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arXiv:1004.0425 · Proceedings in information and communications technology

Limit Theorem for a Time-Dependent Coined Quantum Walk on the Line

Takuya Machida, Norio Konno

Published Jan 1, 2010• 22 citations
arXivHTMLPDF
DOI
10.1007/978-4-431-53868-4_26

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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.