qat.lang.vendors.K

qat.lang.vendors.K

Definition of the \(K\) gate (of arity \(1\)). This gate is not included in the default gate set of myQLM, but in the gate set quobly_gate_set().

Apply gate

from qat.lang import qrout
from qat.lang.vendors import K

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

Control gate

from qat.lang import qrout
from qat.lang.vendors import K

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

Multi-controlled gate

from qat.lang import qrout
from qat.lang.vendors import K

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

Reverse gate

from qat.lang import qrout
from qat.lang.vendors import K

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

This \(K\) gate is defined by:

\[\begin{split}\forall \phi \in\rm I\!R: \frac{1}{\sqrt{2}} \begin{vmatrix} 1 & -i \cdot e^{-i\phi} \\ -i \cdot e^{i\phi} & 1 \\ \end{vmatrix} = R_Z(\phi) \cdot R_X(\frac{\pi}{2}) \cdot R_Z(-\phi)\end{split}\]