  Rydberg quantum gate serving as an indispensable computing unit for
neutral-atom quantum computation, has attracted intense research efforts for
the last decade. However the state-of-the-art experiments have not reached the
high gate fidelity as predicted by most theories due to the unexpected large
loss remaining in Rydberg and intermediate states. In this paper we report our
findings in constructing a native two-qubit controlled-NOT gate based on pulse
optimization. We focus on the method of commonly-used two-photon Rydberg
excitation with smooth Gaussian-shaped pulses which is straightforward for
experimental demonstration. By utilizing optimized pulse shapes the scheme
reveals a remarkable reduction in the decays from Rydberg and intermediate
states, as well as a high-tolerance to the residual thermal motion of atoms. We
extract a conservative lower bound for the gate fidelity > 0.992 after taking
into account the experimental imperfections. Our results not only reduce the
gap between experimental and theoretical prediction because of the optimal
control, but also facilitate the connectivity of distant atomic qubits in a
larger atom array by reducing the requirement of strong blockade, which is
promising for developing multiqubit quantum computation in large-scale atomic
arrays.
