How does Grover walk recognize the shape of crystal lattice?

Chul Ki Ko, Norio Konno, Etsuo Segawa, Hyun Jae Yoo

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)


We consider the support of the limit distribution of the Grover walk on crystal lattices with the linear scaling. The orbit of the Grover walk is denoted by the parametric plot of the pseudo-velocity of the Grover walk in the wave space. The region of the orbit is the support of the limit distribution. In this paper, we compute the regions of the orbits for the triangular, hexagonal and kagome lattices. We show every outer frame of the support is described by an ellipse. The shape of the ellipse depends only on the realization of the fundamental lattice of the crystal lattice in R2.

Original languageEnglish
Article number167
JournalQuantum Information Processing
Issue number7
Publication statusPublished - 2018 Jul 1


  • Crystal lattice
  • Grover walks
  • Limit theorem

ASJC Scopus subject areas

  • Electronic, Optical and Magnetic Materials
  • Statistical and Nonlinear Physics
  • Theoretical Computer Science
  • Signal Processing
  • Modelling and Simulation
  • Electrical and Electronic Engineering


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