Interdisciplinary Information Sciences
Online ISSN : 1347-6157
Print ISSN : 1340-9050
ISSN-L : 1340-9050
Quantum Simulation and Quantum Walks
Periodicity for the Hadamard Walk on Cycles
Norio KONNOYuki SHIMIZUMasato TAKEI
Author information
JOURNALS FREE ACCESS

2017 Volume 23 Issue 1 Pages 1-8

Details
Abstract

The present paper treats the period TN of the Hadamard walk on a cycle CN with N vertices. Dukes (2014) considered the periodicity of more general quantum walks on CN and showed T2=2, T4=8, T8=24 for the Hadamard walk case. We prove that the Hadamard walk does not have any period except for his case, i.e., N = 2,4,8. Our method is based on a path counting and cyclotomic polynomials which is different from his approach based on the property of eigenvalues for unitary matrix that determines the evolution of the walk.

Information related to the author
© 2017 by the Graduate School of Information Sciences (GSIS), Tohoku University
Top