Periodicity of Grover walks on bipartite regular graphs with at most five distinct eigenvalues

2021/11/30 by Kubota, Sho · 2 citations
#05C50 #81Q99 #Combinatorics (math.CO) #FOS: Mathematics #FOS: Physical sciences #Quantum Physics (quant-ph)

paper · doi:10.48550/arxiv.2111.15074

Abstract

We determine connected bipartite regular graphs with four distinct adjacency eigenvalues that induce periodic Grover walks, and show that it is only C₆. We also show that there are only three kinds of the second largest eigenvalues of bipartite regular periodic graphs with five distinct eigenvalues. Using walk-regularity, we enumerate feasible spectra for such graphs.

Cited by

• Perfect state transfer in Grover walks on association schemes and distance-regular graphs
• Strongly regular and strongly walk-regular graphs that admit perfect state transfer

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