Towards Quantum Operator-Valued Kernels
This is an incremental position paper aimed at researchers in quantum machine learning, suggesting a new direction to explore quantum kernels' potential.
The paper argues that quantum kernel research should shift focus from scalar-valued kernels to more expressive operator-valued kernels to overcome limitations in outperforming classical methods on classical data, proposing guidelines for developing new quantum kernel machines.
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.