Quantum mixture-density network for multimodal probabilistic prediction

TL;DR

The paper addresses modeling multimodal probabilistic outputs in systems with potentially many or unknown modes. It introduces the Quantum Mixture-Density Network (Q-MDN), which uses parameterized quantum circuits to represent an exponential number of mixture components with a compact qubit-based parameter set, encoding Gaussian parameters via log-ratio mappings from quantum state probabilities. Across electron double-slit–like data and chaotic logistic bifurcation tasks, Q-MDN demonstrates superior mode separability and sharper density predictions under equal parameter budgets compared to classical MDNs, highlighting a potential quantum advantage in probabilistic regression. The work also discusses practical considerations for real quantum hardware and points toward future extensions in reinforcement learning and continuous-action settings, with code availability for reproducibility.

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.