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

Abstract

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.

Journal

• Interdisciplinary Information Sciences

  Interdisciplinary Information Sciences 23 (1), 105-114, 2017

  The Editorial Committee of the Interdisciplinary Information Sciences

Keywords

• quantum walk model
• spectral mapping theorem
• generalized eigenspace

Details

• CRID: 1390282679413294464
• NII Article ID: 120006237466
• NII Article 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
• Text Lang: en
• Data Source:
  • JaLC
  • IRDB
  • Crossref
  • CiNii Articles
  • KAKEN
• Abstract License Flag: Disallowed