  We utilize numerical linked-cluster expansions (NLCEs) and the determinantal
quantum Monte Carlo algorithm to study pairing correlations in the square
lattice Hubbard model. To benchmark the NLCE, we first locate the
finite-temperature phase transition of the attractive model to a
superconducting state away from half filling. We then explore the
superconducting properties of the repulsive model for the d-wave and extended
s-wave pairing symmetries. The pairing structure factor shows a strong tendency
to d-wave pairing and peaks at an interaction strength comparable to the
bandwidth. The extended s-wave structure factor and correlation length are
larger at higher temperatures but clearly saturate as temperature is lowered,
whereas the d-wave counterparts, which start off lower at high temperatures,
continue to rise near half filling. This rise is even more dramatic in the
d-wave susceptibility. The convergence of NLCEs breaks down as the
susceptibilities and correlation lengths become large, so we are unable to
determine the onset of long-range order. However, our results extend the
conclusion, previously restricted to only magnetic and charge correlations,
that NLCEs offer unique window into pairing in the Hubbard model at strong
coupling.
