Abstract
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.
Subject
General Physics and Astronomy,Mathematical Physics,Modeling and Simulation,Statistics and Probability,Statistical and Nonlinear Physics
Cited by
2 articles.
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