Mitigating Temporal Fragility in the XY Surface Code,Physical Review X

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Mitigating Temporal Fragility in the XY Surface Code
Physical Review X ( IF 11.6 ) Pub Date : 2024-07-09 , DOI: 10.1103/physrevx.14.031003
Pei-Kai Tsai _{1,

1} , Yue Wu _{1,

1} , Shruti Puri _{1,

1}

Affiliation

An important outstanding challenge that must be overcome in order to fully utilize the XY surface code for correcting biased Pauli noise is the phenomenon of fragile temporal boundaries that arises during the standard logical state-preparation and measurement protocols. To address this challenge we propose a new logical state-preparation protocol based on locally entangling qubits into small Greenberger-Horne-Zeilinger-like states prior to making the stabilizer measurements that place them in the XY-code state. We prove that in this new procedure

O (\sqrt{n})

high-rate errors along a single lattice boundary can cause a logical failure, leading to an almost quadratic reduction in the number of fault configurations compared to the standard state-preparation approach. Moreover, the code becomes equivalent to a repetition code for high-rate errors, guaranteeing a 50% code-capacity threshold during state preparation for infinitely biased noise. With a simple matching decoder we confirm that our preparation protocol outperforms the standard protocol in terms of both threshold and logical error rate in the fault-tolerant regime where measurements are unreliable and at experimentally realistic biases. We also discuss how our state-preparation protocol can be inverted for similar fragile-boundary-mitigated logical-state measurement.

中文翻译：

减轻 XY 表面代码中的时间脆弱性

为了充分利用 XY 表面代码来校正有偏差的泡利噪声，必须克服的一个重要的突出挑战是在标准逻辑状态准备和测量协议期间出现的脆弱时间边界现象。为了应对这一挑战，我们提出了一种新的逻辑状态准备协议，该协议基于在进行将量子位置于 XY 代码状态的稳定器测量之前，将量子位局部纠缠成类似 Greenberger-Horne-Zeilinger 的小状态。我们证明，在这个新过程中，沿单个晶格边界的高速率错误可能会导致逻辑故障，与标准状态准备方法相比，导致故障配置数量几乎呈二次方减少。此外，该代码等效于高错误率的重复代码，从而在无限偏置噪声的状态准备期间保证 50% 的代码容量阈值。通过简单的匹配解码器，我们确认我们的准备协议在容错机制中的阈值和逻辑错误率方面均优于标准协议，在容错机制中测量不可靠且存在实验上现实的偏差。我们还讨论了如何反转我们的状态准备协议以实现类似的脆弱边界缓解逻辑状态测量。

更新日期：2024-07-09

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