  Quantum kernel methods have been widely recognized as one of promising
quantum machine learning algorithms that have potential to achieve quantum
advantages. In this paper, we theoretically characterize the power of noisy
quantum kernels and demonstrate that under global depolarization noise, for
different input data the predictions of the optimal hypothesis inferred by the
noisy quantum kernel approximately concentrate towards some fixed value. In
particular, we depict the convergence rate in terms of the strength of quantum
noise, the size of training samples, the number of qubits, the number of layers
affected by quantum noises, as well as the number of measurement shots. Our
results show that noises may make quantum kernel methods to only have poor
prediction capability, even when the generalization error is small. Thus, we
provide a crucial warning to employ noisy quantum kernel methods for quantum
computation and the theoretical results can also serve as guidelines when
developing practical quantum kernel algorithms for achieving quantum
advantages.
