mlsanityData to 7 Oct 2026

Classical versus Quantum: comparing Tensor Network-based Quantum Circuits on LHC data

arXiv 2202.10471 ↗First posted 21 Feb 2022quant-ph cs.LG hep-excited by 7

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Abstract (arXiv)

Tensor Networks (TN) are approximations of high-dimensional tensors designed to represent locally entangled quantum many-body systems efficiently. This study provides a comprehensive comparison between classical TNs and TN-inspired quantum circuits in the context of Machine Learning on highly complex, simulated LHC data. We show that classical TNs require exponentially large bond dimensions and higher Hilbert-space mapping to perform comparably to their quantum counterparts. While such an expansion in the dimensionality allows better performance, we observe that, with increased dimensionality, classical TNs lead to a highly flat loss landscape, rendering the usage of gradient-based optimization methods highly challenging. Furthermore, by employing quantitative metrics, such as the Fisher information and effective dimensions, we show that classical TNs require a more extensive training sample to represent the data as efficiently as TN-inspired quantum circuits. We also engage with the idea of hybrid classical-quantum TNs and show possible architectures to employ a larger phase-space from the data. We offer our results using three main TN ansatz: Tree Tensor Networks, Matrix Product States, and Multi-scale Entanglement Renormalisation Ansatz.

Key facts. Cited by 7 papers in the map (data through 7 Oct 2026). Builds on 29 of its 119 references that are in the map. First posted on arXiv 21 Feb 2022.

Builds on

29 of 119 references.

References · 29

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17 more
  1. 2016Supervised Learning with Quantum-Inspired Tensor Networkscited by 35
  2. 2016Convolutional Rectifier Networks as Generalized Tensor Decompositionscited by 32
  3. 2020Quantum-inspired Machine Learning on high-energy physics datacited by 30
  4. 2019TensorNetwork for Machine Learningcited by 29
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  6. 2020Tensor Networks for Medical Image Classificationcited by 20
  7. 2021Hybrid Quantum Classical Graph Neural Networks for Particle Track Reconstructioncited by 20
  8. 2021Style-based quantum generative adversarial networks for Monte Carlo eventscited by 19
  9. 2020Entanglement and Tensor Networks for Supervised Image Classificationcited by 18
  10. 2020A scale-dependent notion of effective dimensioncited by 17
  11. 2021Higgs analysis with quantum classifierscited by 14
  12. 2019Matrix Product State Based Quantum Classifiercited by 13
  13. 2020A Multi-Scale Tensor Network Architecture for Classification and Regressioncited by 13
  14. 2021Quantum Tensor Network in Machine Learning: An Application to Tiny Object Classificationcited by 9
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  16. 2021Quantum Optimisation of Complex Systems with a Quantum Annealercited by 6
  17. 2020Quantum-Classical Machine learning by Hybrid Tensor Networkscited by 3

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Cited by year

Citing papers per year: 2022: 1; 2023: 5; 2024: 0; 2025: 1.

7 papers.

  1. 2023Tensor networks for quantum machine learningcited by 16
  2. 2023Quantum Machine Learning on Near-Term Quantum Devices: Current State of Supervised and Unsupervised Techniques for Real-World Applicationscited by 14
  3. 2023Quantum-Inspired Machine Learning: a Surveycited by 11
  4. 2022Completely Quantum Neural Networkscited by 6
  5. 2023mathbbZ2× mathbbZ2 Equivariant Quantum Neural Networks: Benchmarking against Classical Neural Networkscited by 4
  6. 2023Generative Invertible Quantum Neural Networkscited by 3
  7. 2025Hybrid quantum recurrent neural network for remaining useful life prediction of turbofan enginescited by 0