Multiparticle quantum walks for distinguishing hard graphs

Fuente: arXiv
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Autores principales: Kasture, Sachin, Acheche, Shaheen, Henriet, Loic, Henry, Louis-Paul
Formato: Preprint
Publicado: 2025
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author Kasture, Sachin
Acheche, Shaheen
Henriet, Loic
Henry, Louis-Paul
author_facet Kasture, Sachin
Acheche, Shaheen
Henriet, Loic
Henry, Louis-Paul
contents Quantum random walks have been shown to be powerful quantum algorithms for certain tasks on graphs like database searching, quantum simulations etc. In this work we focus on its applications for the graph isomorphism problem. In particular we look at how we can compare multi-particle quantum walks and well known classical WL tests and how quantum walks can be used to distinguish hard graphs like CFI graphs which k-WL tests cannot distinguish. We provide theoretical proofs and empirical results to show that a k-QW with input superposition states distinguishes k-CFI graphs. In addition we also prove that a k-1 QW with localized input states distinguishes k-CFI graphs. We also prove some additional results about strongly regular graphs (SRGs).
format Preprint
id arxiv_https___arxiv_org_abs_2501_03683
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Multiparticle quantum walks for distinguishing hard graphs
Kasture, Sachin
Acheche, Shaheen
Henriet, Loic
Henry, Louis-Paul
Quantum Physics
Quantum random walks have been shown to be powerful quantum algorithms for certain tasks on graphs like database searching, quantum simulations etc. In this work we focus on its applications for the graph isomorphism problem. In particular we look at how we can compare multi-particle quantum walks and well known classical WL tests and how quantum walks can be used to distinguish hard graphs like CFI graphs which k-WL tests cannot distinguish. We provide theoretical proofs and empirical results to show that a k-QW with input superposition states distinguishes k-CFI graphs. In addition we also prove that a k-1 QW with localized input states distinguishes k-CFI graphs. We also prove some additional results about strongly regular graphs (SRGs).
title Multiparticle quantum walks for distinguishing hard graphs
topic Quantum Physics
url https://arxiv.org/abs/2501.03683