Maximum-Likelihood Detection With QAOA for Massive MIMO and Sherrington-Kirkpatrick Model With Local Field at Infinite Size

Abstract

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 × 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 ∈ [1, 14] and signal-to-noise (SNR) < 12 dB achieving near-optimum ML performance for 25 × 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.