Banca de DEFESA: LUIGY MADSON SANTANA PINTO

Uma banca de DEFESA de MESTRADO foi cadastrada pelo programa.
STUDENT : LUIGY MADSON SANTANA PINTO
DATE: 30/09/2025
TIME: 14:30
LOCAL: Plataforma Google Meet
TITLE:

On Topological Quantum Field Theories and Applications

KEY WORDS:

Quantum field theory, topological qubits, Wilson loops, anyons, braid groups, knots and links

PAGES: 68
BIG AREA: Ciências Exatas e da Terra
AREA: Física
SUMMARY:

This work investigates information storage in states of Topological Quantum Field Theories (TQFTs), with an emphasis on the level-k Chern-Simons model and Atiyah's axiomatic framework. We explore the non-local and redundant nature of information in physical systems that realize TQFTs, such as collections of defects on S² manifolds, a feature that provides robust protection against data loss and local corruption. The structure of the work begins with theoretical foundations, reviewing the connection between Chern-Simons theory and knot and link invariants. The main result is the development and analysis of two distinct protocols to encode one logical qubit into four physical qubits and recover it in case one is lost: The first consists of working with Hilbert spaces formed by tensor products of individual qubits, while the second is a deterministic protocol that embeds the qubits in a larger Hilbert space without a tensor product structure, which is a more natural setup for physical implementations such as those involving anyons. This study demonstrates concrete schemes for the implementation of topological quantum error correction.

COMMITTEE MEMBERS:
Externo à Instituição - ALEKSANDR NIKOLAIEVICH PINZUL - UnB
Presidente - ***.839.841-** - DMITRY MELNIKOV - UFRN
Interno - 1313663 - RODRIGO GONCALVES PEREIRA