  Quantum computers are reaching one crucial milestone after another. Motivated
by their progress in quantum chemistry, we have performed an extensive series
of simulations of quantum-computer runs that were aimed at inspecting
best-practice aspects of these calculations. In order to compare the
performance of different set-ups, the ground-state energy of hydrogen molecule
has been chosen as a benchmark for which the exact solution exists in
literature. Applying variational quantum eigensolver (VQE) to a qubit
Hamiltonian obtained by the Bravyi-Kitaev transformation we have analyzed the
impact of various computational technicalities. These include (i) the choice of
optimization methods, (ii) the architecture of quantum circuits, as well as
(iii) different types of noise when simulating real quantum processors. On
these we eventually performed a series of experimental runs as a complement to
our simulations. The SPSA and COBYLA optimization methods have clearly
outperformed the Nelder-Mead and Powell methods. The results obtained when
using the $R_{\mathrm{y}}$ variational form were better than those obtained
when the $R_{\mathrm{y}}R_{\mathrm{z}}$ form was used. The choice of an optimum
{entangling layer} was sensitively interlinked with the choice of the
optimization method. The circular {entangling layer} has been found to worsen
the performance of the COBYLA method while the full {entangling layer} improved
it. All four optimization methods sometimes lead to an energy that corresponds
to an excited state rather than the ground state. We also show that a
similarity analysis of measured probabilities can provide a useful insight.
