Fig. 4
An example of a quantum state rotation on the Bloch sphere. The |0 > 0, |1⟩ indicates the σz-axis, the X and Y the σx and σy axes respectively. In (a), the vector is residing in a +1 σx eigenstate. By rotating about the σz axis by π/4, the vector is rotated to the right, to the +1 σy eigenstate. A rotation about the σZ axis by angle θ is equivalent to the application of the unitary \(U(\theta )=\exp (-i{\theta }_{z}{\sigma }_{z}/2)\).
