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：本文系统比较了等变量子神经网络（EQNN）与量子神经网络（QNN）的性能，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）进行对比。我们通过两个二元分类任务的简单示例，从模型复杂度（以参数数量衡量）和训练数据集规模两个维度评估各网络性能。结果表明，在参数集较小且训练数据样本适中的情况下，$\mathbb{Z}_2\times \mathbb{Z}_2$ EQNN 和 QNN 展现出更优性能。