We study a family of structure-preserving deterministic numerical schemes for Lindblad equations. This family of schemes has a simple form and can systemically achieve arbitrary high-order accuracy in theory. Moreover, these schemes can also overcome the non-physical issues that arise from many traditional numerical schemes. Due to their preservation of physical nature, these schemes can be straightforwardly used as backbones for further developing randomized and quantum algorithms in simulating Lindblad equations. In this work, we systematically study these methods and perform a detailed error analysis, which is validated through numerical examples.

翻译：我们研究一族用于林德布拉德方程的保持结构的确定性数值格式。这族格式具有简单形式，理论上能够系统性地实现任意高阶精度。此外，这些格式还能克服许多传统数值格式中出现的非物理问题。由于保留了物理本质，这些格式可直接用作进一步开发模拟林德布拉德方程的随机算法和量子算法的基础框架。本文系统性地研究了这些方法，并进行了详细的误差分析，该分析通过数值算例得到验证。