标题： 开放量子系统中的变分微扰理论用于高效稳态计算 显示英文标题

标题： Variational Perturbation Theory in Open Quantum Systems for Efficient Steady State Computation

摘要： 确定开放量子系统的稳态对于表征量子器件和研究各种物理现象至关重要。通常，计算单一稳态是不够的，需要探索其对外部参数的依赖性。在这种情况下，针对每个参数组合独立计算稳态很快变得难以处理。微扰理论（PT）可以通过在参考参数周围展开稳态来缓解这一挑战，在相邻参数值之间最小化冗余计算。然而，PT有两个显著的局限性：它依赖于伪逆——一种数值上代价高昂的操作，并且具有有限的收敛半径。在这项工作中，我们消除了这两个障碍。首先，我们引入了变分微扰理论（VPT）及其多点推广，即使在存在非解析效应（如耗散相变）的情况下，也能显著扩展收敛半径。然后，我们开发了两种数值策略以消除计算伪逆的需求。第一种方法依赖于一次LU分解，以高效地构建收敛区域内的稳态；第二种方法将VPT重新表述为Krylov空间循环问题，并使用预处理迭代方法。我们在各种模型中验证了这些方法，展示了它们的广泛适用性和相对于标准PT的重大改进。 显示英文摘要

摘要： Determining the steady state of an open quantum system is crucial for characterizing quantum devices and studying various physical phenomena. Often, computing a single steady state is insufficient, and it is necessary to explore its dependence on multiple external parameters. In such cases, calculating the steady state independently for each combination of parameters quickly becomes intractable. Perturbation theory (PT) can mitigate this challenge by expanding steady states around reference parameters, minimizing redundant computations across neighboring parameter values. However, PT has two significant limitations: it relies on the pseudo-inverse -- a numerically costly operation -- and has a limited radius of convergence. In this work, we remove both of these roadblocks. First, we introduce a variational perturbation theory (VPT) and its multipoint generalization that significantly extends the radius of convergence even in the presence of non-analytic effects such as dissipative phase transitions. Then, we develop two numerical strategies that eliminate the need to compute pseudo-inverses. The first relies on a single LU decomposition to efficiently construct the steady state within the convergence region, while the second reformulates VPT as a Krylov space recycling problem and uses preconditioned iterative methods. We benchmark these approaches across various models, demonstrating their broad applicability and significant improvements over standard PT.