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}
}
  • Yusuke Higuchi, Norio Konno, +1 author Etsuo Segawa
  • Published 2013
  • Mathematics, Physics
  • arXiv: Probability
  • 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

    Figures from this paper.

    Citations

    Publications citing this paper.
    SHOWING 1-10 OF 42 CITATIONS

    Quaternionic quantum walks of Szegedy type and zeta functions of graphs

    VIEW 2 EXCERPTS
    CITES BACKGROUND

    Staggered Quantum Walks on Graphs

    VIEW 1 EXCERPT
    CITES RESULTS

    FILTER CITATIONS BY YEAR

    2014
    2020

    CITATION STATISTICS

    • 3 Highly Influenced Citations

    • Averaged 8 Citations per year from 2018 through 2020

    References

    Publications referenced by this paper.
    SHOWING 1-10 OF 24 REFERENCES