Fig. 3
Diagram of the neural network (a) and plot of the convergence of the cost function (b) for the neural network discovery of the teleportation protocol. a A circuit diagram of a quantum neural network that can learn and carry out teleportation of the state \(\left| \psi \right\rangle\) from Alice to Bob using quantum entanglement. The standard teleportation protocol allows only classical communication of 2 bits20; this is enforced by only allowing two connections, which are dephased in the Z-basis (D). U 1,U 2 and U 3 are unitaries. The blue line is the boundary between Alice and Bob. b 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 to converge to zero. The non-monotonic decrease is to be expected as we are varying the input states. The network now teleports any qubit state: picking 1000 states at random from the Haar measure (uniform distribution over the Bloch sphere) gives a cost function distribution with mean 5.0371 × 10−4 and standard deviation 1.7802 × 10−4, which is effectively zero
