One Dimensional Quantum Walks with Memory

Abstract

We investigate the quantum versions of a one-dimensional random walk, whose corresponding Markov Chain is of order 2. This corresponds to the walk having a memory of up to two previous steps. We derive the amplitudes and probabilities for these walks, and point out how they differ from both classical random walks, and quantum walks without memory.

arXiv comment18 pages, 3 figures: second version has small changes: some corrections, extra references, better diagrams.