Periodicity of quantum walks defined by mixed paths and mixed cycles

نویسندگان

چکیده

In this paper, we determine periodicity of quantum walks defined by mixed paths and cycles. By the spectral mapping theorem walks, consideration is reduced to eigenvalue analysis $\eta$-Hermitian adjacency matrices. First, investigate coefficients characteristic polynomials We show that trees their underlying graphs are same. also define $n+1$ types cycles every cycle switching equivalent one them. use these results discuss periodicity. periodic for any $\eta$. addition, provide a necessary sufficient condition be periods.

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ژورنال

عنوان ژورنال: Linear Algebra and its Applications

سال: 2021

ISSN: ['1873-1856', '0024-3795']

DOI: https://doi.org/10.1016/j.laa.2021.07.022