Multi-hop fault-tolerant teleportation of arbitrary two-qubit states with cluster channel

In this paper, we propose one multi-hop fault-tolerant teleportation scheme leveraging non-maximally entangled cluster states as the quantum channel, which is crucial for efficient transmission over extended distances. During quantum communication, environmental noise may introduce operational errors between adjacent nodes. In order to uphold the maximum transmission efficiency, error correction operations are exclusively conducted by the ultimate receiver rather than intermediate nodes. Error outcomes from each node can be synchronously relayed to the receiver via the classical channel, effectively diminishing the delays and operational intricacies, thereby significantly bolstering the transmission efficiency. Moreover, we utilize the Quirk simulation software to simulate the teleportation process.