

                // Update global best
                if fitness < global_best_fitness {
                    global_best_fitness = fitness;
                    global_best = particles[i].clone();
                }
            }

            self.state.best_objective = global_best_fitness;
            self.state.best_solution = global_best.clone();
            self.state.convergence_history.push(global_best_fitness);

            // Check convergence
            if self.check_convergence()? {
                break;
            }
        }

        Ok(OptimizationResult {
            solution: global_best,
            objective_value: global_best_fitness,
            iterations: self.state.iteration,
            converged: self.check_convergence()?,
            runtime_stats: self.state.runtime_stats.clone(),
            metadata: HashMap::new(),
        })
    }

    /// Quantum-inspired simulated annealing
    fn quantum_simulated_annealing(&mut self) -> Result<OptimizationResult> {
        let max_iterations = self.config.algorithm_config.max_iterations;
        let temperature_schedule = self.config.algorithm_config.temperature_schedule;
        let quantum_parameters = self.config.algorithm_config.quantum_parameters.clone();
        let bounds = self.config.optimization_config.bounds.clone();
        let num_vars = self.config.num_variables;

        // Initialize current solution randomly
        let mut current_solution = Array1::zeros(num_vars);
        let mut rng = self.rng.lock().expect("RNG lock poisoned");

        for i in 0..num_vars {
            let (min_bound, max_bound) = if i < bounds.len() {
                bounds[i]
            } else {
                (-10.0, 10.0)
            };
            current_solution[i] = rng.gen::<f64>().mul_add(max_bound - min_bound, min_bound);
        }
        drop(rng);

        let mut current_energy = self.evaluate_objective(&current_solution)?;
        let mut best_solution = current_solution.clone();
        let mut best_energy = current_energy;

        self.state.runtime_stats.function_evaluations += 1;

        // Initial temperature
        let initial_temp: f64 = 100.0;
        let final_temp: f64 = 0.01;

        for iteration in 0..max_iterations {
            self.state.iteration = iteration;

            // Calculate temperature based on schedule
            let temp = match temperature_schedule {
                TemperatureSchedule::Exponential => {
                    initial_temp
                        * (final_temp / initial_temp).powf(iteration as f64 / max_iterations as f64)
                }
                TemperatureSchedule::Linear => (initial_temp - final_temp)
                    .mul_add(-(iteration as f64 / max_iterations as f64), initial_temp),
                TemperatureSchedule::Logarithmic => initial_temp / (1.0 + (iteration as f64).ln()),
                TemperatureSchedule::QuantumAdiabatic => {
                    // Quantum adiabatic schedule
                    let s = iteration as f64 / max_iterations as f64;
                    initial_temp.mul_add(1.0 - s, final_temp * s * (1.0 - (1.0 - s).powi(3)))
                }
                TemperatureSchedule::Custom => initial_temp * 0.95_f64.powi(iteration as i32),
            };

            // Generate neighbor solution with quantum-inspired moves
            let mut neighbor = current_solution.clone();
            let quantum_params = &quantum_parameters;
            let mut rng = self.rng.lock().expect("RNG lock poisoned");

            for i in 0..num_vars {
                if rng.gen::<f64>() < 0.5 {
                    let (min_bound, max_bound) = if i < bounds.len() {
                        bounds[i]
                    } else {
                        (-10.0, 10.0)
                    };

                    // Quantum-inspired neighbor generation
                    let step_size = temp / initial_temp;
                    let gaussian_step =
                        rng.gen::<f64>() * step_size * (max_bound - min_bound) * 0.1;

                    // Quantum tunneling move
                    let tunneling_move = if rng.gen::<f64>() < quantum_params.tunneling_probability
                    {
                        (rng.gen::<f64>() - 0.5) * (max_bound - min_bound) * 0.5
                    } else {
                        0.0
                    };

                    neighbor[i] = (current_solution[i] + gaussian_step + tunneling_move)
                        .clamp(min_bound, max_bound);
                }
            }
            drop(rng);

            let neighbor_energy = self.evaluate_objective(&neighbor)?;
            self.state.runtime_stats.function_evaluations += 1;

            // Quantum-inspired acceptance probability
            let delta_energy = neighbor_energy - current_energy;
            let acceptance_prob = if delta_energy < 0.0 {
                1.0
            } else {
                // Classical Boltzmann factor with quantum corrections
                let boltzmann_factor = (-delta_energy / temp).exp();

                // Quantum interference correction
                let quantum_correction = quantum_params.interference_strength
                    * (2.0 * PI * iteration as f64 / max_iterations as f64).cos()
                    * 0.1;

                (boltzmann_factor + quantum_correction).clamp(0.0, 1.0)
            };

            // Accept or reject
            let mut rng = self.rng.lock().expect("RNG lock poisoned");
            if rng.gen::<f64>() < acceptance_prob {
                current_solution = neighbor;
                current_energy = neighbor_energy;

                // Update best solution
                if current_energy < best_energy {
                    best_solution = current_solution.clone();
                    best_energy = current_energy;
                }
            }
            drop(rng);

            self.state.best_objective = best_energy;
            self.state.best_solution = best_solution.clone();
            self.state.convergence_history.push(best_energy);

            // Check convergence
            if temp < final_temp || self.check_convergence()? {
                break;
            }
        }

        Ok(OptimizationResult {
            solution: best_solution,
            objective_value: best_energy,
            iterations: self.state.iteration,
            converged: self.check_convergence()?,
            runtime_stats: self.state.runtime_stats.clone(),
            metadata: HashMap::new(),
        })
    }

    /// Quantum differential evolution
    fn quantum_differential_evolution(&self) -> Result<OptimizationResult> {
        // Implement quantum-inspired differential evolution
        // This is a placeholder for the full implementation
        Err(SimulatorError::NotImplemented(
            "Quantum Differential Evolution not yet implemented".to_string(),
        ))
    }

    /// Classical QAOA simulation
    fn classical_qaoa_simulation(&self) -> Result<OptimizationResult> {
        // Implement classical simulation of QAOA
        // This is a placeholder for the full implementation
        Err(SimulatorError::NotImplemented(
            "Classical QAOA simulation not yet implemented".to_string(),
        ))
    }

    /// Classical VQE simulation
    fn classical_vqe_simulation(&self) -> Result<OptimizationResult> {
        // Implement classical simulation of VQE
        // This is a placeholder for the full implementation
        Err(SimulatorError::NotImplemented(
            "Classical VQE simulation not yet implemented".to_string(),
        ))
    }

    /// Quantum ant colony optimization
    fn quantum_ant_colony_optimization(&self) -> Result<OptimizationResult> {
        // Implement quantum-inspired ant colony optimization
        // This is a placeholder for the full implementation
        Err(SimulatorError::NotImplemented(
            "Quantum Ant Colony Optimization not yet implemented".to_string(),
        ))
    }

    /// Quantum harmony search
    fn quantum_harmony_search(&self) -> Result<OptimizationResult> {
        // Implement quantum-inspired harmony search
        // This is a placeholder for the full implementation
        Err(SimulatorError::NotImplemented(
            "Quantum Harmony Search not yet implemented".to_string(),
        ))
    }

    /// Evaluate objective function
    fn evaluate_objective(&self, solution: &Array1<f64>) -> Result<f64> {
        let result = match self.config.optimization_config.objective_function {
            ObjectiveFunction::Quadratic => solution.iter().map(|&x| x * x).sum(),
            ObjectiveFunction::Rastrigin => {
                let n = solution.len() as f64;
                let a = 10.0;
                a * n
                    + solution
                        .iter()
                        .map(|&x| x.mul_add(x, -(a * (2.0 * PI * x).cos())))
                        .sum::<f64>()
            }
            ObjectiveFunction::Rosenbrock => {
                if solution.len() < 2 {
                    return Ok(0.0);
                }
                let mut result = 0.0;
                for i in 0..solution.len() - 1 {
                    let x = solution[i];
                    let y = solution[i + 1];
                    result += (1.0 - x).mul_add(1.0 - x, 100.0 * x.mul_add(-x, y).powi(2));
                }
                result
            }
            ObjectiveFunction::Ackley => {
                let n = solution.len() as f64;
                let a: f64 = 20.0;
                let b: f64 = 0.2;
                let c: f64 = 2.0 * PI;

                let sum1 = solution.iter().map(|&x| x * x).sum::<f64>() / n;
                let sum2 = solution.iter().map(|&x| (c * x).cos()).sum::<f64>() / n;

                (-a).mul_add((-b * sum1.sqrt()).exp(), -sum2.exp()) + a + std::f64::consts::E
            }
            ObjectiveFunction::Sphere => solution.iter().map(|&x| x * x).sum(),
            ObjectiveFunction::Griewank => {
                let sum_sq = solution.iter().map(|&x| x * x).sum::<f64>() / 4000.0;
                let prod_cos = solution
                    .iter()
                    .enumerate()
                    .map(|(i, &x)| (x / ((i + 1) as f64).sqrt()).cos())
                    .product::<f64>();
                1.0 + sum_sq - prod_cos
            }
            ObjectiveFunction::Custom => {
                // Custom objective function - placeholder
                solution.iter().map(|&x| x * x).sum()
            }
        };

        Ok(result)
    }

    /// Check convergence
    fn check_convergence(&self) -> Result<bool> {
        if self.state.convergence_history.len() < 2 {
            return Ok(false);
        }

        let tolerance = self.config.algorithm_config.tolerance;
        let recent_improvements = &self.state.convergence_history
            [self.state.convergence_history.len().saturating_sub(10)..];

        if recent_improvements.len() < 2 {
            return Ok(false);
        }

        // Check for convergence by comparing consecutive recent values
        // Safety: length check above guarantees at least 2 elements
        let last_value = recent_improvements
            .last()
            .expect("recent_improvements has at least 2 elements");
        let second_last_value = recent_improvements[recent_improvements.len() - 2];
        let change = (last_value - second_last_value).abs();
        Ok(change < tolerance)
    }

    /// Train machine learning model
    pub fn train_ml_model(
        &mut self,
        training_data: &[(Array1<f64>, Array1<f64>)],
    ) -> Result<MLTrainingResult> {
        // Implement quantum-inspired machine learning training
        // This is a placeholder for the full implementation
        Err(SimulatorError::NotImplemented(
            "ML training not yet implemented".to_string(),
        ))
    }

    /// Perform sampling
    pub fn sample(&mut self) -> Result<SamplingResult> {
        // Implement quantum-inspired sampling
        // This is a placeholder for the full implementation
        Err(SimulatorError::NotImplemented(
            "Sampling not yet implemented".to_string(),
        ))
    }

    /// Solve linear algebra problem
    pub fn solve_linear_algebra(
        &mut self,
        matrix: &Array2<Complex64>,
        rhs: &Array1<Complex64>,
    ) -> Result<LinalgResult> {
        // Implement quantum-inspired linear algebra
        // This is a placeholder for the full implementation
        Err(SimulatorError::NotImplemented(
            "Linear algebra solving not yet implemented".to_string(),
        ))
    }

    /// Solve graph problem
    pub fn solve_graph_problem(&mut self, adjacency_matrix: &Array2<f64>) -> Result<GraphResult> {
        // Implement quantum-inspired graph algorithms
        // This is a placeholder for the full implementation
        Err(SimulatorError::NotImplemented(
            "Graph algorithms not yet implemented".to_string(),
        ))
    }

    /// Get current statistics
    #[must_use]
    pub const fn get_stats(&self) -> &QuantumInspiredStats {
        &self.stats
    }

    /// Get current state
    #[must_use]
    pub const fn get_state(&self) -> &QuantumInspiredState {
        &self.state
    }

    /// Get mutable state access
    pub const fn get_state_mut(&mut self) -> &mut QuantumInspiredState {
        &mut self.state
    }

    /// Evaluate objective function (public version)
    pub fn evaluate_objective_public(&mut self, solution: &Array1<f64>) -> Result<f64> {
        self.evaluate_objective(solution)
    }

    /// Check convergence (public version)
    pub fn check_convergence_public(&self) -> Result<bool> {
        self.check_convergence()
    }

    /// Reset framework state
    pub fn reset(&mut self) {
        self.state = QuantumInspiredState {
            variables: Array1::zeros(self.config.num_variables),
            objective_value: f64::INFINITY,
            iteration: 0,
            best_solution: Array1::zeros(self.config.num_variables),
            best_objective: f64::INFINITY,
            convergence_history: Vec::new(),
            runtime_stats: RuntimeStats::default(),
        };

        self.stats = QuantumInspiredStats::default();
    }
}

/// Utility functions for quantum-inspired algorithms
pub struct QuantumInspiredUtils;

impl QuantumInspiredUtils {
    /// Generate synthetic optimization problems
    #[must_use]
    pub fn generate_optimization_problem(
        problem_type: ObjectiveFunction,
        dimension: usize,
        bounds: (f64, f64),
    ) -> (ObjectiveFunction, Vec<(f64, f64)>, Array1<f64>) {
        let bounds_vec = vec![bounds; dimension];
        let optimal_solution = Array1::zeros(dimension); // Placeholder

        (problem_type, bounds_vec, optimal_solution)
    }

    /// Analyze convergence behavior
    #[must_use]
    pub fn analyze_convergence(convergence_history: &[f64]) -> ConvergenceAnalysis {
        if convergence_history.len() < 2 {
            return ConvergenceAnalysis::default();
        }

        // Safety: length check above guarantees at least 2 elements
        let final_value = *convergence_history
            .last()
            .expect("convergence_history has at least 2 elements");
        let initial_value = convergence_history[0];
        let improvement = initial_value - final_value;

        // Estimate convergence rate
        let convergence_rate = if improvement > 0.0 {
            improvement / convergence_history.len() as f64
        } else {
            0.0
        };

        // Find convergence point by checking for stable windows
        let mut convergence_iteration = convergence_history.len();

        // Check if we have enough data for window analysis
        if convergence_history.len() >= 5 {
            for (i, window) in convergence_history.windows(5).enumerate() {
                let mean = window.iter().sum::<f64>() / window.len() as f64;
                let variance =
                    window.iter().map(|&x| (x - mean).powi(2)).sum::<f64>() / window.len() as f64;

                // Use adaptive tolerance based on the magnitude of values
                let adaptive_tolerance = (mean.abs() * 0.1).max(0.1);

                if variance < adaptive_tolerance {
                    convergence_iteration = i + 5;
                    break;
                }
            }
        }

        ConvergenceAnalysis {
            convergence_rate,
            iterations_to_convergence: convergence_iteration,
            final_gradient_norm: 0.0, // Placeholder
            converged: convergence_iteration < convergence_history.len(),
            convergence_criterion: "variance".to_string(),
        }
    }

    /// Compare algorithm performances
    #[must_use]
    pub fn compare_algorithms(
        results1: &[OptimizationResult],
        results2: &[OptimizationResult],
    ) -> ComparisonStats {
        let perf1 = results1
            .iter()
            .map(|r| r.objective_value)
            .collect::<Vec<_>>();
        let perf2 = results2
            .iter()
            .map(|r| r.objective_value)
            .collect::<Vec<_>>();

        let mean1 = perf1.iter().sum::<f64>() / perf1.len() as f64;
        let mean2 = perf2.iter().sum::<f64>() / perf2.len() as f64;

        let speedup = if mean2 > 0.0 { mean2 / mean1 } else { 1.0 };

        ComparisonStats {
            quantum_inspired_performance: mean1,
            classical_performance: mean2,
            speedup_factor: speedup,
            solution_quality_ratio: mean1 / mean2,
            convergence_speed_ratio: 1.0, // Placeholder
        }
    }

    /// Estimate quantum advantage
    #[must_use]
    pub fn estimate_quantum_advantage(
        problem_size: usize,
        algorithm_type: OptimizationAlgorithm,
    ) -> QuantumAdvantageMetrics {
        let theoretical_speedup = match algorithm_type {
            OptimizationAlgorithm::QuantumGeneticAlgorithm => (problem_size as f64).sqrt(),
            OptimizationAlgorithm::QuantumParticleSwarm => (problem_size as f64).log2(),
            OptimizationAlgorithm::ClassicalQAOA => (problem_size as f64 / 2.0).exp2(),
            _ => 1.0,
        };

        QuantumAdvantageMetrics {
            theoretical_speedup,
            practical_advantage: theoretical_speedup * 0.5, // Conservative estimate
            complexity_class: "BQP".to_string(),
            quantum_resource_requirements: problem_size * 10,
            classical_resource_requirements: problem_size * problem_size,
        }
    }
}

/// Benchmark quantum-inspired algorithms
pub fn benchmark_quantum_inspired_algorithms(
    config: &QuantumInspiredConfig,
) -> Result<BenchmarkingResults> {
    let mut framework = QuantumInspiredFramework::new(config.clone())?;
    let num_runs = config.benchmarking_config.num_runs;

    let mut execution_times = Vec::new();
    let mut solution_qualities = Vec::new();
    let mut convergence_rates = Vec::new();
    let mut memory_usage = Vec::new();

    for _ in 0..num_runs {
        let start_time = std::time::Instant::now();
        let result = framework.optimize()?;
        let execution_time = start_time.elapsed().as_secs_f64();

        execution_times.push(execution_time);
        solution_qualities.push(result.objective_value);

        let convergence_analysis =
            QuantumInspiredUtils::analyze_convergence(&framework.state.convergence_history);
        convergence_rates.push(convergence_analysis.convergence_rate);
        memory_usage.push(framework.state.runtime_stats.memory_usage);

        framework.reset();
    }

    // Statistical analysis
    let mean_performance = solution_qualities.iter().sum::<f64>() / solution_qualities.len() as f64;
    let variance = solution_qualities
        .iter()
        .map(|&x| (x - mean_performance).powi(2))
        .sum::<f64>()
        / solution_qualities.len() as f64;
    let std_deviation = variance.sqrt();

    let statistical_analysis = StatisticalAnalysis {
        mean_performance,
        std_deviation,
        confidence_intervals: (
            1.96f64.mul_add(-std_deviation, mean_performance),
            1.96f64.mul_add(std_deviation, mean_performance),
        ),
        p_value: 0.05, // Placeholder
        effect_size: mean_performance / std_deviation,
    };

    Ok(BenchmarkingResults {
        performance_metrics: solution_qualities.clone(),
        execution_times,
        memory_usage,
        solution_qualities,
        convergence_rates,
        statistical_analysis,
    })
}

#[cfg(test)]
mod tests {
    use super::*;

    #[test]
    fn test_quantum_inspired_config() {
        let config = QuantumInspiredConfig::default();
        assert_eq!(config.num_variables, 16);
        assert_eq!(config.algorithm_category, AlgorithmCategory::Optimization);
        assert!(config.enable_quantum_heuristics);
    }

    #[test]
    fn test_framework_creation() {
        let config = QuantumInspiredConfig::default();
        let framework = QuantumInspiredFramework::new(config);
        assert!(framework.is_ok());
    }

    #[test]
    fn test_objective_functions() {
        let config = QuantumInspiredConfig::default();
        let mut framework =
            QuantumInspiredFramework::new(config).expect("Failed to create framework");

        let solution = Array1::from(vec![1.0, 2.0, 3.0, 4.0]);
        let result = framework.evaluate_objective(&solution);
        assert!(result.is_ok());
        assert!(result.expect("Failed to evaluate objective") > 0.0);
    }

    #[test]
    fn test_quantum_genetic_algorithm() {
        let mut config = QuantumInspiredConfig::default();
        config.algorithm_config.max_iterations = 10; // Short test
        config.num_variables = 4;

        let mut framework =
            QuantumInspiredFramework::new(config).expect("Failed to create framework");
        let result = framework.optimize();
        assert!(result.is_ok());

        let opt_result = result.expect("Failed to optimize");
        assert!(opt_result.iterations <= 10);
        assert!(opt_result.objective_value.is_finite());
    }

    #[test]
    fn test_quantum_particle_swarm() {
        let mut config = QuantumInspiredConfig::default();
        config.optimization_config.algorithm_type = OptimizationAlgorithm::QuantumParticleSwarm;
        config.algorithm_config.max_iterations = 10;
        config.num_variables = 4;

        let mut framework =
            QuantumInspiredFramework::new(config).expect("Failed to create framework");
        let result = framework.optimize();
        assert!(result.is_ok());
    }

    #[test]
    fn test_quantum_simulated_annealing() {
        let mut config = QuantumInspiredConfig::default();
        config.optimization_config.algorithm_type =
            OptimizationAlgorithm::QuantumSimulatedAnnealing;
        config.algorithm_config.max_iterations = 10;
        config.num_variables = 4;

        let mut framework =
            QuantumInspiredFramework::new(config).expect("Failed to create framework");
        let result = framework.optimize();
        assert!(result.is_ok());
    }

    #[test]
    fn test_convergence_analysis() {
        let history = vec![100.0, 90.0, 80.0, 70.0, 65.0, 64.9, 64.8, 64.8, 64.8];
        let analysis = QuantumInspiredUtils::analyze_convergence(&history);
        assert!(analysis.convergence_rate > 0.0);
        assert!(analysis.converged);
    }

    #[test]
    fn test_quantum_parameters() {
        let params = QuantumParameters::default();
        assert!(params.superposition_strength > 0.0);
        assert!(params.entanglement_strength > 0.0);
        assert!(params.tunneling_probability > 0.0);
    }

    #[test]
    fn test_benchmarking() {
        let mut config = QuantumInspiredConfig::default();
        config.algorithm_config.max_iterations = 5;
        config.benchmarking_config.num_runs = 3;
        config.num_variables = 4;

        let result = benchmark_quantum_inspired_algorithms(&config);
        assert!(result.is_ok());

        let benchmark = result.expect("Failed to benchmark");
        assert_eq!(benchmark.execution_times.len(), 3);
        assert_eq!(benchmark.solution_qualities.len(), 3);
    }
}