Machine Learning Entanglement Freedom Or: How I Learned to Stop Worrying and Love Linear Regression

TL;DR

This paper explores using machine learning techniques, including linear regression and auto-encoders, to estimate the interaction distance in quantum many-body systems, facilitating the analysis of their entanglement spectra.

Contribution

It introduces machine learning methods to efficiently approximate the interaction distance, a key measure of interactions in quantum states, using supervised and semi-supervised learning.

Findings

Linear regression can predict interaction distance from entanglement spectra.

Auto-encoders can estimate an alternative interaction measure with similar behavior.

Machine learning approaches offer a computationally efficient way to analyze quantum entanglement.

Abstract

Quantum many-body systems realise many different phases of matter characterised by their exotic emergent phenomena. While some simple versions of these properties can occur in systems of free fermions, their occurrence generally implies that the physics is dictated by an interacting Hamiltonian. The interaction distance has been successfully used to quantify the effect of interactions in a variety of states of matter via the entanglement spectrum [Nat. Commun. 8, 14926 (2017), arXiv:1705.09983]. The computation of the interaction distance reduces to a global optimisation problem whose goal is to search for the free-fermion entanglement spectrum closest to the given entanglement spectrum. In this work, we employ techniques from machine learning in order to perform this same task. In a supervised learning setting, we use labelled data obtained by computing the interaction distance and predict its value via linear regression. Moving to a semi-supervised setting, we train an auto-encoder to estimate an alternative measure to the interaction distance, and we show that it behaves in a similar manner.