Qubit Lattice Algorithm for electromagnetic wave scattering from scalar dielectric media

A Qubit Lattice Algorithm (QLA) consisting of an interleaved sequence of unitary streaming and collision non-commuting operators which together with an appropriate set of potential operators is a discrete representation of a set of continuum equations. Using an 8-spinor representation [1], we have developed an initial value QLA for Maxwell equations to study the scattering of spatially confined electromagnetic pulses by inhomogeneous 2D scalar dielectric objects. For homogeneous media, there is a direct analogy between Maxwell equations and the Dirac equation for a free particle, with the corresponding 4-qubit QLA fully unitary. In its simplest forms, the inhomogeneous 8-qubit QLA introduces a Hermitian operator. Numerical simulations show that the scattering of an initial 1D pulse by dielectric cylinders and cones show multiple internal reflections and subsequent refractions into the surrounding vacuum region. The refractions are not 1D as they are affected by the geometry of the scatterer. QLA simulations show new magnetic field components in the scattered field so that div B = 0.

[1] S. A. Khan, Physica Scripta 71, 440 (2005)