Fig. 2: Cavity state tomography with a Kerr-cat qubit.

a Gate sequence (upper) and pulse sequence (lower) for performing characteristic function tomography of a coherent state of amplitude 1 in the storage cavity with the KCQ. The pulse lengths are not to scale. b Experimental (upper) and theoretical (lower) characteristic function tomography of a coherent state with amplitude 1 in the cavity, demonstrating the coherence of the conditional displacement interaction. Note that the characteristic function of a coherent state \(\left\vert \eta \right\rangle\) is given by \({{{\mathcal{C}}}}(\beta )=\exp (-| \beta {| }^{2}/2)\exp (\beta {\eta }^{*}-\eta {\beta }^{*})\), where the second exponential term provides the interference fringes observed in the plot. This expression originates from the geometric phase associated with displacements according to \(D(\eta )D(\beta )=\exp (2iA)D(\beta )D(\eta )\) with \(A={{{\rm{Im}}}}[\eta {\beta }^{*}]\).