Periodicity for the Hadamard Walk on Cycles

• KONNO Norio

  Department of Applied Mathematics, Faculty of Engineering, Yokohama National University

• SHIMIZU Yuki

  Department of Applied Mathematics, Faculty of Engineering, Yokohama National University

• TAKEI Masato

  Department of Applied Mathematics, Faculty of Engineering, Yokohama National University

抄録

The present paper treats the period T_N of the Hadamard walk on a cycle C_N with N vertices. Dukes (2014) considered the periodicity of more general quantum walks on C_N and showed T₂=2, T₄=8, T₈=24 for the Hadamard walk case. We prove that the Hadamard walk does not have any period except for his case, i.e., N = 2,4,8. Our method is based on a path counting and cyclotomic polynomials which is different from his approach based on the property of eigenvalues for unitary matrix that determines the evolution of the walk.

収録刊行物

• Interdisciplinary Information Sciences

  Interdisciplinary Information Sciences 23 (1), 1-8, 2017

  東北大学大学院情報科学研究科ジャーナル編集委員会

キーワード

• Quantum walk
• Hadamard walk
• periodicity
• cycle

詳細情報

• CRID: 1390001204436603648
• NII論文ID: 120006237474
• NII論文ID: 130005519585
• DOI: 10.4036/iis.2017.a.01
• ISSN: 13476157
• ISSN: 13409050
• HANDLE: 10097/00120625
• Web Site: https://tohoku.repo.nii.ac.jp/records/123212
• Web Site: https://www.jstage.jst.go.jp/article/iis/23/1/23_2017.A.01/_pdf
• 本文言語コード: en
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