发表机构
Quantum AI Research Group, School of Computer Science and Mathematics, Kingston University London（伦敦金斯顿大学计算机科学与数学学院量子人工智能研究组）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
研究量子学习模型中谱几何的出现及其诊断方法，通过图正则化网络、双玻色干涉和混合量子自编码器，建立谱几何框架，利用玻色和布洛赫探针诊断量子学习系统。
AI 中文摘要
本文研究谱几何如何在量子学习模型中出现，以及如何用物理基础的探针进行诊断。在图正则化量子网络中，训练重新组织输出相似性图，增加有效谱维数 Delta S = +0.23，并重塑拉普拉斯谱。边缘分辨的双玻色干涉直接探测这种重构：玻色增强 Delta P_uv 与 Fiedler 边缘分裂 |Delta v_2| 相关（r = -0.50），将学习到的谱划分与干涉特征联系起来。相图显示性能对耦合强度 gamma 和噪声 delta 呈非单调依赖，图正则化仅在受限区域提高保真度；硬件实验在散粒噪声不确定性内确认了预测的干涉行为。我们还分析了一个混合量子自编码器，并引入布洛赫空间漂移作为其潜在表示的几何诊断。通过无监督良性数据阈值，模型实现了高排名性能（ROC-AUC 约 0.99）和可忽略的假阴性率。绝对布洛赫漂移强烈区分异常（ROC-AUC 至少约 0.9），而连续漂移接近随机（ROC-AUC 约 0.5），表明检测源于持久的状态空间位移而非局部波动。通过约化单量子比特态的几何和相关的量子 Fisher 信息，这些结果表明学习诱导的谱组织表现为可测量的量子态结构，建立了一个统一的谱几何框架，用于用玻色和布洛赫探针诊断量子学习系统。
英文摘要
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.
