This paper addresses the question: what processes take polynomial time on a quantum computer that require exponential time classically? We show that the hitting time of the discrete time quantum random walk on the n-bit hypercube from one corner to its opposite is polynomial in n. This gives the first exponential quantum-classical gap in the hitting time of discrete quantum walks. We provide the basic framework for quantum hitting time and give two alternative definitions to set the ground for its study on general graphs. We outline a possible application to sequential packet routing.


Random Walk Cayley Graph Quantum Walk Simple Random Walk Faulty Node 
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© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • Julia Kempe
    • 1
    • 2
  1. 1.CNRS-LRI, UMR 8623Université de Paris-SudOrsayFrance
  2. 2.Computer Science Division and Dept. of ChemistryUniversity of CaliforniaBerkeleyUSA

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