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

Introduction

Finite‑element methods (FEM) are the workhorse for high‑frequency antenna design, but the resulting large sparse linear systems become a bottleneck as mesh resolution increases. Quantum linear system solvers (QLSS) promise asymptotic speed‑ups for solving such systems, yet their output is a quantum superposition, making direct extraction of the full solution vector costly. Recent research therefore focuses on measuring only the physical observables of interest—quantities that can be obtained from the quantum state without full tomography. The paper Finite‑Element Electromagnetic Analysis and Evaluation of Antenna Performance Metrics Using a Quantum Linear System Solver presents a complete end‑to‑end hybrid workflow that integrates FEM, matrix preconditioning, a QLSS, and observable‑based evaluation of antenna metrics.

From FEM to Quantum Observables

The authors begin by formulating the electromagnetic problem for an axisymmetric coaxially fed monopole antenna. After discretizing Maxwell’s equations with FEM, they obtain a sparse matrix equation \(A\mathbf{x}=\mathbf{b}\). Traditional solvers compute the full field vector \(\mathbf{x}\), from which radiated power, angular power distribution, and loss mechanisms are derived.

To leverage a quantum solver, the matrix is first preconditioned to improve condition number and to fit the requirements of the quantum algorithm (e.g., Hermitian, sparse, and efficiently block‑encoded). The preconditioned system is then encoded into a quantum circuit that implements the QLSS—typically a variant of the Harrow‑Hassidim‑Lloyd (HHL) algorithm. Rather than measuring \(\mathbf{x}\) component‑wise, the workflow defines observables that correspond directly to antenna performance metrics:

• Total radiated power – expressed as a quadratic form \(\mathbf{x}^\dagger R \mathbf{x}\) where \(R\) encodes the radiation integral.
• Directional radiated power – similar quadratic forms restricted to a solid‑angle region.
• Dielectric and conductive losses – represented by loss matrices derived from material properties.

These observables are implemented as Hermitian operators that can be measured on the quantum state using techniques such as amplitude estimation, thereby extracting the desired scalar quantities with a number of measurements that scales polylogarithmically with system size.

Hybrid Workflow and Numerical Validation

The paper outlines a practical pipeline:

1. Classical FEM preprocessing – mesh generation, matrix assembly, and preconditioning.
2. Quantum encoding – construction of block‑encodings for \(A\) and the observable operators.
3. Quantum linear system solution – execution of the QLSS on a simulated fault‑tolerant quantum computer.
4. Observable measurement – estimation of the antenna metrics via quantum amplitude estimation.
5. Post‑processing – conversion of measured values into engineering‑relevant units.

To validate the approach, the authors performed numerical experiments on the monopole antenna model. Under idealized, noise‑free quantum simulation conditions, the relative errors for total radiated power and dissipated power were on the order of \(10^{-3}\) compared with the classical FEM solution. These results demonstrate that the observable‑based method preserves the fidelity of key performance metrics while sidestepping the expensive full‑state reconstruction.

Practical Implications and Outlook

The study provides a concrete blueprint for integrating quantum algorithms into electromagnetic design workflows. By targeting specific observables, engineers can obtain the most relevant design information—such as efficiency, gain, and loss—without incurring the overhead of reconstructing the entire field distribution. While the current validation relies on ideal quantum simulations, the methodology is compatible with future fault‑tolerant quantum hardware and can be extended to more complex antenna geometries, multi‑port networks, and broadband analyses.

Future work will need to address realistic noise models, resource estimation for actual quantum devices, and the development of adaptive preconditioning strategies that are themselves quantum‑aware. Nonetheless, the presented hybrid workflow marks a significant step toward practical quantum‑accelerated antenna design, offering a pathway to faster optimization cycles for next‑generation high‑frequency wireless systems.

--- This article synthesizes the key contributions of the referenced arXiv paper, focusing on the workflow, observable formulation, and validation results, without introducing new data or quotations.