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.
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.
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
2M-phase
θ dictionary for optimizing power
∥Aejθ∥2 having
K×N channel matrix
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≥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≤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∈{5,12}. We observe performance reaching a near-optimal multi-start single-flip local-search reference for
N≤16 under order-2 modeling with
25=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.
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 (Jij) for the Quantum Approximate Optimization Algorithm (QAOA), ranging from idealized phase-only to fully dense physical models. Analyzing a 5 × 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.
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.
The design and analysis of reconfigurable meta-surfaces operating within rich multi-path propagation fading is of crucial importance for the development of real-life programmable electromagnetic environments. We incorporate the effect of multi-path fading in an impedance-based model of wireless communication links assisted by reconfigurable surfaces. Previous work has shown that impedance-based channel models under rich multi-path propagation have an isomorphism with Sherrington-Kirkpatrick (SK) Hamiltonians. We focus on received power minimisation, which is equivalent to the hard-to-solve task task of finding the ground state of the SK Hamiltonian. It has been recently discovered that the Quantum Approximate Optimisation Algorithm (QAOA) predicts the ground state of SK Hamiltonians accurately. However, the landscape parameters of QAOA are dependent on the specific realisation of the random SK Hamiltonian, which hinders the full usage of quantum hardware to optimise reconfigurable surfaces dynamically. We show by Montecarlo simulations that a concentration property cures this impediment thus making QAOA an excellent candidate for surface optimisation under fast multi-path fading.