  In this study we have computed the pair correlation functions in the
two-dimensional Hubbard model using a quantum Monte Carlo method. We employ a
new diagonalization algorithm in quantum Monte Carlo method which is free from
the negative sign problem. We show that the d-wave pairing correlation function
is indeed enhanced slightly for the positive on-site Coulomb interaction U when
doping away from the half-filling. When the system size becomes large, the pair
correlation function P_d is increased for U>0 compared to the non-interacting
case, while P_d is suppressed for U>0 when the system size is small. The
enhancement ratio P_d[U]/P_d[U=0] will give a criterion on the existence of
superconductivity. The ratio P_d[U]/P_d[U=0] increases almost linearly \propto
L as the system size L\times L is increased. This increase is a good indication
of an existence of superconducting phase in the two-dimensional Hubbard model.
There is, however, no enhancement of pair correlation functions at
half-filling, which indicates the absence of superconductivity without hole
doping.
