mlsanityData to 7 Oct 2026

Efficient and Equivariant Graph Networks for Predicting Quantum Hamiltonian

arXiv 2306.04922 ↗First posted 8 Jun 2023cs.LG physics.comp-phcited by 38

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Abstract (arXiv)

We consider the prediction of the Hamiltonian matrix, which finds use in quantum chemistry and condensed matter physics. Efficiency and equivariance are two important, but conflicting factors. In this work, we propose a SE(3)-equivariant network, named QHNet, that achieves efficiency and equivariance. Our key advance lies at the innovative design of QHNet architecture, which not only obeys the underlying symmetries, but also enables the reduction of number of tensor products by 92%. In addition, QHNet prevents the exponential growth of channel dimension when more atom types are involved. We perform experiments on MD17 datasets, including four molecular systems. Experimental results show that our QHNet can achieve comparable performance to the state of the art methods at a significantly faster speed. Besides, our QHNet consumes 50% less memory due to its streamlined architecture. Our code is publicly available as part of the AIRS library (urlhttps://github.com/divelab/AIRS).

Key facts. Cited by 38 papers in the map (data through 7 Oct 2026). Builds on 33 of its 51 references that are in the map. First posted on arXiv 8 Jun 2023.

Builds on

33 of 51 references.

References · 33

  1. 2019PyTorch: An Imperative Style, High-Performance Deep Learning Librarycited by 20,160
  2. 2017Neural Message Passing for Quantum Chemistrycited by 3,460
  3. 2019Fast Graph Representation Learning with PyTorch Geometriccited by 2,414
  4. 2021E(n) Equivariant Graph Neural Networkscited by 951
  5. 2018Tensor field networks: Rotation- and translation-equivariant neural networks for 3D point cloudscited by 735
  6. 2021E(3)-Equivariant Graph Neural Networks for Data-Efficient and Accurate Interatomic Potentialscited by 701
  7. 2020SE(3)-Transformers: 3D Roto-Translation Equivariant Attention Networkscited by 602
  8. 2017SchNet: A continuous-filter convolutional neural network for modeling quantum interactionscited by 569
  9. 2020Directional Message Passing for Molecular Graphscited by 556
  10. 2021Equivariant message passing for the prediction of tensorial properties and molecular spectracited by 438
  11. 2021GemNet: Universal Directional Graph Neural Networks for Moleculescited by 342
  12. 2022DiffDock: Diffusion Steps, Twists, and Turns for Molecular Dockingcited by 307
21 more
  1. 2019Cormorant: Covariant Molecular Neural Networkscited by 262
  2. 2020Fast and Uncertainty-Aware Directional Message Passing for Non-Equilibrium Moleculescited by 254
  3. 2021Geometric and Physical Quantities Improve E(3) Equivariant Message Passingcited by 225
  4. 2021Spherical Message Passing for 3D Graph Networkscited by 166
  5. 2021Learning Gradient Fields for Molecular Conformation Generationcited by 162
  6. 2022EquiBind: Geometric Deep Learning for Drug Binding Structure Predictioncited by 143
  7. 2021GeoMol: Torsional Geometric Generation of Molecular 3D Conformer Ensemblescited by 106
  8. 2022Generating 3D Molecules for Target Protein Bindingcited by 104
  9. 2019Molecular geometry prediction using a deep generative graph neural networkcited by 91
  10. 2021Learning Neural Generative Dynamics for Molecular Conformation Generationcited by 87
  11. 2022Periodic Graph Transformers for Crystal Material Property Predictioncited by 87
  12. 2021Independent SE(3)-Equivariant Models for End-to-End Rigid Protein Dockingcited by 81
  13. 2019Unifying machine learning and quantum chemistry -- a deep neural network for molecular wavefunctionscited by 73
  14. 2019A Generative Model for Molecular Distance Geometrycited by 73
  15. 2022ComENet: Towards Complete and Efficient Message Passing for 3D Molecular Graphscited by 69
  16. 2021SE(3)-equivariant prediction of molecular wavefunctions and electronic densitiescited by 67
  17. 2020OrbNet: Deep Learning for Quantum Chemistry Using Symmetry-Adapted Atomic-Orbital Featurescited by 63
  18. 2021An End-to-End Framework for Molecular Conformation Generation via Bilevel Programmingcited by 59
  19. 2020Advanced Graph and Sequence Neural Networks for Molecular Property Prediction and Drug Discoverycited by 46
  20. 2022E3Bind: An End-to-End Equivariant Network for Protein-Ligand Dockingcited by 35
  21. 2021Fast Quantum Property Prediction via Deeper 2D and 3D Graph Networkscited by 10

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2023: 2; 2024: 12; 2025: 12; 2026: 12.

38 papers.

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  1. 2024Enabling Efficient Equivariant Operations in the Fourier Basis via Gaunt Tensor Productscited by 35
  2. 2023QH9: A Quantum Hamiltonian Prediction Benchmark for QM9 Moleculescited by 26
  3. 2024Equivariance via Minimal Frame Averaging for More Symmetries and Efficiencycited by 18
  4. 2025Enhancing the Scalability and Applicability of Kohn-Sham Hamiltonians for Molecular Systemscited by 13
  5. 2024Self-Consistency Training for Density-Functional-Theory Hamiltonian Predictioncited by 12
  6. 2025HIP: Hessian Interatomic Potentials without derivativescited by 11
  7. 2025Autonomous Agents for Scientific Discovery: Orchestrating Scientists, Language, Code, and Physicscited by 11
  8. 2025Efficient and Scalable Density Functional Theory Hamiltonian Prediction through Adaptive Sparsitycited by 10
  9. 2025High-order Equivariant Flow Matching for Density Functional Theory Hamiltonian Predictioncited by 10
  10. 2024A Space Group Symmetry Informed Network for O(3) Equivariant Crystal Tensor Predictioncited by 7
  11. 2024Learning local equivariant representations for quantum operatorscited by 7
  12. 2025Learning from the electronic structure of molecules across the periodic tablecited by 7
26 more
  1. 2024Infusing Self-Consistency into Density Functional Theory Hamiltonian Prediction via Deep Equilibrium Modelscited by 6
  2. 2024Equivariant Graph Network Approximations of High-Degree Polynomials for Force Field Predictioncited by 6
  3. 2025Efficient Prediction of SO(3)-Equivariant Hamiltonian Matrices via SO(2) Local Framescited by 5
  4. 2024Reducing the Cost of Quantum Chemical Data By Backpropagating Through Density Functional Theorycited by 4
  5. 2024TraceGrad: a Framework Learning Expressive SO(3)-equivariant Non-linear Representations for Electronic-Structure Hamiltonian Predictioncited by 4
  6. 2026Transferable SCF-Acceleration through Solver-Aligned Initialization Learningcited by 3
  7. 2023Electronic excited states from physically-constrained machine learningcited by 2
  8. 2024Towards Harmonization of SO(3)-Equivariance and Expressiveness: a Hybrid Deep Learning Framework for Electronic-Structure Hamiltonian Predictioncited by 2
  9. 2024nabla2DFT: A Universal Quantum Chemistry Dataset of Drug-Like Molecules and a Benchmark for Neural Network Potentialscited by 2
  10. 2025Advancing Universal Deep Learning for Electronic-Structure Hamiltonian Prediction of Materialscited by 2
  11. 2025Towards A Transferable Acceleration Method for Density Functional Theorycited by 2
  12. 2026Derivative Informed Learning of Exchange-Correlation Functionalscited by 2
  13. 2024NeuralSCF: Neural network self-consistent fields for density functional theorycited by 1
  14. 2025Self-Refining Training for Amortized Density Functional Theorycited by 1
  15. 2025Tensor Decomposition Networks for Fast Machine Learning Interatomic Potential Computationscited by 1
  16. 2026M=oLe-Lambda: Learning the Coupled-Cluster Response State for Energies, Gradients, and Propertiescited by 1
  17. 2025Distributed Equivariant Graph Neural Networks for Large-Scale Electronic Structure Predictioncited by 0
  18. 2026Coupled Cluster con M=oLe: Molecular Orbital Learning for Neural Wavefunctionscited by 0
  19. 2026Orbital Transformers for Predicting Wavefunctions in Time-Dependent Density Functional Theorycited by 0
  20. 2026A Fixed-Point Neural Operator for Size- and Functional-Transferable Hamiltonian Predictioncited by 0
  21. 2026MALOQ: Massively Accelerated Learning of Operators for Quantum Transportcited by 0
  22. 2026A Density-Matrix Framework for Electronic-Structure Analysis of Electrolytes for Lithium Batteriescited by 0
  23. 2026Coupled-cluster molecular properties across the main group that extrapolate beyond training sizecited by 0
  24. 2026Continuous-Time Quantum Walks based Graph Neural Networkcited by 0
  25. 2026Equivariant Cellular Sheaves for Molecular Electronic Structure: Bridging Sheaf Cohomology and E(3)-Equivariant Hamiltonian Learningcited by 0
  26. 2026Physics-Aligned Electronic Ground-State Learning Improves Generalizationcited by 0