  We propose new applications of Floquet theory in Rydberg atoms for
constructing quantum entangling gates in atomic ground-state manifolds. By
dynamically periodically modulating the Rabi frequencies of transitions between
ground and Rydberg states of atoms, error-resilient two-qubit entangling gates
can be implemented in the regime of Rydberg blockade. According to different
degrees of Floquet theory utilization, the fidelity of the resulting controlled
gates surpasses that of the original reference, and it exhibits high robustness
against Rabi error in two qubits and detuning error in the control qubit. Our
method only uses encoding in the ground states, and compared to the original
scheme using Rydberg state for encoding, it is less susceptible to
environmental interference, making it more practical to implement. Therefore,
our approach may have broader applications or potential for further expansion
of geometric quantum computation with neutral atoms.
