用改进的EM算法训练量子玻尔兹曼机，克服梯度消失问题。
Structured quantum learning via em algorithm for Boltzmann machines
- 基于信息几何的量子EM算法，避免依赖梯度优化。
- 在半量子受限玻尔兹曼机上实现稳定学习，优于传统梯度下降。
- 适合研究量子生成模型与抗退化训练方法的学者。
量子玻尔兹曼机（QBMs）在量子机器学习中具有潜力，但其训练受“贫瘠高原”问题制约——梯度随系统规模指数级消失。本文提出一种量子版EM算法，作为经典期望最大化方法的信息几何推广，可绕过非凸函数上的梯度优化。该方法在半量子受限玻尔兹曼机（sqRBM）上实现，其中量子效应仅限于隐层。实验表明，该方法能实现稳定学习，在多个基准数据集上性能优于梯度下降。结果为量子机器学习中的梯度训练提供了结构化且可扩展的替代方案，有助于缓解贫瘠高原问题，提升量子生成建模能力。
原文摘要 · Abstract (English)
Quantum Boltzmann machines (QBMs) are generative models with potential advantages in quantum machine learning, yet their training is fundamentally limited by the barren plateau problem, where gradients vanish exponentially with system size. We introduce a quantum version of the em algorithm, an information-geometric generalization of the classical Expectation-Maximization method, which circumvents gradient-based optimization on non-convex functions. Implemented on a semi-quantum restricted Boltzmann machine (sqRBM) -- a hybrid architecture with quantum effects confined to the hidden layer -- our method achieves stable learning and outperforms gradient descent on multiple benchmark datasets. These results establish a structured and scalable alternative to gradient-based training in QML, offering a pathway to mitigate barren plateaus and enhance quantum generative modeling.
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