Discrete time quantum walks on percolation graphs

  • Bálint Kollár
  • Jaroslav Novotný
  • Tamás Kiss
  • Igor Jex
Open Access
Regular Article
Part of the following topical collections:
  1. Focus Point on Quantum information and complexity


Randomly breaking connections in a graph alters its transport properties, a model used to describe percolation. In the case of quantum walks, dynamic percolation graphs represent a special type of imperfections, where the connections appear and disappear randomly in each step during the time evolution. The resulting open system dynamics is hard to treat numerically in general. We shortly review the literature on this problem. We then present our method to solve the evolution on finite percolation graphs in the long time limit, applying the asymptotic methods concerning random unitary maps. We work out the case of one-dimensional chains in detail and provide a concrete, step-by-step numerical example in order to give more insight into the possible asymptotic behavior. The results about the case of the two-dimensional integer lattice are summarized, focusing on the Grover-type coin operator.


Edge State Quantum Walk Shift Condition Position Distribution Break Link 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© The Author(s) 2014

Authors and Affiliations

  • Bálint Kollár
    • 1
  • Jaroslav Novotný
    • 2
  • Tamás Kiss
    • 1
  • Igor Jex
    • 2
  1. 1.Wigner RCP, SZFKIBudapestHungary
  2. 2.Department of Physics, Faculty of Nuclear Sciences and Physical EngineeringCzech Technical University in PraguePraha 1 - Staré MěstoCzech Republic

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