Noise-enhanced quantum kernels on analog quantum computers for estimating the non-Markovianity from sparse temporal data

The quantum kernel method, a promising quantum machine learning algorithm, possesses substantial potential for demonstrating a quantum advantage. While most quantum kernels are constructed in the context of gate-based quantum circuits, inspired by the idea of analog quantum computing with Rydberg atoms, here we construct an analog quantum kernel and a hybrid quantum kernel, and demonstrate their competitiveness against other standard baselines in the physically motivated task of estimating the non-Markovianity from sparse temporal data. Crucially, we report a counterintuitive phenomenon where the operational noise can enhance their performance when interatomic distances are appropriately tuned. Our analysis reveals that the noise can help the analog and hybrid quantum models keep the test MSE under control despite closely fitting the training data, yielding models with higher complexity and a training MSE lower than or comparable to their ideal counterparts. Our results not only reveal that the noise can counterintuitively benefit analog and hybrid quantum kernel methods, but also provide an efficient route to estimating the non-Markovianity with alleviated experimental demands.