  Noisy intermediate-scale quantum computers (NISQ computers) are now readily
available, motivating many researchers to experiment with Variational Quantum
Algorithms (VQAs). Among them, the Quantum Approximate Optimization Algorithm
(QAOA) 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.
