One-way quantum repeaters where loss and operational errors are counteracted by quantum error-correcting codes can ensure fast and reliable qubit transmission in quantum networks. It is crucial that the resource requirements of such repeaters, for example, the number of qubits per repeater node and the complexity of the quantum error-correcting operations are kept to a minimum to allow for near-future implementations. To this end, we propose a one-way quantum repeater that targets both the loss and operational error rates in a communication channel in a resource-efficient manner using code concatenation. Specifically, we consider a tree-cluster code as an inner loss-tolerant code concatenated with an outer 5-qubit code for protection against Pauli errors. Adopting flag-based stabilizer measurements, we show that intercontinental distances of up to 10,000 km can be bridged with a minimized resource overhead by interspersing repeater nodes that each specialize in suppressing either loss or operational errors. Our work demonstrates how tailored error-correcting codes can significantly lower the experimental requirements for long-distance quantum communication.

单向量子中继器通过量子纠错码抵消丢失和操作错误，可以确保量子网络中快速可靠的量子比特传输。至关重要的是，此类中继器的资源需求（例如，每个中继器节点的量子比特数和量子纠错操作的复杂性）保持在最低限度，以便在不久的将来实现。为此，我们提出了一种单向量子中继器，它使用代码级联以资源高效的方式降低通信信道中的丢失率和操作错误率。具体来说，我们将树簇代码视为与外部 5 量子位代码连接的内部耐丢失代码，以防止泡利错误。采用基于标志的稳定器测量，我们表明，通过散布中继器节点（每个中继器节点专门用于抑制丢失或操作错误），可以以最小的资源开销桥接长达 10,000 公里的洲际距离。我们的工作展示了定制的纠错码如何显着降低长距离量子通信的实验要求。