We propose a quantum neural network structure that can, on its own, work out the standard protocol for quantum teleportation [@NielsenChuang00].

The design and training of this network is analogous to the autoencoder and the quantum circuit diagram is shown in FIG. \[fig:teleport\_circuit\]. The cost function used was: $$C=\sum_{j=0}^3(\mathrm{Tr}(\ket{\psi}\bra{\psi}\sigma_{j}) - \mathrm{Tr}(\rho_6 \sigma_{j}))^{2}.$$ A fully trained network can teleport the state $\ket{\psi}$ (from Alice) to the output port of qubit 6 (to Bob). Once trained properly, $\rho_{out_{1}}$ will no longer be $\ket{\psi}\bra{\psi}$, as the teleportation has ‘messed up’ Alice’s state [@Wilde13].

In order to train the teleportation for any arbitrary state $\ket{\psi}$ (and to avoid the network simply learning to *copy* $\ket{\psi}$ from Alice to Bob), the training inputs are randomly picked from the axis intersection states on the surface of the Bloch sphere [@NielsenChuang00]. FIG. \[fig:teleportation\_cost\] shows the convergence of the cost function during training, simulated on a classical computer. As can be seen, the training was found to be successful, i.e. the cost function converged towards zero. This held for all tests with randomly initialised weights.

![\[fig:teleportation\_cost\]A plot of the teleportation cost function w.r.t. the number of steps used in the training procedure. The cost function can be seen 