Fig. 4

iSWAP gate implementation a and phase characterization c. a A 3π pulse on the second transition with zero phase defines an iSWAP quantum gate. Probability as a function of the pulse length of each state knowing that the initial state is |−3/2〉, |−1/2〉, |1/2〉, |3/2〉 from bottom to top, respectively. The states |−3/2〉 and |3/2〉 remain unchanged when the state −|1/2〉 and |1/2〉 are swapped. The 3π rotation ensures the accumulation of a dynamic phase equal to π/2. b and c To probe the phase “i = e^iπ/2” of the state after the iSWAP gate we make use of a three-arm Ramsey interferometry. The peculiarity of the latter is that in order to apply the quantum gate phase manipulation on only one arm of the interferometer, an additional π pulse is considered. Consequently, the π/2 pulses are sent on two different transitions. Probabilities P_p,q of each state as a function of the pulse length when the initial state is |−3/2〉, |−1/2〉, |1/2〉, |3/2〉 from bottom to top, respectively. With this sequence, the blue state probability P_{|−1/2〉, |3/2〉} is maximized when the gate phase is equal to −1 and the green state probability P_{|−1/2〉, |1/2〉} is maximized when the gate phase is equal to i