Error correction for reliable quantum computing
Quantum computers herald the arrival of a new era in which previously intractable computational problems will be solved efficiently. However, quantum technology is held down by decoherence, a phenomenon that is omnipresent in the quantum paradigm and that renders quantum information useless when lef...
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| Format: | info:eu-repo/semantics/doctoralThesis |
| Language: | eng |
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Servicio de Publicaciones. Universidad de Navarra
2022
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| Online Access: | https://hdl.handle.net/10171/63067 |
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| author | Fuentes-Ugartemendia, P. (Patricio) Crespo-Bofil, P. (Pedro) |
| author_facet | Fuentes-Ugartemendia, P. (Patricio) Crespo-Bofil, P. (Pedro) |
| author_sort | Fuentes-Ugartemendia, P. (Patricio) |
| collection | DSpace |
| description | Quantum computers herald the arrival of a new era in which previously intractable computational problems will be solved efficiently. However, quantum technology is held down by decoherence, a phenomenon that is omnipresent in the quantum paradigm and that renders quantum information useless when left unchecked. The science of quantum error correction, a discipline that seeks to combine and protect quantum information from the effects of decoherence using structures known as codes, has arisen to meet this challenge. Stabilizer codes, a particular subclass of quantum codes, have enabled fast progress in the field of quantum error correction by allowing parallels to be drawn with the widely studied field of classical error correction. This has resulted in the construction of the quantum counterparts of well-known capacity-approaching classical codes like sparse codes and quantum turbo codes. However, quantum codes obtained in this manner do not entirely evoke the stupendous error correcting abilities of their classical counterparts. This occurs because classical strategies ignore important differences between the quantum and classical paradigms, an issue that needs to be addressed if quantum error correction is to succeed in its battle with decoherence. In this dissertation we study a phenomenon exclusive to the quantum paradigm, known as degeneracy, and its effects on the performance of sparse quantum codes. Furthermore, we also analyze and present methods to improve the performance of a specific family of sparse quantum codes in various different scenarios. |
| format | info:eu-repo/semantics/doctoralThesis |
| id | oai:dadun.unav.edu:10171-63067 |
| institution | Universidad de Navarra |
| language | eng |
| publishDate | 2022 |
| publisher | Servicio de Publicaciones. Universidad de Navarra |
| record_format | dspace |
| spelling | oai:dadun.unav.edu:10171-630672022-03-10T13:44:42Z Error correction for reliable quantum computing Fuentes-Ugartemendia, P. (Patricio) Crespo-Bofil, P. (Pedro) Quantum computing Quantum error correction Sparse quantum codes QLDPC Codes Degeneracy Computación cuántica Códigos cuánticos sparse Quantum computers herald the arrival of a new era in which previously intractable computational problems will be solved efficiently. However, quantum technology is held down by decoherence, a phenomenon that is omnipresent in the quantum paradigm and that renders quantum information useless when left unchecked. The science of quantum error correction, a discipline that seeks to combine and protect quantum information from the effects of decoherence using structures known as codes, has arisen to meet this challenge. Stabilizer codes, a particular subclass of quantum codes, have enabled fast progress in the field of quantum error correction by allowing parallels to be drawn with the widely studied field of classical error correction. This has resulted in the construction of the quantum counterparts of well-known capacity-approaching classical codes like sparse codes and quantum turbo codes. However, quantum codes obtained in this manner do not entirely evoke the stupendous error correcting abilities of their classical counterparts. This occurs because classical strategies ignore important differences between the quantum and classical paradigms, an issue that needs to be addressed if quantum error correction is to succeed in its battle with decoherence. In this dissertation we study a phenomenon exclusive to the quantum paradigm, known as degeneracy, and its effects on the performance of sparse quantum codes. Furthermore, we also analyze and present methods to improve the performance of a specific family of sparse quantum codes in various different scenarios. Los ordenadores cuánticos presagian la llegada de una etapa en la cual seremos capaces de abordar problemas computacionales que actualmente están fuera de nuestro alcance. Para que la computación cuántica se convierta en una realidad es imprescindible que previamente se desarrollen estrategias para paliar los efectos de la decoherencia cuántica, un mecanismo físico que corrompe e invalida los resultados producidos por máquinas cuánticas. Es para dicho fin que surge la disciplina conocida como la corrección de errores cuántica, la cual pretende diseñar métodos, conocidos como códigos, que sean capaces de proteger a la información cuántica de los efectos nocivos de la decoherencia cuántica. Los códigos estabilizadores, una familia particular de códigos cuánticos, han habilitado un rápido progreso en el campo de la corrección de errores cuántica ya que permiten diseñar códigos cuánticos a partir de estrategias de corrección de errores clásicas. Esto ha resultado en la aparición de familias de códigos cuánticos equivalentes a sus versiones clásicas, entre las cuales destacan los códigos cuánticos turbo y los códigos cuánticos sparse. Sin embargo, dichos códigos cuánticos no obtienen el mismo rendimiento que sus equivalentes clásicos cuando se aplican en el nuevo paradigma. Esto se debe a que el diseño de estrategias de corrección cuántica de errores a partir de códigos clásicos ignora diferencias importantes entre los entornos de comunicaciones cuánticos y clásicos y es algo que debe solucionarse para combatir la decoherencia cuántica con éxito. Por ello, en esta tesis doctoral estudiamos el fenómeno cuántico de la degeneración y el impacto que este tiene sobre el rendimiento de los códigos cuánticos sparse. Además, también analizamos y proponemos metodologías para mejorar el rendimiento de una familia en particular de códigos cuánticos sparse. 2022-03-08T07:46:20Z 2022-03-08T07:46:20Z 2022-02 2022-02-14 info:eu-repo/semantics/doctoralThesis https://hdl.handle.net/10171/63067 eng info:eu-repo/semantics/openAccess application/pdf Servicio de Publicaciones. Universidad de Navarra |
| spellingShingle | Quantum computing Quantum error correction Sparse quantum codes QLDPC Codes Degeneracy Computación cuántica Códigos cuánticos sparse Fuentes-Ugartemendia, P. (Patricio) Crespo-Bofil, P. (Pedro) Error correction for reliable quantum computing |
| title | Error correction for reliable quantum computing |
| title_full | Error correction for reliable quantum computing |
| title_fullStr | Error correction for reliable quantum computing |
| title_full_unstemmed | Error correction for reliable quantum computing |
| title_short | Error correction for reliable quantum computing |
| title_sort | error correction for reliable quantum computing |
| topic | Quantum computing Quantum error correction Sparse quantum codes QLDPC Codes Degeneracy Computación cuántica Códigos cuánticos sparse |
| url | https://hdl.handle.net/10171/63067 |
| work_keys_str_mv | AT fuentesugartemendiappatricio errorcorrectionforreliablequantumcomputing AT crespobofilppedro errorcorrectionforreliablequantumcomputing |