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This is spawned from a comment at the answer to one of my previous questions.

Someone suggested to me that claiming the following statement might be NP-hard. Could anyone please help me to figure out whether it is true?

If the eigenstate of the initial Hamiltonian are superposition of all possible states we cannot perform the adiabatic evolution with a diagonal Hamiltonian as the problem Hamiltonian.

Thanks in advance!

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Statements aren't NP-hard. Problems (a family of related yes-or-no questions) can be, however. If you only mean to ask whether or not your statement is true, you should remove the reference to NP-hardness. – Niel de Beaudrap Nov 4 '13 at 18:32

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