2005/12/03 by Lorenzo Stella, Giuseppe E. Santoro, Erio Tosatti · 1 citation
Physics and Astronomy · #cond-mat.dis-nn #quant-ph
paper · pdf · doi:10.1103/physrevb.73.144302
published as Phys. Rev. B 73, 144302 (2006) · 15 pages, 10 figures, REVTex 4
arxiv created 2005/12/03 · arxiv updated 2009/12/01
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 non-trivial 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 one.