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 of the current state of QAOA, encompassing its performance analysis in
diverse scenarios, its applicability across various problem instances, and
considerations of hardware-specific challenges such as error susceptibility and
noise resilience. Additionally, we conduct a comparative study of selected QAOA
extensions and variants, while exploring future prospects and directions for
the algorithm. We aim to provide insights into key questions about the
algorithm, such as whether it can outperform classical algorithms and under
what circumstances it should be used. Towards this goal, we offer specific
practical points in a form of a short guide. Keywords: Quantum Approximate
Optimization Algorithm (QAOA), Variational Quantum Algorithms (VQAs), Quantum
Optimization, Combinatorial Optimization Problems, NISQ AlgorithmsComment: 67 pages, 9 figures, 9 tables; version 2 -- added more discussions
and practical guide