A Quantum Algorithm for Nonlinear Electromagnetic Fluid Dynamics via Koopman-von Neumann Linearization
POSTER
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 Schrödinger equation and evolve the system using Hamiltonian simulation via quantum singular value transformation.
Our algorithm scales O(sNxpolylog(Nx)T) in time complexity with s, Nx, and T being the spatial dimension, the number of spatial grid points per dimension, and the evolution time, respectively.
Comparing the scaling O(sNxs(T5/4+TNx)) for the classical method with the finite volume scheme, this algorithm achieves polynomial speedup in Nx.
The space complexity of this algorithm is exponentially reduced from O(sNxs) to O(spolylog(Nx)).
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.
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 Schrödinger equation and evolve the system using Hamiltonian simulation via quantum singular value transformation.
Our algorithm scales O(sNxpolylog(Nx)T) in time complexity with s, Nx, and T being the spatial dimension, the number of spatial grid points per dimension, and the evolution time, respectively.
Comparing the scaling O(sNxs(T5/4+TNx)) for the classical method with the finite volume scheme, this algorithm achieves polynomial speedup in Nx.
The space complexity of this algorithm is exponentially reduced from O(sNxs) to O(spolylog(Nx)).
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.
*HH gratefully acknowledges the financial support of the Kyushu University Innovator Fellowship Program (Quantum Science Area).YI, KS, and KF are supported by MEXT Quantum Leap Flagship Program (MEXT Q-LEAP) Grant No. JPMXS0120319794 and JST COI-NEXT Grant No. JPMJPF2014.YI and KS are also supported by JST SPRING Grant No. JPMJSP2138 and the $\Sigma$ Doctoral Futures Research Grant Program from The University of Osaka.
Publication: https://doi.org/10.48550/arXiv.2509.22503
Presenters
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Hayato Higuchi
- QunaSys Inc.