Quantum-Inspired Ultra-Massive THz MIMO Sparse Subarray Hybrid Beamforming

Ultra-massive multiple-input multiple-output (MIMO) operating in the terahertz (THz) band has the potential to deliver data rates well beyond those of millimeter-wave and sub-6 GHz systems. However, fully digital beamforming becomes impractical for arrays with hundreds or thousands of antennas because each antenna requires a dedicated radio frequency (RF) chain, data converter, and power amplifier. Hybrid beamforming addresses this limitation by allowing multiple antennas to share a limited number of RF chains. Nevertheless, existing subarray-selection techniques either suffer from high computational complexity, as in Orthogonal Matching Pursuit (OMP), or tend to converge to local optima when using greedy search strategies. This paper presents a Quantum-Inspired Spare Subarray (Q-Sparse) selection framework for hybrid beamforming. The proposed method employs a qubit-inspired rotation-gate search to identify the subarrays that contribute most to channel capacity while satisfying a predefined hardware budget. Performance was evaluated using 50 Monte Carlo realizations of a 512-antenna THz MIMO system with eight RF chains. The results show that activating only about 40% of the available subarrays achieves spectral efficiency within approximately 9% of the fully digital benchmark, while reducing the number of active antenna elements and the associated phase shifters by more than half. Q-Sparse was further compared with OMP, Particle Swarm Optimization (PSO), and Genetic Algorithm (GA) under the same hardware budget and evaluation settings. It achieved spectral efficiency comparable to PSO and GA (95% confidence intervals overlap; two-sample t-test, p = 0.585) while requiring approximately 2.5-3 times less computation time per channel realization. In addition, it consistently outperforms greedy and OMP methods across the evaluated SNR range, RF-chain configurations, and array sizes. A sensitivity analysis over target sparsity levels (20-70%) showed that the energy-efficiency gain over fully digital beamforming decreases from approximately 154% to 28% as more subarrays are activated, providing designers with a practical trade-off between hardware usage and system performance. Repeated optimization on a fixed channel also revealed a statistically significant, although moderate, preference for selecting higher-gain subarrays over random selection. These results demonstrate that Q-Sparse provides a practical and computationally efficient solution for achieving near-optimal hybrid beamforming for ultra-massive THz MIMO systems.