  We simulate $N_f=2+1$ QCD at the physical point combining open and periodic
boundary conditions in a parallel tempering framework, following the original
proposal by M. Hasenbusch for $2d$ $\mathrm{CP}^{N-1}$ models, which has been
recently implemented and widely employed in $4d$ $\mathrm{SU}(N)$ pure
Yang-Mills theories too. We show that using this algorithm it is possible to
achieve an impressive reduction of the auto-correlation time of the topological
charge in dynamical fermions simulations both at zero and finite temperature up
to two orders of magnitude, allowing to avoid topology freezing down to lattice
spacings as fine as $a \sim 0.02$ fm. Therefore, this implementation of the
Parallel Tempering on Boundary Conditions algorithm has the potential to
substantially push forward the investigation of the QCD vacuum properties by
means of lattice simulations.
