type

symbol

graph

matrix

NOT

N

$\left[\begin{array}{cc}0& 1\\ 1& 0\end{array}\right]$

CNOT

C

$\left[\begin{array}{cc}\begin{array}{ccc}1& 0& 0\\ 0& 1& 0\\ 0& 0& 0\end{array}& \begin{array}{c}0\\ 0\\ 1\end{array}\\ \begin{array}{ccc}0& 0& 1\end{array}& 0\end{array}\right]$

Hadamard

H

$\frac{1}{\sqrt{2}}\left[\begin{array}{cc}1& 1\\ 1& -1\end{array}\right]$

T gate

T

$\left[\begin{array}{cc}1& 0\\ 0& e^{\frac{i\pi }{4}}\end{array}\right]$

T gate⁻¹

T⁺

$\left[\begin{array}{cc}1& 0\\ 0& e^{\frac{-i\pi }{4}}\end{array}\right]$

Phase

S

$\left[\begin{array}{cc}1& 0\\ 0& i\end{array}\right]$

Phase⁻¹

S⁺

$\left[\begin{array}{cc}1& 0\\ 0& -i\end{array}\right]$