Monte Carlo studies of quantum and classical annealing on a double well

L Stella*, GE Santoro, E Tosatti

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

17 Citations (Scopus)

Abstract

We present results for a variety of Monte Carlo annealing approaches, both classical and quantum, benchmarked against one another for the textbook optimization exercise of a simple one-dimensional double well. In classical (thermal) annealing, the dependence upon the move chosen in a Metropolis scheme is studied and correlated with the spectrum of the associated Markov transition matrix. In quantum annealing, the path integral Monte Carlo approach is found to yield nontrivial sampling difficulties associated with the tunneling between the two wells. The choice of fictitious quantum kinetic energy is also addressed. We find that a "relativistic" kinetic energy form, leading to a higher probability of long real-space jumps, can be considerably more effective than the standard nonrelativistic one.

Original languageEnglish
Article number144302
Number of pages14
JournalPhysical Review B (Condensed Matter)
Volume73
Issue number14
DOIs
Publication statusPublished - Apr 2006

Keywords

  • GLOBAL OPTIMIZATION
  • ORDER CORRECTION
  • MINIMIZATION
  • SYSTEMS
  • MODEL

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