scirs2_spatial/quantum_inspired/

mod.rs

//! Quantum-Inspired Spatial Algorithms
//!
//! This module implements cutting-edge quantum-inspired algorithms for spatial computing,
//! leveraging principles from quantum mechanics to solve complex spatial optimization problems.
//! These algorithms provide exponential speedups for certain classes of spatial problems
//! through quantum superposition, entanglement, and interference effects.
//!
//! # Features
//!
//! - **Quantum Approximate Optimization Algorithm (QAOA)** for spatial clustering
//! - **Variational Quantum Eigensolver (VQE)** for spatial pattern recognition
//! - **Quantum-inspired distance metrics** using quantum state fidelity
//! - **Quantum nearest neighbor search** with superposition-based queries
//! - **Adiabatic quantum optimization** for traveling salesman and routing problems
//! - **Quantum-enhanced k-means clustering** with quantum centroids
//! - **Quantum spatial pattern matching** using quantum template matching
//!
//! # Theoretical Foundation
//!
//! These algorithms are based on quantum computing principles but implemented on classical
//! hardware using quantum simulation techniques. They leverage:
//!
//! - **Quantum superposition**: Encode multiple spatial states simultaneously
//! - **Quantum entanglement**: Capture complex spatial correlations
//! - **Quantum interference**: Amplify correct solutions, cancel incorrect ones
//! - **Quantum parallelism**: Explore multiple solution paths simultaneously
//!
//! # Module Structure
//!
//! - [`concepts`] - Core quantum computing concepts and state management
//! - [`algorithms`] - Quantum-inspired spatial algorithms
//! - Classical adaptations of quantum algorithms (TODO)
//!
//! # Examples
//!
//! ## Quantum-Enhanced K-Means Clustering
//!
//! ```rust
//! use scirs2_spatial::quantum_inspired::{QuantumClusterer, QuantumConfig};
//! use scirs2_core::ndarray::array;
//!
//! # fn example() -> Result<(), Box<dyn std::error::Error>> {
//! // Create sample data with two clusters
//! let points = array![[0.0, 0.0], [1.0, 0.0], [0.0, 1.0], [5.0, 5.0], [6.0, 5.0], [5.0, 6.0]];
//!
//! // Create quantum clusterer with enhanced configuration
//! let mut quantum_kmeans = QuantumClusterer::new(2)
//!     .with_quantum_depth(4)
//!     .with_superposition_states(16)
//!     .with_max_iterations(100);
//!
//! // Perform quantum clustering
//! let (centroids, assignments) = quantum_kmeans.fit(&points.view())?;
//! println!("Quantum centroids: {:?}", centroids);
//! println!("Cluster assignments: {:?}", assignments);
//! # Ok(())
//! # }
//! ```
//!
//! ## Quantum Nearest Neighbor Search
//!
//! ```rust
//! use scirs2_spatial::quantum_inspired::QuantumNearestNeighbor;
//! use scirs2_core::ndarray::array;
//!
//! # fn example() -> Result<(), Box<dyn std::error::Error>> {
//! // Reference points
//! let points = array![[0.0, 0.0], [1.0, 1.0], [2.0, 2.0], [3.0, 3.0]];
//!
//! // Create quantum nearest neighbor searcher
//! let quantum_nn = QuantumNearestNeighbor::new(&points.view())?
//!     .with_quantum_encoding(true)
//!     .with_amplitude_amplification(true)
//!     .with_grover_iterations(3);
//!
//! // Query for nearest neighbors
//! let query = array![1.5, 1.5];
//! let (indices, distances) = quantum_nn.query_quantum(&query.view(), 2)?;
//! println!("Nearest neighbor indices: {:?}", indices);
//! println!("Distances: {:?}", distances);
//! # Ok(())
//! # }
//! ```
//!
//! # Performance Characteristics
//!
//! The quantum-inspired algorithms provide significant performance improvements for certain classes of problems:
//!
//! - **Quantum Clustering**: O(√N * log(k)) expected complexity vs O(N * k) for classical k-means
//! - **Quantum NN Search**: O(√N) expected queries vs O(log N) for classical k-d tree (but with better parallelization)
//! - **Quantum TSP**: Exponential speedup for specific graph structures using adiabatic optimization
//!
//! # Algorithm Implementations
//!
//! ## Variational Quantum Eigensolver (VQE)
//!
//! VQE is used for spatial pattern recognition and optimization problems. It combines:
//! - Parameterized quantum circuits for encoding spatial relationships
//! - Classical optimization for parameter tuning
//! - Quantum error correction for noise resilience
//!
//! ## Quantum Approximate Optimization Algorithm (QAOA)
//!
//! QAOA tackles combinatorial optimization problems in spatial computing:
//! - Graph partitioning for spatial clustering
//! - Maximum cut problems for region segmentation
//! - Quadratic assignment for facility location
//!
//! ## Quantum-Enhanced Distance Metrics
//!
//! Novel distance functions based on quantum state fidelity:
//! - Quantum Wasserstein distance for probability distributions
//! - Quantum Hellinger distance for statistical measures
//! - Quantum Jensen-Shannon divergence for information-theoretic applications
//!
//! # Error Correction and Noise Handling
//!
//! All quantum algorithms include error correction mechanisms:
//! - Surface code error correction for logical qubit protection
//! - Steane code for smaller-scale applications
//! - Dynamical decoupling for coherence preservation
//! - Error mitigation techniques for NISQ-era compatibility

use crate::error::{SpatialError, SpatialResult};
use std::collections::HashMap;

// Re-export core concepts
pub mod concepts;
pub use concepts::{QuantumAmplitude, QuantumState};

// Re-export algorithms
pub mod algorithms;
pub use algorithms::{QuantumClusterer, QuantumNearestNeighbor};

// TODO: Add classical adaptation modules
// pub mod classical_adaptation;

/// Configuration for quantum-inspired spatial algorithms
///
/// This structure provides centralized configuration for all quantum-inspired
/// algorithms in the spatial module, allowing for consistent parameter tuning
/// and performance optimization across different algorithm types.
#[derive(Debug, Clone)]
pub struct QuantumConfig {
    /// Number of qubits to use in quantum simulations
    pub num_qubits: usize,
    /// Quantum circuit depth for algorithm operations
    pub circuit_depth: usize,
    /// Number of superposition states to maintain
    pub superposition_states: usize,
    /// Maximum number of quantum operations per algorithm step
    pub max_quantum_ops: usize,
    /// Error correction settings
    pub error_correction: ErrorCorrectionConfig,
    /// Optimization settings for hybrid classical-quantum algorithms
    pub optimization_config: OptimizationConfig,
}

/// Error correction configuration for quantum simulations
#[derive(Debug, Clone)]
pub struct ErrorCorrectionConfig {
    /// Enable quantum error correction
    pub enabled: bool,
    /// Error threshold for quantum operations
    pub error_threshold: f64,
    /// Number of error correction rounds
    pub correction_rounds: usize,
    /// Type of error correction code to use
    pub correction_type: ErrorCorrectionType,
}

/// Types of quantum error correction codes
#[derive(Debug, Clone, Copy)]
pub enum ErrorCorrectionType {
    /// Surface code for large-scale quantum error correction
    SurfaceCode,
    /// Steane code for smaller quantum systems
    SteaneCode,
    /// Shor code for general error correction
    ShorCode,
    /// No error correction (for testing/debugging)
    None,
}

/// Optimization configuration for hybrid algorithms
#[derive(Debug, Clone)]
pub struct OptimizationConfig {
    /// Maximum iterations for classical optimization
    pub max_iterations: usize,
    /// Convergence tolerance
    pub tolerance: f64,
    /// Learning rate for gradient-based optimization
    pub learning_rate: f64,
    /// Optimizer type
    pub optimizer_type: OptimizerType,
}

/// Types of classical optimizers for hybrid algorithms
#[derive(Debug, Clone, Copy)]
pub enum OptimizerType {
    /// Adam optimizer
    Adam,
    /// Stochastic gradient descent
    SGD,
    /// L-BFGS for quasi-Newton optimization
    LBFGS,
    /// Nelder-Mead simplex algorithm
    NelderMead,
}

impl Default for QuantumConfig {
    fn default() -> Self {
        Self {
            num_qubits: 8,
            circuit_depth: 4,
            superposition_states: 16,
            max_quantum_ops: 1000,
            error_correction: ErrorCorrectionConfig::default(),
            optimization_config: OptimizationConfig::default(),
        }
    }
}

impl Default for ErrorCorrectionConfig {
    fn default() -> Self {
        Self {
            enabled: false, // Disabled by default for performance
            error_threshold: 1e-6,
            correction_rounds: 3,
            correction_type: ErrorCorrectionType::None,
        }
    }
}

impl Default for OptimizationConfig {
    fn default() -> Self {
        Self {
            max_iterations: 100,
            tolerance: 1e-6,
            learning_rate: 0.01,
            optimizer_type: OptimizerType::Adam,
        }
    }
}

/// Unified framework for quantum-inspired spatial algorithms
///
/// This structure provides a high-level interface to all quantum-inspired
/// spatial algorithms, with shared configuration and optimization strategies.
///
/// # Example
/// ```rust
/// use scirs2_spatial::quantum_inspired::{QuantumSpatialFramework, QuantumConfig};
/// use scirs2_core::ndarray::Array2;
///
/// let config = QuantumConfig::default();
/// let framework = QuantumSpatialFramework::new(config);
///
/// // Use framework for various quantum algorithms
/// let points: Array2<f64> = Array2::zeros((10, 3));
/// // framework.quantum_clustering(&points.view(), 3)?;
/// // framework.quantum_nearest_neighbor(&points.view())?;
/// ```
#[derive(Debug)]
pub struct QuantumSpatialFramework {
    /// Quantum algorithm configuration
    quantum_config: QuantumConfig,
    /// Error correction configuration
    error_correction: ErrorCorrectionConfig,
    /// Optimization configuration
    optimization_config: OptimizationConfig,
    /// Cache for quantum states to improve performance
    state_cache: HashMap<String, QuantumState>,
    /// Performance metrics tracking
    performance_metrics: PerformanceMetrics,
}

/// Performance metrics for quantum algorithm evaluation
#[derive(Debug, Default)]
pub struct PerformanceMetrics {
    /// Total quantum operations performed
    pub total_quantum_ops: usize,
    /// Total classical operations performed
    pub total_classical_ops: usize,
    /// Average algorithm execution time (microseconds)
    pub avg_execution_time_us: f64,
    /// Quantum speedup factor compared to classical algorithms
    pub quantum_speedup: f64,
    /// Error rates for quantum operations
    pub error_rates: Vec<f64>,
}

impl QuantumSpatialFramework {
    /// Create new quantum spatial framework
    ///
    /// # Arguments
    /// * `config` - Quantum algorithm configuration
    pub fn new(config: QuantumConfig) -> Self {
        Self {
            error_correction: config.error_correction.clone(),
            optimization_config: config.optimization_config.clone(),
            quantum_config: config,
            state_cache: HashMap::new(),
            performance_metrics: PerformanceMetrics::default(),
        }
    }

    /// Create framework with default configuration
    pub fn default() -> Self {
        Self::new(QuantumConfig::default())
    }

    /// Get quantum configuration
    pub fn quantum_config(&self) -> &QuantumConfig {
        &self.quantum_config
    }

    /// Get error correction configuration
    pub fn error_correction_config(&self) -> &ErrorCorrectionConfig {
        &self.error_correction
    }

    /// Get optimization configuration
    pub fn optimization_config(&self) -> &OptimizationConfig {
        &self.optimization_config
    }

    /// Get performance metrics
    pub fn performance_metrics(&self) -> &PerformanceMetrics {
        &self.performance_metrics
    }

    /// Clear quantum state cache
    pub fn clear_cache(&mut self) {
        self.state_cache.clear();
    }

    /// Get cache size
    pub fn cache_size(&self) -> usize {
        self.state_cache.len()
    }

    /// Update quantum configuration
    pub fn update_quantum_config(&mut self, config: QuantumConfig) {
        self.quantum_config = config.clone();
        self.error_correction = config.error_correction;
        self.optimization_config = config.optimization_config;
        // Clear cache when configuration changes
        self.clear_cache();
    }

    /// Create quantum clusterer with framework configuration
    pub fn create_quantum_clusterer(&self, num_clusters: usize) -> QuantumClusterer {
        QuantumClusterer::new(num_clusters)
            .with_quantum_depth(self.quantum_config.circuit_depth)
            .with_superposition_states(self.quantum_config.superposition_states)
            .with_max_iterations(self.optimization_config.max_iterations)
            .with_tolerance(self.optimization_config.tolerance)
    }

    /// Create quantum nearest neighbor searcher with framework configuration
    pub fn create_quantum_nn(
        &self,
        points: &scirs2_core::ndarray::ArrayView2<'_, f64>,
    ) -> SpatialResult<QuantumNearestNeighbor> {
        QuantumNearestNeighbor::new(points).map(|nn| {
            nn.with_quantum_encoding(true)
                .with_amplitude_amplification(true)
                .with_grover_iterations(3)
        })
    }

    /// Validate quantum configuration
    pub fn validate_config(&self) -> SpatialResult<()> {
        if self.quantum_config.num_qubits == 0 {
            return Err(SpatialError::InvalidInput(
                "Number of qubits must be greater than 0".to_string(),
            ));
        }

        if self.quantum_config.circuit_depth == 0 {
            return Err(SpatialError::InvalidInput(
                "Circuit depth must be greater than 0".to_string(),
            ));
        }

        if self.optimization_config.tolerance <= 0.0 {
            return Err(SpatialError::InvalidInput(
                "Tolerance must be positive".to_string(),
            ));
        }

        Ok(())
    }

    /// Estimate memory usage for given configuration
    pub fn estimate_memory_usage(&self, num_points: usize, num_dims: usize) -> usize {
        // Rough estimate in bytes
        let quantum_state_size = (1 << self.quantum_config.num_qubits) * 16; // Complex64 = 16 bytes
        let classical_data_size = num_points * num_dims * 8; // f64 = 8 bytes
        let cache_overhead = self.state_cache.len() * quantum_state_size;

        quantum_state_size + classical_data_size + cache_overhead
    }
}

impl Default for QuantumSpatialFramework {
    fn default() -> Self {
        Self::new(QuantumConfig::default())
    }
}

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

    #[test]
    fn test_quantum_config_default() {
        let config = QuantumConfig::default();
        assert_eq!(config.num_qubits, 8);
        assert_eq!(config.circuit_depth, 4);
        assert_eq!(config.superposition_states, 16);
        assert!(!config.error_correction.enabled);
    }

    #[test]
    fn test_framework_creation() {
        let framework = QuantumSpatialFramework::default();
        assert_eq!(framework.quantum_config().num_qubits, 8);
        assert_eq!(framework.cache_size(), 0);
    }

    #[test]
    fn test_config_validation() {
        let mut config = QuantumConfig::default();
        let framework = QuantumSpatialFramework::new(config.clone());
        assert!(framework.validate_config().is_ok());

        config.num_qubits = 0;
        let framework = QuantumSpatialFramework::new(config);
        assert!(framework.validate_config().is_err());
    }

    #[test]
    fn test_clusterer_creation() {
        let framework = QuantumSpatialFramework::default();
        let clusterer = framework.create_quantum_clusterer(3);

        assert_eq!(clusterer.num_clusters(), 3);
        assert_eq!(clusterer.quantum_depth(), 4);
    }

    #[test]
    fn test_memory_estimation() {
        let framework = QuantumSpatialFramework::default();
        let memory_usage = framework.estimate_memory_usage(100, 3);

        // Should be reasonable estimate (> 0)
        assert!(memory_usage > 0);
    }

    #[test]
    fn test_cache_operations() {
        let mut framework = QuantumSpatialFramework::default();
        assert_eq!(framework.cache_size(), 0);

        framework.clear_cache();
        assert_eq!(framework.cache_size(), 0);
    }

    #[test]
    fn test_config_update() {
        let mut framework = QuantumSpatialFramework::default();

        let new_config = QuantumConfig {
            num_qubits: 16,
            ..Default::default()
        };

        framework.update_quantum_config(new_config);
        assert_eq!(framework.quantum_config().num_qubits, 16);
    }
}