Quantum Algorithm to Solve a Maze: Converting the Maze Problem into a Search Problem

kniraj@iitk.ac.inIndian Institute of Technology, KanpurWe propose a di erent methodology towards approaching a Maze problem. We convert theproblem into a Quantum Search Problem (QSP), and its solutions are sought for using the iterativeGrover’s Search Algorithm. Though the category of mazes we are looking at are of the NP completeclass[1], we have redirected such a NP complete problem into a QSP. Our solution deals with twodimensional perfect mazes with no closed loops. We encode all possible individual paths from thestarting point of the maze into a quantum register. A quantum tness operator applied on theregister encodes each individual with its tness value. We propose an oracle design which marks allthe individuals above a certain tness value and use the Grover search algorithm to nd one of themarked states. Iterating over this method, we approach towards the optimum solution.I. INTRODUCTION