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In the application of quantum communication networks, it is an important task to realize the optimal allocation of resources according to the current situation. For example, We need to select the optimal quantum key distribution (QKD) protocol and parameters. Traditionally, the most commonly implemented method is the local search algorithm (LSA), which costs a lot of resources. Here in this work, we propose a machine learning based scheme, in which the regression machine learning is used to simultaneously select the optimal protocol and corresponding parameters. In addition, we make comparisons among a few machine learning models including random forest (RF), K-nearest neighbor (KNN) and logistic regression. Simulation results show that the new scheme takes much less time than the LSA scheme, and the RF achieves the best performance. In addition, through the RF residual analysis, we find that the machine learning scheme has good robustness. In conclusion, this work may play an important role in promoting the practical application of quantum communication networks.
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Keywords:
- quantum communication network /
- quantum key distribution /
- regression machine learning /
- optimal allocation of resources.
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图 1 随机森林回归模型的算法框架.
Figure 1. The algorithm framework of random forest regression model.
图 2 系统参数对随机森林回归模型的重要性.
Figure 2. Importance of system parameters to RF regression model.
图 3 随机森林回归模型的残差图
Figure 3. Residual diagram of RF regression model.
图 4 随机森林回归模型的混淆矩阵
Figure 4. Residual diagram of RF regression model.
表 1 系统参数的特征范围
Table 1. Characteristic range of system parameters.
Y0 ed $ \eta $ N L/km 10–10—10–5 0.00—0.06 0.1—0.9 106—1016 1—600 
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表 2 不同回归模型的评估对比
Table 2. Evaluation and comparison of different regression models.
RF KNN LR MAE 0.002 0.012 0.038 MSE 0.016 0.049 0.131 $ {\mathit{R}}^{2} $ 0.978 0.795 0.397 Accuracy 0.977 0.787 0.365
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表 3 时间资源损耗记录表
Table 3. Time resource wastage table.
机器学习方案 传统方案 Model RF KNN LR LSA Time 1.23 s 2.95 s 5.43 s 24 h以上
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[1] Bennett C H, Brassard G 1984 Proceedings of IEEE International Conference on Computers, System and Signal Processing (Bangalore: IEEE) p175
[2] Busch P, Heinonen T, Lathi P 2007 Phys. Rep. 452 155
Google Scholar
[3] Wootters W K, Zurek W H 1982 Nature. 299 299
Google Scholar
[4] Hwang W Y 2003 Phys. Rev. Lett. 91 057901
Google Scholar
[5] Wang X B 2005 Phys. Rev. Lett. 94 230503
Google Scholar
[6] Lo H K, Ma X F, Chen K 2005 Phys. Rev. Lett. 94 230504
Google Scholar
[7] Makarov V, Hjelme D R 2005 J. Mod. Optic. 52 691
Google Scholar
[8] Qi B, Fung C H F, Lo H K, Ma X F 2007 Quantum. Inf. Comput. 7 73
[9] Lamas L A, Qin L, Gerhardt I, Makarov V, Kurtsiefer C 2009 New. J. Phys. 11 065003
Google Scholar
[10] Lydersen L, Wiechers C, Wittmann C, Elser D, Skaar J 2010 Nat. Photonics. 4 686
Google Scholar
[11] Lo H, Curty M, Qi B 2012 Phys. Rev. Lett. 108 130503
Google Scholar
[12] Braunstein S L, Pirandola S 2012 Phys. Rev. Lett. 108 130502
Google Scholar
[13] Wang X B. 2013 Phys. Rev. A 87 012320
Google Scholar
[14] Rubenok A, Slater J A, Chan P, Lucio M I, Tittel W 2013 Phys. Rev. Lett. 111 130501
Google Scholar
[15] Tang Z Y, Liao Z F, Xu F H, Qi B, Qian L, Lo H K 2014 Phys. Rev. Lett. 112 190503
Google Scholar
[16] Liu Y, Chen T Y, Wang L J, Liang H, Shentu G L, Wang J, Cui K, Yin H L, Liu N L, Li L, Ma X F, Pelc J S, Fejer M M, Peng C Z, Zhang Q, Pan J W 2013 Phys. Rev. Lett. 111 130502
Google Scholar
[17] Zhou X Y, Ding H J, Zhang C H, Wang Q 2020 Opt. Lett. 45 4176
Google Scholar
[18] Liu J Y, Zhou X Y Wang Q 2021 Phys. Rev. A. 103 022602
Google Scholar
[19] Lucamarini M, Yuan Z L, Dynes J F, Shields A J 2018 Nature 557 400
Google Scholar
[20] Takeoka M, Guha S. 2014 Nat. Commun. 5 5235
Google Scholar
[21] Pirandola S, Laurenza R, Ottaviani C 2017 Nat. Commun. 8 15043
Google Scholar
[22] Wang X B, Yu Z W, Hu X L 2018 Phys. Rev. A. 98 062323
Google Scholar
[23] Pittaluga M, Minder M, Lucamarini M, Sanzaro M, Woodward R I, Li M J, Yuan Z L, Shields A J 2021 Nat. Photonics. 15 530
Google Scholar
[24] Wang S, Yin Z Q, Chen W, He D Y, Song X T, Li H W, Zhang L J, Zhou Z, Guo G C, Han Z F 2022 Nat. Photonics. 16 154
Google Scholar
[25] Ren Z A, Chen Y P, Liu J Y, Ding H J, Wang Q 2021 IEEE Commun. Lett. 25 3
Google Scholar
[26] Fan-Yuan G J, Lu F Y, Wang S, Yin Z Q, He D Y, Zhou Z, Teng J, Chen W, Guo G C, Han Z F 2021 Photon. Res. 9 1881
Google Scholar
[27] Ding H J, Liu J Y, Zhang C M, Wang Q 2020 Quantum. Inf. Comput. 19 2548
Google Scholar
[28] Xu F, Xu H, Lo H K. 2014 Phys. Rev. A. 89 052333
Google Scholar
[29] Liu J Y, Ding H J, Zhang C M, Xie S P, Wang Q 2019 Phys. Rev. Appl. 12 014059
Google Scholar
[30] Yang M, Ren C L, Ma Y C, Xiao Y, Ye X J, Song L L, Xun J S, Yung M H, Li C F, Guo G C 2019 Phys. Rev. Lett. 123 190401
Google Scholar
[31] Zhou Y H, Yu Z W, Wang X B. 2016 Phys. Rev. A. 93 042324
Google Scholar
[32] Zhang C H, Zhang C M, Wang Q. 2019 Opt. Lett. 44 1468
Google Scholar
[33] Breiman L 2001 J. Clin. Microbiol. 45 5
Google Scholar
[34] Cover T M, Hart P E 1967 IEEE Trans. Inf. Theory 13 21
Google Scholar
[35] Cox D R 1958 J. R. Stat. Soc. B 20 215
Google Scholar
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