Consider a variant of the SAT problem when for a given boolean formula, we would like to find an assignment that is also in the support of a given quantum state.
Formally let $ A $ be a set of the binary strings at length $ n $ and consider the superposition over the elemens $ |\psi\rangle = \frac{1}{\sqrt{|A|}}\sum_{x \in A}{|x \rangle} $. Given $ |\psi \rangle $, without its classical description, Is that possible to perform the operation $ I - 2| \psi \rangle \langle \psi | $ ? And if so ,how to construct that circuit, and what will be its complexity?
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