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arXiv:2411.01641 · IEEE Transactions on Artificial Intelligence

Lorentz-Equivariant Quantum Graph Neural Network for High-Energy Physics

Md Abrar Jahin, Md. Akmol Masud, Md Wahiduzzaman Suva, M. F. Mridha, Nilanjan Dey

Published Mar 24, 2025• 6 citations
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Abstract

The rapid data surge from the high-luminosity Large Hadron Collider introduces critical computational challenges requiring novel approaches for efficient data processing in particle physics. Quantum machine learning, with its capability to leverage the extensive Hilbert space of quantum hardware, offers a promising solution. However, current quantum graph neural networks (GNNs) lack robustness to noise and are often constrained by fixed symmetry groups, limiting adaptability in complex particle interaction modeling. This article demonstrates that replacing the classical Lorentz group equivariant block modules in LorentzNet with a dressed quantum circuit significantly enhances performance despite using$\approx 5.5$times fewer parameters. Additionally, quantum circuits effectively replace MLPs by inherently preserving symmetries, with Lorentz symmetry integration ensuring robust handling of relativistic invariance. OurLorentz-equivariantquantumgraphneuralnetwork (Lorentz-EQGNN) achieved 74.00% test accuracy and an AUC of 87.38% on the Quark-Gluon jet tagging dataset, outperforming the classical and quantum GNNs with a reduced architecture using only 4 qubits. On the electron–photon dataset, Lorentz-EQGNN reached 67.00% test accuracy and an AUC of 68.20%, demonstrating competitive results with just 800 training samples. Evaluation of our model on generic MNIST and FashionMNIST datasets confirmed Lorentz-EQGNN’s efficiency, achieving 88.10% and 74.80% test accuracy, respectively. Ablation studies validated the impact of quantum components on performance, with notable improvements in background rejection rates over classical counterparts. These results highlight Lorentz-EQGNN’s potential for immediate applications in noise-resilient jet tagging, event classification, and broader data-scarce HEP tasks.

DOI
10.1109/tai.2025.3554461

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The rapid data surge from the high-luminosity Large Hadron Collider introduces critical computational challenges requiring novel approaches for efficient data processing in particle physics. Quantum machine learning, with its capability to leverage the extensive Hilbert space of quantum hardware, offers a promising solution. However, current quantum graph neural networks (GNNs) lack robustness to noise and are often constrained by fixed symmetry groups, limiting adaptability in complex particle interaction modeling. This article demonstrates that replacing the classical Lorentz group equivariant block modules in LorentzNet with a dressed quantum circuit significantly enhances performance despite using≈5.5\approx 5.5≈5.5times fewer parameters. Additionally, quantum circuits effectively replace MLPs by inherently preserving symmetries, with Lorentz symmetry integration ensuring robust handling of relativistic invariance. OurLorentz-equivariantquantumgraphneuralnetwork (Lorentz-EQGNN) achieved 74.00% test accuracy and an AUC of 87.38% on the Quark-Gluon jet tagging dataset, outperforming the classical and quantum GNNs with a reduced architecture using only 4 qubits. On the electron–photon dataset, Lorentz-EQGNN reached 67.00% test accuracy and an AUC of 68.20%, demonstrating competitive results with just 800 training samples. Evaluation of our model on generic MNIST and FashionMNIST datasets confirmed Lorentz-EQGNN’s efficiency, achieving 88.10% and 74.80% test accuracy, respectively. Ablation studies validated the impact of quantum components on performance, with notable improvements in background rejection rates over classical counterparts. These results highlight Lorentz-EQGNN’s potential for immediate applications in noise-resilient jet tagging, event classification, and broader data-scarce HEP tasks.
Discovering new phenomena at the Large Hadron Collider (LHC) involves the identification of rare signals over conventional backgrounds. Thus binary classification tasks are ubiquitous in analyses of the vast amounts of LHC data. We develop a Lie-Equivariant Quantum Graph Neural Network (Lie-EQGNN), a quantum model that is not only data efficient, but also has symmetry-preserving properties. Since Lorentz group equivariance has been shown to be beneficial for jet tagging, we build a Lorentz-equivariant quantum GNN for quark-gluon jet discrimination and show that its performance is on par with its classical state-of-the-art counterpart LorentzNet, making it a viable alternative to the conventional computing paradigm.
Machine learning algorithms are heavily relied on to understand the vast amounts of data from high-energy particle collisions at the CERN Large Hadron Collider (LHC). The data from such collision events can naturally be represented with graph structures. Therefore, deep geometric methods, such as graph neural networks (GNNs), have been leveraged for various data analysis tasks in high-energy physics. One typical task is jet tagging, where jets are viewed as point clouds with distinct features and edge connections between their constituent particles. The increasing size and complexity of the LHC particle datasets, as well as the computational models used for their analysis, have greatly motivated the development of alternative fast and efficient computational paradigms such as quantum computation. In addition, to enhance the validity and robustness of deep networks, we can leverage the fundamental symmetries present in the data through the use of invariant inputs and equivariant layers. In this paper, we provide a fair and comprehensive comparison of classical graph neural networks (GNNs) and equivariant graph neural networks (EGNNs) and their quantum counterparts: quantum graph neural networks (QGNNs) and equivariant quantum graph neural networks (EQGNN). The four architectures were benchmarked on a binary classification task to classify the parton-level particle initiating the jet. Based on their area under the curve (AUC) scores, the quantum networks were found to outperform the classical networks. However, seeing the computational advantage of quantum networks in practice may have to wait for the further development of quantum technology and its associated application programming interfaces (APIs).
Jets are central to the physics programs of both current and future colliders, from precision Standard Model measurements and searches for new physics at the Large Hadron Collider to studies of nucleon structure at the future Electron-Ion Collider. Motivated by these applications, we explore quantum machine learning for jet classification and present a permutation-invariant Quantum Graph Neural Network (QGNN) applied to particle-cloud representations of jets. We apply the model to two such discrimination tasks: quark vs. gluon and up vs. down quark flavor tagging, with the latter being, to our knowledge, the first application of a quantum model to this problem. In the ideal simulation, the QGNN performs competitively against the Particle Flow Network and traditional QCD observables. We further deploy scaled-down models to IBM and IonQ quantum processing units (QPUs), where we train and evaluate them, obtaining promising results. Finally, we perform an interpretability analysis to characterize the observables learned by the quantum model, relating them to generalized angularities for the quark-gluon study and to jet charge for the flavor study.
The integration of symmetry, such as permutation equivariance, into Quantum Graph Neural Networks (QGNNs), referred to as Equivariant Quantum Graph Neural Networks (EQGNNs), markedly improves the model's generalization performance on graph-structured data. Despite this advancement, current research has not yet extended rotational equivariance to QGNN frameworks. Furthermore, processing large-scale graph data increases computational complexity due to numerous inter-node connections, significantly raising the required number of qubits. To address these challenges, a novel Rotationally Equivariant Quantum Graph Neural Network (REQGNN) with trainable compression encoder and entanglement-enhanced aggregation mechanism is proposed. By adopting quantum fidelity as the evaluation metric, we design a quantum autoencoder to effectively compress feature dimensionality, substantially lowering the qubit requirements of the model while preserving essential global structural details. To achieve rotational equivariance in the model, we propose an entanglement-enhanced layer that incorporates distance and angle information between nodes. This layer performs entanglement by extracting diverse edge information, thereby further refining edge feature extraction. Additionally, an auxiliary entanglement layer is introduced to mitigate the over-smoothing issue. Experiment results demonstrate REQGNN is significantly better for graph classification tasks than GIN, Gra+QSVM, and Gra+QCNN on four datasets in all metrics and achieves better results than egoGQNN in accuracy on PTC dataset, and it also has advantage for graph regression tasks over the classical models, including EGNN and EquiformerV2, and reduces the MAE of CvC_vCv​ task unit by 20\% on average compared with a previous quantum model QGCNN. Our approach offers an effective solution for achieving rotational equivariance while providing a novel perspective for exploring symmetry in graph neural networks (GNNs).
Equivariant quantum graph neural networks (EQGNNs) offer a potentially powerful method to process graph data. However, existing EQGNN models only consider the permutation symmetry of graphs, and failing to fully exploit the geometric and non-geometric information in graphs, resulting in suboptimal performance when processing 3D graph data. To address these limitations, we derive constraints of rotation and permutation equivariance, and then propose a novel rotation- and permutation-equivariant quantum graph neural network (RP-EQGNN). An equivariant module is designed to extract the geometric information. Then, a convolution and entanglement module is constructed to extract non-geometric information. To improve performance of our model, an edge entanglement strategy is designed to perform distinguishable entanglement operations based on edge heterogeneity. The experiment results demonstrate that RP-EQGNN is significantly better for graph regression on the QM9 dataset and the OC20 dataset than Q3DGL and EQC in MAE and achieves results comparable to those of EquiformerV2, Geoformer, SO3KRATES and HEGNN. It also has advantage for point cloud classification on the ModelNet40 dataset over quantum models, including sQCNN-3D and PI-QSVM. RP-EQGNN introduces an innovative approach for processing 3D graph data, establishing a basis for future investigations into symmetries within graph neural networks.
Machine learning, particularly deep neural networks, has seen widespread application in high-energy physics. Recently, quantum machine learning has emerged by integrating quantum computing with classical ML techniques. In this work, we propose the Quantum Complete Graph Neural Network (QCGNN), tailored for fully connected graphs and reducing computational complexity from O(N2) to O(N). We apply QCGNN to the jet tagging task in the datasets Top and JetNet for showing the feasibility, achieving AUCs of 0.932 and 0.822 via simulators, respectively, comparable to the leading classical models. On real quantum hardware via the IBM Quantum Platform (IBMQ), however, the AUC drops to around 0.5 due to quantum noise, indicating current devices remain impractical. The scaling behavior of QCGNN on computational complexity is further examined through runtime measurements on actual IBMQ machines.