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

The required superposition is the Bell statePrepare $|00⟩$, apply $H$ to the first qubit, then apply CNOT from the first to the second. The intermediate state is $(|00⟩+|10⟩)/\sqrt{2}$, and the controlled-NOT gate gives the required Bell state. No final basis change is needed: the two displayed expressions represent exactly the same vector.