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 proceedingConference proceeding contributionpeer-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 languageEnglish
    Title of host publicationArtificial Intelligence in Intelligent Systems
    Subtitle of host publicationProceedings of 10th Computer Science on-Line Conference 2021, Vol. 2
    EditorsRadek Silhavy
    Place of PublicationCham, Switzerland
    PublisherSpringer, Springer Nature
    Pages455-468
    Number of pages14
    ISBN (Electronic)9783030774455
    ISBN (Print)9783030774448
    DOIs
    Publication statusPublished - 2021
    Event10th Computer Science Online Conference, CSOC 2021 - Virtual, Online
    Duration: 1 Apr 20211 Apr 2021

    Publication series

    NameLecture Notes in Networks and Systems
    Volume229
    ISSN (Print)2367-3370
    ISSN (Electronic)2367-3389

    Conference

    Conference10th Computer Science Online Conference, CSOC 2021
    CityVirtual, Online
    Period1/04/211/04/21

    Keywords

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

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