Individual subject evaluated difficulty of adjustable mazes generated using quantum annealing

TL;DR

This paper presents a novel method for generating mazes of varying difficulty using quantum annealing, evaluated through human subjects and computational solvers, advancing quantum-based puzzle creation.

Contribution

It reformulates maze generation as a quadratic unconstrained binary optimization problem for quantum annealing and introduces a cost function to control maze difficulty.

Findings

Quantum annealing effectively generates diverse maze difficulties.

Maze difficulty correlates with human solving time.

Hybrid solvers show promising efficiency in maze generation.

Abstract

In this paper, the maze generation using quantum annealing is proposed. We reformulate a standard algorithm to generate a maze into a specific form of a quadratic unconstrained binary optimization problem suitable for the input of the quantum annealer. To generate more difficult mazes, we introduce an additional cost function $Q_{update}$ to increase the difficulty. The difficulty of the mazes was evaluated by the time to solve the maze of 12 human subjects. To check the efficiency of our scheme to create the maze, we investigated the time-to-solution of a quantum processing unit, classical computer, and hybrid solver.