  Among various quantum machine learning (QML) algorithms, the quantum kernel
method has especially attracted attention due to its compatibility with noisy
intermediate-scale quantum devices and its potential to achieve quantum
advantage. This method performs classification and regression by nonlinearly
mapping data into quantum states in a higher dimensional Hilbert space. Thus
far, the quantum kernel method has been implemented only on qubit-based
systems, but continuous-variable (CV) systems can potentially offer superior
computational power by utilizing its infinite-dimensional Hilbert space. Here,
we demonstrate the implementation of the classification task with the CV
quantum kernel method on a programmable photonic quantum processor. We
experimentally prove that the CV quantum kernel method successfully classifies
several datasets robustly even under the experimental imperfections, with high
accuracies comparable to the classical kernel. This demonstration sheds light
on the utility of CV quantum systems for QML and should stimulate further study
in other CV QML algorithms.
