Quantum Optimal Control
​
Quantum Optimal Control is the art of steering the dynamics of a quantum system so that it undergoes some desired quantum operation.

While the field started in the 1970s by engineering chemical reactions of molecules, it has gained increasing interest during the last decade in the emerging field of quantum technology in general and quantum information processing in particular. The control objective, i.e. the desired quantum operation of the system, in this context can be the transfer of a quantum state into another, e.g. to prepare a more
interesting entangled state starting from an experimentally more easily accessible state. Another very important example is the design of quantum gate operations, i.e. unitary operations on a set of computational basis states that encodes a logical operation on these states. The control knobs to engineer these operations usually are external electro-magnetic fields that allow to manipulate the dynamics of the system, such as trap potentials or lasers driving transitions between the internal states of the system. By varying the laser power over time in a sophisticated way as resulting from numerical optimization, quantum operations can be performed at high fidelity also in a range not accessible by analytically designed pulse shapes.

The QDAB group is interested in Quantum Optimal Control mainly as a tool to realize quantum operations in experiments, where the contribution of the group is the design of the control pulses that are developed together with our experimentalist collaborators. The control pulses are calculated by numerical optimization algorithms especially designed and adapted for the precise problem. This allows also to implement the special needs of the experiment and technical equipment of the laboratory, such as constraints on the power and bandwidth of the pulses, along with imperfect arbitrary wave generators. A very established collaboration in Florence exists with the atom chip lab of Francesco S. Cataliotti.

Apart from applying Quantum Optimal Control to experiments we are also interested in developing the control algorithms themselves. Crucial points of interest are the question how experimental constraints and environmental noise can be considered in the control algorithms without too much hindering the ability of the algorithms to find the optimal solution. A current point of our interest that is also linked to our research on „Noisy Quantum Systems“ is the robustness of controlled operations against noise. While the operations are
usually quite robust against a small amount of noise, as also observed experimentally, the question of complete controllability of noisy quantum system is still open. Also memory effects in the noise could be used to reduce the damaging effect of the noise by adapting the controlled dynamic to the correlation length of the noise.