Work

A mathematical framework for maze solving using quantum walks

Year: 2025

Type: article

Abstract: We provide a mathematical framework for identifying the shortest path in a maze using a Grover walk, which becomes non-unitary by introducing absorbing holes. In this study, we define the maze as a network with vertices connected by unweighted edges. Our analysis of the stationary state of the truncated Grover walk on finite graphs, where we strategically place absorbing holes and self-loops on specific vertices, demonstrates that this approach can effectively solve mazes. By setting arbitrary start and goal vertices in the underlying graph, we obtain the following long-time results: (i) in tree structures, the probability amplitude is concentrated exclusively along the shortest path between start and goal; (ii) in ladder-like structures with additional paths, the probability amplitude is maximized near the shortest path.

Source: Quantum Information Processing

DOI: 10.1007/s11128-025-04711-y

Authors: Leo Matsuoka, Hiromichi Ohno, Etsuo Segawa

Institutions: Hiroshima Institute of Technology, Shinshu University, Yokohama National University

Language: English

Topic: Quantum Computing Algorithms and Architecture

Subfield: Artificial Intelligence

Field: Computer Science

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $2,990

Funders: Shinshu University, Japan Society for the Promotion of Science