Portes quantiques - Memo
Pauli gates
$X = \begin{pmatrix} 0 & 1 \\ 1 & 0 \\ \end{pmatrix}, $ $Y = \begin{pmatrix} 0 & -i \\ i & 0 \\ \end{pmatrix}, $ $Z = \begin{pmatrix} 1 & 0 \\ 0 & -1 \\ \end{pmatrix} $
Hadamard gate
$ H = \frac{1}{\sqrt{2}} \begin{pmatrix} 1 & 1 \\ 1 & -1 \\ \end{pmatrix} $
Phase shift gates
$ S = \begin{pmatrix} 1 & 0 \\ 0 & i \\ \end{pmatrix}, $ $ T = \begin{pmatrix} 1 & 0 \\ 0 & e^{i\frac{\pi}{4}} \\ \end{pmatrix} $
Rotation gates
$ R_x(\theta) = \begin{pmatrix} cos(\frac{\theta}{2}) & -isin(\frac{\theta}{2}) \\ -isin(\frac{\theta}{2}) & cos(\frac{\theta}{2}) \end{pmatrix}, $ $ R_y(\theta) = \begin{pmatrix} cos(\frac{\theta}{2}) & -sin(\frac{\theta}{2}) \\ sin(\frac{\theta}{2}) & cos(\frac{\theta}{2}) \end{pmatrix}, $ $ R_z(\theta) = \begin{pmatrix} e^{-i\frac{\theta}{2}} & 0 \\ 0 & e^{i\frac{\theta}{2}} \end{pmatrix} $