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.
Related
- Advances in quantum learning theory with bosonic systems
- Quantum advantage in learning single mode bosonic channels
- Spectral Reduction Selects the Observable Imprint of Dirac Quantum Geometry
- Engineering non-Markovianity from spectral shaping of bosonic and fermionic baths
- Maximizing the spectral gap for free bosonic CFTs
BibTeX
@misc{ganguly2026spectral,
title = {{Spectral Geometry and Bosonic-Bloch Probes: Explorations in Quantum Learning}},
author = {Santanu Ganguly and Xing Liang and Dimitrios Makris},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2607.00063},
eprint = {2607.00063},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2607.00063},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Spectral Geometry and Bosonic-Bloch Probes: Explorations in Quantum Learning
AU - Santanu Ganguly
AU - Xing Liang
AU - Dimitrios Makris
PY - 2026
DA - 2026/09/08
PB - arXiv
DO - 10.48550/arxiv.2607.00063
UR - https://arxiv.org/abs/2607.00063
AB - 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.
ER -