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arXiv · 1404.1509

A limit theorem for a 3-period time-dependent quantum walk

F. Alberto Grünbaum·Takuya Machida
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Abstract

We consider a discrete-time 2-state quantum walk on the line. The state of the quantum walker evolves according to a rule which is determined by a coin-flip operator and a position-shift operator. In this paper we take a 3-periodic time evolution as the rule. For such a quantum walk, we get a limit distribution which expresses the asymptotic behavior of the walker after a long time. The limit distribution is different from that of a time-independent quantum walk or a 2-period time-dependent quantum walk. We give some analytical results and then consider a number of variants of our model and indicate the result of simulations for these ones.

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F. Alberto Grünbaum, Takuya Machida. 2014-04-05. A limit theorem for a 3-period time-dependent quantum walk. https://arxiv.org/abs/1404.1509

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