We introduce a new type of sparse CSS quantum error correcting code based on the homology of hypermaps. Sparse quantum error correcting codes are of interest in the building of quantum computers due to their ease of implementation and the possibility of developing fast decoders for them. Codes based on the homology of embeddings of graphs, such as Kitaev's toric code, have been discussed widely in the literature and our class of codes generalize these. We use embedded hypergraphs, which are a generalization of graphs that can have edges connected to more than two vertices. We develop theorems and examples of our hypermap-homology codes, especially in the case that we choose a special type of basis in our homology chain complex. In particular, the most straightforward generalization of the m × m toric code to hypermap-homology codes gives us a [(3/2)m²,2, m] code as compared to the toric code which is a [2m²,2, m]code. Thus we can protect the same amount of quantum information, with the same error-correcting capability, using less physical qubits.

Made available in DSpace on 2016-04-29T14:23:49Z (GMT). No. of bitstreams: 1 Karen Patricia Reis Figueiredo.pdf: 8523616 bytes, checksum: b668b1fe109e2317bf83ec97fcc86387 (MD5) Previous issue date: 2009-05-28 / The thesis entitled "The Use of Technologies of Intelligence on Demand Management of Cyberspace Products: Case Study 'Captare'", of the Master in Technologies of Intelligence and Digital Design - TIDD, focuses on how the industrial segments can come to know and understand, in a more effective way, the behavior of demand in retail. It was analyzed how intelligence softwares with a cognitive basis can collect, process, classify and interpret data generated from business to business transactions B2B. As a main informational means to be examined, within the case methodological line, it proposes the Captare Software used by industrial segments through an eMarketplace (Genexis.com). Captare is a information product (e-Business solution) supported by technology of algorithm intelligence in cyberspace with cognitive representation pattern. Its conception is based on the hybrid convergence of the multidisciplinarity of statistics, data mining, marketing, trade marketing, technology of information and hypermap, promoting interactive communication strategies of the triad "man", "interface" and "computer", turning it into a set to make the objectives happen, such as action, reaction, service or information / A dissertação intitulada O uso de tecnologias da inteligência para a gestão da demanda de produtos no ciberespaço: estudo de caso Captare do Mestrado em Tecnologias da Inteligência e Design Digital (TIDD) tem como tema central a investigação de como os segmentos industriais podem vir a conhecer e compreender de forma mais eficaz o comportamento da demanda no varejo. Tal processo será levado pela análise de como os softwares de inteligência com base cognitiva coletam, processam, classificam e interpretam os dados gerados a partir de transações business-to-business (B2B). O estudo propõe, como veículo informacional principal a ser investigado, dentro da linha metodológica do case, o software Captare, utilizado pelos segmentos industriais por meio de um eMarketplace (portal de negócios Genexis.com). O Captare constitui-se em um produto de informação (solução de eBusiness) suportado por tecnologia de inteligência algorítma em um ciberespaço, cuja essência centra-se em modelos de representações cognitivas. Sua concepção parte da convergência híbrida da multidisciplinaridade da estatística, datamining, marketing, trademarketing, tecnologia da informação e do hipermapa, possibilitando estratégias de comunicação interativa entre a tríade homem", "interface" e "computador" , formando um conjunto para fazer acontecer o fenômeno da comunicação a fim de alcançar objetivos, sejam esses uma ação, reação, serviço ou informação