  Arrays of neutral atoms have emerged as promising platforms for quantum
computing. Realization of high-fidelity two-qubit gates with robustness is
currently a significant important task for large-scale operations. In this
paper, we present a convenient approach for implementing a two-qubit
controlled-phase gate using Rydberg blockade. We achieve the noncyclic
geometric control with a single modulated pulse. As compared with the control
scheme by cyclic evolution that determined by dynamical parameters, the
robustness of the proposal against systematic errors will be remarkably
improved due to the geometric characteristic. Importantly, the noncyclic
geometric control reduces the gate time for small rotation angles and will be
more insensitive to the decoherence effect. We accelerate the adiabatic control
with the aid of shortcuts to adiabaticity to further shorten the operation
time. We apply our protocol to the algorithm of quantum Fourier transformation
to show the actual acceleration. Therefore, the proposed scheme will provide an
analytical waveforms for arbitrary two-qubit gates and may have important use
in the experiments of atomic arrays.
