Inference from Matrix Products: A Heuristic Spin Glass Algorithm

TL;DR

This paper introduces a heuristic algorithm inspired by quantum matrix product states to efficiently approximate ground states of 2D spin glass systems, outperforming traditional methods in speed and scalability.

Contribution

The authors develop a novel matrix product state-based heuristic for 2D spin glasses, enabling efficient zero-temperature ground state approximation with scalable accuracy.

Findings

Accurate results require polynomially scaling parameter k.

Algorithm performs well on small systems with arbitrary interactions.

Significantly faster than Monte Carlo methods.

Abstract

We present an algorithm for finding ground states of two dimensional spin glass systems based on ideas from matrix product states in quantum information theory. The algorithm works directly at zero temperature and defines an approximate "boundary Hamiltonian" whose accuracy depends on a parameter $k$. We test the algorithm against exact methods on random field and random bond Ising models, and we find that accurate results require a $k$ which scales roughly polynomially with the system size. The algorithm also performs well when tested on small systems with arbitrary interactions, where no fast, exact algorithms exist. The time required is significantly less than Monte Carlo schemes.