Past exam of the mathematics course of the University of Cambridge / 2021 / iii / Paper 324 / 3 / a / i

Table of contents
- Solution i

Solution

Let

P_{G}

project onto the good subspace and write

∣ ψ ⟩ = sin θ ∣ ψ_{G} ⟩ + cos θ ∣ ψ_{B} ⟩ .

The amplitude amplification theorem says that alternating the reflection

I - 2 P_{G}

with the reflection

2∣ ψ ⟩ ⟨ ψ ∣ - I

rotates this two-dimensional plane by

2 θ

. After

j

amplification iterations the good probability is

sin^{2} ((2 j + 1) θ) .

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