Quantum low density parity check codes
| Autor: | Popatia, Tabriz |
|---|---|
| Přispěvatelé: | Ball, Simeon Michael, Universitat Politècnica de Catalunya. Departament de Matemàtiques |
| Jazyk: | angličtina |
| Rok vydání: | 2022 |
| Předmět: | |
| Zdroj: | UPCommons. Portal del coneixement obert de la UPC Universitat Politècnica de Catalunya (UPC) |
| Popis: | Low density Parity Check (LDPC) Codes are asymptotically good codes with a fast decoding algorithm, and hence have extensive applications. A lot of work has been done on constructing a quantum code with LDPC properties. Recent breakthroughs show that it is possible to construct a quantum LDPC code that is asymptotically good (meaning the distance of the code grows at the same rate as the length); however, no explicit construction currently exists. In this thesis we give an explicit construction of a non Calderbank Shor Steane (CSS) quantum LDPC code from projective geometries. The construction we lay out gives a code that at best has a distance that grows at a rate of one quarter root of the length. Despite the limitations on the distance, the code that we give has the nice property that it can be decoded in linear time. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|