Sample-efficient estimation of entanglement entropy through supervised learning

TL;DR

This paper presents a supervised machine learning method to efficiently estimate entanglement entropy and quantum mutual information in multi-qubit systems, outperforming traditional algorithms especially with limited samples.

Contribution

It introduces a novel supervised learning approach that accurately estimates entanglement entropy and uncertainty, demonstrating improved performance over conventional methods in quantum systems.

Findings

Converges with fewer samples than baseline methods

Effective in estimating mutual information under noise

Extrapolates near training data regime

Abstract

We explore a supervised machine learning approach to estimate the entanglement entropy of multi-qubit systems from few experimental samples. We put a particular focus on estimating both aleatoric and epistemic uncertainty of the network's estimate and benchmark against the best known conventional estimation algorithms. For states that are contained in the training distribution, we observe convergence in a regime of sample sizes in which the baseline method fails to give correct estimates, while extrapolation only seems possible for regions close to the training regime. As a further application of our method, highly relevant for quantum simulation experiments, we estimate the quantum mutual information for non-unitary evolution by training our model on different noise strengths.