3. Consider a single qubit operator U that is unitary but also Hermitian with eigenvalues ±1. It is both a gate and an observable. Show that the following circuit measures the observable U in the...

Extracted text: 3. Consider a single qubit operator U that is unitary but also Hermitian with eigenvalues ±1. It is both a gate and an observable. Show that the following circuit measures the observable U in the following sense: we want a measurement result that indicates one of the two eigenvalues of U and leaves |Vout) in a state corresponding to that eigenvector. 「つ tinフ -it> Itout