mlsanityData to 14 Oct 2026

Gauge Invariant and Anyonic Symmetric Transformer and RNN Quantum States for Quantum Lattice Models

arXiv 2101.07243 ↗First posted 18 Jan 2021cond-mat.str-el cond-mat.dis-nn cs.LGcited by 18

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Abstract (arXiv)

Symmetries such as gauge invariance and anyonic symmetry play a crucial role in quantum many-body physics. We develop a general approach to constructing gauge invariant or anyonic symmetric autoregressive neural network quantum states, including a wide range of architectures such as Transformer and recurrent neural network (RNN), for quantum lattice models. These networks can be efficiently sampled and explicitly obey gauge symmetries or anyonic constraint. We prove that our methods can provide exact representation for the ground and excited states of the 2D and 3D toric codes, and the X-cube fracton model. We variationally optimize our symmetry incorporated autoregressive neural networks for ground states as well as real-time dynamics for a variety of models. We simulate the dynamics and the ground states of the quantum link model of U(1) lattice gauge theory, obtain the phase diagram for the 2D mathbbZ2 gauge theory, determine the phase transition and the central charge of the SU(2)3 anyonic chain, and also compute the ground state energy of the SU(2) invariant Heisenberg spin chain. Our approach provides powerful tools for exploring condensed matter physics, high energy physics and quantum information science.

Key facts. Cited by 18 papers in the map (data through 14 Oct 2026). Builds on 17 of its 80 references that are in the map. First posted on arXiv 18 Jan 2021.

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17 of 80 references.

References · 17

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5 more
  1. 2018Quantum Entanglement in Deep Learning Architecturescited by 50
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Cited by year (2026 to 14 Oct)

Citing papers per year: 2022: 1; 2023: 1; 2024: 5; 2025: 4; 2026: 7.

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  1. 2023Diffusion Models as Stochastic Quantization in Lattice Field Theorycited by 24
  2. 2024QuanTA: Efficient High-Rank Fine-Tuning of LLMs with Quantum-Informed Tensor Adaptationcited by 23
  3. 2025L2M: Mutual Information Scaling Law for Long-Context Language Modelingcited by 9
  4. 2024Recurrent neural network wave functions for Rydberg atom arrays on kagome latticecited by 8
  5. 2024Are queries and keys always relevant? A case study on Transformer wave functionscited by 6
  6. 2024Approximately-symmetric neural networks for quantum spin liquidscited by 5
  7. 2024TENG: Time-Evolving Natural Gradient for Solving PDEs With Deep Neural Nets Toward Machine Precisioncited by 4
  8. 2026Gauge-Equivariant Graph Neural Networks for Lattice Gauge Theoriescited by 3
  9. 2025Is attention all you need to solve the correlated electron problem?cited by 2
  10. 2026Graph Neural Networks in the Wilson Loop Representation of Abelian Lattice Gauge Theoriescited by 2
  11. 2026Parallel Scan Recurrent Neural Quantum States for Scalable Variational Monte Carlocited by 2
  12. 2022Learning quantum symmetries with interactive quantum-classical variational algorithmscited by 1
6 more
  1. 2025Diagonal Symmetrization of Neural Network Solvers for the Many-Electron Schr"odinger Equationcited by 1
  2. 2025Adaptive Neural Quantum States: A Recurrent Neural Network Perspectivecited by 1
  3. 2026Geometry-Induced Long-Range Correlations in Recurrent Neural Network Quantum Statescited by 1
  4. 2026Mechanistic Interpretability and Causal Feature Steering of Neural Quantum States via Sparse Autoencoderscited by 1
  5. 2026TENG-BC: Unified Time-Evolving Natural Gradient for Neural PDE Solvers with General Boundary Conditionscited by 0
  6. 2026Emergent Loop Geometry in Gauge-Equivariant Graph Neural Networkscited by 0