  Feature selection is of great importance in Machine Learning, where it can be
used to reduce the dimensionality of classification, ranking and prediction
problems. The removal of redundant and noisy features can improve both the
accuracy and scalability of the trained models. However, feature selection is a
computationally expensive task with a solution space that grows
combinatorically. In this work, we consider in particular a quadratic feature
selection problem that can be tackled with the Quantum Approximate Optimization
Algorithm (QAOA), already employed in combinatorial optimization. First we
represent the feature selection problem with the QUBO formulation, which is
then mapped to an Ising spin Hamiltonian. Then we apply QAOA with the goal of
finding the ground state of this Hamiltonian, which corresponds to the optimal
selection of features. In our experiments, we consider seven different
real-world datasets with dimensionality up to 21 and run QAOA on both a quantum
simulator and, for small datasets, the 7-qubit IBM (ibm-perth) quantum
computer. We use the set of selected features to train a classification model
and evaluate its accuracy. Our analysis shows that it is possible to tackle the
feature selection problem with QAOA and that currently available quantum
devices can be used effectively. Future studies could test a wider range of
classification models as well as improve the effectiveness of QAOA by exploring
better performing optimizers for its classical step.
