The quantum walk is a powerful tool to develop quantum algorithms, which usually are based on searching for a vertex in a graph with multiple marked vertices, Ambainis's quantum algorithm for solving the element distinctness problem being the most shining example. In this work, we address the problem of calculating analytical expressions of the time complexity of finding a marked vertex using quantum walk-based search algorithms with multiple marked vertices on arbitrary graphs, extending previous analytical methods based on Szegedy's quantum walk, which can be applied only to bipartite graphs. Two examples based on the coined quantum walk on two-dimensional lattices and hypercubes show the details of our method.

翻译：量子漫步是开发量子算法的有力工具,它通常基于在带有多标记的脊椎的图表中搜索一个顶点,即Ambainis的量子算法,以解决元素差异性问题的量子辨别问题是最光辉的例子。在这项工作中,我们解决了使用在任意图形上带有多标记的垂直点的量子漫步搜索算法来计算一个标志性顶点的时间复杂性分析表达方式的问题,该算法以量子漫步法为基础,扩展了以前基于Szegedy量子漫步的分析方法,该方法只能应用于双方图。基于在二维层和超立方的硬体上的量子漫步的两个实例显示了我们方法的细节。