quantrs2_ml/

quantum_pinns.rs

//! Quantum Physics-Informed Neural Networks (QPINNs)
//!
//! This module implements Quantum Physics-Informed Neural Networks, which incorporate
//! physical laws and constraints directly into quantum neural network architectures.
//! QPINNs can solve partial differential equations (PDEs) and enforce physical
//! conservation laws using quantum computing advantages.

use crate::error::Result;
use ndarray::{s, Array1, Array2, Array3, ArrayD, IxDyn};
use serde::{Deserialize, Serialize};
use std::collections::HashMap;

/// Configuration for Quantum Physics-Informed Neural Networks
#[derive(Debug, Clone, Serialize, Deserialize)]
pub struct QPINNConfig {
    /// Number of qubits for the quantum neural network
    pub num_qubits: usize,
    /// Number of quantum layers
    pub num_layers: usize,
    /// Spatial domain boundaries
    pub domain_bounds: Vec<(f64, f64)>,
    /// Temporal domain bounds
    pub time_bounds: (f64, f64),
    /// Physical equation type
    pub equation_type: PhysicsEquationType,
    /// Boundary condition types
    pub boundary_conditions: Vec<BoundaryCondition>,
    /// Initial conditions
    pub initial_conditions: Vec<InitialCondition>,
    /// Loss function weights
    pub loss_weights: LossWeights,
    /// Quantum ansatz configuration
    pub ansatz_config: AnsatzConfig,
    /// Training configuration
    pub training_config: TrainingConfig,
    /// Physics constraints
    pub physics_constraints: PhysicsConstraints,
}

impl Default for QPINNConfig {
    fn default() -> Self {
        Self {
            num_qubits: 6,
            num_layers: 4,
            domain_bounds: vec![(-1.0, 1.0), (-1.0, 1.0)],
            time_bounds: (0.0, 1.0),
            equation_type: PhysicsEquationType::Poisson,
            boundary_conditions: vec![],
            initial_conditions: vec![],
            loss_weights: LossWeights::default(),
            ansatz_config: AnsatzConfig::default(),
            training_config: TrainingConfig::default(),
            physics_constraints: PhysicsConstraints::default(),
        }
    }
}

/// Types of physics equations that can be solved
#[derive(Debug, Clone, Serialize, Deserialize)]
pub enum PhysicsEquationType {
    /// Poisson equation: ∇²u = f
    Poisson,
    /// Heat equation: ∂u/∂t = α∇²u
    Heat,
    /// Wave equation: ∂²u/∂t² = c²∇²u
    Wave,
    /// Schrödinger equation: iℏ∂ψ/∂t = Ĥψ
    Schrodinger,
    /// Navier-Stokes equations
    NavierStokes,
    /// Maxwell equations
    Maxwell,
    /// Klein-Gordon equation
    KleinGordon,
    /// Burgers equation: ∂u/∂t + u∇u = ν∇²u
    Burgers,
    /// Custom PDE with user-defined operator
    Custom {
        differential_operator: String,
        equation_form: String,
    },
}

/// Boundary condition specifications
#[derive(Debug, Clone, Serialize, Deserialize)]
pub struct BoundaryCondition {
    /// Boundary location specification
    pub boundary: BoundaryLocation,
    /// Type of boundary condition
    pub condition_type: BoundaryType,
    /// Boundary value function
    pub value_function: String, // Mathematical expression
}

/// Boundary location in the domain
#[derive(Debug, Clone, Serialize, Deserialize)]
pub enum BoundaryLocation {
    /// Left boundary (x = x_min)
    Left,
    /// Right boundary (x = x_max)
    Right,
    /// Bottom boundary (y = y_min)
    Bottom,
    /// Top boundary (y = y_max)
    Top,
    /// Custom boundary defined by equation
    Custom(String),
}

/// Types of boundary conditions
#[derive(Debug, Clone, Serialize, Deserialize)]
pub enum BoundaryType {
    /// Dirichlet boundary condition (fixed value)
    Dirichlet,
    /// Neumann boundary condition (fixed derivative)
    Neumann,
    /// Robin boundary condition (mixed)
    Robin { alpha: f64, beta: f64 },
    /// Periodic boundary condition
    Periodic,
}

/// Initial condition specifications
#[derive(Debug, Clone, Serialize, Deserialize)]
pub struct InitialCondition {
    /// Initial value function
    pub value_function: String,
    /// Derivative initial condition (for second-order equations)
    pub derivative_function: Option<String>,
}

/// Loss function weights for different terms
#[derive(Debug, Clone, Serialize, Deserialize)]
pub struct LossWeights {
    /// Weight for PDE residual loss
    pub pde_loss_weight: f64,
    /// Weight for boundary condition loss
    pub boundary_loss_weight: f64,
    /// Weight for initial condition loss
    pub initial_loss_weight: f64,
    /// Weight for physics constraint loss
    pub physics_constraint_weight: f64,
    /// Weight for data fitting loss (if available)
    pub data_loss_weight: f64,
}

impl Default for LossWeights {
    fn default() -> Self {
        Self {
            pde_loss_weight: 1.0,
            boundary_loss_weight: 10.0,
            initial_loss_weight: 10.0,
            physics_constraint_weight: 1.0,
            data_loss_weight: 1.0,
        }
    }
}

/// Quantum ansatz configuration
#[derive(Debug, Clone, Serialize, Deserialize)]
pub struct AnsatzConfig {
    /// Type of quantum ansatz
    pub ansatz_type: QuantumAnsatzType,
    /// Entanglement pattern
    pub entanglement_pattern: EntanglementPattern,
    /// Number of repetitions
    pub repetitions: usize,
    /// Parameter initialization strategy
    pub parameter_init: ParameterInitialization,
}

impl Default for AnsatzConfig {
    fn default() -> Self {
        Self {
            ansatz_type: QuantumAnsatzType::EfficientSU2,
            entanglement_pattern: EntanglementPattern::Linear,
            repetitions: 3,
            parameter_init: ParameterInitialization::Random,
        }
    }
}

/// Types of quantum ansatz circuits
#[derive(Debug, Clone, Serialize, Deserialize)]
pub enum QuantumAnsatzType {
    /// Efficient SU(2) ansatz
    EfficientSU2,
    /// Two-local ansatz
    TwoLocal,
    /// Alternating operator ansatz
    AlternatingOperator,
    /// Hardware-efficient ansatz
    HardwareEfficient,
    /// Physics-informed ansatz (problem-specific)
    PhysicsInformed,
}

/// Entanglement patterns for quantum circuits
#[derive(Debug, Clone, Serialize, Deserialize)]
pub enum EntanglementPattern {
    /// Linear entanglement (nearest neighbor)
    Linear,
    /// Circular entanglement
    Circular,
    /// Full entanglement (all-to-all)
    Full,
    /// Custom entanglement pattern
    Custom(Vec<(usize, usize)>),
}

/// Parameter initialization strategies
#[derive(Debug, Clone, Serialize, Deserialize)]
pub enum ParameterInitialization {
    /// Random initialization
    Random,
    /// Xavier/Glorot initialization
    Xavier,
    /// He initialization
    He,
    /// Physics-informed initialization
    PhysicsInformed,
    /// Custom initialization
    Custom(Vec<f64>),
}

/// Training configuration
#[derive(Debug, Clone, Serialize, Deserialize)]
pub struct TrainingConfig {
    /// Number of training epochs
    pub epochs: usize,
    /// Learning rate
    pub learning_rate: f64,
    /// Optimizer type
    pub optimizer: OptimizerType,
    /// Batch size for collocation points
    pub batch_size: usize,
    /// Number of collocation points
    pub num_collocation_points: usize,
    /// Adaptive sampling strategy
    pub adaptive_sampling: bool,
}

impl Default for TrainingConfig {
    fn default() -> Self {
        Self {
            epochs: 1000,
            learning_rate: 0.001,
            optimizer: OptimizerType::Adam,
            batch_size: 128,
            num_collocation_points: 1000,
            adaptive_sampling: true,
        }
    }
}

/// Optimizer types
#[derive(Debug, Clone, Serialize, Deserialize)]
pub enum OptimizerType {
    Adam,
    LBFGS,
    SGD,
    QuantumNaturalGradient,
    ParameterShift,
}

/// Physics constraints for the problem
#[derive(Debug, Clone, Serialize, Deserialize)]
pub struct PhysicsConstraints {
    /// Conservation laws to enforce
    pub conservation_laws: Vec<ConservationLaw>,
    /// Symmetries to preserve
    pub symmetries: Vec<Symmetry>,
    /// Physical bounds on the solution
    pub solution_bounds: Option<(f64, f64)>,
    /// Energy constraints
    pub energy_constraints: Vec<EnergyConstraint>,
}

impl Default for PhysicsConstraints {
    fn default() -> Self {
        Self {
            conservation_laws: vec![],
            symmetries: vec![],
            solution_bounds: None,
            energy_constraints: vec![],
        }
    }
}

/// Conservation laws
#[derive(Debug, Clone, Serialize, Deserialize)]
pub enum ConservationLaw {
    /// Conservation of mass
    Mass,
    /// Conservation of momentum
    Momentum,
    /// Conservation of energy
    Energy,
    /// Conservation of charge
    Charge,
    /// Custom conservation law
    Custom(String),
}

/// Symmetries in the problem
#[derive(Debug, Clone, Serialize, Deserialize)]
pub enum Symmetry {
    /// Translational symmetry
    Translational,
    /// Rotational symmetry
    Rotational,
    /// Reflection symmetry
    Reflection,
    /// Time reversal symmetry
    TimeReversal,
    /// Custom symmetry
    Custom(String),
}

/// Energy constraints
#[derive(Debug, Clone, Serialize, Deserialize)]
pub struct EnergyConstraint {
    /// Type of energy constraint
    pub constraint_type: EnergyConstraintType,
    /// Target energy value
    pub target_value: f64,
    /// Tolerance for constraint satisfaction
    pub tolerance: f64,
}

/// Types of energy constraints
#[derive(Debug, Clone, Serialize, Deserialize)]
pub enum EnergyConstraintType {
    /// Total energy constraint
    Total,
    /// Kinetic energy constraint
    Kinetic,
    /// Potential energy constraint
    Potential,
    /// Custom energy functional
    Custom(String),
}

/// Main Quantum Physics-Informed Neural Network
#[derive(Debug, Clone)]
pub struct QuantumPINN {
    config: QPINNConfig,
    quantum_circuit: QuantumCircuit,
    parameters: Array1<f64>,
    collocation_points: Array2<f64>,
    training_history: Vec<TrainingMetrics>,
    physics_evaluator: PhysicsEvaluator,
}

/// Quantum circuit for the PINN
#[derive(Debug, Clone)]
pub struct QuantumCircuit {
    gates: Vec<QuantumGate>,
    num_qubits: usize,
    parameter_map: HashMap<usize, usize>, // Gate index to parameter index
}

/// Individual quantum gates
#[derive(Debug, Clone)]
pub struct QuantumGate {
    gate_type: GateType,
    qubits: Vec<usize>,
    parameters: Vec<usize>, // Parameter indices
    is_parametric: bool,
}

/// Gate types for quantum circuits
#[derive(Debug, Clone)]
pub enum GateType {
    RX,
    RY,
    RZ,
    CNOT,
    CZ,
    CY,
    Hadamard,
    S,
    T,
    Custom(String),
}

/// Physics evaluator for computing PDE residuals
#[derive(Debug, Clone)]
pub struct PhysicsEvaluator {
    equation_type: PhysicsEquationType,
    differential_operators: HashMap<String, DifferentialOperator>,
}

/// Differential operators for computing derivatives
#[derive(Debug, Clone)]
pub struct DifferentialOperator {
    operator_type: OperatorType,
    order: usize,
    direction: Vec<usize>, // Spatial directions for mixed derivatives
}

/// Types of differential operators
#[derive(Debug, Clone)]
pub enum OperatorType {
    Gradient,
    Laplacian,
    Divergence,
    Curl,
    TimeDerivative,
    Mixed,
}

/// Training metrics for QPINNs
#[derive(Debug, Clone)]
pub struct TrainingMetrics {
    epoch: usize,
    total_loss: f64,
    pde_loss: f64,
    boundary_loss: f64,
    initial_loss: f64,
    physics_constraint_loss: f64,
    quantum_fidelity: f64,
    solution_energy: f64,
}

impl QuantumPINN {
    /// Create a new Quantum Physics-Informed Neural Network
    pub fn new(config: QPINNConfig) -> Result<Self> {
        let quantum_circuit = Self::build_quantum_circuit(&config)?;
        let num_parameters = Self::count_parameters(&quantum_circuit);
        let parameters = Self::initialize_parameters(&config, num_parameters)?;
        let collocation_points = Self::generate_collocation_points(&config)?;
        let physics_evaluator = PhysicsEvaluator::new(&config.equation_type)?;

        Ok(Self {
            config,
            quantum_circuit,
            parameters,
            collocation_points,
            training_history: Vec::new(),
            physics_evaluator,
        })
    }

    /// Build the quantum circuit based on configuration
    fn build_quantum_circuit(config: &QPINNConfig) -> Result<QuantumCircuit> {
        let mut gates = Vec::new();
        let mut parameter_map = HashMap::new();
        let mut param_index = 0;

        match config.ansatz_config.ansatz_type {
            QuantumAnsatzType::EfficientSU2 => {
                for rep in 0..config.ansatz_config.repetitions {
                    // Single-qubit rotations
                    for qubit in 0..config.num_qubits {
                        // RY gate
                        gates.push(QuantumGate {
                            gate_type: GateType::RY,
                            qubits: vec![qubit],
                            parameters: vec![param_index],
                            is_parametric: true,
                        });
                        parameter_map.insert(gates.len() - 1, param_index);
                        param_index += 1;

                        // RZ gate
                        gates.push(QuantumGate {
                            gate_type: GateType::RZ,
                            qubits: vec![qubit],
                            parameters: vec![param_index],
                            is_parametric: true,
                        });
                        parameter_map.insert(gates.len() - 1, param_index);
                        param_index += 1;
                    }

                    // Entangling gates
                    match config.ansatz_config.entanglement_pattern {
                        EntanglementPattern::Linear => {
                            for qubit in 0..config.num_qubits - 1 {
                                gates.push(QuantumGate {
                                    gate_type: GateType::CNOT,
                                    qubits: vec![qubit, qubit + 1],
                                    parameters: vec![],
                                    is_parametric: false,
                                });
                            }
                        }
                        EntanglementPattern::Circular => {
                            for qubit in 0..config.num_qubits {
                                gates.push(QuantumGate {
                                    gate_type: GateType::CNOT,
                                    qubits: vec![qubit, (qubit + 1) % config.num_qubits],
                                    parameters: vec![],
                                    is_parametric: false,
                                });
                            }
                        }
                        EntanglementPattern::Full => {
                            for i in 0..config.num_qubits {
                                for j in i + 1..config.num_qubits {
                                    gates.push(QuantumGate {
                                        gate_type: GateType::CNOT,
                                        qubits: vec![i, j],
                                        parameters: vec![],
                                        is_parametric: false,
                                    });
                                }
                            }
                        }
                        _ => {
                            return Err(crate::error::MLError::InvalidConfiguration(
                                "Unsupported entanglement pattern".to_string(),
                            ));
                        }
                    }
                }
            }
            QuantumAnsatzType::PhysicsInformed => {
                // Build physics-informed ansatz based on the equation type
                gates = Self::build_physics_informed_ansatz(
                    config,
                    &mut param_index,
                    &mut parameter_map,
                )?;
            }
            _ => {
                return Err(crate::error::MLError::InvalidConfiguration(
                    "Ansatz type not implemented".to_string(),
                ));
            }
        }

        Ok(QuantumCircuit {
            gates,
            num_qubits: config.num_qubits,
            parameter_map,
        })
    }

    /// Build physics-informed ansatz specific to the equation type
    fn build_physics_informed_ansatz(
        config: &QPINNConfig,
        param_index: &mut usize,
        parameter_map: &mut HashMap<usize, usize>,
    ) -> Result<Vec<QuantumGate>> {
        let mut gates = Vec::new();

        match config.equation_type {
            PhysicsEquationType::Schrodinger => {
                // Use time-evolution inspired ansatz
                for layer in 0..config.num_layers {
                    // Kinetic energy terms (hopping)
                    for qubit in 0..config.num_qubits - 1 {
                        gates.push(QuantumGate {
                            gate_type: GateType::RX,
                            qubits: vec![qubit],
                            parameters: vec![*param_index],
                            is_parametric: true,
                        });
                        parameter_map.insert(gates.len() - 1, *param_index);
                        *param_index += 1;

                        gates.push(QuantumGate {
                            gate_type: GateType::CNOT,
                            qubits: vec![qubit, qubit + 1],
                            parameters: vec![],
                            is_parametric: false,
                        });

                        gates.push(QuantumGate {
                            gate_type: GateType::RZ,
                            qubits: vec![qubit + 1],
                            parameters: vec![*param_index],
                            is_parametric: true,
                        });
                        parameter_map.insert(gates.len() - 1, *param_index);
                        *param_index += 1;

                        gates.push(QuantumGate {
                            gate_type: GateType::CNOT,
                            qubits: vec![qubit, qubit + 1],
                            parameters: vec![],
                            is_parametric: false,
                        });
                    }

                    // Potential energy terms
                    for qubit in 0..config.num_qubits {
                        gates.push(QuantumGate {
                            gate_type: GateType::RZ,
                            qubits: vec![qubit],
                            parameters: vec![*param_index],
                            is_parametric: true,
                        });
                        parameter_map.insert(gates.len() - 1, *param_index);
                        *param_index += 1;
                    }
                }
            }
            PhysicsEquationType::Heat => {
                // Diffusion-inspired ansatz
                for layer in 0..config.num_layers {
                    for qubit in 0..config.num_qubits {
                        gates.push(QuantumGate {
                            gate_type: GateType::RY,
                            qubits: vec![qubit],
                            parameters: vec![*param_index],
                            is_parametric: true,
                        });
                        parameter_map.insert(gates.len() - 1, *param_index);
                        *param_index += 1;
                    }

                    // Nearest-neighbor interactions for diffusion
                    for qubit in 0..config.num_qubits - 1 {
                        gates.push(QuantumGate {
                            gate_type: GateType::CZ,
                            qubits: vec![qubit, qubit + 1],
                            parameters: vec![],
                            is_parametric: false,
                        });
                    }
                }
            }
            _ => {
                // Default to efficient SU(2) for other equation types
                for qubit in 0..config.num_qubits {
                    gates.push(QuantumGate {
                        gate_type: GateType::RY,
                        qubits: vec![qubit],
                        parameters: vec![*param_index],
                        is_parametric: true,
                    });
                    parameter_map.insert(gates.len() - 1, *param_index);
                    *param_index += 1;
                }
            }
        }

        Ok(gates)
    }

    /// Count parameters in the quantum circuit
    fn count_parameters(circuit: &QuantumCircuit) -> usize {
        circuit
            .gates
            .iter()
            .filter(|gate| gate.is_parametric)
            .map(|gate| gate.parameters.len())
            .sum()
    }

    /// Initialize parameters based on configuration
    fn initialize_parameters(config: &QPINNConfig, num_params: usize) -> Result<Array1<f64>> {
        match &config.ansatz_config.parameter_init {
            ParameterInitialization::Random => Ok(Array1::from_shape_fn(num_params, |_| {
                fastrand::f64() * 2.0 * std::f64::consts::PI
            })),
            ParameterInitialization::Xavier => {
                let limit = (6.0 / num_params as f64).sqrt();
                Ok(Array1::from_shape_fn(num_params, |_| {
                    (fastrand::f64() - 0.5) * 2.0 * limit
                }))
            }
            ParameterInitialization::PhysicsInformed => {
                // Initialize based on physical intuition
                match config.equation_type {
                    PhysicsEquationType::Schrodinger => {
                        // Small random values for quantum evolution
                        Ok(Array1::from_shape_fn(num_params, |_| {
                            (fastrand::f64() - 0.5) * 0.1
                        }))
                    }
                    PhysicsEquationType::Heat => {
                        // Initialize for diffusive behavior
                        Ok(Array1::from_shape_fn(num_params, |i| {
                            0.1 * (i as f64 / num_params as f64)
                        }))
                    }
                    _ => {
                        // Default random initialization
                        Ok(Array1::from_shape_fn(num_params, |_| {
                            fastrand::f64() * std::f64::consts::PI
                        }))
                    }
                }
            }
            ParameterInitialization::Custom(values) => {
                if values.len() != num_params {
                    return Err(crate::error::MLError::InvalidConfiguration(
                        "Custom parameter length mismatch".to_string(),
                    ));
                }
                Ok(Array1::from_vec(values.clone()))
            }
            _ => Ok(Array1::zeros(num_params)),
        }
    }

    /// Generate collocation points for training
    fn generate_collocation_points(config: &QPINNConfig) -> Result<Array2<f64>> {
        let num_points = config.training_config.num_collocation_points;
        let num_dims = config.domain_bounds.len() + 1; // spatial + time
        let mut points = Array2::zeros((num_points, num_dims));

        for i in 0..num_points {
            // Spatial coordinates
            for (j, &(min_val, max_val)) in config.domain_bounds.iter().enumerate() {
                points[[i, j]] = min_val + fastrand::f64() * (max_val - min_val);
            }

            // Temporal coordinate
            let (t_min, t_max) = config.time_bounds;
            points[[i, config.domain_bounds.len()]] = t_min + fastrand::f64() * (t_max - t_min);
        }

        Ok(points)
    }

    /// Forward pass through the quantum network
    pub fn forward(&self, input_points: &Array2<f64>) -> Result<Array2<f64>> {
        let batch_size = input_points.nrows();
        let num_outputs = 1; // Single output for scalar PDE solutions
        let mut outputs = Array2::zeros((batch_size, num_outputs));

        for i in 0..batch_size {
            let point = input_points.row(i);
            let quantum_state = self.encode_input(&point.to_owned())?;
            let evolved_state = self.apply_quantum_circuit(&quantum_state)?;
            let output = self.decode_output(&evolved_state)?;
            outputs[[i, 0]] = output;
        }

        Ok(outputs)
    }

    /// Encode input coordinates into quantum state
    fn encode_input(&self, point: &Array1<f64>) -> Result<Array1<f64>> {
        let num_amplitudes = 1 << self.config.num_qubits;
        let mut quantum_state = Array1::zeros(num_amplitudes);

        // Amplitude encoding of coordinates
        let norm = point.iter().map(|x| x * x).sum::<f64>().sqrt();
        if norm > 1e-10 {
            for (i, &coord) in point.iter().enumerate() {
                if i < num_amplitudes {
                    quantum_state[i] = coord / norm;
                }
            }
        } else {
            quantum_state[0] = 1.0;
        }

        // Normalize the quantum state
        let state_norm = quantum_state.iter().map(|x| x * x).sum::<f64>().sqrt();
        if state_norm > 1e-10 {
            quantum_state /= state_norm;
        }

        Ok(quantum_state)
    }

    /// Apply the parameterized quantum circuit
    fn apply_quantum_circuit(&self, input_state: &Array1<f64>) -> Result<Array1<f64>> {
        let mut state = input_state.clone();

        for gate in &self.quantum_circuit.gates {
            match gate.gate_type {
                GateType::RY => {
                    let angle = if gate.is_parametric {
                        self.parameters[gate.parameters[0]]
                    } else {
                        0.0
                    };
                    state = self.apply_ry_gate(&state, gate.qubits[0], angle)?;
                }
                GateType::RZ => {
                    let angle = if gate.is_parametric {
                        self.parameters[gate.parameters[0]]
                    } else {
                        0.0
                    };
                    state = self.apply_rz_gate(&state, gate.qubits[0], angle)?;
                }
                GateType::RX => {
                    let angle = if gate.is_parametric {
                        self.parameters[gate.parameters[0]]
                    } else {
                        0.0
                    };
                    state = self.apply_rx_gate(&state, gate.qubits[0], angle)?;
                }
                GateType::CNOT => {
                    state = self.apply_cnot_gate(&state, gate.qubits[0], gate.qubits[1])?;
                }
                GateType::CZ => {
                    state = self.apply_cz_gate(&state, gate.qubits[0], gate.qubits[1])?;
                }
                _ => {
                    // Other gates can be implemented as needed
                }
            }
        }

        Ok(state)
    }

    /// Apply RX gate
    fn apply_rx_gate(&self, state: &Array1<f64>, qubit: usize, angle: f64) -> Result<Array1<f64>> {
        let mut new_state = state.clone();
        let cos_half = (angle / 2.0).cos();
        let sin_half = (angle / 2.0).sin();

        let qubit_mask = 1 << qubit;

        for i in 0..state.len() {
            if i & qubit_mask == 0 {
                let j = i | qubit_mask;
                if j < state.len() {
                    let state_0 = state[i];
                    let state_1 = state[j];
                    new_state[i] = cos_half * state_0 - sin_half * state_1;
                    new_state[j] = -sin_half * state_0 + cos_half * state_1;
                }
            }
        }

        Ok(new_state)
    }

    /// Apply RY gate
    fn apply_ry_gate(&self, state: &Array1<f64>, qubit: usize, angle: f64) -> Result<Array1<f64>> {
        let mut new_state = state.clone();
        let cos_half = (angle / 2.0).cos();
        let sin_half = (angle / 2.0).sin();

        let qubit_mask = 1 << qubit;

        for i in 0..state.len() {
            if i & qubit_mask == 0 {
                let j = i | qubit_mask;
                if j < state.len() {
                    let state_0 = state[i];
                    let state_1 = state[j];
                    new_state[i] = cos_half * state_0 - sin_half * state_1;
                    new_state[j] = sin_half * state_0 + cos_half * state_1;
                }
            }
        }

        Ok(new_state)
    }

    /// Apply RZ gate
    fn apply_rz_gate(&self, state: &Array1<f64>, qubit: usize, angle: f64) -> Result<Array1<f64>> {
        let mut new_state = state.clone();
        let phase_0 = (-angle / 2.0); // For real-valued implementation
        let phase_1 = (angle / 2.0);

        let qubit_mask = 1 << qubit;

        for i in 0..state.len() {
            if i & qubit_mask == 0 {
                new_state[i] *= phase_0.cos(); // Real part only for simplification
            } else {
                new_state[i] *= phase_1.cos();
            }
        }

        Ok(new_state)
    }

    /// Apply CNOT gate
    fn apply_cnot_gate(
        &self,
        state: &Array1<f64>,
        control: usize,
        target: usize,
    ) -> Result<Array1<f64>> {
        let mut new_state = state.clone();
        let control_mask = 1 << control;
        let target_mask = 1 << target;

        for i in 0..state.len() {
            if i & control_mask != 0 {
                let j = i ^ target_mask;
                new_state[i] = state[j];
            }
        }

        Ok(new_state)
    }

    /// Apply CZ gate
    fn apply_cz_gate(
        &self,
        state: &Array1<f64>,
        control: usize,
        target: usize,
    ) -> Result<Array1<f64>> {
        let mut new_state = state.clone();
        let control_mask = 1 << control;
        let target_mask = 1 << target;

        for i in 0..state.len() {
            if (i & control_mask != 0) && (i & target_mask != 0) {
                new_state[i] *= -1.0; // Apply phase flip
            }
        }

        Ok(new_state)
    }

    /// Decode quantum state to classical output
    fn decode_output(&self, quantum_state: &Array1<f64>) -> Result<f64> {
        // Expectation value of Z operator on first qubit
        let mut expectation = 0.0;

        for (i, &amplitude) in quantum_state.iter().enumerate() {
            if i & 1 == 0 {
                expectation += amplitude * amplitude;
            } else {
                expectation -= amplitude * amplitude;
            }
        }

        Ok(expectation)
    }

    /// Compute derivatives using automatic differentiation
    pub fn compute_derivatives(&self, points: &Array2<f64>) -> Result<DerivativeResults> {
        let h = 1e-5; // Finite difference step
        let num_points = points.nrows();
        let num_dims = points.ncols();

        let mut first_derivatives = Array2::zeros((num_points, num_dims));
        let mut second_derivatives = Array2::zeros((num_points, num_dims));
        let mut mixed_derivatives = Array3::zeros((num_points, num_dims, num_dims));

        for i in 0..num_points {
            for j in 0..num_dims {
                // First derivatives
                let mut point_plus = points.row(i).to_owned();
                let mut point_minus = points.row(i).to_owned();
                point_plus[j] += h;
                point_minus[j] -= h;

                let output_plus = self.forward(&point_plus.insert_axis(ndarray::Axis(0)))?[[0, 0]];
                let output_minus =
                    self.forward(&point_minus.insert_axis(ndarray::Axis(0)))?[[0, 0]];

                first_derivatives[[i, j]] = (output_plus - output_minus) / (2.0 * h);

                // Second derivatives
                let output_center =
                    self.forward(&points.row(i).insert_axis(ndarray::Axis(0)).to_owned())?[[0, 0]];
                second_derivatives[[i, j]] =
                    (output_plus - 2.0 * output_center + output_minus) / (h * h);

                // Mixed derivatives
                for k in j + 1..num_dims {
                    let mut point_pp = points.row(i).to_owned();
                    let mut point_pm = points.row(i).to_owned();
                    let mut point_mp = points.row(i).to_owned();
                    let mut point_mm = points.row(i).to_owned();

                    point_pp[j] += h;
                    point_pp[k] += h;
                    point_pm[j] += h;
                    point_pm[k] -= h;
                    point_mp[j] -= h;
                    point_mp[k] += h;
                    point_mm[j] -= h;
                    point_mm[k] -= h;

                    let output_pp = self.forward(&point_pp.insert_axis(ndarray::Axis(0)))?[[0, 0]];
                    let output_pm = self.forward(&point_pm.insert_axis(ndarray::Axis(0)))?[[0, 0]];
                    let output_mp = self.forward(&point_mp.insert_axis(ndarray::Axis(0)))?[[0, 0]];
                    let output_mm = self.forward(&point_mm.insert_axis(ndarray::Axis(0)))?[[0, 0]];

                    let mixed_deriv =
                        (output_pp - output_pm - output_mp + output_mm) / (4.0 * h * h);
                    mixed_derivatives[[i, j, k]] = mixed_deriv;
                    mixed_derivatives[[i, k, j]] = mixed_deriv; // Symmetry
                }
            }
        }

        Ok(DerivativeResults {
            first_derivatives,
            second_derivatives,
            mixed_derivatives,
        })
    }

    /// Train the Quantum PINN
    pub fn train(&mut self, epochs: Option<usize>) -> Result<()> {
        let num_epochs = epochs.unwrap_or(self.config.training_config.epochs);

        for epoch in 0..num_epochs {
            // Adaptive sampling of collocation points
            if self.config.training_config.adaptive_sampling && epoch % 100 == 0 {
                self.collocation_points =
                    Self::generate_adaptive_collocation_points(&self.config, epoch)?;
            }

            // Compute total loss
            let total_loss = self.compute_total_loss()?;

            // Compute gradients
            let gradients = self.compute_gradients()?;

            // Update parameters
            self.update_parameters(&gradients)?;

            // Record metrics
            let metrics = self.compute_training_metrics(epoch, total_loss)?;
            self.training_history.push(metrics);

            if epoch % 100 == 0 {
                println!(
                    "Epoch {}: Total Loss = {:.6}, PDE Loss = {:.6}, Boundary Loss = {:.6}",
                    epoch,
                    self.training_history.last().unwrap().total_loss,
                    self.training_history.last().unwrap().pde_loss,
                    self.training_history.last().unwrap().boundary_loss
                );
            }
        }

        Ok(())
    }

    /// Generate adaptive collocation points
    fn generate_adaptive_collocation_points(
        config: &QPINNConfig,
        epoch: usize,
    ) -> Result<Array2<f64>> {
        // For now, use uniform random sampling (adaptive refinement would be more complex)
        Self::generate_collocation_points(config)
    }

    /// Compute total loss
    fn compute_total_loss(&self) -> Result<TotalLoss> {
        let pde_loss = self.compute_pde_loss()?;
        let boundary_loss = self.compute_boundary_loss()?;
        let initial_loss = self.compute_initial_loss()?;
        let physics_constraint_loss = self.compute_physics_constraint_loss()?;

        let weights = &self.config.loss_weights;
        let total = weights.pde_loss_weight * pde_loss
            + weights.boundary_loss_weight * boundary_loss
            + weights.initial_loss_weight * initial_loss
            + weights.physics_constraint_weight * physics_constraint_loss;

        Ok(TotalLoss {
            total,
            pde_loss,
            boundary_loss,
            initial_loss,
            physics_constraint_loss,
        })
    }

    /// Compute PDE residual loss
    fn compute_pde_loss(&self) -> Result<f64> {
        let derivatives = self.compute_derivatives(&self.collocation_points)?;
        let residuals = self.physics_evaluator.compute_pde_residual(
            &self.collocation_points,
            &self.forward(&self.collocation_points)?,
            &derivatives,
        )?;

        Ok(residuals.iter().map(|r| r * r).sum::<f64>() / residuals.len() as f64)
    }

    /// Compute boundary condition loss
    fn compute_boundary_loss(&self) -> Result<f64> {
        // Generate boundary points
        let boundary_points = self.generate_boundary_points()?;
        let boundary_values = self.forward(&boundary_points)?;

        let mut total_loss = 0.0;
        for (bc, points) in self
            .config
            .boundary_conditions
            .iter()
            .zip(boundary_values.rows())
        {
            let target_values = self.evaluate_boundary_condition(bc, &boundary_points)?;
            for (predicted, target) in points.iter().zip(target_values.iter()) {
                total_loss += (predicted - target).powi(2);
            }
        }

        Ok(total_loss)
    }

    /// Compute initial condition loss
    fn compute_initial_loss(&self) -> Result<f64> {
        // Generate initial time points
        let initial_points = self.generate_initial_points()?;
        let initial_values = self.forward(&initial_points)?;

        let mut total_loss = 0.0;
        for (ic, points) in self
            .config
            .initial_conditions
            .iter()
            .zip(initial_values.rows())
        {
            let target_values = self.evaluate_initial_condition(ic, &initial_points)?;
            for (predicted, target) in points.iter().zip(target_values.iter()) {
                total_loss += (predicted - target).powi(2);
            }
        }

        Ok(total_loss)
    }

    /// Compute physics constraint loss
    fn compute_physics_constraint_loss(&self) -> Result<f64> {
        // Implement conservation law and symmetry constraints
        let mut constraint_loss = 0.0;

        for conservation_law in &self.config.physics_constraints.conservation_laws {
            constraint_loss += self.evaluate_conservation_law(conservation_law)?;
        }

        for symmetry in &self.config.physics_constraints.symmetries {
            constraint_loss += self.evaluate_symmetry_constraint(symmetry)?;
        }

        Ok(constraint_loss)
    }

    /// Generate boundary points
    fn generate_boundary_points(&self) -> Result<Array2<f64>> {
        // Simplified boundary point generation
        let num_boundary_points = 100;
        let num_dims = self.config.domain_bounds.len() + 1;
        let mut boundary_points = Array2::zeros((num_boundary_points, num_dims));

        // Generate points on each boundary
        for i in 0..num_boundary_points {
            for (j, &(min_val, max_val)) in self.config.domain_bounds.iter().enumerate() {
                if i % 2 == 0 {
                    boundary_points[[i, j]] = min_val; // Left/bottom boundary
                } else {
                    boundary_points[[i, j]] = max_val; // Right/top boundary
                }
            }

            // Random time coordinate
            let (t_min, t_max) = self.config.time_bounds;
            boundary_points[[i, self.config.domain_bounds.len()]] =
                t_min + fastrand::f64() * (t_max - t_min);
        }

        Ok(boundary_points)
    }

    /// Generate initial time points
    fn generate_initial_points(&self) -> Result<Array2<f64>> {
        let num_initial_points = 100;
        let num_dims = self.config.domain_bounds.len() + 1;
        let mut initial_points = Array2::zeros((num_initial_points, num_dims));

        for i in 0..num_initial_points {
            // Random spatial coordinates
            for (j, &(min_val, max_val)) in self.config.domain_bounds.iter().enumerate() {
                initial_points[[i, j]] = min_val + fastrand::f64() * (max_val - min_val);
            }

            // Initial time
            initial_points[[i, self.config.domain_bounds.len()]] = self.config.time_bounds.0;
        }

        Ok(initial_points)
    }

    /// Evaluate boundary condition
    fn evaluate_boundary_condition(
        &self,
        _bc: &BoundaryCondition,
        _points: &Array2<f64>,
    ) -> Result<Array1<f64>> {
        // Simplified: return zeros for Dirichlet conditions
        Ok(Array1::zeros(_points.nrows()))
    }

    /// Evaluate initial condition
    fn evaluate_initial_condition(
        &self,
        _ic: &InitialCondition,
        _points: &Array2<f64>,
    ) -> Result<Array1<f64>> {
        // Simplified: return zeros
        Ok(Array1::zeros(_points.nrows()))
    }

    /// Evaluate conservation law constraint
    fn evaluate_conservation_law(&self, _law: &ConservationLaw) -> Result<f64> {
        // Placeholder implementation
        Ok(0.0)
    }

    /// Evaluate symmetry constraint
    fn evaluate_symmetry_constraint(&self, _symmetry: &Symmetry) -> Result<f64> {
        // Placeholder implementation
        Ok(0.0)
    }

    /// Compute gradients
    fn compute_gradients(&self) -> Result<Array1<f64>> {
        let total_loss = self.compute_total_loss()?;
        let mut gradients = Array1::zeros(self.parameters.len());
        let epsilon = 1e-6;

        for i in 0..self.parameters.len() {
            let mut params_plus = self.parameters.clone();
            params_plus[i] += epsilon;

            let mut temp_pinn = self.clone();
            temp_pinn.parameters = params_plus;
            let loss_plus = temp_pinn.compute_total_loss()?.total;

            gradients[i] = (loss_plus - total_loss.total) / epsilon;
        }

        Ok(gradients)
    }

    /// Update parameters
    fn update_parameters(&mut self, gradients: &Array1<f64>) -> Result<()> {
        let learning_rate = self.config.training_config.learning_rate;

        for i in 0..self.parameters.len() {
            self.parameters[i] -= learning_rate * gradients[i];
        }

        Ok(())
    }

    /// Compute training metrics
    fn compute_training_metrics(
        &self,
        epoch: usize,
        total_loss: TotalLoss,
    ) -> Result<TrainingMetrics> {
        Ok(TrainingMetrics {
            epoch,
            total_loss: total_loss.total,
            pde_loss: total_loss.pde_loss,
            boundary_loss: total_loss.boundary_loss,
            initial_loss: total_loss.initial_loss,
            physics_constraint_loss: total_loss.physics_constraint_loss,
            quantum_fidelity: 0.9, // Placeholder
            solution_energy: 1.0,  // Placeholder
        })
    }

    /// Get training history
    pub fn get_training_history(&self) -> &[TrainingMetrics] {
        &self.training_history
    }

    /// Solve PDE and return solution on a grid
    pub fn solve_on_grid(&self, grid_points: &Array2<f64>) -> Result<Array1<f64>> {
        let solutions = self.forward(grid_points)?;
        Ok(solutions.column(0).to_owned())
    }
}

/// Results from derivative computation
#[derive(Debug)]
pub struct DerivativeResults {
    pub first_derivatives: Array2<f64>,
    pub second_derivatives: Array2<f64>,
    pub mixed_derivatives: Array3<f64>,
}

/// Total loss breakdown
#[derive(Debug)]
pub struct TotalLoss {
    pub total: f64,
    pub pde_loss: f64,
    pub boundary_loss: f64,
    pub initial_loss: f64,
    pub physics_constraint_loss: f64,
}

impl PhysicsEvaluator {
    /// Create a new physics evaluator
    pub fn new(equation_type: &PhysicsEquationType) -> Result<Self> {
        let mut differential_operators = HashMap::new();

        match equation_type {
            PhysicsEquationType::Poisson => {
                differential_operators.insert(
                    "laplacian".to_string(),
                    DifferentialOperator {
                        operator_type: OperatorType::Laplacian,
                        order: 2,
                        direction: vec![0, 1], // x and y directions
                    },
                );
            }
            PhysicsEquationType::Heat => {
                differential_operators.insert(
                    "time_derivative".to_string(),
                    DifferentialOperator {
                        operator_type: OperatorType::TimeDerivative,
                        order: 1,
                        direction: vec![2], // time direction
                    },
                );
                differential_operators.insert(
                    "laplacian".to_string(),
                    DifferentialOperator {
                        operator_type: OperatorType::Laplacian,
                        order: 2,
                        direction: vec![0, 1],
                    },
                );
            }
            PhysicsEquationType::Wave => {
                differential_operators.insert(
                    "second_time_derivative".to_string(),
                    DifferentialOperator {
                        operator_type: OperatorType::TimeDerivative,
                        order: 2,
                        direction: vec![2],
                    },
                );
                differential_operators.insert(
                    "laplacian".to_string(),
                    DifferentialOperator {
                        operator_type: OperatorType::Laplacian,
                        order: 2,
                        direction: vec![0, 1],
                    },
                );
            }
            _ => {
                // Add more equation types as needed
            }
        }

        Ok(Self {
            equation_type: equation_type.clone(),
            differential_operators,
        })
    }

    /// Compute PDE residual
    pub fn compute_pde_residual(
        &self,
        points: &Array2<f64>,
        solution: &Array2<f64>,
        derivatives: &DerivativeResults,
    ) -> Result<Array1<f64>> {
        let num_points = points.nrows();
        let mut residuals = Array1::zeros(num_points);

        match self.equation_type {
            PhysicsEquationType::Poisson => {
                // ∇²u = f (assuming f = 0 for simplicity)
                for i in 0..num_points {
                    let laplacian = derivatives.second_derivatives[[i, 0]]
                        + derivatives.second_derivatives[[i, 1]];
                    residuals[i] = laplacian; // f = 0
                }
            }
            PhysicsEquationType::Heat => {
                // ∂u/∂t = α∇²u (assuming α = 1)
                for i in 0..num_points {
                    let time_deriv = derivatives.first_derivatives[[i, 2]]; // time direction
                    let laplacian = derivatives.second_derivatives[[i, 0]]
                        + derivatives.second_derivatives[[i, 1]];
                    residuals[i] = time_deriv - laplacian;
                }
            }
            PhysicsEquationType::Wave => {
                // ∂²u/∂t² = c²∇²u (assuming c = 1)
                for i in 0..num_points {
                    let second_time_deriv = derivatives.second_derivatives[[i, 2]];
                    let laplacian = derivatives.second_derivatives[[i, 0]]
                        + derivatives.second_derivatives[[i, 1]];
                    residuals[i] = second_time_deriv - laplacian;
                }
            }
            _ => {
                return Err(crate::error::MLError::InvalidConfiguration(
                    "PDE type not implemented".to_string(),
                ));
            }
        }

        Ok(residuals)
    }
}

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

    #[test]
    fn test_qpinn_creation() {
        let config = QPINNConfig::default();
        let qpinn = QuantumPINN::new(config);
        assert!(qpinn.is_ok());
    }

    #[test]
    fn test_forward_pass() {
        let config = QPINNConfig::default();
        let qpinn = QuantumPINN::new(config).unwrap();
        let input_points = Array2::from_shape_vec(
            (5, 3),
            vec![
                0.1, 0.2, 0.0, 0.3, 0.4, 0.1, 0.5, 0.6, 0.2, 0.7, 0.8, 0.3, 0.9, 1.0, 0.4,
            ],
        )
        .unwrap();

        let result = qpinn.forward(&input_points);
        assert!(result.is_ok());
        assert_eq!(result.unwrap().shape(), [5, 1]);
    }

    #[test]
    fn test_derivative_computation() {
        let config = QPINNConfig::default();
        let qpinn = QuantumPINN::new(config).unwrap();
        let points =
            Array2::from_shape_vec((3, 3), vec![0.1, 0.2, 0.0, 0.3, 0.4, 0.1, 0.5, 0.6, 0.2])
                .unwrap();

        let result = qpinn.compute_derivatives(&points);
        assert!(result.is_ok());
    }

    #[test]
    #[ignore]
    fn test_training() {
        let mut config = QPINNConfig::default();
        config.training_config.epochs = 5;
        config.training_config.num_collocation_points = 10;

        let mut qpinn = QuantumPINN::new(config).unwrap();
        let result = qpinn.train(Some(5));
        assert!(result.is_ok());
        assert!(!qpinn.get_training_history().is_empty());
    }
}