QERNEL: Quantum Expert-Routed Neural Learner
ORAL
Abstract
QERNEL is a neural variational solver that learns ground states and observables for entire families of Hamiltonians in a single training run. Rather than re-optimizing per instance, QERNEL conditions on continuous control parameters (e.g., potential depth, dielectric constant), enabling smooth interpolation and amortized evaluation across parameter space. We apply it to interacting electrons in semiconductor moiré heterobilayers with periodic boundary conditions, obtaining accurate energies, correlations and trace phase boundaries. A lightweight expert-routing mechanism directs electron configurations to specialized subnetworks; combined with optimized attention and custom nonlinearities, this yields higher expressivity with several-fold fewer parameters and stable training. Once trained, scanning new parameter points requires only a forward pass, turning dense phase-diagram sweeps from repeated optimizations into rapid evaluations.
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Publication: [1] M. Geier, Kh. Nazaryan, T. Zaklama, and L. Fu, "Self-attention neural network for solving correlated electron problems in solids," Phys. Rev. B, vol. 112, no. 4, p. 045119, Jul. 2025.
[2] Kh. Nazaryan, F. Gaggioli, Y. Teng, and L. Fu, "Artificial Intelligence for Quantum Matter: Finding a Needle in a Haystack," arXiv preprint arXiv:2507.13322, 2025, doi:10.48550/arXiv.2507.13322
[3] I. von Glehn, J. S. Spencer, and D. Pfau, "A Self-Attention Ansatz for Ab-initio Quantum Chemistry," arXiv preprint arXiv:2211.13672, 2022, doi:10.48550/arXiv.2211.13672
Presenters
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Khachatur Nazaryan
- Massachusetts Institute of Technology