Provably efficient machine learning for quantum many-body problems
Provably efficient machine learning for quantum many-body problems
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DOI：
10.1126/science.abk3333
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发表时间：
2022-09-23
期刊：
影响因子：
56.9
通讯作者：
Preskill, John
中科院分区：
文献类型：
--
作者：
Huang, Hsin-Yuan;Kueng, Richard;Preskill, John
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，最大似然法相对于传统方法的优势还没有被牢固地确立。在这项工作中，我们证明了经典的ML算法在学习了同一量子相物质中的其他哈密顿量后，可以有效地预测有隙哈密顿量的基态性质。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最大似然算法可以有效地对大范围的量子相位进行分类。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、对称性保护的拓扑相和拓扑有序相。
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.