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 × 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 ≪ 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(m n p) quantum and O(m n2) classical operations with low complexity. We experimentally implement QAOA combined with MV (QAOA-MV) for n ϵ [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. © 2025 Elsevier B.V. All rights reserved.