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arXiv:2505.03914

Hybrid Quantum-Classical Maximum-Likelihood Detection via Grover-based Adaptive Search for RIS-assisted Broadband Wireless Systems

Maryam Tariq, Raneem F. Abdelrahim, Omar Alhussein, Sami Muhaidat

Published May 6, 2025• 0 citations
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Abstract

The escalating complexity and stringent performance demands of sixth-generation wireless systems necessitate advanced signal processing methods capable of simultaneously achieving high spectral efficiency and low computational complexity, especially under frequency-selective propagation conditions. In this paper, we propose a hybrid quantum-classical detection framework for broadband systems enhanced by reconfigurable intelligent surfaces (RISs). We address the maximum likelihood detection (MLD) problem for RIS-aided broadband wireless communications by formulating it as a quadratic unconstrained binary optimization problem, that is then solved using Grover adaptive search (GAS). To accelerate convergence, we initialize the GAS algorithm with a threshold based on a classical minimum mean-squared error detector. The simulation results show that the proposed hybrid classical-quantum detection scheme achieves near-optimal MLD performance while substantially reducing query complexity. These findings highlight the potential of quantum-enhanced detection strategies combined with RIS technology, offering efficient and near-optimal solutions for broadband wireless communications.

DOI
10.48550/arxiv.2505.03914

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The escalating complexity and stringent performance demands of sixth-generation wireless systems necessitate advanced signal processing methods capable of simultaneously achieving high spectral efficiency and low computational complexity, especially under frequency-selective propagation conditions. In this paper, we propose a hybrid quantum-classical detection framework for broadband systems enhanced by reconfigurable intelligent surfaces (RISs). We address the maximum likelihood detection (MLD) problem for RIS-aided broadband wireless communications by formulating it as a quadratic unconstrained binary optimization problem, that is then solved using Grover adaptive search (GAS). To accelerate convergence, we initialize the GAS algorithm with a threshold based on a classical minimum mean-squared error detector. The simulation results show that the proposed hybrid classical-quantum detection scheme achieves near-optimal MLD performance while substantially reducing query complexity. These findings highlight the potential of quantum-enhanced detection strategies combined with RIS technology, offering efficient and near-optimal solutions for broadband wireless communications.
Wideband and low-latency requirements in sixth-generation (6G) networks demand detectors that approach maximum-likelihood (ML) performance without incurring exponential complexity. This work develops a hybrid quantum-classical detection framework for reconfigurable intelligent surface (RIS)-assisted single-carrier (SC) frequency-domain equalization (FDE) over frequency-selective channels. The ML detection objective is reformulated as a quadratic unconstrained binary optimization (QUBO) problem and solved via Grover adaptive search (GAS). To accelerate convergence, we introduce a frequency-domain MMSE threshold that exploits the circulant structure of SC-FDE channels, yielding low-complexity initialization. The framework is evaluated across varying channel lengths and RIS sizes, confirming robustness and scalability. In addition, GAS requirements are quantified through register widths and gate counts, and its query complexity is analyzed to characterize the algorithm's cost for block transmission in frequency-selective channels. Quantum circuit simulations are conducted in Qiskit under both ideal and noisy conditions. In the ideal case, the detector achieves near-optimal performance while benefiting from Grover's quadratic speedup, reducing the search cost from from O(M^N) exhaustive evaluations to O(SQRT(M^N)) oracle queries. Under noise, the shallow depth of the GAS circuits, aided by MMSE initialization, makes depolarizing errors negligible, while readout errors introduce moderate degradation yet still preserve performance close to the MMSE baseline. These results establish the feasibility of quantum-enhanced detection for RIS-assisted broadband communications, highlighting both algorithmic scalability and practical robustness for 6G networks.
In this paper, we propose a quantum-native formulation of maximum likelihood detection (MLD) for overloaded multiple-input multiple-output (MIMO) systems in a random access channel, where numerous user terminals share the same channel resource and asynchronously transmit signals. Classical linear detectors suffer from significant performance degradation in this scenario, whereas the exhaustive-search MLD achieves the optimal performance but incurs an exponential computational complexity. To overcome this trade-off, we formulate the MLD as a binary optimization problem and solve it via Grover adaptive search (GAS) -- a quantum exhaustive search algorithm offering quadratic speedup in fault-tolerant quantum computing. We then introduce a search space reduction technique to substantially decrease the required computational resources. In addition, we investigate efficient parameter settings for GAS through probability analysis to improve convergence performance. We demonstrate that the proposed detector achieves the optimal detection performance while reducing the required Grover rotation count to reach the solution by up to approximately 65% compared with the conventional GAS, showing its potential as a viable solution for future quantum-accelerated wireless systems.
In this paper, we propose a quantum-native formulation of maximum likelihood detection in random access channel with overloaded multiple-input multiple-output (MIMO), where a number of user terminals share the same channel resource and asynchronously transmit signals. Classical low-complexity linear detectors suffer from significant performance degradation in this scenario, while the exhaustive-search-based maximum likelihood detection achieves the optimal performance but induces an exponential increase in time complexity. To strike this fundamental tradeoff, we formulate the maximum likelihood detection as a binary optimization problem and solve it via the Grover adaptive search (GAS), a quantum exhaustive search algorithm offering quadratic speedup. We further introduce a search space reduction technique using quantum W states and controlled-H gates, which substantially decreases complexity. In addition, we investigate the effects of efficient parameter settings in GAS. Our simulation results show that the proposed detector achieved the optimal detection performance while reducing the query complexity, thereby highlighting its potential as a solution for future quantum-accelerated overloaded MIMO systems.
We propose a new quantum-assisted maximum likelihood detection (MLD) scheme for generalized spatial modulation (GSM) systems. To that end, we first present a novel MLD formulation for GSM, and then describe a corresponding novel method to prepare the initial state for an associated quantum-computing Grover adaptive search (GAS) algorithm. Simulation results are presented to show that our approach achieves optimal performance and reduces query complexity compared both to the classical MLD and to earlier quantum search methods, which do not achieve an advantage over classical MLD for some parameter settings.
In this paper, we address the joint maximum-likelihood detection of power-domain non-orthogonal multiple access and transform the detection problem into a binary optimization problem. Then, we solve it by a quantum algorithm, Grover adaptive search (GAS), and further accelerate the algorithm. Assuming fault-tolerant quantum computing, GAS provides a quadratic speedup for binary optimization problems in terms of query complexity. The proposed method designs the number of Grover operators using a time-invariant distribution of the number of solutions, which can be obtained in advance. Simulation results demonstrate that the proposed method is capable of reducing the query complexity in the classical domain while achieving the optimal performance.
We propose a quantum-assisted solution for the maximum likelihood detection (MLD) of generalized spatial modulation (GSM) signals. Specifically, the MLD of GSM is first formulated as a novel polynomial optimization problem, followed by the application of a quantum algorithm, namely, the Grover adaptive search. The performance in terms of query complexity of the proposed method is evaluated and compared to the classical alternative via a numerical analysis, which reveals that under fault-tolerant quantum computation, the proposed method outperforms the classical solution if the number of data symbols and the constellation size are relatively large.