Supercharging Quantum Optimal Control with Efficient Automatic Differentiation*

Numerical optimal control theory has proven an essential tool for achieving a core requirement of both quantum information and quantum metrology: the creation of particular non-classical states, respectively of quantum processes that produce such states. Finding the most general solutions to the relevant control problems would require the direct optimization of, e.g., measures for entanglement, spin squeezing, or the quantum Fisher information. To date, such measures have generally not been considered suitable for optimal control due to the lack of an analytic derivative. We show how the use of automatic differentiation (AD) allows to directly optimize these non-classical measures, and virtually any other functional.  We further show how AD can be \emph{combined} with existing numerical techniques of quantum control to allow the formulation of a ``semi-automatic differentiation'' approach that eliminates the often exponential overhead associated with previous attempts to use AD in quantum control. Thus, our methods scale to large Hilbert space dimensions and open quantum systems. We illustrate the use of the technique for the optimization of entangling quantum gates and the creation of spin-squeezed states.

The proposed methods are realized in a new open-source software framework for numerical quantum control, QuantumControl.jl, written in the Julia language. Designed for extensibility and performance, the framework consists of a collection of packages that implement a wide variety of control algorithms, including Krotov's method, several variations of gradient-ascent methods (GRAPE, GROUP, GOAT), and gradient-free methods such a CRAB. These are enhanced with methods of automatic differentiation for unparalleled flexibility.