Optimization in random field Ising models by quantum annealing

Details Optimization in random field Ising models by quantum annealing Optimization in random field Ising models by quantum annealing

2005-11-21

arxiv.org/abs/cond-mat/0511515v3

J. Stat. Mech. (2006) P01008

Physics

Condensed Matter

Disordered Systems and Neural Networks

7 pages (2 columns), 9 figures, published with minor changes, one reference updated after the publication

Scientific paper

10.1088/1742-5468/2006/01/P01008

We investigate the properties of quantum annealing applied to the random field Ising model in one, two and three dimensions. The decay rate of the residual energy, defined as the energy excess from the ground state, is find to be $e_{res}\sim \log(N_{MC})^{-\zeta}$ with $\zeta$ in the range $2...6$, depending on the strength of the random field. Systems with ``large clusters'' are harder to optimize as measured by $\zeta$. Our numerical results suggest that in the ordered phase $\zeta=2$ whereas in the paramagnetic phase the annealing procedure can be tuned so that $\zeta\to6$.

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