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Figure 1 | EPJ Quantum Technology

Figure 1

From: Hybrid optimization schemes for quantum control

Figure 1

Population dynamics under guess and optimized pulse. The figure shows the population dynamics of the initial state \(\vert \Psi \rangle(t=0) = \vert 00 \rangle \) for the guess pulse, panels (a)-(d), and the pulse obtained from direct optimization of the \(J_{T}^{\mathrm {geo}}\) functional, panels (e)-(h). In panels (a), (e), expectation value \(\langle n \rangle\) of the cavity excitation, plus-minus the standard deviation \(\sigma_{n}\). In panels (b), (f), and (c), (g), expectation values and standard deviations for the excitation of the right and left qubit, respectively. In panels (d), (h), population in the state \(\vert 00 \rangle\). The pulse shape (normalized by the peak amplitude \(E_{0} = 300\mbox{ MHz}\), cf. Figure 2) is shown in the background of panels (d), (h). The guess pulse implements a geometric phase gate with a gate error of \(\varepsilon _{\mathrm {avg}}= 8.3 \times10^{-2}\), with concurrence error \(\varepsilon _{C}= 1.9 \times10^{-1}\) and population loss from the logical subspace \(\varepsilon _{\mathrm {pop}}= 5.9 \times10^{-3}\). The optimized pulse decreases the gate error to \(\varepsilon _{\mathrm {avg}}= 1.4 \times10^{-4}\), with \(\varepsilon _{C}= 1.8 \times10^{-6}\) and \(\varepsilon _{\mathrm {pop}}= 1.4 \times10^{-4}\), see Table 2.

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