A study of the thermal properties of two-dimensional topological lattice models is presented. This work is relevant to assess the usefulness of these systems as a quantum memory. For our purposes, we use the topological mutual information $I_{\mathrm{topo}}$ as a "topological order parameter". For Abelian models, we show how $I_{\mathrm{topo}}$ depends on the thermal topological charge probability distribution. More generally, we present a conjecture that $I_{\mathrm{topo}}$ can (asymptotically) be written as a Kullback-Leitner distance between this probability distribution and that induced by the quantum dimensions of the model at hand. We also explain why $I_{\mathrm{topo}}$ is more suitable for our purposes than the more familiar entanglement entropy $S_{\mathrm{topo}}$. A scaling law, encoding the interplay of volume and temperature effects, as well as different limit procedures, are derived in detail. A non-Abelian model is next analysed and similar results are found. Finally, we also consider, in the case of a one-plaquette toric code, an environment model giving rise to a simulation of thermal effects in time.
Hanbury Brown-Twiss interferometry at the $ν=2/5$ fractional quantum Hall edge
Institute for Solid State Physics, The University of Tokyo（东京大学固体物理研究所）；Aix Marseille Univ, Université de Toulon, CNRS, CPT（艾克斯-马赛大学、土伦大学、法国国家科学研究中心、CPT）
Unveiling Topological Fusion in Quantum Hall Systems from Microscopic Principles
Jagiellonian University（雅盖隆大学）；Max-Planck-Institut für Quantenoptik（马克斯·普朗克量子光学研究所）；Munich Center for Quantum Science and Technology（慕尼黑量子科学与工程中心）；Princeton University（普林斯顿大学）；Karlstads Universitet（卡尔斯特大学）；Institute for Advanced Study, Princeton（普林斯顿高等研究院）；Indiana University（印第安纳大学）
Unified approach to topological quantum computation with anyons: From qubit encoding to Toffoli gate
拓扑量子计算可以提供一种鲁棒的方法，用于利用任意子准粒子激发的拓扑性质来编码和操纵信息。针对Chern-Simons-Witten SU（2）$_k$理论中的所有任意子模型，我们提出了一种有效的方法来映射量子信息（qubit）的密集和稀疏表示，并简单地构造了多量子比特门，该理论支持通过编织进行通用量子计算（$k\geq 3,\ k \neq 4$）.在这个过程中，我们展示了如何拓扑量子存储器和门的$k=2,4$连接自然那些$k\geq 3,\ k \neq 4$，统一这些概念在一个简单的框架。此外，我们说明了这些想法的潜在扩展到其他任何子模型以外的陈-西蒙斯-威滕场论。
