Banca de DEFESA: DENNIS RODOLFO AQUILES BARBOSA LIMA

Uma banca de DEFESA de MESTRADO foi cadastrada pelo programa.
STUDENT : DENNIS RODOLFO AQUILES BARBOSA LIMA
DATE: 25/07/2022
TIME: 14:00
LOCAL: Google Meet
TITLE:

Random Braid Gates for Topological Quantum Circuits

KEY WORDS:

braid group, topological quantum circuits, random matrices.

PAGES: 53
BIG AREA: Ciências Exatas e da Terra
AREA: Física
SUMMARY:

Abelian anyons 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 T-matrix 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 its transmission probability distribution.

COMMITTEE MEMBERS:
Externo à Instituição - ALEKSANDR NIKOLAIEVICH PINZUL
Presidente - ***.839.841-** - DMITRY MELNIKOV - UFRN
Externo à Instituição - FRANCESO TOPPAN
Interno - 1313663 - RODRIGO GONCALVES PEREIRA
Interno - ***.624.208-** - THIAGO SIMONETTI FLEURY - UNESP