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arXiv:2606.24540

Offline Channel-Independent QAOA Angles for RIS Power Aggregation: Unit-Circle Phase Dictionaries and Infinite-Size Spin-Glass Limits

Burhan Gulbahar

quant-pheess.SPSubmitted Jun 23, 2026• Announced Jun 24, 2026• 0 citations
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Abstract

Reconfigurable intelligent surfaces (RIS) maximize received power by setting per-element phases. Discrete-phase optimization is NP-hard in the worst case, while the quantum approximate optimization algorithm (QAOA) applied to RIS faces limited phase alphabets, either per-problem angle optimization or uncharacterized training cost exposed to barren plateaus, and no scalable performance benchmark. We introduce a $2^{M}$-phase $θ$ dictionary for optimizing power $\|\mathbf{A} \, e^{jθ}\|^{2}$ having $K \times N$ channel matrix $\mathbf{A}$ and QAOA angle offline optimization with instance and size-independent infinite-size limit of the mixed-$q$ Gaussian ensemble of Basso et al. Our design bounds the spin-Hamiltonian interaction order to at most quartic for any $M$, and the deployed order-2 reduction lies below the even-$q\!\ge\!4$ regime in which constant-level QAOA limitations are proved. We perform analytical, state-vector, matrix-product-state and Pauli-path-simulation numerical studies for $N=K \leq 100$ and QAOA depth $p=9$, verifying offline angle transfer to Rayleigh, Rician/line-of-sight, cascaded double-fading and spatially-correlated RIS channels at $N\!\in\!\{5,12\}$. We observe performance reaching a near-optimal multi-start single-flip local-search reference for $N\!\le\!16$ under order-2 modeling with $2^{5}{=}32$-phase dictionary while the order-4 model shows a performance ceiling below the classical reference. The approach suggests a route to near-optimal large-$N$ performance on future fault-tolerant (FTQ) quantum computers, which enable the higher-depth QAOA circuits.

Comments
11 pages, 8 figures

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IEEE Open Journal of Vehicular Technology•Jan 1, 2026•0 citations
Reconfigurable intelligent surfaces (RIS) maximize received power by setting per-element phases. Discrete-phase optimization is NP-hard in the worst case, while the quantum approximate optimization algorithm (QAOA) applied to RIS faces limited phase alphabets, either per-problem angle optimization or uncharacterized training cost exposed to barren plateaus, and no scalable performance benchmark. We introduce a 2M2^{M}2M-phase θθθ dictionary for optimizing power ∥A ejθ∥2\|\mathbf{A} \, e^{jθ}\|^{2}∥Aejθ∥2 having K×NK \times NK×N channel matrix A\mathbf{A}A and QAOA angle offline optimization with instance and size-independent infinite-size limit of the mixed-qqq Gaussian ensemble of Basso et al. Our design bounds the spin-Hamiltonian interaction order to at most quartic for any MMM, and the deployed order-2 reduction lies below the even-q ⁣≥ ⁣4q\!\ge\!4q≥4 regime in which constant-level QAOA limitations are proved. We perform analytical, state-vector, matrix-product-state and Pauli-path-simulation numerical studies for N=K≤100N=K \leq 100N=K≤100 and QAOA depth p=9p=9p=9, verifying offline angle transfer to Rayleigh, Rician/line-of-sight, cascaded double-fading and spatially-correlated RIS channels at N ⁣∈ ⁣{5,12}N\!\in\!\{5,12\}N∈{5,12}. We observe performance reaching a near-optimal multi-start single-flip local-search reference for N ⁣≤ ⁣16N\!\le\!16N≤16 under order-2 modeling with 25=322^{5}{=}3225=32-phase dictionary while the order-4 model shows a performance ceiling below the classical reference. The approach suggests a route to near-optimal large-NNN performance on future fault-tolerant (FTQ) quantum computers, which enable the higher-depth QAOA circuits.
The quantum approximate optimization algorithm (QAOA) targets NP-hard maximum-likelihood (ML) detection in multiple-input multiple-output (MIMO) systems. Existing MMM-ary quadrature amplitude modulation (M-QAM) detectors design angles by expected Ising energy: online per instance, warm-started, or ramped, while train-once designs remain B/QPSK-only or block-local, leaving M-QAM without a size-scalable benchmark. Their infinite-size spin-glass theory assumes independent disorder, matching the retained covariances at B/QPSK but not M-QAM's correlated couplings and fields. We develop a correlated infinite-size multi-species spin-glass framework whose covariance-matched evaluators make that energy an offline objective with a size-scalable benchmark. In addition, the ML rate, the exponential rate of sampling the ML string, is for the first time exploited for QAOA angle design in MIMO detection. The energy evaluator is qqq-free at O(p 4p)O(p\,4^p)O(p4p) cost while the ML rate transfers angles from a fixed qrefq_{\rm ref}qref​-qubit reference. Tests reach 4096-QAM, 128 antennas, p=30p=30p=30 and per-symbol SNR 0-45 dB. In simulations, ML rates fall as a power law r0 p−αr_0\,p^{-α}r0​p−α, with larger exponents for the sampling design, which tracks exact ML at 5×55\times55×5 16-QAM (0-20 dB) and 3×33\times33×3 64-QAM (8-28 dB) while its bit-error rate (BER) advantage widens with SNR to two orders of magnitude. The approach points toward near-optimum decoding on deeper noiseless fault-tolerant quantum (FTQ) circuits.
Reconfigurable intelligent surface (RIS) optimization is a high-dimensional combinatorial problem, where classical methods face significant scalability challenges. The quantum approximate optimization algorithm (QAOA) offers a promising alternative by encoding the optimization problem into a quantum Hamiltonian and finding its ground state through a parameterized quantum circuit, known as the ansatz [1]. In the quantum framework, the RIS optimization problem is mapped onto the Sherrington-Kirkpatrick (SK) Hamiltonian, which models the transfer function between the transmitting antenna (TX) and the receiver (RX) [2], [3] as follows:
Wireless communication systems play a pivotal role in modern society, yet they face significant challenges such as latency and multipath fading. Reconfigurable intelligent surface (RIS) is emerged as a promising solution to manipulate electromagnetic waves to enhance transmission quality, although their optimization presents several limitations. In this study, we propose a hybrid approach utilizing the quantum approximate optimization algorithm (QAOA) to effectively configure RIS in multipath environments, addressing the shortcomings of classical methods. The computational model trained by the Sherrington- Kirkpatrick Hamiltonian, demonstrates high accuracy in identifying optimal RIS configurations across various scenarios, without running optimization at each condition. However, the analysis of barren plateaus reveals that the cost function gradient diminishes exponentially as the number of cells increases, making hard the training for large-scale systems. To mitigate these issues, we conclude by suggesting some potential strategies for future research aimed at enhancing RIS performance in practical applications.
Simultaneously transmitting and reflecting reconfigurable intelligent surface (STAR-RIS) enables 360-degree full-space coverage by controlling both transmitted and reflected signals through each element. However, the coupled phase-shift model, where the transmission and reflection coefficients are physically interdependent, transforms the phase optimization into an extremely complex non-convex combinatorial problem that classical algorithms struggle to solve efficiently. In this paper, we propose a hybrid quantum-classical framework that employs the Quantum Approximate Optimization Algorithm (QAOA) to optimize the coupled phase-shift configuration of STAR-RIS. Each discrete phase configuration is mapped to a qubit-based Ising Hamiltonian, enabling QAOA to explore the exponentially large solution space through quantum superposition and entanglement. To address the scalability challenge of simulating large antenna arrays (e.g., 8 × 8 = 64 elements), we introduce a variable grouping (tiling) strategy that partitions the RIS into manageable sub-arrays of 2 × 2 elements, each requiring only 8 qubits for 2-bit phase quantization. Our comprehensive simulations demonstrate that the proposed QAOA-based optimizer achieves an approximation ratio exceeding 0.94 with 10 QAOA layers, maintains over 86% fidelity under 2% gate error rates in noisy intermediate-scale quantum (NISQ) environments, and exhibits robust performance under imperfect channel state information with less than 5% degradation at 30% CSI error variance. The energy efficiency analysis confirms that the QAOA-optimized STAR-RIS achieves approximately 1.7× higher spectral efficiency per unit energy compared to conventional reflect-only RIS. Furthermore, the proposed tiling framework scales linearly with array size, enabling deployment on arrays up to 16 × 16 elements while maintaining constant per-group quantum resource requirements.
Wireless communication technology has become important in modern life. Real-world radio environments present significant challenges, particularly concerning latency and multipath fading. A promising solution is represented by reconfigurable intelligent surfaces (RIS), which can manipulate electromagnetic waves to enhance transmission quality. In this study, we introduce a novel approach that employs the quantum approximate optimization algorithm (QAOA) to efficiently configure RIS in multipath environments. Applying the spin glass (SG) theoretical framework to describe chaotic systems, along with a variable noise model, we propose a quantum-based minimization algorithm to optimize RIS in various electromagnetic scenarios affected by multipath fading. The method involves training a parameterized quantum circuit using a mathematical model that scales with the size of the RIS. When applied to different EM scenarios, it directly identifies the optimal RIS configuration. This approach eliminates the need for large datasets for training, validation, and testing, streamlines, and accelerates the training process. Furthermore, the algorithm will not need to be rerun for each individual scenario. In particular, our analysis considers a system with one transmitting antenna, multiple receiving antennas, and varying noise levels. The results show that QAOA enhances the performance of RIS in both noise-free and noisy environments, highlighting the potential of quantum computing to address the complexities of RIS optimization and improve the performance of the wireless network.
This paper considers a multi-antenna base station (BS) communicating with a single-antenna user through a reconfigurable intelligent surface (RIS). In large RIS deployments, feeding back the high-dimensional phase vector θ∈[0,2π)N\boldsymbol{\theta }\in [0,2\pi)^{N}θ∈[0,2π)N , where NNN is the number of RIS elements, poses a major scalability challenge. Conventional codebook-based compression is limited to fixed linear subspaces. To address this, we propose Phase-Aware Quantum RIS (PAQ-RIS), a hybrid quantum–classical autoencoder that compresses RIS phase profiles using variational quantum circuits. Phase shifts are angle-encoded into quantum states, processed by parameterized quantum circuits, and reconstructed by a classical decoder. Results show that PAQ-RIS improves beamforming accuracy by up to 14.5% over classical autoencoders for an RIS with N=512N=512N=512 elements using q=9q=9q=9 qubits at a feedback compression ratio of approximately 19%. For N=1024N=1024N=1024 , the framework continues to provide performance gains, achieving beamforming accuracy improvements of up to 11.33%. However, for larger RIS configurations with N=2048N=2048N=2048 elements, the performance gain decreases, with the best improvement dropping to 4.44% due to barren plateaus and near-Haar-random latent states, establishing the practical scalability limits of quantum-assisted compression.