标题： 对称保持量子动力学中的非马尔可夫噪声 显示英文标题

标题： Non-Markovian Noise in Symmetry-Preserving Quantum Dynamics

摘要： 在量子动力学中，对称性对于识别和评估支配量子系统演化的守恒量至关重要。 当提升到开放量子系统设置时，动力学对称性可能会因系统与环境的相互作用而被负面改变，从而使其分析变得更加复杂。 先前关于噪声对称量子动力学的研究主要集中在马尔可夫设置中，尽管非马尔可夫噪声在许多广泛使用的量子技术中普遍存在。 在本研究中，我们开发了一个框架，通过根空间分解和滤波函数形式主义来量化非马尔可夫噪声对对称量子演化的影响。 我们通过分析证明，保持对称性的噪声会维持对称子空间，而非对称噪声会导致高度特定的泄漏误差。 我们通过一个受时空相关噪声影响的横向场伊辛模型的数值研究来支持我们的发现。 我们的结果具有广泛的应用性，为开放量子系统动力学的控制和表征提供了新的分析见解。 显示英文摘要

摘要： In quantum dynamics, symmetries are vital for identifying and assessing conserved quantities that govern the evolution of a quantum system. When promoted to the open quantum system setting, dynamical symmetries can be negatively altered by system-environment interactions, thus, complicating their analysis. Previous work on noisy symmetric quantum dynamics has focused on the Markovian setting, despite the ubiquity of non-Markovian noise in a number of widely used quantum technologies. In this study, we develop a framework for quantifying the impact of non-Markovian noise on symmetric quantum evolution via root space decompositions and the filter function formalism. We demonstrate analytically that symmetry-preserving noise maintains the symmetric subspace, while non-symmetric noise leads to highly specific leakage errors. We support our findings with a numerical study of the transverse field Ising model subject to spatiotemporally correlated noise. Our results are broadly applicable, providing new analytic insights into the control and characterization of open quantum system dynamics.