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

Lorenzo Stella; Giuseppe E. Santoro; Erio Tosatti

doi:10.1103/physrevb.73.144302

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

Lorenzo Stella·Giuseppe E. Santoro·Erio Tosatti

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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 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.

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Lorenzo Stella, Giuseppe E. Santoro, Erio Tosatti. 2005-12-03. Monte Carlo studies of quantum and classical annealing on a double-well. https://doi.org/10.1103/physrevb.73.144302

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