mlsanityData to 7 Oct 2026

Investigating Topological Order using Recurrent Neural Networks

arXiv 2303.11207 ↗First posted 20 Mar 2023cond-mat.str-el cond-mat.dis-nn cs.LGcited by 6

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Abstract (arXiv)

Recurrent neural networks (RNNs), originally developed for natural language processing, hold great promise for accurately describing strongly correlated quantum many-body systems. Here, we employ 2D RNNs to investigate two prototypical quantum many-body Hamiltonians exhibiting topological order. Specifically, we demonstrate that RNN wave functions can effectively capture the topological order of the toric code and a Bose-Hubbard spin liquid on the kagome lattice by estimating their topological entanglement entropies. We also find that RNNs favor coherent superpositions of minimally-entangled states over minimally-entangled states themselves. Overall, our findings demonstrate that RNN wave functions constitute a powerful tool to study phases of matter beyond Landau's symmetry-breaking paradigm.

Key facts. Cited by 6 papers in the map (data through 7 Oct 2026). Builds on 18 of its 99 references that are in the map. First posted on arXiv 20 Mar 2023.

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18 of 99 references.

References · 18

  1. 2014Adam: A Method for Stochastic Optimizationcited by 36,960
  2. 2019Monte Carlo Gradient Estimation in Machine Learningcited by 281
  3. 2015A Critical Review of Recurrent Neural Networks for Sequence Learningcited by 223
  4. 2019Ab-Initio Solution of the Many-Electron Schr"odinger Equation with Deep Neural Networkscited by 195
  5. 2019Deep neural network solution of the electronic Schr"odinger equationcited by 124
  6. 2021Variational Neural Annealingcited by 45
  7. 2016Minimal Gated Unit for Recurrent Neural Networkscited by 40
  8. 2017Neural-Network Quantum States, String-Bond States, and Chiral Topological Statescited by 31
  9. 2017Equivalence of restricted Boltzmann machines and tensor network statescited by 26
  10. 2020Locally Masked Convolution for Autoregressive Modelscited by 22
  11. 2021Neural Error Mitigation of Near-Term Quantum Simulationscited by 15
  12. 2019Mutual Information Scaling and Expressive Power of Sequence Modelscited by 14
6 more
  1. 2021Machine learning discovery of new phases in programmable quantum simulator snapshotscited by 13
  2. 2022From Tensor Network Quantum States to Tensorial Recurrent Neural Networkscited by 13
  3. 2020Dynamical large deviations of two-dimensional kinetically constrained models using a neural-network state ansatzcited by 6
  4. 2022Supplementing Recurrent Neural Networks with Annealing to Solve Combinatorial Optimization Problemscited by 6
  5. 2022Supplementing Recurrent Neural Network Wave Functions with Symmetry and Annealing to Improve Accuracycited by 6
  6. 2019TensorNetwork on TensorFlow: A Spin Chain Application Using Tree Tensor Networkscited by 3

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Cited by year

Citing papers per year: 2024: 2; 2025: 4.

6 papers.

  1. 2024Recurrent neural network wave functions for Rydberg atom arrays on kagome latticecited by 8
  2. 2024When can classical neural networks represent quantum states?cited by 6
  3. 2025Tensorization of neural networks for improved privacy and interpretabilitycited by 3
  4. 2025Lattice Protein Folding with Variational Annealingcited by 3
  5. 2025Adaptive Neural Quantum States: A Recurrent Neural Network Perspectivecited by 1
  6. 2025Large-scale portfolio optimization with variational neural annealingcited by 0