Efficient machine-learning representations of a surface code with boundaries, defects, domain walls, and twists

Jia, Zhih-Ahn1,2,3,4; Zhang, Yuan-Hang5; Wu, Yu-Chun3,4; Kong, Liang6,7; Guo, Guang-Can3,4; Guo, Guo-Ping3,4

2019-01-04

10.1103/PhysRevA.99.012307

PHYSICAL REVIEW A   影响因子和分区

2469-9926

2469-9934

Machine-learning representations of many-body quantum states have recently been introduced as an ansatz to describe the ground states and unitary evolutions of many-body quantum systems. We investigate one of the most important representations, the restricted Boltzmann machine (RBM), in the stabilizer formalism. A general method to construct RBM representations for stabilizer code states is given, and exact RBM representations for several types of stabilizer groups with the number of hidden neurons equal to or less than the number of visible neurons are presented. The result indicates that the representation is extremely efficient. Then we analyze a surface code with boundaries, defects, domain walls, and twists in full detail and find that almost all the models can be efficiently represented via the RBM ansatz: the RBM parameters of the perfect case, boundary case, and defect case are constructed analytically using the method we provide in the stabilizer formalism, and the domain wall and twist case is studied numerically. In addition, the case for Kitaev's D (Z(d)) model, which is a generalized model of the surface code, is also investigated.

SCI ; EI

英语

通讯

Anhui Initiative in Quantum Information Technologies[AHY080000]

Optics ; Physics

Optics ; Physics, Atomic, Molecular & Chemical

WOS:000455050600003

AMER PHYSICAL SOC

20190306370851

Artificial intelligence ; Codes (symbols) ; Ground state ; Learning systems ; Quantum optics

Data Processing and Image Processing:723.2 ; Artificial Intelligence:723.4 ; Light/Optics:741.1

PHYSICS

Web of Science

1.Univ Calif Santa Barbara, Microsoft Stn Q, Santa Barbara, CA 93106 USA
2.Univ Calif Santa Barbara, Dept Math, Santa Barbara, CA 93106 USA
3.Univ Sci & Technol China, Sch Phys, Chinese Acad Sci, Key Lab Quantum Informat, Hefei 230026, Anhui, Peoples R China
4.Univ Sci & Technol China, Synerget Innovat Ctr Quantum Informat & Quantum P, Hefei 230026, Anhui, Peoples R China
5.Univ Sci & Technol China, Sch Gifted Young, Hefei 230026, Anhui, Peoples R China
6.Southern Univ Sci & Technol, Shenzhen Inst Quantum Sci & Engn, Shenzhen 518055, Peoples R China
7.Southern Univ Sci & Technol, Dept Phys, Shenzhen 518055, Peoples R China

Jia, Zhih-Ahn,Zhang, Yuan-Hang,Wu, Yu-Chun,et al. Efficient machine-learning representations of a surface code with boundaries, defects, domain walls, and twists[J]. PHYSICAL REVIEW A,2019,99(1).

Jia, Zhih-Ahn,Zhang, Yuan-Hang,Wu, Yu-Chun,Kong, Liang,Guo, Guang-Can,&Guo, Guo-Ping.(2019).Efficient machine-learning representations of a surface code with boundaries, defects, domain walls, and twists.PHYSICAL REVIEW A,99(1).

Jia, Zhih-Ahn,et al."Efficient machine-learning representations of a surface code with boundaries, defects, domain walls, and twists".PHYSICAL REVIEW A 99.1(2019).