We develop a pairing-based graph neural network for simulating quantum many-body systems. Our architecture augments a BCS-type geminal wave function with a generalized pair amplitude parametrized by a graph neural network. Variational Monte Carlo with our neural network simultaneously provides an accurate, flexible, and scalable method for simulating many-electron systems. We apply this method to two-dimensional semiconductor electron-hole bilayers and obtain accurate results on a variety of interaction-induced phases with one unified neural network, including the exciton Bose-Einstein condensate, electron-hole superconductor, and bilayer Wigner crystal. Our study demonstrates the potential of physically motivated neural network wave functions for quantum materials simulations.

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• Electronic structure
• Two-dimensional electron system
• BCS theory
• Machine learning
• Mean field theory
• Superconductivity
• Variational wave functional methods