Using quantum mechanics to find your way through a maze

Guy Vandegrift

Students can explore quantum mechanics with a concept map that uses only the most elementary solutions to Schrödinger's equation. The content has been slightly modified from the traditional introduction to the subject because the issue of interpretation is postponed until Parseval's theorem is reached and used to postulate two fundamental equations of probability, simultaneously. A set of canonical but approximate equations can describe wavepacket motion for most linear waves. If restricted to certain special cases, these equations of wavepacket motion are easily derived and can serve as a temporary substitute for Ehrenfest's theorem. A number of exercises can be incorporated into this maze of quantum mechanics.

Konstantin K. Likharev

Yuto Ishikawa, Takuma Yoshihara, Keita Okamura +1 more

In this study, 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 difficulty mazes, we introduce an additional cost function Qupdate 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. The results show that Qupdate generates difficult mazes tailored to the individual. Furthermore, it show that the quantum processing unit is more efficient at generating mazes than other solvers. Finally, we also present applications how our results could be used in the future.

Jean Bricmont

Lauren Peters