  Understanding the formation of the supermassive black holes (SMBHs) present
in the centers of galaxies is a crucial topic in modern astrophysics.
Observations have detected the SMBHs with mass $M$ of $10^{9}\, \rm M_\odot$ in
the high-redshift galaxies with $\rm z\sim7$. However, how SMBHs grew to such
huge masses within the first billion years after the big bang remains elusive.
One possible explanation is that SMBHs grow quickly through the frequent
mergers of galaxies, which provides sustainable gas to maintain rapid growth.
This study presents the hydrodynamics simulations of the SMBHs' growth with
their host galaxies using the GIZMO code. In contrast to previous simulations,
we have developed a giant molecular cloud (GMC) model by separating
molecular-gas particles from the atomic-gas particles and then evolving them
independently. During major mergers, we show that the more massive molecular
gas particles cloud bear stronger dynamical friction. Consequently, GMCs are
substantially accreted onto the galactic centers that grow SMBHs from $\sim
10^{7}$ $\rm M_\odot$ to $\sim 10^{9}\, \rm M_\odot$ within $300$ Myr,
explaining the rapid growth of SMBHs, and this accretion also triggers a
violent starburst at the galactic center. Furthermore, we examine the impact of
minor mergers on the bulge of a Milky-Way-like galaxy and find that the size
and mass of the bulge can increase from $0.92$ kpc to $1.9$ kpc and from
$4.7\times 10^{10}\, \rm M_\odot$ to $7\times 10^{10}\, \rm M_\odot$.
