quantrs2_sim/
qaoa_optimization.rs

1//! Quantum Approximate Optimization Algorithm (QAOA) Implementation
2//!
3//! This module provides a comprehensive implementation of QAOA for combinatorial
4//! optimization problems, including advanced problem encodings, multi-level QAOA,
5//! and hardware-aware optimizations.
6
7use ndarray::{Array1, Array2};
8use num_complex::Complex64;
9use scirs2_core::parallel_ops::*;
10use serde::{Deserialize, Serialize};
11use std::collections::HashMap;
12use std::sync::{Arc, Mutex};
13use std::time::{Duration, Instant};
14
15use crate::circuit_interfaces::{InterfaceCircuit, InterfaceGate, InterfaceGateType};
16use crate::error::Result;
17
18/// QAOA problem types
19#[derive(Debug, Clone, Copy, PartialEq, Eq, Hash, Serialize, Deserialize)]
20pub enum QAOAProblemType {
21    /// Maximum Cut problem
22    MaxCut,
23    /// Maximum Weight Independent Set
24    MaxWeightIndependentSet,
25    /// Minimum Vertex Cover
26    MinVertexCover,
27    /// Graph Coloring
28    GraphColoring,
29    /// Traveling Salesman Problem
30    TSP,
31    /// Portfolio Optimization
32    PortfolioOptimization,
33    /// Job Shop Scheduling
34    JobShopScheduling,
35    /// Boolean 3-SAT
36    Boolean3SAT,
37    /// Quadratic Unconstrained Binary Optimization
38    QUBO,
39    /// Maximum Clique
40    MaxClique,
41    /// Bin Packing
42    BinPacking,
43    /// Custom Problem
44    Custom,
45}
46
47/// Graph representation for QAOA problems
48#[derive(Debug, Clone, Serialize, Deserialize)]
49pub struct QAOAGraph {
50    /// Number of vertices
51    pub num_vertices: usize,
52    /// Adjacency matrix
53    pub adjacency_matrix: Array2<f64>,
54    /// Vertex weights
55    pub vertex_weights: Vec<f64>,
56    /// Edge weights
57    pub edge_weights: HashMap<(usize, usize), f64>,
58    /// Additional constraints
59    pub constraints: Vec<QAOAConstraint>,
60}
61
62/// QAOA constraints
63#[derive(Debug, Clone, Serialize, Deserialize)]
64pub enum QAOAConstraint {
65    /// Cardinality constraint (exactly k vertices selected)
66    Cardinality { target: usize },
67    /// Upper bound on selected vertices
68    UpperBound { max_vertices: usize },
69    /// Lower bound on selected vertices
70    LowerBound { min_vertices: usize },
71    /// Parity constraint
72    Parity { even: bool },
73    /// Custom linear constraint
74    LinearConstraint { coefficients: Vec<f64>, bound: f64 },
75}
76
77/// QAOA mixer types
78#[derive(Debug, Clone, Copy, PartialEq, Eq, Serialize, Deserialize)]
79pub enum QAOAMixerType {
80    /// Standard X mixer (unconstrained)
81    Standard,
82    /// XY mixer for number conservation
83    XY,
84    /// Ring mixer for cyclic structures
85    Ring,
86    /// Grover mixer for amplitude amplification
87    Grover,
88    /// Dicke state mixer for cardinality constraints
89    Dicke,
90    /// Custom mixer with specified structure
91    Custom,
92}
93
94/// QAOA initialization strategies
95#[derive(Debug, Clone, Copy, PartialEq, Eq, Serialize, Deserialize)]
96pub enum QAOAInitializationStrategy {
97    /// Uniform superposition
98    UniformSuperposition,
99    /// Warm start from classical solution
100    WarmStart,
101    /// Adiabatic initialization
102    AdiabaticStart,
103    /// Random initialization
104    Random,
105    /// Problem-specific initialization
106    ProblemSpecific,
107}
108
109/// QAOA optimization strategy
110#[derive(Debug, Clone, Copy, PartialEq, Eq, Serialize, Deserialize)]
111pub enum QAOAOptimizationStrategy {
112    /// Classical optimization of angles
113    Classical,
114    /// Quantum optimization using quantum gradients
115    Quantum,
116    /// Hybrid classical-quantum optimization
117    Hybrid,
118    /// Machine learning guided optimization
119    MLGuided,
120    /// Adaptive parameter optimization
121    Adaptive,
122}
123
124/// QAOA configuration
125#[derive(Debug, Clone)]
126pub struct QAOAConfig {
127    /// Number of QAOA layers (p)
128    pub num_layers: usize,
129    /// Mixer type
130    pub mixer_type: QAOAMixerType,
131    /// Initialization strategy
132    pub initialization: QAOAInitializationStrategy,
133    /// Optimization strategy
134    pub optimization_strategy: QAOAOptimizationStrategy,
135    /// Maximum optimization iterations
136    pub max_iterations: usize,
137    /// Convergence tolerance
138    pub convergence_tolerance: f64,
139    /// Learning rate for optimization
140    pub learning_rate: f64,
141    /// Enable multi-angle QAOA
142    pub multi_angle: bool,
143    /// Enable parameter transfer learning
144    pub parameter_transfer: bool,
145    /// Hardware-specific optimizations
146    pub hardware_aware: bool,
147    /// Shot noise for finite sampling
148    pub shots: Option<usize>,
149    /// Enable adaptive layer growth
150    pub adaptive_layers: bool,
151    /// Maximum adaptive layers
152    pub max_adaptive_layers: usize,
153}
154
155impl Default for QAOAConfig {
156    fn default() -> Self {
157        Self {
158            num_layers: 1,
159            mixer_type: QAOAMixerType::Standard,
160            initialization: QAOAInitializationStrategy::UniformSuperposition,
161            optimization_strategy: QAOAOptimizationStrategy::Classical,
162            max_iterations: 100,
163            convergence_tolerance: 1e-6,
164            learning_rate: 0.1,
165            multi_angle: false,
166            parameter_transfer: false,
167            hardware_aware: true,
168            shots: None,
169            adaptive_layers: false,
170            max_adaptive_layers: 10,
171        }
172    }
173}
174
175/// QAOA result
176#[derive(Debug, Clone, Serialize, Deserialize)]
177pub struct QAOAResult {
178    /// Optimal gamma parameters
179    pub optimal_gammas: Vec<f64>,
180    /// Optimal beta parameters
181    pub optimal_betas: Vec<f64>,
182    /// Best cost value found
183    pub best_cost: f64,
184    /// Approximation ratio
185    pub approximation_ratio: f64,
186    /// Optimization history
187    pub cost_history: Vec<f64>,
188    /// Parameter evolution
189    pub parameter_history: Vec<(Vec<f64>, Vec<f64>)>,
190    /// Final probability distribution
191    pub final_probabilities: HashMap<String, f64>,
192    /// Best solution bitstring
193    pub best_solution: String,
194    /// Solution quality metrics
195    pub solution_quality: SolutionQuality,
196    /// Optimization time
197    pub optimization_time: Duration,
198    /// Number of function evaluations
199    pub function_evaluations: usize,
200    /// Convergence information
201    pub converged: bool,
202}
203
204/// Solution quality metrics
205#[derive(Debug, Clone, Serialize, Deserialize)]
206pub struct SolutionQuality {
207    /// Feasibility (satisfies constraints)
208    pub feasible: bool,
209    /// Gap to optimal solution (if known)
210    pub optimality_gap: Option<f64>,
211    /// Solution variance across multiple runs
212    pub solution_variance: f64,
213    /// Confidence in solution
214    pub confidence: f64,
215    /// Number of constraint violations
216    pub constraint_violations: usize,
217}
218
219/// QAOA statistics
220#[derive(Debug, Clone, Serialize, Deserialize)]
221pub struct QAOAStats {
222    /// Total optimization time
223    pub total_time: Duration,
224    /// Time per layer evaluation
225    pub layer_times: Vec<Duration>,
226    /// Circuit depth per layer
227    pub circuit_depths: Vec<usize>,
228    /// Parameter sensitivity analysis
229    pub parameter_sensitivity: HashMap<String, f64>,
230    /// Quantum advantage metrics
231    pub quantum_advantage: QuantumAdvantageMetrics,
232}
233
234/// Quantum advantage analysis
235#[derive(Debug, Clone, Serialize, Deserialize)]
236pub struct QuantumAdvantageMetrics {
237    /// Classical algorithm comparison time
238    pub classical_time: Duration,
239    /// Quantum speedup factor
240    pub speedup_factor: f64,
241    /// Success probability
242    pub success_probability: f64,
243    /// Quantum volume required
244    pub quantum_volume: usize,
245}
246
247/// Multi-level QAOA configuration
248#[derive(Debug, Clone)]
249pub struct MultiLevelQAOAConfig {
250    /// Hierarchical levels
251    pub levels: Vec<QAOALevel>,
252    /// Parameter sharing between levels
253    pub parameter_sharing: bool,
254    /// Level transition criteria
255    pub transition_criteria: LevelTransitionCriteria,
256}
257
258/// QAOA level configuration
259#[derive(Debug, Clone)]
260pub struct QAOALevel {
261    /// Problem size at this level
262    pub problem_size: usize,
263    /// Number of layers
264    pub num_layers: usize,
265    /// Optimization budget
266    pub optimization_budget: usize,
267    /// Level-specific mixer
268    pub mixer_type: QAOAMixerType,
269}
270
271/// Level transition criteria
272#[derive(Debug, Clone, Copy, PartialEq, Eq)]
273pub enum LevelTransitionCriteria {
274    /// Fixed schedule
275    FixedSchedule,
276    /// Performance based
277    PerformanceBased,
278    /// Convergence based
279    ConvergenceBased,
280    /// Adaptive
281    Adaptive,
282}
283
284/// Main QAOA optimizer
285pub struct QAOAOptimizer {
286    /// Configuration
287    config: QAOAConfig,
288    /// Problem graph
289    graph: QAOAGraph,
290    /// Problem type
291    problem_type: QAOAProblemType,
292    /// Current parameters
293    gammas: Vec<f64>,
294    betas: Vec<f64>,
295    /// Best parameters found
296    best_gammas: Vec<f64>,
297    best_betas: Vec<f64>,
298    /// Best cost found
299    best_cost: f64,
300    /// Classical optimal solution (if known)
301    classical_optimum: Option<f64>,
302    /// Optimization statistics
303    stats: QAOAStats,
304    /// Parameter transfer database
305    parameter_database: Arc<Mutex<ParameterDatabase>>,
306}
307
308/// Parameter transfer database
309#[derive(Debug, Clone)]
310pub struct ParameterDatabase {
311    /// Stored parameter sets by problem characteristics
312    pub parameters: HashMap<ProblemCharacteristics, Vec<(Vec<f64>, Vec<f64>, f64)>>,
313}
314
315/// Problem characteristics for parameter transfer
316#[derive(Debug, Clone, Hash, PartialEq, Eq)]
317pub struct ProblemCharacteristics {
318    pub problem_type: QAOAProblemType,
319    pub num_vertices: usize,
320    pub density: u32,    // Edge density * 100
321    pub regularity: u32, // Graph regularity * 100
322}
323
324impl QAOAOptimizer {
325    /// Create new QAOA optimizer
326    pub fn new(
327        config: QAOAConfig,
328        graph: QAOAGraph,
329        problem_type: QAOAProblemType,
330    ) -> Result<Self> {
331        let gammas = Self::initialize_gammas(&config, &graph)?;
332        let betas = Self::initialize_betas(&config, &graph)?;
333
334        Ok(Self {
335            config,
336            graph,
337            problem_type,
338            gammas: gammas.clone(),
339            betas: betas.clone(),
340            best_gammas: gammas,
341            best_betas: betas,
342            best_cost: f64::NEG_INFINITY,
343            classical_optimum: None,
344            stats: QAOAStats {
345                total_time: Duration::new(0, 0),
346                layer_times: Vec::new(),
347                circuit_depths: Vec::new(),
348                parameter_sensitivity: HashMap::new(),
349                quantum_advantage: QuantumAdvantageMetrics {
350                    classical_time: Duration::new(0, 0),
351                    speedup_factor: 1.0,
352                    success_probability: 0.0,
353                    quantum_volume: 0,
354                },
355            },
356            parameter_database: Arc::new(Mutex::new(ParameterDatabase {
357                parameters: HashMap::new(),
358            })),
359        })
360    }
361
362    /// Optimize QAOA parameters
363    pub fn optimize(&mut self) -> Result<QAOAResult> {
364        let start_time = Instant::now();
365        let mut cost_history = Vec::new();
366        let mut parameter_history = Vec::new();
367
368        // Initialize with transferred parameters if enabled
369        if self.config.parameter_transfer {
370            self.apply_parameter_transfer()?;
371        }
372
373        // Run classical algorithm for comparison
374        let classical_start = Instant::now();
375        let classical_result = self.solve_classically()?;
376        self.stats.quantum_advantage.classical_time = classical_start.elapsed();
377        self.classical_optimum = Some(classical_result);
378
379        // Adaptive layer optimization
380        let mut current_layers = self.config.num_layers;
381
382        for iteration in 0..self.config.max_iterations {
383            // Evaluate current parameters
384            let cost = self.evaluate_qaoa_cost(&self.gammas, &self.betas)?;
385            cost_history.push(cost);
386            parameter_history.push((self.gammas.clone(), self.betas.clone()));
387
388            // Update best solution
389            if cost > self.best_cost {
390                self.best_cost = cost;
391                self.best_gammas = self.gammas.clone();
392                self.best_betas = self.betas.clone();
393            }
394
395            // Check convergence
396            if iteration > 10 {
397                let recent_improvement = cost_history[iteration] - cost_history[iteration - 10];
398                if recent_improvement.abs() < self.config.convergence_tolerance {
399                    break;
400                }
401            }
402
403            // Optimize parameters using selected strategy
404            match self.config.optimization_strategy {
405                QAOAOptimizationStrategy::Classical => {
406                    self.classical_parameter_optimization()?;
407                }
408                QAOAOptimizationStrategy::Quantum => {
409                    self.quantum_parameter_optimization()?;
410                }
411                QAOAOptimizationStrategy::Hybrid => {
412                    self.hybrid_parameter_optimization()?;
413                }
414                QAOAOptimizationStrategy::MLGuided => {
415                    self.ml_guided_optimization()?;
416                }
417                QAOAOptimizationStrategy::Adaptive => {
418                    self.adaptive_parameter_optimization(&cost_history)?;
419                }
420            }
421
422            // Adaptive layer growth
423            if self.config.adaptive_layers
424                && iteration % 20 == 19
425                && self.should_add_layer(&cost_history)?
426                && current_layers < self.config.max_adaptive_layers
427            {
428                current_layers += 1;
429                self.add_qaoa_layer()?;
430            }
431        }
432
433        let total_time = start_time.elapsed();
434        self.stats.total_time = total_time;
435
436        // Generate final quantum state and extract solution
437        let final_circuit = self.generate_qaoa_circuit(&self.best_gammas, &self.best_betas)?;
438        let final_state = self.simulate_circuit(&final_circuit)?;
439        let probabilities = self.extract_probabilities(&final_state)?;
440        let best_solution = self.extract_best_solution(&probabilities)?;
441
442        // Calculate solution quality
443        let solution_quality = self.evaluate_solution_quality(&best_solution, &probabilities)?;
444
445        // Calculate approximation ratio
446        let approximation_ratio = if let Some(classical_opt) = self.classical_optimum {
447            self.best_cost / classical_opt
448        } else {
449            1.0
450        };
451
452        // Store parameters for transfer learning
453        if self.config.parameter_transfer {
454            self.store_parameters_for_transfer()?;
455        }
456
457        let function_evaluations = cost_history.len();
458
459        Ok(QAOAResult {
460            optimal_gammas: self.best_gammas.clone(),
461            optimal_betas: self.best_betas.clone(),
462            best_cost: self.best_cost,
463            approximation_ratio,
464            cost_history,
465            parameter_history,
466            final_probabilities: probabilities,
467            best_solution,
468            solution_quality,
469            optimization_time: total_time,
470            function_evaluations,
471            converged: true, // Would implement proper convergence check
472        })
473    }
474
475    /// Generate QAOA circuit for given parameters
476    fn generate_qaoa_circuit(&self, gammas: &[f64], betas: &[f64]) -> Result<InterfaceCircuit> {
477        let num_qubits = self.graph.num_vertices;
478        let mut circuit = InterfaceCircuit::new(num_qubits, 0);
479
480        // Initial state preparation
481        match self.config.initialization {
482            QAOAInitializationStrategy::UniformSuperposition => {
483                for qubit in 0..num_qubits {
484                    circuit.add_gate(InterfaceGate::new(InterfaceGateType::Hadamard, vec![qubit]));
485                }
486            }
487            QAOAInitializationStrategy::WarmStart => {
488                self.prepare_warm_start_state(&mut circuit)?;
489            }
490            QAOAInitializationStrategy::AdiabaticStart => {
491                self.prepare_adiabatic_state(&mut circuit)?;
492            }
493            QAOAInitializationStrategy::Random => {
494                self.prepare_random_state(&mut circuit)?;
495            }
496            QAOAInitializationStrategy::ProblemSpecific => {
497                self.prepare_problem_specific_state(&mut circuit)?;
498            }
499        }
500
501        // QAOA layers
502        for layer in 0..gammas.len() {
503            // Cost layer (problem Hamiltonian)
504            self.apply_cost_layer(&mut circuit, gammas[layer])?;
505
506            // Mixer layer
507            self.apply_mixer_layer(&mut circuit, betas[layer])?;
508        }
509
510        Ok(circuit)
511    }
512
513    /// Apply cost layer to circuit
514    fn apply_cost_layer(&self, circuit: &mut InterfaceCircuit, gamma: f64) -> Result<()> {
515        match self.problem_type {
516            QAOAProblemType::MaxCut => {
517                self.apply_maxcut_cost_layer(circuit, gamma)?;
518            }
519            QAOAProblemType::MaxWeightIndependentSet => {
520                self.apply_mwis_cost_layer(circuit, gamma)?;
521            }
522            QAOAProblemType::TSP => {
523                self.apply_tsp_cost_layer(circuit, gamma)?;
524            }
525            QAOAProblemType::PortfolioOptimization => {
526                self.apply_portfolio_cost_layer(circuit, gamma)?;
527            }
528            QAOAProblemType::Boolean3SAT => {
529                self.apply_3sat_cost_layer(circuit, gamma)?;
530            }
531            QAOAProblemType::QUBO => {
532                self.apply_qubo_cost_layer(circuit, gamma)?;
533            }
534            _ => {
535                self.apply_generic_cost_layer(circuit, gamma)?;
536            }
537        }
538        Ok(())
539    }
540
541    /// Apply MaxCut cost layer
542    fn apply_maxcut_cost_layer(&self, circuit: &mut InterfaceCircuit, gamma: f64) -> Result<()> {
543        // Apply exp(-i*gamma*H_C) where H_C = sum_{(i,j)} w_{ij} * (1 - Z_i Z_j) / 2
544        for i in 0..self.graph.num_vertices {
545            for j in i + 1..self.graph.num_vertices {
546                let weight = self
547                    .graph
548                    .edge_weights
549                    .get(&(i, j))
550                    .or_else(|| self.graph.edge_weights.get(&(j, i)))
551                    .unwrap_or(&self.graph.adjacency_matrix[[i, j]]);
552
553                if weight.abs() > 1e-10 {
554                    let angle = gamma * weight;
555
556                    // Apply ZZ interaction: exp(-i*angle*Z_i*Z_j)
557                    circuit.add_gate(InterfaceGate::new(InterfaceGateType::CNOT, vec![i, j]));
558                    circuit.add_gate(InterfaceGate::new(InterfaceGateType::RZ(angle), vec![j]));
559                    circuit.add_gate(InterfaceGate::new(InterfaceGateType::CNOT, vec![i, j]));
560                }
561            }
562        }
563        Ok(())
564    }
565
566    /// Apply Maximum Weight Independent Set cost layer
567    fn apply_mwis_cost_layer(&self, circuit: &mut InterfaceCircuit, gamma: f64) -> Result<()> {
568        // H_C = sum_i w_i * Z_i + penalty * sum_{(i,j)} Z_i * Z_j
569
570        // Single-qubit terms (vertex weights)
571        for i in 0..self.graph.num_vertices {
572            let weight = self.graph.vertex_weights.get(i).unwrap_or(&1.0);
573            let angle = gamma * weight;
574            circuit.add_gate(InterfaceGate::new(InterfaceGateType::RZ(angle), vec![i]));
575        }
576
577        // Two-qubit penalty terms (prevent adjacent vertices)
578        let penalty = 10.0; // Large penalty for violating independence
579        for i in 0..self.graph.num_vertices {
580            for j in i + 1..self.graph.num_vertices {
581                if self.graph.adjacency_matrix[[i, j]] > 0.0 {
582                    let angle = gamma * penalty;
583                    circuit.add_gate(InterfaceGate::new(InterfaceGateType::CNOT, vec![i, j]));
584                    circuit.add_gate(InterfaceGate::new(InterfaceGateType::RZ(angle), vec![j]));
585                    circuit.add_gate(InterfaceGate::new(InterfaceGateType::CNOT, vec![i, j]));
586                }
587            }
588        }
589        Ok(())
590    }
591
592    /// Apply TSP cost layer
593    fn apply_tsp_cost_layer(&self, circuit: &mut InterfaceCircuit, gamma: f64) -> Result<()> {
594        let num_cities = (self.graph.num_vertices as f64).sqrt() as usize;
595
596        // Distance cost terms
597        for t in 0..num_cities {
598            for i in 0..num_cities {
599                for j in 0..num_cities {
600                    if i != j {
601                        let distance = self.graph.adjacency_matrix[[i, j]];
602                        if distance > 0.0 {
603                            let angle = gamma * distance;
604
605                            // Encode: city i at time t and city j at time t+1
606                            let qubit_i_t = i * num_cities + t;
607                            let qubit_j_t1 = j * num_cities + ((t + 1) % num_cities);
608
609                            if qubit_i_t < circuit.num_qubits && qubit_j_t1 < circuit.num_qubits {
610                                circuit.add_gate(InterfaceGate::new(
611                                    InterfaceGateType::CNOT,
612                                    vec![qubit_i_t, qubit_j_t1],
613                                ));
614                                circuit.add_gate(InterfaceGate::new(
615                                    InterfaceGateType::RZ(angle),
616                                    vec![qubit_j_t1],
617                                ));
618                                circuit.add_gate(InterfaceGate::new(
619                                    InterfaceGateType::CNOT,
620                                    vec![qubit_i_t, qubit_j_t1],
621                                ));
622                            }
623                        }
624                    }
625                }
626            }
627        }
628
629        // Constraint penalty terms (each city visited exactly once, each time slot used exactly once)
630        let penalty = 10.0;
631
632        // Each city visited exactly once
633        for i in 0..num_cities {
634            for t1 in 0..num_cities {
635                for t2 in t1 + 1..num_cities {
636                    let qubit1 = i * num_cities + t1;
637                    let qubit2 = i * num_cities + t2;
638                    if qubit1 < circuit.num_qubits && qubit2 < circuit.num_qubits {
639                        let angle = gamma * penalty;
640                        circuit.add_gate(InterfaceGate::new(
641                            InterfaceGateType::CNOT,
642                            vec![qubit1, qubit2],
643                        ));
644                        circuit.add_gate(InterfaceGate::new(
645                            InterfaceGateType::RZ(angle),
646                            vec![qubit2],
647                        ));
648                        circuit.add_gate(InterfaceGate::new(
649                            InterfaceGateType::CNOT,
650                            vec![qubit1, qubit2],
651                        ));
652                    }
653                }
654            }
655        }
656
657        Ok(())
658    }
659
660    /// Apply portfolio optimization cost layer
661    fn apply_portfolio_cost_layer(&self, circuit: &mut InterfaceCircuit, gamma: f64) -> Result<()> {
662        // Portfolio optimization: maximize return - risk
663        // H_C = -sum_i r_i * Z_i + lambda * sum_{i,j} sigma_{ij} * Z_i * Z_j
664
665        let lambda = 1.0; // Risk aversion parameter
666
667        // Return terms (negative for maximization)
668        for i in 0..self.graph.num_vertices {
669            let return_rate = self.graph.vertex_weights.get(i).unwrap_or(&0.1);
670            let angle = -gamma * return_rate; // Negative for maximization
671            circuit.add_gate(InterfaceGate::new(InterfaceGateType::RZ(angle), vec![i]));
672        }
673
674        // Risk terms (covariance matrix)
675        for i in 0..self.graph.num_vertices {
676            for j in i..self.graph.num_vertices {
677                let covariance = self.graph.adjacency_matrix[[i, j]];
678                if covariance.abs() > 1e-10 {
679                    let angle = gamma * lambda * covariance;
680
681                    if i == j {
682                        // Diagonal terms (variance)
683                        circuit.add_gate(InterfaceGate::new(InterfaceGateType::RZ(angle), vec![i]));
684                    } else {
685                        // Off-diagonal terms (covariance)
686                        circuit.add_gate(InterfaceGate::new(InterfaceGateType::CNOT, vec![i, j]));
687                        circuit.add_gate(InterfaceGate::new(InterfaceGateType::RZ(angle), vec![j]));
688                        circuit.add_gate(InterfaceGate::new(InterfaceGateType::CNOT, vec![i, j]));
689                    }
690                }
691            }
692        }
693        Ok(())
694    }
695
696    /// Apply 3-SAT cost layer
697    fn apply_3sat_cost_layer(&self, circuit: &mut InterfaceCircuit, gamma: f64) -> Result<()> {
698        // For 3-SAT, we need to encode clauses
699        // Each clause contributes to the cost if not satisfied
700
701        // This is a simplified implementation - would need actual clause encoding
702        for constraint in &self.graph.constraints {
703            match constraint {
704                QAOAConstraint::LinearConstraint {
705                    coefficients,
706                    bound,
707                } => {
708                    let angle = gamma * bound;
709
710                    // Apply constraint penalty (simplified)
711                    for (i, &coeff) in coefficients.iter().enumerate() {
712                        if i < circuit.num_qubits && coeff.abs() > 1e-10 {
713                            circuit.add_gate(InterfaceGate::new(
714                                InterfaceGateType::RZ(angle * coeff),
715                                vec![i],
716                            ));
717                        }
718                    }
719                }
720                _ => {
721                    // Other constraint types would be handled here
722                }
723            }
724        }
725        Ok(())
726    }
727
728    /// Apply QUBO cost layer
729    fn apply_qubo_cost_layer(&self, circuit: &mut InterfaceCircuit, gamma: f64) -> Result<()> {
730        // QUBO: minimize x^T Q x where Q is the QUBO matrix
731
732        // Linear terms (diagonal of Q)
733        for i in 0..self.graph.num_vertices {
734            let coeff = self.graph.adjacency_matrix[[i, i]];
735            if coeff.abs() > 1e-10 {
736                let angle = gamma * coeff;
737                circuit.add_gate(InterfaceGate::new(InterfaceGateType::RZ(angle), vec![i]));
738            }
739        }
740
741        // Quadratic terms (off-diagonal of Q)
742        for i in 0..self.graph.num_vertices {
743            for j in i + 1..self.graph.num_vertices {
744                let coeff = self.graph.adjacency_matrix[[i, j]];
745                if coeff.abs() > 1e-10 {
746                    let angle = gamma * coeff;
747                    circuit.add_gate(InterfaceGate::new(InterfaceGateType::CNOT, vec![i, j]));
748                    circuit.add_gate(InterfaceGate::new(InterfaceGateType::RZ(angle), vec![j]));
749                    circuit.add_gate(InterfaceGate::new(InterfaceGateType::CNOT, vec![i, j]));
750                }
751            }
752        }
753        Ok(())
754    }
755
756    /// Apply generic cost layer
757    fn apply_generic_cost_layer(&self, circuit: &mut InterfaceCircuit, gamma: f64) -> Result<()> {
758        // Generic cost layer based on adjacency matrix
759        for i in 0..self.graph.num_vertices {
760            for j in i + 1..self.graph.num_vertices {
761                let weight = self.graph.adjacency_matrix[[i, j]];
762                if weight.abs() > 1e-10 {
763                    let angle = gamma * weight;
764                    circuit.add_gate(InterfaceGate::new(InterfaceGateType::CNOT, vec![i, j]));
765                    circuit.add_gate(InterfaceGate::new(InterfaceGateType::RZ(angle), vec![j]));
766                    circuit.add_gate(InterfaceGate::new(InterfaceGateType::CNOT, vec![i, j]));
767                }
768            }
769        }
770        Ok(())
771    }
772
773    /// Apply mixer layer to circuit
774    fn apply_mixer_layer(&self, circuit: &mut InterfaceCircuit, beta: f64) -> Result<()> {
775        match self.config.mixer_type {
776            QAOAMixerType::Standard => {
777                self.apply_standard_mixer(circuit, beta)?;
778            }
779            QAOAMixerType::XY => {
780                self.apply_xy_mixer(circuit, beta)?;
781            }
782            QAOAMixerType::Ring => {
783                self.apply_ring_mixer(circuit, beta)?;
784            }
785            QAOAMixerType::Grover => {
786                self.apply_grover_mixer(circuit, beta)?;
787            }
788            QAOAMixerType::Dicke => {
789                self.apply_dicke_mixer(circuit, beta)?;
790            }
791            QAOAMixerType::Custom => {
792                self.apply_custom_mixer(circuit, beta)?;
793            }
794        }
795        Ok(())
796    }
797
798    /// Apply standard X mixer
799    fn apply_standard_mixer(&self, circuit: &mut InterfaceCircuit, beta: f64) -> Result<()> {
800        for qubit in 0..circuit.num_qubits {
801            circuit.add_gate(InterfaceGate::new(InterfaceGateType::RX(beta), vec![qubit]));
802        }
803        Ok(())
804    }
805
806    /// Apply XY mixer for number conservation
807    fn apply_xy_mixer(&self, circuit: &mut InterfaceCircuit, beta: f64) -> Result<()> {
808        // XY mixer: exp(-i*beta*(X_i X_j + Y_i Y_j)) for adjacent qubits
809        for i in 0..circuit.num_qubits {
810            for j in i + 1..circuit.num_qubits {
811                if self.graph.adjacency_matrix[[i, j]] > 0.0 {
812                    // Apply XX interaction
813                    circuit.add_gate(InterfaceGate::new(InterfaceGateType::Hadamard, vec![i]));
814                    circuit.add_gate(InterfaceGate::new(InterfaceGateType::Hadamard, vec![j]));
815                    circuit.add_gate(InterfaceGate::new(InterfaceGateType::CNOT, vec![i, j]));
816                    circuit.add_gate(InterfaceGate::new(InterfaceGateType::RZ(beta), vec![j]));
817                    circuit.add_gate(InterfaceGate::new(InterfaceGateType::CNOT, vec![i, j]));
818                    circuit.add_gate(InterfaceGate::new(InterfaceGateType::Hadamard, vec![i]));
819                    circuit.add_gate(InterfaceGate::new(InterfaceGateType::Hadamard, vec![j]));
820
821                    // Apply YY interaction
822                    circuit.add_gate(InterfaceGate::new(
823                        InterfaceGateType::RY(std::f64::consts::PI / 2.0),
824                        vec![i],
825                    ));
826                    circuit.add_gate(InterfaceGate::new(
827                        InterfaceGateType::RY(std::f64::consts::PI / 2.0),
828                        vec![j],
829                    ));
830                    circuit.add_gate(InterfaceGate::new(InterfaceGateType::CNOT, vec![i, j]));
831                    circuit.add_gate(InterfaceGate::new(InterfaceGateType::RZ(beta), vec![j]));
832                    circuit.add_gate(InterfaceGate::new(InterfaceGateType::CNOT, vec![i, j]));
833                    circuit.add_gate(InterfaceGate::new(
834                        InterfaceGateType::RY(-std::f64::consts::PI / 2.0),
835                        vec![i],
836                    ));
837                    circuit.add_gate(InterfaceGate::new(
838                        InterfaceGateType::RY(-std::f64::consts::PI / 2.0),
839                        vec![j],
840                    ));
841                }
842            }
843        }
844        Ok(())
845    }
846
847    /// Apply ring mixer
848    fn apply_ring_mixer(&self, circuit: &mut InterfaceCircuit, beta: f64) -> Result<()> {
849        // Ring mixer with periodic boundary conditions
850        for i in 0..circuit.num_qubits {
851            let next = (i + 1) % circuit.num_qubits;
852
853            // Apply X_i X_{i+1} interaction
854            circuit.add_gate(InterfaceGate::new(InterfaceGateType::Hadamard, vec![i]));
855            circuit.add_gate(InterfaceGate::new(InterfaceGateType::Hadamard, vec![next]));
856            circuit.add_gate(InterfaceGate::new(InterfaceGateType::CNOT, vec![i, next]));
857            circuit.add_gate(InterfaceGate::new(InterfaceGateType::RZ(beta), vec![next]));
858            circuit.add_gate(InterfaceGate::new(InterfaceGateType::CNOT, vec![i, next]));
859            circuit.add_gate(InterfaceGate::new(InterfaceGateType::Hadamard, vec![i]));
860            circuit.add_gate(InterfaceGate::new(InterfaceGateType::Hadamard, vec![next]));
861        }
862        Ok(())
863    }
864
865    /// Apply Grover mixer
866    fn apply_grover_mixer(&self, circuit: &mut InterfaceCircuit, beta: f64) -> Result<()> {
867        // Grover diffusion operator: 2|s><s| - I where |s> is uniform superposition
868
869        // Apply H gates
870        for qubit in 0..circuit.num_qubits {
871            circuit.add_gate(InterfaceGate::new(InterfaceGateType::Hadamard, vec![qubit]));
872        }
873
874        // Apply Z gates (conditional phase)
875        for qubit in 0..circuit.num_qubits {
876            circuit.add_gate(InterfaceGate::new(InterfaceGateType::PauliZ, vec![qubit]));
877        }
878
879        // Multi-controlled Z gate (simplified implementation)
880        if circuit.num_qubits > 1 {
881            let controls: Vec<usize> = (0..circuit.num_qubits - 1).collect();
882            let target = circuit.num_qubits - 1;
883
884            // Simplified multi-controlled Z using Toffoli decomposition
885            circuit.add_gate(InterfaceGate::new(
886                InterfaceGateType::CNOT,
887                vec![controls[0], target],
888            ));
889            circuit.add_gate(InterfaceGate::new(
890                InterfaceGateType::RZ(beta),
891                vec![target],
892            ));
893            circuit.add_gate(InterfaceGate::new(
894                InterfaceGateType::CNOT,
895                vec![controls[0], target],
896            ));
897        }
898
899        // Apply Z gates again
900        for qubit in 0..circuit.num_qubits {
901            circuit.add_gate(InterfaceGate::new(InterfaceGateType::PauliZ, vec![qubit]));
902        }
903
904        // Apply H gates
905        for qubit in 0..circuit.num_qubits {
906            circuit.add_gate(InterfaceGate::new(InterfaceGateType::Hadamard, vec![qubit]));
907        }
908
909        Ok(())
910    }
911
912    /// Apply Dicke mixer for cardinality constraints
913    fn apply_dicke_mixer(&self, circuit: &mut InterfaceCircuit, beta: f64) -> Result<()> {
914        // Dicke state mixer preserves the number of excited qubits
915        // This is a simplified implementation
916
917        for i in 0..circuit.num_qubits - 1 {
918            // Apply partial SWAP operation
919            circuit.add_gate(InterfaceGate::new(InterfaceGateType::CNOT, vec![i, i + 1]));
920            circuit.add_gate(InterfaceGate::new(InterfaceGateType::RY(beta), vec![i]));
921            circuit.add_gate(InterfaceGate::new(InterfaceGateType::CNOT, vec![i + 1, i]));
922            circuit.add_gate(InterfaceGate::new(
923                InterfaceGateType::RY(-beta),
924                vec![i + 1],
925            ));
926            circuit.add_gate(InterfaceGate::new(InterfaceGateType::CNOT, vec![i, i + 1]));
927        }
928        Ok(())
929    }
930
931    /// Apply custom mixer
932    fn apply_custom_mixer(&self, circuit: &mut InterfaceCircuit, beta: f64) -> Result<()> {
933        // Custom mixer based on problem structure
934        match self.problem_type {
935            QAOAProblemType::TSP => {
936                // Custom TSP mixer that respects route constraints
937                self.apply_tsp_custom_mixer(circuit, beta)?;
938            }
939            QAOAProblemType::PortfolioOptimization => {
940                // Portfolio-specific mixer
941                self.apply_portfolio_custom_mixer(circuit, beta)?;
942            }
943            _ => {
944                // Default to standard mixer
945                self.apply_standard_mixer(circuit, beta)?;
946            }
947        }
948        Ok(())
949    }
950
951    /// TSP-specific custom mixer
952    fn apply_tsp_custom_mixer(&self, circuit: &mut InterfaceCircuit, beta: f64) -> Result<()> {
953        let num_cities = (circuit.num_qubits as f64).sqrt() as usize;
954
955        // Swap operations that preserve TSP constraints
956        for t in 0..num_cities {
957            for i in 0..num_cities {
958                for j in i + 1..num_cities {
959                    let qubit_i = i * num_cities + t;
960                    let qubit_j = j * num_cities + t;
961
962                    if qubit_i < circuit.num_qubits && qubit_j < circuit.num_qubits {
963                        // Partial SWAP between cities at same time
964                        circuit.add_gate(InterfaceGate::new(
965                            InterfaceGateType::CNOT,
966                            vec![qubit_i, qubit_j],
967                        ));
968                        circuit.add_gate(InterfaceGate::new(
969                            InterfaceGateType::RY(beta),
970                            vec![qubit_i],
971                        ));
972                        circuit.add_gate(InterfaceGate::new(
973                            InterfaceGateType::CNOT,
974                            vec![qubit_j, qubit_i],
975                        ));
976                        circuit.add_gate(InterfaceGate::new(
977                            InterfaceGateType::RY(-beta),
978                            vec![qubit_j],
979                        ));
980                        circuit.add_gate(InterfaceGate::new(
981                            InterfaceGateType::CNOT,
982                            vec![qubit_i, qubit_j],
983                        ));
984                    }
985                }
986            }
987        }
988        Ok(())
989    }
990
991    /// Portfolio-specific custom mixer
992    fn apply_portfolio_custom_mixer(
993        &self,
994        circuit: &mut InterfaceCircuit,
995        beta: f64,
996    ) -> Result<()> {
997        // Portfolio mixer that respects budget constraints
998        for i in 0..circuit.num_qubits - 1 {
999            for j in i + 1..circuit.num_qubits {
1000                // Conditional rotations based on correlation
1001                let correlation = self.graph.adjacency_matrix[[i, j]].abs();
1002                if correlation > 0.1 {
1003                    let angle = beta * correlation;
1004                    circuit.add_gate(InterfaceGate::new(
1005                        InterfaceGateType::CRY(angle),
1006                        vec![i, j],
1007                    ));
1008                }
1009            }
1010        }
1011        Ok(())
1012    }
1013
1014    /// Initialize gamma parameters
1015    fn initialize_gammas(config: &QAOAConfig, _graph: &QAOAGraph) -> Result<Vec<f64>> {
1016        let mut gammas = Vec::with_capacity(config.num_layers);
1017
1018        for i in 0..config.num_layers {
1019            let gamma = match config.initialization {
1020                QAOAInitializationStrategy::Random => {
1021                    (rand::random::<f64>() - 0.5) * std::f64::consts::PI
1022                }
1023                QAOAInitializationStrategy::AdiabaticStart => {
1024                    // Start with small values for adiabatic evolution
1025                    0.1 * (i + 1) as f64 / config.num_layers as f64
1026                }
1027                _ => {
1028                    // Default linear schedule
1029                    0.5 * (i + 1) as f64 / config.num_layers as f64
1030                }
1031            };
1032            gammas.push(gamma);
1033        }
1034
1035        Ok(gammas)
1036    }
1037
1038    /// Initialize beta parameters
1039    fn initialize_betas(config: &QAOAConfig, _graph: &QAOAGraph) -> Result<Vec<f64>> {
1040        let mut betas = Vec::with_capacity(config.num_layers);
1041
1042        for i in 0..config.num_layers {
1043            let beta = match config.initialization {
1044                QAOAInitializationStrategy::Random => {
1045                    (rand::random::<f64>() - 0.5) * std::f64::consts::PI
1046                }
1047                QAOAInitializationStrategy::AdiabaticStart => {
1048                    // Start with large values for mixer
1049                    std::f64::consts::PI * (config.num_layers - i) as f64 / config.num_layers as f64
1050                }
1051                _ => {
1052                    // Default linear schedule
1053                    0.5 * std::f64::consts::PI * (config.num_layers - i) as f64
1054                        / config.num_layers as f64
1055                }
1056            };
1057            betas.push(beta);
1058        }
1059
1060        Ok(betas)
1061    }
1062
1063    /// Evaluate QAOA cost function
1064    fn evaluate_qaoa_cost(&self, gammas: &[f64], betas: &[f64]) -> Result<f64> {
1065        let circuit = self.generate_qaoa_circuit(gammas, betas)?;
1066        let state = self.simulate_circuit(&circuit)?;
1067
1068        // Calculate expectation value of cost Hamiltonian
1069        let cost = self.calculate_cost_expectation(&state)?;
1070        Ok(cost)
1071    }
1072
1073    /// Calculate cost expectation value
1074    fn calculate_cost_expectation(&self, state: &Array1<Complex64>) -> Result<f64> {
1075        let mut expectation = 0.0;
1076
1077        // Iterate over all basis states
1078        for (idx, amplitude) in state.iter().enumerate() {
1079            let probability = amplitude.norm_sqr();
1080            if probability > 1e-10 {
1081                let bitstring = format!("{:0width$b}", idx, width = self.graph.num_vertices);
1082                let cost = self.evaluate_classical_cost(&bitstring)?;
1083                expectation += probability * cost;
1084            }
1085        }
1086
1087        Ok(expectation)
1088    }
1089
1090    /// Evaluate classical cost for a bitstring
1091    fn evaluate_classical_cost(&self, bitstring: &str) -> Result<f64> {
1092        let bits: Vec<bool> = bitstring.chars().map(|c| c == '1').collect();
1093
1094        match self.problem_type {
1095            QAOAProblemType::MaxCut => self.evaluate_maxcut_cost(&bits),
1096            QAOAProblemType::MaxWeightIndependentSet => self.evaluate_mwis_cost(&bits),
1097            QAOAProblemType::TSP => self.evaluate_tsp_cost(&bits),
1098            QAOAProblemType::PortfolioOptimization => self.evaluate_portfolio_cost(&bits),
1099            QAOAProblemType::QUBO => self.evaluate_qubo_cost(&bits),
1100            _ => self.evaluate_generic_cost(&bits),
1101        }
1102    }
1103
1104    /// Evaluate MaxCut cost
1105    fn evaluate_maxcut_cost(&self, bits: &[bool]) -> Result<f64> {
1106        let mut cost = 0.0;
1107
1108        for i in 0..self.graph.num_vertices {
1109            for j in i + 1..self.graph.num_vertices {
1110                let weight = self
1111                    .graph
1112                    .edge_weights
1113                    .get(&(i, j))
1114                    .or_else(|| self.graph.edge_weights.get(&(j, i)))
1115                    .unwrap_or(&self.graph.adjacency_matrix[[i, j]]);
1116
1117                if weight.abs() > 1e-10 && bits[i] != bits[j] {
1118                    cost += weight;
1119                }
1120            }
1121        }
1122
1123        Ok(cost)
1124    }
1125
1126    /// Evaluate MWIS cost
1127    fn evaluate_mwis_cost(&self, bits: &[bool]) -> Result<f64> {
1128        let mut cost = 0.0;
1129        let mut valid = true;
1130
1131        // Check independence constraint
1132        for i in 0..self.graph.num_vertices {
1133            if bits[i] {
1134                for j in 0..self.graph.num_vertices {
1135                    if i != j && bits[j] && self.graph.adjacency_matrix[[i, j]] > 0.0 {
1136                        valid = false;
1137                        break;
1138                    }
1139                }
1140                if valid {
1141                    cost += self.graph.vertex_weights.get(i).unwrap_or(&1.0);
1142                }
1143            }
1144        }
1145
1146        // Return large penalty if invalid
1147        if !valid {
1148            cost = -1000.0;
1149        }
1150
1151        Ok(cost)
1152    }
1153
1154    /// Evaluate TSP cost
1155    fn evaluate_tsp_cost(&self, bits: &[bool]) -> Result<f64> {
1156        let num_cities = (self.graph.num_vertices as f64).sqrt() as usize;
1157        let mut cost = 0.0;
1158        let mut valid = true;
1159
1160        // Check if valid TSP solution
1161        let mut city_times = vec![-1i32; num_cities];
1162        let mut time_cities = vec![-1i32; num_cities];
1163
1164        for city in 0..num_cities {
1165            for time in 0..num_cities {
1166                let qubit = city * num_cities + time;
1167                if qubit < bits.len() && bits[qubit] {
1168                    if city_times[city] != -1 || time_cities[time] != -1 {
1169                        valid = false;
1170                        break;
1171                    }
1172                    city_times[city] = time as i32;
1173                    time_cities[time] = city as i32;
1174                }
1175            }
1176            if !valid {
1177                break;
1178            }
1179        }
1180
1181        if valid && city_times.iter().all(|&t| t != -1) {
1182            // Calculate tour cost
1183            for t in 0..num_cities {
1184                let current_city = time_cities[t] as usize;
1185                let next_city = time_cities[(t + 1) % num_cities] as usize;
1186                cost += self.graph.adjacency_matrix[[current_city, next_city]];
1187            }
1188        } else {
1189            cost = 1000.0; // Large penalty for invalid solution
1190        }
1191
1192        Ok(cost)
1193    }
1194
1195    /// Evaluate portfolio cost
1196    fn evaluate_portfolio_cost(&self, bits: &[bool]) -> Result<f64> {
1197        let mut expected_return = 0.0;
1198        let mut risk = 0.0;
1199        let lambda = 1.0; // Risk aversion parameter
1200
1201        // Calculate expected return
1202        for i in 0..self.graph.num_vertices {
1203            if bits[i] {
1204                expected_return += self.graph.vertex_weights.get(i).unwrap_or(&0.1);
1205            }
1206        }
1207
1208        // Calculate risk (portfolio variance)
1209        for i in 0..self.graph.num_vertices {
1210            for j in 0..self.graph.num_vertices {
1211                if bits[i] && bits[j] {
1212                    risk += self.graph.adjacency_matrix[[i, j]];
1213                }
1214            }
1215        }
1216
1217        // Portfolio objective: maximize return - risk
1218        Ok(expected_return - lambda * risk)
1219    }
1220
1221    /// Evaluate QUBO cost
1222    fn evaluate_qubo_cost(&self, bits: &[bool]) -> Result<f64> {
1223        let mut cost = 0.0;
1224
1225        // Linear terms
1226        for i in 0..self.graph.num_vertices {
1227            if bits[i] {
1228                cost += self.graph.adjacency_matrix[[i, i]];
1229            }
1230        }
1231
1232        // Quadratic terms
1233        for i in 0..self.graph.num_vertices {
1234            for j in i + 1..self.graph.num_vertices {
1235                if bits[i] && bits[j] {
1236                    cost += self.graph.adjacency_matrix[[i, j]];
1237                }
1238            }
1239        }
1240
1241        Ok(cost)
1242    }
1243
1244    /// Evaluate generic cost
1245    fn evaluate_generic_cost(&self, bits: &[bool]) -> Result<f64> {
1246        // Default to MaxCut-like cost
1247        self.evaluate_maxcut_cost(bits)
1248    }
1249
1250    /// Solve problem classically for comparison
1251    fn solve_classically(&self) -> Result<f64> {
1252        match self.problem_type {
1253            QAOAProblemType::MaxCut => self.solve_maxcut_classically(),
1254            QAOAProblemType::MaxWeightIndependentSet => self.solve_mwis_classically(),
1255            _ => {
1256                // Brute force for small problems
1257                self.solve_brute_force()
1258            }
1259        }
1260    }
1261
1262    /// Solve MaxCut classically (greedy approximation)
1263    fn solve_maxcut_classically(&self) -> Result<f64> {
1264        let mut best_cost = 0.0;
1265        let num_vertices = self.graph.num_vertices;
1266
1267        // Simple greedy algorithm
1268        let mut assignment = vec![false; num_vertices];
1269
1270        for _ in 0..10 {
1271            // Random starting assignment
1272            for i in 0..num_vertices {
1273                assignment[i] = rand::random();
1274            }
1275
1276            // Local optimization
1277            let mut improved = true;
1278            while improved {
1279                improved = false;
1280                for i in 0..num_vertices {
1281                    assignment[i] = !assignment[i];
1282                    let cost = self.evaluate_classical_cost(
1283                        &assignment
1284                            .iter()
1285                            .map(|&b| if b { '1' } else { '0' })
1286                            .collect::<String>(),
1287                    )?;
1288                    if cost > best_cost {
1289                        best_cost = cost;
1290                        improved = true;
1291                    } else {
1292                        assignment[i] = !assignment[i];
1293                    }
1294                }
1295            }
1296        }
1297
1298        Ok(best_cost)
1299    }
1300
1301    /// Solve MWIS classically (greedy)
1302    fn solve_mwis_classically(&self) -> Result<f64> {
1303        let mut vertices: Vec<usize> = (0..self.graph.num_vertices).collect();
1304        vertices.sort_by(|&a, &b| {
1305            let weight_a = self.graph.vertex_weights.get(a).unwrap_or(&1.0);
1306            let weight_b = self.graph.vertex_weights.get(b).unwrap_or(&1.0);
1307            weight_b.partial_cmp(weight_a).unwrap()
1308        });
1309
1310        let mut selected = vec![false; self.graph.num_vertices];
1311        let mut total_weight = 0.0;
1312
1313        for &v in &vertices {
1314            let mut can_select = true;
1315            for &u in &vertices {
1316                if selected[u] && self.graph.adjacency_matrix[[u, v]] > 0.0 {
1317                    can_select = false;
1318                    break;
1319                }
1320            }
1321            if can_select {
1322                selected[v] = true;
1323                total_weight += self.graph.vertex_weights.get(v).unwrap_or(&1.0);
1324            }
1325        }
1326
1327        Ok(total_weight)
1328    }
1329
1330    /// Brute force solver for small problems
1331    fn solve_brute_force(&self) -> Result<f64> {
1332        if self.graph.num_vertices > 20 {
1333            return Ok(0.0); // Too large for brute force
1334        }
1335
1336        let mut best_cost = f64::NEG_INFINITY;
1337        let num_states = 1 << self.graph.num_vertices;
1338
1339        for state in 0..num_states {
1340            let bitstring = format!("{:0width$b}", state, width = self.graph.num_vertices);
1341            let cost = self.evaluate_classical_cost(&bitstring)?;
1342            if cost > best_cost {
1343                best_cost = cost;
1344            }
1345        }
1346
1347        Ok(best_cost)
1348    }
1349
1350    /// Parameter optimization methods
1351    /// Classical parameter optimization
1352    fn classical_parameter_optimization(&mut self) -> Result<()> {
1353        // Gradient descent optimization
1354        let epsilon = 1e-4;
1355        let mut gamma_gradients = vec![0.0; self.gammas.len()];
1356        let mut beta_gradients = vec![0.0; self.betas.len()];
1357
1358        // Calculate gradients using finite differences
1359        for i in 0..self.gammas.len() {
1360            let mut gammas_plus = self.gammas.clone();
1361            let mut gammas_minus = self.gammas.clone();
1362            gammas_plus[i] += epsilon;
1363            gammas_minus[i] -= epsilon;
1364
1365            let cost_plus = self.evaluate_qaoa_cost(&gammas_plus, &self.betas)?;
1366            let cost_minus = self.evaluate_qaoa_cost(&gammas_minus, &self.betas)?;
1367            gamma_gradients[i] = (cost_plus - cost_minus) / (2.0 * epsilon);
1368        }
1369
1370        for i in 0..self.betas.len() {
1371            let mut betas_plus = self.betas.clone();
1372            let mut betas_minus = self.betas.clone();
1373            betas_plus[i] += epsilon;
1374            betas_minus[i] -= epsilon;
1375
1376            let cost_plus = self.evaluate_qaoa_cost(&self.gammas, &betas_plus)?;
1377            let cost_minus = self.evaluate_qaoa_cost(&self.gammas, &betas_minus)?;
1378            beta_gradients[i] = (cost_plus - cost_minus) / (2.0 * epsilon);
1379        }
1380
1381        // Update parameters
1382        for i in 0..self.gammas.len() {
1383            self.gammas[i] += self.config.learning_rate * gamma_gradients[i];
1384        }
1385        for i in 0..self.betas.len() {
1386            self.betas[i] += self.config.learning_rate * beta_gradients[i];
1387        }
1388
1389        Ok(())
1390    }
1391
1392    /// Quantum parameter optimization using parameter shift rule
1393    fn quantum_parameter_optimization(&mut self) -> Result<()> {
1394        let shift = std::f64::consts::PI / 2.0;
1395
1396        // Parameter shift rule for gammas
1397        for i in 0..self.gammas.len() {
1398            let mut gammas_plus = self.gammas.clone();
1399            let mut gammas_minus = self.gammas.clone();
1400            gammas_plus[i] += shift;
1401            gammas_minus[i] -= shift;
1402
1403            let cost_plus = self.evaluate_qaoa_cost(&gammas_plus, &self.betas)?;
1404            let cost_minus = self.evaluate_qaoa_cost(&gammas_minus, &self.betas)?;
1405            let gradient = (cost_plus - cost_minus) / 2.0;
1406
1407            self.gammas[i] += self.config.learning_rate * gradient;
1408        }
1409
1410        // Parameter shift rule for betas
1411        for i in 0..self.betas.len() {
1412            let mut betas_plus = self.betas.clone();
1413            let mut betas_minus = self.betas.clone();
1414            betas_plus[i] += shift;
1415            betas_minus[i] -= shift;
1416
1417            let cost_plus = self.evaluate_qaoa_cost(&self.gammas, &betas_plus)?;
1418            let cost_minus = self.evaluate_qaoa_cost(&self.gammas, &betas_minus)?;
1419            let gradient = (cost_plus - cost_minus) / 2.0;
1420
1421            self.betas[i] += self.config.learning_rate * gradient;
1422        }
1423
1424        Ok(())
1425    }
1426
1427    /// Hybrid classical-quantum optimization
1428    fn hybrid_parameter_optimization(&mut self) -> Result<()> {
1429        // Alternate between classical and quantum optimization
1430        if self.stats.total_time.as_secs() % 2 == 0 {
1431            self.classical_parameter_optimization()?;
1432        } else {
1433            self.quantum_parameter_optimization()?;
1434        }
1435        Ok(())
1436    }
1437
1438    /// Machine learning guided optimization
1439    fn ml_guided_optimization(&mut self) -> Result<()> {
1440        // Use ML model to predict good parameter updates
1441        // This is a simplified implementation
1442
1443        let problem_features = self.extract_problem_features()?;
1444        let predicted_update = self.predict_parameter_update(&problem_features)?;
1445
1446        // Apply predicted updates
1447        for i in 0..self.gammas.len() {
1448            self.gammas[i] += self.config.learning_rate * predicted_update.0[i];
1449        }
1450        for i in 0..self.betas.len() {
1451            self.betas[i] += self.config.learning_rate * predicted_update.1[i];
1452        }
1453
1454        Ok(())
1455    }
1456
1457    /// Adaptive parameter optimization
1458    fn adaptive_parameter_optimization(&mut self, cost_history: &[f64]) -> Result<()> {
1459        // Adapt learning rate based on cost history
1460        if cost_history.len() > 5 {
1461            let recent_improvement =
1462                cost_history[cost_history.len() - 1] - cost_history[cost_history.len() - 5];
1463
1464            if recent_improvement > 0.0 {
1465                self.config.learning_rate *= 1.1; // Increase learning rate
1466            } else {
1467                self.config.learning_rate *= 0.9; // Decrease learning rate
1468            }
1469        }
1470
1471        // Use classical optimization with adaptive learning rate
1472        self.classical_parameter_optimization()
1473    }
1474
1475    /// Helper methods
1476    fn apply_parameter_transfer(&mut self) -> Result<()> {
1477        // Load similar problem parameters from database
1478        let characteristics = self.extract_problem_characteristics()?;
1479        let database = self.parameter_database.lock().unwrap();
1480
1481        if let Some(similar_params) = database.parameters.get(&characteristics) {
1482            if let Some((gammas, betas, _cost)) = similar_params.first() {
1483                self.gammas = gammas.clone();
1484                self.betas = betas.clone();
1485            }
1486        }
1487        Ok(())
1488    }
1489
1490    fn store_parameters_for_transfer(&mut self) -> Result<()> {
1491        let characteristics = self.extract_problem_characteristics()?;
1492        let mut database = self.parameter_database.lock().unwrap();
1493
1494        let entry = database
1495            .parameters
1496            .entry(characteristics)
1497            .or_insert_with(Vec::new);
1498        entry.push((
1499            self.best_gammas.clone(),
1500            self.best_betas.clone(),
1501            self.best_cost,
1502        ));
1503
1504        // Keep only best parameters
1505        entry.sort_by(|a, b| b.2.partial_cmp(&a.2).unwrap());
1506        entry.truncate(5);
1507
1508        Ok(())
1509    }
1510
1511    fn extract_problem_characteristics(&self) -> Result<ProblemCharacteristics> {
1512        let num_edges = self
1513            .graph
1514            .adjacency_matrix
1515            .iter()
1516            .map(|&x| if x.abs() > 1e-10 { 1 } else { 0 })
1517            .sum::<usize>();
1518
1519        let max_edges = self.graph.num_vertices * (self.graph.num_vertices - 1) / 2;
1520        let density = if max_edges > 0 {
1521            (100.0 * num_edges as f64 / max_edges as f64) as u32
1522        } else {
1523            0
1524        };
1525
1526        Ok(ProblemCharacteristics {
1527            problem_type: self.problem_type,
1528            num_vertices: self.graph.num_vertices,
1529            density,
1530            regularity: 50, // Simplified regularity measure
1531        })
1532    }
1533
1534    fn extract_problem_features(&self) -> Result<Vec<f64>> {
1535        let mut features = Vec::new();
1536
1537        // Graph features
1538        features.push(self.graph.num_vertices as f64);
1539        features.push(self.graph.adjacency_matrix.sum());
1540        features.push(self.graph.vertex_weights.iter().sum::<f64>());
1541
1542        // Problem type encoding
1543        features.push(self.problem_type as u32 as f64);
1544
1545        Ok(features)
1546    }
1547
1548    fn predict_parameter_update(&self, _features: &[f64]) -> Result<(Vec<f64>, Vec<f64>)> {
1549        // Simplified ML prediction - would use trained model
1550        let gamma_updates = vec![0.01; self.gammas.len()];
1551        let beta_updates = vec![0.01; self.betas.len()];
1552        Ok((gamma_updates, beta_updates))
1553    }
1554
1555    fn should_add_layer(&self, cost_history: &[f64]) -> Result<bool> {
1556        if cost_history.len() < 10 {
1557            return Ok(false);
1558        }
1559
1560        // Add layer if improvement has plateaued
1561        let recent_improvement =
1562            cost_history[cost_history.len() - 1] - cost_history[cost_history.len() - 10];
1563        Ok(recent_improvement.abs() < self.config.convergence_tolerance * 10.0)
1564    }
1565
1566    fn add_qaoa_layer(&mut self) -> Result<()> {
1567        // Add new gamma and beta parameters
1568        self.gammas.push(0.1);
1569        self.betas.push(0.1);
1570        self.best_gammas.push(0.1);
1571        self.best_betas.push(0.1);
1572        Ok(())
1573    }
1574
1575    fn simulate_circuit(&self, circuit: &InterfaceCircuit) -> Result<Array1<Complex64>> {
1576        // Simplified circuit simulation - would integrate with actual simulator
1577        let state_size = 1 << circuit.num_qubits;
1578        let mut state = Array1::zeros(state_size);
1579        state[0] = Complex64::new(1.0, 0.0);
1580        Ok(state)
1581    }
1582
1583    fn extract_probabilities(&self, state: &Array1<Complex64>) -> Result<HashMap<String, f64>> {
1584        let mut probabilities = HashMap::new();
1585
1586        for (idx, amplitude) in state.iter().enumerate() {
1587            let probability = amplitude.norm_sqr();
1588            if probability > 1e-10 {
1589                let bitstring = format!("{:0width$b}", idx, width = self.graph.num_vertices);
1590                probabilities.insert(bitstring, probability);
1591            }
1592        }
1593
1594        Ok(probabilities)
1595    }
1596
1597    fn extract_best_solution(&self, probabilities: &HashMap<String, f64>) -> Result<String> {
1598        let mut best_solution = String::new();
1599        let mut best_cost = f64::NEG_INFINITY;
1600
1601        for (bitstring, _probability) in probabilities {
1602            let cost = self.evaluate_classical_cost(bitstring)?;
1603            if cost > best_cost {
1604                best_cost = cost;
1605                best_solution = bitstring.clone();
1606            }
1607        }
1608
1609        Ok(best_solution)
1610    }
1611
1612    fn evaluate_solution_quality(
1613        &self,
1614        solution: &str,
1615        _probabilities: &HashMap<String, f64>,
1616    ) -> Result<SolutionQuality> {
1617        let cost = self.evaluate_classical_cost(solution)?;
1618        let feasible = self.check_feasibility(solution)?;
1619
1620        let optimality_gap = if let Some(classical_opt) = self.classical_optimum {
1621            Some((classical_opt - cost) / classical_opt)
1622        } else {
1623            None
1624        };
1625
1626        Ok(SolutionQuality {
1627            feasible,
1628            optimality_gap,
1629            solution_variance: 0.0, // Would calculate from multiple runs
1630            confidence: 0.9,        // Would calculate based on probability
1631            constraint_violations: if feasible { 0 } else { 1 },
1632        })
1633    }
1634
1635    fn check_feasibility(&self, solution: &str) -> Result<bool> {
1636        let bits: Vec<bool> = solution.chars().map(|c| c == '1').collect();
1637
1638        // Check problem-specific constraints
1639        match self.problem_type {
1640            QAOAProblemType::MaxWeightIndependentSet => {
1641                // Check independence constraint
1642                for i in 0..self.graph.num_vertices {
1643                    if bits[i] {
1644                        for j in 0..self.graph.num_vertices {
1645                            if i != j && bits[j] && self.graph.adjacency_matrix[[i, j]] > 0.0 {
1646                                return Ok(false);
1647                            }
1648                        }
1649                    }
1650                }
1651            }
1652            QAOAProblemType::TSP => {
1653                // Check TSP constraints
1654                let num_cities = (self.graph.num_vertices as f64).sqrt() as usize;
1655                let mut city_counts = vec![0; num_cities];
1656                let mut time_counts = vec![0; num_cities];
1657
1658                for city in 0..num_cities {
1659                    for time in 0..num_cities {
1660                        let qubit = city * num_cities + time;
1661                        if qubit < bits.len() && bits[qubit] {
1662                            city_counts[city] += 1;
1663                            time_counts[time] += 1;
1664                        }
1665                    }
1666                }
1667
1668                // Each city exactly once, each time exactly once
1669                if !city_counts.iter().all(|&count| count == 1)
1670                    || !time_counts.iter().all(|&count| count == 1)
1671                {
1672                    return Ok(false);
1673                }
1674            }
1675            _ => {
1676                // No specific constraints for other problems
1677            }
1678        }
1679
1680        // Check general constraints
1681        for constraint in &self.graph.constraints {
1682            match constraint {
1683                QAOAConstraint::Cardinality { target } => {
1684                    let count = bits.iter().filter(|&&b| b).count();
1685                    if count != *target {
1686                        return Ok(false);
1687                    }
1688                }
1689                QAOAConstraint::UpperBound { max_vertices } => {
1690                    let count = bits.iter().filter(|&&b| b).count();
1691                    if count > *max_vertices {
1692                        return Ok(false);
1693                    }
1694                }
1695                QAOAConstraint::LowerBound { min_vertices } => {
1696                    let count = bits.iter().filter(|&&b| b).count();
1697                    if count < *min_vertices {
1698                        return Ok(false);
1699                    }
1700                }
1701                QAOAConstraint::Parity { even } => {
1702                    let count = bits.iter().filter(|&&b| b).count();
1703                    if (count % 2 == 0) != *even {
1704                        return Ok(false);
1705                    }
1706                }
1707                QAOAConstraint::LinearConstraint {
1708                    coefficients,
1709                    bound,
1710                } => {
1711                    let mut sum = 0.0;
1712                    for (i, &coeff) in coefficients.iter().enumerate() {
1713                        if i < bits.len() && bits[i] {
1714                            sum += coeff;
1715                        }
1716                    }
1717                    if (sum - bound).abs() > 1e-10 {
1718                        return Ok(false);
1719                    }
1720                }
1721            }
1722        }
1723
1724        Ok(true)
1725    }
1726
1727    /// State preparation methods
1728    fn prepare_warm_start_state(&self, circuit: &mut InterfaceCircuit) -> Result<()> {
1729        // Use classical solution as starting point
1730        let classical_solution = self.get_classical_solution()?;
1731
1732        for (i, bit) in classical_solution.chars().enumerate() {
1733            if bit == '1' && i < circuit.num_qubits {
1734                circuit.add_gate(InterfaceGate::new(InterfaceGateType::PauliX, vec![i]));
1735            }
1736        }
1737
1738        // Add some superposition
1739        for qubit in 0..circuit.num_qubits {
1740            circuit.add_gate(InterfaceGate::new(InterfaceGateType::RY(0.1), vec![qubit]));
1741        }
1742
1743        Ok(())
1744    }
1745
1746    fn prepare_adiabatic_state(&self, circuit: &mut InterfaceCircuit) -> Result<()> {
1747        // Start from uniform superposition and evolve towards problem state
1748        for qubit in 0..circuit.num_qubits {
1749            circuit.add_gate(InterfaceGate::new(InterfaceGateType::Hadamard, vec![qubit]));
1750        }
1751
1752        // Apply small evolution towards problem Hamiltonian
1753        self.apply_cost_layer(circuit, 0.01)?;
1754
1755        Ok(())
1756    }
1757
1758    fn prepare_random_state(&self, circuit: &mut InterfaceCircuit) -> Result<()> {
1759        for qubit in 0..circuit.num_qubits {
1760            let angle = (rand::random::<f64>() - 0.5) * std::f64::consts::PI;
1761            circuit.add_gate(InterfaceGate::new(
1762                InterfaceGateType::RY(angle),
1763                vec![qubit],
1764            ));
1765        }
1766        Ok(())
1767    }
1768
1769    fn prepare_problem_specific_state(&self, circuit: &mut InterfaceCircuit) -> Result<()> {
1770        match self.problem_type {
1771            QAOAProblemType::MaxCut => {
1772                // Start with a balanced cut
1773                for qubit in 0..circuit.num_qubits {
1774                    if qubit % 2 == 0 {
1775                        circuit
1776                            .add_gate(InterfaceGate::new(InterfaceGateType::PauliX, vec![qubit]));
1777                    }
1778                }
1779            }
1780            QAOAProblemType::TSP => {
1781                // Start with a valid tour
1782                let num_cities = (circuit.num_qubits as f64).sqrt() as usize;
1783                for time in 0..num_cities {
1784                    let city = time; // Simple tour: 0->1->2->...->0
1785                    let qubit = city * num_cities + time;
1786                    if qubit < circuit.num_qubits {
1787                        circuit
1788                            .add_gate(InterfaceGate::new(InterfaceGateType::PauliX, vec![qubit]));
1789                    }
1790                }
1791            }
1792            _ => {
1793                // Default to uniform superposition
1794                for qubit in 0..circuit.num_qubits {
1795                    circuit.add_gate(InterfaceGate::new(InterfaceGateType::Hadamard, vec![qubit]));
1796                }
1797            }
1798        }
1799        Ok(())
1800    }
1801
1802    fn get_classical_solution(&self) -> Result<String> {
1803        // Get classical solution (simplified)
1804        let classical_cost = self.solve_classically()?;
1805
1806        // For now, return a random valid solution
1807        let mut solution = String::new();
1808        for _ in 0..self.graph.num_vertices {
1809            solution.push(if rand::random() { '1' } else { '0' });
1810        }
1811        Ok(solution)
1812    }
1813}
1814
1815/// Benchmark QAOA performance
1816pub fn benchmark_qaoa() -> Result<HashMap<String, f64>> {
1817    let mut results = HashMap::new();
1818
1819    // Test MaxCut problem
1820    let start = Instant::now();
1821    let graph = QAOAGraph {
1822        num_vertices: 4,
1823        adjacency_matrix: Array2::from_shape_vec(
1824            (4, 4),
1825            vec![
1826                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,
1827            ],
1828        )
1829        .unwrap(),
1830        vertex_weights: vec![1.0; 4],
1831        edge_weights: HashMap::new(),
1832        constraints: Vec::new(),
1833    };
1834
1835    let config = QAOAConfig {
1836        num_layers: 2,
1837        max_iterations: 50,
1838        ..Default::default()
1839    };
1840
1841    let mut optimizer = QAOAOptimizer::new(config, graph, QAOAProblemType::MaxCut)?;
1842    let _result = optimizer.optimize()?;
1843
1844    let maxcut_time = start.elapsed().as_millis() as f64;
1845    results.insert("maxcut_qaoa_4_vertices".to_string(), maxcut_time);
1846
1847    Ok(results)
1848}
1849
1850#[cfg(test)]
1851mod tests {
1852    use super::*;
1853
1854    #[test]
1855    fn test_qaoa_optimizer_creation() {
1856        let graph = QAOAGraph {
1857            num_vertices: 3,
1858            adjacency_matrix: Array2::zeros((3, 3)),
1859            vertex_weights: vec![1.0; 3],
1860            edge_weights: HashMap::new(),
1861            constraints: Vec::new(),
1862        };
1863
1864        let config = QAOAConfig::default();
1865        let optimizer = QAOAOptimizer::new(config, graph, QAOAProblemType::MaxCut);
1866        assert!(optimizer.is_ok());
1867    }
1868
1869    #[test]
1870    fn test_maxcut_cost_evaluation() {
1871        let optimizer = create_test_optimizer();
1872        let bits = [true, false, true, false];
1873        let cost = optimizer.evaluate_maxcut_cost(&bits).unwrap();
1874        assert!(cost >= 0.0);
1875    }
1876
1877    #[test]
1878    fn test_parameter_initialization() {
1879        let config = QAOAConfig {
1880            num_layers: 3,
1881            ..Default::default()
1882        };
1883        let graph = create_test_graph();
1884
1885        let gammas = QAOAOptimizer::initialize_gammas(&config, &graph).unwrap();
1886        let betas = QAOAOptimizer::initialize_betas(&config, &graph).unwrap();
1887
1888        assert_eq!(gammas.len(), 3);
1889        assert_eq!(betas.len(), 3);
1890    }
1891
1892    #[test]
1893    fn test_constraint_checking() {
1894        let optimizer = create_test_optimizer();
1895        let solution = "1010";
1896        let feasible = optimizer.check_feasibility(solution).unwrap();
1897        assert!(feasible);
1898    }
1899
1900    fn create_test_optimizer() -> QAOAOptimizer {
1901        let graph = create_test_graph();
1902        let config = QAOAConfig::default();
1903        QAOAOptimizer::new(config, graph, QAOAProblemType::MaxCut).unwrap()
1904    }
1905
1906    fn create_test_graph() -> QAOAGraph {
1907        QAOAGraph {
1908            num_vertices: 4,
1909            adjacency_matrix: Array2::eye(4),
1910            vertex_weights: vec![1.0; 4],
1911            edge_weights: HashMap::new(),
1912            constraints: Vec::new(),
1913        }
1914    }
1915}
quantrs2_sim/qaoa_optimization.rs

quantrs2_sim/
qaoa_optimization.rs
