AI 中文总结
针对多门隐形传输中相关错误导致容错性下降的问题，提出基于旋转表面码的容错数据包大小设计规则，并通过模拟验证其有效性，在降低纠缠成本的同时保持容错性。
AI 中文摘要
多门隐形传输（MGT）通过一个1-ebit扇出量子电路将$n$个远程门打包成一个ebit，相比顺序门隐形传输节省了$n{-}1$个纠缠对。代价是相关的故障模式：单个网络故障通过扇出树传播，注入一个权重为$n$的泡利错误。我们推导了容错数据包大小的设计规则，对于距离为$d$的旋转表面码，使用相关性感知解码器时$\nmax^{\text{corr}}(d) = \lceil d/2 \rceil$（无感知时$\nmax^{\text{naive}} = \lfloor d/2 \rfloor$），限制了在保持容错性的前提下可打包的门数量。使用PyMatching的模拟表明，基于数据包电路噪声模型构建的标准MWPM解码器自然纠正了相关错误：在网络-本地噪声比$\gamma = \pnet/\pgate$高达100时，数据包在中高$\gamma$下匹配或超过每链路顺序LER，优势随$\gamma$和$d$增长，同时将纠缠成本从$n$个ebit降低到1个。当网络成为瓶颈时（$\gamma \gg 1$），打包化获胜；在$\gamma \approx 1$时，额外的$n{-}1$个本地扇出门抵消了网络节省。无需自定义解码器：电路级噪声模型已经编码了相关性。这些结果使得噪声感知的分布式电路编译器能够在不牺牲容错性的情况下倾向于扇出打包化。
英文摘要
Multi-gate teleportation (MGT) packages $n$ remote gates into a single ebit via a 1-ebit fan-out quantum circuit, saving $n{-}1$ entangled pairs relative to sequential gate teleportation. The cost is a correlated failure mode: a single network fault propagates through the fan-out tree, injecting a weight-$n$ Pauli error on the target register (weight $n{+}1$ including the control). We establish a design rule for fault-tolerant packet sizes in rotated surface codes of odd distance~$d$: a rigorous decoder-independent floor $\lfloor d/2 \rfloor$, extended to $\lceil d/2 \rceil$ by a local weight argument confirmed by simulation when the decoder is correlation-aware. Simulation with PyMatching shows the standard MWPM decoder built from the packet circuit's detector error model (DEM) naturally corrects the correlated error: at $n=\lfloor d/2\rfloor$ the packet matches or surpasses the per-link sequential LER for moderate-to-high $γ$, with the crossover $γ^\star$ decreasing as $d$ grows (from $γ^\star{\approx}17$ at $d{=}5$ to $γ^\star{<}1$ at $d{=}9$, extrapolated), whilst reducing the entanglement cost from $n$ ebits to~$1$. Packetisation wins when the network is the bottleneck ($γ\gg 1$); at $γ\approx 1$ the packet is marginally worse ($\leq1.13\times$ at $d\in\{5,7\}$, reversing by $d{=}9$) as the $n{-}1$ extra local fan-out gates offset the network savings. No custom decoding algorithm is required: the standard MWPM decoder, built from the packet circuit's DEM, already encodes the correlation.
Comments4 pages, 2 figures, 1 table
