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Abstract We present the HelioCubed, a high-order magnetohydrodynamic (MHD) code designed for modeling the inner heliosphere. The code is designed to achieve 4th order accuracy both in space and in time. In addition, HelioCubed can perform simulations on mapped grids, such as those based on cubed spheres, which makes it possible to overcome stability limitations caused by the geometrical singularity at the polar axis of a spherical grid, thus enabling substantially larger time steps. HelioCubed has been developed using the high-level Proto library, ensures performance portability across CPU and GPU architectures, and supports back-end implementations, e.g., CUDA, HIP, OpenMP, and MPI. The code is compatible with the HDF5 library, which facilitates seamless data handling for simulations and boundary conditions derived from semi-empirical and MHD models of the solar corona. While presenting the results of preliminary simulations, we demonstrate that our simulations are indeed performed with 4th order of accuracy. Our approach ensures that HelioCubed solves the MHD equations preserving the radial flow to machine round-off error even on cubed-sphere grids. Solar wind simulations are performed using the boundary conditions provided by the Wang–Sheeley–Arge coronal model of the ambient solar wind. It also allows us to to simulate coronal mass ejections using observation-driven flux rope models. These capabilities make HelioCubed a versatile and powerful tool to advance heliophysics research and space weather forecasting.