Continuous-time Quantum Walks on Cayley Graphs of Extraspecial Groups

Sin, Peter; Sorci, Julien

doi:10.48550/arxiv.2011.07566

Cited by 1 publication

(1 citation statement)

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“…Quantum walks have been discussed on different types of graphs such as Cayley graphs, percolation graphs, glued trees graphs, cyclic graphs, etc. for discrete [34][35][36][37] as well as continuous [38][39][40][41] quantum walks. Topological behavior (topological invariants and topological phases) of quantum walks has also been illustrated, both theoretically [7,[42][43][44] and experimentally [45][46][47][48][49].…”

Section: Introductionmentioning

confidence: 99%

Response to glassy disorder in coin on spread of quantum walker

Ghosh¹,

Sen²,

Sen³

2021

Preprint

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We analyze the response to incorporation of glassy disorder in the coin operation of a discrete-time quantum walk in one dimension. We find that the ballistic spread of the disorder-free quantum walker is inhibited by the insertion of disorder, for all the disorder distributions that we have chosen for our investigation, but remains faster than the dispersive spread of the classical random walker. While the inhibition to spread is common to all the distributions investigated, there are marked differences between the further behavior of the scalings for the different distributions. In particular, for disorder chosen from Haar-uniform and circular distributions, the response to weak disorder is weak, so that the scaling exponent falls off like a Gaussian against the disorder strength. However, for the spherical normal distribution and the two spherical Cauchy-Lorentz distributions, the response is strong even to weak disorder, and the fall-off is an exponential decay. Strong disorder universally leads to near, but faster than, the classical dispersive spread.

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