Quantum Computing for Future Super Large-Scale Plasma Simulations: A Novel Approach for Simulating the Vlasov-Maxwell System

The space plasma environment, extending from the Sun to the Earth, includes regions of frozen conditions, zones of anomalous resistance caused by electromagnetic turbulence, interconnected regions characterized by weakly ionized gas systems in strong magnetic fields, coupled neutral-atmosphere chemical processes, and pure neutral-atmosphere collision systems. Owing to their complex interactions, an inclusive understanding and forecasting of the space environment remains an elusive goal, even with the advancements in high-performance instrumentation and in-situ observation of satellites. Therefore, it is imperative to develop space plasma simulations capable of providing comprehensive insights, ranging from local spatial domains to the global schematic.

Historically, the development of space plasma simulations has been constrained by computational time, memory capacity, and data storage limitations, resolving complex phenomena with restricted physics at local space scales.

Recently, as quantum computing hardware has advanced, quantum algorithms have proven to benefit exponential speedups. There has been a focus on the practical applications of quantum computing in finance, chemistry, fluids, and a variety of fields (e.g., Bouland et al.,[2020], Cao et al.,[2019], Egger et al.,[2020] and Budinski, [2022]). Then a quantum algorithm for the collisionless Boltzmann equation using the discrete velocity method was developed by (Todorova and Steijl, [2020]).

We have developed a quantum algorithm for the six-dimensional Boltzmann-Maxwell equations for collisionless plasmas with reference to (Higuchi, et al.,[2023]). We applied this methodology to propose a quantum approach that predicts kinetic and multiscale plasma dynamics.

In this presentation, we will introduce a quantum algorithm for performing super large- scale plasma simulations in a quantum computer and estimate the performance required by this task for future quantum error tolerant large-scale quantum computers. We will also discuss the prospects for applications that can be expected in our field, based on trends in the development of quantum computer hardware and software.