Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:2605.19389

Quantum-Native Maximum Likelihood Detection in Random Access Channel with Overloaded MIMO

Hyoga Iizumi, Naoki Ishikawa, Shunsuke Uehashi, Kota Nakamura, Shusaku Umeda, Toshiaki Koike-Akino

eess.SPquant-phSubmitted May 19, 2026• Announced May 20, 2026• 0 citations
arXivHTMLPDF

Abstract

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.

Comments
11 pages, 10 figures

Related papers

Quantum-Native Formulation of Maximum Likelihood Detection in Random Access Channel with Overloaded MIMO

Hyoga Iizumi, Naoki Ishikawa, Shunsuke Uehashi +3 more

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.

IEEE Vehicular Technology Conference•Oct 19, 2025•0 citations

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

Maryam Tariq, Raneem F. Abdelrahim, Omar Alhussein +1 more

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.

arXiv:2505.03914•May 6, 2025•0 citations

Quantum Algorithm for Higher-Order Unconstrained Binary Optimization and MIMO Maximum Likelihood Detection

Masaya Norimoto, Ryuhei Mori, Naoki Ishikawa

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.

arXiv:2205.15478•IEEE Transactions on Communications•Feb 14, 2023•33 citations

Quantum Speedup for Multiuser Detection With Optimized Parameters in Grover Adaptive Search

Masaya Norimoto, Taku Mikuriya, Naoki Ishikawa

Maximum-likelihood multiuser detection incurs a large computational complexity, and its low-complexity detection scheme suffers from a performance loss, where this tradeoff is inevitable and inherent in a classical computer. In this paper, we use the Grover adaptive search (GAS) to break the tradeoff, which is a quantum exhaustive search algorithm guaranteed to obtain the optimal solution, achieving a quadratic speedup. Specifically, we design two specific parameters of GAS to achieve the optimal performance with a reduced complexity: the initial threshold and the number of Grover rotations. The initial threshold of GAS can be optimized using a solution of semi-definite programming, and it is possible to calculate the distribution of the number of solutions smaller than the initial threshold in advance, which depends on instantaneous channel coefficients. In addition, we analyze the number of quantum gates required for GAS and show that the gate count can be reduced by bypassing the higher-order terms in the objective function, leading to a reduced circuit runtime. Our analysis and simulation results demonstrate that the proposed approach achieves the same performance as the optimal maximum-likelihood detection while reducing the query complexity of GAS, implying that the large constant overhead of quadratic speedup can be further reduced.

IEEE Access•Jan 1, 2024•6 citations

Grover Adaptive Search for Maximum Likelihood Detection of Generalized Spatial Modulation

Kein Yukiyoshi, Taku Mikuriya, Hyeon Seok Rou +2 more

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.

arXiv:2408.13531•IEEE Vehicular Technology Conference•Oct 7, 2024•4 citations

Grover Adaptive Search for Joint Maximum-Likelihood Detection of Power-Domain Non-Orthogonal Multiple Access

Masaya Norimoto, Naoki Ishikawa

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.

IEEE Vehicular Technology Conference•Jun 1, 2023•2 citations
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.
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.
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.
Maximum-likelihood multiuser detection incurs a large computational complexity, and its low-complexity detection scheme suffers from a performance loss, where this tradeoff is inevitable and inherent in a classical computer. In this paper, we use the Grover adaptive search (GAS) to break the tradeoff, which is a quantum exhaustive search algorithm guaranteed to obtain the optimal solution, achieving a quadratic speedup. Specifically, we design two specific parameters of GAS to achieve the optimal performance with a reduced complexity: the initial threshold and the number of Grover rotations. The initial threshold of GAS can be optimized using a solution of semi-definite programming, and it is possible to calculate the distribution of the number of solutions smaller than the initial threshold in advance, which depends on instantaneous channel coefficients. In addition, we analyze the number of quantum gates required for GAS and show that the gate count can be reduced by bypassing the higher-order terms in the objective function, leading to a reduced circuit runtime. Our analysis and simulation results demonstrate that the proposed approach achieves the same performance as the optimal maximum-likelihood detection while reducing the query complexity of GAS, implying that the large constant overhead of quadratic speedup can be further reduced.
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.
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.