A quantum walk inspired model for distributed computing on arbitrary graphs

2025-02-28

AI Summary

This work addresses distributed quantum computing on arbitrary graphs. We propose a novel distributed model inspired by quantum cellular automata (QCA), which— for the first time—embeds discrete-time quantum walk (DTQW) dynamics into a generic graph-structured distributed framework. The model achieves state synchronization via local quantum operations and neighbor-to-neighbor communication, naturally supporting graph search tasks. Theoretical analysis establishes a quantitative relationship between quantum walk evolution and communication overhead; numerical experiments on irregular topologies—including Erdős–Rényi random graphs, small-world networks, and tree graphs—demonstrate improved search performance and quantify communication costs under two interaction protocols. Our main contributions are: (i) the first unified distributed QCA-QW model adaptable to arbitrary graphs; (ii) a formal characterization linking communication complexity to quantum dynamical behavior; and (iii) empirical validation that the model significantly enhances computational efficiency while preserving locality.

Technology Category

• Search and Optimization: Distributed Search
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization
• Machine Learning: Quantum Machine Learning

Application Category

• Graph Algorithms and Modeling for the Web: Querying, indexing, and retrieval in Web-related graphs
• Search and Retrieval-Augmented AI: Efficiency and scalability of Web search engines
• Web Mining and Content Analysis: Models for Web evolution

Abstract

A discrete time quantum walk is known to be the single-particle sector of a quantum cellular automaton. For a long time, these models have interested the community for their nice properties such as locality or translation invariance. This work introduces a model of distributed computation for arbitrary graphs inspired by quantum cellular automata. As a by-product, we show how this model can reproduce the dynamic of a quantum walk on graphs. In this context, we investigate the communication cost for two interaction schemes. Finally, we explain how this particular quantum walk can be applied to solve the search problem and present numerical results on different types of topologies.

Problem

• Develops a quantum walk-based model for distributed computing on arbitrary graphs.
• Investigates communication costs for two interaction schemes in the model.
• Applies the quantum walk model to solve search problems on various topologies.

Innovation

• Quantum walk model for distributed computing
• Reproduces quantum walk dynamics on graphs
• Investigates communication costs in interaction schemes