标题： 关于量子算符值核函数 显示英文标题

标题： Towards Quantum Operator-Valued Kernels

摘要： 量子核是利用量子力学原理构建的再生核函数，并且研究它们的目的是超越其经典的对应物。 最近研究表明，当在经典数据上进行学习时，量子核可能无法提供加速，这使人们对量子核机器的热情有所降温。 然而，该领域的大多数研究都集中在标量值核上，这些核用于标准分类或回归设置的经典核方法效率很高，因此量子核几乎没有改进的空间。 本文认为，量子核研究应集中于更具表达能力的核类。 我们基于算符值核的最新进展，提出了研究量子核的指导方针。 这将有助于设计新一代的量子核机器，并充分挖掘其潜力。 显示英文摘要

摘要： Quantum kernels are reproducing kernel functions built using quantum-mechanical principles and are studied with the aim of outperforming their classical counterparts. The enthusiasm for quantum kernel machines has been tempered by recent studies that have suggested that quantum kernels could not offer speed-ups when learning on classical data. However, most of the research in this area has been devoted to scalar-valued kernels in standard classification or regression settings for which classical kernel methods are efficient and effective, leaving very little room for improvement with quantum kernels. This position paper argues that quantum kernel research should focus on more expressive kernel classes. We build upon recent advances in operator-valued kernels, and propose guidelines for investigating quantum kernels. This should help to design a new generation of quantum kernel machines and fully explore their potentials.