Enhancing classical pathfinding via probabilistically guided search governed by Grover probability distributions

Abstract

Pathfinding on grid maps with obstacles is a fundamental problem in robotics, autonomous mechatronic systems, and artificial intelligence. Classical algorithms such as BFS, Dijkstra, and A* guarantee optimal solutions under specific conditions, but often explore many redundant nodes, leading to increased computational overhead and memory saturation. This paper introduces an advanced, probabilistically guided path planning method based on the Grover probability distribution. The quantum-inspired heuristic leverages Grover’s algorithm framework to generate a highly targeted probabilistic guidance map, biasing the search toward more promising spatial corridors. To ensure methodological rigor, benchmarks are scaled up to a 30 × 30 grid and comprehensively evaluated across 30 randomly generated map instances with strict statistical analysis. Furthermore, the 8-directional movement framework is corrected to incorporate an exact geometric cost of √ 2 for diagonal transitions, preventing valuation errors common in simplified benchmarks. Experiments demonstrate that the Grover-guided approach significantly reduces the number of visited nodes compared to classical BFS and Dijkstra while maintaining strict path quality and completeness. Finally, I report and discuss the actual execution times, addressing the classical computational overhead introduced by simulating quantum iterations on conventional hardware, and charting a path toward real-time deployment on genuine quantum processing units (QPUs) for future mechatronic applications.