Rmw

class qililab.Rmw(qubit, *, theta, phase)

Bases: BasicGate

Microwave rotation in the equatorial plane (native single-qubit pulse).

This gate represents a resonant microwave (e.g., DRAG-shaped) pulse implementing a rotation by angle theta around an axis in the XY plane defined by the drive phase phase.

Mathematically, it can be written as a Z-X-Z decomposition .. math:

R_{MW}(\theta, \phi) = Z_{\phi}\, X_{\theta}\, Z_{-\phi},

which is equivalent to a rotation generated by \(\cos\phi\,\sigma_x + \sin\phi\,\sigma_y\): .. math:

R_{MW}(\theta,\phi)
= \exp\!\left(-\frac{i\theta}{2}\left(\cos\phi\,\sigma_x + \sin\phi\,\sigma_y\right)\right)
=
\begin{pmatrix}
    \cos(\tfrac{\theta}{2}) & -i e^{-i\phi}\sin(\tfrac{\theta}{2}) \\
    -i e^{i\phi}\sin(\tfrac{\theta}{2}) & \cos(\tfrac{\theta}{2})
\end{pmatrix}.

Implementation note (hardware-aware): In pulse-level execution, \(Z\) rotations are virtual frame updates. The trailing \(Z_{\phi}\) can be absorbed into subsequent operations, so a common realization is a single Virtual-Z by \(-\phi\) followed by a microwave pulse of area \(\theta\) with drive phase \(\phi\).

Together with Virtual-Z gates, any single-qubit unitary can be expressed as .. math:

U(\theta,\phi,\lambda) = Z_\phi X_\theta Z_\lambda
= R_{MW}(\theta,\phi)\, Z_{\lambda+\phi}
= Z_{\phi+\lambda}\, R_{MW}(\theta,-\lambda).

Parameters:

qubit (int) – Target qubit index.
theta (float) – Rotation angle in radians.
phase (float) – Microwave drive phase in radians (sets the rotation axis in the XY plane).

Attributes Summary

`PARAMETER_NAMES`
`name`	Retrieve the name of the gate.
`phase`
`theta`
`yaml_tag`

Attributes Documentation

PARAMETER_NAMES = ['theta', 'phase']

name

phase

theta

yaml_tag = '!Rmw'

Ramp

Sample