Experimental Bayesian calibration of trapped ion entangling operations

The performance of quantum gate operations is experimentally determined by how correct operational parameters can be determined and set, and how stable these parameters can be maintained. In addition, gates acting on different sets of qubits require unique sets of control parameters. Thus, an efficient multi-dimensional parameter estimation procedure is crucial to calibrate even medium sized quantum processors. Here, we develop and characterize an efficient calibration protocol to automatically estimate and adjust experimental parameters of the widely used Molmer-Sorensen entangling gate operation in a trapped ion quantum information processor. The protocol exploits Bayesian parameter estimation methods which includes a stopping criterion based on a desired gate infidelity. We experimentally demonstrate a median gate infidelity of $1.3(1)\cdot10^{-3}$, requiring only $1200\pm500$ experimental cycles, while completing the entire gate calibration procedure in less than one minute. This approach is applicable to other quantum information processor architectures with known or sufficiently characterized theoretical models.