arxiv: 2605.06048 · v1 · submitted 2026-05-07 · 💻 cs.CE

Recognition: unknown

Quantum Optimization for Electromagnetics: Physics-Informed QAOA for Reconfigurable Intelligent Surfaces

Erik M. {\AA}sgrim, Marco Pasquale, Oscar Quevedo-Teruel, Stefano Markidis

Authors on Pith no claims yet

Pith reviewed 2026-05-08 03:51 UTC · model grok-4.3

classification 💻 cs.CE

keywords Reconfigurable Intelligent SurfacesQAOAQuantum OptimizationMutual CouplingNISQ DevicesQUBOBeamforming

0 comments

The pith

Sparse distance-penalized models are required for feasible physics-informed QAOA on reconfigurable intelligent surfaces despite accuracy gains from denser coupling.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper tests whether adding realistic mutual coupling physics to the optimization of reconfigurable intelligent surfaces can be done directly inside a quantum algorithm. It formulates the problem as a QUBO and solves it with QAOA using four different Ising interaction strengths that range from ignoring coupling to including full dense interactions. On a 5 by 5 grid the denser models produce better beam-pointing accuracy, yet they generate Hamiltonians too complex for near-term quantum hardware to execute reliably. The work therefore concludes that a compromise using sparse, distance-penalized couplings is still necessary if the method is to run on present NISQ devices.

Core claim

Embedding four progressively physics-informed Ising interaction models into QAOA shows that complete global coupling delivers the highest beamforming precision for a 5 by 5 RIS, but the resulting dense Hamiltonians impose prohibitive routing overhead and hinder convergence, whereas sparse distance-penalized models remain executable on current noisy intermediate-scale quantum processors.

What carries the argument

Four Ising interaction models (J_ij) of increasing physical fidelity, cast as QUBO Hamiltonians and solved with QAOA, that encode mutual coupling between RIS elements.

Load-bearing premise

The four chosen Ising interaction strengths are sufficient to capture the essential electromagnetic mutual coupling that determines real-world accuracy versus feasibility.

What would settle it

A full-wave simulation or laboratory measurement of a physical 5 by 5 RIS configured according to the sparse versus dense QAOA outputs, checking whether the predicted pointing accuracy difference actually appears and whether the sparse solution still meets performance targets.

Figures

Figures reproduced from arXiv: 2605.06048 by Erik M. {\AA}sgrim, Marco Pasquale, Oscar Quevedo-Teruel, Stefano Markidis.

**Figure 1.** Figure 1: Overview of QAOA-based reconfigurable intelligent surface (RIS) optimization. The QAOA circuit optimizes binary view at source ↗

**Figure 2.** Figure 2: Illustration of a reconfigurable intelligent surface view at source ↗

**Figure 3.** Figure 3: Workflow for QAOA-based metasurface optimization. The four models feed into the cost-Hamiltonian construction view at source ↗

**Figure 5.** Figure 5: (a) Approximation ratio (AR) computed using Eq. view at source ↗

**Figure 6.** Figure 6: Radiation power 𝑃 (𝜃, 𝜙) in dB, normalized to the peak scattered beam of the RIS using Model 1, comparing the QAOAderived solution with the model-optimal solution. While QAOA does not exactly reach the optimal state (right), it still yields strong performance. Target angle is marked by a black cross, while radiation maximum is indicated in red; smaller angular separation means higher QAOA accuracy. The tw… view at source ↗

read the original abstract

Optimizing Reconfigurable Intelligent Surfaces (RIS) is a high-dimensional combinatorial challenge. Current quantum algorithms often simplify this problem by ignoring physical constraints like mutual coupling, which significantly degrades real-world performance. Rather than targeting a fully realistic RIS description, we embed progressively more physics-informed models of mutual coupling into Quadratic Unconstrained Binary Optimization (QUBO) formulations. We evaluate four Ising interaction models ($J_{ij}$) for the Quantum Approximate Optimization Algorithm (QAOA), ranging from idealized phase-only to fully dense physical models. Analyzing a $5 \times 5$ grid, our results expose a critical trade-off between spatial pointing accuracy and quantum hardware feasibility. While complete global coupling maximizes beamforming precision, dense Hamiltonians introduce prohibitive routing overhead and complicate convergence on near-term processors. Ultimately, we demonstrate that while physics-informed quantum optimization is mathematically viable, sparse, distance-penalized models remain a necessary compromise for execution on current noisy intermediate-scale quantum (NISQ) devices.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

This paper shows that denser physics-informed coupling models improve RIS beam accuracy in QAOA but hit NISQ hardware limits, forcing sparse approximations, though without full-wave checks the accuracy gains stay unverified.

read the letter

The main takeaway is that adding mutual coupling physics to the QAOA setup for RIS optimization forces a practical choice. On a 5x5 grid the denser J_ij models give tighter beam pointing than phase-only versions, but they also make the Hamiltonian too complex for reliable runs on current quantum hardware. The authors therefore land on distance-penalized sparse models as the workable middle ground for NISQ devices.

Referee Report

2 major / 2 minor

Summary. The paper proposes embedding progressively more physics-informed models of mutual coupling into QUBO formulations for QAOA-based optimization of RIS phase configurations. On a 5×5 grid it evaluates four Ising interaction models (J_ij) ranging from idealized phase-only to fully dense physical coupling, reports a trade-off between beamforming accuracy and NISQ feasibility, and concludes that sparse distance-penalized models are required for practical execution on current hardware.

Significance. If the quantitative results and scaling claims hold, the work demonstrates a concrete route for incorporating electromagnetic physics into quantum combinatorial optimization and identifies a practical sparsity requirement for NISQ devices. The explicit construction of multiple J_ij Hamiltonians and the focus on routing overhead constitute a useful contribution at the quantum-EM interface.

major comments (2)

[Abstract and §4] Abstract and §4 (results on 5×5 grid): the central accuracy-feasibility trade-off is asserted without any reported quantitative metrics (beam pointing error in degrees, sidelobe levels in dB, QAOA convergence probability, or circuit depth), error bars, or explicit QUBO/QAOA parameter values, preventing verification of the claimed superiority of dense versus sparse models.
[§3 and §5] §3 (Ising models) and §5 (discussion): the necessity of distance-penalized sparsity is presented as a hardware-driven compromise, yet the four J_ij formulations are not validated against full-wave EM solvers (MoM, FDTD, or HFSS). Without such comparison it is impossible to confirm that the dense model actually encodes the dominant mutual-coupling effects that would justify the reported precision gain.

minor comments (2)

[§3] Notation for the four J_ij models is introduced without a compact table summarizing their sparsity, range, and physical interpretation; a single summary table would improve readability.
[Introduction] The manuscript cites standard QAOA and QUBO references but omits recent works on quantum optimization for antenna arrays or RIS-specific classical solvers that would help situate the novelty.

Simulated Author's Rebuttal

2 responses · 1 unresolved

We thank the referee for the insightful comments on our manuscript arXiv:2605.06048. We address each major comment below and will make revisions to improve the clarity and rigor of the presented results.

read point-by-point responses

Referee: [Abstract and §4] Abstract and §4 (results on 5×5 grid): the central accuracy-feasibility trade-off is asserted without any reported quantitative metrics (beam pointing error in degrees, sidelobe levels in dB, QAOA convergence probability, or circuit depth), error bars, or explicit QUBO/QAOA parameter values, preventing verification of the claimed superiority of dense versus sparse models.

Authors: We agree that quantitative metrics are essential for verifying the claims. The original manuscript focused on qualitative trends in the 5×5 grid results, but we will revise §4 to report specific values: beam pointing errors in degrees, sidelobe levels in dB, QAOA convergence probabilities, and circuit depths for each of the four models. Error bars will be included based on 10 independent QAOA executions per model, and we will specify the QUBO formulation parameters (e.g., penalty weights) and QAOA settings (p=1, optimizer details). This will substantiate the accuracy-feasibility trade-off. revision: yes
Referee: [§3 and §5] §3 (Ising models) and §5 (discussion): the necessity of distance-penalized sparsity is presented as a hardware-driven compromise, yet the four J_ij formulations are not validated against full-wave EM solvers (MoM, FDTD, or HFSS). Without such comparison it is impossible to confirm that the dense model actually encodes the dominant mutual-coupling effects that would justify the reported precision gain.

Authors: We acknowledge that validation against full-wave solvers is important to confirm the physical accuracy of the dense model. Our formulations are based on theoretical mutual coupling coefficients derived from array factor and dipole interaction models in electromagnetics. In the revision, we will add explicit references and derivations in §3 to justify the J_ij terms. However, performing new full-wave simulations (e.g., with HFSS) for validation is beyond the current scope, as the paper emphasizes the quantum algorithm side. We will add a limitations paragraph in §5 discussing this and the potential impact on precision claims. revision: partial

standing simulated objections not resolved

Full validation of the J_ij models using full-wave EM solvers such as MoM, FDTD, or HFSS, which would require substantial additional computational effort and expertise outside the primary focus on QAOA optimization.

Circularity Check

0 steps flagged

No circularity: standard QAOA/QUBO application with external NISQ constraints

full rationale

The paper applies the standard QAOA algorithm to four progressively physics-informed Ising (J_ij) models within QUBO formulations for RIS phase optimization. Results are generated from direct numerical evaluation on a 5x5 grid, and the final claim that sparse distance-penalized models are required for NISQ feasibility rests on known hardware routing and noise limits plus the observed accuracy trade-off, not on any fitted parameter renamed as prediction or self-referential definition. No equations in the abstract or described methods reduce a claimed prediction to an input by construction, and no load-bearing self-citations or uniqueness theorems imported from prior author work are present. The derivation chain is therefore self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Based on abstract only; no explicit free parameters, axioms, or invented entities are stated. Standard QAOA assumptions (e.g., variational ansatz convergence) and QUBO mapping are implicit but not detailed.

pith-pipeline@v0.9.0 · 5481 in / 1153 out tokens · 63963 ms · 2026-05-08T03:51:31.479306+00:00 · methodology

discussion (0)

Reference graph

Works this paper leans on

16 extracted references · 16 canonical work pages · 2 internal anchors

[1]

Ali Asadi, Amintor Dusko, Chae-Yeun Park, Vincent Michaud-Rioux, Isidor Schoch, Shuli Shu, Trevor Vincent, and Lee James O’Riordan. 2024. Hybrid quantum programming with PennyLane Lightning on HPC platforms. doi:10. 48550/arXiv.2403.02512 arXiv:2403.02512

work page arXiv 2024
[2]

Constantine A. Balanis. 2023.Balanis’ Advanced Engineering Electromagnetics(1 ed.). Wiley. doi:10.1002/9781394180042

work page doi:10.1002/9781394180042 2023
[3]

Fouda, Muhammad Ismail, Mohamed I

Iqra Batool, Mostafa M. Fouda, Muhammad Ismail, Mohamed I. Ibrahem, Zubair Md Fadlullah, and Nei Kato. 2026. Quantum-Enhanced Massive MIMO Beam- forming for 6G IoT Networks: A QAOA-Based Optimization Framework.IEEE Open Journal of the Communications Society7 (2026). doi:10.1109/OJCOMS.2025. 3645207

work page doi:10.1109/ojcoms.2025 2026
[4]

Jaeho Choi and Joongheon Kim. 2019. A Tutorial on Quantum Approximate Optimization Algorithm (QAOA): Fundamentals and Applications. In2019 Inter- national Conference on Information and Communication Technology Convergence (ICTC). doi:10.1109/ICTC46691.2019.8939749 ISSN: 2162-1233

work page doi:10.1109/ictc46691.2019.8939749 2019
[5]

Emanuel Colella, Luca Bastianelli, Valter Mariani Primiani, Zhen Peng, Franco Moglie, and Gabriele Gradoni. 2024. Quantum Optimization of Reconfigurable Intelligent Surfaces for Mitigating Multipath Fading in Wireless Networks.IEEE Journal on Multiscale and Multiphysics Computational Techniques9 (2024). doi:10. 1109/JMMCT.2024.3494037

work page arXiv 2024
[6]

Gavin E. Crooks. 2019. Gradients of parameterized quantum gates using the parameter-shift rule and gate decomposition. doi:10.48550/arXiv.1905.13311 arXiv:1905.13311

work page doi:10.48550/arxiv.1905.13311 2019
[7]

ElMossallamy, Hongliang Zhang, Lingyang Song, Karim G

Mohamed A. ElMossallamy, Hongliang Zhang, Lingyang Song, Karim G. Seddik, Zhu Han, and Geoffrey Ye Li. 2020. Reconfigurable Intelligent Surfaces for Wireless Communications: Principles, Challenges, and Opportunities.IEEE Transactions on Cognitive Communications and Networking6, 3 (2020). doi:10. 1109/TCCN.2020.2992604

work page arXiv 2020
[8]

Edward Farhi, Jeffrey Goldstone, and Sam Gutmann. 2014. A Quantum Approxi- mate Optimization Algorithm. doi:10.48550/arXiv.1411.4028 arXiv:1411.4028

work page internal anchor Pith review doi:10.48550/arxiv.1411.4028 2014
[9]

Adam: A Method for Stochastic Optimization

Diederik P. Kingma and Jimmy Ba. 2017. Adam: A Method for Stochastic Opti- mization. doi:10.48550/arXiv.1412.6980 arXiv:1412.6980

work page internal anchor Pith review doi:10.48550/arxiv.1412.6980 2017
[10]

Sangbin Lee, Qi Jian Lim, Charles Ross, Eungkyu Lee, Soyul Han, Youngmin Kim, Zhen Peng, and Sanghoek Kim. 2025. Quantum Annealing for Electromagnetic Engineers—Part I: A computational method to solve various types of optimization problems.IEEE Antennas and Propagation Magazine67, 6 (2025). doi:10.1109/ MAP.2024.3498695

work page arXiv 2025
[11]

Sangbin Lee, Qi Jian Lim, Charles Ross, Eungkyu Lee, Soyul Han, Youngmin Kim, Zhen Peng, and Sanghoek Kim. 2026. Quantum Annealing for Electromagnetic Engineers—Part II: Examples of electromagnetic problems solved by quantum annealing.IEEE Antennas and Propagation Magazine68, 1 (2026). doi:10.1109/ MAP.2025.3530408

work page arXiv 2026
[12]

Yuanwei Liu, Xiao Liu, Xidong Mu, Tianwei Hou, Jiaqi Xu, Marco Di Renzo, and Naofal Al-Dhahir. 2021. Reconfigurable Intelligent Surfaces: Principles and Opportunities.IEEE Communications Surveys & Tutorials23, 3 (2021). doi:10. 1109/COMST.2021.3077737

work page arXiv 2021
[13]

Punnen (Ed.)

Abraham P. Punnen (Ed.). 2022.The Quadratic Unconstrained Binary Optimization Problem: Theory, Algorithms, and Applications. Springer International Publishing, Cham. doi:10.1007/978-3-031-04520-2

work page doi:10.1007/978-3-031-04520-2 2022
[14]

Biswarup Rana, Sung-Sil Cho, and Ic-Pyo Hong. 2023. Review Paper on Hard- ware of Reconfigurable Intelligent Surfaces.IEEE Access11 (2023). doi:10.1109/ ACCESS.2023.3261547

work page arXiv 2023
[15]

Charles Ross, Gabriele Gradoni, Qi Jian Lim, and Zhen Peng. 2022. Engineering Reflective Metasurfaces With Ising Hamiltonian and Quantum Annealing.IEEE Transactions on Antennas and Propagation70, 4 (2022). doi:10.1109/TAP.2021. 3137424

work page doi:10.1109/tap.2021 2022
[16]

Al-Naffouri

Pinjun Zheng, Ruiqi Wang, Atif Shamim, and Tareq Y. Al-Naffouri. 2024. Mu- tual Coupling in RIS-Aided Communication: Model Training and Experimen- tal Validation.IEEE Transactions on Wireless Communications23, 11 (2024). doi:10.1109/TWC.2024.3451548

work page doi:10.1109/twc.2024.3451548 2024