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Take for example a variational algorithm which has a classical optimization part and a quantum sampling part. In principle, the quantum part can be simulated by another classical computer given sufficient amount of resources ("exponential" in general). Now, if the hybrid algorithm performs better than any known classical algorithm, does this imply that the quantum part of the algorithm that performs sampling from a quantum distribution can show this "quantum advantage" on its own (In the same sense as, say, the boson sampling)?

If this is so, should not the efforts in the variational algorithms than be focused entirely on the quantum sampling part? Or the whole point is to use the classical optimization to drive the quantum circuit in a regime where its sampling can not be efficiently reproduced classicaly?

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