Training quantum embedding kernels on near-term quantum computers

Kernel methods are a cornerstone of classical machine learning. The idea using quantum computers to compute kernels has recently attracted attention. Quantum embedding (QEKs), constructed by data into the Hilbert space computer, particular kernel technique that is particularly suitable for noisy intermediate-scale devices. Unfortunately, face three major problems: Constructing matrix quadratic computational complexity in number training samples, choosing right function nontrivial, and effects noise unknown. In this work, we addressed latter two. particular, introduced notion trainable QEKs, based on model optimization methods. To train parameters QEK, proposed use kernel-target alignment. We verified feasibility method, showed our experimental setup could reduce error significantly. Furthermore, investigated device finite sampling noise, evaluated various mitigation techniques numerically hardware. took best performing strategy it from real processing unit. found demonstrated an increased quality.