The geometry of quantum codes
Quantum particles are continuously interacting with the environment hence quantum information is always susceptible to errors. Consequently when encoding information into quantum bits a special treatment is required such that there is a recovery map between the information sent and the information r...
| Autor: | |
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| Tipo de recurso: | tesis de maestría |
| Fecha de publicación: | 2021 |
| País: | España |
| Institución: | Universitat Politècnica de Catalunya (UPC) |
| Repositorio: | UPCommons. Portal del coneixement obert de la UPC |
| Idioma: | inglés |
| OAI Identifier: | oai:upcommons.upc.edu:2117/349594 |
| Acceso en línea: | https://hdl.handle.net/2117/349594 |
| Access Level: | acceso abierto |
| Palabra clave: | Error-correcting codes (Information theory) Error Correcting Quantum Codes Qubits Stabilizer Codes Non Additive Quantum Codes Pauli Group Projective Space Codis de correcció d'errors (Teoria de la informació) Classificació AMS::94 Information And Communication, Circuits::94B Theory of error-correcting codes and error-detecting codes Àrees temàtiques de la UPC::Matemàtiques i estadística |
| Sumario: | Quantum particles are continuously interacting with the environment hence quantum information is always susceptible to errors. Consequently when encoding information into quantum bits a special treatment is required such that there is a recovery map between the information sent and the information received capable to correct certain class of errors. We allow the quantum bits to take two orthogonal values (qubits) and we encode k logical qubits on n physical qubits. We first present the already well known class of quantum codes called stabiliser codes and its geometry from which one can deduce the code parameters. Finally we shall study the much less known class of quantum codes called non additive codes, result of direct sums of stabilizer codes, and for which we provide a geometric framework which appears to be new. |
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