Related papers: Simulated annealing, optimization, searching for g…
We investigate the computational hardness of spin-glass instances on a square lattice, generated via a recently introduced tunable and scalable approach for planting solutions. The method relies on partitioning the problem graph into…
We review the main methods used to study spin glasses. In the first part, we focus on methods for fully connected models and systems defined on a tree, such as the replica method, the Thouless-Anderson-Palmer formalism, the cavity method,…
A huge number of independent true ground-state configurations is calculated for two-, three- and four-dimensional +- J spin-glass models. Using the genetic cluster-exact approximation method, system sizes up to N=20^2,8^3,6^4 spins are…
Particle based optimization algorithms have recently been developed as sampling methods that iteratively update a set of particles to approximate a target distribution. In particular Stein variational gradient descent has gained attention…
We explore the role of entanglement in adiabatic quantum optimization by performing approximate simulations of the real-time evolution of a quantum system while limiting the amount of entanglement. To classically simulate the time evolution…
Limited resources motivate decomposing large-scale problems into smaller,``local" subsystems and stitching together the so-found solutions. We explore the physics underlying this approach and discuss the concept of ``local hardness", i.e.,…
An introduction to the application of combinatorial optimization methods to ground state calculations of frustrated, disordered systems is given. We discuss the interface problem in the random bond Ising ferromagnet, the random field Ising…
As spin glass materials have extremely slow dynamics, devious numerical methods are needed to study low-temperature states. A simple and fast optimization version of the classical Kasteleyn treatment of the Ising model is described and…
Many scientific problems seek to find the ground state in a rugged energy landscape, a task that becomes prohibitively difficult for large systems. Within a particular class of problems, however, the short-range correlations within energy…
In a recent article [Phys. Rev. Lett. 97 (2006), 107206], we have presented a class of states which is suitable as a variational set to find ground states in spin systems of arbitrary spatial dimension and with long-range entanglement.…
The use of combinatorial optimization algorithms has contributed substantially to the major progress that has occurred in recent years in the understanding of the physics of disordered systems, such as the random-field Ising model. While…
Finding the ground state of Ising spin glasses is notoriously difficult due to disorder and frustration. Often, this challenge is framed as a combinatorial optimization problem, for which a common strategy employs simulated annealing, a…
We introduce an algorithm to generate (not solve) spin-glass instances with planted solutions of arbitrary size and structure. First, a set of small problem patches with open boundaries is solved either exactly or with a heuristic, and then…
To provide a novel tool for the investigation of the energy landscape of the Edwards-Anderson spin-glass model we introduce an algorithm that allows an efficient execution of a greedy optimization based on data from a previously performed…
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…
An overview of some methods of statistical physics applied to the analysis of algorithms for optimization problems (satisfiability of Boolean constraints, vertex cover of graphs, decoding, ...) with distributions of random inputs is…
Replica symmetry breaking postulates that near optima of spin glass Hamiltonians have an ultrametric structure. Namely, near optima can be associated to leaves of a tree, and the Euclidean distance between them corresponds to the distance…
In a recent Letter [Europhys. Lett. 40, 429 (1997)], Hartmann presented results for the structure of the degenerate ground states of the three-dimensional +/- J spin glass model obtained using a genetic algorithm. In this Comment, I argue…
Spin glasses are disordered magnets with random interactions that are, generally, in conflict with each other. Finding the ground states of spin glasses is not only essential for the understanding of the nature of disordered magnetic and…
In this talk I will review the approach to spin glasses based on the spontaneously broken replica symmetry. I will concentrate my attention mostly on more general ideas, skipping technical details and stressing the characteristic…