# 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 Norio Konno and Iwao Sato and Etsuo 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… CONTINUE READING

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#### References

##### Publications referenced by this paper.

SHOWING 1-10 OF 24 REFERENCES

## Quantum walks on graphs and quantum scattering theory

VIEW 1 EXCERPT

## Quantum speed-up of Markov chain based algorithms

VIEW 1 EXCERPT

## Quantum Random Walks in One Dimension

VIEW 1 EXCERPT

## Quantum graph walks II: Quantum walks on graph coverings

VIEW 1 EXCERPT