Full-revivals in 2-D Quantum Walks
Quantum Physics
2010-11-10 v1
Abstract
Recurrence of a random walk is described by the Polya number. For quantum walks, recurrence is understood as the return of the walker to the origin, rather than the full-revival of its quantum state. Localization for two dimensional quantum walks is known to exist in the sense of non-vanishing probability distribution in the asymptotic limit. We show on the example of the 2-D Grover walk that one can exploit the effect of localization to construct stationary solutions. Moreover, we find full-revivals of a quantum state with a period of two steps. We prove that there cannot be longer cycles for a four-state quantum walk. Stationary states and revivals result from interference which has no counterpart in classical random walks.
Cite
@article{arxiv.1011.2066,
title = {Full-revivals in 2-D Quantum Walks},
author = {M. Stefanak and B. Kollar and T. Kiss and I. Jex},
journal= {arXiv preprint arXiv:1011.2066},
year = {2010}
}