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Recursive-Repetitive Truncated QAOA-MVSIC for mMIMO Detection: Matrix Product State Simulation and Experimental Evaluation

Burhan Gülbahar

Published Sep 4, 2025• 0 citations
Publisher

Abstract

Quantum approximate optimization algorithm (QAOA) promises near-optimal decoding for n × n massive multiple-input multiple-output (mMIMO) systems. QAOA-MVSIC, recently formulated for Noisy Intermediate-Scale Quantum (NISQ) settings, combines truncated QAOA of small depth p with majority voting (MV) and successive-interference cancellation (SIC) for robustness to noise. We introduce RRT-Q, a recursive, repetitive extension of truncated QAOA-MVSIC, and demonstrate strong noise tolerance, markedly outperforming QAOA and QAOA-MVSIC. We report, to our knowledge, the first experimental bit-error-rate (BER) results for QAOA-based decoding: on an IBM Eagle processor, performance matches semidefinite relaxation with Gaussian randomization (SDR-GR) at signal-to-noise ratio (SNR) ≤ 10 dB for n = 120 (BPSK) and n = 32 (QPSK). Matrix-product-state tensor-network simulations up to n ≤ 256 reach SDR-GR with p = 1. We derive RRT-Q complexity bounds; empirically, we observe that for n ≤ 256 and SNR ≤ 10 dB with Ns QAOA samples, average cost per instance is n α +Ns n β (classical) and Nsn η (quantum) with α ∈ [2.8, 3.4], β ∈ [1.8, 2.2] and η ∈ [1.6, 2.2] while RRT-Q-ML version with maximum-likelihood detection at the final step adds n ζ term with ζ ∈ [2.7, 4.6]. The tunable, low-complexity design targets near-optimal NISQ performance and is expected to scale to the fault-tolerant regime (n ≫ 256).

DOI
10.22541/au.175700359.95812012/v1

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In the massive multiple-input and multiple-output (Massive MIMO) systems, the maximum likelihood (ML) detection problem is NP-hard and becoming classically intricate with the number of transmitting antennas and symbols increasing. The quantum approximate optimization algorithm (QAOA), a leading candidate algorithm running in the noisy intermediate-scale quantum (NISQ) devices, can show quantum advantage for approximately solving combinatorial optimization problems. In this paper, we propose the QAOA based on the maximum likelihood detection solver of binary symbols. In the proposed scheme, we first conduct a universal and compact analytical expression for the expectation value of the 1-level QAOA. Second, a Bayesian optimization based parameters initialization is presented, which can speedup the convergence of the QAOA to a lower local minimum and improve the probability of measuring the exact solution. Compared to the state-of-the-art QAOA based ML detection algorithm, our scheme has the more universal and compact expectation value expression of the 1-level QAOA, and requires few quantum resources and has the higher probability to obtain the exact solution.