Quantum neural networks (QNNs) and quantum kernels stand as prominent figures in the realm of quantum machine learning, poised to leverage the nascent capabilities of near-term quantum computers to surmount classical machine learning challenges. Nonetheless, the training efficiency challenge poses a limitation on both QNNs and quantum kernels, curbing their efficacy when applied to extensive datasets. To confront this concern, we present a unified approach: coreset selection, aimed at expediting the training of QNNs and quantum kernels by distilling a judicious subset from the original training dataset. Furthermore, we analyze the generalization error bounds of QNNs and quantum kernels when trained on such coresets, unveiling the comparable performance with those training on the complete original dataset. Through systematic numerical simulations, we illuminate the potential of coreset selection in expediting tasks encompassing synthetic data classification, identification of quantum correlations, and quantum compiling. Our work offers a useful way to improve diverse quantum machine learning models with a theoretical guarantee while reducing the training cost.

翻译：量子神经网络（QNNs）与量子核作为量子机器学习领域的两大核心模型，有望利用近期量子计算机的初步能力来攻克经典机器学习难题。然而，训练效率问题对QNNs和量子核均构成限制，削弱了它们在大规模数据集上的应用效果。为此，我们提出统一方法：通过从原始训练数据集中提取精炼子集的核心集选取，加速QNNs与量子核的训练进程。进一步，我们分析了基于此类核心集训练的QNNs与量子核的泛化误差界，揭示了其与完整原始数据集训练方案相当的性能表现。通过系统性数值模拟，我们阐明了核心集选取在加速合成数据分类、量子关联识别及量子编译等任务中的潜力。本研究为在降低训练成本的同时提升多种量子机器学习模型性能提供了兼具理论保障的有效途径。