The optimal creation of a targeted unitary transformation W is considered under the influence of an external control field. The controlled dynamics produces the unitary transformation U and the goal is to seek a control field that minimizes the cost JU. The optimal control landscape is the cost J as a functional of the control field. For a controllable quantum system with N states and without restrictions placed on the controls, the optimal control landscape is shown to have extrema with N+1 possible distinct values, where the desired transformation at U=W is a minimum and the maximum value is at UW. The other distinct N1 extrema values of J are saddle points. The results of this analysis have significance for the practical construction of unitary transformations.
|Physical Review A - Atomic, Molecular, and Optical Physics
|Published - Nov 1 2005
All Science Journal Classification (ASJC) codes
- Atomic and Molecular Physics, and Optics