任意旋转表面码布局上分布式晶格手术的综合征提取框架
A Syndrome-Extraction Framework for Distributed Lattice Surgery on Arbitrary Rotated Surface-Code Layouts
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- Brandeis University（布兰迪斯大学）
- Argonne National Laboratory（阿贡国家实验室）
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中文总结 AI 辅助
提出一种接缝构造框架，将任意旋转表面码布局分割为均匀补丁，通过贝尔对和CXX门限制链路错误，实现低且稳定的逻辑错误率。
中文摘要 AI 辅助
模块化量子计算是可扩展容错量子计算的主要候选方案。在不同模块中使用表面码补丁执行晶格手术需要使用模块间门，这些门比本地门噪声更大。此外，晶格手术期间合并的布局暴露了多个方向，钩子错误可以沿这些方向传播以降低容错距离。现有的避免钩子的调度要么增加综合征提取电路深度，要么让链路故障传播到体区域。我们引入了一种接缝构造，允许将任意合并的旋转表面码布局分割成具有均匀边界的较小补丁，这些补丁可以保持自己的避免钩子的N/Z形调度。在接缝处，我们将权重为4的稳定子拆分为由贝尔对介导的权重为2的稳定子对，并在CNOT深度为4的范围内测量。我们还采用三量子比特的CXX门用于接缝处的奇偶校验测量，以保持最小CNOT深度。通过这种接缝构造，我们将升高的链路错误限制在接缝处，保护体区域免受更高错误率的影响。我们还为这种接缝提供了自定义探测器注释器，可以找到探测器空间，在Stim电路中注释探测器，并确保它们适合匹配解码器使用。我们针对逻辑Pauli-XX测量晶格手术和十字形空间结实现了我们的构造，并将链路错误率从固定体错误率的10倍扫描到100倍，结果表明我们的构造在比较的其他框架中给出了最低且最稳定的逻辑错误率。
英文摘要
Modular quantum computing is a leading candidate for scalable fault tolerant quantum computation. Performing lattice surgery using surface code patches in different modules requires the use of inter-module gates that are noisier than the local gates. Furthermore, the merged layouts during lattice surgery expose multiple directions in which hook errors can propagate to reduce the fault distance. Existing hook-avoiding schedules either increase the syndrome extraction circuit depth, or let link faults propagate into the bulk. We introduce a seam construction that allows splitting arbitrary merged rotated surface code layout into smaller patches with uniform boundaries that could keep their own hook-avoiding N/Z shaped schedule. At the seam we split weight-4 stabilizers into pairs of weight-2 stabilizers that are mediated through a Bell pair and measured within a CNOT depth of 4. We also employ the use of three-qubit $\texttt{CXX}$ gates for parity measurements at the seam to maintain the minimum CNOT depth. Through this seam construction, we confine the elevated link error at the seam, protecting the bulk from higher error rate. We also give a custom detector annotator for such seams that can find the detector space, annotate detectors in the Stim circuits, and ensure that they are suitable to use by matching decoders. We implement our construction for the logical Pauli-$XX$ measurement lattice surgery and a cross-shaped spatial junction and sweep the link error rate from $10$ times to $100$ times a fixed bulk error rate, and show that our construction gives the lowest and most stable logical error rate than the other frameworks compared here.
