Past exam of the computer science course of the University of Oxford / 2021 / Quantum information / 3 / a / i / Solution

Prepare $|0⟩$, then apply $H$, then $T$. With $T=\mathrm{diag}(1,e^{i\pi /4})$,This uses only the allowed state preparation and elementary gates. The rightmost operator acts first, so $TH$ denotes the temporal order $H$ followed by $T$.