  Previously only considered a frontier area of Physics, nowadays quantum
computing is one of the fastest growing research field, precisely because of
its technological applications in optimization problems, machine learning,
information security and simulations. The goal of this article is to introduce
the fundamentals of quantum computing, focusing on a promising quantum
algorithm and its application to a financial market problem. More specifically,
we discuss the portfolio optimization problem using the \textit{Quantum
Approximate Optimization Algorithm} (QAOA). We not only describe the main
concepts involved but also consider simple practical examples, involving
financial assets available on the Brazilian stock exchange, with codes, both
classic and quantum, freely available as a Jupyter Notebook. We also analyze in
details the quality of the combinatorial portfolio optimization solutions
through QAOA using SENAI/CIMATEC's ATOS QLM quantum simulator.
