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

Hai, Yong-Ju1,2; Zhang, Ze2; Zheng, Hao1,3,4; Kong, Liang1,3,4; Wu, Jiansheng1,3,4; Yu, Dapeng1,2,3,4

2023-02-28

10.1093/nsr/nwac264

National Science Review   Impact Factor & Quartile

2095-5138

2053-714X

["Topological order is a new quantum phase that is beyond Landau's symmetry-breaking 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.","A protocol to uniquely identify topological orders by measuring the fingerprints of anyons is proposed and demonstrated in few-qubit systems."]

topological order R matrix F matrix bulk-boundary duality anyon condensation

SCI

English

First ; Corresponding

National Natural Science Foundation of China (NSFC)["11674152","11681240276"] ; Guangdong Innovative and Entrepreneurial Research Team Program[2016ZT06D348] ; Natural Science Foundation of Guangdong Province[2017B030308003] ; Science, Technology and Innovation Commission of Shenzhen Municipality["JCYJ20170412152620376","KYT-DPT20181011104202253","ZDSYS20170303165926217"] ; Guangdong Provincial Key Laboratory[2019B121203002] ; NSFC["11871078","11971219"]

Science & Technology - Other Topics

Multidisciplinary Sciences

WOS:000947388700001

OXFORD UNIV PRESS

Web of Science

1.Southern Univ Sci & Technol, Shenzhen Inst Quantum Sci & Engn, Shenzhen 518055, Peoples R China
2.Southern Univ Sci & Technol, Dept Phys, Shenzhen 518055, Peoples R China
3.Int Quantum Acad, Shenzhen 518048, Peoples R China
4.Guangdong Prov Key Lab Quantum Sci & Engn, Shenzhen 518055, Peoples R China

Hai, Yong-Ju,Zhang, Ze,Zheng, Hao,et al. Uniquely identifying topological order based on boundary-bulk duality and anyon condensation[J]. National Science Review,2023,10(3).

Hai, Yong-Ju,Zhang, Ze,Zheng, Hao,Kong, Liang,Wu, Jiansheng,&Yu, Dapeng.(2023).Uniquely identifying topological order based on boundary-bulk duality and anyon condensation.National Science Review,10(3).

Hai, Yong-Ju,et al."Uniquely identifying topological order based on boundary-bulk duality and anyon condensation".National Science Review 10.3(2023).