Constraint optimization and SU ( N ) quantum control landscapes

Abstract We develop the embedded gradient vector field method, introduced in 8, 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.