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dc.contributor.authorNoormandipour, Mohammadreza
dc.contributor.authorYouran, Sun
dc.contributor.authorHaghighat, Babak
dc.date.accessioned2022-01-04T12:01:28Z
dc.date.available2022-01-04T12:01:28Z
dc.date.issued2022-03-01
dc.date.submitted2021-05-23
dc.identifier.issn2632-2153
dc.identifier.othermlstac3ddf
dc.identifier.otherac3ddf
dc.identifier.othermlst-100386.r1
dc.identifier.urihttps://www.repository.cam.ac.uk/handle/1810/331862
dc.description.abstract<jats:title>Abstract</jats:title> <jats:p>In 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><?CDATA $3 \times 3$?></jats:tex-math> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mn>3</mml:mn> <mml:mo>×</mml:mo> <mml:mn>3</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><?CDATA $0.09\%$?></jats:tex-math> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mn>0.09</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><?CDATA $99.89\%$?></jats:tex-math> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mn>99.89</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>
dc.languageen
dc.publisherIOP Publishing
dc.subjectPaper
dc.subjectFocus on Machine Learning for Quantum Physics
dc.subjecttopological field theory
dc.subjectconformal blocks
dc.subjectrestricted Boltzmann machine
dc.subjectmachine learning
dc.subjectKitaev honeycomb model
dc.titleRestricted Boltzmann machine representation for the groundstate and excited states of Kitaev Honeycomb model
dc.typeArticle
dc.date.updated2022-01-04T12:01:28Z
prism.issueIdentifier1
prism.publicationNameMachine Learning: Science and Technology
prism.volume3
dc.identifier.doi10.17863/CAM.79312
dcterms.dateAccepted2021-11-26
rioxxterms.versionofrecord10.1088/2632-2153/ac3ddf
rioxxterms.versionVoR
rioxxterms.licenseref.urihttp://creativecommons.org/licenses/by/4.0
dc.contributor.orcidNoormandipour, Mohammadreza [0000-0001-9294-2035]
dc.identifier.eissn2632-2153
cam.issuedOnline2021-12-10


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