quantrs2-anneal 0.1.3

# Performance Optimization Guide

This guide provides comprehensive strategies for optimizing performance across all components of QuantRS2-Anneal, from algorithm selection to cloud service optimization.

## Performance Overview

### Algorithm Performance Characteristics

| Algorithm | Problem Size | Time Complexity | Memory | Quality | Best Use Case |
|-----------|--------------|-----------------|--------|---------|---------------|
| Classical Annealing | < 10K vars | O(n²·t) | O(n²) | Good | General purpose |
| Population Annealing | < 1K vars | O(p·n²·t) | O(p·n) | Excellent | High-quality solutions |
| Coherent Ising Machine | < 100K vars | O(n·t) | O(n) | Good | Large continuous problems |
| Reverse Annealing | < 5K vars | O(n²·t) | O(n²) | Excellent | Solution refinement |
| Hybrid Classical-Quantum | > 10K vars | Variable | Cloud | Good | Very large problems |

## Core Algorithm Optimization

### 1. Classical Annealing Optimization

```rust
use quantrs2_anneal::simulator::{
    ClassicalAnnealingSimulator, AnnealingParams, TemperatureSchedule, 
    NeighborhoodStrategy
};

// Optimized parameters for different problem types
let optimized_params = match problem_type {
    ProblemType::MaxCut => AnnealingParams {
        num_sweeps: 5000,
        num_repetitions: 50,
        initial_temperature: 10.0,
        final_temperature: 0.01,
        temperature_schedule: TemperatureSchedule::Exponential { decay: 0.99 },
        neighborhood_strategy: NeighborhoodStrategy::Random,
        parallel_tempering: Some(ParallelTemperingConfig {
            num_replicas: 8,
            exchange_frequency: 100,
        }),
    },
    ProblemType::GraphColoring => AnnealingParams {
        num_sweeps: 10000,
        num_repetitions: 20,
        initial_temperature: 5.0,
        final_temperature: 0.001,
        temperature_schedule: TemperatureSchedule::Linear,
        neighborhood_strategy: NeighborhoodStrategy::Greedy,
        parallel_tempering: None,
    },
    ProblemType::Portfolio => AnnealingParams {
        num_sweeps: 3000,
        num_repetitions: 100,
        initial_temperature: 2.0,
        final_temperature: 0.1,
        temperature_schedule: TemperatureSchedule::Logarithmic,
        neighborhood_strategy: NeighborhoodStrategy::Constraint,
        parallel_tempering: Some(ParallelTemperingConfig {
            num_replicas: 4,
            exchange_frequency: 50,
        }),
    },
};

// Use adaptive parameters that adjust based on problem characteristics
let adaptive_params = AnnealingParams::adaptive_for_problem(
    &ising_model,
    target_quality: 0.95,
    time_budget: Duration::from_secs(60),
)?;
```

### 2. Memory Optimization

```rust
use quantrs2_anneal::{
    ising::IsingModel,
    memory::{MemoryOptimizer, SparseMatrixConfig}
};

// Configure sparse matrix storage for large problems
let sparse_config = SparseMatrixConfig {
    storage_format: StorageFormat::CSR, // Compressed Sparse Row
    block_size: 1024,
    memory_pool_size: Some(1_000_000), // Pre-allocate 1MB
    compression_threshold: 0.1, // Compress if < 10% non-zero
};

let mut model = IsingModel::with_config(num_qubits, sparse_config)?;

// Use memory-efficient operations
let memory_optimizer = MemoryOptimizer::new();
memory_optimizer.optimize_model_memory(&mut model)?;

// Monitor memory usage
println!("Memory usage: {:.2} MB", model.memory_usage_mb());
println!("Sparsity: {:.2}%", model.sparsity_percentage());
```

### 3. Parallel Processing

```rust
use quantrs2_anneal::{
    simulator::ParallelAnnealingSimulator,
    parallel::{ThreadPoolConfig, WorkDistribution}
};

// Configure parallel execution
let thread_config = ThreadPoolConfig {
    num_threads: num_cpus::get(),
    stack_size: 2 * 1024 * 1024, // 2MB per thread
    work_distribution: WorkDistribution::Dynamic,
    load_balancing: true,
};

// Use parallel simulator for large problems
let parallel_simulator = ParallelAnnealingSimulator::new(
    base_params,
    thread_config,
)?;

// Run with work stealing for better load distribution
let results = parallel_simulator.solve_with_work_stealing(&model)?;

// Combine results from multiple threads
let best_result = results.into_iter()
    .min_by_key(|r| OrderedFloat(r.best_energy))
    .unwrap();
```

## Cloud Service Optimization

### 1. D-Wave Leap Optimization

```rust
use quantrs2_anneal::dwave::{
    DWaveClient, PerformanceOptimizer, SolverPerformanceMetrics
};

// Monitor solver performance
let performance_monitor = SolverPerformanceMetrics::new();

// Auto-select optimal solver based on performance history
let solver_selector = SolverSelector {
    category: SolverCategory::QPU,
    performance_criteria: vec![
        PerformanceCriterion::MinimizeQueueTime,
        PerformanceCriterion::MaximizeSolutionQuality,
        PerformanceCriterion::MinimizeChainBreaks,
    ],
    historical_data: performance_monitor.get_historical_data(),
    ..Default::default()
};

// Optimize problem parameters based on solver characteristics
let optimizer = PerformanceOptimizer::new();
let optimized_params = optimizer.optimize_for_solver(
    &problem_params,
    &selected_solver,
    &performance_history,
)?;

// Use batching for multiple similar problems
let batch_optimizer = BatchOptimizer::new();
let optimized_batch = batch_optimizer.optimize_batch_submission(
    &problems,
    &solver_performance_data,
)?;
```

#### D-Wave Specific Optimizations

```rust
// Optimize for specific D-Wave topologies
match solver.topology() {
    Topology::Chimera => {
        // Chimera-specific optimizations
        params.programming_thermalization = Some(1000);
        params.readout_thermalization = Some(100);
        params.annealing_time = Some(20);
    }
    Topology::Pegasus => {
        // Pegasus-specific optimizations
        params.programming_thermalization = Some(2000);
        params.readout_thermalization = Some(200);
        params.annealing_time = Some(50);
    }
    Topology::Zephyr => {
        // Zephyr-specific optimizations
        params.programming_thermalization = Some(1500);
        params.readout_thermalization = Some(150);
        params.annealing_time = Some(30);
    }
}

// Adaptive chain strength based on problem and hardware
let chain_strength_optimizer = ChainStrengthOptimizer::new();
let optimal_chain_strength = chain_strength_optimizer.optimize(
    &ising_model,
    &embedding,
    &solver_properties,
    target_chain_break_rate: 0.05,
)?;
```

### 2. AWS Braket Optimization

```rust
use quantrs2_anneal::braket::{
    BraketClient, CostOptimizer, DevicePerformanceAnalyzer
};

// Cost-performance optimization
let cost_optimizer = CostOptimizer::new();

// Analyze device performance vs. cost
let device_analyzer = DevicePerformanceAnalyzer::new();
let performance_data = device_analyzer.analyze_all_devices()?;

// Select optimal device for cost-performance ratio
let optimal_device = cost_optimizer.select_optimal_device(
    &problem_characteristics,
    &performance_data,
    cost_budget: 100.0, // $100
    quality_threshold: 0.9,
)?;

// Use spot pricing for non-urgent tasks
let spot_config = SpotPricingConfig {
    max_wait_time: Duration::from_hours(6),
    cost_savings_target: 0.3, // 30% savings
    fallback_device: Some("SV1".to_string()), // Simulator fallback
};

let task_result = client.submit_with_spot_pricing(
    &ising_model,
    &optimal_device,
    Some(params),
    Some(spot_config),
)?;
```

#### Device-Specific Optimizations

```rust
// Optimize parameters for different device types
match device.device_type {
    DeviceType::IonQ => {
        // IonQ optimization
        params.shots = std::cmp::min(params.shots, 10000); // Max shots limit
        params.optimization_level = 3; // Use maximum optimization
    }
    DeviceType::Rigetti => {
        // Rigetti optimization
        params.shots = std::cmp::min(params.shots, 100000);
        params.use_parametric_compilation = true;
    }
    DeviceType::Simulator => {
        // Simulator optimization
        params.shots = 100000; // Simulators are cheap
        params.noise_model = Some(NoiseModel::None);
    }
}
```

## Problem-Specific Optimizations

### 1. Max-Cut Problems

```rust
use quantrs2_anneal::applications::graph_problems::{
    MaxCutOptimizer, GraphAnalyzer
};

// Analyze graph structure for optimization opportunities
let graph_analyzer = GraphAnalyzer::new();
let graph_properties = graph_analyzer.analyze(&graph);

let maxcut_optimizer = MaxCutOptimizer::new();

// Use graph-specific optimizations
let optimized_model = if graph_properties.is_planar {
    maxcut_optimizer.optimize_for_planar_graph(&graph)?
} else if graph_properties.is_sparse {
    maxcut_optimizer.optimize_for_sparse_graph(&graph)?
} else {
    maxcut_optimizer.optimize_for_dense_graph(&graph)?
};

// Use degree-based variable ordering
let variable_ordering = maxcut_optimizer.compute_optimal_ordering(&graph);
let reordered_model = optimized_model.reorder_variables(&variable_ordering)?;
```

### 2. Portfolio Optimization

```rust
use quantrs2_anneal::applications::finance::{
    PortfolioOptimizer, RiskAnalyzer, ConstraintOptimizer
};

// Optimize constraint penalties
let constraint_optimizer = ConstraintOptimizer::new();
let optimized_penalties = constraint_optimizer.optimize_penalties(
    &portfolio_problem,
    target_violation_rate: 0.01,
    penalty_search_range: (1.0, 100.0),
)?;

// Use risk-adjusted optimization
let risk_analyzer = RiskAnalyzer::new();
let risk_factors = risk_analyzer.analyze_correlation_matrix(&returns)?;

let portfolio_optimizer = PortfolioOptimizer::with_risk_factors(risk_factors);
let optimized_formulation = portfolio_optimizer.create_risk_adjusted_qubo(
    &expected_returns,
    &covariance_matrix,
    risk_aversion: 0.5,
)?;
```

### 3. Logistics Optimization

```rust
use quantrs2_anneal::applications::logistics::{
    VehicleRoutingOptimizer, RoutingHeuristics
};

// Use problem-specific heuristics
let routing_optimizer = VehicleRoutingOptimizer::new();

// Pre-solve with heuristics for better initial solutions
let heuristic_solution = RoutingHeuristics::nearest_neighbor(&problem)?;
let warm_start_model = routing_optimizer.create_warm_start_model(
    &problem,
    &heuristic_solution,
)?;

// Use decomposition for large routing problems
if problem.num_customers() > 100 {
    let decomposed_problems = routing_optimizer.decompose_problem(
        &problem,
        cluster_size: 20,
        overlap_size: 5,
    )?;
    
    // Solve subproblems in parallel
    let subproblem_solutions: Vec<_> = decomposed_problems
        .into_par_iter()
        .map(|subproblem| solve_subproblem(subproblem))
        .collect::<Result<Vec<_>, _>>()?;
    
    // Merge solutions
    let final_solution = routing_optimizer.merge_solutions(subproblem_solutions)?;
}
```

## Advanced Optimization Techniques

### 1. Adaptive Parameter Tuning

```rust
use quantrs2_anneal::optimization::{
    AdaptiveParameterTuner, ParameterSpace, TuningStrategy
};

// Define parameter space to explore
let parameter_space = ParameterSpace::new()
    .add_parameter("temperature_schedule", vec!["linear", "exponential", "logarithmic"])
    .add_parameter("num_sweeps", (1000, 10000))
    .add_parameter("chain_strength", (0.1, 10.0))
    .add_parameter("annealing_time", (10, 100));

// Use Bayesian optimization for parameter tuning
let tuner = AdaptiveParameterTuner::new(
    TuningStrategy::BayesianOptimization {
        acquisition_function: AcquisitionFunction::ExpectedImprovement,
        num_initial_samples: 10,
        max_iterations: 50,
    }
);

// Optimize parameters for specific problem class
let optimal_params = tuner.optimize_for_problem_class(
    &problem_examples,
    &parameter_space,
    objective: OptimizationObjective::MinimizeEnergy,
)?;

println!("Optimal parameters found:");
for (name, value) in optimal_params {
    println!("  {}: {:?}", name, value);
}
```

### 2. Multi-Level Optimization

```rust
use quantrs2_anneal::optimization::MultiLevelOptimizer;

// Use coarse-to-fine optimization for large problems
let ml_optimizer = MultiLevelOptimizer::new()
    .add_level(CoarseLevel { reduction_factor: 0.25 })
    .add_level(MediumLevel { reduction_factor: 0.5 })
    .add_level(FineLevel { reduction_factor: 1.0 });

// Optimize across multiple resolution levels
let ml_solution = ml_optimizer.solve_multilevel(&large_problem)?;

println!("Multi-level optimization complete:");
println!("  Levels processed: {}", ml_solution.levels_processed);
println!("  Final energy: {}", ml_solution.best_energy);
println!("  Speedup: {:.2}x", ml_solution.speedup_factor);
```

### 3. Hybrid Optimization Strategies

```rust
use quantrs2_anneal::{
    hybrid::{HybridOptimizer, ClassicalQuantumBridge},
    classical::TabuSearch,
    quantum::QuantumAnnealingSimulator,
};

// Combine classical and quantum approaches
let hybrid_optimizer = HybridOptimizer::new()
    .add_classical_stage(
        TabuSearch::new(tabu_size: 100, max_iterations: 1000)
    )
    .add_quantum_stage(
        QuantumAnnealingSimulator::new(num_trotter_slices: 100)
    )
    .add_classical_refinement(
        LocalSearch::new(neighborhood_size: 50)
    );

// Use bridge between classical and quantum solutions
let bridge = ClassicalQuantumBridge::new();

// Solve with hybrid approach
let classical_solution = hybrid_optimizer.solve_classical(&problem)?;
let quantum_initial = bridge.classical_to_quantum(&classical_solution)?;
let quantum_solution = hybrid_optimizer.solve_quantum(&problem, Some(quantum_initial))?;
let final_solution = bridge.quantum_to_classical(&quantum_solution)?;
```

## Benchmarking and Profiling

### 1. Performance Benchmarking

```rust
use quantrs2_anneal::{
    benchmarks::{BenchmarkSuite, BenchmarkConfig, PerformanceReport},
    profiling::{Profiler, ProfileConfig}
};

// Set up comprehensive benchmarking
let benchmark_config = BenchmarkConfig {
    problem_sizes: vec![10, 50, 100, 500, 1000],
    algorithms: vec![
        Algorithm::ClassicalAnnealing,
        Algorithm::PopulationAnnealing,
        Algorithm::CoherentIsingMachine,
    ],
    num_trials: 10,
    timeout_per_trial: Duration::from_secs(300),
    metrics: vec![
        Metric::BestEnergy,
        Metric::TimeToSolution,
        Metric::MemoryUsage,
        Metric::SolutionQuality,
    ],
};

let benchmark_suite = BenchmarkSuite::new(benchmark_config);
let report = benchmark_suite.run_full_benchmark()?;

// Generate performance report
report.print_summary();
report.save_detailed_report("benchmark_results.json")?;
report.generate_plots("benchmark_plots/")?;
```

### 2. Real-time Profiling

```rust
// Profile algorithm performance
let profiler = Profiler::new(ProfileConfig {
    sample_rate: 1000, // Hz
    track_memory: true,
    track_cpu: true,
    track_custom_metrics: true,
});

profiler.start();

// Run optimization with profiling
let result = {
    let _guard = profiler.section("main_optimization");
    
    // Memory allocation profiling
    let _memory_guard = profiler.memory_section("model_creation");
    let model = create_large_ising_model(num_vars)?;
    
    // CPU profiling
    let _cpu_guard = profiler.cpu_section("annealing");
    simulator.solve(&model)?
};

profiler.stop();

// Analyze profile data
let profile_data = profiler.get_profile_data();
println!("Performance Profile:");
println!("  Total time: {:?}", profile_data.total_time);
println!("  Peak memory: {:.2} MB", profile_data.peak_memory_mb);
println!("  CPU utilization: {:.1}%", profile_data.avg_cpu_usage);

// Identify bottlenecks
let bottlenecks = profile_data.identify_bottlenecks();
for bottleneck in bottlenecks {
    println!("Bottleneck: {} - {:.2}% of total time", 
             bottleneck.section, bottleneck.percentage);
}
```

### 3. A/B Testing for Algorithm Selection

```rust
use quantrs2_anneal::testing::{ABTestFramework, AlgorithmComparison};

// Set up A/B testing framework
let ab_test = ABTestFramework::new()
    .add_algorithm_variant("classical", ClassicalAnnealingSimulator::default())
    .add_algorithm_variant("population", PopulationAnnealingSimulator::default())
    .add_algorithm_variant("coherent", CoherentIsingMachine::default());

// Run statistical comparison
let comparison_results = ab_test.run_comparison(
    &test_problems,
    confidence_level: 0.95,
    min_sample_size: 30,
)?;

// Analyze results
for (algorithm, stats) in comparison_results.iter() {
    println!("Algorithm: {}", algorithm);
    println!("  Mean energy: {:.6} ± {:.6}", stats.mean_energy, stats.std_energy);
    println!("  Success rate: {:.2}%", stats.success_rate * 100.0);
    println!("  Avg. time: {:?}", stats.avg_time);
}

// Statistical significance testing
let significance_test = comparison_results.statistical_significance_test();
println!("Statistical significance: p-value = {:.6}", significance_test.p_value);
```

## Best Practices Summary

### 1. Algorithm Selection Guidelines

```rust
fn select_optimal_algorithm(problem: &OptimizationProblem) -> Box<dyn Optimizer> {
    match (problem.size(), problem.structure(), problem.constraints()) {
        // Small, dense problems
        (size, _, _) if size < 100 => {
            Box::new(ClassicalAnnealingSimulator::with_high_quality_params())
        }
        
        // Medium problems with high-quality requirements
        (size, _, ConstraintType::Hard) if size < 1000 => {
            Box::new(PopulationAnnealingSimulator::default())
        }
        
        // Large, sparse problems
        (size, StructureType::Sparse, _) if size > 1000 => {
            Box::new(CoherentIsingMachine::default())
        }
        
        // Very large problems
        (size, _, _) if size > 10000 => {
            Box::new(HybridCloudOptimizer::default())
        }
        
        // Default case
        _ => Box::new(ClassicalAnnealingSimulator::default())
    }
}
```

### 2. Memory Management

- Use sparse representations for large, sparse problems
- Pre-allocate memory pools for repeated optimizations
- Monitor memory usage and implement garbage collection
- Use memory mapping for very large datasets

### 3. Parallel Processing

- Use thread pools for CPU-intensive computations
- Implement work-stealing for dynamic load balancing
- Consider NUMA topology for multi-socket systems
- Use async/await for I/O-bound cloud operations

### 4. Cloud Optimization

- Monitor queue times and adjust submission timing
- Use batch submission for multiple similar problems
- Implement cost tracking and budget management
- Cache embeddings and parameter configurations

## Performance Monitoring Dashboard

```rust
use quantrs2_anneal::monitoring::{PerformanceDashboard, Metrics};

// Set up real-time performance monitoring
let dashboard = PerformanceDashboard::new()
    .add_metric(Metrics::ThroughputProblemsPerSecond)
    .add_metric(Metrics::AverageEnergyQuality)
    .add_metric(Metrics::CloudCostPerProblem)
    .add_metric(Metrics::MemoryUtilization)
    .add_metric(Metrics::CPUUtilization);

// Start monitoring
dashboard.start_monitoring();

// Get real-time statistics
let current_stats = dashboard.get_current_statistics();
println!("Current Performance:");
println!("  Throughput: {:.2} problems/sec", current_stats.throughput);
println!("  Avg. Quality: {:.4}", current_stats.avg_quality);
println!("  Cost Rate: ${:.4}/problem", current_stats.cost_per_problem);

// Set up alerts
dashboard.add_alert(
    AlertCondition::ThroughputBelow(0.1),
    AlertAction::EmailNotification("admin@example.com"),
);

dashboard.add_alert(
    AlertCondition::CostAbove(10.0),
    AlertAction::PauseSubmissions,
);
```

This comprehensive performance optimization guide should help you get the best performance from QuantRS2-Anneal across all use cases and deployment scenarios.