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

2024-11-03

arXiv.org

AI Summary

Existing quantum graph neural networks (QGNNs) for jet identification and event classification in high-energy physics suffer from rigid Lorentz symmetry adaptation, poor noise robustness, and low data efficiency. This work introduces the first Lorentz-covariant QGNN: it replaces conventional learnable covariant modules with a native-covariant “decorated” parameterized quantum circuit, rigorously preserving Lorentz group representation invariance using only four qubits. Integrated with covariant feature embedding and few-shot training, the model achieves 74.00% accuracy (AUC 87.38%) on the Quark-Gluon dataset; 67.00% accuracy on the Electron-Photon dataset using merely 800 samples; and 88.10% and 74.80% accuracy on MNIST and FashionMNIST, respectively—outperforming both classical baselines and state-of-the-art QGNNs across all benchmarks.

Technology Category

• Machine Learning: Quantum Machine Learning
• Computer Vision: Learning & Optimization for CV
• Search and Optimization: Learning to Search

Application Category

• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs

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.

Problem

• High-speed Data Processing
• Quantum Graph Neural Networks
• Complex Particle Interaction Analysis

Innovation

• Lorentz-EQGNN
• Quantum Machine Learning
• Relativistic Symmetry Preservation