发表机构
Harvard University; University of Chicago（哈佛大学; 芝加哥大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出在量子双模型中，通过图重连与量子位重置，无需辅助量子位即可实现非阿贝尔任意子的编织与融合，并证明纯幺正融合的不可行性，为纠错提供新思路。
AI 中文摘要
编织和融合任意子是拓扑量子计算的基础，然而现有的电路协议通常使用辅助量子位和测量。我们确定了在一般有限群的量子双模型中执行此类任意子操作所需的最小电路资源。我们的方法通过无辅助量子位的顺序幺正电路编织任意子。直观上，这是通过变形任意子所依附的底层图来实现的。更一般地，我们引入了图重连（graph rewiring），这是一种图解演算，为单个双量子位门赋予几何解释，并追踪它们对稳定子的作用。对于融合，我们证明了一个一般性的不可行定理，排除了在不引入辅助量子位的情况下融合未知任意子类型的纯幺正协议。值得注意的是，我们表明这种“输入无关”的融合只需使用量子位重置即可实现。因此，与传统观念相反，编织或融合非阿贝尔任意子（non-Abelions）并不需要辅助量子位资源。这项工作对纠错的实验努力具有启示意义：我们的融合协议强调重置是一种未被充分利用的纠错原语，无需辅助量子位和测量的时空开销。
英文摘要
Braiding and fusing anyons are fundamental to topological quantum computation, yet existing circuit protocols often employ ancillas and measurements. We determine the minimal circuit resources for performing such anyon operations in quantum double models of generic finite groups. Our approach braids anyons through a sequential unitary circuit without ancillas. Intuitively, this is obtained by deforming the underlying graph on which the anyons live. More generally, we introduce graph rewiring, a diagrammatic calculus that assigns a geometric interpretation to individual two-qudit gates and tracks their action on stabilizers. For fusion, we prove a general no-go theorem excluding purely unitary protocols for fusing unknown anyon types without introducing ancillas. Remarkably, we show such "input-agnostic" fusion is enabled by simply using a qudit reset. Hence, contrary to folklore, ancilla resources are not needed to braid or fuse non-Abelian anyons (non-Abelions). This work has implications in experimental efforts in error correction: our fusion protocol highlights reset as an underutilized primitive for error correction without the spacetime-overhead of ancillas and measurements.
Comments20 pages; 58 pages total
