Majority Voting With Recursive QAOA and Cost-Restricted Uniform Sampling for Maximum-Likelihood Detection in Massive MIMO

Abstract

Quantum approximate optimization algorithm (QAOA) with layer depth p is promising near-optimum performance and low complexity for NP-hard maximum-likelihood (ML) detection in $n \times n$ multi-input multi-output (MIMO) systems. Experimental challenges for ML detection on Noisy Intermediate-Scale Quantum (NISQ) computers arise from accumulated errors with large p and n. Recursive QAOA (RQAOA) is promising with small p by reducing complexity over n steps. In this article, we modify RQAOA for $p \ll n$ with cost sorting and post-selection in $m \ll n$ steps, and then integrate it with majority voting (MV) and successive interference cancellation (SIC) into the QAOA-MVSIC algorithm to tackle experimental challenges. We truncate QAOA circuits to further improve experimental feasibility. Simulations with $n = 24$ and 12 for BPSK and QPSK modulations, respectively, show near-optimum bit-error rate (BER) with $p = 1$ and $m \leq 4$ . Truncated version requires $O(m \,n \, p)$ quantum and $O(m \, n^{2})$ classical operations with low complexity. We experimentally implement QAOA combined with MV (QAOA-MV) for $n \in [{17, 64}]$ in IBM Eagle processor by observing superior performance of QAOA-MV over QAOA and reducing problem dimensions by at least $n / 4$ . We generalize QAOA as cost-restricted uniform sampling (CRUS) oracle and approximately simulate for $n \leq 128$ to obtain comparison benchmark for future QAOA experiments.