AI 中文总结
本研究提出零开销的moonwalking表面码，结合三态测量与分支定界解码器，可在无需中间电路擦除校验的情况下，实现表面码类似擦除的逻辑错误率缩放，提升了对泄漏和擦除的处理能力。
AI 中文摘要
量子纠错（QEC）码可纠正的擦除错误数量是泡利错误的两倍。凭借这一缩放优势，学界对开发能通过中间电路擦除校验将主导错误通道转化为擦除的量子比特兴趣浓厚，但这类擦除校验在实际应用中存在硬件开销。终端三态读出可同时测量量子比特的擦除状态与计算状态，是中间电路擦除校验的替代方案，通常更易实现。本研究系统探究了表面码实现擦除性能（即翻倍纠错容量）所需的条件，涵盖有无中间电路擦除校验的情况。我们提出了「moonwalking表面码」，即「walking表面码」的时间反演版本，这是一种零开销电路，对泄漏和擦除的处理能力更优。具体而言，若泄漏量子比特会导致两量子比特门被跳过，且采用合适的解码器，结合三态测量时，该码可实现类似擦除的逻辑错误率缩放。我们的解码器基于分支定界算法，专门纳入了跳过门泄漏量子比特效应的噪声结构。
英文摘要
Quantum error correction (QEC) codes can correct twice as many erasure errors as Pauli errors. Because of this scaling advantage, there is significant interest in developing qubits whose dominant error channel can be converted into erasures via mid-circuit erasure checks. However, such erasure checks come with hardware overhead in practice. End-of-the-line three-state readout, in which one simultaneously measures a qubit's erasure status and computational state, is an alternative to mid-circuit erasure checks that is generally simpler to implement. In this work, we systematically study the conditions required to enable erasure performance---the doubled error-correction capacity---in the surface code with and without mid-circuit erasure checks. We introduce the moonwalking surface code, the time-reversal of the walking surface code, as a zero-overhead circuit with superior handling of leakage and erasure. Specifically, we show that it enables erasure-like logical error rate scaling when combined with three-state measurement if leaked qubits cause two-qubit gates to be skipped and an appropriate decoder is used. Our decoder, based on a branch-and-bound algorithm, specifically incorporates the noise structure of the skip-gate leaked-qubit effect.
Comments10 pages main text (5 figures), 9 pages appendix. See also separate Supplementary Materials. v2: added missing funding acknowledgement. v3: updated results after fixing bug in simulation code. Minimal effect. v4: fixed analytical error in Sec. V.A, Table IV
