Handling leakage with subsystem codes
Handling leakage with subsystem codes
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DOI：
10.1088/1367-2630/ab3372
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发表时间：
2019-03
影响因子：
3.3
通讯作者：
N. C. Brown;M. Newman;K. Brown
中科院分区：
文献类型：
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作者：
N. C. Brown;M. Newman;K. Brown
泄漏是一种特别具有破坏性的错误，当量子位状态脱离其两级计算子空间时就会发生。与独立的去极化噪声相比，泄漏的量子位可能在纠错过程中产生更多有害相关错误的配置。在这项工作中，我们研究了泄漏门错误模型的低错误状态下的不同本地代码。当限制裸辅助提取时，我们观察到子系统代码是处理泄漏的良好候选者，因为它们的局部性可以限制破坏性的相关错误。作为案例研究，我们将子空间表面代码与 Bravyi 等人引入的子系统表面代码进行比较。与去极化噪声相比，子系统表面代码的性能优于同距离子空间表面代码，错误率高达 ⪅ 7.5 × 10−4，同时提供更好的每量子位距离保护。此外，我们表明，在低到中距离，Bacon-Shor 码提供了更好的每量子位错误保护，防止离子陷阱驱动的错误模型中的泄漏，错误率高达 ⪅ 1.2 × 10−3。对于受限泄漏模型，通过放松到表面代码中未经验证的双量子位猫状态提取，可以将这一优势扩展到更长的距离。这些结果凸显了子系统代码局部性对纠错性能的内在好处。
Leakage is a particularly damaging error that occurs when a qubit state falls out of its two-level computational subspace. Compared to independent depolarizing noise, leaked qubits may produce many more configurations of harmful correlated errors during error-correction. In this work, we investigate different local codes in the low-error regime of a leakage gate error model. When restricting to bare-ancilla extraction, we observe that subsystem codes are good candidates for handling leakage, as their locality can limit damaging correlated errors. As a case study, we compare subspace surface codes to the subsystem surface codes introduced by Bravyi et al. In contrast to depolarizing noise, subsystem surface codes outperform same-distance subspace surface codes below error rates as high as ⪅ 7.5 × 10−4 while offering better per-qubit distance protection. Furthermore, we show that at low to intermediate distances, Bacon–Shor codes offer better per-qubit error protection against leakage in an ion-trap motivated error model below error rates as high as ⪅ 1.2 × 10−3. For restricted leakage models, this advantage can be extended to higher distances by relaxing to unverified two-qubit cat state extraction in the surface code. These results highlight an intrinsic benefit of subsystem code locality to error-corrective performance.