An introduction to variational quantum algorithms for combinatorial optimization problems

Camille Grange (), Michael Poss and Eric Bourreau
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Camille Grange: University of Montpellier, CNRS
Michael Poss: University of Montpellier, CNRS
Eric Bourreau: University of Montpellier, CNRS

Annals of Operations Research, 2024, vol. 343, issue 2, No 9, 847-884

Abstract: Abstract Noisy intermediate-scale quantum computers are now readily available, motivating many researchers to experiment with Variational Quantum Algorithms. Among them, the Quantum Approximate Optimization Algorithm is one of the most popular one studied by the combinatorial optimization community. In this tutorial, we provide a mathematical description of the class of Variational Quantum Algorithms, assuming no previous knowledge of quantum physics from the readers. We introduce precisely the key aspects of these hybrid algorithms on the quantum side (parametrized quantum circuit) and the classical side (guiding function, optimizer). We devote a particular attention to QAOA, detailing the quantum circuits involved in that algorithm, as well as the properties satisfied by its possible guiding functions. Finally, we discuss the recent literature on QAOA, highlighting several research trends.

Keywords: Variational quantum algorithm; QAOA; Combinatorial optimization; Metaheuristics (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s10479-024-06253-5

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