Quantum lattice gas approach for the Maxwell equations

We show that a quantum lattice gas approach can provide a viable means for numerically solving the classical Maxwell equations. By casting the Maxwell equations in Dirac form, the propagator may be discretized, and we describe how the accuracy relative to the time step may be systematically increased. The quantum lattice gas form of the discretization is suitable for implementation on hybrid classical-quantum computers. We discuss a number of extensions, including application to inhomogeneous media.