Clifford Algebras, Quantum Neural Networks and Generalized Quantum Fourier Transform

TL;DR

This paper introduces quantum neural network models based on Clifford algebras, enabling geometric data analysis and entanglement, along with a generalized quantum Fourier transform for quantum machine learning.

Contribution

It presents a novel framework combining Clifford algebras with quantum neural networks and introduces a parameterized generalization of the quantum Fourier transform.

Findings

Clifford algebra-based models capture geometric features and produce entanglement.

A generalized quantum Fourier transform with additional parameters is developed.

Properties of the generalized transform are theoretically proven.

Abstract

We propose models of quantum neural networks through Clifford algebras, which are capable of capturing geometric features of systems and to produce entanglement. Due to their representations in terms of Pauli matrices, the Clifford algebras are the natural framework for multidimensional data analysis in a quantum setting. 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. Furthermore, some interesting properties of the generalized quantum Fourier transform have been proved.