Warm-Start Quantum Approximate Optimization Algorithm for QAM MIMO Data Detection

Data detection in large-scale multiple-input multiple-output (MIMO) systems with higher-order quadrature amplitude modulation (QAM) remains a challenging problem due to the exponential complexity of the classical maximum likelihood (ML) detector. This challenge is further amplified by Gray-coded modulation, which introduces nonlinear symbol-to-bit mappings and transforms the problem into a higher-order unconstrained binary optimization (HUBO) formulation. To address this problem, this paper presents a hybrid quantum-classical detection framework that leverages a warm-start linear-ramp Quantum Approximate Optimization Algorithm (WSLR-QAOA) for solving the resulting HUBO problem. A structured warm-start based on a low-rank semidefinite relaxation, solved via a block coordinate descent (BCD) method, provides an efficient and high-quality initialization, while a linear ramp parameterization guides the QAOA optimization. Simulation results show that the proposed framework outperforms classical methods in terms of symbol error rate (SER) and converges faster than standard QAOA, while achieving performance close to the optimal ML detector. Furthermore, the WSLR-QAOA algorithm is validated on actual IBM quantum hardware, where it achieves near-ML performance at low SNR and maintains competitive accuracy at higher SNR despite moderate degradation due to hardware noise. This demonstrates the practical potential of the HUBO-based WSLR-QAOA algorithm for large-scale MIMO data detection.