[P-EM17] Space Plasma Science

[PEM17-14] Estimation of Simulation Size with Quantum Advantage in Quantum Computation of the Vlasov-Maxwell Equations vs. a Classical High-Accuracy Computational Method.

*Hayato Higuchi¹, Juan William Pedersen², Chusei Kiumi³, Kohji Yoshikawa⁴, Kiichiro Toyoizumi⁵, Akimasa Yoshikawa¹ (1.Kyushu University , 2.RIKEN, 3.Osaka University, 4.University of Tsukuba, 5.Keio University)

Keywords:Quantum computing, Vlasov simulation, Kinetic simulation, Computational fluid technique

Recently, with advances in both the software and hardware aspects of quantum computing, quantum algorithms have shown to provide many benefits. Practical applications of quantum computing in finance, chemistry, fluids, and various fields have focused much research and development (e.g., Bouland et al.,[2020], Cao et al.,[2019], Egger et al.,[2020] and Budinski, [2022]). We have developed a quantum algorithm for the 6D Boltzmann-Maxwell equations with quantum walks for application to collisionless space plasma simulations (Higuchi et al.,[2023]). While it provided computational speedup on a logarithmic scale with respect to the number of spatial grids, the issue was that it increased computational complexity with respect to the number of time steps. Moreover, only the time evolution of one step was accelerated, and it was not assured that the speed-up would be achieved at any given time evolution.
Therefore, we took as a reference the quantum algorithm for the linear Vlasov-Poisson equation (Toyoizumi et al., [2023]) using a quantum numerical method called Hamiltonian Simulation based on Quantum Singular Value Transformation. Using the same framework, we reconstructed the quantum algorithm for the Vlasov-Maxwell equations. This improved exponentially the computational complexity, including the number of time steps, and ensured smooth arbitrary time evolution. In addition, we found that the implementation of the quantum algorithm in the method can be applied to other fluid numerical methods universally. The reason is that it features a simple quantum circuit structure. Because it has a simple quantum circuit structure and can be implemented simply by changing the Hamiltonian according to the governing equations of the target.
In this presentation, we will introduce Quantum Singular Value Transformation that is suitable for plasma simulation in quantum computing. We will show the results solved on a quantum computer simulator, and then explain the simulation size estimates that exceed the high-precision calculations by classical computers. We will also discuss the future prospects of applications that can be expected in our field, based on the development trends of hardware and software for quantum computers.