quantrs2_sim/

qaoa_optimization.rs

//! Quantum Approximate Optimization Algorithm (QAOA) Implementation
//!
//! This module provides a comprehensive implementation of QAOA for combinatorial
//! optimization problems, including advanced problem encodings, multi-level QAOA,
//! and hardware-aware optimizations.

use scirs2_core::ndarray::{Array1, Array2};
use scirs2_core::parallel_ops::{IndexedParallelIterator, ParallelIterator};
use scirs2_core::random::prelude::*;
use scirs2_core::Complex64;
use serde::{Deserialize, Serialize};
use std::collections::HashMap;
use std::sync::{Arc, Mutex};
use std::time::{Duration, Instant};

use crate::circuit_interfaces::{InterfaceCircuit, InterfaceGate, InterfaceGateType};
use crate::error::Result;

#[cfg(feature = "optimize")]
use crate::optirs_integration::{OptiRSConfig, OptiRSQuantumOptimizer};

/// QAOA problem types
#[derive(Debug, Clone, Copy, PartialEq, Eq, Hash, Serialize, Deserialize)]
pub enum QAOAProblemType {
    /// Maximum Cut problem
    MaxCut,
    /// Maximum Weight Independent Set
    MaxWeightIndependentSet,
    /// Minimum Vertex Cover
    MinVertexCover,
    /// Graph Coloring
    GraphColoring,
    /// Traveling Salesman Problem
    TSP,
    /// Portfolio Optimization
    PortfolioOptimization,
    /// Job Shop Scheduling
    JobShopScheduling,
    /// Boolean 3-SAT
    Boolean3SAT,
    /// Quadratic Unconstrained Binary Optimization
    QUBO,
    /// Maximum Clique
    MaxClique,
    /// Bin Packing
    BinPacking,
    /// Custom Problem
    Custom,
}

/// Graph representation for QAOA problems
#[derive(Debug, Clone, Serialize, Deserialize)]
pub struct QAOAGraph {
    /// Number of vertices
    pub num_vertices: usize,
    /// Adjacency matrix
    pub adjacency_matrix: Array2<f64>,
    /// Vertex weights
    pub vertex_weights: Vec<f64>,
    /// Edge weights
    pub edge_weights: HashMap<(usize, usize), f64>,
    /// Additional constraints
    pub constraints: Vec<QAOAConstraint>,
}

/// QAOA constraints
#[derive(Debug, Clone, Serialize, Deserialize)]
pub enum QAOAConstraint {
    /// Cardinality constraint (exactly k vertices selected)
    Cardinality { target: usize },
    /// Upper bound on selected vertices
    UpperBound { max_vertices: usize },
    /// Lower bound on selected vertices
    LowerBound { min_vertices: usize },
    /// Parity constraint
    Parity { even: bool },
    /// Custom linear constraint
    LinearConstraint { coefficients: Vec<f64>, bound: f64 },
}

/// QAOA mixer types
#[derive(Debug, Clone, Copy, PartialEq, Eq, Serialize, Deserialize)]
pub enum QAOAMixerType {
    /// Standard X mixer (unconstrained)
    Standard,
    /// XY mixer for number conservation
    XY,
    /// Ring mixer for cyclic structures
    Ring,
    /// Grover mixer for amplitude amplification
    Grover,
    /// Dicke state mixer for cardinality constraints
    Dicke,
    /// Custom mixer with specified structure
    Custom,
}

/// QAOA initialization strategies
#[derive(Debug, Clone, Copy, PartialEq, Eq, Serialize, Deserialize)]
pub enum QAOAInitializationStrategy {
    /// Uniform superposition
    UniformSuperposition,
    /// Warm start from classical solution
    WarmStart,
    /// Adiabatic initialization
    AdiabaticStart,
    /// Random initialization
    Random,
    /// Problem-specific initialization
    ProblemSpecific,
}

/// QAOA optimization strategy
#[derive(Debug, Clone, Copy, PartialEq, Eq, Serialize, Deserialize)]
pub enum QAOAOptimizationStrategy {
    /// Classical optimization of angles
    Classical,
    /// Quantum optimization using quantum gradients
    Quantum,
    /// Hybrid classical-quantum optimization
    Hybrid,
    /// Machine learning guided optimization
    MLGuided,
    /// Adaptive parameter optimization
    Adaptive,
    /// `OptiRS` optimization (Adam, SGD, `RMSprop`, etc.) - requires "optimize" feature
    #[cfg(feature = "optimize")]
    OptiRS,
}

/// QAOA configuration
#[derive(Debug, Clone)]
pub struct QAOAConfig {
    /// Number of QAOA layers (p)
    pub num_layers: usize,
    /// Mixer type
    pub mixer_type: QAOAMixerType,
    /// Initialization strategy
    pub initialization: QAOAInitializationStrategy,
    /// Optimization strategy
    pub optimization_strategy: QAOAOptimizationStrategy,
    /// Maximum optimization iterations
    pub max_iterations: usize,
    /// Convergence tolerance
    pub convergence_tolerance: f64,
    /// Learning rate for optimization
    pub learning_rate: f64,
    /// Enable multi-angle QAOA
    pub multi_angle: bool,
    /// Enable parameter transfer learning
    pub parameter_transfer: bool,
    /// Hardware-specific optimizations
    pub hardware_aware: bool,
    /// Shot noise for finite sampling
    pub shots: Option<usize>,
    /// Enable adaptive layer growth
    pub adaptive_layers: bool,
    /// Maximum adaptive layers
    pub max_adaptive_layers: usize,
}

impl Default for QAOAConfig {
    fn default() -> Self {
        Self {
            num_layers: 1,
            mixer_type: QAOAMixerType::Standard,
            initialization: QAOAInitializationStrategy::UniformSuperposition,
            optimization_strategy: QAOAOptimizationStrategy::Classical,
            max_iterations: 100,
            convergence_tolerance: 1e-6,
            learning_rate: 0.1,
            multi_angle: false,
            parameter_transfer: false,
            hardware_aware: true,
            shots: None,
            adaptive_layers: false,
            max_adaptive_layers: 10,
        }
    }
}

/// QAOA result
#[derive(Debug, Clone, Serialize, Deserialize)]
pub struct QAOAResult {
    /// Optimal gamma parameters
    pub optimal_gammas: Vec<f64>,
    /// Optimal beta parameters
    pub optimal_betas: Vec<f64>,
    /// Best cost value found
    pub best_cost: f64,
    /// Approximation ratio
    pub approximation_ratio: f64,
    /// Optimization history
    pub cost_history: Vec<f64>,
    /// Parameter evolution
    pub parameter_history: Vec<(Vec<f64>, Vec<f64>)>,
    /// Final probability distribution
    pub final_probabilities: HashMap<String, f64>,
    /// Best solution bitstring
    pub best_solution: String,
    /// Solution quality metrics
    pub solution_quality: SolutionQuality,
    /// Optimization time
    pub optimization_time: Duration,
    /// Number of function evaluations
    pub function_evaluations: usize,
    /// Convergence information
    pub converged: bool,
}

/// Solution quality metrics
#[derive(Debug, Clone, Serialize, Deserialize)]
pub struct SolutionQuality {
    /// Feasibility (satisfies constraints)
    pub feasible: bool,
    /// Gap to optimal solution (if known)
    pub optimality_gap: Option<f64>,
    /// Solution variance across multiple runs
    pub solution_variance: f64,
    /// Confidence in solution
    pub confidence: f64,
    /// Number of constraint violations
    pub constraint_violations: usize,
}

/// QAOA statistics
#[derive(Debug, Clone, Serialize, Deserialize)]
pub struct QAOAStats {
    /// Total optimization time
    pub total_time: Duration,
    /// Time per layer evaluation
    pub layer_times: Vec<Duration>,
    /// Circuit depth per layer
    pub circuit_depths: Vec<usize>,
    /// Parameter sensitivity analysis
    pub parameter_sensitivity: HashMap<String, f64>,
    /// Quantum advantage metrics
    pub quantum_advantage: QuantumAdvantageMetrics,
}

/// Quantum advantage analysis
#[derive(Debug, Clone, Serialize, Deserialize)]
pub struct QuantumAdvantageMetrics {
    /// Classical algorithm comparison time
    pub classical_time: Duration,
    /// Quantum speedup factor
    pub speedup_factor: f64,
    /// Success probability
    pub success_probability: f64,
    /// Quantum volume required
    pub quantum_volume: usize,
}

/// Multi-level QAOA configuration
#[derive(Debug, Clone)]
pub struct MultiLevelQAOAConfig {
    /// Hierarchical levels
    pub levels: Vec<QAOALevel>,
    /// Parameter sharing between levels
    pub parameter_sharing: bool,
    /// Level transition criteria
    pub transition_criteria: LevelTransitionCriteria,
}

/// QAOA level configuration
#[derive(Debug, Clone)]
pub struct QAOALevel {
    /// Problem size at this level
    pub problem_size: usize,
    /// Number of layers
    pub num_layers: usize,
    /// Optimization budget
    pub optimization_budget: usize,
    /// Level-specific mixer
    pub mixer_type: QAOAMixerType,
}

/// Level transition criteria
#[derive(Debug, Clone, Copy, PartialEq, Eq)]
pub enum LevelTransitionCriteria {
    /// Fixed schedule
    FixedSchedule,
    /// Performance based
    PerformanceBased,
    /// Convergence based
    ConvergenceBased,
    /// Adaptive
    Adaptive,
}

/// Main QAOA optimizer
pub struct QAOAOptimizer {
    /// Configuration
    config: QAOAConfig,
    /// Problem graph
    graph: QAOAGraph,
    /// Problem type
    problem_type: QAOAProblemType,
    /// Current parameters
    gammas: Vec<f64>,
    betas: Vec<f64>,
    /// Best parameters found
    best_gammas: Vec<f64>,
    best_betas: Vec<f64>,
    /// Best cost found
    best_cost: f64,
    /// Classical optimal solution (if known)
    classical_optimum: Option<f64>,
    /// Optimization statistics
    stats: QAOAStats,
    /// Parameter transfer database
    parameter_database: Arc<Mutex<ParameterDatabase>>,
    /// `OptiRS` optimizer (optional, for `OptiRS` strategy)
    #[cfg(feature = "optimize")]
    optirs_optimizer: Option<OptiRSQuantumOptimizer>,
}

/// Parameter transfer database
#[derive(Debug, Clone)]
pub struct ParameterDatabase {
    /// Stored parameter sets by problem characteristics
    pub parameters: HashMap<ProblemCharacteristics, Vec<(Vec<f64>, Vec<f64>, f64)>>,
}

/// Problem characteristics for parameter transfer
#[derive(Debug, Clone, Hash, PartialEq, Eq)]
pub struct ProblemCharacteristics {
    pub problem_type: QAOAProblemType,
    pub num_vertices: usize,
    pub density: u32,    // Edge density * 100
    pub regularity: u32, // Graph regularity * 100
}

impl QAOAOptimizer {
    /// Create new QAOA optimizer
    pub fn new(
        config: QAOAConfig,
        graph: QAOAGraph,
        problem_type: QAOAProblemType,
    ) -> Result<Self> {
        let gammas = Self::initialize_gammas(&config, &graph)?;
        let betas = Self::initialize_betas(&config, &graph)?;

        Ok(Self {
            config,
            graph,
            problem_type,
            gammas: gammas.clone(),
            betas: betas.clone(),
            best_gammas: gammas,
            best_betas: betas,
            best_cost: f64::NEG_INFINITY,
            classical_optimum: None,
            stats: QAOAStats {
                total_time: Duration::new(0, 0),
                layer_times: Vec::new(),
                circuit_depths: Vec::new(),
                parameter_sensitivity: HashMap::new(),
                quantum_advantage: QuantumAdvantageMetrics {
                    classical_time: Duration::new(0, 0),
                    speedup_factor: 1.0,
                    success_probability: 0.0,
                    quantum_volume: 0,
                },
            },
            parameter_database: Arc::new(Mutex::new(ParameterDatabase {
                parameters: HashMap::new(),
            })),
            #[cfg(feature = "optimize")]
            optirs_optimizer: None,
        })
    }

    /// Optimize QAOA parameters
    pub fn optimize(&mut self) -> Result<QAOAResult> {
        let start_time = Instant::now();
        let mut cost_history = Vec::new();
        let mut parameter_history = Vec::new();

        // Initialize with transferred parameters if enabled
        if self.config.parameter_transfer {
            self.apply_parameter_transfer()?;
        }

        // Run classical algorithm for comparison
        let classical_start = Instant::now();
        let classical_result = self.solve_classically()?;
        self.stats.quantum_advantage.classical_time = classical_start.elapsed();
        self.classical_optimum = Some(classical_result);

        // Adaptive layer optimization
        let mut current_layers = self.config.num_layers;

        for iteration in 0..self.config.max_iterations {
            // Evaluate current parameters
            let cost = self.evaluate_qaoa_cost(&self.gammas, &self.betas)?;
            cost_history.push(cost);
            parameter_history.push((self.gammas.clone(), self.betas.clone()));

            // Update best solution
            if cost > self.best_cost {
                self.best_cost = cost;
                self.best_gammas = self.gammas.clone();
                self.best_betas = self.betas.clone();
            }

            // Check convergence
            if iteration > 10 {
                let recent_improvement = cost_history[iteration] - cost_history[iteration - 10];
                if recent_improvement.abs() < self.config.convergence_tolerance {
                    break;
                }
            }

            // Optimize parameters using selected strategy
            match self.config.optimization_strategy {
                QAOAOptimizationStrategy::Classical => {
                    self.classical_parameter_optimization()?;
                }
                QAOAOptimizationStrategy::Quantum => {
                    self.quantum_parameter_optimization()?;
                }
                QAOAOptimizationStrategy::Hybrid => {
                    self.hybrid_parameter_optimization()?;
                }
                QAOAOptimizationStrategy::MLGuided => {
                    self.ml_guided_optimization()?;
                }
                QAOAOptimizationStrategy::Adaptive => {
                    self.adaptive_parameter_optimization(&cost_history)?;
                }
                #[cfg(feature = "optimize")]
                QAOAOptimizationStrategy::OptiRS => {
                    self.optirs_parameter_optimization()?;
                }
            }

            // Adaptive layer growth
            if self.config.adaptive_layers
                && iteration % 20 == 19
                && self.should_add_layer(&cost_history)?
                && current_layers < self.config.max_adaptive_layers
            {
                current_layers += 1;
                self.add_qaoa_layer()?;
            }
        }

        let total_time = start_time.elapsed();
        self.stats.total_time = total_time;

        // Generate final quantum state and extract solution
        let final_circuit = self.generate_qaoa_circuit(&self.best_gammas, &self.best_betas)?;
        let final_state = self.simulate_circuit(&final_circuit)?;
        let probabilities = self.extract_probabilities(&final_state)?;
        let best_solution = self.extract_best_solution(&probabilities)?;

        // Calculate solution quality
        let solution_quality = self.evaluate_solution_quality(&best_solution, &probabilities)?;

        // Calculate approximation ratio
        let approximation_ratio = if let Some(classical_opt) = self.classical_optimum {
            self.best_cost / classical_opt
        } else {
            1.0
        };

        // Store parameters for transfer learning
        if self.config.parameter_transfer {
            self.store_parameters_for_transfer()?;
        }

        let function_evaluations = cost_history.len();

        Ok(QAOAResult {
            optimal_gammas: self.best_gammas.clone(),
            optimal_betas: self.best_betas.clone(),
            best_cost: self.best_cost,
            approximation_ratio,
            cost_history,
            parameter_history,
            final_probabilities: probabilities,
            best_solution,
            solution_quality,
            optimization_time: total_time,
            function_evaluations,
            converged: true, // Would implement proper convergence check
        })
    }

    /// Generate QAOA circuit for given parameters
    fn generate_qaoa_circuit(&self, gammas: &[f64], betas: &[f64]) -> Result<InterfaceCircuit> {
        let num_qubits = self.graph.num_vertices;
        let mut circuit = InterfaceCircuit::new(num_qubits, 0);

        // Initial state preparation
        match self.config.initialization {
            QAOAInitializationStrategy::UniformSuperposition => {
                for qubit in 0..num_qubits {
                    circuit.add_gate(InterfaceGate::new(InterfaceGateType::Hadamard, vec![qubit]));
                }
            }
            QAOAInitializationStrategy::WarmStart => {
                self.prepare_warm_start_state(&mut circuit)?;
            }
            QAOAInitializationStrategy::AdiabaticStart => {
                self.prepare_adiabatic_state(&mut circuit)?;
            }
            QAOAInitializationStrategy::Random => {
                self.prepare_random_state(&mut circuit)?;
            }
            QAOAInitializationStrategy::ProblemSpecific => {
                self.prepare_problem_specific_state(&mut circuit)?;
            }
        }

        // QAOA layers
        for layer in 0..gammas.len() {
            // Cost layer (problem Hamiltonian)
            self.apply_cost_layer(&mut circuit, gammas[layer])?;

            // Mixer layer
            self.apply_mixer_layer(&mut circuit, betas[layer])?;
        }

        Ok(circuit)
    }

    /// Apply cost layer to circuit
    fn apply_cost_layer(&self, circuit: &mut InterfaceCircuit, gamma: f64) -> Result<()> {
        match self.problem_type {
            QAOAProblemType::MaxCut => {
                self.apply_maxcut_cost_layer(circuit, gamma)?;
            }
            QAOAProblemType::MaxWeightIndependentSet => {
                self.apply_mwis_cost_layer(circuit, gamma)?;
            }
            QAOAProblemType::TSP => {
                self.apply_tsp_cost_layer(circuit, gamma)?;
            }
            QAOAProblemType::PortfolioOptimization => {
                self.apply_portfolio_cost_layer(circuit, gamma)?;
            }
            QAOAProblemType::Boolean3SAT => {
                self.apply_3sat_cost_layer(circuit, gamma)?;
            }
            QAOAProblemType::QUBO => {
                self.apply_qubo_cost_layer(circuit, gamma)?;
            }
            _ => {
                self.apply_generic_cost_layer(circuit, gamma)?;
            }
        }
        Ok(())
    }

    /// Apply `MaxCut` cost layer
    fn apply_maxcut_cost_layer(&self, circuit: &mut InterfaceCircuit, gamma: f64) -> Result<()> {
        // Apply exp(-i*gamma*H_C) where H_C = sum_{(i,j)} w_{ij} * (1 - Z_i Z_j) / 2
        for i in 0..self.graph.num_vertices {
            for j in i + 1..self.graph.num_vertices {
                let weight = self
                    .graph
                    .edge_weights
                    .get(&(i, j))
                    .or_else(|| self.graph.edge_weights.get(&(j, i)))
                    .unwrap_or(&self.graph.adjacency_matrix[[i, j]]);

                if weight.abs() > 1e-10 {
                    let angle = gamma * weight;

                    // Apply ZZ interaction: exp(-i*angle*Z_i*Z_j)
                    circuit.add_gate(InterfaceGate::new(InterfaceGateType::CNOT, vec![i, j]));
                    circuit.add_gate(InterfaceGate::new(InterfaceGateType::RZ(angle), vec![j]));
                    circuit.add_gate(InterfaceGate::new(InterfaceGateType::CNOT, vec![i, j]));
                }
            }
        }
        Ok(())
    }

    /// Apply Maximum Weight Independent Set cost layer
    fn apply_mwis_cost_layer(&self, circuit: &mut InterfaceCircuit, gamma: f64) -> Result<()> {
        // H_C = sum_i w_i * Z_i + penalty * sum_{(i,j)} Z_i * Z_j

        // Single-qubit terms (vertex weights)
        for i in 0..self.graph.num_vertices {
            let weight = self.graph.vertex_weights.get(i).unwrap_or(&1.0);
            let angle = gamma * weight;
            circuit.add_gate(InterfaceGate::new(InterfaceGateType::RZ(angle), vec![i]));
        }

        // Two-qubit penalty terms (prevent adjacent vertices)
        let penalty = 10.0; // Large penalty for violating independence
        for i in 0..self.graph.num_vertices {
            for j in i + 1..self.graph.num_vertices {
                if self.graph.adjacency_matrix[[i, j]] > 0.0 {
                    let angle = gamma * penalty;
                    circuit.add_gate(InterfaceGate::new(InterfaceGateType::CNOT, vec![i, j]));
                    circuit.add_gate(InterfaceGate::new(InterfaceGateType::RZ(angle), vec![j]));
                    circuit.add_gate(InterfaceGate::new(InterfaceGateType::CNOT, vec![i, j]));
                }
            }
        }
        Ok(())
    }

    /// Apply TSP cost layer
    fn apply_tsp_cost_layer(&self, circuit: &mut InterfaceCircuit, gamma: f64) -> Result<()> {
        let num_cities = (self.graph.num_vertices as f64).sqrt() as usize;

        // Distance cost terms
        for t in 0..num_cities {
            for i in 0..num_cities {
                for j in 0..num_cities {
                    if i != j {
                        let distance = self.graph.adjacency_matrix[[i, j]];
                        if distance > 0.0 {
                            let angle = gamma * distance;

                            // Encode: city i at time t and city j at time t+1
                            let qubit_i_t = i * num_cities + t;
                            let qubit_j_t1 = j * num_cities + ((t + 1) % num_cities);

                            if qubit_i_t < circuit.num_qubits && qubit_j_t1 < circuit.num_qubits {
                                circuit.add_gate(InterfaceGate::new(
                                    InterfaceGateType::CNOT,
                                    vec![qubit_i_t, qubit_j_t1],
                                ));
                                circuit.add_gate(InterfaceGate::new(
                                    InterfaceGateType::RZ(angle),
                                    vec![qubit_j_t1],
                                ));
                                circuit.add_gate(InterfaceGate::new(
                                    InterfaceGateType::CNOT,
                                    vec![qubit_i_t, qubit_j_t1],
                                ));
                            }
                        }
                    }
                }
            }
        }

        // Constraint penalty terms (each city visited exactly once, each time slot used exactly once)
        let penalty = 10.0;

        // Each city visited exactly once
        for i in 0..num_cities {
            for t1 in 0..num_cities {
                for t2 in t1 + 1..num_cities {
                    let qubit1 = i * num_cities + t1;
                    let qubit2 = i * num_cities + t2;
                    if qubit1 < circuit.num_qubits && qubit2 < circuit.num_qubits {
                        let angle = gamma * penalty;
                        circuit.add_gate(InterfaceGate::new(
                            InterfaceGateType::CNOT,
                            vec![qubit1, qubit2],
                        ));
                        circuit.add_gate(InterfaceGate::new(
                            InterfaceGateType::RZ(angle),
                            vec![qubit2],
                        ));
                        circuit.add_gate(InterfaceGate::new(
                            InterfaceGateType::CNOT,
                            vec![qubit1, qubit2],
                        ));
                    }
                }
            }
        }

        Ok(())
    }

    /// Apply portfolio optimization cost layer
    fn apply_portfolio_cost_layer(&self, circuit: &mut InterfaceCircuit, gamma: f64) -> Result<()> {
        // Portfolio optimization: maximize return - risk
        // H_C = -sum_i r_i * Z_i + lambda * sum_{i,j} sigma_{ij} * Z_i * Z_j

        let lambda = 1.0; // Risk aversion parameter

        // Return terms (negative for maximization)
        for i in 0..self.graph.num_vertices {
            let return_rate = self.graph.vertex_weights.get(i).unwrap_or(&0.1);
            let angle = -gamma * return_rate; // Negative for maximization
            circuit.add_gate(InterfaceGate::new(InterfaceGateType::RZ(angle), vec![i]));
        }

        // Risk terms (covariance matrix)
        for i in 0..self.graph.num_vertices {
            for j in i..self.graph.num_vertices {
                let covariance = self.graph.adjacency_matrix[[i, j]];
                if covariance.abs() > 1e-10 {
                    let angle = gamma * lambda * covariance;

                    if i == j {
                        // Diagonal terms (variance)
                        circuit.add_gate(InterfaceGate::new(InterfaceGateType::RZ(angle), vec![i]));
                    } else {
                        // Off-diagonal terms (covariance)
                        circuit.add_gate(InterfaceGate::new(InterfaceGateType::CNOT, vec![i, j]));
                        circuit.add_gate(InterfaceGate::new(InterfaceGateType::RZ(angle), vec![j]));
                        circuit.add_gate(InterfaceGate::new(InterfaceGateType::CNOT, vec![i, j]));
                    }
                }
            }
        }
        Ok(())
    }

    /// Apply 3-SAT cost layer
    fn apply_3sat_cost_layer(&self, circuit: &mut InterfaceCircuit, gamma: f64) -> Result<()> {
        // For 3-SAT, we need to encode clauses
        // Each clause contributes to the cost if not satisfied

        // This is a simplified implementation - would need actual clause encoding
        for constraint in &self.graph.constraints {
            if let QAOAConstraint::LinearConstraint {
                coefficients,
                bound,
            } = constraint
            {
                let angle = gamma * bound;

                // Apply constraint penalty (simplified)
                for (i, &coeff) in coefficients.iter().enumerate() {
                    if i < circuit.num_qubits && coeff.abs() > 1e-10 {
                        circuit.add_gate(InterfaceGate::new(
                            InterfaceGateType::RZ(angle * coeff),
                            vec![i],
                        ));
                    }
                }
            } else {
                // Other constraint types would be handled here
            }
        }
        Ok(())
    }

    /// Apply QUBO cost layer
    fn apply_qubo_cost_layer(&self, circuit: &mut InterfaceCircuit, gamma: f64) -> Result<()> {
        // QUBO: minimize x^T Q x where Q is the QUBO matrix

        // Linear terms (diagonal of Q)
        for i in 0..self.graph.num_vertices {
            let coeff = self.graph.adjacency_matrix[[i, i]];
            if coeff.abs() > 1e-10 {
                let angle = gamma * coeff;
                circuit.add_gate(InterfaceGate::new(InterfaceGateType::RZ(angle), vec![i]));
            }
        }

        // Quadratic terms (off-diagonal of Q)
        for i in 0..self.graph.num_vertices {
            for j in i + 1..self.graph.num_vertices {
                let coeff = self.graph.adjacency_matrix[[i, j]];
                if coeff.abs() > 1e-10 {
                    let angle = gamma * coeff;
                    circuit.add_gate(InterfaceGate::new(InterfaceGateType::CNOT, vec![i, j]));
                    circuit.add_gate(InterfaceGate::new(InterfaceGateType::RZ(angle), vec![j]));
                    circuit.add_gate(InterfaceGate::new(InterfaceGateType::CNOT, vec![i, j]));
                }
            }
        }
        Ok(())
    }

    /// Apply generic cost layer
    fn apply_generic_cost_layer(&self, circuit: &mut InterfaceCircuit, gamma: f64) -> Result<()> {
        // Generic cost layer based on adjacency matrix
        for i in 0..self.graph.num_vertices {
            for j in i + 1..self.graph.num_vertices {
                let weight = self.graph.adjacency_matrix[[i, j]];
                if weight.abs() > 1e-10 {
                    let angle = gamma * weight;
                    circuit.add_gate(InterfaceGate::new(InterfaceGateType::CNOT, vec![i, j]));
                    circuit.add_gate(InterfaceGate::new(InterfaceGateType::RZ(angle), vec![j]));
                    circuit.add_gate(InterfaceGate::new(InterfaceGateType::CNOT, vec![i, j]));
                }
            }
        }
        Ok(())
    }

    /// Apply mixer layer to circuit
    fn apply_mixer_layer(&self, circuit: &mut InterfaceCircuit, beta: f64) -> Result<()> {
        match self.config.mixer_type {
            QAOAMixerType::Standard => {
                self.apply_standard_mixer(circuit, beta)?;
            }
            QAOAMixerType::XY => {
                self.apply_xy_mixer(circuit, beta)?;
            }
            QAOAMixerType::Ring => {
                self.apply_ring_mixer(circuit, beta)?;
            }
            QAOAMixerType::Grover => {
                self.apply_grover_mixer(circuit, beta)?;
            }
            QAOAMixerType::Dicke => {
                self.apply_dicke_mixer(circuit, beta)?;
            }
            QAOAMixerType::Custom => {
                self.apply_custom_mixer(circuit, beta)?;
            }
        }
        Ok(())
    }

    /// Apply standard X mixer
    fn apply_standard_mixer(&self, circuit: &mut InterfaceCircuit, beta: f64) -> Result<()> {
        for qubit in 0..circuit.num_qubits {
            circuit.add_gate(InterfaceGate::new(InterfaceGateType::RX(beta), vec![qubit]));
        }
        Ok(())
    }

    /// Apply XY mixer for number conservation
    fn apply_xy_mixer(&self, circuit: &mut InterfaceCircuit, beta: f64) -> Result<()> {
        // XY mixer: exp(-i*beta*(X_i X_j + Y_i Y_j)) for adjacent qubits
        for i in 0..circuit.num_qubits {
            for j in i + 1..circuit.num_qubits {
                if self.graph.adjacency_matrix[[i, j]] > 0.0 {
                    // Apply XX interaction
                    circuit.add_gate(InterfaceGate::new(InterfaceGateType::Hadamard, vec![i]));
                    circuit.add_gate(InterfaceGate::new(InterfaceGateType::Hadamard, vec![j]));
                    circuit.add_gate(InterfaceGate::new(InterfaceGateType::CNOT, vec![i, j]));
                    circuit.add_gate(InterfaceGate::new(InterfaceGateType::RZ(beta), vec![j]));
                    circuit.add_gate(InterfaceGate::new(InterfaceGateType::CNOT, vec![i, j]));
                    circuit.add_gate(InterfaceGate::new(InterfaceGateType::Hadamard, vec![i]));
                    circuit.add_gate(InterfaceGate::new(InterfaceGateType::Hadamard, vec![j]));

                    // Apply YY interaction
                    circuit.add_gate(InterfaceGate::new(
                        InterfaceGateType::RY(std::f64::consts::PI / 2.0),
                        vec![i],
                    ));
                    circuit.add_gate(InterfaceGate::new(
                        InterfaceGateType::RY(std::f64::consts::PI / 2.0),
                        vec![j],
                    ));
                    circuit.add_gate(InterfaceGate::new(InterfaceGateType::CNOT, vec![i, j]));
                    circuit.add_gate(InterfaceGate::new(InterfaceGateType::RZ(beta), vec![j]));
                    circuit.add_gate(InterfaceGate::new(InterfaceGateType::CNOT, vec![i, j]));
                    circuit.add_gate(InterfaceGate::new(
                        InterfaceGateType::RY(-std::f64::consts::PI / 2.0),
                        vec![i],
                    ));
                    circuit.add_gate(InterfaceGate::new(
                        InterfaceGateType::RY(-std::f64::consts::PI / 2.0),
                        vec![j],
                    ));
                }
            }
        }
        Ok(())
    }

    /// Apply ring mixer
    fn apply_ring_mixer(&self, circuit: &mut InterfaceCircuit, beta: f64) -> Result<()> {
        // Ring mixer with periodic boundary conditions
        for i in 0..circuit.num_qubits {
            let next = (i + 1) % circuit.num_qubits;

            // Apply X_i X_{i+1} interaction
            circuit.add_gate(InterfaceGate::new(InterfaceGateType::Hadamard, vec![i]));
            circuit.add_gate(InterfaceGate::new(InterfaceGateType::Hadamard, vec![next]));
            circuit.add_gate(InterfaceGate::new(InterfaceGateType::CNOT, vec![i, next]));
            circuit.add_gate(InterfaceGate::new(InterfaceGateType::RZ(beta), vec![next]));
            circuit.add_gate(InterfaceGate::new(InterfaceGateType::CNOT, vec![i, next]));
            circuit.add_gate(InterfaceGate::new(InterfaceGateType::Hadamard, vec![i]));
            circuit.add_gate(InterfaceGate::new(InterfaceGateType::Hadamard, vec![next]));
        }
        Ok(())
    }

    /// Apply Grover mixer
    fn apply_grover_mixer(&self, circuit: &mut InterfaceCircuit, beta: f64) -> Result<()> {
        // Grover diffusion operator: 2|s><s| - I where |s> is uniform superposition

        // Apply H gates
        for qubit in 0..circuit.num_qubits {
            circuit.add_gate(InterfaceGate::new(InterfaceGateType::Hadamard, vec![qubit]));
        }

        // Apply Z gates (conditional phase)
        for qubit in 0..circuit.num_qubits {
            circuit.add_gate(InterfaceGate::new(InterfaceGateType::PauliZ, vec![qubit]));
        }

        // Multi-controlled Z gate (simplified implementation)
        if circuit.num_qubits > 1 {
            let controls: Vec<usize> = (0..circuit.num_qubits - 1).collect();
            let target = circuit.num_qubits - 1;

            // Simplified multi-controlled Z using Toffoli decomposition
            circuit.add_gate(InterfaceGate::new(
                InterfaceGateType::CNOT,
                vec![controls[0], target],
            ));
            circuit.add_gate(InterfaceGate::new(
                InterfaceGateType::RZ(beta),
                vec![target],
            ));
            circuit.add_gate(InterfaceGate::new(
                InterfaceGateType::CNOT,
                vec![controls[0], target],
            ));
        }

        // Apply Z gates again
        for qubit in 0..circuit.num_qubits {
            circuit.add_gate(InterfaceGate::new(InterfaceGateType::PauliZ, vec![qubit]));
        }

        // Apply H gates
        for qubit in 0..circuit.num_qubits {
            circuit.add_gate(InterfaceGate::new(InterfaceGateType::Hadamard, vec![qubit]));
        }

        Ok(())
    }

    /// Apply Dicke mixer for cardinality constraints
    fn apply_dicke_mixer(&self, circuit: &mut InterfaceCircuit, beta: f64) -> Result<()> {
        // Dicke state mixer preserves the number of excited qubits
        // This is a simplified implementation

        for i in 0..circuit.num_qubits - 1 {
            // Apply partial SWAP operation
            circuit.add_gate(InterfaceGate::new(InterfaceGateType::CNOT, vec![i, i + 1]));
            circuit.add_gate(InterfaceGate::new(InterfaceGateType::RY(beta), vec![i]));
            circuit.add_gate(InterfaceGate::new(InterfaceGateType::CNOT, vec![i + 1, i]));
            circuit.add_gate(InterfaceGate::new(
                InterfaceGateType::RY(-beta),
                vec![i + 1],
            ));
            circuit.add_gate(InterfaceGate::new(InterfaceGateType::CNOT, vec![i, i + 1]));
        }
        Ok(())
    }

    /// Apply custom mixer
    fn apply_custom_mixer(&self, circuit: &mut InterfaceCircuit, beta: f64) -> Result<()> {
        // Custom mixer based on problem structure
        match self.problem_type {
            QAOAProblemType::TSP => {
                // Custom TSP mixer that respects route constraints
                self.apply_tsp_custom_mixer(circuit, beta)?;
            }
            QAOAProblemType::PortfolioOptimization => {
                // Portfolio-specific mixer
                self.apply_portfolio_custom_mixer(circuit, beta)?;
            }
            _ => {
                // Default to standard mixer
                self.apply_standard_mixer(circuit, beta)?;
            }
        }
        Ok(())
    }

    /// TSP-specific custom mixer
    fn apply_tsp_custom_mixer(&self, circuit: &mut InterfaceCircuit, beta: f64) -> Result<()> {
        let num_cities = (circuit.num_qubits as f64).sqrt() as usize;

        // Swap operations that preserve TSP constraints
        for t in 0..num_cities {
            for i in 0..num_cities {
                for j in i + 1..num_cities {
                    let qubit_i = i * num_cities + t;
                    let qubit_j = j * num_cities + t;

                    if qubit_i < circuit.num_qubits && qubit_j < circuit.num_qubits {
                        // Partial SWAP between cities at same time
                        circuit.add_gate(InterfaceGate::new(
                            InterfaceGateType::CNOT,
                            vec![qubit_i, qubit_j],
                        ));
                        circuit.add_gate(InterfaceGate::new(
                            InterfaceGateType::RY(beta),
                            vec![qubit_i],
                        ));
                        circuit.add_gate(InterfaceGate::new(
                            InterfaceGateType::CNOT,
                            vec![qubit_j, qubit_i],
                        ));
                        circuit.add_gate(InterfaceGate::new(
                            InterfaceGateType::RY(-beta),
                            vec![qubit_j],
                        ));
                        circuit.add_gate(InterfaceGate::new(
                            InterfaceGateType::CNOT,
                            vec![qubit_i, qubit_j],
                        ));
                    }
                }
            }
        }
        Ok(())
    }

    /// Portfolio-specific custom mixer
    fn apply_portfolio_custom_mixer(
        &self,
        circuit: &mut InterfaceCircuit,
        beta: f64,
    ) -> Result<()> {
        // Portfolio mixer that respects budget constraints
        for i in 0..circuit.num_qubits - 1 {
            for j in i + 1..circuit.num_qubits {
                // Conditional rotations based on correlation
                let correlation = self.graph.adjacency_matrix[[i, j]].abs();
                if correlation > 0.1 {
                    let angle = beta * correlation;
                    circuit.add_gate(InterfaceGate::new(
                        InterfaceGateType::CRY(angle),
                        vec![i, j],
                    ));
                }
            }
        }
        Ok(())
    }

    /// Initialize gamma parameters
    fn initialize_gammas(config: &QAOAConfig, _graph: &QAOAGraph) -> Result<Vec<f64>> {
        let mut gammas = Vec::with_capacity(config.num_layers);

        for i in 0..config.num_layers {
            let gamma = match config.initialization {
                QAOAInitializationStrategy::Random => {
                    (thread_rng().gen::<f64>() - 0.5) * std::f64::consts::PI
                }
                QAOAInitializationStrategy::AdiabaticStart => {
                    // Start with small values for adiabatic evolution
                    0.1 * (i + 1) as f64 / config.num_layers as f64
                }
                _ => {
                    // Default linear schedule
                    0.5 * (i + 1) as f64 / config.num_layers as f64
                }
            };
            gammas.push(gamma);
        }

        Ok(gammas)
    }

    /// Initialize beta parameters
    fn initialize_betas(config: &QAOAConfig, _graph: &QAOAGraph) -> Result<Vec<f64>> {
        let mut betas = Vec::with_capacity(config.num_layers);

        for i in 0..config.num_layers {
            let beta = match config.initialization {
                QAOAInitializationStrategy::Random => {
                    (thread_rng().gen::<f64>() - 0.5) * std::f64::consts::PI
                }
                QAOAInitializationStrategy::AdiabaticStart => {
                    // Start with large values for mixer
                    std::f64::consts::PI * (config.num_layers - i) as f64 / config.num_layers as f64
                }
                _ => {
                    // Default linear schedule
                    0.5 * std::f64::consts::PI * (config.num_layers - i) as f64
                        / config.num_layers as f64
                }
            };
            betas.push(beta);
        }

        Ok(betas)
    }

    /// Evaluate QAOA cost function
    fn evaluate_qaoa_cost(&self, gammas: &[f64], betas: &[f64]) -> Result<f64> {
        let circuit = self.generate_qaoa_circuit(gammas, betas)?;
        let state = self.simulate_circuit(&circuit)?;

        // Calculate expectation value of cost Hamiltonian
        let cost = self.calculate_cost_expectation(&state)?;
        Ok(cost)
    }

    /// Calculate cost expectation value
    fn calculate_cost_expectation(&self, state: &Array1<Complex64>) -> Result<f64> {
        let mut expectation = 0.0;

        // Iterate over all basis states
        for (idx, amplitude) in state.iter().enumerate() {
            let probability = amplitude.norm_sqr();
            if probability > 1e-10 {
                let bitstring = format!("{:0width$b}", idx, width = self.graph.num_vertices);
                let cost = self.evaluate_classical_cost(&bitstring)?;
                expectation += probability * cost;
            }
        }

        Ok(expectation)
    }

    /// Evaluate classical cost for a bitstring
    fn evaluate_classical_cost(&self, bitstring: &str) -> Result<f64> {
        let bits: Vec<bool> = bitstring.chars().map(|c| c == '1').collect();

        match self.problem_type {
            QAOAProblemType::MaxCut => self.evaluate_maxcut_cost(&bits),
            QAOAProblemType::MaxWeightIndependentSet => self.evaluate_mwis_cost(&bits),
            QAOAProblemType::TSP => self.evaluate_tsp_cost(&bits),
            QAOAProblemType::PortfolioOptimization => self.evaluate_portfolio_cost(&bits),
            QAOAProblemType::QUBO => self.evaluate_qubo_cost(&bits),
            _ => self.evaluate_generic_cost(&bits),
        }
    }

    /// Evaluate `MaxCut` cost
    fn evaluate_maxcut_cost(&self, bits: &[bool]) -> Result<f64> {
        let mut cost = 0.0;

        for i in 0..self.graph.num_vertices {
            for j in i + 1..self.graph.num_vertices {
                let weight = self
                    .graph
                    .edge_weights
                    .get(&(i, j))
                    .or_else(|| self.graph.edge_weights.get(&(j, i)))
                    .unwrap_or(&self.graph.adjacency_matrix[[i, j]]);

                if weight.abs() > 1e-10 && bits[i] != bits[j] {
                    cost += weight;
                }
            }
        }

        Ok(cost)
    }

    /// Evaluate MWIS cost
    fn evaluate_mwis_cost(&self, bits: &[bool]) -> Result<f64> {
        let mut cost = 0.0;
        let mut valid = true;

        // Check independence constraint
        for i in 0..self.graph.num_vertices {
            if bits[i] {
                for j in 0..self.graph.num_vertices {
                    if i != j && bits[j] && self.graph.adjacency_matrix[[i, j]] > 0.0 {
                        valid = false;
                        break;
                    }
                }
                if valid {
                    cost += self.graph.vertex_weights.get(i).unwrap_or(&1.0);
                }
            }
        }

        // Return large penalty if invalid
        if !valid {
            cost = -1000.0;
        }

        Ok(cost)
    }

    /// Evaluate TSP cost
    fn evaluate_tsp_cost(&self, bits: &[bool]) -> Result<f64> {
        let num_cities = (self.graph.num_vertices as f64).sqrt() as usize;
        let mut cost = 0.0;
        let mut valid = true;

        // Check if valid TSP solution
        let mut city_times = vec![-1i32; num_cities];
        let mut time_cities = vec![-1i32; num_cities];

        for city in 0..num_cities {
            for time in 0..num_cities {
                let qubit = city * num_cities + time;
                if qubit < bits.len() && bits[qubit] {
                    if city_times[city] != -1 || time_cities[time] != -1 {
                        valid = false;
                        break;
                    }
                    city_times[city] = time as i32;
                    time_cities[time] = city as i32;
                }
            }
            if !valid {
                break;
            }
        }

        if valid && city_times.iter().all(|&t| t != -1) {
            // Calculate tour cost
            for t in 0..num_cities {
                let current_city = time_cities[t] as usize;
                let next_city = time_cities[(t + 1) % num_cities] as usize;
                cost += self.graph.adjacency_matrix[[current_city, next_city]];
            }
        } else {
            cost = 1000.0; // Large penalty for invalid solution
        }

        Ok(cost)
    }

    /// Evaluate portfolio cost
    fn evaluate_portfolio_cost(&self, bits: &[bool]) -> Result<f64> {
        let mut expected_return = 0.0;
        let mut risk = 0.0;
        let lambda = 1.0; // Risk aversion parameter

        // Calculate expected return
        for i in 0..self.graph.num_vertices {
            if bits[i] {
                expected_return += self.graph.vertex_weights.get(i).unwrap_or(&0.1);
            }
        }

        // Calculate risk (portfolio variance)
        for i in 0..self.graph.num_vertices {
            for j in 0..self.graph.num_vertices {
                if bits[i] && bits[j] {
                    risk += self.graph.adjacency_matrix[[i, j]];
                }
            }
        }

        // Portfolio objective: maximize return - risk
        Ok(expected_return - lambda * risk)
    }

    /// Evaluate QUBO cost
    fn evaluate_qubo_cost(&self, bits: &[bool]) -> Result<f64> {
        let mut cost = 0.0;

        // Linear terms
        for i in 0..self.graph.num_vertices {
            if bits[i] {
                cost += self.graph.adjacency_matrix[[i, i]];
            }
        }

        // Quadratic terms
        for i in 0..self.graph.num_vertices {
            for j in i + 1..self.graph.num_vertices {
                if bits[i] && bits[j] {
                    cost += self.graph.adjacency_matrix[[i, j]];
                }
            }
        }

        Ok(cost)
    }

    /// Evaluate generic cost
    fn evaluate_generic_cost(&self, bits: &[bool]) -> Result<f64> {
        // Default to MaxCut-like cost
        self.evaluate_maxcut_cost(bits)
    }

    /// Solve problem classically for comparison
    fn solve_classically(&self) -> Result<f64> {
        match self.problem_type {
            QAOAProblemType::MaxCut => self.solve_maxcut_classically(),
            QAOAProblemType::MaxWeightIndependentSet => self.solve_mwis_classically(),
            _ => {
                // Brute force for small problems
                self.solve_brute_force()
            }
        }
    }

    /// Solve `MaxCut` classically (greedy approximation)
    fn solve_maxcut_classically(&self) -> Result<f64> {
        let mut best_cost = 0.0;
        let num_vertices = self.graph.num_vertices;

        // Simple greedy algorithm
        let mut assignment = vec![false; num_vertices];

        for _ in 0..10 {
            // Random starting assignment
            for i in 0..num_vertices {
                assignment[i] = thread_rng().gen();
            }

            // Local optimization
            let mut improved = true;
            while improved {
                improved = false;
                for i in 0..num_vertices {
                    assignment[i] = !assignment[i];
                    let cost = self.evaluate_classical_cost(
                        &assignment
                            .iter()
                            .map(|&b| if b { '1' } else { '0' })
                            .collect::<String>(),
                    )?;
                    if cost > best_cost {
                        best_cost = cost;
                        improved = true;
                    } else {
                        assignment[i] = !assignment[i];
                    }
                }
            }
        }

        Ok(best_cost)
    }

    /// Solve MWIS classically (greedy)
    fn solve_mwis_classically(&self) -> Result<f64> {
        let mut vertices: Vec<usize> = (0..self.graph.num_vertices).collect();
        vertices.sort_by(|&a, &b| {
            let weight_a = self.graph.vertex_weights.get(a).unwrap_or(&1.0);
            let weight_b = self.graph.vertex_weights.get(b).unwrap_or(&1.0);
            weight_b
                .partial_cmp(weight_a)
                .unwrap_or(std::cmp::Ordering::Equal)
        });

        let mut selected = vec![false; self.graph.num_vertices];
        let mut total_weight = 0.0;

        for &v in &vertices {
            let mut can_select = true;
            for &u in &vertices {
                if selected[u] && self.graph.adjacency_matrix[[u, v]] > 0.0 {
                    can_select = false;
                    break;
                }
            }
            if can_select {
                selected[v] = true;
                total_weight += self.graph.vertex_weights.get(v).unwrap_or(&1.0);
            }
        }

        Ok(total_weight)
    }

    /// Brute force solver for small problems
    fn solve_brute_force(&self) -> Result<f64> {
        if self.graph.num_vertices > 20 {
            return Ok(0.0); // Too large for brute force
        }

        let mut best_cost = f64::NEG_INFINITY;
        let num_states = 1 << self.graph.num_vertices;

        for state in 0..num_states {
            let bitstring = format!("{:0width$b}", state, width = self.graph.num_vertices);
            let cost = self.evaluate_classical_cost(&bitstring)?;
            if cost > best_cost {
                best_cost = cost;
            }
        }

        Ok(best_cost)
    }

    /// Parameter optimization methods
    /// Classical parameter optimization
    fn classical_parameter_optimization(&mut self) -> Result<()> {
        // Gradient descent optimization
        let epsilon = 1e-4;
        let mut gamma_gradients = vec![0.0; self.gammas.len()];
        let mut beta_gradients = vec![0.0; self.betas.len()];

        // Calculate gradients using finite differences
        for i in 0..self.gammas.len() {
            let mut gammas_plus = self.gammas.clone();
            let mut gammas_minus = self.gammas.clone();
            gammas_plus[i] += epsilon;
            gammas_minus[i] -= epsilon;

            let cost_plus = self.evaluate_qaoa_cost(&gammas_plus, &self.betas)?;
            let cost_minus = self.evaluate_qaoa_cost(&gammas_minus, &self.betas)?;
            gamma_gradients[i] = (cost_plus - cost_minus) / (2.0 * epsilon);
        }

        for i in 0..self.betas.len() {
            let mut betas_plus = self.betas.clone();
            let mut betas_minus = self.betas.clone();
            betas_plus[i] += epsilon;
            betas_minus[i] -= epsilon;

            let cost_plus = self.evaluate_qaoa_cost(&self.gammas, &betas_plus)?;
            let cost_minus = self.evaluate_qaoa_cost(&self.gammas, &betas_minus)?;
            beta_gradients[i] = (cost_plus - cost_minus) / (2.0 * epsilon);
        }

        // Update parameters
        for i in 0..self.gammas.len() {
            self.gammas[i] += self.config.learning_rate * gamma_gradients[i];
        }
        for i in 0..self.betas.len() {
            self.betas[i] += self.config.learning_rate * beta_gradients[i];
        }

        Ok(())
    }

    /// Quantum parameter optimization using parameter shift rule
    fn quantum_parameter_optimization(&mut self) -> Result<()> {
        let shift = std::f64::consts::PI / 2.0;

        // Parameter shift rule for gammas
        for i in 0..self.gammas.len() {
            let mut gammas_plus = self.gammas.clone();
            let mut gammas_minus = self.gammas.clone();
            gammas_plus[i] += shift;
            gammas_minus[i] -= shift;

            let cost_plus = self.evaluate_qaoa_cost(&gammas_plus, &self.betas)?;
            let cost_minus = self.evaluate_qaoa_cost(&gammas_minus, &self.betas)?;
            let gradient = (cost_plus - cost_minus) / 2.0;

            self.gammas[i] += self.config.learning_rate * gradient;
        }

        // Parameter shift rule for betas
        for i in 0..self.betas.len() {
            let mut betas_plus = self.betas.clone();
            let mut betas_minus = self.betas.clone();
            betas_plus[i] += shift;
            betas_minus[i] -= shift;

            let cost_plus = self.evaluate_qaoa_cost(&self.gammas, &betas_plus)?;
            let cost_minus = self.evaluate_qaoa_cost(&self.gammas, &betas_minus)?;
            let gradient = (cost_plus - cost_minus) / 2.0;

            self.betas[i] += self.config.learning_rate * gradient;
        }

        Ok(())
    }

    /// Hybrid classical-quantum optimization
    fn hybrid_parameter_optimization(&mut self) -> Result<()> {
        // Alternate between classical and quantum optimization
        if self.stats.total_time.as_secs() % 2 == 0 {
            self.classical_parameter_optimization()?;
        } else {
            self.quantum_parameter_optimization()?;
        }
        Ok(())
    }

    /// Machine learning guided optimization
    fn ml_guided_optimization(&mut self) -> Result<()> {
        // Use ML model to predict good parameter updates
        // This is a simplified implementation

        let problem_features = self.extract_problem_features()?;
        let predicted_update = self.predict_parameter_update(&problem_features)?;

        // Apply predicted updates
        for i in 0..self.gammas.len() {
            self.gammas[i] += self.config.learning_rate * predicted_update.0[i];
        }
        for i in 0..self.betas.len() {
            self.betas[i] += self.config.learning_rate * predicted_update.1[i];
        }

        Ok(())
    }

    /// Adaptive parameter optimization
    fn adaptive_parameter_optimization(&mut self, cost_history: &[f64]) -> Result<()> {
        // Adapt learning rate based on cost history
        if cost_history.len() > 5 {
            let recent_improvement =
                cost_history[cost_history.len() - 1] - cost_history[cost_history.len() - 5];

            if recent_improvement > 0.0 {
                self.config.learning_rate *= 1.1; // Increase learning rate
            } else {
                self.config.learning_rate *= 0.9; // Decrease learning rate
            }
        }

        // Use classical optimization with adaptive learning rate
        self.classical_parameter_optimization()
    }

    /// `OptiRS` parameter optimization using Adam, SGD, `RMSprop`, etc.
    ///
    /// This method uses state-of-the-art ML optimizers from `OptiRS` to optimize
    /// QAOA parameters more efficiently than classical gradient descent.
    #[cfg(feature = "optimize")]
    fn optirs_parameter_optimization(&mut self) -> Result<()> {
        // Initialize OptiRS optimizer if not already created
        if self.optirs_optimizer.is_none() {
            let config = OptiRSConfig {
                optimizer_type: crate::optirs_integration::OptiRSOptimizerType::Adam,
                learning_rate: self.config.learning_rate,
                convergence_tolerance: self.config.convergence_tolerance,
                max_iterations: self.config.max_iterations,
                ..Default::default()
            };
            self.optirs_optimizer = Some(OptiRSQuantumOptimizer::new(config)?);
        }

        // Combine gammas and betas into a single parameter vector
        let mut all_params = Vec::new();
        all_params.extend_from_slice(&self.gammas);
        all_params.extend_from_slice(&self.betas);

        // Calculate gradients using finite differences
        let epsilon = 1e-4;
        let mut all_gradients = vec![0.0; all_params.len()];
        let num_gammas = self.gammas.len();

        // Gradients for gammas
        for i in 0..num_gammas {
            let mut gammas_plus = self.gammas.clone();
            let mut gammas_minus = self.gammas.clone();
            gammas_plus[i] += epsilon;
            gammas_minus[i] -= epsilon;

            let cost_plus = self.evaluate_qaoa_cost(&gammas_plus, &self.betas)?;
            let cost_minus = self.evaluate_qaoa_cost(&gammas_minus, &self.betas)?;
            all_gradients[i] = (cost_plus - cost_minus) / (2.0 * epsilon);
        }

        // Gradients for betas
        for i in 0..self.betas.len() {
            let mut betas_plus = self.betas.clone();
            let mut betas_minus = self.betas.clone();
            betas_plus[i] += epsilon;
            betas_minus[i] -= epsilon;

            let cost_plus = self.evaluate_qaoa_cost(&self.gammas, &betas_plus)?;
            let cost_minus = self.evaluate_qaoa_cost(&self.gammas, &betas_minus)?;
            all_gradients[num_gammas + i] = (cost_plus - cost_minus) / (2.0 * epsilon);
        }

        // Evaluate current cost
        let current_cost = self.evaluate_qaoa_cost(&self.gammas, &self.betas)?;

        // OptiRS optimization step
        let optimizer = self.optirs_optimizer.as_mut().ok_or_else(|| {
            crate::error::SimulatorError::InvalidInput(
                "OptiRS optimizer not initialized".to_string(),
            )
        })?;
        let new_params = optimizer.optimize_step(&all_params, &all_gradients, -current_cost)?; // Negate cost for minimization

        // Split updated parameters back into gammas and betas
        self.gammas = new_params[..num_gammas].to_vec();
        self.betas = new_params[num_gammas..].to_vec();

        Ok(())
    }

    /// Helper methods
    fn apply_parameter_transfer(&mut self) -> Result<()> {
        // Load similar problem parameters from database
        let characteristics = self.extract_problem_characteristics()?;
        let database = self.parameter_database.lock().map_err(|e| {
            crate::error::SimulatorError::InvalidInput(format!(
                "Failed to lock parameter database: {}",
                e
            ))
        })?;

        if let Some(similar_params) = database.parameters.get(&characteristics) {
            if let Some((gammas, betas, _cost)) = similar_params.first() {
                self.gammas = gammas.clone();
                self.betas = betas.clone();
            }
        }
        Ok(())
    }

    fn store_parameters_for_transfer(&self) -> Result<()> {
        let characteristics = self.extract_problem_characteristics()?;
        let mut database = self.parameter_database.lock().map_err(|e| {
            crate::error::SimulatorError::InvalidInput(format!(
                "Failed to lock parameter database: {}",
                e
            ))
        })?;

        let entry = database.parameters.entry(characteristics).or_default();
        entry.push((
            self.best_gammas.clone(),
            self.best_betas.clone(),
            self.best_cost,
        ));

        // Keep only best parameters
        entry.sort_by(|a, b| b.2.partial_cmp(&a.2).unwrap_or(std::cmp::Ordering::Equal));
        entry.truncate(5);

        Ok(())
    }

    fn extract_problem_characteristics(&self) -> Result<ProblemCharacteristics> {
        let num_edges = self
            .graph
            .adjacency_matrix
            .iter()
            .map(|&x| usize::from(x.abs() > 1e-10))
            .sum::<usize>();

        let max_edges = self.graph.num_vertices * (self.graph.num_vertices - 1) / 2;
        let density = if max_edges > 0 {
            (100.0 * num_edges as f64 / max_edges as f64) as u32
        } else {
            0
        };

        Ok(ProblemCharacteristics {
            problem_type: self.problem_type,
            num_vertices: self.graph.num_vertices,
            density,
            regularity: 50, // Simplified regularity measure
        })
    }

    fn extract_problem_features(&self) -> Result<Vec<f64>> {
        // Graph features and problem type encoding
        let features = vec![
            self.graph.num_vertices as f64,
            self.graph.adjacency_matrix.sum(),
            self.graph.vertex_weights.iter().sum::<f64>(),
            f64::from(self.problem_type as u32),
        ];

        Ok(features)
    }

    fn predict_parameter_update(&self, _features: &[f64]) -> Result<(Vec<f64>, Vec<f64>)> {
        // Simplified ML prediction - would use trained model
        let gamma_updates = vec![0.01; self.gammas.len()];
        let beta_updates = vec![0.01; self.betas.len()];
        Ok((gamma_updates, beta_updates))
    }

    fn should_add_layer(&self, cost_history: &[f64]) -> Result<bool> {
        if cost_history.len() < 10 {
            return Ok(false);
        }

        // Add layer if improvement has plateaued
        let recent_improvement =
            cost_history[cost_history.len() - 1] - cost_history[cost_history.len() - 10];
        Ok(recent_improvement.abs() < self.config.convergence_tolerance * 10.0)
    }

    fn add_qaoa_layer(&mut self) -> Result<()> {
        // Add new gamma and beta parameters
        self.gammas.push(0.1);
        self.betas.push(0.1);
        self.best_gammas.push(0.1);
        self.best_betas.push(0.1);
        Ok(())
    }

    fn simulate_circuit(&self, circuit: &InterfaceCircuit) -> Result<Array1<Complex64>> {
        // Simplified circuit simulation - would integrate with actual simulator
        let state_size = 1 << circuit.num_qubits;
        let mut state = Array1::zeros(state_size);
        state[0] = Complex64::new(1.0, 0.0);
        Ok(state)
    }

    fn extract_probabilities(&self, state: &Array1<Complex64>) -> Result<HashMap<String, f64>> {
        let mut probabilities = HashMap::new();

        for (idx, amplitude) in state.iter().enumerate() {
            let probability = amplitude.norm_sqr();
            if probability > 1e-10 {
                let bitstring = format!("{:0width$b}", idx, width = self.graph.num_vertices);
                probabilities.insert(bitstring, probability);
            }
        }

        Ok(probabilities)
    }

    fn extract_best_solution(&self, probabilities: &HashMap<String, f64>) -> Result<String> {
        let mut best_solution = String::new();
        let mut best_cost = f64::NEG_INFINITY;

        for bitstring in probabilities.keys() {
            let cost = self.evaluate_classical_cost(bitstring)?;
            if cost > best_cost {
                best_cost = cost;
                best_solution = bitstring.clone();
            }
        }

        Ok(best_solution)
    }

    fn evaluate_solution_quality(
        &self,
        solution: &str,
        _probabilities: &HashMap<String, f64>,
    ) -> Result<SolutionQuality> {
        let cost = self.evaluate_classical_cost(solution)?;
        let feasible = self.check_feasibility(solution)?;

        let optimality_gap = self
            .classical_optimum
            .map(|classical_opt| (classical_opt - cost) / classical_opt);

        Ok(SolutionQuality {
            feasible,
            optimality_gap,
            solution_variance: 0.0, // Would calculate from multiple runs
            confidence: 0.9,        // Would calculate based on probability
            constraint_violations: usize::from(!feasible),
        })
    }

    fn check_feasibility(&self, solution: &str) -> Result<bool> {
        let bits: Vec<bool> = solution.chars().map(|c| c == '1').collect();

        // Check problem-specific constraints
        match self.problem_type {
            QAOAProblemType::MaxWeightIndependentSet => {
                // Check independence constraint
                for i in 0..self.graph.num_vertices {
                    if bits[i] {
                        for j in 0..self.graph.num_vertices {
                            if i != j && bits[j] && self.graph.adjacency_matrix[[i, j]] > 0.0 {
                                return Ok(false);
                            }
                        }
                    }
                }
            }
            QAOAProblemType::TSP => {
                // Check TSP constraints
                let num_cities = (self.graph.num_vertices as f64).sqrt() as usize;
                let mut city_counts = vec![0; num_cities];
                let mut time_counts = vec![0; num_cities];

                for city in 0..num_cities {
                    for time in 0..num_cities {
                        let qubit = city * num_cities + time;
                        if qubit < bits.len() && bits[qubit] {
                            city_counts[city] += 1;
                            time_counts[time] += 1;
                        }
                    }
                }

                // Each city exactly once, each time exactly once
                if !city_counts.iter().all(|&count| count == 1)
                    || !time_counts.iter().all(|&count| count == 1)
                {
                    return Ok(false);
                }
            }
            _ => {
                // No specific constraints for other problems
            }
        }

        // Check general constraints
        for constraint in &self.graph.constraints {
            match constraint {
                QAOAConstraint::Cardinality { target } => {
                    let count = bits.iter().filter(|&&b| b).count();
                    if count != *target {
                        return Ok(false);
                    }
                }
                QAOAConstraint::UpperBound { max_vertices } => {
                    let count = bits.iter().filter(|&&b| b).count();
                    if count > *max_vertices {
                        return Ok(false);
                    }
                }
                QAOAConstraint::LowerBound { min_vertices } => {
                    let count = bits.iter().filter(|&&b| b).count();
                    if count < *min_vertices {
                        return Ok(false);
                    }
                }
                QAOAConstraint::Parity { even } => {
                    let count = bits.iter().filter(|&&b| b).count();
                    if (count % 2 == 0) != *even {
                        return Ok(false);
                    }
                }
                QAOAConstraint::LinearConstraint {
                    coefficients,
                    bound,
                } => {
                    let mut sum = 0.0;
                    for (i, &coeff) in coefficients.iter().enumerate() {
                        if i < bits.len() && bits[i] {
                            sum += coeff;
                        }
                    }
                    if (sum - bound).abs() > 1e-10 {
                        return Ok(false);
                    }
                }
            }
        }

        Ok(true)
    }

    /// State preparation methods
    fn prepare_warm_start_state(&self, circuit: &mut InterfaceCircuit) -> Result<()> {
        // Use classical solution as starting point
        let classical_solution = self.get_classical_solution()?;

        for (i, bit) in classical_solution.chars().enumerate() {
            if bit == '1' && i < circuit.num_qubits {
                circuit.add_gate(InterfaceGate::new(InterfaceGateType::PauliX, vec![i]));
            }
        }

        // Add some superposition
        for qubit in 0..circuit.num_qubits {
            circuit.add_gate(InterfaceGate::new(InterfaceGateType::RY(0.1), vec![qubit]));
        }

        Ok(())
    }

    fn prepare_adiabatic_state(&self, circuit: &mut InterfaceCircuit) -> Result<()> {
        // Start from uniform superposition and evolve towards problem state
        for qubit in 0..circuit.num_qubits {
            circuit.add_gate(InterfaceGate::new(InterfaceGateType::Hadamard, vec![qubit]));
        }

        // Apply small evolution towards problem Hamiltonian
        self.apply_cost_layer(circuit, 0.01)?;

        Ok(())
    }

    fn prepare_random_state(&self, circuit: &mut InterfaceCircuit) -> Result<()> {
        for qubit in 0..circuit.num_qubits {
            let angle = (thread_rng().gen::<f64>() - 0.5) * std::f64::consts::PI;
            circuit.add_gate(InterfaceGate::new(
                InterfaceGateType::RY(angle),
                vec![qubit],
            ));
        }
        Ok(())
    }

    fn prepare_problem_specific_state(&self, circuit: &mut InterfaceCircuit) -> Result<()> {
        match self.problem_type {
            QAOAProblemType::MaxCut => {
                // Start with a balanced cut
                for qubit in 0..circuit.num_qubits {
                    if qubit % 2 == 0 {
                        circuit
                            .add_gate(InterfaceGate::new(InterfaceGateType::PauliX, vec![qubit]));
                    }
                }
            }
            QAOAProblemType::TSP => {
                // Start with a valid tour
                let num_cities = (circuit.num_qubits as f64).sqrt() as usize;
                for time in 0..num_cities {
                    let city = time; // Simple tour: 0->1->2->...->0
                    let qubit = city * num_cities + time;
                    if qubit < circuit.num_qubits {
                        circuit
                            .add_gate(InterfaceGate::new(InterfaceGateType::PauliX, vec![qubit]));
                    }
                }
            }
            _ => {
                // Default to uniform superposition
                for qubit in 0..circuit.num_qubits {
                    circuit.add_gate(InterfaceGate::new(InterfaceGateType::Hadamard, vec![qubit]));
                }
            }
        }
        Ok(())
    }

    fn get_classical_solution(&self) -> Result<String> {
        // Get classical solution (simplified)
        let classical_cost = self.solve_classically()?;

        // For now, return a random valid solution
        let mut solution = String::new();
        for _ in 0..self.graph.num_vertices {
            solution.push(if thread_rng().gen() { '1' } else { '0' });
        }
        Ok(solution)
    }
}

/// Benchmark QAOA performance
pub fn benchmark_qaoa() -> Result<HashMap<String, f64>> {
    let mut results = HashMap::new();

    // Test MaxCut problem
    let start = Instant::now();
    let graph = QAOAGraph {
        num_vertices: 4,
        adjacency_matrix: Array2::from_shape_vec(
            (4, 4),
            vec![
                0.0, 1.0, 1.0, 0.0, 1.0, 0.0, 1.0, 1.0, 1.0, 1.0, 0.0, 1.0, 0.0, 1.0, 1.0, 0.0,
            ],
        )
        .map_err(|e| {
            crate::error::SimulatorError::InvalidInput(format!(
                "Failed to create adjacency matrix: {}",
                e
            ))
        })?,
        vertex_weights: vec![1.0; 4],
        edge_weights: HashMap::new(),
        constraints: Vec::new(),
    };

    let config = QAOAConfig {
        num_layers: 2,
        max_iterations: 50,
        ..Default::default()
    };

    let mut optimizer = QAOAOptimizer::new(config, graph, QAOAProblemType::MaxCut)?;
    let _result = optimizer.optimize()?;

    let maxcut_time = start.elapsed().as_millis() as f64;
    results.insert("maxcut_qaoa_4_vertices".to_string(), maxcut_time);

    Ok(results)
}

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

    #[test]
    fn test_qaoa_optimizer_creation() {
        let graph = QAOAGraph {
            num_vertices: 3,
            adjacency_matrix: Array2::zeros((3, 3)),
            vertex_weights: vec![1.0; 3],
            edge_weights: HashMap::new(),
            constraints: Vec::new(),
        };

        let config = QAOAConfig::default();
        let optimizer = QAOAOptimizer::new(config, graph, QAOAProblemType::MaxCut);
        assert!(optimizer.is_ok());
    }

    #[test]
    fn test_maxcut_cost_evaluation() {
        let optimizer = create_test_optimizer();
        let bits = [true, false, true, false];
        let cost = optimizer
            .evaluate_maxcut_cost(&bits)
            .expect("MaxCut cost evaluation should succeed");
        assert!(cost >= 0.0);
    }

    #[test]
    fn test_parameter_initialization() {
        let config = QAOAConfig {
            num_layers: 3,
            ..Default::default()
        };
        let graph = create_test_graph();

        let gammas = QAOAOptimizer::initialize_gammas(&config, &graph)
            .expect("Gamma initialization should succeed");
        let betas = QAOAOptimizer::initialize_betas(&config, &graph)
            .expect("Beta initialization should succeed");

        assert_eq!(gammas.len(), 3);
        assert_eq!(betas.len(), 3);
    }

    #[test]
    fn test_constraint_checking() {
        let optimizer = create_test_optimizer();
        let solution = "1010";
        let feasible = optimizer
            .check_feasibility(solution)
            .expect("Feasibility check should succeed");
        assert!(feasible);
    }

    fn create_test_optimizer() -> QAOAOptimizer {
        let graph = create_test_graph();
        let config = QAOAConfig::default();
        QAOAOptimizer::new(config, graph, QAOAProblemType::MaxCut)
            .expect("Test optimizer creation should succeed")
    }

    fn create_test_graph() -> QAOAGraph {
        QAOAGraph {
            num_vertices: 4,
            adjacency_matrix: Array2::eye(4),
            vertex_weights: vec![1.0; 4],
            edge_weights: HashMap::new(),
            constraints: Vec::new(),
        }
    }
}