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Classes of High-Performance Quantum LDPC Codes From Finte Projective Geometries

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dc.contributor.advisor Agnarsson, Geir Farinholt, Jacob M.
dc.creator Farinholt, Jacob M. 2012-07-05 2012-10-05T14:21:27Z NO_RESTRICTION en_US 2012-10-05T14:21:27Z 2012-10-05
dc.description.abstract Due to their fast decoding algorithms, quantum generalizations of low-density parity check, or LDPC, codes have been invesitgated as a solution to the problem of decoherence in fragile quantum states [1, 2]. However, the additional twisted inner product requirements of quantum stabilizer codes force four-cycles and eliminate the possibility of randomly generated quantum LDPC codes. Moreover, the classes of quantum LDPC codes discovered thus far generally have unknown or small minimum distance, or a fixed rate (see [3, 4] and references therin). This paper presents several new classes of quantum LDPC codes constructed from finite projective planes. These codes have rates that increase with the block length n and minimum weights proportional to n1=2. For the sake of completeness, we include an introduction to classical error correction and LDPC codes, and provide a review of quantum communication, quantum stabilizer codes, and finite projective geometry.
dc.language.iso en en_US
dc.subject quantum error correction en_US
dc.subject error correcting codes en_US
dc.subject finite geometry en_US
dc.title Classes of High-Performance Quantum LDPC Codes From Finte Projective Geometries en_US
dc.type Thesis en Master of Science in Mathematics en_US Master's en Mathematics en George Mason University en

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