Clifford Algebras, Quantum Neural Networks and Generalized Quantum Fourier Transform

Abstract

We propose models of quantum perceptrons and quantum neural networks based on Clifford algebras. These models are capable to capture geometric features of classical and quantum data as well as producing data entanglement. Due to their representations in terms of Pauli matrices, the Clifford algebras seem to be a natural framework for multidimensional data analysis in a quantum setting. In this context, the implementation of activation functions, and unitary learning rules are discussed. In this scheme, we also provide an algebraic generalization of the quantum Fourier transform containing additional parameters that allow performing quantum machine learning based on variational algorithms. Furthermore, some interesting properties of the generalized quantum Fourier transform have been proved.