Affiliation:
1. College of Mathematics and Statistics, Northwest Normal University, Lanzhou 730070, P. R. China
Abstract
In this paper, we successfully obtain an explicit expression of the limit distribution [Formula: see text] of three-state quantum walks on cycles, the total variation distance between [Formula: see text] and the average probability [Formula: see text], and lower bound on the difference between two eigenvalues, among others. Based on the above conclusions, we finally get the mixing time [Formula: see text] of the quantum walk of Grover coin on the N-cycle. [Formula: see text] is the time required to characterize [Formula: see text] approaching [Formula: see text]. Our results show that the average probability of a three-state quantum walk on a cycle can approach its limit distribution faster than that of a two-state quantum walk, which might be of significance to quantum computation.
Funder
National Natural Science Foundation of China
Natural Science Foundation of Gansu province
Higher Education Innovation Fund of Gansu Provincial Department of Education
Publisher
World Scientific Pub Co Pte Ltd
Subject
Condensed Matter Physics,Statistical and Nonlinear Physics
Cited by
2 articles.
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