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With their constantly increasing peak performance and memory capacity, modernsupercomputers offer new perspectives on numerical studies of open many-bodyquantum systems. These systems are often modeled by using Markovian quantummaster equations describing the evolution of the system density operators. Inthis paper we address master equations of the Lindblad form, which are apopular theoretical tool in quantum optics, cavity quantum electrodynamics, andoptomechanics. By using the generalized Gell-Mann matrices as a basis, anyLindblad equation can be transformed into a system of ordinary differentialequations with real coefficients. This allows us to use standardhigh-performance parallel algorithms to integrate the equations and thus toemulate open quantum dynamics in a computationally efficient way. Recently wepresented an implementation of the transform with the computational complexityscaling as $O(N^5 log N)$ for dense Lindbaldians and $O(N^3 log N)$ for sparseones. However, infeasible memory costs remain a serious obstacle on the way tolarge models. Here we present a parallel cluster-based implementation of thealgorithm and demonstrate that it allows us to integrate a sparse Lindbladianmodel of the dimension $N=2000$ and a dense random Lindbladian model of thedimension $N=200$ by using $25$ nodes with $64$ GB RAM per node.

Transforming the Lindblad Equation into a System of Linear Equations: Performance Optimization and Parallelization of an Algorithm