用于自适应纠缠辅助稳定子码的穿刺

中文摘要 AI 辅助

量子纠错码对于可靠的量子通信至关重要。通过使用纠缠辅助稳定子，可以改进可达到的参数，但代价是消耗预共享的贝尔对。如果这种贝尔对的可用性是间歇性的，那么能够将码适应于可用资源的能力将是有益的。也就是说，选择一个单一的母码，可以适应不同的纠缠预算。为实现这一点，我们将现有的用于标准/无辅助稳定子的穿刺构造扩展到纠缠辅助设置，通过三步过程：将码解释为无辅助稳定子，穿刺接收端的一个量子比特，并恢复纠缠辅助表示。该过程将所需的贝尔对数量减少一个，同时保持传输和逻辑量子比特的数量。我们推导了由此产生的距离损失的一个界限，并建立了保持原始码距离的条件。最后，我们分析了五个到八个传输量子比特的、不同的、随机生成的纠缠辅助稳定子。在这些码中，14.75%的码具有比其相关的无辅助表示更大的距离。在这个子集中，81.4%的码允许至少一个穿刺选择，该选择保持原始的纠缠辅助距离。这些结果说明了穿刺如何在保持码距离的同时减少纠缠需求。

英文摘要

Quantum error-correcting codes are essential for reliable quantum communication. The achievable parameters can be improved by using entanglement-assisted stabilizers at the cost of consuming pre-shared Bell pairs. If the availability of such Bell pairs is intermittent, the ability to adapt the code to available resources is beneficial. That is, to pick a single mother code that can be adapted to different entanglement budgets. To achieve this, we extend an existing puncturing construction for standard/unassisted stabilizers to the entanglement-assisted setting through a three-step procedure: Interpreting the code as an unassisted stabilizer, puncturing a receiver-side qubit, and recovering an entanglement-assisted representation. This procedure reduces the number of required Bell pairs by one while preserving the number of transmitted and logical qubits. We derive a bound on the resulting distance loss and establish conditions for preserving the original code distance. Finally, we analyse distinct, randomly generated, entanglement-assisted stabilizers with five to eight transmitted qubits. Of these codes, 14.75% have a greater distance than their associated unassisted representations. Among this subset, 81.4% admit at least one puncturing choice that preserves the original entanglement-assisted distance. These results illustrate how puncturing can reduce entanglement requirements while maintaining code distance.

发表机构

• Aalborg University（奥尔堡大学）

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