Maximum-Likelihood Detection With QAOA for Massive MIMO and Sherrington-Kirkpatrick Model With Local Field at Infinite Size
Burhan Gülbahar · IEEE Transactions on Wireless Communications · 2024
Quantum-approximate optimization algorithm (QAOA) is promising in Noisy Intermediate-Scale Quantum (NISQ) computers with applications for NP-hard combinatorial optimization problems. It is recently utilized for NP-hard maximum-likelihood (ML) detection problem with challenges of optimization, simulation and performance analysis forn×nmultiple-input multiple output (MIMO) systems with largen. QAOA is recently applied by Farhi et al. on infinite size limit of Sherrington-Kirkpatrick (SK) model with a cost model including only quadratic terms. In this article, we extend the model by including also linear terms and then realize SK modeling of massive MIMO ML detection. The proposed design targets near ML performance while with complexity includingO(16p) initial operations independent from problem instance and sizenfor optimizing QAOA angles andO(n2p) quantum operations for each instance. We provide both optimized and extrapolated angles forp∈ [1, 14] and signal-to-noise (SNR)p≥ 4 for 25×25 and 12 × 12 MIMO systems modulated with BPSK and QPSK, respectively. We present two conjectures about concentration properties of QAOA and near-optimum performance for next generation massive MIMO systems coveringn< 300.