论文标题
非马克维亚开放量子动态的描述和复杂性
Description and complexity of Non-markovian open quantum dynamics
论文作者
论文摘要
在开放量子系统理论中，理解和模拟非马克维亚量子动力学仍然是一个重要的挑战。这项努力的关键进步是开发对非马克维亚动力学的统一数学描述，并在多体设置中对其复杂性进行分类。在本文中，我们确定了一类通用的非马克维亚记忆内核，该内核通过复杂值ra的测量来描述，并通过构建相应的系统 - 环境统一组的正规化程序来定义其动力学。然后，在此定义的基础上，我们考虑了$ k-$本地多体非马尔可夫系统，对内存内核的总变化和平滑度具有物理上动机的假设。我们确定可以在量子计算机上有效地近似它们的动态，从而为这类非马克维亚开放量子系统的一般类别提供了对扩展教会培养论文的严格验证。
Understanding and simulating non-Markovian quantum dynamics remains an important challenge in open quantum system theory. A key advance in this endeavour would be to develop a unified mathematical description of non-Markovian dynamics, and classify its complexity in the many-body setting. In this paper, we identify a general class of non-Markovian memory kernels, described by complex-valued radon measures, and define their dynamics through a regularization procedure constructing the corresponding system-environment unitary groups. Building on this definition, we then consider $k-$local many-body non-Markovian systems with physically motivated assumptions on the total variation and smoothness of the memory kernels. We establish that their dynamics can be efficiently approximated on quantum computers, thus providing a rigorous verification of the Extended Church-Turing thesis for this general class of non-Markovian open quantum systems.
