标题： 利用非阿贝尔拓扑序生成逻辑魔术态 显示英文标题

标题： Generating logical magic states with the aid of non-Abelian topological order

摘要： 在使用表面码的容错量子计算中，非克莱夫门对于通用计算至关重要。 然而，使用诸如魔术态提纯和码切换等方法实现这些门需要大量的资源。 在本工作中，我们提出了一种新协议，将魔术态制备和码变换相结合，以在潜在容错的情况下实现逻辑非克莱夫操作。 我们的方法从 $\mathbb{Z}_4$ 表面码中的一个特殊逻辑态开始。 通过应用一系列变换，系统会经历不同的拓扑码，包括非阿贝尔的 $D_4$ 量子双模型。 此过程最终会在 $\mathbb{Z}_{2}$ 表面码中产生一个编码的魔术态。 可以通过门遥测在标准的 $\mathbb{Z}_2$ 表面码中实现逻辑 $T$ 门。 在我们的分析中，我们采用了一个框架，其中拓扑码由其拓扑序表示，所有变换都被视为拓扑操作，如对称性规范和任意子凝聚。 这种观点对于理解拓扑码之间的变换特别有用。 显示英文摘要

摘要： In fault-tolerant quantum computing with the surface code, non-Clifford gates are crucial for universal computation. However, implementing these gates using methods like magic state distillation and code switching requires significant resources. In this work, we propose a new protocol that combines magic state preparation and code transformation to realize logical non-Clifford operations with the potential for fault tolerance. Our approach begins with a special logical state in the $\mathbb{Z}_4$ surface code. By applying a sequence of transformations, the system goes through different topological codes, including the non-Abelian $D_4$ quantum double model. This process ultimately produces a magic state encoded in the $\mathbb{Z}_{2}$ surface code. A logical $T$ gate can be implemented in the standard $\mathbb{Z}_2$ surface code by gate teleportation. In our analysis, we employ a framework where the topological codes are represented by their topological orders and all the transformations are considered as topological manipulations such as gauging symmetries and condensing anyons. This perspective is particularly useful for understanding transformations between topological codes.