# TwoModeSqueezing¶

Module: pennylane

class TwoModeSqueezing(r, phi, wires)[source]

Phase space two-mode squeezing.

$S_2(z) = \exp\left(z^* \a \hat{b} -z \ad \hat{b}^\dagger \right) = \exp\left(r (e^{-i\phi} \a\hat{b} -e^{i\phi} \ad \hat{b}^\dagger \right).$

where $$z = r e^{i\phi}$$.

Details:

• Number of wires: 2

• Number of parameters: 2

• Gradient recipe: $$\frac{d}{dr}f(S_2(r,\phi)) = \frac{1}{2\sinh s} \left[f(S_2(r+s, \phi)) - f(S_2(r-s, \phi))\right]$$, where $$s$$ is an arbitrary real number ($$0.1$$ by default) and $$f$$ is an expectation value depending on $$S_2(r,\phi)$$.

• Heisenberg representation:

$\begin{split}M = \begin{bmatrix} 1 & 0 & 0 & 0 & 0 \\ 0 & \cosh r & 0 & \sinh r \cos \phi & \sinh r \sin \phi\\ 0 & 0 & \cosh r & \sinh r \sin \phi & -\sinh r \cos \phi\\ 0 & \sinh r \cos \phi & \sinh r \sin \phi & \cosh r & 0\\ 0 & \sinh r \sin \phi & -\sinh r \cos \phi & 0 & \cosh r \end{bmatrix}\end{split}$
Parameters: r (float) – squeezing amount phi (float) – squeezing phase angle $$\phi$$ wires (Sequence[int] or int) – the wire the operation acts on