Automatic Contraction of Unstructured Tensor Networks

TL;DR

This paper introduces a new algorithm for contracting unstructured tensor networks, enabling efficient computation of partition functions in statistical physics without relying on network structure assumptions.

Contribution

The paper presents a novel algorithm that effectively contracts unstructured tensor networks, broadening applicability beyond structured networks.

Findings

Performs well on both structured and unstructured networks

No assumptions needed about network structure

Effective when correlation structure is local

Abstract

The evaluation of partition functions is a central problem in statistical physics. For lattice systems and other discrete models the partition function may be expressed as the contraction of a tensor network. Unfortunately computing such contractions is difficult, and many methods to make this tractable require periodic or otherwise structured networks. Here I present a new algorithm for contracting unstructured tensor networks. This method makes no assumptions about the structure of the network and performs well in both structured and unstructured cases so long as the correlation structure is local.