从可训练性诊断到优化声明：变分量子优化中的边界与控制
From Trainability Diagnostics to Optimization Claims: Boundaries and Controls in Variational Quantum Optimization
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中文总结 AI 辅助
本研究揭示变分量子优化中可训练性与优化成效的差距，提出步长级诊断并证明原始梯度在固定范数下最优，强调优化收益需匹配控制验证。
中文摘要 AI 辅助
贫瘠高原诊断用于表征梯度信号在训练过程中是否仍然可用，但信号的存续并不必然转化为成功的优化。我们在优化器步长层面研究这种可训练性与优化之间的差距。将系数加权的哈密顿量项梯度视为类任务组件，我们引入了步长级诊断，并推导出带符号的逐项组织、方向活动性与一阶下降之间的精确桥梁。将该桥梁分解为标准一阶几何结构表明，表面上的组织-活动性因子并非独立的优化轴，并且在固定状态和更新范数下，原始梯度使求和目标的一阶下降最大化。我们比较了普通梯度下降、确定性哈密顿量项PCGrad变体以及探针门控的LSO-PCGrad在横场伊辛模型实例上的表现，这些实例采用硬件高效和哈密顿量变分拟设，并配有更新范数和探针预算的匹配控制。盲目投影可以改善组织诊断，但同时会恶化最终能量和一阶可预测性。在基于标准一阶几何结构进行条件化后，残差项空间组成与实现下降之间没有可复现的实质性增量关联，而优化器相对更新范数在某些设置中显示出正向实质性关联，但缺乏跨体制的可复现性。匹配控制未提供可归因于投影方向的最终能量改善，且LSO-PCGrad的改进更一致地归因于基于探针的搜索和步长范数自适应，而非哈密顿量项投影本身。这些结果表明，梯度结构诊断可以表征可训练性和更新几何结构，但不能作为优化收益的独立证据，优化收益需要匹配更新范数和搜索预算的控制。
英文摘要
Barren plateau diagnostics characterize whether gradient signal remains available for training, but surviving signal need not translate into successful optimization. We study this trainability--optimization gap at the level of optimizer steps. Treating coefficient-weighted Hamiltonian-term gradients as task-like components, we introduce step-level diagnostics and derive an exact bridge between signed termwise organization, directional activity, and first-order descent. Resolving this bridge into standard first-order geometry shows that the apparent organization--activity factors are not independent optimization axes and that, at fixed state and update norm, the raw gradient maximizes first-order descent of the summed objective. We compare vanilla gradient descent, a deterministic Hamiltonian-term PCGrad variant, and probe-gated LSO-PCGrad on transverse-field Ising model instances with hardware-efficient and Hamiltonian variational ansatzes, together with matched controls for update norm and probe budget. Blind projection can improve an organization diagnostic while worsening final energy and first-order predictability. After conditioning on standard first-order geometry, residual term-space composition shows no reproducible material incremental association with realized descent, while optimizer-relative update norm shows positive material associations in some settings without cross-regime reproducibility. Matched controls provide no resolved final-energy benefit attributable to the projected direction, and the improvement of LSO-PCGrad is more consistent with probe-based search and step-norm adaptation than with Hamiltonian-term projection itself. These results show that gradient-structure diagnostics can characterize trainability and update geometry without serving as standalone evidence of optimization benefit, which requires controls matched on update norm and search budget.
