Fig. 1. The optical drivings and atomic transition linkage structure of atom-laser interaction under study. The two driving lasers ω0,ω1 form a Λ-like transition pattern on a single qubit atom. The detailed transition linkage pattern with respect to the two-qubit basis states is shown in the right, which can also be interpreted by the Morris-Shore transform [40].

Fig. 2. Numerical simulation of Rydberg blockade SWAP gate with hybrid modulation, for idealized Rydberg blockade effect. (a) Waveforms of modulation. (b) Populations of wave functions corresponding to (a). (c) Phases of wave functions corresponding to (a). The calculated gate errors are less than 10−4.

Fig. 3. Numerical simulation of Rydberg blockade SWAP gate with only amplitude modulation under off-resonant drivings, for idealized Rydberg blockade effect. (a) Waveforms of modulation. (b) Populations of wave functions corresponding to (a). (c) Phases of wave functions corresponding to (a). The calculated gate errors are less than 10−4.

Fig. 4. Numerical simulation of gate errors with respect to changes of Rabi frequencies and detunings. (a) Varying ratios of Ω0,Ω1. (b) Adding constant shifts to the detunings.

Fig. 5. Numerical simulation of gate errors with respect to changes of Rydberg dipole-dipole interaction strength. (a) Estimated performance of waveforms designed for B=∞. (b) Estimated performance of waveforms designed for B=2π×125  MHz.

Fig. 6. Comparison of Rydberg blockade SWAP gates via one-photon ground-Rydberg transition (on the left) and two-photon transition (on the right).

Fig. 7. Numerical simulation of Rydberg blockade SWAP gate with only amplitude modulation under almost-resonant drivings. (a) Waveforms of modulation. (b) Populations of wave functions corresponding to (a). (c) Phases of wave functions corresponding to (a). The calculated gate errors are less than 10−4.

Fig. 8. Numerical simulation of Rydberg blockade SWAP gate with only amplitude modulation under off-resonant drivings. (a) Waveforms of modulation, in particular, the Rabi frequency amplitudes of Ω0,Ω1, are identical. (b) Populations of wave functions corresponding to (a). (c) Phases of wave functions corresponding to (a). The calculated gate errors are less than 10−4.

Table 1. Two Formats of SWAP Gate under Consideration^a