Module quantum_machine_learning 

Quantum-Inspired Machine Learning Algorithms

This module provides quantum-inspired machine learning algorithms for spatial classification and pattern recognition tasks. The algorithms leverage quantum computing principles — specifically quantum feature maps and kernel methods — to achieve enhanced classification performance on complex spatial data.

Algorithms

• QuantumSVMModel: Quantum-enhanced Support Vector Machine using quantum kernel functions computed via random Fourier features (Rahimi-Recht method)
• QuantumClassifier: Hybrid quantum-classical classifier wrapping the quantum SVM with optional preprocessing

Theoretical Foundation

The quantum feature map φ: ℝᵈ → ℝᴰ (D >> d) approximates a quantum kernel k(x, z) = ⟨φ(x), φ(z)⟩ ≈ exp(-‖x - z‖² / (2σ²)) by drawing random frequencies ω from a distribution whose Fourier transform is the kernel’s spectral density. This is the Rahimi-Recht random Fourier feature approach.

The SVM dual problem is solved via Sequential Minimal Optimization (SMO) to find support vectors and dual coefficients α.

Structs

QuantumClassifier

Quantum-Classical Hybrid Classifier

QuantumSVMModel

Quantum-Enhanced Support Vector Machine