  Geometric deep learning refers to the scenario in which the symmetries of a
dataset are used to constrain the parameter space of a neural network and thus,
improve their trainability and generalization. Recently this idea has been
incorporated into the field of quantum machine learning, which has given rise
to equivariant quantum neural networks (EQNNs). In this work, we investigate
the role of classical-to-quantum embedding on the performance of equivariant
quantum convolutional neural networks (EQCNNs) for the classification of
images. We discuss the connection between the data embedding method and the
resulting representation of a symmetry group and analyze how changing
representation affects the expressibility of an EQCNN. We numerically compare
the classification accuracy of EQCNNs with three different basis-permuted
amplitude embeddings to the one obtained from a non-equivariant quantum
convolutional neural network (QCNN). Our results show a clear dependence of
classification accuracy on the underlying embedding, especially for initial
training iterations. The improvement in classification accuracy of EQCNN over
non-equivariant QCNN may be present or absent depending on the particular
embedding and dataset used. It is expected that the results of this work can be
useful to the community for a better understanding of the importance of data
embedding choice in the context of geometric quantum machine learning.
