Variational Quantum-Based Simulation of Waveguide Modes

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