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Discrete Quantum Walks Hit Exponentially Faster
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  • Published: 10 February 2005

Discrete Quantum Walks Hit Exponentially Faster

  • Julia Kempe1,2 

Probability Theory and Related Fields volume 133, pages 215–235 (2005)Cite this article

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Abstract.

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 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.

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Authors and Affiliations

  1. CNRS-LRI, UMR 8623, Université de Paris-Sud, 91405, Orsay, France

    Julia Kempe

  2. Computer Science Division and Dept. of Chemistry, University of California, Berkeley, USA

    Julia Kempe

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  1. Julia Kempe
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Correspondence to Julia Kempe.

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Kempe, J. Discrete Quantum Walks Hit Exponentially Faster. Probab. Theory Relat. Fields 133, 215–235 (2005). https://doi.org/10.1007/s00440-004-0423-2

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  • Received: 23 March 2004

  • Revised: 01 December 2004

  • Published: 10 February 2005

  • Issue Date: October 2005

  • DOI: https://doi.org/10.1007/s00440-004-0423-2

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Keywords

  • Stochastic Process
  • Probability Theory
  • Polynomial Time
  • Discrete Time
  • Mathematical Biology
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