# Towards Quantum Machine Learning with Tensor Networks

arXiv: https://arxiv.org/abs/1803.11537 · HTML: https://mlsanity.com/paper/1803.11537/

## Key facts

- Cited by 76 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 30 Mar 2018.

## Built on by (most cited first, 30 of 76)

- [Variational Quantum Reinforcement Learning via Evolutionary Optimization](https://mlsanity.com/paper/2109.00540/) (2021)
- [Recent Advances for Quantum Neural Networks in Generative Learning](https://mlsanity.com/paper/2206.03066/) (2022)
- [Subtractive Mixture Models via Squaring: Representation and Learning](https://mlsanity.com/paper/2310.00724/) (2023)
- [Tensor Networks Meet Neural Networks: A Survey and Future Perspectives](https://mlsanity.com/paper/2302.09019/) (2023)
- [QTN-VQC: An End-to-End Learning framework for Quantum Neural Networks](https://mlsanity.com/paper/2110.03861/) (2021)
- [Theoretical Error Performance Analysis for Variational Quantum Circuit Based Functional Regression](https://mlsanity.com/paper/2206.04804/) (2022)
- [Certified Robustness of Quantum Classifiers against Adversarial Examples through Quantum Noise](https://mlsanity.com/paper/2211.00887/) (2022)
- [Tensor networks for quantum machine learning](https://mlsanity.com/paper/2303.11735/) (2023)
- [Tensor networks for interpretable and efficient quantum-inspired machine learning](https://mlsanity.com/paper/2311.11258/) (2023)
- [Machine learning with tree tensor networks, CP rank constraints, and tensor dropout](https://mlsanity.com/paper/2305.19440/) (2023)
- [Quantum Machine Learning on Near-Term Quantum Devices: Current State of Supervised and Unsupervised Techniques for Real-World Applications](https://mlsanity.com/paper/2307.00908/) (2023)
- [Tensor networks and efficient descriptions of classical data](https://mlsanity.com/paper/2103.06872/) (2021)
- [Permutation Search of Tensor Network Structures via Local Sampling](https://mlsanity.com/paper/2206.06597/) (2022)
- [Quantum-PEFT: Ultra parameter-efficient fine-tuning](https://mlsanity.com/paper/2503.05431/) (2025)
- [The Hintons in your Neural Network: a Quantum Field Theory View of Deep Learning](https://mlsanity.com/paper/2103.04913/) (2021)
- [Generative Learning of Continuous Data by Tensor Networks](https://mlsanity.com/paper/2310.20498/) (2023)
- [Quantum Circuit Synthesis and Compilation Optimization: Overview and Prospects](https://mlsanity.com/paper/2407.00736/) (2024)
- [Quantum Embedding Search for Quantum Machine Learning](https://mlsanity.com/paper/2105.11853/) (2021)
- [Classical versus Quantum: comparing Tensor Network-based Quantum Circuits on LHC data](https://mlsanity.com/paper/2202.10471/) (2022)
- [Quantum-probabilistic Hamiltonian learning for generative modelling & anomaly detection](https://mlsanity.com/paper/2211.03803/) (2022)
- [Federated Hierarchical Tensor Networks: a Collaborative Learning Quantum AI-Driven Framework for Healthcare](https://mlsanity.com/paper/2405.07735/) (2024)
- [Generalization Error Bound for Quantum Machine Learning in NISQ Era -- A Survey](https://mlsanity.com/paper/2409.07626/) (2024)
- [AutoQML: Automated Quantum Machine Learning for Wi-Fi Integrated Sensing and Communications](https://mlsanity.com/paper/2205.09115/) (2022)
- [Quantum Neural Networks under Depolarization Noise: Exploring White-Box Attacks and Defenses](https://mlsanity.com/paper/2311.17458/) (2023)
- [Deep Tree Tensor Networks](https://mlsanity.com/paper/2502.09928/) (2025)
- [When Federated Learning Meets Quantum Computing: Survey and Research Opportunities](https://mlsanity.com/paper/2504.08814/) (2025)
- [Entangled q-Convolutional Neural Nets](https://mlsanity.com/paper/2103.11785/) (2021)
- [Residual Tensor Train: A Quantum-inspired Approach for Learning Multiple Multilinear Correlations](https://mlsanity.com/paper/2108.08659/) (2021)
- [Classical Simulation of Variational Quantum Classifiers using Tensor Rings](https://mlsanity.com/paper/2201.08878/) (2022)
- [A hybrid quantum-classical conditional generative adversarial network algorithm for human-centered paradigm in cloud](https://mlsanity.com/paper/2310.00246/) (2023)

## Abstract (arXiv)

Machine learning is a promising application of quantum computing, but challenges remain as near-term devices will have a limited number of physical qubits and high error rates. Motivated by the usefulness of tensor networks for machine learning in the classical context, we propose quantum computing approaches to both discriminative and generative learning, with circuits based on tree and matrix product state tensor networks that could have benefits for near-term devices. The result is a unified framework where classical and quantum computing can benefit from the same theoretical and algorithmic developments, and the same model can be trained classically then transferred to the quantum setting for additional optimization. Tensor network circuits can also provide qubit-efficient schemes where, depending on the architecture, the number of physical qubits required scales only logarithmically with, or independently of the input or output data sizes. We demonstrate our proposals with numerical experiments, training a discriminative model to perform handwriting recognition using a optimization procedure that could be carried out on quantum hardware, and testing the noise resilience of the trained model.