  Realizing quantum Hall states in a fast rotating Bose gas is a long sought
goal in cold atom research. The effort is very challenging because Bose
statistics fights against quantum Hall correlations. In contrast, Fermi
statistics does not cause such conflict. Here, we show that by sweeping the
integer quantum Hall states of a spin-1/2 Fermi gas across the Feshbach
resonance from the BCS side to the BEC side at a "projection" rate similar to
that in the "projection" experiment of fermion superfluid, these states can be
"fused" into a bosonic quantum Hall states. A projection sweep means the pair
association is sufficiently fast so that the center of mass of the pair remains
unchanged in the process. We show that the fusion of integer fermion states
with filling factor $\nu_{\uparrow}=\nu_{\downarrow}=n$ will result in a
bosonic Laughlin state and Pfaffian state for $n=1$ and 2. The is due to a
hidden property of the fermionic integer quantum Hall states -- for any
grouping of opposite spin into pairs, their centers of mass automatically
assume a bosonic quantum Hall structure.
