Towards understanding the power of quantum kernels in the NISQ era

Xinbiao Wang; Yuxuan Du; Yong Luo; Dacheng Tao

doi:10.22331/q-2021-08-30-531

Towards understanding the power of quantum kernels in the NISQ era

Xinbiao Wang^1,2, Yuxuan Du², Yong Luo¹, and Dacheng Tao²

¹Institute of Artificial Intelligence, School of Computer Science, Wuhan University
²JD Explore Academy

Published:	2021-08-30, volume 5, page 531
Eprint:	arXiv:2103.16774v2
Doi:	https://doi.org/10.22331/q-2021-08-30-531
Citation:	Quantum 5, 531 (2021).

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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.

Featured image: The paradigm of classical and quantum kernels. Both of the classical and quantum kernels embed the data points from data space $\mathcal{X}$ into a high-dimensional space, and then compute the kernel as the inner product of feature maps. The quantum kernel leverages variational quantum circuits to achieve this goal, as indicated by the blue color. In the ideal scenario, quantum kernels promise better performance over classical kernels for certain datasets.

► BibTeX data

@article{Wang2021towards,
  doi = {10.22331/q-2021-08-30-531},
  url = {https://doi.org/10.22331/q-2021-08-30-531},
  title = {Towards understanding the power of quantum kernels in the {NISQ} era},
  author = {Wang, Xinbiao and Du, Yuxuan and Luo, Yong and Tao, Dacheng},
  journal = {{Quantum}},
  issn = {2521-327X},
  publisher = {{Verein zur F{\"{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}},
  volume = {5},
  pages = {531},
  month = aug,
  year = {2021}
}

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