  Motivated by recent experimental studies on superconductivity found in
nickelate-based materials, we study the temperature dependence of the spin
correlation and the superconducting pairing interaction within an effective
two-band Hubbard model by the quantum Monte Carlo method. Based on parameters
extracted from first-principles calculations, our intensive numerical results
reveal that the pairing with a $d_{xy}$-wave symmetry firmly dominates over
other pairings at low temperature, which is mainly determined by the Ni 3$d$
orbital. It is also found that the effective pairing interaction is enhanced as
the on-site interaction increases, demonstrating that the superconductivity is
driven by strong electron-electron correlation. Even though the $(\pi,\pi)$
antiferromagnetic correlation could be enhanced by electronic interaction,
there is no evidence for long-range antiferromagnetic order exhibited in
nickelate-based superconductors. Moreover, our results offer possible evidence
that the pure electron correlation may not account for the charge density wave
state observed in nickelates.
