# mathbbZ2× mathbbZ2 Equivariant Quantum Neural Networks: Benchmarking against Classical Neural Networks

arXiv: https://arxiv.org/abs/2311.18744 · HTML: https://mlsanity.com/paper/2311.18744/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 19 of its 51 references that are in the map.
- First posted on arXiv 30 Nov 2023.

## Builds on (most cited first, 19 of 19)

- [Group Equivariant Convolutional Networks](https://mlsanity.com/paper/1602.07576/) (2016)
- [Gauge Equivariant Convolutional Networks and the Icosahedral CNN](https://mlsanity.com/paper/1902.04615/) (2019)
- [Lorentz Group Equivariant Neural Network for Particle Physics](https://mlsanity.com/paper/2006.04780/) (2020)
- [Sampling using SU(N) gauge equivariant flows](https://mlsanity.com/paper/2008.05456/) (2020)
- [A Living Review of Machine Learning for Particle Physics](https://mlsanity.com/paper/2102.02770/) (2021)
- [Exploiting symmetry in variational quantum machine learning](https://mlsanity.com/paper/2205.06217/) (2022)
- [Theory for Equivariant Quantum Neural Networks](https://mlsanity.com/paper/2210.08566/) (2022)
- [Lattice gauge equivariant convolutional neural networks](https://mlsanity.com/paper/2012.12901/) (2020)
- [Equivariant quantum circuits for learning on weighted graphs](https://mlsanity.com/paper/2205.06109/) (2022)
- [PELICAN: Permutation Equivariant and Lorentz Invariant or Covariant Aggregator Network for Particle Physics](https://mlsanity.com/paper/2211.00454/) (2022)
- [EPiC-GAN: Equivariant Point Cloud Generation for Particle Jets](https://mlsanity.com/paper/2301.08128/) (2023)
- [Hybrid Quantum-Classical Graph Convolutional Network](https://mlsanity.com/paper/2101.06189/) (2021)
- [Generalization capabilities of translationally equivariant neural networks](https://mlsanity.com/paper/2103.14686/) (2021)
- [A General Framework for Equivariant Neural Networks on Reductive Lie Groups](https://mlsanity.com/paper/2306.00091/) (2023)
- [Lorentz group equivariant autoencoders](https://mlsanity.com/paper/2212.07347/) (2022)
- [Snowmass 2021 Computational Frontier CompF03 Topical Group Report: Machine Learning](https://mlsanity.com/paper/2209.07559/) (2022)
- [Approximately Equivariant Quantum Neural Network for p4m Group Symmetries in Images](https://mlsanity.com/paper/2310.02323/) (2023)
- [Quantum Optimisation of Complex Systems with a Quantum Annealer](https://mlsanity.com/paper/2105.13945/) (2021)
- [Classical versus Quantum: comparing Tensor Network-based Quantum Circuits on LHC data](https://mlsanity.com/paper/2202.10471/) (2022)

## Built on by (most cited first, 4 of 4)

- [A Primer on Quantum Machine Learning](https://mlsanity.com/paper/2511.15969/) (2025)
- [Quantum Vision Transformers for Quark-Gluon Classification](https://mlsanity.com/paper/2405.10284/) (2024)
- [Lorentz-Equivariant Quantum Graph Neural Network for High-Energy Physics](https://mlsanity.com/paper/2411.01641/) (2024)
- [Lie-Equivariant Quantum Graph Neural Networks](https://mlsanity.com/paper/2411.15315/) (2024)

## Abstract (arXiv)

This paper presents a comprehensive comparative analysis of the performance of Equivariant Quantum Neural Networks (EQNN) and Quantum Neural Networks (QNN), juxtaposed against their classical counterparts: Equivariant Neural Networks (ENN) and Deep Neural Networks (DNN). We evaluate the performance of each network with two toy examples for a binary classification task, focusing on model complexity (measured by the number of parameters) and the size of the training data set. Our results show that the mathbbZ2× mathbbZ2 EQNN and the QNN provide superior performance for smaller parameter sets and modest training data samples.