  The precise and automated calibration of quantum gates is a key requirement
for building a reliable quantum computer. Unlike errors from decoherence,
systematic errors can in principle be completely removed by tuning experimental
parameters. Here, we present an iterative calibration routine which can remove
systematic gate errors on several qubits. A central ingredient is the
construction of pulse sequences that extract independent indicators for every
linearly independent error generator. We show that decoherence errors only
moderately degrade the achievable infidelity due to systematic errors.
Furthermore, we investigate the convergence properties of our approach by
performing simulations for a specific qubit encoded in a pair of spins. Our
results indicate that a gate set with 230 gate parameters can be calibrated in
about ten iterations, after which incoherent errors limit the gate fidelity.
