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Elsevier eBooks

Quantum approximate optimization algorithm: a review study and problems

Laith Abualigah, Saif AlNajdawi, Abiodun Motunrayo Ikotun, Agostino Forestiero, Faiza Gul, Absalom El-Shamir Ezugwu, Heming Jia, Mohsen Zare, Shubham Mahajan, Mohammad Alshinwan

Published Jan 1, 2024• 16 citations
Publisher
DOI
10.1016/b978-0-443-13925-3.00007-8

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Among quantum algorithms, the quantum approximation optimization algorithm (QAOA) is an algorithm that finds approximate solutions. Recursive QAOA is proposed to overcome the limitation that QAOA has lower performance than Goemans-Williamson algorithm in the MAX-CUT problem [Physical Review Letter, 125, 260504, 2020]. In this paper, we introduce a method with lower complexity than RQAOA and compare its numerical results in the MAX-CUT problem. At the same level, the performance of the proposed method is lower than that of RQAOA, but the number of computations of quantum and classical parts is very small.
Quantum Approximate Optimization Algorithm (QAOA) is the notable advancement in quantum computing, which allows us to solve optimization problems differently. In this paper, we provide a detailed investigation of the possible applications of QAOA accompanied by an overview of previous implementations. This is where QAOA shines and can spin out solutions where ordinary methods takes millennia to converge with acceptable results for NP-hard optimization problems that involve transfer of n\mathbf{n}n qubits between a quantum state. We present a comprehensive literature review in this paper, and potential areas of application where QAOA could be successfully used such as logistics, finance and Artificial Intelligence.
Quantum computing has emerged as a transformative technology, particularly for solving optimization problems, which are notoriously difficult for classical computers. Quantum algorithms, leveraging quantum parallelism and entanglement, promise significant speedups for a wide range of optimization tasks, from combinatorial optimization to machine learning. This paper reviews recent advancements in quantum algorithms for optimization problems, highlighting key algorithms such as Grover’s search algorithm, the Quantum Approximate Optimization Algorithm (QAOA), and the Quantum Alternating Operator Ansatz (QAOA). We also explore the challenges and potential of quantum computing in addressing real-world optimization problems, such as in logistics, finance, and machine learning. The paper discusses the current state of quantum hardware, as well as theoretical and practical limitations in implementing these quantum algorithms. Finally, we propose future research directions to overcome existing challenges and enhance the application of quantum algorithms in solving complex optimization problems