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

In this work, the capability of restricted Boltzmann machines (RBMs) to find solutions for the Kitaev honeycomb model is investigated. The measured groundstate (GS) energy of the system is compared and shown to reside within less than $5\%$ error of the analytically derived value of the energy. Moreover, given a set of single shot measurements of exact solutions of the model, an RBM is used to perform quantum state tomography and the obtained result has a $97\%$ overlap with the exact analytic result. Furthermore, the possibility of realizing anyons in the RBM is discussed and an algorithm is given to build these anyonic excitations and braid them as a proof of concept for performing quantum gates and doing quantum computation.