Quantum walks with history dependence

A. P. Flitney; D. Abbott; N. F. Johnson

doi:10.1088/0305-4470/37/30/013

Quantum walks with history dependence

A. P. Flitney, D. Abbott, N. F. Johnson

Physics

Research output: Contribution to journal › Article › peer-review

34 Scopus citations

Abstract

We introduce a multi-coin discrete quantum walk where the amplitude for a coin flip depends upon previous tosses. Although the corresponding classical random walk is unbiased, a bias can be introduced into the quantum walk by varying the history dependence. By mixing the biased walk with an unbiased one, the direction of the bias can be reversed leading to a new quantum version of Parrondo's paradox.

Original language	English (US)
Pages (from-to)	7581-7591
Number of pages	11
Journal	Journal of Physics A: Mathematical and General
Volume	37
Issue number	30
DOIs	https://doi.org/10.1088/0305-4470/37/30/013
State	Published - Jul 30 2004

ASJC Scopus subject areas

Statistical and Nonlinear Physics
Mathematical Physics
Physics and Astronomy(all)

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10.1088/0305-4470/37/30/013

Cite this

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title = "Quantum walks with history dependence",

abstract = "We introduce a multi-coin discrete quantum walk where the amplitude for a coin flip depends upon previous tosses. Although the corresponding classical random walk is unbiased, a bias can be introduced into the quantum walk by varying the history dependence. By mixing the biased walk with an unbiased one, the direction of the bias can be reversed leading to a new quantum version of Parrondo's paradox.",

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N2 - We introduce a multi-coin discrete quantum walk where the amplitude for a coin flip depends upon previous tosses. Although the corresponding classical random walk is unbiased, a bias can be introduced into the quantum walk by varying the history dependence. By mixing the biased walk with an unbiased one, the direction of the bias can be reversed leading to a new quantum version of Parrondo's paradox.

AB - We introduce a multi-coin discrete quantum walk where the amplitude for a coin flip depends upon previous tosses. Although the corresponding classical random walk is unbiased, a bias can be introduced into the quantum walk by varying the history dependence. By mixing the biased walk with an unbiased one, the direction of the bias can be reversed leading to a new quantum version of Parrondo's paradox.

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JO - Journal of Physics A: Mathematical and Theoretical

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Quantum walks with history dependence

Abstract

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