Figure 5

(a) Time evolution of the dc applied electric fields \(\Delta E_{z,1}(t)\) and \(\Delta E_{z,2}(t)\) and of the mean values of the operators \(\sigma ^{\mathrm{ff}}_{z,(1,2)}\), \(\sigma ^{id}_{z,(1,2)}\) and the charge operator \(|e\rangle \langle e|-|g\rangle \langle g|\) for the two flip-flop qubits during the evolution of the \(\sqrt{\mathit{iSWAP}}\) gate for the initial state \(|\psi _{0}\rangle =|\psi _{0_{1}}\rangle \otimes |\psi _{0_{2}} \rangle \) with \(|\psi _{0_{1}}\rangle =|1\rangle \) and \(|\psi _{0_{2}}\rangle =|0\rangle \). (b) Bloch sphere representation of the \(\sqrt{\mathit{iSWAP}}\) gate. The blue (yellow) arrow represents the initial (final) state for \(Q_{1}\) (left) and \(Q_{2}\) (right) in the rotating frame