Clifford Algebras, Quantum Neural Networks and Generalized Quantum Fourier Transform

2022/06/03 by Marco A. S. Trindade, Trindade, Marco A. S., Vinicius N. L. Rocha +3 · 1 citation
Computer Science · Mathematics · #FOS: Physical sciences #Mathematical Analysis and Transform Methods #Mathematical Physics (math-ph) #Quantum Computing Algorithms and Architecture #Quantum Physics (quant-ph)

paper · pdf · doi:10.48550/arxiv.2206.01808

openalex publication_date 2022/06/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Cited by

• FoGE: Fock Space inspired encoding for graph prompting

Related

• Quantum Circuit C^*-algebra Net
• Quantum Algorithms for Unsupervised Machine Learning and Neural Networks
• A quantum neural network framework for scalable quantum circuit approximation of unitary matrices
• Topographic Representation for Quantum Machine Learning
• Quantum activation functions for quantum neural networks