[论文解读] Implementing Fault-tolerant Entangling Gates on the Five-qubit Code and the Color Code

C. Ryan-Anderson, N. C. Brown+35 more|arXiv (Cornell University)|Aug 3, 2022

Quantum Computing Algorithms and Architecture被引用 54

一句话总结

本文在受约束离子实现平台上，实验性比较两种量子误差纠正编码的容错纠缠门实现——使用可分段容错的 [[5,1,3]] 代码与 [[7,1,3]] 颜色码——并通过态保真度和过程界限（含实时解码）来评估性能。

ABSTRACT

We compare two different implementations of fault-tolerant entangling gates on logical qubits. In one instance, a twelve-qubit trapped-ion quantum computer is used to implement a non-transversal logical CNOT gate between two five qubit codes. The operation is evaluated with varying degrees of fault tolerance, which are provided by including quantum error correction circuit primitives known as flagging and pieceable fault tolerance. In the second instance, a twenty-qubit trapped-ion quantum computer is used to implement a transversal logical CNOT gate on two [[7,1,3]] color codes. The two codes were implemented on different but similar devices, and in both instances, all of the quantum error correction primitives, including the determination of corrections via decoding, are implemented during runtime using a classical compute environment that is tightly integrated with the quantum processor. For different combinations of the primitives, logical state fidelity measurements are made after applying the gate to different input states, providing bounds on the process fidelity. We find the highest fidelity operations with the color code, with the fault-tolerant SPAM operation achieving fidelities of 0.99939(15) and 0.99959(13) when preparing eigenstates of the logical X and Z operators, which is higher than the average physical qubit SPAM fidelities of 0.9968(2) and 0.9970(1) for the physical X and Z bases, respectively. When combined with a logical transversal CNOT gate, we find the color code to perform the sequence--state preparation, CNOT, measure out--with an average fidelity bounded by [0.9957,0.9963]. The logical fidelity bounds are higher than the analogous physical-level fidelity bounds, which we find to be [0.9850,0.9903], reflecting multiple physical noise sources such as SPAM errors for two qubits, several single-qubit gates, a two-qubit gate and some amount of memory error.

研究动机与目标

• 评估两种量子纠错编码上的实际容错（FT）纠缠门实现：五量子位代码与颜色码。
• 评估不同 FT 原语（标记、可分段FT、FT SPAM、FT 测量输出、QEC 循环）对逻辑态保真度的影响。
• 在现实噪声下比较逻辑门性能与物理层性能。
• 展示与量子处理器整合的实时解码。
• 提供仿真以在较低物理错误率下理解代码性能。

提出的方法

• 在 [[5,1,3]] 代码中，使用带中间 QEC 和标记的可分段 FT 对两个逻辑量子位实现逻辑 CNOT。
• 在 [[7,1,3]] 颜色码中，实现跨越的逻辑 CNOT（横向传输）。
• 通过使用从 QASM 脱钩的 Look-Up Table 解码器并由现场外部的经典协处理器嵌入运行时解码（采用 WebAssembly 的解码器）来实现。
• 对具有不同 FT 原语（初始化、QEC 循环、标记、测量输出）的电路进行表征，并在 X、Z 与 Bell 基底下测量态保真度以界定过程保真度。
• 使用两个不同的 Quantinuum 寄存离子系统（五量子位代码为 H1-2；颜色码为 H1-1），实现集成的 SPAM、QEC 与解码。

实验结果

研究问题

• RQ1 你如何用翻译后的研究问题列表替换原文中的空条？

主要发现

• 在所测试条件下，使用 [[7,1,3]] 颜色码的实验在保真度方面高于五量子位代码。
• 颜色码的 FT SPAM 将 X、Z 基底的本征态制备保真度提升至接近 0.9994–0.9996。
• 采用颜色码的逻辑 CNOT 的平均保真度界约为 [0.9957, 0.9963]，高于相应的物理层界 [0.9850, 0.9903]。
• 五量子位代码的实验表明，在所考察的噪声环境下，较高的 FT 电路复杂度并不总是提升保真度；CNOT1f（非 FT SPAM）在测试的五量子位代码序列中提供了最高保真度。
• 仅 SPAM 与 FT-SPAM 的结果表明，在某些设置中逻辑 SPAM 可接近或超过物理 SPAM，但总体逻辑保真度仍受现实噪声和门数量的约束。
• 仿真显示在较低物理错误率下可能获得性能提升，展示了这些量子纠错编码的长期潜力。