发表机构
Technische Universität Berlin（柏林工业大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究提出QAOA参数空间的动力学表示框架，揭示其梯度景观的粗组织特性，发现近优解位于特定中间动力学 regime，为解释QAOA跨尺度可训练性提供依据。
AI 中文摘要
表征量子近似优化算法（QAOA）的可训练性，需要理解其梯度景观如何随电路参数和问题规模变化。然而，这些梯度通常用QAOA的原生角度来描述，难以区分参数特定特征与底层电路动力学的更广泛变化。在此，我们基于范数加权层强度和代价-混频器不平衡性，引入QAOA参数空间的动力学表示，将演化的整体尺度与两个生成器的相对贡献分离开来。利用MaxCut的精确态模拟，我们发现梯度景观在这些动力学变量中呈现出粗粒度组织，该组织在电路深度和调度结构变化时仍保持，而更精细的干涉模式则依赖于调度。近优解并不简单地与最大局部梯度重合，而是占据一个独特的中间动力学 regime。均匀调度可恢复该 regime 的大致位置，而非均匀调度则主要重组其精细结构。在所研究的系统规模中，近优解区域在动力学表示中保持扩展，而它们在QAOA原生角度中的预像在更大规模时会被显著压缩。这些结果将有用的QAOA动力学的持续性与它们在原生参数化中的可访问性分离开来，并提供了一个动力学框架，用于解释QAOA在电路和问题尺度上的可训练性。
英文摘要
Characterizing the trainability of the Quantum Approximate Optimization Algorithm (QAOA) requires understanding how its gradient landscape changes across circuit parameters and problem size. Yet these gradients are usually described in terms of the native QAOA angles, making it difficult to distinguish parameter specific features from broader changes in the underlying circuit dynamics. Here we introduce a dynamical representation of the QAOA parameter space based on a norm-weighted layer strength and a cost--mixer imbalance, separating the overall scale of the evolution from the relative contribution of the two generators. Using exact-state simulations of MaxCut, we find that the gradient landscape exhibits a coarse organization in these dynamical variables that persists across changes in circuit depth and schedule structure, while the finer interference pattern remains schedule dependent. Near-optimal solutions do not simply coincide with the largest local gradients, but instead occupy a distinct intermediate dynamical regime. Uniform schedules recover the broad location of this regime, whereas nonuniform schedules mainly reorganize its fine structure. Across the system sizes studied, near-optimal solution regions remain extended in the dynamical representation while their preimages in the native QAOA angles become substantially compressed at larger sizes. These results separate the persistence of useful QAOA dynamics from their accessibility in the native parameterization, and provide a dynamical framework for interpreting QAOA trainability across circuit and problem scales.
Commentsv2: Added a new formula and shortened the manuscript
