One Dimensional Quantum Walks with Two-step Memory

Abstract: In this paper we investigate one dimensional quantum walks with two-step memory, which can be viewed as an extension of quantum walks with one-step memory. We develop a general formula for the amplitudes of the two-step-memory walk with Hadamard coin by using path integral approach, and numerically simulate its process. The simulation shows that the probability distribution of this new walk is different from that of the Hadamard quantum walk with one-step memory, while it presents some similarities with that of the normal Hadamard quantum walk without memory.