Monte Carlo studies of quantum and classical annealing on a double-well
  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. 
Lorenzo Stella (1), Giuseppe E. Santoro (1,2), Erio Tosatti (1,2) ((1)   SISSA and INFM-Democritos, Trieste, Italy, (2) ICTP...