Lackadaisical quantum walks on triangular and honeycomb 2D grids
英文摘要：
In the typical model, a discrete-time coined quantum walk search has the same running time of $O(\sqrt{N} \log{N})$ for 2D rectangular, triangular and honeycomb grids. It is known that for 2D rectangular grid the running time can be improved to $O(\sqrt{N \log{N}})$ using several different techniques. One of such techniques is adding a self-loop of weight $4/N$ to each vertex (i.e. making the walk lackadaisical). In this paper we apply lackadaisical approach to quantum walk search on triangular and honeycomb 2D grids. We show that for both types of grids adding a self-loop of weight $6/N$ and $3/N$ for triangular and honeycomb grids, respectively, results in $O(\sqrt{N \log{N}})$ running time.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
