Abstract: Gaussian Quantum Monte Carlo (GQMC) is a stochastic method to simulate fermionic systems with positive weights. However, in the example of the Hubbard model close to half filling it fails to reproduce all the symmetries of the ground state leading to systematic errors at low temperatures. We propose to restore these symmetries a posteriori by a projection onto the ground state symmetry sector. Recent results for Hubbard ladders are presented. We show that non-vanishing boundary terms (fat tailed distributions) are a possible source of the systematic errors.