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

Let $P_G$ project onto the good subspace and writeThe amplitude amplification theorem says that alternating the reflection $I-2P_G$ with the reflection $2|\psi ⟩⟨\psi |-I$ rotates this two-dimensional plane by $2\theta$. After $j$ amplification iterations the good probability is