# Seeding neural network quantum states with tensor network states

arXiv: https://arxiv.org/abs/2506.23550 · HTML: https://mlsanity.com/paper/2506.23550/

## 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.

## Builds on (most cited first, 12 of 12)

- [Entity Embeddings of Categorical Variables](https://mlsanity.com/paper/1604.06737/) (2016)
- [Deep autoregressive models for the efficient variational simulation of many-body quantum systems](https://mlsanity.com/paper/1902.04057/) (2019)
- [Quantum Entanglement in Deep Learning Architectures](https://mlsanity.com/paper/1803.09780/) (2018)
- [Neural-Network Quantum States, String-Bond States, and Chiral Topological States](https://mlsanity.com/paper/1710.04045/) (2017)
- [Equivalence of restricted Boltzmann machines and tensor network states](https://mlsanity.com/paper/1701.04831/) (2017)
- [Neural tensor contractions and the expressive power of deep neural quantum states](https://mlsanity.com/paper/2103.10293/) (2021)
- [From Tensor Network Quantum States to Tensorial Recurrent Neural Networks](https://mlsanity.com/paper/2206.12363/) (2022)
- [Boltzmann machines as two-dimensional tensor networks](https://mlsanity.com/paper/2105.04130/) (2021)
- [Legendre Decomposition for Tensors](https://mlsanity.com/paper/1802.04502/) (2018)
- [Tensorization is a powerful but underexplored tool for compression and interpretability of neural networks](https://mlsanity.com/paper/2505.20132/) (2025)
- [Mixed State Entanglement Classification using Artificial Neural Networks](https://mlsanity.com/paper/2102.06053/) (2021)
- [Experimental Analysis of Legendre Decomposition in Machine Learning](https://mlsanity.com/paper/2008.05095/) (2020)

## 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.