Periodicity of Grover walks on complete graphs with self-loops
Periodicity of Grover walks on complete graphs with self-loops
复制标题
Grover 在具有自循环的完整图上行走的周期性
DOI：
10.1016/j.laa.2020.04.003
复制
发表时间：
2020
影响因子：
1.1
通讯作者：
Tatsuya Tsurii
中科院分区：
文献类型：
--
作者：
N. Ito;T. Matsuyama;Tatsuya Tsurii
研究了顶点有自环的完全图上Grover行走的周期性。用代数方法研究了一种阶跃概率振幅矢量状态的演化矩阵。然后我们发现了一个周期性的行为，即每个顶点的概率振幅向量经过一些步骤后会回到初始状态。证明了格罗弗行走在完全图上，每个顶点都有一个自环，其周期为2n。
We investigate a periodicity of Grover walk on complete graphs with a self-loop at each vertex. We study an evolution matrix which steps forward a state of probability amplitude vector by using algebraic method. Then we find a periodic behaviour that the probability amplitude vector at each vertex gets back to initial state after some steps. It is shown that Grover walk on complete graphs onnvertices with a self-loop at each vertex is periodic with period 2n.