Learning Fourier series with parametrized quantum circuits

TL;DR

This paper compares various parametrized quantum circuit architectures in learning Fourier series, introduces a data reupload structure for dissipative quantum neural networks, and offers guidelines for designing efficient PQCs.

Contribution

It provides a comparative analysis of PQC ansätze for Fourier series learning and proposes a novel data reupload method for dissipative quantum neural networks.

Findings

Certain PQC architectures outperform others in learning Fourier series.

Data reupload enhances the capability of dissipative quantum neural networks.

Guidelines for designing efficient PQCs are established.

Abstract

Variational quantum algorithms (VQAs) and their applications in the field of quantum machine learning through parametrized quantum circuits (PQCs) are thought to be one major way of leveraging noisy intermediate-scale quantum computing devices. However, differences in the performance of certain VQA architectures are often unclear since established best practices, as well as detailed studies, are missing. In this paper, we build upon the work by Schuld et al. [Phys. Rev. A 103, 032430 (2021)] and Vidal et al. [Front. Phys. 8, 297 (2020)] by comparing how well popular ans\"atze for PQCs learn different one-dimensional truncated Fourier series. We also examine dissipative quantum neural networks (dQNN) as introduced by Beer et al. [Nat. Commun. 11, 808 (2020)] and propose a data reupload structure for dQNNs to increase their capability for this regression task. By comparing the results for different PQC architectures, we can provide guidelines for designing efficient PQCs.