  We develop an all-electron quantum Monte Carlo (QMC) method for solids that
does not rely on pseudopotentials, and use it to construct a primary ultra-high
pressure calibration based the equation of state of cubic boron nitride(c-BN).
We compute the static contribution to the free energy with QMC, and obtain the
phonon contribution from density functional theory, yielding a high-accuracy
calibration up to 900 GPa usable directly in experiment. Furthermore, we
compute the anharmonic Raman frequency shift with QMC as a function of pressure
and temperature, allowing optical pressure calibration in table-top
experiments. In contrast to present experimental approaches, small systematic
errors in the theoretical EOS do not increase with pressure, and no
extrapolation is needed. This all-electron methodology is generally applicable
to first-row solids, and can be used to provide a new reference for ab initio
calculations of solids and to benchmark pseudopotential accuracy.
