Prospects for a Quantum Speedup of Classical Nonlinear Plasma Simulations

Large nonlinear dynamical systems, including systems generated by discretization of hyperbolic partial differential equations, are important in both fluid and kinetic computational plasma physics. The simulation of these systems can be extremely computationally demanding, which motivates exploring whether a future error-corrected quantum computer could perform these simulations more efficiently than any classical computer. Quantum computers are expected to provide a dramatic speedup for many linear computations, e.g. through the application of quantum linear systems algorithms, but obtaining any large speedup for nonlinear computations is made difficult by the linearity of quantum mechanics. We describe a method for mapping any finite nonlinear dynamical system to an infinite linear dynamical system, which can then be approximated with finite linear systems if the nonlinearity is sufficiently weak [1]. Using this approach, a quantum computer could approximate the simulation of weakly nonlinear dynamical systems using a number of qubits only logarithmic in the size of the nonlinear system.

[1] "Linear embedding of nonlinear dynamical systems and prospects for efficient quantum algorithms," A. Engel, G. Smith, S. E. Parker, Phys. Plasmas 28, 062305 (2021).