Symmetry Breaking in Geometric Quantum Machine Learning in the Presence of Noise - Strategies for Preserving Equivariance Under Pauli Noise

Aug 3, 2026

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This work investigates how equivariant quantum neural networks (EQNNs) behave when hardware noise is present, extending geometric quantum machine learning beyond idealized theory. It shows that certain EQNN architectures can preserve equivariance under Pauli channels, while equivariance is lost under the nonunital amplitude damping channel. The symmetry breaking is characterized by newly introduced metrics and is found to grow approximately linearly with both the number of layers and noise strength. Results are supported by simulations and hardware experiments up to 64 qubits, together with strategies such as representation choice and adaptive thresholding to improve symmetry protection.

LanguageEnglish

CategoryResearch & Report

FormatPDF

Pages19

Reading Time48 min

AccessFree to download

Introduction

Variational quantum algorithms and noise challenges

Geometric quantum machine learning and equivariant neural networks

Framework

Equivariant quantum neural networks

Quantum feature maps and predictions

Symmetry breaking in geometric quantum machine learning in the presence of noise arXiv :2401 . 10293v1 [ quant-ph] 17 Jan 2024 Cenk Tüysüz, 1, 2, ∗ Su Yeon Chang,3, 4 Maria Demidik, 1, 5 Karl Jansen, 1, 5 Sofia Vallecorsa,3 and Michele Grossi3,† 1 Deutsches Elektronen-Synchrotron DESY, 15738 Zeuthen, Germany 2 Institut für Physik, Humboldt-Universität zu Berlin, 12489 Berlin, Germany 3 European Organization for Nuclear Research (CERN), 1211 Geneva, Switzerland 4 Institute of Physics, École Polytechnique Fédérale de Lausanne (EPFL), 1015 Lausanne, Switzerland 5 Computation-Based Science and Technology Research Center, The Cyprus Institute, 2121 Nicosia, Cyprus 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 isnot 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. I. INTRODUCTION Variational quantum algorithms (VQAs) appear to be one of the promising algorithms of the noisy intermediate scale quantum (NISQ) era [1] in the literature [2] . Furthermore, recent results showed noise resilience of VQAs, which further increased hope [3] . However, there exist many roadblocks to making this promise a reality. Some problems that are common to most VQAs are barren plateaus (BPs) i. e. number of shots needed to estimate the sufficiently precise values of the cost function grows exponentially [4, 5], many local minima [6–8] and lack of efficient gradient computation (e.g. parameter shift rules require circuit executions that scale linearly in number of parameters) [9] . While certain issues can be partially alleviated through a range of methods [10–14], faithfully running these algorithms on NISQ hardware, beyond what is classically simulable (e.g. n > 40 qubits and at least log (n) depth), is still a practical challenge. Proposals of geometric quantum machine learning (GQML) opened new avenues, which in theory bring VQAs closer to practicality [15] . The GQML framework leverages inductive biases on problems and uses this to construct algorithms with improved trainability and generalization [16] . This requires the circuit to have a certain structure from the initial state until the final measurements. On the other hand, this is where the NISQ hardware fails to provide due to coherent and incoherent errors present [1, 17] . In the literature, this topic has been explored in the context of state preparation and time evolution of quantum systems, in which many physical symmetries arise [18, 19] . However, these results don’t directly translate to the setting of GQML. For this reason, we study the behavior of these algorithms, specifically equivariant quantum neural networks (EQNNs), under hardware noise in this work. ∗ cenk.tueysuez@desy.de † michele.grossi@cern.ch In this paper, we study the behavior of EQNN models in the presence of noise. Our theoretical and numerical results indicate that, for the models considered, equivariance can be protected under realistic Pauli channels. We further show that the symmetry is broken under the nonunital amplitude damping channel. We characterize this with metrics that we introduce and show that symmetry breaking grows approximately linearly in the number of layers and the noise strength. Moreover, we provide strategies such as choice of representation and adaptive thres

FAQs

How does noise affect equivariance in EQNN models?

The study shows that EQNN models may preserve equivariance under Pauli channels, but symmetry breaks under the amplitude damping channel.

How is symmetry breaking quantified in the paper?

The paper introduces metrics to measure symmetry breaking and uses them to characterize how it changes across settings.

What factors make symmetry breaking stronger?

Symmetry breaking grows approximately linearly with the number of layers and the noise strength.

Aug 3, 2026

Upload by Maeve