First-Principles Optical Descriptors and Hybrid Classical-Quantum Classification of Er-Doped CaF${}_2$

Abstract

We present a physics-informed classical-quantum machine learning framework for discriminating pristine CaF${}_2$ from Er-doped CaF${}_2$ using first-principles optical descriptors. Finite Ca${}_8$F${}_{16}$ and Ca${}_7$ErF${}_{16}$ clusters were constructed from the fluorite structure (a=5.46~$\mathring{A}$) and treated using density functional theory (DFT) and linear-response time-dependent DFT (LR-TDDFT) within the GPAW code. Geometry optimization was performed in LCAO mode with a DZP basis and PBE exchange-correlation functional, followed by real-space finite-difference ground-state calculations with grid spacing h=0.30~$\mathring{A}$ and N${}_{bands}$=N${}_{occ}$+20. Optical excitations up to 10~eV were obtained via the Casida formalism and converted into continuous absorption spectra using Gaussian broadening ($\sigma$=0.1-0.2~eV). From 1,589 energy-resolved points per system, physically interpretable descriptors including transition energy $E$, extinction coefficient $\kappa$, and absorption coefficient $\alpha$ were extracted. A classical RBF-kernel support vector machine (SVM) achieves a test accuracy (ACC) of 0.983 and ROC-AUC of 0.999. Quantum support vector machines (QSVMs) evaluated on statevector and noisy simulators reach accuracies of 0.851 and 0.817, respectively, while execution on IBM quantum hardware yields a test-slice accuracy of 0.733 under finite-shot and decoherence constraints. A hybrid quantum neural network (QNN) with a 3-qubit feature map and depth-4 ansatz achieves a test accuracy of 0.93 and AUC of 0.96. Results here demonstrate that dopant-induced optical fingerprints form a robust, physically grounded feature space for benchmarking near-term quantum learning models against strong classical baselines.

References in corpus (10)

• Quantum Machine Learning
• A real-space grid implementation of the Projector Augmented Wave method
• Quantum support vector machine for big data classification
• Evaluating analytic gradients on quantum hardware
• Expressibility and entangling capability of parameterized quantum circuits for hybrid quantum-classical algorithms
• An Artificial Neuron Implemented on an Actual Quantum Processor
• Is quantum advantage the right goal for quantum machine learning?
• Hybrid quantum-classical neural network for calculating ground state energies of molecules
• Neural quantum kernels: training quantum kernels with quantum neural networks
• Quantum Convolutional Neural Network for Phase Recognition in Two Dimensions