论文标题
量子状态的自适应在线学习
Adaptive Online Learning of Quantum States
论文作者
论文摘要
高效的量子状态学习的问题（也称为阴影层析成像）旨在通过POVMS理解未知的$ D $维量子状态。然而，这些国家很少静态。它们由于测量，环境噪声或固有的哈密顿状态过渡等因素而发展。本文利用自适应在线学习的技术来保持这种状态变化的步伐。 在这些可变环境中学习的关键指标是增强的遗憾概念，特别是适应性和动态的遗憾。我们为在线影子层析成像提供了自适应和动态的遗憾界限，这些范围在测量量的量子数和sublinear的数量中是多项式。为了支持我们的理论发现，我们包括验证我们提出的模型的数值实验。
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.
