Localization of two-dimensional quantum walks defined by generalized Grover coins
Quantum Physics
2022-09-14 v3 Combinatorics
Abstract
Localization phenomena of quantum walks makes the propagation dynamics of a walker strikingly different from that corresponding to classical random walks. In this paper, we study the localization phenomena of four-state discrete-time quantum walks on two-dimensional lattices with coin operators as one-parameter orthogonal matrices that are also permutative, a combinatorial structure of the Grover matrix. We show that the proposed walks localize at its initial position for canonical initial coin states when the coin belongs to classes which contain the Grover matrix that we consider in this paper, however, the localization phenomena depends on the coin parameter when the class of parametric coins does not contain the Grover matrix.
Keywords
Cite
@article{arxiv.2103.00515,
title = {Localization of two-dimensional quantum walks defined by generalized Grover coins},
author = {Amrita Mandal and Rohit Sarma Sarkar and Bibhas Adhikari},
journal= {arXiv preprint arXiv:2103.00515},
year = {2022}
}