Melnikov, DmitryLima, Dennis Rodolfo Aquiles Barbosa2022-09-022022-09-022022-07-25LIMA, Dennis Rodolfo Aquiles Barbosa. Random braid gates for topological quantum circuits. 2022. 59f. Dissertação (Mestrado em Física) - Centro de Ciências Exatas e da Terra, Universidade Federal do Rio Grande do Norte, Natal, 2022.https://repositorio.ufrn.br/handle/123456789/49261Anyons are many-body states of electrons characterized by a permutation phase between 0 and π. The non-abelian generalization of this concept was proposed by Kitaev to make fault-tolerant quantum computers. For non-abelian anyons, the phased permutation operators give rise to matrix representations of the permutation group, among them the braid groups. Knot Theory and Braid Group have all the tools that are needed to build quantum braid circuits. Taking advantage of existing technologies of study of transport properties of interacting systems, we use the Tmatrix formalism to analyze random T-matrix models and random R-matrix models as circuits of random braids. A special attention is given to Chalker-Coddington’s percolation model and renormalization approaches that rely on solving systems of linear equations or performing tensor contractions. As a simple example we introduce a quasi-1D random braid model in polynomial representation and analyze the transmission probability, that is a function of chain pieces.Acesso AbertoBraid groupTopological quantum circuitsRandom matricesmasterThesisCNPQ::CIENCIAS EXATAS E DA TERRA::FISICA