  Combining the complementary capabilities of two of the most powerful modern
computational methods, we find superconductivity in both the electron- and
hole-doped regimes of the two-dimensional Hubbard model (with next nearest
neighbor hopping). In the electron-doped regime, superconductivity is weaker
and is accompanied by antiferromagnetic N\'eel correlations at low doping. The
strong superconductivity on the hole-doped side coexists with stripe order,
which persists into the overdoped region with weaker hole density modulation.
These stripe orders, neither filled as in the pure Hubbard model (no next
nearest neighbor hopping) nor half-filled as seen in previous state-of-the-art
calculations, vary in fillings between 0.6 and 0.8. The resolution of the tiny
energy scales separating competing orders requires exceedingly high accuracy
combined with averaging and extrapolating with a wide range of system sizes and
boundary conditions. These results validate the applicability of this iconic
model for describing cuprate high-$T_c$ superconductivity.
