Some Comments on Unitary Qubit Lattice Algorithms for Classical Problems

$\bf{Abstract}$: A qubit lattice algorithm (QLA) for normal incidence of an rectangular electromagnetic pulse onto a dielectric slab is examined and shows that the transmission coefficient is indeed augmented over the Fresnel boundary value infinite plane wave result by the square root of the ratio of the refractive indices of the two media. For an oscillatory wave packet, this transmission coefficient is further increased. As the QLA is not fully unitary, due to one evolution operator being Hermitian, first steps are taken in correcting a similar problem of determining a fully unitary QLA for the Korteweg-de Vries equation. This is achieved by appropriate perturbation of the unitary collision angle.