A quantum walk inspired model for distributed computing on arbitrary graphs

TL;DR

This paper introduces a quantum walk inspired distributed computing model for arbitrary graphs, demonstrating its ability to replicate quantum walk dynamics, analyze communication costs, and solve search problems with numerical validation.

Contribution

It presents a novel distributed computation model based on quantum walks applicable to any graph topology, bridging quantum cellular automata and quantum walk dynamics.

Findings

Model reproduces quantum walk dynamics on graphs

Communication costs vary with interaction schemes

Numerical results show effectiveness on different topologies

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.