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Qubit Lattice Algorithm Simulations of Maxwell's Equations for Scattering from Anisotropic Dielectric Objects
preprintposted on 2023-02-02, 17:02 authored by George Vahala, Min Soe, Linda Vahala, Abhay K. Ram, Efstratios Koukoutsis, Kyriakos Hizanidis
A Dyson map explicitly determines the appropriate basis of electromagnetic fields which yields a unitary representation of the Maxwell equations in an inhomogeneous medium. A qubit lattice algorithm (QLA) is then developed perturbatively to solve this representation of Maxwell equations. QLA consists of an interleaved unitary sequence of collision operators (that entangle on lattice-site qubits) and streaming operators (that move this entanglement throughout the lattice). External potential operators are introduced to handle gradients in the refractive indices, and these operators are typically non-unitary, but sparse matrices. By also interleaving the external potential operators with the unitary collide-stream operators one achieves a QLA which conserves energy to high accuracy. Some two dimensional simulations results are presented for the scattering of a one-dimensional (1D) pulse off a localized anisotropic dielectric object.