Publication: Modelos con anyones en códigos cuánticos y superconductores topológicos
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2021-05-18
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Universidad Complutense de Madrid
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Abstract
En esta tesis estudiamos dos temas relacionados con la información cuántica y la topología: los superconductores topológicos y la corrección cuántica topológica de errores. Los superconductores topológicos han sido ampliamente estudiados, hecho parcialmente motivado por la búsqueda de fermiones de Majorana en sistemas de materia condensada. Estas cuasipartículas son anyones no abelianos y se pueden utilizar para el procesamiento de información cuántica. Recientemente se han presentado varias propuestas y experimentos en los que se obtienen superconductores topológicos mediante la construcción de heteroestructuras. Dichas heteroestructuras generalmente consisten en un superconductor de onda s acoplado a un semiconductor. En la publicación [P1] exploramos la posibilidad de diseñar un superconductor topológico utilizando un superconductor padre de onda d acoplado a un gas de electrones bidimensional con interacción de espín-órbita y un campo Zeeman. Hallamos una expresión analítica de los estados de Majorana y comparamos estos resultados con los obtenidos cuando se usa un superconductor de ondas convencional.
In this thesis we study two main topics related to the interplay between quantum information and topology: topological superconductors and topological quantum error correction. Topological superconductors have been extensively studied, partly motivated by the search of a condensed-matter realization of Majorana fermions. These quasiparticles are non-Abelian anyons and can be used for quantum information processing. There have been several proposals and experiments where topological superconductors are realized by building heterostructures. These heterostructures usually consist of an s-wave superconductor proximity-coupled to a semiconductor. In publication [P1] we explore the possibility of engineering a topological superconductor using a d-wave parent superconductor coupled to a two-dimensional electron gas with spin-orbit coupling and a Zeeman field. We determine an analytical expression of the Majorana states and compare these results to the ones obtained using a conventional s-wave superconductor...
In this thesis we study two main topics related to the interplay between quantum information and topology: topological superconductors and topological quantum error correction. Topological superconductors have been extensively studied, partly motivated by the search of a condensed-matter realization of Majorana fermions. These quasiparticles are non-Abelian anyons and can be used for quantum information processing. There have been several proposals and experiments where topological superconductors are realized by building heterostructures. These heterostructures usually consist of an s-wave superconductor proximity-coupled to a semiconductor. In publication [P1] we explore the possibility of engineering a topological superconductor using a d-wave parent superconductor coupled to a two-dimensional electron gas with spin-orbit coupling and a Zeeman field. We determine an analytical expression of the Majorana states and compare these results to the ones obtained using a conventional s-wave superconductor...
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Tesis inédita de la Universidad Complutense de Madrid, Facultad de Ciencias Físicas, Departamento de Física Teórica, leída el 27-11-2020