Related papers: Periodicity of lively quantum walks on cycles with generalized Grover coin

Periodicity of lively quantum walks on cycles with generalized Grover coin

URL: http://arxiv.org/abs/2003.12955v2
Date: Tue, 31 Mar 2020 00:59:12 GMT
Title: Periodicity of lively quantum walks on cycles with generalized Grover coin
Authors: Rohit Sarma Sarkar, Amrita Mandal, Bibhas Adhikari
Abstract summary: We extend the study of three state lively quantum walks on cycles by considering the coin operator as a linear sum of permutation matrices. We establish that an orthogonal matrix of order $3times 3$ is a linear sum of permutation matrices if and only if it is permutative.
Score: 0.17205106391379021
License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
Abstract: 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.

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