  We apply the method of compressed sensing (CS) quantum process tomography
(QPT) to characterize quantum gates based on superconducting Xmon and phase
qubits. Using experimental data for a two-qubit controlled-Z gate, we obtain an
estimate for the process matrix $\chi$ with reasonably high fidelity compared
to full QPT, but using a significantly reduced set of initial states and
measurement configurations. We show that the CS method still works when the
amount of used data is so small that the standard QPT would have an
underdetermined system of equations. We also apply the CS method to the
analysis of the three-qubit Toffoli gate with numerically added noise, and
similarly show that the method works well for a substantially reduced set of
data. For the CS calculations we use two different bases in which the process
matrix $\chi$ is approximately sparse, and show that the resulting estimates of
the process matrices match each ther with reasonably high fidelity. For both
two-qubit and three-qubit gates, we characterize the quantum process by not
only its process matrix and fidelity, but also by the corresponding standard
deviation, defined via variation of the state fidelity for different initial
states.
