# Spectral and asymptotic properties of Grover walks on crystal lattice

@article{Higuchi2013SpectralAA, title={Spectral and asymptotic properties of Grover walks on crystal lattice}, author={Yusuke Higuchi and N. Konno and I. Sato and E. Segawa}, journal={arXiv: Probability}, year={2013} }

We propose a twisted Szegedy walk for estimating the limit behavior of a discrete-time quantum walk on a crystal lattice, an infinite abelian covering graph, whose notion was introduced by [14]. First, we show that the spectrum of the twisted Szegedy walk on the quotient graph can be expressed by mapping the spectrum of a twisted random walk onto the unit circle. Secondly, we show that the spatial Fourier transform of the twisted Szegedy walk on a finite graph with appropriate parameters… Expand

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