Periodicity of lively quantum walks on cycles with generalized Grover coin
Periodicity of lively quantum walks on cycles with generalized Grover coin
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DOI：
10.1016/j.laa.2020.07.006
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发表时间：
2020-11-01
影响因子：
1.1
通讯作者：
Adhikari, Bibhas
中科院分区：
文献类型：
--
作者：
Sarkar, Rohit Sarma;Mandal, Amrita;Adhikari, Bibhas
本文扩展了环上三态活泼量子行走的研究，将硬币算子看作是置换矩阵的线性和，这是Grover矩阵的推广。首先，我们给出了3 × 3阶正交矩阵的一个完整表征，它是置换矩阵的线性和。因此，我们确定了几组复、实、有理正交矩阵。证明了一个3 × 3阶正交矩阵是置换矩阵的线性和，当且仅当它是置换矩阵。最后，我们确定了当硬币算子属于（实）排列矩阵线性和的正交群时，在环上活泼量子行走的周期。(C) 2020爱思唯尔公司版权所有。
In this paper we extend the study of three state lively quantum walks on cycles by considering the coin operator as 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 x 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 x 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 orthogonal group of (real) linear sum of permutation matrices. (C) 2020 Elsevier Inc. All rights reserved.