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

Choon Lin Ho, Yusuke Ide, Norio Konno, Etsuo Segawa, Kentaro Takumi

研究成果: Article査読

2 被引用数 (Scopus)

抄録

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.

本文言語English
ページ(範囲)207-219
ページ数13
ジャーナルJournal of Statistical Physics
171
2
DOI
出版ステータスPublished - 2018 4月 1

ASJC Scopus subject areas

  • 統計物理学および非線形物理学
  • 数理物理学

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