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Motivated by high-temperature superconductivity in the bilayer nickelateLa$_3$Ni$_2$O$_7$, we investigate the pair correlations in the two-orbitalHubbard ladder, which consists of the nearly half-filled and nearlyquarter-filled orbitals. By employing the density matrix renormalization groupmethod, we demonstrate that the pair correlation exhibits a power-law decayagainst the distance while the spin correlation decays exponentially. The decayexponent of the pair correlation of the nearly half-filled orbital iscomparable to the exponent of the quasi-long-range superconducting correlationin the doped single-orbital Hubbard ladder, which suggests the importance ofthe $d_{3z^2-r^2}$ orbital in La$_3$Ni$_2$O$_7$.

Pair correlations in the two-orbital Hubbard ladder: Implications on superconductivity in the bilayer nickelate