  Variational quantum algorithms are one of the most promising methods that can
be implemented on noisy intermediate-scale quantum (NISQ) machines to achieve a
quantum advantage over classical computers. This article describes the use of a
variational quantum algorithm in conjunction with the finite difference method
for the calculation of propagation modes of an electromagnetic wave in a hollow
metallic waveguide. The two-dimensional (2D) waveguide problem, described by
the Helmholtz equation, is approximated by a system of linear equations, whose
solutions are expressed in terms of simple quantum expectation values that can
be evaluated efficiently on quantum hardware. Numerical examples are presented
to validate the proposed method for solving 2D waveguide problems.
