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.

中文翻译：

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使用扩散图的量子相变无监督机器学习

实验性的量子模拟器已经变得足够大和复杂，以至于从大量的测量数据中发现新的物理学将是非常具有挑战性的，特别是在对模拟模型的理论了解很少的情况下。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是针对以简单阶次参数为特征的相变而开发的，这些阶跃参数通常在所测量的可观测值中呈线性。但是，此类方法通常无法实现更复杂的相变，例如涉及不相称的相，价键固体，拓扑顺序和多体定位的方法。我们证明了扩散图法 它执行非线性降维和测量数据的频谱聚类，对于学习这种无监督的复杂相变具有巨大的潜力。该方法可以在单个基础上测量局部可观测物，因此可以很容易地应用于许多实验量子模拟器，作为学习各种量子相和相变的通用工具。