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Seeding neural network quantum states with tensor network states

arXiv 2506.23550 ↗First posted 30 Jun 2025cond-mat.str-el cs.LG cs.NAcited by 0

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Abstract (arXiv)

We find an efficient approach to approximately convert matrix product states (MPSs) into restricted Boltzmann machine wave functions consisting of a multinomial hidden unit through a canonical polyadic (CP) decomposition of the MPSs. This method allows us to generate well-behaved initial neural network quantum states for quantum many-body ground-state calculations in polynomial time of the number of variational parameters and systematically shorten the distance between the initial states and the ground states while increasing the rank of the CP decomposition. We demonstrate the efficiency of our method by taking the transverse-field Ising model as an example and discuss possible applications of our method to more general quantum many-body systems in which the ground-state wave functions possess complex nodal structures.

Key facts. No citing papers in the map yet (data through 14 Oct 2026). Builds on 12 of its 113 references that are in the map. First posted on arXiv 30 Jun 2025.

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References · 12

  1. 2016Entity Embeddings of Categorical Variablescited by 87
  2. 2019Deep autoregressive models for the efficient variational simulation of many-body quantum systemscited by 64
  3. 2018Quantum Entanglement in Deep Learning Architecturescited by 50
  4. 2017Neural-Network Quantum States, String-Bond States, and Chiral Topological Statescited by 31
  5. 2017Equivalence of restricted Boltzmann machines and tensor network statescited by 27
  6. 2021Neural tensor contractions and the expressive power of deep neural quantum statescited by 21
  7. 2022From Tensor Network Quantum States to Tensorial Recurrent Neural Networkscited by 14
  8. 2021Boltzmann machines as two-dimensional tensor networkscited by 7
  9. 2018Legendre Decomposition for Tensorscited by 5
  10. 2025Tensorization is a powerful but underexplored tool for compression and interpretability of neural networkscited by 4
  11. 2021Mixed State Entanglement Classification using Artificial Neural Networkscited by 3
  12. 2020Experimental Analysis of Legendre Decomposition in Machine Learningcited by 1

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