This paper analyzes the numerical approximation of the Lindblad master equation on infinite-dimensional Hilbert spaces. We employ a classical Galerkin approach for spatial discretization and investigate the convergence of the discretized solution to the exact solution. Using \textit{a priori} estimates, we derive explicit convergence rates and demonstrate the effectiveness of our method through examples motivated by autonomous quantum error correction.

翻译：本文分析了无限维希尔伯特空间中Lindblad主方程的数值近似方法。我们采用经典的Galerkin方法进行空间离散化，并研究了离散化解向精确解的收敛性。通过先验估计，我们推导出显式收敛速率，并以自主量子纠错为背景的算例验证了该方法的有效性。