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This short tutorial provides an introduction to the Quantum Approximation Optimization Algorithm (QAOA). Specifically, how to use QAOA with the Simultaneous Perturbation Stochastic Approximation (SPSA) algorithm to solve the Max-Cut…

Quantum Physics · Physics 2021-06-04 Salonik Resch

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

Photonic quantum computers, programmed within the framework of the measurement-based quantum computing (MBQC), currently concur with gate-based platforms in the race towards useful quantum advantage, and some algorithms emerged as main…

Quantum Physics · Physics 2023-04-10 Massimiliano Proietti , Filippo Cerocchi , Massimiliano Dispenza

Understanding the best known parameters, performance, and systematic behavior of the Quantum Approximate Optimization Algorithm (QAOA) remain open research questions, even as the algorithm gains popularity. We introduce QAOAKit, a Python…

Quantum Physics · Physics 2022-04-19 Ruslan Shaydulin , Kunal Marwaha , Jonathan Wurtz , Phillip C. Lotshaw

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

Running quantum circuits on quantum computers does not always generate "clean" results, unlike on a simulator, as noise plays a significant role in any quantum device. To explore this, we experimented with the Quantum Approximate…

Quantum Physics · Physics 2025-10-09 Abyan Khabir Irfan , Chansu Yu

The emergent practical applicability of the Quantum Approximate Optimization Algorithm (QAOA) for approximate combinatorial optimization is a subject of considerable interest. One of the primary limitations of QAOA is the task of finding a…

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

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

We propose an Indirect Quantum Approximate Optimization Algorithm (referred to as IQAOA) where the Quantum Alternating Operator Ansatz takes into consideration a general parameterized family of unitary operators to efficiently model the…

Quantum Physics · Physics 2023-11-07 Eric Bourreau , Gerard Fleury , Philippe Lacomme

We show through numerical simulation that the Quantum Approximate Optimization Algorithm (QAOA) for higher-order, random-coefficient, heavy-hex compatible spin glass Ising models has strong parameter concentration across problem sizes from…

Quantum Physics · Physics 2024-11-13 Elijah Pelofske , Andreas Bärtschi , Lukasz Cincio , John Golden , Stephan Eidenbenz

The task of Multiple Sequence Alignment (MSA) is a constrained combinatorial optimization problem that is generally considered a complex computational problem. In this paper, we first present a binary encoding of MSA and devise a…

The Quantum Approximate Optimization Algorithm (QAOA) is a highly promising variational quantum algorithm that aims to solve combinatorial optimization problems that are classically intractable. This comprehensive review offers an overview…

The quantum approximate optimization algorithm (QAOA) is a leading iterative variational quantum algorithm for heuristically solving combinatorial optimization problems. A large portion of the computational effort in QAOA is spent by the…

Quantum Physics · Physics 2022-08-23 Ohad Amosy , Tamuz Danzig , Ely Porat , Gal Chechik , Adi Makmal

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…

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

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 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

Quantum computers and simulators may offer significant advantages over their classical counterparts, providing insights into quantum many-body systems and possibly improving performance for solving exponentially hard problems, such as…

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,…