  We propose a protocol to realize atomic nonadiabatic holonomic quantum
computation (NHQC) with two computational atoms and an auxiliary atom. Dynamics
of the system is analyzed in the regime of Rydberg blockade, and robust laser
pulses are designed via reverse engineering, so that quantum gates can be
easily realized with high fidelities. In addition, we also study the evolution
suffering from dissipation with a master equation. The result indicates that
decays of atoms can be heralded by measuring the state of the auxiliary atom,
and nearly perfect unitary evolution can be obtained if the auxiliary atom
remains in its Rydberg state. Therefore, the protocol may be helpful to realize
NHQC in dissipative environment.
