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The quantum approximate optimization algorithm (QAOA) is a hybrid quantum-classical algorithm that seeks to achieve approximate solutions to optimization problems by iteratively alternating between intervals of controlled quantum evolution.…

The quantum approximate optimization algorithm (QAOA) is one of the most prominent proposed applications for near-term quantum computing. Here we study the ability of QAOA to solve hard constraint satisfaction problems, as opposed to…

Quantum Physics · Physics 2022-08-16 Sami Boulebnane , Ashley Montanaro

We explore strategies aimed at reducing the amount of computation, both quantum and classical, required to run the Quantum Approximate Optimization Algorithm (QAOA). First, following Wurtz et al. [Phys.Rev A 104:052419], we consider the…

We introduce a variational algorithm based on the quantum alternating operator ansatz (QAOA) for the approximate solution of computationally hard counting problems. Our algorithm, dubbed VQCount, is based on the equivalence between random…

Quantum Physics · Physics 2026-04-16 Julien Drapeau , Shreya Banerjee , Stefanos Kourtis

This research explores the integration of the Quantum Approximate Optimization Algorithm (QAOA) into Hybrid Quantum-HPC systems for solving the Max-Cut problem, comparing its performance with classical algorithms like brute-force search and…

Quantum Physics · Physics 2024-10-22 Ishan Patwardhan , Akhil Akkapelli

The Quantum Approximate Optimization Algorithm (QAOA) finds approximate solutions to combinatorial optimization problems. Its performance monotonically improves with its depth $p$. We apply the QAOA to MaxCut on large-girth $D$-regular…

Quantum Physics · Physics 2022-07-08 Joao Basso , Edward Farhi , Kunal Marwaha , Benjamin Villalonga , Leo Zhou

It is hoped that quantum computers will offer advantages over classical computers for combinatorial optimization. Here, we introduce a feedback-based strategy for quantum optimization, where the results of qubit measurements are used to…

Quantum Physics · Physics 2023-01-05 Alicia B. Magann , Kenneth M. Rudinger , Matthew D. Grace , Mohan Sarovar

The quantum approximate optimization algorithm (QAOA) is one of the most promising candidates for achieving quantum advantage through quantum-enhanced combinatorial optimization. A near-optimal solution to the combinatorial optimization…

Quantum Physics · Physics 2023-07-12 Alexey Galda , Eesh Gupta , Jose Falla , Xiaoyuan Liu , Danylo Lykov , Yuri Alexeev , Ilya Safro

The quantum approximate optimization algorithm (QAOA) is a leading candidate algorithm for solving optimization problems on quantum computers. However, the potential of QAOA to tackle classically intractable problems remains unclear. Here,…

Designing noisy-resilience quantum algorithms is indispensable for practical applications on Noisy Intermediate-Scale Quantum~(NISQ) devices. Here we propose a quantum approximate optimization algorithm~(QAOA) with a very shallow circuit,…

Quantum Physics · Physics 2021-09-27 Fang-Gang Duan , Dan-Bo Zhang

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

The Quantum Approximate Optimization Algorithm (QAOA) is a powerful tool in solving various combinatorial problems such as Maximum Satisfiability and Maximum Cut. Hard computational problems, however, require deep circuits that place high…

Quantum Physics · Physics 2025-10-28 Malick A. Gaye , Omar Shehab , Paraj Titum , Gregory Quiroz

Solving combinatorial optimization problems on near-term quantum devices has gained a lot of attraction in recent years. Currently, most works have focused on single-objective problems, whereas many real-world applications need to consider…

Quantum Physics · Physics 2025-06-06 Linus Ekstrom , Hao Wang , Sebastian Schmitt

The quantum approximate optimization algorithm (QAOA) is a method of approximately solving combinatorial optimization problems. While QAOA is developed to solve a broad class of combinatorial optimization problems, it is not clear which…

Quantum Physics · Physics 2020-08-13 James Ostrowski , Rebekah Herrman , Travis S. Humble , George Siopsis

Quantum computing exploits basic quantum phenomena such as state superposition and entanglement to perform computations. The Quantum Approximate Optimization Algorithm (QAOA) is arguably one of the leading quantum algorithms that can…

Machine Learning · Computer Science 2022-06-16 Sami Khairy , Ruslan Shaydulin , Lukasz Cincio , Yuri Alexeev , Prasanna Balaprakash

Quantum computers are expected to accelerate solving combinatorial optimization problems, including algorithms such as Grover adaptive search and quantum approximate optimization algorithm (QAOA). However, many combinatorial optimization…

Quantum Physics · Physics 2023-05-05 Takuya Yoshioka , Keita Sasada , Yuichiro Nakano , Keisuke Fujii

The quantum approximate optimization algorithm (QAOA) is a near-term quantum algorithm aimed at solving combinatorial optimization problems. Since its introduction, various generalizations have emerged, spanning modifications to the initial…

Quantum Physics · Physics 2024-11-18 Truman Yu Ng , Jin Ming Koh , Dax Enshan Koh

The quantum approximate optimization algorithm (QAOA) has become a cornerstone of contemporary quantum applications development. In QAOA, a quantum circuit is trained -- by repeatedly adjusting circuit parameters -- to solve a problem.…

Quantum Physics · Physics 2021-08-17 V. Akshay , D. Rabinovich , E. Campos , J. Biamonte

The quantum approximate optimization algorithm (QAOA) is designed to determine optimum and near optimum solutions of quadratic (and higher order) unconstrained binary optimization (QUBO or HUBO) problems, which in turn accurately model…

Quantum Physics · Physics 2025-03-18 Prashanti Priya Angara , Danylo Lykov , Ulrike Stege , Yuri Alexeev , Hausi Müller

The Quantum Approximate Optimization Algorithm (QAOA) has shown promise in solving combinatorial optimization problems by leveraging quantum computational power. We propose a simple approach, the Two-Step QAOA, which aims to improve the…

Quantum Physics · Physics 2025-02-25 Yuichiro Minato