Full-revivals in 2-D Quantum Walks

Details Full-revivals in 2-D Quantum Walks Full-revivals in 2-D Quantum Walks

2010-11-09

arxiv.org/abs/1011.2066v1

Phys. Scr. T140, 014035 (2010)

Physics

Quantum Physics

Scientific paper

10.1088/0031-8949/2010/T140/0140

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.

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