Quantum Superalgebraic Entanglement Classification with Generative AI

Abstract: This paper presents a novel framework for classifying and synthesizing entangled quantum states using the mathematical structure of quantum superalgebras integrated with generative artificial intelligence. While traditional entanglement classification methods struggle with scalability and symmetry-awareness in systems governed by supersymmetric dynamics, this work introduces a hybrid model that leverages Lie superalgebras—such as sl(2∣1) and osp(1∣2)—to construct algebraically constrained entangled state spaces. A generative AI model, specifically a conditional diffusion model, is trained on datasets of quantum states annotated with entanglement metrics and superalgebraic invariants including Casimir operators and parity labels. The model achieves over 90% classification accuracy on known entanglement types and successfully generalizes to unseen state classes while preserving algebraic structure. Validation through quantum fidelity and entropic measures demonstrates that the generated states are physically realizable and symmetry-consistent. This research bridges algebraic theory and machine learning, opening new directions for interpretable, scalable, and symmetry-aware quantum state classification and synthesis. Keywords: Quantum entanglement, Lie superalgebras, entanglement classification, generative AI, quantum machine learning, sl(2∣1), osp(1∣2), Casimir operators, diffusion models, symmetry-preserving quantum systems