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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References

SHOWING 1-10 OF 24 REFERENCES
Quantum walks on graphs and quantum scattering theory
Localization of quantum walks induced by recurrence properties of random walks
Limit measures of inhomogeneous discrete-time quantum walks in one dimension
Quantum speed-up of Markov chain based algorithms
  • M. Szegedy
  • Mathematics, Computer Science
  • 45th Annual IEEE Symposium on Foundations of Computer Science
  • 2004
Albanese Maps and Off Diagonal Long Time Asymptotics for the Heat Kernel
Quantum Random Walks in One Dimension
  • N. Konno
  • Physics, Computer Science
  • Quantum Inf. Process.
  • 2002
Quantum graph walks II: Quantum walks on graph coverings
Quantum Simulations of Classical Random Walks and Undirected Graph Connectivity
  • J. Watrous
  • Computer Science, Physics
  • J. Comput. Syst. Sci.
  • 2001
...
1
2
3
...