Variational Quantum Circuits (VQCs) have emerged as a promising paradigm for quantum machine learning in the NISQ era. While parameter sharing in VQCs can reduce the parameter space dimensionality and potentially mitigate the barren plateau phenomenon, it introduces a complex trade-off that has been largely overlooked. This paper investigates how parameter sharing, despite creating better global optima with fewer parameters, fundamentally alters the optimization landscape through deceptive gradients -- regions where gradient information exists but systematically misleads optimizers away from global optima. Through systematic experimental analysis, we demonstrate that increasing degrees of parameter sharing generate more complex solution landscapes with heightened gradient magnitudes and measurably higher deceptiveness ratios. Our findings reveal that traditional gradient-based optimizers (Adam, SGD) show progressively degraded convergence as parameter sharing increases, with performance heavily dependent on hyperparameter selection. We introduce a novel gradient deceptiveness detection algorithm and a quantitative framework for measuring optimization difficulty in quantum circuits, establishing that while parameter sharing can improve circuit expressivity by orders of magnitude, this comes at the cost of significantly increased landscape deceptiveness. These insights provide important considerations for quantum circuit design in practical applications, highlighting the fundamental mismatch between classical optimization strategies and quantum parameter landscapes shaped by parameter sharing.

翻译：变分量子电路（VQC）已成为NISQ时代量子机器学习的一种重要范式。尽管VQC中的参数共享能够降低参数空间维度并可能缓解贫瘠高原现象，但它引入了一种复杂的权衡关系，这一点在很大程度上被忽视了。本文研究表明，参数共享虽然能以更少的参数创建更优的全局最优解，但会通过欺骗性梯度——即存在梯度信息但系统性地将优化器引离全局最优解的区域——从根本上改变优化地形。通过系统性实验分析，我们证明参数共享程度的增加会生成更复杂的解空间地形，其梯度幅值更高且欺骗性比率可测量地提升。我们的研究结果表明，传统基于梯度的优化器（Adam、SGD）随着参数共享的增加呈现出逐渐恶化的收敛性，其性能高度依赖于超参数选择。我们提出了一种新颖的梯度欺骗性检测算法和用于量化量子电路优化难度的框架，证实了虽然参数共享能将电路表达能力提升数个数量级，但这会以显著增加地形欺骗性为代价。这些发现为实际应用中的量子电路设计提供了重要参考，揭示了经典优化策略与由参数共享塑造的量子参数地形之间存在根本性不匹配。