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.

Monte Carlo studies of quantum and classical annealing on a double well / Stella, L; Santoro, Giuseppe Ernesto; Tosatti, E.. - In: PHYSICAL REVIEW. B, CONDENSED MATTER AND MATERIALS PHYSICS. - ISSN 1098-0121. - 73:14(2006), pp. 144302.1-144302.15. [10.1103/PhysRevB.73.144302]

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

Santoro, Giuseppe Ernesto;Tosatti E.
2006-01-01

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.
2006
73
14
1
15
144302
https://arxiv.org/abs/cond-mat/0512064
Stella, L; Santoro, Giuseppe Ernesto; Tosatti, E.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/20.500.11767/13610
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