mlsanityData to 13 Oct 2026

Gauge Equivariant Neural Networks for 2+1D U(1) Gauge Theory Simulations in Hamiltonian Formulation

arXiv 2211.03198 ↗First posted 6 Nov 2022hep-lat cond-mat.dis-nn cond-mat.str-elcited by 11

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Abstract (arXiv)

Gauge Theory plays a crucial role in many areas in science, including high energy physics, condensed matter physics and quantum information science. In quantum simulations of lattice gauge theory, an important step is to construct a wave function that obeys gauge symmetry. In this paper, we have developed gauge equivariant neural network wave function techniques for simulating continuous-variable quantum lattice gauge theories in the Hamiltonian formulation. We have applied the gauge equivariant neural network approach to find the ground state of 2+1-dimensional lattice gauge theory with U(1) gauge group using variational Monte Carlo. We have benchmarked our approach against the state-of-the-art complex Gaussian wave functions, demonstrating improved performance in the strong coupling regime and comparable results in the weak coupling regime.

Key facts. Cited by 11 papers in the map (data through 13 Oct 2026). Builds on 19 of its 47 references that are in the map. First posted on arXiv 6 Nov 2022.

Builds on

19 of 47 references.

References · 19

  1. 2016Group Equivariant Convolutional Networkscited by 1,157
  2. 2018Tensor field networks: Rotation- and translation-equivariant neural networks for 3D point cloudscited by 739
  3. 20183D Steerable CNNs: Learning Rotationally Equivariant Features in Volumetric Datacited by 350
  4. 2019Gauge Equivariant Convolutional Networks and the Icosahedral CNNcited by 263
  5. 2019Cormorant: Covariant Molecular Neural Networkscited by 263
  6. 2019Ab-Initio Solution of the Many-Electron Schr"odinger Equation with Deep Neural Networkscited by 197
  7. 2018Clebsch-Gordan Nets: a Fully Fourier Space Spherical Convolutional Neural Networkcited by 170
  8. 2019Deep neural network solution of the electronic Schr"odinger equationcited by 125
  9. 2020Equivariant flow-based sampling for lattice gauge theorycited by 102
  10. 2020Gauge Equivariant Mesh CNNs: Anisotropic convolutions on geometric graphscited by 90
  11. 2020Sampling using SU(N) gauge equivariant flowscited by 83
  12. 2018Quantum Entanglement in Deep Learning Architecturescited by 50
7 more
  1. 2020Lattice gauge equivariant convolutional neural networkscited by 45
  2. 2017Neural-Network Quantum States, String-Bond States, and Chiral Topological Statescited by 31
  3. 2022Gauge-equivariant flow models for sampling in lattice field theories with pseudofermionscited by 30
  4. 2020Gauge equivariant neural networks for quantum lattice gauge theoriescited by 27
  5. 2021Neural tensor contractions and the expressive power of deep neural quantum statescited by 21
  6. 2020Phases of two-dimensional spinless lattice fermions with first-quantized deep neural-network quantum statescited by 15
  7. 2021Spacetime Neural Network for High Dimensional Quantum Dynamicscited by 9

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Cited by year (2026 to 13 Oct)

Citing papers per year: 2022: 1; 2023: 4; 2024: 2; 2025: 3; 2026: 1.

11 papers.

  1. 2022Simulating 2+1D Lattice Quantum Electrodynamics at Finite Density with Neural Flow Wavefunctionscited by 10
  2. 2023Pairing-based graph neural network for simulating quantum materialscited by 9
  3. 2023ANTN: Bridging Autoregressive Neural Networks and Tensor Networks for Quantum Many-Body Simulationcited by 8
  4. 2024Approximately-symmetric neural networks for quantum spin liquidscited by 5
  5. 2023Q-Flow: Generative Modeling for Differential Equations of Open Quantum Dynamics with Normalizing Flowscited by 4
  6. 2025Gauge-covariant stochastic neural fields: Stability and finite-width effectscited by 3
  7. 2024Current Symmetry Group Equivariant Convolution Frameworks for Representation Learningcited by 2
  8. 2023Artificial intelligence for artificial materials: moir'e atomcited by 1
  9. 2025Reduced Density Matrices Through Machine Learningcited by 1
  10. 2025Gauge-Equivariant Graph Networks via Self-Interference Cancellationcited by 1
  11. 2026Representability-Aware Neural Networks for Reduced Density Matrices: Application to Fractional Chern Insulatorscited by 0