发表机构
Joint Center for Quantum Information and Computer Science; NIST; University of Maryland; IBM Quantum; IBM T.J. Watson Research Center; Center for Theoretical Physics; Leinweber Institute; Massachusetts Institute of Technology（量子信息与计算机科学联合中心; 美国国家标准与技术研究院; 马里兰大学; IBM量子; IBM托马斯·J·沃森研究中心; 理论物理中心; 莱因韦伯研究所; 麻省理工学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
我们利用对称性和AI辅助方法搜索魔法态工厂，提出统一二进制矩阵表述，发现699个工厂类别，包括564个新类别，并实现了γ<1的最小纯T工厂，为容错量子计算提供开源协议库。
AI 中文摘要
魔法态蒸馏是容错量子计算中的一项主要资源成本。魔法态工厂的成本强烈依赖于其失败率，而失败率随输入魔法态数量的增加而增长。尽管最近对称性限制的方法使得距离为二的搜索变得可行，但在中等输入数量下，距离为三及以上的搜索仍然难以实现。我们开发了对称性和AI辅助的方法来搜索这一领域。我们提出了一种统一的二进制矩阵表述，涵盖了三正交码和直接电路搜索。我们证明距离至少为三等价于非零、成对不同的综合征，从而将综合征的选择与兼容输出门的搜索分离开来。我们利用群对称性和语言模型代理来限制综合征搜索，随后进行确定性求解和独立验证。我们的搜索产生了699个工厂类别，其中564个是新的。这些包括纯T态工厂以及具有纠缠输出的工厂，纠缠输出包含T、CS和CCZ魔法态的组合。纯T工厂[[63, 11, 3]]和[[850, 128, 6]]在分别最多100和1000个输入的协议中达到了我们所知的最低开销指数，γ分别为1.589和1.057。我们的[[1715, 287, 6]]工厂，γ=0.998，是已知最小的γ<1的纯T工厂。我们还提供了一个搜索简报和活动笔记的上下文目录，读者可以用它来训练自己的代理并根据需求定制搜索。凭借这些结果，我们开始为量子社区构建一个活跃的开源魔法态蒸馏协议库，辅以我们的方法和数据，用于实用容错量子计算领域。
英文摘要
Magic-state distillation is a major resource cost in fault-tolerant quantum computing. The cost of a magic-state factory depends strongly on its failure rate, which grows with the number of input magic states. Although symmetry-restricted methods have recently made distance two searches tractable, distance three and above have remained elusive at moderate input counts. We develop symmetry- and AI-assisted methods to search this regime. We present a unified binary-matrix formulation encompassing both triorthogonal-code and direct circuit searches. We show that distance at least three is equivalent to nonzero, pairwise distinct syndromes, separating the choice of syndromes from the search for compatible output gates. We restrict the syndrome search using group symmetry and language-model agents, followed by deterministic solving and independent verification. Our searches yield 699 factory classes, including 564 new ones. These include factories for pure-T states and factories with entangled outputs comprising combinations of T, CS, and CCZ magic states. The pure-T factories [[63, 11, 3]] and [[850, 128, 6]] achieve the lowest overhead exponents we know among protocols with at most 100 and 1000 inputs, respectively, with $γ= 1.589$ and $γ= 1.057$. Our [[1715, 287, 6]] factory, with $γ= 0.998$, is the smallest known pure-T factory with $γ< 1$. We also provide a context directory of search briefs and campaign notes with which readers can train their own agents and tailor the search to their requirements. With these results, we begin constructing an active, open-source repository of magic-state distillation protocols for the quantum community, supplemented by our methods and data, for the practical fault-tolerant quantum computing regime.
