 Solution

ID: past-exam-of-the-computer-science-course-of-the-university-of-oxford/2020/quantum-information/3/b/iii/solution

For the marked subset,

⟨ e_{0} ∣ A_{1} ⟩ = S_{1} / N

by the same summation of the individual inner products. Consequently

W ∣ A_{1} ⟩ = 2∣ e_{0} ⟩ \frac{S _{1}}{N} - ∣ A_{1} ⟩ = \frac{2 S _{1}}{N} ∣ J ⟩ - ∣ A_{1} ⟩ .

S_{1}

here. Its sign will reverse when this expression is used for the oracle's negative marked component.

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