Restricted Boltzmann machines and matrix product states of one-dimensional translationally invariant stabilizer codes

doi:https://doi.org/10.1103/physrevb.99.155129

Title: Restricted Boltzmann machines and matrix product states of one-dimensional translationally invariant stabilizer codes

Abstract

Not provided.

Authors:: Zheng, Yunqin; He, Huan; Regnault, Nicolas; Bernevig, B. Andrei

Publication Date:: 2019-04-01

Research Org.:: Princeton Univ., NJ (United States)

Sponsoring Org.:: USDOE Office of Science (SC)

OSTI Identifier:: 1612432

DOE Contract Number:: SC0016239

Resource Type:: Journal Article

Journal Name:: Physical Review B

Additional Journal Information:: Journal Volume: 99; Journal Issue: 15; Journal ID: ISSN 2469-9950

Publisher:: American Physical Society (APS)

Country of Publication:: United States

Language:: English

Subject:: Materials Science; Physics

Citation Formats


                    Zheng, Yunqin, He, Huan, Regnault, Nicolas, and Bernevig, B. Andrei. Restricted Boltzmann machines and matrix product states of one-dimensional translationally invariant stabilizer codes.  United States: N. p., 2019. 
        Web.  doi:10.1103/physrevb.99.155129.

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                    Zheng, Yunqin, He, Huan, Regnault, Nicolas, & Bernevig, B. Andrei. Restricted Boltzmann machines and matrix product states of one-dimensional translationally invariant stabilizer codes.  United States.  https://doi.org/10.1103/physrevb.99.155129

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                    Zheng, Yunqin, He, Huan, Regnault, Nicolas, and Bernevig, B. Andrei. Mon .  
        "Restricted Boltzmann machines and matrix product states of one-dimensional translationally invariant stabilizer codes".  United States.  https://doi.org/10.1103/physrevb.99.155129.

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@article{osti_1612432,

  title        = {Restricted Boltzmann machines and matrix product states of one-dimensional translationally invariant stabilizer codes},

  author       = {Zheng, Yunqin and He, Huan and Regnault, Nicolas and Bernevig, B. Andrei},

  abstractNote = {Not provided.},

  doi          = {10.1103/physrevb.99.155129},

  url          = {https://www.osti.gov/biblio/1612432},
  journal      = {Physical Review B},

  issn         = {2469-9950},

  number       = 15,

  volume       = 99,

  place        = {United States},

  year         = {2019},

  month        = {4}

}

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Works referenced in this record:

Solving the quantum many-body problem with artificial neural networks
journal, February 2017

Carleo, Giuseppe; Troyer, Matthias
Science, Vol. 355, Issue 6325
https://doi.org/10.1126/science.aag2302

Neural-network quantum state tomography
journal, February 2018

Torlai, Giacomo; Mazzola, Guglielmo; Carrasquilla, Juan
Nature Physics, Vol. 14, Issue 5
https://doi.org/10.1038/s41567-018-0048-5

Constructing exact representations of quantum many-body systems with deep neural networks
journal, December 2018

Carleo, Giuseppe; Nomura, Yusuke; Imada, Masatoshi
Nature Communications, Vol. 9, Issue 1
https://doi.org/10.1038/s41467-018-07520-3

Efficient machine-learning representations of a surface code with boundaries, defects, domain walls, and twists
journal, January 2019

Jia, Zhih-Ahn; Zhang, Yuan-Hang; Wu, Yu-Chun
Physical Review A, Vol. 99, Issue 1
https://doi.org/10.1103/PhysRevA.99.012307

Chiral topological phases from artificial neural networks
journal, May 2018

Kaubruegger, Raphael; Pastori, Lorenzo; Budich, Jan Carl
Physical Review B, Vol. 97, Issue 19
https://doi.org/10.1103/PhysRevB.97.195136

Neural-Network Quantum States, String-Bond States, and Chiral Topological States
journal, January 2018

Glasser, Ivan; Pancotti, Nicola; August, Moritz
Physical Review X, Vol. 8, Issue 1
https://doi.org/10.1103/PhysRevX.8.011006

Unifying neural-network quantum states and correlator product states via tensor networks
journal, February 2018

Clark, Stephen R.
Journal of Physics A: Mathematical and Theoretical, Vol. 51, Issue 13
https://doi.org/10.1088/1751-8121/aaaaf2

Restricted Boltzmann machine learning for solving strongly correlated quantum systems
journal, November 2017

Nomura, Yusuke; Darmawan, Andrew S.; Yamaji, Youhei
Physical Review B, Vol. 96, Issue 20
https://doi.org/10.1103/PhysRevB.96.205152

Identifying product order with restricted Boltzmann machines
journal, March 2018

Rao, Wen-Jia; Li, Zhenyu; Zhu, Qiong
Physical Review B, Vol. 97, Issue 9
https://doi.org/10.1103/PhysRevB.97.094207

Efficient representation of quantum many-body states with deep neural networks
journal, September 2017

Gao, Xun; Duan, Lu-Ming
Nature Communications, Vol. 8, Issue 1
https://doi.org/10.1038/s41467-017-00705-2

Quantum Entanglement in Neural Network States
journal, May 2017

Deng, Dong-Ling; Li, Xiaopeng; Das Sarma, S.
Physical Review X, Vol. 7, Issue 2
https://doi.org/10.1103/PhysRevX.7.021021

Equivalence of restricted Boltzmann machines and tensor network states
journal, February 2018

Chen, Jing; Cheng, Song; Xie, Haidong
Physical Review B, Vol. 97, Issue 8
https://doi.org/10.1103/PhysRevB.97.085104

Restricted Boltzmann machines for the long range Ising models
journal, December 2016

Aoki, Ken-Ichi; Kobayashi, Tamao
Modern Physics Letters B, Vol. 30, Issue 34
https://doi.org/10.1142/S0217984916504017

Emergence of Compositional Representations in Restricted Boltzmann Machines
journal, March 2017

Tubiana, J.; Monasson, R.
Physical Review Letters, Vol. 118, Issue 13
https://doi.org/10.1103/PhysRevLett.118.138301

Approximating quantum many-body wave functions using artificial neural networks
journal, January 2018

Cai, Zi; Liu, Jinguo
Physical Review B, Vol. 97, Issue 3
https://doi.org/10.1103/PhysRevB.97.035116

Accelerated Monte Carlo simulations with restricted Boltzmann machines
journal, January 2017

Huang, Li; Wang, Lei
Physical Review B, Vol. 95, Issue 3
https://doi.org/10.1103/PhysRevB.95.035105

Representational Power of Restricted Boltzmann Machines and Deep Belief Networks
journal, June 2008

Le Roux, Nicolas; Bengio, Yoshua
Neural Computation, Vol. 20, Issue 6
https://doi.org/10.1162/neco.2008.04-07-510

Rigorous results on valence-bond ground states in antiferromagnets
journal, August 1987

Affleck, Ian; Kennedy, Tom; Lieb, Elliott H.
Physical Review Letters, Vol. 59, Issue 7
https://doi.org/10.1103/PhysRevLett.59.799

Finitely correlated states on quantum spin chains
journal, March 1992

Fannes, M.; Nachtergaele, B.; Werner, R. F.
Communications in Mathematical Physics, Vol. 144, Issue 3
https://doi.org/10.1007/BF02099178

Density matrix formulation for quantum renormalization groups
journal, November 1992

White, Steven R.
Physical Review Letters, Vol. 69, Issue 19
https://doi.org/10.1103/PhysRevLett.69.2863

Thermodynamic Limit of Density Matrix Renormalization
journal, November 1995

Östlund, Stellan; Rommer, Stefan
Physical Review Letters, Vol. 75, Issue 19
https://doi.org/10.1103/PhysRevLett.75.3537

Matrix product states, projected entangled pair states, and variational renormalization group methods for quantum spin systems
journal, March 2008

Verstraete, F.; Murg, V.; Cirac, J. I.
Advances in Physics, Vol. 57, Issue 2
https://doi.org/10.1080/14789940801912366

Entropy Scaling and Simulability by Matrix Product States
journal, January 2008

Schuch, Norbert; Wolf, Michael M.; Verstraete, Frank
Physical Review Letters, Vol. 100, Issue 3
https://doi.org/10.1103/PhysRevLett.100.030504

The density-matrix renormalization group in the age of matrix product states
journal, January 2011

Schollwöck, Ulrich
Annals of Physics, Vol. 326, Issue 1
https://doi.org/10.1016/j.aop.2010.09.012

Quantum Neural Network States: A Brief Review of Methods and Applications
journal, March 2019

Jia, Zhih‐Ahn; Yi, Biao; Zhai, Rui
Advanced Quantum Technologies, Vol. 2, Issue 7-8
https://doi.org/10.1002/qute.201800077

Fault-tolerant quantum computation by anyons
journal, January 2003

Kitaev, A. Yu.
Annals of Physics, Vol. 303, Issue 1
https://doi.org/10.1016/S0003-4916(02)00018-0

Machine learning topological states
journal, November 2017

Deng, Dong-Ling; Li, Xiaopeng; Das Sarma, S.
Physical Review B, Vol. 96, Issue 19
https://doi.org/10.1103/PhysRevB.96.195145

Field-Theory Representation of Gauge-Gravity Symmetry-Protected Topological Invariants, Group Cohomology, and Beyond
journal, January 2015

Wang, Juven C.; Gu, Zheng-Cheng; Wen, Xiao-Gang
Physical Review Letters, Vol. 114, Issue 3
https://doi.org/10.1103/PhysRevLett.114.031601

Entanglement entropy from tensor network states for stabilizer codes
journal, March 2018

He, Huan; Zheng, Yunqin; Bernevig, B. Andrei
Physical Review B, Vol. 97, Issue 12
https://doi.org/10.1103/PhysRevB.97.125102

Spurious long-range entanglement and replica correlation length
journal, August 2016

Zou, Liujun; Haah, Jeongwan
Physical Review B, Vol. 94, Issue 7
https://doi.org/10.1103/PhysRevB.94.075151

Topological entanglement entropy of fracton stabilizer codes
journal, March 2018

Ma, Han; Schmitz, A. T.; Parameswaran, S. A.
Physical Review B, Vol. 97, Issue 12
https://doi.org/10.1103/PhysRevB.97.125101

Topological gauge theories and group cohomology
journal, April 1990

Dijkgraaf, Robbert; Witten, Edward
Communications in Mathematical Physics, Vol. 129, Issue 2
https://doi.org/10.1007/BF02096988

Symmetry protected topological orders and the group cohomology of their symmetry group
journal, April 2013

Chen, Xie; Gu, Zheng-Cheng; Liu, Zheng-Xin
Physical Review B, Vol. 87, Issue 15
https://doi.org/10.1103/PhysRevB.87.155114

Twisted quantum double model of topological phases in two dimensions
journal, March 2013

Hu, Yuting; Wan, Yidun; Wu, Yong-Shi
Physical Review B, Vol. 87, Issue 12
https://doi.org/10.1103/PhysRevB.87.125114

Twisted gauge theory model of topological phases in three dimensions
journal, July 2015

Wan, Yidun; Wang, Juven C.; He, Huan
Physical Review B, Vol. 92, Issue 4
https://doi.org/10.1103/PhysRevB.92.045101

Rokhsar-Kivelson models of bosonic symmetry-protected topological states
journal, April 2015

Santos, Luiz H.
Physical Review B, Vol. 91, Issue 15
https://doi.org/10.1103/PhysRevB.91.155150

Superconductivity and the Quantum Hard-Core Dimer Gas
journal, November 1988

Rokhsar, Daniel S.; Kivelson, Steven A.
Physical Review Letters, Vol. 61, Issue 20
https://doi.org/10.1103/PhysRevLett.61.2376

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Title: Restricted Boltzmann machines and matrix product states of one-dimensional translationally invariant stabilizer codes

Abstract

Citation Formats

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Approximating quantum many-body wave functions using artificial neural networks journal, January 2018

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Thermodynamic Limit of Density Matrix Renormalization journal, November 1995

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Twisted quantum double model of topological phases in two dimensions journal, March 2013

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Constructing exact representations of quantum many-body systems with deep neural networks
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Efficient machine-learning representations of a surface code with boundaries, defects, domain walls, and twists
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Neural-Network Quantum States, String-Bond States, and Chiral Topological States
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