量子模型的认证成本：测量相关性，而非参数数量
Certification cost of quantum models: measurement correlation, not parameter count
- Zurich University of Applied Sciences (ZHAW)（苏黎世应用科学大学（ZHAW））
- University of Zurich（苏黎世大学）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
本研究证明量子模型Fisher矩阵的认证成本由测量相关性决定而非参数数量，提出统一成本公式，并在硬件上验证了成本最优读出权重可显著降低采样预算。
AI中文摘要：
报告训练后的变分量子模型的Fisher几何是常规操作；但引用建立该几何所需的采样预算则不然。在坐标方向参数位移下，将经验Fisher矩阵认证到相对Frobenius误差$\varepsilon$需要$\Theta(B p^{2} V/(\varepsilon^{2} G))$次电路执行，其中$V$是测量的读出方差，$G$是测量的平方梯度范数，均匀分配在该类中是最优的。一个常数重现了两个电路族的成本，其指数相差$p$的整个幂次。该指数是$nV$和$nG$随寄存器规模缩放方式的恒等式，在去除有限$p$前因子后，在624个矩阵乘积态单元上逐族保持到0.001。因此，三次方成本是一个有限尺寸窗口，由读出光锥是否随寄存器增长决定。一个乘积族到256量子比特给出1.966（95%置信区间1.934--1.997）；一个砖墙纠缠器从十量子比特以下的2.853降至六十四量子比特以上的1.715；一个分块纠缠器在固定锥宽下给出1.984，而在比例锥宽下为3.034。固定的设备连接性固定了光锥，因此来自小规模模拟的三次方预算会高估大型机器，此外硬件乘数在ibm_marrakesh、ibm_fez和ibm_kingston上分别为2.07倍（1.41--3.02）、2.38倍和1.91倍。成本最优的读出权重在硬件上将测量的采样预算削减了2.67倍（1.33--4.00），在四到十二量子比特上保持平稳。在廉价电路上拟合的差异模型将其均值转移到校准网格内部，而在数据之前指定的六个更大尺寸上则不然：名义90%区间覆盖36%，而分裂共形是唯一保持接近名义水平的层级。
英文摘要：
Reporting the Fisher geometry of a trained variational quantum model is routine; quoting the shot budget that would establish it is not. Certifying an empirical Fisher matrix to relative Frobenius error $\varepsilon$ under coordinate-wise parameter shift costs $Θ(B p^{2} V/(\varepsilon^{2} G))$ circuit executions, where $V$ is the measured readout variance and $G$ the measured squared gradient norm, with uniform allocation optimal in that class. One constant reproduces the cost of two circuit families whose exponents differ by a full power of $p$. The exponent is an identity in how $nV$ and $nG$ scale with the register, holding family by family to $0.001$ across 624 matrix-product-state cells once the finite-$p$ prefactor is removed. The cubic cost is therefore a finite-size window, set by whether the readout light cone grows with the register. A product family to 256 qubits gives $1.966$ (95% CI $1.934$--$1.997$); a brickwork entangler falls from $2.853$ below ten qubits to $1.715$ beyond sixty-four; a blocked entangler gives $1.984$ at a fixed cone width against $3.034$ at a proportional one. Fixed device connectivity fixes the cone, so a cubic budget from a small simulation overestimates a large machine, on top of hardware multipliers $2.07\times$ ($1.41$--$3.02$), $2.38\times$ and $1.91\times$ on ibm_marrakesh, ibm_fez and ibm_kingston. Cost-optimal readout weights cut the measured shot budget by $2.67\times$ ($1.33$--$4.00$) on hardware, flat from four to twelve qubits. A discrepancy model fitted on cheap circuits transfers its mean inside the calibration grid and, at six larger sizes named before the data, does not: nominal 90% intervals cover 36%, and split conformal is the only rung that stays near nominal.
