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

arXiv: https://arxiv.org/abs/2202.10471 · HTML: https://mlsanity.com/paper/2202.10471/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Builds on 29 of its 119 references that are in the map.
- First posted on arXiv 21 Feb 2022.

## Builds on (most cited first, 29 of 29)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Barren plateaus in quantum neural network training landscapes](https://mlsanity.com/paper/1803.11173/) (2018)
- [New insights and perspectives on the natural gradient method](https://mlsanity.com/paper/1412.1193/) (2014)
- [The power of quantum neural networks](https://mlsanity.com/paper/2011.00027/) (2020)
- [Quantum Natural Gradient](https://mlsanity.com/paper/1909.02108/) (2019)
- [Quantum machine learning: a classical perspective](https://mlsanity.com/paper/1707.08561/) (2017)
- [Universal Statistics of Fisher Information in Deep Neural Networks: Mean Field Approach](https://mlsanity.com/paper/1806.01316/) (2018)
- [Towards Quantum Machine Learning with Tensor Networks](https://mlsanity.com/paper/1803.11537/) (2018)
- [On the Quantum versus Classical Learnability of Discrete Distributions](https://mlsanity.com/paper/2007.14451/) (2020)
- [Ultimate tensorization: compressing convolutional and FC layers alike](https://mlsanity.com/paper/1611.03214/) (2016)
- [Quantum Entanglement in Deep Learning Architectures](https://mlsanity.com/paper/1803.09780/) (2018)
- [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)
- [Convolutional Rectifier Networks as Generalized Tensor Decompositions](https://mlsanity.com/paper/1603.00162/) (2016)
- [Quantum-inspired Machine Learning on high-energy physics data](https://mlsanity.com/paper/2004.13747/) (2020)
- [TensorNetwork for Machine Learning](https://mlsanity.com/paper/1906.06329/) (2019)
- [Hybrid quantum-classical classifier based on tensor network and variational quantum circuit](https://mlsanity.com/paper/2011.14651/) (2020)
- [Tensor Networks for Medical Image Classification](https://mlsanity.com/paper/2004.10076/) (2020)
- [Hybrid Quantum Classical Graph Neural Networks for Particle Track Reconstruction](https://mlsanity.com/paper/2109.12636/) (2021)
- [Style-based quantum generative adversarial networks for Monte Carlo events](https://mlsanity.com/paper/2110.06933/) (2021)
- [Entanglement and Tensor Networks for Supervised Image Classification](https://mlsanity.com/paper/2007.06082/) (2020)
- [A scale-dependent notion of effective dimension](https://mlsanity.com/paper/2001.10872/) (2020)
- [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)
- [Higgs analysis with quantum classifiers](https://mlsanity.com/paper/2104.07692/) (2021)
- [Quantum Tensor Network in Machine Learning: An Application to Tiny Object Classification](https://mlsanity.com/paper/2101.03154/) (2021)
- [Quantum-inspired event reconstruction with Tensor Networks: Matrix Product States](https://mlsanity.com/paper/2106.08334/) (2021)
- [Quantum Optimisation of Complex Systems with a Quantum Annealer](https://mlsanity.com/paper/2105.13945/) (2021)
- [Quantum-Classical Machine learning by Hybrid Tensor Networks](https://mlsanity.com/paper/2005.09428/) (2020)

## Built on by (most cited first, 7 of 7)

- [Tensor networks for quantum machine learning](https://mlsanity.com/paper/2303.11735/) (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)
- [Quantum-Inspired Machine Learning: a Survey](https://mlsanity.com/paper/2308.11269/) (2023)
- [Completely Quantum Neural Networks](https://mlsanity.com/paper/2202.11727/) (2022)
- [mathbbZ2× mathbbZ2 Equivariant Quantum Neural Networks: Benchmarking against Classical Neural Networks](https://mlsanity.com/paper/2311.18744/) (2023)
- [Generative Invertible Quantum Neural Networks](https://mlsanity.com/paper/2302.12906/) (2023)
- [Hybrid quantum recurrent neural network for remaining useful life prediction of turbofan engines](https://mlsanity.com/paper/2504.20823/) (2025)

## 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.