Quantum analogs of classical codes
(English) The main focus of this thesis are stabilizer codes, a type of error-correcting code used to correct quantum information that has been corrupted by noise. We introduce several new general constructions of stabilizer codes. In particular we use one of the constructions to construct quantum c...
| Autor: | |
|---|---|
| Tipo de recurso: | tesis doctoral |
| Estado: | Versión publicada |
| Fecha de publicación: | 2025 |
| País: | España |
| Institución: | CBUC, CESCA |
| Repositorio: | TDR. Tesis Doctorales en Red |
| OAI Identifier: | oai:www.tdx.cat:10803/694186 |
| Acceso en línea: | http://hdl.handle.net/10803/694186 https://dx.doi.org/10.5821/dissertation-2117-427443 |
| Access Level: | acceso abierto |
| Palabra clave: | Quàntica Codis Correcció Quàntica CRC Codis Reed Solomon Correcció de ràfegues Àrees temàtiques de la UPC::Matemàtiques i estadística Àrees temàtiques de la UPC::Informàtica 519.1 - Teoria general de l'anàlisi combinatòria. Teoria de grafs 004 - Informàtica |
| Sumario: | (English) The main focus of this thesis are stabilizer codes, a type of error-correcting code used to correct quantum information that has been corrupted by noise. We introduce several new general constructions of stabilizer codes. In particular we use one of the constructions to construct quantum cyclic redundancy check codes, an error-correcting code which is used in classical information to correct burst errors. We show how to use a quantum version of such codes to correct burst errors on systems of quantum bits. We include a geometric description of stabilizer codes, extending previous constructions which work only for the qubit case to quantum systems in which the quantum particles have local dimension p, where p is any prime number. Finally, we reduce the problem of ascertaining when a generalised Reed-Solomon code is contained in its Hermitian dual and therefore can be used to construct a stabilizer code. This reduction allows us to determine the shortest and longest length of generalised Reed-Solomon codes which are contained in their Hermitian dual, verifying a conjecture of Grassl and Rotteler. |
|---|