  We apply recently developed smooth boundary conditions to the quantum Monte
Carlo simulation of the two-dimensional Hubbard model. At half-filling, where
there is no sign problem, we show that the thermodynamic limit is reached more
rapidly with smooth rather than with periodic or open boundary conditions. Away
from half-filling, where ordinarily the simulation cannot be carried out at low
temperatures due to the existence of the sign problem, we show that smooth
boundary conditions allow us to reach significantly lower temperatures. We
examine pairing correlation functions away from half-filling in order to
determine the possible existence of a superconducting state. On a $10\times 10$
lattice for $U=4$, at a filling of $\langle n \rangle = 0.87$ and an inverse
temperature of $\beta=10$, we did find enhancement of the $d$-wave correlations
with respect to the non-interacting case, a possible sign of $d$-wave
superconductivity.
