Interpretable representation learning of quantum data enabled by probabilistic variational autoencoders

TL;DR

This paper introduces a probabilistic VAE framework tailored for quantum data, enabling the extraction of interpretable physical features and phase structures without supervision, even in complex quantum regimes.

Contribution

The authors develop two key modifications to VAEs—quantum state-faithful decoders and a probabilistic loss—that improve interpretability of quantum data representations.

Findings

Successfully applied to quantum spin models, revealing regimes where standard methods fail.

Unsupervised discovery of phase structures in Rydberg atom array data.

Enhanced interpretability of quantum features learned by the model.

Abstract

Interpretable machine learning is rapidly becoming a crucial tool for scientific discovery. Among existing approaches, variational autoencoders (VAEs) have shown promise in extracting the hidden physical features of some input data, with no supervision nor prior knowledge of the system at study. Yet, the ability of VAEs to create meaningful, interpretable representations relies on their accurate approximation of the underlying probability distribution of their input. When dealing with quantum data, VAEs must hence account for its intrinsic randomness and complex correlations. While VAEs have been previously applied to quantum data, they have often neglected its probabilistic nature, hindering the extraction of meaningful physical descriptors. Here, we demonstrate that two key modifications enable VAEs to learn physically meaningful latent representations: a decoder capable of faithfully reproduce quantum states and a probabilistic loss tailored to this task. Using benchmark quantum spin models, we identify regimes where standard methods fail while the representations learned by our approach remain meaningful and interpretable. Applied to experimental data from Rydberg atom arrays, the model autonomously uncovers the phase structure without access to prior labels, Hamiltonian details, or knowledge of relevant order parameters, highlighting its potential as an unsupervised and interpretable tool for the study of quantum systems.