Globally Optimal Quantum Control

Abstract: 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.