Squeezing

Module: pennylane

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

Phase space squeezing.

\[S(z) = \exp\left(\frac{1}{2}(z^* \a^2 -z {\a^\dagger}^2)\right).\]

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

Details:

  • Number of wires: 1

  • Number of parameters: 2

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

  • Heisenberg representation:

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