Quantum algorithms are emerging tools in the design of functional materials due to their powerful solution space search capability. How to balance the high price of quantum computing resources and the growing computing needs has become an urgent problem to be solved. We propose a novel optimization strategy based on an active learning scheme that combines the Quantum-inspired Genetic Algorithm (QGA) with machine learning surrogate model regression. Using Random Forests as the surrogate model circumvents the time-consuming physical modeling or experiments, thereby improving the optimization efficiency. QGA, a genetic algorithm embedded with quantum mechanics, combines the advantages of quantum computing and genetic algorithms, enabling faster and more robust convergence to the optimum. Using the design of planar multilayer photonic structures for transparent radiative cooling as a testbed, we show superiority of our algorithm over the classical genetic algorithm (CGA). Additionally, we show the precision advantage of the Random Forest (RF) model as a flexible surrogate model, which relaxes the constraints on the type of surrogate model that can be used in other quantum computing optimization algorithms (e.g., quantum annealing needs Ising model as a surrogate).

量子算法因其强大的解决方案空间搜索能力而成为功能材料设计中的新兴工具。如何平衡量子计算资源的高价格和不断增长的计算需求，成为亟待解决的问题。我们提出了一种基于主动学习方案的新型优化策略，该方案将量子启发遗传算法 （QGA） 与机器学习代理模型回归相结合。使用随机森林作为代理模型可以避免耗时的物理建模或实验，从而提高优化效率。QGA 是一种嵌入量子力学的遗传算法，结合了量子计算和遗传算法的优势，能够更快、更稳健地收敛到最佳状态。使用用于透明辐射冷却的平面多层光子结构设计作为测试台，我们展示了我们的算法优于经典遗传算法 （CGA）。此外，我们还展示了随机森林 （RF） 模型作为灵活代理模型的精度优势，它放宽了对可用于其他量子计算优化算法的代理模型类型的限制（例如，量子退火需要 Ising 模型作为代理）。