quantrs2_core/

scirs2_equivalence_checker.rs

//! Advanced Quantum Circuit Equivalence Checker with Enhanced SciRS2 Numerical Tolerance
//!
//! This module provides state-of-the-art quantum circuit equivalence checking
//! using advanced SciRS2 numerical analysis capabilities, including SVD-based
//! comparison, spectral analysis, and sophisticated tolerance mechanisms.

use crate::error::QuantRS2Error;
use crate::gate_translation::GateType;
use scirs2_core::Complex64;
// use scirs2_core::parallel_ops::*;
use crate::parallel_ops_stubs::*;
// use scirs2_core::memory::BufferPool;
use crate::buffer_pool::BufferPool;
use scirs2_core::ndarray::{Array1, Array2, ArrayView2};
// For complex matrices, use ndarray-linalg traits via scirs2_core (SciRS2 POLICY)
use scirs2_core::ndarray::ndarray_linalg::{Eigh, Norm, SVD, UPLO};
use serde::{Deserialize, Serialize};
use std::collections::{HashMap, HashSet};
use std::sync::Arc;

/// Advanced configuration for SciRS2-enhanced equivalence checking
#[derive(Debug, Clone, Serialize, Deserialize)]
pub struct AdvancedEquivalenceConfig {
    /// Base configuration
    pub base_config: crate::equivalence_checker::EquivalenceConfig,

    /// Advanced comparison methods
    pub comparison_methods: Vec<ComparisonMethod>,

    /// SVD truncation threshold for noise resilience
    pub svd_truncation_threshold: f64,

    /// Enable circuit canonicalization
    pub enable_canonicalization: bool,

    /// Maximum circuit depth for canonicalization
    pub max_canonicalization_depth: usize,

    /// Enable quantum process tomography verification
    pub enable_qpt_verification: bool,

    /// Number of Pauli basis measurements for QPT
    pub qpt_measurement_count: usize,

    /// Enable circuit fingerprinting for fast comparison
    pub enable_fingerprinting: bool,

    /// Fingerprint hash size in bits
    pub fingerprint_bits: usize,

    /// Enable state space partitioning for large circuits
    pub enable_partitioning: bool,

    /// Partition size threshold (qubits)
    pub partition_threshold: usize,

    /// Advanced tolerance settings
    pub tolerance_settings: ToleranceSettings,

    /// Circuit symmetry detection depth
    pub symmetry_detection_depth: usize,

    /// Enable statistical equivalence testing
    pub enable_statistical_testing: bool,

    /// Statistical confidence level (0.0 to 1.0)
    pub statistical_confidence: f64,
}

impl Default for AdvancedEquivalenceConfig {
    fn default() -> Self {
        Self {
            base_config: Default::default(),
            comparison_methods: vec![
                ComparisonMethod::FrobeniusNorm,
                ComparisonMethod::SpectralNorm,
                ComparisonMethod::SvdBased,
            ],
            svd_truncation_threshold: 1e-10,
            enable_canonicalization: true,
            max_canonicalization_depth: 100,
            enable_qpt_verification: false,
            qpt_measurement_count: 1000,
            enable_fingerprinting: true,
            fingerprint_bits: 256,
            enable_partitioning: true,
            partition_threshold: 20,
            tolerance_settings: ToleranceSettings::default(),
            symmetry_detection_depth: 10,
            enable_statistical_testing: true,
            statistical_confidence: 0.99,
        }
    }
}

/// Advanced comparison methods for numerical equivalence
#[derive(Debug, Clone, Copy, PartialEq, Eq, Serialize, Deserialize)]
pub enum ComparisonMethod {
    /// Frobenius norm comparison
    FrobeniusNorm,
    /// Spectral norm (largest singular value)
    SpectralNorm,
    /// SVD-based comparison with tolerance
    SvdBased,
    /// Eigenvalue spectrum comparison
    EigenvalueBased,
    /// Trace distance comparison
    TraceDistance,
    /// Diamond norm approximation
    DiamondNorm,
    /// Choi matrix comparison
    ChoiMatrix,
    /// Process fidelity
    ProcessFidelity,
}

/// Advanced tolerance settings with adaptive thresholds
#[derive(Debug, Clone, Serialize, Deserialize)]
pub struct ToleranceSettings {
    /// Base absolute tolerance
    pub absolute_tolerance: f64,
    /// Base relative tolerance
    pub relative_tolerance: f64,
    /// Machine epsilon multiplier
    pub epsilon_multiplier: f64,
    /// Adaptive tolerance based on circuit size
    pub size_adaptive_factor: f64,
    /// Noise-aware tolerance adjustment
    pub noise_tolerance_factor: f64,
    /// Condition number threshold for ill-conditioned matrices
    pub condition_threshold: f64,
}

impl Default for ToleranceSettings {
    fn default() -> Self {
        Self {
            absolute_tolerance: 1e-12,
            relative_tolerance: 1e-10,
            epsilon_multiplier: 10.0,
            size_adaptive_factor: 1.5,
            noise_tolerance_factor: 2.0,
            condition_threshold: 1e12,
        }
    }
}

/// Circuit fingerprint for fast comparison
#[derive(Debug, Clone, Hash, PartialEq, Eq)]
pub struct CircuitFingerprint {
    /// Gate count by type
    pub gate_counts: std::collections::BTreeMap<String, usize>,
    /// Circuit depth
    pub depth: usize,
    /// Connectivity hash
    pub connectivity_hash: u64,
    /// Parameter hash for parametric gates
    pub parameter_hash: u64,
    /// Structural hash
    pub structural_hash: u64,
}

/// Advanced quantum circuit equivalence checker
pub struct AdvancedEquivalenceChecker {
    config: AdvancedEquivalenceConfig,
    buffer_pool: Arc<BufferPool<Complex64>>,
    fingerprint_cache: HashMap<Vec<u8>, CircuitFingerprint>,
    canonical_cache: HashMap<Vec<u8>, Vec<crate::equivalence_checker::QuantumGate>>,
}

impl AdvancedEquivalenceChecker {
    /// Create a new advanced equivalence checker
    pub fn new() -> Self {
        Self::with_config(AdvancedEquivalenceConfig::default())
    }

    /// Create with custom configuration
    pub fn with_config(config: AdvancedEquivalenceConfig) -> Self {
        Self {
            config,
            buffer_pool: Arc::new(BufferPool::new()),
            fingerprint_cache: HashMap::new(),
            canonical_cache: HashMap::new(),
        }
    }

    /// Perform comprehensive equivalence check with all advanced features
    pub fn comprehensive_equivalence_check(
        &mut self,
        circuit1: &[crate::equivalence_checker::QuantumGate],
        circuit2: &[crate::equivalence_checker::QuantumGate],
        num_qubits: usize,
    ) -> Result<AdvancedEquivalenceResult, QuantRS2Error> {
        // Quick fingerprint check
        if self.config.enable_fingerprinting {
            let fp1 = self.compute_fingerprint(circuit1)?;
            let fp2 = self.compute_fingerprint(circuit2)?;

            if fp1 == fp2 {
                return Ok(AdvancedEquivalenceResult {
                    equivalent: true,
                    confidence: 1.0,
                    comparison_methods_used: vec!["Fingerprint".to_string()],
                    numerical_error: 0.0,
                    phase_factor: Some(Complex64::new(1.0, 0.0)),
                    canonical_forms_computed: false,
                    symmetries_detected: vec![],
                    performance_metrics: PerformanceMetrics::default(),
                });
            }
        }

        // Canonicalize circuits if enabled
        let (canonical1, canonical2) = if self.config.enable_canonicalization {
            (
                self.canonicalize_circuit(circuit1, num_qubits)?,
                self.canonicalize_circuit(circuit2, num_qubits)?,
            )
        } else {
            (circuit1.to_vec(), circuit2.to_vec())
        };

        // Perform multiple comparison methods
        let mut results = Vec::new();
        let mut methods_used = Vec::new();

        for method in &self.config.comparison_methods {
            let result = match method {
                ComparisonMethod::FrobeniusNorm => {
                    self.frobenius_norm_comparison(&canonical1, &canonical2, num_qubits)?
                }
                ComparisonMethod::SpectralNorm => {
                    self.spectral_norm_comparison(&canonical1, &canonical2, num_qubits)?
                }
                ComparisonMethod::SvdBased => {
                    self.svd_based_comparison(&canonical1, &canonical2, num_qubits)?
                }
                ComparisonMethod::EigenvalueBased => {
                    self.eigenvalue_comparison(&canonical1, &canonical2, num_qubits)?
                }
                ComparisonMethod::TraceDistance => {
                    self.trace_distance_comparison(&canonical1, &canonical2, num_qubits)?
                }
                ComparisonMethod::ProcessFidelity => {
                    self.process_fidelity_comparison(&canonical1, &canonical2, num_qubits)?
                }
                _ => continue,
            };

            results.push(result);
            methods_used.push(format!("{method:?}"));
        }

        // Aggregate results with confidence scoring
        let (equivalent, confidence, numerical_error) = self.aggregate_results(&results);

        // Detect symmetries if enabled
        let symmetries = if self.config.base_config.enable_symmetry_detection {
            self.detect_circuit_symmetries(&canonical1, num_qubits)?
        } else {
            vec![]
        };

        // Extract phase factor if circuits are equivalent up to phase
        let phase_factor = if equivalent {
            Some(Complex64::new(1.0, 0.0))
        } else {
            self.extract_global_phase(&canonical1, &canonical2, num_qubits)
                .ok()
        };

        Ok(AdvancedEquivalenceResult {
            equivalent,
            confidence,
            comparison_methods_used: methods_used,
            numerical_error,
            phase_factor,
            canonical_forms_computed: self.config.enable_canonicalization,
            symmetries_detected: symmetries,
            performance_metrics: PerformanceMetrics::default(),
        })
    }

    /// Compute circuit fingerprint for fast comparison
    fn compute_fingerprint(
        &mut self,
        circuit: &[crate::equivalence_checker::QuantumGate],
    ) -> Result<CircuitFingerprint, QuantRS2Error> {
        let circuit_hash = self.hash_circuit(circuit);

        if let Some(cached) = self.fingerprint_cache.get(&circuit_hash) {
            return Ok(cached.clone());
        }

        let mut gate_counts = std::collections::BTreeMap::new();
        let mut connectivity = HashSet::new();
        let mut depth = 0;
        let mut current_layer = HashSet::new();

        for gate in circuit {
            let gate_type = format!("{:?}", gate.gate_type());
            *gate_counts.entry(gate_type).or_insert(0) += 1;

            // Track connectivity
            for target in gate.target_qubits() {
                connectivity.insert(*target);
                current_layer.insert(*target);
            }
            if let Some(controls) = gate.control_qubits() {
                for control in controls {
                    connectivity.insert(*control);
                    current_layer.insert(*control);
                }
            }

            // Simple depth calculation
            if current_layer.len() > depth {
                depth = current_layer.len();
            }
        }

        let connectivity_hash = self.hash_set(&connectivity);
        let parameter_hash = self.hash_parameters(circuit);
        let structural_hash = self.hash_structure(circuit);

        let fingerprint = CircuitFingerprint {
            gate_counts,
            depth,
            connectivity_hash,
            parameter_hash,
            structural_hash,
        };

        self.fingerprint_cache
            .insert(circuit_hash, fingerprint.clone());
        Ok(fingerprint)
    }

    /// Canonicalize circuit for comparison
    fn canonicalize_circuit(
        &mut self,
        circuit: &[crate::equivalence_checker::QuantumGate],
        num_qubits: usize,
    ) -> Result<Vec<crate::equivalence_checker::QuantumGate>, QuantRS2Error> {
        let circuit_hash = self.hash_circuit(circuit);

        if let Some(cached) = self.canonical_cache.get(&circuit_hash) {
            return Ok(cached.clone());
        }

        let mut canonical = circuit.to_vec();

        // Apply canonicalization rules
        for _ in 0..self.config.max_canonicalization_depth {
            let mut changed = false;

            // Rule 1: Commute compatible gates
            changed |= self.apply_commutation_rules(&mut canonical)?;

            // Rule 2: Merge adjacent gates
            changed |= self.apply_gate_fusion(&canonical)?;

            // Rule 3: Cancel inverse gates
            changed |= self.apply_inverse_cancellation(&mut canonical)?;

            // Rule 4: Normalize phases
            changed |= self.apply_phase_normalization(&canonical)?;

            if !changed {
                break;
            }
        }

        // Sort gates by a canonical ordering
        self.apply_canonical_ordering(&mut canonical);

        self.canonical_cache.insert(circuit_hash, canonical.clone());
        Ok(canonical)
    }

    /// Frobenius norm comparison with adaptive tolerance
    fn frobenius_norm_comparison(
        &self,
        circuit1: &[crate::equivalence_checker::QuantumGate],
        circuit2: &[crate::equivalence_checker::QuantumGate],
        num_qubits: usize,
    ) -> Result<ComparisonResult, QuantRS2Error> {
        let matrix1 = self.compute_unitary_matrix(circuit1, num_qubits)?;
        let matrix2 = self.compute_unitary_matrix(circuit2, num_qubits)?;

        let diff = &matrix1 - &matrix2;
        // Use Norm trait via scirs2_core::ndarray (SciRS2 POLICY)
        let frobenius_norm = diff.norm_l2()?;
        let matrix_size = (1 << num_qubits) as f64;

        // Adaptive tolerance based on matrix size
        let tolerance = self.config.tolerance_settings.absolute_tolerance
            * matrix_size.sqrt()
            * self
                .config
                .tolerance_settings
                .size_adaptive_factor
                .powf(num_qubits as f64 / 10.0);

        Ok(ComparisonResult {
            equivalent: frobenius_norm < tolerance,
            error_measure: frobenius_norm,
            confidence: 1.0 - (frobenius_norm / matrix_size.sqrt()).min(1.0),
        })
    }

    /// Spectral norm comparison (largest singular value)
    fn spectral_norm_comparison(
        &self,
        circuit1: &[crate::equivalence_checker::QuantumGate],
        circuit2: &[crate::equivalence_checker::QuantumGate],
        num_qubits: usize,
    ) -> Result<ComparisonResult, QuantRS2Error> {
        let matrix1 = self.compute_unitary_matrix(circuit1, num_qubits)?;
        let matrix2 = self.compute_unitary_matrix(circuit2, num_qubits)?;

        let diff = &matrix1 - &matrix2;

        // Compute SVD to get spectral norm (use SVD trait via scirs2_core - SciRS2 POLICY)
        let (_, singular_values, _) = diff
            .svd(true, true)
            .map_err(|_| QuantRS2Error::ComputationError("SVD computation failed".into()))?;

        let spectral_norm = singular_values[0];
        let tolerance = self.config.tolerance_settings.absolute_tolerance;

        Ok(ComparisonResult {
            equivalent: spectral_norm < tolerance,
            error_measure: spectral_norm,
            confidence: 1.0 - spectral_norm.min(1.0),
        })
    }

    /// SVD-based comparison with truncation
    fn svd_based_comparison(
        &self,
        circuit1: &[crate::equivalence_checker::QuantumGate],
        circuit2: &[crate::equivalence_checker::QuantumGate],
        num_qubits: usize,
    ) -> Result<ComparisonResult, QuantRS2Error> {
        let matrix1 = self.compute_unitary_matrix(circuit1, num_qubits)?;
        let matrix2 = self.compute_unitary_matrix(circuit2, num_qubits)?;

        // Compute SVD of both matrices (use SVD trait via scirs2_core - SciRS2 POLICY)
        let (_, singular_values1, _) = matrix1.svd(true, true).map_err(|_| {
            QuantRS2Error::ComputationError("SVD computation failed for matrix 1".into())
        })?;

        let (_, singular_values2, _) = matrix2.svd(true, true).map_err(|_| {
            QuantRS2Error::ComputationError("SVD computation failed for matrix 2".into())
        })?;

        // Compare singular values with truncation
        let mut total_error: f64 = 0.0;
        let threshold = self.config.svd_truncation_threshold;

        for i in 0..singular_values1.len() {
            if singular_values1[i] > threshold || singular_values2[i] > threshold {
                let diff = (singular_values1[i] - singular_values2[i]).abs();
                total_error += diff * diff;
            }
        }

        let error = total_error.sqrt();
        let tolerance = self.config.tolerance_settings.absolute_tolerance;

        Ok(ComparisonResult {
            equivalent: error < tolerance,
            error_measure: error,
            confidence: 1.0 - error.min(1.0),
        })
    }

    /// Eigenvalue spectrum comparison
    fn eigenvalue_comparison(
        &self,
        circuit1: &[crate::equivalence_checker::QuantumGate],
        circuit2: &[crate::equivalence_checker::QuantumGate],
        num_qubits: usize,
    ) -> Result<ComparisonResult, QuantRS2Error> {
        let matrix1 = self.compute_unitary_matrix(circuit1, num_qubits)?;
        let matrix2 = self.compute_unitary_matrix(circuit2, num_qubits)?;

        // For unitary matrices, we can compute eigenvalues efficiently
        // Since U†U = I, all eigenvalues have magnitude 1
        // We'll compare the phases of eigenvalues

        // Convert to hermitian for eigenvalue computation: U + U†
        let herm1 = &matrix1 + &matrix1.t().mapv(|x| x.conj());
        let herm2 = &matrix2 + &matrix2.t().mapv(|x| x.conj());

        // Use ndarray-linalg trait via scirs2_core for complex hermitian matrices (SciRS2 POLICY)
        let (evals1, _) = herm1.eigh(UPLO::Upper).map_err(|_| {
            QuantRS2Error::ComputationError("Eigenvalue computation failed for matrix 1".into())
        })?;

        let (evals2, _) = herm2.eigh(UPLO::Upper).map_err(|_| {
            QuantRS2Error::ComputationError("Eigenvalue computation failed for matrix 2".into())
        })?;

        // Sort eigenvalues for comparison
        let mut sorted_evals1: Vec<f64> = evals1.iter().copied().collect();
        let mut sorted_evals2: Vec<f64> = evals2.iter().copied().collect();
        sorted_evals1.sort_by(|a, b| a.partial_cmp(b).unwrap_or(std::cmp::Ordering::Equal));
        sorted_evals2.sort_by(|a, b| a.partial_cmp(b).unwrap_or(std::cmp::Ordering::Equal));

        // Compare sorted eigenvalues
        let mut max_diff: f64 = 0.0;
        for (e1, e2) in sorted_evals1.iter().zip(sorted_evals2.iter()) {
            max_diff = max_diff.max((e1 - e2).abs());
        }

        let tolerance = self.config.tolerance_settings.absolute_tolerance;

        Ok(ComparisonResult {
            equivalent: max_diff < tolerance,
            error_measure: max_diff,
            confidence: 1.0 - max_diff.min(1.0),
        })
    }

    /// Trace distance comparison
    fn trace_distance_comparison(
        &self,
        circuit1: &[crate::equivalence_checker::QuantumGate],
        circuit2: &[crate::equivalence_checker::QuantumGate],
        num_qubits: usize,
    ) -> Result<ComparisonResult, QuantRS2Error> {
        let matrix1 = self.compute_unitary_matrix(circuit1, num_qubits)?;
        let matrix2 = self.compute_unitary_matrix(circuit2, num_qubits)?;

        // Compute trace distance: 0.5 * Tr(|U1 - U2|)
        let diff = &matrix1 - &matrix2;

        // For trace distance, we need the trace of the absolute value
        // This requires computing eigenvalues of (U1 - U2)†(U1 - U2)
        let diff_dag_diff = diff.t().mapv(|x| x.conj()).dot(&diff);

        // Use ndarray-linalg trait via scirs2_core for complex hermitian matrices (SciRS2 POLICY)
        let (eigenvalues, _) = diff_dag_diff.eigh(UPLO::Upper).map_err(|_| {
            QuantRS2Error::ComputationError(
                "Eigenvalue computation failed for trace distance".into(),
            )
        })?;

        let trace_distance: f64 =
            eigenvalues.iter().map(|&lambda| lambda.sqrt()).sum::<f64>() * 0.5;

        let tolerance = self.config.tolerance_settings.absolute_tolerance;

        Ok(ComparisonResult {
            equivalent: trace_distance < tolerance,
            error_measure: trace_distance,
            confidence: 1.0 - (trace_distance / num_qubits as f64).min(1.0),
        })
    }

    /// Process fidelity comparison
    fn process_fidelity_comparison(
        &self,
        circuit1: &[crate::equivalence_checker::QuantumGate],
        circuit2: &[crate::equivalence_checker::QuantumGate],
        num_qubits: usize,
    ) -> Result<ComparisonResult, QuantRS2Error> {
        let matrix1 = self.compute_unitary_matrix(circuit1, num_qubits)?;
        let matrix2 = self.compute_unitary_matrix(circuit2, num_qubits)?;

        let dim = 1 << num_qubits;

        // Process fidelity: |Tr(U1† U2)|² / d²
        let u1_dag_u2 = matrix1.t().mapv(|x| x.conj()).dot(&matrix2);
        let trace: Complex64 = (0..dim).map(|i| u1_dag_u2[[i, i]]).sum();
        let fidelity = (trace.norm_sqr()) / (dim * dim) as f64;

        // Convert fidelity to error measure (1 - fidelity)
        let error = 1.0 - fidelity;
        let tolerance = self.config.tolerance_settings.absolute_tolerance;

        Ok(ComparisonResult {
            equivalent: error < tolerance,
            error_measure: error,
            confidence: fidelity,
        })
    }

    /// Compute unitary matrix representation
    fn compute_unitary_matrix(
        &self,
        circuit: &[crate::equivalence_checker::QuantumGate],
        num_qubits: usize,
    ) -> Result<Array2<Complex64>, QuantRS2Error> {
        let dim = 1 << num_qubits;
        let mut matrix = Array2::eye(dim);

        // Apply gates in order (quantum circuit convention)
        for gate in circuit {
            let gate_matrix = self.gate_to_ndarray_matrix(gate, num_qubits)?;
            // For quantum circuits, we apply gates from left to right: U_total = U_n * ... * U_2 * U_1
            // Since we're building up the matrix, we do: matrix = gate_matrix * matrix
            matrix = gate_matrix.dot(&matrix);
        }

        Ok(matrix)
    }

    /// Convert gate to ndarray matrix
    fn gate_to_ndarray_matrix(
        &self,
        gate: &crate::equivalence_checker::QuantumGate,
        num_qubits: usize,
    ) -> Result<Array2<Complex64>, QuantRS2Error> {
        let dim = 1 << num_qubits;
        let mut matrix = Array2::eye(dim);

        // Apply gate-specific transformations
        match gate.gate_type() {
            GateType::X => self.apply_pauli_x(&mut matrix, gate.target_qubits()[0], num_qubits),
            GateType::Y => self.apply_pauli_y(&mut matrix, gate.target_qubits()[0], num_qubits),
            GateType::Z => self.apply_pauli_z(&mut matrix, gate.target_qubits()[0], num_qubits),
            GateType::H => self.apply_hadamard(&mut matrix, gate.target_qubits()[0], num_qubits),
            GateType::CNOT => {
                if gate.target_qubits().len() >= 2 {
                    self.apply_cnot(
                        &mut matrix,
                        gate.target_qubits()[0],
                        gate.target_qubits()[1],
                        num_qubits,
                    );
                }
            }
            _ => {} // Other gates would be implemented similarly
        }

        Ok(matrix)
    }

    /// Apply Pauli X gate
    fn apply_pauli_x(&self, matrix: &mut Array2<Complex64>, target: usize, num_qubits: usize) {
        let target_bit = 1 << target;
        let dim = 1 << num_qubits;

        for i in 0..dim {
            if i & target_bit == 0 {
                let j = i | target_bit;
                for k in 0..dim {
                    let temp = matrix[[i, k]];
                    matrix[[i, k]] = matrix[[j, k]];
                    matrix[[j, k]] = temp;
                }
            }
        }
    }

    /// Apply Pauli Y gate
    fn apply_pauli_y(&self, matrix: &mut Array2<Complex64>, target: usize, num_qubits: usize) {
        let target_bit = 1 << target;
        let dim = 1 << num_qubits;
        let i_unit = Complex64::new(0.0, 1.0);

        for i in 0..dim {
            if i & target_bit == 0 {
                let j = i | target_bit;
                for k in 0..dim {
                    let temp = matrix[[i, k]];
                    matrix[[i, k]] = -i_unit * matrix[[j, k]];
                    matrix[[j, k]] = i_unit * temp;
                }
            }
        }
    }

    /// Apply Pauli Z gate
    fn apply_pauli_z(&self, matrix: &mut Array2<Complex64>, target: usize, num_qubits: usize) {
        let target_bit = 1 << target;
        let dim = 1 << num_qubits;

        for i in 0..dim {
            if i & target_bit != 0 {
                for k in 0..dim {
                    matrix[[i, k]] *= -1.0;
                }
            }
        }
    }

    /// Apply Hadamard gate
    fn apply_hadamard(&self, matrix: &mut Array2<Complex64>, target: usize, num_qubits: usize) {
        let target_bit = 1 << target;
        let dim = 1 << num_qubits;
        let inv_sqrt2 = 1.0 / std::f64::consts::SQRT_2;

        for i in 0..dim {
            if i & target_bit == 0 {
                let j = i | target_bit;
                for k in 0..dim {
                    let temp = matrix[[i, k]];
                    matrix[[i, k]] = inv_sqrt2 * (temp + matrix[[j, k]]);
                    matrix[[j, k]] = inv_sqrt2 * (temp - matrix[[j, k]]);
                }
            }
        }
    }

    /// Apply CNOT gate
    fn apply_cnot(
        &self,
        matrix: &mut Array2<Complex64>,
        control: usize,
        target: usize,
        num_qubits: usize,
    ) {
        let control_bit = 1 << control;
        let target_bit = 1 << target;
        let dim = 1 << num_qubits;

        for i in 0..dim {
            if i & control_bit != 0 && i & target_bit == 0 {
                let j = i | target_bit;
                for k in 0..dim {
                    let temp = matrix[[i, k]];
                    matrix[[i, k]] = matrix[[j, k]];
                    matrix[[j, k]] = temp;
                }
            }
        }
    }

    /// Aggregate multiple comparison results
    fn aggregate_results(&self, results: &[ComparisonResult]) -> (bool, f64, f64) {
        if results.is_empty() {
            return (false, 0.0, f64::INFINITY);
        }

        // Circuits are equivalent only if EVERY comparison method agrees.
        // A single dissenting result (equivalent=false) is enough to declare
        // non-equivalence, regardless of how confident the other methods are
        // in saying they *are* equivalent.  This prevents unreliable methods
        // (e.g. SVD singular-value comparison, which cannot distinguish
        // circuits with the same singular-value spectrum) from overriding
        // correct matrix-based comparisons.
        let all_equivalent = results.iter().all(|r| r.equivalent);
        let max_error = results.iter().map(|r| r.error_measure).fold(0.0, f64::max);

        // Confidence: for equivalent circuits take the minimum method confidence;
        // for non-equivalent circuits take the complement of the minimum error.
        let confidence = if all_equivalent {
            results.iter().map(|r| r.confidence).fold(1.0_f64, f64::min)
        } else {
            // Confidence in non-equivalence: comes from the method with the
            // largest error measure (most certain about difference).
            let max_conf_of_disagreeing = results
                .iter()
                .filter(|r| !r.equivalent)
                .map(|r| r.confidence)
                .fold(0.0_f64, f64::max);
            max_conf_of_disagreeing
        };

        (all_equivalent, confidence, max_error)
    }

    /// Detect circuit symmetries
    fn detect_circuit_symmetries(
        &self,
        circuit: &[crate::equivalence_checker::QuantumGate],
        num_qubits: usize,
    ) -> Result<Vec<String>, QuantRS2Error> {
        let mut symmetries = Vec::new();

        // Check for time-reversal symmetry
        if self.check_time_reversal_symmetry(circuit, num_qubits)? {
            symmetries.push("Time-reversal".to_string());
        }

        // Check for spatial symmetries (qubit permutations)
        let spatial_syms = self.check_spatial_symmetries(circuit, num_qubits)?;
        symmetries.extend(spatial_syms);

        // Check for phase symmetries
        if self.check_phase_symmetries(circuit, num_qubits)? {
            symmetries.push("Phase-invariant".to_string());
        }

        Ok(symmetries)
    }

    /// Extract global phase between circuits
    fn extract_global_phase(
        &self,
        circuit1: &[crate::equivalence_checker::QuantumGate],
        circuit2: &[crate::equivalence_checker::QuantumGate],
        num_qubits: usize,
    ) -> Result<Complex64, QuantRS2Error> {
        let matrix1 = self.compute_unitary_matrix(circuit1, num_qubits)?;
        let matrix2 = self.compute_unitary_matrix(circuit2, num_qubits)?;

        // Find first non-zero element
        let dim = 1 << num_qubits;
        for i in 0..dim {
            for j in 0..dim {
                if matrix1[[i, j]].norm() > self.config.tolerance_settings.absolute_tolerance
                    && matrix2[[i, j]].norm() > self.config.tolerance_settings.absolute_tolerance
                {
                    return Ok(matrix2[[i, j]] / matrix1[[i, j]]);
                }
            }
        }

        Ok(Complex64::new(1.0, 0.0))
    }

    // Helper methods for canonicalization
    fn apply_commutation_rules(
        &self,
        circuit: &mut [crate::equivalence_checker::QuantumGate],
    ) -> Result<bool, QuantRS2Error> {
        let mut changed = false;

        for i in 0..circuit.len().saturating_sub(1) {
            if self.gates_commute(&circuit[i], &circuit[i + 1]) {
                // Sort by some canonical order (e.g., gate type, then target qubits)
                if self.gate_priority(&circuit[i]) > self.gate_priority(&circuit[i + 1]) {
                    circuit.swap(i, i + 1);
                    changed = true;
                }
            }
        }

        Ok(changed)
    }

    const fn apply_gate_fusion(
        &self,
        circuit: &[crate::equivalence_checker::QuantumGate],
    ) -> Result<bool, QuantRS2Error> {
        // Simplified gate fusion - would be expanded in full implementation
        Ok(false)
    }

    fn apply_inverse_cancellation(
        &self,
        circuit: &mut Vec<crate::equivalence_checker::QuantumGate>,
    ) -> Result<bool, QuantRS2Error> {
        let mut changed = false;
        let mut i = 0;

        while i < circuit.len().saturating_sub(1) {
            if self.are_inverse_gates(&circuit[i], &circuit[i + 1]) {
                circuit.remove(i);
                circuit.remove(i);
                changed = true;
            } else {
                i += 1;
            }
        }

        Ok(changed)
    }

    const fn apply_phase_normalization(
        &self,
        circuit: &[crate::equivalence_checker::QuantumGate],
    ) -> Result<bool, QuantRS2Error> {
        // Simplified phase normalization
        Ok(false)
    }

    fn apply_canonical_ordering(&self, circuit: &mut [crate::equivalence_checker::QuantumGate]) {
        // Bubble-sort respecting commutativity: only swap adjacent gates that
        // are proven to commute (act on disjoint qubits).  When two gates
        // commute, put the one with the lower minimum qubit index first so
        // that the representation is canonical regardless of the original
        // insertion order.  This preserves circuit semantics for
        // non-commuting gates while creating a unique normal form for all
        // parallel (disjoint-qubit) pairs.
        let n = circuit.len();
        if n < 2 {
            return;
        }
        let mut swapped = true;
        while swapped {
            swapped = false;
            for i in 0..n - 1 {
                if self.gates_commute(&circuit[i], &circuit[i + 1]) {
                    let min_qubit_i = circuit[i]
                        .target_qubits()
                        .iter()
                        .chain(circuit[i].control_qubits().unwrap_or(&[]).iter())
                        .copied()
                        .min()
                        .unwrap_or(usize::MAX);
                    let min_qubit_next = circuit[i + 1]
                        .target_qubits()
                        .iter()
                        .chain(circuit[i + 1].control_qubits().unwrap_or(&[]).iter())
                        .copied()
                        .min()
                        .unwrap_or(usize::MAX);
                    // Secondary key: gate-type priority for equal qubit indices
                    let priority_i = self.gate_priority(&circuit[i]);
                    let priority_next = self.gate_priority(&circuit[i + 1]);
                    let should_swap = (min_qubit_i, priority_i) > (min_qubit_next, priority_next);
                    if should_swap {
                        circuit.swap(i, i + 1);
                        swapped = true;
                    }
                }
            }
        }
    }

    // Helper methods
    fn gates_commute(
        &self,
        gate1: &crate::equivalence_checker::QuantumGate,
        gate2: &crate::equivalence_checker::QuantumGate,
    ) -> bool {
        // Check if gates operate on disjoint qubits
        let qubits1: HashSet<_> = gate1
            .target_qubits()
            .iter()
            .chain(gate1.control_qubits().unwrap_or(&[]).iter())
            .collect();
        let qubits2: HashSet<_> = gate2
            .target_qubits()
            .iter()
            .chain(gate2.control_qubits().unwrap_or(&[]).iter())
            .collect();

        qubits1.is_disjoint(&qubits2)
    }

    const fn gate_priority(&self, gate: &crate::equivalence_checker::QuantumGate) -> u32 {
        match gate.gate_type() {
            GateType::X => 1,
            GateType::Y => 2,
            GateType::Z => 3,
            GateType::H => 4,
            GateType::CNOT => 10,
            _ => 100,
        }
    }

    fn are_inverse_gates(
        &self,
        gate1: &crate::equivalence_checker::QuantumGate,
        gate2: &crate::equivalence_checker::QuantumGate,
    ) -> bool {
        if gate1.target_qubits() != gate2.target_qubits() {
            return false;
        }

        match (gate1.gate_type(), gate2.gate_type()) {
            (GateType::X, GateType::X)
            | (GateType::Y, GateType::Y)
            | (GateType::Z, GateType::Z)
            | (GateType::H, GateType::H) => true,
            (GateType::CNOT, GateType::CNOT) => gate1.control_qubits() == gate2.control_qubits(),
            _ => false,
        }
    }

    // Hashing utilities
    fn hash_circuit(&self, circuit: &[crate::equivalence_checker::QuantumGate]) -> Vec<u8> {
        use std::collections::hash_map::DefaultHasher;
        use std::hash::{Hash, Hasher};

        let mut hasher = DefaultHasher::new();
        for gate in circuit {
            format!("{:?}", gate.gate_type()).hash(&mut hasher);
            gate.target_qubits().hash(&mut hasher);
            if let Some(controls) = gate.control_qubits() {
                controls.hash(&mut hasher);
            }
        }

        hasher.finish().to_le_bytes().to_vec()
    }

    fn hash_set(&self, set: &HashSet<usize>) -> u64 {
        use std::collections::hash_map::DefaultHasher;
        use std::hash::{Hash, Hasher};

        let mut hasher = DefaultHasher::new();
        let mut sorted: Vec<_> = set.iter().collect();
        sorted.sort();
        for item in sorted {
            item.hash(&mut hasher);
        }

        hasher.finish()
    }

    const fn hash_parameters(&self, circuit: &[crate::equivalence_checker::QuantumGate]) -> u64 {
        // Placeholder - would hash parametric gate parameters
        0
    }

    fn hash_structure(&self, circuit: &[crate::equivalence_checker::QuantumGate]) -> u64 {
        use std::collections::hash_map::DefaultHasher;
        use std::hash::{Hash, Hasher};

        let mut hasher = DefaultHasher::new();
        circuit.len().hash(&mut hasher);

        // Hash gate types and targets in order to capture structure
        for (i, gate) in circuit.iter().enumerate() {
            i.hash(&mut hasher);
            format!("{:?}", gate.gate_type()).hash(&mut hasher);
            gate.target_qubits().hash(&mut hasher);
            if let Some(controls) = gate.control_qubits() {
                controls.hash(&mut hasher);
            }
        }

        hasher.finish()
    }

    // Symmetry checking methods
    const fn check_time_reversal_symmetry(
        &self,
        _circuit: &[crate::equivalence_checker::QuantumGate],
        _num_qubits: usize,
    ) -> Result<bool, QuantRS2Error> {
        // Placeholder implementation
        Ok(false)
    }

    const fn check_spatial_symmetries(
        &self,
        _circuit: &[crate::equivalence_checker::QuantumGate],
        _num_qubits: usize,
    ) -> Result<Vec<String>, QuantRS2Error> {
        // Placeholder implementation
        Ok(vec![])
    }

    const fn check_phase_symmetries(
        &self,
        _circuit: &[crate::equivalence_checker::QuantumGate],
        _num_qubits: usize,
    ) -> Result<bool, QuantRS2Error> {
        // Placeholder implementation
        Ok(false)
    }
}

/// Result of a single comparison method
#[derive(Debug, Clone)]
struct ComparisonResult {
    /// Whether circuits are equivalent according to this method
    pub equivalent: bool,
    /// Numerical error measure
    pub error_measure: f64,
    /// Confidence in the result (0.0 to 1.0)
    pub confidence: f64,
}

/// Comprehensive result of advanced equivalence checking
#[derive(Debug, Clone)]
pub struct AdvancedEquivalenceResult {
    /// Overall equivalence determination
    pub equivalent: bool,
    /// Confidence in the equivalence (0.0 to 1.0)
    pub confidence: f64,
    /// List of comparison methods used
    pub comparison_methods_used: Vec<String>,
    /// Maximum numerical error across all methods
    pub numerical_error: f64,
    /// Global phase factor if circuits are equivalent up to phase
    pub phase_factor: Option<Complex64>,
    /// Whether canonical forms were computed
    pub canonical_forms_computed: bool,
    /// Detected symmetries in the circuits
    pub symmetries_detected: Vec<String>,
    /// Performance metrics
    pub performance_metrics: PerformanceMetrics,
}

/// Performance metrics for equivalence checking
#[derive(Debug, Clone, Default)]
pub struct PerformanceMetrics {
    /// Time spent in matrix computation (ms)
    pub matrix_computation_time: f64,
    /// Time spent in comparison algorithms (ms)
    pub comparison_time: f64,
    /// Time spent in canonicalization (ms)
    pub canonicalization_time: f64,
    /// Memory peak usage (MB)
    pub peak_memory_usage: f64,
    /// Number of cache hits
    pub cache_hits: usize,
    /// Number of cache misses
    pub cache_misses: usize,
}

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

    #[test]
    fn test_advanced_equivalence_basic() {
        let mut checker = AdvancedEquivalenceChecker::new();

        let circuit1 = vec![
            QuantumGate::new(GateType::H, vec![0], None),
            QuantumGate::new(GateType::X, vec![0], None),
        ];

        let circuit2 = vec![
            QuantumGate::new(GateType::X, vec![0], None),
            QuantumGate::new(GateType::H, vec![0], None),
        ];

        let result = checker
            .comprehensive_equivalence_check(&circuit1, &circuit2, 1)
            .expect("Failed to perform comprehensive equivalence check");
        assert!(!result.equivalent); // H and X don't commute
    }

    #[test]
    fn test_fingerprint_matching() {
        let mut checker = AdvancedEquivalenceChecker::new();

        let circuit = vec![
            QuantumGate::new(GateType::H, vec![0], None),
            QuantumGate::new(GateType::CNOT, vec![0, 1], None),
        ];

        let fp1 = checker
            .compute_fingerprint(&circuit)
            .expect("Failed to compute fingerprint 1");
        let fp2 = checker
            .compute_fingerprint(&circuit)
            .expect("Failed to compute fingerprint 2");

        assert_eq!(fp1, fp2);
    }

    #[test]
    fn test_svd_based_comparison() {
        let checker = AdvancedEquivalenceChecker::new();

        let circuit1 = vec![QuantumGate::new(GateType::X, vec![0], None)];
        let circuit2 = vec![QuantumGate::new(GateType::X, vec![0], None)];

        let result = checker
            .svd_based_comparison(&circuit1, &circuit2, 1)
            .expect("Failed to perform SVD-based comparison");
        assert!(result.equivalent);
        assert!(result.error_measure < 1e-10);
    }

    #[test]
    fn test_canonicalization() {
        let mut checker = AdvancedEquivalenceChecker::new();

        // Two X gates should cancel
        let circuit = vec![
            QuantumGate::new(GateType::X, vec![0], None),
            QuantumGate::new(GateType::X, vec![0], None),
        ];

        let canonical = checker
            .canonicalize_circuit(&circuit, 1)
            .expect("Failed to canonicalize circuit");
        assert_eq!(canonical.len(), 0); // Should be empty after cancellation
    }

    #[test]
    fn test_commutation_ordering() {
        let mut checker = AdvancedEquivalenceChecker::new();

        // Gates on different qubits commute
        let circuit = vec![
            QuantumGate::new(GateType::X, vec![1], None),
            QuantumGate::new(GateType::Z, vec![0], None),
        ];

        let mut canonical = circuit.clone();
        checker.apply_canonical_ordering(&mut canonical);

        // Should be reordered by gate priority
        assert_eq!(canonical[0].gate_type(), &GateType::Z);
        assert_eq!(canonical[1].gate_type(), &GateType::X);
    }
}