Multiple classical noise mitigation by multiobjective robust quantum optimal control

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 to 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 classical stochastic 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 robust entangling gate in a 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.