We introduce a technique that uses gauge fixing to significantly improve the quantum-error-correcting performance of subsystem codes. By changing the order in which check operators are measured, valuable additional information can be gained, and we introduce a new method for decoding which uses this information to improve performance. Applied to the subsystem toric code with three-qubit check operators, we increase the threshold under circuit-level depolarizing noise from 0.67% to 0.81%. The threshold increases further under a circuit-level noise model with small finite bias, up to 2.22% for infinite bias. Furthermore, we construct families of finite-rate subsystem low-density parity-check codes with three-qubit check operators and optimal-depth parity-check measurement schedules. To the best of our knowledge, these finite-rate subsystem codes outperform all known codes at circuit-level depolarizing error rates as high as 0.2%, where they have a qubit overhead that is $4.3\times$ lower than the most efficient version of the surface code and $5.1\times$ lower than the subsystem toric code. Their threshold and pseudo-threshold exceeds 0.42% for circuit-level depolarizing noise, increasing to 2.4% under infinite bias using gauge fixing.

中文翻译：

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通过规范固定和减少量子位开销的具有高阈值的子系统代码

我们介绍了一种使用规范固定来显着提高子系统代码的量子纠错性能的技术。通过更改检查运算符的测量顺序，可以获得有价值的附加信息，并且我们引入了一种新的解码方法，该方法使用这些信息来提高性能。应用于具有三量子位校验算子的子系统复曲面代码，我们将电路级去极化噪声下的阈值从 0.67% 增加到 0.81%。在具有小的有限偏差的电路级噪声模型下，阈值进一步增加，对于无限偏差高达 2.22%。此外，我们使用三量子位校验算子和最佳深度奇偶校验测量计划构建了有限速率子系统低密度奇偶校验码系列。据我们所知，$4.3\times$ 低于表面代码的最有效版本，并且 $5.1\times$低于子系统环面代码。对于电路级去极化噪声，它们的阈值和伪阈值超过 0.42%，使用仪表固定在无限偏置下增加到 2.4%。