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In the context of quantum control theory, it is common to see references to both quantum control and quantum optimal control (e.g. 0910.2350 or the guide on qutip quantrum control functions). Sometimes it seems like the two terms are used interchangeably, while sometimes they are treated as different things.

For example, from the above link, it seems that quantum optimal control is (unsurprisingly) a special kind of quantum control. It is however not too clear what the exact difference is between the two. For example, are both approaches used to tackle the same classes of problems? Is the only difference in quantum optimal control theory looking for optimal solutions, while quantum control techniques have less strict requirements?

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    $\begingroup$ To be called optimal quantum control, the control strategy (for example a specific NMR pulse sequence) must be optimal for a certain goal, for example to achieve maximum fidelity or minimum time. That's the only difference to (non-optimal) quantum control. $\endgroup$ – pyramids Mar 30 '18 at 11:56
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    $\begingroup$ @pyramids great, that is the answer then! Can you provide some references which make this point explicit? $\endgroup$ – glS Mar 30 '18 at 12:40
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    $\begingroup$ Take the first sentence in the second paragraph under section 3.2 "Optimal control" from your own reference (0910.2350): "In the optimal control approach, the quantum control problem can be formulated as a problem of seeking a set of admissible controls satisfying the system dynamic equations and simultaneously minimizing a cost functional. " $\endgroup$ – pyramids Mar 30 '18 at 12:58
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    $\begingroup$ @pyramids I still do not understand whether quantum optimal control uses different methodologies, or whether one calls it "optimal control" only when for some reason it is possible to prove that the found strategy is indeed optimal $\endgroup$ – glS Mar 30 '18 at 13:18
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    $\begingroup$ I think it is both (using different methodologies AND called "optimal control" because its results are optimal in a certain sense). But I'm not enough of an expert to be comfortable answering it as such. $\endgroup$ – pyramids Mar 30 '18 at 13:26

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