  Within an extended Hubbard model, we investigate the superconducting pairing
behavior of infinite-layer nickelate $\mathrm{NdNiO_2}$ and cuprates
superconductors by using the determinant quantum Monte Carlo method. Our focus
is on comparing their dominant pairing symmetries. The results indicate that
the $d_{x^2-y^2}$ pairing interaction is significantly enhanced at low
temperatures in both doped nickelates and cuprates, while other typical pairing
symmetries are effectively suppressed, highlighting the dominance of
$d_{x^2-y^2}$ pairing form. Additionally, we find that the effective pairing
interaction for $d_{x^2-y^2}$ pairing in doped nickelates is slightly lower
than that in doped cuprates, which may be attributed to the different degrees
of Fermi surface warping caused by the third nearest hopping $t''$. Further
studies show that the hole doping and interaction strength have significant
effects on the $d_{x^2-y^2}$ pairing interaction within the selected parameter
range. The $d_{x^2-y^2}$ pairing interaction is notably weakened when the hole
doping increases, while it is significantly enhanced with increasing Coulomb
interaction strength $U$. This comparative analysis reveals the similarities
and differences in the pairing behaviors of doped nickelates and cuprates,
which may provide further insights into understanding the superconducting
properties of these two classes of materials.
