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arXiv:2510.15935 · IEEE Journal of Selected Topics in Signal Processing

Quantum Approximate Optimization Algorithm for MIMO With Quantized bbb-Bit Beamforming

Nikos A. Mitsiou, Ioannis Krikidis, George K. Karagiannidis

Published Sep 1, 2025• 5 citations
arXivHTMLPDF

Abstract

Multiple-input multiple-output (MIMO) is critical for 6G communication, offering improved spectral efficiency and reliability. However, conventional fully digital designs face significant challenges due to high hardware complexity and power consumption. Low-bit MIMO architectures, such as those employing$b$-bit quantized phase shifters, provide a cost-effective alternative but introduce NP-hard combinatorial problems in the pre- and post-coding design. This paper explores the use of the Quantum Approximate Optimization Algorithm (QAOA) and alternating optimization to address the problem of$b$-bit quantized phase shifters both at the transmitter and the receiver. We demonstrate that the structure of this quantized beamforming problem aligns naturally with hybrid-classical methods like QAOA, as the phase shifts used in beamforming can be directly mapped to rotation gates in a quantum circuit. Notably, this paper is the first to show that theoretical connection. Then, the Hamiltonian derivation analysis for the$b$-bit case is presented, which could have applications in different fields, such as integrated sensing and communication, and emerging quantum algorithms such as quantum machine learning. In addition, a warm-start QAOA approach is studied which improves computational efficiency. Numerical results highlight the effectiveness of the proposed methods in achieving an improved quantized beamforming gain over their classical optimization benchmarks from the literature.

DOI
10.1109/jstsp.2025.3615537

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Multiple-input multiple-output (MIMO) is critical for 6G communication, offering improved spectral efficiency and reliability. However, conventional fully digital designs face significant challenges due to high hardware complexity and power consumption. Low-bit MIMO architectures, such as those employingbbb-bit quantized phase shifters, provide a cost-effective alternative but introduce NP-hard combinatorial problems in the pre- and post-coding design. This paper explores the use of the Quantum Approximate Optimization Algorithm (QAOA) and alternating optimization to address the problem ofbbb-bit quantized phase shifters both at the transmitter and the receiver. We demonstrate that the structure of this quantized beamforming problem aligns naturally with hybrid-classical methods like QAOA, as the phase shifts used in beamforming can be directly mapped to rotation gates in a quantum circuit. Notably, this paper is the first to show that theoretical connection. Then, the Hamiltonian derivation analysis for thebbb-bit case is presented, which could have applications in different fields, such as integrated sensing and communication, and emerging quantum algorithms such as quantum machine learning. In addition, a warm-start QAOA approach is studied which improves computational efficiency. Numerical results highlight the effectiveness of the proposed methods in achieving an improved quantized beamforming gain over their classical optimization benchmarks from the literature.
In this letter, we study the analogue pre/post-coding vector design for a point-to-point multiple-input multiple-output (MIMO) system with 1-bit phase shifters. Specifically, we focus on the signal-to-noise ratio (SNR) maximization problem which corresponds to a combinatorial NP-hard due to the binary phase resolution. Two classical computation heuristics are proposed i.e., i) an 1-bit real-valued approximation of the optimal digital designs, and ii) an alternating optimization where a Rayleigh quotient problem is solved at each iteration. An iterative quantum annealing (QA)-based heuristic is also investigated, which outperforms classical counterparts and achieves near-optimal performance while ensuring polynomial time complexity. Experimental results in a real-world D-WAVE QA device validate the efficiency of the proposed QA approach.
Massive MIMO beamforming for 6G networks faces a fundamental tradeoff between solution quality and computational complexity. Exhaustive search guarantees optimal antenna selection; however, this becomes prohibitively expensive for arrays exceeding 16 elements, while polynomial-time classical heuristics sacrifice 15–25% performance to achieve practical scalability. This paper introduces a quantum-enhanced optimization framework using the Quantum Approximate Optimization Algorithm (QAOA) to address this challenge for IoT-integrated 6G massive MIMO systems. Our approach combines quantum solution exploration with classical parameter optimization, integrating realistic 3GPP TR 38.901 channel models across 28–60 GHz bands and heterogeneous IoT device characteristics (mMTC, URLLC, eMBB). The framework incorporates an adaptive penalty mechanism that achieves constraint satisfaction within five iterations while maintaining polynomial complexity. Statistical validation across 50 independent channel realizations demonstrates significant advantages: 10–20% spectral efficiency improvement over classical heuristics (p<0.001, Cohen’s d=1.24), 35–42% IoT energy reduction, and 90–95% near-optimal solution quality compared to 65–85% for polynomial-time classical methods. Hardware validation on IBM quantum platforms (127–133 qubits) confirms practical feasibility for medium-scale systems with M≤16 antennas, achieving 89.3% of ideal performance with 22% measurement success rate. Current hardware limitations restrict deployment to proof-of-concept demonstrations, with full-scale 6G implementations requiring quantum error correction projected for 2030+.
We propose a Quantum Approximate Optimization Algorithm with a deterministic linear ramp schedule (QAOA-LR) for phase optimization of a 1-bit RIS-assisted MIMO communication system. Each RIS element is restricted to a binary phase shift of 0 or π, turning the passive beamforming design problem with N elements into a combinatorial optimization problem over 2^N configurations. Instead of running a classical optimizer, QAOA-LR uses a fixed linear ramp to set the variational parameters across p layers and finds the best scale via a simple one-dimensional grid search over a single parameter. Monte Carlo simulations over Rayleigh-fading MIMO channels confirm that QAOA-LR closely tracks the optimum maximum-likelihood (ML) solution. Furthermore, the proposed algorithm reduces the computational complexity compared with classical optimization, and real hardware experiments on the IBM Quantum processor confirm near-ML capacity performance with polynomial scaling of quantum processing unit execution time as the number of RIS elements increases.
Beamforming optimization in 6G networks is essential for ensuring energy-efficient and interference-aware transmission, where ultra-reliable low-latency communication (URLLC) and scalable antenna technologies play a key role. Classical optimization methods face scalability challenges, making real-time beamforming infeasible. This paper applies the quantum approximate optimization algorithm (QAOA) to minimize transmit power while ensuring signal quality constraints. The problem is formulated as a quadratic unconstrained binary optimization (QUBO) and solved using quantum simulation. Simulation results demonstrate that QAOA achieves lower transmit power compared to classical solvers, with faster convergence and improved efficiency. These findings suggest that quantum computing can significantly enhance beamforming optimization, paving the way for its integration into future wireless networks.
In this paper, we study the problem of digital pre/post-coding design in multiple-input multiple-output (MIMO) systems with 1-bit resolution per complex dimension. The optimal solution that maximizes the received signal-to-noise ratio relies on an NP-hard combinatorial problem that requires exhaustive searching with exponential complexity. By using the principles of alternating optimization and quantum annealing (QA), an iterative QA-based algorithm is proposed that achieves near-optimal performance with polynomial complexity. The algorithm is associated with a rigorous mathematical framework that casts the pre/post-coding vector design to appropriate real-valued quadratic unconstrained binary optimization (QUBO) problems. Experimental results in a state-of-the-art D-WAVE QA device validate the efficiency of the proposed algorithm. To further improve the efficiency of the D-WAVE quantum device, a new pre-processing technique which preserves the quadratic QUBO matrix from the detrimental effects of the Hamiltonian noise through non-linear companding, is proposed. The proposed pre-processing technique significantly improves the quality of the D-WAVE solutions as well as the occurrence probability of the optimal solution.
As wireless networks advance toward the Sixth Generation (6G), which will support highly heterogeneous scenarios and massive data traffic, conventional computing methods may struggle to meet the immense processing demands in a resource-efficient manner. This paper explores the potential of quantum computing (QC) to address these challenges, specifically by enhancing the efficiency of Maximum-Likelihood detection in Multiple-Input Multiple-Output (MIMO) Non-Orthogonal Multiple Access (NOMA) communication systems, an essential technology anticipated for 6G. The study proposes the use of the Quantum Approximate Optimization Algorithm (QAOA), a variational quantum algorithm known for providing quantum advantages in certain combinatorial optimization problems. While current quantum systems are not yet capable of managing millions of physical qubits or performing high-fidelity, long gate sequences, the results indicate that QAOA is a promising QC approach for radio signal processing tasks. This research provides valuable insights into the potential transformative impact of QC on future wireless networks. This sets the stage for discussions on practical implementation challenges, such as constrained problem sizes and sensitivity to noise, and opens pathways for future research aimed at fully harnessing the potential of QC for 6G and beyond.