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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…
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…
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…
Parameterized quantum circuits are attractive candidates for potential quantum advantage in the near term and beyond. At the same time, as quantum computing hardware not only continues to improve but also begins to incorporate new features…
A combinatorial optimization problem becomes very difficult in situations where the energy landscape is rugged, and the global minimum locates in a narrow region of the configuration space. When using the quantum approximate optimization…
The Quantum Approximate Optimization Algorithm (QAOA) has been suggested as a promising candidate for the solution of combinatorial optimization problems. Yet, whether - or under what conditions - it may offer an advantage compared to…
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…
Current state-of-the-art quantum optimization algorithms require representing the original problem as a binary optimization problem, which is then converted into an equivalent cost Hamiltonian suitable for the quantum device. Implementing…
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…
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 variational algorithms have garnered significant interest recently, due to their feasibility of being implemented and tested on noisy intermediate scale quantum (NISQ) devices. We examine the robustness of the quantum approximate…
Quantum approximate optimization algorithms are hybrid quantum-classical variational algorithms designed to approximately solve combinatorial optimization problems such as the MAX-CUT problem. In spite of its potential for near-term quantum…
In this work, we compare the performance of the Quantum Approximate Optimization Algorithm (QAOA) with state-of-the-art classical solvers such as Gurobi and MQLib to solve the combinatorial optimization problem MaxCut on 3-regular graphs.…
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…
Combinatorial optimization is a promising area for achieving quantum speedup. Quantum approximate optimization algorithm (QAOA) is designed to search for low-energy states of the Ising model, which correspond to near-optimal solutions of…
Quantum Approximate Optimization Algorithm (QAOA) is a promising hybrid quantum-classical algorithm for solving combinatorial optimization problems. However, it cannot overcome qubit limitation for large-scale problems. Furthermore, the…
Quantum optimization allows for up to exponential quantum speedups for specific, possibly industrially relevant problems. As the key algorithm in this field, we motivate and discuss the Quantum Approximate Optimization Algorithm (QAOA),…
Constrained combinatorial optimization with strict linear constraints underpins applications in drug discovery, power grids, logistics, and finance, yet remains computationally demanding for classical algorithms, especially at large scales.…
The quantum approximate optimization algorithm (QAOA) is a promising quantum-classical hybrid technique to solve combinatorial optimization problems in near-term gate-based noisy quantum devices. In QAOA, the objective is a function of the…
Constrained combinatorial optimization problems are challenging for quantum computing, particularly at utility-relevant scales and on near-term hardware. At the same time, these problems are of practical significance in industry; for…