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Advanced Quantum Technologies

A Machine Learning Based Optimization Approach for Continuous‐Variable Quantum Key Distribution

Xueqin Jiang, Na Wang, Jiangliang Jin, Yan Feng, Han Hai, Jisheng Dai, Peng Huang

Published Jun 11, 2025• 5 citations
Publisher

Abstract

Abstract In the continuous‐variable quantum key distribution (CV‐QKD) system, the secret key rate and transmission distance are important factors to evaluate the quality of the system. Numerical methods are commonly employed to calculate the secret key rate of QKD, but they often face challenges to find the optimal parameter to enhance the secret key rate. In this study, a machine learning based parameter optimization approach is proposed for the Gaussian‐modulated CV‐QKD system. The proposed approach adopts the genetic algorithm backpropagation (GA‐BP) based approach to enhance the secret key rate by optimize parameters of the CV‐QKD system. Furthermore, under certain assumptions, some theoretical results are established, which enables us to identify the maximum secret key rate under a given GA‐BP network. Based on these results, a bisection based method is proposed that can effectively find the optimal modulation variance and the corresponding maximum secret key rate. Finally, the simulation results show that the proposed approach can achieve a higher secret key rate than the conventional methods under the numerical settings.

DOI
10.1002/qute.202500269

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Abstract In the continuous‐variable quantum key distribution (CV‐QKD) system, the secret key rate and transmission distance are important factors to evaluate the quality of the system. Numerical methods are commonly employed to calculate the secret key rate of QKD, but they often face challenges to find the optimal parameter to enhance the secret key rate. In this study, a machine learning based parameter optimization approach is proposed for the Gaussian‐modulated CV‐QKD system. The proposed approach adopts the genetic algorithm backpropagation (GA‐BP) based approach to enhance the secret key rate by optimize parameters of the CV‐QKD system. Furthermore, under certain assumptions, some theoretical results are established, which enables us to identify the maximum secret key rate under a given GA‐BP network. Based on these results, a bisection based method is proposed that can effectively find the optimal modulation variance and the corresponding maximum secret key rate. Finally, the simulation results show that the proposed approach can achieve a higher secret key rate than the conventional methods under the numerical settings.
In the continuous-variable quantum key distribution (CV-QKD) system, the secret key rate (SKR) and transmission distance are important factors to evaluate the quality of system. Numerical methods are commonly employed to compute SKR of QKD systems in practice, but it is difficult to find the optimal parameter to enhance SKR. In this paper, we propose a machine learning-based parameter optimization scheme of CV-QKD. The proposed scheme applies the genetic algorithm-back propagation neural network (GA-BPNN) to CV-QKD to learn the mapping relationship between SKR and modulation variance. According to the property that the mapping relationship is a concave function, the optimal modulation variance can be determined by bisection, and then SKR can be enhanced. Simulation results demonstrate that the proposed scheme can enhance SKR and transmission distance.
Abstract In the continuous-variable quantum key distribution (CV-QKD) system, the secure key rate and the throughput of secure keys are important factors in measuring system quality. However, the secure key rate and the throughput of secure keys depend on various nonlinearly related parameters, which makes it difficult to effectively find the optimal parameters. In this paper, we introduce machine learning into the CV-QKD system and propose a parameter optimization scheme for the CV-QKD system based on the back-propagation (BP) neural network. The proposed scheme improves the secure key rate and throughput of secure keys by optimizing the code rate and the number of decoding iterations in the error correction process. Furthermore, under some reasonable assumptions, we prove that the optimization objective is a concave function of the optimization parameters under the BP neural network, which ensures that there exists a global optimal solution in a certain domain and provides a theoretical basis for the optimization based on BP neural networks. Simulation results show that compared with traditional optimization schemes, the proposed scheme can improve the secure key rate and transmission distance.
Continuous-variable quantum key distribution (CV-QKD) offers the advantages of high secret key rates in metropolitan areas. Optimization of modulation variance is an efficient method to improve the secret key rate of CVQKD system. However, in practical CV-QKD system, inevitable slight parameter fluctuation could occur after the modification of modulation variance, and controlling the modulation variance with arbitrary accuracy is also difficult. In this paper, we propose a two-step optimization for practical CV-QKD. The first step is to determine the optimal working state by combining the modulation variance optimization with error correction matrix optimization. The second step is to optimize the rate-adaptive reconciliation parameters to compensate the loss of secret key rate caused by inaccuracy modulation variance. Our results show that the secret key rate can be improved by 17.8% in comparison to one-step optimization method. Our method can be conveniently applied to CV-QKD protocol with homodyne and heterodyne detection, which will pave the way to the deployment of high stable and high performance for CV-QKD.
Abstract For a practical continuous-variable quantum key distribution (CV-QKD) system, the optimization of modulation variance is crucial for promoting protocol performance. The optimization relies on algorithms like local search in general. But the efficiency of local search methods is limited in low latency and limited computing power scenarios due to their high computational consumption. Hence, this optimization approach is infeasible for satellite-based CV-QKD due to satellites’ low power feature. In this paper, a neural network model that directly predicting the optimal modulation variance in nearly real time is proposed for free space gaussian modulated CV-QKD protocols. This work enhances the feasibility of implementing CV-QKD in low-Earth-orbit satellite scenarios, where typical link durations of few seconds demand rapid parameter optimization. Moreover, a simulation platform for free space CV-QKD protocol, which employs the precise orbital model to extract the elevation angle and the transmission length, is designed and developed to generate training sets that make the neural network model more practical. Our work can be used as a foundation to support parameter prediction for future quantum communication satellite missions.
The discrete-modulated continuous-variable quantum key distribution (DM-CV-QKD) could break the distance limitation of Gaussian-modulated CV-QKD. In practice, the high-performance error correction code plays an important role in DM-CV-QKD and affects the secure transmission distance. However, DM-CV-QKD usually works under low signal-to-noise ratio (SNR) and the design of high-performance error correction code under this condition is difficult, so that it would impose a limitation on further improvement of the secure distance. We propose a DM-CV-QKD with the machine-learning-based detector to further improve the secure distance. The numerical result shows that the proposed scheme could validly improve the system performance. Viewed from another perspective, the proposed scheme could be employed to overcome various impairments induced by the channel and thereby lower the demand of error correction codes on the SNR threshold of the quantum channel without compromising the system performance. The proposed scheme opens the door to applying machine leaning to directly process the raw secret key and improve the performance for CV-QKD systems.
Continuous-variable quantum key distribution (CV-QKD) with discrete modulation has received widespread attentions because of its experimental simplicity, lower-cost implementation and ease to multiplex with classical optical communication. Recently, some inspiring numerical methods have been applied to analyse the security of discrete-modulated CV-QKD against collective attacks, which promises to obtain considerable key rate over one hundred kilometers of fiber distance. However, numerical methods require up to ten minutes to calculate a secure key rate one time using a high-performance personal computer, which means that extracting the real-time secure key rate is impossible for discrete-modulated CV-QKD system. Here, we present a neural network model to quickly predict the secure key rate of homodyne detection discrete-modulated CV-QKD with good accuracy based on experimental parameters and experimental results. With the excess noise of about 0.010.010.01, the speed of our method is improved by about seven orders of magnitude compared to that of the conventional numerical method. Our method can be extended to quickly solve complex security key rate calculation of a variety of other unstructured quantum key distribution protocols.