Turaev-Viro码量子计算
Quantum computation with Turaev-Viro codes
摘要：
闭三维流形的Turaev-Viro不变量被定义为某个张量网络的收缩。张量对应于流形三角剖分中的四面体，其值由固定的球面范畴确定。对于一个有边界的流形，张量网络有自由的指数，可以与qudit相关联，它的收缩给出了量子纠错码的系数。该代码具有由Levin和Wen确定的局部稳定器。例如，应用于使用Z_2范畴的亏格一的双曲体，这种构造产生了众所周知的复曲面代码。对于其他类别，如斐波那契类别，该构造实现了离散格上的非阿贝尔任意子模型。通过研究辫子群表示作用于等价类的彩色丝带图嵌入穿孔球，我们确定了任意子，并给出了一个简单的食谱映射融合基态的双重类别的丝带图。我们解释了如何有效地准备合适的初始状态，如何实现辫子，通过连续改变使用一个固定的五qudit本地酉门的三角剖分，以及如何测量拓扑电荷。结合已知的普适性结果的任意子系统，这提供了一个大家庭的计划，量子计算的基础上局部变形的稳定剂代码。这些计划可以作为一个起点，发展容错计划，使用连续的稳定器测量和主动纠错。
英文摘要：
The Turaev-Viro invariant for a closed 3-manifold is defined as the contraction of a certain tensor network. The tensors correspond to tetrahedra in a triangulation of the manifold, with values determined by a fixed spherical category. For a manifold with boundary, the tensor network has free indices that can be associated to qudits, and its contraction gives the coefficients of a quantum error-correcting code. The code has local stabilizers determined by Levin and Wen. For example, applied to the genus-one handlebody using the Z_2 category, this construction yields the well-known toric code. For other categories, such as the Fibonacci category, the construction realizes a non-abelian anyon model over a discrete lattice. By studying braid group representations acting on equivalence classes of colored ribbon graphs embedded in a punctured sphere, we identify the anyons, and give a simple recipe for mapping fusion basis states of the doubled category to ribbon graphs. We explain how suitable initial states can be prepared efficiently, how to implement braids, by successively changing the triangulation using a fixed five-qudit local unitary gate, and how to measure the topological charge. Combined with known universality results for anyonic systems, this provides a large family of schemes for quantum computation based on local deformations of stabilizer codes. These schemes may serve as a starting point for developing fault-tolerance schemes using continuous stabilizer measurements and active error-correction.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
