Quantum-Enhanced Generative Models for Rare Event Prediction

Rare events such as financial crashes, climate extremes, and biological anomalies are notoriously difficult to model due to their scarcity and heavy-tailed distributions. Classical deep generative models often struggle to capture these rare occurrences, either collapsing low-probability modes or producing poorly calibrated uncertainty estimates. In this work, we propose the Quantum-Enhanced Generative Model (QEGM), a hybrid classical-quantum framework that integrates deep latent-variable models with variational quantum circuits. The framework introduces two key innovations: (1) a hybrid loss function that jointly optimizes reconstruction fidelity and tail-aware likelihood, and (2) quantum randomness-driven noise injection to enhance sample diversity and mitigate mode collapse. Training proceeds via a hybrid loop where classical parameters are updated through backpropagation while quantum parameters are optimized using parameter-shift gradients. We evaluate QEGM on synthetic Gaussian mixtures and real-world datasets spanning finance, climate, and protein structure. Results demonstrate that QEGM reduces tail KL divergence by up to 50 percent compared to state-of-the-art baselines (GAN, VAE, Diffusion), while improving rare-event recall and coverage calibration. These findings highlight the potential of QEGM as a principled approach for rare-event prediction, offering robustness beyond what is achievable with purely classical methods.