Generative modeling using samples drawn from the probability distribution constitutes a powerful approach for unsupervised machine learning. Quantum mechanical systems can produce probability distributions that exhibit quantum correlations which are difficult to capture using classical models. We show theoretically that such quantum-inspired correlations provide a powerful resource for generative modeling. In particular, we provide an unconditional proof of separation in expressive power between a class of widely used generative models, known as Bayesian networks, and its minimal quantum-inspired extension. We show that this expressivity enhancement is associated with quantum nonlocality and quantum contextuality. Furthermore, we numerically test this separation on standard machine-learning data sets and show that it holds for practical problems. The possibility of quantum-inspired enhancement demonstrated in this work not only sheds light on the design of useful quantum machine-learning protocols but also provides inspiration to draw on ideas from quantum foundations to improve purely classical algorithms.

中文翻译：

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通过量子相关增强生成模型

使用从概率分布中抽取的样本进行生成建模构成了一种强大的无监督机器学习方法。量子力学系统可以产生概率分布，这些概率分布表现出使用经典模型难以捕捉的量子相关性。我们从理论上证明，这种受量子启发的相关性为生成建模提供了强大的资源。特别是，我们无条件地证明了一类广泛使用的生成模型（称为贝叶斯网络）与其最小的量子启发扩展之间的表达能力分离。我们表明，这种表达能力增强与量子非定域性和量子上下文相关。此外，我们在标准机器学习数据集上对这种分离进行了数值测试，并表明它适用于实际问题。