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- Title
Periodicity for the Hadamard Walk on Cycles.
- Authors
Norio KONNO; Yuki SHIMIZU; Masato TAKEI
- 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.
- Subjects
HADAMARD matrices; MATRICES (Mathematics); CYCLOTOMIC fields; FIELD extensions (Mathematics); POLYNOMIALS; EIGENVALUES
- Publication
Interdisciplinary Information Sciences, 2017, Vol 23, Issue 1, p1
- ISSN
1340-9050
- Publication type
Article
- DOI
10.4036/iis.2017.A.01