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The present tutorial aims to provide a comprehensible and easily accessible introduction into the theory and implementation of the famous Quantum Approximate Optimization Algorithm (QAOA). We lay our focus on practical aspects and…

Quantum Physics · Physics 2023-01-24 Andreas Sturm

The Quantum Approximate Optimization Algorithm (QAOA) has been suggested as a promising candidate for the solution of combinatorial optimization problems. Yet, whether - or under what conditions - it may offer an advantage compared to…

Quantum Physics · Physics 2025-04-14 Vanessa Dehn , Martin Zaefferer , Gerhard Hellstern , Florentin Reiter , Thomas Wellens

Variational quantum algorithms (VQAs) have demonstrated considerable potential in solving NP-hard combinatorial problems in the contemporary near intermediate-scale quantum (NISQ) era. The quantum approximate optimisation algorithm (QAOA)…

Quantum Physics · Physics 2024-05-09 Boy Choy , David J. Wales

Parameterized quantum circuits are attractive candidates for potential quantum advantage in the near term and beyond. At the same time, as quantum computing hardware not only continues to improve but also begins to incorporate new features…

Quantum Physics · Physics 2024-03-19 Tobias Stollenwerk , Stuart Hadfield

Quantum computers and simulators may offer significant advantages over their classical counterparts, providing insights into quantum many-body systems and possibly improving performance for solving exponentially hard problems, such as…

The Quantum Approximate Optimization Algorithm (QAOA) is a variational quantum algorithm that can be used to approximately solve combinatorial optimization problems. However, a major limitation of QAOA is that it is a "local" algorithm for…

Quantum Physics · Physics 2025-04-10 Quinn Langfitt , Reuben Tate , Stephan Eidenbenz

We implement two Quantum Approximate Optimisation Algorithm (QAOA) variants for a battery revenue optimisation problem, equivalent to the weakly NP-hard Knapsack Problem. Both approaches investigate how to tackle constrained problems with…

Emerging Technologies · Computer Science 2019-08-16 Pierre Dupuy de la Grand'rive , Jean-Francois Hullo

Bayesian network structure learning is an NP-hard problem that has been faced by a number of traditional approaches in recent decades. Currently, quantum technologies offer a wide range of advantages that can be exploited to solve…

Quantum Physics · Physics 2022-03-07 Vicente P. Soloviev , Concha Bielza , Pedro Larrañaga

Combinatorial optimization is among the main applications envisioned for near-term and fault-tolerant quantum computers. In this work, we consider a well-studied quantum algorithm for combinatorial optimization: the Quantum Approximate…

Quantum Physics · Physics 2020-11-12 Sami Boulebnane

To overcome the limitations of classical partially connected Boltzmann machines and mainstream quantum Boltzmann machines (QBMs), this work extends the conventional circuit of the quantum approximate optimization algorithm (QAOA) to a…

Quantum Physics · Physics 2026-05-13 Jun Liu

The quantum approximate optimization algorithm (QAOA) is a variational quantum algorithm (VQA) ideal for noisy intermediate-scale quantum (NISQ) processors, and is highly successful in solving combinatorial optimization problems (COPs). It…

Quantum Physics · Physics 2026-03-23 Francesco Aldo Venturelli , Sreetama Das , Filippo Caruso

Binary optimization problems are emerging as potential candidates for useful applications of quantum computing. Among quantum algorithms, the quantum approximate optimization algorithm (QAOA) is currently considered the most promising…

Quantum Physics · Physics 2025-03-31 Bruno Oziel Fernandez , Rodrigo Bloot , Marcelo Moret

Test case optimization (TCO) reduces software testing cost while preserving its effectiveness, but solving TCO problems for large-scale and complex systems requires substantial computational resources. Quantum approximate optimization…

Software Engineering · Computer Science 2026-01-21 Xinyi Wang , Shaukat Ali , Tao Yue , Paolo Arcaini

Quantum approximate optimization algorithm (QAOA) is a promising hybrid quantum-classical algorithm to solve combinatorial optimization problems in the era of noisy intermediate-scale quantum computers. Recently warm-start approaches have…

Quantum Physics · Physics 2024-01-19 Ken N. Okada , Hirofumi Nishi , Taichi Kosugi , Yu-ichiro Matsushita

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

The quantum approximate optimization algorithm (QAOA) applies two Hamiltonians to a quantum system in alternation. The original goal of the algorithm was to drive the system close to the ground state of one of the Hamiltonians. This paper…

Quantum Physics · Physics 2018-12-31 Seth Lloyd

The quantum approximate optimization algorithm (QAOA) has the potential of providing a useful quantum advantage on noisy intermediate-scale quantum (NISQ) devices. The effects of uncorrelated noise on variational quantum algorithms such as…

Quantum Physics · Physics 2023-05-08 Joris Kattemölle , Guido Burkard

Despite its popularity, several empirical and theoretical studies suggest that the quantum approximate optimization algorithm (QAOA) has persistent issues in providing a substantial practical advantage. Numerical results for few qubits and…

Quantum Physics · Physics 2025-10-15 Gereon Koßmann , Lennart Binkowski , Lauritz van Luijk , Timo Ziegler , René Schwonnek

Quantum Approximate Optimization Algorithm (QAOA) is one of the most promising quantum heuristics for combinatorial optimization. While QAOA has been shown to perform well on small-scale instances and to provide an asymptotic speedup over…

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