Qubit Lattice Algorithm Simulations of Maxwell's Equations for Scattering from Anisotropic Dielectric Objects

TL;DR

This paper develops a qubit lattice algorithm to simulate Maxwell's equations in inhomogeneous media, enabling efficient quantum simulations of electromagnetic scattering from anisotropic dielectric objects.

Contribution

It introduces a novel perturbative qubit lattice algorithm that incorporates external potentials for accurate energy conservation in simulating Maxwell's equations.

Findings

Successfully simulated 1D pulse scattering off anisotropic dielectric objects.

Demonstrated high energy conservation in the qubit lattice algorithm.

Provided initial 2D simulation results for electromagnetic scattering.

Abstract

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.