Exponential speedup of quantum algorithms for the pathfinding problem

Jianqiang Li

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arXiv · 2307.12492

Exponential speedup of quantum algorithms for the pathfinding problem

Jianqiang Li

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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.

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Jianqiang Li. 2023-07-24. Exponential speedup of quantum algorithms for the pathfinding problem. https://arxiv.org/abs/2307.12492

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