mlstMLSTCKMachine Learning: Science and TechnologyMLSTMach. Learn.: Sci. Technol.2632-2153IOP Publishingmlstac3ddf10.1088/2632-2153/ac3ddfac3ddfMLST-100386.R1PaperFocus on Machine Learning for Quantum PhysicsRestricted Boltzmann machine representation for the groundstate and excited states of Kitaev Honeycomb model0000-0001-9294-2035NoormandipourMohammadreza1YouranSun2HaghighatBabak2 * babakhaghighat@tsinghua.edu.cn TCM Group, Cavendish Laboratory, University of Cambridge, J.J. Thomson Avenue, Cambridge CB3 0HE, United Kingdom Yau Mathematical Sciences Center, Tsinghua University, Beijing 100084, People’s Republic of China

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3202210122021101220213101501023520211112021261120212112021© 2021 The Author(s). Published by IOP Publishing Ltd2021 Original content from this work may be used under the terms of the Creative Commons Attribution 4.0 license. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI.Abstract

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. 3×3 with 18 spinors), shown to agree with the analytically derived value of the energy up to a deviation of 0.09% . Moreover, the wave-functions we find have 99.89% 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.

topological field theoryconformal blocksrestricted Boltzmann machinemachine learningKitaev honeycomb modelccc2632-2153/21/015010+25$33.00printedPrinted in the UKcrossmarkyes