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Running kinetic plasma physics simulations using grid-based solvers is very demanding both in terms of memory as well as computational cost. This is primarily due to the up to six-dimensional phase space and the associated unfavorable scaling of the computational cost as a function of grid spacing (often termed the curse of dimensionality). In this article, we present 4d, 5d, and 6d simulations of the Vlasov–Poisson equation with a split-step semi-Lagrangian discontinuous Galerkin scheme on graphic processing units (GPUs). The local communication pattern of this method allows an efficient implementation on large-scale GPU-based systems and emphasizes the importance of considering algorithmic and high-performance computing aspects in unison. We demonstrate a single node performance above 2 TB/s effective memory bandwidth (on a node with four A100 GPUs) and show excellent scaling (parallel efficiency between 30% and 67%) for up to 1536 A100 GPUs on JUWELS Booster. Graphical Abstract [ABSTRACT FROM AUTHOR]