mlsanityData to 14 Oct 2026

From Tensor Network Quantum States to Tensorial Recurrent Neural Networks

arXiv 2206.12363 ↗First posted 24 Jun 2022quant-ph cond-mat.str-el cs.LGcited by 14

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Abstract (arXiv)

We show that any matrix product state (MPS) can be exactly represented by a recurrent neural network (RNN) with a linear memory update. We generalize this RNN architecture to 2D lattices using a multilinear memory update. It supports perfect sampling and wave function evaluation in polynomial time, and can represent an area law of entanglement entropy. Numerical evidence shows that it can encode the wave function using a bond dimension lower by orders of magnitude when compared to MPS, with an accuracy that can be systematically improved by increasing the bond dimension.

Key facts. Cited by 14 papers in the map (data through 14 Oct 2026). Builds on 1 of its 20 references that are in the map. First posted on arXiv 24 Jun 2022.

Builds on

1 of 20 references.

References · 1

  1. 2021Variational Neural Annealingcited by 47

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Cited by year (2026 to 14 Oct)

Citing papers per year: 2022: 1; 2023: 5; 2024: 3; 2025: 3; 2026: 2.

14 papers.

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  1. 2023Tensor Networks Meet Neural Networks: A Survey and Future Perspectivescited by 32
  2. 2022Grokking phase transitions in learning local rules with gradient descentcited by 28
  3. 2023Tensor networks for quantum machine learningcited by 17
  4. 2023Tensor networks for interpretable and efficient quantum-inspired machine learningcited by 17
  5. 2025L2M: Mutual Information Scaling Law for Long-Context Language Modelingcited by 9
  6. 2023ANTN: Bridging Autoregressive Neural Networks and Tensor Networks for Quantum Many-Body Simulationcited by 8
  7. 2024Certifying almost all quantum states with few single-qubit measurementscited by 7
  8. 2023Investigating Topological Order using Recurrent Neural Networkscited by 6
  9. 2024When can classical neural networks represent quantum states?cited by 6
  10. 2026Parallel Scan Recurrent Neural Quantum States for Scalable Variational Monte Carlocited by 2
  11. 2025Adaptive Neural Quantum States: A Recurrent Neural Network Perspectivecited by 1
  12. 2024Simulating Non-Markovian Open Quantum Dynamics with Neural Quantum Statescited by 0
2 more
  1. 2025Seeding neural network quantum states with tensor network statescited by 0
  2. 2026Gaussian Universality and Its Breakdown in Tensor-Network Machine Learningcited by 0