好的量子卷积纠错码及其译码算法
Good Quantum Convolutional Error Correction Codes And Their Decoding Algorithm Exist
摘要：
量子卷积码是近年来提出的一种保护重要量子信息的新方法。为了完成对量子卷积码的分析，本文提出了一种基于经典Viterbi译码算法的量子卷积码的译码方法。这种译码算法对于无记忆信道是最优的。我还报告了三个简单的标准来测试量子卷积码中的解码错误是否会在有限数量的解码步骤后终止，只要每个量子寄存器的希尔伯特空间维度是素数幂。最后，我证明了某些量子卷积码实际上是稳定子码。因此，这些量子稳定器卷积码具有容错实现。
英文摘要：
Quantum convolutional code was introduced recently as an alternative way to protect vital quantum information. To complete the analysis of quantum convolutional code, I report a way to decode certain quantum convolutional codes based on the classical Viterbi decoding algorithm. This decoding algorithm is optimal for a memoryless channel. I also report three simple criteria to test if decoding errors in a quantum convolutional code will terminate after a finite number of decoding steps whenever the Hilbert space dimension of each quantum register is a prime power. Finally, I show that certain quantum convolutional codes are in fact stabilizer codes. And hence, these quantum stabilizer convolutional codes have fault-tolerant implementations.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
