A Grover-Based Quantum Algorithm for Solving Perfect Mazes via Fitness-Guided Search

TL;DR

This paper introduces a quantum algorithm leveraging Grover's search to efficiently solve perfect mazes by encoding paths in superposition and iteratively refining the search with a fitness-guided oracle.

Contribution

It presents a novel quantum algorithm that encodes maze paths in superposition and uses a fitness-based oracle with adaptive cutoff to improve maze solving efficiency.

Findings

Algorithm scales efficiently with maze size and path length.

Formal definitions and convergence guarantees are provided.

Framework is extensible to other search domains.

Abstract

We present a quantum algorithm for solving perfect mazes by casting the pathfinding task as a structured search problem. Building on Grover's amplitude amplification, the algorithm encodes all candidate paths in superposition and evaluates their proximity to the goal using a reversible fitness operator based on quantum arithmetic. A Grover-compatible oracle marks high-fitness states, and an adaptive cutoff strategy refines the search iteratively. We provide formal definitions, unitary constructions, and convergence guarantees, along with a resource analysis showing efficient scaling with maze size and path length. The framework serves as a foundation for quantum-hybrid pathfinding and planning. The full algorithmic pipeline is specified from encoding to amplification, including oracle design and fitness evaluation. The approach is readily extensible to other search domains, including navigation over tree-like or acyclic graphs.