Developing quantum optimal control methods is at the interface of theory and experiment. The constructive results have been successfully applied, e.g., in NV centres in diamond, coupled Josephson elements, cavity grids in QED as well as in ion traps.
Given an experimental set-up, which quantum states can be reached from a given initial state in closed and open systems? Which systems can form universal quantum processors? What are the requirements of a quantum system A to simulate another system B? ---
In the theory group, we aim at a unifying framework of quantum systems theory to answer these questions in a constructive way that helps engineering quantum devices in concrete experimental set-ups (of NV centres, Josephson elements, cavity grids etc). At the same time we use the mathematical rigour and geometric intuition of Lie theory (Fig.1), where, e.g., group (or semigroup) orbits determine reachable sets in closed (or open) systems.
Among the recent achievements, there is an easy-to-use algorithmic platform for numerical optimal quantum control (DYNAMO), first necessary and sufficient symmetry condition for full controllability, a comprehensive symmetry characteri-sation of spin systems, fermionic & bosonic systems, first characterisation of Markovian open quantum systems as Lie semigroups, first parallelized optimal-control based quantum compiler, and first exploitation of switchable noise enabling arbitrary quantum state transfer (Fig.2).
Other recent results include optimal-control based high-fidelity gates for entangling NV centres in diamond as well as optimal-control tools for error-corrected single-shot readout in NV centres (Fig.3) for quantum memories.