quantrs2_core/

symbolic_optimization.rs

//! Symbolic optimization module for quantum circuits and algorithms
//!
//! This module provides symbolic optimization capabilities for quantum circuits,
//! including automatic differentiation for variational algorithms, circuit
//! simplification using symbolic computation, and parameter optimization.

use crate::error::{QuantRS2Error, QuantRS2Result};
use crate::symbolic_hamiltonian::SymbolicHamiltonian;
use num_complex::Complex64;
use std::collections::HashMap;

/// Symbolic optimization configuration
#[derive(Debug, Clone)]
pub struct SymbolicOptimizationConfig {
    /// Maximum number of optimization iterations
    pub max_iterations: usize,
    /// Convergence tolerance
    pub tolerance: f64,
    /// Learning rate for gradient-based optimization
    pub learning_rate: f64,
    /// Whether to use analytical gradients when available
    pub use_analytical_gradients: bool,
    /// Finite difference step size for numerical gradients
    pub finite_difference_step: f64,
}

impl Default for SymbolicOptimizationConfig {
    fn default() -> Self {
        SymbolicOptimizationConfig {
            max_iterations: 1000,
            tolerance: 1e-6,
            learning_rate: 0.01,
            use_analytical_gradients: true,
            finite_difference_step: 1e-8,
        }
    }
}

/// Optimization result
#[derive(Debug, Clone)]
pub struct OptimizationResult {
    /// Optimal parameter values
    pub optimal_parameters: HashMap<String, f64>,
    /// Final objective function value
    pub final_value: f64,
    /// Number of iterations performed
    pub iterations: usize,
    /// Whether optimization converged
    pub converged: bool,
    /// Optimization history
    pub history: Vec<(HashMap<String, f64>, f64)>,
}

/// Symbolic objective function for optimization
pub trait SymbolicObjective {
    /// Evaluate the objective function
    fn evaluate(&self, parameters: &HashMap<String, f64>) -> QuantRS2Result<f64>;

    /// Compute gradients (analytical if available, numerical otherwise)
    fn gradients(&self, parameters: &HashMap<String, f64>) -> QuantRS2Result<HashMap<String, f64>>;

    /// Get parameter names
    fn parameter_names(&self) -> Vec<String>;

    /// Get parameter bounds (if any)
    fn parameter_bounds(&self) -> HashMap<String, (Option<f64>, Option<f64>)> {
        HashMap::new()
    }
}

/// Hamiltonian expectation value objective for VQE
pub struct HamiltonianExpectation {
    /// The Hamiltonian
    pub hamiltonian: SymbolicHamiltonian,
    /// Parametric quantum circuit (simplified representation)
    pub circuit_parameters: Vec<String>,
    /// State preparation function (placeholder)
    pub state_prep: Option<Box<dyn Fn(&HashMap<String, f64>) -> QuantRS2Result<Vec<Complex64>>>>,
}

impl std::fmt::Debug for HamiltonianExpectation {
    fn fmt(&self, f: &mut std::fmt::Formatter<'_>) -> std::fmt::Result {
        f.debug_struct("HamiltonianExpectation")
            .field("hamiltonian", &self.hamiltonian)
            .field("circuit_parameters", &self.circuit_parameters)
            .field(
                "state_prep",
                &self.state_prep.as_ref().map(|_| "<function>"),
            )
            .finish()
    }
}

impl Clone for HamiltonianExpectation {
    fn clone(&self) -> Self {
        Self {
            hamiltonian: self.hamiltonian.clone(),
            circuit_parameters: self.circuit_parameters.clone(),
            state_prep: None, // Cannot clone closures
        }
    }
}

impl HamiltonianExpectation {
    /// Create a new Hamiltonian expectation objective
    pub fn new(hamiltonian: SymbolicHamiltonian) -> Self {
        HamiltonianExpectation {
            circuit_parameters: hamiltonian.variables(),
            hamiltonian,
            state_prep: None,
        }
    }

    /// Set the state preparation function
    pub fn with_state_prep<F>(mut self, state_prep: F) -> Self
    where
        F: Fn(&HashMap<String, f64>) -> QuantRS2Result<Vec<Complex64>> + 'static,
    {
        self.state_prep = Some(Box::new(state_prep));
        self
    }
}

impl SymbolicObjective for HamiltonianExpectation {
    fn evaluate(&self, parameters: &HashMap<String, f64>) -> QuantRS2Result<f64> {
        // Get the evaluated Hamiltonian terms
        let terms = self.hamiltonian.evaluate(parameters)?;

        // For this example, we'll use a simple computational basis state
        // In practice, you'd use the actual quantum circuit state
        let n_qubits = self.hamiltonian.n_qubits;
        let mut state_vector = vec![Complex64::new(0.0, 0.0); 1 << n_qubits];

        if let Some(ref state_prep) = self.state_prep {
            state_vector = state_prep(parameters)?;
        } else {
            // Default to |0...0⟩ state
            state_vector[0] = Complex64::new(1.0, 0.0);
        }

        // Compute expectation value
        let mut expectation = 0.0;
        for (coeff, pauli_string) in terms {
            let pauli_expectation = compute_pauli_expectation_real(&pauli_string, &state_vector)?;
            expectation += coeff * pauli_expectation;
        }

        Ok(expectation)
    }

    fn gradients(&self, parameters: &HashMap<String, f64>) -> QuantRS2Result<HashMap<String, f64>> {
        let mut gradients = HashMap::new();

        #[cfg(feature = "symbolic")]
        {
            // Use analytical gradients if available
            if self
                .hamiltonian
                .variables()
                .iter()
                .all(|v| parameters.contains_key(v))
            {
                let grad_hamiltonians = self.hamiltonian.gradients(&self.parameter_names())?;

                for (param_name, grad_hamiltonian) in grad_hamiltonians {
                    let grad_obj = HamiltonianExpectation {
                        hamiltonian: grad_hamiltonian,
                        circuit_parameters: self.circuit_parameters.clone(),
                        state_prep: None, // Cannot clone function
                    };

                    let grad_value = grad_obj.evaluate(parameters)?;
                    gradients.insert(param_name, grad_value);
                }

                return Ok(gradients);
            }
        }

        // Fallback to numerical gradients
        let step = 1e-8;
        let _base_value = self.evaluate(parameters)?;

        for param_name in self.parameter_names() {
            let mut params_plus = parameters.clone();
            let mut params_minus = parameters.clone();

            let current_value = parameters.get(&param_name).unwrap_or(&0.0);
            params_plus.insert(param_name.clone(), current_value + step);
            params_minus.insert(param_name.clone(), current_value - step);

            let value_plus = self.evaluate(&params_plus)?;
            let value_minus = self.evaluate(&params_minus)?;

            let gradient = (value_plus - value_minus) / (2.0 * step);
            gradients.insert(param_name, gradient);
        }

        Ok(gradients)
    }

    fn parameter_names(&self) -> Vec<String> {
        let mut names = self.hamiltonian.variables();
        names.extend(self.circuit_parameters.iter().cloned());
        names.sort();
        names.dedup();
        names
    }
}

/// Quantum circuit cost function for QAOA
#[derive(Debug, Clone)]
pub struct QAOACostFunction {
    /// Cost Hamiltonian
    pub cost_hamiltonian: SymbolicHamiltonian,
    /// Mixer Hamiltonian  
    pub mixer_hamiltonian: SymbolicHamiltonian,
    /// Number of QAOA layers
    pub p_layers: usize,
}

impl QAOACostFunction {
    /// Create a new QAOA cost function
    pub fn new(
        cost_hamiltonian: SymbolicHamiltonian,
        mixer_hamiltonian: SymbolicHamiltonian,
        p_layers: usize,
    ) -> Self {
        QAOACostFunction {
            cost_hamiltonian,
            mixer_hamiltonian,
            p_layers,
        }
    }
}

impl SymbolicObjective for QAOACostFunction {
    fn evaluate(&self, parameters: &HashMap<String, f64>) -> QuantRS2Result<f64> {
        // Simplified QAOA evaluation
        // In practice, you'd simulate the full QAOA circuit

        // Extract beta and gamma parameters
        let mut total_cost = 0.0;

        for layer in 0..self.p_layers {
            let gamma_key = format!("gamma_{}", layer);
            let beta_key = format!("beta_{}", layer);

            let gamma = parameters.get(&gamma_key).unwrap_or(&0.0);
            let beta = parameters.get(&beta_key).unwrap_or(&0.0);

            // Simplified cost calculation
            total_cost += gamma * gamma + beta * beta;
        }

        Ok(total_cost)
    }

    fn gradients(&self, parameters: &HashMap<String, f64>) -> QuantRS2Result<HashMap<String, f64>> {
        let mut gradients = HashMap::new();

        // Simplified gradients for the example
        for layer in 0..self.p_layers {
            let gamma_key = format!("gamma_{}", layer);
            let beta_key = format!("beta_{}", layer);

            let gamma = parameters.get(&gamma_key).unwrap_or(&0.0);
            let beta = parameters.get(&beta_key).unwrap_or(&0.0);

            gradients.insert(gamma_key, 2.0 * gamma);
            gradients.insert(beta_key, 2.0 * beta);
        }

        Ok(gradients)
    }

    fn parameter_names(&self) -> Vec<String> {
        let mut names = Vec::new();
        for layer in 0..self.p_layers {
            names.push(format!("gamma_{}", layer));
            names.push(format!("beta_{}", layer));
        }
        names
    }

    fn parameter_bounds(&self) -> HashMap<String, (Option<f64>, Option<f64>)> {
        let mut bounds = HashMap::new();
        for layer in 0..self.p_layers {
            // QAOA parameters typically bounded by [0, 2π]
            bounds.insert(
                format!("gamma_{}", layer),
                (Some(0.0), Some(2.0 * std::f64::consts::PI)),
            );
            bounds.insert(
                format!("beta_{}", layer),
                (Some(0.0), Some(std::f64::consts::PI)),
            );
        }
        bounds
    }
}

/// Symbolic optimizer
pub struct SymbolicOptimizer {
    config: SymbolicOptimizationConfig,
}

impl SymbolicOptimizer {
    /// Create a new symbolic optimizer
    pub fn new(config: SymbolicOptimizationConfig) -> Self {
        SymbolicOptimizer { config }
    }

    /// Create with default configuration
    pub fn default() -> Self {
        SymbolicOptimizer::new(SymbolicOptimizationConfig::default())
    }

    /// Optimize using gradient descent
    pub fn optimize<O: SymbolicObjective>(
        &self,
        objective: &O,
        initial_parameters: HashMap<String, f64>,
    ) -> QuantRS2Result<OptimizationResult> {
        let mut parameters = initial_parameters;
        let mut history = Vec::new();
        let mut converged = false;

        let mut prev_value = objective.evaluate(&parameters)?;
        history.push((parameters.clone(), prev_value));

        for iteration in 0..self.config.max_iterations {
            // Compute gradients
            let gradients = objective.gradients(&parameters)?;

            // Gradient descent update
            let mut max_gradient: f64 = 0.0;
            for param_name in objective.parameter_names() {
                if let Some(gradient) = gradients.get(&param_name) {
                    let current_value = parameters.get(&param_name).unwrap_or(&0.0);
                    let new_value = current_value - self.config.learning_rate * gradient;

                    // Apply bounds if they exist
                    let bounded_value = if let Some((lower, upper)) =
                        objective.parameter_bounds().get(&param_name)
                    {
                        let mut val = new_value;
                        if let Some(lower_bound) = lower {
                            val = val.max(*lower_bound);
                        }
                        if let Some(upper_bound) = upper {
                            val = val.min(*upper_bound);
                        }
                        val
                    } else {
                        new_value
                    };

                    parameters.insert(param_name.clone(), bounded_value);
                    max_gradient = max_gradient.max(gradient.abs());
                }
            }

            // Evaluate new objective value
            let current_value = objective.evaluate(&parameters)?;
            history.push((parameters.clone(), current_value));

            // Check convergence
            let value_change = (current_value - prev_value).abs();
            if value_change < self.config.tolerance && max_gradient < self.config.tolerance {
                converged = true;
                break;
            }

            prev_value = current_value;

            // Optional: Print progress
            if iteration % 100 == 0 {
                println!(
                    "Iteration {}: objective = {:.6e}, max_grad = {:.6e}",
                    iteration, current_value, max_gradient
                );
            }
        }

        Ok(OptimizationResult {
            optimal_parameters: parameters,
            final_value: prev_value,
            iterations: history.len() - 1,
            converged,
            history,
        })
    }

    /// Optimize using BFGS (simplified implementation)
    pub fn optimize_bfgs<O: SymbolicObjective>(
        &self,
        objective: &O,
        initial_parameters: HashMap<String, f64>,
    ) -> QuantRS2Result<OptimizationResult> {
        // For now, fall back to gradient descent
        // A full BFGS implementation would maintain an approximation to the inverse Hessian
        self.optimize(objective, initial_parameters)
    }
}

/// Circuit parameter optimization utilities
pub mod circuit_optimization {
    use super::*;
    use crate::parametric::ParametricGate;

    /// Optimize a parametric quantum circuit
    pub fn optimize_parametric_circuit<O: SymbolicObjective>(
        _gates: &[Box<dyn ParametricGate>],
        objective: &O,
        initial_parameters: HashMap<String, f64>,
    ) -> QuantRS2Result<OptimizationResult> {
        let optimizer = SymbolicOptimizer::default();
        optimizer.optimize(objective, initial_parameters)
    }

    /// Extract parameters from a list of parametric gates
    pub fn extract_circuit_parameters(gates: &[Box<dyn ParametricGate>]) -> Vec<String> {
        let mut parameters = Vec::new();
        for gate in gates {
            parameters.extend(gate.parameter_names());
        }
        parameters.sort();
        parameters.dedup();
        parameters
    }

    /// Apply optimized parameters to a circuit
    pub fn apply_optimized_parameters(
        gates: &[Box<dyn ParametricGate>],
        parameters: &HashMap<String, f64>,
    ) -> QuantRS2Result<Vec<Box<dyn ParametricGate>>> {
        let mut optimized_gates = Vec::new();

        for gate in gates {
            let param_assignments: Vec<(String, f64)> = gate
                .parameter_names()
                .into_iter()
                .filter_map(|name| parameters.get(&name).map(|&value| (name, value)))
                .collect();

            let optimized_gate = gate.assign(&param_assignments)?;
            optimized_gates.push(optimized_gate);
        }

        Ok(optimized_gates)
    }
}

// Helper functions

fn compute_pauli_expectation_real(
    pauli_string: &crate::symbolic_hamiltonian::PauliString,
    state_vector: &[Complex64],
) -> QuantRS2Result<f64> {
    // Simplified implementation - in practice you'd use more efficient algorithms
    use crate::symbolic_hamiltonian::PauliOperator;

    let n_qubits = pauli_string.n_qubits;
    let n_states = 1 << n_qubits;

    if state_vector.len() != n_states {
        return Err(QuantRS2Error::InvalidInput(
            "State vector size mismatch".to_string(),
        ));
    }

    let mut expectation = 0.0;

    for i in 0..n_states {
        for j in 0..n_states {
            let mut matrix_element = Complex64::new(1.0, 0.0);

            for qubit in 0..n_qubits {
                let op = pauli_string.get_operator(qubit.into());
                let bit_i = (i >> qubit) & 1;
                let bit_j = (j >> qubit) & 1;

                let local_element = match op {
                    PauliOperator::I => {
                        if bit_i == bit_j {
                            Complex64::new(1.0, 0.0)
                        } else {
                            Complex64::new(0.0, 0.0)
                        }
                    }
                    PauliOperator::X => {
                        if bit_i != bit_j {
                            Complex64::new(1.0, 0.0)
                        } else {
                            Complex64::new(0.0, 0.0)
                        }
                    }
                    PauliOperator::Y => {
                        if bit_i != bit_j {
                            if bit_j == 1 {
                                Complex64::new(0.0, 1.0)
                            } else {
                                Complex64::new(0.0, -1.0)
                            }
                        } else {
                            Complex64::new(0.0, 0.0)
                        }
                    }
                    PauliOperator::Z => {
                        if bit_i == bit_j {
                            if bit_i == 0 {
                                Complex64::new(1.0, 0.0)
                            } else {
                                Complex64::new(-1.0, 0.0)
                            }
                        } else {
                            Complex64::new(0.0, 0.0)
                        }
                    }
                };

                matrix_element *= local_element;
                if matrix_element.norm() < 1e-12 {
                    break;
                }
            }

            let contribution = state_vector[i].conj() * matrix_element * state_vector[j];
            expectation += contribution.re;
        }
    }

    Ok(expectation)
}

#[cfg(test)]
mod tests {
    use super::*;
    use crate::parametric::Parameter;
    use crate::qubit::QubitId;
    use crate::symbolic_hamiltonian::hamiltonians;

    #[test]
    fn test_hamiltonian_expectation() {
        let hamiltonian = hamiltonians::transverse_field_ising(
            2,
            Parameter::constant(1.0),
            Parameter::constant(0.5),
        );

        let objective = HamiltonianExpectation::new(hamiltonian);
        let parameters = HashMap::new();

        let result = objective.evaluate(&parameters);
        assert!(result.is_ok());
    }

    #[test]
    fn test_qaoa_cost_function() {
        let cost_h = hamiltonians::maxcut(&[(QubitId::from(0), QubitId::from(1), 1.0)], 2);
        let mixer_h = hamiltonians::transverse_field_ising(
            2,
            Parameter::constant(0.0),
            Parameter::constant(1.0),
        );

        let objective = QAOACostFunction::new(cost_h, mixer_h, 1);

        let mut parameters = HashMap::new();
        parameters.insert("gamma_0".to_string(), 0.5);
        parameters.insert("beta_0".to_string(), 0.3);

        let result = objective.evaluate(&parameters);
        assert!(result.is_ok());

        let gradients = objective.gradients(&parameters);
        assert!(gradients.is_ok());
    }

    #[test]
    fn test_symbolic_optimizer() {
        let cost_h = hamiltonians::maxcut(&[(QubitId::from(0), QubitId::from(1), 1.0)], 2);
        let mixer_h = hamiltonians::transverse_field_ising(
            2,
            Parameter::constant(0.0),
            Parameter::constant(1.0),
        );

        let objective = QAOACostFunction::new(cost_h, mixer_h, 1);

        let mut initial_params = HashMap::new();
        initial_params.insert("gamma_0".to_string(), 1.0);
        initial_params.insert("beta_0".to_string(), 1.0);

        let mut config = SymbolicOptimizationConfig::default();
        config.max_iterations = 10; // Limit for test

        let optimizer = SymbolicOptimizer::new(config);
        let result = optimizer.optimize(&objective, initial_params);

        assert!(result.is_ok());
        let opt_result = result.unwrap();
        assert_eq!(opt_result.iterations, 10);
    }
}