Fuzzy C-Means and Explainable AI for Quantum Entanglement Classification and Noise Analysis

Quantum 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. The results indicate that while moderate noise levels allow for partial state recovery, strong decoherence, particularly under depolarization, remains a major challenge. Rather than relying solely on noise suppression, a classification-based strategy is proposed to identify states that retain computational feasibility despite the effects of noise. This hybrid approach combining quantum-state classification with AI-based interpretability offers a new framework for assessing the resilience of quantum systems. The results have practical implications in quantum error correction, quantum cryptography, and the optimization of quantum technologies under realistic conditions.