This paper proposes a hybrid quantum optimization framework for large-scale antenna-array beamforming with jointly optimized discrete phases and continuous amplitudes. The method combines quantum-inspired search with classical gradient refinement to handle mixed discrete-continuous variables efficiently. For phase optimization, a Gray-code and odd-combination encoding scheme is introduced to improve robustness and avoid the complexity explosion of higher-order Ising models. For amplitude optimization, a geometric spin-combination encoding and a two-stage strategy are developed, using quantum-inspired optimization for coarse search and gradient optimization for fine refinement. To enhance solution diversity and quality, a rainbow quantum-inspired algorithm integrates multiple optimizers for parallel exploration, followed by hierarchical-clustering-based candidate refinement. In addition, a double outer-product method and an augmented version are proposed to construct the coupling matrix and bias vector efficiently, improving numerical precision and implementation efficiency. Under the scoring rules of the 7th National Quantum Computing Hackathon, simulations on a 32-element antenna array show that the proposed method achieves a score of 461.58 under constraints on near-main-lobe sidelobes, wide-angle sidelobes, beamwidth, and optimization time, nearly doubling the baseline score. The proposed framework provides an effective reference for beamforming optimization in future wireless communication systems.
This paper proposes a hybrid quantum optimization framework for large-scale antenna-array beamforming with jointly optimized discrete phases and continuous amplitudes. The method combines quantum-inspired search with classical gradient refinement to handle mixed discrete-continuous variables efficiently. For phase optimization, a Gray-code and odd-combination encoding scheme is introduced to improve robustness and avoid the complexity explosion of higher-order Ising models. For amplitude optimization, a geometric spin-combination encoding and a two-stage strategy are developed, using quantum-inspired optimization for coarse search and gradient optimization for fine refinement. To enhance solution diversity and quality, a rainbow quantum-inspired algorithm integrates multiple optimizers for parallel exploration, followed by hierarchical-clustering-based candidate refinement. In addition, a double outer-product method and an augmented version are proposed to construct the coupling matrix and bias vector efficiently, improving numerical precision and implementation efficiency. Under the scoring rules of the 7th National Quantum Computing Hackathon, simulations on a 32-element antenna array show that the proposed method achieves a score of 461.58 under constraints on near-main-lobe sidelobes, wide-angle sidelobes, beamwidth, and optimization time, nearly doubling the baseline score. The proposed framework provides an effective reference for beamforming optimization in future wireless communication systems.
Massive multiple-input multiple-output (MIMO) systems are a key enabling technology for 5G-Advanced and emerging 6G networks, yet their performance is fundamentally constrained by high-dimensional, non-convex optimization problems arising from beamforming, power allocation, and user scheduling under imperfect channel state information (CSI).This paper proposes a hybrid quantum-classical optimization framework that formulates discrete and continuous massive MIMO resource allocation problems using Quadratic Unconstrained Binary Optimization (QUBO) and variational quantum algorithms.Discrete beam selection is addressed using quantum annealing, while continuous power control and hybrid beamforming are refined using variational quantum circuits within a classical feedback loop.Simulation results demonstrate improvements in aggregate spectral efficiency, runtime scalability, and robustness under imperfect CSI compared to conventional ZF and WMMSE baselines.The benefits of using the proposed solution include scalable runtime performance with respect to larger numbers of antennas; thus, it highlights the potential of optimizing quantum-assisted technologies for the future of wireless networks based on realistic assumptions regarding near-term NISQ-era performance.
Massive MIMO beamforming for 6G networks faces a fundamental tradeoff between solution quality and computational complexity. Exhaustive search guarantees optimal antenna selection; however, this becomes prohibitively expensive for arrays exceeding 16 elements, while polynomial-time classical heuristics sacrifice 15–25% performance to achieve practical scalability. This paper introduces a quantum-enhanced optimization framework using the Quantum Approximate Optimization Algorithm (QAOA) to address this challenge for IoT-integrated 6G massive MIMO systems. Our approach combines quantum solution exploration with classical parameter optimization, integrating realistic 3GPP TR 38.901 channel models across 28–60 GHz bands and heterogeneous IoT device characteristics (mMTC, URLLC, eMBB). The framework incorporates an adaptive penalty mechanism that achieves constraint satisfaction within five iterations while maintaining polynomial complexity. Statistical validation across 50 independent channel realizations demonstrates significant advantages: 10–20% spectral efficiency improvement over classical heuristics (p<0.001, Cohen’s d=1.24), 35–42% IoT energy reduction, and 90–95% near-optimal solution quality compared to 65–85% for polynomial-time classical methods. Hardware validation on IBM quantum platforms (127–133 qubits) confirms practical feasibility for medium-scale systems with M≤16 antennas, achieving 89.3% of ideal performance with 22% measurement success rate. Current hardware limitations restrict deployment to proof-of-concept demonstrations, with full-scale 6G implementations requiring quantum error correction projected for 2030+.
Scalable combinatorial optimization under resource-constrained quantum hardware remains a fundamental challenge in the Noisy Intermediate-Scale Quantum (NISQ) era, due to the mismatch between exponentially growing solution spaces and limited quantum computational capacity. In this work, we propose a NISQ-aware hybrid quantum-classical optimization framework that reformulates large-scale combinatorial optimization as a resource-bounded distribution evolution process. Instead of directly optimizing individual solutions, the proposed framework operates on a probabilistic representation of the solution space, enabling efficient exploration under hardware constraints. Specifically, large problem instances are decomposed into qubit-compatible subproblems via clustering-based decomposition, ensuring resource-bounded optimization. Within each subproblem, a quantum genetic algorithm evolves the solution distribution, while periodically embedded amplitude amplification acts as a controlled quantum enhancement mechanism that accelerates convergence without increasing circuit depth. A classical refinement stage ensures global solution consistency. Extensive experiments on benchmark and synthetic datasets demonstrate that the proposed framework consistently outperforms classical and quantum-inspired baselines, with performance gains that become more pronounced as problem scale increases. This scale-dependent behavior indicates that scalability is achieved through structured decomposition rather than increased quantum complexity. Noise simulations further confirm robustness under realistic NISQ conditions, and ablation studies validate that both quantum evolutionary search and amplitude amplification contribute significantly to performance improvements.
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.
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.
Large-scale optimization (LSO) problems—those with hundreds to thousands of decision variables—are prevalent in engineering design, logistics, telecommunications, and machine learning hyperparameter search. Classical evolutionary algorithms often struggle in this regime due to premature convergence and prohibitive search costs. This manuscript presents a Quantum-Inspired Genetic Algorithm (QIGA) that transfers three ideas from quantum computation into a purely classical algorithm: (i) Q-bit angle encoding that maintains a compact, uncertainty-aware distribution over decision values, (ii) rotation-gate adaptation that updates search probabilities toward promising regions while preserving exploration, and (iii) quantum observation that draws diverse candidate solutions from the encoded amplitudes at each generation. We further couple the core QIGA with (a) an island-model decomposition for ultra-high dimensionality, (b) surrogate-assisted local refinement for exploitation at low cost, and (c) a feasibility-aware penalty for constraints. We evaluate the approach on five canonical continuous benchmarks in 1,000 dimensions (Sphere, Rosenbrock, Rastrigin, Ackley, Griewank) under a fixed computational budget. Across 30 independent runs per function, QIGA achieves lower final objective values and higher success rates than classical GA, PSO, and DE baselines. A non-parametric Wilcoxon signed-rank test indicates statistically significant improvements for QIGA (adjusted p < 0.01) on all functions. We analyze the algorithm’s scaling behavior, the role of angle-space step control, and the contribution of island-level diversity. The results suggest that quantum-inspired probability evolution provides a robust inductive bias for LSO by decoupling representation capacity from point estimates and by enabling distribution-aware search moves. We conclude with practical guidelines for tuning and discuss extensions to constrained and mixed-variable problems.