Spectral Geometry and Bosonic-Bloch Probes: Explorations in Quantum Learning

The latest research explored the emergence mechanism of spectral geometry in graph regularization quantum networks and its physical detection methods. Experiments revealed that the training process reorganized the output similarity graph, increasing the effective spectral dimension Delta S to +0.23 and reshaping the Laplace spectrum. Edge-differentiated bosonic interference directly detected this reorganization: the bosonic enhancement Delta P_uv showed a significant correlation with Fiedler edge splitting |Delta v_2| (r = -0.50), successfully linking the learned spectral partitions with interference characteristics. Phase diagram analysis indicated that model performance had a non-monotonic dependence on coupling strength gamma and noise delta, and graph regularization could improve fidelity only in specific restricted regions. Hardware experiments confirmed the predicted interference behavior. Additionally, the study analyzed hybrid quantum autoencoders, introducing Bloch space drift as a geometric diagnostic tool for potential representations. Through the analysis of the geometric structure of reduced single-qubit states and related quantum Fisher information, the results showed that learned-induced spectral groups…