# sf.ops.Fourier¶

Fourier = <strawberryfields.ops.Fouriergate object>

Fourier gate.

Also accessible via the shortcut variable Fourier.

A special case of the phase space rotation gate, where $$\theta=\pi/2$$.

$F = R(\pi/2) = e^{i (\pi/2) a^\dagger a}$

Definition

A special case of the rotation operator is the case $$\phi=\pi/2$$; this corresponds to the Fourier gate,

$F = R(\pi/2) = e^{i (\pi/2) \ad \a}.$

The Fourier gate transforms the quadratures as follows:

$\begin{split}& F^\dagger\x F = -\p,\\ & F^\dagger\p F = \x.\end{split}$