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IEEE Access

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

Masaya Norimoto, Taku Mikuriya, Naoki Ishikawa

Published Jan 1, 2024• 6 citations
Publisher

Abstract

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.

DOI
10.1109/access.2024.3413084

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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.
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.
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.
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 binary optimization problems, where the goal is to find the inputx\boldsymbol {x}xthat minimizes a given objective function, Grover adaptive search (GAS) is a well-known quantum algorithm that provides quadratic speedup when compared with the brute-force approaches of classical computers. GAS calls a renowned quantum search algorithm, Grover search (GS), as a subroutine to search for inputs with function values less than the threshold value. If such an input is found, the threshold value is updated with the function value and the search targets are narrowed. To search efficiently for a solution, an appropriate number of queries must be selected to amplify the desired state of the GS in each step. This paper discusses this issue and proposes a new method for selecting the number of queries and provides proof that our method achieves quadratic speedup as well as the original GAS. Furthermore, the simulation results for 40-bit problems confirm that our method allows an optimal solution with 22% fewer queries than the standard method, thus offering the possibility of significantly reduced computation times for combinatorial optimization problems.
Conventional decoding algorithms for polar codes strive to balance achievable performance and computational complexity in classical computing. While maximum likelihood (ML) decoding guarantees optimal performance, its NP-hard nature makes it impractical for real-world systems. In this letter, we propose a novel ML decoding architecture for polar codes based on the Grover adaptive search, a quantum exhaustive search algorithm. Unlike conventional studies, our approach, enabled by a newly formulated objective function, uniquely supports Gray-coded multi-level modulation without expanding the search space size compared to the classical ML decoding. Simulation results demonstrate that our proposed quantum decoding achieves ML performance while providing a pure quadratic speedup in query complexity.
Grover adaptive search (GAS) is a quantum exhaustive search algorithm designed to solve binary optimization problems. In this article, we propose higher order binary formulations that can simultaneously reduce the numbers of qubits and gates required for GAS. Specifically, we consider two novel strategies: one that reduces the number of gates through polynomial factorization, and the other that halves the order of the objective function, subsequently decreasing circuit runtime and implementation cost. Our analysis demonstrates that the proposed higher order formulations improve the convergence performance of GAS by reducing both the search space size and the number of quantum gates. Our strategies are also beneficial for general combinatorial optimization problems using one-hot encoding.