Past exam of the computer science course of the University of Oxford / 2020 / Quantum information / 3 / b / ii

Table of contents
- Solution ii

Solution

Summing part (i) over the

S_{0}

unmarked indices gives

⟨ e_{0} ∣ A_{0} ⟩ = S_{0} / N

. The Grover diffusion operator therefore acts as

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

This is an identity for an unnormalized subset sum; it does not require replacing its norm by one.

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