层码作为量子存储器：综合征提取、阈值与空闲鲁棒性
Layer codes as quantum memories: syndrome extraction, thresholds and idle robustness
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中文总结 AI 辅助
本文提出层码的综合征提取调度器，在电路级噪声下评估其性能，发现其阈值与表面码相当，但空闲鲁棒性更优，代价是更多操作和物理量子比特。
中文摘要 AI 辅助
层码是校验权重至多为六的三维局部CSS码，通过将CSS输入码与未旋转的表面码补丁进行准级联而获得。现有关于它们的研究描述的是码本身，而非测量它的电路。在本工作中，我们将它们作为电路级噪声下的主动存储器进行评估。这样做首先需要综合征提取电路，而连接各补丁的结稳定子排除了借用表面码补丁的CNOT调度方案。我们提出了一种无需解码器的调度器，该调度器首先约束钩子传播，随后压缩深度，为四种输入码下的十八种层码生成电路，并将它们与相同距离、以相同方式模拟和解码的表面码进行比较。在可负担电路距离证明的情况下，这些电路在[[4,2,2]]输入码上不会因钩子错误而损失距离，并且其逻辑错误率低于通用CSS码调度器，而每轮CNOT深度约为后者的一半。我们基于[[4,2,2]]输入码构建的主要码族达到了$5.06(7)\ imes 10^{-3}$的电路级阈值。在空闲鲁棒性方面，层码优于表面码：在相同距离下，它能容忍的综合征提取轮次间隔比旋转表面码长1.7至3.0倍。这是以每单位时间操作数增加1.7至5.0倍以及每个逻辑量子比特的物理量子比特数增加约五倍为代价的。最后，我们对构建所要求的超越二维的跨平面CNOT的成本进行了建模，发现其速度远比其保真度重要。
英文摘要
Layer codes are three-dimensional local CSS codes of check weight at most six, obtained by quasi-concatenating a CSS input code with unrotated surface code patches. What is established about them describes the code, not the circuit that measures it. In this work, we evaluate them as active memories under circuit-level noise. Doing so first requires a syndrome extraction circuit, and the junction stabilizers that couple the patches rule out borrowing a surface code patch's CNOT schedule. We present a decoder-free scheduler that constrains hook propagation first and compresses depth afterwards, generate circuits for eighteen layer codes across four input codes, and compare them with surface codes of the same distance, simulated and decoded in the same way. The circuits lose no distance to hook errors on [[4,2,2]]-input codes wherever a circuit-distance proof is affordable, and reach a lower logical error rate than those of a general-purpose scheduler for CSS codes at roughly half its CNOT depth per round. Our primary family built from a [[4,2,2]] input code reaches a circuit-level threshold of $5.06(7)\times10^{-3}$. The layer code outperforms the surface code in terms of idle robustness: at the same distance it tolerates an interval between syndrome extraction rounds 1.7-3.0 times longer than the rotated surface code. This comes at the cost of 1.7-5.0 times more operations per unit time and approximately five times more physical qubits, both per logical qubit. Finally, we model the cost of the beyond-2D cross-plane CNOTs that the construction demands, and find that their speed matters far more than their fidelity.
发表机构
- University of Oxford（牛津大学）
- Quantum Motion（量子运动）
- Imperial College London（伦敦帝国理工学院）
机构由 AI 辅助整理，请以论文原文为准。
