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
References: Add references at CitEc
Citations:
Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0378437115001788
Full text for ScienceDirect subscribers only. Journal offers the option of making the article available online on Science direct for a fee of $3,000
Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.
Export reference: BibTeX
RIS (EndNote, ProCite, RefMan)
HTML/Text
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
Access Statistics for this article
Physica A: Statistical Mechanics and its Applications is currently edited by K. A. Dawson, J. O. Indekeu, H.E. Stanley and C. Tsallis
More articles in Physica A: Statistical Mechanics and its Applications from Elsevier
Bibliographic data for series maintained by Catherine Liu (repec@elsevier.com).