Rotation

Module: pennylane

class Rotation(phi, wires)[source]

Phase space rotation.

\[R(\phi) = \exp\left(i \phi \ad \a\right)=\exp\left(i \frac{\phi}{2} \left(\frac{\x^2+ \p^2}{\hbar}-\I\right)\right).\]

Details:

  • Number of wires: 1

  • Number of parameters: 1

  • Gradient recipe: \(\frac{d}{dr}f(R(r)) = \frac{1}{2} \left[f(R(\phi+\pi/2)) - f(R(\phi-\pi/2))\right]\) where \(f\) is an expectation value depending on \(R(r)\).

  • Heisenberg representation:

    \[\begin{split}M = \begin{bmatrix} 1 & 0 & 0\\ 0 & \cos\phi & -\sin\phi\\ 0 & \sin\phi & \cos\phi \end{bmatrix}\end{split}\]
Parameters:phi (float) – the rotation angle