The Gate command converts a string symbol of the quantum gate into a Matrix representation of the gate.

The Gate command without arguments yields a list of the known gates.

$\mathrm{with}\left(\mathrm{QuantumChemistry}\right)\:$

$\mathrm{with}\left(\mathrm{QuantumComputing}\right)\;$

$\left[\mathrm{ConvertDirac}\,\mathrm{Gate}\,\mathrm{InitialState}\,\mathrm{MeasureState}\,\mathrm{PrepareState}\,\mathrm{QubitPopulations}\,\mathrm{QubitPopulationsPlot}\right]$

$\mathrm{Uz} ≔ \mathrm{Gate}\left(''Z''\right)\;$

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

$\mathrm{Uz}\,\mathrm{Uy} ≔ \mathrm{Gate}\left(''X''\right)\,\mathrm{Gate}\left(''Y''\right)\;$

$\mathrm{Uz},\mathrm{Uy}≔\left[\begin{array}{cc}0& 1\\ 1& 0\end{array}\right],\left[\begin{array}{cc}0& \mathrm{-I}\\ \mathrm{I}& 0\end{array}\right]$

$\mathrm{Uu} ≔ \mathrm{Gate}\left(''U''\,\mathrm{theta}\=\mathrm{theta}\,\mathrm{phi}\=\mathrm{phi}\,\mathrm{lambda}\=\mathrm{lambda}\right)\;$

$\mathrm{Uu}≔\left[\begin{array}{cc}\cos \left(\frac{\mathrm{\theta }}{2}\right)& -{\ⅇ}^{\mathrm{I}\mathrm{\lambda }}\sin \left(\frac{\mathrm{\theta }}{2}\right)\\ {\ⅇ}^{\mathrm{I}\mathrm{\phi }}\sin \left(\frac{\mathrm{\theta }}{2}\right)& {\ⅇ}^{\mathrm{I}\left(\mathrm{\phi }+\mathrm{\lambda }\right)}\cos \left(\frac{\mathrm{\theta }}{2}\right)\end{array}\right]$

$\mathrm{Ucnot} ≔ \mathrm{Gate}\left(''CNOT''\right)\;$

$\mathrm{Ucnot}≔\left[\begin{array}{cccc}1& 0& 0& 0\\ 0& 0& 0& 1\\ 0& 0& 1& 0\\ 0& 1& 0& 0\end{array}\right]$

$\mathrm{Gate}\left(\right)\;$

$\left\{''CH''\,''CNOT''\,''CP''\,''CPhase''\,''CS''\,''CT''\,''CU''\,''CX''\,''CY''\,''CZ''\,''H''\,''I''\,''P''\,''Rx''\,''Ry''\,''Rz''\,''S''\,''SWAP''\,''T''\,''U''\,''X''\,''Y''\,''Z''\,''fSWAP''\,''iSWAP''\right\}$