Quantum walks induced by Dirichlet random walks on infinite trees

Yusuke Higuchi, Etsuo Segawa

Research output: Contribution to journalArticlepeer-review

11 Citations (Scopus)


We consider the Grover walk on infinite trees from the viewpoint of spectral analysis. From the previous work, infinite regular trees provide localization. In this paper, we give the complete characterization of the eigenspace of this Grover walk, which involves localization of its behavior and recovers the previous work. Our result suggests that the Grover walk on infinite trees may be regarded as a limit of the quantum walk induced by the isotropic random walk with the Dirichlet boundary condition at the n-th depth rather than one with the Neumann boundary condition.

Original languageEnglish
Article number075303
JournalJournal of Physics A: Mathematical and Theoretical
Issue number7
Publication statusPublished - 2018 Jan 19


  • Dirichlet condition
  • eigenspace
  • flow
  • infinite tree
  • quantum walk

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Statistics and Probability
  • Modelling and Simulation
  • Mathematical Physics
  • Physics and Astronomy(all)


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