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An Example of the Difference Between Quantum and Classical Random Walks

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Abstract

In this note, we discuss a general definition of quantum random walks on graphs and illustrate with a simple graph the possibility of very different behavior between a classical random walk and its quantum analog. In this graph, propagation between a particular pair of nodes is exponentially faster in the quantum case.

PACS: 03.67.Hk

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Authors and Affiliations

  1. Center for Theoretical Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts, 02139

    Andrew M. Childs & Edward Farhi

  2. Department of Mathematics, Northeastern University, Boston, Massachusetts, 02115

    Sam Gutmann

Authors
  1. Andrew M. Childs
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  2. Edward Farhi
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  3. Sam Gutmann
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Childs, A.M., Farhi, E. & Gutmann, S. An Example of the Difference Between Quantum and Classical Random Walks. Quantum Information Processing 1, 35–43 (2002). https://doi.org/10.1023/A:1019609420309

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  • DOI: https://doi.org/10.1023/A:1019609420309

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