qat.lang.RZ

qat.lang.RZ

Definition of the \(RZ\) gate (of arity \(1\)). This gate is part of the default gate set of myQLM and is defined in the default gate set default_gate_set().

Apply gate

from qat.lang import qrout, RZ

@qrout
def circ(alpha):
    RZ(alpha)(0)

Control gate

from qat.lang import qrout, RZ

@qrout
def ctrl_circ(alpha):
    RZ(alpha).ctrl()(0, 1)

Multi-controlled gate

from qat.lang import qrout, RZ

@qrout
def multi_ctrl_circ(alpha):
    RZ(alpha).ctrl(2)(0, 1, 2)

Reverse gate

from qat.lang import qrout, RZ

@qrout
def reversed_circ(alpha):
    RZ(alpha).dag()(0)

This \(RZ\) gate is defined by:

\[\begin{split}\forall \theta \in\rm I\!R: R_Z[\theta] = \begin{vmatrix} e^{-i\frac{\theta}{2}} & 0 \\ 0 & e^{i\frac{\theta}{2}} \\ \end{vmatrix}\end{split}\]