Detailed simulations are presented on a quantum lattice algorithm (QLA) for the solution of pulse propagation in a two dimensional (2D) refractive index medium. In particular, the initial value problem of an electromagnetic pulse scattering from a localized dielectric object is considered. The properties of the scattered waves depend on the scale length of the transition layer separating the vacuum from the core of the dielectric. The QLA perturbatively recovers the Maxwell equations to second order in a perturbation parameter ε that is just the normalized initial speed of light. QLA simulations show that the Maxwell equations are still recovered when ε = 1.