Classical machine learning (ML) provides a potentially powerful approach to solving challenging quantum many-body problems in physics and chemistry. However, the advantages of ML over traditional methods have not been firmly established. In this work, we prove that classical ML algorithms can efficiently predict ground-state properties of gapped Hamiltonians after learning from other Hamiltonians in the same quantum phase of matter. By contrast, under a widely accepted conjecture, classical algorithms that do not learn from data cannot achieve the same guarantee. We also prove that classical ML algorithms can efficiently classify a wide range of quantum phases. Extensive numerical experiments corroborate our theoretical results in a variety of scenarios, including Rydberg atom systems, two-dimensional random Heisenberg models, symmetry-protected topological phases, and topologically ordered phases.

中文翻译：

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用于量子多体问题的可证明有效的机器学习

经典机器学习 (ML) 为解决物理和化学中具有挑战性的量子多体问题提供了一种潜在的强大方法。然而，ML 相对于传统方法的优势尚未得到牢固确立。在这项工作中，我们证明了经典的 ML 算法在向物质相同量子相中的其他哈密顿量学习后，可以有效地预测带隙哈密顿量的基态特性。相比之下，在一个被广泛接受的猜想下，不从数据中学习的经典算法无法实现同样的保证。我们还证明了经典的 ML 算法可以有效地对各种量子相进行分类。大量的数值实验证实了我们在各种场景中的理论结果，包括里德堡原子系统、二维随机海森堡模型、