Quantum mixture-density network for multimodal probabilistic prediction

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 a practical quantum advantage in probabilistic regression and highlight the potential of quantum machine learning in capturing complex stochastic behavior beyond the reach of classical models.