Figure 3

(a) Initial-state-specified fidelity at the time \(T = 4\pi /\Omega _{\mathrm{0m}}\) for executing the SWAP gate \({\hat{U}}_{\text{SWAP}}\) with different values of \(\omega _{0}/\Omega _{\mathrm{0m}}\) and \(\omega _{1}/\Omega _{\mathrm{0m}}\) with \(\Omega _{\mathrm{1m}}=2\sqrt {2}\omega _{0}\) and \(V=\omega _{1}\). For clarity, we roughly plot contour lines of 0.99 (solid-blue) and 0.995 (dashed-red). (b) Initial-state-specified fidelity and populations of related states with evolution of time. \(\Omega _{\mathrm{0m}}/2\pi =1\text{ MHz}\), \(\omega _{0}/2\pi =2.5\text{ MHz}\), and \(d=4.8~\mu{\mathrm{m}}\) (\(C_{6}/2 \pi =858.4~{\text{GHz}}\cdot \mu{\mathrm{m}}^{6}\))