Enhancing Generative Models via Quantum Correlations

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-inspired 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-inspired extension. We show that this expressivity enhancement 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-inspired enhancement 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.

Automated summary

This research demonstrates the powerful resource of generative modeling derived from quantum correlations. It provides an unconditional proof that quantum-inspired models surpass conventional Bayesian networks in expressive power and verifies their applicability through numerical tests. This has significant implications for designing quantum machine learning protocols and improving classical algorithms using ideas from quantum foundations.