  We propose several schemes for implementing a fast two-qubit quantum gate for
neutral atoms with the gate operation time much faster than the time scales
associated with the external motion of the atoms in the trapping potential. In
our example, the large interaction energy required to perform fast gate
operations is provided by the dipole-dipole interaction of atoms excited to
low-lying Rydberg states in constant electric fields. A detailed analysis of
imperfections of the gate operation is given.
