有限资源下的影子层析最优策略
Optimal strategies for shadow tomography with limited resources
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中文总结 AI 辅助
该研究针对有限资源下的影子层析问题，构建最优测量策略，证明克利福德测量在多场景下最优，为哈密顿量能量估计提供改进方差界的构造性策略。
中文摘要 AI 辅助
影子层析旨在通过对相对少量的量子态副本进行随机测量，高效预测未知量子态的大量期望值。现有分析表明其具有显著的缩放优势，但实现这些保证的最优策略并不总是已知的，且所需测量在当前硬件上可能难以实现。我们针对泡利可观测量解决这一缺口，计算最优样本复杂度参数，并在现实资源约束下构建最优测量策略。我们聚焦于无记忆协议（每个副本仅被测量一次）和具有有界相互作用范围的测量。我们的方法将问题简化为对编码泡利反对易关系的 frustration 图的图参数分析。我们为一般情况提供高效数值方法，并解析证明克利福德测量在许多场景下是最优的，包括所有完美图、所有单量子比特、所有两量子比特测量场景等。将其应用于哈密顿量能量估计，我们的框架为分子基准测试提供了构造性策略和改进的方差界。
英文摘要
Shadow tomography addresses the task of efficiently predicting many expectation values of an unknown quantum state from randomized measurements on comparatively few copies. Existing analyses promise large scaling advantages, but the optimal strategies realizing these guarantees are not always known, and the required measurements are potentially challenging to implement on current hardware. We address this gap for Pauli observables by computing optimal sample-complexity parameters and constructing optimal measurement strategies under realistic resource constraints. We focus on memoryless protocols, where each copy is measured only once, and on measurements with bounded interaction range. Our approach reduces the problem to the analysis of graph parameters of the frustration graph encoding the Pauli anticommutation relations. We provide efficient numerical methods for the general case and analytically prove that Clifford measurements are optimal in many situations. This includes all perfect graphs, all single-qubit, all two-qubit measurement scenarios, and more. Applied to Hamiltonian energy estimation, our framework yields constructive strategies and improved variance bounds for molecular benchmarks.
