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Grover’s search uses an equal superposition of all basis states in the search space both as its starting state and as a part of “reflection about the mean” step. So if you're searching among these 4 states, you need to have an operation that prepares this superposition from the $|0000\rangle$ state to start with, and then your "reflection about the mean&...


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I do not believe there are known quantum algorithms based on amplitude amplification that do not rely on an oracle to flip the phase of the desired state. Popular algorithms using amplitude amplification, including Grover Search, rely on the same idea proposed by Brassard/Hoyer and Grover, requiring an oracle. Technically you do not always need an additional ...


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