Quantum walks with memory provided by recycled coins and a memory of the coin-flip history

Peter P. Rohde*, Gavin K. Brennen, Alexei Gilchrist

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

21 Citations (Scopus)
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Abstract

Quantum walks have emerged as an interesting approach to quantum information processing, exhibiting many unique properties compared to the analogous classical random walk. Here we introduce a model for a discrete-time quantum walk with memory by endowing the walker with multiple recycled coins and using a physical memory function via a history dependent coin flip. By numerical simulation we observe several phenomena. First in one dimension, walkers with memory have persistent quantum ballistic speed up over classical walks just as found in previous studies of multicoined walks with trivial memory function. However, measurement of the multicoin state can dramatically shift the mean of the spatial distribution. Second, we consider spatial entanglement in a two-dimensional quantum walk with memory and find that memory destroys entanglement between the spatial dimensions, even when entangling coins are employed. Finally, we explore behavior in the presence of spatial randomness and find that in the time regime where single-coined walks localize, multicoined walks do not and in fact a memory function can speed up the walk relative to a multicoin walker with no memory. We explicitly show how to construct linear optics circuits implementing the walks, and discuss prospects for classical simulation.

Original languageEnglish
Article number052302
Pages (from-to)1-11
Number of pages11
JournalPhysical Review A - Atomic, Molecular, and Optical Physics
Volume87
Issue number5
DOIs
Publication statusPublished - 2 May 2013

Bibliographical note

Rohde, P. P., Brennen, G. K., & Gilchrist, A. (2013). Quantum walks with memory provided by recycled coins and a memory of the coin-flip history. Physical Review A, 87(5), 052302. Copyright (2013) by the American Physical Society. The original article can be found at http://dx.doi.org/10.1103/PhysRevA.87.052302.

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