Using constrained-path quantum Monte Carlo simulations on a bilayer two-orbital Hubbard model, we systematically investigate the pairing symmetry competition in ${\mathrm{La}}_3{\mathrm{Ni}}_2{\mathrm{O}}_7$. Our findings reveal that Hund's coupling $J_H$ and crystal field splitting $\mathrm{\Delta }E$ are the key factors controlling the ground-state pairing symmetry. Increasing either $J_H$ or $\mathrm{\Delta }E$ robustly enhances the interlayer $s_{\pm }$-wave pairing, driven by interlayer antiferromagnetic correlations, while simultaneously suppressing the intralayer $d$-wave pairing, which is mediated by intralayer antiferromagnetic spin fluctuations. In the physically relevant parameter regime for ${\mathrm{La}}_3{\mathrm{Ni}}_2{\mathrm{O}}_7$, the $s_{\pm }$-wave emerges as the dominant pairing symmetry. Crucially, this robust $s_{\pm }$-wave pairing persists even when the $\gamma$ pocket is absent, providing theoretical support for the recent experimental observations of high-temperature superconductivity in thin films.

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• Nickelates
• Strongly correlated systems
• Hubbard model
• Quantum Monte Carlo