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

Abstract:This paper studies how spectral geometry emerges in quantum learning models and how it can be diagnosed with physically grounded probes. In graph-regularized quantum networks, training reorganizes the output similarity graph, increases the effective spectral dimension Delta S = +0.23, and reshapes the Laplacian spectrum. Edge-resolved two-boson interference directly probes this restructuring: the bosonic enhancement Delta P_uv correlates with the Fiedler edge split |Delta v_2| (r = -0.50), linking learned spectral partitions to interference signatures. A phase diagram shows a nonmonotonic dependence of performance on coupling strength gamma and noise delta, with graph regularization improving fidelity only in a restricted regime; hardware experiments confirm the predicted interference behavior within shot-noise uncertainty. We also analyze a hybrid quantum autoencoder and introduce Bloch-space drift as a geometric diagnostic of its latent representation. With an unsupervised benign-data threshold, the model achieves high ranking performance (ROC-AUC about 0.99) and negligible false-negative rates. Absolute Bloch drift strongly discriminates anomalies (ROC-AUC at least about 0.9), while consecutive drift is near random (ROC-AUC about 0.5), showing that detection arises from persistent state-space displacement rather than local fluctuations. Through the geometry of reduced single-qubit states and associated quantum Fisher information, these results show that learning-induced spectral organization appears as measurable quantum-state structure, establishing a unified spectral-geometric framework for diagnosing quantum learning systems with bosonic and Bloch probes.

Quantum Physics (quant-ph); Artificial Intelligence (cs.AI)

arXiv:2607.00063 [quant-ph]

(or arXiv:2607.00063v4 [quant-ph] for this version)

https://doi.org/10.48550/arXiv.2607.00063 Focus to learn more arXiv-issued DOI via DataCite

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