Finding and proving the exact ground state of a generalized Ising model by convex optimization and MAX-SAT

  title={Finding and proving the exact ground state of a generalized Ising model by convex optimization and MAX-SAT},
  author={Wenxuan Huang and Daniil A. Kitchaev and Stephen T. Dacek and Ziqin Rong and Alexander Urban and Shan Cao and Chuan Luo and Gerbrand Ceder},
  journal={Physical Review B},
This paper was supported primarily by the US Department of Energy (DOE) under Contract No. DE-FG02-96ER45571. In addition, some of the test cases for ground states were supported by the Office of Naval Research under contract N00014-14-1-0444. 

Figures from this paper

Learning from survey propagation: a neural network for MAX-E-3-SAT

  • Raffaele Marino
  • Computer Science
    Machine Learning: Science and Technology
  • 2021
This paper presents a new algorithm for computing approximate solutions in Θ(N) for the maximum exact 3-satisfiability (MAX-E-3-SAT) problem by using supervised learning methodology and shows that this new algorithm can build assignments better than a random one, even if the convergence of the messages is not found.

Maximum Satisfiability

This chapter provides a detailed overview of the approaches to MaxSAT solving that have in recent years been most successful in solving real-world optimization problems.

Empirical investigation of stochastic local search for maximum satisfiability

Experimental results show that the enhanced SLS algorithm developed here performs better than its state-of-the-art SLS competitors on a large number of industrial MAX-SAT instances.

CCEHC: An Efficient Local Search Algorithm for Weighted Partial Maximum Satisfiability (Extended Abstract)

A new SLS algorithm named CCEHC for WPMS is presented, mainly based on a heuristic emphasizing hard clauses, which has three components: a variable selection mechanism focusing on configuration checking based only on hard clause, a weighting scheme forhard clauses, and a biased random walk component.

Construction of ground-state preserving sparse lattice models for predictive materials simulations

This paper presents a systematic and mathematically sound method to obtain cluster expansion models that are guaranteed to preserve the ground states of their reference data and shows that out-of-sample ground-state preservation up to relatively large supercell size is achievable through a rapidly converging iterative refinement.

Pure MaxSAT and Its Applications to Combinatorial Optimization via Linear Local Search

This work designs a novel local search method for Pure MaxSAT, which combines the idea of linear search and local search and is dubbed as linear local search, which significantly outperforms state of the art MaxSat solvers on PureMaxSAT instances.

Implementation of a Multiple Target Tracking Filter on an Adiabatic Quantum Computer

Recent work at Fraunhofer FKIE shows that More-field's method for multiple target data association can in theory be solved on an adiabatic quantum computer. The present paper validates the theory and

Partial lifting of degeneracy in the $J_1-J_2-J_3$ Ising antiferromagnet on the kagome lattice

Motivated by dipolar-coupled artificial spin systems, we present a theoretical study of the classical J 1 − J 2 − J 3 Ising antiferromagnet on the kagome lattice. We establish the ground-state phase

Solving frustrated Ising models using tensor networks

It is shown that optimizing the choice of clusters, including the weight on shared bonds, is crucial for the contractibility of the tensor networks, and some basic rules are derived and a linear program to implement them are derived.



A Method of Determining the Ground State of the Extended-Range Classical Lattice Gas Model

A method of deriving geometrical inequalities by the use of which the ground state of the extended-range classica:l lattice gas model can be analytically determined is developed. As illustrative

Pseudo-Boolean optimization

CCLS: An Efficient Local Search Algorithm for Weighted Maximum Satisfiability

Experimental results illustrate that the quality of solution found by CCLS is much better than that found by IRoTS, akmaxsat_ls and New WPM2 on most industrial, crafted and random instances, indicating the efficiency and the robustness of the CCRS algorithm.

The First and Second Max-SAT Evaluations

The main objectives of both evaluations were assessing the advancements in the field of Max-SAT solvers through a comparison of their performances, identifying successful solving techniques and encouraging researchers to develop new ones, and creating a publicly available collection of challenging Max- SAT benchmarks.

Engineering Ising-XY spin-models in a triangular lattice using tunable artificial gauge fields

A quantum gas trapped in an optical lattice of triangular symmetry can now be driven from a paramagnetic to an antiferromagnetic state by a tunable artificial magnetic field.

Satisfiability Solvers

The efficiency of subgradient projection methods for convex optimization, part I: general level methods

Subgradient methods for convex optimization that use projections onto successive approximations of level sets of the objective corresponding to estimates of the optimal value enjoy almost optimal efficiency estimates.