Quantum Finance: a tutorial on quantum computing applied to the financial market

TL;DR

This paper introduces quantum computing fundamentals and demonstrates how the Quantum Approximate Optimization Algorithm (QAOA) can be applied to portfolio optimization in financial markets, with practical examples and simulations.

Contribution

It provides a tutorial on quantum computing with a focus on applying QAOA to real-world financial portfolio optimization problems, including code and simulation analysis.

Findings

QAOA can effectively optimize financial portfolios.

Practical examples using Brazilian stock data illustrate the approach.

Simulations show promising solution quality for quantum algorithms in finance.

Abstract

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.