发表机构
Universit\'e de Lorraine, CNRS, LPCT, F-54000 Nancy, France
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文综述并比较了四种基于Matrix Product State的Lindblad方程数值积分算法，包括直接积分与随机展开两类方法，并讨论了其原理、实现、精度和效率，且与精确可解模型进行了基准对比。
AI 中文摘要
在这篇入门综述中，我们介绍并比较了四种用于一维量子晶格系统Lindblad方程数值积分的算法。这四种方法均基于Matrix Product State表示，可视为Time-Evolving Block Decimation (TEBD)算法向开放量子系统的扩展。其中两种方法直接对向量化的Lindblad方程进行积分，其中一种显式强制密度矩阵的正定性。另外两种方法依赖于Lindblad方程的随机展开，即quantum trajectory和quantum state diffusion方法。我们讨论了不同方法的原理、数值实现、精度和计算效率，并将其与一个可精确求解的自由费米子模型进行了基准测试。
英文摘要
In this introductory review, we present and compare four algorithms for the numerical integration of the Lindblad equation for one-dimensional quantum lattice systems. All four methods are based on Matrix Product State representations and can be viewed as extensions of the Time-Evolving Block Decimation (TEBD) algorithm to open quantum systems. Two approaches directly integrate the vectorized Lindblad equation, one of them explicitly enforcing the positivity of the density matrix. The other two rely on stochastic unravelings of the Lindblad equation, namely the quantum trajectory and quantum state diffusion approaches. We discuss the principles, numerical implementation, accuracy, and computational efficiency of the different methods, and benchmark them against an exactly solvable free fermion model.
