Organizer: Jacqueline Brendel, CROSSING
In this talk I will try to demonstrate the use of Lie-algebraic concepts in the quantum control of interacting qubit arrays, with examples from both operator (gate)- and state control. I will start from the basics of quantum control and briefly review the Lie-algebraic underpinnings of the concept of complete controllability. I will then specialize to qubit arrays with Heisenberg-type interactions, summarizing the conditions for their complete controllability and showing a few examples of quantum-gate realization.
The second part of the talk will be devoted to a rather unconventional use of Lie-algebraic concepts within a dynamical-symmetry-based approach to the deterministic conversion between W- and Greenberger-Horne-Zeilinger (three-qubit) states. The underlying physical system consists of three neutral atoms subject to several external laser pulses, where the atomic ground state and a highly-excited Rydberg state play the role of the two relevant logical qubit states. In particular, it will be demonstrated that our approach -- based on the explicit use of the dynamical symmetry so(4) of the system -- allows a much more time-efficient and robust state conversion than conventional quantum-control methods.