Module quantum_inspired

scirs2_spatial

Module quantum_inspired 

Source
Expand description

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

use scirs2_spatial::quantum_inspired::{QuantumClusterer, QuantumConfig};
use scirs2_core::ndarray::array;

// 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);
use scirs2_spatial::quantum_inspired::QuantumNearestNeighbor;
use scirs2_core::ndarray::array;

// 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);

§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

Re-exports§

pub use concepts::QuantumAmplitude;
pub use concepts::QuantumState;
pub use algorithms::QuantumClusterer;
pub use algorithms::QuantumNearestNeighbor;

Modules§

algorithms
Quantum-Inspired Algorithms
concepts
Core Quantum Computing Concepts

Structs§

ErrorCorrectionConfig
Error correction configuration for quantum simulations
OptimizationConfig
Optimization configuration for hybrid algorithms
PerformanceMetrics
Performance metrics for quantum algorithm evaluation
QuantumConfig
Configuration for quantum-inspired spatial algorithms
QuantumSpatialFramework
Unified framework for quantum-inspired spatial algorithms

Enums§

ErrorCorrectionType
Types of quantum error correction codes
OptimizerType
Types of classical optimizers for hybrid algorithms