Quantum Calculation of Classical Kinetic Equations: A Novel Approach for Numerical Analysis of 6D Boltzmann-Maxwell Equations in Collisionless Plasmas Using Quantum Computing

Abstract: A novel quantum algorithm for solving the Boltzmann-Maxwell equations of the 6D collisionless plasma is proposed. The equation describes the kinetic behavior of plasma particles in electromagnetic fields and is known for the classical first-principles equations in various domains, from space to laboratory plasmas. We have constructed a quantum algorithm for a future large-scale quantum computer to accelerate its costly computation. This algorithm consists mainly of two routines: the Boltzmann solver and the Maxwell solver. Quantum algorithms undertake these dual procedures, while classical algorithms facilitate their interplay. Each solver has a similar structure consisting of three steps: Encoding, Propagation, and Integration. We conducted a preliminary implementation of the quantum algorithm and performed a parallel validation against a comparable classical approach. IBM Qiskit was used to implement all quantum circuits.