  While spin qubits based on gate-defined quantum dots have demonstrated very
favorable properties for quantum computing, one remaining hurdle is the need to
tune each of them into a good operating regime by adjusting the voltages
applied to electrostatic gates. The automation of these tuning procedures is a
necessary requirement for the operation of a quantum processor based on
gate-defined quantum dots, which is yet to be fully addressed. We present an
algorithm for the automated fine-tuning of quantum dots, and demonstrate its
performance on a semiconductor singlet-triplet qubit in GaAs. The algorithm
employs a Kalman filter based on Bayesian statistics to estimate the gradients
of the target parameters as function of gate voltages, thus learning the system
response. The algorithm's design is focused on the reduction of the number of
required measurements. We experimentally demonstrate the ability to change the
operation regime of the qubit within 3 to 5 iterations, corresponding to 10 to
15 minutes of lab-time.
