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New Journal of Physics

Back-propagation neural network based optimization for high secret key rate continuous-variable quantum key distribution systems

Yang Liu, Jiangliang Jin, Xueqin Jiang, Han Hai, Jisheng Dai, Yinghua Xie

Published Mar 27, 2026• 0 citations
Publisher

Abstract

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.

DOI
10.1088/1367-2630/ae5842

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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.
The goal of continuous variable quantum key distribution (CVQKD) is to be diffusely used and adopted in diverse scenarios, so the adhibition of atmospheric channel will play a crucial part in constituting global secure quantum communications. Atmospheric channel transmittance is affected by many factors and does not vary linearly, leading to great changes in signal-to-noise ratio. It is crucial to choose the appropriate modulation variance under different turbulence intensities to acquire the optimal secret key rate. In this paper, the four-state protocol, back-propagation neural network (BPNN) algorithm was discussed in the proposed scheme. We employ BPNN to CVQKD, which could adjust the modulation variance to an optimum value for ensuring the system security and making the system performance optimal. The numerical results show that the proposed scheme is equipped to improve the secret key rate efficiently.
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.
Abstract Numerical methods are widely used to calculate the secure key rate of many quantum key distribution protocols in practice, but they consumes many computing resources and are too time-consuming. In this work, we take the homodyne detection discrete-modulated continuous-variable quantum key distribution (CV-QKD) as an example, and construct a neural network that can quickly predict the secure key rate based on the experimental parameters and experimental results. Compared to traditional numerical methods, the speed of the neural network is improved by several orders of magnitude. Importantly, the predicted key rates are not only highly accurate but also highly likely to be secure. This allows the secure key rate of discrete-modulated CV-QKD to be extracted in real time on a low-power platform. Furthermore, our method is versatile and can be extended to quickly calculate the complex secure key rates of various other unstructured quantum key distribution protocols.
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.