Construction of robust Rydberg controlled-phase gates

One scheme is presented to construct the robust multi-qubit arbitrary-phase controlled-phase gate (CPG) with one control and multiple target qubits in Rydberg atoms using the Lewis-Riesenfeld (LR) invariant method. The scheme is not limited by adiabatic condition while preserves the robustness against control parameter variations of adiabatic evolution. Comparing with the adiabatic case, our scheme does not require very strong Rydberg interaction strength. Taking the construction of two-qubit $\pi$ CPG as an example, our scheme is more robust against control parameter variations than non-adiabatic scheme and faster than adiabatic scheme.