  Using exact quantum Monte Carlo method, we examine the recent novel
electronic states seen in magic-angle graphene superlattices. From the Hubbard
model on a double-layer honeycomb lattice with a rotation angle
$\theta=1.08^{\circ}$, we reveal that an antiferromagnetically ordered Mott
insulator emerges beyond a critical $U_c$ at half filling, and with a small
doping, the pairing with $d+id$ symmetry dominates over other pairings at low
temperature. The effective $d+id$ pairing interaction strongly increase as the
on-site Coulomb interaction increases, indicating that the superconductivity is
driven by electron-electron correlation. Our non-biased numerical results
demonstrate that the twisted bilayer graphene share the similar superconducting
mechanism of high temperature superconductors, which is a new and idea platform
for further investigating the strongly correlated phenomena.
