Unitary Qubit Lattice Algorithms for Electromagnetic Scattering in Anisotropic Dielectric Media

A fully unitary representation of the Faraday-Ampere subset of Maxwell equations has been developed recently for a medium represented by an anisotropic permittivity tensor [1]. Using pseudo-Hermitian theory[1], an appropriate metric is found in which the Faraday-Ampere equations take on a fully Hermitian form. The corresponding transformation leads to a Dyson map that yields a fully unitary representation of the curl-Maxwell equations in the standard Hilbert space. We are developing a unitary Qubit Lattice Algorithm (QLA) for this new representation, devising the required sequence and form of the interleaved sequence of unitary collision-stream operators on a chosen set of qubits. We first consider a simple splitting of the similarity Dyson transformation. While this splitting results in a QLA which is not fully unitary, the QLA simulates electromagnetic scattering in a tensor anisotropic dielectric media. Our earlier studies were restricted to scalar dielectric media. QLA simulations will be presented for both 1D and 2D scattering from tensor dielectric media and eventually in a cold plasma dielectric media. A fully unitary QLA is required for direct implementation on quantum computers.

[1] E. Koukoutsis et. al. (poster this DPP meeting)