论文标题
同源产品代码的Union-Find解码器
Union-Find Decoders For Homological Product Codes
论文作者
论文摘要
同源产品代码是一类代码，可以提高距离，同时保持相对较低的稳定剂重量。我们展示了如何为这些代码构建Union-Find解码器，并使用Union-Find解码器为产品中的一个代码和其他代码中的蛮力解码器进行构建。我们将此构造应用于具有小型代码的表面代码产品的特定情况，例如$ [[4,2,2]] $代码，我们称之为增强的表面代码。增强表面代码的距离是表面代码与小型代码的距离的乘积，而通过轻微修改的联合获取解码器可以解释错误最多是距离的一半。我们提出数值模拟，表明尽管这些增强代码的阈值低于表面代码的阈值，但低噪声性能得到了改善。
Homological product codes are a class of codes that can have improved distance while retaining relatively low stabilizer weight. We show how to build union-find decoders for these codes, using a union-find decoder for one of the codes in the product and a brute force decoder for the other code. We apply this construction to the specific case of the product of a surface code with a small code such as a $[[4,2,2]]$ code, which we call an augmented surface code. The distance of the augmented surface code is the product of the distance of the surface code with that of the small code, and the union-find decoder, with slight modifications, can decode errors up to half the distance. We present numerical simulations, showing that while the threshold of these augmented codes is lower than that of the surface code, the low noise performance is improved.
