Correcting errors in real time is essential for reliable large-scale quantum computations. Realizing this high-level function requires a system capable of several low-level primitives, including single-qubit and two-qubit operations, midcircuit measurements of subsets of qubits, real-time processing of measurement outcomes, and the ability to condition subsequent gate operations on those measurements. In this work, we use a 10-qubit quantum charge-coupled device trapped-ion quantum computer to encode a single logical qubit using the $[[7,1,3]]$ color code, first proposed by Steane [Phys. Rev. Lett. 77, 793 (1996)]. The logical qubit is initialized into the eigenstates of three mutually unbiased bases using an encoding circuit, and we measure an average logical state preparation and measurement (SPAM) error of $1.7(2)\times {10}^{-3}$, compared to the average physical SPAM error $2.4(4)\times {10}^{-3}$ of our qubits. We then perform multiple syndrome measurements on the encoded qubit, using a real-time decoder to determine any necessary corrections that are done either as software updates to the Pauli frame or as physically applied gates. Moreover, these procedures are done repeatedly while maintaining coherence, demonstrating a dynamically protected logical qubit memory. Additionally, we demonstrate non-Clifford qubit operations by encoding a $\overline{T}|+{⟩}_L$ magic state with an error rate below the threshold required for magic state distillation. Finally, we present system-level simulations that allow us to identify key hardware upgrades that may enable the system to reach the pseudothreshold.

中文翻译：

---

实时容错量子纠错的实现

实时纠正错误对于可靠的大规模量子计算至关重要。实现这一高级功能需要一个能够执行多个低级原语的系统，包括单量子位和双量子位操作、量子位子集的中间电路测量、测量结果的实时处理以及调节后续门操作的能力在这些测量上。在这项工作中，我们使用 10 量子位量子电荷耦合器件俘获离子量子计算机来编码单个逻辑量子位。$[[7,1,3]]$颜色代码，首先由 Steane [ Phys. 牧师莱特。 77 , 793 (1996)]。使用编码电路将逻辑量子位初始化为三个相互无偏基的本征态，我们测量平均逻辑状态准备和测量 (SPAM) 误差为$1.7(2)\times {10}^{-3}$, 与平均物理垃圾邮件错误相比 $2.4(4)\times {10}^{-3}$我们的量子位。然后，我们使用实时解码器对编码的量子位执行多个校正子测量，以确定作为泡利帧的软件更新或物理应用的门完成的任何必要的校正。此外，这些过程在保持一致性的同时重复执行，展示了动态保护的逻辑量子位存储器。此外，我们通过编码一个非 Clifford 量子位操作来演示$\overline{吨}|+{⟩}_{升}$错误率低于魔术状态蒸馏所需阈值的魔术状态。最后，我们展示了系统级模拟，使我们能够识别可能使系统达到伪阈值的关键硬件升级。