Classes of High-Performance Quantum LDPC Codes From Finte Projective Geometries
| dc.contributor.advisor | Agnarsson, Geir | |
| dc.contributor.author | Farinholt, Jacob M. | |
| dc.creator | Farinholt, Jacob M. | |
| dc.date | 2012-07-05 | |
| dc.date.accessioned | 2012-10-05T14:21:27Z | |
| dc.date.available | NO_RESTRICTION | |
| dc.date.available | 2012-10-05T14:21:27Z | |
| dc.date.issued | 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.identifier.uri | https://hdl.handle.net/1920/7947 | |
| dc.language.iso | en | |
| dc.subject | Quantum error correction | |
| dc.subject | Error correcting codes | |
| dc.subject | Finite geometry | |
| dc.title | Classes of High-Performance Quantum LDPC Codes From Finte Projective Geometries | |
| dc.type | Thesis | |
| thesis.degree.discipline | Mathematics | |
| thesis.degree.grantor | George Mason University | |
| thesis.degree.level | Master's | |
| thesis.degree.name | Master of Science in Mathematics |