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Periodicity of quantum walks defined by mixed paths and mixed cycles
- Source :
- Linear Algebra and its Applications. 630:15-38
- Publication Year :
- 2021
- Publisher :
- Elsevier BV, 2021.
-
Abstract
- In this paper, we determine periodicity of quantum walks defined by mixed paths and mixed cycles. By the spectral mapping theorem of quantum walks, consideration of periodicity is reduced to eigenvalue analysis of $\eta$-Hermitian adjacency matrices. First, we investigate coefficients of the characteristic polynomials of $\eta$-Hermitian adjacency matrices. We show that the characteristic polynomials of mixed trees and their underlying graphs are same. We also define $n+1$ types of mixed cycles and show that every mixed cycle is switching equivalent to one of them. We use these results to discuss periodicity. We show that the mixed paths are periodic for any $\eta$. In addition, we provide a necessary and sufficient condition for a mixed cycle to be periodic and determine their periods.<br />Comment: 22 pages, 12 figures
- Subjects :
- Quantum Physics
05C50, 81Q99, 05C20, 05C81
Numerical Analysis
Pure mathematics
Algebra and Number Theory
FOS: Physical sciences
Spectral mapping
Eigenvalue analysis
FOS: Mathematics
Mathematics - Combinatorics
Discrete Mathematics and Combinatorics
Quantum walk
Combinatorics (math.CO)
Geometry and Topology
Adjacency matrix
Quantum Physics (quant-ph)
Mathematics
Subjects
Details
- ISSN :
- 00243795
- Volume :
- 630
- Database :
- OpenAIRE
- Journal :
- Linear Algebra and its Applications
- Accession number :
- edsair.doi.dedup.....2f882d3d9a5fc968e148960b355ce50a