标题： 经典和量子图神经网络的不变性与等变性比较 显示英文标题

标题： A Comparison Between Invariant and Equivariant Classical and Quantum Graph Neural Networks

摘要： 机器学习算法被广泛依赖于理解欧洲核子研究中心大型强子对撞机（LHC）中高能粒子碰撞产生的大量数据。 此类碰撞事件的数据可以自然地用图结构表示。 因此，深度几何方法，如图神经网络（GNNs），已被用于高能物理中的各种数据分析任务。 一个典型的任务是喷注标签，其中喷注被视为具有独特特征和粒子间边连接的点云。 LHC粒子数据集的规模和复杂性，以及用于分析它们的计算模型，极大地推动了替代快速高效计算范式的开发，例如量子计算。 此外，为了增强深度网络的有效性和鲁棒性，可以通过使用不变输入和等变层来利用数据中存在的基本对称性。 在本文中，我们对经典图神经网络（GNNs）和等变图神经网络（EGNNs）及其量子对应物：量子图神经网络（QGNNs）和等变量子图神经网络（EQGNN）进行了公平且全面的比较。 这四种架构在二分类任务上进行了基准测试，以分类引发喷注的粒子层次粒子。 根据它们的AUC分数，量子网络被证明优于经典网络。 然而，在实践中看到量子网络的计算优势可能需要等待量子技术及其相关API的进一步发展。 显示英文摘要

摘要： 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, greatly motivate the development of alternative fast and efficient computational paradigms such as quantum computation. In addition, to enhance the validity and robustness of deep networks, one can leverage the fundamental symmetries present in the data through the use of invariant inputs and equivariant layers. In this paper, we perform a fair and comprehensive comparison between 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 AUC scores, the quantum networks were shown to outperform the classical networks. However, seeing the computational advantage of the quantum networks in practice may have to wait for the further development of quantum technology and its associated APIs.