Hanoi network (HN) has a one-dimensional periodic lattice as its main structure with additional long-range edges, which allow having efficient quantum walk algorithm that can find a target state on the network faster than the exhaustive classical search. In this paper, we use regular quantum walks and lackadaisical quantum walks, respectively, to search for a target state. From the curve fitting of the numerical results for HN of degrees three and four, we find that their running time for the regular quantum walks are followed by amplitude amplification scales as [Formula: see text] and [Formula: see text], respectively. For the search by lackadaisical quantum walks, the running time scales are as [Formula: see text] and [Formula: see text], respectively.

中文翻译：

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河内网络上的量子搜索

Hanoi 网络 (HN) 以一维周期格为主要结构，并带有附加的长程边，这使得高效的量子游走算法可以比穷举经典搜索更快地在网络上找到目标状态。在本文中，我们分别使用常规的量子游走和懒散的量子游走来搜索目标状态。从三度和四度 HN 的数值结果的曲线拟合中，我们发现它们在常规量子游走的运行时间之后是幅度放大尺度，分别为 [公式：见文本] 和 [公式：见文本]。对于懒散量子游走的搜索，运行时间尺度分别为[公式：见正文]和[公式：见正文]。