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The Quantum Approximate Optimization Algorithm (QAOA), which is a variational quantum algorithm, aims to give sub-optimal solutions of combinatorial optimization problems. It is widely believed that QAOA has the potential to demonstrate…

We investigate the potential of the Quantum Approximate Optimization Algorithm (QAOA) for reducing energy consumption in route planning, a key challenge in logistics due to the NP-hard nature of the Traveling Salesman and Vehicle Routing…

Emerging Technologies · Computer Science 2026-04-21 Ayush Nadiger , Adriana Caraeni , Katie Schouten

We demonstrate the application of the Google Sycamore superconducting qubit quantum processor to combinatorial optimization problems with the quantum approximate optimization algorithm (QAOA). Like past QAOA experiments, we study…

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

Quantum Approximate Optimization Algorithm (QAOA) is a hybrid algorithm whose control parameters are classically optimized. In addition to the variational parameters, the right choice of hyperparameter is crucial for improving the…

Quantum Physics · Physics 2022-06-30 Yu Pan , Yifan Tong , Yi Yang

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

In the search for quantum advantage in real--world problems, one promising avenue is to use a quantum algorithm to improve on the solution found using an efficient classical algorithm. The quantum approximate optimization algorithm (QAOA)…

Quantum Physics · Physics 2025-07-25 Yunlong Yu , Xiang-Bin Wang , Nic Shannon , Robert Joynt

Many combinatorial optimization problems admit a maximin fairness variant, where the aim is to find a distribution over possible solutions which maximizes an expected worst-case outcome. However, the support for an optimal distribution may…

Quantum Physics · Physics 2026-04-17 Bao Bach , Cameron Ibrahim , Reuben Tate , Jad Salem , Stephan Eidenbenz , Ilya Safro

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

We introduce a quantum approximate optimization algorithm (QAOA) for continuous optimization. The algorithm is based on the dynamics of a quantum system moving in an energy potential which encodes the objective function. By approximating…

Quantum Physics · Physics 2019-02-04 Guillaume Verdon , Juan Miguel Arrazola , Kamil Brádler , Nathan Killoran

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

The Quantum Approximate Optimization Algorithm (QAOA) adopts a hybrid quantum-classical approach to find approximate solutions to variational optimization problems. In fact, it relies on a classical subroutine to optimize the parameters of…

Quantum Physics · Physics 2023-07-31 Simone Tibaldi , Davide Vodola , Edoardo Tignone , Elisa Ercolessi

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

The quantum approximate optimisation algorithm (QAOA) is at the core of many scenarios that aim to combine the power of quantum computers and classical high-performance computing appliances for combinatorial optimisation. Several obstacles…

Quantum Physics · Physics 2026-02-26 Simon Thelen , Hila Safi , Wolfgang Mauerer

The Quantum Approximate Optimization Algorithm (QAOA) requires that circuit parameters are determined that allow one to sample from high-quality solutions to combinatorial optimization problems. Such parameters can be obtained using either…

Quantum Physics · Physics 2023-01-11 David Headley , Frank K. Wilhelm

The quantum approximate optimization algorithm (QAOA) is a promising method of solving combinatorial optimization problems using quantum computing. QAOA on the MaxCut problem has been studied extensively on specific families of graphs,…

Quantum algorithms must be scaled up to tackle real-world applications. Doing so requires overcoming the noise present on today's hardware. The quantum approximate optimization algorithm (QAOA) is a promising candidate for scaling up, due…

Quantum Physics · Physics 2026-02-23 Zichang He , David Amaro , Ruslan Shaydulin , Marco Pistoia

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

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

Quantum computing exploits basic quantum phenomena such as state superposition and entanglement to perform computations. The Quantum Approximate Optimization Algorithm (QAOA) is arguably one of the leading quantum algorithms that can…

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