AI 中文总结
研究量子测量约简的两个全局优化层问题，用二阶锥规划求解内层，RANGE优化器处理外层，可实现测量字典压缩，降低认证最优成本，在不同模型和场景下有显著效果，还能避免一些策略的测量次数冗余。
AI 中文摘要
量子测量约简包含两个不同的全局优化层：一个是在固定测量字典内分割可观测量并分配测量次数的连续问题，另一个是设计字典并校准其数据驱动不确定性模型的非凸外部问题。我们将内层作为二阶锥规划（SOCP）全局且可认证地求解，并使用RANGE（一种强大的自适应自然启发全局优化器）处理组合和统计外层。对于任何声明的上下文集、单次成本、评分函数和协方差模型，SOCP返回无偏线性分层估计器中的最小领先测量成本。圆锥对偶提供可独立检查的下界见证；可行性修复后，外部验证器可从存储数据重新计算\(L \le \Phi \le U\)而无需信任优化器。先导测量产生同时的有限样本协方差括号，对偶成为遗漏上下文的定价预言机。离散RANGE搜索覆盖子字典、帕累托压缩前沿和候选上下文；连续RANGE对协方差半径模型进行明确的经验性、覆盖约束校准，同时严格证书保留已证明的有限样本半径。RANGE将分子上下文字典压缩4.3 - 6.1倍，认证前沿超额为0.2 - 2.1%。标准策略对H2恰好最优，但对H2O在其自身设置下测量次数有2.1 - 7.7倍的冗余。添加完全可交换上下文可将认证最优降低多达56%；在声明的哈特里 - 福克代理协方差模型下，对于29 - 35量子比特的生产f元素哈密顿量， capped - 字典扩展节省3% - 70%的测量次数，且降低块编码成本的变换不一定会降低采样成本。
英文摘要
Quantum-measurement reduction contains two distinct global-optimization layers: a continuous problem of splitting an observable and allocating shots within a fixed measurement dictionary, and a nonconvex outer problem of designing the dictionary and calibrating its data-driven uncertainty model. We solve the inner layer globally and certifiably as a second-order cone program (SOCP), and use RANGE, a robust adaptive nature-inspired global optimizer, for the combinatorial and statistical outer layer. For any declared set of contexts, per-shot costs, score functions, and covariance model, the SOCP returns the minimum leading shot cost among unbiased linear stratified estimators. The conic dual supplies an independently checkable lower-bound witness; after feasibility repair, an external verifier recomputes $L \le Φ\le U$ from stored data without trusting the optimizer. Pilot measurements yield simultaneous finite-sample covariance brackets, and the dual becomes a pricing oracle for omitted contexts. Discrete RANGE searches covering sub-dictionaries, Pareto compression fronts, and candidate contexts; continuous RANGE performs an explicitly empirical, coverage-constrained calibration of covariance-radius models, while rigorous certificates retain the proved finite-sample radius. RANGE compresses molecular context dictionaries by 4.3-6.1x at 0.2-2.1% certified-frontier excess. Standard strategies are exactly optimal for H2 yet leave factors of 2.1-7.7 in shots within their own settings by H2O. Adding fully commuting contexts lowers the certified optimum by up to 56%; on 29-35-qubit production f-element Hamiltonians under a declared Hartree-Fock-proxy covariance model, the capped-dictionary enlargement saves 31-70% of the shots, and transformations reducing block-encoding cost need not reduce sampling cost.
Comments20 pages; companion paper to "Beyond Orbital Rotations: Correlation-Rank Limits and Clifford-Accessible Measurement, from Algebra and Global Optimization"
