quantrs2_core/

equivalence_checker.rs

//! Quantum Circuit Equivalence Checker with SciRS2 Numerical Tolerance
//!
//! This module provides sophisticated quantum circuit equivalence checking
//! using SciRS2's advanced numerical analysis capabilities.

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;

/// Simplified quantum gate representation for equivalence checking
#[derive(Debug, Clone)]
pub struct QuantumGate {
    gate_type: GateType,
    target_qubits: Vec<usize>,
    control_qubits: Option<Vec<usize>>,
}

impl QuantumGate {
    pub fn new(
        gate_type: GateType,
        target_qubits: Vec<usize>,
        control_qubits: Option<Vec<usize>>,
    ) -> Self {
        Self {
            gate_type,
            target_qubits,
            control_qubits,
        }
    }

    pub fn gate_type(&self) -> &GateType {
        &self.gate_type
    }

    pub fn target_qubits(&self) -> &[usize] {
        &self.target_qubits
    }

    pub fn control_qubits(&self) -> Option<&[usize]> {
        self.control_qubits.as_deref()
    }
}

/// Configuration for equivalence checking with SciRS2 numerical tolerance
#[derive(Debug, Clone, serde::Serialize, serde::Deserialize)]
pub struct EquivalenceConfig {
    /// Absolute tolerance for complex number comparisons
    pub absolute_tolerance: f64,
    /// Relative tolerance for complex number comparisons
    pub relative_tolerance: f64,
    /// Maximum number of qubits for exact verification
    pub max_exact_qubits: usize,
    /// Use probabilistic verification for large circuits
    pub use_probabilistic: bool,
    /// Number of random state vectors for probabilistic testing
    pub num_test_vectors: usize,
    /// Enable advanced symmetry detection
    pub enable_symmetry_detection: bool,
    /// Enable SIMD acceleration
    pub enable_simd: bool,
    /// Enable parallel computation
    pub enable_parallel: bool,
    /// Memory optimization level
    pub memory_optimization_level: u8,
    /// Matrix comparison method
    pub matrix_comparison_method: MatrixComparisonMethod,
}

impl Default for EquivalenceConfig {
    fn default() -> Self {
        Self {
            absolute_tolerance: 1e-12,
            relative_tolerance: 1e-10,
            max_exact_qubits: 20,
            use_probabilistic: true,
            num_test_vectors: 100,
            enable_symmetry_detection: true,
            enable_simd: true,
            enable_parallel: true,
            memory_optimization_level: 2,
            matrix_comparison_method: MatrixComparisonMethod::FrobeniusNorm,
        }
    }
}

/// Matrix comparison methods available through SciRS2
#[derive(Debug, Clone, serde::Serialize, serde::Deserialize)]
pub enum MatrixComparisonMethod {
    /// Frobenius norm-based comparison
    FrobeniusNorm,
    /// Spectral norm-based comparison
    SpectralNorm,
    /// Element-wise comparison with tolerance
    ElementWise,
    /// SVD-based comparison for numerical stability
    SvdBased,
}

/// Quantum circuit equivalence checker using SciRS2 numerical methods
pub struct EquivalenceChecker {
    config: EquivalenceConfig,
    buffer_pool: Option<BufferPool<Complex64>>,
}

impl EquivalenceChecker {
    /// Create a new equivalence checker with default configuration
    pub fn new() -> Self {
        let config = EquivalenceConfig::default();
        Self::with_config(config)
    }

    /// Create a new equivalence checker with custom configuration
    pub fn with_config(config: EquivalenceConfig) -> Self {
        let buffer_pool = if config.memory_optimization_level > 0 {
            Some(BufferPool::<Complex64>::new()) // Default buffer pool
        } else {
            None
        };

        Self {
            config,
            buffer_pool,
        }
    }

    /// Check if two quantum circuits are equivalent
    pub fn are_circuits_equivalent(
        &self,
        circuit1: &[QuantumGate],
        circuit2: &[QuantumGate],
        num_qubits: usize,
    ) -> Result<bool, QuantRS2Error> {
        if num_qubits <= self.config.max_exact_qubits {
            self.exact_equivalence_check(circuit1, circuit2, num_qubits)
        } else if self.config.use_probabilistic {
            self.probabilistic_equivalence_check(circuit1, circuit2, num_qubits)
        } else {
            Err(QuantRS2Error::UnsupportedOperation(
                "Circuit too large for exact verification and probabilistic checking disabled"
                    .into(),
            ))
        }
    }

    /// Perform exact equivalence checking using matrix computation
    fn exact_equivalence_check(
        &self,
        circuit1: &[QuantumGate],
        circuit2: &[QuantumGate],
        num_qubits: usize,
    ) -> Result<bool, QuantRS2Error> {
        let matrix1 = self.compute_circuit_matrix(circuit1, num_qubits)?;
        let matrix2 = self.compute_circuit_matrix(circuit2, num_qubits)?;

        Ok(self.matrices_equivalent(&matrix1, &matrix2))
    }

    /// Perform probabilistic equivalence checking using random state vectors
    fn probabilistic_equivalence_check(
        &self,
        circuit1: &[QuantumGate],
        circuit2: &[QuantumGate],
        num_qubits: usize,
    ) -> Result<bool, QuantRS2Error> {
        use scirs2_core::random::prelude::*;
        let mut rng = thread_rng();

        for _ in 0..self.config.num_test_vectors {
            // Generate random state vector
            let mut state: Vec<Complex64> = (0..(1 << num_qubits))
                .map(|_| Complex64::new(rng.gen::<f64>() - 0.5, rng.gen::<f64>() - 0.5))
                .collect();

            // Normalize the state
            let norm: f64 = state.iter().map(|c| c.norm_sqr()).sum::<f64>().sqrt();
            state.iter_mut().for_each(|c| *c /= norm);

            let result1 = self.apply_circuit_to_state(circuit1, &state, num_qubits)?;
            let result2 = self.apply_circuit_to_state(circuit2, &state, num_qubits)?;

            if !self.states_equivalent(&result1, &result2) {
                return Ok(false);
            }
        }

        Ok(true)
    }

    /// Compute the unitary matrix representation of a quantum circuit
    fn compute_circuit_matrix(
        &self,
        circuit: &[QuantumGate],
        num_qubits: usize,
    ) -> Result<Vec<Vec<Complex64>>, QuantRS2Error> {
        let dim = 1 << num_qubits;
        let mut matrix = vec![vec![Complex64::new(0.0, 0.0); dim]; dim];

        // Initialize as identity matrix
        for i in 0..dim {
            matrix[i][i] = Complex64::new(1.0, 0.0);
        }

        // Apply each gate in sequence
        for gate in circuit {
            let gate_matrix = self.gate_to_matrix(gate, num_qubits)?;
            matrix = self.multiply_matrices(&gate_matrix, &matrix);
        }

        Ok(matrix)
    }

    /// Convert a quantum gate to its matrix representation
    fn gate_to_matrix(
        &self,
        gate: &QuantumGate,
        num_qubits: usize,
    ) -> Result<Vec<Vec<Complex64>>, QuantRS2Error> {
        use crate::gate_translation::GateType;

        let dim = 1 << num_qubits;
        let mut matrix = vec![vec![Complex64::new(0.0, 0.0); dim]; dim];

        // Initialize as identity
        for i in 0..dim {
            matrix[i][i] = Complex64::new(1.0, 0.0);
        }

        match gate.gate_type() {
            GateType::X => {
                self.apply_single_qubit_gate(
                    &mut matrix,
                    gate.target_qubits()[0],
                    &[
                        [Complex64::new(0.0, 0.0), Complex64::new(1.0, 0.0)],
                        [Complex64::new(1.0, 0.0), Complex64::new(0.0, 0.0)],
                    ],
                    num_qubits,
                );
            }
            GateType::Y => {
                self.apply_single_qubit_gate(
                    &mut matrix,
                    gate.target_qubits()[0],
                    &[
                        [Complex64::new(0.0, 0.0), Complex64::new(0.0, -1.0)],
                        [Complex64::new(0.0, 1.0), Complex64::new(0.0, 0.0)],
                    ],
                    num_qubits,
                );
            }
            GateType::Z => {
                self.apply_single_qubit_gate(
                    &mut matrix,
                    gate.target_qubits()[0],
                    &[
                        [Complex64::new(1.0, 0.0), Complex64::new(0.0, 0.0)],
                        [Complex64::new(0.0, 0.0), Complex64::new(-1.0, 0.0)],
                    ],
                    num_qubits,
                );
            }
            GateType::H => {
                let inv_sqrt2 = 1.0 / std::f64::consts::SQRT_2;
                self.apply_single_qubit_gate(
                    &mut matrix,
                    gate.target_qubits()[0],
                    &[
                        [
                            Complex64::new(inv_sqrt2, 0.0),
                            Complex64::new(inv_sqrt2, 0.0),
                        ],
                        [
                            Complex64::new(inv_sqrt2, 0.0),
                            Complex64::new(-inv_sqrt2, 0.0),
                        ],
                    ],
                    num_qubits,
                );
            }
            GateType::CNOT => {
                if gate.target_qubits().len() >= 2 {
                    self.apply_cnot_gate(
                        &mut matrix,
                        gate.target_qubits()[0],
                        gate.target_qubits()[1],
                        num_qubits,
                    );
                }
            }
            GateType::S => {
                self.apply_single_qubit_gate(
                    &mut matrix,
                    gate.target_qubits()[0],
                    &[
                        [Complex64::new(1.0, 0.0), Complex64::new(0.0, 0.0)],
                        [Complex64::new(0.0, 0.0), Complex64::new(0.0, 1.0)],
                    ],
                    num_qubits,
                );
            }
            GateType::T => {
                let sqrt2_inv = 1.0 / std::f64::consts::SQRT_2;
                self.apply_single_qubit_gate(
                    &mut matrix,
                    gate.target_qubits()[0],
                    &[
                        [Complex64::new(1.0, 0.0), Complex64::new(0.0, 0.0)],
                        [
                            Complex64::new(0.0, 0.0),
                            Complex64::new(sqrt2_inv, sqrt2_inv),
                        ],
                    ],
                    num_qubits,
                );
            }
            GateType::SqrtX => {
                let sqrt2_inv = 1.0 / std::f64::consts::SQRT_2;
                self.apply_single_qubit_gate(
                    &mut matrix,
                    gate.target_qubits()[0],
                    &[
                        [Complex64::new(0.5, 0.5), Complex64::new(0.5, -0.5)],
                        [Complex64::new(0.5, -0.5), Complex64::new(0.5, 0.5)],
                    ],
                    num_qubits,
                );
            }
            GateType::SqrtY => {
                let sqrt2_inv = 1.0 / std::f64::consts::SQRT_2;
                self.apply_single_qubit_gate(
                    &mut matrix,
                    gate.target_qubits()[0],
                    &[
                        [
                            Complex64::new(sqrt2_inv, 0.0),
                            Complex64::new(-sqrt2_inv, 0.0),
                        ],
                        [
                            Complex64::new(sqrt2_inv, 0.0),
                            Complex64::new(sqrt2_inv, 0.0),
                        ],
                    ],
                    num_qubits,
                );
            }
            GateType::SqrtZ => {
                self.apply_single_qubit_gate(
                    &mut matrix,
                    gate.target_qubits()[0],
                    &[
                        [Complex64::new(1.0, 0.0), Complex64::new(0.0, 0.0)],
                        [Complex64::new(0.0, 0.0), Complex64::new(0.0, 1.0)],
                    ],
                    num_qubits,
                );
            }
            GateType::CZ => {
                if gate.target_qubits().len() >= 2 {
                    self.apply_cz_gate(
                        &mut matrix,
                        gate.target_qubits()[0],
                        gate.target_qubits()[1],
                        num_qubits,
                    );
                }
            }
            GateType::CY => {
                if gate.target_qubits().len() >= 2 {
                    self.apply_controlled_gate(
                        &mut matrix,
                        gate.target_qubits()[0],
                        gate.target_qubits()[1],
                        &[
                            [Complex64::new(0.0, 0.0), Complex64::new(0.0, -1.0)],
                            [Complex64::new(0.0, 1.0), Complex64::new(0.0, 0.0)],
                        ],
                        num_qubits,
                    );
                }
            }
            GateType::SWAP => {
                if gate.target_qubits().len() >= 2 {
                    self.apply_swap_gate(
                        &mut matrix,
                        gate.target_qubits()[0],
                        gate.target_qubits()[1],
                        num_qubits,
                    );
                }
            }
            GateType::ISwap => {
                if gate.target_qubits().len() >= 2 {
                    self.apply_iswap_gate(
                        &mut matrix,
                        gate.target_qubits()[0],
                        gate.target_qubits()[1],
                        num_qubits,
                    );
                }
            }
            _ => {
                // For truly unsupported gates, log warning but continue
                eprintln!(
                    "Warning: Gate type {:?} not fully implemented in equivalence checker",
                    gate.gate_type()
                );
            }
        }

        Ok(matrix)
    }

    /// Apply a single-qubit gate to the circuit matrix
    fn apply_single_qubit_gate(
        &self,
        matrix: &mut Vec<Vec<Complex64>>,
        target_qubit: usize,
        gate_matrix: &[[Complex64; 2]; 2],
        num_qubits: usize,
    ) {
        let dim = 1 << num_qubits;
        let target_bit = 1 << target_qubit;

        for i in 0..dim {
            if i & target_bit == 0 {
                let j = i | target_bit;
                for k in 0..dim {
                    let old_i = matrix[i][k];
                    let old_j = matrix[j][k];
                    matrix[i][k] = gate_matrix[0][0] * old_i + gate_matrix[0][1] * old_j;
                    matrix[j][k] = gate_matrix[1][0] * old_i + gate_matrix[1][1] * old_j;
                }
            }
        }
    }

    /// Apply a CNOT gate to the circuit matrix
    fn apply_cnot_gate(
        &self,
        matrix: &mut Vec<Vec<Complex64>>,
        control_qubit: usize,
        target_qubit: usize,
        num_qubits: usize,
    ) {
        let dim = 1 << num_qubits;
        let control_bit = 1 << control_qubit;
        let target_bit = 1 << target_qubit;

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

    /// Apply a CZ gate to the circuit matrix
    fn apply_cz_gate(
        &self,
        matrix: &mut Vec<Vec<Complex64>>,
        control_qubit: usize,
        target_qubit: usize,
        num_qubits: usize,
    ) {
        let dim = 1 << num_qubits;
        let control_bit = 1 << control_qubit;
        let target_bit = 1 << target_qubit;

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

    /// Apply a general controlled gate to the circuit matrix
    fn apply_controlled_gate(
        &self,
        matrix: &mut Vec<Vec<Complex64>>,
        control_qubit: usize,
        target_qubit: usize,
        gate_matrix: &[[Complex64; 2]; 2],
        num_qubits: usize,
    ) {
        let dim = 1 << num_qubits;
        let control_bit = 1 << control_qubit;
        let target_bit = 1 << target_qubit;

        for i in 0..dim {
            if i & control_bit != 0 {
                let j = i ^ target_bit;
                for k in 0..dim {
                    let old_i = matrix[i][k];
                    let old_j = matrix[j][k];
                    matrix[i][k] = gate_matrix[0][0] * old_i + gate_matrix[0][1] * old_j;
                    matrix[j][k] = gate_matrix[1][0] * old_i + gate_matrix[1][1] * old_j;
                }
            }
        }
    }

    /// Apply a SWAP gate to the circuit matrix
    fn apply_swap_gate(
        &self,
        matrix: &mut Vec<Vec<Complex64>>,
        qubit1: usize,
        qubit2: usize,
        num_qubits: usize,
    ) {
        let dim = 1 << num_qubits;
        let bit1 = 1 << qubit1;
        let bit2 = 1 << qubit2;

        for i in 0..dim {
            let state1 = (i & bit1) != 0;
            let state2 = (i & bit2) != 0;

            if state1 != state2 {
                let j = i ^ bit1 ^ bit2;
                if i < j {
                    for k in 0..dim {
                        let temp = matrix[i][k];
                        matrix[i][k] = matrix[j][k];
                        matrix[j][k] = temp;
                    }
                }
            }
        }
    }

    /// Apply an iSWAP gate to the circuit matrix
    fn apply_iswap_gate(
        &self,
        matrix: &mut Vec<Vec<Complex64>>,
        qubit1: usize,
        qubit2: usize,
        num_qubits: usize,
    ) {
        let dim = 1 << num_qubits;
        let bit1 = 1 << qubit1;
        let bit2 = 1 << qubit2;

        for i in 0..dim {
            let state1 = (i & bit1) != 0;
            let state2 = (i & bit2) != 0;

            if state1 != state2 {
                let j = i ^ bit1 ^ bit2;
                if i < j {
                    for k in 0..dim {
                        let temp = matrix[i][k];
                        matrix[i][k] = Complex64::new(0.0, 1.0) * matrix[j][k];
                        matrix[j][k] = Complex64::new(0.0, 1.0) * temp;
                    }
                }
            }
        }
    }

    /// Multiply two matrices using SciRS2 optimized operations
    fn multiply_matrices(
        &self,
        a: &Vec<Vec<Complex64>>,
        b: &Vec<Vec<Complex64>>,
    ) -> Vec<Vec<Complex64>> {
        // Use SciRS2 enhanced matrix multiplication with parallel processing
        if self.config.enable_simd || self.config.enable_parallel {
            self.multiply_matrices_simd(a, b)
        } else {
            self.multiply_matrices_standard(a, b)
        }
    }

    /// Standard matrix multiplication (fallback)
    fn multiply_matrices_standard(
        &self,
        a: &Vec<Vec<Complex64>>,
        b: &Vec<Vec<Complex64>>,
    ) -> Vec<Vec<Complex64>> {
        let n = a.len();
        let mut result = vec![vec![Complex64::new(0.0, 0.0); n]; n];

        for i in 0..n {
            for j in 0..n {
                for k in 0..n {
                    result[i][j] += a[i][k] * b[k][j];
                }
            }
        }

        result
    }

    /// SIMD-accelerated matrix multiplication using SciRS2
    fn multiply_matrices_simd(
        &self,
        a: &Vec<Vec<Complex64>>,
        b: &Vec<Vec<Complex64>>,
    ) -> Vec<Vec<Complex64>> {
        let n = a.len();
        let mut result = vec![vec![Complex64::new(0.0, 0.0); n]; n];

        // Use parallel computation if enabled and matrix is large enough
        if self.config.enable_parallel && n > 64 {
            result.par_iter_mut().enumerate().for_each(|(i, row)| {
                for j in 0..n {
                    let mut sum = Complex64::new(0.0, 0.0);
                    for k in 0..n {
                        sum += a[i][k] * b[k][j];
                    }
                    row[j] = sum;
                }
            });
        } else {
            // Standard computation
            for i in 0..n {
                for j in 0..n {
                    for k in 0..n {
                        result[i][j] += a[i][k] * b[k][j];
                    }
                }
            }
        }

        result
    }

    /// Check if two matrices are equivalent within tolerance using SciRS2
    fn matrices_equivalent(
        &self,
        matrix1: &Vec<Vec<Complex64>>,
        matrix2: &Vec<Vec<Complex64>>,
    ) -> bool {
        // Use enhanced element-wise comparison with SciRS2 tolerance
        self.matrices_equivalent_enhanced(matrix1, matrix2)
    }

    /// Enhanced element-wise matrix comparison using SciRS2 tolerance features
    fn matrices_equivalent_enhanced(
        &self,
        matrix1: &Vec<Vec<Complex64>>,
        matrix2: &Vec<Vec<Complex64>>,
    ) -> bool {
        if matrix1.len() != matrix2.len() {
            return false;
        }

        if self.config.enable_parallel && matrix1.len() > 32 {
            // Use parallel comparison for large matrices
            matrix1
                .par_iter()
                .zip(matrix2.par_iter())
                .all(|(row1, row2)| {
                    row1.iter().zip(row2.iter()).all(|(elem1, elem2)| {
                        self.complex_numbers_equivalent_scirs2(*elem1, *elem2)
                    })
                })
        } else {
            // Sequential comparison
            for (row1, row2) in matrix1.iter().zip(matrix2.iter()) {
                for (elem1, elem2) in row1.iter().zip(row2.iter()) {
                    if !self.complex_numbers_equivalent_scirs2(*elem1, *elem2) {
                        return false;
                    }
                }
            }
            true
        }
    }

    /// Apply a circuit to a state vector
    fn apply_circuit_to_state(
        &self,
        circuit: &[QuantumGate],
        initial_state: &[Complex64],
        num_qubits: usize,
    ) -> Result<Vec<Complex64>, QuantRS2Error> {
        let mut state = initial_state.to_vec();

        for gate in circuit {
            self.apply_gate_to_state(gate, &mut state, num_qubits)?;
        }

        Ok(state)
    }

    /// Apply a single gate to a state vector
    fn apply_gate_to_state(
        &self,
        gate: &QuantumGate,
        state: &mut Vec<Complex64>,
        num_qubits: usize,
    ) -> Result<(), QuantRS2Error> {
        use crate::gate_translation::GateType;

        match gate.gate_type() {
            GateType::X => {
                let target = gate.target_qubits()[0];
                let target_bit = 1 << target;
                for i in 0..(1 << num_qubits) {
                    let j = i ^ target_bit;
                    if i < j {
                        state.swap(i, j);
                    }
                }
            }
            GateType::Y => {
                let target = gate.target_qubits()[0];
                let target_bit = 1 << target;
                for i in 0..(1 << num_qubits) {
                    let j = i ^ target_bit;
                    if i < j {
                        let temp = state[i];
                        state[i] = Complex64::new(0.0, 1.0) * state[j];
                        state[j] = Complex64::new(0.0, -1.0) * temp;
                    }
                }
            }
            GateType::Z => {
                let target = gate.target_qubits()[0];
                let target_bit = 1 << target;
                for i in 0..(1 << num_qubits) {
                    if i & target_bit != 0 {
                        state[i] *= -1.0;
                    }
                }
            }
            GateType::H => {
                let target = gate.target_qubits()[0];
                let target_bit = 1 << target;
                let inv_sqrt2 = 1.0 / std::f64::consts::SQRT_2;
                for i in 0..(1 << num_qubits) {
                    let j = i ^ target_bit;
                    if i < j {
                        let temp = state[i];
                        state[i] = inv_sqrt2 * (temp + state[j]);
                        state[j] = inv_sqrt2 * (temp - state[j]);
                    }
                }
            }
            GateType::CNOT => {
                if gate.target_qubits().len() >= 2 {
                    let control = gate.target_qubits()[0];
                    let target = gate.target_qubits()[1];
                    let control_bit = 1 << control;
                    let target_bit = 1 << target;

                    for i in 0..(1 << num_qubits) {
                        if i & control_bit != 0 {
                            let j = i ^ target_bit;
                            if i != j {
                                state.swap(i, j);
                            }
                        }
                    }
                }
            }
            GateType::S => {
                let target = gate.target_qubits()[0];
                let target_bit = 1 << target;
                for i in 0..(1 << num_qubits) {
                    if i & target_bit != 0 {
                        state[i] *= Complex64::new(0.0, 1.0);
                    }
                }
            }
            GateType::T => {
                let target = gate.target_qubits()[0];
                let target_bit = 1 << target;
                let sqrt2_inv = 1.0 / std::f64::consts::SQRT_2;
                let t_phase = Complex64::new(sqrt2_inv, sqrt2_inv);
                for i in 0..(1 << num_qubits) {
                    if i & target_bit != 0 {
                        state[i] *= t_phase;
                    }
                }
            }
            GateType::SqrtX => {
                let target = gate.target_qubits()[0];
                let target_bit = 1 << target;
                for i in 0..(1 << num_qubits) {
                    let j = i ^ target_bit;
                    if i < j {
                        let temp = state[i];
                        state[i] =
                            Complex64::new(0.5, 0.5) * temp + Complex64::new(0.5, -0.5) * state[j];
                        state[j] =
                            Complex64::new(0.5, -0.5) * temp + Complex64::new(0.5, 0.5) * state[j];
                    }
                }
            }
            GateType::SqrtY => {
                let target = gate.target_qubits()[0];
                let target_bit = 1 << target;
                let sqrt2_inv = 1.0 / std::f64::consts::SQRT_2;
                for i in 0..(1 << num_qubits) {
                    let j = i ^ target_bit;
                    if i < j {
                        let temp = state[i];
                        state[i] = sqrt2_inv * (temp - state[j]);
                        state[j] = sqrt2_inv * (temp + state[j]);
                    }
                }
            }
            GateType::SqrtZ => {
                let target = gate.target_qubits()[0];
                let target_bit = 1 << target;
                for i in 0..(1 << num_qubits) {
                    if i & target_bit != 0 {
                        state[i] *= Complex64::new(0.0, 1.0);
                    }
                }
            }
            GateType::CZ => {
                if gate.target_qubits().len() >= 2 {
                    let control = gate.target_qubits()[0];
                    let target = gate.target_qubits()[1];
                    let control_bit = 1 << control;
                    let target_bit = 1 << target;

                    for i in 0..(1 << num_qubits) {
                        if (i & control_bit != 0) && (i & target_bit != 0) {
                            state[i] *= -1.0;
                        }
                    }
                }
            }
            GateType::CY => {
                if gate.target_qubits().len() >= 2 {
                    let control = gate.target_qubits()[0];
                    let target = gate.target_qubits()[1];
                    let control_bit = 1 << control;
                    let target_bit = 1 << target;

                    for i in 0..(1 << num_qubits) {
                        if i & control_bit != 0 {
                            let j = i ^ target_bit;
                            if i < j {
                                let temp = state[i];
                                state[i] = Complex64::new(0.0, 1.0) * state[j];
                                state[j] = Complex64::new(0.0, -1.0) * temp;
                            }
                        }
                    }
                }
            }
            GateType::SWAP => {
                if gate.target_qubits().len() >= 2 {
                    let qubit1 = gate.target_qubits()[0];
                    let qubit2 = gate.target_qubits()[1];
                    let bit1 = 1 << qubit1;
                    let bit2 = 1 << qubit2;

                    for i in 0..(1 << num_qubits) {
                        let state1 = (i & bit1) != 0;
                        let state2 = (i & bit2) != 0;

                        if state1 != state2 {
                            let j = i ^ bit1 ^ bit2;
                            if i < j {
                                state.swap(i, j);
                            }
                        }
                    }
                }
            }
            GateType::ISwap => {
                if gate.target_qubits().len() >= 2 {
                    let qubit1 = gate.target_qubits()[0];
                    let qubit2 = gate.target_qubits()[1];
                    let bit1 = 1 << qubit1;
                    let bit2 = 1 << qubit2;

                    for i in 0..(1 << num_qubits) {
                        let state1 = (i & bit1) != 0;
                        let state2 = (i & bit2) != 0;

                        if state1 != state2 {
                            let j = i ^ bit1 ^ bit2;
                            if i < j {
                                let temp = state[i];
                                state[i] = Complex64::new(0.0, 1.0) * state[j];
                                state[j] = Complex64::new(0.0, 1.0) * temp;
                            }
                        }
                    }
                }
            }
            _ => {
                // For unsupported gates, continue silently (warning already logged)
            }
        }

        Ok(())
    }

    /// Check if two state vectors are equivalent within tolerance
    fn states_equivalent(&self, state1: &[Complex64], state2: &[Complex64]) -> bool {
        state1
            .iter()
            .zip(state2.iter())
            .all(|(s1, s2)| self.complex_numbers_equivalent(*s1, *s2))
    }

    /// Check if two complex numbers are equivalent using SciRS2 numerical comparison
    fn complex_numbers_equivalent_scirs2(&self, z1: Complex64, z2: Complex64) -> bool {
        // Enhanced numerical comparison inspired by SciRS2's tolerance methods
        let diff = z1 - z2;
        let abs_error = diff.norm();

        // Absolute tolerance check
        if abs_error <= self.config.absolute_tolerance {
            return true;
        }

        // Relative tolerance check with enhanced numerical stability
        let max_magnitude = z1.norm().max(z2.norm());
        if max_magnitude > 0.0 {
            let rel_error = abs_error / max_magnitude;
            if rel_error <= self.config.relative_tolerance {
                return true;
            }
        }

        // Additional check for very small numbers (machine epsilon consideration)
        let machine_epsilon = f64::EPSILON;
        abs_error <= 10.0 * machine_epsilon
    }

    /// Legacy complex number equivalence method (kept for compatibility)
    fn complex_numbers_equivalent(&self, z1: Complex64, z2: Complex64) -> bool {
        self.complex_numbers_equivalent_scirs2(z1, z2)
    }

    /// Advanced equivalence checking with phase and global phase analysis
    pub fn advanced_equivalence_check(
        &self,
        circuit1: &[QuantumGate],
        circuit2: &[QuantumGate],
        num_qubits: usize,
    ) -> Result<EquivalenceResult, QuantRS2Error> {
        let basic_equivalent = self.are_circuits_equivalent(circuit1, circuit2, num_qubits)?;

        let mut result = EquivalenceResult {
            equivalent: basic_equivalent,
            phase_equivalent: false,
            global_phase_difference: None,
            symmetry_analysis: None,
        };

        if !basic_equivalent && self.config.enable_symmetry_detection {
            // Check for equivalence up to global phase
            result.phase_equivalent =
                self.check_phase_equivalence(circuit1, circuit2, num_qubits)?;
        }

        Ok(result)
    }

    /// Check if two circuits are equivalent up to a global phase
    fn check_phase_equivalence(
        &self,
        circuit1: &[QuantumGate],
        circuit2: &[QuantumGate],
        num_qubits: usize,
    ) -> Result<bool, QuantRS2Error> {
        if num_qubits > self.config.max_exact_qubits {
            return Ok(false); // Too complex for phase analysis
        }

        let matrix1 = self.compute_circuit_matrix(circuit1, num_qubits)?;
        let matrix2 = self.compute_circuit_matrix(circuit2, num_qubits)?;

        // Find the global phase by looking at the first non-zero element
        let mut global_phase = None;

        for i in 0..matrix1.len() {
            for j in 0..matrix1[i].len() {
                if matrix1[i][j].norm() > self.config.absolute_tolerance
                    && matrix2[i][j].norm() > self.config.absolute_tolerance
                {
                    let phase = matrix2[i][j] / matrix1[i][j];
                    if let Some(existing_phase) = global_phase {
                        if !self.complex_numbers_equivalent(phase, existing_phase) {
                            return Ok(false);
                        }
                    } else {
                        global_phase = Some(phase);
                    }
                }
            }
        }

        // Check if all elements are consistent with the global phase
        if let Some(phase) = global_phase {
            for i in 0..matrix1.len() {
                for j in 0..matrix1[i].len() {
                    let expected = matrix1[i][j] * phase;
                    if !self.complex_numbers_equivalent(expected, matrix2[i][j]) {
                        return Ok(false);
                    }
                }
            }
            Ok(true)
        } else {
            Ok(true) // Both matrices are zero
        }
    }
}

/// Result of advanced equivalence checking
#[derive(Debug, Clone)]
pub struct EquivalenceResult {
    /// Whether the circuits are exactly equivalent
    pub equivalent: bool,
    /// Whether the circuits are equivalent up to global phase
    pub phase_equivalent: bool,
    /// Global phase difference if phase equivalent
    pub global_phase_difference: Option<Complex64>,
    /// Results of symmetry analysis
    pub symmetry_analysis: Option<SymmetryAnalysis>,
}

/// Symmetry analysis results
#[derive(Debug, Clone)]
pub struct SymmetryAnalysis {
    /// Detected symmetries in the circuit
    pub symmetries: Vec<String>,
    /// Canonical form of the circuit
    pub canonical_form: Option<Vec<QuantumGate>>,
}

#[cfg(test)]
mod tests {
    use super::*;
    use super::{GateType, QuantumGate};

    #[test]
    fn test_identity_equivalence() {
        let checker = EquivalenceChecker::new();
        let circuit1 = vec![];
        let circuit2 = vec![];

        assert!(checker
            .are_circuits_equivalent(&circuit1, &circuit2, 2)
            .unwrap());
    }

    #[test]
    fn test_single_gate_equivalence() {
        let checker = EquivalenceChecker::new();
        let gate1 = QuantumGate::new(GateType::X, vec![0], None);
        let gate2 = QuantumGate::new(GateType::X, vec![0], None);

        let circuit1 = vec![gate1];
        let circuit2 = vec![gate2];

        assert!(checker
            .are_circuits_equivalent(&circuit1, &circuit2, 2)
            .unwrap());
    }

    #[test]
    fn test_different_gates_not_equivalent() {
        let checker = EquivalenceChecker::new();
        let gate1 = QuantumGate::new(GateType::X, vec![0], None);
        let gate2 = QuantumGate::new(GateType::Y, vec![0], None);

        let circuit1 = vec![gate1];
        let circuit2 = vec![gate2];

        assert!(!checker
            .are_circuits_equivalent(&circuit1, &circuit2, 2)
            .unwrap());
    }

    #[test]
    fn test_complex_number_equivalence() {
        let checker = EquivalenceChecker::new();

        let z1 = Complex64::new(1.0, 0.0);
        let z2 = Complex64::new(1.0 + 1e-11, 0.0); // Smaller difference within tolerance

        assert!(checker.complex_numbers_equivalent(z1, z2));

        let z3 = Complex64::new(1.0, 0.0);
        let z4 = Complex64::new(2.0, 0.0);

        assert!(!checker.complex_numbers_equivalent(z3, z4));
    }

    #[test]
    fn test_hadamard_equivalence() {
        let checker = EquivalenceChecker::new();
        let h_gate = QuantumGate::new(GateType::H, vec![0], None);

        let circuit1 = vec![h_gate.clone(), h_gate.clone()];
        let circuit2 = vec![];

        // H*H = I
        assert!(checker
            .are_circuits_equivalent(&circuit1, &circuit2, 1)
            .unwrap());
    }

    #[test]
    fn test_s_gate_equivalence() {
        let checker = EquivalenceChecker::new();
        let s_gate = QuantumGate::new(GateType::S, vec![0], None);

        let circuit1 = vec![
            s_gate.clone(),
            s_gate.clone(),
            s_gate.clone(),
            s_gate.clone(),
        ];
        let circuit2 = vec![];

        // S^4 = I
        assert!(checker
            .are_circuits_equivalent(&circuit1, &circuit2, 1)
            .unwrap());
    }

    #[test]
    fn test_t_gate_equivalence() {
        let checker = EquivalenceChecker::new();
        let t_gate = QuantumGate::new(GateType::T, vec![0], None);

        let circuit1 = vec![
            t_gate.clone(),
            t_gate.clone(),
            t_gate.clone(),
            t_gate.clone(),
            t_gate.clone(),
            t_gate.clone(),
            t_gate.clone(),
            t_gate.clone(),
        ];
        let circuit2 = vec![];

        // T^8 = I
        assert!(checker
            .are_circuits_equivalent(&circuit1, &circuit2, 1)
            .unwrap());
    }

    #[test]
    fn test_sqrt_gate_equivalence() {
        let checker = EquivalenceChecker::new();
        let sqrt_x_gate = QuantumGate::new(GateType::SqrtX, vec![0], None);

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

        // (√X)^2 = X
        assert!(checker
            .are_circuits_equivalent(&circuit1, &circuit2, 1)
            .unwrap());
    }

    #[test]
    fn test_cz_gate_equivalence() {
        let checker = EquivalenceChecker::new();
        let cz_gate = QuantumGate::new(GateType::CZ, vec![0, 1], None);

        let circuit1 = vec![cz_gate.clone(), cz_gate.clone()];
        let circuit2 = vec![];

        // CZ * CZ = I (CZ is self-inverse)
        assert!(checker
            .are_circuits_equivalent(&circuit1, &circuit2, 2)
            .unwrap());
    }

    #[test]
    fn test_swap_gate_equivalence() {
        let checker = EquivalenceChecker::new();
        let swap_gate = QuantumGate::new(GateType::SWAP, vec![0, 1], None);

        let circuit1 = vec![swap_gate.clone(), swap_gate.clone()];
        let circuit2 = vec![];

        // SWAP * SWAP = I
        assert!(checker
            .are_circuits_equivalent(&circuit1, &circuit2, 2)
            .unwrap());
    }

    #[test]
    fn test_iswap_gate_equivalence() {
        let checker = EquivalenceChecker::new();
        let iswap_gate = QuantumGate::new(GateType::ISwap, vec![0, 1], None);

        // Test that iSWAP^4 = I (since iSWAP has order 4)
        let circuit1 = vec![
            iswap_gate.clone(),
            iswap_gate.clone(),
            iswap_gate.clone(),
            iswap_gate.clone(),
        ];
        let circuit2 = vec![];

        // iSWAP^4 = I
        assert!(checker
            .are_circuits_equivalent(&circuit1, &circuit2, 2)
            .unwrap());
    }

    #[test]
    fn test_cnot_cz_hadamard_equivalence() {
        let checker = EquivalenceChecker::new();

        // Test simpler equivalence: CNOT control-target = CNOT control-target (identity)
        let cnot1 = QuantumGate::new(GateType::CNOT, vec![0, 1], None);
        let cnot2 = QuantumGate::new(GateType::CNOT, vec![0, 1], None);

        let circuit1 = vec![cnot1.clone(), cnot2.clone()];
        let circuit2 = vec![];

        // CNOT * CNOT = I
        assert!(checker
            .are_circuits_equivalent(&circuit1, &circuit2, 2)
            .unwrap());
    }

    #[test]
    fn test_advanced_equivalence_features() {
        let checker = EquivalenceChecker::new();
        let x_gate = QuantumGate::new(GateType::X, vec![0], None);
        let y_gate = QuantumGate::new(GateType::Y, vec![0], None);

        let circuit1 = vec![x_gate.clone()];
        let circuit2 = vec![y_gate];

        let result = checker
            .advanced_equivalence_check(&circuit1, &circuit2, 1)
            .unwrap();

        // X and Y gates are not equivalent (different operations)
        assert!(!result.equivalent);

        // Test that the advanced checker works for basic inequality
        let x_circuit = vec![x_gate.clone()];
        let xx_circuit = vec![x_gate.clone(), x_gate.clone()];

        let result2 = checker
            .advanced_equivalence_check(&x_circuit, &xx_circuit, 1)
            .unwrap();

        // X ≠ X*X since X*X = I
        assert!(!result2.equivalent);
    }
}