  The growth process of proto-planets can be sped-up by accreting a large
number of solid, pebble-sized objects that are still present in the
protoplanetary disc. It is still an open question on how efficient this process
works in realistic turbulent discs. Here, we investigate the accretion of
pebbles in turbulent discs that are driven by the purely hydrodynamical
vertical shear instability (VSI). For this purpose, we perform global
three-dimensional simulations of locally isothermal, VSI turbulent discs with
embedded protoplanetary cores from 5 to 100 $M_\oplus$ that are placed at 5.2
au distance from the star. In addition, we follow the evolution of a swarm of
embedded pebbles of different size under the action of drag forces between gas
and particles in this turbulent flow. Simultaneously, we perform a set of
comparison simulations for laminar viscous discs where the particles experience
stochastic kicks. For both cases, we measure the accretion rate onto the cores
as a function of core mass and Stokes number ($\tau_s$) of the particles and
compare it to recent MRI turbulence simulations. Overall the dynamic is very
similar for the particles in the VSI turbulent disc and the laminar case with
stochastic kicks. For the small mass planets (i.e. 5 and 10 $M_\oplus$),
well-coupled particles with $\tau_s = 1$, which have a size of about one meter
at this location, we find an accretion efficiency (rate of particles accreted
over drifting inward) of about 1.6-3%. For smaller and larger particles this
efficiency is higher. However, the fast inward drift for $\tau_s = 1$ particles
makes them the most effective for rapid growth, leading to mass doubling times
of about 20,000 yr. For masses between 10 and 30 $M_\oplus$ the core reaches
the pebble isolation mass and the particles are trapped at the pressure maximum
just outside of the planet, shutting off further particle accretion.
