Quantum Information Processing

, Volume 11, Issue 5, pp 1273–1286 | Cite as

Enhancing the spreading of quantum walks on star graphs by additional bonds

  • Anastasiia Anishchenko
  • Alexander Blumen
  • Oliver Mülken


We study the dynamics of continuous-time quantum walks (CTQW) on networks with highly degenerate eigenvalue spectra of the corresponding connectivity matrices. In particular, we consider the two cases of a star graph and of a complete graph, both having one highly degenerate eigenvalue, while displaying different topologies. While the CTQW spreading over the network—in terms of the average probability to return or to stay at an initially excited node—is in both cases very slow, also when compared to the corresponding classical continuous-time random walk (CTRW), we show how the spreading is enhanced by randomly adding bonds to the star graph or removing bonds from the complete graph. Then, the spreading of the excitations may become very fast, even outperforming the corresponding CTRW. Our numerical results suggest that the maximal spreading is reached halfway between the star graph and the complete graph. We further show how this disorder-enhanced spreading is related to the networks’ eigenvalues.


Continuous-time quantum walk Continuous-time random walk Star graph Complete graph Distinct eigenvalue sets Transition probability 


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Copyright information

© Springer Science+Business Media, LLC 2012

Authors and Affiliations

  • Anastasiia Anishchenko
    • 1
  • Alexander Blumen
    • 1
  • Oliver Mülken
    • 1
  1. 1.Theoretische PolymerphysikUniversität FreiburgFreiburgGermany

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