Variational Quantum Algorithms (VQAs) have emerged as pivotal strategies for
attaining quantum advantages in diverse scientific and technological domains,
notably within Quantum Neural Networks. However, despite their potential, VQAs
encounter significant obstacles, chief among them being the gradient vanishing
problem, commonly referred to as barren plateaus. In this study, we unveil a
direct correlation between the dimension of qudits and the occurrence of barren
plateaus, a connection previously overlooked. 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. Additionally, despite the proposition of
various error mitigation techniques, our results call for further scrutiny
about their efficacy in the context of VQAs with qudits.

通过细致的分析，本研究揭示了多维量子比特的维度与贫瘠平台之间的直接关联，并通过数值结果展示了多维量子比特对贫瘠平台的影响，同时对基于多维量子比特的 VQA 的误差缓解技术的功效提出了进一步的审视。