The hitting time of quantum walk on 2D lattice

Abstract

The hitting time, which refers to the time required to find the marked element in the search algorithm, is one of the most interesting properties of quantum walk. In this paper we briefly analyze the hitting time on a finite 2D lattice in the classical case, focusing on the quantum version of the hitting time and give specific expressions for each. It is well known that the quantum hitting time has the same order as the square of the classical case, and our work also happens to verify this particular property.