Geometric Algebra Quantum Convolutional Neural Network: A model using geometric (Clifford) algebras and quantum computing [Hypercomplex Signal and Image Processing]

Abstract

A hybrid model called the geometric (Clifford) quanvolutional neural network ( GQNN ) that merges elements of geometric (Clifford) convolutional neural networks (GCNNs) and variational quantum circuits (VQCs) is presented. In this model, a randomized quantum convolution operation is applied to the input image, giving as a result four output channels, which are treated as a single entity (quaternion image) by the subsequent quaternion layers. This approach is extended to Clifford algebras by choosing the number of qubits of the quantum circuit according to the dimension of the Clifford algebra so that the resulting output channels are regarded as the components of a multivector image to be further processed by Clifford layers.