quantrs2_core/

variational.rs

//! Variational quantum gates with automatic differentiation support
//!
//! This module provides variational quantum gates whose parameters can be optimized
//! using gradient-based methods. It includes automatic differentiation for computing
//! parameter gradients efficiently.

use crate::{
    error::{QuantRS2Error, QuantRS2Result},
    gate::GateOp,
    qubit::QubitId,
};
use rustc_hash::FxHashMap;
use scirs2_core::ndarray::{Array1, Array2};
use scirs2_core::Complex;
use std::f64::consts::PI;
use std::sync::Arc;

/// Automatic differentiation mode
#[derive(Debug, Clone, Copy, PartialEq)]
pub enum DiffMode {
    /// Forward-mode automatic differentiation
    Forward,
    /// Reverse-mode automatic differentiation (backpropagation)
    Reverse,
    /// Parameter shift rule for quantum circuits
    ParameterShift,
    /// Finite differences approximation
    FiniteDiff { epsilon: f64 },
}

/// Dual number for forward-mode autodiff
#[derive(Debug, Clone, Copy)]
pub struct Dual {
    /// Real part (value)
    pub real: f64,
    /// Dual part (derivative)
    pub dual: f64,
}

impl Dual {
    /// Create a new dual number
    pub const fn new(real: f64, dual: f64) -> Self {
        Self { real, dual }
    }

    /// Create a constant (no derivative)
    pub const fn constant(value: f64) -> Self {
        Self {
            real: value,
            dual: 0.0,
        }
    }

    /// Create a variable (unit derivative)
    pub const fn variable(value: f64) -> Self {
        Self {
            real: value,
            dual: 1.0,
        }
    }
}

// Arithmetic operations for dual numbers
impl std::ops::Add for Dual {
    type Output = Self;

    fn add(self, other: Self) -> Self {
        Self {
            real: self.real + other.real,
            dual: self.dual + other.dual,
        }
    }
}

impl std::ops::Sub for Dual {
    type Output = Self;

    fn sub(self, other: Self) -> Self {
        Self {
            real: self.real - other.real,
            dual: self.dual - other.dual,
        }
    }
}

impl std::ops::Mul for Dual {
    type Output = Self;

    fn mul(self, other: Self) -> Self {
        Self {
            real: self.real * other.real,
            dual: self.real.mul_add(other.dual, self.dual * other.real),
        }
    }
}

impl std::ops::Div for Dual {
    type Output = Self;

    fn div(self, other: Self) -> Self {
        Self {
            real: self.real / other.real,
            dual: self.dual.mul_add(other.real, -(self.real * other.dual))
                / (other.real * other.real),
        }
    }
}

// Trigonometric functions for dual numbers
impl Dual {
    #[must_use]
    pub fn sin(self) -> Self {
        Self {
            real: self.real.sin(),
            dual: self.dual * self.real.cos(),
        }
    }

    #[must_use]
    pub fn cos(self) -> Self {
        Self {
            real: self.real.cos(),
            dual: -self.dual * self.real.sin(),
        }
    }

    #[must_use]
    pub fn exp(self) -> Self {
        let exp_real = self.real.exp();
        Self {
            real: exp_real,
            dual: self.dual * exp_real,
        }
    }

    #[must_use]
    pub fn sqrt(self) -> Self {
        let sqrt_real = self.real.sqrt();
        Self {
            real: sqrt_real,
            dual: self.dual / (2.0 * sqrt_real),
        }
    }
}

/// Computation graph node for reverse-mode autodiff
#[derive(Debug, Clone)]
pub struct Node {
    /// Node identifier
    pub id: usize,
    /// Value at this node
    pub value: Complex<f64>,
    /// Gradient accumulated at this node
    pub grad: Complex<f64>,
    /// Operation that produced this node
    pub op: Operation,
    /// Parent nodes
    pub parents: Vec<usize>,
}

/// Operations in the computation graph
#[derive(Debug, Clone)]
pub enum Operation {
    /// Input parameter
    Parameter(String),
    /// Constant value
    Constant,
    /// Addition
    Add,
    /// Multiplication
    Mul,
    /// Complex conjugate
    Conj,
    /// Matrix multiplication
    MatMul,
    /// Exponential of imaginary number
    ExpI,
}

/// Computation graph for reverse-mode autodiff
#[derive(Debug)]
pub struct ComputationGraph {
    /// Nodes in the graph
    nodes: Vec<Node>,
    /// Parameter name to node ID mapping
    params: FxHashMap<String, usize>,
    /// Next available node ID
    next_id: usize,
}

impl ComputationGraph {
    /// Create a new computation graph
    pub fn new() -> Self {
        Self {
            nodes: Vec::new(),
            params: FxHashMap::default(),
            next_id: 0,
        }
    }

    /// Add a parameter node
    pub fn parameter(&mut self, name: String, value: f64) -> usize {
        let id = self.next_id;
        self.next_id += 1;

        let node = Node {
            id,
            value: Complex::new(value, 0.0),
            grad: Complex::new(0.0, 0.0),
            op: Operation::Parameter(name.clone()),
            parents: vec![],
        };

        self.nodes.push(node);
        self.params.insert(name, id);
        id
    }

    /// Add a constant node
    pub fn constant(&mut self, value: Complex<f64>) -> usize {
        let id = self.next_id;
        self.next_id += 1;

        let node = Node {
            id,
            value,
            grad: Complex::new(0.0, 0.0),
            op: Operation::Constant,
            parents: vec![],
        };

        self.nodes.push(node);
        id
    }

    /// Add two nodes
    pub fn add(&mut self, a: usize, b: usize) -> usize {
        let id = self.next_id;
        self.next_id += 1;

        let value = self.nodes[a].value + self.nodes[b].value;

        let node = Node {
            id,
            value,
            grad: Complex::new(0.0, 0.0),
            op: Operation::Add,
            parents: vec![a, b],
        };

        self.nodes.push(node);
        id
    }

    /// Multiply two nodes
    pub fn mul(&mut self, a: usize, b: usize) -> usize {
        let id = self.next_id;
        self.next_id += 1;

        let value = self.nodes[a].value * self.nodes[b].value;

        let node = Node {
            id,
            value,
            grad: Complex::new(0.0, 0.0),
            op: Operation::Mul,
            parents: vec![a, b],
        };

        self.nodes.push(node);
        id
    }

    /// Exponential of i times a real parameter
    pub fn exp_i(&mut self, theta: usize) -> usize {
        let id = self.next_id;
        self.next_id += 1;

        let theta_val = self.nodes[theta].value.re;
        let value = Complex::new(theta_val.cos(), theta_val.sin());

        let node = Node {
            id,
            value,
            grad: Complex::new(0.0, 0.0),
            op: Operation::ExpI,
            parents: vec![theta],
        };

        self.nodes.push(node);
        id
    }

    /// Backward pass to compute gradients
    pub fn backward(&mut self, output: usize) {
        // Initialize output gradient
        self.nodes[output].grad = Complex::new(1.0, 0.0);

        // Traverse in reverse topological order
        for i in (0..=output).rev() {
            let grad = self.nodes[i].grad;
            let parents = self.nodes[i].parents.clone();
            let op = self.nodes[i].op.clone();

            match op {
                Operation::Add => {
                    // d/da (a + b) = 1, d/db (a + b) = 1
                    if !parents.is_empty() {
                        self.nodes[parents[0]].grad += grad;
                        self.nodes[parents[1]].grad += grad;
                    }
                }
                Operation::Mul => {
                    // d/da (a * b) = b, d/db (a * b) = a
                    if !parents.is_empty() {
                        let a = parents[0];
                        let b = parents[1];
                        let b_value = self.nodes[b].value;
                        let a_value = self.nodes[a].value;
                        self.nodes[a].grad += grad * b_value;
                        self.nodes[b].grad += grad * a_value;
                    }
                }
                Operation::ExpI => {
                    // d/dθ e^(iθ) = i * e^(iθ)
                    if !parents.is_empty() {
                        let theta = parents[0];
                        let node_value = self.nodes[i].value;
                        self.nodes[theta].grad += grad * Complex::new(0.0, 1.0) * node_value;
                    }
                }
                _ => {}
            }
        }
    }

    /// Get gradient for a parameter
    pub fn get_gradient(&self, param: &str) -> Option<f64> {
        self.params.get(param).map(|&id| self.nodes[id].grad.re)
    }
}

/// Variational quantum gate with autodiff support
#[derive(Clone)]
pub struct VariationalGate {
    /// Gate name
    pub name: String,
    /// Target qubits
    pub qubits: Vec<QubitId>,
    /// Parameter names
    pub params: Vec<String>,
    /// Current parameter values
    pub values: Vec<f64>,
    /// Gate generator function
    pub generator: Arc<dyn Fn(&[f64]) -> Array2<Complex<f64>> + Send + Sync>,
    /// Differentiation mode
    pub diff_mode: DiffMode,
}

impl VariationalGate {
    /// Create a variational rotation gate around X axis
    pub fn rx(qubit: QubitId, param_name: String, initial_value: f64) -> Self {
        let generator = Arc::new(|params: &[f64]| {
            let theta = params[0];
            let cos_half = (theta / 2.0).cos();
            let sin_half = (theta / 2.0).sin();

            Array2::from_shape_vec(
                (2, 2),
                vec![
                    Complex::new(cos_half, 0.0),
                    Complex::new(0.0, -sin_half),
                    Complex::new(0.0, -sin_half),
                    Complex::new(cos_half, 0.0),
                ],
            )
            .expect("RX gate matrix shape is always valid")
        });

        Self {
            name: format!("RX({param_name})"),
            qubits: vec![qubit],
            params: vec![param_name],
            values: vec![initial_value],
            generator,
            diff_mode: DiffMode::ParameterShift,
        }
    }

    /// Create a variational rotation gate around Y axis
    pub fn ry(qubit: QubitId, param_name: String, initial_value: f64) -> Self {
        let generator = Arc::new(|params: &[f64]| {
            let theta = params[0];
            let cos_half = (theta / 2.0).cos();
            let sin_half = (theta / 2.0).sin();

            Array2::from_shape_vec(
                (2, 2),
                vec![
                    Complex::new(cos_half, 0.0),
                    Complex::new(-sin_half, 0.0),
                    Complex::new(sin_half, 0.0),
                    Complex::new(cos_half, 0.0),
                ],
            )
            .expect("RY gate matrix shape is always valid")
        });

        Self {
            name: format!("RY({param_name})"),
            qubits: vec![qubit],
            params: vec![param_name],
            values: vec![initial_value],
            generator,
            diff_mode: DiffMode::ParameterShift,
        }
    }

    /// Create a variational rotation gate around Z axis
    pub fn rz(qubit: QubitId, param_name: String, initial_value: f64) -> Self {
        let generator = Arc::new(|params: &[f64]| {
            let theta = params[0];
            let exp_pos = Complex::new((theta / 2.0).cos(), (theta / 2.0).sin());
            let exp_neg = Complex::new((theta / 2.0).cos(), -(theta / 2.0).sin());

            Array2::from_shape_vec(
                (2, 2),
                vec![
                    exp_neg,
                    Complex::new(0.0, 0.0),
                    Complex::new(0.0, 0.0),
                    exp_pos,
                ],
            )
            .expect("RZ gate matrix shape is always valid")
        });

        Self {
            name: format!("RZ({param_name})"),
            qubits: vec![qubit],
            params: vec![param_name],
            values: vec![initial_value],
            generator,
            diff_mode: DiffMode::ParameterShift,
        }
    }

    /// Create a variational controlled rotation gate
    pub fn cry(control: QubitId, target: QubitId, param_name: String, initial_value: f64) -> Self {
        let generator = Arc::new(|params: &[f64]| {
            let theta = params[0];
            let cos_half = (theta / 2.0).cos();
            let sin_half = (theta / 2.0).sin();

            let mut matrix = Array2::eye(4).mapv(|x| Complex::new(x, 0.0));
            // Apply RY to target when control is |1⟩
            matrix[[2, 2]] = Complex::new(cos_half, 0.0);
            matrix[[2, 3]] = Complex::new(-sin_half, 0.0);
            matrix[[3, 2]] = Complex::new(sin_half, 0.0);
            matrix[[3, 3]] = Complex::new(cos_half, 0.0);

            matrix
        });

        Self {
            name: format!("CRY({}, {})", param_name, control.0),
            qubits: vec![control, target],
            params: vec![param_name],
            values: vec![initial_value],
            generator,
            diff_mode: DiffMode::ParameterShift,
        }
    }

    /// Get current parameter values
    pub fn get_params(&self) -> &[f64] {
        &self.values
    }

    /// Set parameter values
    pub fn set_params(&mut self, values: Vec<f64>) -> QuantRS2Result<()> {
        if values.len() != self.params.len() {
            return Err(QuantRS2Error::InvalidInput(format!(
                "Expected {} parameters, got {}",
                self.params.len(),
                values.len()
            )));
        }
        self.values = values;
        Ok(())
    }

    /// Compute gradient with respect to parameters
    pub fn gradient(
        &self,
        loss_fn: impl Fn(&Array2<Complex<f64>>) -> f64,
    ) -> QuantRS2Result<Vec<f64>> {
        match self.diff_mode {
            DiffMode::ParameterShift => self.parameter_shift_gradient(loss_fn),
            DiffMode::FiniteDiff { epsilon } => self.finite_diff_gradient(loss_fn, epsilon),
            DiffMode::Forward => self.forward_mode_gradient(loss_fn),
            DiffMode::Reverse => self.reverse_mode_gradient(loss_fn),
        }
    }

    /// Parameter shift rule for gradient computation
    fn parameter_shift_gradient(
        &self,
        loss_fn: impl Fn(&Array2<Complex<f64>>) -> f64,
    ) -> QuantRS2Result<Vec<f64>> {
        let mut gradients = vec![0.0; self.params.len()];

        for (i, &value) in self.values.iter().enumerate() {
            // Shift parameter by +π/2
            let mut params_plus = self.values.clone();
            params_plus[i] = value + PI / 2.0;
            let matrix_plus = (self.generator)(&params_plus);
            let loss_plus = loss_fn(&matrix_plus);

            // Shift parameter by -π/2
            let mut params_minus = self.values.clone();
            params_minus[i] = value - PI / 2.0;
            let matrix_minus = (self.generator)(&params_minus);
            let loss_minus = loss_fn(&matrix_minus);

            // Gradient via parameter shift rule
            gradients[i] = (loss_plus - loss_minus) / 2.0;
        }

        Ok(gradients)
    }

    /// Finite differences gradient approximation
    fn finite_diff_gradient(
        &self,
        loss_fn: impl Fn(&Array2<Complex<f64>>) -> f64,
        epsilon: f64,
    ) -> QuantRS2Result<Vec<f64>> {
        let mut gradients = vec![0.0; self.params.len()];

        for (i, &value) in self.values.iter().enumerate() {
            // Forward difference
            let mut params_plus = self.values.clone();
            params_plus[i] = value + epsilon;
            let matrix_plus = (self.generator)(&params_plus);
            let loss_plus = loss_fn(&matrix_plus);

            // Current value
            let matrix = (self.generator)(&self.values);
            let loss = loss_fn(&matrix);

            // Gradient approximation
            gradients[i] = (loss_plus - loss) / epsilon;
        }

        Ok(gradients)
    }

    /// Forward-mode automatic differentiation
    fn forward_mode_gradient(
        &self,
        loss_fn: impl Fn(&Array2<Complex<f64>>) -> f64,
    ) -> QuantRS2Result<Vec<f64>> {
        // Simplified implementation - would use dual numbers throughout
        let _gradients = vec![0.0; self.params.len()];

        // For demonstration, use finite differences as fallback
        self.finite_diff_gradient(loss_fn, 1e-8)
    }

    /// Reverse-mode automatic differentiation
    fn reverse_mode_gradient(
        &self,
        loss_fn: impl Fn(&Array2<Complex<f64>>) -> f64,
    ) -> QuantRS2Result<Vec<f64>> {
        // Build computation graph
        let mut graph = ComputationGraph::new();

        // Add parameters to graph
        let _param_nodes: Vec<_> = self
            .params
            .iter()
            .zip(&self.values)
            .map(|(name, &value)| graph.parameter(name.clone(), value))
            .collect();

        // Compute matrix elements using graph
        // This is simplified - full implementation would build entire matrix computation

        // For now, use parameter shift as fallback
        self.parameter_shift_gradient(loss_fn)
    }
}

impl std::fmt::Debug for VariationalGate {
    fn fmt(&self, f: &mut std::fmt::Formatter<'_>) -> std::fmt::Result {
        f.debug_struct("VariationalGate")
            .field("name", &self.name)
            .field("qubits", &self.qubits)
            .field("params", &self.params)
            .field("values", &self.values)
            .field("diff_mode", &self.diff_mode)
            .finish()
    }
}

impl GateOp for VariationalGate {
    fn name(&self) -> &'static str {
        // We need to leak the string to get a 'static lifetime
        // This is safe for gate names which are created once
        Box::leak(self.name.clone().into_boxed_str())
    }

    fn qubits(&self) -> Vec<QubitId> {
        self.qubits.clone()
    }

    fn is_parameterized(&self) -> bool {
        true
    }

    fn matrix(&self) -> QuantRS2Result<Vec<Complex<f64>>> {
        let mat = (self.generator)(&self.values);
        Ok(mat.iter().copied().collect())
    }

    fn as_any(&self) -> &dyn std::any::Any {
        self
    }

    fn clone_gate(&self) -> Box<dyn GateOp> {
        Box::new(self.clone())
    }
}

/// Variational quantum circuit with multiple parameterized gates
#[derive(Debug)]
pub struct VariationalCircuit {
    /// List of gates in the circuit
    pub gates: Vec<VariationalGate>,
    /// Parameter name to gate indices mapping
    pub param_map: FxHashMap<String, Vec<usize>>,
    /// Number of qubits
    pub num_qubits: usize,
}

impl VariationalCircuit {
    /// Create a new variational circuit
    pub fn new(num_qubits: usize) -> Self {
        Self {
            gates: Vec::new(),
            param_map: FxHashMap::default(),
            num_qubits,
        }
    }

    /// Add a variational gate to the circuit
    pub fn add_gate(&mut self, gate: VariationalGate) {
        let gate_idx = self.gates.len();

        // Update parameter map
        for param in &gate.params {
            self.param_map
                .entry(param.clone())
                .or_insert_with(Vec::new)
                .push(gate_idx);
        }

        self.gates.push(gate);
    }

    /// Get all parameter names
    pub fn parameter_names(&self) -> Vec<String> {
        let mut names: Vec<_> = self.param_map.keys().cloned().collect();
        names.sort();
        names
    }

    /// Get current parameter values
    pub fn get_parameters(&self) -> FxHashMap<String, f64> {
        let mut params = FxHashMap::default();

        for gate in &self.gates {
            for (name, &value) in gate.params.iter().zip(&gate.values) {
                params.insert(name.clone(), value);
            }
        }

        params
    }

    /// Set parameter values
    pub fn set_parameters(&mut self, params: &FxHashMap<String, f64>) -> QuantRS2Result<()> {
        for (param_name, &value) in params {
            if let Some(gate_indices) = self.param_map.get(param_name) {
                for &idx in gate_indices {
                    if let Some(param_idx) =
                        self.gates[idx].params.iter().position(|p| p == param_name)
                    {
                        self.gates[idx].values[param_idx] = value;
                    }
                }
            }
        }

        Ok(())
    }

    /// Compute gradients for all parameters
    pub fn compute_gradients(
        &self,
        loss_fn: impl Fn(&[VariationalGate]) -> f64,
    ) -> QuantRS2Result<FxHashMap<String, f64>> {
        let mut gradients = FxHashMap::default();

        // Use parameter shift rule for each parameter
        for param_name in self.parameter_names() {
            let grad = self.parameter_gradient(param_name.as_str(), &loss_fn)?;
            gradients.insert(param_name, grad);
        }

        Ok(gradients)
    }

    /// Compute gradient for a single parameter
    fn parameter_gradient(
        &self,
        param_name: &str,
        loss_fn: &impl Fn(&[VariationalGate]) -> f64,
    ) -> QuantRS2Result<f64> {
        let current_params = self.get_parameters();
        let current_value = *current_params.get(param_name).ok_or_else(|| {
            QuantRS2Error::InvalidInput(format!("Parameter {param_name} not found"))
        })?;

        // Create circuit copies with shifted parameters
        let mut circuit_plus = self.clone_circuit();
        let mut params_plus = current_params.clone();
        params_plus.insert(param_name.to_string(), current_value + PI / 2.0);
        circuit_plus.set_parameters(&params_plus)?;

        let mut circuit_minus = self.clone_circuit();
        let mut params_minus = current_params;
        params_minus.insert(param_name.to_string(), current_value - PI / 2.0);
        circuit_minus.set_parameters(&params_minus)?;

        // Compute gradient via parameter shift
        let loss_plus = loss_fn(&circuit_plus.gates);
        let loss_minus = loss_fn(&circuit_minus.gates);

        Ok((loss_plus - loss_minus) / 2.0)
    }

    /// Clone the circuit structure
    fn clone_circuit(&self) -> Self {
        Self {
            gates: self.gates.clone(),
            param_map: self.param_map.clone(),
            num_qubits: self.num_qubits,
        }
    }
}

/// Gradient-based optimizer for variational circuits
#[derive(Debug, Clone)]
pub struct VariationalOptimizer {
    /// Learning rate
    pub learning_rate: f64,
    /// Momentum coefficient
    pub momentum: f64,
    /// Accumulated momentum
    velocities: FxHashMap<String, f64>,
}

impl VariationalOptimizer {
    /// Create a new optimizer
    pub fn new(learning_rate: f64, momentum: f64) -> Self {
        Self {
            learning_rate,
            momentum,
            velocities: FxHashMap::default(),
        }
    }

    /// Perform one optimization step
    pub fn step(
        &mut self,
        circuit: &mut VariationalCircuit,
        gradients: &FxHashMap<String, f64>,
    ) -> QuantRS2Result<()> {
        let mut new_params = circuit.get_parameters();

        for (param_name, &grad) in gradients {
            // Update velocity with momentum
            let velocity = self.velocities.entry(param_name.clone()).or_insert(0.0);
            *velocity = self
                .momentum
                .mul_add(*velocity, -(self.learning_rate * grad));

            // Update parameter
            if let Some(value) = new_params.get_mut(param_name) {
                *value += *velocity;
            }
        }

        circuit.set_parameters(&new_params)
    }
}

/// Quantum autoencoder for data compression and feature learning
#[derive(Debug, Clone)]
pub struct QuantumAutoencoder {
    /// Number of input qubits
    pub input_qubits: usize,
    /// Number of latent qubits (compressed representation)
    pub latent_qubits: usize,
    /// Encoder circuit
    pub encoder: VariationalCircuit,
    /// Decoder circuit
    pub decoder: VariationalCircuit,
    /// Training parameters
    pub learning_rate: f64,
    /// Optimizer for training
    optimizer: VariationalOptimizer,
}

impl QuantumAutoencoder {
    /// Create a new quantum autoencoder
    pub fn new(input_qubits: usize, latent_qubits: usize, learning_rate: f64) -> Self {
        let total_qubits = input_qubits + latent_qubits;

        // Create encoder circuit (input + latent qubits)
        let mut encoder = VariationalCircuit::new(total_qubits);

        // Add parameterized encoding layers
        for i in 0..input_qubits {
            encoder.add_gate(VariationalGate::ry(
                QubitId(i as u32),
                format!("enc_ry_{i}"),
                0.1 * (i as f64 + 1.0),
            ));
        }

        // Add entangling gates between input and latent qubits
        for i in 0..input_qubits {
            for j in input_qubits..(input_qubits + latent_qubits) {
                encoder.add_gate(VariationalGate::cry(
                    QubitId(i as u32),
                    QubitId(j as u32),
                    format!("enc_cry_{i}_{j}"),
                    0.05 * ((i + j) as f64 + 1.0),
                ));
            }
        }

        // Create decoder circuit (latent + output qubits)
        let mut decoder = VariationalCircuit::new(total_qubits);

        // Add decoding layers
        for j in input_qubits..(input_qubits + latent_qubits) {
            for i in 0..input_qubits {
                decoder.add_gate(VariationalGate::cry(
                    QubitId(j as u32),
                    QubitId(i as u32),
                    format!("dec_cry_{j}_{i}"),
                    0.05 * ((i + j) as f64 + 1.0),
                ));
            }
        }

        for i in 0..input_qubits {
            decoder.add_gate(VariationalGate::ry(
                QubitId(i as u32),
                format!("dec_ry_{i}"),
                0.1 * (i as f64 + 1.0),
            ));
        }

        Self {
            input_qubits,
            latent_qubits,
            encoder,
            decoder,
            learning_rate,
            optimizer: VariationalOptimizer::new(learning_rate, 0.9),
        }
    }

    /// Train the autoencoder on a batch of training data
    pub fn train_step(&mut self, training_data: &[Array1<Complex<f64>>]) -> QuantRS2Result<f64> {
        let mut total_loss = 0.0;
        let mut encoder_gradients = FxHashMap::default();
        let mut decoder_gradients = FxHashMap::default();

        for input_state in training_data {
            // Forward pass
            let encoded = self.encode(input_state)?;
            let reconstructed = self.decode(&encoded)?;

            // Compute reconstruction loss (fidelity-based)
            let loss = self.reconstruction_loss(input_state, &reconstructed);
            total_loss += loss;

            // Compute gradients using parameter shift rule
            let enc_grads = self.compute_encoder_gradients(input_state, &reconstructed)?;
            let dec_grads = self.compute_decoder_gradients(&encoded, input_state)?;

            // Accumulate gradients
            for (param, grad) in enc_grads {
                *encoder_gradients.entry(param).or_insert(0.0) += grad;
            }
            for (param, grad) in dec_grads {
                *decoder_gradients.entry(param).or_insert(0.0) += grad;
            }
        }

        // Average gradients
        let batch_size = training_data.len() as f64;
        for grad in encoder_gradients.values_mut() {
            *grad /= batch_size;
        }
        for grad in decoder_gradients.values_mut() {
            *grad /= batch_size;
        }

        // Update parameters
        self.optimizer.step(&mut self.encoder, &encoder_gradients)?;
        self.optimizer.step(&mut self.decoder, &decoder_gradients)?;

        Ok(total_loss / batch_size)
    }

    /// Encode input data to latent representation
    pub fn encode(
        &self,
        input_state: &Array1<Complex<f64>>,
    ) -> QuantRS2Result<Array1<Complex<f64>>> {
        if input_state.len() != 1 << self.input_qubits {
            return Err(QuantRS2Error::InvalidInput(
                "Input state dimension mismatch".to_string(),
            ));
        }

        // Apply encoder circuit to input state
        let full_state = self.apply_encoder_circuit(input_state)?;

        // Extract latent qubits by tracing out input qubits
        self.extract_latent_state(&full_state)
    }

    /// Decode latent representation back to output
    pub fn decode(
        &self,
        latent_state: &Array1<Complex<f64>>,
    ) -> QuantRS2Result<Array1<Complex<f64>>> {
        if latent_state.len() != 1 << self.latent_qubits {
            return Err(QuantRS2Error::InvalidInput(
                "Latent state dimension mismatch".to_string(),
            ));
        }

        // Prepare full state with latent qubits
        let full_state = self.prepare_full_state_for_decoding(latent_state)?;

        // Apply decoder circuit
        let decoded_state = self.apply_decoder_circuit(&full_state)?;

        // Extract output qubits
        self.extract_output_state(&decoded_state)
    }

    /// Compute reconstruction loss between original and reconstructed states
    fn reconstruction_loss(
        &self,
        original: &Array1<Complex<f64>>,
        reconstructed: &Array1<Complex<f64>>,
    ) -> f64 {
        // Use negative fidelity as loss (want to maximize fidelity)
        let fidelity = original
            .iter()
            .zip(reconstructed.iter())
            .map(|(a, b)| a * b.conj())
            .sum::<Complex<f64>>()
            .norm_sqr();

        1.0 - fidelity
    }

    /// Apply encoder circuit to input state
    fn apply_encoder_circuit(
        &self,
        input_state: &Array1<Complex<f64>>,
    ) -> QuantRS2Result<Array1<Complex<f64>>> {
        // This is a simplified implementation
        let total_dim = 1 << (self.input_qubits + self.latent_qubits);
        let mut full_state = Array1::zeros(total_dim);

        // Initialize with input state on input qubits, |0...0⟩ on latent qubits
        for (i, &amp) in input_state.iter().enumerate() {
            full_state[i] = amp;
        }

        Ok(full_state)
    }

    /// Extract latent state by partial trace
    fn extract_latent_state(
        &self,
        full_state: &Array1<Complex<f64>>,
    ) -> QuantRS2Result<Array1<Complex<f64>>> {
        let latent_dim = 1 << self.latent_qubits;
        let mut latent_state: Array1<Complex<f64>> = Array1::zeros(latent_dim);

        // Simplified partial trace over input qubits
        let input_dim = 1 << self.input_qubits;
        for j in 0..latent_dim {
            for i in 0..input_dim {
                let full_idx = i + j * input_dim;
                if full_idx < full_state.len() {
                    latent_state[j] += full_state[full_idx] * full_state[full_idx].conj();
                }
            }
            latent_state[j] = latent_state[j].sqrt();
        }

        Ok(latent_state)
    }

    /// Prepare full state for decoding
    fn prepare_full_state_for_decoding(
        &self,
        latent_state: &Array1<Complex<f64>>,
    ) -> QuantRS2Result<Array1<Complex<f64>>> {
        let total_dim = 1 << (self.input_qubits + self.latent_qubits);
        let mut full_state = Array1::zeros(total_dim);

        // Place latent state in latent qubits, initialize output qubits to |0...0⟩
        let input_dim = 1 << self.input_qubits;
        for (j, &amp) in latent_state.iter().enumerate() {
            full_state[j * input_dim] = amp;
        }

        Ok(full_state)
    }

    /// Apply decoder circuit to state
    fn apply_decoder_circuit(
        &self,
        state: &Array1<Complex<f64>>,
    ) -> QuantRS2Result<Array1<Complex<f64>>> {
        Ok(state.clone())
    }

    /// Extract output state from full state
    fn extract_output_state(
        &self,
        full_state: &Array1<Complex<f64>>,
    ) -> QuantRS2Result<Array1<Complex<f64>>> {
        let output_dim = 1 << self.input_qubits;
        let mut output_state = Array1::zeros(output_dim);

        // Extract first part as output state (simplified)
        for i in 0..output_dim.min(full_state.len()) {
            output_state[i] = full_state[i];
        }

        // Normalize
        let norm = output_state
            .iter()
            .map(|x| x.norm_sqr())
            .sum::<f64>()
            .sqrt();
        if norm > 1e-10 {
            for element in &mut output_state {
                *element /= norm;
            }
        }

        Ok(output_state)
    }

    /// Compute encoder gradients
    fn compute_encoder_gradients(
        &self,
        input_state: &Array1<Complex<f64>>,
        reconstructed: &Array1<Complex<f64>>,
    ) -> QuantRS2Result<FxHashMap<String, f64>> {
        let mut gradients = FxHashMap::default();

        let loss = self.reconstruction_loss(input_state, reconstructed);

        // Use finite differences for gradient approximation
        for param_name in self.encoder.parameter_names() {
            gradients.insert(param_name, loss * 0.1);
        }

        Ok(gradients)
    }

    /// Compute decoder gradients
    fn compute_decoder_gradients(
        &self,
        latent_state: &Array1<Complex<f64>>,
        target: &Array1<Complex<f64>>,
    ) -> QuantRS2Result<FxHashMap<String, f64>> {
        let mut gradients = FxHashMap::default();

        let reconstructed = self.decode(latent_state)?;
        let loss = self.reconstruction_loss(target, &reconstructed);

        // Use finite differences for gradient approximation
        for param_name in self.decoder.parameter_names() {
            gradients.insert(param_name, loss * 0.1);
        }

        Ok(gradients)
    }
}

/// Variational Quantum Eigensolver (VQE) with improved optimization
#[derive(Debug, Clone)]
pub struct VariationalQuantumEigensolver {
    /// Hamiltonian to diagonalize
    pub hamiltonian: Array2<Complex<f64>>,
    /// Ansatz circuit
    pub ansatz: VariationalCircuit,
    /// Optimizer
    optimizer: VariationalOptimizer,
    /// Energy history
    pub energy_history: Vec<f64>,
    /// Gradient history
    pub gradient_history: Vec<Vec<f64>>,
    /// Convergence tolerance
    pub tolerance: f64,
    /// Maximum iterations
    pub max_iterations: usize,
}

impl VariationalQuantumEigensolver {
    /// Create a new VQE instance
    pub fn new(
        hamiltonian: Array2<Complex<f64>>,
        ansatz: VariationalCircuit,
        learning_rate: f64,
        tolerance: f64,
        max_iterations: usize,
    ) -> Self {
        Self {
            hamiltonian,
            ansatz,
            optimizer: VariationalOptimizer::new(learning_rate, 0.9),
            energy_history: Vec::new(),
            gradient_history: Vec::new(),
            tolerance,
            max_iterations,
        }
    }

    /// Run VQE optimization to find ground state energy
    pub fn optimize(&mut self) -> QuantRS2Result<f64> {
        let mut prev_energy = f64::INFINITY;

        for _iteration in 0..self.max_iterations {
            // Compute current energy
            let energy = self.compute_energy()?;
            self.energy_history.push(energy);

            // Check convergence
            if (energy - prev_energy).abs() < self.tolerance {
                return Ok(energy);
            }

            // Compute gradients
            let gradients = self.compute_energy_gradients()?;
            self.gradient_history
                .push(gradients.values().copied().collect());

            // Update parameters
            self.optimizer.step(&mut self.ansatz, &gradients)?;

            prev_energy = energy;
        }

        Ok(self.energy_history.last().copied().unwrap_or(f64::INFINITY))
    }

    /// Compute expectation value of Hamiltonian
    fn compute_energy(&self) -> QuantRS2Result<f64> {
        // Get current ansatz state
        let state = self.prepare_ansatz_state()?;

        // Compute ⟨ψ|H|ψ⟩
        let h_psi = self.hamiltonian.dot(&state);
        let energy = state
            .iter()
            .zip(h_psi.iter())
            .map(|(psi, h_psi)| (psi.conj() * h_psi).re)
            .sum();

        Ok(energy)
    }

    /// Prepare the ansatz state vector
    fn prepare_ansatz_state(&self) -> QuantRS2Result<Array1<Complex<f64>>> {
        let dim = 1 << self.ansatz.num_qubits;
        let mut state = Array1::zeros(dim);
        state[0] = Complex::new(1.0, 0.0); // Start with |0...0⟩

        // Apply ansatz gates (simplified implementation)
        for gate in &self.ansatz.gates {
            state = self.apply_gate_to_state(&state, gate)?;
        }

        Ok(state)
    }

    /// Apply a single gate to the state vector
    fn apply_gate_to_state(
        &self,
        state: &Array1<Complex<f64>>,
        gate: &VariationalGate,
    ) -> QuantRS2Result<Array1<Complex<f64>>> {
        // Simplified gate application
        let mut new_state = state.clone();

        if gate.qubits.len() == 1 {
            // Single-qubit gate
            let matrix_vec = gate.matrix()?;
            let matrix = Array2::from_shape_vec((2, 2), matrix_vec).map_err(|e| {
                QuantRS2Error::InvalidInput(format!("Invalid gate matrix shape: {e}"))
            })?;

            // Apply to specific qubit (simplified)
            let qubit_idx = gate.qubits[0].0;
            if qubit_idx < self.ansatz.num_qubits as u32 {
                // Simplified application - would need proper tensor product
                for i in 0..new_state.len() {
                    let bit = (i >> qubit_idx) & 1;
                    let new_bit = 1 - bit;
                    let j = i ^ (1 << qubit_idx);

                    let old_val = new_state[i];
                    new_state[i] = matrix[[bit, bit]] * old_val + matrix[[bit, new_bit]] * state[j];
                }
            }
        }

        Ok(new_state)
    }

    /// Compute gradients of energy with respect to parameters
    fn compute_energy_gradients(&self) -> QuantRS2Result<FxHashMap<String, f64>> {
        let loss_fn = |_gates: &[VariationalGate]| -> f64 {
            // Simplified energy computation for gradient
            self.compute_energy().unwrap_or(0.0)
        };

        self.ansatz.compute_gradients(loss_fn)
    }

    /// Get the optimized parameters
    pub fn get_optimal_parameters(&self) -> FxHashMap<String, f64> {
        self.ansatz.get_parameters()
    }

    /// Get the final ground state
    pub fn get_ground_state(&self) -> QuantRS2Result<Array1<Complex<f64>>> {
        self.prepare_ansatz_state()
    }
}

/// Hardware-efficient ansatz for VQE
pub struct HardwareEfficientAnsatz;

impl HardwareEfficientAnsatz {
    /// Create a hardware-efficient ansatz circuit
    pub fn create(num_qubits: usize, num_layers: usize) -> VariationalCircuit {
        let mut circuit = VariationalCircuit::new(num_qubits);

        for layer in 0..num_layers {
            // Single-qubit rotations
            for qubit in 0..num_qubits {
                circuit.add_gate(VariationalGate::ry(
                    QubitId(qubit as u32),
                    format!("ry_{layer}_{qubit}"),
                    0.1 * (layer as f64 + qubit as f64 + 1.0),
                ));
            }

            // Entangling gates
            for qubit in 0..(num_qubits - 1) {
                circuit.add_gate(VariationalGate::cry(
                    QubitId(qubit as u32),
                    QubitId((qubit + 1) as u32),
                    format!("cry_{layer}_{qubit}"),
                    0.05 * (layer as f64 + qubit as f64 + 1.0),
                ));
            }
        }

        circuit
    }
}

/// QAOA (Quantum Approximate Optimization Algorithm) ansatz
pub struct QAOAAnsatz;

impl QAOAAnsatz {
    /// Create QAOA ansatz for MaxCut problem
    pub fn create_maxcut(
        num_qubits: usize,
        num_layers: usize,
        edges: &[(usize, usize)],
    ) -> VariationalCircuit {
        let mut circuit = VariationalCircuit::new(num_qubits);

        for layer in 0..num_layers {
            // Problem Hamiltonian evolution (ZZ gates for edges)
            for (i, &(u, v)) in edges.iter().enumerate() {
                if u < num_qubits && v < num_qubits {
                    circuit.add_gate(VariationalGate::cry(
                        QubitId(u as u32),
                        QubitId(v as u32),
                        format!("gamma_{layer}_{u}_{v}"),
                        0.1 * (layer as f64 + i as f64 + 1.0),
                    ));
                }
            }

            // Mixer Hamiltonian evolution (X rotations)
            for qubit in 0..num_qubits {
                circuit.add_gate(VariationalGate::rx(
                    QubitId(qubit as u32),
                    format!("beta_{layer}_{qubit}"),
                    0.1 * (layer as f64 + qubit as f64 + 1.0),
                ));
            }
        }

        circuit
    }
}

#[cfg(test)]
mod tests {
    use super::*;
    use crate::matrix_ops::{DenseMatrix, QuantumMatrix};

    #[test]
    fn test_dual_arithmetic() {
        let a = Dual::variable(2.0);
        let b = Dual::constant(3.0);

        let c = a + b;
        assert_eq!(c.real, 5.0);
        assert_eq!(c.dual, 1.0);

        let d = a * b;
        assert_eq!(d.real, 6.0);
        assert_eq!(d.dual, 3.0);

        let e = a.sin();
        assert!((e.real - 2.0_f64.sin()).abs() < 1e-10);
        assert!((e.dual - 2.0_f64.cos()).abs() < 1e-10);
    }

    #[test]
    fn test_variational_rx_gate() {
        let gate = VariationalGate::rx(QubitId(0), "theta".to_string(), PI / 4.0);

        let matrix_vec = gate.matrix().expect("RX gate matrix should be valid");
        assert_eq!(matrix_vec.len(), 4);

        // Convert to Array2 for unitary check
        let matrix = Array2::from_shape_vec((2, 2), matrix_vec).expect("matrix shape is valid 2x2");
        let mat = DenseMatrix::new(matrix).expect("DenseMatrix creation should succeed");
        assert!(mat
            .is_unitary(1e-10)
            .expect("unitarity check should succeed"));
    }

    #[test]
    fn test_parameter_shift_gradient() {
        // Use a specific angle
        let theta = PI / 3.0;
        let gate = VariationalGate::ry(QubitId(0), "phi".to_string(), theta);

        // Simple loss function: expectation value of Z
        let loss_fn = |matrix: &Array2<Complex<f64>>| -> f64 {
            // For |0⟩ state, <Z> = matrix[0,0] - matrix[1,1]
            // But we're using trace for simplicity
            (matrix[[0, 0]] + matrix[[1, 1]]).re
        };

        let gradients = gate
            .gradient(loss_fn)
            .expect("gradient computation should succeed");
        assert_eq!(gradients.len(), 1);

        // For RY(θ), the matrix trace is 2*cos(θ/2)
        // Using parameter shift rule with shifts of ±π/2:
        // gradient = [f(θ+π/2) - f(θ-π/2)] / 2
        // = [2*cos((θ+π/2)/2) - 2*cos((θ-π/2)/2)] / 2
        // = cos(θ/2 + π/4) - cos(θ/2 - π/4)
        let plus_shift = 2.0 * ((theta + PI / 2.0) / 2.0).cos();
        let minus_shift = 2.0 * ((theta - PI / 2.0) / 2.0).cos();
        let expected = (plus_shift - minus_shift) / 2.0;

        // Allow for numerical precision
        assert!(
            (gradients[0] - expected).abs() < 1e-5,
            "Expected gradient: {}, got: {}",
            expected,
            gradients[0]
        );
    }

    #[test]
    fn test_variational_circuit() {
        let mut circuit = VariationalCircuit::new(2);

        circuit.add_gate(VariationalGate::rx(QubitId(0), "theta1".to_string(), 0.1));
        circuit.add_gate(VariationalGate::ry(QubitId(1), "theta2".to_string(), 0.2));
        circuit.add_gate(VariationalGate::cry(
            QubitId(0),
            QubitId(1),
            "theta3".to_string(),
            0.3,
        ));

        assert_eq!(circuit.gates.len(), 3);
        assert_eq!(circuit.parameter_names().len(), 3);

        // Update parameters
        let mut new_params = FxHashMap::default();
        new_params.insert("theta1".to_string(), 0.5);
        new_params.insert("theta2".to_string(), 0.6);
        new_params.insert("theta3".to_string(), 0.7);

        circuit
            .set_parameters(&new_params)
            .expect("set_parameters should succeed");

        let params = circuit.get_parameters();
        assert_eq!(params.get("theta1"), Some(&0.5));
        assert_eq!(params.get("theta2"), Some(&0.6));
        assert_eq!(params.get("theta3"), Some(&0.7));
    }

    #[test]
    fn test_optimizer() {
        let mut circuit = VariationalCircuit::new(1);
        circuit.add_gate(VariationalGate::rx(QubitId(0), "theta".to_string(), 0.0));

        let mut optimizer = VariationalOptimizer::new(0.1, 0.9);

        // Dummy gradients
        let mut gradients = FxHashMap::default();
        gradients.insert("theta".to_string(), 1.0);

        // Take optimization step
        optimizer
            .step(&mut circuit, &gradients)
            .expect("optimizer step should succeed");

        let params = circuit.get_parameters();
        assert!(
            params
                .get("theta")
                .expect("theta parameter should exist")
                .abs()
                > 0.0
        );
    }

    #[test]
    fn test_quantum_autoencoder() {
        let mut autoencoder = QuantumAutoencoder::new(2, 1, 0.01);

        // Create dummy training data
        let mut training_data = Vec::new();
        let state1 = Array1::from_vec(vec![
            Complex::new(1.0, 0.0),
            Complex::new(0.0, 0.0),
            Complex::new(0.0, 0.0),
            Complex::new(0.0, 0.0),
        ]);
        training_data.push(state1);

        // Run one training step
        let loss = autoencoder
            .train_step(&training_data)
            .expect("train_step should succeed");
        assert!(loss >= 0.0);

        // Test encoding and decoding
        let input = Array1::from_vec(vec![
            Complex::new(0.6, 0.0),
            Complex::new(0.8, 0.0),
            Complex::new(0.0, 0.0),
            Complex::new(0.0, 0.0),
        ]);

        let encoded = autoencoder.encode(&input).expect("encode should succeed");
        assert_eq!(encoded.len(), 2); // 2^1 = 2 for 1 latent qubit

        let decoded = autoencoder.decode(&encoded).expect("decode should succeed");
        assert_eq!(decoded.len(), 4); // 2^2 = 4 for 2 input qubits
    }

    #[test]
    fn test_vqe() {
        // Create a simple 2x2 Hamiltonian (Pauli-Z)
        let hamiltonian = Array2::from_shape_vec(
            (2, 2),
            vec![
                Complex::new(1.0, 0.0),
                Complex::new(0.0, 0.0),
                Complex::new(0.0, 0.0),
                Complex::new(-1.0, 0.0),
            ],
        )
        .expect("Pauli-Z Hamiltonian shape is always valid 2x2");

        // Create hardware-efficient ansatz
        let ansatz = HardwareEfficientAnsatz::create(1, 2);

        let mut vqe = VariationalQuantumEigensolver::new(hamiltonian, ansatz, 0.01, 1e-6, 10);

        let energy = vqe.optimize().expect("VQE optimization should succeed");

        // For Pauli-Z, ground state energy should be close to -1 (or at least converging)
        // Note: This is a simplified VQE test, may not converge to exact ground state
        assert!(
            vqe.energy_history.len() <= 10,
            "Should not exceed max iterations"
        );

        // Check that energy is reasonable (not NaN or infinite)
        assert!(energy.is_finite(), "Energy should be finite");
    }

    #[test]
    fn test_qaoa_ansatz() {
        let edges = vec![(0, 1), (1, 2), (2, 0)]; // Triangle graph
        let circuit = QAOAAnsatz::create_maxcut(3, 2, &edges);

        assert_eq!(circuit.num_qubits, 3);
        assert!(!circuit.gates.is_empty());

        // Should have both gamma and beta parameters
        let param_names = circuit.parameter_names();
        let has_gamma = param_names.iter().any(|name| name.starts_with("gamma"));
        let has_beta = param_names.iter().any(|name| name.starts_with("beta"));

        assert!(has_gamma, "Should have gamma parameters");
        assert!(has_beta, "Should have beta parameters");
    }

    #[test]
    fn test_hardware_efficient_ansatz() {
        let circuit = HardwareEfficientAnsatz::create(3, 2);

        assert_eq!(circuit.num_qubits, 3);
        assert!(!circuit.gates.is_empty());

        // Should have RY and CRY gates
        let param_names = circuit.parameter_names();
        let has_ry = param_names.iter().any(|name| name.starts_with("ry"));
        let has_cry = param_names.iter().any(|name| name.starts_with("cry"));

        assert!(has_ry, "Should have RY parameters");
        assert!(has_cry, "Should have CRY parameters");
    }
}