831 research outputs found
Quantum Optimization of Fully-Connected Spin Glasses
The Sherrington-Kirkpatrick model with random couplings is programmed
on the D-Wave Two annealer featuring 509 qubits interacting on a Chimera-type
graph. The performance of the optimizer compares and correlates to simulated
annealing. When considering the effect of the static noise, which degrades the
performance of the annealer, one can estimate an improvement on the comparative
scaling of the two methods in favor of the D-Wave machine. The optimal choice
of parameters of the embedding on the Chimera graph is shown to be associated
to the emergence of the spin-glass critical temperature of the embedded
problem.Comment: includes supplemental materia
The high temperature region of the Viana-Bray diluted spin glass model
In this paper, we study the high temperature or low connectivity phase of the
Viana-Bray model. This is a diluted version of the well known
Sherrington-Kirkpatrick mean field spin glass. In the whole replica symmetric
region, we obtain a complete control of the system, proving annealing for the
infinite volume free energy, and a central limit theorem for the suitably
rescaled fluctuations of the multi-overlaps. Moreover, we show that free energy
fluctuations, on the scale 1/N, converge in the infinite volume limit to a
non-Gaussian random variable, whose variance diverges at the boundary of the
replica-symmetric region. The connection with the fully connected
Sherrington-Kirkpatrick model is discussed.Comment: 24 page
Spin Glasses: a Perspective
A brief personal perspective is given of issues, questions, formulations,
methods, some answers and selected extensions posed by the spin glass problem,
showing how considerations of an apparently insignificant and practically
unimportant group of metallic alloys stimulated an explosion of new insights
and opportunities in the general area of complex many-body systems and still is
doing soComment: For publication in the proceedings of International Conference on
"Equilibrium and Dynamics of Spin Glasses" (Ascona, Switzerland: April 2004).
V2 has minor changes to clarify and correct typo
Hysteretic Optimization For Spin Glasses
The recently proposed Hysteretic Optimization (HO) procedure is applied to
the 1D Ising spin chain with long range interactions. To study its
effectiveness, the quality of ground state energies found as a function of the
distance dependence exponent, , is assessed. It is found that the
transition from an infinite-range to a long-range interaction at
is accompanied by a sharp decrease in the performance . The transition is
signaled by a change in the scaling behavior of the average avalanche size
observed during the hysteresis process. This indicates that HO requires the
system to be infinite-range, with a high degree of interconnectivity between
variables leading to large avalanches, in order to function properly. An
analysis of the way auto-correlations evolve during the optimization procedure
confirm that the search of phase space is less efficient, with the system
becoming effectively stuck in suboptimal configurations much earlier. These
observations explain the poor performance that HO obtained for the
Edwards-Anderson spin glass on finite-dimensional lattices, and suggest that
its usefulness might be limited in many combinatorial optimization problems.Comment: 6 pages, 9 figures. To appear in JSTAT. Author website:
http://www.bgoncalves.co
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