Control theories are at the heart of the effort to turn scientific knowledge into technology. The scope of control theory is to find a control law for accomplishing a certain task, e.g. driving a system from some initial state to a final target state under a set of constraints, or optimizing the performance of some quantum device.
Typically, external electromagnetic fields are applied in order to execute the control law. The two main goals of quantum control theory are: (i) to determine whether, and under what conditions, a quantum system is controllable, i.e. if a target state or a process outcome can be reached; and (ii) to develop systematic and robust methods for manipulating quantum systems and processes at the atomic and molecular level.
While quantum control theories are elementary to quantum state preparation and to achieving desired quantum protocols, the methods are still limited to closed systems that follow a unitary evolution. Because all quantum systems are subject to noise that may arise from parasitic couplings to the environment or from sensitivities in the control fields, we are interested in developing systematic methods that minimize these effects or even utilize them to obtain a control law.
Another challenge control theory is facing are the scaling of the methods with the particle number. For many-body system the Hilbert space of the system grows exponentially with particle number and control over long range interaction becomes difficult both theoretically and experimentally.