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IEEE Access

Hybrid Quantum-Classical Algorithm Design for Coupled Phase-Shift Optimization of STAR-RIS

Su-Chang Lim, Jong-Chan Kim

Published Jan 1, 2026• 0 citations
Publisher

Abstract

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.

DOI
10.1109/access.2026.3690802

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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.
In this paper, we investigate the potential of a near-optimal hybrid quantum-classical optimization approach to jointly optimizing beamforming and discrete phase shifts of the simultaneous transmitting and reflecting reconfigurable intelligent surface (STAR-RIS) assisted wireless network. We first formulate a discrete optimization problem to maximize the total power transmitted to the ground users by optimizing the beamforming at the base station (BS) and STAR-RIS phase shift cells under minimal power allocation for each user and the power budget at the BS. Then, we propose a quantum approximate optimization algorithm with alternating optimization (QAOA-AO) method that iteratively addresses beamform-ing components and discrete phase shifts to search for the near-optimal solutions for the problem. Numerical results validate the effectiveness and robustness of the proposed QAOA-AO compared to the classical benchmarks, and further highlight its potential for practical applicability for solving medium-to-large-scale optimization problems.
Quantum-classical hybrid communication is emerging as a key enabler for future 6G networks, where THz communication and quantum services are expected to coexist over intelligent and reconfigurable wireless infrastructures. A fundamental challenge in such systems is that reconfigurable intelligent surface (RIS) phase control simultaneously influences classical communication performance and quantum-state evolution, making reliable entanglement preservation difficult in dynamic propagation environments. To address this challenge, this paper proposes an AI-native Entanglement-Sustained Reconfigurable Intelligent Surface (AI-ES-RIS) framework for hybrid quantum-classical THz communication. A unified model is developed to jointly characterize THz-wave propagation and Bell-state evolution through a phase-flip-inspired decoherence representation. To capture RIS-induced quantum degradation, a weighted mismatch-based decoherence model is introduced that links RIS phase perturbations, channel-dependent element significance, and entanglement fidelity degradation. Furthermore, a Proximal Policy Optimization (PPO)-based controller is designed to adapt RIS phase configurations by jointly optimizing communication reliability and quantum-state preservation. Simulation results demonstrate that the proposed framework consistently achieves higher entanglement fidelity, lower decoherence probability, and competitive communication performance compared with communication-centric and model-based RIS optimization strategies. Distributional analysis further confirms improved quantum-state robustness across diverse channel realizations, while scalability studies demonstrate favorable runtime characteristics for larger RIS dimensions. Additional meta-learning and federated learning extensions show enhanced adaptation and convergence under heterogeneous propagation environments. The results establish that RIS control in hybrid quantum-classical networks should be treated as a joint communication-and-quantum optimization problem rather than as independent design objectives, providing a promising foundation for future THz-enabled quantum-aware 6G systems.
Due to the limited coverage of reflecting-only reconfigurable intelligent surfaces (RIS), the existing RIS-assisted physical-layer key generation (PKG) scheme limits its overall performance in the full space. This paper proposes a novel simultaneously transmitting and reflecting (STAR)-RIS-assisted PKG protocol for multiple-input multiple-output (MIMO) systems, where the closed-form sum secret key rate is derived in the presence of full-space eavesdroppers. Two optimization problems are formulated to maximize the sum secret key rate by designing the transmit beamforming (TBF) and transmitting and reflecting coefficients (TRCs) for energy splitting (ES) with coupled phase-shift and mode switching (MS) mode. For ES mode with coupled phase-shift, a penalty-based alternating optimization (AO) algorithm is proposed to address its non-convexity. For MS mode, the semidefinite relaxation-successive convex approximation-based AO algorithm is utilized to achieve continuous solutions and then quantize to binary value for the MS mode. Simulation results demonstrate that the coupled phase-shift STAR-RIS incurs a slight KGR loss in comparison to the independent phase-shift STAR-RIS. Additionally, the ES mode outperforms the MS mode in terms of KGR performance. Finally, STAR-RIS can achieve a higher sum secret key rate than traditional reflecting-only RIS.
Physical-layer key generation (PLKG) is an information-theoretic security technique aimed at addressing key distribution challenges among resource-constrained legitimate users in the Internet of Things (IoT). However, in quasi-static or blocked environments, key generation faces significant limitations owing to its low entropy. To overcome this challenge, we propose leveraging a simultaneously transmitting and reflecting (STAR) reconfigurable intelligent surface (RIS). In this study, we introduce a STAR-RIS-aided multiuser PLKG framework and formulate an optimization problem focused on minimizing the average bit disagreement ratio through optimal phase-shift matrix adjustments. Initially, we derive closed-form solutions for optimal phase shifts, simplifying the problem to depend solely on amplitude coefficients. We then employ a Newton-Raphson algorithm under the energy-splitting (ES) protocol and a traversal method under the mode-switching (MS) and time-switching (TS) protocols to solve the optimization problem. Simulation results confirm the efficacy of our proposed schemes by comparison with existing benchmark schemes.
We propose a Quantum Approximate Optimization Algorithm with a deterministic linear ramp schedule (QAOA-LR) for phase optimization of a 1-bit RIS-assisted MIMO communication system. Each RIS element is restricted to a binary phase shift of 0 or π, turning the passive beamforming design problem with N elements into a combinatorial optimization problem over 2^N configurations. Instead of running a classical optimizer, QAOA-LR uses a fixed linear ramp to set the variational parameters across p layers and finds the best scale via a simple one-dimensional grid search over a single parameter. Monte Carlo simulations over Rayleigh-fading MIMO channels confirm that QAOA-LR closely tracks the optimum maximum-likelihood (ML) solution. Furthermore, the proposed algorithm reduces the computational complexity compared with classical optimization, and real hardware experiments on the IBM Quantum processor confirm near-ML capacity performance with polynomial scaling of quantum processing unit execution time as the number of RIS elements increases.
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.