Past exam of the computer science course of the University of Oxford / 2023 / Quantum information / 2 / b / ii

Table of contents
- Solution ii

Solution

Initialize three qubits in

∣000 ⟩

. Apply a Hadamard gate on the first, then controlled-NOT gates

1 \to 2

and

1 \to 3

:

∣000 ⟩ ⟼ \frac{∣000 ⟩ + ∣100 ⟩}{2} ⟼ \frac{∣000 ⟩ + ∣111 ⟩}{2} .

Apply the T gate twice to the first qubit. Because

T^{2} = diag (1, i)

, the resulting GHZ state with the specified relative quantum phase is

T_{1}^{2} CNOT_{1 \to 3} CNOT_{1 \to 2} H_{1} ∣000 ⟩ = \frac{∣000 ⟩ + i ∣111 ⟩}{2} .

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