Qubit Lattice Algorithm for an Electromagnetic Pulse Interacting with a Two-Dimensional (2D) Dielectric Obstacle

A qubit lattice algorithm (QLA) is developed for the solution of Maxwell equations in a scalar dielectric 2D medium.  QLA consists of an interleaved sequence of collide-stream operators appropriately chosen so that Maxwell equations in an arbitrary scalar medium are recovered to second order.  Using the Riemann-Silberstein-Weber representation, the qubit evolution equations will have both Hermitian and antiHermitian operators.  1D QLA is extended to 2D by tensor products, requiring just 16 qubits/lattice site.  Here we consider the propagation of a 1D electromagnetic pulse past a 2D dielectric cylinder whose diameter is several times larger than the pulse width.  As in the 1D QLA simulations we find transmission and reflection of the pulse.  There is a phase change in the electric field component on reflection off the dielectric cylinder while an additional component of the magnetic field is created due to the 2D dielectric so as to maintain div B = 0. The refraction of the incident pulse at the dielectric boundary and multiple reflections within the dielectric lead to circular wavefronts propagating in the surrounding medium.  If desired, the antiHermitian operators can be readily coaxed into Hermitian form by doubling the number of qubits/lattice site.