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Recently, Hadfield et al. proposed the quantum alternating operator ansatz algorithm (QAOA+), an extension of the quantum approximate optimization algorithm (QAOA), to solve constrained combinatorial optimization problems (CCOPs). Compared…

While variational quantum algorithms (VQAs) have demonstrated considerable success in unconstrained optimization, their application to constrained combinatorial problems face a trade-off. Penalty-based methods, despite their circuit…

Solving hard optimization problems is one of the most promising application domains for quantum computers due to the ubiquity of such problems in industry and the availability of broadly applicable quantum speedups. However, the ability of…

One of the most promising attempts towards solving optimization problems with quantum computers in the noisy intermediate scale era of quantum computing are variational quantum algorithms. The Quantum Alternating Operator Ansatz provides an…

Variational Quantum optimization algorithms, such as the Variational Quantum Eigensolver (VQE) or the Quantum Approximate Optimization Algorithm (QAOA), are among the most studied quantum algorithms. In our work, we evaluate and improve an…

Solving combinatorial optimization problems using variational quantum algorithms (VQAs) has emerged as a promising research direction. Since the introduction of the Quantum Approximate Optimization Algorithm (QAOA), numerous variants have…

The Quantum Approximate Optimization Algorithm (QAOA) is a standard method for combinatorial optimization with a gate-based quantum computer. The QAOA consists of a particular ansatz for the quantum circuit architecture, together with a…

Hadfield et al. proposed a novel Quantum Alternating Operator Ansatz algorithm (QAOA+), and this algorithm has wide applications in solving constrained combinatorial optimization problems (CCOPs) because of the advantages of QAOA+ ansatz in…

In the near-term, hybrid quantum-classical algorithms hold great potential for outperforming classical approaches. Understanding how these two computing paradigms work in tandem is critical for identifying areas where such hybrid algorithms…

The Quantum Approximate Optimization Algorithm and its generalization to Quantum Alternating Operator Ansatz (QAOA) is a promising approach for applying quantum computers to challenging problems such as combinatorial optimization and…

We present a quantum alternating operator ansatz (QAOA$^+$) that solves a class of linearly constrained optimization problems by evolving a quantum state within a Hilbert subspace of feasible problem solutions. Our main focus is on a class…

We introduce a variational algorithm based on the quantum alternating operator ansatz (QAOA) for the approximate solution of computationally hard counting problems. Our algorithm, dubbed VQCount, is based on the equivalence between random…

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 promising variational quantum algorithm introduced to tackle classically intractable combinatorial optimization problems. This tutorial offers a comprehensive, first-principles…

The Quantum Approximate Optimization Algorithm (QAOA) is a leading framework for quantum combinatorial optimization. The Vehicle Routing Problem (VRP), a core problem in logistics and transportation, is a natural application target, but it…

Optimization problems are critical across various domains, yet existing quantum algorithms, despite their great potential, struggle with scalability and accuracy due to excessive reliance on entanglement. To address these limitations, we…

The Quantum Alternating Operator Ansatz (QAOA) represents a branch of quantum algorithms for solving combinatorial optimization problems. A specific variant, the Grover-Mixer Quantum Alternating Operator Ansatz (GM-QAOA), ensures uniform…

Quantum computing is an emerging field on the multidisciplinary interface between physics, engineering, and computer science with the potential to make a large impact on computational intelligence (CI). The aim of this paper is to introduce…

Variational quantum algorithms are believed to be promising for solving computationally hard problems and are often comprised of repeated layers of quantum gates. An example thereof is the quantum approximate optimization algorithm (QAOA),…

The Capacitated Vehicle Routing Problem (CVRP) is an NP-optimization problem (NPO) that arises in various fields including transportation and logistics. The CVRP extends from the Vehicle Routing Problem (VRP), aiming to determine the most…