A Quantum Algorithm for Nonlinear Electromagnetic Fluid Dynamics via Koopman-von Neumann Linearization

• URL: http://arxiv.org/abs/2509.22503v1
• Date: Fri, 26 Sep 2025 15:44:51 GMT
• Title: A Quantum Algorithm for Nonlinear Electromagnetic Fluid Dynamics via Koopman-von Neumann Linearization
• Authors: Hayato Higuchi, Yuki Ito, Kazuki Sakamoto, Keisuke Fujii, Akimasa Yoshikawa,
• Abstract summary: This study presents a quantum algorithm for the nonlinear electromagnetic fluid dynamics that govern space plasmas.<n>We map it, by applying Koopman-von Neumann linearization, to the Schr"odinger equation and evolve the system via quantum singular value transformation.<n> Numerical experiments validate that accurate solutions are attainable with smaller $m$ than theoretically anticipated.
• Score: 4.485267685992102
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: To simulate plasma phenomena, large-scale computational resources have been employed in developing high-precision and high-resolution plasma simulations. One of the main obstacles in plasma simulations is the requirement of computational resources that scale polynomially with the number of spatial grids, which poses a significant challenge for large-scale modeling. To address this issue, this study presents a quantum algorithm for simulating the nonlinear electromagnetic fluid dynamics that govern space plasmas. We map it, by applying Koopman-von Neumann linearization, to the Schr\"{o}dinger equation and evolve the system using Hamiltonian simulation via quantum singular value transformation. Our algorithm scales $O \left(s N_x \, \mathrm{polylog} \left( N_x \right) T \right)$ in time complexity with $s$, $N_x$, and $T$ being the spatial dimension, the number of spatial grid points per dimension, and the evolution time, respectively. Comparing the scaling $O \left( s N_x^s \left(T^{5/4}+T N_x\right) \right)$ for the classical method with the finite volume scheme, this algorithm achieves polynomial speedup in $N_x$. The space complexity of this algorithm is exponentially reduced from $O\left( s N_x^s \right)$ to $O\left( s \, \mathrm{polylog} \left( N_x \right) \right)$. Numerical experiments validate that accurate solutions are attainable with smaller $m$ than theoretically anticipated and with practical values of $m$ and $R$, underscoring the feasibility of the approach. As a practical demonstration, the method accurately reproduces the Kelvin-Helmholtz instability, underscoring its capability to tackle more intricate nonlinear dynamics. These results suggest that quantum computing can offer a viable pathway to overcome the computational barriers of multiscale plasma modeling.

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