Correlator convolutional neural networks as an interpretable architecture for image-like quantum matter data

Cole Miles, Annabelle Bohrdt, Ruihan Wu, Christie Chiu, Muqing Xu, Geoffrey Ji, Markus Greiner, Kilian Q. Weinberger, Eugene Demler and Eun-Ah Kim ()
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Cole Miles: Cornell University
Annabelle Bohrdt: Harvard University
Ruihan Wu: Cornell University
Christie Chiu: Harvard University
Muqing Xu: Harvard University
Geoffrey Ji: Harvard University
Markus Greiner: Harvard University
Kilian Q. Weinberger: Cornell University
Eugene Demler: Harvard University
Eun-Ah Kim: Cornell University

Nature Communications, 2021, vol. 12, issue 1, 1-7

Abstract: Abstract Image-like data from quantum systems promises to offer greater insight into the physics of correlated quantum matter. However, the traditional framework of condensed matter physics lacks principled approaches for analyzing such data. Machine learning models are a powerful theoretical tool for analyzing image-like data including many-body snapshots from quantum simulators. Recently, they have successfully distinguished between simulated snapshots that are indistinguishable from one and two point correlation functions. Thus far, the complexity of these models has inhibited new physical insights from such approaches. Here, we develop a set of nonlinearities for use in a neural network architecture that discovers features in the data which are directly interpretable in terms of physical observables. Applied to simulated snapshots produced by two candidate theories approximating the doped Fermi-Hubbard model, we uncover that the key distinguishing features are fourth-order spin-charge correlators. Our approach lends itself well to the construction of simple, versatile, end-to-end interpretable architectures, thus paving the way for new physical insights from machine learning studies of experimental and numerical data.

Date: 2021
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DOI: 10.1038/s41467-021-23952-w

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