A Spectral Analysis of Discrete-Time Quantum Walks Related to the Birth and Death Chains

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Title:	A Spectral Analysis of Discrete-Time Quantum Walks Related to the Birth and Death Chains
Authors:	Ho, Choon-Lin;Ide, Yusuke;Konno, Norio;Segawa, Etsuo;Takumi, Kentaro
Keywords:	Quantum walk;Birth and death chain;Ehrenfest model;Krawtchouk polynomials
Date:	2018-03-08
Issue Date:	2019-09-20 12:10:14 (UTC+8)
Publisher:	Springer Nature
Abstract:	In this paper, we consider a spectral analysis of discrete time quantum walks on the path. For isospectral coin cases, we show that the time averaged distribution and stationary distributions of the quantum walks are described by the pair of eigenvalues of the coins as well as the eigenvalues and eigenvectors of the corresponding random walks which are usually referred as the birth and death chains. As an example of the results, we derive the time averaged distribution of so-called Szegedy’s walk which is related to the Ehrenfest model. It is represented by Krawtchouk polynomials which is the eigenvectors of the model and includes the arcsine law.
Relation:	Journal of Statistical Physics 171(2), p.207-219
DOI:	10.1007/s10955-018-1998-9
Appears in Collections:	[Graduate Institute & Department of Physics] Journal Article

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