We develop the embedded gradient vector field method, introduced in [8] and [9], for the case of the special unitary group SU(N) regarded as a constraint submanifold of the unitary group U(N). The optimization problem associated to the trace fidelity cost function defined on SU(N) that appears in the context of SU(N) quantum control landscapes is completely solved using the embedded gradient vector field method. We prove that for N≥5, the landscape is not SU(N)-trap free, there are always kinematic local extrema that are not global extrema.
Cite
@article{arxiv.2103.11132,
title = {Constraint optimization and $\mathcal{SU}(N)$ quantum control landscapes},
author = {Petre Birtea and Ioan Casu and Dan Comanescu},
journal= {arXiv preprint arXiv:2103.11132},
year = {2022}
}