Quantum Computational Methods for Higher Order Modes Detection in Transmission Lines

The efficient computation of higher-order modes in multiconductor transmission lines is crucial, as these modes alter the distribution of TEM modes and increase cross-talk, affecting electromagnetic compatibility and signal integrity in high-frequency circuits. Traditional numerical methods face challenges in handling large-scale eigenvalue problems due to increasing computational complexity. Quantum computing offers a promising alternative by leveraging quantum principles such as superposition and entanglement to solve large eigenvalue problems more efficiently than classical solvers. In this work, we explore the variational quantum eigensolver as a quantum-assisted method for waveguide modal analysis. Starting from the Helmholtz equation for TM modes, we discretize the system using the finite difference method, map the Hamiltonian onto the Pauli basis, and implement the VQE with a hardware-efficient ansatz optimized via BFGS on the Qiskit statevector simulator of IBM [1]. As a test case, we analyze a shielded stripline. The quantum eigensolver successfully computes the first two TM modes and their cutoff frequencies while reconstructing the Ez and Ex field distributions at 1 GHz. This preliminary study shows the feasibility of quantum algorithms for solving large eigenvalue problems in computational electromagnetics where classical computing can fail, opening new possibilities for the efficient analysis of shielded multiconductor transmission lines, where higher-order modes significantly impact cross-talk and signal integrity. Future work will focus on scaling this approach to analyze multiconductor propagation in complex transmission-line structures.