We propose an architecture of quantum-error-correction-based quantum repeaters that combines 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 encoding the qubit in a single bosonic mode. On the second level we use a small discrete-variable code. Such an architecture has two important features. Firstly, errors on each of the two levels are corrected in repeaters of two different types. This enables for achieving performance needed in practical scenarios with a reduced cost with respect to an architecture for which all repeaters are the same. Secondly, the use of continuous-variable GKP code on the lower level generates additional analog information which enhances the error-correcting capabilities of the second-level code such that long-distance communication becomes possible with encodings consisting of only four or seven optical modes.

我们提出了一种基于量子纠错的量子中继器架构，该架构结合了离散和连续可变量子信息中使用的技术。具体来说，我们建议将传输的量子位编码为由两个级别组成的级联代码。在第一级，我们使用连续变量 GKP 代码以单一玻色子模式对量子位进行编码。在第二层，我们使用一个小的离散变量代码。这种架构有两个重要的特征。首先，在两种不同类型的中继器中纠正两个级别中每一个级别的错误。相对于所有中继器都相同的架构，这能够以降低的成本实现实际场景中所需的性能。第二，