自适应差分进化与多起点搜索用于含噪QAOA优化
Adaptive Differential Evolution and Multistart Search for Noisy QAOA Optimization
- VSB–Technical University of Ostrava（俄斯特拉发科技大学）
- IT4Innovations National Supercomputing Center, VSB–Technical University of Ostrava（俄斯特拉发科技大学 IT4创新国家超级计算中心）
- Marine Research Institute, Klaipeda University（克莱佩达大学海洋研究所）
- Indian Statistical Institute（印度统计研究所）
- Università dell’Aquila（阿奎拉大学）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
本研究在含噪QAOA优化中基准测试十种优化器，发现自适应差分进化方法在噪声下更具竞争力，且优化器选择取决于景观、噪声和最终点识别。
AI中文摘要：
我们在$N=12$、$p=3$和$D=6$的条件下，对固定低深度量子近似优化算法（QAOA）拟设的经典优化在四个代价哈密顿量族上进行了基准测试。在10,000和30,000次函数评估（FEs）的共同上限下，对十种优化器进行了25次独立运行的比较，首先使用精确态矢量目标，然后使用两种加性观测噪声水平。精确目标有利于多起点BFGS和多起点CMA-ES。在噪声反馈下，自适应群体方法变得更具竞争力，但排名取决于性能是通过访问的最佳精确点还是从噪声观测中选择的点来衡量。对所有每个家族中三个预筛选实例的定向扩展证实了这种机制变化，同时表明命名的自适应差分进化（DE）获胜者依赖于实例：jSO-lite在低噪声预言机搜索中领先，iL-SHADE在高噪声预言机搜索中领先，而L-SRTDE在相等实例摘要中的高噪声选定解决方案中领先。自举分析量化了不可忽略的高噪声搜索-选择差距，而回顾性固定预算验证代理表明，预留少量测量预算用于最终重新评估，在30,000次FEs下提高了所有十种方法的选定质量。一项补充的结构感知研究进一步表明，在这些条件下，QAOA跨深度限制和连续盆地细化比独立的蒙特卡洛树搜索选择更有用。总体而言，优化器的选择共同取决于景观结构、观测噪声和最终点识别。
英文摘要：
We benchmark classical optimization of a fixed low-depth Quantum Approximate Optimization Algorithm (QAOA) ansatz across four cost-Hamiltonian families at $N=12$, $p=3$, and $D=6$. Ten optimizers are compared over 25 independent runs under common ceilings of 10\,000 and 30\,000 function evaluations (FEs), first with exact statevector objectives and then with two additive observation-noise levels. Exact objectives favor multistart BFGS and multistart CMA-ES. Under noisy feedback, adaptive population methods become more competitive, but the ranking depends on whether performance is measured by the best exact point visited or by the point selected from noisy observations. A targeted extension over all three pre-screened instances per family confirms this regime change while showing that named adaptive-DE winners are instance dependent: jSO-lite leads low-noise oracle search, iL-SHADE high-noise oracle search, and L-SRTDE high-noise selected solutions in the equal-instance summaries. Bootstrap analysis quantifies a non-negligible high-noise search--selection gap, and a retrospective fixed-budget verification proxy shows that reserving a small measurement budget for final re-evaluation improves selected quality across all ten methods at 30\,000 FEs. A supplementary structure-aware study further shows that QAOA cross-depth restriction and continuous basin refinement are more useful in these conditions than standalone Monte Carlo tree-search selection. Overall, optimizer choice depends jointly on landscape structure, observation noise, and final-point identification.
