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arXiv:2404.08993 · IEEE Transactions on Green Communications and Networking

An Unsupervised Machine Learning to Optimize Hybrid Quantum Noise Clusters for Gaussian Quantum Channel

Mouli Chakraborty, Anshu Mukherjee, Ioannis Krikidis, Avishek Nag, Subhash Chandra

Published Jul 9, 2025• 3 citations
arXivHTMLPDF

Abstract

Quantum communication systems are essential for secure information transmission, but their performance is significantly impeded by complex hybrid quantum noise (HQN) in Gaussian quantum channels. Accurately modeling this noise is crucial for optimizing channel achievable rates, a problem compounded by the complex nature of hybrid noise, which combines quantum shot noise and classical additive-white-Gaussian noise (AWGN) and is typically represented as an infinite mixture of Gaussian distributions. This work focuses on optimizing the HQN model to improve the achievable rate of Gaussian quantum channels using Machine Learning (ML) optimized clusters. The work specifically leverages Gaussian mixture model (GMM) and the Expectation-Maximization (EM) algorithm to model the complex noise characteristics of quantum channels. The study proposes modeling of hybrid noise as an infinite mixture of Gaussian distributions weighted by Poissonian parameters, with a novel cluster reduction technique that minimizes the number of Gaussian components while maintaining accuracy within acceptable error tolerances. Simulation results demonstrate that the GMM-EM enhanced clustering method significantly improves channel achievable rates in general quantum communication and satellite-based quantum communication systems. The GMMEM method substantially outperforms conventional clustering techniques, including K-means and Density-Based Spatial Clustering of Applications with Noise (DBSCAN) algorithms, in terms of maximizing achievable rates and characterizing noise accuracy. This advancement provides a practical and efficient solution for real-time quantum noise modeling, representing a significant improvement over existing state-of-the-art approaches in quantum communication network optimization

DOI
10.1109/tgcn.2025.3587144

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Quantum communication systems are essential for secure information transmission, but their performance is significantly impeded by complex hybrid quantum noise (HQN) in Gaussian quantum channels. Accurately modeling this noise is crucial for optimizing channel achievable rates, a problem compounded by the complex nature of hybrid noise, which combines quantum shot noise and classical additive-white-Gaussian noise (AWGN) and is typically represented as an infinite mixture of Gaussian distributions. This work focuses on optimizing the HQN model to improve the achievable rate of Gaussian quantum channels using Machine Learning (ML) optimized clusters. The work specifically leverages Gaussian mixture model (GMM) and the Expectation-Maximization (EM) algorithm to model the complex noise characteristics of quantum channels. The study proposes modeling of hybrid noise as an infinite mixture of Gaussian distributions weighted by Poissonian parameters, with a novel cluster reduction technique that minimizes the number of Gaussian components while maintaining accuracy within acceptable error tolerances. Simulation results demonstrate that the GMM-EM enhanced clustering method significantly improves channel achievable rates in general quantum communication and satellite-based quantum communication systems. The GMMEM method substantially outperforms conventional clustering techniques, including K-means and Density-Based Spatial Clustering of Applications with Noise (DBSCAN) algorithms, in terms of maximizing achievable rates and characterizing noise accuracy. This advancement provides a practical and efficient solution for real-time quantum noise modeling, representing a significant improvement over existing state-of-the-art approaches in quantum communication network optimization
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Clustering algorithms are a cornerstone of machine learning applications. Recently, a quantum algorithm for clustering based on the kkk-means algorithm has been proposed by Kerenidis, Landman, Luongo, and Prakash. Based on their work, we propose a quantum expectation-maximization algorithm for Gaussian mixture models (GMMs). The robustness and quantum speedup of the algorithm are shown. We also show numerically the advantage of GMM over kkk-means algorithm for nontrivial cluster data.
This research advances the application of QKD in FSO satellite-based quantum communication. It proposes an innovative satellite quantum channel model and derives the secret quantum key distribution rate achievable through this channel. Unlike existing models that approximate the noise in quantum channels as merely Gaussian distributed, this model incorporates a hybrid quantum noise analysis, accounting for both quantum Poissonian noise and classical AWGN. This hybrid approach acknowledges the dual vulnerability of CV Gaussian quantum channels to both quantum and classical noise under collective attack with RR setting, thereby offering a more realistic assessment of the quantum SKR. This work delves into the variation of asymptotic SKR with the SNR and satellite altitudes under various influencing parameters. We identify and analyze critical factors such as reconciliation efficiency, electrical noise, transmission coefficient, detection efficiency, transmission efficiency, excess noise, and the quantum Poissonian noise parameter impacting the SKR. These parameters are pivotal in determining the asymptotic SKR in FSO satellite quantum channels, highlighting the challenges of satellite-based quantum communication. A comparative study has been provided based on the finite-size and asymptotic SKR. It provides a comprehensive framework for understanding and optimizing asymptotic SKR in satellite-based QKD systems, paving the way for more efficient and secure quantum communication networks.
The Expectation-Maximization (EM) algorithm is a fundamental tool in unsupervised machine learning. It is often used as an efficient way to solve Maximum Likelihood (ML) estimation problems, especially for models with latent variables. It is also the algorithm of choice to fit mixture models: generative models that represent unlabelled points originating from kkk different processes, as samples from kkk multivariate distributions. In this work we define and use a quantum version of EM to fit a Gaussian Mixture Model. Given quantum access to a dataset of nnn vectors of dimension ddd, our algorithm has convergence and precision guarantees similar to the classical algorithm, but the runtime is only polylogarithmic in the number of elements in the training set, and is polynomial in other parameters - as the dimension of the feature space, and the number of components in the mixture. We generalize further the algorithm in two directions. First, we show how to fit any mixture model of probability distributions in the exponential family. Then, we show how to use this algorithm to compute the Maximum a Posteriori (MAP) estimate of a mixture model: the Bayesian approach to likelihood estimation problems. We discuss the performance of the algorithm on a dataset that is expected to be classified successfully by this algorithm, arguing that on those cases we can give strong guarantees on the runtime.
This paper develops a hybrid quantum channel model tailored for finite-regime quantum key distribution (QKD) in free-space satellite quantum communication. The channel model addresses the fading characteristics of satellite-to-ground links while incorporating the dynamics of satellite orbits. By conducting a comprehensive security analysis under finite-size effects and collective attacks, the research bridges the theoretical and practical aspects of satellite-based QKD. Critical parameters, such as reconciliation efficiency, transmission coefficient, detection efficiency, receiver telescope aperture, beam waist, and effective communication time, are systematically investigated to optimize the secret key rate. The study reveals key trade-offs between the influence of satellite altitude on communication windows, noise levels, and synchronization, which significantly impact quantum channel efficiency. The model improves the accuracy of free-space quantum channel evaluations by presenting a hybrid noise framework that combines quantum Poissonian noise with classical additive white Gaussian noise (AWGN). Our numerical results demonstrate the feasibility and robustness of finite-regime QKD for uplink and downlink configurations in various atmospheric conditions, highlighting the superiority of satellite-based quantum communication over conventional networks.
Noise is a vital factor in determining the accuracy of processing the information of the quantum channel. One must consider classical noise effects associated with quantum noise sources for more realistic modelling of quantum channels. A hybrid quantum noise model incorporating both quantum Poisson noise and classical additive white Gaussian noise (AWGN) can be interpreted as an infinite mixture of Gaussians with weightage from the Poisson distribution. The entropy measure of this function is difficult to calculate. This research developed how the infinite mixture can be well approximated by a finite mixture distribution depending on the Poisson parametric setting compared to the number of mixture components. The mathematical analysis of the characterization of hybrid quantum noise has been demonstrated based on Gaussian and Poisson parametric analysis. This helps in the pattern analysis of the parametric values of the component distribution, and it also helps in the calculation of hybrid noise entropy to understand hybrid quantum noise better.