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arXiv · 2103.11132

Constraint optimization and $\mathcal{SU}(N)$ quantum control landscapes

Petre Birtea·Ioan Casu·Dan Comanescu
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Abstract

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

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Petre Birtea, Ioan Casu, Dan Comanescu. 2021-03-20. Constraint optimization and $\mathcal{SU}(N)$ quantum control landscapes. https://doi.org/10.1088/1751-8121%2Fac5189

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