This paper presents a comprehensive comparative analysis of the performance of Equivariant Quantum Neural Networks (EQNN) and Quantum Neural Networks (QNN), juxtaposed against their classical counterparts: Equivariant Neural Networks (ENN) and Deep Neural Networks (DNN). We evaluate the performance of each network with two toy examples for a binary classification task, focusing on model complexity (measured by the number of parameters) and the size of the training data set. Our results show that the $\mathbb{Z}_2\times \mathbb{Z}_2$ EQNN and the QNN provide superior performance for smaller parameter sets and modest training data samples.

翻译：本文对等变量子神经网络（EQNN）和量子神经网络（QNN）的性能进行了全面的比较分析，并将其与经典对应模型——等变神经网络（ENN）和深度神经网络（DNN）进行了对比。我们通过两个二分类任务的简单示例评估了每种网络的性能，重点考察了模型复杂度（以参数数量衡量）和训练数据集规模。结果表明，$\mathbb{Z}_2\times \mathbb{Z}_2$ EQNN 和 QNN 在参数集较小且训练数据样本适中的情况下展现出更优的性能。