Selection and Optimization of Hyperparameters in Warm-Started Quantum Optimization for the MaxCut Problem

Round 1

Reviewer 1 Report

In this work the authors proposed some methods to address the problem of hyperparameter selection in WS-QAOA for the maximum cut problem， including regularization parameter, optimization strategies, and objective functions. The manuscript is well written and clear. The author also provides convincing numerical results to demonstrate the effectiveness of their methods. I could recommend the publication of this manuscript in Electronics after several revisions as suggested below.

1) The authors do not give any indication of the effectiveness of their method as the graph size grows, which is an important factor that must be considered.

2) When the authors introduce quantum computing in the ``Introduction'' section, it may raise interest to a broader readership if some references about the development of different quantum computing systems are provided, such as

(i) Krantz P, Kjaergaard M, Yan F, et al. A quantum engineer's guide to superconducting qubits. Appl. Phys. Rev., 2019, 6: 021318
(ii) Huang, He-Liang, et al. Superconducting quantum computing: a review. Science China Information Sciences 63, 180501 (2020).
(iii) Blatt, Rainer, and Christian F. Roos. Quantum simulations with trapped ions. Nature Physics 8.4 (2012): 277-284.
(iv) Bruzewicz, Colin D., et al. Trapped-ion quantum computing: Progress and challenges. Applied Physics Reviews 6.2 (2019): 021314.

Also some theories and experiments related to quantum artificial intelligence are necessary to be mentioned, such as 

(i) Havlíček, V., Córcoles, A. D., Temme, K., Harrow, A. W., Kandala, A., Chow, J. M., & Gambetta, J. M. (2019). Supervised learning with quantum-enhanced feature spaces. Nature, 567(7747), 209-212.
(ii) Huang, H. L., Du, Y., Gong, M., Zhao, Y., Wu, Y., Wang, C., ... & Pan, J. W. (2021). Experimental quantum generative adversarial networks for image generation. Physical Review Applied, 16(2), 024051.
(iii) Harrigan, M. P., Sung, K. J., Neeley, M., Satzinger, K. J., Arute, F., Arya, K., ... & Babbush, R. (2021). Quantum approximate optimization of non-planar graph problems on a planar superconducting processor. Nature Physics, 17(3), 332-336.
(iv)Liu, J., Lim, K. H., Wood, K. L., Huang, W., Guo, C., & Huang, H. L. (2021). Hybrid quantum-classical convolutional neural networks. Science China Physics, Mechanics & Astronomy, 64, 290311 (2021).
(v)Cong, I., Choi, S., & Lukin, M. D. (2019). Quantum convolutional neural networks. Nature Physics, 15(12), 1273-1278.

Author Response

Thank you very much for the review. Please find a point-by-point list of how we adapted the manuscript regarding your suggestions attached.

Author Response File: Author Response.pdf

Reviewer 2 Report

The authors consider a very important method of warm-started quantum optimization (WS-QAOA) for the MaxCut Problem with particular emphasis on the selection of hyperparameters, which is especially important in the context of limited sizes of executable quantum circuits. In addition, the Goemans-Williamson algorithm for precomputations was used. The analysis of how the regularization parameter tunes the bias of the warm-started quantum algorithm towards the precomputed solution was correctly performed. Three optimization strategies were compared, and finally evaluate five objective functions for the classical optimization. The presented results justify the conclusions drawn. There are also minor shortcomings in the work:
1. The Related Work section appears at the end of the article, and it is customary to familiarize the Reader with other publications on the subject matter at the beginning, after the Introduction.
2. How large instances of the MaxCut optimization problem were solved? Figure 4 suggests that three qubits are considered. How will it be for larger instances? First of all, how to enable CNOT gates for 4, 5 and more qubits?
3. How to interpret the determined solution, eg 001?
In addition, it should be emphasized that the article is well written, and the shortcomings noticed can be corrected by the Authors without the need to re-review.

Author Response

Thank you very much for the review. Please find a point-by-point list of how we adapted the manuscript regarding your suggestions attached.

Author Response File: Author Response.pdf