Fourier series weight in quantum machine learning

TL;DR

This paper investigates the influence of Fourier series on quantum machine learning models, proposing new models and methods to analyze and utilize Fourier coefficients within quantum algorithms.

Contribution

It introduces quantum machine learning models leveraging Hamiltonian encoding and proposes a novel approach to estimate Fourier coefficients using quantum techniques.

Findings

Demonstrated the effectiveness of Fourier-based quantum models

Developed a method for approximate Fourier coefficient determination

Validated models using Pennylane framework

Abstract

In this work, we aim to confirm the impact of the Fourier series on the quantum machine learning model. We will propose models, tests, and demonstrations to achieve this objective. We designed a quantum machine learning leveraged on the Hamiltonian encoding. With a subtle change, we performed the trigonometric interpolation, binary and multiclass classifier, and a quantum signal processing application. We also proposed a block diagram of determining approximately the Fourier coefficient based on quantum machine learning. We performed and tested all the proposed models using the Pennylane framework.