The reliable provision of entangled qubits is an essential precondition in a variety of schemes for distributed quantum computing. This is challenged by multiple nuisances, such as errors during the transmission over quantum links, but also due to degradation of the entanglement over time due to decoherence. The latter can be seen as a constraint on the latency of the quantum protocol, which brings the problem of quantum protocol design into the context of latency-reliability constraints. We address the problem through hybrid schemes that combine: (1) indirect transmission based on teleportation and purification; (2) direct transmission, based on quantum error correction (QEC). The intuition is that, at present, the quantum hardware offers low fidelity, which demands purification; on the other hand, low latency can be obtained by QEC techniques. It is shown that, in the proposed framework, the purification protocol gives rise to asymmetries that can be exploited by asymmetric quantum error correcting code (QECC), which sets the basis for unique hybrid purification and coding design. Our results show that ad-hoc asymmetric codes give, compared to conventional QEC, a performance boost and codeword size reduction both in a single link and in a quantum network scenario.

翻译：纠缠量子比特的可靠提供是分布式量子计算多种方案中的关键前提。这一目标面临多重挑战，例如量子链路传输过程中的错误，以及退相干导致纠缠随时间退化的现象。后者可视为对量子协议延迟时间的约束，从而将量子协议设计问题引入延迟-可靠性约束的范畴。我们通过混合方案解决该问题，该方案结合了：(1)基于量子隐形传态与纯化的间接传输；(2)基于量子纠错码的直接传输。其核心思想在于：当前量子硬件保真度较低，需要纯化技术；而量子纠错技术可实现低延迟。研究表明，在该框架中，纯化协议会产生可被非对称量子纠错码利用的非对称性，这为独特的混合纯化与编码设计奠定了基础。我们的结果表明，相较于传统量子纠错码，定制化非对称码在单链路和量子网络场景中均能提升性能并缩减码字长度。