  Recent JWST observations have uncovered an unexpectedly large population of
massive quiescent galaxies at $z>3$. Using the cosmological simulations
IllustrisTNG and ASTRID, we identify analogous galaxies and investigate their
abundance, formation, quenching mechanisms, and post-quenching evolution for
stellar masses $9.5 < \log_{10}{(M_\star/{\rm M}_\odot)} < 12$. We apply three
different quenching definitions and find that both simulations significantly
underestimate the comoving number density of quenched massive galaxies at $z
\gtrsim 3$ compared to JWST observations by up to $\sim 2$ dex. This fact
highlights the necessity for improved physical models of AGN feedback in galaxy
formation simulations. In both simulations, the high-$z$ quenched massive
galaxies often host overmassive central black holes above the standard
$M_{BH}-M_\star$ relation, implying that the AGN feedback plays a crucial role
in quenching galaxies in the early Universe. The typical quenching timescales
for these galaxies are $\sim 200-600$ Myr. IllustrisTNG primarily employs AGN
kinetic feedback, while ASTRID relies on AGN thermal feedback, which is less
effective and has a longer quenching timescale. We also study the
post-quenching evolution of the high-$z$ massive quiescent galaxies and find
that many experience subsequent reactivation of star formation, evolving into
primary progenitors of $z=0$ brightest cluster galaxies.
