Abstract
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 language | English |
|---|---|
| Article number | 167 |
| Journal | Quantum Information Processing |
| Volume | 17 |
| Issue number | 7 |
| DOIs | |
| Publication status | Published - 2018 Jul 1 |
Keywords
- 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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Cite this
Ko, C. K., Konno, N., Segawa, E., & Yoo, H. J. (2018). How does Grover walk recognize the shape of crystal lattice? Quantum Information Processing, 17(7), [167]. https://doi.org/10.1007/s11128-018-1886-x