Contracting Arbitrary Tensor Networks: General Approximate Algorithm and Applications in Graphical Models and Quantum Circuit Simulations

TL;DR

This paper introduces a versatile approximate tensor network contraction algorithm applicable to arbitrary graph connectivities, significantly advancing inference in graphical models and quantum circuit simulation.

Contribution

It provides a novel general algorithm for tensor network contraction on arbitrary graphs, enabling broader applications in inference and quantum simulations.

Findings

Outperforms existing algorithms in estimating free energy of spin glasses

Enables simulation of larger quantum circuits than current methods

Achieves negligible truncation errors with high computational efficiency

Abstract

We present a general method for approximately contracting tensor networks with an arbitrary connectivity. This enables us to release the computational power of tensor networks to wide use in inference and learning problems defined on general graphs. We show applications of our algorithm in graphical models, specifically on estimating free energy of spin glasses defined on various of graphs, where our method largely outperforms existing algorithms including the mean-field methods and the recently proposed neural-network-based methods. We further apply our method to the simulation of random quantum circuits, and demonstrate that, with a trade off of negligible truncation errors, our method is able to simulate large quantum circuits that are out of reach of the state-of-the-art simulation methods.