# Quantum Entanglement in Deep Learning Architectures

arXiv: https://arxiv.org/abs/1803.09780 · HTML: https://mlsanity.com/paper/1803.09780/

## Key facts

- Cited by 50 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 26 Mar 2018.

## Built on by (most cited first, 30 of 50)

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- [Generative Learning of Continuous Data by Tensor Networks](https://mlsanity.com/paper/2310.20498/) (2023)
- [ANTN: Bridging Autoregressive Neural Networks and Tensor Networks for Quantum Many-Body Simulation](https://mlsanity.com/paper/2304.01996/) (2023)
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- [Classical versus Quantum: comparing Tensor Network-based Quantum Circuits on LHC data](https://mlsanity.com/paper/2202.10471/) (2022)
- [Lattice Convolutional Networks for Learning Ground States of Quantum Many-Body Systems](https://mlsanity.com/paper/2206.07370/) (2022)
- [Compositionality Unlocks Deep Interpretable Models](https://mlsanity.com/paper/2504.02667/) (2025)
- [Entangled q-Convolutional Neural Nets](https://mlsanity.com/paper/2103.11785/) (2021)
- [Scaling of neural-network quantum states for time evolution](https://mlsanity.com/paper/2104.10696/) (2021)
- [Tensor network to learn the wavefunction of data](https://mlsanity.com/paper/2111.08014/) (2021)
- [Quantum Split Neural Network Learning using Cross-Channel Pooling](https://mlsanity.com/paper/2211.06524/) (2022)
- [What Makes Data Suitable for a Locally Connected Neural Network? A Necessary and Sufficient Condition Based on Quantum Entanglement](https://mlsanity.com/paper/2303.11249/) (2023)
- [Review of Ansatz Designing Techniques for Variational Quantum Algorithms](https://mlsanity.com/paper/2212.04913/) (2022)
- [Provable learning of quantum states with graphical models](https://mlsanity.com/paper/2309.09235/) (2023)
- [Blind Estimation of a Doubly Selective OFDM Channel: A Deep Learning Algorithm and Theory](https://mlsanity.com/paper/2206.07483/) (2022)
- [Identification of quantum entanglement with Siamese convolutional neural networks and semi-supervised learning](https://mlsanity.com/paper/2210.07410/) (2022)
- [Data-driven criteria for quantum correlations](https://mlsanity.com/paper/2307.11091/) (2023)

## Abstract (arXiv)

Modern deep learning has enabled unprecedented achievements in various domains. Nonetheless, employment of machine learning for wave function representations is focused on more traditional architectures such as restricted Boltzmann machines (RBMs) and fully-connected neural networks. In this letter, we establish that contemporary deep learning architectures, in the form of deep convolutional and recurrent networks, can efficiently represent highly entangled quantum systems. By constructing Tensor Network equivalents of these architectures, we identify an inherent reuse of information in the network operation as a key trait which distinguishes them from standard Tensor Network based representations, and which enhances their entanglement capacity. Our results show that such architectures can support volume-law entanglement scaling, polynomially more efficiently than presently employed RBMs. Thus, beyond a quantification of the entanglement capacity of leading deep learning architectures, our analysis formally motivates a shift of trending neural-network based wave function representations closer to the state-of-the-art in machine learning.