quantrs2_tytan/
quantum_advantage_analysis.rs

1//! Quantum Advantage Analysis Suite
2//!
3//! This module provides tools to analyze when quantum optimization approaches
4//! provide theoretical and practical advantages over classical methods.
5
6#![allow(dead_code)]
7
8use scirs2_core::ndarray::Array2;
9use serde::{Deserialize, Serialize};
10use std::collections::HashMap;
11use std::time::{Duration, Instant};
12
13/// Quantum advantage analysis engine
14pub struct QuantumAdvantageAnalyzer {
15    /// Configuration for analysis
16    config: AnalysisConfig,
17    /// Classical complexity estimator
18    classical_estimator: ClassicalComplexityEstimator,
19    /// Quantum resource estimator
20    quantum_estimator: QuantumResourceEstimator,
21    /// Benchmarking suite
22    benchmarker: QuantumSupremacyBenchmarker,
23}
24
25#[derive(Debug, Clone, Serialize, Deserialize)]
26pub struct AnalysisConfig {
27    /// Problem size range for analysis
28    pub problem_size_range: (usize, usize),
29    /// Number of samples for statistical analysis
30    pub num_samples: usize,
31    /// Confidence level for advantage detection
32    pub confidence_level: f64,
33    /// Classical algorithms to compare against
34    pub classical_baselines: Vec<ClassicalAlgorithm>,
35    /// Quantum algorithms to analyze
36    pub quantum_algorithms: Vec<QuantumAlgorithm>,
37    /// Hardware models to consider
38    pub hardware_models: Vec<HardwareModel>,
39    /// Noise models for realistic analysis
40    pub noise_models: Vec<NoiseModel>,
41}
42
43impl Default for AnalysisConfig {
44    fn default() -> Self {
45        Self {
46            problem_size_range: (10, 1000),
47            num_samples: 100,
48            confidence_level: 0.95,
49            classical_baselines: vec![
50                ClassicalAlgorithm::SimulatedAnnealing,
51                ClassicalAlgorithm::TabuSearch,
52                ClassicalAlgorithm::GeneticAlgorithm,
53                ClassicalAlgorithm::BranchAndBound,
54            ],
55            quantum_algorithms: vec![
56                QuantumAlgorithm::QuantumAnnealing,
57                QuantumAlgorithm::QAOA,
58                QuantumAlgorithm::VQE,
59                QuantumAlgorithm::QFAST,
60            ],
61            hardware_models: vec![
62                HardwareModel::IdealQuantum,
63                HardwareModel::NoisyNISQ { error_rate: 0.001 },
64                HardwareModel::DigitalAnnealer,
65                HardwareModel::PhotonicIsing,
66            ],
67            noise_models: vec![
68                NoiseModel::None,
69                NoiseModel::Depolarizing { rate: 0.001 },
70                NoiseModel::AmplitudeDamping { rate: 0.01 },
71                NoiseModel::Realistic {
72                    decoherence_time: Duration::from_micros(100),
73                },
74            ],
75        }
76    }
77}
78
79#[derive(Debug, Clone, Serialize, Deserialize, PartialEq, Eq, Hash)]
80pub enum ClassicalAlgorithm {
81    SimulatedAnnealing,
82    TabuSearch,
83    GeneticAlgorithm,
84    BranchAndBound,
85    ConstraintProgramming,
86    LinearProgramming,
87    SDP,
88}
89
90#[derive(Debug, Clone, Serialize, Deserialize, PartialEq, Eq, Hash)]
91pub enum QuantumAlgorithm {
92    QuantumAnnealing,
93    QAOA,
94    VQE,
95    QFAST,
96    QuantumWalk,
97    AdiabaticQuantumComputing,
98}
99
100#[derive(Debug, Clone, Serialize, Deserialize)]
101pub enum HardwareModel {
102    IdealQuantum,
103    NoisyNISQ { error_rate: f64 },
104    DigitalAnnealer,
105    PhotonicIsing,
106    CoherentIsingMachine,
107    SuperconductingAnnealer,
108}
109
110#[derive(Debug, Clone, Serialize, Deserialize)]
111pub enum NoiseModel {
112    None,
113    Depolarizing { rate: f64 },
114    AmplitudeDamping { rate: f64 },
115    PhaseDamping { rate: f64 },
116    Realistic { decoherence_time: Duration },
117}
118
119/// Results of quantum advantage analysis
120#[derive(Debug, Clone, Serialize, Deserialize)]
121pub struct AdvantageAnalysisResult {
122    /// Problem characteristics
123    pub problem_info: ProblemCharacteristics,
124    /// Classical performance estimates
125    pub classical_performance: HashMap<ClassicalAlgorithm, PerformanceMetrics>,
126    /// Quantum performance estimates
127    pub quantum_performance: HashMap<QuantumAlgorithm, QuantumPerformanceMetrics>,
128    /// Advantage analysis
129    pub advantage_analysis: AdvantageAnalysis,
130    /// Threshold analysis
131    pub threshold_analysis: ThresholdAnalysis,
132    /// Recommendations
133    pub recommendations: Vec<AlgorithmRecommendation>,
134}
135
136#[derive(Debug, Clone, Serialize, Deserialize)]
137pub struct ProblemCharacteristics {
138    /// Problem type
139    pub problem_type: String,
140    /// Number of variables
141    pub num_variables: usize,
142    /// Problem density (fraction of non-zero coefficients)
143    pub density: f64,
144    /// Connectivity structure
145    pub connectivity: ConnectivityStructure,
146    /// Problem hardness indicators
147    pub hardness_indicators: HardnessIndicators,
148    /// Symmetry properties
149    pub symmetries: Vec<SymmetryType>,
150}
151
152#[derive(Debug, Clone, Serialize, Deserialize)]
153pub enum ConnectivityStructure {
154    FullyConnected,
155    Sparse { avg_degree: f64 },
156    Grid { dimensions: Vec<usize> },
157    Tree,
158    Planar,
159    SmallWorld { clustering_coefficient: f64 },
160}
161
162#[derive(Debug, Clone, Serialize, Deserialize)]
163pub struct HardnessIndicators {
164    /// Estimated classical complexity class
165    pub complexity_class: ComplexityClass,
166    /// Problem-specific difficulty metrics
167    pub difficulty_metrics: HashMap<String, f64>,
168    /// Approximation ratio bounds
169    pub approximation_bounds: Option<(f64, f64)>,
170}
171
172#[derive(Debug, Clone, Serialize, Deserialize)]
173pub enum ComplexityClass {
174    P,
175    NP,
176    NPComplete,
177    NPHard,
178    PSpace,
179    ExpTime,
180}
181
182#[derive(Debug, Clone, Serialize, Deserialize)]
183pub enum SymmetryType {
184    Permutation,
185    Reflection,
186    Rotation,
187    Translation,
188    Scale,
189}
190
191#[derive(Debug, Clone, Serialize, Deserialize)]
192pub struct PerformanceMetrics {
193    /// Time complexity estimate
194    pub time_complexity: TimeComplexity,
195    /// Space complexity estimate
196    pub space_complexity: SpaceComplexity,
197    /// Solution quality estimate
198    pub solution_quality: QualityMetrics,
199    /// Success probability
200    pub success_probability: f64,
201    /// Scaling behavior
202    pub scaling_behavior: ScalingBehavior,
203}
204
205#[derive(Debug, Clone, Serialize, Deserialize)]
206pub struct QuantumPerformanceMetrics {
207    /// Base performance metrics
208    pub base_metrics: PerformanceMetrics,
209    /// Quantum-specific metrics
210    pub quantum_metrics: QuantumSpecificMetrics,
211    /// Hardware requirements
212    pub hardware_requirements: HardwareRequirements,
213    /// Noise sensitivity
214    pub noise_sensitivity: NoiseSensitivity,
215}
216
217#[derive(Debug, Clone, Serialize, Deserialize)]
218pub struct QuantumSpecificMetrics {
219    /// Number of qubits required
220    pub qubits_required: usize,
221    /// Circuit depth
222    pub circuit_depth: usize,
223    /// Number of quantum operations
224    pub quantum_operations: usize,
225    /// Entanglement measures
226    pub entanglement_measures: EntanglementMeasures,
227    /// Coherence time requirements
228    pub coherence_time_required: Duration,
229}
230
231#[derive(Debug, Clone, Serialize, Deserialize)]
232pub struct HardwareRequirements {
233    /// Minimum qubit count
234    pub min_qubits: usize,
235    /// Required connectivity
236    pub connectivity_requirements: ConnectivityRequirement,
237    /// Gate fidelity requirements
238    pub gate_fidelity_threshold: f64,
239    /// Measurement fidelity requirements
240    pub measurement_fidelity_threshold: f64,
241    /// Operating temperature requirements
242    pub temperature_requirements: Option<f64>,
243}
244
245#[derive(Debug, Clone, Serialize, Deserialize)]
246pub enum ConnectivityRequirement {
247    AllToAll,
248    NearestNeighbor,
249    Specific { required_edges: Vec<(usize, usize)> },
250    MinDegree { min_degree: usize },
251}
252
253#[derive(Debug, Clone, Serialize, Deserialize)]
254pub struct NoiseSensitivity {
255    /// Threshold error rates for different noise types
256    pub error_thresholds: HashMap<String, f64>,
257    /// Degradation rates under noise
258    pub degradation_rates: HashMap<String, f64>,
259    /// Error mitigation effectiveness
260    pub mitigation_effectiveness: HashMap<String, f64>,
261}
262
263#[derive(Debug, Clone, Serialize, Deserialize)]
264pub struct EntanglementMeasures {
265    /// Average entanglement entropy
266    pub avg_entanglement_entropy: f64,
267    /// Maximum entanglement entropy
268    pub max_entanglement_entropy: f64,
269    /// Entanglement depth
270    pub entanglement_depth: usize,
271    /// Multipartite entanglement measures
272    pub multipartite_measures: HashMap<String, f64>,
273}
274
275#[derive(Debug, Clone, Serialize, Deserialize)]
276pub struct TimeComplexity {
277    /// Best case complexity
278    pub best_case: ComplexityFunction,
279    /// Average case complexity
280    pub average_case: ComplexityFunction,
281    /// Worst case complexity
282    pub worst_case: ComplexityFunction,
283}
284
285#[derive(Debug, Clone, Serialize, Deserialize)]
286pub struct SpaceComplexity {
287    /// Memory requirements
288    pub memory_complexity: ComplexityFunction,
289    /// Storage requirements
290    pub storage_complexity: ComplexityFunction,
291}
292
293#[derive(Debug, Clone, Serialize, Deserialize)]
294pub enum ComplexityFunction {
295    Constant,
296    Logarithmic,
297    Linear,
298    Linearithmic,
299    Quadratic,
300    Cubic,
301    Polynomial { degree: f64 },
302    Exponential { base: f64 },
303    Factorial,
304}
305
306#[derive(Debug, Clone, Serialize, Deserialize)]
307pub struct QualityMetrics {
308    /// Expected approximation ratio
309    pub approximation_ratio: f64,
310    /// Solution variance
311    pub solution_variance: f64,
312    /// Probability of optimal solution
313    pub optimal_probability: f64,
314    /// Expected energy gap
315    pub energy_gap: f64,
316}
317
318#[derive(Debug, Clone, Serialize, Deserialize)]
319pub struct ScalingBehavior {
320    /// Scaling exponent
321    pub scaling_exponent: f64,
322    /// Scaling constant
323    pub scaling_constant: f64,
324    /// Confidence interval
325    pub confidence_interval: (f64, f64),
326    /// R-squared of fit
327    pub fit_quality: f64,
328}
329
330#[derive(Debug, Clone, Serialize, Deserialize)]
331pub struct AdvantageAnalysis {
332    /// Overall advantage assessment
333    pub has_quantum_advantage: bool,
334    /// Advantage confidence level
335    pub confidence: f64,
336    /// Advantage factors by metric
337    pub advantage_factors: HashMap<String, f64>,
338    /// Conditional advantages
339    pub conditional_advantages: Vec<ConditionalAdvantage>,
340    /// Break-even analysis
341    pub break_even_points: HashMap<String, f64>,
342}
343
344#[derive(Debug, Clone, Serialize, Deserialize)]
345pub struct ConditionalAdvantage {
346    /// Conditions under which advantage exists
347    pub conditions: Vec<String>,
348    /// Advantage magnitude under these conditions
349    pub advantage_magnitude: f64,
350    /// Probability conditions are met
351    pub condition_probability: f64,
352}
353
354#[derive(Debug, Clone, Serialize, Deserialize)]
355pub struct ThresholdAnalysis {
356    /// Problem size thresholds for quantum advantage
357    pub size_thresholds: HashMap<String, usize>,
358    /// Noise thresholds for quantum advantage
359    pub noise_thresholds: HashMap<String, f64>,
360    /// Hardware requirement thresholds
361    pub hardware_thresholds: HashMap<String, f64>,
362    /// Time-to-advantage predictions
363    pub time_to_advantage: HashMap<String, Duration>,
364}
365
366#[derive(Debug, Clone, Serialize, Deserialize)]
367pub struct AlgorithmRecommendation {
368    /// Recommended algorithm
369    pub algorithm: String,
370    /// Algorithm type (classical or quantum)
371    pub algorithm_type: AlgorithmType,
372    /// Confidence in recommendation
373    pub confidence: f64,
374    /// Expected performance
375    pub expected_performance: PerformanceMetrics,
376    /// Justification for recommendation
377    pub justification: String,
378    /// Alternative algorithms
379    pub alternatives: Vec<String>,
380}
381
382#[derive(Debug, Clone, Serialize, Deserialize)]
383pub enum AlgorithmType {
384    Classical,
385    Quantum,
386    Hybrid,
387}
388
389/// Classical complexity estimator
390pub struct ClassicalComplexityEstimator {
391    /// Known complexity results
392    complexity_database: HashMap<String, ComplexityInfo>,
393    /// Heuristic estimators
394    heuristic_estimators: Vec<Box<dyn ComplexityHeuristic>>,
395}
396
397pub trait ComplexityHeuristic {
398    fn estimate_complexity(&self, problem: &ProblemCharacteristics) -> PerformanceMetrics;
399    fn algorithm_name(&self) -> &str;
400}
401
402#[derive(Debug, Clone)]
403pub struct ComplexityInfo {
404    pub time_complexity: TimeComplexity,
405    pub space_complexity: SpaceComplexity,
406    pub approximation_bounds: Option<(f64, f64)>,
407    pub practical_scaling: ScalingBehavior,
408}
409
410/// Quantum resource estimator
411pub struct QuantumResourceEstimator {
412    /// Quantum algorithm database
413    algorithm_database: HashMap<String, QuantumAlgorithmInfo>,
414    /// Hardware model database
415    hardware_database: HashMap<String, HardwareCharacteristics>,
416}
417
418#[derive(Debug, Clone)]
419pub struct QuantumAlgorithmInfo {
420    pub resource_requirements: HardwareRequirements,
421    pub performance_model: QuantumPerformanceModel,
422    pub noise_sensitivity: NoiseSensitivity,
423    pub theoretical_advantage: Option<AdvantageEstimate>,
424}
425
426pub struct QuantumPerformanceModel {
427    pub time_to_solution: Box<dyn Fn(usize) -> Duration>,
428    pub success_probability: Box<dyn Fn(usize, f64) -> f64>,
429    pub resource_scaling: ScalingBehavior,
430}
431
432impl std::fmt::Debug for QuantumPerformanceModel {
433    fn fmt(&self, f: &mut std::fmt::Formatter<'_>) -> std::fmt::Result {
434        f.debug_struct("QuantumPerformanceModel")
435            .field("time_to_solution", &"<function>")
436            .field("success_probability", &"<function>")
437            .field("resource_scaling", &self.resource_scaling)
438            .finish()
439    }
440}
441
442impl Clone for QuantumPerformanceModel {
443    fn clone(&self) -> Self {
444        Self {
445            time_to_solution: Box::new(|_| Duration::from_secs(1)),
446            success_probability: Box::new(|_, _| 0.5),
447            resource_scaling: self.resource_scaling.clone(),
448        }
449    }
450}
451
452#[derive(Debug, Clone)]
453pub struct AdvantageEstimate {
454    pub speedup_factor: f64,
455    pub advantage_type: AdvantageType,
456    pub confidence_level: f64,
457    pub conditions: Vec<String>,
458}
459
460#[derive(Debug, Clone)]
461pub enum AdvantageType {
462    Polynomial { degree_reduction: f64 },
463    Exponential { base_improvement: f64 },
464    Constant { factor: f64 },
465    Conditional { conditions: Vec<String> },
466}
467
468#[derive(Debug, Clone)]
469pub struct HardwareCharacteristics {
470    pub qubit_count: usize,
471    pub connectivity: ConnectivityStructure,
472    pub gate_fidelities: HashMap<String, f64>,
473    pub measurement_fidelity: f64,
474    pub coherence_times: HashMap<String, Duration>,
475    pub operating_parameters: HashMap<String, f64>,
476}
477
478/// Quantum supremacy benchmarker
479pub struct QuantumSupremacyBenchmarker {
480    /// Benchmark problem generators
481    problem_generators: Vec<Box<dyn BenchmarkProblemGenerator>>,
482    /// Performance trackers
483    performance_trackers: HashMap<String, PerformanceTracker>,
484}
485
486pub trait BenchmarkProblemGenerator {
487    fn generate_problem(&self, size: usize, seed: Option<u64>) -> BenchmarkProblem;
488    fn problem_type(&self) -> &str;
489    fn difficulty_level(&self) -> DifficultyLevel;
490}
491
492#[derive(Debug, Clone)]
493pub struct BenchmarkProblem {
494    pub qubo: Array2<f64>,
495    pub metadata: ProblemMetadata,
496    pub known_optimal: Option<f64>,
497    pub theoretical_properties: TheoreticalProperties,
498}
499
500#[derive(Debug, Clone)]
501pub struct ProblemMetadata {
502    pub problem_type: String,
503    pub size: usize,
504    pub density: f64,
505    pub generation_seed: Option<u64>,
506    pub generation_time: Instant,
507}
508
509#[derive(Debug, Clone)]
510pub struct TheoreticalProperties {
511    pub complexity_class: ComplexityClass,
512    pub approximation_hardness: Option<f64>,
513    pub spectral_gap: Option<f64>,
514    pub landscape_features: LandscapeFeatures,
515}
516
517#[derive(Debug, Clone)]
518pub struct LandscapeFeatures {
519    pub num_local_minima: Option<usize>,
520    pub barrier_heights: Vec<f64>,
521    pub correlation_length: f64,
522    pub ruggedness_measure: f64,
523}
524
525#[derive(Debug, Clone)]
526pub enum DifficultyLevel {
527    Easy,
528    Medium,
529    Hard,
530    ExtremelyHard,
531}
532
533#[derive(Debug, Clone)]
534pub struct PerformanceTracker {
535    pub algorithm_name: String,
536    pub performance_history: Vec<PerformanceDataPoint>,
537    pub scaling_model: Option<ScalingBehavior>,
538}
539
540#[derive(Debug, Clone)]
541pub struct PerformanceDataPoint {
542    pub problem_size: usize,
543    pub execution_time: Duration,
544    pub solution_quality: f64,
545    pub success_rate: f64,
546    pub timestamp: Instant,
547}
548
549impl QuantumAdvantageAnalyzer {
550    /// Create new quantum advantage analyzer
551    pub fn new(config: AnalysisConfig) -> Self {
552        Self {
553            config,
554            classical_estimator: ClassicalComplexityEstimator::new(),
555            quantum_estimator: QuantumResourceEstimator::new(),
556            benchmarker: QuantumSupremacyBenchmarker::new(),
557        }
558    }
559
560    /// Analyze quantum advantage for a given problem
561    pub fn analyze_advantage(
562        &self,
563        qubo: &Array2<f64>,
564        problem_metadata: Option<ProblemMetadata>,
565    ) -> Result<AdvantageAnalysisResult, String> {
566        // Characterize the problem
567        let problem_chars = self.characterize_problem(qubo, problem_metadata)?;
568
569        // Estimate classical performance
570        let classical_performance = self
571            .classical_estimator
572            .estimate_classical_performance(&problem_chars, &self.config.classical_baselines)?;
573
574        // Estimate quantum performance
575        let quantum_performance = self
576            .quantum_estimator
577            .estimate_quantum_performance(&problem_chars, &self.config.quantum_algorithms)?;
578
579        // Perform advantage analysis
580        let advantage_analysis = self.analyze_quantum_advantage(
581            &classical_performance,
582            &quantum_performance,
583            &problem_chars,
584        )?;
585
586        // Perform threshold analysis
587        let threshold_analysis =
588            self.analyze_thresholds(&classical_performance, &quantum_performance, &problem_chars)?;
589
590        // Generate recommendations
591        let recommendations = self.generate_recommendations(
592            &classical_performance,
593            &quantum_performance,
594            &advantage_analysis,
595            &problem_chars,
596        )?;
597
598        Ok(AdvantageAnalysisResult {
599            problem_info: problem_chars,
600            classical_performance,
601            quantum_performance,
602            advantage_analysis,
603            threshold_analysis,
604            recommendations,
605        })
606    }
607
608    /// Characterize problem structure and properties
609    fn characterize_problem(
610        &self,
611        qubo: &Array2<f64>,
612        metadata: Option<ProblemMetadata>,
613    ) -> Result<ProblemCharacteristics, String> {
614        let num_variables = qubo.shape()[0];
615
616        // Calculate density
617        let non_zero_count = qubo.iter().filter(|&&x| x.abs() > 1e-10).count();
618        let density = non_zero_count as f64 / (num_variables * num_variables) as f64;
619
620        // Analyze connectivity
621        let connectivity = self.analyze_connectivity(qubo)?;
622
623        // Compute hardness indicators
624        let hardness_indicators = self.compute_hardness_indicators(qubo)?;
625
626        // Detect symmetries
627        let symmetries = self.detect_symmetries(qubo)?;
628
629        Ok(ProblemCharacteristics {
630            problem_type: metadata
631                .as_ref()
632                .map_or_else(|| "Unknown".to_string(), |m| m.problem_type.clone()),
633            num_variables,
634            density,
635            connectivity,
636            hardness_indicators,
637            symmetries,
638        })
639    }
640
641    /// Analyze connectivity structure of QUBO
642    fn analyze_connectivity(&self, qubo: &Array2<f64>) -> Result<ConnectivityStructure, String> {
643        let n = qubo.shape()[0];
644        let mut edge_count = 0;
645        let mut degree_sum = 0;
646
647        for i in 0..n {
648            let mut degree = 0;
649            for j in 0..n {
650                if i != j && qubo[[i, j]].abs() > 1e-10 {
651                    if i < j {
652                        edge_count += 1;
653                    }
654                    degree += 1;
655                }
656            }
657            degree_sum += degree;
658        }
659
660        let avg_degree = degree_sum as f64 / n as f64;
661
662        // Determine connectivity type based on density and structure
663        if edge_count == n * (n - 1) / 2 {
664            Ok(ConnectivityStructure::FullyConnected)
665        } else if avg_degree < n as f64 / 4.0 {
666            Ok(ConnectivityStructure::Sparse { avg_degree })
667        } else {
668            // Check for grid-like structure (simplified heuristic)
669            let expected_grid_degree = 4.0; // For 2D grid
670            if (avg_degree - expected_grid_degree).abs() < 1.0 {
671                Ok(ConnectivityStructure::Grid {
672                    dimensions: vec![(n as f64).sqrt() as usize, (n as f64).sqrt() as usize],
673                })
674            } else {
675                Ok(ConnectivityStructure::Sparse { avg_degree })
676            }
677        }
678    }
679
680    /// Compute hardness indicators for the problem
681    fn compute_hardness_indicators(
682        &self,
683        qubo: &Array2<f64>,
684    ) -> Result<HardnessIndicators, String> {
685        let n = qubo.shape()[0];
686
687        // Estimate complexity class based on structure
688        let complexity_class = if n < 100 {
689            ComplexityClass::P
690        } else {
691            ComplexityClass::NPComplete // Most QUBO problems are NP-complete
692        };
693
694        // Compute difficulty metrics
695        let mut difficulty_metrics = HashMap::new();
696
697        // Compute coefficient variance as a measure of heterogeneity
698        let coeffs: Vec<f64> = qubo.iter().copied().collect();
699        let mean = coeffs.iter().sum::<f64>() / coeffs.len() as f64;
700        let variance = coeffs.iter().map(|x| (x - mean).powi(2)).sum::<f64>() / coeffs.len() as f64;
701        difficulty_metrics.insert("coefficient_variance".to_string(), variance);
702
703        // Compute spectral gap estimate (simplified)
704        let max_coeff = coeffs.iter().map(|x| x.abs()).fold(0.0, f64::max);
705        let min_coeff = coeffs
706            .iter()
707            .map(|x| x.abs())
708            .filter(|&x| x > 1e-10)
709            .fold(f64::INFINITY, f64::min);
710        if min_coeff.is_finite() {
711            difficulty_metrics.insert("dynamic_range".to_string(), max_coeff / min_coeff);
712        }
713
714        // Frustration measure (simplified)
715        let mut frustration = 0.0;
716        for i in 0..n {
717            for j in i + 1..n {
718                if qubo[[i, j]] > 0.0 {
719                    frustration += qubo[[i, j]];
720                }
721            }
722        }
723        difficulty_metrics.insert("frustration_measure".to_string(), frustration);
724
725        Ok(HardnessIndicators {
726            complexity_class,
727            difficulty_metrics,
728            approximation_bounds: None, // Would require more sophisticated analysis
729        })
730    }
731
732    /// Detect symmetries in the QUBO
733    fn detect_symmetries(&self, qubo: &Array2<f64>) -> Result<Vec<SymmetryType>, String> {
734        let mut symmetries = Vec::new();
735        let n = qubo.shape()[0];
736
737        // Check for permutation symmetries (simplified check)
738        let mut is_symmetric = true;
739        for i in 0..n {
740            for j in 0..n {
741                if (qubo[[i, j]] - qubo[[j, i]]).abs() > 1e-10 {
742                    is_symmetric = false;
743                    break;
744                }
745            }
746            if !is_symmetric {
747                break;
748            }
749        }
750
751        if is_symmetric {
752            symmetries.push(SymmetryType::Permutation);
753        }
754
755        // Additional symmetry detection could be added here
756
757        Ok(symmetries)
758    }
759
760    /// Analyze quantum advantage by comparing performance metrics
761    fn analyze_quantum_advantage(
762        &self,
763        classical_perf: &HashMap<ClassicalAlgorithm, PerformanceMetrics>,
764        quantum_perf: &HashMap<QuantumAlgorithm, QuantumPerformanceMetrics>,
765        _problem_chars: &ProblemCharacteristics,
766    ) -> Result<AdvantageAnalysis, String> {
767        let mut advantage_factors = HashMap::new();
768        let mut conditional_advantages = Vec::new();
769        let break_even_points = HashMap::new();
770
771        // Find best classical performance
772        let best_classical = classical_perf.values().min_by(|a, b| {
773            a.time_complexity
774                .average_case
775                .partial_cmp(&b.time_complexity.average_case)
776                .unwrap_or(std::cmp::Ordering::Equal)
777        });
778
779        // Find best quantum performance
780        let best_quantum = quantum_perf.values().min_by(|a, b| {
781            a.base_metrics
782                .time_complexity
783                .average_case
784                .partial_cmp(&b.base_metrics.time_complexity.average_case)
785                .unwrap_or(std::cmp::Ordering::Equal)
786        });
787
788        let has_quantum_advantage = if let (Some(classical), Some(quantum)) =
789            (best_classical, best_quantum)
790        {
791            // Simplified advantage analysis based on success probability and scaling
792            let classical_quality = classical.solution_quality.approximation_ratio;
793            let quantum_quality = quantum.base_metrics.solution_quality.approximation_ratio;
794
795            advantage_factors.insert("quality".to_string(), quantum_quality / classical_quality);
796
797            let classical_success = classical.success_probability;
798            let quantum_success = quantum.base_metrics.success_probability;
799
800            advantage_factors.insert(
801                "success_rate".to_string(),
802                quantum_success / classical_success,
803            );
804
805            // Consider noise effects
806            if quantum
807                .noise_sensitivity
808                .error_thresholds
809                .values()
810                .any(|&x| x < 0.01)
811            {
812                conditional_advantages.push(ConditionalAdvantage {
813                    conditions: vec!["Low noise environment".to_string()],
814                    advantage_magnitude: 2.0,
815                    condition_probability: 0.3,
816                });
817            }
818
819            quantum_quality > classical_quality || quantum_success > classical_success
820        } else {
821            false
822        };
823
824        // Compute overall confidence (simplified)
825        let confidence = if has_quantum_advantage {
826            0.7 // This would be computed based on statistical analysis
827        } else {
828            0.3
829        };
830
831        Ok(AdvantageAnalysis {
832            has_quantum_advantage,
833            confidence,
834            advantage_factors,
835            conditional_advantages,
836            break_even_points,
837        })
838    }
839
840    /// Analyze thresholds for quantum advantage
841    fn analyze_thresholds(
842        &self,
843        _classical_perf: &HashMap<ClassicalAlgorithm, PerformanceMetrics>,
844        quantum_perf: &HashMap<QuantumAlgorithm, QuantumPerformanceMetrics>,
845        problem_chars: &ProblemCharacteristics,
846    ) -> Result<ThresholdAnalysis, String> {
847        let mut size_thresholds = HashMap::new();
848        let mut noise_thresholds = HashMap::new();
849        let mut hardware_thresholds = HashMap::new();
850        let mut time_to_advantage = HashMap::new();
851
852        // Estimate problem size threshold
853        let estimated_threshold = if problem_chars.num_variables < 100 {
854            500 // Classical methods likely better for small problems
855        } else {
856            100 // Quantum advantage may exist for larger problems
857        };
858
859        size_thresholds.insert("general".to_string(), estimated_threshold);
860
861        // Noise thresholds
862        for (alg, perf) in quantum_perf {
863            if let Some(min_threshold) = perf
864                .noise_sensitivity
865                .error_thresholds
866                .values()
867                .min_by(|a, b| a.partial_cmp(b).unwrap_or(std::cmp::Ordering::Equal))
868            {
869                noise_thresholds.insert(format!("{alg:?}"), *min_threshold);
870            }
871        }
872
873        // Hardware thresholds
874        for (alg, perf) in quantum_perf {
875            hardware_thresholds.insert(
876                format!("{alg:?}_qubits"),
877                perf.hardware_requirements.min_qubits as f64,
878            );
879            hardware_thresholds.insert(
880                format!("{alg:?}_fidelity"),
881                perf.hardware_requirements.gate_fidelity_threshold,
882            );
883        }
884
885        // Time to advantage (simplified projection)
886        time_to_advantage.insert(
887            "conservative".to_string(),
888            Duration::from_secs(365 * 24 * 3600 * 5),
889        ); // 5 years
890        time_to_advantage.insert(
891            "optimistic".to_string(),
892            Duration::from_secs(365 * 24 * 3600 * 2),
893        ); // 2 years
894
895        Ok(ThresholdAnalysis {
896            size_thresholds,
897            noise_thresholds,
898            hardware_thresholds,
899            time_to_advantage,
900        })
901    }
902
903    /// Generate algorithm recommendations
904    fn generate_recommendations(
905        &self,
906        classical_perf: &HashMap<ClassicalAlgorithm, PerformanceMetrics>,
907        quantum_perf: &HashMap<QuantumAlgorithm, QuantumPerformanceMetrics>,
908        advantage_analysis: &AdvantageAnalysis,
909        problem_chars: &ProblemCharacteristics,
910    ) -> Result<Vec<AlgorithmRecommendation>, String> {
911        let mut recommendations = Vec::new();
912
913        // Find best classical algorithm
914        if let Some((best_classical_alg, best_classical_perf)) =
915            classical_perf.iter().max_by(|a, b| {
916                a.1.solution_quality
917                    .approximation_ratio
918                    .partial_cmp(&b.1.solution_quality.approximation_ratio)
919                    .unwrap_or(std::cmp::Ordering::Equal)
920            })
921        {
922            recommendations.push(AlgorithmRecommendation {
923                algorithm: format!("{best_classical_alg:?}"),
924                algorithm_type: AlgorithmType::Classical,
925                confidence: 0.8,
926                expected_performance: best_classical_perf.clone(),
927                justification: "Best performing classical algorithm for this problem type"
928                    .to_string(),
929                alternatives: classical_perf.keys().map(|k| format!("{k:?}")).collect(),
930            });
931        }
932
933        // Find best quantum algorithm if quantum advantage exists
934        if advantage_analysis.has_quantum_advantage {
935            if let Some((best_quantum_alg, best_quantum_perf)) =
936                quantum_perf.iter().max_by(|a, b| {
937                    a.1.base_metrics
938                        .solution_quality
939                        .approximation_ratio
940                        .partial_cmp(&b.1.base_metrics.solution_quality.approximation_ratio)
941                        .unwrap_or(std::cmp::Ordering::Equal)
942                })
943            {
944                recommendations.push(AlgorithmRecommendation {
945                    algorithm: format!("{best_quantum_alg:?}"),
946                    algorithm_type: AlgorithmType::Quantum,
947                    confidence: advantage_analysis.confidence,
948                    expected_performance: best_quantum_perf.base_metrics.clone(),
949                    justification: "Quantum advantage detected for this problem".to_string(),
950                    alternatives: quantum_perf.keys().map(|k| format!("{k:?}")).collect(),
951                });
952            }
953        }
954
955        // Always recommend hybrid approach for large problems
956        if problem_chars.num_variables > 1000 {
957            recommendations.push(AlgorithmRecommendation {
958                algorithm: "Hybrid Quantum-Classical".to_string(),
959                algorithm_type: AlgorithmType::Hybrid,
960                confidence: 0.6,
961                expected_performance: PerformanceMetrics {
962                    time_complexity: TimeComplexity {
963                        best_case: ComplexityFunction::Linear,
964                        average_case: ComplexityFunction::Quadratic,
965                        worst_case: ComplexityFunction::Cubic,
966                    },
967                    space_complexity: SpaceComplexity {
968                        memory_complexity: ComplexityFunction::Linear,
969                        storage_complexity: ComplexityFunction::Linear,
970                    },
971                    solution_quality: QualityMetrics {
972                        approximation_ratio: 0.9,
973                        solution_variance: 0.1,
974                        optimal_probability: 0.1,
975                        energy_gap: 0.1,
976                    },
977                    success_probability: 0.8,
978                    scaling_behavior: ScalingBehavior {
979                        scaling_exponent: 1.5,
980                        scaling_constant: 1.0,
981                        confidence_interval: (1.2, 1.8),
982                        fit_quality: 0.85,
983                    },
984                },
985                justification: "Hybrid approaches often perform well for large-scale problems"
986                    .to_string(),
987                alternatives: vec!["Pure classical".to_string(), "Pure quantum".to_string()],
988            });
989        }
990
991        Ok(recommendations)
992    }
993
994    /// Run comprehensive benchmark suite
995    pub fn run_supremacy_benchmark(&mut self) -> Result<SupremacyBenchmarkResult, String> {
996        self.benchmarker.run_comprehensive_benchmark(&self.config)
997    }
998
999    /// Export analysis results
1000    pub fn export_results(
1001        &self,
1002        results: &AdvantageAnalysisResult,
1003        format: ExportFormat,
1004    ) -> Result<String, String> {
1005        match format {
1006            ExportFormat::JSON => serde_json::to_string_pretty(results)
1007                .map_err(|e| format!("JSON export failed: {e}")),
1008            ExportFormat::Python => {
1009                // Generate Python code for visualization and further analysis
1010                Ok(self.generate_python_analysis_code(results))
1011            }
1012            ExportFormat::Rust => {
1013                // Generate Rust code for reproducible analysis
1014                Ok(self.generate_rust_analysis_code(results))
1015            }
1016            ExportFormat::QUBO => {
1017                Err("QUBO export not applicable for analysis results".to_string())
1018            }
1019        }
1020    }
1021
1022    fn generate_python_analysis_code(&self, results: &AdvantageAnalysisResult) -> String {
1023        format!(
1024            r#"
1025# Quantum Advantage Analysis Results
1026# Generated by QuantRS2-Tytan
1027
1028import numpy as np
1029import matplotlib.pyplot as plt
1030
1031# Problem characteristics
1032problem_size = {}
1033problem_density = {:.3}
1034has_quantum_advantage = {}
1035confidence = {:.3}
1036
1037# Visualization code
1038plt.figure(figsize=(12, 8))
1039plt.subplot(2, 2, 1)
1040plt.title('Quantum vs Classical Performance')
1041# Add your performance comparison plots here
1042
1043plt.subplot(2, 2, 2)
1044plt.title('Advantage Factors')
1045# Add advantage factor visualization here
1046
1047plt.tight_layout()
1048plt.show()
1049
1050print(f"Problem size: {{problem_size}}")
1051print(f"Quantum advantage detected: {{has_quantum_advantage}}")
1052print(f"Confidence level: {{confidence:.1%}}")
1053"#,
1054            results.problem_info.num_variables,
1055            results.problem_info.density,
1056            results.advantage_analysis.has_quantum_advantage,
1057            results.advantage_analysis.confidence,
1058        )
1059    }
1060
1061    fn generate_rust_analysis_code(&self, results: &AdvantageAnalysisResult) -> String {
1062        format!(
1063            r#"
1064// Quantum Advantage Analysis Results
1065// Generated by QuantRS2-Tytan
1066
1067use quantrs2_tytan::quantum_advantage_analysis::*;
1068
1069fn reproduce_analysis() {{
1070    let problem_size = {};
1071    let has_advantage = {};
1072    let confidence = {:.3};
1073
1074    println!("Problem size: {{}}", problem_size);
1075    println!("Quantum advantage: {{}}", has_advantage);
1076    println!("Confidence: {{:.1%}}", confidence);
1077
1078    // Add your analysis reproduction code here
1079}}
1080"#,
1081            results.problem_info.num_variables,
1082            results.advantage_analysis.has_quantum_advantage,
1083            results.advantage_analysis.confidence,
1084        )
1085    }
1086}
1087
1088impl Default for ClassicalComplexityEstimator {
1089    fn default() -> Self {
1090        Self::new()
1091    }
1092}
1093
1094impl ClassicalComplexityEstimator {
1095    pub fn new() -> Self {
1096        Self {
1097            complexity_database: Self::build_complexity_database(),
1098            heuristic_estimators: vec![],
1099        }
1100    }
1101
1102    fn build_complexity_database() -> HashMap<String, ComplexityInfo> {
1103        let mut db = HashMap::new();
1104
1105        // Add known complexity results for common problems
1106        db.insert(
1107            "max_cut".to_string(),
1108            ComplexityInfo {
1109                time_complexity: TimeComplexity {
1110                    best_case: ComplexityFunction::Exponential { base: 2.0 },
1111                    average_case: ComplexityFunction::Exponential { base: 2.0 },
1112                    worst_case: ComplexityFunction::Exponential { base: 2.0 },
1113                },
1114                space_complexity: SpaceComplexity {
1115                    memory_complexity: ComplexityFunction::Linear,
1116                    storage_complexity: ComplexityFunction::Linear,
1117                },
1118                approximation_bounds: Some((0.878, 1.0)),
1119                practical_scaling: ScalingBehavior {
1120                    scaling_exponent: 1.8,
1121                    scaling_constant: 10.0,
1122                    confidence_interval: (1.6, 2.0),
1123                    fit_quality: 0.9,
1124                },
1125            },
1126        );
1127
1128        db
1129    }
1130
1131    pub fn estimate_classical_performance(
1132        &self,
1133        problem: &ProblemCharacteristics,
1134        algorithms: &[ClassicalAlgorithm],
1135    ) -> Result<HashMap<ClassicalAlgorithm, PerformanceMetrics>, String> {
1136        let mut results = HashMap::new();
1137
1138        for algorithm in algorithms {
1139            let performance = self.estimate_algorithm_performance(algorithm, problem)?;
1140            results.insert(algorithm.clone(), performance);
1141        }
1142
1143        Ok(results)
1144    }
1145
1146    fn estimate_algorithm_performance(
1147        &self,
1148        algorithm: &ClassicalAlgorithm,
1149        problem: &ProblemCharacteristics,
1150    ) -> Result<PerformanceMetrics, String> {
1151        // Simplified performance estimation based on algorithm type and problem characteristics
1152        let base_complexity = match algorithm {
1153            ClassicalAlgorithm::SimulatedAnnealing => {
1154                ComplexityFunction::Polynomial { degree: 2.0 }
1155            }
1156            ClassicalAlgorithm::TabuSearch => ComplexityFunction::Polynomial { degree: 2.5 },
1157            ClassicalAlgorithm::GeneticAlgorithm => ComplexityFunction::Polynomial { degree: 3.0 },
1158            ClassicalAlgorithm::BranchAndBound => ComplexityFunction::Exponential { base: 2.0 },
1159            ClassicalAlgorithm::ConstraintProgramming => {
1160                ComplexityFunction::Exponential { base: 1.5 }
1161            }
1162            ClassicalAlgorithm::LinearProgramming => ComplexityFunction::Polynomial { degree: 3.5 },
1163            ClassicalAlgorithm::SDP => ComplexityFunction::Polynomial { degree: 4.0 },
1164        };
1165
1166        // Adjust for problem characteristics
1167        let scaling_factor = match problem.connectivity {
1168            ConnectivityStructure::FullyConnected => 1.5,
1169            ConnectivityStructure::Sparse { .. } => 0.8,
1170            ConnectivityStructure::Grid { .. } => 0.9,
1171            ConnectivityStructure::Tree => 0.6,
1172            ConnectivityStructure::Planar => 0.7,
1173            ConnectivityStructure::SmallWorld { .. } => 1.1,
1174        };
1175
1176        let approximation_ratio = match algorithm {
1177            ClassicalAlgorithm::SimulatedAnnealing => 0.85,
1178            ClassicalAlgorithm::TabuSearch => 0.9,
1179            ClassicalAlgorithm::GeneticAlgorithm => 0.8,
1180            ClassicalAlgorithm::BranchAndBound => 1.0, // Exact for small instances
1181            ClassicalAlgorithm::ConstraintProgramming => 0.95,
1182            ClassicalAlgorithm::LinearProgramming => 0.99, // If problem is relaxable
1183            ClassicalAlgorithm::SDP => 0.878,              // For Max-Cut
1184        };
1185
1186        Ok(PerformanceMetrics {
1187            time_complexity: TimeComplexity {
1188                best_case: base_complexity.clone(),
1189                average_case: base_complexity.clone(),
1190                worst_case: base_complexity,
1191            },
1192            space_complexity: SpaceComplexity {
1193                memory_complexity: ComplexityFunction::Linear,
1194                storage_complexity: ComplexityFunction::Linear,
1195            },
1196            solution_quality: QualityMetrics {
1197                approximation_ratio,
1198                solution_variance: 0.1,
1199                optimal_probability: if matches!(algorithm, ClassicalAlgorithm::BranchAndBound) {
1200                    1.0
1201                } else {
1202                    0.1
1203                },
1204                energy_gap: 0.05,
1205            },
1206            success_probability: 0.9,
1207            scaling_behavior: ScalingBehavior {
1208                scaling_exponent: scaling_factor,
1209                scaling_constant: 1.0,
1210                confidence_interval: (scaling_factor * 0.8, scaling_factor * 1.2),
1211                fit_quality: 0.8,
1212            },
1213        })
1214    }
1215}
1216
1217impl Default for QuantumResourceEstimator {
1218    fn default() -> Self {
1219        Self::new()
1220    }
1221}
1222
1223impl QuantumResourceEstimator {
1224    pub fn new() -> Self {
1225        Self {
1226            algorithm_database: Self::build_algorithm_database(),
1227            hardware_database: Self::build_hardware_database(),
1228        }
1229    }
1230
1231    fn build_algorithm_database() -> HashMap<String, QuantumAlgorithmInfo> {
1232        let mut db = HashMap::new();
1233
1234        // Add quantum algorithm information
1235        db.insert(
1236            "QAOA".to_string(),
1237            QuantumAlgorithmInfo {
1238                resource_requirements: HardwareRequirements {
1239                    min_qubits: 10,
1240                    connectivity_requirements: ConnectivityRequirement::AllToAll,
1241                    gate_fidelity_threshold: 0.99,
1242                    measurement_fidelity_threshold: 0.95,
1243                    temperature_requirements: Some(0.01), // Kelvin
1244                },
1245                performance_model: QuantumPerformanceModel {
1246                    time_to_solution: Box::new(|n| {
1247                        Duration::from_millis((n as f64 * n as f64 * 0.1) as u64)
1248                    }),
1249                    success_probability: Box::new(|n, error_rate| {
1250                        (1.0 - error_rate).powf(n as f64)
1251                    }),
1252                    resource_scaling: ScalingBehavior {
1253                        scaling_exponent: 1.0,
1254                        scaling_constant: 1.0,
1255                        confidence_interval: (0.8, 1.2),
1256                        fit_quality: 0.85,
1257                    },
1258                },
1259                noise_sensitivity: NoiseSensitivity {
1260                    error_thresholds: {
1261                        let mut map = HashMap::new();
1262                        map.insert("gate_error".to_string(), 0.001);
1263                        map.insert("measurement_error".to_string(), 0.01);
1264                        map
1265                    },
1266                    degradation_rates: HashMap::new(),
1267                    mitigation_effectiveness: HashMap::new(),
1268                },
1269                theoretical_advantage: Some(AdvantageEstimate {
1270                    speedup_factor: 1.5,
1271                    advantage_type: AdvantageType::Polynomial {
1272                        degree_reduction: 0.5,
1273                    },
1274                    confidence_level: 0.7,
1275                    conditions: vec![
1276                        "Low noise".to_string(),
1277                        "Sufficient circuit depth".to_string(),
1278                    ],
1279                }),
1280            },
1281        );
1282
1283        db
1284    }
1285
1286    fn build_hardware_database() -> HashMap<String, HardwareCharacteristics> {
1287        let mut db = HashMap::new();
1288
1289        // Add hardware characteristics
1290        db.insert(
1291            "ideal_quantum".to_string(),
1292            HardwareCharacteristics {
1293                qubit_count: 10000,
1294                connectivity: ConnectivityStructure::FullyConnected,
1295                gate_fidelities: {
1296                    let mut map = HashMap::new();
1297                    map.insert("single_qubit".to_string(), 1.0);
1298                    map.insert("two_qubit".to_string(), 1.0);
1299                    map
1300                },
1301                measurement_fidelity: 1.0,
1302                coherence_times: {
1303                    let mut map = HashMap::new();
1304                    map.insert("T1".to_string(), Duration::from_secs(1000));
1305                    map.insert("T2".to_string(), Duration::from_secs(1000));
1306                    map
1307                },
1308                operating_parameters: HashMap::new(),
1309            },
1310        );
1311
1312        db
1313    }
1314
1315    pub fn estimate_quantum_performance(
1316        &self,
1317        problem: &ProblemCharacteristics,
1318        algorithms: &[QuantumAlgorithm],
1319    ) -> Result<HashMap<QuantumAlgorithm, QuantumPerformanceMetrics>, String> {
1320        let mut results = HashMap::new();
1321
1322        for algorithm in algorithms {
1323            let performance = self.estimate_quantum_algorithm_performance(algorithm, problem)?;
1324            results.insert(algorithm.clone(), performance);
1325        }
1326
1327        Ok(results)
1328    }
1329
1330    fn estimate_quantum_algorithm_performance(
1331        &self,
1332        algorithm: &QuantumAlgorithm,
1333        problem: &ProblemCharacteristics,
1334    ) -> Result<QuantumPerformanceMetrics, String> {
1335        // Estimate quantum-specific requirements
1336        let qubits_required = match algorithm {
1337            QuantumAlgorithm::QuantumAnnealing => problem.num_variables,
1338            QuantumAlgorithm::QAOA => problem.num_variables,
1339            QuantumAlgorithm::VQE => problem.num_variables,
1340            QuantumAlgorithm::QFAST => problem.num_variables + 10, // Extra ancilla qubits
1341            QuantumAlgorithm::QuantumWalk => (problem.num_variables as f64).log2().ceil() as usize,
1342            QuantumAlgorithm::AdiabaticQuantumComputing => problem.num_variables,
1343        };
1344
1345        let circuit_depth = match algorithm {
1346            QuantumAlgorithm::QuantumAnnealing => 1, // Continuous evolution
1347            QuantumAlgorithm::QAOA => 10,            // Typical QAOA depth
1348            QuantumAlgorithm::VQE => 50,
1349            QuantumAlgorithm::QFAST => 100,
1350            QuantumAlgorithm::QuantumWalk => 20,
1351            QuantumAlgorithm::AdiabaticQuantumComputing => 1,
1352        };
1353
1354        // Base performance estimation
1355        let base_metrics = PerformanceMetrics {
1356            time_complexity: TimeComplexity {
1357                best_case: ComplexityFunction::Linear,
1358                average_case: ComplexityFunction::Linearithmic,
1359                worst_case: ComplexityFunction::Quadratic,
1360            },
1361            space_complexity: SpaceComplexity {
1362                memory_complexity: ComplexityFunction::Linear,
1363                storage_complexity: ComplexityFunction::Linear,
1364            },
1365            solution_quality: QualityMetrics {
1366                approximation_ratio: 0.95, // Generally better than classical heuristics
1367                solution_variance: 0.05,
1368                optimal_probability: 0.3,
1369                energy_gap: 0.1,
1370            },
1371            success_probability: 0.8,
1372            scaling_behavior: ScalingBehavior {
1373                scaling_exponent: 1.2,
1374                scaling_constant: 0.5,
1375                confidence_interval: (1.0, 1.4),
1376                fit_quality: 0.75,
1377            },
1378        };
1379
1380        // Quantum-specific metrics
1381        let quantum_metrics = QuantumSpecificMetrics {
1382            qubits_required,
1383            circuit_depth,
1384            quantum_operations: circuit_depth * qubits_required,
1385            entanglement_measures: EntanglementMeasures {
1386                avg_entanglement_entropy: 2.0,
1387                max_entanglement_entropy: (qubits_required as f64).log2(),
1388                entanglement_depth: circuit_depth / 5,
1389                multipartite_measures: HashMap::new(),
1390            },
1391            coherence_time_required: Duration::from_micros(circuit_depth as u64 * 10),
1392        };
1393
1394        // Hardware requirements
1395        let hardware_requirements = HardwareRequirements {
1396            min_qubits: qubits_required,
1397            connectivity_requirements: ConnectivityRequirement::AllToAll,
1398            gate_fidelity_threshold: 0.99,
1399            measurement_fidelity_threshold: 0.95,
1400            temperature_requirements: Some(0.01),
1401        };
1402
1403        // Noise sensitivity
1404        let noise_sensitivity = NoiseSensitivity {
1405            error_thresholds: {
1406                let mut map = HashMap::new();
1407                map.insert("gate_error".to_string(), 1.0 / circuit_depth as f64);
1408                map.insert("measurement_error".to_string(), 0.01);
1409                map
1410            },
1411            degradation_rates: HashMap::new(),
1412            mitigation_effectiveness: HashMap::new(),
1413        };
1414
1415        Ok(QuantumPerformanceMetrics {
1416            base_metrics,
1417            quantum_metrics,
1418            hardware_requirements,
1419            noise_sensitivity,
1420        })
1421    }
1422}
1423
1424impl Default for QuantumSupremacyBenchmarker {
1425    fn default() -> Self {
1426        Self::new()
1427    }
1428}
1429
1430impl QuantumSupremacyBenchmarker {
1431    pub fn new() -> Self {
1432        Self {
1433            problem_generators: vec![],
1434            performance_trackers: HashMap::new(),
1435        }
1436    }
1437
1438    pub fn run_comprehensive_benchmark(
1439        &mut self,
1440        config: &AnalysisConfig,
1441    ) -> Result<SupremacyBenchmarkResult, String> {
1442        let mut results = Vec::new();
1443
1444        for size in (config.problem_size_range.0..=config.problem_size_range.1).step_by(50) {
1445            let benchmark_result = self.run_size_benchmark(size, config)?;
1446            results.push(benchmark_result);
1447        }
1448
1449        Ok(SupremacyBenchmarkResult {
1450            benchmark_results: results.clone(),
1451            summary: self.generate_summary(&results)?,
1452        })
1453    }
1454
1455    fn run_size_benchmark(
1456        &self,
1457        size: usize,
1458        _config: &AnalysisConfig,
1459    ) -> Result<SizeBenchmarkResult, String> {
1460        // This would run actual benchmarks
1461        // For now, return simulated results
1462        Ok(SizeBenchmarkResult {
1463            problem_size: size,
1464            classical_times: HashMap::new(),
1465            quantum_times: HashMap::new(),
1466            solution_qualities: HashMap::new(),
1467            advantage_detected: size > 100, // Simplified threshold
1468        })
1469    }
1470
1471    fn generate_summary(
1472        &self,
1473        results: &[SizeBenchmarkResult],
1474    ) -> Result<BenchmarkSummary, String> {
1475        let advantage_threshold = results
1476            .iter()
1477            .find(|r| r.advantage_detected)
1478            .map_or(usize::MAX, |r| r.problem_size);
1479
1480        Ok(BenchmarkSummary {
1481            total_benchmarks: results.len(),
1482            advantage_threshold,
1483            confidence_level: 0.8,
1484            recommendations: vec![
1485                "Quantum advantage likely for problems > 100 variables".to_string()
1486            ],
1487        })
1488    }
1489}
1490
1491#[derive(Debug, Clone, Serialize, Deserialize)]
1492pub struct SupremacyBenchmarkResult {
1493    pub benchmark_results: Vec<SizeBenchmarkResult>,
1494    pub summary: BenchmarkSummary,
1495}
1496
1497#[derive(Debug, Clone, Serialize, Deserialize)]
1498pub struct SizeBenchmarkResult {
1499    pub problem_size: usize,
1500    pub classical_times: HashMap<String, Duration>,
1501    pub quantum_times: HashMap<String, Duration>,
1502    pub solution_qualities: HashMap<String, f64>,
1503    pub advantage_detected: bool,
1504}
1505
1506#[derive(Debug, Clone, Serialize, Deserialize)]
1507pub struct BenchmarkSummary {
1508    pub total_benchmarks: usize,
1509    pub advantage_threshold: usize,
1510    pub confidence_level: f64,
1511    pub recommendations: Vec<String>,
1512}
1513
1514#[derive(Debug, Clone, Serialize, Deserialize)]
1515pub enum ExportFormat {
1516    JSON,
1517    Python,
1518    Rust,
1519    QUBO,
1520}
1521
1522// Additional trait implementations for missing partial comparisons
1523impl PartialOrd for ComplexityFunction {
1524    fn partial_cmp(&self, other: &Self) -> Option<std::cmp::Ordering> {
1525        use ComplexityFunction::{
1526            Constant, Cubic, Exponential, Factorial, Linear, Linearithmic, Logarithmic, Polynomial,
1527            Quadratic,
1528        };
1529        match (self, other) {
1530            (Constant, Constant) => Some(std::cmp::Ordering::Equal),
1531            (Constant, _) => Some(std::cmp::Ordering::Less),
1532            (_, Constant) => Some(std::cmp::Ordering::Greater),
1533            (Logarithmic, Logarithmic) => Some(std::cmp::Ordering::Equal),
1534            (Logarithmic, _) => Some(std::cmp::Ordering::Less),
1535            (_, Logarithmic) => Some(std::cmp::Ordering::Greater),
1536            (Linear, Linear) => Some(std::cmp::Ordering::Equal),
1537            (Linear, _) => Some(std::cmp::Ordering::Less),
1538            (_, Linear) => Some(std::cmp::Ordering::Greater),
1539            (Linearithmic, Linearithmic) => Some(std::cmp::Ordering::Equal),
1540            (Linearithmic, _) => Some(std::cmp::Ordering::Less),
1541            (_, Linearithmic) => Some(std::cmp::Ordering::Greater),
1542            (Quadratic, Quadratic) => Some(std::cmp::Ordering::Equal),
1543            (Quadratic, _) => Some(std::cmp::Ordering::Less),
1544            (_, Quadratic) => Some(std::cmp::Ordering::Greater),
1545            (Cubic, Cubic) => Some(std::cmp::Ordering::Equal),
1546            (Cubic, _) => Some(std::cmp::Ordering::Less),
1547            (_, Cubic) => Some(std::cmp::Ordering::Greater),
1548            (Polynomial { degree: d1 }, Polynomial { degree: d2 }) => d1.partial_cmp(d2),
1549            (Polynomial { .. }, _) => Some(std::cmp::Ordering::Less),
1550            (_, Polynomial { .. }) => Some(std::cmp::Ordering::Greater),
1551            (Exponential { base: b1 }, Exponential { base: b2 }) => b1.partial_cmp(b2),
1552            (Exponential { .. }, Factorial) => Some(std::cmp::Ordering::Less),
1553            (Factorial, Exponential { .. }) => Some(std::cmp::Ordering::Greater),
1554            (Factorial, Factorial) => Some(std::cmp::Ordering::Equal),
1555        }
1556    }
1557}
1558
1559impl PartialEq for ComplexityFunction {
1560    fn eq(&self, other: &Self) -> bool {
1561        matches!(self.partial_cmp(other), Some(std::cmp::Ordering::Equal))
1562    }
1563}
quantrs2_tytan/quantum_advantage_analysis.rs

quantrs2_tytan/
quantum_advantage_analysis.rs
