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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

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

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

We investigate the Maximum Cut (MaxCut) problem on different graph classes with the Quantum Approximate Optimization Algorithm (QAOA) using symmetries. In particular, heuristics on the relationship between graph symmetries and the…

Quantum Physics · Physics 2025-11-04 Leonardo Lavagna , Simone Piperno , Andrea Ceschini , Massimo Panella

The Quantum Approximate Optimization Algorithm (QAOA) is a hybrid quantum-classical variational algorithm designed to tackle combinatorial optimization problems. Despite its promise for near-term quantum applications, not much is currently…

Quantum Physics · Physics 2020-06-26 Leo Zhou , Sheng-Tao Wang , Soonwon Choi , Hannes Pichler , Mikhail D. Lukin

Quadratic unconstrained binary optimization (QUBO) tasks are very important in chemistry, finance, job scheduling, and so on, which can be represented using graph structures, with the variables as nodes and the interaction between them as…

Quantum Physics · Physics 2024-04-10 Yuhan Huang , Ferris Prima Nugraha , Siyuan Jin , Yichi Zhang , Bei Zeng , Qiming Shao

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…

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

Introducing additional tunable parameters to quantum circuits is a powerful way of improving performance without increasing hardware requirements. A recently introduced multiangle extension of the quantum approximate optimization algorithm…

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

As combinatorial optimization is one of the main quantum computing applications, many methods based on parameterized quantum circuits are being developed. In general, a set of parameters are being tweaked to optimize a cost function out of…

Quantum Physics · Physics 2022-05-09 Charles Moussa , Hao Wang , Thomas Bäck , Vedran Dunjko

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

In recent years, quantum computing has emerged as a transformative force in the field of combinatorial optimization, offering novel approaches to tackling complex problems that have long challenged classical computational methods. Among…

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

Maximum cut (MaxCut) on graphs is a classic NP-hard problem. In quantum computing, Farhi, Gutmann, and Goldstone proposed the Quantum Approximate Optimization Algorithm (QAOA) for solving the MaxCut problem. Its guarantee on cut fraction…

Quantum Physics · Physics 2025-02-11 Tongyang Li , Yuexin Su , Ziyi Yang , Shengyu Zhang

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) 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

Combinatorial optimization is regarded as a potentially promising application of near and long-term quantum computers. The best-known heuristic quantum algorithm for combinatorial optimization on gate-based devices, the Quantum Approximate…

Quantum Physics · Physics 2021-10-22 Sami Boulebnane , Ashley Montanaro

Quantum Approximate Optimization Algorithm (QAOA) is a hybrid classical-quantum algorithm to approximately solve NP optimization problems such as MAX-CUT. We describe a new application area of QAOA circuits: graph structure discovery. We…

Quantum Physics · Physics 2020-01-01 Mario Szegedy

A promising approach to the practical application of the Quantum Approximate Optimization Algorithm (QAOA) is finding QAOA parameters classically in simulation and sampling the solutions from QAOA with optimized parameters on a quantum…

Quantum Physics · Physics 2021-10-29 Ruslan Shaydulin , Stefan M. Wild