Compact machines quantum entangler8/11/2023 ![]() ![]() 3, including corresponding software development, for which we highlight publicly available software packages. We review progress on these methodologies in Sect. ![]() These can be classified into analytical vs numerical approaches and the latter into approaches evaluating only the target functional (gradient-free methods) and those based on variational calculus such as the Pontryagin maximum principle (PMP). Section 3 presents the current state of the art in quantum optimal control methodologies. We provide a brief summary of basic definitions together with a review of recent progress towards these goals and open questions in Sect. Such a theory also forms the basis for the derivation of optimal control strategies by ensuring the well-posedness of problems and existence of solutions. For training future quantum engineers, such a framework is yet to emerge.Ī rigorous and unified quantum systems theory is therefore among the current overarching research goals - it will interface not only theory and experiment but teaching programmes in quantum physics and engineering as well. For classical (mostly linear) systems, a rigorous systems and control theoretical framework exists and is core to the teaching programme of every engineer. For example: To which extent can a quantum system be (i) controlled, (ii) observed (sensed or tomographed), (iii) stabilised, etc. Under this specific perspective, quantum optimal control sets out to answer typical engineering questions. Here we provide an update to Ref. , focussing on progress in QOCT and its applications relevant to the development of quantum technologies. The next challenge for QOCT will be to become an integral part of practical quantum devices or, in other words, of practical quantum engineering. Conversely, QOCT has matured to the stage that it is nowadays readily used in experiments. It is this very feature that makes them an ideal testbed for QOCT, compared to other fields where QOCT has been used, such as chemical reaction dynamics. Quantum technologies require comparatively well-isolated and well-characterized quantum systems. Over the past few years, QOCT has become an integral part of the emerging quantum technologies , testifying to the fact that it is control that turns scientific knowledge into technology : If the superposition principle is the core feature of quantum mechanics, quantum control is the superposition principle at work. Quantum processes are no exception to this general framework, but certain aspects of control theory must be adapted to take into account the particularities of the quantum world. The main goal is for the dynamical system under study to operate optimally and reach its physical limits while satisfying constraints imposed by the devices at hand. It builds on control theory in more general terms which evolves at the interface between applied mathematics, engineering, and physics and concerns the manipulation of dynamical processes to realize specific tasks. Quantum optimal control theory (QOCT) refers to a set of methods to devise and implement shapes of external electromagnetic fields that manipulate quantum dynamical processes at the atomic or molecular scale in the best way possible .
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