scirs2_cluster/advanced/

quantum.rs

//! Quantum-inspired clustering algorithms
//!
//! This module provides implementations of quantum-inspired clustering algorithms
//! that leverage quantum computing principles such as superposition, entanglement,
//! and quantum annealing to potentially find better local optima than classical methods.

use scirs2_core::ndarray::{Array1, Array2, ArrayView1, ArrayView2, Zip};
use scirs2_core::numeric::{Float, FromPrimitive, Zero};
use scirs2_core::random::{Rng, SeedableRng};
use serde::{Deserialize, Serialize};
use std::fmt::Debug;

use crate::error::{ClusteringError, Result};
use crate::vq::euclidean_distance;

/// Configuration for quantum-inspired clustering algorithms
#[derive(Debug, Clone, Serialize, Deserialize)]
pub struct QuantumConfig {
    /// Number of quantum states (superposition states)
    pub n_quantum_states: usize,
    /// Quantum decoherence factor (0.0 to 1.0)
    pub decoherence_factor: f64,
    /// Number of quantum iterations
    pub quantum_iterations: usize,
    /// Entanglement strength between quantum states
    pub entanglement_strength: f64,
    /// Measurement probability threshold
    pub measurement_threshold: f64,
    /// Temperature parameter for quantum annealing
    pub temperature: f64,
    /// Cooling rate for simulated quantum annealing
    pub cooling_rate: f64,
}

impl Default for QuantumConfig {
    fn default() -> Self {
        Self {
            n_quantum_states: 8,
            decoherence_factor: 0.95,
            quantum_iterations: 50,
            entanglement_strength: 0.3,
            measurement_threshold: 0.1,
            temperature: 1.0,
            cooling_rate: 0.95,
        }
    }
}

/// Quantum-inspired K-means clustering algorithm
///
/// This algorithm uses quantum superposition principles to maintain multiple
/// possible cluster assignments simultaneously, potentially finding better
/// local optima than classical K-means.
pub struct QuantumKMeans<F: Float> {
    config: QuantumConfig,
    n_clusters: usize,
    quantum_centroids: Option<Array2<F>>,
    quantum_amplitudes: Option<Array2<F>>,
    classical_centroids: Option<Array2<F>>,
    quantum_states: Vec<QuantumState<F>>,
    initialized: bool,
}

/// Represents a quantum state in the clustering algorithm
#[derive(Debug, Clone)]
pub struct QuantumState<F: Float> {
    /// Amplitude of this quantum state
    amplitude: F,
    /// Phase of this quantum state
    phase: F,
    /// Cluster assignment probabilities
    cluster_probabilities: Array1<F>,
}

impl<F: Float + FromPrimitive + Debug> QuantumKMeans<F> {
    /// Create a new quantum K-means instance
    pub fn new(nclusters: usize, config: QuantumConfig) -> Self {
        Self {
            config,
            n_clusters: nclusters,
            quantum_centroids: None,
            quantum_amplitudes: None,
            classical_centroids: None,
            quantum_states: Vec::new(),
            initialized: false,
        }
    }

    /// Initialize quantum states and centroids
    pub fn fit(&mut self, data: ArrayView2<F>) -> Result<()> {
        let (n_samples, n_features) = data.dim();

        if n_samples == 0 || n_features == 0 {
            return Err(ClusteringError::InvalidInput(
                "Data cannot be empty".to_string(),
            ));
        }

        // Initialize quantum centroids with superposition
        let mut quantum_centroids =
            Array2::zeros((self.config.n_quantum_states * self.n_clusters, n_features));
        let mut quantum_amplitudes = Array2::zeros((self.config.n_quantum_states, self.n_clusters));

        // Initialize classical centroids using K-means++
        let mut classical_centroids = Array2::zeros((self.n_clusters, n_features));
        self.initialize_classical_centroids(&mut classical_centroids, data)?;

        // Create quantum superposition of centroids
        for quantum_state in 0..self.config.n_quantum_states {
            for cluster in 0..self.n_clusters {
                let idx = quantum_state * self.n_clusters + cluster;

                // Add quantum noise to classical centroids
                let noise_scale = F::from(0.1).unwrap();
                for feature in 0..n_features {
                    let noise = self.quantum_noise() * noise_scale;
                    quantum_centroids[[idx, feature]] =
                        classical_centroids[[cluster, feature]] + noise;
                }

                // Initialize quantum amplitudes with equal superposition
                quantum_amplitudes[[quantum_state, cluster]] =
                    F::from(1.0 / (self.config.n_quantum_states as f64).sqrt()).unwrap();
            }
        }

        // Initialize quantum states for each data point
        self.quantum_states = Vec::with_capacity(n_samples);
        for _ in 0..n_samples {
            let amplitude = F::from(1.0 / (n_samples as f64).sqrt()).unwrap();
            let phase = F::zero();
            let cluster_probabilities = Array1::from_elem(
                self.n_clusters,
                F::from(1.0 / self.n_clusters as f64).unwrap(),
            );

            self.quantum_states.push(QuantumState {
                amplitude,
                phase,
                cluster_probabilities,
            });
        }

        self.quantum_centroids = Some(quantum_centroids);
        self.quantum_amplitudes = Some(quantum_amplitudes);
        self.classical_centroids = Some(classical_centroids);
        self.initialized = true;

        // Run quantum optimization
        self.quantum_optimization(data)?;

        Ok(())
    }

    /// Initialize classical centroids using K-means++
    fn initialize_classical_centroids(
        &self,
        centroids: &mut Array2<F>,
        data: ArrayView2<F>,
    ) -> Result<()> {
        let n_samples = data.nrows();

        // Choose first centroid randomly
        centroids.row_mut(0).assign(&data.row(0));

        // Choose remaining centroids using K-means++
        for i in 1..self.n_clusters {
            let mut distances = Array1::zeros(n_samples);
            let mut total_distance = F::zero();

            for j in 0..n_samples {
                let mut min_dist = F::infinity();
                for k in 0..i {
                    let dist = euclidean_distance(data.row(j), centroids.row(k));
                    if dist < min_dist {
                        min_dist = dist;
                    }
                }
                distances[j] = min_dist * min_dist;
                total_distance = total_distance + distances[j];
            }

            // Select next centroid probabilistically
            let target = total_distance * F::from(0.5).unwrap();
            let mut cumsum = F::zero();
            for j in 0..n_samples {
                cumsum = cumsum + distances[j];
                if cumsum >= target {
                    centroids.row_mut(i).assign(&data.row(j));
                    break;
                }
            }
        }

        Ok(())
    }

    /// Generate quantum noise for superposition
    fn quantum_noise(&self) -> F {
        // Simplified quantum noise generation
        let mut rng = scirs2_core::random::thread_rng();
        F::from(rng.gen_range(-1.0..1.0)).unwrap()
    }

    /// Perform quantum optimization iterations
    fn quantum_optimization(&mut self, data: ArrayView2<F>) -> Result<()> {
        let mut temperature = F::from(self.config.temperature).unwrap();
        let cooling_rate = F::from(self.config.cooling_rate).unwrap();

        for iteration in 0..self.config.quantum_iterations {
            // Quantum evolution step
            self.quantum_evolution_step(data)?;

            // Entanglement operation
            self.apply_entanglement()?;

            // Measurement and decoherence
            self.measure_and_decohere(temperature)?;

            // Cool down temperature for quantum annealing
            temperature = temperature * cooling_rate;

            // Update classical centroids based on quantum measurements
            if iteration % 10 == 0 {
                self.update_classical_centroids(data)?;
            }
        }

        Ok(())
    }

    /// Quantum evolution step - evolve quantum states
    fn quantum_evolution_step(&mut self, data: ArrayView2<F>) -> Result<()> {
        let quantum_centroids = self.quantum_centroids.as_ref().unwrap();
        let quantum_amplitudes = self.quantum_amplitudes.as_ref().unwrap();

        for (point_idx, point) in data.rows().into_iter().enumerate() {
            let quantum_state = &mut self.quantum_states[point_idx];

            // Calculate quantum distances to all quantum centroids
            for cluster in 0..self.n_clusters {
                let mut total_amplitude = F::zero();

                for quantum_idx in 0..self.config.n_quantum_states {
                    let centroid_idx = quantum_idx * self.n_clusters + cluster;
                    let centroid = quantum_centroids.row(centroid_idx);
                    let distance = euclidean_distance(point, centroid);

                    // Quantum amplitude contribution
                    let amplitude = quantum_amplitudes[[quantum_idx, cluster]];
                    let quantum_weight =
                        amplitude * F::from((-distance.to_f64().unwrap()).exp()).unwrap();
                    total_amplitude = total_amplitude + quantum_weight;
                }

                quantum_state.cluster_probabilities[cluster] = total_amplitude;
            }

            // Normalize probabilities
            let sum: F = quantum_state.cluster_probabilities.sum();
            if sum > F::zero() {
                quantum_state
                    .cluster_probabilities
                    .mapv_inplace(|x| x / sum);
            }
        }

        Ok(())
    }

    /// Apply quantum entanglement between states
    fn apply_entanglement(&mut self) -> Result<()> {
        let entanglement = F::from(self.config.entanglement_strength).unwrap();

        // Simple entanglement: correlate neighboring quantum states
        for i in 0..(self.quantum_states.len() - 1) {
            let (left, right) = self.quantum_states.split_at_mut(i + 1);
            let state_i = &mut left[i];
            let state_j = &mut right[0];

            // Entangle cluster probabilities
            for cluster in 0..self.n_clusters {
                let prob_i = state_i.cluster_probabilities[cluster];
                let prob_j = state_j.cluster_probabilities[cluster];

                let entangled_i = prob_i + entanglement * (prob_j - prob_i);
                let entangled_j = prob_j + entanglement * (prob_i - prob_j);

                state_i.cluster_probabilities[cluster] = entangled_i;
                state_j.cluster_probabilities[cluster] = entangled_j;
            }

            // Normalize after entanglement
            let sum_i: F = state_i.cluster_probabilities.sum();
            let sum_j: F = state_j.cluster_probabilities.sum();

            if sum_i > F::zero() {
                state_i.cluster_probabilities.mapv_inplace(|x| x / sum_i);
            }
            if sum_j > F::zero() {
                state_j.cluster_probabilities.mapv_inplace(|x| x / sum_j);
            }
        }

        Ok(())
    }

    /// Measure quantum states and apply decoherence
    fn measure_and_decohere(&mut self, temperature: F) -> Result<()> {
        let decoherence = F::from(self.config.decoherence_factor).unwrap();
        let threshold = F::from(self.config.measurement_threshold).unwrap();
        let quantum_noise = self.quantum_noise();

        for quantum_state in &mut self.quantum_states {
            // Apply quantum decoherence
            quantum_state.amplitude = quantum_state.amplitude * decoherence;

            // Thermal noise based on temperature
            let thermal_noise = temperature * quantum_noise * F::from(0.01).unwrap();
            quantum_state.phase = quantum_state.phase + thermal_noise;

            // Measurement collapse - if probability is high enough, collapse to classical state
            for cluster in 0..self.n_clusters {
                if quantum_state.cluster_probabilities[cluster] > threshold {
                    // Partial collapse - increase probability of measured state
                    quantum_state.cluster_probabilities[cluster] =
                        quantum_state.cluster_probabilities[cluster] * F::from(1.1).unwrap();
                }
            }

            // Renormalize after measurement
            let sum: F = quantum_state.cluster_probabilities.sum();
            if sum > F::zero() {
                quantum_state
                    .cluster_probabilities
                    .mapv_inplace(|x| x / sum);
            }
        }

        Ok(())
    }

    /// Update classical centroids based on quantum measurements
    fn update_classical_centroids(&mut self, data: ArrayView2<F>) -> Result<()> {
        let classical_centroids = self.classical_centroids.as_mut().unwrap();
        classical_centroids.fill(F::zero());

        let mut cluster_weights = Array1::zeros(self.n_clusters);

        // Weighted update based on quantum probabilities
        for (point_idx, point) in data.rows().into_iter().enumerate() {
            let quantum_state = &self.quantum_states[point_idx];

            for cluster in 0..self.n_clusters {
                let weight = quantum_state.cluster_probabilities[cluster];
                cluster_weights[cluster] = cluster_weights[cluster] + weight;

                // Add weighted contribution to centroid
                Zip::from(classical_centroids.row_mut(cluster))
                    .and(point)
                    .for_each(|centroid_val, &point_val| {
                        *centroid_val = *centroid_val + weight * point_val;
                    });
            }
        }

        // Normalize centroids by weights
        for cluster in 0..self.n_clusters {
            if cluster_weights[cluster] > F::zero() {
                let mut row = classical_centroids.row_mut(cluster);
                row.mapv_inplace(|x| x / cluster_weights[cluster]);
            }
        }

        Ok(())
    }

    /// Predict cluster assignments using quantum probabilities
    pub fn predict(&self, data: ArrayView2<F>) -> Result<Array1<usize>> {
        if !self.initialized {
            return Err(ClusteringError::InvalidInput(
                "Model must be fitted before prediction".to_string(),
            ));
        }

        let classical_centroids = self.classical_centroids.as_ref().unwrap();
        let n_samples = data.nrows();
        let mut labels = Array1::zeros(n_samples);

        for (i, point) in data.rows().into_iter().enumerate() {
            let mut min_distance = F::infinity();
            let mut best_cluster = 0;

            for cluster in 0..self.n_clusters {
                let distance = euclidean_distance(point, classical_centroids.row(cluster));
                if distance < min_distance {
                    min_distance = distance;
                    best_cluster = cluster;
                }
            }

            labels[i] = best_cluster;
        }

        Ok(labels)
    }

    /// Get the final classical centroids
    pub fn cluster_centers(&self) -> Option<&Array2<F>> {
        self.classical_centroids.as_ref()
    }

    /// Get quantum state information for analysis
    pub fn quantum_states(&self) -> &[QuantumState<F>] {
        &self.quantum_states
    }
}

/// Convenience function to perform quantum K-means clustering
pub fn quantum_kmeans<F: Float + FromPrimitive + Debug>(
    data: ArrayView2<F>,
    n_clusters: usize,
    config: Option<QuantumConfig>,
) -> Result<(Array2<F>, Array1<usize>)> {
    let config = config.unwrap_or_default();
    let mut clusterer = QuantumKMeans::new(n_clusters, config);
    clusterer.fit(data)?;

    let centroids = clusterer.cluster_centers().unwrap().clone();
    let labels = clusterer.predict(data)?;

    Ok((centroids, labels))
}

#[cfg(test)]
mod tests {
    use super::*;
    use scirs2_core::ndarray::Array2;

    #[test]
    fn test_quantum_config_default() {
        let config = QuantumConfig::default();
        assert_eq!(config.n_quantum_states, 8);
        assert_eq!(config.quantum_iterations, 50);
        assert!((config.decoherence_factor - 0.95).abs() < 1e-10);
    }

    #[test]
    fn test_quantum_kmeans_creation() {
        let config = QuantumConfig::default();
        let clusterer = QuantumKMeans::<f64>::new(3, config);
        assert_eq!(clusterer.n_clusters, 3);
        assert!(!clusterer.initialized);
    }

    #[test]
    fn test_quantum_kmeans_simple() {
        let data = Array2::from_shape_vec(
            (6, 2),
            vec![0.0, 0.0, 1.0, 1.0, 0.0, 1.0, 1.0, 0.0, 5.0, 5.0, 6.0, 6.0],
        )
        .unwrap();
        let config = QuantumConfig {
            quantum_iterations: 10,
            ..Default::default()
        };

        let result = quantum_kmeans(data.view(), 2, Some(config));
        assert!(result.is_ok());

        let (centroids, labels) = result.unwrap();
        assert_eq!(centroids.nrows(), 2);
        assert_eq!(centroids.ncols(), 2);
        assert_eq!(labels.len(), 6);
    }

    #[test]
    fn test_quantum_state() {
        let amplitude = 0.5f64;
        let phase = 0.0f64;
        let cluster_probs = Array1::from_vec(vec![0.3, 0.7]);

        let state = QuantumState {
            amplitude,
            phase,
            cluster_probabilities: cluster_probs,
        };

        assert!((state.amplitude - 0.5).abs() < 1e-10);
        assert_eq!(state.cluster_probabilities.len(), 2);
    }

    #[test]
    fn test_quantum_noise_generation() {
        let config = QuantumConfig::default();
        let clusterer = QuantumKMeans::<f64>::new(2, config);

        let noise = clusterer.quantum_noise();
        assert!(noise >= -1.0 && noise <= 1.0);
    }
}