Quantum error correction codes were introduced as a means to protect quantum information from decoherance and operational errors. Based on their approach to error control, error correcting codes can be divided into two different classes: block codes and convolutional codes. There has been significant development towards finding quantum block codes, since they were first discovered in 1995. In contrast, quantum convolutional codes remained mainly uninvestigated. In this thesis, we develop the stabilizer formalism for quantum convolutional codes. We define distance properties of these codes and give a general method for constructing encoding circuits, given a set of generators of the stabilizer of a quantum convolutional stabilizer code, is shown. The resulting encoding circuit enables online encoding of the qubits, i.e., the encoder does not have to wait for the input transmission to end before starting the encoding process. We develop the quantum analogue of the Viterbi algorithm. The quantum Viterbi algorithm (QVA) is a maximum likehood error estimation algorithm, the complexity of which grows linearly with the number of encoded qubits. A variation of the quantum Viterbi algorithm, the Windowed QVA, is also discussed. Using Windowed QVA, we can estimate the most likely error without waiting for the entire received sequence.

Quantum error correction codes were introduced as a means to protect quantum information from decoherance and operational errors. Based on their approach to error control, error correcting codes can be divided into two different classes: block codes and convolutional codes. There has been significant development towards finding quantum block codes, since they were first discovered in 1995. In contrast, quantum convolutional codes remained mainly uninvestigated. In this thesis, we develop the stabilizer formalism for quantum convolutional codes. We define distance properties of these codes and give a general method for constructing encoding circuits, given a set of generators of the stabilizer of a quantum convolutional stabilizer code, is shown. The resulting encoding circuit enables online encoding of the qubits, i.e., the encoder does not have to wait for the input transmission to end before starting the encoding process. We develop the quantum analogue of the Viterbi algorithm. The quantum Viterbi algorithm (QVA) is a maximum likehood error estimation algorithm, the complexity of which grows linearly with the number of encoded qubits. A variation of the quantum Viterbi algorithm, the Windowed QVA, is also discussed. Using Windowed QVA, we can estimate the most likely error without waiting for the entire received sequence.

Orientador: Reginaldo Palazzo Junior / Dissertação (mestrado) - Universidade Estadual de Campinas, Faculdade de Engenharia Eletrica e de Computação / Made available in DSpace on 2018-08-12T20:22:38Z (GMT). No. of bitstreams: 1 Santos_PolyaneAlves_M.pdf: 825808 bytes, checksum: f4b4d556a54cfca0cb0a84dd5e07a7a3 (MD5) Previous issue date: 2008 / Resumo: A proposta de um sistema criptográfico de chave pública que utiliza códigos convolucionais de memória-unitária clássicos e quânticos apresentada neste trabalho, está baseada na utilização de transformações armadilha que, ao serem aplicadas as submatrizes reduzem a capacidade de correção de erros do código. Este processo proporciona um aumento no grau de privacidade da informação a ser enviada devido a dois fatores: para a determinação de códigos ótimos de memória unitária è necessário resolver o Problema da Mochila e a redução da capacidade de correção de erro dos códigos ocasionada pelo embaralhamento das colunas das submatrizes geradoras. São também apresentados neste trabalho, novos códigos convolucionais quânticos concatenados [(4, 1, 3)]. / Abstract: The proposal of a cryptographic system of public key that uses classical and quantum convolutional codes of unit-memory presented in this work, is based on the use of trapdoors functions which when applied to submatrices reduce the capacity of correction of errors of the code. This process gives us an increase in the degree of privacy of information being sent, because of two factors, namely: to establish good unit-memory codes is necessary to solve the knapsack problem, and the reduction of the capacity of correcting errors of codes provided by scrambling the columns of generating submatrices. We also present in this work, news quantum convolutional codes [(4, 1, 3)]. / Mestrado / Telecomunicações e Telemática / Mestre em Engenharia Elétrica

Orientador : Reginaldo Palazzo Junior / Tese (doutorado) - Universidade Estadual de Campinas, Faculdade de Engenharia Eletrica e de Computação / Made available in DSpace on 2018-08-04T00:27:05Z (GMT). No. of bitstreams: 1 Almeida_AntonioCarlosAidode_D.pdf: 2149041 bytes, checksum: 427f77a8e0ec2774c7b152dd209ba9fa (MD5) Previous issue date: 2004 / Resumo: A decoerencia é um dos maiores desafios obstrutivos da computação quantica. Os codigos corretores de erros quanticos tem sido desenvolvidos com o intuito de enfrentar este desafio. Uma estrutura de grupos e uma classe associada de codigos, a classe dos codigos estabilizadores, tem-se mostrado uteis na produção de codigos e no entendimento da estrutura de classes de codigos. Todos os codigos estabilizadores descobertos ate o momentos são codigos de bloco. Nesta tese, construiremos uma classe de codigos convolucional quanticos concatenados. Introduziremos o conceito de memoria convolucional quantica e algumas tecnicas simples para produzir bons codigos convolucionais quanticos a partir de classes de codigos concolucionais classicos / Abstract: Decoherence is one of the major challenges facing the field of quantum computation. The field of quantum error correction has developed to meet this challenge. A group-theoretical structure and associated class of quantum codes, the stabilizer codes, has proved particularly fruitful in producing codes and in understanding the structure of both specified codes and class of codes. All stabilizer codes discovered so far are block codes. In this thesis we will construct a class of concatenated quantum convolutional codes. We will introduce the concept of quantum convolutional memory and some simple techniques to produce good quantum convolutional codes from classes of classical convolutional codes / Doutorado / Telecomunicações e Telemática / Doutor em Engenharia Elétrica