标题： 带有擦除量子位的魔术态注入 显示英文标题

标题： Magic State Injection with Erasure Qubits

摘要： 擦除量子比特是一种有前景的方法，用于解决容错量子计算所需的庞大资源问题。 通过引导擦除错误，纠错阈值和逻辑错误率的次阈值缩放显著提高。 虽然之前的研究主要集中在容错量子存储器上，但我们将其研究扩展到魔术态注入——这是容错量子计算中一个关键但资源密集的组成部分。 我们表明，在对擦除进行后选择之后，注入的魔术态的逻辑错误率由残留的保罗错误决定，而与具有类似噪声强度的非擦除量子比特相比，时空开销仅略有增加。 这些结论既适用于表面码中的注入，也适用于颜色码中的注入和培养。 对于前者，我们表明，通过在表面码块中仅使用三个战略性放置的擦除量子比特就可以实现大部分优势，与块大小无关。 而对于后者，相反，让培养块中的所有量子比特都是擦除量子比特是有益的。 我们的培养结果表明，对于擦除率$\lesssim 4\times 10^{-3}$和残留保罗错误率$\sim 10^{-4}$，算法相关的逻辑错误率可能无需魔术态纯化即可达到。 显示英文摘要

摘要： Erasure qubits constitute a promising approach for tackling the daunting resources required for fault-tolerant quantum computing. By heralding erasure errors, both the error-correction threshold and the sub-threshold scaling of the logical error rate are significantly improved. While previous research has focused primarily on fault-tolerant quantum memories, we extend this investigation to magic state injection--a critical yet resource-intensive component of fault-tolerant quantum computation. We show that, after postselecting on erasures, the logical error rate of the injected magic state is set by the residual Pauli error, while the space-time overhead is only marginally increased as compared to non-erasure qubits with a similar noise strength. These conclusions hold both for injection into the surface code, and for injection and cultivation on the color code. For the former, we show that most of the gains can be achieved by using just three strategically placed erasure qubits in the surface code patch, independent of the patch size. For the latter, in contrast, it is beneficial to have all the qubits in the cultivation patch be erasure qubits. Our results for cultivation suggest that algorithmically relevant logical error rates may be within reach without magic state distillation for erasure rates $\lesssim 4\times 10^{-3}$ and residual Pauli error rates $\sim 10^{-4}$.