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Restricted Boltzmann machine representation for the groundstate and excited states of Kitaev Honeycomb model

Published version
Peer-reviewed

Repository DOI


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Authors

Noormandipour, Mohammadreza  ORCID logo  https://orcid.org/0000-0001-9294-2035
Youran, Sun 
Haghighat, Babak 

Abstract

jats:titleAbstract</jats:title> jats:pIn this work, the capability of restricted Boltzmann machines (RBMs) to find solutions for the Kitaev honeycomb model with periodic boundary conditions is investigated. The measured groundstate energy of the system is compared and, for small lattice sizes (e.g. jats:inline-formula jats:tex-math</jats:tex-math> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> mml:mn3</mml:mn> mml:mo×</mml:mo> mml:mn3</mml:mn> </mml:math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="mlstac3ddfieqn1.gif" xlink:type="simple" /> </jats:inline-formula> with 18 spinors), shown to agree with the analytically derived value of the energy up to a deviation of jats:inline-formula jats:tex-math</jats:tex-math> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> mml:mn0.09</mml:mn> <mml:mi mathvariant="normal">%</mml:mi> </mml:math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="mlstac3ddfieqn2.gif" xlink:type="simple" /> </jats:inline-formula>. Moreover, the wave-functions we find have jats:inline-formula jats:tex-math</jats:tex-math> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> mml:mn99.89</mml:mn> <mml:mi mathvariant="normal">%</mml:mi> </mml:math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="mlstac3ddfieqn3.gif" xlink:type="simple" /> </jats:inline-formula> overlap with the exact ground state wave-functions. Furthermore, the possibility of realizing anyons in the RBM is discussed and an algorithm is given to build these anyonic excitations and braid them for possible future applications in quantum computation. Using the correspondence between topological field theories in (2 + 1)d and 2d conformal field theories, we propose an identification between our RBM states with the Moore-Read state and conformal blocks of the 2d Ising model.</jats:p>

Description

Keywords

46 Information and Computing Sciences, 4601 Applied Computing, 4611 Machine Learning

Journal Title

Machine Learning: Science and Technology

Conference Name

Journal ISSN

2632-2153
2632-2153

Volume Title

3

Publisher

IOP Publishing