标题： 漫不经心的量子行走与多个标记顶点 显示英文标题

标题： Lackadaisical quantum walks with multiple marked vertices

摘要： 懒散量子行走的概念——带有自环的量子行走——最初是在一维线上的离散时间量子行走中引入的。 后来它成功地应用于改进二维网格上的空间搜索的运行时间。 在本文中，我们研究了在具有多个标记顶点的二维网格上通过懒散量子行走进行的搜索。 首先，我们证明懒散量子行走与常规（非懒散）量子行走一样，存在异常配置，即对于这些标记顶点的放置，该行走相对于经典穷尽搜索没有加速效果。 接下来，我们演示前文提出的自环权重对于多个标记顶点并不最优。 最后，我们展示如何调整自环的权重以克服上述问题。 显示英文摘要

摘要： The concept of lackadaisical quantum walk -- quantum walk with self loops -- was first introduced for discrete-time quantum walk on one-dimensional line. Later it was successfully applied to improve the running time of the spacial search on two-dimensional grid. In this paper we study search by lackadaisical quantum walk on the two-dimensional grid with multiple marked vertices. First, we show that the lackadaisical quantum walk, similarly to the regular (non-lackadaisical) quantum walk, has exceptional configuration, i.e. placements of marked vertices for which the walk has no speed-up over the classical exhaustive search. Next, we demonstrate that the weight of the self-loop suggested in the previous papers is not optimal for multiple marked vertices. And, last, we show how to adjust the weight of the self-loop to overcome the aforementioned problem.