Abstract
The optimal creation of a targeted unitary transformation is considered under the influence of an external control field. The controlled dynamics produces the unitary transformation and the goal is to seek a control field that minimizes the cost . The optimal control landscape is the cost as a functional of the control field. For a controllable quantum system with states and without restrictions placed on the controls, the optimal control landscape is shown to have extrema with possible distinct values, where the desired transformation at is a minimum and the maximum value is at . The other distinct extrema values of are saddle points. The results of this analysis have significance for the practical construction of unitary transformations.
- Received 14 October 2003
DOI:https://doi.org/10.1103/PhysRevA.72.052337
©2005 American Physical Society