Approximate Dynamics Lead to Optimal Control: Efficient Calculation of Exact Derivatives
Jesper Hasseriis Mohr Jensen, Frederik Møller, Jens Jakob Sørensen, Jacob Friis Sherson · arXiv (Cornell University) · 2020
We discuss the importance of accurate derivatives for efficiently locally traversing and converging in optimization landscapes. In the context of quantum optimal control, we find that the feasibility of meeting this central requirement critically depends on the choice of propagation scheme and problem representation by deriving analytically exact control derivatives (gradient and Hessian). Even when exact propagation is sufficiently cheap, we find, perhaps surprisingly, that it is always much more efficient to optimize the (appropriately) approximate propagators: in a certain sense, approximations in the dynamics is traded off for significant complexity reductions in the exact derivative calculations. We quantitatively verify these claims for two concrete problems of increasing Hilbert space dimensionality and find that the best schemes obtain unit fidelity to machine precision, whereas the results for other schemes are separated consistently by orders of magnitude in computation time and in worst case 10 orders of magnitude in achievable fidelity. Since these gaps will continually increase with system size and complexity, this methodology unlocks efficient optimization of many-body dynamics operating in the unprecedented high-fidelity regime which will be published separately.