 Solution

ID: past-exam-of-the-computer-science-course-of-the-university-of-oxford/2023/quantum-information/2/b/i/solution

Initialize one qubit in

∣0 ⟩

, then apply a Hadamard gate, a T gate, and a Hadamard gate, in that temporal order. Defining the Pauli X eigenstates

∣ \pm ⟩ = (∣0 ⟩ \pm ∣1 ⟩) / 2

, the successive quantum states are

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

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