On the relation between quantum walks and zeta functions
classification
🪐 quant-ph
math-phmath.COmath.MPmath.PR
keywords
matrixquantumtransitionzetaapplicationscharacteristicdiscrete-timeexplicit
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We present an explicit formula for the characteristic polynomial of the transition matrix of the discrete-time quantum walk on a graph via the second weighted zeta function. As applications, we obtain new proofs for the results on spectra of the transition matrix and its positive support.
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