# TensorNetwork: A Library for Physics and Machine Learning

arXiv: https://arxiv.org/abs/1905.01330 · HTML: https://mlsanity.com/paper/1905.01330/

## Key facts

- Cited by 21 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 3 May 2019.

## Built on by (most cited first, 21 of 21)

- [Tensor Networks Meet Neural Networks: A Survey and Future Perspectives](https://mlsanity.com/paper/2302.09019/) (2023)
- [TedNet: A Pytorch Toolkit for Tensor Decomposition Networks](https://mlsanity.com/paper/2104.05018/) (2021)
- [Quantum-inspired event reconstruction with Tensor Networks: Matrix Product States](https://mlsanity.com/paper/2106.08334/) (2021)
- [tntorch: Tensor Network Learning with PyTorch](https://mlsanity.com/paper/2206.11128/) (2022)
- [Verifying Fairness in Quantum Machine Learning](https://mlsanity.com/paper/2207.11173/) (2022)
- [Demonstration of Robust and Efficient Quantum Property Learning with Shallow Shadows](https://mlsanity.com/paper/2402.17911/) (2024)
- [Federated Hierarchical Tensor Networks: a Collaborative Learning Quantum AI-Driven Framework for Healthcare](https://mlsanity.com/paper/2405.07735/) (2024)
- [tn4ml: Tensor Network Training and Customization for Machine Learning](https://mlsanity.com/paper/2502.13090/) (2025)
- [Entangled q-Convolutional Neural Nets](https://mlsanity.com/paper/2103.11785/) (2021)
- [Identification of quantum entanglement with Siamese convolutional neural networks and semi-supervised learning](https://mlsanity.com/paper/2210.07410/) (2022)
- [Quantum-inspired tensor network for Earth science](https://mlsanity.com/paper/2301.07528/) (2023)
- [The cross-sectional stock return predictions via quantum neural network and tensor network](https://mlsanity.com/paper/2304.12501/) (2023)
- [Probabilistic Regular Tree Priors for Scientific Symbolic Reasoning](https://mlsanity.com/paper/2306.08506/) (2023)
- [No-Free-Lunch Theories for Tensor-Network Machine Learning Models](https://mlsanity.com/paper/2412.05674/) (2024)
- [Derandomized shallow shadows: Efficient Pauli learning with bounded-depth circuits](https://mlsanity.com/paper/2412.18973/) (2024)
- [Tensor Network for Supervised Learning at Finite Temperature](https://mlsanity.com/paper/2104.05439/) (2021)
- [Stack operation of tensor networks](https://mlsanity.com/paper/2203.16338/) (2022)
- [Symbolically integrating tensor networks over various random tensors by the second version of Python RTNI](https://mlsanity.com/paper/2309.01167/) (2023)
- [A Tensor Network Implementation of Multi Agent Reinforcement Learning](https://mlsanity.com/paper/2401.03896/) (2024)
- [Application of Quantum Tensor Networks for Protein Classification](https://mlsanity.com/paper/2403.06890/) (2024)
- [Quantum-inspired tensor networks in machine learning models](https://mlsanity.com/paper/2604.14287/) (2026)

## Abstract (arXiv)

TensorNetwork is an open source library for implementing tensor network algorithms. Tensor networks are sparse data structures originally designed for simulating quantum many-body physics, but are currently also applied in a number of other research areas, including machine learning. We demonstrate the use of the API with applications both physics and machine learning, with details appearing in companion papers.