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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.
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Birtea et al. (2022) studied this question.
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