  In the quest to achieve scalable quantum information processing technologies,
gradient-based optimal control algorithms (e.g., GRAPE) are broadly used for
implementing high-precision quantum gates, but their performance is often
hindered by deterministic or random errors in the system model and the control
electronics. In this paper, we show that GRAPE can be taught to be more
effective by jointly learning from the design model and the experimental data
obtained from process tomography. The resulting data-driven gradient
optimization algorithm (d-GRAPE) can in principle correct all deterministic
gate errors, with a mild efficiency loss. The d-GRAPE algorithm may become more
powerful with broadband controls that involve a large number of control
parameters, while other algorithms usually slow down due to the increased size
of the search space. These advantages are demonstrated by simulating the
implementation of a two-qubit CNOT gate.
