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A quantum lattice algorithm (QLA) is developed for the solution of Maxwellequations in scalar dielectric media using the Riemann-Silbersteinrepresentation. For x-dependent and y-dependent inhomogeneities, thecorresponding QLA requries 8 qubits/spatial lattice site. This is because thecorresponding Pauli spin matrices have off-diagonal components which permit thecollisional entanglement of two qubits. However, z-dependent inhomogeneitiesrequire a QLA with 16 qubits/lattice site since the Pauli spin matrix$\sigma_z$ is diagonal. QLA simulations are performed for the time evolution ofan initial electromagnetic pulse propagating normally to a boundary layerregion joining two media of different refractive index. There is excellentagreement between all three representations, as well as very good agreementwith nearly all the standard plane wave boundary condition results forreflection and transmission off a dielectric discontinuity. In the QLAsimulation, no boundary conditions are imposed at the continuous, but sharplyincreasing, boundary layer.

The Effect of the Pauli Spin Matrices on the Quantum Lattice Algorithm for Maxwell Equations in Inhomogeneous Media