To sum up the last couple nodes, here are all the single-qubit gates we've met so far, shown with their matrix representations, circuit elements, and their actions on the basis states. Feel free to come back to this node any time and use it as a reference.

Gate	Matrix	Basis state action
$X$	$\begin{pmatrix} 0 & 1 \\1 & 0 \\ \end{pmatrix}$	$$\begin{align} X\vert 0 \rangle &= \vert 1 \rangle \\ X\vert 1 \rangle &= \vert 0 \rangle \end{align}$$
$H$	$\frac{1}{\sqrt{2}}\begin{pmatrix} 1 & 1 \\ 1 & -1 \end{pmatrix}$	$$\begin{align} H\vert 0 \rangle &= \frac{1}{\sqrt{2}} (\vert 0 \rangle + \vert 1 \rangle) \\ H\vert 1 \rangle &= \frac{1}{\sqrt{2}} (\vert 0 \rangle - \vert 1 \rangle) \end{align}$$
$Z$	$\begin{pmatrix} 1 & 0 \\ 0 & -1 \end{pmatrix}$	$$\begin{align} Z\vert 0 \rangle &= \vert 0 \rangle \\ Z\vert 1 \rangle &= -\vert 1 \rangle \end{align}$$
$S$	$\begin{pmatrix} 1 & 0 \\ 0 & i \end{pmatrix}$	$$\begin{align} S\vert 0 \rangle &= \vert 0 \rangle \\ S\vert 1 \rangle &= i\vert 1 \rangle \end{align}$$
$T$	$\begin{pmatrix} 1 & 0 \\ 0 & e^{i\pi/4} \end{pmatrix}$	$$\begin{align} T\vert 0 \rangle &= \vert 0 \rangle \\ T\vert 1 \rangle &= e^{i\pi/4}\vert 1 \rangle \end{align}$$
$Y$	$\begin{pmatrix} 0 & -i \\ i & 0 \end{pmatrix}$	$$\begin{align} Y\vert 0 \rangle &= i \vert 1 \rangle \\ Y\vert 1 \rangle &= -i\vert 0 \rangle \end{align}$$
$RZ$	$\begin{pmatrix} e^{-i \frac{\theta}{2}} & 0 \\ 0 & e^{i \frac{\theta}{2}} \end{pmatrix}$	$$\begin{align} RZ(\theta)\vert 0 \rangle &= e^{-i \frac{\theta}{2}} \vert 0 \rangle \\ RZ(\theta)\vert 1 \rangle &= e^{i \frac{\theta}{2}} \vert 1 \rangle \end{align}$$
$RX$	$\begin{pmatrix} \cos \left(\frac{\theta}{2} \right) & -i \sin \left(\frac{\theta}{2} \right) \\ -i\sin \left(\frac{\theta}{2} \right)& \cos \left(\frac{\theta}{2} \right) \end{pmatrix}$	$$\begin{align} RX(\theta)\vert 0 \rangle &= \cos \frac{\theta}{2} \vert 0 \rangle - i \sin \frac{\theta}{2} \vert 1\rangle \\ RX(\theta) \vert 1 \rangle &= - i \sin \frac{\theta}{2} \vert 0 \rangle + \cos \frac{\theta}{2} \vert 1\rangle \end{align}$$
$RY$	$\begin{pmatrix} \cos \left(\frac{\theta}{2} \right) & - \sin \left(\frac{\theta}{2} \right) \\ \sin \left(\frac{\theta}{2} \right)& \cos \left(\frac{\theta}{2} \right) \end{pmatrix}$	$$\begin{align} RY(\theta)\vert 0 \rangle &= \cos \frac{\theta}{2} \vert 0 \rangle + \sin \frac{\theta}{2} \vert 1 \rangle \\ RY(\theta) \vert 1 \rangle &= - \sin \frac{\theta}{2} \vert 0 \rangle + \cos \frac{\theta}{2} \vert 1 \rangle \end{align}$$

Codercise I.8.1 — State preparation

Codercise I.8.2 — State preparation revisited

Codercise I.8.3 — State preparation with Mottonen's method

Single-Qubit Unitaries Table