QERNEL: a Scalable Large Electron Model
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Abstract (arXiv)
We introduce QERNEL, a foundational neural wavefunction that variationally solves families of parameterized many-electron Hamiltonians and captures their ground states throughout parameter space within a single model. QERNEL combines FiLM-based parameter conditioning with scale-efficient architectural elements -- mixture of experts and grouped-query attention, substantially improving expressivity at low computational cost. We apply QERNEL to interacting electrons in semiconductor moir'e heterobilayers, training a single weight-shared model for systems of up to 150 electrons. By solving the many-electron Schr"odinger equation conditioned on moir'e potential depth, QERNEL captures both quantum liquid and crystal states and discovers the sharp phase transition between them, marked by abrupt changes in interaction energy and charge density. Our work establishes a foundation model for moir'e quantum materials and a scalable architecture toward a Large Electron Model for solids.
Key facts. Cited by 3 papers in the map (data through 14 Oct 2026). Builds on 10 of its 26 references that are in the map. First posted on arXiv 28 Apr 2026.
Builds on
10 of 26 references.
References · 10
- 2017Outrageously Large Neural Networks: The Sparsely-Gated Mixture-of-Experts Layercited by 3,509
- 2017FiLM: Visual Reasoning with a General Conditioning Layercited by 2,333
- 2023GQA: Training Generalized Multi-Query Transformer Models from Multi-Head Checkpointscited by 1,346
- 2019Ab-Initio Solution of the Many-Electron Schr"odinger Equation with Deep Neural Networkscited by 200
- 2022A Self-Attention Ansatz for Ab-initio Quantum Chemistrycited by 49
- 2022Discovering Quantum Phase Transitions with Fermionic Neural Networkscited by 26
- 2025An ab initio foundation model of wavefunctions that accurately describes chemical bond breakingcited by 14
- 2023Pairing-based graph neural network for simulating quantum materialscited by 10
- 2023Forward Laplacian: A New Computational Framework for Neural Network-based Variational Monte Carlocited by 6
- 2026Large Electron Model: A Universal Ground State Predictorcited by 4
Built on by
Citing papers per year: 2026: 3.
3 papers.
- 2026Low-variance estimators overcome the phase-gradient bottleneck in complex-valued neural quantum statescited by 1
- 2026Hamilton-Zero: A Neural Tensor-Network Foundation Model for Ground States of Arbitrary Quadratic Qubit Hamiltonianscited by 1
- 2026Representability-Aware Neural Networks for Reduced Density Matrices: Application to Fractional Chern Insulatorscited by 0
- 2026Hamilton-Zero: A Neural Tensor-Network Foundation Model for Ground States of Arbitrary Quadratic Qubit Hamiltonians12 Aug 2026
- 2026Low-variance estimators overcome the phase-gradient bottleneck in complex-valued neural quantum states11 Jun 2026
- 2026Representability-Aware Neural Networks for Reduced Density Matrices: Application to Fractional Chern Insulators19 May 2026
Similar, not cited
Close in wording, no citation either way
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- 2026Foundation Neural-Network Quantum States for Molecular Potential Energy Surfaces in Second Quantization
- 2026QuPAINT: Physics-Aware Instruction Tuning Approach to Quantum Material Discovery
- 2026Agentic multi-fidelity learning of quasiparticle and excitonic properties
- 2025Large Language Model Scaling Laws for Neural Quantum States in Quantum Chemistry
- 2025TensorRL-QAS: Reinforcement learning with tensor networks for improved quantum architecture search
- 2023A Score-Based Model for Learning Neural Wavefunctions
- 2026One More Time: Revisiting Neural Quantum States from a Reinforcement Learning Perspective