发表机构
Fritz Haber Research Center for Molecular Dynamics, Institute of Chemistry, The Hebrew University of Jerusalem（弗里茨·哈伯分子动力学研究中心，化学研究所，耶路撒冷希伯来大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究提出海森堡回声对称化（HES）方法，结合插入门（GI）与海森堡表象启发的回声，可降低1-2个数量级的保真度误差，兼容任意硬件，适用于秩一或近似秩一可观测量。
AI 中文摘要
插入门（GI）量子误差缓解将对合门（如CZ和CX）替换为相同门的2j+1次重复，以名义上将噪声放大相同倍数。分析和实验结果表明，对于实际器件中常见的非对易门噪声，这种放大缩放会失效。本文提出海森堡回声对称化（HES），它结合标准GI与受海森堡表象启发的回声，以抵消主要的GI误差。在模拟中，与GI相比，HES将绝对保真度误差降低1至2个数量级。与更准确的Layered-KIK方法不同，HES兼容任何硬件，仅需电路级访问，可实现跨平台的虚拟噪声缩放，有望大幅减少采样开销。其与噪声无关的放大还能完全抵御时间噪声漂移。不过，对于纯初始态，高秩可观测量会使回声方差相对于无回声电路显著增加，而秩一可观测量与GI或Layered-KIK相比无额外采样开销，因此HES特别适用于秩一或近似秩一的可观测量。
英文摘要
Gate insertion (GI) quantum error mitigation replaces involutory gates such as CZ and CX with 2j+1 repetitions of the same gates to nominally amplify noise by the same factor. Analytical and experimental results show that this amplification scaling fails for non-commuting gate noise, as typically encountered in realistic devices. Here we introduce Heisenberg-echo symmetrization (HES), which combines standard GI with an echo inspired by the Heisenberg representation to cancel the leading GI error. In our simulations, HES reduces the absolute fidelity error by one to two orders of magnitude compared with GI. Unlike the more accurate Layered-KIK method, HES is compatible with any hardware and requires only circuit-level access. It enables virtual noise scaling across platforms, potentially reducing sampling overhead substantially. Its agnostic noise amplification also provides full resilience to temporal noise drift. For pure initial states, however, high-rank observables can substantially increase the echo variance relative to non-echoed circuits, whereas rank-one observables incur no additional sampling overhead compared with GI or Layered-KIK. HES is therefore particularly suited to rank-one or nearly rank-one observables.
