  In this work, we develop a supervised learning model for implementing robust
quantum control in composite-pulse systems, where the training parameters can
be either phases, detunings, or Rabi frequencies. This model exhibits great
resistance to all kinds of systematic errors, including single, multiple, and
time-varying errors. We propose a modified gradient descent algorithm for
adapting the training of phase parameters, and show that different sampling
methods result in different robust performances. In particular, there is a
trade-off between high fidelity and robustness for a given number of training
parameters, and both can be simultaneously enhanced by increasing the number of
training parameters (pulses). For its applications, we demonstrate that the
current model can be used for achieving high-fidelity arbitrary superposition
states and universal quantum gates in a robust manner. This work provides a
highly efficient learning model for fault-tolerant quantum computation by
training various physical parameters.
