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It is well known that Maxwell equations can be expressed in a unitarySchrodinger-Dirac representation for homogeneous media. However, difficultiesarise when considering inhomogeneous media. A Dyson map points to a unitaryfield qubit basis, but the standard qubit lattice algorithm of interleavedunitary collision-stream operators must be augmented by some sparse non-unitarypotential operators that recover the derivatives on the refractive indices. Theeffect of the steepness of these derivatives on two dimensional scattering isexamined with simulations showing quite complex wavefronts emitted due totransmissions/reflections within the dielectric objects. Maxwell equations areextended to handle dissipation using Kraus operators. Then, our theoreticalalgorithms are extended to these open quantum systems. A quantum circuitdiagram is presented as well as estimates on the required number of quantumgates for implementation on a quantum computer.

Qubit Lattice Algorithms based on the Schrodinger-Dirac representation of Maxwell Equations and their Extensions