AI 中文总结
该研究针对素数维量子位上基于泡利的量子纠错码提出叶状化框架，获得可用于容错测量量子计算的图态，讨论多个例子，在简单错误模型下计算叶状量子位环面码阈值，结果与非叶状版本相当。
AI 中文摘要
我们提出了一个框架，用于对素数维量子位上的任何基于泡利的量子纠错码进行叶状化。对于任何此类码，我们得到一个量子位图态，可通过测量来执行容错的基于测量的量子计算。这种范式在光子学等平台中很有意义，其中基于测量的协议很自然且高维态很容易获得。我们讨论了任意素数维\(d\)的几个例子，如量子位环面码（稳定子码，CSS）、\(d\)维完美\([[5,1,3]]\)码（稳定子码，非CSS）以及CSS蜂巢码的直接\(d\)维推广（动态，CSS）。在一个简单的错误模型下，我们数值计算了叶状量子位环面码的阈值，并证明它们与非叶状版本相当。
英文摘要
We present a framework for foliating any Pauli-based quantum error-correcting code over prime-dimensional qudits. For any such code, we obtain a qudit graph state that can be measured to perform fault-tolerant measurement-based quantum computing. Such a paradigm is of interest in platforms such as photonics, where measurement-based protocols are natural and high-dimensional states are readily available. We discuss several examples for arbitrary prime dimension $d$, such as the qudit toric code (stabilizer, CSS), the $d$-dimensional perfect $[[5,1,3]]$ code (stabilizer, non-CSS), and a straightforward $d$-dimensional generalization of the CSS honeycomb code (dynamical, CSS). Under a simple error model, we numerically calculate thresholds for the foliated qudit toric code and demonstrate that they are comparable to the non-foliated version.
Comments15 Figures in total (5 in the main text and appendices, 10 in Supplementary Material.) and 1 table
