Comment on "Are there Traps in Quantum Control Landscapes?"

Physics – Quantum Physics

Scientific paper

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Scientific paper

Many quantum control problems are formulated as a search for an optimal field that maximizes a physical objective. This search is performed over a landscape defined as the objective $J$ as a function of the control field $\epsilon(t)$. Therefore, it is important to investigate the likelihood of encountering traps at suboptimal values of $J$ on the landscape, which possibly could hinder reaching the highest objective value. Pechen and Tannor report [Phys. Rev. Lett. {\bf 106}, 120402 (2011)] special traps under unusual conditions and then claim that "This observation can have profound implications for both theoretical and experimental quantum control studies." We point out here that their special cases of zero and DC (constant) fields with strictly limited systems drawn from a null set of Hamiltonians and controls correspond to extraordinarily demanding conditions which are not broadly applicable. The fundamental issue is not that traps may exist under unusually restricted conditions, but rather their likelihood of being encountered under broad physical circumstances.

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