Maximum-likelihood detection with QAOA for massive MIMO and Sherrington-Kirkpatrick model with local field at infinite size

<p>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 fundamental challenges of optimization, simulation and performance analysis for  n x n multiple-input multiple output (MIMO) systems with large n. 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 application of QAOA on SK model by including also linear terms  and then realize SK modeling of massive MIMO ML detection by ensuring independence from specific problem instance and size  n while preserving computational complexity of O(16^p) designed by Farhi et al. We provide both optimized and extrapolated angles for p in the set [1, 14] and signal-to-noise (SNR) < 12  dB achieving near-optimum ML performance for 25 x 25 MIMO system with p >= 4  in extensive simulations where  236500 different QAOA circuits are simulated.  We present two conjectures about the concentration properties of QAOA  and  its near-optimum performance for massive MIMO systems with large sizes covering n  < 300 promising significant performance for next generation massive MIMO systems.</p>