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It seems to me that the diagonalisation arguments that can be used are only slightly different from a standard one, e.g. such as can be found in these lecture notes about the Baker–Gill–Solovay Theorem (i.e., that there are oracles $A$ for which $\mathsf P^A = \mathsf{NP}^A$ and also oracles $A$ for which $\mathsf P^A \ne \mathsf{NP}^A$...


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I found the answer in these notes: For an ​NP​-complete problem like CircuitSAT, we can be pretty confident that the Grover speedup is real, because no one has found any classical algorithm that’s even slightly better than brute force. On the other hand, for more “structured” ​NP​-complete problems, we ​do​ know exponential-time algorithms that are ...


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Grover Search Algorithm has complexity of O(√(N/n) oracle queries, where N is the total no. of elements in search space & n is the number of acceptable solutions. And is very useful for all problems where we do not know the structure or insight about the problem. Further, even if we know the structure / insight / domain information about the practical / ...


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