Structure of optimal policies in quantum control
Abstract
Using the Pontryagin maximum principle, the generic structure of optimal policies is deduced for typical quantum control tasks involving coherent lasers, magnetic fields and reservoir engineering. In addition, the periodic optimization is considered for the first time in view of prospective applications. We proved that nearly all optimal policies are actively constrained by technical bounds on control parameter but reduce to entirely bang-bang sequences only in special cases, such as the environmental control by random collisions. The results allow to arguably refute two generally accepted and concurring conjectures regarding the structure of optimal controls.
Cite
@article{arxiv.1709.09423,
title = {Structure of optimal policies in quantum control},
author = {Dmitry V. Zhdanov and Tamar Seideman},
journal= {arXiv preprint arXiv:1709.09423},
year = {2018}
}
Comments
The following major changes were made compared to the previous version. 1) The original literature review (which dates back to 2009-2012) is updated. 2) Incorrect theorem 2 is removed. 3) Mistakes in treating branch points in the proof of theorem 1 are fixed. 4) The detailed discussions on the physical meaning of each formal mathematical result are added. 12 pages, 3 figures, 2 tables