Experimental Bayesian Calibration of Trapped-Ion Entangling Operations

The performance of quantum gate operations is experimentally determined by how correctly 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 multidimensional 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 two-qubit Mølmer-Sørensen entangling gate operation in a trapped-ion quantum information processor. The protocol exploits Bayesian parameter estimation methods that include a stopping criterion based on a desired gate infidelity. We experimentally demonstrate a tune-up procedure that leads to a residual median gate infidelity due to miscalibration of 1.3(1)×10^{−3}, requiring 1200±500 experimental cycles, while completing the entire gate calibration procedure in less than one minute, which provides a significant speedup over commonly used manual tune-up routines. This approach is applicable to other quantum information processor architectures with known or sufficiently characterized theoretical models.