论文标题
接近具有近似误差校正的量子单例绑定
Approaching the Quantum Singleton Bound with Approximate Error Correction
论文作者
论文摘要
众所周知，没有量子错误纠正费率$ r $的代码可以纠正超过$（1-r）/4 $符号分数的对抗错误。但是，如果我们只要求我们的代码 *大致 *恢复消息怎么办？对于任何恒定速率$ r $，我们构建了有效地定位的近似量子代码，以接近$（1-r）/2 $的量子单例界限。此外，字母的大小是一个常数独立于消息长度的常数，并且恢复误差在消息长度中成倍小。我们构造的核心是量子列表解码的概念和涉及折叠式芦苇 - 固体代码的实现。
It is well known that no quantum error correcting code of rate $R$ can correct adversarial errors on more than a $(1-R)/4$ fraction of symbols. But what if we only require our codes to *approximately* recover the message? We construct efficiently-decodable approximate quantum codes against adversarial error rates approaching the quantum Singleton bound of $(1-R)/2$, for any constant rate $R$. Moreover, the size of the alphabet is a constant independent of the message length and the recovery error is exponentially small in the message length. Central to our construction is a notion of quantum list decoding and an implementation involving folded quantum Reed-Solomon codes.
