A Note on the Spectral Mapping Theorem of Quantum Walk Models

• MATSUE Kaname

  Institute of Mathematics for Industry/International Institute for Carbon-Neutral Energy Research, Kyushu University

• OGURISU Osamu

  Division of Mathematical and Physical Sciences, Kanazawa University

• SEGAWA Etsuo

  Graduate School of Information Sciences, Tohoku University

抄録

We discuss the description of eigenspace of a quantum walk model U with an associating linear operator T in abstract settings of quantum walk including the Szegedy walk on graphs. In particular, we provide the spectral mapping theorem of U without the spectral decomposition of T. Arguments in this direction reveal the eigenspaces of U characterized by the generalized kernels of linear operators given by T.

収録刊行物

• Interdisciplinary Information Sciences

  Interdisciplinary Information Sciences 23 (1), 105-114, 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 model
• spectral mapping theorem
• generalized eigenspace

詳細情報

• CRID: 1390282679413294464
• NII論文ID: 120006237466
• NII論文ID: 130005519648
• DOI: 10.4036/iis.2017.a.13
• ISSN: 13476157
• ISSN: 13409050
• HANDLE: 10097/00120637
• Web Site: https://tohoku.repo.nii.ac.jp/records/123224
• Web Site: https://www.jstage.jst.go.jp/article/iis/23/1/23_2017.A.13/_pdf
• 本文言語コード: en
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