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The parameter configuration of quantum key distribution (QKD) has a great effect on the communication effect, and in the practical application of the QKD network in the future, it is necessary to quickly realize the parameter configuration optimization of the asymmetric channel measurement-device-independent QKD according to the communication state, so as to ensure the good communication effect of the mobile users, which is an inevitable requirement for real-time quantum communication. Aiming at the problem that the traditional QKD parameter optimization configuration scheme cannot guarantee real-time, in this paper we propose to apply the supervised machine learning algorithm to the QKD parameter optimization configuration, and predict the optimal parameters of TF-QKD and MDI-QKD under different conditions through the machine learning model. First, we delineate the range of system parameters and evenly spaced (linear or logarithmic) values through experimental experience, and then use the traditional local search algorithm (LSA) to obtain the optimal parameters and take them as the optimal parameters in this work. Finally, we train various machine learning models based on the above data and compare their performances. We compare the supervised regression learning models such as neural network, K-nearest neighbors, random forest, gradient tree boosting and classification and regression tree (CART), and the results show that the CART decision tree model has the best performance in the regression evaluation index, and the average value of the key rate (of the prediction parameters) and the optimal key rate ratio is about 0.995, which can meet the communication needs in the actual environment. At the same time, the CART decision tree model shows good environmental robustness in the residual analysis of asymmetric QKD protocol. In addition, compared with the traditional scheme, the new scheme based on CART decision tree greatly improves the real-time performance of computing, shortening the single prediction time of the optimal parameters of different environments to the microsecond level, which well meets the real-time communication needs of the communicator in the movable state. This work mainly focuses on the parameter optimization of discrete variable QKD (DV-QKD). In recent years, the continuous variable QKD (CV-QKD) has developed also rapidly. At the end of the paper, we briefly introduce academic attempts of applying machine learning to the parameter optimization of CV-QKD system, and discuss the applicability of the scheme in CV-QKD system.
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Keywords:
- quantum key distribution /
- measurement-device-independent /
- classification and regression tree /
- parameter optimization
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图 1 MDI-QKD系统示意图
Figure 1. Schematic diagram of MDI-QKD system.
图 2 不同类别监督学习算法
$ {R^2} $ 比较Figure 2. Comparison of R2 of supervised learning algorithms in different categories.
图 3 标准情况决策树模型残差图
Figure 3. Decision tree model residual plot for standard cases.
图 4 标准情况神经网络模型残差图
Figure 4. Neural networks model residual plot for standard cases.
图 5 标准情况KNN模型残差图
Figure 5. KNN model residual plot for standard cases.
图 6 CART构建过程
Figure 6. CART construction process.
图 7 TF-QKD模型比例柱状图
Figure 7. Model scale histogram of TF-QKD.
图 8 MDI-QKD模型比例柱状图
Figure 8. Model scale histogram of MDI-QKD.
图 9 回归决策树模型比例柱状图
Figure 9. Regression decision tree model scale histogram.
图 10 RF模型比例柱状图
Figure 10. Random forest model scale histogram.
图 11 超精度情况决策树模型残差图
Figure 11. Decision tree model residual plot for super-precision cases.
图 12 超精度情况RF模型残差图
Figure 12. RF model residual plot for super-precision cases.
表 1 系统参数范围
Table 1. System parameter range.
参数 $ L $/km $ \Delta L $/km $ N $ $ \eta $ $ {Y_0} $ $ {e_{\text{d}}} $ 范围 0—300 0, 25, 50, 75, 100 109—1014 0.1—0.9 10–11—10–6 0.01—0.10 
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表 2 不同方案时间消耗对比
Table 2. Comparison of time loss between different schemes.
协议 决策树/s 神经网络/s KNN/s 传统/h TF-QKD 0.713 0.825 1.509 163 MDI-QKD 0.608 0.710 1.301 116
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表 3 标准情况下模型结果评估
Table 3. Evaluation of the results under standard conditions.
协议 R2 MAE/10–3 MSE/10–5 TF-QKD 0.9916 3.42 8.05 MDI-QKD 0.9993 0.37 1.70
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表 4 不同使用场景模型结果评估
Table 4. Evaluation of the results of different usage scenarios.
模型 $ {R^2} $ MAE/10–2 MSE/10–4 超范围 决策树 0.9529 1.64 8.75 RF 0.9494 1.68 9.12 梯度提升 0.8579 2.76 40.0 超精度 决策树 0.9659 1.14 3.52 RF 0.9654 1.15 3.54 梯度提升 0.9154 1.94 8.74 注: 粗体数据为该指标最好的结果.
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表 5 不同方案时间消耗对比
Table 5. Comparison of time loss between different schemes.
协议 RF/s 决策树/s 梯度提升树/s 传统/h TF-QKD 1.426 0.713 6.748 163 MDI-QKD 1.221 0.608 5.631 116
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[1] Gisin N, Thew R 2007 Nat. Photonics. 1 165
Google Scholar
[2] Scarani V, Bechmann P H, Cerf N J, Dusek M, Lutkenhaus N, Peev M 2009 Rev. Mod. Phys. 81 1301
Google Scholar
[3] Wootters W K, Zurek W H 1982 Nature 299 802
Google Scholar
[4] Busch P, Heinonen T, Lathi P 2007 Phys. Rep. 452 155
Google Scholar
[5] Deutsch D, Ekert A, Jozsa R, Macchiavello C, Popescu S, Sanpera A 1996 Phys. Rev. Lett. 77 2818
Google Scholar
[6] Bennett C H, Brassard G 2014 Theoret. Comput. Sci. 560 7
Google Scholar
[7] 杨林轩, 苏志锟 2022 中国高新科技 11 82
Google Scholar
Yang L X, Su Z K 2022 China High and New Technol. 11 82
Google Scholar
[8] Lütkenhaus N 2000 Phys. Rev. A 61 052304
Google Scholar
[9] Acin A, Gisin N, Scarani V 2004 Phys. Rev. A 69 012309
Google Scholar
[10] Lydersen L, Wiechers C, Wittmann C, Elser D, Skaar J, Makarov V 2010 Nat. Photonics. 4 686
Google Scholar
[11] Lo H K, 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] Lucamarini M, Yuan Z L, Dynes J F, Shields A J 2018 Nature. 557 400
Google Scholar
[14] Takeoka M, Guha S, Wilde M M 2014 Nat. Commun. 5 5235
Google Scholar
[15] Wang X B, Yu Z W, Hu X L 2018 Phys. Rev. A 98 062323
Google Scholar
[16] Ma X, Zeng P, Zhou H 2018 Phys. Rev. X 8 031043
[17] 王华, 赵永利 2019 通信学报 40 168
Google Scholar
Wang H, Zhao Y L 2019 J. Commun. 40 168
Google Scholar
[18] Hughes R J, Morgan G L, Peterson C G 2000 J. Mod. Opt. 47 533
[19] Ren Z A, Chen Y P, Liu J Y, Ding H J, Wang Q 2020 IEEE Commun. Lett. 25 940
[20] Ding H J, Liu J Y, Zhang C M, Wang Q 2020 Quant. Inform. Proces. 19 1
Google Scholar
[21] Xu F, Xu H, Lo H K 2014 Phys. Rev. A 89 052333
Google Scholar
[22] Liu W, Huang P, Peng J, Fan J, Zeng G 2018 Phys. Rev. A 97 022316
Google Scholar
[23] Wang W, Lo H K 2019 Phys. Rev. A 100 062334
Google Scholar
[24] Lu F Y, Yin Z Q, Wang C, Cui C H, Teng J, Wang S, Chen W, Huang W, Xu B J, Guo G C, Han Z F 2019 JOSA B 36 B92
Google Scholar
[25] 陈以鹏, 刘靖阳, 朱佳莉, 方伟, 王琴 2022 物理学报 71 220301
Google Scholar
Chen Y P, Liu J Y, Zhu J L, Fang W, Wang Q 2022 Acta Phys. Sin. 71 220301
Google Scholar
[26] 王琴, 陈以鹏 2020 南京邮电大学学报 40 141
Wang Q, Chen Y P 2020 J. Nanjing University of Posts and Telecommun. 40 141
[27] Cao Y, Li Y H, Yang K X, et al. 2020 Phys. Rev. Lett. 125 260503
Google Scholar
[28] Zhou X Y, Zhang C H, Zhang C M, Wang Q 2019 Phys. Rev. A 99 062316
Google Scholar
[29] Wang W, Xu F, Lo H K 2019 Phys. Rev. X 9 041012
[30] Quinlan J R 1986 Mach. Learn. 1 81
[31] Rumelhart D E, Hinton G E, Williams R J 1986 Nature. 323 533
Google Scholar
[32] Gordon A D, Breiman L, Friedman J H, Olshen R A, Stone C J 1984 Biometrics. 40 874
Google Scholar
[33] 申媛媛, 邬锦雯, 刘鑫东 2020 科技管理研究 40 91
Shen Y Y, Wu T W, Liu X D 2020 Sci. Technol. Manage. Res. 40 91
[34] 刘勇洪, 牛铮, 王长耀 2005 遥感学报 9 405
Google Scholar
Liu Y H, Niu Z, Wang C Y 2005 J. Remote Sens. 9 405
Google Scholar
[35] 王辉, 张文杰, 刘杰, 陈林烽, 李泽南 2022 中国民航大学学报 40 35
Google Scholar
Wang H, Zhang W J, Liu J, Chen L F, Li Z N 2022 J. Civil Aviation University of China 40 35
Google Scholar
[36] 刘玉茹, 赵成萍, 臧军, 宁芊, 周新志 2017 计算机应用 37 57
Liu Y R, Zhao C P, Zang J, Ning Q, Zhou X Z 2017 Comput. Appl. 37 57
[37] S. Pirandola, Andersen U L, Banchi L, et al. 2020 Adv. Opt. Photonics 12 1012
Google Scholar
[38] Huang D, Liu S, Zhang L 2021 Photonics 8 511
Google Scholar
[39] Liu Z P, Zhou M G, Liu W B, Li C L, Gu J, Yin H L, Chen Z B 2022 Opt. Express 30 15024
Google Scholar
[40] Luo H, Wang Y J, Ye W, Zhong H, Mao Y Y, Guo Y 2022 Phys. B 31 020306
[41] Zhou M G, Liu Z P, Liu W B, Li C L, Bai J L, Xue Y R, Fu Y, Yin H L, Chen Z B 2022 Sci. Rep. 12 8879
Google Scholar
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