A quantum algorithm for nonlinear electromagnetic fluid dynamics using Koopman-von Neumann linearization

To predict and simulate plasma phenomena, large-scale computational resources have been employed to develop high-precision, high-resolution plasma simulations. However, multi-scale plasma simulations require computational resources that scale polynomially with the number of spatial grids, posing a significant challenge for large-scale modeling. In this study, we present a quantum algorithm for simulating the nonlinear electromagnetic fluid dynamics systems that govern space plasmas. By applying Koopman–von Neumann (KvN) linearization, we map the nonlinear electromagnetic fluid dynamics systems to a Schrödinger equation and evolve it using Hamiltonian simulation via quantum singular value transformation (QSVT). The resulting algorithm reduces the computational complexity from O(Nx4) scaling of classical finite volume schemes to O(Nx log Nx), where Nx is the number of spatial grid points per dimension. And numerical experiments quantify behaviors of combined errors of discretization, KvN linearization, and QSVT-Hamiltonian simulation. As a practical demonstration, the method accurately reproduces the Kelvin-Helmholtz instability, underscoring its capability to tackle intricate nonlinear dynamics. These results suggest that quantum computing can offer a viable pathway to overcome the computational barriers of traditional multiscale plasma modeling.