A Brief on Quantum Systems Theory and Control Engineering
Thomas Schulte‐Herbrüggen, Robert Zeier, Michael Keyl, Gunther Dirr · 2016
This chapter illustrates a unified frame of quantum systems theory in view of control engineering. In the chapter, controllability criteria is shifted from the well-known Lie-algebra rank condition to symmetry conditions that are easy to check yet rigorously rooted in the branching diagrams for simple subalgebras of Su(N). The chapter applies quantum systems theory for bilinear control systems of closed and open systems. It then shows how the emerging quantum systems theory links to many applications in quantum simulation and control without sacrificing mathematical rigor. The chapter points out how gradient flows form the missing link to numerical optimal control algorithms for explicit steerings (control amplitudes) for manipulating closed and open (Markovian and non-Markovian) systems in finite dimensions. Finally, it gives an outlook on a Lie picture of systems and control theory in infinite dimensions and its application to Jaynes-Cummings systems, for example, like atoms in a cavity.