Localization of two dimensional quantum walks defined by generalized Grover coins

Abstract Localization phenomena of quantum walks makes the propagation dynamics a walker strikingly different from that corresponding to classical random walks. In this paper, we study localization four-state discrete-time on two-dimensional lattices with coin operators as one-parameter orthogonal matrices are also permutative, combinatorial structure Grover matrix. We show proposed localize at its initial position for canonical states when belongs classes which contain matrix consider in however, depends parameter class parametric coins does not