Quantum annealing by the path-integral Monte Carlo method: The two-dimensional random Ising model

Roman Martoňák, Giuseppe E. Santoro, and Erio Tosatti
Phys. Rev. B 66, 094203 – Published 13 September 2002
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Abstract

Quantum annealing was recently found experimentally in a disordered spin-12 magnet to be more effective than its classical, thermal counterpart. We use the random two-dimensional Ising model as a test example and perform on it both classical and quantum (path-integral) Monte Carlo annealing. A systematic study of the dependence of the final residual energy on the annealing Monte Carlo time quantitatively demonstrates the superiority of quantum relative to classical annealing in this system. In order to determine the parameter regime for optimal efficiency of the quantum annealing procedure we explore a range of values of Trotter slice number P and temperature T. This identifies two different regimes of freezing with respect to efficiency of the algorithm, and leads to useful guidelines for the optimal choice of quantum annealing parameters.

  • Received 22 March 2002

DOI:https://doi.org/10.1103/PhysRevB.66.094203

©2002 American Physical Society

Authors & Affiliations

Roman Martoňák1,*, Giuseppe E. Santoro2, and Erio Tosatti2,3

  • 1Swiss Center for Scientific Computing, Via Cantonale, CH-6928 Manno, SwitzerlandETH Zurich, Physical Chemistry, Hoenggerberg, CH-8093 Zurich, Switzerland
  • 2International School for Advanced Studies (SISSA) and INFM (UdR SISSA), Trieste, Italy
  • 3International Center for Theoretical Physics (ICTP), P.O. Box 586, Trieste, Italy

  • *Permanent address: Department of Physics, Faculty of Electrical Engineering and Information Technology, Slovak University of Technology, Ilkovičova 3, 812 19 Bratislava, Slovakia.

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Vol. 66, Iss. 9 — 1 September 2002

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