Past exam of the atomic and Optical Physics course of the University of Cambridge / 2012 / Paper 1 / 2 / a / Solution

Following the pure state through the first two gates gives $(|1⟩+e^{i\alpha }|2⟩)/\sqrt{2}$. After the last Hadamard gate it isUsing the qubit polarization convention defined above,The output remains pure and has unit Bloch vector length. The population oscillation is the Ramsey interferometry fringe: the first gate supplies quantum coherence, and the last turns the acquired relative quantum phase into a measurable population difference.