Localization of two-dimensional quantum walks

摘要: The Grover walk, which is related to Grover's search algorithm on a quantum computer, one of the typical discrete time walks. However, localization two-dimensional walk starting from fixed point strikingly different other types present paper explains reason why walker who moves according degree-four operator can remain at with high probability. It shown that key factor for due degeneration eigenvalues evolution operator. In fact, global large lattice mainly determined by degree degeneration. dependence initial state also considered calculating wave function analytically.