Yi Zhengzhong, Liang Zhipeng, Wu Yulin, Wang Xuan
Harbin Institute of Technology, Xili University Town, Nanshan District, Shenzhen 518055, China.
Entropy (Basel). 2024 Sep 25;26(10):818. doi: 10.3390/e26100818.
Inspired by classical polar codes, whose coding rate can asymptotically achieve the Shannon capacity, researchers are trying to find their analogs in the quantum information field, which are called quantum polar codes. However, no one has designed a quantum polar coding scheme that applies to quantum computing yet. There are two intuitions in previous research. The first is that directly converting classical polar coding circuits to quantum ones will produce the polarization phenomenon of a pure quantum channel, which has been proved in our previous work. The second is that based on this quantum polarization phenomenon, one can design a quantum polar coding scheme that applies to quantum computing. There are several previous work following the second intuition, none of which has been verified by experiments. In this paper, we follow the second intuition and propose a more reasonable quantum polar stabilizer code construction algorithm than any previous ones by using the theory of stabilizer codes. Unfortunately, simulation experiments show that even the stabilizer codes obtained from this more reasonable construction algorithm do not work, which implies that the second intuition leads to a dead end. Based on the analysis of why the second intuition does not work, we provide a possible future direction for designing quantum stabilizer codes with a high coding rate by borrowing the idea of classical polar codes. Following this direction, we find a class of quantum stabilizer codes with a coding rate of 0.5, which can correct two of the Pauli errors.
受经典极化码启发，其编码率可渐近达到香农容量，研究人员试图在量子信息领域找到其类似物，即所谓的量子极化码。然而，尚未有人设计出适用于量子计算的量子极化编码方案。先前的研究有两种思路。第一种是直接将经典极化编码电路转换为量子电路会产生纯量子信道的极化现象，这在我们之前的工作中已得到证明。第二种是基于这种量子极化现象，可以设计出适用于量子计算的量子极化编码方案。先前有几项工作遵循了第二种思路，但均未经过实验验证。在本文中，我们遵循第二种思路，利用稳定子码理论提出了一种比以往任何算法都更合理的量子极化稳定子码构造算法。不幸的是，仿真实验表明，即使是从这种更合理的构造算法得到的稳定子码也不起作用，这意味着第二种思路走入了死胡同。基于对第二种思路为何行不通的分析，我们借鉴经典极化码的思想，为设计高编码率的量子稳定子码提供了一个可能的未来方向。沿着这个方向，我们找到了一类编码率为0.5的量子稳定子码，它可以纠正两个泡利错误。
