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History dependent quantum walk on the cycle with an unbalanced coin

Walter O. Krawec

Physica A: Statistical Mechanics and its Applications, 2015, vol. 428, issue C, 319-331

Abstract: Recently, a new model of quantum walk, utilizing recycled coins, was introduced; however little is yet known about its properties. In this paper, we study its behavior on the cycle graph. In particular, we will consider its time averaged distribution and how it is affected by the walk’s “memory parameter”—a real parameter, between zero and eight, which affects the walk’s coin flip operator. Despite an infinite number of different parameters, our analysis provides evidence that only a few produce non-uniform behavior. Our analysis also shows that the initial state, and cycle size modulo four all affect the behavior of this walk. We also prove an interesting relationship between the recycled coin model and a different memory-based quantum walk recently proposed.

Keywords: Quantum random walks; History dependent walk; Recycled coin model (search for similar items in EconPapers)
Date: 2015
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:428:y:2015:i:c:p:319-331

DOI: 10.1016/j.physa.2015.02.061

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