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The Quantum Approximate Optimization Algorithm (QAOA) is a standard method for combinatorial optimization with a gate-based quantum computer. The QAOA consists of a particular ansatz for the quantum circuit architecture, together with a…

Quantum Physics · Physics 2020-04-28 Li Li , Minjie Fan , Marc Coram , Patrick Riley , Stefan Leichenauer

The Quantum Approximate Optimization Algorithm (QAOA) is a promising variational algorithm for solving combinatorial optimization problems on near-term devices. However, as the number of layers in a QAOA circuit increases, which is…

Machine Learning · Computer Science 2025-04-24 Owain Parry , Phil McMinn

Noisy Intermediate-Scale Quantum (NISQ) devices are restricted by their limited number of qubits and their short decoherence times. An approach addressing these problems is quantum circuit cutting. It decomposes the execution of a large…

The Quantum Approximate Optimization Algorithm (QAOA) is a promising algorithm for solving combinatorial optimization problems (COPs), with performance governed by variational parameters $\{\gamma_i, \beta_i\}_{i=0}^{p-1}$. While most prior…

Quantum Physics · Physics 2025-08-07 J. A. Montanez-Barrera , Kristel Michielsen

Quantum computers are devices, which allow more efficient solutions of problems as compared to their classical counterparts. As the timeline to developing a quantum-error corrected computer is unclear, the quantum computing community has…

Quantum Physics · Physics 2023-02-16 Marko J. Rančić

The Quantum Approximate Optimization Algorithm (QAOA) is an algorithmic framework for finding approximate solutions to combinatorial optimization problems, derived from an approximation to the Quantum Adiabatic Algorithm (QAA). In solving…

Quantum Physics · Physics 2020-02-05 Yue Ruan , Samuel Marsh , Xilin Xue , Xi Li , Zhihao Liu , Jingbo Wang

Quantum computers are expected to offer significant advantages in solving complex optimization problems that are challenging for classical computers. Quadratic Unconstrained Binary Optimization (QUBO) problems represent an important class…

Quantum Physics · Physics 2025-10-15 Teemu Pihkakoski , Aravind Plathanam Babu , Pauli Taipale , Petri Liimatta , Matti Silveri

Noise on near-term quantum devices will inevitably limit the performance of Quantum Approximate Optimization Algorithm (QAOA). One significant consequence is that the performance of QAOA may fail to monotonically improve with depth. In…

Quantum Physics · Physics 2022-07-12 Yu Pan , Yifan Tong , Shibei Xue , Guofeng Zhang

Quantum approximate optimization algorithm (QAOA) has shown promise in solving combinatorial optimization problems by providing quantum speedup on near-term gate-based quantum computing systems. However, QAOA faces challenges for…

Distributed, Parallel, and Cluster Computing · Computer Science 2025-03-24 Seongmin Kim , Vincent R. Pascuzzi , Zhihao Xu , Tengfei Luo , Eungkyu Lee , In-Saeng Suh

Quantum computers may provide good solutions to combinatorial optimization problems by leveraging the Quantum Approximate Optimization Algorithm (QAOA). The QAOA is often presented as an algorithm for noisy hardware. However, hardware…

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

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

The quantum approximate optimization algorithm (QAOA) is known for its capability and universality in solving combinatorial optimization problems on near-term quantum devices. The results yielded by QAOA depend strongly on its initial…

Quantum Physics · Physics 2022-09-29 Xinwei Lee , Ningyi Xie , Yoshiyuki Saito , Dongsheng Cai , Nobuyoshi Asai

The Quantum Approximate Optimization Algorithm (QAOA) is one of the most promising candidates for achieving quantum advantage over classical computers. However, existing compilers lack specialized methods for optimizing QAOA circuits. There…

Quantum Physics · Physics 2024-08-19 Yuchen Zhu , Yidong Zhou , Jinglei Cheng , Yuwei Jin , Boxi Li , Siyuan Niu , Zhiding Liang

Quantum computers have now surpassed classical simulation limits, yet noise continues to limit their practical utility. As the field shifts from proof-of-principle demonstrations to early deployments, there is no standard method for…

Quantum Physics · Physics 2025-05-29 J. A. Montanez-Barrera , Kristel Michielsen , David E. Bernal Neira

The quantum approximate optimization algorithm (QAOA) is a quantum heuristic for combinatorial optimization that has been demonstrated to scale better than state-of-the-art classical solvers for some problems. For a given problem instance,…

Quantum Physics · Physics 2026-02-23 Tianyi Hao , Zichang He , Ruslan Shaydulin , Jeffrey Larson , Marco Pistoia

Structured variational quantum algorithms such as the Quantum Approximate Optimisation Algorithm (QAOA) have emerged as leading candidates for exploiting advantages of near-term quantum hardware. They interlace classical computation, in…

Quantum Physics · Physics 2026-05-05 Vincent Eichenseher , Maja Franz , Christian Wolff , Wolfgang Mauerer

QAOA is a hybrid quantum-classical algorithm to solve optimization problems in gate-based quantum computers. It is based on a variational quantum circuit that can be interpreted as a discretization of the annealing process that quantum…

Quantum Physics · Physics 2025-05-28 Francisco Chicano , Zakaria Abdelmoiz Dahi , Gabriel Luque

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

Optimization is often cited as a promising application of quantum computers. However, the low degree of provable quantum speedups has led prior rigorous end-to-end resource analyses to conclude that a quantum computer is unlikely to surpass…