Related papers: Finding Ground States of Sherrington-Kirkpatrick S…
Ground states of Ising spin glasses on fully connected graphs are studied for a broadly distributed bond family. In particular, bonds $J$ distributed according to a Levy distribution P(J)\propto 1/|J|^{1+\alpha}, |J|>1, are investigated for…
Across many scientific and engineering disciplines, it is important to consider how much the output of a given system changes due to perturbations of the input. Here, we investigate the glassy phase of $\pm J$ spin glasses at zero…
Let ${\boldsymbol A}\in{\mathbb R}^{n\times n}$ be a symmetric random matrix with independent and identically distributed Gaussian entries above the diagonal. We consider the problem of maximizing $\langle{\boldsymbol \sigma},{\boldsymbol…
We demonstrate that a recently introduced heuristic optimization algorithm [Phys. Rev. E 83, 046709 (2011)] that combines a local search with triadic crossover genetic updates is capable of sampling nearly uniformly among ground-state…
The Sherrington--Kirkpatrick model of spin glasses, the Hopfield model of neural networks and the Ising spin glass are all models of binary data belonging to the one-parameter exponential family with quadratic sufficient statistic. Under…
Spin glasses are fundamental probability distributions at the core of statistical physics, the theory of average-case computational complexity, and modern high-dimensional statistical inference. In the mean-field setting, we design…
We consider whether it is possible to find ground states of frustrated spin systems by solving them locally. Using spin glass physics and Imry-Ma arguments in addition to numerical benchmarks we quantify the power of such local solution…
Motivated by the recent development of quantum technology using quantum annealing technique and the recent works on the static properties of the Sherrington-Kirkpatrick (SK) spin glass model, we study quantum annealing of the spin glass…
The probability distribution function (PDF) of the ground-state energy in the Sherrington-Kirkpatrick spin-glass model is numerically determined by collecting a large statistical sample of ground states, computed using a genetic algorithm.…
Computing the ground state of Ising spin-glass models with p-spin interactions is, in general, an NP-hard problem. In this work we show that unlike in the case of the standard Ising spin glass with two-spin interactions, computing ground…
Some interesting recent advances in the theoretical understanding of neural networks have been informed by results from the physics of disordered many-body systems. Motivated by these findings, this work uses the replica technique to study…
The genetic cluster-exact approximation algorithm is an efficient method to calculate ground states of EA spin glasses. The method can be used to study ground-state landscapes by calculating many independent ground states for each…
We present an ansatz for the ground states of the Quantum Sherrington-Kirkpatrick model, a paradigmatic model for quantum spin glasses. Our ansatz, based on the concept of generalized coherent states, very well captures the fundamental…
A new approach to combinatorial optimization based on systematic move-class deflation is proposed. The algorithm combines heuristics of genetic algorithms and simulated annealing, and is mainly entropy-driven. It is tested on two problems…
The concept of replica symmetry breaking found in the solution of the mean-field Sherrington-Kirkpatrick spin-glass model has been applied to a variety of problems in science ranging from biological to computational and even financial…
The chapter starts with a historical summary of first attempts to optimize the spin glass Hamiltonian, comparing it to recent results on searching largest cliques in random graphs. Exact algorithms to find ground states in generic spin…
We developed a genetic algorithm (GA) in the Heisenberg model that combines a triadic crossover and a parameter-free genetic algorithm. Using the algorithm, we examined the ground-state stiffness of the $\pm J$ Heisenberg model in three…
Ground states of three-dimensional EA Ising spin glasses are calculated for sizes up to 14^3 using a combination of a genetic algorithm and cluster-exact approximation. For each realization several independent ground states are obtained.…
It is a folklore belief in the theory of spin glasses and disordered systems that out-of-equilibrium dynamics fail to find stable local optima exhibiting e.g. local strict convexity on physical time-scales. In the context of the…
We propose and demonstrate numerically a fast classical annealing scheme for the Sherrington-Kirkpatrick (SK) spin glass model, employing the Suzuki-Kubo meanfield Ising dynamics (supplemented by a modified Thouless-Anderson-Palmer reaction…