Finite-Element Electromagnetic Analysis and Evaluation of Antenna Performance Metrics Using a Quantum Linear System Solver

Abstract

Electromagnetic analysis based on the finite element method is widely used in antenna design. At higher frequencies, however, the required mesh refinement makes solving large sparse linear systems the main contributor to computational cost. Quantum linear system solvers offer a potential means of accelerating this step, but their output is a superposition state: reconstructing all components of the classical solution vector would forfeit the quantum speedup. Prior studies have proposed methods for obtaining physical quantities such as scattering cross sections and scattering parameters from the solution state. To support antenna design using fault-tolerant quantum computers, we formulate the total radiated power, the radiated power within a prescribed solid angle, and the dielectric and conductive losses as observables for efficient evaluation from a quantum solution state. These observables avoid the measurement cost of reconstructing all components of the output quantum state. We develop an end-to-end hybrid quantum--classical workflow that combines finite-element electromagnetic analysis, matrix preconditioning, a quantum linear system solver, and the evaluation of antenna design metrics. To validate the workflow, we performed numerical experiments evaluating these observables for an axisymmetric coaxially fed monopole antenna. Under idealized conditions, the relative errors in the total radiated power and the dissipated power with respect to the classical finite-element solution were on the order of $10^{-3}$, confirming the consistency of the workflow. The proposed method is expected to provide a basis for using quantum linear system solvers to evaluate antenna performance and, in the future, to design high-frequency wireless devices.

The paper asks how antenna performance metrics can be extracted from a quantum linear-system solver’s normalized finite-element solution state without reconstructing the full electromagnetic field. It expresses total and solid-angle-restricted radiated power, Huygens-surface power flux, and dielectric and conductive losses as quadratic forms $x^\dagger Qx$. Radiation observables are constructed from far-field linear functionals; loss observables follow from volume and surface integrals of finite-element basis fields. The workflow combines Ruiz diagonal equilibration, Hermitian embedding of the complex indefinite Maxwell matrix, and HHL-type solution-state preparation. Observables are transformed consistently with preconditioning, and physical power scales are recovered using the solution norm inferred from postselection probability. Validation uses idealized classical simulation for an axisymmetric coaxially fed monopole with 519 complex degrees of freedom. Equilibration reduces the condition number from $6.16\times10^5$ to $9.34\times10^3$; the simulation uses 14 phase qubits and has postselection probability $1.29\times10^{-5}$ at the reference frequency. Relative errors against the classical discrete solution are $0.769\%$ for total radiated power and $0.662\%$ for angular-band power. Across a 21-frequency sweep, radiated-power errors remain below $0.693\%$, and total-loss errors below $0.313\%$. The classical far-field and Huygens-surface powers differ by $6.64\%$, requiring electromagnetic convergence studies. Finite-shot estimation, gate-synthesis precision, fault-tolerant resources, and end-to-end complexity are not evaluated. Observable formulation alone does not establish efficient measurement or quantum advantage; matrix access, state preparation, preconditioning, spectral bounds, and readout costs remain to be assessed.