In this talk, we present continuous-adjoint sensitivity methods for hybrid differential equations (i.e., ordinary or stochastic differential equations with callbacks) modeling explicit and implicit events. The methods are implemented in the SciMLSensitivity.jl package. As a concrete example, we consider the sensitivity analysis of dosing times in pharmacokinetic models. We discuss different options for the automatic differentiation backend.

Feedback control policies for quantum systems often lack performance targets and certificates of optimality. Here, we will show how bounds on the best possible control performance are readily computable for a wide range of quantum control problems by means of convex optimization using Julia's optimization ecosystem. We discuss how these bounds provide targets and certificates to improve the design of quantum feedback controllers.