This thesis focuses on the progress made toward constructing Majorana-based topological qubits using nanowire-based hybrid superconducting-semiconductor quantum dot systems. It specifically investigates the application of dispersive gate sensing in these systems, emphasizing the characterization of diverse charge tunneling events and the understanding of forthcoming parity readout signals for potential topological qubits in their simplified forms. Through a combination of chip design, fabrication, cryogenic measurements at base temperatures, data analysis, and theoretical simulations, our findings have emerged.

The main idea of this thesis is to separate the two interfering paths required for qubit readout and to understand each path individually. One path connects two quantum dots through a semiconductor reference arm, while the other connects them via a superconducting island. Key achievements include the implementation of dispersive gate sensing on normal dots within dot-island systems, revealing charge tunneling processes and demonstrating the efficacy of this technique for investigating subgap excitations. Our work extends to characterizing spin-orbit field orientations in InSb nanowire-based double quantum dots, emphasizing that dispersive gate sensing is an effective tool for situations where transport measurements are not feasible. Additionally, novel methods for measuring capacitance in micro- and nanoscale devices using RF resonators have been validated, showcasing sensitivity suitable for both room temperature and cryogenic applications. The latest developments return to the exploration of one of the core segments of topological qubits, focusing on charge tunneling processes in a hybrid dot-island-dot system, and highlighting the tunability between elastic cotunneling and cross-Andreev reflection.

The findings presented in this thesis not only contribute to the understanding of hybrid quantum systems but also pave the way for future research in topological quantum computing, emphasizing the potential of dispersive gate sensing in advancing the field.

This thesis investigates gate-defined quantum dots (QDs) in a two-dimensional electron gas as a minimal platform to explore Kitaev chain physics and zero-energy states. By coupling two QDs through Andreev bound states (ABS) induced in a planar Josephson junction, we realize and control coherent interactions such as Cooper pair splitting and elastic co-tunneling. The devices are fabricated using multi-layer electron-beam lithography, wet and dry etching, and thin-film deposition techniques. To characterize these systems, we employ both DC transport and radio-frequency (RF) reflectometry measurements. We demonstrate tunable dot-dot coupling over micrometer distances using gate voltages and magnetic flux, and access a "poor man’s Majorana" regime. Finally, we explore an isolated QD-ABS-QD system using RF gate reflectometry to resolve states without tunnelling probes, revealing parity-dependent behaviour limited by measurement sensitivity and quasiparticle poisoning. These results advance the control and understanding of hybrid mesoscopic devices and lay a foundation for future experiments with confined structures in hybrid systems.

Kitaev chains have recently been realized in semiconductor quantum dots (QD) coupled to
each other through Andreev bound states (ABS) emerging from the superconducting proximity effect. These chains are a promising platform for the detection and manipulation of Majorana bound states, which are predicted to have interesting properties for quantum information experiments such as non-Abelian statistics and robustness to charge noise. In this thesis, we show strong coupling in a relatively long 2-site Kitaev chain in a QD-ABS-QD setup and demonstrate that control over the superconducting phase of the ABS allows tuning of the Kitaev chain regime. We also investigate the Majorana wavefunction overlap in the ABS in the strong coupling regime. We then discuss a 3-site Kitaev chain in the QD-ABS-QD-ABS-QD system, where we demonstrate the importance of superconducting phase control for stable Majorana bound states in this system and directly probe the excitation gap in the bulk of the
chain, showing the delocalization of the Majorana bound states. Lastly, we study the
Majorana protection against chemical potential fluctuations in the 3-site chain.

The search for Majoranas bound states has witnessed heated efforts in the past decade. This field of research lies at the intersection of both scientific and commercial interests. The Majorana quasiparticle, being its own antiparticle and exhibiting non-abelian exchange statistics, is a unique member of the family of condensed-matter quasiparticles, distinct from most fermions or bosons. These properties are predicted to be instrumental in the building of a new type of qubits, having no energy splitting between qubit states and intrinsically protected from decoherence. In addition, the theory describing Majorana modes has a rich connection to the mathematical language of topology, making its study also of theoretical value. Thus, the prediction of the existence of Majorana zero modes in hybrid semiconducting-superconducting nanowires has been a strong driving force behind the recent technological progress in the making of these materials and devices.
In this thesis, the most recent advance in materials, specifically the making of clean interfaces between semiconductors and superconductors, are applied to the study of the physical properties of superconducting-proximitized electronic states in semiconductors. This technology is combined with quantum dot techniques to investigate electron transport between individual quantum states in proximitized nanowires. The findings include better understanding of electron transport in these systems as well as presenting new potential applications to the field of Majoranas and beyond.
Following the introductory chapters, this thesis first demonstrates a high-efficiency Cooper-pair splitter, enabled by quantum dots with narrow linewidth and a superconductor with a hard gap. The techniques behind the improved efficiency can be used to make a generator of entangled pairs of electrons. We also demonstrate the use of quantum dots as spin detectors capable of revealing the spin structure of individual Cooper pairs. Next, we report the effect of a Cooper-pair splitter's peculiar response to the tuning of electrical gates in both experiment and theory. This includes the discovery of a new interference effect in electron co-tunneling processes through a superconductor. The key to observing this response is to ensure the hybrid nanowire is also a discrete quantum state instead of a superconducting bulk. The discovery above forms the foundation of fine-tuning the types of electron couplings between two quantum dots coupled via a superconductor. The power of this tunability can been seen via the successful making of a minimal artificial Kitaev chain, opening up new possibilities in the search for Majorana zero modes. This approach is less prone to difficulties encountered in other platforms such as material disorder and the interpretability of data.
Moving from studying quantum dots under the influence of a superconducting hybrid, later chapters of this thesis focus on investigating electron properties in the hybrid nanowire using quantum dots as spin-, charge- and energy-selective probes.
We first use them to detect and quantify the spin polarization of Andreev bound states in the hybrid nanowire. Using quantum dots as charge and energy detectors instead, we observe how electrons traverse through the bulk of a hybrid nanowire and reveal a thermoelectric conversion process in the conductance measurements of these devices. Finally, we report on the selective-area growth of InSb, the semiconductor used throughout this thesis, that can form the basis of future developments.

Quantum computers can solve some problems exponentially faster than classical computers. Unfortunately, the computational power of quantum computers is currently limited by the number of working qubits. It is difficult to scale up these systems, because qubits are easily affected by noise in their environment. This noise leads to decoherence: loss of the qubit’s encoded information. A possible solution to diminish decoherence is using Majorana box qubits, as these qubits are predicted to be insensitive to local noise. However, this promising type of qubit does not exist yet.

With the research described in this thesis, we aim to contribute to the development of Majorana box qubits (MBQs). In these qubits, Majorana zero modes, the basic elements of MBQs, are contained within a superconducting island to suppress Majorana parity fluctuations caused by quasiparticle poisoning. To enable parity readout of the MBQ, these modes are coupled to quantum dots within a nanowire network.
To help realize MBQs, we need a better understanding of quasiparticles in superconducting islands, parity-readout techniques, and ways to fabricate nanowire networks. These three aspects are the focus of the experiments presented in this thesis.

To study superconducting islands and readout techniques, we used InAs semiconductor nanowires with an epitaxially grown Al shell. Majorana signatures have already been observed in such nanowires. We addressed quasiparticle dynamics in superconducting islands by measuring the gate-charge modulation of the switching current. We found a consistent 2e-periodic modulation at zero magnetic field, and an exponential decrease of parity lifetime with increasing magnetic field. We explored MBQ readout, using a quantum dot level as a proxy for a Majorana zero mode, and measured its charge hybridization with another dot using gate-based readout. We showed that we can rapidly discriminate between two settings with different tunnel couplings, demonstrating the potential of gate-based readout to measure MBQs. And, using gate-based readout, we could study charge-transfer processes occurring in hybrid structures of superconducting islands coupled to quantum dots.

Finally, to find a good material platform for nanowire networks, we characterized two two-dimensional systems. We realized quantum point contacts in InSb, which we used to measure the $g$-factor anisotropy, and effective electron mass in this system. And, we studied the spin-orbit interaction in InAs/GaSb by extracting the difference in density between electrons with different spin orientations.

This thesis finishes with a proposal for a series experiments to realize MBQs. These experiments make use of superconducting islands and the reflectometry setup we developed for gate-based readout.