Kernel methods map data into high-dimensional spaces, enabling linear algorithms to learn nonlinear functions without explicitly storing the feature vectors. Quantum kernel methods promise efficient learning by encoding feature maps into exponentially large Hilbert spaces inherent in quantum systems. In this work we implement quantum kernels on a 10-qubit star-topology register in a nuclear magnetic resonance (NMR) platform. We experimentally encode classical data in the evolution of multiple quantum coherence orders using data-dependent unitary transformations and then demonstrate one-dimensional regression and two-dimensional classification tasks. By extending the register to a double-layered star configuration, we propose an extended quantum kernel to handle non-parametrized operator inputs. By numerically simulating the extended quantum kernel, we show classification of entangling and nonentangling unitaries. These results confirm that quantum kernels exhibit strong capabilities in classical as well as quantum machine learning tasks.

翻译：核方法将数据映射到高维空间，使得线性算法能够学习非线性函数而无需显式存储特征向量。量子核方法通过将特征映射编码到量子系统固有的指数级大希尔伯特空间中，有望实现高效学习。本研究在核磁共振平台的10量子比特星型拓扑寄存器上实现了量子核。我们通过数据相关的幺正变换将经典数据实验性地编码到多量子相干阶的演化中，进而演示了一维回归和二维分类任务。通过将寄存器扩展为双层星型构型，我们提出了一种扩展量子核以处理非参数化算子输入。通过对扩展量子核进行数值模拟，我们展示了纠缠与非纠缠幺正算子的分类能力。这些结果证实了量子核在经典及量子机器学习任务中均表现出强大能力。