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Recently, a programmable quantum annealing machine has been built that minimizes the cost function of hard optimization problems by adiabatically quenching quantum fluctuations.
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Note that the statements made are independent of which theory (droplet Fisher and Huse 1986 ; Fisher and Huse 1987 ; Fisher and Huse 1988 ; Bray and Moore 1986 vs replica symmetry breaking Parisi 1979 ; Parisi 1980 ; Parisi 1983 ; Mézard et al. 1987 ) describes the low-temperature state of spin glasses best. For the numerically accessible system sizes N N , there are features in the overlap distribution like in the mean-field model. The replica symmetry breaking versus droplet picture question, however, only affects results in the thermodynamic limit and not in the finite systems probed in simulations. In the replica symmetry breaking picture for the mean-field model, the number of states increases by around N 1 / 6 N^{1/6} Aspelmeier et al. 2008 . For the droplet model, there is only one dominant state in the thermodynamic limit. Furthermore, in the mean-field limit, barriers should increase by around N 1 / 3 N^{1/3} , whereas for a short-range model the growth is to date unclear. Therefore, at low, but finite temperature, the replica symmetry breaking vs droplet picture controversy should not play a role if N < ∞ N<\infty . In both pictures (below a finite T c T_{c} ), barriers in the energy landscape appear that grow with increasing system size and decreasing temperature (at least for any numerically accessible system sizes). We emphasize that what matters is that barriers grow for any temperature T ≤ T c T\leq T_{c}
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Note that simulated annealing—by design—is unable to climb over barriers because temperature is monotonically quenched to zero. However, more efficient algorithms like exchange Monte Carlo Hukushima and Nemoto 1996 are able to “climb” over barriers
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Detailed tests of the distributions of time scales show that the speedup claimed in Ref. Santoro et al. 2002 could be explained by the fact that the analysis focused only on average times scales and not the distribution of time scales. (M. Troyer, private communication)
2002
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Note that the disorder vs temperature phase diagrams are typically reentrant for disordered ferromagnets. Therefore, it is safe to assume that a spin-glass phase at zero temperature might exist for values of p p slightly smaller than p c p_{c} . For examples of reentrant phase diagrams for very different model systems, see Refs. Katzgraber et al. 2009b and Thomas and Katzgraber 2011
2011
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2013
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2013
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2014
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A. Lucas, Ising formulations of many NP problems , Front. Physics 12
2014
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