Tomography is the main method used for measuring the fidelity of an experimentally implemented quantum process. However, it is a very inefficient method since the number of measurements as well as the time needed for the data post-processing scale exponentially with the number of qubits. With the ongoing experimental progress and growth in system size, quantum process tomography will soon become infeasible in state-of-the art experiments. Nevertheless, the task of certifying how an experimental implementation of a process compares to the corresponding ideal process is crucial in any quantum system. A more practical approach to determine the fidelity of an experimental quantum
process has recently been proposed, where the experimental data is compared directly to an ideal process using Monte Carlo sampling. The significant advantage of Monte Carlo process certification is that the number of measurements needed to be performed to obtain some desired accuracy depends only polynomially rather than exponentially on said accuray and not on the size of the system. We realized an experimental implementation of this scheme in a circuit quantum electrodynamics setup  to determine the fidelity of two qubit gates, such as the CPHASE- and the CNOT-gate, and three qubit gates, such as the Toffoli gate and two sequential CPHASE-gates. By comparing the obtained fidelities with the ones obtained from quantum process tomography, we find that all estimates are consistent, while Monte Carlo process certification gives more accurate estimates of the fidelity with fewer measurements.
L. Steffen, M. P. da Silva, A. Fedorov, M. Baur, and A. Wallraff, Physical Review Letters 108, 260506