Marín Díaz, Gabriel2025-12-302025-12-302025Marín Díaz, G. (2025). Fuzzy c-means and explainable ai for quantum entanglement classification and noise analysis. Mathematics, 13(7), 1056. https://doi.org/10.3390/math130710562227-7390https://hdl.handle.net/11268/16658Quantum entanglement plays a fundamental role in quantum mechanics, with applications in quantum computing. This study introduces a new approach that integrates quantum simulations, noise analysis, and fuzzy clustering to classify and evaluate the stability of quantum entangled states under noisy conditions. The Fuzzy C-Means clustering model (FCM) is applied to identify different categories of quantum states based on fidelity and entropy trends, allowing for a structured assessment of the impact of noise. The presented methodology follows five key phases: a simulation of the Bell state, the introduction of the noise channel (depolarization and phase damping), noise suppression using corrective operators, clustering-based state classification, and interpretability analysis using Explainable Artificial Intelligence (XAI) techniques.engAttribution 4.0 Internationalhttp://creativecommons.org/licenses/by/4.0/journal article10.3390/math13071056open accessTeoría cuánticaFísicaInteligencia artificialGoal 7: Ensure access to affordable, reliable, sustainable and modern energy