  Maxwells equations are fundamental to our understanding of electromagnetic
fields, but their solution can be computationally demanding, even for
high-performance computing clusters. Quantum computers offer a promising
alternative for solving these equations, as they can simulate larger and more
complex systems more efficiently both in time and resources. In this paper we
investigate the potential of using the variational quantum imaginary time
evolution (VarQITE) algorithm on near-term quantum hardware to solve for the
Maxwells equations. Our objective is to analyze the trade-off between the
accuracy of the simulated fields and the depth of the quantum circuit required
to implement the VarQITE algorithm. We demonstrate that VarQITE can efficiently
approximate the solution of these equations with high accuracy, and show that
its performance can be enhanced by optimizing the quantum circuit depth. Our
findings suggest that VarQITE on near-term quantum devices could provide a
powerful tool for solving PDEs in electromagnetics and other fields.
