QAOA applied to the portfolio optimization problem

Abstract

Quantum computing is no longer in its early stages. There already exists quantum computers with more qubits than a classical computer is capable of efficiently simulating. This current stage is considered intermediate and is therefore called the NISQ era (noisy intermediate-scale quantum). The main feature of this current stage is that there are still not enough qubits to perform quantum error correction, hence the noisy name. In this context of quantum computing without quantum error correction and with an intermediate number of qubits, variational algorithms gained prominence and, among them, there is one called QAOA (quantum approximate optimization algorithm). As the name suggests, this is a quantum algorithm that approximates the solution of optimization problems. The objective of this work was to apply this algorithm to solve an optimization problem in the finance area known as portfolio optimization. This application took place both in an ideal way (without noise) and in a way consistent with the current capacity of quantum computers (with noise). Both were simulated using IBM’s Python tool for simulation and access of quantum computers via cloud called Qiskit. The results suggest that the QAOA performance with noise was, as expected, worse than the ideal case, but still satisfactory within the limitations of the method.