  As Juno is presently measuring Jupiter's gravitational moments to
unprecedented accuracy, models for the interior structure of the planet are
putted to the test. While equations of state based on first principles or ab
initio simulations have been available and used for the two most abundant
elements constituting the envelope, hydrogen and helium, significant
discrepancies remain regarding the predictions of the inner structure of
Jupiter. The differences are severe enough to clutter the analysis of Juno's
data and even cast doubts on the usefulness of these computationally expensive
EOSs for the modeling of the interior of Jupiter and exoplanets at large. Using
our newly developed equations of state for hydrogen and helium, we asses the ab
initio equations of state currently available and establish their efficiency at
predicting the interior structure of Jupiter in a two-layers model. By
adjusting our free energy parameterization to reproduce previous ab initio EOS
behavior, we identify the source of the disagreement previously reported for
the interior structure of Jupiter. We further point to area where care should
be taken when building EOS for the modeling of giant planets. This concerns the
interpolation between the ab initio results and the physical models used to
cover the low density range as well as the interpolation of the {\sl ab initio}
simulation results at high densities. This sensitivity falls well within the
uncertainties of the ab initio simulations. This suggests that hydrogen EOS
should be carefully benchmarked using a simple planetary model before being
used in the more advanced planetary models needed to interpret the Juno data.
We finally provide an updated version of our ab initio hydrogen EOS recently
published.
