Quantum Diffusion Simulator

Quantum Walks for Information Spread Modeling

Qiskit Fall Fest 2025 - Quantum Walks Hackathon

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Overview

This project implements a quantum walk simulator to explore how quantum interference changes the dynamics of information spread across networks. We compare quantum walks with classical random walks, demonstrating the unique properties of quantum diffusion.

Key Features

• 1D Quantum Walk Implementation using Qiskit
• Classical Random Walk Baseline for comparison
• Quantitative Metrics (entropy, coverage, interference visibility)
• Multiple Network Topologies (ring, star, random)

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Quick Start

Installation

# Clone repository
git clone https://github.com/TeyjK/quantum-diffusion-simulator
cd quantum-diffusion-simulator

# Install dependencies
pip install -r requirements.txt

Run the Demo

# Launch Jupyter notebook
jupyter notebook main_ring.ipynb

# Or run as Python script (after converting)
# jupyter nbconvert --to script main_ring.ipynb
# python main.py

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How It Works

Classical Random Walk

In a classical random walk, a walker moves to a random neighbor at each step with equal probability. The probability distribution spreads smoothly and symmetrically.

Algorithm:

1. Start at a single node with probability
2. At each step, distribute probability equally to neighbors
3. Result: Smooth + predictable diffusion (like heat spreading)

Quantum Walk

In a quantum walk, we use:

• Coin qubit: Creates superposition of left/right directions
• Position qubits: Encode walker's location on the network
• Interference: Different paths combine, creating peaks and valleys

Algorithm:

1. Initialize walker at starting position
2. Apply coin operator (rotation gate)
3. Apply shift operator (conditional position update based on coin)
4. Repeat for multiple steps
5. Measure final probability distribution

Key Difference: Quantum interference causes constructive and destructive interference, creating wave-like patterns that differ dramatically from classical diffusion.