发表机构
Virginia Tech; California Institute of Technology; Duke University（弗吉尼亚理工大学; 加州理工学院; 杜克大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文研究SPAM噪声下局部Lindbladian的学习问题，刻画了规范变换导致的不可学习性，并提出了仅用可信单量子比特操作、无需辅助比特的SPAM鲁棒算法，可高效学习所有普适规范不变分量。
AI 中文摘要
我们研究了在态制备与测量（SPAM）噪声存在的情况下学习局部Lindbladian的问题。尽管近期工作已在理想化访问假设下开发出可扩展的学习算法，但SPAM可能使不同的Lindbladian在实验上无法区分，从而使得部分Lindbladian从根本上不可学习。我们对于有界度的局部Lindbladian给出了这一阻碍的精确刻画。我们识别出一族保持局域性的规范变换，这些变换与可信的单量子比特控制对易，并利用它们对Lindbladian分量进行分类。对于一般规范依赖的分量，我们构造Lindbladian以表明即使施加完全正性约束，它们仍可能具有与系统大小无关的Ω(1)不确定性。我们通过用于学习每个普适规范不变分量的SPAM鲁棒算法来补充这一刻画。我们的算法仅使用可信的单量子比特操作，既不需要辅助比特也不需要纠缠控制，并且在常数局域性和度下使用Õ(ε^{-2}log(N/δ))次实验和总演化时间。我们的保证允许全局SPAM随着N增长而任意偏离理想状态，仅要求非零的局域可见性。我们还建立了在物理正性约束下边界诱导的额外哈密顿量系数的规范不变性的充分条件，尽管在一般情况下学习这些额外参数仍然是一个开放问题。更广泛地说，我们的规范感知框架和SPAM消除技术为开放量子系统的可扩展表征提供了实用工具包。
英文摘要
We study the problem of learning a local Lindbladian in the presence of state-preparation-and-measurement (SPAM) noise. Although recent work has developed scalable learning algorithms under idealized access assumptions, SPAM can make distinct Lindbladians experimentally indistinguishable, thus making part of the Lindbladian fundamentally unlearnable. We give a sharp characterization of this obstruction for bounded-degree local Lindbladians. We identify a family of locality-preserving gauge transformations that commutes with trusted single-qubit control, and use it to classify Lindbladian components. For the generically gauge dependent components, we construct Lindbladians to show that they can have $Ω(1)$ uncertainty independent of system size, even after imposing complete positivity. We complement this characterization with SPAM-robust algorithms for learning every universally gauge-invariant component. Our algorithms use only trusted single-qubit operations, require neither ancillas nor entangling control, and use $\widetilde{\mathcal O}\left(ε^{-2}\log(N/δ)\right)$ experiments and total evolution time for constant locality and degree. Our guarantees allow global SPAM to become arbitrarily far from ideal as $N$ grows, requiring only nonvanishing local visibility. We also establish sufficient conditions for boundary-induced gauge invariance of additional Hamiltonian coefficients under physical positivity constraints, though learning these additional parameters in general remains an open problem. More broadly, our gauge-aware framework and SPAM-cancellation techniques offer a practical toolkit for the scalable characterization of open quantum systems.
