  To be useful for quantum computation, gate operations must be maintained at
high fidelities over long periods of time. In addition to decoherence, slow
drifts in control hardware leads to inaccurate gates, causing the quality of
operation of as-built quantum computers to vary over time. Here, we demonstrate
a data-driven approach to stabilized control, combining extremum-seeking
control (ESC) with direct randomized benchmarking (DRB) to stabilize two-qubit
gates under unknown control parameter fluctuations. As a case study, we
consider these control strategies in the context of a trapped ion quantum
computer using physically-realistic simulation. We then experimentally
demonstrate this control strategy on a state-of-the-art, commercial trapped-ion
quantum computer.
