🤖 AI Summary
This work addresses the barren plateau problem—gradient vanishing—in variational quantum algorithms (VQAs) arising from high-dimensional qudits. Through rigorous theoretical analysis and numerical simulations, we establish for the first time that qudit dimensionality acts as a critical amplification factor: gradient variance decays exponentially with increasing qudit dimension, severely exacerbating trainability challenges. This finding fundamentally challenges the implicit assumption underlying existing error-mitigation techniques—that their efficacy extends to high-dimensional qudit settings. Leveraging the statistical properties of gradients in parameterized quantum circuits, we develop a quantitative analytical model characterizing this dimensional dependence. Our framework provides both foundational theoretical guidance and practical caution for the design, optimization, and error mitigation of qudit-based VQAs. The results underscore the necessity of dimension-aware ansatz construction and gradient estimation strategies, particularly as qudit systems gain prominence in near-term quantum hardware.
📝 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.