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Quantum neural networks (QNNs) have generated excitement around the possibility of efficiently analyzing quantum data. But this excitement has been tempered by the existence of exponentially vanishing gradients, known as barren plateau…

Quantum Physics · Physics 2021-11-02 Arthur Pesah , M. Cerezo , Samson Wang , Tyler Volkoff , Andrew T. Sornborger , Patrick J. Coles

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

Quantum Annealing (QA) is a computational framework where a quantum system's continuous evolution is used to find the global minimum of an objective function over an unstructured search space. It can be seen as a general metaheuristic for…

Quantum Physics · Physics 2022-02-04 Arthur Braida , Simon Martiel , Ioan Todinca

The quantum approximate optimization algorithm (QAOA) is one of the canonical algorithms designed to find approximate solutions to combinatorial optimization problems in current noisy intermediate-scale quantum (NISQ) devices. It is an…

Quantum Physics · Physics 2023-12-12 Ping Zou

The recently proposed QAOA-GPT framework demonstrated that generative pre-trained transformers can learn mappings between problem graphs and optimized quantum circuits for the Quantum Approximate Optimization Algorithm (QAOA). In this work,…

Quantum Physics · Physics 2025-11-11 Leanto Sunny , Abhinav Rijal , George Siopsis

The Quantum Approximate Optimization Algorithm (QAOA) is a leading candidate for demonstrating quantum advantage on near-term devices, yet the physical origins of its efficacy remain poorly understood. In this work, we study QAOA for random…

Quantum Physics · Physics 2026-05-21 Mingyou Wu , Hanwu Chen

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

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) has emerged as a promising approach for solving NP hard combinatorial optimization problems on noisy intermediate-scale quantum (NISQ) hardware. However, its performance is critically…

Quantum Physics · Physics 2025-11-13 Rakesh Saini , Nora Mohamed , Saif Al-Kuwari , Ahmed Farouk

The Quantum Approximate Optimization Algorithm (QAOA) has emerged as a promising variational quantum algorithm for addressing NP hard combinatorial optimization problems. However, a significant limitation lies in optimizing its classical…

Quantum Physics · Physics 2023-09-22 Peter Gleißner , Georg Kruse , Andreas Roßkopf

Parameterized quantum circuits (PQCs) are fundamental to quantum machine learning (QML), quantum optimization, and variational quantum algorithms (VQAs). The expressibility of PQCs is a measure that determines their capability to harness…

The Quantum Approximate Optimization Algorithm (QAOA) was originally developed to solve combinatorial optimization problems, but has become a standard for assessing the performance of quantum computers. Fully descriptive benchmarking…

Quantum Physics · Physics 2024-02-29 Anthony M. Polloreno , Graeme Smith

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…

High error rates and limited fidelity of quantum gates in near-term quantum devices are the central obstacles to successful execution of the Quantum Approximate Optimization Algorithm (QAOA). In this paper we introduce an…

Quantum Physics · Physics 2022-06-16 Ruslan Shaydulin , Alexey Galda

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 overparameterization of variational quantum circuits, as a model of Quantum Neural Networks (QNN), not only improves their trainability but also serves as a method for evaluating the property of a given ansatz by investigating their…

Quantum Physics · Physics 2023-05-23 Ali Rad

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

The capability of the quantum approximate optimization algorithm (QAOA) in solving the combinatorial optimization problems has been intensively studied in recent years due to its application in the quantum-classical hybrid regime. Despite…

Quantum Physics · Physics 2025-04-15 Xinwei Lee , Xinjian Yan , Ningyi Xie , Yoshiyuki Saito , Dongsheng Cai , Nobuyoshi Asai

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 Optimization Algorithm can naturally be applied to combinatorial search problems on graphs. The quantum circuit has p applications of a unitary operator that respects the locality of the graph. On a graph with…

Quantum Physics · Physics 2020-04-21 Edward Farhi , David Gamarnik , Sam Gutmann