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