Title: Simulation complexity of open quantum dynamics: Connection with tensor networks Show Chinese title

Title: 开放量子动力学的仿真复杂度：与张量网络的联系

Abstract: The difficulty to simulate the dynamics of open quantum systems resides in their coupling to many-body reservoirs with exponentially large Hilbert space. Applying a tensor network approach in the time domain, we demonstrate that effective small reservoirs can be defined and used for modeling open quantum dynamics. The key element of our technique is the timeline reservoir network (TRN), which contains all the information on the reservoir's characteristics, in particular, the memory effects timescale. The TRN has a one-dimensional tensor network structure, which can be effectively approximated in full analogy with the matrix product approximation of spin-chain states. We derive the sufficient bond dimension in the approximated TRN with a reduced set of physical parameters: coupling strength, reservoir correlation time, minimal timescale, and the system's number of degrees of freedom interacting with the environment. The bond dimension can be viewed as a measure of the open dynamics complexity. Simulation is based on the semigroup dynamics of the system and effective reservoir of finite dimension. We provide an illustrative example showing scope for new numerical and machine learning-based methods for open quantum systems. Show Chinese abstract

Abstract: 模拟开放量子系统动力学的困难在于它们与具有指数级大希尔伯特空间的多体辐射场耦合。 在时域中应用张量网络方法，我们证明可以定义并使用有效的小型辐射场来建模开放量子动力学。 我们技术的关键要素是时间线辐射场网络（TRN），它包含关于辐射场特征的所有信息，特别是记忆效应的时间尺度。 TRN 具有一维张量网络结构，可以完全类比自旋链态的矩阵乘积近似进行有效近似。 我们通过一组简化的物理参数推导出近似 TRN 中足够的键维数：耦合强度、辐射场相关时间、最小时间尺度以及与环境相互作用的系统的自由度数量。 键维数可以视为开放动力学复杂性的度量。 模拟基于系统的半群动力学和有限维的有效辐射场。 我们提供了一个示例，展示了针对开放量子系统的新数值和机器学习方法的应用前景。