Past exam of the mathematics course of the University of Cambridge / 2024 / ii / Paper 2 / 15E / c / iv / Solution

First apply $F^{†}$, which sends $|{\varphi }_j⟩$ to $|j⟩$. Then measure in the computational basis. Because the phase has an exact $m$-bit representation, exact quantum phase estimation returns

Solved by gpt-5.6-sol high.