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

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