Exploring the transition-probability-control landscape of open quantum systems: Application to a two-level case

This paper explores the state-to-state transition-probability-control landscape for n-level open quantum systems governed by the Lindblad equation. For generic two-level systems, we show analytically that the control landscape does not possess critical points in the space of square-integrable control fields. Numerical simulations show that for a given target state the transition probability reaches its highest value at a particular finite time, and the corresponding control contains temporal subpulses, similar to that for the time optimal control of analogous closed quantum systems with unbounded controls.