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

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

TL;DR

The paper tackles the computational and data-efficiency challenges posed by the HL-LHC era by introducing the Lorentz-EQGNN, a Lie-algebra adaptive quantum GNN that preserves Lorentz symmetry while using a compact 4-qubit architecture. By replacing LorentzNet’s MLPs with parameterized quantum circuits and integrating Minkowski-based attention, the model achieves robust, symmetry-preserving learning with far fewer parameters than classical counterparts. Across quark-gluon jet tagging, electron-photon discrimination, and generic image benchmarks, Lorentz-EQGNN demonstrates competitive or superior performance in data-scarce settings, underscoring the value of symmetry adaptation in QML. The work highlights practical benefits for noise resilience and resource efficiency in NISQ devices and outlines future directions for error mitigation, scalability to larger graphs, and broader applicability beyond particle physics.

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 paper demonstrates that replacing the Lorentz Group Equivariant Block modules in LorentzNet with a dressed quantum circuit significantly enhances performance despite using nearly 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. Our Lorentz-Equivariant Quantum Graph Neural Network (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.

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

TL;DR

The paper tackles the computational and data-efficiency challenges posed by the HL-LHC era by introducing the Lorentz-EQGNN, a Lie-algebra adaptive quantum GNN that preserves Lorentz symmetry while using a compact 4-qubit architecture. By replacing LorentzNet’s MLPs with parameterized quantum circuits and integrating Minkowski-based attention, the model achieves robust, symmetry-preserving learning with far fewer parameters than classical counterparts. Across quark-gluon jet tagging, electron-photon discrimination, and generic image benchmarks, Lorentz-EQGNN demonstrates competitive or superior performance in data-scarce settings, underscoring the value of symmetry adaptation in QML. The work highlights practical benefits for noise resilience and resource efficiency in NISQ devices and outlines future directions for error mitigation, scalability to larger graphs, and broader applicability beyond particle physics.

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 paper demonstrates that replacing the Lorentz Group Equivariant Block modules in LorentzNet with a dressed quantum circuit significantly enhances performance despite using nearly 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. Our Lorentz-Equivariant Quantum Graph Neural Network (Lorentz-EQGNN) achieved test accuracy and an AUC of 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 test accuracy and an AUC of , demonstrating competitive results with just 800 training samples. Evaluation of our model on generic MNIST and FashionMNIST datasets confirmed Lorentz-EQGNN's efficiency, achieving and 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.

Paper Structure

This paper contains 37 sections, 1 theorem, 24 equations, 2 figures, 7 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Related Work
  3. Geometric Deep Learning and Transformer Models
  4. Classical Graph Neural Networks
  5. Quantum Graph Neural Networks (QGNNs)
  6. Invariant-Equivariant Machine Learning
  7. Methodology
  8. Equivariant Quantum Graph Neural Networks (EQGNN)
  9. Proposed Lorentz-EQGNN
  10. Input Layer
  11. Dressed Quantum Circuit
  12. Lorentz Group Equivariant Quantum Block (LGEQB)
  13. Infrared and Collinear Safety
  14. Decoding layer
  15. Theoretical Analysis
  16. ...and 22 more sections

Key Result

Proposition III.1

The coordinate embedding $x^{l} = \{x_1^{l}, x_2^{l}, \dots, x_n^{l}\}$ exhibits Lie group equivariance, whereas the node embedding $h^{l} = \{h_1^{l}, h_2^{l}, \dots, h_n^{l}\}$, which signifies the particle scalars, maintains Lie group invariance.

Figures (2)

  • Figure 1: Proposed architecture of Lorentz-EQGNN. Within LGEQB, we replace standard $\phi$ modules with customized MLPs and PQCs. Here, only the MLP replacement in $\phi_e$ is shown. Dimension reducers are applied before $\phi_e$ and $\phi_m$ to ensure input compatibility across LGEQB, minimizing qubit requirement.
  • Figure 2: Dressed quantum circuit architecture for the LGEQB in the Lorentz-EQGNN framework. Here, the figure was generated for depth size = 2 to illustrate the varying entanglement operation in both even and odd depth sizes.

Theorems & Definitions (2)

  • Proposition III.1
  • proof