Constraint optimization and SU(N) quantum control landscapes

We develop the embedded gradient vector field method, introduced in [8] and [9], for case of special unitary group $\mathcal{SU}(N)$ regarded as a constraint submanifold $\mathcal{U}(N)$. The optimization problem associated to trace fidelity cost function defined on that appears context quantum control landscapes is completely solved using method. prove $N\geq 5$, landscape not $\mathcal{SU}(N)$-trap free, there are always kinematic local extrema global extrema.