NCON: A tensor network contractor for MATLAB

TL;DR

The paper introduces ncon(), a MATLAB function that efficiently contracts tensor networks by following specified contraction sequences, simplifying the implementation of tensor network algorithms.

Contribution

It presents a new MATLAB tool, ncon(), for contracting tensor networks based on user-defined sequences, enhancing ease and flexibility in tensor computations.

Findings

Provides a MATLAB implementation for tensor network contraction

Enables flexible contraction sequences for complex networks

Facilitates development of tensor network algorithms

Abstract

A fundamental process in the implementation of any numerical tensor network algorithm is that of contracting a tensor network. In this process, a network made up of multiple tensors connected by summed indices is reduced to a single tensor or a number by evaluating the index sums. This article presents a MATLAB function ncon(), or "Network CONtractor", which accepts as its input a tensor network and a contraction sequence describing how this network may be reduced to a single tensor or number. As its output it returns that single tensor or number. The function ncon() may be obtained by downloading the source of this preprint.