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.

翻译：罕见事件（如金融崩盘、极端气候和生物异常）因其稀缺性和重尾分布特性而极难建模。经典深度生成模型在捕捉此类罕见事件时往往表现不佳，容易出现低概率模式塌缩或产生校准不佳的不确定性估计。本研究提出量子增强生成模型（QEGM），这是一种融合深度隐变量模型与变分量子电路的经典-量子混合框架。该框架引入两项关键创新：（1）联合优化重构保真度与尾部感知似然的混合损失函数；（2）利用量子随机性驱动的噪声注入以增强样本多样性并缓解模式塌缩。训练通过混合循环进行：经典参数通过反向传播更新，而量子参数则采用参数平移梯度法优化。我们在合成高斯混合数据集及涵盖金融、气候和蛋白质结构的真实数据集上评估QEGM。结果表明，相较于前沿基线模型（GAN、VAE、Diffusion），QEGM将尾部KL散度降低达50%，同时提升了罕见事件召回率与覆盖校准度。这些发现彰显了QEGM作为罕见事件预测原则性方法的潜力，其鲁棒性超越了纯经典方法所能达到的范畴。