(color online) (a) Schematic diagram of the controlled-phase gate with one control and multiple target qubits. (b) Energy level and the corresponding laser coupling for control (1) and target (k = 2, 3, ···, n) atoms. Ω_1(k) is the Rabi frequency of the transitions |1〉 ↔ |R_(r)〉 of atom 1(k). |R〉 denotes high-lying Rydberg state. The principal quantum number of the Rydberg state |r〉 is not equal to that of |R〉, which induces the asymmetric RRI strength V_Rr ≫ V_rr (suppose V_Rr(V_rr) is identical for different target atoms for simplicity) through choosing different energy levels, as described in Ref. [69]. |0〉 and |1〉 are two ground states used to encode the quantum information.