# Tensor networks for quantum machine learning

arXiv: https://arxiv.org/abs/2303.11735 · HTML: https://mlsanity.com/paper/2303.11735/

## Key facts

- Cited by 17 papers in the map (data through 14 Oct 2026).
- Builds on 41 of its 125 references that are in the map.
- First posted on arXiv 21 Mar 2023.

## Builds on (most cited first, 30 of 41)

- [Barren plateaus in quantum neural network training landscapes](https://mlsanity.com/paper/1803.11173/) (2018)
- [The power of quantum neural networks](https://mlsanity.com/paper/2011.00027/) (2020)
- [The effect of data encoding on the expressive power of variational quantum machine learning models](https://mlsanity.com/paper/2008.08605/) (2020)
- [Tensorizing Neural Networks](https://mlsanity.com/paper/1509.06569/) (2015)
- [Generalization in quantum machine learning from few training data](https://mlsanity.com/paper/2111.05292/) (2021)
- [Absence of Barren Plateaus in Quantum Convolutional Neural Networks](https://mlsanity.com/paper/2011.02966/) (2020)
- [Unsupervised Generative Modeling Using Matrix Product States](https://mlsanity.com/paper/1709.01662/) (2017)
- [Towards Quantum Machine Learning with Tensor Networks](https://mlsanity.com/paper/1803.11537/) (2018)
- [Tree Tensor Networks for Generative Modeling](https://mlsanity.com/paper/1901.02217/) (2019)
- [Expressive power of tensor-network factorizations for probabilistic modeling, with applications from hidden Markov models to quantum machine learning](https://mlsanity.com/paper/1907.03741/) (2019)
- [Tensor Networks for Dimensionality Reduction and Large-Scale Optimizations. Part 2 Applications and Future Perspectives](https://mlsanity.com/paper/1708.09165/) (2017)
- [Learning Relevant Features of Data with Multi-scale Tensor Networks](https://mlsanity.com/paper/1801.00315/) (2017)
- [An end-to-end trainable hybrid classical-quantum classifier](https://mlsanity.com/paper/2102.02416/) (2021)
- [Quantum Entanglement in Deep Learning Architectures](https://mlsanity.com/paper/1803.09780/) (2018)
- [Variational Quantum Reinforcement Learning via Evolutionary Optimization](https://mlsanity.com/paper/2109.00540/) (2021)
- [Machine Learning by Unitary Tensor Network of Hierarchical Tree Structure](https://mlsanity.com/paper/1710.04833/) (2017)
- [Supervised Learning with Quantum-Inspired Tensor Networks](https://mlsanity.com/paper/1605.05775/) (2016)
- [From probabilistic graphical models to generalized tensor networks for supervised learning](https://mlsanity.com/paper/1806.05964/) (2018)
- [Quantum-inspired Machine Learning on high-energy physics data](https://mlsanity.com/paper/2004.13747/) (2020)
- [Analyzing the barren plateau phenomenon in training quantum neural networks with the ZX-calculus](https://mlsanity.com/paper/2102.01828/) (2021)
- [Equivalence of restricted Boltzmann machines and tensor network states](https://mlsanity.com/paper/1701.04831/) (2017)
- [Anomaly Detection with Tensor Networks](https://mlsanity.com/paper/2006.02516/) (2020)
- [Theoretical Error Performance Analysis for Variational Quantum Circuit Based Functional Regression](https://mlsanity.com/paper/2206.04804/) (2022)
- [Generative Tensor Network Classification Model for Supervised Machine Learning](https://mlsanity.com/paper/1903.10742/) (2019)
- [Dynamic Portfolio Optimization with Real Datasets Using Quantum Processors and Quantum-Inspired Tensor Networks](https://mlsanity.com/paper/2007.00017/) (2020)
- [Entanglement-guided architectures of machine learning by quantum tensor network](https://mlsanity.com/paper/1803.09111/) (2018)
- [Matrix Product State Based Quantum Classifier](https://mlsanity.com/paper/1905.01426/) (2019)
- [A Multi-Scale Tensor Network Architecture for Classification and Regression](https://mlsanity.com/paper/2001.08286/) (2020)
- [From Tensor Network Quantum States to Tensorial Recurrent Neural Networks](https://mlsanity.com/paper/2206.12363/) (2022)
- [Machine Learning Phase Transitions with a Quantum Processor](https://mlsanity.com/paper/1906.10155/) (2019)

## Built on by (most cited first, 17 of 17)

- [Quantum-Inspired Machine Learning: a Survey](https://mlsanity.com/paper/2308.11269/) (2023)
- [Federated Hierarchical Tensor Networks: a Collaborative Learning Quantum AI-Driven Framework for Healthcare](https://mlsanity.com/paper/2405.07735/) (2024)
- [TensorRL-QAS: Reinforcement learning with tensor networks for improved quantum architecture search](https://mlsanity.com/paper/2505.09371/) (2025)
- [tn4ml: Tensor Network Training and Customization for Machine Learning](https://mlsanity.com/paper/2502.13090/) (2025)
- [Tensorization is a powerful but underexplored tool for compression and interpretability of neural networks](https://mlsanity.com/paper/2505.20132/) (2025)
- [Application of Tensorized Neural Networks for Cloud Classification](https://mlsanity.com/paper/2405.10946/) (2024)
- [Quantum Methods for Managing Ambiguity in Natural Language Processing](https://mlsanity.com/paper/2504.00040/) (2025)
- [Trainable Quantum Neural Network for Multiclass Image Classification with the Power of Pre-trained Tree Tensor Networks](https://mlsanity.com/paper/2504.14995/) (2025)
- [Explaining Anomalies with Tensor Networks](https://mlsanity.com/paper/2505.03911/) (2025)
- [Dimension reduction with structure-aware quantum circuits for hybrid machine learning](https://mlsanity.com/paper/2508.00048/) (2025)
- [Hybrid quantum tensor networks for aeroelastic applications](https://mlsanity.com/paper/2508.05169/) (2025)
- [Tensor Computing Interface: An Application-Oriented, Lightweight Interface for Portable High-Performance Tensor Network Applications](https://mlsanity.com/paper/2512.23917/) (2025)
- [Embedded Quantum Machine Learning in Embedded Systems: Feasibility, Hybrid Architectures, and Quantum Co-Processors](https://mlsanity.com/paper/2603.12540/) (2026)
- [Quantum-inspired tensor networks in machine learning models](https://mlsanity.com/paper/2604.14287/) (2026)
- [Mitigating Measurement-Induced Training Instability in Hybrid Quantum Neural Networks for Protein Classification](https://mlsanity.com/paper/2606.22551/) (2026)
- [Quantum Tensor Network Learning with DMRG](https://mlsanity.com/paper/2608.18901/) (2026)
- [Gaussian Universality and Its Breakdown in Tensor-Network Machine Learning](https://mlsanity.com/paper/2610.06080/) (2026)

## Abstract (arXiv)

Once developed for quantum theory, tensor networks have been established as a successful machine learning paradigm. Now, they have been ported back to the quantum realm in the emerging field of quantum machine learning to assess problems that classical computers are unable to solve efficiently. Their nature at the interface between physics and machine learning makes tensor networks easily deployable on quantum computers. In this review article, we shed light on one of the major architectures considered to be predestined for variational quantum machine learning. In particular, we discuss how layouts like MPS, PEPS, TTNs and MERA can be mapped to a quantum computer, how they can be used for machine learning and data encoding and which implementation techniques improve their performance.