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.
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.
Data detection in large-scale multiple-input multiple-output (MIMO) systems with higher-order quadrature amplitude modulation (QAM) remains a challenging problem due to the exponential complexity of the classical maximum likelihood (ML) detector. This challenge is further amplified by Gray-coded modulation, which introduces nonlinear symbol-to-bit mappings and transforms the problem into a higher-order unconstrained binary optimization (HUBO) formulation. To address this problem, this paper presents a hybrid quantum-classical detection framework that leverages a warm-start linear-ramp Quantum Approximate Optimization Algorithm (WSLR-QAOA) for solving the resulting HUBO problem. A structured warm-start based on a low-rank semidefinite relaxation, solved via a block coordinate descent (BCD) method, provides an efficient and high-quality initialization, while a linear ramp parameterization guides the QAOA optimization. Simulation results show that the proposed framework outperforms classical methods in terms of symbol error rate (SER) and converges faster than standard QAOA, while achieving performance close to the optimal ML detector. Furthermore, the WSLR-QAOA algorithm is validated on actual IBM quantum hardware, where it achieves near-ML performance at low SNR and maintains competitive accuracy at higher SNR despite moderate degradation due to hardware noise. This demonstrates the practical potential of the HUBO-based WSLR-QAOA algorithm for large-scale MIMO data detection.
Simultaneously transmitting and reflecting reconfigurable intelligent surface (STAR-RIS) enables 360-degree full-space coverage by controlling both transmitted and reflected signals through each element. However, the coupled phase-shift model, where the transmission and reflection coefficients are physically interdependent, transforms the phase optimization into an extremely complex non-convex combinatorial problem that classical algorithms struggle to solve efficiently. In this paper, we propose a hybrid quantum-classical framework that employs the Quantum Approximate Optimization Algorithm (QAOA) to optimize the coupled phase-shift configuration of STAR-RIS. Each discrete phase configuration is mapped to a qubit-based Ising Hamiltonian, enabling QAOA to explore the exponentially large solution space through quantum superposition and entanglement. To address the scalability challenge of simulating large antenna arrays (e.g., 8 × 8 = 64 elements), we introduce a variable grouping (tiling) strategy that partitions the RIS into manageable sub-arrays of 2 × 2 elements, each requiring only 8 qubits for 2-bit phase quantization. Our comprehensive simulations demonstrate that the proposed QAOA-based optimizer achieves an approximation ratio exceeding 0.94 with 10 QAOA layers, maintains over 86% fidelity under 2% gate error rates in noisy intermediate-scale quantum (NISQ) environments, and exhibits robust performance under imperfect channel state information with less than 5% degradation at 30% CSI error variance. The energy efficiency analysis confirms that the QAOA-optimized STAR-RIS achieves approximately 1.7× higher spectral efficiency per unit energy compared to conventional reflect-only RIS. Furthermore, the proposed tiling framework scales linearly with array size, enabling deployment on arrays up to 16 × 16 elements while maintaining constant per-group quantum resource requirements.
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.
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 employingb-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 ofb-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 theb-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.
Abstract The quantum approximate optimization algorithm (QAOA) is a promising algorithm for solving combinatorial optimization problems (COPs), with performance governed by variational parameters {γi,βi}i=0p−1 { γ i , β i } i = 0 p − 1 . While most prior work has focused on classically optimizing these parameters, we demonstrate that fixed linear ramp schedules, linear ramp QAOA (LR-QAOA), can efficiently approximate optimal solutions across diverse COPs. Simulations with up to N q = 42 qubits and p = 400 layers suggest that the success probability scales as P(x∗)≈2−η(p)Nq+C P ( x * ) ≈ 2 − η ( p ) N q + C , where η ( p ) decreases with increasing p . For example, in Weighted Maxcut instances, η (10) = 0.22 improves to η (100) = 0.05. Comparisons with classical algorithms, including simulated annealing, Tabu Search, and branch-and-bound, show a scaling advantage for LR-QAOA. We show results of LR-QAOA on multiple QPUs (IonQ, Quantinuum, IBM) with up to N q = 109 qubits, p = 100, and circuits requiring 21,200 CNOT gates. Finally, we present a noise model based on two-qubit gate counts that accurately reproduces the experimental behavior of LR-QAOA.
In this paper, we investigate the potential of a near-optimal hybrid quantum-classical optimization approach to jointly optimizing beamforming and discrete phase shifts of the simultaneous transmitting and reflecting reconfigurable intelligent surface (STAR-RIS) assisted wireless network. We first formulate a discrete optimization problem to maximize the total power transmitted to the ground users by optimizing the beamforming at the base station (BS) and STAR-RIS phase shift cells under minimal power allocation for each user and the power budget at the BS. Then, we propose a quantum approximate optimization algorithm with alternating optimization (QAOA-AO) method that iteratively addresses beamform-ing components and discrete phase shifts to search for the near-optimal solutions for the problem. Numerical results validate the effectiveness and robustness of the proposed QAOA-AO compared to the classical benchmarks, and further highlight its potential for practical applicability for solving medium-to-large-scale optimization problems.