mlsanityData to 7 Oct 2026

Gauge equivariant neural networks for quantum lattice gauge theories

arXiv 2012.05232 ↗First posted 9 Dec 2020cond-mat.str-el cond-mat.dis-nn cs.LGcited by 27

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Abstract (arXiv)

Gauge symmetries play a key role in physics appearing in areas such as quantum field theories of the fundamental particles and emergent degrees of freedom in quantum materials. Motivated by the desire to efficiently simulate many-body quantum systems with exact local gauge invariance, gauge equivariant neural-network quantum states are introduced, which exactly satisfy the local Hilbert space constraints necessary for the description of quantum lattice gauge theory with Zd gauge group on different geometries. Focusing on the special case of Z2 gauge group on a periodically identified square lattice, the equivariant architecture is analytically shown to contain the loop-gas solution as a special case. Gauge equivariant neural-network quantum states are used in combination with variational quantum Monte Carlo to obtain compact descriptions of the ground state wavefunction for the Z2 theory away from the exactly solvable limit, and to demonstrate the confining/deconfining phase transition of the Wilson loop order parameter.

Key facts. Cited by 27 papers in the map (data through 7 Oct 2026). First posted on arXiv 9 Dec 2020.

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Citing papers per year: 2021: 8; 2022: 5; 2023: 4; 2024: 3; 2025: 2; 2026: 5.

27 papers.

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  1. 2021Scalars are universal: Equivariant machine learning, structured like classical physicscited by 127
  2. 2021Geometric Deep Learning and Equivariant Neural Networkscited by 64
  3. 2021Introduction to Normalizing Flows for Lattice Field Theorycited by 35
  4. 2024QuanTA: Efficient High-Rank Fine-Tuning of LLMs with Quantum-Informed Tensor Adaptationcited by 23
  5. 2021Homogeneous vector bundles and G-equivariant convolutional neural networkscited by 21
  6. 2021Gauge Invariant and Anyonic Symmetric Transformer and RNN Quantum States for Quantum Lattice Modelscited by 17
  7. 2022Gauge Equivariant Neural Networks for 2+1D U(1) Gauge Theory Simulations in Hamiltonian Formulationcited by 11
  8. 2022Simulating 2+1D Lattice Quantum Electrodynamics at Finite Density with Neural Flow Wavefunctionscited by 10
  9. 2023Pairing-based graph neural network for simulating quantum materialscited by 9
  10. 2023ANTN: Bridging Autoregressive Neural Networks and Tensor Networks for Quantum Many-Body Simulationcited by 8
  11. 2022Algorithmic Differentiation for Automated Modeling of Machine Learned Force Fieldscited by 7
  12. 2024Approximately-symmetric neural networks for quantum spin liquidscited by 5
15 more
  1. 2021Infinite Neural Network Quantum States: Entanglement and Training Dynamicscited by 4
  2. 2021Machine Learning in Nuclear Physicscited by 4
  3. 2022Why self-attention is Natural for Sequence-to-Sequence Problems? A Perspective from Symmetriescited by 3
  4. 2021Continuous-variable neural-network quantum states and the quantum rotor modelcited by 2
  5. 2023Densely Connected G-invariant Deep Neural Networks with Signed Permutation Representationscited by 2
  6. 2024Current Symmetry Group Equivariant Convolution Frameworks for Representation Learningcited by 2
  7. 2025Learning Chern Numbers of Topological Insulators with Gauge Equivariant Neural Networkscited by 2
  8. 2025SESaMo: Symmetry-Enforcing Stochastic Modulation for Normalizing Flowscited by 2
  9. 2026Gauge-Equivariant Graph Neural Networks for Lattice Gauge Theoriescited by 2
  10. 2023Artificial intelligence for artificial materials: moir'e atomcited by 1
  11. 2026Graph Neural Networks in the Wilson Loop Representation of Abelian Lattice Gauge Theoriescited by 1
  12. 2026Mechanistic Interpretability and Causal Feature Steering of Neural Quantum States via Sparse Autoencoderscited by 1
  13. 2022Learning quantum symmetries with interactive quantum-classical variational algorithmscited by 0
  14. 2026Holographic Quantum Transformer: A Generalist Neuro-Symbolic Architecture for Solving Frustrated Systems via Generative Attentioncited by 0
  15. 2026Learning Discrete Riemannian Metrics for Physical Fields with Cochain-Frame Equivarianccited by 0