 Solution

ID: 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 = diag (1, e^{iπ /4})

T H ∣0 ⟩ = T \frac{∣0 ⟩ + ∣1 ⟩}{2} = \frac{∣0 ⟩ + e ^{iπ /4} ∣1 ⟩}{2} .

This uses only the allowed state preparation and elementary gates. The rightmost operator acts first, so

T H

denotes the temporal order

H

followed by

T

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