多轭表面码
Multi-Yoked Surface Codes
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中文总结 AI 辅助
本文提出多轭表面码，通过多级级联链码和分层轭间隔的补丁分配，在保持平面连接的同时提高编码密度，在teraquop区域密度提升4至4.5倍。
中文摘要 AI 辅助
表面码因其平面最近邻连接、高阈值和高效解码而成为容错量子计算的主要候选方案，但其低编码率在teraquop区域每个逻辑量子比特需要约一千个物理量子比特。轭表面码通过在表面码之上级联高密度奇偶校验码，同时保持平面最近邻连接，将密度提高了两到三倍。在这项工作中，我们将这一思想推广到多层级联，并引入了多轭表面码。我们的构造基于两个新要素。首先，我们提出了一类称为链码的外码族，通过链接种子码的副本构建，该种子码检测下一级代码的块错误；所得代码使用较低级别的所有逻辑量子比特，并在几级级联内实现高编码率。其次，我们设计了一种补丁分配方案，其中可移动工作区通过具有轭间隔层次结构的晶格手术执行轭检查，使得较低级别的检查频繁执行，而较高级别的检查较少执行，从而避免了单个大距离外码所需的长轭间隔。作为基准，我们构建了一个具有$[[256,166,8]]$外码的三轭表面码，并在SI1000噪声模型下使用表面码解码器的软信息进行数值评估。逻辑错误率在内码距离上呈指数级抑制，在teraquop区域，三轭表面码的密度大约是未轭表面码的4到4.5倍。
英文摘要
The surface code is the leading candidate for fault-tolerant quantum computation owing to its planar nearest-neighbor connectivity, high threshold, and efficient decoding, but its low encoding rate demands on the order of a thousand physical qubits per logical qubit in the teraquop regime. Yoked surface codes improve the density by a factor of two or three by concatenating a high-density parity check code on top of the surface code while retaining planar nearest-neighbor connectivity. In this work, we generalize this idea to multiple levels of concatenation and introduce multi-yoked surface codes. Our construction rests on two new ingredients. First, we propose a family of outer codes called chain codes, built by chaining copies of a seed code that detects the block errors of the code one level below; the resulting codes use all logical qubits of the lower level and achieve a high encoding rate within a few concatenation levels. Second, we design a patch allocation in which movable workspaces perform the yoking checks by lattice surgery with a hierarchy of yoking intervals, so that lower-level checks are performed frequently while higher-level checks are performed less often, which avoids the long yoking intervals that a single large-distance outer code would require. As a benchmark, we construct a three-yoked surface code with a $[[256,166,8]]$ outer code and evaluate it numerically under the SI1000 noise model using soft information from the surface code decoder. The logical error rate is suppressed exponentially in the inner code distance, and in the teraquop regime the three-yoked surface code is about 4 to 4.5$\times$ denser than the unyoked surface code.
发表机构
- Keio University（庆应义塾大学）
- RIKEN（理化学研究所）
机构由 AI 辅助整理，请以论文原文为准。
