quantumwalks 1.0.1

A comprehensive Python package for simulating quantum walks in various dimensions and on complex networks

# Quantum Walks

A comprehensive Python package for simulating quantum walks in various dimensions and on complex networks.

## Features

- **Multi-dimensional quantum walks**: 1D, 2D, and 3D discrete-time quantum walks
- **Graph-based quantum walks**: Quantum walks on arbitrary graphs using various coin operators
- **Szegedy quantum walks**: Advanced quantum walks for complex network analysis
- **Quantum ranking algorithms**: Quantum PageRank and node ranking for network analysis
- **Comprehensive visualization**: Built-in plotting utilities for all walk types
- **Performance analysis**: Convergence analysis and comparison tools

## Installation

```bash
pip install quantumwalks

Quick Start

import numpy as np
import networkx as nx
from quantumwalks import DTQW1D, GraphDTQW, QuantumPageRank

# 1D quantum walk
qw1d = DTQW1D(N=100, coin_type='hadamard')
qw1d.initialize_state(init_pos=0)
qw1d.evolve(50)
qw1d.plot()

# Graph quantum walk
graph = nx.karate_club_graph()
gqw = GraphDTQW(graph, coin_type='grover', initial_node=0)
gqw.evolve(10)
gqw.plot()

# Quantum PageRank
qpr = QuantumPageRank(graph)
ranking = qpr.get_ranking()
qpr.plot(plot_type='bar')

Documentation

Full documentation is available at quantumwalks.readthedocs.io

Examples

Check the examples/ directory for comprehensive usage examples:

• basic_usage.py: Basic quantum walk simulations
• network_analysis.py: Network analysis with quantum walks
• visualization_demo.py: Advanced visualization techniques

Basic 1D Walk Example

from quantumwalks import DTQW1D
import numpy as np

# Initialize 1D quantum walk
qw = DTQW1D(N=100, coin_type='hadamard')
qw.initialize_state(init_pos=0, init_coin=np.array([1, 1j])/np.sqrt(2))

# Evolve and plot
qw.evolve(100)
qw.plot()

Network Analysis Example

import networkx as nx
from quantumwalks import GraphDTQW, QuantumPageRank

# Create complex network
graph = nx.connected_watts_strogatz_graph(20, 4, 0.3)

# Quantum walk on graph
gqw = GraphDTQW(graph, coin_type='grover', initial_node=0)
gqw.evolve(10)
gqw.plot()

# Quantum PageRank analysis
qpr = QuantumPageRank(graph)
ranking = qpr.get_sorted_ranking()
print("Top nodes:", ranking[:5])

Supported Quantum Walk Types

Discrete-Time Quantum Walks

• 1D Walks: Line graphs with various coin operators
• 2D Walks: Lattice graphs with 4-direction movement
• 3D Walks: Cubic lattices with 6-direction movement

Graph-Based Walks

• GraphDTQW: Quantum walks on arbitrary graphs
• SzegedyQW: Szegedy quantum walks for complex networks
• DTQWPageRank: Discrete-time quantum walk for node ranking
• QuantumPageRank: Quantum PageRank using Szegedy formalism

Coin Operators

• Hadamard coin
• Grover coin
• Fourier coin
• SU(n) coin

Advanced Usage

Convergence Analysis

from quantumwalks import analyze_convergence, plot_convergence_analysis

graph = nx.barabasi_albert_graph(30, 2)
gqw = GraphDTQW(graph, coin_type='grover', initial_node=0)

# Analyze convergence behavior
convergence_data = analyze_convergence(gqw, max_steps=50)
plot_convergence_analysis(convergence_data)

Quantum vs Classical Comparison

from quantumwalks import compare_classical_quantum

graph = nx.connected_caveman_graph(3, 8)
comparison = compare_classical_quantum(graph)

print(f"Correlation: {comparison['correlation']:.4f}")
print(f"KL Divergence: {comparison['kl_divergence']:.4f}")

API Overview

Core Classes

• DTQW1D, DTQW2D, DTQW3D: Multi-dimensional quantum walks
• GraphDTQW: Quantum walks on arbitrary graphs
• SzegedyQW: Szegedy quantum walks
• DTQWPageRank, QuantumPageRank: Quantum ranking algorithms

Key Methods

• evolve(num_steps): Evolve quantum walk for specified steps
• get_probabilities(): Get current probability distribution
• plot(): Visualize results
• get_ranking(): Compute node ranking scores

Dependencies

• Python >= 3.8
• NumPy >= 1.21.0
• SciPy >= 1.7.0
• Matplotlib >= 3.5.0
• NetworkX >= 2.6.0

Development

To contribute to this project:

# Clone repository
git clone https://github.com/TDSKS-123/quantumwalks
cd quantumwalks

# Install in development mode
pip install -e .

# Install development dependencies
pip install -e ".[dev]"

# Run tests
pytest tests/

Citation

If you use this package in your research, please cite:

@software{quantumwalks2025,
  title = {Quantum Walks: A Python package for quantum walk simulations},
  author = {LiangWen},
  year = {2025},
  url = {https://github.com/TDSKS-123/quantumwalks}
}

License

This project is licensed under the MIT License - see the LICENSE file for details.

Contributing

Contributions are welcome! Please feel free to submit a Pull Request.

1. Fork the project
2. Create your feature branch (git checkout -b feature/AmazingFeature)
3. Commit your changes (git commit -m 'Add some AmazingFeature')
4. Push to the branch (git push origin feature/AmazingFeature)
5. Open a Pull Request

Support

If you encounter any problems or have questions:

• Open an issue on GitHub
• Check the documentation

Changelog

Version 1.0.1

• Initial release with comprehensive quantum walk implementations
• Support for 1D, 2D, and 3D quantum walks
• Graph-based quantum walks and ranking algorithms
• Advanced visualization and analysis tools
• Fixed some issues that prevented operation, and now all examples can run.