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Liu, Jin-Guo; Wang, Lei1,4; Zhang, Pan5,6,7
Tropical Tensor Network for Ground States of Spin Glasses
Source PublicationPHYSICAL REVIEW LETTERS
Language英语
AbstractWe present a unified exact tensor network approach to compute the ground state energy, identify the optimal configuration, and count the number of solutions for spin glasses. The method is based on tensor networks with the tropical algebra defined on the semiring of (R boolean OR {-infinity}, circle plus circle dot). Contracting the tropical tensor network gives the ground state energy; differentiating through the tensor network contraction gives the ground state configuration; mixing the tropical algebra and the ordinary algebra counts the ground state degeneracy. The approach brings together the concepts from graphical models, tensor networks, differentiable programming, and quantum circuit simulation, and easily utilizes the computational power of graphical processing units (GPUs). For applications, we compute the exact ground state energy of Ising spin glasses on square lattice up to 1024 spins, on cubic lattice up to 216 spins, and on three regular random graphs up to 220 spins, on a single GPU; we obtain exact ground state energy of +/- J Ising spin glass on the chimera graph of D-Wave quantum annealer of 512 qubits in less than 100 s and investigate the exact value of the residual entropy of +/- J spin glasses on the chimera graph; finally, we investigate ground-state energy and entropy of three-state Potts glasses on square lattices up to size 18 x 18. Our approach provides baselines and benchmarks for exact algorithms for spin glasses and combinatorial optimization problems, and for evaluating heuristic algorithms and mean-field theories.
2021
ISSN0031-9007
Volume126Issue:9Pages:90506
Cooperation Status国际
Subject AreaPhysics
MOST Discipline CataloguePhysics, Multidisciplinary
DOI10.1103/PhysRevLett.126.090506
Indexed BySCIE
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Document Type期刊论文
Identifierhttp://ir.itp.ac.cn/handle/311006/27524
CollectionSCI期刊论文
Affiliation1.Chinese Acad Sci, Beijing Natl Lab Condensed Matter Phys, Beijing 100190, Peoples R China
2.Chinese Acad Sci, Inst Phys, Beijing 100190, Peoples R China
3.Harvard Univ, Cambridge, MA 02138 USA
4.QuEra Comp Inc, Boston, MA 02143 USA
5.Songshan Lake Mat Lab, Dongguan 523808, Guangdong, Peoples R China
6.Chinese Acad Sci, Inst Theoret Phys, CAS Key Lab Theoret Phys, Beijing 100190, Peoples R China
7.UCAS, Hangzhou Inst Adv Study, Sch Fundamental Phys & Math Sci, Hangzhou 310024, Peoples R China
8.Int Ctr Theoret Phys Asia Pacific, Beijing, Peoples R China
Recommended Citation
GB/T 7714
Liu, Jin-Guo,Wang, Lei,Zhang, Pan. Tropical Tensor Network for Ground States of Spin Glasses[J]. PHYSICAL REVIEW LETTERS,2021,126(9):90506.
APA Liu, Jin-Guo,Wang, Lei,&Zhang, Pan.(2021).Tropical Tensor Network for Ground States of Spin Glasses.PHYSICAL REVIEW LETTERS,126(9),90506.
MLA Liu, Jin-Guo,et al."Tropical Tensor Network for Ground States of Spin Glasses".PHYSICAL REVIEW LETTERS 126.9(2021):90506.
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