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.
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.
Quantum computing, with its powerful parallel computing capabilities, is considered one of the promising candidates for solving complex communication problems. This paper proposes a new detection scheme by combining quantum approximation optimization algorithms (QAOA) with maximum likelihood (ML) detection. The scheme addresses the computational complexity problem faced by ML detection in large-scale multiple-input multiple-output (MIMO) channels. The primary focus lies in the warm-start optimization based on the QAOA-ML detection. We use semi-definite relaxation (SDR) to calculate the temporary solution of ML for initializing quantum circuits. The feasibility of the scheme is verified through simulation. The proposed detection scheme is evaluated and compared with classical computer-based ML detection and Minimum Mean Square Error (MMSE) detection, demonstrating similar bit error rate (BER) performance. The enormous potential of quantum algorithms in computing power solving the drawbacks of traditional ML detection algorithms provides new possibilities for improving detection efficiency.
Recent advances in quantum technologies pave the way for noisy intermediate-scale quantum (NISQ) devices, where the quantum approximation optimization algorithm (QAOA) constitutes a promising candidate for demonstrating tangible quantum advantages based on NISQ devices. In this paper, we consider the maximum likelihood (ML) detection problem of binary symbols transmitted over a multiple-input and multiple-output (MIMO) channel, where finding the optimal solution is exponentially hard using classical computers. Here, we apply the QAOA for the ML detection by encoding the problem of interest into a level-pQAOA circuit having2pvariational parameters, which can be optimized by classical optimizers. This level-pQAOA circuit is constructed by applying the prepared Hamiltonian to our problem and the initial Hamiltonian alternately inpconsecutive rounds. More explicitly, we first encode the optimal solution of the ML detection problem into the ground state of a problem Hamiltonian. Using the quantum adiabatic evolution technique, we provide both analytical and numerical results for characterizing the evolution of the eigenvalues of the quantum system used for ML detection. Then, for level-1 QAOA circuits, we derive the analytical expressions of the expectation values of the QAOA and discuss the complexity of the QAOA based ML detector. Explicitly, we evaluate the computational complexity of the classical optimizer used and the storage requirement of simulating the QAOA. Finally, we evaluate the bit error rate (BER) of the QAOA based ML detector and compare it both to the classical ML detector and to the classical minimum mean squared error (MMSE) detector, demonstrating that the QAOA based ML detector is capable of approaching the performance of the classical ML detector.
In this paper, we propose a quantum algorithm that supports a real-valued higher-order unconstrained binary optimization (HUBO) problem. This algorithm is based on the Grover adaptive search that originally supported HUBO with integer coefficients. Next, as an application example, we formulate multiple-input multiple-output maximum likelihood detection as a HUBO problem with real-valued coefficients, where we use the Gray-coded bit-to-symbol mapping specified in the 5G standard. The proposed approach allows us to construct an efficient quantum circuit for the detection problem and to analyze specific numbers of required qubits and quantum gates, whereas other conventional studies have assumed that such a circuit is feasible as a quantum oracle. To further accelerate the quantum algorithm, we also derive a probability distribution of the objective function value and determine a unique threshold to sample better states. Assuming a future fault-tolerant quantum computing, our proposed algorithm has the potential for significantly reducing query complexity in the classical domain and providing a quadratic speedup in the quantum domain.
Beyond Binary Encoding: Qudit-Based QAOA Framework for ML Detection in M-QAM MIMO Systems
Maximum likelihood (ML) detection in massive multiple-input multiple-output (MIMO) systems is an NP-hard combinatorial problem whose complexity grows exponentially with the number of transmit antennas and the modulation order. The Quantum Approximate Optimization Algorithm (QAOA) has recently emerged as a promising near-term quantum heuristic for such problems; however, existing qubit-based formulations require log2M qubits per M-QAM symbol, inflating both circuit width and depth. In this paper, we propose a qudit-based QAOA framework that encodes each M-QAM symbol directly into a pair of d-dimensional quantum states, where d=M. We derive a Hermitian cost Hamiltonian via a real-imaginary decomposition of the constellation, and introduce a generalized cyclic-shift mixer that ensures ergodic exploration of the search space without binary encoding. The proposed formulation reduces the number of quantum carriers from O(Ntlog2M) to O(Nt) and the Hamiltonian interaction complexity from O((Ntlog2M)2) to O(Nt2), while preserving the geometric structure of the constellation. Bit-error-rate (BER) simulations for 2×2 MIMO systems employing 4-QAM and 16-QAM over Rayleigh fading channels, with circuit depth p=3, demonstrate that the proposed detector closely approximates the performance of the optimal classical maximum-likelihood (ML) detector, while consistently outperforming the conventional minimum mean square error (MMSE) detector.
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.
In this research, the goal is to assess the performance and computational efficiency of the Quantum Approximate Optimization Algorithm for signal detection in MIMO-NOMA systems compared with classical detection methods. The deep learning detection framework supported by the Quantum Approximate Optimization Algorithm (QAOA). The Quantum Approximate Optimization Algorithm (QAOA) assistance in the deep learning-based detection system. For this group, the sample size of signal examples considered is 5,000, and the simulations are carried out based on various signal to noise ratios, antenna array, modulations, and channel estimation errors. The bit error rate, accuracy of detection, channel estimation error, complexity, and throughput of the system are evaluated. The output of the simulation showed that, for a given detection performance, the QAOA-assisted deep learning detection framework outperforms other detection methods in terms of 18% lower bit error rate, 14% higher detection accuracy, 12% lower channel estimation error, 10% lower computational complexity, and 16% higher throughput. The result of the experiment suggests that the proposed framework for signal detection using the assistance of the QAOA-based deep learning algorithm is capable of carrying out the detection of the multiple users' signal compared to other signal detection methods in terms of the mentioned criteria.