For paving the way to novel applications in quantum simulation, computation, and technology, increasingly large quantum systems have to be steered with high precision. It is a typical task amenable to numerical optimal control to turn the time course of pulses, i.e. piecewise constant control amplitudes, iteratively into an optimised shape. Here, we present the first comparative study of optimal control algorithms for a wide range of finite-dimensional applications. We focus on the most commonly used algorithms: grape methods which update all controls concurrently, and Krotov-type methods which do so sequentially. Guidelines for their use are given and open research questions are pointed out. -Moreover we introduce a novel unifying algorithmic framework, dynamo (dynamic optimisation platform) designed to provide the quantum-technology community with a convenient matlab-based toolset for optimal control. In addition, it gives researchers in optimal-control techniques a framework for benchmarking and comparing new proposed algorithms to the state-of-the-art. It allows for a mix-and-match approach with various types of gradients, update and step-size methods as well as subspace choices. Open-source code including examples is made available at http://qlib.info.

No abstract

Both equations of motion take the form of a standard bilinear control system (~) known in classical system and control theory(3) (4) (1) (A, B j Ij = 1,2, ... ,m)Lie = eMat N(