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 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(16p) 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.