  We apply a diagrammatic Monte Carlo method to the problem of an impurity
interacting resonantly with a homogeneous Fermi bath for a
quasi-two-dimensional setup. Notwithstanding the series divergence, we can show
numerically that the three particle-hole diagrammatic contributions are not
contributing significantly to the final answer, thus demonstrating a nearly
perfect destructive interference of contributions in subspaces with
higher-order particle-hole lines. Consequently, for strong enough confinement
in the third direction, the transition between the polaron and the molecule
ground state is found to be in good agreement with the pure two-dimensional
case and agrees very well with the one found by the wave-function approach in
the two-particle-hole subspace.
