Definition of all avalaible gates

In the following table, we list and give the definition of all available gates on the QLM.

Gate name	pyAQASM name	# qubits	Matrix
Hadamard	H	1	$ \begin{vmatrix} \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{2}} \\ \frac{1}{\sqrt{2}} & -\frac{1}{\sqrt{2}} \\ \end{vmatrix}$
Pauli X	X	1	$ \begin{vmatrix} 0 & 1 \\ 1 & 0 \\ \end{vmatrix}$
Pauli Y	Y	1	$ \begin{vmatrix} 0 & -i \\ i & 0 \\ \end{vmatrix}$
Pauli Z	Z	1	$ \begin{vmatrix} 1 & 0 \\ 0 & -1 \\ \end{vmatrix}$
Identity	I	1	$ \begin{vmatrix} 1 & 0 \\ 0 & 1 \\ \end{vmatrix}$
Phase Shift	PH($\theta$)	1	$\forall \theta \in\rm I\!R$: $\begin{vmatrix} 1 & 0 \\ 0 & e^{i\theta} \\ \end{vmatrix}$
Phase Shift gate of $\frac{\pi}{2}$	S	1	$ \begin{vmatrix} 1 & 0 \\ 0 & i \\ \end{vmatrix}$
Phase Shift gate of $\frac{\pi}{4}$	T	1	$ \begin{vmatrix} 1 & 0 \\ 0 & e^{i\frac{\pi}{4}} \\ \end{vmatrix}$
X Rotation	RX($\theta$)	1	$\forall \theta \in\rm I\!R$: $\begin{vmatrix} \cos(\frac{\theta}{2}) & -i\sin(\frac{\theta}{2}) ~\\ -i\sin(\frac{\theta}{2}) & \cos(\frac{\theta}{2}) \\ \end{vmatrix}$
Y Rotation	RY($\theta$)	1	$\forall \theta \in\rm I\!R$: $\begin{vmatrix} \cos(\frac{\theta}{2}) & -\sin(\frac{\theta}{2}) ~\\ \sin(\frac{\theta}{2}) & \cos(\frac{\theta}{2}) \\ \end{vmatrix}$
Z Rotation	RZ($\theta$)	1	$\forall \theta \in\rm I\!R$: $\begin{vmatrix} e^{-i\frac{\theta}{2}} & 0 \\ 0 & e^{i\frac{\theta}{2}} \\ \end{vmatrix}$
Controlled NOT	CNOT	2	$\begin{vmatrix} 1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 0 & 1 \\ 0 & 0 & 1 & 0 \\ \end{vmatrix}$
SWAP	SWAP	2	$\begin{vmatrix} 1 & 0 & 0 & 0 \\ 0 & 0 & 1 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 0 & 1 \\ \end{vmatrix}$
iSWAP	ISWAP	2	$\begin{vmatrix} 1 & 0 & 0 & 0 \\ 0 & 0 & i & 0 \\ 0 & i & 0 & 0 \\ 0 & 0 & 0 & 1 \\ \end{vmatrix}$
$\sqrt{\text{SWAP}}$	SQRTSWAP	2	$\begin{vmatrix} 1 & 0 & 0 & 0 \\ 0 & \frac{1}{2}(1 + i) & \frac{1}{2}(1 - i) & 0 \\ 0 & \frac{1}{2}(1 - i) & \frac{1}{2}(1 + i) & 0 \\ 0 & 0 & 0 & 1 \\ \end{vmatrix}$
Toffoli	CCNOT	3	$\begin{vmatrix} 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 \\ 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 \\ \end{vmatrix}$

Short example

Here is a short example to illustrate the creation of a quantum program with all those gates:

from qat.lang.AQASM import Program, H, X, Y, Z, I, PH, S, T, RX, RY, RZ, CNOT, ISWAP, SQRTSWAP, CCNOT, SWAP

p = Program()
reg = p.qalloc(3)

p.apply(H, reg[0])
p.apply(X, reg[0])
p.apply(Y, reg[2])
p.apply(Z, reg[1])
p.apply(I, reg[1])
p.apply(S, reg[0])
p.apply(T, reg[0])
p.apply(PH(0.3), reg[0])
p.apply(RX(-0.3), reg[0])
p.apply(RY(0.6), reg[1])
p.apply(RZ(0.3), reg[0])
p.apply(CNOT, reg[0:2])
p.apply(SWAP, reg[0], reg[2])
p.apply(ISWAP, reg[1:3])
p.apply(SQRTSWAP, reg[0:2])
p.apply(CCNOT, reg)

circuit = p.to_circ()

circuit.display()

To learn more about how to write a quantum program with the Python AQASM library, check out this basic tutorial or this advanced tutorial