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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 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 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

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 optimization algorithm (QAOA) is a leading variational approach to combinatorial optimization, but its practical performance depends strongly on objective design, parameter search, and shot allocation. We present a…

Quantum Physics · Physics 2026-04-09 Siran Zhang , Shuming Cheng

This article consists of a short introduction to the quantum approximation optimisation algorithm (QAOA). The mathematical structure of the QAOA, as well as its basic properties, are described. The implementation of the QAOA on MaxCut…

Quantum Physics · Physics 2021-03-25 Behzad Mansouri

A new methodology is proposed to solve classical Boolean problems as Hamiltonians, using the quantum approximate optimization algorithm (QAOA). Our methodology successfully finds all optimized approximated solutions for Boolean problems,…

Quantum Physics · Physics 2024-07-11 Ali Al-Bayaty , Marek Perkowski

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…

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.…

Quantum computing is a computational paradigm with the potential to outperform classical methods for a variety of problems. Proposed recently, the Quantum Approximate Optimization Algorithm (QAOA) is considered as one of the leading…

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

Combinatorial optimization lies at the heart of numerous real-world applications. For a broad category of optimization problems, quantum computing is expected to exhibit quantum speed-up over classic computing. Among various quantum…

Quantum Physics · Physics 2025-09-23 Zixu Wang , Jack Mandell , Yangyang Xu , Jian Shi

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

The Quantum Approximate Optimisation Algorithm (QAOA) is a leading candidate for near-term quantum advantage, yet its practical impact is hindered by limited performance on symmetric local Hamiltonians and the costly optimisation of…

The quantum approximate optimization algorithm (QAOA) is widely seen as a possible usage of noisy intermediate-scale quantum (NISQ) devices. We analyze the algorithm as a bang-bang protocol with fixed total time and a randomized greedy…

Quantum Physics · Physics 2020-09-16 Daniel Liang , Li Li , Stefan Leichenauer

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

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

Quantum approximate optimization algorithm (QAOA) is one of the popular quantum algorithms that are used to solve combinatorial optimization problems via approximations. QAOA is able to be evaluated on both physical and virtual quantum…

Quantum Physics · Physics 2023-12-07 Yu-Cheng Lin , Chuan-Chi Wang , Chia-Heng Tu , Shih-Hao Hung

The quantum approximate optimization algorithm (QAOA) is an approach for near-term quantum computers to potentially demonstrate computational advantage in solving combinatorial optimization problems. However, the viability of the QAOA…

We apply digitized Quantum Annealing (QA) and Quantum Approximate Optimization Algorithm (QAOA) to a paradigmatic task of supervised learning in artificial neural networks: the optimization of synaptic weights for the binary perceptron. At…

Quantum Physics · Physics 2021-12-21 Pietro Torta , Glen B. Mbeng , Carlo Baldassi , Riccardo Zecchina , Giuseppe E. Santoro

Quantum Approximate Optimization algorithm (QAOA) aims to search for approximate solutions to discrete optimization problems with near-term quantum computers. As there are no algorithmic guarantee possible for QAOA to outperform classical…

Quantum Physics · Physics 2022-07-25 Bingzhi Zhang , Akira Sone , Quntao Zhuang