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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?

glS
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Indeed,quantum control theory studies whether a system is controllable or not. For example, if you have a Hamiltonian, there are several tests that rely on the Lie algebra, such as the Lie-Trotter theorem (including universal controllability) and the commutator formula. These allow you to check whether your system is controllable or not. However, these methods say nothing about efficiency. They are more useful if the system is not controllable. This is because in the case of a non-controllable system, these methods directly tell you that your system is not controllable. However, if you implement a pulse or gate in your system and have used the commutator formula to verify that your system is controllable, you have no indication of what the efficiency of your gate will be. In this case, quantum optimum theory comes into play, and there are several algorithms for finding optimal pulses, such as the CRAB algorithm. Quantum optimal theory looks for the best method/best pulse for your system (such as time optimal pulses, reshaping pulses etc..) whereas quantum control theory checks if the system is controllable or not.(you can find a solution by using quantum control theory but the result has not to be the best solution)

Some useful readings: quantum optimal control, quantum control theory

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