Optimal Quantum Control

In this talk I will present a framework to prepare quantum states and gates which are insensitive to any kind of weak perturbation by using optimal control. To this end, I will show that the fidelity susceptibility, which quantifies the perturbative error to leading order and corresponds to the quantum Fisher Information of the dynamical process, can be expressed in superoperator form. This allows us to numerically search for control pulses which are robust to any class of systematic unknown errors by minimizing the norm of a suitably-defined dynamical robustness superoperator. We show that the proposed optimal control protocol is equivalent to searching for a sequence of unitaries that mimics the first-order moments of the Haar distribution, i.e. it constitutes a 1-design. This connection, in turn, demonstrates the existence of universally robust quantum control protocols for any Hilbert space dimension. I will illustrate the power of this framework by showing its application to the generation of robust one- and two-qubit gates, and discussing how generalized robustness requirements can be built into the formalism. If time allows, I will talk about how to apply this formalism to problems related to quantum sensing and quantum computing, and how this can be connected to quantum chaos.