The problem of efficient quantum state learning, also called shadow tomography, aims to comprehend an unknown $d$-dimensional quantum state through POVMs. Yet, these states are rarely static; they evolve due to factors such as measurements, environmental noise, or inherent Hamiltonian state transitions. This paper leverages techniques from adaptive online learning to keep pace with such state changes.
The key metrics considered for learning in these mutable environments are enhanced notions of regret, specifically adaptive and dynamic regret. We present adaptive and dynamic regret bounds for online shadow tomography, which are polynomial in the number of qubits and sublinear in the number of measurements. To support our theoretical findings, we include numerical experiments that validate our proposed models.

中文翻译：

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量子态的自适应在线学习


高效量子态学习问题，也称为影子断层扫描，旨在通过 POVM 理解未知的 $d$ 维量子态。然而，这些状态很少是静态的；它们由于测量、环境噪声或固有的哈密顿状态转换等因素而演变。本文利用自适应在线学习技术来跟上这种状态变化。

在这些可变环境中学习所考虑的关键指标是增强的后悔概念，特别是适应性和动态后悔。我们提出了在线阴影断层扫描的自适应和动态遗憾界限，其在量子位数量上是多项式，在测量数量上是次线性的。为了支持我们的理论发现，我们进行了数值实验来验证我们提出的模型。