Barren plateaus are amplified by the dimension of qudits

TL;DR

This paper investigates how the dimensionality of qudits influences the emergence of barren plateaus in Variational Quantum Algorithms, revealing that higher dimensions can amplify the vanishing gradient problem and challenging existing mitigation strategies.

Contribution

The study provides a detailed analysis and numerical evidence showing the impact of qudit dimensionality on barren plateaus in VQAs, highlighting the need for new approaches.

Findings

Qudit dimensionality affects barren plateau severity

Numerical results demonstrate increased vanishing gradients with higher dimensions

Current error mitigation techniques may be insufficient for high-dimensional qudits

Abstract

Variational Quantum Algorithms (VQAs) have emerged as pivotal strategies for attaining quantum advantage in diverse scientific and technological domains, notably within Quantum Neural Networks. However, despite their potential, VQAs encounter significant obstacles, chief among them being the vanishing gradient problem, commonly referred to as barren plateaus. In this article, through meticulous analysis, we demonstrate that existing literature implicitly suggests the intrinsic influence of qudit dimensionality on barren plateaus. To instantiate these findings, we present numerical results that exemplify the impact of qudit dimensionality on barren plateaus. Therefore, despite the proposition of various error mitigation techniques, our results call for further scrutiny about their efficacy in the context of VQAs with qudits.