  High-quality control is a fundamental requirement for quantum computation,
but practically it is often hampered by the presence of various types of
noises, which can be static or time-dependent. In many realistic scenarios,
multiple noise sources coexist, and their resulting noise effects need be
corrected to a sufficient order, posing significant challenges for the design
of effective robust control methods. Here, we explore the method of robust
quantum optimal control to generally tackle the problem of resisting multiple
noises from a complicated noise environment. Specifically, we confine our
analysis to unitary noises that can be described by classical noise models.
This method employs a gradient-based multiobjective optimization algorithm to
maximize the control figure of merit, and meanwhile to minimize the
perturbative effects of the noises that are allowed for. To verify its
effectiveness, we apply this method to a number of examples, including roubust
entangling gate in trapped ion system and robust controlled-Z gate in
superconducting qubits, under commonly encountered static and time-dependent
noises. Our simulation results reveal that robust optimal control can find
smooth, robust pulses that can simultaneously resist several noises and thus
achieve high-fidelity gates. Therefore, we expect that this method will find
wide applications on current noisy quantum computing devices.
