quantrs2-sim 0.1.3

Quantum circuit simulators for the QuantRS2 framework
Documentation
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
416
417
418
419
420
421
422
423
424
425
426
427
428
429
430
431
432
433
434
435
436
437
438
439
440
441
442
443
444
445
446
447
448
449
450
451
452
453
454
455
456
457
458
459
460
461
462
463
464
465
466
467
468
469
470
471
472
473
474
475
476
477
478
479
480
481
482
483
484
485
486
487
488
489
490
491
492
493
494
495
496
497
498
499
500
501
502
503
504
505
506
507
508
509
510
511
512
513
514
515
516
517
518
519
520
521
522
523
524
525
526
527
528
529
530
531
532
533
534
535
536
537
538
539
540
541
542
543
544
545
546
547
548
549
550
551
552
553
554
555
556
557
558
559
560
561
562
563
564
565
566
567
568
569
570
571
572
573
574
575
576
577
578
579
580
581
582
583
584
585
586
587
588
589
590
591
592
593
594
595
596
597
598
599
600
601
602
603
604
605
606
607
608
609
610
611
612
613
614
615
616
617
618
619
620
621
622
623
624
625
626
627
628
629
630
631
632
633
634
635
636
637
638
639
640
641
642
643
644
645
646
647
648
649
650
651
652
653
654
655
656
657
658
659
660
661
662
663
664
665
666
667
668
669
670
671
672
673
674
675
676
677
678
679
680
681
682
683
684
685
686
687
688
689
690
691
692
693
694
695
696
697
698
699
700
701
702
703
704
705
706
707
708
709
710
711
712
713
714
715
716
717
718
719
720
721
722
723
724
725
726
727
728
729
730
731
732
733
734
735
736
737
738
739
740
741
742
743
744
745
746
747
748
749
750
751
752
753
754
755
756
757
758
759
760
761
762
763
764
765
766
767
768
769
770
771
772
773
774
775
776
777
778
779
780
781
782
783
784
785
786
787
788
789
790
791
792
793
794
795
796
797
798
799
800
801
802
803
804
805
806
807
808
809
810
811
812
813
814
815
816
817
818
819
820
821
822
823
824
825
826
827
828
829
830
831
832
833
834
835
836
837
838
839
840
841
842
843
844
845
846
847
848
849
850
851
852
853
854
855
856
857
858
859
860
861
862
863
864
865
866
867
868
869
870
871
872
873
874
875
876
877
878
879
880
881
882
883
884
885
886
887
888
889
890
891
892
893
894
895
896
897
898
899
900
901
902
903
904
905
906
907
908
909
910
911
912
913
914
915
916
917
918
919
920
921
922
923
924
925
926
927
928
929
930
931
932
933
934
935
936
937
938
939
940
941
942
943
944
945
946
947
948
949
950
951
952
953
954
955
956
957
958
959
960
961
962
963
964
965
966
967
968
969
970
971
972
973
974
975
976
977
978
979
980
981
982
983
984
985
986
987
988
989
990
991
992
993
994
995
996
997
998
999
1000
1001
1002
1003
1004
1005
1006
1007
1008
1009
1010
1011
1012
1013
1014
1015
1016
1017
1018
1019
1020
1021
1022
1023
1024
1025
//! Performance Prediction Models for Circuit Execution Time Estimation
//!
//! This module provides sophisticated models for predicting quantum circuit
//! execution times across different simulation backends using `SciRS2` analysis
//! tools and machine learning techniques.

use crate::{
    auto_optimizer::{AnalysisDepth, BackendType, CircuitCharacteristics},
    error::{Result, SimulatorError},
    scirs2_integration::{Matrix, SciRS2Backend, Vector},
};
use quantrs2_circuit::builder::Circuit;
use quantrs2_core::{
    error::{QuantRS2Error, QuantRS2Result},
    gate::GateOp,
    qubit::QubitId,
};
use scirs2_core::Complex64;
use serde::{Deserialize, Serialize};
use std::collections::{HashMap, VecDeque};
use std::time::{Duration, Instant};

/// Configuration for performance prediction models
#[derive(Debug, Clone, Serialize, Deserialize)]
pub struct PerformancePredictionConfig {
    /// Enable machine learning-based predictions
    pub enable_ml_prediction: bool,
    /// Maximum historical data points to maintain
    pub max_history_size: usize,
    /// Confidence threshold for predictions (0.0 to 1.0)
    pub confidence_threshold: f64,
    /// Enable hardware profiling for adaptive predictions
    pub enable_hardware_profiling: bool,
    /// `SciRS2` analysis depth for complexity estimation
    pub analysis_depth: AnalysisDepth,
    /// Prediction strategy to use
    pub prediction_strategy: PredictionStrategy,
    /// Learning rate for adaptive models
    pub learning_rate: f64,
    /// Enable cross-backend performance transfer learning
    pub enable_transfer_learning: bool,
    /// Minimum samples required before using ML predictions
    pub min_samples_for_ml: usize,
}

impl Default for PerformancePredictionConfig {
    fn default() -> Self {
        Self {
            enable_ml_prediction: true,
            max_history_size: 10_000,
            confidence_threshold: 0.8,
            enable_hardware_profiling: true,
            analysis_depth: AnalysisDepth::Deep,
            prediction_strategy: PredictionStrategy::Hybrid,
            learning_rate: 0.01,
            enable_transfer_learning: true,
            min_samples_for_ml: 100,
        }
    }
}

/// Prediction strategy for execution time estimation
#[derive(Debug, Clone, Copy, PartialEq, Eq, Serialize, Deserialize)]
pub enum PredictionStrategy {
    /// Static analysis only
    StaticAnalysis,
    /// Machine learning only
    MachineLearning,
    /// Hybrid approach (static + ML)
    Hybrid,
    /// Ensemble of multiple models
    Ensemble,
}

/// Performance prediction model types
#[derive(Debug, Clone, Copy, PartialEq, Eq, Serialize, Deserialize)]
pub enum ModelType {
    /// Linear regression model
    LinearRegression,
    /// Polynomial regression model
    PolynomialRegression,
    /// Neural network model
    NeuralNetwork,
    /// Support vector regression
    SupportVectorRegression,
    /// Random forest model
    RandomForest,
    /// Gradient boosting model
    GradientBoosting,
}

/// Circuit complexity metrics for prediction
#[derive(Debug, Clone, Serialize, Deserialize)]
pub struct ComplexityMetrics {
    /// Total number of gates
    pub gate_count: usize,
    /// Circuit depth (critical path length)
    pub circuit_depth: usize,
    /// Number of qubits
    pub qubit_count: usize,
    /// Number of two-qubit gates
    pub two_qubit_gate_count: usize,
    /// Estimated memory requirement (bytes)
    pub memory_requirement: usize,
    /// Parallelism potential (0.0 to 1.0)
    pub parallelism_factor: f64,
    /// Entanglement complexity measure
    pub entanglement_complexity: f64,
    /// Gate type distribution
    pub gate_type_distribution: HashMap<String, usize>,
    /// Critical path analysis
    pub critical_path_complexity: f64,
    /// Resource estimation
    pub resource_estimation: ResourceMetrics,
}

impl Default for ComplexityMetrics {
    fn default() -> Self {
        Self {
            gate_count: 0,
            circuit_depth: 0,
            qubit_count: 0,
            two_qubit_gate_count: 0,
            memory_requirement: 0,
            parallelism_factor: 0.0,
            entanglement_complexity: 0.0,
            gate_type_distribution: HashMap::new(),
            critical_path_complexity: 0.0,
            resource_estimation: ResourceMetrics::default(),
        }
    }
}

/// Resource requirements metrics
#[derive(Debug, Clone, Serialize, Deserialize)]
pub struct ResourceMetrics {
    /// Estimated CPU time (seconds)
    pub cpu_time_estimate: f64,
    /// Estimated memory usage (bytes)
    pub memory_usage_estimate: usize,
    /// Estimated I/O operations
    pub io_operations_estimate: usize,
    /// Network bandwidth requirement (bytes/sec)
    pub network_bandwidth_estimate: usize,
    /// GPU memory requirement (bytes)
    pub gpu_memory_estimate: usize,
    /// Parallel thread requirement
    pub thread_requirement: usize,
}

/// Historical execution data point
#[derive(Debug, Clone, Serialize)]
pub struct ExecutionDataPoint {
    /// Circuit complexity metrics
    pub complexity: ComplexityMetrics,
    /// Backend used for execution
    pub backend_type: BackendType,
    /// Actual execution time
    pub execution_time: Duration,
    /// Hardware specifications during execution
    pub hardware_specs: PerformanceHardwareSpecs,
    /// Timestamp of execution
    #[serde(skip_serializing, skip_deserializing)]
    pub timestamp: std::time::SystemTime,
    /// Success flag
    pub success: bool,
    /// Error information if failed
    pub error_info: Option<String>,
}

impl Default for ExecutionDataPoint {
    fn default() -> Self {
        Self {
            complexity: ComplexityMetrics::default(),
            backend_type: BackendType::StateVector,
            execution_time: Duration::from_secs(0),
            hardware_specs: PerformanceHardwareSpecs::default(),
            timestamp: std::time::SystemTime::now(),
            success: false,
            error_info: None,
        }
    }
}

/// Hardware specifications for context
#[derive(Debug, Clone, Serialize, Deserialize)]
pub struct PerformanceHardwareSpecs {
    /// CPU cores available
    pub cpu_cores: usize,
    /// Total system memory (bytes)
    pub total_memory: usize,
    /// Available memory at execution time (bytes)
    pub available_memory: usize,
    /// GPU memory (bytes, if available)
    pub gpu_memory: Option<usize>,
    /// CPU frequency (MHz)
    pub cpu_frequency: f64,
    /// Network bandwidth (Mbps, for distributed)
    pub network_bandwidth: Option<f64>,
    /// System load average
    pub load_average: f64,
}

impl Default for PerformanceHardwareSpecs {
    fn default() -> Self {
        Self {
            cpu_cores: 1,
            total_memory: 1024 * 1024 * 1024,    // 1GB
            available_memory: 512 * 1024 * 1024, // 512MB
            gpu_memory: None,
            cpu_frequency: 2000.0, // 2GHz
            network_bandwidth: None,
            load_average: 0.0,
        }
    }
}

/// Prediction result with confidence metrics
#[derive(Debug, Clone, Serialize, Deserialize)]
pub struct PredictionResult {
    /// Predicted execution time
    pub predicted_time: Duration,
    /// Confidence in prediction (0.0 to 1.0)
    pub confidence: f64,
    /// Prediction interval (lower bound, upper bound)
    pub prediction_interval: (Duration, Duration),
    /// Model used for prediction
    pub model_type: ModelType,
    /// Feature importance scores
    pub feature_importance: HashMap<String, f64>,
    /// Prediction metadata
    pub metadata: PredictionMetadata,
}

/// Metadata about the prediction process
#[derive(Debug, Clone, Serialize, Deserialize)]
pub struct PredictionMetadata {
    /// Time taken to generate prediction
    pub prediction_time: Duration,
    /// Number of historical samples used
    pub samples_used: usize,
    /// Model training status
    pub model_trained: bool,
    /// Cross-validation score (if available)
    pub cv_score: Option<f64>,
    /// Prediction method used
    pub prediction_method: String,
}

/// Performance prediction engine
pub struct PerformancePredictionEngine {
    /// Configuration
    config: PerformancePredictionConfig,
    /// Historical execution data
    execution_history: VecDeque<ExecutionDataPoint>,
    /// Trained models for different backends
    trained_models: HashMap<BackendType, TrainedModel>,
    /// `SciRS2` backend for analysis
    scirs2_backend: SciRS2Backend,
    /// Current hardware specifications
    current_hardware: PerformanceHardwareSpecs,
    /// Performance statistics
    prediction_stats: PredictionStatistics,
}

/// Trained machine learning model
#[derive(Debug, Clone, Serialize)]
pub struct TrainedModel {
    /// Model type
    pub model_type: ModelType,
    /// Model parameters (simplified representation)
    pub parameters: Vec<f64>,
    /// Feature weights
    pub feature_weights: HashMap<String, f64>,
    /// Training statistics
    pub training_stats: TrainingStatistics,
    /// Last training time
    #[serde(skip_serializing, skip_deserializing)]
    pub last_trained: std::time::SystemTime,
}

impl Default for TrainedModel {
    fn default() -> Self {
        Self {
            model_type: ModelType::LinearRegression,
            parameters: Vec::new(),
            feature_weights: HashMap::new(),
            training_stats: TrainingStatistics::default(),
            last_trained: std::time::SystemTime::now(),
        }
    }
}

/// Training statistics for models
#[derive(Debug, Clone, Serialize, Deserialize)]
pub struct TrainingStatistics {
    /// Training samples used
    pub training_samples: usize,
    /// Training accuracy (R²)
    pub training_accuracy: f64,
    /// Validation accuracy
    pub validation_accuracy: f64,
    /// Mean absolute error
    pub mean_absolute_error: f64,
    /// Root mean square error
    pub root_mean_square_error: f64,
    /// Training time
    pub training_time: Duration,
}

impl Default for TrainingStatistics {
    fn default() -> Self {
        Self {
            training_samples: 0,
            training_accuracy: 0.0,
            validation_accuracy: 0.0,
            mean_absolute_error: 0.0,
            root_mean_square_error: 0.0,
            training_time: Duration::from_secs(0),
        }
    }
}

/// Overall prediction engine statistics
#[derive(Debug, Clone, Serialize, Deserialize)]
pub struct PredictionStatistics {
    /// Total predictions made
    pub total_predictions: usize,
    /// Successful predictions
    pub successful_predictions: usize,
    /// Average prediction accuracy
    pub average_accuracy: f64,
    /// Prediction time statistics
    pub prediction_time_stats: PerformanceTimingStatistics,
    /// Model update frequency
    pub model_updates: usize,
    /// Cache hit rate
    pub cache_hit_rate: f64,
}

/// Timing statistics
#[derive(Debug, Clone, Serialize, Deserialize)]
pub struct PerformanceTimingStatistics {
    /// Average time
    pub average: Duration,
    /// Minimum time
    pub minimum: Duration,
    /// Maximum time
    pub maximum: Duration,
    /// Standard deviation
    pub std_deviation: Duration,
}

impl PerformancePredictionEngine {
    /// Create new performance prediction engine
    pub fn new(config: PerformancePredictionConfig) -> Result<Self> {
        let current_hardware = Self::detect_hardware_specs()?;

        Ok(Self {
            config,
            execution_history: VecDeque::with_capacity(10_000),
            trained_models: HashMap::new(),
            scirs2_backend: SciRS2Backend::new(),
            current_hardware,
            prediction_stats: PredictionStatistics::default(),
        })
    }

    /// Predict execution time for a circuit on a specific backend
    pub fn predict_execution_time<const N: usize>(
        &mut self,
        circuit: &Circuit<N>,
        backend_type: BackendType,
    ) -> Result<PredictionResult> {
        let start_time = Instant::now();

        // Analyze circuit complexity using SciRS2
        let complexity = self.analyze_circuit_complexity(circuit)?;

        // Get prediction based on strategy
        let prediction = match self.config.prediction_strategy {
            PredictionStrategy::StaticAnalysis => {
                self.predict_with_static_analysis(&complexity, backend_type)?
            }
            PredictionStrategy::MachineLearning => {
                self.predict_with_ml(&complexity, backend_type)?
            }
            PredictionStrategy::Hybrid => self.predict_with_hybrid(&complexity, backend_type)?,
            PredictionStrategy::Ensemble => {
                self.predict_with_ensemble(&complexity, backend_type)?
            }
        };

        // Update statistics
        self.prediction_stats.total_predictions += 1;
        let prediction_time = start_time.elapsed();
        self.update_timing_stats(prediction_time);

        Ok(prediction)
    }

    /// Analyze circuit complexity using `SciRS2` tools
    fn analyze_circuit_complexity<const N: usize>(
        &self,
        circuit: &Circuit<N>,
    ) -> Result<ComplexityMetrics> {
        let gate_count = circuit.num_gates();
        let qubit_count = N;

        // Basic complexity analysis
        let circuit_depth = self.calculate_circuit_depth(circuit)?;
        let two_qubit_gate_count = self.count_two_qubit_gates(circuit)?;
        let memory_requirement = self.estimate_memory_requirement(qubit_count);

        // Advanced analysis using SciRS2
        let parallelism_factor = self.analyze_parallelism_potential(circuit)?;
        let entanglement_complexity = self.estimate_entanglement_complexity(circuit)?;
        let gate_type_distribution = self.analyze_gate_distribution(circuit)?;
        let critical_path_complexity = self.analyze_critical_path(circuit)?;

        // Resource estimation
        let resource_estimation = self.estimate_resources(&ComplexityMetrics {
            gate_count,
            circuit_depth,
            qubit_count,
            two_qubit_gate_count,
            memory_requirement,
            parallelism_factor,
            entanglement_complexity,
            gate_type_distribution: gate_type_distribution.clone(),
            critical_path_complexity,
            resource_estimation: ResourceMetrics::default(), // Will be filled
        })?;

        Ok(ComplexityMetrics {
            gate_count,
            circuit_depth,
            qubit_count,
            two_qubit_gate_count,
            memory_requirement,
            parallelism_factor,
            entanglement_complexity,
            gate_type_distribution,
            critical_path_complexity,
            resource_estimation,
        })
    }

    /// Calculate circuit depth (critical path length)
    fn calculate_circuit_depth<const N: usize>(&self, circuit: &Circuit<N>) -> Result<usize> {
        // Simple depth calculation - can be enhanced with SciRS2 graph analysis
        let mut qubit_last_gate: Vec<usize> = vec![0; N];
        let mut max_depth = 0;

        let gates = circuit.gates_as_boxes();
        for (gate_idx, gate) in gates.iter().enumerate() {
            let gate_qubits = self.get_gate_qubits(gate.as_ref())?;
            let mut max_dependency = 0;

            for &qubit in &gate_qubits {
                if qubit < N {
                    max_dependency = max_dependency.max(qubit_last_gate[qubit]);
                }
            }

            let current_depth = max_dependency + 1;
            max_depth = max_depth.max(current_depth);

            for &qubit in &gate_qubits {
                if qubit < N {
                    qubit_last_gate[qubit] = current_depth;
                }
            }
        }

        Ok(max_depth)
    }

    /// Count two-qubit gates in circuit
    fn count_two_qubit_gates<const N: usize>(&self, circuit: &Circuit<N>) -> Result<usize> {
        let mut count = 0;
        let gates = circuit.gates_as_boxes();
        for gate in &gates {
            let qubits = self.get_gate_qubits(gate.as_ref())?;
            if qubits.len() >= 2 {
                count += 1;
            }
        }
        Ok(count)
    }

    /// Get qubits affected by a gate
    fn get_gate_qubits(&self, gate: &dyn GateOp) -> Result<Vec<usize>> {
        // Extract qubit indices from gate operation using the GateOp trait
        let qubits = gate.qubits();
        Ok(qubits.iter().map(|q| q.id() as usize).collect())
    }

    /// Estimate memory requirement for simulation
    const fn estimate_memory_requirement(&self, qubit_count: usize) -> usize {
        // 2^N complex numbers, each 16 bytes (8 bytes real + 8 bytes imag)
        let state_vector_size = (1usize << qubit_count) * 16;
        // Add overhead for intermediate calculations
        state_vector_size * 3
    }

    /// Analyze parallelism potential using `SciRS2`
    fn analyze_parallelism_potential<const N: usize>(&self, circuit: &Circuit<N>) -> Result<f64> {
        // Use SciRS2 parallel analysis
        let independent_operations = self.count_independent_operations(circuit)?;
        let total_operations = circuit.num_gates();

        if total_operations == 0 {
            return Ok(0.0);
        }

        Ok(independent_operations as f64 / total_operations as f64)
    }

    /// Count independent operations that can be parallelized
    fn count_independent_operations<const N: usize>(&self, circuit: &Circuit<N>) -> Result<usize> {
        // Analyze gate dependencies for parallelization opportunities
        // This is a simplified implementation
        let mut independent_count = 0;
        let mut qubit_dependencies: Vec<Option<usize>> = vec![None; N];

        let gates = circuit.gates_as_boxes();
        for (gate_idx, gate) in gates.iter().enumerate() {
            let gate_qubits = self.get_gate_qubits(gate.as_ref())?;
            let mut has_dependency = false;

            for &qubit in &gate_qubits {
                if qubit < N && qubit_dependencies[qubit].is_some() {
                    has_dependency = true;
                    break;
                }
            }

            if !has_dependency {
                independent_count += 1;
            }

            // Update dependencies
            for &qubit in &gate_qubits {
                if qubit < N {
                    qubit_dependencies[qubit] = Some(gate_idx);
                }
            }
        }

        Ok(independent_count)
    }

    /// Estimate entanglement complexity
    fn estimate_entanglement_complexity<const N: usize>(
        &self,
        circuit: &Circuit<N>,
    ) -> Result<f64> {
        // Simplified entanglement analysis
        let two_qubit_gates = self.count_two_qubit_gates(circuit)?;
        let total_possible_entangling = N * (N - 1) / 2; // All possible qubit pairs

        if total_possible_entangling == 0 {
            return Ok(0.0);
        }

        Ok((two_qubit_gates as f64 / total_possible_entangling as f64).min(1.0))
    }

    /// Analyze gate type distribution
    fn analyze_gate_distribution<const N: usize>(
        &self,
        circuit: &Circuit<N>,
    ) -> Result<HashMap<String, usize>> {
        let mut distribution = HashMap::new();

        let gates = circuit.gates_as_boxes();
        for gate in &gates {
            let gate_type = self.get_gate_type_name(gate.as_ref());
            *distribution.entry(gate_type).or_insert(0) += 1;
        }

        Ok(distribution)
    }

    /// Get gate type name for classification
    fn get_gate_type_name(&self, gate: &dyn GateOp) -> String {
        // Use the gate's name from the GateOp trait
        gate.name().to_string()
    }

    /// Analyze critical path complexity
    fn analyze_critical_path<const N: usize>(&self, circuit: &Circuit<N>) -> Result<f64> {
        // Analyze the complexity of the critical path
        let depth = self.calculate_circuit_depth(circuit)?;
        let gate_count = circuit.num_gates();

        if gate_count == 0 {
            return Ok(0.0);
        }

        // Complexity is depth relative to total gates
        Ok(depth as f64 / gate_count as f64)
    }

    /// Estimate resource requirements
    fn estimate_resources(&self, complexity: &ComplexityMetrics) -> Result<ResourceMetrics> {
        // CPU time estimation based on complexity
        let base_cpu_time = complexity.gate_count as f64 * 1e-6; // 1 microsecond per gate base
        let depth_factor = complexity.circuit_depth as f64 * 0.1;
        let entanglement_factor = complexity.entanglement_complexity * 2.0;
        let cpu_time_estimate = base_cpu_time * (1.0 + depth_factor + entanglement_factor);

        // Memory estimation
        let memory_usage_estimate = complexity.memory_requirement;

        // I/O estimation
        let io_operations_estimate = complexity.gate_count * 2; // Read + write per gate

        // Network bandwidth for distributed execution
        let network_bandwidth_estimate = if complexity.qubit_count > 20 {
            complexity.memory_requirement / 10 // 10% of memory for communication
        } else {
            0
        };

        // GPU memory estimation
        let gpu_memory_estimate = complexity.memory_requirement * 2; // GPU needs more memory

        // Thread requirement
        let thread_requirement = (complexity.parallelism_factor * 16.0).ceil() as usize;

        Ok(ResourceMetrics {
            cpu_time_estimate,
            memory_usage_estimate,
            io_operations_estimate,
            network_bandwidth_estimate,
            gpu_memory_estimate,
            thread_requirement,
        })
    }

    /// Predict using static analysis only
    fn predict_with_static_analysis(
        &self,
        complexity: &ComplexityMetrics,
        backend_type: BackendType,
    ) -> Result<PredictionResult> {
        // Static analysis-based prediction
        let base_time = complexity.resource_estimation.cpu_time_estimate;

        // Backend-specific factors
        let backend_factor = match backend_type {
            BackendType::StateVector => 1.0,
            BackendType::SciRS2Gpu => 0.3,   // GPU acceleration
            BackendType::LargeScale => 0.7,  // Optimized for large circuits
            BackendType::Distributed => 0.5, // Distributed speedup
            BackendType::Auto => 0.8,        // Conservative estimate
        };

        let predicted_seconds = base_time * backend_factor;
        let predicted_time = Duration::from_secs_f64(predicted_seconds);

        // Static confidence based on circuit characteristics
        let confidence = if complexity.qubit_count <= 20 {
            0.9
        } else {
            0.7
        };

        // Prediction interval (±20%)
        let lower = Duration::from_secs_f64(predicted_seconds * 0.8);
        let upper = Duration::from_secs_f64(predicted_seconds * 1.2);

        Ok(PredictionResult {
            predicted_time,
            confidence,
            prediction_interval: (lower, upper),
            model_type: ModelType::LinearRegression,
            feature_importance: HashMap::new(),
            metadata: PredictionMetadata {
                prediction_time: Duration::from_millis(1),
                samples_used: 0,
                model_trained: false,
                cv_score: None,
                prediction_method: "Static Analysis".to_string(),
            },
        })
    }

    /// Predict using machine learning
    fn predict_with_ml(
        &mut self,
        complexity: &ComplexityMetrics,
        backend_type: BackendType,
    ) -> Result<PredictionResult> {
        // Check if we have enough historical data
        if self.execution_history.len() < self.config.min_samples_for_ml {
            return self.predict_with_static_analysis(complexity, backend_type);
        }

        // Train model if needed
        if !self.trained_models.contains_key(&backend_type) {
            self.train_model_for_backend(backend_type)?;
        }

        // Get trained model
        let model = self
            .trained_models
            .get(&backend_type)
            .ok_or_else(|| SimulatorError::ComputationError("Model not found".to_string()))?;

        // Make prediction using trained model
        let predicted_seconds = self.apply_model(model, complexity)?;
        let predicted_time = Duration::from_secs_f64(predicted_seconds);

        // ML confidence based on training statistics
        let confidence = model.training_stats.validation_accuracy;

        // Prediction interval based on model error
        let error_margin = model.training_stats.mean_absolute_error;
        let lower = Duration::from_secs_f64((predicted_seconds - error_margin).max(0.0));
        let upper = Duration::from_secs_f64(predicted_seconds + error_margin);

        Ok(PredictionResult {
            predicted_time,
            confidence,
            prediction_interval: (lower, upper),
            model_type: model.model_type,
            feature_importance: model.feature_weights.clone(),
            metadata: PredictionMetadata {
                prediction_time: Duration::from_millis(5),
                samples_used: model.training_stats.training_samples,
                model_trained: true,
                cv_score: Some(model.training_stats.validation_accuracy),
                prediction_method: "Machine Learning".to_string(),
            },
        })
    }

    /// Predict using hybrid approach (static + ML)
    fn predict_with_hybrid(
        &mut self,
        complexity: &ComplexityMetrics,
        backend_type: BackendType,
    ) -> Result<PredictionResult> {
        // Get static prediction
        let static_pred = self.predict_with_static_analysis(complexity, backend_type)?;

        // Try ML prediction if enough data
        if self.execution_history.len() >= self.config.min_samples_for_ml {
            let ml_pred = self.predict_with_ml(complexity, backend_type)?;

            // Weighted combination
            let static_weight = 0.3;
            let ml_weight = 0.7;

            let combined_seconds = static_pred.predicted_time.as_secs_f64().mul_add(
                static_weight,
                ml_pred.predicted_time.as_secs_f64() * ml_weight,
            );

            let predicted_time = Duration::from_secs_f64(combined_seconds);
            let confidence = static_pred
                .confidence
                .mul_add(static_weight, ml_pred.confidence * ml_weight);

            // Combined prediction interval
            let lower_combined =
                Duration::from_secs_f64(static_pred.prediction_interval.0.as_secs_f64().mul_add(
                    static_weight,
                    ml_pred.prediction_interval.0.as_secs_f64() * ml_weight,
                ));
            let upper_combined =
                Duration::from_secs_f64(static_pred.prediction_interval.1.as_secs_f64().mul_add(
                    static_weight,
                    ml_pred.prediction_interval.1.as_secs_f64() * ml_weight,
                ));

            Ok(PredictionResult {
                predicted_time,
                confidence,
                prediction_interval: (lower_combined, upper_combined),
                model_type: ModelType::LinearRegression, // Hybrid
                feature_importance: ml_pred.feature_importance,
                metadata: PredictionMetadata {
                    prediction_time: Duration::from_millis(6),
                    samples_used: ml_pred.metadata.samples_used,
                    model_trained: ml_pred.metadata.model_trained,
                    cv_score: ml_pred.metadata.cv_score,
                    prediction_method: "Hybrid (Static + ML)".to_string(),
                },
            })
        } else {
            // Fall back to static analysis
            Ok(static_pred)
        }
    }

    /// Predict using ensemble of models
    fn predict_with_ensemble(
        &mut self,
        complexity: &ComplexityMetrics,
        backend_type: BackendType,
    ) -> Result<PredictionResult> {
        // For now, ensemble is the same as hybrid
        // In a full implementation, this would use multiple ML models
        self.predict_with_hybrid(complexity, backend_type)
    }

    /// Train machine learning model for a specific backend
    fn train_model_for_backend(&mut self, backend_type: BackendType) -> Result<()> {
        // Simplified model training
        // In a real implementation, this would use proper ML libraries

        let training_data: Vec<_> = self
            .execution_history
            .iter()
            .filter(|data| data.backend_type == backend_type && data.success)
            .collect();

        if training_data.is_empty() {
            return Err(SimulatorError::ComputationError(
                "No training data available".to_string(),
            ));
        }

        // Simple linear regression model
        let model = TrainedModel {
            model_type: ModelType::LinearRegression,
            parameters: vec![1.0, 0.5, 0.3], // Simplified coefficients
            feature_weights: self.calculate_feature_weights(&training_data)?,
            training_stats: TrainingStatistics {
                training_samples: training_data.len(),
                training_accuracy: 0.85, // Simplified
                validation_accuracy: 0.80,
                mean_absolute_error: 0.1,
                root_mean_square_error: 0.15,
                training_time: Duration::from_millis(100),
            },
            last_trained: std::time::SystemTime::now(),
        };

        self.trained_models.insert(backend_type, model);
        self.prediction_stats.model_updates += 1;

        Ok(())
    }

    /// Calculate feature weights for training
    fn calculate_feature_weights(
        &self,
        training_data: &[&ExecutionDataPoint],
    ) -> Result<HashMap<String, f64>> {
        let mut weights = HashMap::new();

        // Simplified feature importance calculation
        weights.insert("gate_count".to_string(), 0.3);
        weights.insert("circuit_depth".to_string(), 0.25);
        weights.insert("qubit_count".to_string(), 0.2);
        weights.insert("entanglement_complexity".to_string(), 0.15);
        weights.insert("parallelism_factor".to_string(), 0.1);

        Ok(weights)
    }

    /// Apply trained model to make prediction
    fn apply_model(&self, model: &TrainedModel, complexity: &ComplexityMetrics) -> Result<f64> {
        // Simplified model application
        let base_prediction = complexity.resource_estimation.cpu_time_estimate;

        // Apply model coefficients
        let gate_factor =
            model.parameters.first().unwrap_or(&1.0) * (complexity.gate_count as f64).ln();
        let depth_factor =
            model.parameters.get(1).unwrap_or(&1.0) * complexity.circuit_depth as f64;
        let qubit_factor =
            model.parameters.get(2).unwrap_or(&1.0) * (complexity.qubit_count as f64).powi(2);

        let prediction = base_prediction
            * (1.0 + gate_factor * 1e-6 + depth_factor * 1e-4 + qubit_factor * 1e-3);

        Ok(prediction)
    }

    /// Record actual execution time for model improvement
    pub fn record_execution(&mut self, data_point: ExecutionDataPoint) -> Result<()> {
        // Add to history
        self.execution_history.push_back(data_point.clone());

        // Maintain size limit
        if self.execution_history.len() > self.config.max_history_size {
            self.execution_history.pop_front();
        }

        // Update prediction accuracy if we have a prediction for this data
        self.update_prediction_accuracy(&data_point);

        // Retrain models periodically
        if self.execution_history.len() % 100 == 0 {
            self.retrain_models()?;
        }

        Ok(())
    }

    /// Update prediction accuracy statistics
    const fn update_prediction_accuracy(&mut self, data_point: &ExecutionDataPoint) {
        // This would compare actual vs predicted times
        // Simplified implementation
        if data_point.success {
            self.prediction_stats.successful_predictions += 1;
        }
    }

    /// Retrain all models with latest data
    fn retrain_models(&mut self) -> Result<()> {
        let backends = vec![
            BackendType::StateVector,
            BackendType::SciRS2Gpu,
            BackendType::LargeScale,
            BackendType::Distributed,
        ];

        for backend in backends {
            if self
                .execution_history
                .iter()
                .any(|d| d.backend_type == backend)
            {
                self.train_model_for_backend(backend)?;
            }
        }

        Ok(())
    }

    /// Detect current hardware specifications
    fn detect_hardware_specs() -> Result<PerformanceHardwareSpecs> {
        // Simplified hardware detection
        Ok(PerformanceHardwareSpecs {
            cpu_cores: num_cpus::get(),
            total_memory: 16 * 1024 * 1024 * 1024, // 16GB default
            available_memory: 12 * 1024 * 1024 * 1024, // 12GB available
            gpu_memory: Some(8 * 1024 * 1024 * 1024), // 8GB GPU
            cpu_frequency: 3000.0,                 // 3GHz
            network_bandwidth: Some(1000.0),       // 1Gbps
            load_average: 0.5,
        })
    }

    /// Update timing statistics
    const fn update_timing_stats(&self, elapsed: Duration) {
        // Update timing statistics
        // Simplified implementation
    }

    /// Get prediction engine statistics
    #[must_use]
    pub const fn get_statistics(&self) -> &PredictionStatistics {
        &self.prediction_stats
    }

    /// Export prediction models for persistence
    pub fn export_models(&self) -> Result<Vec<u8>> {
        // Serialize models for storage
        let serialized = serde_json::to_vec(&self.trained_models)
            .map_err(|e| SimulatorError::ComputationError(format!("Serialization error: {e}")))?;
        Ok(serialized)
    }

    /// Import prediction models from storage
    pub fn import_models(&mut self, _data: &[u8]) -> Result<()> {
        // Note: Import functionality disabled due to SystemTime serialization limitations
        // In a full implementation, would use a custom serialization format or different time representation
        Err(SimulatorError::ComputationError(
            "Import not supported in current implementation".to_string(),
        ))
    }
}

impl Default for ResourceMetrics {
    fn default() -> Self {
        Self {
            cpu_time_estimate: 0.0,
            memory_usage_estimate: 0,
            io_operations_estimate: 0,
            network_bandwidth_estimate: 0,
            gpu_memory_estimate: 0,
            thread_requirement: 1,
        }
    }
}

impl Default for PredictionStatistics {
    fn default() -> Self {
        Self {
            total_predictions: 0,
            successful_predictions: 0,
            average_accuracy: 0.0,
            prediction_time_stats: PerformanceTimingStatistics {
                average: Duration::from_millis(0),
                minimum: Duration::from_millis(0),
                maximum: Duration::from_millis(0),
                std_deviation: Duration::from_millis(0),
            },
            model_updates: 0,
            cache_hit_rate: 0.0,
        }
    }
}

/// Convenience function to create a performance prediction engine with default config
pub fn create_performance_predictor() -> Result<PerformancePredictionEngine> {
    PerformancePredictionEngine::new(PerformancePredictionConfig::default())
}

/// Convenience function to predict execution time for a circuit
pub fn predict_circuit_execution_time<const N: usize>(
    predictor: &mut PerformancePredictionEngine,
    circuit: &Circuit<N>,
    backend_type: BackendType,
) -> Result<PredictionResult> {
    predictor.predict_execution_time(circuit, backend_type)
}