quantrs2-core 0.1.3

//! Logical gate synthesis for fault-tolerant computing
//!
//! This module provides the ability to implement logical operations on encoded quantum states
//! without decoding them first, which is essential for fault-tolerant quantum computation.

use super::pauli::{Pauli, PauliString};
use super::stabilizer::StabilizerCode;
use crate::error::{QuantRS2Error, QuantRS2Result};

/// Logical gate operation that can be applied to encoded quantum states
#[derive(Debug, Clone)]
pub struct LogicalGateOp {
    /// The stabilizer code this logical gate operates on
    pub code: StabilizerCode,
    /// Physical gate operations that implement the logical gate
    pub physical_operations: Vec<PhysicalGateSequence>,
    /// Which logical qubit(s) this gate acts on
    pub logical_qubits: Vec<usize>,
    /// Error propagation analysis
    pub error_propagation: ErrorPropagationAnalysis,
}

/// Sequence of physical gates that implement part of a logical gate
#[derive(Debug, Clone)]
pub struct PhysicalGateSequence {
    /// Target physical qubits
    pub target_qubits: Vec<usize>,
    /// Pauli operators to apply
    pub pauli_sequence: Vec<PauliString>,
    /// Timing constraints (if any)
    pub timing_constraints: Option<TimingConstraints>,
    /// Error correction rounds needed
    pub error_correction_rounds: usize,
}

/// Analysis of how errors propagate through logical gates
#[derive(Debug, Clone)]
pub struct ErrorPropagationAnalysis {
    /// How single-qubit errors propagate
    pub single_qubit_propagation: Vec<ErrorPropagationPath>,
    /// How two-qubit errors propagate
    pub two_qubit_propagation: Vec<ErrorPropagationPath>,
    /// Maximum error weight after gate application
    pub max_error_weight: usize,
    /// Fault-tolerance threshold
    pub fault_tolerance_threshold: f64,
}

/// Path of error propagation through a logical gate
#[derive(Debug, Clone)]
pub struct ErrorPropagationPath {
    /// Initial error location
    pub initial_error: PauliString,
    /// Final error after gate application
    pub final_error: PauliString,
    /// Probability of this propagation path
    pub probability: f64,
    /// Whether this path can be corrected
    pub correctable: bool,
}

/// Timing constraints for fault-tolerant gate implementation
#[derive(Debug, Clone)]
pub struct TimingConstraints {
    /// Maximum time between operations
    pub max_operation_time: std::time::Duration,
    /// Required synchronization points
    pub sync_points: Vec<usize>,
    /// Parallel operation groups
    pub parallel_groups: Vec<Vec<usize>>,
}

/// Logical gate synthesis engine
pub struct LogicalGateSynthesizer {
    /// Available error correction codes
    codes: Vec<StabilizerCode>,
    /// Synthesis strategies
    #[allow(dead_code)]
    strategies: Vec<SynthesisStrategy>,
    /// Error threshold for fault tolerance
    error_threshold: f64,
}

/// Strategy for synthesizing logical gates
#[derive(Debug, Clone)]
pub enum SynthesisStrategy {
    /// Transversal gates (apply same gate to all qubits)
    Transversal,
    /// Magic state distillation and injection
    MagicStateDistillation,
    /// Lattice surgery operations
    LatticeSurgery,
    /// Code deformation
    CodeDeformation,
    /// Braiding operations (for topological codes)
    Braiding,
}

impl LogicalGateSynthesizer {
    /// Create a new logical gate synthesizer
    pub fn new(error_threshold: f64) -> Self {
        Self {
            codes: Vec::new(),
            strategies: vec![
                SynthesisStrategy::Transversal,
                SynthesisStrategy::MagicStateDistillation,
                SynthesisStrategy::LatticeSurgery,
            ],
            error_threshold,
        }
    }

    /// Add an error correction code to the synthesizer
    pub fn add_code(&mut self, code: StabilizerCode) {
        self.codes.push(code);
    }

    /// Synthesize a logical Pauli-X gate
    pub fn synthesize_logical_x(
        &self,
        code: &StabilizerCode,
        logical_qubit: usize,
    ) -> QuantRS2Result<LogicalGateOp> {
        if logical_qubit >= code.k {
            return Err(QuantRS2Error::InvalidInput(format!(
                "Logical qubit {} exceeds code dimension {}",
                logical_qubit, code.k
            )));
        }

        // For most stabilizer codes, logical X can be implemented transversally
        let logical_x_operator = &code.logical_x[logical_qubit];

        let physical_ops = vec![PhysicalGateSequence {
            target_qubits: (0..code.n).collect(),
            pauli_sequence: vec![logical_x_operator.clone()],
            timing_constraints: None,
            error_correction_rounds: 1,
        }];

        let error_analysis = self.analyze_error_propagation(code, &physical_ops)?;

        Ok(LogicalGateOp {
            code: code.clone(),
            physical_operations: physical_ops,
            logical_qubits: vec![logical_qubit],
            error_propagation: error_analysis,
        })
    }

    /// Synthesize a logical Pauli-Z gate
    pub fn synthesize_logical_z(
        &self,
        code: &StabilizerCode,
        logical_qubit: usize,
    ) -> QuantRS2Result<LogicalGateOp> {
        if logical_qubit >= code.k {
            return Err(QuantRS2Error::InvalidInput(format!(
                "Logical qubit {} exceeds code dimension {}",
                logical_qubit, code.k
            )));
        }

        let logical_z_operator = &code.logical_z[logical_qubit];

        let physical_ops = vec![PhysicalGateSequence {
            target_qubits: (0..code.n).collect(),
            pauli_sequence: vec![logical_z_operator.clone()],
            timing_constraints: None,
            error_correction_rounds: 1,
        }];

        let error_analysis = self.analyze_error_propagation(code, &physical_ops)?;

        Ok(LogicalGateOp {
            code: code.clone(),
            physical_operations: physical_ops,
            logical_qubits: vec![logical_qubit],
            error_propagation: error_analysis,
        })
    }

    /// Synthesize a logical Hadamard gate
    pub fn synthesize_logical_h(
        &self,
        code: &StabilizerCode,
        logical_qubit: usize,
    ) -> QuantRS2Result<LogicalGateOp> {
        if logical_qubit >= code.k {
            return Err(QuantRS2Error::InvalidInput(format!(
                "Logical qubit {} exceeds code dimension {}",
                logical_qubit, code.k
            )));
        }

        // Hadamard can often be implemented transversally
        // H|x⟩ = |+⟩ if x=0, |-⟩ if x=1, and H swaps X and Z operators
        let physical_ops = vec![PhysicalGateSequence {
            target_qubits: (0..code.n).collect(),
            pauli_sequence: self.generate_hadamard_sequence(code, logical_qubit)?,
            timing_constraints: Some(TimingConstraints {
                max_operation_time: std::time::Duration::from_micros(100),
                sync_points: vec![code.n / 2],
                parallel_groups: vec![(0..code.n).collect()],
            }),
            error_correction_rounds: 2, // Need more rounds for non-Pauli gates
        }];

        let error_analysis = self.analyze_error_propagation(code, &physical_ops)?;

        Ok(LogicalGateOp {
            code: code.clone(),
            physical_operations: physical_ops,
            logical_qubits: vec![logical_qubit],
            error_propagation: error_analysis,
        })
    }

    /// Synthesize a logical CNOT gate
    pub fn synthesize_logical_cnot(
        &self,
        code: &StabilizerCode,
        control_qubit: usize,
        target_qubit: usize,
    ) -> QuantRS2Result<LogicalGateOp> {
        if control_qubit >= code.k || target_qubit >= code.k {
            return Err(QuantRS2Error::InvalidInput(
                "Control or target qubit exceeds code dimension".to_string(),
            ));
        }

        if control_qubit == target_qubit {
            return Err(QuantRS2Error::InvalidInput(
                "Control and target qubits must be different".to_string(),
            ));
        }

        // CNOT can be implemented transversally for many codes
        let cnot_sequence = self.generate_cnot_sequence(code, control_qubit, target_qubit)?;

        let physical_ops = vec![PhysicalGateSequence {
            target_qubits: (0..code.n).collect(),
            pauli_sequence: cnot_sequence,
            timing_constraints: Some(TimingConstraints {
                max_operation_time: std::time::Duration::from_micros(200),
                sync_points: vec![],
                parallel_groups: vec![], // CNOT requires sequential operations
            }),
            error_correction_rounds: 2,
        }];

        let error_analysis = self.analyze_error_propagation(code, &physical_ops)?;

        Ok(LogicalGateOp {
            code: code.clone(),
            physical_operations: physical_ops,
            logical_qubits: vec![control_qubit, target_qubit],
            error_propagation: error_analysis,
        })
    }

    /// Synthesize a T gate using magic state distillation
    pub fn synthesize_logical_t(
        &self,
        code: &StabilizerCode,
        logical_qubit: usize,
    ) -> QuantRS2Result<LogicalGateOp> {
        if logical_qubit >= code.k {
            return Err(QuantRS2Error::InvalidInput(format!(
                "Logical qubit {} exceeds code dimension {}",
                logical_qubit, code.k
            )));
        }

        // T gate requires magic state distillation for fault-tolerant implementation
        let magic_state_prep = self.prepare_magic_state(code)?;
        let injection_sequence = self.inject_magic_state(code, logical_qubit, &magic_state_prep)?;

        let physical_ops = vec![magic_state_prep, injection_sequence];

        let error_analysis = self.analyze_error_propagation(code, &physical_ops)?;

        Ok(LogicalGateOp {
            code: code.clone(),
            physical_operations: physical_ops,
            logical_qubits: vec![logical_qubit],
            error_propagation: error_analysis,
        })
    }

    /// Generate Hadamard gate sequence for a logical qubit
    fn generate_hadamard_sequence(
        &self,
        code: &StabilizerCode,
        _logical_qubit: usize,
    ) -> QuantRS2Result<Vec<PauliString>> {
        // For transversal Hadamard, apply H to each physical qubit
        // This swaps X and Z logical operators
        let mut sequence = Vec::new();

        // Create a Pauli string that represents applying H to all qubits
        // Since H|0⟩ = |+⟩ = (|0⟩ + |1⟩)/√2 and H|1⟩ = |-⟩ = (|0⟩ - |1⟩)/√2
        // We represent this as identity for simplicity in this implementation
        sequence.push(PauliString::new(vec![Pauli::I; code.n]));

        Ok(sequence)
    }

    /// Generate CNOT gate sequence for logical qubits
    fn generate_cnot_sequence(
        &self,
        code: &StabilizerCode,
        _control: usize,
        _target: usize,
    ) -> QuantRS2Result<Vec<PauliString>> {
        // For transversal CNOT, apply CNOT between corresponding physical qubits
        // This is a simplified implementation
        let mut sequence = Vec::new();

        // Represent CNOT as identity for this implementation
        sequence.push(PauliString::new(vec![Pauli::I; code.n]));

        Ok(sequence)
    }

    /// Prepare magic state for T gate implementation
    fn prepare_magic_state(&self, code: &StabilizerCode) -> QuantRS2Result<PhysicalGateSequence> {
        // Magic state |T⟩ = (|0⟩ + e^(iπ/4)|1⟩)/√2 for T gate
        // This is a simplified implementation
        Ok(PhysicalGateSequence {
            target_qubits: (0..code.n).collect(),
            pauli_sequence: vec![PauliString::new(vec![Pauli::I; code.n])],
            timing_constraints: Some(TimingConstraints {
                max_operation_time: std::time::Duration::from_millis(1),
                sync_points: vec![],
                parallel_groups: vec![(0..code.n).collect()],
            }),
            error_correction_rounds: 5, // Magic state prep requires many rounds
        })
    }

    /// Inject magic state to implement T gate
    fn inject_magic_state(
        &self,
        code: &StabilizerCode,
        _logical_qubit: usize,
        _magic_state: &PhysicalGateSequence,
    ) -> QuantRS2Result<PhysicalGateSequence> {
        // Inject magic state using teleportation-based approach
        Ok(PhysicalGateSequence {
            target_qubits: (0..code.n).collect(),
            pauli_sequence: vec![PauliString::new(vec![Pauli::I; code.n])],
            timing_constraints: Some(TimingConstraints {
                max_operation_time: std::time::Duration::from_micros(500),
                sync_points: vec![code.n / 2],
                parallel_groups: vec![],
            }),
            error_correction_rounds: 3,
        })
    }

    /// Analyze error propagation through logical gate operations
    fn analyze_error_propagation(
        &self,
        code: &StabilizerCode,
        physical_ops: &[PhysicalGateSequence],
    ) -> QuantRS2Result<ErrorPropagationAnalysis> {
        let mut single_qubit_propagation = Vec::new();
        let mut two_qubit_propagation = Vec::new();
        let mut max_error_weight = 0;

        // Analyze single-qubit errors
        for i in 0..code.n {
            for pauli in [Pauli::X, Pauli::Y, Pauli::Z] {
                let mut initial_error = vec![Pauli::I; code.n];
                initial_error[i] = pauli;
                let initial_pauli_string = PauliString::new(initial_error);

                // Simulate error propagation through the logical gate
                let final_error = self.propagate_error(&initial_pauli_string, physical_ops)?;
                let error_weight = final_error.weight();
                max_error_weight = max_error_weight.max(error_weight);

                // Check if error is correctable
                let correctable = self.is_error_correctable(code, &final_error)?;

                single_qubit_propagation.push(ErrorPropagationPath {
                    initial_error: initial_pauli_string,
                    final_error,
                    probability: 1.0 / (3.0 * code.n as f64), // Uniform for now
                    correctable,
                });
            }
        }

        // Analyze two-qubit errors (simplified)
        for i in 0..code.n.min(5) {
            // Limit to first 5 for performance
            for j in (i + 1)..code.n.min(5) {
                let mut initial_error = vec![Pauli::I; code.n];
                initial_error[i] = Pauli::X;
                initial_error[j] = Pauli::X;
                let initial_pauli_string = PauliString::new(initial_error);

                let final_error = self.propagate_error(&initial_pauli_string, physical_ops)?;
                let error_weight = final_error.weight();
                max_error_weight = max_error_weight.max(error_weight);

                let correctable = self.is_error_correctable(code, &final_error)?;

                two_qubit_propagation.push(ErrorPropagationPath {
                    initial_error: initial_pauli_string,
                    final_error,
                    probability: 1.0 / (code.n * (code.n - 1)) as f64,
                    correctable,
                });
            }
        }

        Ok(ErrorPropagationAnalysis {
            single_qubit_propagation,
            two_qubit_propagation,
            max_error_weight,
            fault_tolerance_threshold: self.error_threshold,
        })
    }

    /// Propagate an error through physical gate operations
    fn propagate_error(
        &self,
        error: &PauliString,
        _physical_ops: &[PhysicalGateSequence],
    ) -> QuantRS2Result<PauliString> {
        // Simplified error propagation - in reality this would track
        // how each gate operation transforms the error
        Ok(error.clone())
    }

    /// Check if an error is correctable by the code
    fn is_error_correctable(
        &self,
        code: &StabilizerCode,
        error: &PauliString,
    ) -> QuantRS2Result<bool> {
        // An error is correctable if its weight is less than (d+1)/2
        // where d is the minimum distance of the code
        Ok(error.weight() <= (code.d + 1) / 2)
    }
}

/// Logical circuit synthesis for fault-tolerant quantum computing
pub struct LogicalCircuitSynthesizer {
    gate_synthesizer: LogicalGateSynthesizer,
    optimization_passes: Vec<OptimizationPass>,
}

/// Optimization pass for logical circuits
#[derive(Debug, Clone)]
pub enum OptimizationPass {
    /// Combine adjacent Pauli gates
    PauliOptimization,
    /// Optimize error correction rounds
    ErrorCorrectionOptimization,
    /// Parallelize commuting operations
    ParallelizationOptimization,
    /// Reduce magic state usage
    MagicStateOptimization,
}

impl LogicalCircuitSynthesizer {
    pub fn new(error_threshold: f64) -> Self {
        Self {
            gate_synthesizer: LogicalGateSynthesizer::new(error_threshold),
            optimization_passes: vec![
                OptimizationPass::PauliOptimization,
                OptimizationPass::ErrorCorrectionOptimization,
                OptimizationPass::ParallelizationOptimization,
                OptimizationPass::MagicStateOptimization,
            ],
        }
    }

    /// Add a code to the synthesizer
    pub fn add_code(&mut self, code: StabilizerCode) {
        self.gate_synthesizer.add_code(code);
    }

    /// Synthesize a logical circuit from a sequence of gate names
    pub fn synthesize_circuit(
        &self,
        code: &StabilizerCode,
        gate_sequence: &[(&str, Vec<usize>)], // (gate_name, target_qubits)
    ) -> QuantRS2Result<Vec<LogicalGateOp>> {
        let mut logical_gates = Vec::new();

        for (gate_name, targets) in gate_sequence {
            match gate_name.to_lowercase().as_str() {
                "x" | "pauli_x" => {
                    if targets.len() != 1 {
                        return Err(QuantRS2Error::InvalidInput(
                            "X gate requires exactly one target".to_string(),
                        ));
                    }
                    logical_gates.push(
                        self.gate_synthesizer
                            .synthesize_logical_x(code, targets[0])?,
                    );
                }
                "z" | "pauli_z" => {
                    if targets.len() != 1 {
                        return Err(QuantRS2Error::InvalidInput(
                            "Z gate requires exactly one target".to_string(),
                        ));
                    }
                    logical_gates.push(
                        self.gate_synthesizer
                            .synthesize_logical_z(code, targets[0])?,
                    );
                }
                "h" | "hadamard" => {
                    if targets.len() != 1 {
                        return Err(QuantRS2Error::InvalidInput(
                            "H gate requires exactly one target".to_string(),
                        ));
                    }
                    logical_gates.push(
                        self.gate_synthesizer
                            .synthesize_logical_h(code, targets[0])?,
                    );
                }
                "cnot" | "cx" => {
                    if targets.len() != 2 {
                        return Err(QuantRS2Error::InvalidInput(
                            "CNOT gate requires exactly two targets".to_string(),
                        ));
                    }
                    logical_gates.push(
                        self.gate_synthesizer
                            .synthesize_logical_cnot(code, targets[0], targets[1])?,
                    );
                }
                "t" => {
                    if targets.len() != 1 {
                        return Err(QuantRS2Error::InvalidInput(
                            "T gate requires exactly one target".to_string(),
                        ));
                    }
                    logical_gates.push(
                        self.gate_synthesizer
                            .synthesize_logical_t(code, targets[0])?,
                    );
                }
                _ => {
                    return Err(QuantRS2Error::UnsupportedOperation(format!(
                        "Unsupported logical gate: {gate_name}"
                    )));
                }
            }
        }

        // Apply optimization passes
        self.optimize_circuit(logical_gates)
    }

    /// Apply optimization passes to the logical circuit
    fn optimize_circuit(
        &self,
        mut circuit: Vec<LogicalGateOp>,
    ) -> QuantRS2Result<Vec<LogicalGateOp>> {
        for pass in &self.optimization_passes {
            circuit = self.apply_optimization_pass(circuit, pass)?;
        }
        Ok(circuit)
    }

    /// Apply a specific optimization pass
    const fn apply_optimization_pass(
        &self,
        circuit: Vec<LogicalGateOp>,
        pass: &OptimizationPass,
    ) -> QuantRS2Result<Vec<LogicalGateOp>> {
        match pass {
            OptimizationPass::PauliOptimization => self.optimize_pauli_gates(circuit),
            OptimizationPass::ErrorCorrectionOptimization => {
                self.optimize_error_correction(circuit)
            }
            OptimizationPass::ParallelizationOptimization => self.optimize_parallelization(circuit),
            OptimizationPass::MagicStateOptimization => self.optimize_magic_states(circuit),
        }
    }

    /// Optimize Pauli gate sequences
    const fn optimize_pauli_gates(
        &self,
        circuit: Vec<LogicalGateOp>,
    ) -> QuantRS2Result<Vec<LogicalGateOp>> {
        // Combine adjacent Pauli gates that act on the same logical qubits
        Ok(circuit) // Simplified implementation
    }

    /// Optimize error correction rounds
    const fn optimize_error_correction(
        &self,
        circuit: Vec<LogicalGateOp>,
    ) -> QuantRS2Result<Vec<LogicalGateOp>> {
        // Reduce redundant error correction rounds
        Ok(circuit) // Simplified implementation
    }

    /// Optimize parallelization of commuting operations
    const fn optimize_parallelization(
        &self,
        circuit: Vec<LogicalGateOp>,
    ) -> QuantRS2Result<Vec<LogicalGateOp>> {
        // Identify and parallelize commuting gates
        Ok(circuit) // Simplified implementation
    }

    /// Optimize magic state usage
    const fn optimize_magic_states(
        &self,
        circuit: Vec<LogicalGateOp>,
    ) -> QuantRS2Result<Vec<LogicalGateOp>> {
        // Reduce number of magic states required
        Ok(circuit) // Simplified implementation
    }

    /// Estimate resource requirements for the logical circuit
    pub fn estimate_resources(&self, circuit: &[LogicalGateOp]) -> LogicalCircuitResources {
        let mut total_physical_operations = 0;
        let mut total_error_correction_rounds = 0;
        let mut max_parallelism = 0;
        let mut magic_states_required = 0;

        for gate in circuit {
            total_physical_operations += gate.physical_operations.len();
            for op in &gate.physical_operations {
                total_error_correction_rounds += op.error_correction_rounds;
                if let Some(constraints) = &op.timing_constraints {
                    max_parallelism = max_parallelism.max(constraints.parallel_groups.len());
                }
            }

            // Count T gates which require magic states
            if gate.logical_qubits.len() == 1 {
                // This is a heuristic - in practice we'd check the gate type
                magic_states_required += 1;
            }
        }

        LogicalCircuitResources {
            total_physical_operations,
            total_error_correction_rounds,
            max_parallelism,
            magic_states_required,
            estimated_depth: circuit.len(),
            estimated_time: std::time::Duration::from_millis(
                (total_error_correction_rounds * 10) as u64,
            ),
        }
    }
}

/// Resource requirements for a logical circuit
#[derive(Debug, Clone)]
pub struct LogicalCircuitResources {
    pub total_physical_operations: usize,
    pub total_error_correction_rounds: usize,
    pub max_parallelism: usize,
    pub magic_states_required: usize,
    pub estimated_depth: usize,
    pub estimated_time: std::time::Duration,
}