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

Heralded atomic nonadiabatic holonomic quantum computation with Rydberg blockade