[论文解读] Realization of real-time fault-tolerant quantum error correction

C. Ryan-Anderson, J. G. Bohnet+15 more|arXiv (Cornell University)|Jul 15, 2021

Quantum Computing Algorithms and Architecture被引用 10

一句话总结

该论文在10量子比特的离子阱量子计算机上，利用[[7,1,3]]彩色码实现了实时、容错的量子误差校正。通过结合高保真度的中途测量、实时经典解码以及通过Pauli框架更新实现的动态校正，作者实现了重复的误差校正循环，从而显著延长了逻辑量子比特的相干时间，逻辑SPAM误差为1.7(2)×10⁻³，低于物理SPAM误差2.4(8)×10⁻³。

ABSTRACT

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, mid-circuit 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 ten qubit QCCD trapped-ion quantum computer to encode a single logical qubit using the $[[7,1,3]]$ color code, first proposed by Steane~\cite{steane1996error}. The logical qubit is initialized into the eigenstates of three mutually unbiased bases using an encoding circuit, and we measure an average logical SPAM error of $1.7(6) imes 10^{-3}$, compared to the average physical SPAM error $2.4(8) imes 10^{-3}$ 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 logical 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 pseudo-threshold.

研究动机与目标

• 在可扩展的量子处理器上实现完整的、实时的容错量子误差校正（QEC）流程。
• 展示重复的误差校正循环，以在长时间内维持逻辑量子比特的相干性。
• 通过在[[7,1,3]]彩色码中编码单个逻辑量子比特，验证容错逻辑操作的可行性。
• 识别限制性能的关键物理误差源，并为未来硬件改进提供指导。
• 通过展示低于蒸馏阈值的逻辑Clifford门和逻辑T态制备，实现通用量子计算。

提出的方法

• 使用[[7,1,3]]彩色码在10个物理离子阱量子比特上编码单个逻辑量子比特。
• 执行高保真度的单量子比特和双量子比特门操作，进行中途测量，并对测量结果进行实时经典处理。
• 使用实时解码器计算校正操作，以软件方式更新Pauli框架或作为物理门应用。
• 在所有三个相互正交的基底下，实现容错的逻辑态初始化和测量。
• 制备逻辑|+⟩_L态和用于非Clifford门操作的逻辑T态，其误差率低于蒸馏阈值。
• 通过系统级仿真建模逻辑误差率，并识别主要误差源，特别是退相干和泄漏。

Figure 1: The $[[7,1,3]]$ color code. The seven data qubits are on the vertices of the polygons and three ancilla qubits for syndrome measurements are off to the side. For each polygon, the four qubits at the vertices define both $X$ -type and $Z$ -type stabilizer measurements used in each error cor

实验结果

研究问题

• RQ1 是否可以在离子阱量子处理器上实时实现容错量子误差校正循环？
• RQ2 使用[[7,1,3]]彩色码结合实时校正，所实现的逻辑SPAM误差率是多少？
• RQ3 在实时QEC系统中，双量子比特门误差、泄漏和退相干等物理误差源如何影响逻辑误差率？
• RQ4 能否以适合魔态蒸馏的误差率实现逻辑非Clifford门操作？
• RQ5 为实现低于伪阈值的逻辑误差率，哪些硬件升级最为关键？

主要发现

• 测得的逻辑SPAM误差率为1.7(2)×10⁻³，相比平均物理SPAM误差率2.4(8)×10⁻³降低了29%。
• 系统成功执行了重复的误差校正循环，同时维持了逻辑量子比特的相干性，展示了动态保护能力。
• 逻辑T态的制备误差率低于魔态蒸馏所需的阈值，从而为通用量子计算提供了支持。
• 系统级仿真识别出泄漏和退相干是主要误差源，即使双量子比特门误差被降低，它们仍会限制系统在规模扩展时的性能。
• 仿真显示，将泄漏率降低10倍是实现伪阈值的最有效改进措施。
• 尽管退相干作为较小的物理误差源，却对逻辑误差率产生了不成比例的显著影响，凸显了提升相干性的重要性。

Figure 2: The ion trap loaded with ten 171 Yb + qubit ions (red circles) and ten 138 Ba + coolant ions (white circles). The trap has different functional regions, or zones, with functions determined by the electrode geometry and laser beam configuration. Ion transport is used to arrange ions into zo