Dokument: Majorana Box Systems: From Quantum Transport To Self-Correcting Qubits

Titel:	Majorana Box Systems: From Quantum Transport To Self-Correcting Qubits
URL für Lesezeichen:	https://docserv.uni-duesseldorf.de/servlets/DocumentServlet?id=53760
URN (NBN):	urn:nbn:de:hbz:061-20200723-110134-3
Kollektion:	Dissertationen
Sprache:	Englisch
Dokumententyp:	Wissenschaftliche Abschlussarbeiten » Dissertation
Medientyp:	Text
Autor:	Gau, Matthias [Autor]
Dateien:	[Dateien anzeigen] Adobe PDF [Details] 4,36 MB in einer Datei [ZIP-Datei erzeugen] Dateien vom 20.07.2020 / geändert 20.07.2020
Beitragende:	Prof. Dr. Egger, Reinhold [Gutachter] Dr. Kampermann, Hermann [Gutachter]
Dewey Dezimal-Klassifikation:	500 Naturwissenschaften und Mathematik » 530 Physik
Beschreibung:	In engineered condensed matter systems, Majorana fermions are realised as quasiparticle excitations, called Majorana bound states, at the surface of the aforementioned topological superconductors. Majorana bound states are their own antiparticles and thereby have zero charge, energy, and no spin. While those properties make them hard to detect, they give rise to several interesting features, such as their non-Abelian exchange statistics. Consequently, Majorana bound states are of immense fundamental interest and applications in quantum information processing are promising. Within the context of this thesis, Majorana boxes, which are mesoscopic charging islands harbouring Majorana bound states, are considered from two different perspectives. Setups with multiple coupled Majorana boxes, which are connected by short nanowire segments, are key ingredients to recent Majorana qubit and code network proposals. Therefore, the first perspective is concerned with quantum transport in such coupled Majorana box systems. It includes the construction and study of the low-energy theory for multi-terminal junctions with normal leads connected to the coupled box devices. Starting with a single box, where the topological Kondo effect is reproduced, a distinction between simple and non-simple Majorana-lead junctions is made. The latter breaks local fermion parities and thereby results in a low-energy theory, which, in contrast to previously discussed single box systems, is not purely bosonic. Within the scope of this thesis two examples with non-simple Majorana-lead junctions are discussed in terms of their transport characteristics. Those transport signatures can be used to test the nonlocality of Majorana-based systems and thereby the integrity of the underlying Majorana qubits. The second perspective is given by Majorana boxes in the presence of environmental electromagnetic noise. Coupling the Majorana box setups to quantum dots, one can engineer driven dissipative protocols for stabilisation and manipulation of robust quantum states. Within this thesis it is shown that the time evolution of the Majorana sector is governed by a Lindblad master equation over a wide parameter regime. For a single Majorana box, arbitrary pure states, alternatively dark states, can be stabilised by adjusting suitable gate voltages. If the Majorana box harbours more than four Majorana bound states, the introduced protocols also allow for the stabilisation of fault-tolerant Bell states. Thereby, a single driven dissipative Majorana box works as a self-correcting quantum memory. For devices with two coupled boxes, one can engineer manifolds of degenerate dark states, which allow for the encoding of a dark qubit. For such a qubit, not only the stored quantum information, but also manipulation protocols are protected by the driven dissipative mechanism. Therefore, one can anticipate exceptionally high fault tolerance levels due to a conspiracy of autonomous error correction and topology.
Lizenz:	Urheberrechtsschutz
Fachbereich / Einrichtung:	Mathematisch- Naturwissenschaftliche Fakultät » WE Physik » Theoretische Physik
Dokument erstellt am:	23.07.2020
Dateien geändert am:	23.07.2020
Promotionsantrag am:	23.04.2020
Datum der Promotion:	08.07.2020