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

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 nxn 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 << n with cost sorting and post-selection in m << 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 <= 4 . Truncated version requires O(mnp) quantum and O(mn2) classical operations with low complexity. We experimentally implement QAOA combined with MV (QAOA-MV) for n is an element of[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 <= 128 to obtain comparison benchmark for future QAOA experiments.