  The two-dimensional (2D) Hubbard model is widely believed to capture key
ingredients of high-$T_c$ superconductivity in cuprate materials. However,
compelling evidence remains elusive. In particular, various magnetic orders may
emerge as strong competitors of superconducting orders. Here, we study the
ground state properties of the doped 2D $t$-$t'$ Hubbard model on a square
lattice via the infinite Projected Entangled-Pair State (iPEPS) method with
$\mathrm{U}(1)$ or $\mathrm{SU}(2)$ spin symmetry. The former is compatible
with antiferromagnetic orders, while the latter forbids them. Therefore, we
obtain by comparison a detailed understanding of the magnetic impact on
superconductivity. Moreover, an additional $t'$ term accommodates the
particle-hole asymmetry, which facilitates studies on the discrepancies between
electron- and hole-doped systems. We demonstrate that (i) a positive $t'/t$
significantly amplifies the strength of superconducting orders; (ii) at
sufficiently large doping levels, the $t$-$t'$ Hubbard model favors a uniform
state with superconducting orders instead of stripe states with charge and spin
modulations; and (iii) the enhancement of magnetic frustration, by increasing
either the strength of NNN interactions or the charge doping, impairs stripe
orders and helps stabilize superconductivity.
