Quantum mixture-density network for multimodal probabilistic prediction

TL;DR

The paper introduces a Quantum Mixture-Density Network that uses quantum circuits to efficiently model complex multimodal probability distributions, outperforming classical methods in key quantum and chaotic systems.

Contribution

It presents a novel quantum-based approach to modeling multimodal distributions, reducing parameter complexity and enhancing prediction accuracy over classical mixture-density networks.

Findings

Q-MDN outperforms classical MDNs in mode separability.

Q-MDN achieves sharper predictions with fewer parameters.

Demonstrated effectiveness on quantum and chaotic systems.

Abstract

Multimodal probability distributions are common in both quantum and classical systems, yet modeling them remains challenging when the number of modes is large or unknown. Classical methods such as mixture-density networks (MDNs) scale poorly, requiring parameter counts that grow quadratically with the number of modes. We introduce a Quantum Mixture-Density Network (Q-MDN) that employs parameterized quantum circuits to efficiently model multimodal distributions. By representing an exponential number of modes with a compact set of qubits and parameters, Q-MDN predicts Gaussian mixture components with high resolution. We evaluate Q-MDN on two benchmark tasks: the quantum double-slit experiment and chaotic logistic bifurcation. In both cases, Q-MDN outperforms classical MDNs in mode separability and prediction sharpness under equal parameter budgets. Our results demonstrate an efficiency in probabilistic regression and highlight the potential of quantum machine learning in capturing complex stochastic behavior.