Identifying Abelian and non-Abelian topological orders in the string-net model using a quantum scattering circuit

Zhang, Ze1,2; Long, Xinyue1,2; Zhao, Xiuzhu1,2; Lin, Zidong1,2; Tang, Kai1,2; Liu, Hongfeng1,2; Yang, Xiaodong1,2; Nie, Xinfang1,2,3; Wu, Jiansheng1,2,3; Li, Jun1,2,3; Xin, Tao1,2,3; Li, Keren1,2,4; Lu, Dawei1,2,3,5

2022-03-29

10.1103/PhysRevA.105.L030402

PHYSICAL REVIEW A   影响因子和分区

2469-9926

2469-9934

Realizing universal topological quantum computers requires the manipulation of non-Abelian topological orders in a physical system, which presents great challenges. Conversely, the rapid development in circuit-based quantum computing offers a reliable quantum simulation approach to study these topological orders. The preliminary problem is how to identify distinct topological orders. Here, we develop a framework based on the quantum scattering circuit to directly and efficiently measure the modular transformation matrix, which is widely deemed as the fingerprint of a given topological order. The information of the modular transformation matrix is encoded in the probe qubit, and the readout merely requires single-qubit Pauli measurements. We further implement the scheme in a nuclear magnetic resonance quantum simulator to emulate the string-net model, where an Abelian Z(2) toric code and a non-Abelian Fibonacci order emerge. In particular, the latter is predicted to be the simplest candidate for universal topological quantum computers. The two topological orders are unambiguously distinguished by the experimentally measured modular transformation matrices. As an experimental demonstration of a non-Abelian topological order with efficient readout, our work may open avenues toward investigating topological orders in circuit-based quantum simulators.

SCI ; EI

英语

第一 ; 通讯

National Key Research and Development Program of China[2019YFA0308100] ; National Natural Science Foundation of China[12075110,11975117,11905099,11875159,11905111,"U1801661"] ; Guangdong Basic and Applied Basic Research Foundation[2019A1515011383] ; Guangdong International Collaboration Program[2020A0505100001] ; Science, Technology and Innovation Commission of Shenzhen Municipality["ZDSYS20190902092905285","KQTD20190929173815000","JCYJ20200109140803865","JCYJ20180302174036418"] ; Pengcheng Scholars, Guangdong Innovative and Entrepreneurial Research Team Program[2019ZT08C044] ; Guangdong Provincial Key Laboratory[2019B121203002]

Optics ; Physics

Optics ; Physics, Atomic, Molecular & Chemical

WOS:000779849500008

AMER PHYSICAL SOC

20221712027907

Linear transformations ; Matrix algebra ; Qubits ; Timing circuits ; Topology

Pulse Circuits:713.4 ; Light, Optics and Optical Devices:741 ; Nanotechnology:761 ; Physical Chemistry:801.4 ; Algebra:921.1 ; Mathematical Transformations:921.3 ; Combinatorial Mathematics, Includes Graph Theory, Set Theory:921.4

PHYSICS

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.Guangdong Prov Key Lab Quantum Sci & Engn, Shenzhen 518055, Peoples R China
4.Peng Cheng Lab, Shenzhen 518066, Peoples R China
5.Southern Univ Sci & Technol, Shenzhen Key Lab Adv Quantum Funct Mat & Devices, Shenzhen 518055, Peoples R China

Zhang, Ze,Long, Xinyue,Zhao, Xiuzhu,et al. Identifying Abelian and non-Abelian topological orders in the string-net model using a quantum scattering circuit[J]. PHYSICAL REVIEW A,2022,105(3).

Zhang, Ze.,Long, Xinyue.,Zhao, Xiuzhu.,Lin, Zidong.,Tang, Kai.,...&Lu, Dawei.(2022).Identifying Abelian and non-Abelian topological orders in the string-net model using a quantum scattering circuit.PHYSICAL REVIEW A,105(3).

Zhang, Ze,et al."Identifying Abelian and non-Abelian topological orders in the string-net model using a quantum scattering circuit".PHYSICAL REVIEW A 105.3(2022).