Mapping classical nonlinear plasma dynamics to mean-field theory approximations of many-body quantum systems

Mean-field theory can be applied to approximate various quantum systems in the limit of many quantum particles. For example, the Gross–Pitaevskii equation approximates the dynamics of a system of many interacting bosons with a nonlinear partial differential equation for a single-particle wavefunction. Conversely, by considering the reverse of mean-field mappings, nonlinear dynamical systems including some classical plasma systems can be associated with many-body quantum systems. Simulating these many-body quantum systems on a quantum computer could allow for approximations to nonlinear plasma dynamics with significantly different computational complexity than classical simulation methods. Whether a quantum speedup is possible depends on how many quantum particles are needed to approximate the desired output quantity. We investigate this question theoretically and numerically. Output quantities must be well behaved in order to be approximated with only a small number of quantum particles. We also consider the inclusion of measurements into the quantum dynamics as a strategy for improving the approximation of the nonlinear mean-field dynamics.