  An array of ultracold neutral atoms held in optical micro-traps is a
promising platform for quantum computation. One of the major bottlenecks of
this platform is the weak coupling strength between adjacent atoms, which
limits the speed of two-qubit gates. Here, we present a method to perform a
fast universal square-root-SWAP gate with fermionic atoms. The basic idea of
the gate is to release the atoms into a harmonic potential positioned in
between the two atoms. By properly tailoring the interaction parameter, the
collision process between the atoms generates entanglement and yields the
desired gate. We prove analytically that in the limit of broad atomic
wave-packets, the fidelity of the gate approaches unity. We demonstrate
numerically that with typical experimental parameters, our gate can operate on
a microsecond timescale and achieves a fidelity higher than 0.998. Moreover,
the gate duration is independent of the initial distance between the atoms. A
gate with such features is an important milestone towards all-to-all
connectivity and fault tolerance in quantum computation with neutral atoms.
