论文标题
活泼的量子行走的周期性在带有广义的格罗弗硬币的周期上
Periodicity of lively quantum walks on cycles with generalized Grover coin
论文作者
论文摘要
在本文中，我们通过将硬币操作员视为置换矩阵的线性总和，扩展了三个状态生动的量子步行，这是Grover矩阵的概括。首先，我们提供了订单的正交矩阵$ 3 \ times 3 $的完整表征，即置换矩阵的线性总和。因此，我们确定了几组复杂，真实和理性的正交矩阵。我们确定订单的正交矩阵$ 3 \ times 3 $是且仅在置换时才是置换矩阵的线性总和。最后，当硬币操作员属于置换矩阵的正交（真）线性总和时，我们确定了在循环上生动量子行走的时期。
In this paper we extend the study of three state lively quantum walks on cycles by considering the coin operator as a linear sum of permutation matrices, which is a generalization of the Grover matrix. First we provide a complete characterization of orthogonal matrices of order $3\times 3$ which are linear sum of permutation matrices. Consequently, we determine several groups of complex, real and rational orthogonal matrices. We establish that an orthogonal matrix of order $3\times 3$ is a linear sum of permutation matrices if and only if it is permutative. Finally we determine period of lively quantum walk on cycles when the coin operator belongs to the group of orthogonal (real) linear sum of permutation matrices.
