Enhancing Generative Models via Quantum Correlations

TL;DR

This paper demonstrates that quantum correlations, such as nonlocality and contextuality, can significantly enhance the expressive power of generative models, offering potential quantum advantages in machine learning tasks.

Contribution

It provides a theoretical proof of the separation in expressive power between classical Bayesian networks and their quantum extensions, supported by numerical experiments on standard datasets.

Findings

Quantum correlations improve generative model expressivity.

Quantum advantage is linked to nonlocality and contextuality.

Numerical results confirm practical benefits on real datasets.

Abstract

Generative modeling using samples drawn from the probability distribution constitutes a powerful approach for unsupervised machine learning. Quantum mechanical systems can produce probability distributions that exhibit quantum correlations which are difficult to capture using classical models. We show theoretically that such quantum correlations provide a powerful resource for generative modeling. In particular, we provide an unconditional proof of separation in expressive power between a class of widely-used generative models, known as Bayesian networks, and its minimal quantum extension. We show that this expressivity advantage is associated with quantum nonlocality and quantum contextuality. Furthermore, we numerically test this separation on standard machine learning data sets and show that it holds for practical problems. The possibility of quantum advantage demonstrated in this work not only sheds light on the design of useful quantum machine learning protocols but also provides inspiration to draw on ideas from quantum foundations to improve purely classical algorithms.