动力学关联器的复杂性：算符阴影与指数学习分离
The Complexity of Dynamical Correlators: Operator Shadows and Exponential Learning Separations
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中文总结 AI 辅助
研究量子平台动力学关联器完整读出难的问题，引入算符阴影概念，通过泡利和克利福德算符阴影分别估计局部OTOC和两点关联器，还证明学习OTOC的信息论下界及指数分离，刻画查询复杂性与测量效率优势。
中文摘要 AI 辅助
量子平台能够实现超越经典模拟的多体动力学，但完整读出仍然难以处理：提取可访问信息的成本随系统大小呈指数增长。经典阴影和贝尔采样提供了可扩展的、多可观测量的估计，这些估计来自随机或纠缠辅助测量。本文旨在将这些想法从静态快照扩展到动力学关联器，包括乱序关联器（OTOC）和两点函数。特别地，我们引入了算符阴影的概念，定义为矢量化时间演化算符的经典阴影。泡利算符阴影能够同时估计所有局部OTOC，而克利福德算符阴影能够高效地同时估计所有两点关联器。另外，贝尔采样允许同时计算所有对角OTOC。我们还证明了学习OTOC的信息论下界，在许多情况下完全刻画了它们的查询复杂性，并给出了指数分离，从而形式化了矢量化方法何时提供测量效率优势。
英文摘要
Quantum platforms can realize many-body dynamics beyond classical simulation yet complete readout remains intractable: the cost of extracting accessible information scales exponentially with system size. Classical shadows and Bell sampling offer scalable, multi-observable estimation from randomized or entanglement-assisted measurements. Here we aim to push these ideas beyond static snapshots to dynamical correlators, including out-of-time-ordered correlators (OTOCs) and two-point functions. In particular, we introduce the notion of the shadow of an operator, defined as the classical shadow of the vectorized time-evolved operator. Pauli operator-shadows enable simultaneous estimation of all local OTOCs, while Clifford operator-shadows enable efficient simultaneous estimation of all two-point correlators. Alternatively, Bell sampling allows one to simultaneously compute all diagonal OTOCs. We also prove information-theoretic lower bounds for learning OTOCs, fully characterizing their query complexities in many cases, and yielding exponential separations that formalize when the vectorized approach provides measurement-efficiency advantages.
