Matrix product state representations for machine learning

Eric Howard; Iftekher S. Chowdhury; Ian Nagle

doi:10.1007/978-3-030-77445-5_43

Matrix product state representations for machine learning

Eric Howard^*, Iftekher S. Chowdhury, Ian Nagle

^*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceeding › Conference proceeding contribution › peer-review

1 Citation (Scopus)

Abstract

Machine learning architectures provide a novel perspective on the study of quantum many body states. Restricted Boltzmann machines (RBM) tool is used to represent quantum many-body states in order to find connections to tensor network tools for studying quantum many-body physics, for a deeper understanding of the origin of entanglement entropy in quantum systems. Here, we seek the conditions for the optimal mapping of RBMs into Matrix Product States (MPS), with the aim to show that machine learning methods are a powerful tool for quantum state representations. We here showcase an efficient algorithm for translating RBMs into MPS, with a particular proof for Ising model. We also study the upper entropy bound condition and the entanglement properties of such mapping.

Original language	English
Title of host publication	Artificial Intelligence in Intelligent Systems
Subtitle of host publication	Proceedings of 10th Computer Science on-Line Conference 2021, Vol. 2
Editors	Radek Silhavy
Place of Publication	Cham, Switzerland
Publisher	Springer, Springer Nature
Pages	455-468
Number of pages	14
ISBN (Electronic)	9783030774455
ISBN (Print)	9783030774448
DOIs	https://doi.org/10.1007/978-3-030-77445-5_43
Publication status	Published - 2021
Event	10th Computer Science Online Conference, CSOC 2021 - Virtual, Online Duration: 1 Apr 2021 → 1 Apr 2021

Publication series

Name	Lecture Notes in Networks and Systems
Volume	229
ISSN (Print)	2367-3370
ISSN (Electronic)	2367-3389

Conference

Conference	10th Computer Science Online Conference, CSOC 2021
City	Virtual, Online
Period	1/04/21 → 1/04/21

Keywords

Deep learning
Machine learning
Matrix product states
Restricted Boltzmann machines
Tensor networks

Access to Document

10.1007/978-3-030-77445-5_43

Cite this

Howard, E., Chowdhury, I. S., & Nagle, I. (2021). Matrix product state representations for machine learning. In R. Silhavy (Ed.), Artificial Intelligence in Intelligent Systems: Proceedings of 10th Computer Science on-Line Conference 2021, Vol. 2 (pp. 455-468). (Lecture Notes in Networks and Systems; Vol. 229). Springer, Springer Nature. https://doi.org/10.1007/978-3-030-77445-5_43

@inproceedings{2437a57ea414492998fc622f11ba7a65,

title = "Matrix product state representations for machine learning",

abstract = "Machine learning architectures provide a novel perspective on the study of quantum many body states. Restricted Boltzmann machines (RBM) tool is used to represent quantum many-body states in order to find connections to tensor network tools for studying quantum many-body physics, for a deeper understanding of the origin of entanglement entropy in quantum systems. Here, we seek the conditions for the optimal mapping of RBMs into Matrix Product States (MPS), with the aim to show that machine learning methods are a powerful tool for quantum state representations. We here showcase an efficient algorithm for translating RBMs into MPS, with a particular proof for Ising model. We also study the upper entropy bound condition and the entanglement properties of such mapping.",

keywords = "Deep learning, Machine learning, Matrix product states, Restricted Boltzmann machines, Tensor networks",

author = "Eric Howard and Chowdhury, {Iftekher S.} and Ian Nagle",

year = "2021",

doi = "10.1007/978-3-030-77445-5_43",

language = "English",

isbn = "9783030774448",

series = "Lecture Notes in Networks and Systems",

publisher = "Springer, Springer Nature",

pages = "455--468",

editor = "Radek Silhavy",

booktitle = "Artificial Intelligence in Intelligent Systems",

address = "United States",

note = "10th Computer Science Online Conference, CSOC 2021 ; Conference date: 01-04-2021 Through 01-04-2021",

}

Howard, E, Chowdhury, IS & Nagle, I 2021, Matrix product state representations for machine learning. in R Silhavy (ed.), Artificial Intelligence in Intelligent Systems: Proceedings of 10th Computer Science on-Line Conference 2021, Vol. 2. Lecture Notes in Networks and Systems, vol. 229, Springer, Springer Nature, Cham, Switzerland, pp. 455-468, 10th Computer Science Online Conference, CSOC 2021, Virtual, Online, 1/04/21. https://doi.org/10.1007/978-3-030-77445-5_43

Matrix product state representations for machine learning. / Howard, Eric; Chowdhury, Iftekher S.; Nagle, Ian.
Artificial Intelligence in Intelligent Systems: Proceedings of 10th Computer Science on-Line Conference 2021, Vol. 2. ed. / Radek Silhavy. Cham, Switzerland: Springer, Springer Nature, 2021. p. 455-468 (Lecture Notes in Networks and Systems; Vol. 229).

Research output: Chapter in Book/Report/Conference proceeding › Conference proceeding contribution › peer-review

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T1 - Matrix product state representations for machine learning

AU - Howard, Eric

AU - Chowdhury, Iftekher S.

AU - Nagle, Ian

PY - 2021

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N2 - Machine learning architectures provide a novel perspective on the study of quantum many body states. Restricted Boltzmann machines (RBM) tool is used to represent quantum many-body states in order to find connections to tensor network tools for studying quantum many-body physics, for a deeper understanding of the origin of entanglement entropy in quantum systems. Here, we seek the conditions for the optimal mapping of RBMs into Matrix Product States (MPS), with the aim to show that machine learning methods are a powerful tool for quantum state representations. We here showcase an efficient algorithm for translating RBMs into MPS, with a particular proof for Ising model. We also study the upper entropy bound condition and the entanglement properties of such mapping.

AB - Machine learning architectures provide a novel perspective on the study of quantum many body states. Restricted Boltzmann machines (RBM) tool is used to represent quantum many-body states in order to find connections to tensor network tools for studying quantum many-body physics, for a deeper understanding of the origin of entanglement entropy in quantum systems. Here, we seek the conditions for the optimal mapping of RBMs into Matrix Product States (MPS), with the aim to show that machine learning methods are a powerful tool for quantum state representations. We here showcase an efficient algorithm for translating RBMs into MPS, with a particular proof for Ising model. We also study the upper entropy bound condition and the entanglement properties of such mapping.

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KW - Machine learning

KW - Matrix product states

KW - Restricted Boltzmann machines

KW - Tensor networks

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DO - 10.1007/978-3-030-77445-5_43

M3 - Conference proceeding contribution

AN - SCOPUS:85115820681

SN - 9783030774448

T3 - Lecture Notes in Networks and Systems

SP - 455

EP - 468

BT - Artificial Intelligence in Intelligent Systems

A2 - Silhavy, Radek

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T2 - 10th Computer Science Online Conference, CSOC 2021

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Howard E, Chowdhury IS, Nagle I. Matrix product state representations for machine learning. In Silhavy R, editor, Artificial Intelligence in Intelligent Systems: Proceedings of 10th Computer Science on-Line Conference 2021, Vol. 2. Cham, Switzerland: Springer, Springer Nature. 2021. p. 455-468. (Lecture Notes in Networks and Systems). doi: 10.1007/978-3-030-77445-5_43

Matrix product state representations for machine learning

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