Variational quantum simulation of the Fokker–Planck equation applied to quantum radiation reaction

Abstract Near-future experiments with Petawatt class lasers are expected to produce a high flux of gamma-ray photons and electron–positron pairs through strong field quantum electrodynamical processes. Simulations of the expected regime of laser–matter interaction are computationally intensive due to the disparity of the spatial and temporal scales, and because quantum and classical descriptions need to be accounted for simultaneously (classical for collective effects and quantum for nearly instantaneous events of hard photon emission and pair creation). We study the stochastic cooling of an electron beam in a strong, constant, uniform magnetic field, both its particle distribution functions and their energy momenta. We start by obtaining approximate closed-form analytical solutions to the relevant observables. Then, we apply the quantum-hybrid variational quantum imaginary time evolution to the Fokker–Planck equation describing this process and compare it against theory and results from particle-in-cell simulations and classical partial differential equation solvers, showing good agreement. This work will be useful as a first step towards quantum simulation of plasma physics scenarios where diffusion processes are important, particularly in strong electromagnetic fields.