  The recent literature on near-term applications for quantum computers
contains several examples of the applications of hybrid quantum/classical
variational approaches. This methodology can be applied to a variety of
optimization problems, but its practical performance is not well studied yet.
This paper moves some steps in the direction of characterizing the practical
performance of the methodology, in the context of finding solutions to
classical combinatorial optimization problems. Our study is based on numerical
results obtained applying several classical nonlinear optimization algorithms
to Hamiltonians for six combinatorial optimization problems; the experiments
are conducted via noise-free classical simulation of the quantum circuits
implemented in Qiskit. We empirically verify that: (1) finding the ground state
is harder for Hamiltonians with many Pauli terms; (2) classical global
optimization methods are more successful than local methods due to their
ability of avoiding the numerous local optima; (3) there does not seem to be a
clear advantage in introducing entanglement in the variational form.
