Quantum repeaters with encoding on nitrogen-vacancy center platforms

We investigate quantum repeater protocols that rely on three-qubit repetition codes using nitrogen-vacancy (NV) centers in diamond as quantum memories. NV centers offer a two-qubit register, corresponding to their electron and nuclear spins, which makes it possible to perform deterministic two-qubit operations within one NV center. For quantum repeater applications, we, however, need to do joint operations on two separate NV centers. Here, we study two NV-center based repeater structures that enable such deterministic joint operations. One structure offers less consumption of classical communication, at the cost of more computation overhead, whereas the other one relies on a fewer number of physical resources and operations. We assess and compare their performance for the task of secret key generation under the influence of noise and decoherence with current and near-term experimental parameters. We quantify the regimes of operation, where one structure outperforms the other, and find the regions where encoded quantum repeaters offer practical advantages over their non-encoded counterparts.