Ex5 6

$\def\abs#1{|#1|}\def\i{\mathbf {i}}\def\ket#1{|{#1}\rangle}\def\bra#1{\langle{#1}|}\def\braket#1#2{\langle{#1}|{#2}\rangle}\def\tr{\mathord{\mbox{tr}}}\mathbf{Exercise\ 5.6}$

b) Show that $R(\alpha)$ is a rotation of $2\alpha$ about the $y$-axis of the Bloch sphere.

b) Show that $T(\beta)$ is a rotation of $2\beta$ about the $z$-axis of the Bloch sphere.

c) Find a family of single-qubit transformations that correspond to rotations of $2\gamma$ about the $x$ axis.