# Solving Spin Glasses with Optimized Trees of Clustered Spins

## TL;DR

This paper introduces an algorithm that constructs optimized trees of clustered spins for efficient optimization and thermal sampling of spin glasses, outperforming existing methods on various problem classes.

## Contribution

The paper proposes a novel algorithm combining tree construction and thermal sampling for spin glasses, improving efficiency and scalability over prior approaches.

## Key findings

- Outperforms existing algorithms on benchmark problems.
- Effectively balances tree size and sampling complexity.
- Demonstrates versatility across different graph connectivities.

## Abstract

We present an algorithm for the optimization and thermal equilibration of spin glasses - or more generally, cost functions of the Ising form $H=\sum_{\langle i j\rangle} J_{ij} s_i s_j + \sum_i h_i s_i$, defined on graphs with arbitrary connectivity. The algorithm consists of two repeated steps: i) the optimized construction of a random tree of spin clusters on the input problem graph, and ii) the thermal sampling of the generated tree. The randomly generated trees are constructed so as to optimize a balance between the size of the tree and the complexity required to draw Boltzmann samples from it. We benchmark the algorithm on several classes of problems and demonstrate its advantages over existing approaches.