Figure 3

Population dynamics under (pre-optimized) guess and optimized pulse. The figure follows the conventions of Figure 1. Panels (a)-(d) show the dynamics resulting from a simplex optimization, see text for details. The resulting pulse is the starting point for a continued optimization using Krotov’s method with the \(J_{T}^{\mathrm {sm}}\) functional. The optimized dynamics are shown in panels (e)-(h). The pulse amplitude indicated in the background of panels (d), (h) is normalized to the peak amplitude of \(E_{0} \approx 400\mbox{ MHz}\). The simplex-optimized pulse implements a geometric phase gate with a gate error of \(\varepsilon _{\mathrm {avg}}= 1.4 \times10^{-2}\), with \(\varepsilon _{C}= 2.0 \times10^{-2}\) and \(\varepsilon _{\mathrm {pop}}= 1.4 \times10^{-2}\). The continued optimization decreases the gate error to \(\varepsilon _{\mathrm {avg}}= 3.4 \times10^{-5}\), with \(\varepsilon _{C}= 5.1 \times10^{-5}\) and \(\varepsilon _{\mathrm {pop}}= 1.1 \times10^{-5}\), see Table 2.