{"title":"Exponential speedup of quantum algorithms for the pathfinding problem","authors":"Jianqiang Li","doi":"10.1007/s11128-025-04689-7","DOIUrl":null,"url":null,"abstract":"<div><p>Given <i>x</i>, <i>y</i> on an unweighted undirected graph <i>G</i>, the goal of the pathfinding problem is to find an <i>x</i>–<i>y</i> path. In this work, we first construct a graph <i>G</i> based on welded trees and define a pathfinding problem in the adjacency list oracle <i>O</i>. Then we provide an efficient quantum algorithm to find an <i>x</i>–<i>y</i> path in the graph <i>G</i>. Finally, we prove that no classical algorithm can find an <i>x</i>–<i>y</i> path in subexponential time with high probability. The pathfinding problem is one of the fundamental graph-related problems. Our findings suggest that quantum algorithms could potentially offer advantages in more types of graphs to solve the pathfinding problem.</p></div>","PeriodicalId":746,"journal":{"name":"Quantum Information Processing","volume":"24 3","pages":""},"PeriodicalIF":2.2000,"publicationDate":"2025-02-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Quantum Information Processing","FirstCategoryId":"101","ListUrlMain":"https://link.springer.com/article/10.1007/s11128-025-04689-7","RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"PHYSICS, MATHEMATICAL","Score":null,"Total":0}
引用次数: 0
Abstract
Given x, y on an unweighted undirected graph G, the goal of the pathfinding problem is to find an x–y path. In this work, we first construct a graph G based on welded trees and define a pathfinding problem in the adjacency list oracle O. Then we provide an efficient quantum algorithm to find an x–y path in the graph G. Finally, we prove that no classical algorithm can find an x–y path in subexponential time with high probability. The pathfinding problem is one of the fundamental graph-related problems. Our findings suggest that quantum algorithms could potentially offer advantages in more types of graphs to solve the pathfinding problem.
期刊介绍：
Quantum Information Processing is a high-impact, international journal publishing cutting-edge experimental and theoretical research in all areas of Quantum Information Science. Topics of interest include quantum cryptography and communications, entanglement and discord, quantum algorithms, quantum error correction and fault tolerance, quantum computer science, quantum imaging and sensing, and experimental platforms for quantum information. Quantum Information Processing supports and inspires research by providing a comprehensive peer review process, and broadcasting high quality results in a range of formats. These include original papers, letters, broadly focused perspectives, comprehensive review articles, book reviews, and special topical issues. The journal is particularly interested in papers detailing and demonstrating quantum information protocols for cryptography, communications, computation, and sensing.
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