  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.
