High Performance Entanglement-Assisted Quantum LDPC Codes Need Little Entanglement
High Performance Entanglement-Assisted Quantum LDPC Codes Need Little Entanglement
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DOI：
10.1109/tit.2011.2104590
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发表时间：
2011-03-01
影响因子：
2.5
通讯作者：
Hsu, Li-Yi
中科院分区：
文献类型：
--
作者：
Hsieh, Min-Hsiu;Yen, Wen-Tai;Hsu, Li-Yi
虽然纠缠辅助形式提供了经典线性码和纠缠辅助量子纠错码(EAQECC)之间的普遍联系，但在构造EAQECC时保持大量的纯最大纠缠态的问题是其实际应用的障碍。也有人推测，纠缠辅助形式主义转换这些好的经典码的能力来自于对最大纠缠态的大量消耗。通过给EAQECC族提供一个纠缠消耗率与码长成线性关系，我们证明了上述猜想是错误的。值得注意的是，本文构造的两类EAQECC，无论码长有多大，都只需要一个最大纠缠态的副本。根据我们的数值模拟，这些由经典的有限几何LDPC码构造的EAQECC具有很好的性能。我们的工作表明，EAQECC不仅在理论上很有趣，而且在物理上也是可以实现的。最后，这些纠缠辅助的高性能LDPC码具有较低的纠缠消耗率，使得人们可以构造具有非常相似参数的高性能标准QECC。
Though the entanglement-assisted formalism provides a universal connection between a classical linear code and an entanglement-assisted quantum error-correcting code (EAQECC), the issue of maintaining large amount of pure maximally entangled states in constructing EAQECCs is a practical obstacle to its use. It is also conjectured that the power of entanglement-assisted formalism to convert those good classical codes comes from massive consumption of maximally entangled states. We show that the above conjecture is wrong by providing families of EAQECCs with an entanglement consumption rate that diminishes linearly as a function of the code length. Notably, two families of EAQECCs constructed in the paper require only one copy of maximally entangled state no matter how large the code length is. These families of EAQECCs that are constructed from classical finite geometric LDPC codes perform very well according to our numerical simulations. Our work indicates that EAQECCs are not only theoretically interesting, but also physically implementable. Finally, these high performance entanglement-assisted LDPC codes with low entanglement consumption rates allow one to construct high-performance standard QECCs with very similar parameters.