Quantum repeaters based on stationary Gottesman-Kitaev-Preskill qubits

Quantum repeaters that incorporate quantum error correction codes have been shown to be a promising alternative compared with the original quantum repeaters that rely upon probabilistic quantum error detection depending on classical communication over remote repeater stations. A particularly efficient way of encoding qubits into an error correction code is through bosonic codes where even a single oscillator mode serves as a sufficiently large, physical system. Here we consider the bosonic Gottesman-Kitaev-Preskill (GKP) code as a natural choice for a loss-correction-based quantum repeater. However, unlike existing treatments, we focus on the excitation loss that occurs in the local, stationary memory qubits as represented by, for instance, collective atomic spin modes. We analyze and assess the performance of such a GKP-based quantum repeater where, apart from the initial state generations and distributions, all operations can be performed via deterministic linear mode transformations, as opposed to other existing memory-based quantum repeater schemes.