Quantum Geometric Machine Learning (QGML) Documentation

Welcome to the comprehensive documentation for Quantum Geometric Machine Learning (QGML), an advanced framework that combines quantum geometric principles with machine learning for intrinsic dimension estimation, manifold learning, and data analysis.

Overview

QGML leverages quantum geometric principles to encode classical data in quantum states, enabling:

  • Intrinsic dimension estimation using quantum geometric techniques

  • Manifold learning with quantum coherent states

  • Topological data analysis via Berry curvature and Chern numbers

  • Advanced quantum information measures for data characterization

  • Quantum-classical hybrid learning algorithms

Key Features

Core Framework

  • Base quantum matrix operations with Hermitian constraints

  • Error Hamiltonian construction and ground state computation

  • Quantum state expectation value calculations

  • Unified architecture for supervised and unsupervised learning

Advanced Topological Analysis

  • Berry curvature field computation over parameter space

  • Chern number calculation for topological invariants

  • Quantum phase transition detection

  • Quantum metric tensor analysis

Quantum Information Measures

  • Von Neumann entropy for entanglement quantification

  • Quantum Fisher information matrix for parameter estimation

  • Quantum coherence and capacity measures

  • Cross-correlation analysis between geometric properties

Specialized Applications

  • Chromosomal instability analysis for cancer research

  • Financial time series forecasting

  • High-dimensional manifold learning

  • Quantum-enhanced feature extraction

Quick Start

Installation

git clone <repository-url>
cd qgml
pip install -e .

Basic Usage

import torch
from qgml.geometry.quantum_geometry_trainer import QuantumGeometryTrainer

# Create trainer with advanced quantum geometric features
trainer = QuantumGeometryTrainer(
    N=8, # Hilbert space dimension
    D=2, # Feature space dimension
    fluctuation_weight=1.0,
    topology_weight=0.1
)

# Generate sample data
points = torch.randn(100, 2)

# Perform complete quantum geometric analysis
analysis = trainer.analyze_complete_quantum_geometry(
    points,
    compute_topology=True,
    compute_information=True,
    output_dir="analysis_results"
)

# Access results
print(f"Berry curvature: {analysis['topology']['sample_berry_curvature']}")
print(f"Von Neumann entropy: {analysis['quantum_information']['von_neumann_entropy']}")

Architecture Overview

digraph qgml_architecture { rankdir=TB; node [shape=box, style=rounded]; base [label="BaseQuantumMatrixTrainer\n(Core quantum operations)"]; unsup [label="UnsupervisedMatrixTrainer\n(Manifold learning)"]; sup [label="SupervisedMatrixTrainer\n(Regression/Classification)"]; geom [label="QuantumGeometryTrainer\n(Advanced geometric features)"]; chromo [label="ChromosomalInstabilityTrainer\n(Specialized genomic analysis)"]; topo [label="TopologicalAnalyzer\n(Berry curvature, Chern numbers)"]; info [label="QuantumInformationAnalyzer\n(Entropy, Fisher information)"]; base -> unsup; base -> sup; base -> geom; sup -> chromo; geom -> topo; geom -> info; {rank=same; unsup, sup} {rank=same; topo, info} }

Contents

User Guide

Visualizations

API Reference

Experimental Results

Indices and tables