Observing Target-Qubit Detuning error

To measure the dynamics of the CR gate, we perform Hamiltonian tomography. This experiment involves driving the CR interaction and performing state tomography on the target qubit, thus allowing one to measure the Bloch dynamics of the target qubit, conditioned on the control qubit state. We run this experiment when with the control qubit in both the ground- and excited-state. Plotting the x-z plane of the target qubit, one can observe a tilt away of the x-axis, corresponding to a Z-rotation, that is not conditioned on the control qubit state. This IZ term in the Hamiltonian is an example of an error induced by the higher levels of the transmon.