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Rather than throwing a negative sign in front of the basis states \ket{11}, \ket{10}, and \ket{01}, and leaving \ket{00} unchanged, we can do the opposite. Adding a negative sign in front of \ket{00} and leaving all other basis states unchanged has the same effect, except for a negative sign. But of course that negative sign just goes along for the ride through any other transformations and makes no difference when we make a measurement. So we can replace these three sets of gates with a single set of gates that negates the coefficient in front of \ket{0}. With this modification we should still find the system to be in the state \ket{x*} upon measurement, in this case \ket{11}. This is a more efficient implementation of the Grover Diffusion Operator.

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