Eigenvalues of two-state quantumwalks induced by the hadamard walk

Shimpei Endo; Takako Endo; Takashi Komatsu; Norio Konno

doi:10.3390/e22010127

Eigenvalues of two-state quantumwalks induced by the hadamard walk

Shimpei Endo, Takako Endo, Takashi Komatsu, Norio Konno

SCI - Physics

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

4 Citations (Scopus)

Abstract

Existence of the eigenvalues of the discrete-time quantumwalks is deeply related to localization of the walks. We revealed, for the first time, the distributions of the eigenvalues given by the splitted generating function method (the SGF method) of the space-inhomogeneous quantum walks in one dimension we had treated in our previous studies. Especially, we clarified the characteristic parameter dependence for the distributions of the eigenvalues with the aid of numerical simulation.

Original language	English
Pages (from-to)	127
Number of pages	1
Journal	Entropy
Volume	22
Issue number	1
DOIs	https://doi.org/10.3390/e22010127
Publication status	Published - 2020 Jan 1

Keywords

Classification
Discrete-time quantum walks
Eigenvalues
Localization
Stationary measure

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abstract = "Existence of the eigenvalues of the discrete-time quantumwalks is deeply related to localization of the walks. We revealed, for the first time, the distributions of the eigenvalues given by the splitted generating function method (the SGF method) of the space-inhomogeneous quantum walks in one dimension we had treated in our previous studies. Especially, we clarified the characteristic parameter dependence for the distributions of the eigenvalues with the aid of numerical simulation.",

keywords = "Classification, Discrete-time quantum walks, Eigenvalues, Localization, Stationary measure",

author = "Shimpei Endo and Takako Endo and Takashi Komatsu and Norio Konno",

note = "Funding Information: Acknowledgments: S. Endo acknowledges support from JSPS KAKENHI Grant-in-Aid for Research Activity Start-up 19K21028. T. Endo is supported by financial support of Postdoctoral Fellowship from Japan Society for the Promotion of Science. Publisher Copyright: {\textcopyright} 2020 by the authors.",

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T1 - Eigenvalues of two-state quantumwalks induced by the hadamard walk

AU - Endo, Shimpei

AU - Endo, Takako

AU - Komatsu, Takashi

AU - Konno, Norio

N1 - Funding Information: Acknowledgments: S. Endo acknowledges support from JSPS KAKENHI Grant-in-Aid for Research Activity Start-up 19K21028. T. Endo is supported by financial support of Postdoctoral Fellowship from Japan Society for the Promotion of Science. Publisher Copyright: © 2020 by the authors.

PY - 2020/1/1

Y1 - 2020/1/1

N2 - Existence of the eigenvalues of the discrete-time quantumwalks is deeply related to localization of the walks. We revealed, for the first time, the distributions of the eigenvalues given by the splitted generating function method (the SGF method) of the space-inhomogeneous quantum walks in one dimension we had treated in our previous studies. Especially, we clarified the characteristic parameter dependence for the distributions of the eigenvalues with the aid of numerical simulation.

AB - Existence of the eigenvalues of the discrete-time quantumwalks is deeply related to localization of the walks. We revealed, for the first time, the distributions of the eigenvalues given by the splitted generating function method (the SGF method) of the space-inhomogeneous quantum walks in one dimension we had treated in our previous studies. Especially, we clarified the characteristic parameter dependence for the distributions of the eigenvalues with the aid of numerical simulation.

KW - Classification

KW - Discrete-time quantum walks

KW - Eigenvalues

KW - Localization

KW - Stationary measure

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Eigenvalues of two-state quantumwalks induced by the hadamard walk

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Keywords

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