From local to global ground states in Ising spin glasses

TL;DR

This paper investigates local solution methods for finding ground states in frustrated spin systems, demonstrating polynomial-time solutions outside the spin-glass phase and introducing a hierarchical heuristic that outperforms existing solvers.

Contribution

It provides a quantitative analysis of local solution methods and introduces a new hierarchical heuristic that surpasses current solvers in efficiency and scalability.

Findings

Exact ground states found in polynomial time outside the spin-glass phase.

Hierarchical heuristic outperforms existing solvers on chimera graphs and 2D/3D lattices.

Significantly better scaling performance than simulated annealing.

Abstract

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 methods and show that for the average low-dimensional spin glass problem outside the spin- glass phase the exact ground state can be found in polynomial time. In the second part we present a heuristic, general-purpose hierarchical approach which for spin glasses on chimera graphs and lattices in two and three dimensions outperforms, to our knowledge, any other solver currently around, with significantly better scaling performance than simulated annealing.