The two modules, Alice and Bob, each hold a 88 Sr + ion (purple) and a 43 Ca + ion (orange). Sr + provides a network qubit, {Q}N , whereas Ca + provides both a long-lived circuit qubit, {Q}C , and an auxiliary qubit, {Q}X . Before the protocol, the circuit qubits are in some arbitrary state. The protocol begins by generating entanglement between the network qubits through a photonic link. On heralding entanglement, each module applies a local CZ gate between the network and circuit qubits, using the auxiliary qubit temporarily to mediate the gate mechanism. The outcomes of mid-circuit parity measurements of the network qubits are exchanged in real time through a classical (TTL) link connecting the control systems of the two modules. This information is used to condition local feed-forward operations, U A and U B , on the circuit qubitscompleting the teleportation of the CZ gate.
