Comparison of Qubit Lattice Algorithms for the Ampere-Faraday Equations with the full set of Maxwell equations.

It is common to consider just the Faraday-Ampere curl equations when studying the propagation of waves in plasmas, with the two divergence equations being treated as initial conditions. However, in numerical computations (e.g., MHD simulations) the effects of discretization can plague the simulation since the constraint div B = 0 can only satisfied approximately. Thus, most MHD codes require divergence cleaning throughout the simulation, even if initially div B = 0. We compare Qubit Lattice Algorithms (QLAs) for the curl-curl Maxwell system with that for the full set of Maxwell equations. A QLA consists of an interleaved sequence of unitary collision-stream operations on a set of qubits with appropriate Hermitian potential operators [1]. In 2D the curl-curl subset requires 6 qubits/lattice node while the full Maxwell system requires 8 qubits/lattice node. We compare the two representations by studying the scattering of an electromagnetic pulse by a 2D scalar dielectric cylinder or cone with large refractive index gradients. The scattered fields have a complex structure arising from internal reflections within the dielectric.

[1] G. Vahala et. al. Rad. Effects Def. Solids 176, 49-732 (2021)