全局进化搜索何时对变分量子算法有用？一项景观优先的研究
When is global evolutionary search useful for variational quantum algorithms? A landscape-first study
- VSB - Technical University of Ostrava（俄斯特拉发理工大学）
- IT4Innovations National Supercomputing Center, VSB - Technical University of Ostrava（俄斯特拉发理工大学 IT4创新国家超算中心）
- Klaipeda University（克莱佩达大学）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
本研究通过景观优先实验，发现参数复用和代价项竞争使局部搜索在QAOA中失效，自适应差分进化在困难实例上优于多起点局部搜索，并提出预测全局搜索效用的景观分数。
AI中文摘要：
变分量子算法将态制备重新表述为经典非凸优化问题，但通常不清楚何时多起点局部搜索足够，以及何时基于种群的全局搜索能证明其评估成本合理。采用景观优先的设计，受控的QAOA实验识别出使局部搜索不可靠的两种机制：跨电路层的参数复用以及2-局部与3-局部代价项之间的竞争。仅增加QAOA深度并不能复现这一效应。我们在八个未见过的自旋玻璃、全新的$N=10$和$N=12$实例以及标准MaxCut、横向场伊辛和海森堡模型上测试了这些机制。在所有八个未见过的自旋玻璃上，自适应差分进化（DE）在两种困难构造上均比多起点BFGS和多起点Powell实现了更低的误差中位数，而独立深度对照组则不然。参数复用效应在两种规模的MaxCut上均得到转移，而标准VQE模型仍有利于局部搜索。一个预基准的景观分数，结合随机起点局部结果和一维参数切片，在评估新优化器之前根据确认数据固定。它预测自适应DE在50个新的量子目标上以80%至86%的条件级准确率，超过多起点BFGS超过一个谱范围百分点。全局搜索效用的最清晰指标是局部搜索经常陷入较差的盆地，而非电路深度或曲率各向异性。这些发现促使我们思考，当存在稳健的全局搜索时，是否可以用更困难的经典优化来换取量子电路复杂度。
英文摘要：
Variational quantum algorithms recast state preparation as classical nonconvex optimization, but it is often unclear when multistart local search suffices and when population-based global search justifies its evaluation cost. Using a landscape-first design, controlled QAOA experiments identify two mechanisms making local search unreliable: parameter reuse across circuit layers and competition between 2-local and 3-local cost terms. Increasing QAOA depth alone does not replicate this effect. We test these mechanisms across eight unseen spin glasses, fresh $N=10$ and $N=12$ instances, and standard MaxCut, transverse-field Ising, and Heisenberg models. On all eight unseen spin glasses, adaptive differential evolution (DE) achieves lower median error than both multistart BFGS and multistart Powell on the two difficult constructions, whereas the independent-depth control does not. The parameter-reuse effect transfers to MaxCut at both sizes, while standard VQE models remain favorable to local search. A pre-benchmark landscape score combining random-start local outcomes and 1D parameter slices is fixed from confirmation data before evaluating new optimizers. It predicts whether adaptive DE outperforms multistart BFGS by over one spectral-range percentage point on 50 new quantum objectives with 80--86% condition-level accuracy. The clearest indicator of global-search utility is that local search frequently traps in inferior basins, rather than circuit depth or curvature anisotropy. The findings motivate whether quantum circuit complexity can be traded for harder classical optimization when robust global search is available.
