arXiv：cs.LG（机器学习，全量分类）· Zeyu Chen·· 14 小时前AI 评分29
量子学习中的对称性发现：从有限测量推断可观测级与任务级对称群
Symmetry Discovery in Quantum Learning: Observable-Level and Task-Level Inference from Finite Measurements
AI 导读
研究提出一套有限测量理论，用于从候选变换中推断量子学习模型应施加的对称群。核心结构结果将"可观测不可见变换"等同于投影态稳定子，并证明有限字典下无偏 shadow 统计量以逆间隙测量速率区分零与正平方期望差异，优于均匀差异估计的逆平方间隙速率。任务验证通过特征核或经典—量子差异检验联合分布，Ising 链计算将有限次恢复、标签依赖对称性与物理扇区漂移联系起来。
正文
Abstract:Symmetry reduces the capacity of a quantum learning model, but the imposed group must match both the measured information and the label transformation. We establish a finite-measurement theory for inferring this group from candidate transformations. The central structural result identifies observable-invisible transformations with the stabilizer of a projected state whenever the probe span is invariant. It turns recovered generators into a valid subgroup and identifies the continuous invisible space with its Lie algebra. For finite dictionaries, an unbiased shadow statistic distinguishes zero from positive squared expectation discrepancies with an inverse-gap measurement rate, improving the inverse-square-gap rate of uniform discrepancy estimation. A commuting qubit lower bound proves the gap dependence optimal at fixed snapshot scale, and simultaneous intervals support data-dependent tolerances. Task validation then tests either the joint distribution through a characteristic kernel or its encoded mean through a classical--quantum discrepancy. An exact group-average identity relates the latter to joint-state asymmetry and specifies its conversion to binary task breaking mass. Projection bias quantifies the cost of excessive symmetry, while an $\ell_1$ readout bound quantifies the capacity gained by relaxing it. At an invariant pure-state backbone, retained and nontrivial breaking sectors are Fisher-orthogonal. Ising-chain calculations connect finite-shot recovery, label-dependent symmetry, and physical sector drift. These results determine which symmetry the measurements support and provide the statistical and geometric basis for a subsequent release decision.
| Subjects: | Quantum Physics (quant-ph); Machine Learning (cs.LG) |
| Cite as: | arXiv:2610.00157 [quant-ph] |
| (or arXiv:2610.00157v1 [quant-ph] for this version) | |
| https://doi.org/10.48550/arXiv.2610.00157 arXiv-issued DOI via DataCite (pending registration) |
Submission history
From: Zeyu Chen [view email]
[v1]
Fri, 11 Sep 2026 14:20:17 UTC (38 KB)
来源：arXiv：cs.LG（机器学习，全量分类） · arxiv.org