Explicit demonstration of nonabelian anyon, braiding matrix and fusion rules in the Kitaev-type spin honeycomb lattice models

非阿贝尔任何子在对称增强拓扑相中的非线性对称碎裂：字符串-网络模型的实现

Nonlinear Symmetry-Fragmentation of Nonabelian Anyons In Symmetry-Enriched Topological Phases: A String-Net Model Realization

本文通过字符串-网络模型揭示非阿贝尔任何子在对称性下的非线性碎裂机制，提出相干表示概念，揭示非阿贝尔SETs的特征。

Demonstrating anyonic fractional statistics with a six-qubit quantum simulator

Anyons are exotic quasiparticles living in two dimensions that do not fit into the usual categories of fermions and bosons, but obey a new form of fractional statistics. Following a recent proposal [Phys. Rev. Lett. 98, 150404 (2007)], we present an experimental demonstration of the fractional statistics of anyons in the Kitaev spin lattice model using a photonic quantum simulator. We dynamically create the ground state and excited states (which are six-qubit graph states) of the Kitaev model Hamiltonian, and implement the anyonic braiding and fusion operations by single-qubit rotations. A pha…

拓扑量子比特的腔调控：融合规则、任意子编织与 Majorana-Schrödinger 猫态

Cavity Control of Topological Qubits: Fusion Rule, Anyon Braiding, and Majorana-Schrödinger Cat States

本文研究电磁腔与拓扑 Kitaev 链的耦合，揭示非阿贝尔融合规则和编织操作，并提出通过宇称测量和 Berry 相位探测 MZMs，以及生成 MZM-极化激元猫态的新方法。

Scrambling via Braiding of Nonabelions

We study how quantum states are scrambled via braiding in systems of non-Abelian anyons through the lens of entanglement spectrum statistics. In particular, we focus on the degree of scrambling, defined as the randomness produced by braiding, at the same amount of entanglement entropy. To quantify the degree of randomness, we define a distance between the entanglement spectrum level spacing distribution of a state evolved under random braids and that of a Haar-random state, using the Kullback-Leibler divergence $D_{\mathrm{KL}}$. We study $D_{\mathrm{KL}}$ numerically for random braids of Majo…

基于拓扑BF理论的扭曲二面体量子双相的构造：从自发对称破缺

Topological BF Theory construction of twisted dihedral quantum double phases from spontaneous symmetry breaking

本文提出基于连续O(2)规范场的非阿贝尔二面体量子双相构造方法，通过拓扑BF理论与任意子的对应关系，结合微观模型与重整化群分析，展示了从二面体相到U(1)库仑或手性相的直接过渡。