Unsupervised Machine Learning of Quantum Phase Transitions Using Diffusion Maps
Unsupervised Machine Learning of Quantum Phase Transitions Using Diffusion Maps
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DOI：
10.1103/physrevlett.125.225701
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发表时间：
2020-11-24
影响因子：
8.6
通讯作者：
Gong, Zhexuan
中科院分区：
文献类型：
--
作者：
Lidiak, Alexander;Gong, Zhexuan
实验量子模拟器已经变得足够大和复杂，从大量的测量数据中发现新的物理学可能是相当具有挑战性的，特别是当对模拟模型的理论理解很少时。无监督机器学习方法在克服这一挑战方面特别有前途。对于学习量子相变的特定任务，无监督机器学习方法主要针对由简单序参数表征的相变开发，通常在测量的可观测量中是线性的。然而，这样的方法往往失败的更复杂的相变，如那些涉及无公度相，价键固体，拓扑秩序，和多体本地化。我们表明，扩散图的方法，它执行非线性降维和谱聚类的测量数据，具有显着的潜力，学习这种复杂的相变无监督。这种方法可以工作在一个单一的基础上的本地可观测量，因此很容易适用于许多实验量子模拟器作为一个通用的工具，用于学习各种量子相位和相变。
Experimental quantum simulators have become large and complex enough that discovering new physics from the huge amount of measurement data can be quite challenging, especially when little theoretical understanding of the simulated model is available. Unsupervised machine learning methods are particularly promising in overcoming this challenge. For the specific task of learning quantum phase transitions, unsupervised machine learning methods have primarily been developed for phase transitions characterized by simple order parameters, typically linear in the measured observables. However, such methods often fail for more complicated phase transitions, such as those involving incommensurate phases, valence-bond solids, topological order, and many-body localization. We show that the diffusion map method, which performs nonlinear dimensionality reduction and spectral clustering of the measurement data, has significant potential for learning such complex phase transitions unsupervised. This method may work for measurements of local observables in a single basis and is thus readily applicable to many experimental quantum simulators as a versatile tool for learning various quantum phases and phase transitions.