Lattice Boltzmann and quantum lattice gas representations of one-dimensional magnetohydrodynamic turbulence

A simplified one-dimensional (1D) magnetohydrodynamics (MHD) is solved using a lattice Boltzmann and a quantum lattice gas model. It is shown that the magnetic field decreases the strength of the velocity shock fronts, with marked spikes in the magnetic field strength that gradually broaden in time. There is very good agreement between the lattice Boltzmann model--a representation of non-linear systems that circumvent the non-local non-linear advection by simple local non-linearities within the collision operator--and the quantum lattice gas--an algorithm that is unconditionally stable and appropriate for a hybrid quantum-classical computer