论文标题
通过量规固定和减少量子的开销，具有较高阈值的子系统代码
Subsystem codes with high thresholds by gauge fixing and reduced qubit overhead
论文作者
论文摘要
我们引入了一种使用量规固定来显着提高子系统代码的量子错误纠正性能的技术。通过更改测量检查操作员的顺序，可以获得宝贵的其他信息，我们引入了一种新方法来解码，该方法使用此信息来提高性能。使用三量校验运算符应用于子系统曲折代码，我们将电路级去极化噪声下的阈值从0.67美元\％$ $ $ $ $ $ $提高。在电路级噪声模型的情况下，阈值进一步增加，无限偏见$ 2.22 \％$。此外，我们使用三量检查操作员和最佳深度均等检查测量时间表来构建有限速率子系统LDPC代码的家族。据我们所知，这些有限速率子系统代码的表现优于电路级的去极化错误率的所有已知代码高达$ 0.2 \％$，在这些量度上，它们的Qubit开销价格为$ 4.3 \ times $ 4.3 \ timper $ $比表面代码的最高效版本低于表面代码的$ 5.1 \ $ 5.1 \ tims $ $比子系统Toric Code低。他们的阈值和伪阈值超过$ 0.42 \％$ $ $ $ $ $ $ $ $ $，使用量规固定在无限偏置下增加到$ 2.4 \％$ $。
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 depolarising 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 LDPC 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 depolarising 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 depolarising noise, increasing to $2.4\%$ under infinite bias using gauge fixing.
