Monte Carlo Tensor Network Renormalization

TL;DR

This paper introduces a Monte Carlo tensor network renormalization method that enhances computational efficiency, accuracy, and provides uncertainty estimates, making it suitable for modern parallel computing architectures.

Contribution

It presents a novel Monte Carlo approach to tensor network renormalization that improves efficiency and accuracy while offering unbiased results and uncertainty quantification.

Findings

Demonstrates the efficiency of the Monte Carlo tensor network renormalization method.

Shows the method provides unbiased estimates with quantifiable uncertainty.

Highlights suitability for modern parallel computing architectures.

Abstract

Techniques for approximately contracting tensor networks are limited in how efficiently they can make use of parallel computing resources. In this work we demonstrate and characterize a Monte Carlo approach to the tensor network renormalization group method which can be used straightforwardly on modern computing architectures. We demonstrate the efficiency of the technique and show that Monte Carlo tensor network renormalization provides an attractive path to improving the accuracy of a wide class of challenging computations while also providing useful estimates of uncertainty and a statistical guarantee of unbiased results.