Related papers: A hierarchical approach for computing spin glass g…
Although many efficient heuristics have been developed to solve binary optimization problems, these typically produce correlated solutions for degenerate problems. Most notably, transverse-field quantum annealing - the heuristic employed in…
An important but little-studied property of spin glasses is the stability of their ground states to changes in one or a finite number of couplings. It was shown in earlier work that, if multiple ground states are assumed to exist, then…
In this talk we review our theoretical understanding of spin glasses paying a particular attention to the basic physical ideas. We introduce the replica method and we describe its probabilistic consequences (we stress the recently…
We present an algorithm for the optimization and thermal equilibration of spin glasses - or more generally, cost functions of the Ising form $H=\sum_{\langle i j\rangle} J_{ij} s_i s_j + \sum_i h_i s_i$, defined on graphs with arbitrary…
We wish to thank Stefan Boettcher for prompting us to further check and highlight the accuracy and scaling of our results. Here we provide a comprehensive response to the Comment written by him. We argue that the Comment did not account for…
We compare the performance of extremal optimization (EO), flat-histogram and equal-hit algorithms for finding spin-glass ground states. The first-passage-times to a ground state are computed. At optimal parameter of tau=1.15, EO outperforms…
We investigate the performance of the recently proposed stationary Fokker-Planck sampling method considering a combinatorial optimization problem from statistical physics. The algorithmic procedure relies upon the numerical solution of a…
Reputation systems seek to infer which members of a community can be trusted based on ratings they issue about each other. We construct a Bayesian inference model and simulate approximate estimates using belief propagation (BP). The model…
We present a theoretical framework to accurately calculate the location of the multicritical point in the phase diagram of spin glasses. The result shows excellent agreement with numerical estimates. The basic idea is a combination of the…
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…
The scaling of fluctuations in the distribution of ground-state energies or costs with the system size N for Ising spin glasses is considered using an extensive set of simulations with the Extremal Optimization heuristic across a range of…
We introduce a variational method for the approximation of ground states of strongly interacting spin systems in arbitrary geometries and spatial dimensions. The approach is based on weighted graph states and superpositions thereof. These…
We analyze operational risk in terms of a spin glass model. Several regimes are investigated, as a functions of the parameters that characterize the dynamics. The system is found to be robust against variations of these parameters. We…
We study the Ising spin glass on random graphs with fixed connectivity z and with a Gaussian distribution of the couplings, with mean \mu and unit variance. We compute exact ground states by using a sophisticated branch-and-cut method for…
Hierarchical spin-glasses are Ising spin models defined by recursively coupling together two equally-sized sub-systems. In this work a new hierarchical spin system is introduced wherein the sub-systems are recursively coupled together…
An extensive list of results for the ground state properties of spin glasses on random graphs is presented. These results provide a timely benchmark for currently developing theoretical techniques based on replica symmetry breaking that are…
Exploiting quantum properties to outperform classical ways of information-processing is an outstanding goal of modern physics. A promising route is quantum simulation, which aims at implementing relevant and computationally hard problems in…
Ground states of spin lattices can serve as a resource for measurement-based quantum computation. Ideally, the ability to perform quantum gates via measurements on such states would be insensitive to small variations in the Hamiltonian.…
We compute and analyze couples of ground states of 3D spin glass systems with the same quenched noise but periodic and anti-periodic boundary conditions for different lattice sizes. We discuss the possible different behaviors of the system,…
Ultrastable glasses, amorphous solids with exceptionally low-energy states and enhanced kinetic, thermodynamic and mechanical stability, have long been a subject of intense experimental interest. Over the past decade, their computational…