The Hamiltonians Generating One-Dimensional Discrete-Time Quantum Walks

• TATE Tatsuya

  Mathematical Institute, Graduate School of Sciences, Tohoku University

Abstract

An explicit formula of the Hamiltonians generating one-dimensional discrete-time quantum walks is given. The formula is deduced by using the algebraic structure introduced before. The square of the Hamiltonian turns out to be an operator without, essentially, the ``coin register,'' and hence it can be compared with the one-dimensional continuous-time quantum walk. It is shown that, under a limit with respect to a parameter, which expresses the magnitude of the diagonal components of the unitary matrix defining the discrete-time quantum walks, the one-dimensional continuous-time quantum walk is obtained from operators defined through the Hamiltonians of the one-dimensional discrete-time quantum walks. Thus, this result can be regarded, in one-dimension, as a partial answer to a problem proposed by Ambainis.

Journal

• Interdisciplinary Information Sciences

  Interdisciplinary Information Sciences 19 (2), 149-156, 2013

  The Editorial Committee of the Interdisciplinary Information Sciences

Keywords

• discrete-time quantum walk
• Hamiltonian
• continuous-time quantum walk

Details

• CRID: 1390001204436797184
• NII Article ID: 120005428627
• NII Article ID: 110009795564
• NII Book ID: AA11032627
• DOI: 10.4036/iis.2013.149
• ISSN: 13476157
• ISSN: 13409050
• HANDLE: 10097/57208
• Web Site: https://tohoku.repo.nii.ac.jp/records/41863
• Text Lang: en
• Data Source:
  • JaLC
  • IRDB
  • Crossref
  • CiNii Articles
  • KAKEN
• Abstract License Flag: Disallowed