Lackadaisical quantum walks on 2D grids with multiple marked vertices
Nikolajs Nahimovs, Raqueline A. M. Santos · Journal of Physics A Mathematical and Theoretical · 2021
Abstract Lackadaisical quantum walk (LQW) is a quantum analog of a classical lazy walk, where each vertex has a self-loop of weight l . For a regular N × N 2D grid LQW can find a single marked vertex with O (1) probability in O ( N log N ) steps using l = d / N , where d is the degree of the vertices of the grid [11]. For multiple marked vertices, however, l = d / N is not optimal as the success probability decreases with the increase of the number of marked vertices [12]. In this paper, we numerically study search by LQW for different types of 2D grids—triangular, rectangular and honeycomb—with multiple marked vertices. We show that in all cases the weight l = m ⋅ d / N , where m is the number of marked vertices, still leads to O (1) success probability.