  A quantum lattice algorithm (QLA) is developed for the solution of Maxwell
equations in scalar dielectric media using the Riemann-Silberstein
representation. For x-dependent and y-dependent inhomogeneities, the
corresponding QLA requries 8 qubits/spatial lattice site. This is because the
corresponding Pauli spin matrices have off-diagonal components which permit the
collisional entanglement of two qubits. However, z-dependent inhomogeneities
require a QLA with 16 qubits/lattice site since the Pauli spin matrix
$\sigma_z$ is diagonal. QLA simulations are performed for the time evolution of
an initial electromagnetic pulse propagating normally to a boundary layer
region joining two media of different refractive index. There is excellent
agreement between all three representations, as well as very good agreement
with nearly all the standard plane wave boundary condition results for
reflection and transmission off a dielectric discontinuity. In the QLA
simulation, no boundary conditions are imposed at the continuous, but sharply
increasing, boundary layer.
