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 η-Hermitian adjacency matrices. First, we investigate coefficients of the characteristic polynomials of η-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 η. In addition, we provide a necessary and sufficient condition for a mixed cycle to be periodic and determine their periods.

Talk to us

Join us for a 30 min session where you can share your feedback and ask us any queries you have

Schedule a call

Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.