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

TL;DR

This paper develops quantum lattice algorithms for Maxwell equations in inhomogeneous and dissipative media, using a Schrodinger-Dirac representation, and explores their implementation on quantum computers.

Contribution

It introduces a novel quantum lattice algorithm framework for Maxwell equations in complex media, including dissipation, with circuit diagrams and gate estimates.

Findings

Simulations show complex wavefronts due to inhomogeneities.

Extended algorithms handle dissipation via Kraus operators.

Quantum circuit estimates for implementation are provided.

Abstract

It is well known that Maxwell equations can be expressed in a unitary Schrodinger-Dirac representation for homogeneous media. However, difficulties arise when considering inhomogeneous media. A Dyson map points to a unitary field qubit basis, but the standard qubit lattice algorithm of interleaved unitary collision-stream operators must be augmented by some sparse non-unitary potential operators that recover the derivatives on the refractive indices. The effect of the steepness of these derivatives on two dimensional scattering is examined with simulations showing quite complex wavefronts emitted due to transmissions/reflections within the dielectric objects. Maxwell equations are extended to handle dissipation using Kraus operators. Then, our theoretical algorithms are extended to these open quantum systems. A quantum circuit diagram is presented as well as estimates on the required number of quantum gates for implementation on a quantum computer.