Role of data embedding in equivariant quantum convolutional neural networks

Geometric deep learning is a scenario in which the symmetries of a dataset are used to constrain the trainable parameter space of a neural network, thus improving trainability and generalization. This idea has been incorporated into quantum domain, to build equivariant quantum neural networks (EQNNs).

We explore the connection between the data embedding method and the resulting representation of a symmetry group, and analyze how changing the representation affects the architecture and expressibility of an equivariant quantum convolutional neural network (EQCNN). We use prototypical datasets e.g. MNIST and Cifar10, as well as dataset of connected and non-connected graphs. Two embedding methods are used, namely Amplitude Embedding and Qubit Embedding. Our results show a clear dependence of classification performance on the underlying embedding. The improvement in accuracy of EQCNN over non-equivariant QCNN may be present or absent depending on the particular embedding and dataset used.

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https://us06web.zoom.us/j/98286706234?pwd=bm1JUFVYcTJkaVl1VU55L0FiWDRIUT09