Fig. 4: Teleportation-based error correction (TEC) circuit for the one-way quantum repeater architecture.
From: Comparing one- and two-way quantum repeater architectures
R and S denote the incoming and locally prepared code blocks, respectively, each encoded using the same (n, m) quantum parity code (QPC). Syndrome measurements are denoted by M{X, Z}. The incoming logical qubit \({\left\vert \psi \right\rangle }_{L}\), which may have suffered photon loss during transmission through the optical fiber, is coupled to a freshly prepared logical Bell pair via transversal CNOT operations and logical Bell measurements. The local logical states are prepared using a fault-tolerant encoding circuit. Based on the measurement outcomes, a Pauli correction—denoted by the unitary U—is applied to the untouched half of the Bell pair, yielding a clean outgoing logical state that preserves the original quantum information. This state is then downloaded onto photonic qubits and transmitted to the next repeater node.
