Towards understanding the power of quantum kernels in the NISQ era

TL;DR

This paper investigates whether quantum kernels maintain their advantage in noisy NISQ devices, revealing limitations under realistic conditions and proposing methods to preserve quantum advantage.

Contribution

The study provides the first theoretical analysis of quantum kernel performance under NISQ noise, showing limitations and proposing indefinite kernel learning to retain quantum advantages.

Findings

Quantum kernel advantage diminishes with large datasets and high noise.

Theoretical proof of quantum advantage loss in NISQ settings.

Numerical simulations support the theoretical results.

Abstract

A key problem in the field of quantum computing is understanding whether quantum machine learning (QML) models implemented on noisy intermediate-scale quantum (NISQ) machines can achieve quantum advantages. Recently, Huang et al. [Nat Commun 12, 2631] partially answered this question by the lens of quantum kernel learning. Namely, they exhibited that quantum kernels can learn specific datasets with lower generalization error over the optimal classical kernel methods. However, most of their results are established on the ideal setting and ignore the caveats of near-term quantum machines. To this end, a crucial open question is: does the power of quantum kernels still hold under the NISQ setting? In this study, we fill this knowledge gap by exploiting the power of quantum kernels when the quantum system noise and sample error are considered. Concretely, we first prove that the advantage of quantum kernels is vanished for large size of datasets, few number of measurements, and large system noise. With the aim of preserving the superiority of quantum kernels in the NISQ era, we further devise an effective method via indefinite kernel learning. Numerical simulations accord with our theoretical results. Our work provides theoretical guidance of exploring advanced quantum kernels to attain quantum advantages on NISQ devices.