Perfect state transfer in products and covers of graphs
Perfect state transfer in products and covers of graphs
复制标题
产品和图表封面的完美状态转移
DOI：
10.1080/03081087.2015.1033381
复制
发表时间：
2015
影响因子：
1.1
通讯作者：
C. Godsil
中科院分区：
文献类型：
--
作者：
G. Coutinho;C. Godsil
图上的连续时间量子行走由复矩阵表示，其中是的邻接矩阵，是非负时间。如果图模拟了一个相互作用的量子比特网络，那么这些量子比特之间的状态转移可以被形式化为连续时间量子行走算符在顶点特征向量中的作用。在这里，我们关心的问题是确定哪些图允许状态的完美转移。更具体地说，我们将研究邻接矩阵是-矩阵的张量积之和的图，重点讨论图是另外两个图的张量积的情况。因此，我们将构造许多新的完美状态转移的例子。
A continuous-time quantum walk on a graph is represented by the complex matrix , where is the adjacency matrix of and is a non-negative time. If the graph models a network of interacting qubits, transfer of state among such qubits throughout time can be formalized as the action of the continuous-time quantum walk operator in the characteristic vectors of the vertices. Here, we are concerned with the problem of determining which graphs admit a perfect transfer of state. More specifically, we will study graphs whose adjacency matrix is a sum of tensor products of -matrices, focusing on the case where a graph is the tensor product of two other graphs. As a result, we will construct many new examples of perfect state transfer.