发表机构
Shenzhen University of Advanced Technology; Guangdong Provincial Key Laboratory of Computility Microelectronics; Pengxin Quantum Technology (Shenzhen) Co., Ltd.; Sun Yat-sen University（深圳先进技术大学; 广东省计算微电子重点实验室; 鹏芯量子技术（深圳）有限公司; 中山大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本研究评估了规范逻辑测量中四个侧条件的相对重要性，发现首尾轮完美条件决定时间容错，扩张条件不影响结果，并精确计算了两种码的故障距离，为阈值估计提供定价依据。
AI 中文摘要
逻辑测量读出受保护的信息，其能承受的噪声决定了量子计算可吸收的噪声量。规范（Gauging）通过在被测量量子比特的图上每条边添加一个额外量子比特，将全局算符转化为局部奇偶校验，从而构建逻辑测量。其容错能力分为两部分：剩余码的距离，以及故障可隐藏的轮数。Williamson 和 Yoder 证明了这两个部分都保持不低于码的距离。该保证依赖于四个侧条件作为一个整体，且均未定价。这里我们表明它们并非同等重要：要求首轮和末轮完美（这看似簿记操作）承担了时间部分。在探测器比较相邻轮次的模型中，舍弃该条件会使故障距离（即未被发现且翻转读出结果的最小权重故障）对每个码和轮数降至一，完整协议在实例测量上崩溃。扩张条件（即没有小集合量子比特被隔离）并不决定结果：在同一量子比特上的两条路径，均处于覆盖范围之外，分别给出距离一和二。在比较轮次是唯一规则的场景中，轮数是紧的；完整协议提前一轮达到距离。两个部分均在证明助手内对规范双变量自行车码和 Bacon-Shor 测量进行了精确计算。阈值估计消耗此类数值；侧条件可以被定价。
英文摘要
A logical measurement reads out protected information, and the noise it survives sets how much a quantum computation can absorb. Gauging builds one from a graph on the measured qubits, one extra qubit on each edge, turning a global operator into local parity checks. Its tolerance splits in two: the distance of the code left behind, and the rounds a fault can hide in. Williamson and Yoder proved both components stay at or above the code's distance. The guarantee rests on four side conditions taken as a package, none of them priced. Here we show they are not worth the same: the demand that the first and last rounds be perfect, which reads like bookkeeping, carries the temporal part. Dropping it flattens the fault distance, the least weight of a fault that passes unseen and flips the readout, to one for every code and round count, in a model whose detectors compare adjacent rounds; the full protocol collapses on the instance measured. The expansion condition, that no small set of qubits be sealed off, does not decide the outcome: two paths on the same qubits, both outside the covered regime, give distances one and two. The round count is tight where comparing rounds is the whole rule; the full protocol reaches the distance a round early. Both components are computed exactly on a gauged bivariate bicycle code and a Bacon--Shor measurement, inside a proof assistant. Threshold estimates consume such numbers; side conditions can be priced.
