Quantum walks on quotient graphs

  title={Quantum walks on quotient graphs},
  author={Hari Krovi and Todd A. Brun},
  journal={Physical Review A},
A discrete-time quantum walk on a graph {gamma} is the repeated application of a unitary evolution operator to a Hilbert space corresponding to the graph. If this unitary evolution operator has an associated group of symmetries, then for certain initial states the walk will be confined to a subspace of the original Hilbert space. Symmetries of the original graph, given by its automorphism group, can be inherited by the evolution operator. We show that a quantum walk confined to the subspace… 
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