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Registers of trapped neutral atoms, excited to Rydberg states to inducestrong long-distance interactions, are extensively studied for directapplications in quantum computing. In this regard, new effective approaches tothe creation of multiqubit quantum gates arise high interest. Here, we presenta novel gate implementation technique based on RF-induced few-body F\"{o}rsterresonances. External radio frequency (RF) control field allows us to manipulatethe phase and population dynamics of many-atom system, thus enabling therealization of universal $CCR_{Z}(\phi)$ quantum gates. We numericallydemonstrate RF-induced resonant interactions, as well as high-precisionthree-qubit gates. The extreme controllability of interactions provided by RFmakes it possible to implement gates for a wide range of parameters of theatomic system, and significantly facilitates their experimental implementation.For the considered error sources, we achieve theoretical gate fidelitiescompatible with error correction ($\sim 99.7\%$) using reasonable experimentalparameters.

High-fidelity $CCR_Z(\phi)$ gates via RF-induced F\"{o}rster resonances