mlsanityData to 7 Oct 2026

Tensor networks for quantum machine learning

arXiv 2303.11735 ↗First posted 21 Mar 2023quant-ph cs.LGcited by 16

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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.

Key facts. Cited by 16 papers in the map (data through 7 Oct 2026). Builds on 41 of its 125 references that are in the map. First posted on arXiv 21 Mar 2023.

Builds on

41 of 125 references.

References · 41

  1. 2018Barren plateaus in quantum neural network training landscapescited by 624
  2. 2020The power of quantum neural networkscited by 377
  3. 2020The effect of data encoding on the expressive power of variational quantum machine learning modelscited by 328
  4. 2015Tensorizing Neural Networkscited by 246
  5. 2021Generalization in quantum machine learning from few training datacited by 214
  6. 2020Absence of Barren Plateaus in Quantum Convolutional Neural Networkscited by 124
  7. 2017Unsupervised Generative Modeling Using Matrix Product Statescited by 87
  8. 2018Towards Quantum Machine Learning with Tensor Networkscited by 74
  9. 2019Tree Tensor Networks for Generative Modelingcited by 63
  10. 2019Expressive power of tensor-network factorizations for probabilistic modeling, with applications from hidden Markov models to quantum machine learningcited by 55
  11. 2017Tensor Networks for Dimensionality Reduction and Large-Scale Optimizations. Part 2 Applications and Future Perspectivescited by 53
  12. 2017Learning Relevant Features of Data with Multi-scale Tensor Networkscited by 50
29 more
  1. 2021Variational Quantum Reinforcement Learning via Evolutionary Optimizationcited by 50
  2. 2018Quantum Entanglement in Deep Learning Architecturescited by 49
  3. 2021An end-to-end trainable hybrid classical-quantum classifiercited by 49
  4. 2017Machine Learning by Unitary Tensor Network of Hierarchical Tree Structurecited by 39
  5. 2016Supervised Learning with Quantum-Inspired Tensor Networkscited by 35
  6. 2018From probabilistic graphical models to generalized tensor networks for supervised learningcited by 31
  7. 2020Quantum-inspired Machine Learning on high-energy physics datacited by 30
  8. 2021Analyzing the barren plateau phenomenon in training quantum neural networks with the ZX-calculuscited by 30
  9. 2017Equivalence of restricted Boltzmann machines and tensor network statescited by 26
  10. 2020Anomaly Detection with Tensor Networkscited by 26
  11. 2022Theoretical Error Performance Analysis for Variational Quantum Circuit Based Functional Regressioncited by 26
  12. 2019Generative Tensor Network Classification Model for Supervised Machine Learningcited by 22
  13. 2020Dynamic Portfolio Optimization with Real Datasets Using Quantum Processors and Quantum-Inspired Tensor Networkscited by 22
  14. 2018Entanglement-guided architectures of machine learning by quantum tensor networkcited by 15
  15. 2019Matrix Product State Based Quantum Classifiercited by 13
  16. 2019Machine Learning Phase Transitions with a Quantum Processorcited by 13
  17. 2020A Multi-Scale Tensor Network Architecture for Classification and Regressioncited by 13
  18. 2021Tensor networks and efficient descriptions of classical datacited by 13
  19. 2022From Tensor Network Quantum States to Tensorial Recurrent Neural Networkscited by 13
  20. 2021Quantum Tensor Network in Machine Learning: An Application to Tiny Object Classificationcited by 9
  21. 2021Quantum-inspired event reconstruction with Tensor Networks: Matrix Product Statescited by 9
  22. 2021Boltzmann machines as two-dimensional tensor networkscited by 7
  23. 2022Classical versus Quantum: comparing Tensor Network-based Quantum Circuits on LHC datacited by 7
  24. 2022Unsupervised Recognition of Informative Features via Tensor Network Machine Learning and Quantum Entanglement Variationscited by 7
  25. 2022Improvements to Gradient Descent Methods for Quantum Tensor Network Machine Learningcited by 6
  26. 2020Quantum-Classical Machine learning by Hybrid Tensor Networkscited by 3
  27. 2021Differentiable Programming of Isometric Tensor Networkscited by 2
  28. 2022Improved Wavelets for Image Compression from Unitary Circuitscited by 2
  29. 2020Multi-layered tensor networks for image classificationcited by 1

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2023: 1; 2024: 2; 2025: 9; 2026: 4.

16 papers.

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  1. 2023Quantum-Inspired Machine Learning: a Surveycited by 11
  2. 2024Federated Hierarchical Tensor Networks: a Collaborative Learning Quantum AI-Driven Framework for Healthcarecited by 7
  3. 2025TensorRL-QAS: Reinforcement learning with tensor networks for improved quantum architecture searchcited by 6
  4. 2025tn4ml: Tensor Network Training and Customization for Machine Learningcited by 4
  5. 2025Tensorization is a powerful but underexplored tool for compression and interpretability of neural networkscited by 3
  6. 2024Application of Tensorized Neural Networks for Cloud Classificationcited by 0
  7. 2025Quantum Methods for Managing Ambiguity in Natural Language Processingcited by 0
  8. 2025Trainable Quantum Neural Network for Multiclass Image Classification with the Power of Pre-trained Tree Tensor Networkscited by 0
  9. 2025Explaining Anomalies with Tensor Networkscited by 0
  10. 2025Dimension reduction with structure-aware quantum circuits for hybrid machine learningcited by 0
  11. 2025Hybrid quantum tensor networks for aeroelastic applicationscited by 0
  12. 2025Tensor Computing Interface: An Application-Oriented, Lightweight Interface for Portable High-Performance Tensor Network Applicationscited by 0
4 more
  1. 2026Embedded Quantum Machine Learning in Embedded Systems: Feasibility, Hybrid Architectures, and Quantum Co-Processorscited by 0
  2. 2026Quantum-inspired tensor networks in machine learning modelscited by 0
  3. 2026Mitigating Measurement-Induced Training Instability in Hybrid Quantum Neural Networks for Protein Classificationcited by 0
  4. 2026Quantum Tensor Network Learning with DMRGcited by 0