Convergence Analysis of Galerkin Approximations for the Lindblad Master Equation

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 $\mathit{\text{a}}\mathit{\text{priori}}$ estimates, we derive explicit convergence rates and demonstrate the effectiveness of our method through examples motivated by autonomous quantum error correction.