Abstract
We propose a nontrivial two-qubit gate scheme in which Rydberg atoms are subject to designed pulses resulting from geometric evolution processes. By utilizing a hybrid robust non-adiabatic and adiabatic geometric operations on the control atom and target atom, respectively, we improve the robustness of two-qubit Rydberg gate against Rabi control errors as well as blockade errors in comparison with the conventional two-qubit blockade gate. Numerical results with the current state-of-the-art experimental parameters corroborates the above mentioned robustness. We also evaluated the influence induced by the motion-induced dephasing and the dipole-dipole interaction and imperfection excitation induced leakage errors, which both could decrease the gate fidelity. Our scheme provides a promising route towards systematic control error (Rabi error) as well as blockade error tolerant geometric quantum computation on neutral atom system.