Quantum Method for Solving S-parameters of Lossless Waveguides Based on the HHL Method and Finite-Element-Method

Quantum computing presents a promising approach to address the computational challenges in electromagnetic (EM) problems. Recently, preliminary studies have been conducted on the application of the Harrow/Hassidim/Lloyd (HHL) quantum method to solve finite-element-method (FEM) equations in the EM domain. Since quantum measurements are typically limited to measuring the magnitude rather than the phase, only the magnitude of the electric field can be calculated by existing quantum computing methods. However, without access to phase information of the electric field, the final S-parameters cannot be solved in a traditional computing way. This paper proposes a new quantum method to calculate the two-port S-parameters of lossless waveguides. Novel formulations are derived to leverage two inner products to develop the complete calculation. The correctness and accuracy of the proposed method are demonstrated using a waveguide example.