Experimentally probing topological order and its breakdown through modular matrices

Luo, Zhihuang1,2,3; Li, Jun3; Li, Zhaokai1,2; Hung, Ling-Yan4,5,6,7; Wan, Yidun5,6,7,8,9,10; Peng, Xinhua1,2,11; Du, Jiangfeng1,2,11

2018-02

10.1038/NPHYS4281

Nature Physics   影响因子和分区

1745-2473

1745-2481

The modern concept of phases of matter has undergone tremendous developments since the first observation of topologically ordered states in fractional quantum Hall systems in the 1980s. In this paper, we explore the following question: in principle, how much detail of the physics of topological orders can be observed using state of the art technologies? We find that using surprisingly little data, namely the toric code Hamiltonian in the presence of generic disorders and detuning from its exactly solvable point, the modular matrices-characterizing anyonic statistics that are some of the most fundamental fingerprints of topological orders-can be reconstructed with very good accuracy solely by experimental means. This is an experimental realization of these fundamental signatures of a topological order, a test of their robustness against perturbations, and a proof of principle-that current technologies have attained the precision to identify phases of matter and, as such, probe an extended region of phase space around the soluble point before its breakdown. Given the special role of anyonic statistics in quantum computation, our work promises myriad applications both in probing and realistically harnessing these exotic phases of matter.

SCI ; EI

英语

NI论文

通讯

Shanghai Pujiang Program[KBH 1512328]

Physics

Physics, Multidisciplinary

WOS:000423846600024

NATURE PUBLISHING GROUP

20190806528855

Matrix algebra ; Phase space methods ; Quantum computers ; Quantum theory

Computer Systems and Equipment:722 ; Mathematics:921 ; Quantum Theory; Quantum Mechanics:931.4

Web of Science

1.Univ Sci & Technol China, CAS Key Lab Microscale Magnet Resonance, Hefei 230026, Anhui, Peoples R China
2.Univ Sci & Technol China, Dept Modern Phys, Hefei 230026, Anhui, Peoples R China
3.Beijing Computat Sci Res Ctr, Beijing 100094, Peoples R China
4.Fudan Univ, State Key Lab Surface Phys, 220 Handan Rd, Shanghai 200433, Peoples R China
5.Fudan Univ, Dept Phys, 220 Handan Rd, Shanghai 200433, Peoples R China
6.Fudan Univ, Ctr Field Theory & Particle Phys, 220 Handan Rd, Shanghai 200433, Peoples R China
7.Collaborat Innovat Ctr Adv Microstruct, Nanjing 210093, Jiangsu, Peoples R China
8.Perimeter Inst Theoret Phys, Waterloo, ON N2L 2Y5, Canada
9.Southern Univ Sci & Technol, Inst Quantum Sci & Engn, Shenzhen 518055, Peoples R China
10.Southern Univ Sci & Technol, Dept Phys, Shenzhen 518055, Peoples R China
11.Univ Sci & Technol China, Synerget Innovat Ctr Quantum Informat & Quantum P, Hefei 230026, Anhui, Peoples R China

Luo, Zhihuang,Li, Jun,Li, Zhaokai,et al. Experimentally probing topological order and its breakdown through modular matrices[J]. Nature Physics,2018,14(2):160-+.

Luo, Zhihuang.,Li, Jun.,Li, Zhaokai.,Hung, Ling-Yan.,Wan, Yidun.,...&Du, Jiangfeng.(2018).Experimentally probing topological order and its breakdown through modular matrices.Nature Physics,14(2),160-+.

Luo, Zhihuang,et al."Experimentally probing topological order and its breakdown through modular matrices".Nature Physics 14.2(2018):160-+.