Convergence Analysis of Galerkin Approximations for the Lindblad Master Equation
Numerical Analysis
2026-05-05 v2 Numerical Analysis
Quantum Physics
Abstract
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.
Keywords
Cite
@article{arxiv.2510.11416,
title = {Convergence Analysis of Galerkin Approximations for the Lindblad Master Equation},
author = {Rémi Robin and Pierre Rouchon},
journal= {arXiv preprint arXiv:2510.11416},
year = {2026}
}