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Lackadaisical quantum walk (LQW) is a quantum analog of a classical lazywalk, where each vertex has a self-loop of weight $l$. For a regular$\sqrt{N}\times\sqrt{N}$ 2D grid LQW can find a single marked vertex with$O(1)$ probability in $O(\sqrt{N\log N})$ steps using $l = d/N$, where $d$ isthe degree of the vertices of the grid. For multiple marked vertices, however,$l = d/N$ is not optimal as the success probability decreases with the increaseof the number of marked vertices. In this paper, we numerically study search byLQW for different types of 2D grids -- triangular, rectangular and honeycomb --with multiple marked vertices. We show that in all cases the weight $l = m\cdotd/N$, where $m$ is the number of marked vertices, still leads to $O(1)$ successprobability.

Lackadaisical quantum walks on 2D grids with multiple marked vertices