发表机构
Independent Researcher, Morocco
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究针对固定计算基测量，推导了各向同性量子切线的读出秩定律，通过理论证明与电路实验揭示了量子信息在不同读出空间的层级分布规律。
AI 中文摘要
深度参数化量子电路可能对参数变化保持敏感，而学习模型保留的可观测量几乎没有响应。我们针对固定的计算基测量研究这种分离。对于纯态切线，我们比较量子费舍尔信息$F_Q$、完整比特串分布中的费舍尔信息$F_{\rm full}$，以及对角读出空间$\boldsymbol{\textit{A}}$可用的最大方差归一化响应$\boldsymbol{\textit{I}_{\textit{A}}}$。若联合态-切线框架是哈尔随机的，我们证明这两个连续信息分数是独立的贝塔变量，其均值为$1/2$和$r/(2^n-1)$，其中$r$是读出的中心维度。因此，任何固定权重$k$的所有计算基泡利串的联合跨度仅保留完整记录信息的$O(n^k2^{-n})$。对六个电路族的精确态矢量实验显示，随着电路深度增加，五个非守恒系综与该层级的有限尺寸一致性不断提高。一个守恒系综即使在校正支撑和读出秩后仍与各向同性预测显著偏离，表明仅靠秩不足以保证切线各向同性。
英文摘要
Deep parameterized quantum circuits may remain sensitive to a parameter change while the observables retained by a learning model barely respond. We study this separation for a fixed computational-basis measurement. For a pure-state tangent, we compare the quantum Fisher information $F_Q$, the Fisher information $F_{\rm full}$ in the complete bitstring distribution, and the largest variance-normalized response $\mathcal I_{\mathcal A}$ available to a diagonal readout space $\mathcal A$. If the joint state--tangent frame is Haar random, we prove that the two successive information fractions are independent Beta variables whose means are $1/2$ and $r/(2^n-1)$, where $r$ is the centered dimension of the readout. Consequently, even the joint span of all computational-basis Pauli strings through any fixed weight $k$ retain only $O(n^k2^{-n})$ of the full-record information. Exact-statevector experiments across six circuit families show increasing finite-size agreement with this hierarchy in five nonconserving ensembles as the circuit depth grows. A number-conserving family departs strongly from the isotropic prediction even after correcting the support and readout rank, showing that rank alone is insufficient without tangent isotropy.
Comments14 pages, 4 figures
