  Optimization methods for constrained quantum control problems power quantum
technologies. Such control problems are notoriously difficult because they are
non-convex and plagued with local extrema. Current optimization methods must be
repeated many times to find good solutions, each time requiring many
simulations of the system. Here we present Quantum Control via Polynomial
Optimization (QCPOp), a method that eliminates this problem by directly finding
globally optimal solutions. This remarkable ability is due to global
optimization methods recently developed for polynomial functions. We
demonstrate the tremendous improvement over current state-of-the-art methods
using a number of non-trivial examples. Global optimization also allows QCPOp
to find the simplest control solutions. Since QCPOp is able to reveal the
optimum performance of quantum control with high confidence, we expect that it
will not only enhance the utility of such control but provide a key tool for
determining the limits of quantum technologies.
