{"ID":5552521,"CreatedAt":"2026-07-02T01:54:51.863792489Z","UpdatedAt":"2026-07-03T11:04:44.15433009Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2607.00063","arxiv_id":"2607.00063","title":"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.","short_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 spectru...","url_abs":"https://arxiv.org/abs/2607.00063","url_pdf":"https://arxiv.org/pdf/2607.00063v1","authors":"[\"Santanu Ganguly\",\"Xing Liang\",\"Dimitrios Makris\"]","published":"2026-06-30T11:06:25Z","proceeding":"quant-ph","tasks":"[\"quant-ph\",\"cs.AI\"]","methods":"[\"LoRA\",\"Generative Adversarial Network\"]","has_code":false}