Abstract
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 language | English |
|---|---|
| Article number | 075303 |
| Journal | Journal of Physics A: Mathematical and Theoretical |
| Volume | 51 |
| Issue number | 7 |
| DOIs | |
| Publication status | Published - 2018 Jan 19 |
Keywords
- 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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Cite this
Higuchi, Y., & Segawa, E. (2018). Quantum walks induced by Dirichlet random walks on infinite trees. Journal of Physics A: Mathematical and Theoretical, 51(7), [075303]. https://doi.org/10.1088/1751-8121/aa8fba