The Effect of the Pauli Spin Matrices on the Quantum Lattice Algorithm for Maxwell Equations in Inhomogeneous Media

TL;DR

This paper develops a quantum lattice algorithm using Pauli spin matrices to solve Maxwell equations in inhomogeneous media, demonstrating accurate simulation of electromagnetic wave propagation and boundary interactions without explicit boundary conditions.

Contribution

It introduces a QLA that accounts for inhomogeneities via Pauli matrices, requiring different qubit counts for different media variations, advancing quantum simulation of electromagnetic phenomena.

Findings

Excellent agreement with standard boundary condition results

Accurate simulation of wave propagation in inhomogeneous media

No explicit boundary conditions needed in the simulation

Abstract

A quantum lattice algorithm (QLA) is developed for the solution of Maxwell equations in scalar dielectric media using the Riemann-Silberstein representation. For x-dependent and y-dependent inhomogeneities, the corresponding QLA requries 8 qubits/spatial lattice site. This is because the corresponding Pauli spin matrices have off-diagonal components which permit the collisional entanglement of two qubits. However, z-dependent inhomogeneities require a QLA with 16 qubits/lattice site since the Pauli spin matrix $\sigma_z$ is diagonal. QLA simulations are performed for the time evolution of an initial electromagnetic pulse propagating normally to a boundary layer region joining two media of different refractive index. There is excellent agreement between all three representations, as well as very good agreement with nearly all the standard plane wave boundary condition results for reflection and transmission off a dielectric discontinuity. In the QLA simulation, no boundary conditions are imposed at the continuous, but sharply increasing, boundary layer.