Finding Is as Easy as Detecting for Quantum Walks

  • Hari Krovi
  • Frédéric Magniez
  • Maris Ozols
  • Jérémie Roland
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6198)


We solve an open problem by constructing quantum walks that not only detect but also find marked vertices in a graph. The number of steps of the quantum walk is quadratically smaller than the classical hitting time of any reversible random walk P on the graph.

Our approach is new, simpler and more general than previous ones. We introduce a notion of interpolation between the walk P and the absorbing walk P′, whose marked states are absorbing. Then our quantum walk is simply the quantum analogue of the interpolation. Contrary to previous approaches, our results remain valid when the random walk P is not state-transitive, and in the presence of multiple marked vertices.

As a consequence we make a progress on an open problem related to the spatial search on the 2D-grid.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Hari Krovi
    • 1
  • Frédéric Magniez
    • 2
  • Maris Ozols
    • 3
    • 4
  • Jérémie Roland
    • 3
  1. 1.University of Connecticut 
  2. 2.LRI, Univ Paris-Sud, CNRS 
  3. 3.NEC Laboratories America, Inc. 
  4. 4.University of Waterloo and Institute for Quantum Computing 

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