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

Area of Science:

• Condensed Matter Physics
• Quantum Information Science
• Machine Learning

Background:

• Traditional condensed matter physics lacks methods for analyzing complex quantum data.
• Machine learning (ML) offers powerful tools for image-like data, including quantum many-body snapshots.
• Current ML models for quantum data are often too complex for direct physical interpretation.

Purpose of the Study:

• To develop interpretable machine learning architectures for analyzing quantum data.
• To uncover physically meaningful features within quantum system snapshots.
• To apply these methods to distinguish between competing theories of correlated quantum matter.

Main Methods:

• Developed novel nonlinearities for neural network architectures.
• Engineered the network to discover features interpretable as physical observables.
• Applied the architecture to analyze simulated snapshots from the doped Fermi-Hubbard model.

Main Results:

• The interpretable neural network successfully identified key distinguishing features in quantum snapshots.
• The primary distinguishing features were found to be fourth-order spin-charge correlators.
• This approach distinguished between different theoretical approximations of the doped Fermi-Hubbard model.

Conclusions:

• The developed ML approach enables the extraction of direct physical insights from quantum data.
• The method facilitates the construction of simple, versatile, and interpretable ML architectures.
• This work paves the way for new discoveries in experimental and numerical quantum matter studies.