Uniquely identifying topological order based on boundary-bulk duality and anyon condensation  

作　　者：Yong-Ju Hai Ze Zhang Hao Zheng Liang Kong Jiansheng Wu Dapeng Yu 

机构地区：[1]Shenzhen Institute for Quantum Science and Engineering,Southern University of Science and Technology,Shenzhen 518055,China [2]Department of Physics,Southern University of Science and Technology,Shenzhen 518055,China [3]International Quantum Academy,Shenzhen 518048,China [4]Guangdong Provincial Key Laboratory of Quantum Science and Engineering,Shenzhen 518055,China

出　　处：《National Science Review》2023年第3期111-120,共10页国家科学评论（英文版）

基　　金：supported by the National Natural Science Foundation of China (NSFC)(11674152 and 11681240276);the Guangdong Innovative and Entrepreneurial Research Team Program (2016ZT06D348);the Natural Science Foundation of Guangdong Province (2017B030308003);the Science,Technology and Innovation Commission of Shenzhen Municipality (JCYJ20170412152620376 and KYTDPT20181011104202253);supported by the Science,Technology and Innovation Commission of Shenzhen Municipality (ZDSYS20170303165926217);the Guangdong Provincial Key Laboratory (2019B121203002);supported by the NSFC (11971219);supported by the NSFC (11871078)。

摘　　要：Topological order is a new quantum phase that is beyond Landau' s symmetry-bre aking paradigm.Its defining features include robust degenerate ground states,long-range entanglement and anyons.It was known that R and F matrices,which characterize the fusion-braiding properties of anyons,can be used to uniquely identify topological order.In this article,we explore an essential question:how can the R and F matrices be experimentally measured?We show that the braidings,i.e.the R matrices,can be completely determined by the half braidings of boundary excitations due to the boundary-bulk duality and the anyon condensation.The F matrices can also be measured by comparing the quantum states involving the fusion of three anyons in two different orders.Thus we provide a model-independent experimental protocol to uniquely identify topological order.By using quantum simulations based on a toric code model with boundaries encoded in three-and four-qubit systems and state-of-the-art technology,we obtain the first experimental measurement of R and F matrices by means of an NMR quantum computer at room temperature.

关 键 词：topological order R matrix F matrix bulk-boundary duality anyon condensation 

分 类 号：O469[理学—凝聚态物理]