Estimating the Density of States of Frustrated Spin Systems

TL;DR

This paper introduces a population annealing sampling method with multi-histogram analysis for estimating the density of states in frustrated spin systems, overcoming issues of metastable minima and enabling large-scale physics discoveries.

Contribution

The authors develop a novel sampling technique that improves density of states estimation in complex systems, with broad applicability and enhanced accuracy over existing methods.

Findings

Demonstrates the method's ability to avoid metastable minima.

Shows large scaling advantages in spin glass systems.

Provides schemes for exact degeneracy counts.

Abstract

Estimating the density of states of systems with rugged free energy landscapes is a notoriously difficult task of the utmost importance in many areas of physics ranging from spin glasses to biopolymers. Density of states estimation has also recently become an indispensable tool for the benchmarking of quantum annealers when these function as samplers. Some of the standard approaches suffer from a spurious convergence of the estimates to metastable minima, and these cases are particularly hard to detect. Here, we introduce a sampling technique based on population annealing enhanced with a multi-histogram analysis and report on its performance for spin glasses. We demonstrate its ability to overcome the pitfalls of other entropic samplers, resulting in some cases in large scaling advantages that can lead to the uncovering of new physics. The new technique avoids some inherent difficulties in established approaches and can be applied to a wide range of systems without relevant tailoring requirements. Benchmarking of the studied techniques is facilitated by the introduction of several schemes that allow us to achieve exact counts of the degeneracies of the tested instances.