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In the era of Noisy Intermediate Scale Quantum (NISQ) computing, available quantum resources are limited. Many NP-hard problems can be efficiently addressed using hybrid classical and quantum computational methods. This paper proposes a…

Quantum Physics · Physics 2025-05-01 Dongmei Liu , Jian Li , Xiubo Cheng , Shibing Zhang , Yan Chang , Lili Yan

Quantum Approximate Optimization Algorithm (QAOA) is a quantum-classical hybrid algorithm proposed with the goal of approximately solving combinatorial optimization problems such as the MAX-CUT problem. It has been considered a potential…

Quantum Physics · Physics 2025-11-26 Eunok Bae , Hyukjoon Kwon , V Vijendran , Soojoon Lee

Quantum approximate optimization algorithms are hybrid quantum-classical variational algorithms designed to approximately solve combinatorial optimization problems such as the MAX-CUT problem. In spite of its potential for near-term quantum…

Quantum Physics · Physics 2024-02-27 Eunok Bae , Soojoon Lee

Quantum computing promises solutions to classically difficult and new-found problems through controlling the subtleties of quantum computing. The Quantum Approximate Optimisation Algorithm (QAOA) is a recently proposed quantum algorithm…

Quantum Physics · Physics 2024-12-24 Nicholas J. Pritchard

The Quantum approximate optimization algorithm (QAOA) is a leading hybrid classical-quantum algorithm for solving complex combinatorial optimization problems. QAOA-in-QAOA (QAOA^2) uses a divide-and-conquer heuristic to solve large-scale…

Quantum Physics · Physics 2024-08-27 Aniello Esposito , Tamuz Danzig

We propose a machine learning based approach to accelerate quantum approximate optimization algorithm (QAOA) implementation which is a promising quantum-classical hybrid algorithm to prove the so-called quantum supremacy. In QAOA, a…

Emerging Technologies · Computer Science 2020-04-07 Mahabubul Alam , Abdullah Ash-Saki , Swaroop Ghosh

The design of a good algorithm to solve NP-hard combinatorial approximation problems requires specific domain knowledge about the problems and often needs a trial-and-error problem solving approach. Graph coloring is one of the essential…

Combinatorial optimization is one of the fields where near term quantum devices are being utilized with hybrid quantum-classical algorithms to demonstrate potentially practical applications of quantum computing. One of the most well studied…

Quantum Physics · Physics 2023-09-22 Anthony Angone , Xioayuan Liu , Ruslan Shaydulin , Ilya Safro

The Quantum Approximate Optimization Algorithm (QAOA) is a hybrid quantum-classical algorithm to solve binary-variable optimization problems. Due to the short circuit depth and its expected robustness to systematic errors, it is one of the…

Quantum Physics · Physics 2022-08-23 Jason Larkin , Matías Jonsson , Daniel Justice , Gian Giacomo Guerreschi

The quantum approximate optimization algorithm (QAOA) is a hybrid variational quantum-classical algorithm that solves combinatorial optimization problems. While there is evidence suggesting that the fixed form of the standard QAOA ansatz is…

Variational quantum algorithms, such as the Recursive Quantum Approximate Optimization Algorithm (RQAOA), have become increasingly popular, offering promising avenues for employing Noisy Intermediate-Scale Quantum devices to address…

Emerging Technologies · Computer Science 2025-06-04 Shuaiqun Pan , Yash J. Patel , Aneta Neumann , Frank Neumann , Thomas Bäck , Hao Wang

Learning the problem structure at multiple levels of coarseness to inform the decomposition-based hybrid quantum-classical combinatorial optimization solvers is a promising approach to scaling up variational approaches. We introduce a…

Quantum Physics · Physics 2025-03-18 Bao Bach , Jose Falla , Ilya Safro

Combinatorial optimization problems on graphs have broad applications in science and engineering. The Quantum Approximate Optimization Algorithm (QAOA) is a method to solve these problems on a quantum computer by applying multiple rounds of…

The Quantum Approximate Optimization Algorithm (QAOA), which is a variational quantum algorithm, aims to give sub-optimal solutions of combinatorial optimization problems. It is widely believed that QAOA has the potential to demonstrate…

Quantum Approximate Optimization Algorithm (QAOA) is a promising hybrid quantum-classical algorithm for solving combinatorial optimization problems. However, it cannot overcome qubit limitation for large-scale problems. Furthermore, the…

Emerging Technologies · Computer Science 2021-03-01 Junde Li , Mahabubul Alam , Swaroop Ghosh

Hybrid quantum-classical algorithms such as the quantum approximate optimization algorithm (QAOA) are considered one of the most promising approaches for leveraging near-term quantum computers for practical applications. Such algorithms are…

Quantum Physics · Physics 2022-06-16 Ruslan Shaydulin , Ilya Safro , Jeffrey Larson

The Quantum Approximate Optimization Algorithm (QAOA) is a promising approach for programming a near-term gate-based hybrid quantum computer to find good approximate solutions of hard combinatorial problems. However, little is currently…

Quantum Physics · Physics 2018-11-21 Gavin E. Crooks

The quantum approximate optimization algorithm (QAOA) is a variational method for noisy, intermediate-scale quantum computers to solve combinatorial optimization problems. Quantifying performance bounds with respect to specific problem…

Quantum Physics · Physics 2021-11-30 Phillip C. Lotshaw , Travis S. Humble , Rebekah Herrman , James Ostrowski , George Siopsis

The quantum approximate optimisation algorithm (QAOA) is a hybrid quantum-classical algorithm used to approximately solve combinatorial optimisation problems. It involves multiple iterations of a parameterised ansatz comprising a problem…

Quantum Physics · Physics 2024-02-16 V. Vijendran , Aritra Das , Dax Enshan Koh , Syed M. Assad , Ping Koy Lam

The quantum approximate optimization algorithm (QAOA) has the potential to approximately solve complex combinatorial optimization problems in polynomial time. However, current noisy quantum devices cannot solve large problems due to…

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