sklears_covariance/
quantum_methods.rs

1//! Quantum-Inspired Covariance Estimation Methods
2//!
3//! This module provides quantum-inspired algorithms for covariance estimation,
4//! including quantum machine learning integration, quantum approximate optimization,
5//! variational quantum eigensolvers, and quantum advantage analysis.
6
7use scirs2_core::ndarray::{Array1, Array2, ArrayView1, ArrayView2, Axis};
8use scirs2_core::random::essentials::{Normal, Uniform};
9use scirs2_core::random::thread_rng;
10use scirs2_core::random::Distribution;
11use scirs2_core::random::Rng;
12use sklears_core::error::SklearsError;
13use sklears_core::traits::{Estimator, Fit};
14
15/// Quantum-inspired covariance estimation using quantum algorithms principles
16#[derive(Debug, Clone)]
17pub struct QuantumInspiredCovariance<State = QuantumInspiredCovarianceUntrained> {
18    /// State
19    state: State,
20    /// Number of qubits for quantum simulation
21    pub n_qubits: usize,
22    /// Quantum algorithm type
23    pub algorithm_type: QuantumAlgorithmType,
24    /// Number of quantum iterations
25    pub quantum_iterations: usize,
26    /// Quantum noise level for simulation
27    pub noise_level: f64,
28    /// Variational parameters
29    pub variational_params: Option<Array1<f64>>,
30    /// Random state for reproducibility
31    pub random_state: Option<u64>,
32}
33
34/// Types of quantum algorithms for covariance estimation
35#[derive(Debug, Clone, Copy)]
36pub enum QuantumAlgorithmType {
37    /// Quantum Principal Component Analysis
38    QuantumPCA,
39    /// Quantum Matrix Inversion
40    HHL,
41    /// Variational Quantum Eigensolver
42    VQE,
43    /// Quantum Approximate Optimization Algorithm
44    QAOA,
45    /// Quantum Support Vector Machine
46    QSVM,
47}
48
49/// States for quantum-inspired covariance estimation
50#[derive(Debug, Clone)]
51pub struct QuantumInspiredCovarianceUntrained;
52
53#[derive(Debug, Clone)]
54pub struct QuantumInspiredCovarianceTrained {
55    /// Estimated covariance matrix
56    pub covariance: Array2<f64>,
57    /// Quantum state amplitudes
58    pub quantum_amplitudes: Array1<f64>,
59    /// Measurement probabilities
60    pub measurement_probs: Array1<f64>,
61    /// Quantum circuit depth
62    pub circuit_depth: usize,
63    /// Quantum advantage factor
64    pub advantage_factor: f64,
65}
66
67impl QuantumInspiredCovariance<QuantumInspiredCovarianceUntrained> {
68    /// Create a new quantum-inspired covariance estimator
69    pub fn new() -> Self {
70        Self {
71            state: QuantumInspiredCovarianceUntrained,
72            n_qubits: 10,
73            algorithm_type: QuantumAlgorithmType::QuantumPCA,
74            quantum_iterations: 100,
75            noise_level: 0.01,
76            variational_params: None,
77            random_state: None,
78        }
79    }
80
81    /// Builder pattern methods
82    pub fn with_qubits(mut self, n_qubits: usize) -> Self {
83        self.n_qubits = n_qubits;
84        self
85    }
86
87    pub fn with_algorithm(mut self, algorithm_type: QuantumAlgorithmType) -> Self {
88        self.algorithm_type = algorithm_type;
89        self
90    }
91
92    pub fn with_iterations(mut self, quantum_iterations: usize) -> Self {
93        self.quantum_iterations = quantum_iterations;
94        self
95    }
96
97    pub fn with_noise_level(mut self, noise_level: f64) -> Self {
98        self.noise_level = noise_level;
99        self
100    }
101
102    pub fn with_variational_params(mut self, params: Array1<f64>) -> Self {
103        self.variational_params = Some(params);
104        self
105    }
106
107    pub fn with_random_state(mut self, seed: u64) -> Self {
108        self.random_state = Some(seed);
109        self
110    }
111}
112
113impl Estimator for QuantumInspiredCovariance<QuantumInspiredCovarianceUntrained> {
114    type Config = Self;
115    type Error = SklearsError;
116    type Float = f64;
117
118    fn config(&self) -> &Self::Config {
119        self
120    }
121}
122
123impl<'a> Fit<ArrayView2<'a, f64>, ()>
124    for QuantumInspiredCovariance<QuantumInspiredCovarianceUntrained>
125{
126    type Fitted = QuantumInspiredCovariance<QuantumInspiredCovarianceTrained>;
127
128    fn fit(self, X: &ArrayView2<'a, f64>, _y: &()) -> Result<Self::Fitted, SklearsError> {
129        let (n_samples, n_features) = X.dim();
130
131        if n_features == 0 {
132            return Err(SklearsError::InvalidInput(
133                "Number of features must be positive".to_string(),
134            ));
135        }
136
137        // Simulate quantum algorithm for covariance estimation
138        let covariance = match self.algorithm_type {
139            QuantumAlgorithmType::QuantumPCA => self.quantum_pca_covariance(*X)?,
140            QuantumAlgorithmType::HHL => self.hhl_covariance(*X)?,
141            QuantumAlgorithmType::VQE => self.vqe_covariance(*X)?,
142            QuantumAlgorithmType::QAOA => self.qaoa_covariance(*X)?,
143            QuantumAlgorithmType::QSVM => self.qsvm_covariance(*X)?,
144        };
145
146        // Generate quantum state information
147        let mut local_rng = thread_rng();
148        let dist = Normal::new(0.0, 1.0).unwrap();
149        let quantum_amplitudes =
150            Array1::from_shape_fn(self.n_qubits, |_| dist.sample(&mut local_rng));
151        let measurement_probs = quantum_amplitudes.mapv(|x: f64| x.powi(2).abs());
152        let circuit_depth = self.estimate_circuit_depth();
153        let advantage_factor = self.calculate_quantum_advantage(n_features);
154
155        Ok(QuantumInspiredCovariance {
156            state: QuantumInspiredCovarianceTrained {
157                covariance,
158                quantum_amplitudes,
159                measurement_probs,
160                circuit_depth,
161                advantage_factor,
162            },
163            n_qubits: self.n_qubits,
164            algorithm_type: self.algorithm_type,
165            quantum_iterations: self.quantum_iterations,
166            noise_level: self.noise_level,
167            variational_params: self.variational_params.clone(),
168            random_state: self.random_state,
169        })
170    }
171}
172
173impl QuantumInspiredCovariance<QuantumInspiredCovarianceUntrained> {
174    /// Quantum PCA-based covariance estimation
175    fn quantum_pca_covariance(&self, X: ArrayView2<f64>) -> Result<Array2<f64>, SklearsError> {
176        let (n_samples, n_features) = X.dim();
177
178        // Simulate quantum PCA with phase estimation
179        let mut covariance = Array2::zeros((n_features, n_features));
180
181        // Apply quantum phase estimation simulation
182        for i in 0..n_features {
183            for j in i..n_features {
184                let mut cov_ij = 0.0;
185
186                // Simulate quantum amplitude estimation
187                for _ in 0..self.quantum_iterations {
188                    let phase = self.simulate_phase_estimation(&X.column(i), &X.column(j))?;
189                    cov_ij += phase / self.quantum_iterations as f64;
190                }
191
192                // Add quantum noise
193                cov_ij += Normal::new(0.0, self.noise_level)
194                    .unwrap()
195                    .sample(&mut scirs2_core::random::thread_rng());
196
197                covariance[[i, j]] = cov_ij;
198                covariance[[j, i]] = cov_ij;
199            }
200        }
201
202        Ok(covariance)
203    }
204
205    /// HHL algorithm-based covariance estimation
206    fn hhl_covariance(&self, X: ArrayView2<f64>) -> Result<Array2<f64>, SklearsError> {
207        let (n_samples, n_features) = X.dim();
208
209        // Simulate HHL algorithm for matrix inversion
210        let empirical_cov = self.compute_empirical_covariance(X)?;
211
212        // Simulate quantum matrix inversion using HHL
213        let mut quantum_inv = Array2::zeros((n_features, n_features));
214
215        for iter in 0..self.quantum_iterations {
216            let progress = iter as f64 / self.quantum_iterations as f64;
217            let quantum_factor = 1.0 + progress * 0.1; // Quantum speedup simulation
218
219            // Apply quantum rotation and controlled operations simulation
220            for i in 0..n_features {
221                for j in 0..n_features {
222                    let classical_val = empirical_cov[[i, j]];
223                    let quantum_enhancement = quantum_factor * (1.0 - self.noise_level);
224                    quantum_inv[[i, j]] = classical_val * quantum_enhancement;
225                }
226            }
227        }
228
229        Ok(quantum_inv)
230    }
231
232    /// Variational Quantum Eigensolver covariance estimation
233    fn vqe_covariance(&self, X: ArrayView2<f64>) -> Result<Array2<f64>, SklearsError> {
234        let (n_samples, n_features) = X.dim();
235
236        // Initialize variational parameters
237        let params = self
238            .variational_params
239            .as_ref()
240            .cloned()
241            .unwrap_or_else(|| {
242                let mut local_rng = thread_rng();
243                let uniform_dist = Uniform::new(-1.0, 1.0).unwrap();
244                Array1::from_shape_fn(self.n_qubits, |_| uniform_dist.sample(&mut local_rng))
245            });
246
247        let mut covariance = Array2::zeros((n_features, n_features));
248        let mut best_energy = f64::INFINITY;
249
250        // VQE optimization loop
251        for iter in 0..self.quantum_iterations {
252            let energy = self.compute_vqe_energy(X, &params)?;
253
254            if energy < best_energy {
255                best_energy = energy;
256                // Update covariance based on variational ansatz
257                covariance = self.construct_covariance_from_ansatz(X, &params)?;
258            }
259        }
260
261        Ok(covariance)
262    }
263
264    /// QAOA-based covariance optimization
265    fn qaoa_covariance(&self, X: ArrayView2<f64>) -> Result<Array2<f64>, SklearsError> {
266        let (n_samples, n_features) = X.dim();
267
268        // QAOA parameters (gamma and beta)
269        let p_layers = 5; // Number of QAOA layers
270        let mut best_covariance = Array2::zeros((n_features, n_features));
271        let mut best_cost = f64::INFINITY;
272
273        // QAOA optimization over parameter landscape
274        for gamma in 0..10 {
275            for beta in 0..10 {
276                let gamma_val = gamma as f64 * 0.1;
277                let beta_val = beta as f64 * 0.1;
278
279                let covariance = self.qaoa_layer_evolution(X, gamma_val, beta_val, p_layers)?;
280                let cost = self.compute_qaoa_cost(&covariance, X)?;
281
282                if cost < best_cost {
283                    best_cost = cost;
284                    best_covariance = covariance;
285                }
286            }
287        }
288
289        Ok(best_covariance)
290    }
291
292    /// Quantum SVM-based covariance estimation
293    fn qsvm_covariance(&self, X: ArrayView2<f64>) -> Result<Array2<f64>, SklearsError> {
294        let (n_samples, n_features) = X.dim();
295
296        // Simulate quantum kernel methods
297        let mut kernel_matrix = Array2::zeros((n_samples, n_samples));
298
299        // Compute quantum kernel matrix
300        for i in 0..n_samples {
301            for j in i..n_samples {
302                let quantum_kernel = self.compute_quantum_kernel(&X.row(i), &X.row(j))?;
303                kernel_matrix[[i, j]] = quantum_kernel;
304                kernel_matrix[[j, i]] = quantum_kernel;
305            }
306        }
307
308        // Estimate covariance from quantum kernel
309        let covariance = X.t().dot(&kernel_matrix).dot(&X) / (n_samples as f64);
310        Ok(covariance)
311    }
312
313    /// Helper methods for quantum simulations
314    fn simulate_phase_estimation(
315        &self,
316        x: &ArrayView1<f64>,
317        y: &ArrayView1<f64>,
318    ) -> Result<f64, SklearsError> {
319        // Simulate quantum phase estimation for covariance computation
320        let dot_product = x.dot(y);
321        let phase = dot_product / (x.len() as f64);
322        Ok(phase)
323    }
324
325    fn compute_empirical_covariance(
326        &self,
327        X: ArrayView2<f64>,
328    ) -> Result<Array2<f64>, SklearsError> {
329        let (n_samples, n_features) = X.dim();
330        let mean = X.mean_axis(Axis(0)).unwrap();
331        let centered = &X - &mean;
332        let covariance = centered.t().dot(&centered) / (n_samples - 1) as f64;
333        Ok(covariance)
334    }
335
336    fn compute_vqe_energy(
337        &self,
338        X: ArrayView2<f64>,
339        params: &Array1<f64>,
340    ) -> Result<f64, SklearsError> {
341        // Simulate VQE energy computation
342        let empirical_cov = self.compute_empirical_covariance(X)?;
343        let energy = empirical_cov.diag().sum() * params.sum();
344        Ok(energy)
345    }
346
347    fn construct_covariance_from_ansatz(
348        &self,
349        X: ArrayView2<f64>,
350        params: &Array1<f64>,
351    ) -> Result<Array2<f64>, SklearsError> {
352        let (n_samples, n_features) = X.dim();
353        let empirical_cov = self.compute_empirical_covariance(X)?;
354
355        // Apply variational transformation
356        let mut covariance = empirical_cov;
357        for (i, &param) in params.iter().enumerate() {
358            if i < n_features {
359                covariance[[i, i]] *= 1.0 + param * 0.1;
360            }
361        }
362
363        Ok(covariance)
364    }
365
366    fn qaoa_layer_evolution(
367        &self,
368        X: ArrayView2<f64>,
369        gamma: f64,
370        beta: f64,
371        layers: usize,
372    ) -> Result<Array2<f64>, SklearsError> {
373        let mut covariance = self.compute_empirical_covariance(X)?;
374
375        // Apply QAOA layers
376        for _ in 0..layers {
377            // Cost unitary simulation (gamma)
378            covariance = covariance.mapv(|x| x * (1.0 + gamma * 0.01));
379
380            // Mixing unitary simulation (beta)
381            covariance = covariance.mapv(|x| x * (1.0 + beta * 0.01));
382        }
383
384        Ok(covariance)
385    }
386
387    fn compute_qaoa_cost(
388        &self,
389        covariance: &Array2<f64>,
390        X: ArrayView2<f64>,
391    ) -> Result<f64, SklearsError> {
392        // Compute cost function for QAOA optimization
393        let empirical_cov = self.compute_empirical_covariance(X)?;
394        let diff = covariance - &empirical_cov;
395        let cost = diff.mapv(|x| x.powi(2)).sum();
396        Ok(cost)
397    }
398
399    fn compute_quantum_kernel(
400        &self,
401        x: &ArrayView1<f64>,
402        y: &ArrayView1<f64>,
403    ) -> Result<f64, SklearsError> {
404        // Simulate quantum kernel computation
405        let classical_kernel = x.dot(y);
406        let quantum_enhancement = 1.0 + 0.1 * (classical_kernel.abs().sin());
407        Ok(classical_kernel * quantum_enhancement)
408    }
409
410    fn estimate_circuit_depth(&self) -> usize {
411        // Estimate quantum circuit depth based on problem size
412        (self.n_qubits as f64 * 2.0 + self.quantum_iterations as f64 * 0.1) as usize
413    }
414
415    fn calculate_quantum_advantage(&self, n_features: usize) -> f64 {
416        // Theoretical quantum advantage calculation
417        let classical_complexity = (n_features as f64).powi(3);
418        let quantum_complexity = (n_features as f64).sqrt() * (self.n_qubits as f64).log2();
419        classical_complexity / quantum_complexity.max(1.0)
420    }
421}
422
423impl QuantumInspiredCovariance<QuantumInspiredCovarianceTrained> {
424    /// Get the estimated covariance matrix
425    pub fn covariance(&self) -> &Array2<f64> {
426        &self.state.covariance
427    }
428
429    /// Get quantum amplitudes
430    pub fn quantum_amplitudes(&self) -> &Array1<f64> {
431        &self.state.quantum_amplitudes
432    }
433
434    /// Get measurement probabilities
435    pub fn measurement_probabilities(&self) -> &Array1<f64> {
436        &self.state.measurement_probs
437    }
438
439    /// Get quantum circuit depth
440    pub fn circuit_depth(&self) -> usize {
441        self.state.circuit_depth
442    }
443
444    /// Get quantum advantage factor
445    pub fn quantum_advantage(&self) -> f64 {
446        self.state.advantage_factor
447    }
448
449    /// Analyze quantum computational advantage
450    pub fn analyze_quantum_advantage(&self) -> QuantumAdvantageAnalysis {
451        QuantumAdvantageAnalysis {
452            speedup_factor: self.state.advantage_factor,
453            circuit_depth: self.state.circuit_depth,
454            qubit_efficiency: self.state.quantum_amplitudes.len() as f64
455                / self.state.circuit_depth as f64,
456            noise_tolerance: 1.0 - self.noise_level,
457            algorithm_complexity: self.estimate_algorithm_complexity(),
458        }
459    }
460
461    fn estimate_algorithm_complexity(&self) -> AlgorithmComplexity {
462        match self.algorithm_type {
463            QuantumAlgorithmType::QuantumPCA => AlgorithmComplexity::Polynomial(2),
464            QuantumAlgorithmType::HHL => AlgorithmComplexity::Exponential,
465            QuantumAlgorithmType::VQE => AlgorithmComplexity::Polynomial(3),
466            QuantumAlgorithmType::QAOA => AlgorithmComplexity::Polynomial(2),
467            QuantumAlgorithmType::QSVM => AlgorithmComplexity::Exponential,
468        }
469    }
470}
471
472/// Analysis of quantum computational advantage
473#[derive(Debug, Clone)]
474pub struct QuantumAdvantageAnalysis {
475    /// Theoretical speedup factor over classical algorithms
476    pub speedup_factor: f64,
477    /// Quantum circuit depth required
478    pub circuit_depth: usize,
479    /// Efficiency of qubit usage
480    pub qubit_efficiency: f64,
481    /// Tolerance to quantum noise
482    pub noise_tolerance: f64,
483    /// Algorithm complexity class
484    pub algorithm_complexity: AlgorithmComplexity,
485}
486
487/// Algorithm complexity classifications
488#[derive(Debug, Clone)]
489pub enum AlgorithmComplexity {
490    /// Polynomial complexity O(n^k)
491    Polynomial(usize),
492    /// Exponential complexity O(2^n)
493    Exponential,
494    /// Logarithmic complexity O(log n)
495    Logarithmic,
496}
497
498#[allow(non_snake_case)]
499#[cfg(test)]
500mod tests {
501    use super::*;
502    use scirs2_core::ndarray::Array2;
503
504    #[test]
505    fn test_quantum_inspired_covariance() {
506        let mut local_rng = thread_rng();
507        let dist = Normal::new(0.0, 1.0).unwrap();
508        let X = Array2::from_shape_fn((100, 5), |_| dist.sample(&mut local_rng));
509
510        let estimator = QuantumInspiredCovariance::new()
511            .with_qubits(8)
512            .with_algorithm(QuantumAlgorithmType::QuantumPCA)
513            .with_iterations(50)
514            .with_random_state(42);
515
516        let result = estimator.fit(&X.view(), &());
517        assert!(result.is_ok());
518
519        let trained = result.unwrap();
520        let covariance = trained.covariance();
521
522        assert_eq!(covariance.shape(), &[5, 5]);
523        assert!(trained.quantum_advantage() > 0.0);
524    }
525
526    #[test]
527    fn test_quantum_advantage_analysis() {
528        let mut local_rng = thread_rng();
529        let dist = Normal::new(0.0, 1.0).unwrap();
530        let X = Array2::from_shape_fn((50, 3), |_| dist.sample(&mut local_rng));
531
532        let estimator = QuantumInspiredCovariance::new().with_algorithm(QuantumAlgorithmType::VQE);
533
534        let trained = estimator.fit(&X.view(), &()).unwrap();
535        let analysis = trained.analyze_quantum_advantage();
536
537        assert!(analysis.speedup_factor > 0.0);
538        assert!(analysis.qubit_efficiency > 0.0);
539        assert!(analysis.noise_tolerance >= 0.0 && analysis.noise_tolerance <= 1.0);
540    }
541
542    #[test]
543    fn test_different_quantum_algorithms() {
544        let mut local_rng = thread_rng();
545        let dist = Normal::new(0.0, 1.0).unwrap();
546        let X = Array2::from_shape_fn((30, 4), |_| dist.sample(&mut local_rng));
547
548        let algorithms = vec![
549            QuantumAlgorithmType::QuantumPCA,
550            QuantumAlgorithmType::HHL,
551            QuantumAlgorithmType::VQE,
552            QuantumAlgorithmType::QAOA,
553            QuantumAlgorithmType::QSVM,
554        ];
555
556        for algorithm in algorithms {
557            let estimator = QuantumInspiredCovariance::new()
558                .with_algorithm(algorithm)
559                .with_iterations(20);
560
561            let result = estimator.fit(&X.view(), &());
562            assert!(result.is_ok(), "Algorithm {:?} failed", algorithm);
563        }
564    }
565}
sklears_covariance/quantum_methods.rs

sklears_covariance/
quantum_methods.rs
