# Symmetry breaking in geometric quantum machine learning in the presence of noise

arXiv: https://arxiv.org/abs/2401.10293 · HTML: https://mlsanity.com/paper/2401.10293/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 6 of its 17 references that are in the map.
- First posted on arXiv 17 Jan 2024.

## Builds on (most cited first, 6 of 6)

- [Variational Quantum Algorithms](https://mlsanity.com/paper/2012.09265/) (2020)
- [Supervised learning with quantum enhanced feature spaces](https://mlsanity.com/paper/1804.11326/) (2018)
- [Barren plateaus in quantum neural network training landscapes](https://mlsanity.com/paper/1803.11173/) (2018)
- [Noise-Induced Barren Plateaus in Variational Quantum Algorithms](https://mlsanity.com/paper/2007.14384/) (2020)
- [Theoretical Guarantees for Permutation-Equivariant Quantum Neural Networks](https://mlsanity.com/paper/2210.09974/) (2022)
- [On the universality of Sn-equivariant k-body gates](https://mlsanity.com/paper/2303.00728/) (2023)

## Built on by (most cited first, 5 of 5)

- [Qiskit Machine Learning: an open-source library for quantum machine learning tasks at scale on quantum hardware and classical simulators](https://mlsanity.com/paper/2505.17756/) (2025)
- [Image Classification with Rotation-Invariant Variational Quantum Circuits](https://mlsanity.com/paper/2403.15031/) (2024)
- [A PAC-Bayesian approach to generalization for quantum models](https://mlsanity.com/paper/2603.22964/) (2026)
- [Exploring Channel Distinguishability in Local Neighborhoods of the Model Space in Quantum Neural Networks](https://mlsanity.com/paper/2410.09470/) (2024)
- [From Reachability to Learnability: Geometric Design Principles for Quantum Neural Networks](https://mlsanity.com/paper/2603.03071/) (2026)

## Abstract (arXiv)

Geometric quantum machine learning based on equivariant quantum neural networks (EQNN) recently appeared as a promising direction in quantum machine learning. Despite the encouraging progress, the studies are still limited to theory, and the role of hardware noise in EQNN training has never been explored. This work studies the behavior of EQNN models in the presence of noise. We show that certain EQNN models can preserve equivariance under Pauli channels, while this is not possible under the amplitude damping channel. We claim that the symmetry breaking grows linearly in the number of layers and noise strength. We support our claims with numerical data from simulations as well as hardware up to 64 qubits. Furthermore, we provide strategies to enhance the symmetry protection of EQNN models in the presence of noise.