Cubic Phase Gate Operation to Decrease the Error of Two-Mode Transformations

The paper considers a strategy to decrease the error of the two-mode entanglement transformation Controlled-Z by introducing non-Gaussian nodes in the cluster. Non-Gaussian nodes are obtained by using a cubic phase gate. We have shown that this strategy can significantly decrease the transformation error. The considered implementation of the Controlled-Z operation contains a teleportation scheme with the cubic phase gate. We have shown that the correct selection of phases during measurement allows for lower errors than in the initial teleportation protocol with the cubic phase gate and the original teleportation protocol.