Abstract
In recent decades, there has been a growing interest in designing new quantum devices that utilise topological states of matter. The exploitation, for instance, of the protected surface states of topological insulator (TI) nanowires, or the Majorana zero modes (MZMs) that can be formed at their edges, can potentially yield new, improved devices. This thesis analyses three platforms that can be used respectively to implement quantum information processing, quantum state tomography for device characterisation, and single-electron pumping. Regarding QIP applications, the first part of this thesis studies the coherent control and the coherence in the recently proposed Majorana transmon, where a nanowire hosting MZMs is embedded in a superconducting transmon qubit. In this platform, a single-qubit gate protocol based on the modulation of the offset charge parameter is introduced, showing that it can lead to high-fidelity qubit operations. Moreover, the system’s dynamics under 1/f charge noise is analysed, obtaining long coherence times. These results make the proposed device suitable for quantum computing applications. Since the characterisation of these novel nanowire-based junctions is essential for the development of hybrid devices, the second part of this thesis explores the quantum state tomography of circuits made out of these junctions, using projective measurements of the relative number of Cooper pairs and starting from the density matrix reconstruction of a pure Josephson junction. The use of TI nanowires is not limited to hybrid junctions, and in fact, they are suitable candidates for quantum transport applications. In this regard, the last part of the thesis investigates a quantum device that employs the topologically protected surface states of a TI nanowire to implement an adiabatic quantum pump. Because of the robustness of their surface states against non-magnetic disorder, this platform can be beneficial for the advance of single-electron sources. The charge confinement of these states can be achieved via a radius reduction in two regions of the nanowire so that the adiabatic pumping can be implemented via the only use of electrostatic gates. Conditions for obtaining quantised charge pumping and their optimisation are thus presented, together with an analysis of the possible extension to finite frequencies.