Qubit lattice algorithms for electromagnetic scattering from 2D tensor dielectric objects*

A qubit lattice algorithm (QLA) is devised for the scattering of an electromagnetic pulse from localized 2D inhomogeneous  dielectric objects

with tensor permittivity ε.  A Dyson map: (E, B) ⇒ (ε.E, B) determines a particular qubit basis for which the evolution of the qubit amplitudes is unitary. 

Conservation of energy is automatically guaranteed from the norm of the qubits.  However, it is non-trivial to preserve  unitarity of the algorithm as one approximates the full exponential operator perturbatively on a spatial lattice spacing δ. Various techniques are considered, including the use of linear combination of unitary operators for quantum encoding.   As δ→0, total electromagnetic energy is conserved.  QLA is an initial value solver.  No internal boundary conditions are imposed between interfaces. 

Significant differences in the scattered fields are seen for a 1D pulse interacting with either a cylindrical dielectric (with a steep transition in refractive index) or a conic dielectric (with a slowly varying transition region). In particular, the pulse bounces within the cylindrical dielectric giving rise to multiple wavefronts, whereas for the conic dielectric there is only one appreciable scattering from around the apex of the cone.