Exponential algorithmic speedup by a quantum walk

  • Authors:

  • Andrew M. Childs;Richard Cleve;Enrico Deotto;Edward Farhi;Sam Gutmann;Daniel A. Spielman

  • Affiliations:

  • Massachusetts Institute of Technology, Cambridge, MA;University of Calgary, Calgary, Alberta, Canada;Massachusetts Institute of Technology, Cambridge, MA;Massachusetts Institute of Technology, Cambridge, MA;Northeastern University, Boston, MA;Massachusetts Institute of Technology, Cambridge, MA

  • Venue:
  • Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
  • Year:
  • 2003

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Abstract

We construct a black box graph traversal problem that can be solved exponentially faster on a quantum computer than on a classical computer. The quantum algorithm is based on a continuous time quantum walk, and thus employs a different technique from previous quantum algorithms based on quantum Fourier transforms. We show how to implement the quantum walk efficiently in our black box setting. We then show how this quantum walk solves our problem by rapidly traversing a graph. Finally, we prove that no classical algorithm can solve the problem in subexponential time.