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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

The Quantum approximate optimization algorithm (QAOA) is a quantum-classical hybrid algorithm aiming to produce approximate solutions for combinatorial optimization problems. In the QAOA, the quantum part prepares a quantum parameterized…

Quantum Physics · Physics 2024-04-23 Ningyi Xie , Xinwei Lee , Dongsheng Cai , Yoshiyuki Saito , Nobuyoshi Asai

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

Motivated by the recent advancement of quantum processors, we investigate quantum approximate optimization algorithm (QAOA) to employ quasi-maximum-likelihood (ML) decoding of classical channel codes. QAOA is a hybrid quantum-classical…

Information Theory · Computer Science 2019-03-07 Toshiki Matsumine , Toshiaki Koike-Akino , Ye Wang

The quantum approximate optimization algorithm (QAOA) transforms a simple many-qubit wavefunction into one which encodes a solution to a difficult classical optimization problem. It does this by optimizing the schedule according to which…

Quantum Physics · Physics 2022-06-29 Yunlong Yu , Chenfeng Cao , Carter Dewey , Xiang-Bin Wang , Nic Shannon , Robert Joynt

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

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) has emerged as a promising approach for addressing combinatorial optimization problems on near-term quantum hardware. In this work, we conduct an empirical evaluation of QAOA on the…

Quantum Physics · Physics 2026-04-27 Evgenii Dolzhkov , Franz G. Fuchs , Dirk Oliver Theis

Farhi et al. recently proposed a class of quantum algorithms, the Quantum Approximate Optimization Algorithm (QAOA), for approximately solving combinatorial optimization problems. A level-p QAOA circuit consists of p steps; in each step a…

Quantum Physics · Physics 2021-01-01 Zhihui Wang , Stuart Hadfield , Zhang Jiang , Eleanor G. Rieffel

The Quantum Approximate Optimisation Algorithm (QAOA) is a hybrid quantum-classical algorithm for solving combinatorial optimisation problems. QAOA encodes solutions into the ground state of a Hamiltonian, approximated by a $p$-level…

Quantum Physics · Physics 2025-05-16 V Vijendran , Dax Enshan Koh , Eunok Bae , Hyukjoon Kwon , Ping Koy Lam , Syed M Assad

The promise of quantum computing to address complex problems requiring high computational resources has long been hindered by the intrinsic and demanding requirements of quantum hardware development. Nonetheless, the current state of…

Quantum Physics · Physics 2024-07-10 Daniel F Perez-Ramirez

We introduce a novel quantum optimization paradigm: the Fixed-Parameter-Count Quantum Approximate Optimization Algorithm (FPC-QAOA). It is a scalable variational framework that maintains a constant number of trainable parameters regardless…

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

The quantum approximate optimisation ansatz (QAOA) is one of the flagship algorithms used to tackle combinatorial optimisation on graphs problems using a quantum computer, and is considered a strong candidate for early fault-tolerant…

Quantum Physics · Physics 2025-06-24 Yann Beaujeault-Taudière

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

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

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

Quantum Approximate Optimization Algorithm (QAOA) is a leading candidate algorithm for solving combinatorial optimization problems on quantum computers. However, in many cases QAOA requires computationally intensive parameter optimization.…

The design of fast algorithms for combinatorial optimization greatly contributes to a plethora of domains such as logistics, finance, and chemistry. Quantum approximate optimization algorithms (QAOAs), which utilize the power of quantum…

Quantum Physics · Physics 2022-05-25 Zeqiao Zhou , Yuxuan Du , Xinmei Tian , Dacheng Tao

The Quantum Approximate Optimization Algorithm (QAOA) is a promising variational quantum algorithm introduced to tackle classically intractable combinatorial optimization problems. This tutorial offers a comprehensive, first-principles…

Quantum Physics · Physics 2025-11-25 Alessandro Giovagnoli