Quantum Simulations of Classical Annealing Processes

R. D. Somma, S. Boixo, H. Barnum, and E. Knill
Phys. Rev. Lett. 101, 130504 – Published 26 September 2008

Abstract

We describe a quantum algorithm that solves combinatorial optimization problems by quantum simulation of a classical simulated annealing process. Our algorithm exploits quantum walks and the quantum Zeno effect induced by evolution randomization. It requires order 1/δ steps to find an optimal solution with bounded error probability, where δ is the minimum spectral gap of the stochastic matrices used in the classical annealing process. This is a quadratic improvement over the order 1/δ steps required by the latter.

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  • Received 8 April 2008

DOI:http://dx.doi.org/10.1103/PhysRevLett.101.130504

©2008 American Physical Society

Authors & Affiliations

R. D. Somma1,*, S. Boixo2,3, H. Barnum2, and E. Knill4

  • 1Perimeter Institute for Theoretical Physics, Waterloo, ON N2L 2Y5, Canada
  • 2CCS-3 (Information Sciences), Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
  • 3Department of Physics and Astronomy, University of New Mexico, Albuquerque, New Mexico 87131, USA
  • 4National Institute of Standards and Technology, Boulder, Colorado 80305, USA

  • *rsomma@perimeterinstitute.ca

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Vol. 101, Iss. 13 — 26 September 2008

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