  We investigate quasar outflows at $z \geq 6$ by performing zoom-in
cosmological hydrodynamical simulations. By employing the SPH code GADGET-3, we
zoom in the $2 R_{200}$ region around a $2 \times 10^{12} M_{\odot}$ halo at $z
= 6$, inside a $(500 ~ {\rm Mpc})^3$ comoving volume. We compare the results of
our AGN runs with a control simulation in which only stellar/SN feedback is
considered. Seeding $10^5 M_{\odot}$ BHs at the centers of $10^{9} M_{\odot}$
halos, we find the following results. BHs accrete gas at the Eddington rate
over $z = 9 - 6$. At $z = 6$, our most-massive BH has grown to $M_{\rm BH} = 4
\times 10^9 M_{\odot}$. Fast ($v_{r} > 1000$ km/s), powerful ($\dot{M}_{\rm
out} \sim 2000 M_{\odot}$/yr) outflows of shock-heated low-density gas form at
$z \sim 7$, and propagate up to hundreds kpc. Star-formation is quenched over
$z = 8 - 6$, and the total SFR (SFR surface density near the galaxy center) is
reduced by a factor of $5$ ($1000$). We analyse the relative contribution of
multiple physical process: (i) disrupting cosmic filamentary cold gas inflows,
(ii) reducing central gas density, (iii) ejecting gas outside the galaxy; and
find that AGN feedback has the following effects at $z = 6$. The inflowing gas
mass fraction is reduced by $\sim 12 \%$, the high-density gas fraction is
lowered by $\sim 13 \%$, and $\sim 20 \%$ of the gas outflows at a speed larger
than the escape velocity ($500$ km/s). We conclude that quasar-host galaxies at
$z \geq 6$ are accreting non-negligible amount of cosmic gas, nevertheless AGN
feedback quenches their star formation dominantly by powerful outflows ejecting
gas out of the host galaxy halo.
