发表机构
QPerfect SAS; European Center for Quantum Sciences; University of Strasbourg and CNRS, CESQ and ISIS (UMR 7006)（QPerfect SAS; 欧洲量子科学中心; 斯特拉斯堡大学与法国国家科学研究中心，CESQ和ISIS（联合研究单位7006））
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本研究使用矩阵乘积态方法精确比较两类折叠横向魔法态培育方案，发现新方案在$d=5$时时空成本降低约1.3倍且逻辑错误率达$10^{-9}$，并提出了加速模拟的预筛选方法。
AI 中文摘要
魔法态培育以较低的预期时空成本制备高保真魔法态；然而，由于非克利福德电路模拟的困难，某些方案的确切性能尚未确定。在此，我们使用基于矩阵乘积态（MPS）的方法来计算两类折叠横向培育方案的精确性能：（i）基于常规表面码S门的Sahay等人方法，以及（ii）我们提出的基于部分容错折叠横向S门的方法。我们表明，对于前者在$d=5$时，$|T\ angle$输出达到与$|S\ angle$输出相似的逻辑错误率，后者传统上用作廉价的完全克利福德代理。这与Gidney等人报告的$d=5$颜色码方案约$10\ imes$的差异形成对比。我们还发现，我们新的$d=5$方案具有约$1.3\ imes$更低的预期时空成本，同时仍达到$10^{-9}$的逻辑错误率。我们表明，MPS和克利福德增强MPS（CAMPS）在最具挑战性的$d=5$常规表面码方案上，性能与最近引入的近克利福德模拟器Clifft相当甚至更好。此外，为了加速模拟，我们提出了一种基于简单泡利传播的新预筛选方法，将所需精确模拟次数降低多达三个数量级，并使用若干模拟器无关的采样方法，如子集采样。
英文摘要
Magic state cultivation prepares high-fidelity magic states at low expected space-time costs; however, the exact performance of some schemes is unsettled due to the difficulty in simulating non-Clifford circuits. Here, we use matrix-product states (MPS) based methods to compute the exact performance of two types of fold-transversal cultivation schemes: (i) the Sahay et al method based on the regular surface code S gate, and (ii) a method we propose based on a partially fault-tolerant fold-transversal S gate. We show that for the former protocol at $d=5$, the $|T\rangle$ output reaches similar logical error rates to the $|S\rangle$ output, traditionally used as a cheap full Clifford proxy. This contrasts with the $\sim10\times$ discrepancy reported for the $d=5$ colour-code scheme of Gidney et al. We also find that our new $d=5$ scheme has $\sim1.3\times$ lower expected space-time cost while still reaching $10^{-9}$ logical error rate. We show that MPS and Clifford-augmented MPS (CAMPS) perform on par with or even better than the recently introduced near-Clifford simulator Clifft on the hardest $d=5$ regular surface code scheme. Additionally, to speed up simulation, we propose a new pre-screening method based on simple Pauli propagation, lowering by up to three orders of magnitude the required number of exact simulations, and use several simulator-agnostic sampling methods such as subset sampling.
