Fig. 1. (a) Schematic for implementing a SWAP gate. Two identical atoms are driven resonantly by two AM laser fields, excited from two ground (computational) states |0⟩ and |1⟩ to a Rydberg (mediated) state |r⟩, respectively, with modulated Rabi frequencies Ω0(t) and Ω1(t). Two atoms are coupled to each other by RRI with strength V=C6/d6, C6 being the van der Waals coefficient and d the interatomic distance. The effective Λ-type RAB dynamics is shown in the shadow of (b). (b) Schematic for implementing a CSWAP gate. Inset circle: the control atom c is coupled to target atoms 1 and 2 described in (a), with RRI strengths V1c and V2c corresponding to interatomic distances d1c and d2c, respectively. The effective Λ-type system of the target atoms is coupled to the control atom with RRI strength (V1c+V2c). In addition, the control atom is excited resonantly by another AM field from |0⟩c to |r⟩c with Rabi frequency Ωc(t).

Fig. 2. Time-dependent average fidelities of the SWAP gate with {δ′=0, T=3.87  μs} and {δ′/2π=1.11  MHz, T=33.28  μs}, respectively. Atomic decay is not considered.

Fig. 3. Rydberg excitation probabilities during the SWAP gate procedure with different excitation numbers for (a) the resonant RAB with δ′=0 and (b) the modified RAB with δ′/2π=1.11  MHz, respectively. Two-atom initial product state |Ψ0⟩=(|0⟩1+|1⟩1)/2⊗|1⟩2 is specified.

Fig. 4. Infidelities of the SWAP gates caused by (a) atomic decay with different lifetimes of the Rydberg state, (b) motional dephasing with different atomic temperatures, (c) standard deviations of the interatomic distance, and (d) deviations in the RRI strength. Each point in (b), (c), and (d) denotes the average of 201 results.

Fig. 5. Time-dependent average fidelities of the CSWAP gate with {δ′=0, T=3.87  μs} and {δ′/2π=1.11  MHz, T=33.28  μs}, respectively. Atomic decay is not considered. Ωcm/2π=12  MHz and ωc/2π=142  MHz, and V1c/2π=V2c/2π=70.98  MHz.

Fig. 6. Rydberg excitation probabilities during the CSWAP gate procedure with different excitation numbers for (a) the resonant RAB with δ′=0 and (b) the modified RAB with δ′/2π=1.11  MHz, respectively. Three-atom initial product state |Ψ0⟩=(0⟩1−|1⟩1)/2⊗(|0⟩2−|1⟩2)/2⊗(|0⟩c−|1⟩c)/2 is specified.

Fig. 7. Infidelities of the CSWAP gates caused by (a) atomic decay with different lifetimes of the Rydberg state, (b) motional dephasing with different atomic temperatures, (c) standard deviations of the distance between the two target atoms, and (d) deviations in the RRI strength between the two target atoms. Each point in (b), (c), and (d) denotes the average of 201 results.