quantrs2-sim 0.1.3

//! Quantum Error Correction
//!
//! This module provides implementations of quantum error correction codes
//! for protecting quantum information against noise and errors.

use quantrs_circuit::builder::Circuit;
use quantrs_core::qubit::QubitId;

/// Trait for quantum error correction codes
pub trait ErrorCorrection {
    /// Get the number of physical qubits required
    fn physical_qubits(&self) -> usize;

    /// Get the number of logical qubits encoded
    fn logical_qubits(&self) -> usize;

    /// Get the distance of the code (minimum number of errors it can detect)
    fn distance(&self) -> usize;

    /// Create a circuit to encode logical qubits into the error correction code
    fn encode_circuit(&self, logical_qubits: &[QubitId], ancilla_qubits: &[QubitId]) -> Circuit<16>;

    /// Create a circuit to decode and correct errors
    fn decode_circuit(&self, encoded_qubits: &[QubitId], syndrome_qubits: &[QubitId]) -> Circuit<16>;
}

/// The 3-qubit bit flip code
///
/// This code can detect and correct single bit flip errors.
/// It encodes a single logical qubit into 3 physical qubits.
pub struct BitFlipCode;

impl ErrorCorrection for BitFlipCode {
    fn physical_qubits(&self) -> usize {
        3
    }

    fn logical_qubits(&self) -> usize {
        1
    }

    fn distance(&self) -> usize {
        3
    }

    fn encode_circuit(&self, logical_qubits: &[QubitId], ancilla_qubits: &[QubitId]) -> Circuit<16> {
        // We limit the circuit to 16 qubits maximum
        let mut circuit = Circuit::<16>::new();

        // Check if we have enough qubits
        if logical_qubits.len() < 1 || ancilla_qubits.len() < 2 {
            panic!("BitFlipCode requires 1 logical qubit and 2 ancilla qubits");
        }

        // Extract qubit IDs
        let q0 = logical_qubits[0];
        let q1 = ancilla_qubits[0];
        let q2 = ancilla_qubits[1];

        // Encode |ψ⟩ -> |ψψψ⟩
        // CNOT from logical qubit to each ancilla qubit
        circuit.cnot(q0, q1).expect("CNOT should succeed with validated qubit indices");
        circuit.cnot(q0, q2).expect("CNOT should succeed with validated qubit indices");

        circuit
    }

    fn decode_circuit(&self, encoded_qubits: &[QubitId], syndrome_qubits: &[QubitId]) -> Circuit<16> {
        let mut circuit = Circuit::<16>::new();

        // Check if we have enough qubits
        if encoded_qubits.len() < 3 || syndrome_qubits.len() < 2 {
            panic!("BitFlipCode requires 3 encoded qubits and 2 syndrome qubits");
        }

        // Extract qubit IDs
        let q0 = encoded_qubits[0];
        let q1 = encoded_qubits[1];
        let q2 = encoded_qubits[2];
        let s0 = syndrome_qubits[0];
        let s1 = syndrome_qubits[1];

        // Syndrome extraction: CNOT from data qubits to syndrome qubits
        circuit.cnot(q0, s0).expect("CNOT should succeed with validated qubit indices");
        circuit.cnot(q1, s0).expect("CNOT should succeed with validated qubit indices");
        circuit.cnot(q1, s1).expect("CNOT should succeed with validated qubit indices");
        circuit.cnot(q2, s1).expect("CNOT should succeed with validated qubit indices");

        // Apply corrections based on syndrome
        // Syndrome 01 (s1=0, s0=1): bit flip on q0
        circuit.x(s1).expect("X gate should succeed with validated qubit index");
        circuit.cx(s0, q0).expect("CX gate should succeed with validated qubit indices");
        circuit.x(s1).expect("X gate should succeed with validated qubit index");

        // Syndrome 10 (s1=1, s0=0): bit flip on q1
        circuit.x(s0).expect("X gate should succeed with validated qubit index");
        circuit.cx(s1, q1).expect("CX gate should succeed with validated qubit indices");
        circuit.x(s0).expect("X gate should succeed with validated qubit index");

        // Syndrome 11 (s1=1, s0=1): bit flip on q2
        circuit.cx(s0, q2).expect("CX gate should succeed with validated qubit indices");
        circuit.cx(s1, q2).expect("CX gate should succeed with validated qubit indices");

        circuit
    }
}

/// The 3-qubit phase flip code
///
/// This code can detect and correct single phase flip errors.
/// It encodes a single logical qubit into 3 physical qubits.
pub struct PhaseFlipCode;

impl ErrorCorrection for PhaseFlipCode {
    fn physical_qubits(&self) -> usize {
        3
    }

    fn logical_qubits(&self) -> usize {
        1
    }

    fn distance(&self) -> usize {
        3
    }

    fn encode_circuit(&self, logical_qubits: &[QubitId], ancilla_qubits: &[QubitId]) -> Circuit<16> {
        // We limit the circuit to 16 qubits maximum
        let mut circuit = Circuit::<16>::new();

        // Check if we have enough qubits
        if logical_qubits.len() < 1 || ancilla_qubits.len() < 2 {
            panic!("PhaseFlipCode requires 1 logical qubit and 2 ancilla qubits");
        }

        // Extract qubit IDs
        let q0 = logical_qubits[0];
        let q1 = ancilla_qubits[0];
        let q2 = ancilla_qubits[1];

        // Apply Hadamard to all qubits
        circuit.h(q0).expect("H gate should succeed with validated qubit index");
        circuit.h(q1).expect("H gate should succeed with validated qubit index");
        circuit.h(q2).expect("H gate should succeed with validated qubit index");

        // Encode using bit flip code
        circuit.cnot(q0, q1).expect("CNOT should succeed with validated qubit indices");
        circuit.cnot(q0, q2).expect("CNOT should succeed with validated qubit indices");

        // Apply Hadamard to all qubits again
        circuit.h(q0).expect("H gate should succeed with validated qubit index");
        circuit.h(q1).expect("H gate should succeed with validated qubit index");
        circuit.h(q2).expect("H gate should succeed with validated qubit index");

        circuit
    }

    fn decode_circuit(&self, encoded_qubits: &[QubitId], syndrome_qubits: &[QubitId]) -> Circuit<16> {
        let mut circuit = Circuit::<16>::new();

        // Check if we have enough qubits
        if encoded_qubits.len() < 3 || syndrome_qubits.len() < 2 {
            panic!("PhaseFlipCode requires 3 encoded qubits and 2 syndrome qubits");
        }

        // Extract qubit IDs
        let q0 = encoded_qubits[0];
        let q1 = encoded_qubits[1];
        let q2 = encoded_qubits[2];
        let s0 = syndrome_qubits[0];
        let s1 = syndrome_qubits[1];

        // Apply Hadamard to all encoded qubits
        circuit.h(q0).expect("H gate should succeed with validated qubit index");
        circuit.h(q1).expect("H gate should succeed with validated qubit index");
        circuit.h(q2).expect("H gate should succeed with validated qubit index");

        // Syndrome extraction: CNOT from data qubits to syndrome qubits
        circuit.cnot(q0, s0).expect("CNOT should succeed with validated qubit indices");
        circuit.cnot(q1, s0).expect("CNOT should succeed with validated qubit indices");
        circuit.cnot(q1, s1).expect("CNOT should succeed with validated qubit indices");
        circuit.cnot(q2, s1).expect("CNOT should succeed with validated qubit indices");

        // Apply corrections based on syndrome in X basis
        // Syndrome 01 (s1=0, s0=1): bit flip on q0
        circuit.x(s1).expect("X gate should succeed with validated qubit index");
        circuit.cx(s0, q0).expect("CX gate should succeed with validated qubit indices");
        circuit.x(s1).expect("X gate should succeed with validated qubit index");

        // Syndrome 10 (s1=1, s0=0): bit flip on q1
        circuit.x(s0).expect("X gate should succeed with validated qubit index");
        circuit.cx(s1, q1).expect("CX gate should succeed with validated qubit indices");
        circuit.x(s0).expect("X gate should succeed with validated qubit index");

        // Syndrome 11 (s1=1, s0=1): bit flip on q2
        circuit.cx(s0, q2).expect("CX gate should succeed with validated qubit indices");
        circuit.cx(s1, q2).expect("CX gate should succeed with validated qubit indices");

        // Apply Hadamard to all encoded qubits to go back to computational basis
        circuit.h(q0).expect("H gate should succeed with validated qubit index");
        circuit.h(q1).expect("H gate should succeed with validated qubit index");
        circuit.h(q2).expect("H gate should succeed with validated qubit index");

        circuit
    }
}

/// The 9-qubit Shor code
///
/// This code can detect and correct arbitrary single-qubit errors
/// (bit flips, phase flips, or both). It encodes a single logical
/// qubit into 9 physical qubits.
pub struct ShorCode;

impl ErrorCorrection for ShorCode {
    fn physical_qubits(&self) -> usize {
        9
    }

    fn logical_qubits(&self) -> usize {
        1
    }

    fn distance(&self) -> usize {
        3
    }

    fn encode_circuit(&self, logical_qubits: &[QubitId], ancilla_qubits: &[QubitId]) -> Circuit<16> {
        let mut circuit = Circuit::<16>::new();

        // Check if we have enough qubits
        if logical_qubits.len() < 1 || ancilla_qubits.len() < 8 {
            panic!("ShorCode requires 1 logical qubit and 8 ancilla qubits");
        }

        // Extract qubit IDs for easier reading
        let q = logical_qubits[0];  // logical qubit
        let a = &ancilla_qubits[0..8];  // ancilla qubits

        // Step 1: First encode the qubit for phase-flip protection
        // This is done by applying Hadamard and creating a 3-qubit GHZ-like state
        circuit.h(q).expect("H gate should succeed with validated qubit index");

        // Create 3 blocks with one qubit each
        circuit.cnot(q, a[0]).expect("CNOT should succeed with validated qubit indices");   // Block 1 - first qubit
        circuit.cnot(q, a[3]).expect("CNOT should succeed with validated qubit indices");   // Block 2 - first qubit

        // Step 2: Encode each of these 3 qubits against bit-flips
        // using the 3-qubit bit-flip code

        // Encode Block 1 (qubits q, a[0], a[1], a[2])
        circuit.cnot(q, a[1]).expect("CNOT should succeed with validated qubit indices");
        circuit.cnot(q, a[2]).expect("CNOT should succeed with validated qubit indices");

        // Encode Block 2 (qubits a[3], a[4], a[5])
        circuit.cnot(a[3], a[4]).expect("CNOT should succeed with validated qubit indices");
        circuit.cnot(a[3], a[5]).expect("CNOT should succeed with validated qubit indices");

        // Encode Block 3 (qubits a[6], a[7])
        // CNOT with logical qubit to create the third block
        circuit.cnot(q, a[6]).expect("CNOT should succeed with validated qubit indices");
        circuit.cnot(a[6], a[7]).expect("CNOT should succeed with validated qubit indices");

        // At this point, we have encoded our logical |0⟩ as:
        // (|000_000_000⟩ + |111_111_111⟩)/√2 and
        // logical |1⟩ as: (|000_000_000⟩ - |111_111_111⟩)/√2

        // Apply Hadamards again to transform into the final Shor code state
        // For the standard Shor code representation, we would apply Hadamards again
        // to all qubits. For this implementation we'll leave it in the current basis.

        circuit
    }

    fn decode_circuit(&self, encoded_qubits: &[QubitId], syndrome_qubits: &[QubitId]) -> Circuit<16> {
        let mut circuit = Circuit::<16>::new();

        // Check if we have enough qubits
        if encoded_qubits.len() < 9 || syndrome_qubits.len() < 8 {
            panic!("ShorCode requires 9 encoded qubits and 8 syndrome qubits");
        }

        // Extract qubit IDs for more readable code
        let data = encoded_qubits;
        let synd = syndrome_qubits;

        // Step 1: Bit-flip error detection within each group

        // Group 1 (qubits 0,1,2) syndrome detection
        circuit.cnot(data[0], synd[0]).expect("CNOT should succeed with validated qubit indices");
        circuit.cnot(data[1], synd[0]).expect("CNOT should succeed with validated qubit indices");
        circuit.cnot(data[1], synd[1]).expect("CNOT should succeed with validated qubit indices");
        circuit.cnot(data[2], synd[1]).expect("CNOT should succeed with validated qubit indices");

        // Group 2 (qubits 3,4,5) syndrome detection
        circuit.cnot(data[3], synd[2]).expect("CNOT should succeed with validated qubit indices");
        circuit.cnot(data[4], synd[2]).expect("CNOT should succeed with validated qubit indices");
        circuit.cnot(data[4], synd[3]).expect("CNOT should succeed with validated qubit indices");
        circuit.cnot(data[5], synd[3]).expect("CNOT should succeed with validated qubit indices");

        // Group 3 (qubits 6,7,8) syndrome detection
        circuit.cnot(data[6], synd[4]).expect("CNOT should succeed with validated qubit indices");
        circuit.cnot(data[7], synd[4]).expect("CNOT should succeed with validated qubit indices");
        circuit.cnot(data[7], synd[5]).expect("CNOT should succeed with validated qubit indices");
        circuit.cnot(data[8], synd[5]).expect("CNOT should succeed with validated qubit indices");

        // Step 2: Apply bit-flip corrections based on syndromes

        // Group 1 corrections
        // Syndrome 01 (s1=0, s0=1): bit flip on q0
        circuit.x(synd[1]).expect("X gate should succeed with validated qubit index");
        circuit.cx(synd[0], data[0]).expect("CX gate should succeed with validated qubit indices");
        circuit.x(synd[1]).expect("X gate should succeed with validated qubit index");

        // Syndrome 10 (s1=1, s0=0): bit flip on q1
        circuit.x(synd[0]).expect("X gate should succeed with validated qubit index");
        circuit.cx(synd[1], data[1]).expect("CX gate should succeed with validated qubit indices");
        circuit.x(synd[0]).expect("X gate should succeed with validated qubit index");

        // Syndrome 11 (s1=1, s0=1): bit flip on q2
        circuit.cx(synd[0], data[2]).expect("CX gate should succeed with validated qubit indices");
        circuit.cx(synd[1], data[2]).expect("CX gate should succeed with validated qubit indices");

        // Group 2 corrections
        // Syndrome 01 (s3=0, s2=1): bit flip on q3
        circuit.x(synd[3]).expect("X gate should succeed with validated qubit index");
        circuit.cx(synd[2], data[3]).expect("CX gate should succeed with validated qubit indices");
        circuit.x(synd[3]).expect("X gate should succeed with validated qubit index");

        // Syndrome 10 (s3=1, s2=0): bit flip on q4
        circuit.x(synd[2]).expect("X gate should succeed with validated qubit index");
        circuit.cx(synd[3], data[4]).expect("CX gate should succeed with validated qubit indices");
        circuit.x(synd[2]).expect("X gate should succeed with validated qubit index");

        // Syndrome 11 (s3=1, s2=1): bit flip on q5
        circuit.cx(synd[2], data[5]).expect("CX gate should succeed with validated qubit indices");
        circuit.cx(synd[3], data[5]).expect("CX gate should succeed with validated qubit indices");

        // Group 3 corrections
        // Syndrome 01 (s5=0, s4=1): bit flip on q6
        circuit.x(synd[5]).expect("X gate should succeed with validated qubit index");
        circuit.cx(synd[4], data[6]).expect("CX gate should succeed with validated qubit indices");
        circuit.x(synd[5]).expect("X gate should succeed with validated qubit index");

        // Syndrome 10 (s5=1, s4=0): bit flip on q7
        circuit.x(synd[4]).expect("X gate should succeed with validated qubit index");
        circuit.cx(synd[5], data[7]).expect("CX gate should succeed with validated qubit indices");
        circuit.x(synd[4]).expect("X gate should succeed with validated qubit index");

        // Syndrome 11 (s5=1, s4=1): bit flip on q8
        circuit.cx(synd[4], data[8]).expect("CX gate should succeed with validated qubit indices");
        circuit.cx(synd[5], data[8]).expect("CX gate should succeed with validated qubit indices");

        // Step 3: Phase-flip error detection between groups

        // Apply Hadamard gates to convert phase errors to bit errors
        for &q in &[data[0], data[3], data[6]] {
            circuit.h(q).expect("H gate should succeed with validated qubit index");
        }

        // Detect phase errors by comparing the first qubit of each group
        circuit.cnot(data[0], synd[6]).expect("CNOT should succeed with validated qubit indices");
        circuit.cnot(data[3], synd[6]).expect("CNOT should succeed with validated qubit indices");
        circuit.cnot(data[3], synd[7]).expect("CNOT should succeed with validated qubit indices");
        circuit.cnot(data[6], synd[7]).expect("CNOT should succeed with validated qubit indices");

        // Step 4: Apply phase-flip corrections based on syndrome

        // Syndrome 01 (s7=0, s6=1): phase flip on group 1 (qubits 0,1,2)
        circuit.x(synd[7]).expect("X gate should succeed with validated qubit index");
        for &q in &[data[0], data[1], data[2]] {
            circuit.cz(synd[6], q).expect("CZ gate should succeed with validated qubit indices");
        }
        circuit.x(synd[7]).expect("X gate should succeed with validated qubit index");

        // Syndrome 10 (s7=1, s6=0): phase flip on group 2 (qubits 3,4,5)
        circuit.x(synd[6]).expect("X gate should succeed with validated qubit index");
        for &q in &[data[3], data[4], data[5]] {
            circuit.cz(synd[7], q).expect("CZ gate should succeed with validated qubit indices");
        }
        circuit.x(synd[6]).expect("X gate should succeed with validated qubit index");

        // Syndrome 11 (s7=1, s6=1): phase flip on group 3 (qubits 6,7,8)
        for &q in &[data[6], data[7], data[8]] {
            circuit.cz(synd[6], q).expect("CZ gate should succeed with validated qubit indices");
            circuit.cz(synd[7], q).expect("CZ gate should succeed with validated qubit indices");
        }

        // Step 5: Transform back from Hadamard basis
        for &q in &[data[0], data[3], data[6]] {
            circuit.h(q).expect("H gate should succeed with validated qubit index");
        }

        circuit
    }
}

/// The 5-qubit code
///
/// This is the smallest code that can correct an arbitrary single-qubit error.
/// It encodes a single logical qubit into 5 physical qubits.
pub struct FiveQubitCode;

impl ErrorCorrection for FiveQubitCode {
    fn physical_qubits(&self) -> usize {
        5
    }

    fn logical_qubits(&self) -> usize {
        1
    }

    fn distance(&self) -> usize {
        3
    }

    fn encode_circuit(&self, logical_qubits: &[QubitId], ancilla_qubits: &[QubitId]) -> Circuit<16> {
        let mut circuit = Circuit::<16>::new();

        // Check if we have enough qubits
        if logical_qubits.len() < 1 || ancilla_qubits.len() < 4 {
            panic!("FiveQubitCode requires 1 logical qubit and 4 ancilla qubits");
        }

        // Extract qubit IDs
        let q0 = logical_qubits[0];
        let ancs = ancilla_qubits;

        // The encoding circuit for the 5-qubit perfect code
        // This implements the circuit described in Nielsen & Chuang

        // Initialize all ancilla qubits to |0⟩ (they start in this state by default)

        // Step 1: Apply the initial gates to start creating the superposition
        circuit.h(ancs[0]).expect("H gate should succeed with validated qubit index");
        circuit.h(ancs[1]).expect("H gate should succeed with validated qubit index");
        circuit.h(ancs[2]).expect("H gate should succeed with validated qubit index");
        circuit.h(ancs[3]).expect("H gate should succeed with validated qubit index");

        // Step 2: Apply the controlled encoding operations
        // CNOT from data qubit to ancilla qubits
        circuit.cnot(q0, ancs[0]).expect("CNOT should succeed with validated qubit indices");
        circuit.cnot(q0, ancs[1]).expect("CNOT should succeed with validated qubit indices");
        circuit.cnot(q0, ancs[2]).expect("CNOT should succeed with validated qubit indices");
        circuit.cnot(q0, ancs[3]).expect("CNOT should succeed with validated qubit indices");

        // Step 3: Apply the stabilizer operations
        // These specific gates implement the [[5,1,3]] perfect code

        // X stabilizer operations
        circuit.h(q0).expect("H gate should succeed with validated qubit index");
        circuit.h(ancs[1]).expect("H gate should succeed with validated qubit index");
        circuit.h(ancs[3]).expect("H gate should succeed with validated qubit index");

        circuit.cnot(q0, ancs[0]).expect("CNOT should succeed with validated qubit indices");
        circuit.cnot(ancs[1], ancs[0]).expect("CNOT should succeed with validated qubit indices");
        circuit.cnot(ancs[0], ancs[2]).expect("CNOT should succeed with validated qubit indices");
        circuit.cnot(ancs[2], ancs[3]).expect("CNOT should succeed with validated qubit indices");

        // Z stabilizer operations
        circuit.cz(q0, ancs[1]).expect("CZ gate should succeed with validated qubit indices");
        circuit.cz(ancs[0], ancs[2]).expect("CZ gate should succeed with validated qubit indices");
        circuit.cz(ancs[1], ancs[3]).expect("CZ gate should succeed with validated qubit indices");

        circuit.h(ancs[0]).expect("H gate should succeed with validated qubit index");
        circuit.h(ancs[2]).expect("H gate should succeed with validated qubit index");

        // This encodes the logical qubit into a 5-qubit entangled state that can
        // detect and correct any single-qubit error

        circuit
    }

    fn decode_circuit(&self, encoded_qubits: &[QubitId], syndrome_qubits: &[QubitId]) -> Circuit<16> {
        let mut circuit = Circuit::<16>::new();

        // Check if we have enough qubits
        if encoded_qubits.len() < 5 || syndrome_qubits.len() < 4 {
            panic!("FiveQubitCode requires 5 encoded qubits and 4 syndrome qubits");
        }

        // Extract qubit IDs
        let data = encoded_qubits;
        let synd = syndrome_qubits;

        // The 5-qubit code uses 4 stabilizer generators to detect errors
        // We'll implement the syndrome extraction circuit that measures these stabilizers

        // Generator 1: XZZXI
        circuit.h(synd[0]).expect("H gate should succeed with validated qubit index");
        circuit.cnot(synd[0], data[0]).expect("CNOT should succeed with validated qubit indices");
        circuit.cz(synd[0], data[1]).expect("CZ gate should succeed with validated qubit indices");
        circuit.cz(synd[0], data[2]).expect("CZ gate should succeed with validated qubit indices");
        circuit.cnot(synd[0], data[3]).expect("CNOT should succeed with validated qubit indices");
        circuit.h(synd[0]).expect("H gate should succeed with validated qubit index");

        // Generator 2: IXZZX
        circuit.h(synd[1]).expect("H gate should succeed with validated qubit index");
        circuit.cnot(synd[1], data[1]).expect("CNOT should succeed with validated qubit indices");
        circuit.cz(synd[1], data[2]).expect("CZ gate should succeed with validated qubit indices");
        circuit.cz(synd[1], data[3]).expect("CZ gate should succeed with validated qubit indices");
        circuit.cnot(synd[1], data[4]).expect("CNOT should succeed with validated qubit indices");
        circuit.h(synd[1]).expect("H gate should succeed with validated qubit index");

        // Generator 3: XIXZZ
        circuit.h(synd[2]).expect("H gate should succeed with validated qubit index");
        circuit.cnot(synd[2], data[0]).expect("CNOT should succeed with validated qubit indices");
        circuit.cnot(synd[2], data[2]).expect("CNOT should succeed with validated qubit indices");
        circuit.cz(synd[2], data[3]).expect("CZ gate should succeed with validated qubit indices");
        circuit.cz(synd[2], data[4]).expect("CZ gate should succeed with validated qubit indices");
        circuit.h(synd[2]).expect("H gate should succeed with validated qubit index");

        // Generator 4: ZXIXZ
        circuit.h(synd[3]).expect("H gate should succeed with validated qubit index");
        circuit.cz(synd[3], data[0]).expect("CZ gate should succeed with validated qubit indices");
        circuit.cnot(synd[3], data[1]).expect("CNOT should succeed with validated qubit indices");
        circuit.cnot(synd[3], data[3]).expect("CNOT should succeed with validated qubit indices");
        circuit.cz(synd[3], data[4]).expect("CZ gate should succeed with validated qubit indices");
        circuit.h(synd[3]).expect("H gate should succeed with validated qubit index");

        // After measuring the syndrome, we would apply the appropriate correction
        // The 5-qubit code has a complex error correction table with 16 possible syndromes
        // We'll implement a simplified version that corrects the most common errors

        // First, we'll correct bit flips (X errors)
        // Syndrome 0001: X error on qubit 0
        let syndrome_0001 = [false, false, false, true];
        self.add_conditional_correction(&mut circuit, synd, syndrome_0001, data[0], 'X');

        // Syndrome 0010: X error on qubit 1
        let syndrome_0010 = [false, false, true, false];
        self.add_conditional_correction(&mut circuit, synd, syndrome_0010, data[1], 'X');

        // Syndrome 0100: X error on qubit 2
        let syndrome_0100 = [false, true, false, false];
        self.add_conditional_correction(&mut circuit, synd, syndrome_0100, data[2], 'X');

        // Syndrome 1000: X error on qubit 3
        let syndrome_1000 = [true, false, false, false];
        self.add_conditional_correction(&mut circuit, synd, syndrome_1000, data[3], 'X');

        // Now, we'll correct phase flips (Z errors)
        // Syndrome 0011: Z error on qubit 0
        let syndrome_0011 = [false, false, true, true];
        self.add_conditional_correction(&mut circuit, synd, syndrome_0011, data[0], 'Z');

        // Syndrome 0101: Z error on qubit 1
        let syndrome_0101 = [false, true, false, true];
        self.add_conditional_correction(&mut circuit, synd, syndrome_0101, data[1], 'Z');

        // Syndrome 1001: Z error on qubit 2
        let syndrome_1001 = [true, false, false, true];
        self.add_conditional_correction(&mut circuit, synd, syndrome_1001, data[2], 'Z');

        // Syndrome 1100: Z error on qubit 3
        let syndrome_1100 = [true, true, false, false];
        self.add_conditional_correction(&mut circuit, synd, syndrome_1100, data[3], 'Z');

        // And finally, Y errors (both bit and phase flips)
        // Syndrome 0111: Y error on qubit 0
        let syndrome_0111 = [false, true, true, true];
        self.add_conditional_correction(&mut circuit, synd, syndrome_0111, data[0], 'Y');

        // Syndrome 1011: Y error on qubit 1
        let syndrome_1011 = [true, false, true, true];
        self.add_conditional_correction(&mut circuit, synd, syndrome_1011, data[1], 'Y');

        // Syndrome 1101: Y error on qubit 2
        let syndrome_1101 = [true, true, false, true];
        self.add_conditional_correction(&mut circuit, synd, syndrome_1101, data[2], 'Y');

        // Syndrome 1110: Y error on qubit 3
        let syndrome_1110 = [true, true, true, false];
        self.add_conditional_correction(&mut circuit, synd, syndrome_1110, data[3], 'Y');

        circuit
    }
}

impl FiveQubitCode {
    /// Helper function to add conditionally controlled gates based on syndrome measurement
    fn add_conditional_correction(
        &self,
        circuit: &mut Circuit<16>,
        syndrome_qubits: &[QubitId],
        syndrome: [bool; 4],
        target: QubitId,
        error_type: char,
    ) {
        // In a real quantum circuit, this would involve classical control
        // For our simulator, we simulate classical control using quantum gates

        // For each syndrome bit, apply X gate to negate it if needed
        for (i, &should_be_one) in syndrome.iter().enumerate() {
            if !should_be_one {
                circuit.x(syndrome_qubits[i]).expect("X gate should succeed with validated qubit index");
            }
        }

        // Apply the correction controlled on all syndrome bits being 1
        // We need to control the correction based on all syndrome bits
        // For more accuracy, we'd use a multi-controlled gate, but for this simulation
        // we'll implement a simplified approach

        // First, combine all syndrome bits into one control qubit
        // We do this by applying a series of controlled-X gates
        for i in 1..syndrome_qubits.len() {
            circuit.cx(syndrome_qubits[i], syndrome_qubits[0]).expect("CX gate should succeed with validated qubit indices");
        }

        // Now apply the appropriate correction controlled by the first syndrome bit
        match error_type {
            'X' => {
                // Apply X correction (for bit flip)
                circuit.cx(syndrome_qubits[0], target).expect("CX gate should succeed with validated qubit indices");
            },
            'Z' => {
                // Apply Z correction (for phase flip)
                circuit.cz(syndrome_qubits[0], target).expect("CZ gate should succeed with validated qubit indices");
            },
            'Y' => {
                // Apply Y correction (for bit-phase flip)
                // We can implement Y as Z followed by X
                circuit.cz(syndrome_qubits[0], target).expect("CZ gate should succeed with validated qubit indices");
                circuit.cx(syndrome_qubits[0], target).expect("CX gate should succeed with validated qubit indices");
            },
            _ => panic!("Unsupported error type"),
        }

        // Undo the combination of syndrome bits
        for i in 1..syndrome_qubits.len() {
            circuit.cx(syndrome_qubits[i], syndrome_qubits[0]).expect("CX gate should succeed with validated qubit indices");
        }

        // Reset syndrome bits to their original states
        for (i, &should_be_one) in syndrome.iter().enumerate() {
            if !should_be_one {
                circuit.x(syndrome_qubits[i]).expect("X gate should succeed with validated qubit index");
            }
        }
    }
}

/// The 7-qubit Steane code
///
/// This code is a CSS code that can correct an arbitrary single-qubit error.
/// It encodes a single logical qubit into 7 physical qubits.
pub struct SteaneCode;

impl ErrorCorrection for SteaneCode {
    fn physical_qubits(&self) -> usize {
        7
    }

    fn logical_qubits(&self) -> usize {
        1
    }

    fn distance(&self) -> usize {
        3
    }

    fn encode_circuit(&self, logical_qubits: &[QubitId], ancilla_qubits: &[QubitId]) -> Circuit<16> {
        let mut circuit = Circuit::<16>::new();

        // Check if we have enough qubits
        if logical_qubits.len() < 1 || ancilla_qubits.len() < 6 {
            panic!("SteaneCode requires 1 logical qubit and 6 ancilla qubits");
        }

        // Steane code encoding circuit
        // The Steane code is a [7,1,3] CSS code derived from the classical Hamming code

        let data = encoded_qubits[0];
        let parity_x = &encoded_qubits[1..4];
        let parity_z = &encoded_qubits[4..7];

        // X-basis encoding (for bit-flip protection)
        for &p in parity_x {
            circuit.cnot(data, p).expect("CNOT should succeed with validated qubit indices");
        }

        // Additional X parity checks
        circuit.cnot(encoded_qubits[1], encoded_qubits[3]).expect("CNOT should succeed with validated qubit indices");
        circuit.cnot(encoded_qubits[2], encoded_qubits[3]).expect("CNOT should succeed with validated qubit indices");

        // Z-basis encoding (for phase-flip protection)
        for &p in parity_z {
            circuit.h(p).expect("H gate should succeed with validated qubit index");
            circuit.cnot(data, p).expect("CNOT should succeed with validated qubit indices");
            circuit.h(p).expect("H gate should succeed with validated qubit index");
        }

        // Additional Z parity checks
        circuit.h(encoded_qubits[4]).expect("H gate should succeed with validated qubit index");
        circuit.h(encoded_qubits[5]).expect("H gate should succeed with validated qubit index");
        circuit.cnot(encoded_qubits[4], encoded_qubits[6]).expect("CNOT should succeed with validated qubit indices");
        circuit.cnot(encoded_qubits[5], encoded_qubits[6]).expect("CNOT should succeed with validated qubit indices");
        circuit.h(encoded_qubits[4]).expect("H gate should succeed with validated qubit index");
        circuit.h(encoded_qubits[5]).expect("H gate should succeed with validated qubit index");

        circuit
    }

    fn decode_circuit(&self, encoded_qubits: &[QubitId], syndrome_qubits: &[QubitId]) -> Circuit<16> {
        let mut circuit = Circuit::<16>::new();

        // Check if we have enough qubits
        if encoded_qubits.len() < 7 || syndrome_qubits.len() < 6 {
            panic!("SteaneCode requires 7 encoded qubits and 6 syndrome qubits");
        }

        // Steane code decoding circuit
        // Measure syndrome qubits to detect and correct errors

        // X-syndrome measurement (detects Z errors)
        for i in 0..3 {
            circuit.h(syndrome_qubits[i]).expect("H gate should succeed with validated qubit index");
            for j in 0..7 {
                if (j + 1) & (1 << i) != 0 {
                    circuit.cnot(syndrome_qubits[i], encoded_qubits[j]).expect("CNOT should succeed with validated qubit indices");
                }
            }
            circuit.h(syndrome_qubits[i]).expect("H gate should succeed with validated qubit index");
        }

        // Z-syndrome measurement (detects X errors)
        for i in 3..6 {
            for j in 0..7 {
                if (j + 1) & (1 << (i - 3)) != 0 {
                    circuit.cnot(encoded_qubits[j], syndrome_qubits[i]).expect("CNOT should succeed with validated qubit indices");
                }
            }
        }

        // Error correction based on syndrome
        // In a real implementation, this would involve classical processing
        // For simulation, we apply corrections based on syndrome patterns

        // X error corrections (based on Z syndrome)
        for error_pos in 1..8 {
            let mut control_qubits = Vec::new();
            for i in 0..3 {
                if error_pos & (1 << i) != 0 {
                    control_qubits.push(syndrome_qubits[i]);
                }
            }

            // Multi-controlled X gate (simplified)
            if !control_qubits.is_empty() {
                let target = encoded_qubits[error_pos - 1];
                for &ctrl in &control_qubits {
                    circuit.cnot(ctrl, target).expect("CNOT should succeed with validated qubit indices");
                }
            }
        }

        // Z error corrections (based on X syndrome)
        for error_pos in 1..8 {
            let mut control_qubits = Vec::new();
            for i in 3..6 {
                if error_pos & (1 << (i - 3)) != 0 {
                    control_qubits.push(syndrome_qubits[i]);
                }
            }

            // Multi-controlled Z gate (simplified)
            if !control_qubits.is_empty() {
                let target = encoded_qubits[error_pos - 1];
                for &ctrl in &control_qubits {
                    circuit.h(target).expect("H gate should succeed with validated qubit index");
                    circuit.cnot(ctrl, target).expect("CNOT should succeed with validated qubit indices");
                    circuit.h(target).expect("H gate should succeed with validated qubit index");
                }
            }
        }

        circuit
    }
}