  Robust control design for quantum unitary transformations has been recognized
as a fundamental and challenging task in the development of quantum information
processing due to unavoidable decoherence or operational errors in the
experimental implementation of quantum operations. In this paper, we extend the
systematic methodology of sampling-based learning control (SLC) approach with a
gradient flow algorithm for the design of robust quantum unitary
transformations. The SLC approach first uses a "training" process to find an
optimal control strategy robust against certain ranges of uncertainties. Then a
number of randomly selected samples are tested and the performance is evaluated
according to their average fidelity. The approach is applied to three typical
examples of robust quantum transformation problems including robust quantum
transformations in a three-level quantum system, in a superconducting quantum
circuit, and in a spin chain system. Numerical results demonstrate the
effectiveness of the SLC approach and show its potential applications in
various implementation of quantum unitary transformations.
