Multi-Metric Quantum State Analysis and Decoherence Profiling in Quantum Dot Systems: A Theoretical Approach with Deep Learning-Based Validation

Quantum coherence and fidelity are essential ingredients for scalable quantum technologies, particularly in solid-state platforms such as quantum dots (QDs). In this work, we introduce a physics-inspired framework for the multi-metric characterization of QDs confined to a spherical potential. We obtain the energy eigenvalues using Nikiforov-Uvarov Functional Analysis (NUFA) and calculate the thermodynamic and information-theoretic quantities of purity, Rényi-2 entropy, and dynamical loss of coherence, to give quantitative descriptors of the confinement geometry, excitation dynamics, and decoherence sensitivity. For predictive modeling, we develop a supervised deep neural network (DNN) that learns to map quantum energy features to the corresponding state metrics, providing a quick and accurate estimator that adheres to the underlying physics. Our findings indicate that the low-energy and highly localized states have the lowest entropy and highest purity, whereas the higher excited states exhibit significant decoherence and thermal leakage. This hybrid data-modeling strategy not only enables a systematic connection between the energy-level physics and quantum information-theoretic measures but also provides an enabling step towards intelligent coherence management in QD systems. The framework can be readily extended to other related near-term intermediate-scale quantum (NISQ) systems for a generalized pathway to fidelity-guided quantum design and diagnostics.