Periodicity of Grover walks on generalized Bethe trees
Periodicity of Grover walks on generalized Bethe trees
复制标题
格罗弗在广义贝特树上行走的周期性
DOI：
10.1016/j.laa.2018.05.023
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发表时间：
2018
影响因子：
1.1
通讯作者：
Yusuke Yoshie
中科院分区：
文献类型：
--
作者：
Sho Kubota;Etsuo Segawa;Tetsuji Taniguchi;Yusuke Yoshie
我们专注于周期性的Grover行走的广义Bethe树，这是一个有根树，使得在每个级别的顶点有相同的程度。由于Grover行走是由底层图诱导的，因此它的性质取决于图。本文证明了图诱导周期Grover游动当且仅当存在k∈ N使得时间演化算子的k次幂成为单位算子.我们的目标是刻画这样的图。我们给出了诱导周期Grover游动的广义Bethe树的完美刻画。
We focus on the periodicity of the Grover walk on the generalized Bethe tree, which is a rooted tree such that in each level the vertices have the same degree. Since the Grover walk is induced by the underlying graph, its properties depend on the graph. In this paper, we say that the graph induces periodic Grover walks if and only if there exists k∈ N such that the k-th power of the time evolution operator becomes the identity operator. Our aim is to characterize such graphs. We give the perfect characterizations of the generalized Bethe trees which induce periodic Grover walks.