Trapping and spreading properties of quantum walk in homological structure

@article{Machida2015TrappingAS,
  title={Trapping and spreading properties of quantum walk in homological structure},
  author={T. Machida and E. Segawa},
  journal={Quantum Information Processing},
  year={2015},
  volume={14},
  pages={1539-1558}
}
  • T. Machida, E. Segawa
  • Published 2015
  • Mathematics, Physics, Computer Science
  • Quantum Information Processing
  • We attempt to extract a homological structure of two kinds of graphs by the Grover walk. The first one consists of a cycle and two semi-infinite lines, and the second one is assembled by a periodic embedding of the cycles in $$\mathbb {Z}$$Z. We show that both of them have essentially the same eigenvalues induced by the existence of cycles in the infinite graphs. The eigenspace of the homological structure appears as so called localization in the Grover walks, in which the walk is partially… CONTINUE READING

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    References

    Publications referenced by this paper.
    SHOWING 1-10 OF 22 REFERENCES
    Quantum walks on graphs and quantum scattering theory
    15
    Free quantum motion on a branching graph
    125
    Quantum speed-up of Markov chain based algorithms
    436
    Quantum Random Walks in One Dimension
    208
    A new type of limit theorems for the one-dimensional quantum random walk
    179
    Quantum Simulations of Classical Random Walks and Undirected Graph Connectivity
    143
    Periodic-orbit theory of anderson localization on graphs
    49
    Weak limits for quantum random walks.
    160
    Quantum graphs: Applications to quantum chaos and universal spectral statistics
    213