  We introduce a variational quantum algorithm to solve unconstrained black box
binary optimization problems, i.e., problems in which the objective function is
given as black box. This is in contrast to the typical setting of quantum
algorithms for optimization where a classical objective function is provided as
a given Quadratic Unconstrained Binary Optimization problem and mapped to a sum
of Pauli operators. Furthermore, we provide theoretical justification for our
method based on convergence guarantees of quantum imaginary time evolution. To
investigate the performance of our algorithm and its potential advantages, we
tackle a challenging real-world optimization problem: feature selection. This
refers to the problem of selecting a subset of relevant features to use for
constructing a predictive model such as fraud detection. Optimal feature
selection -- when formulated in terms of a generic loss function -- offers
little structure on which to build classical heuristics, thus resulting
primarily in 'greedy methods'. This leaves room for (near-term) quantum
algorithms to be competitive to classical state-of-the-art approaches. We apply
our quantum-optimization-based feature selection algorithm, termed VarQFS, to
build a predictive model for a credit risk data set with 20 and 59 input
features (qubits) and train the model using quantum hardware and
tensor-network-based numerical simulations, respectively. We show that the
quantum method produces competitive and in certain aspects even better
performance compared to traditional feature selection techniques used in
today's industry.
