Quantum repeaters based on concatenated bosonic and discrete-variable quantum codes

We propose a novel architecture of quantum-error-correction-based quantum repeaters that combines the techniques used in discrete and continuous variable quantum information. Specifically, we propose to encode the transmitted qubits in a concatenated code consisting of two levels. On the first level we use a continuous variable GKP code which encodes the qubit in a single bosonic mode. On the second level we use a small discrete variable code. Such an architecture introduces two major novelties which allow us to make efficient use of resources. Firstly, our architecture makes use of two types of quantum repeaters: the simpler GKP repeaters that need to only be able to store and correct errors on a single GKP qubit and more powerful but more costly multi-qubit repeaters that additionally can correct errors on the higher level. The combination of using the two types of repeaters enables us to achieve performance needed in practical scenarios with a significantly reduced cost with respect to an architecture based solely on multiqubit repeaters. Secondly, the use of the GKP code on the lower level provides us with the information about the success probability of the specific GKP correction round. This analog information offers significant boost in performance of our scheme.