Nanotechnology enables the study of various quantum phenomena on real hardware. For instance, semiconducting and superconducting nanostructures can define single-electron transistors, quantum dots, Josephson junctions, and many other examples of quantum devices. It's a wonderful sandbox.
In this thesis, we exploit such a technology to bring the Kitaev chain model to life. The Kitaev Hamiltonian, discussed in the second chapter of this dissertation, describes a chain of N fermionic sites coupled by a standard tunneling and a more exotic superconducting pairing. It is one of the simplest models able to bring the concept of topology into condensed matter physics. Proposed more than twenty years ago, it attracted many experimental groups around the world, due to the promise of realizing a topologically protected qubit. This would be encoded into the Majorana bound states predicted to appear at the ends of the chain. However, such a qubit was never made, due to the difficulty of reproducing the Kitaev model with realistic, hence imperfect, materials.
Here, we demonstrate that engineering Kitaev chains with state-of-the-art materials is possible, by compensating imperfections with fine tuning. As opposed to top-down approaches, this requires building the chain site-by-site and tuning carefully each of them. In this work, each site is represented by a semiconducting quantum dot, while short semiconducting-superconducting hybrids mediate the inter-dot couplings. First, we describe minimal arrays of two quantum dots, show how to control every term of the Kitaev Hamiltonian, and detect the appearance of Majorana bound states. Then, we generalize the tuning procedure to three-site Kitaev chain devices. We also study the additional complications caused by multiple superconductors on the same device.
The main downside of a few-site Kitaev chain is the lack of topological protection. Nevertheless, we demonstrate that its Majorana bound states already exhibit partial protection (against some parameter perturbations), which increases substantially from two- to three-site chains. In the outlook, we propose to generalize the techniques described here to realize a rudimentary Majorana qubit and scale up to even longer Kitaev chains, whose partial protection evolves into topological as N grows.

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.

Andreev bound states arise in low-dimensional confined systems, coupled to superconductors. They show great similarity to the highly sought-after Majorana bound states, yet they lack the desirable non-Abelian statistics or topological protection. Except for these, Andreev bound states possess a multitude of unique and interesting properties. This thesis explores several of these properties, using semiconductor quantum dots as a measurement tool. In addition, quantum dots are hybridized with Andreev bound states to form novel systems, including Andreev molecules, and Kitaev chains.

In the theory section, we introduce several basic concepts, followed by a discussion of the properties of Andreev bound states and similar Yu-Shiba-Rusinov states. We then extend the concept of Andreev bound states to Kitaev chains in various implementations. In the first chapter, we use a quantum dot as both a spin and energy filter to probe an Andreev bound state. We observe pure spin states despite the strong spin-orbit interaction in the host semiconductor. Utilizing a three-terminal measurement setup, we can change the spin-relaxation process of the Andreev bound state by changing tunnel barrier strengths. Next, we configure a quantum dot as a charge sensor to study Andreev bound states. We observe smooth changes in ground state charge due to hybridization of the even-occupation states. We additionally detect abrupt loading of electrons during the singlet-doublet transition, which agrees with a change of ground state parity. Having used quantum dots as a measurement tool, we then hybridize them with Andreev bound states to form an Andreev molecule. We demonstrate readout of the ground state parity of the combined system using the charge sensor. We argue that parity-to-charge conversion in semiconductorsuperconductor systems is a viable scheme for reading out Kitaev chains and associated qubits.

We proceed by strongly coupling two quantum dots to a single Andreev bound state. This coupling mediates tunneling and Cooper pair splitting processes between the quantum dots, effectively constituting a Kitaev chain. For each Andreev bound state, we can find two gate voltages at which the rates of these processes are equal and non-zero. Spectroscopic measurements reveal localized Majorana zero modes on the quantum dots that are robust against local electrostatic changes.

Engineering Kitaev chain-based qubits requires consistently finding Majorana zero modes. In the final experimental chapter of this thesis, we present an algorithm that tunes gate voltages until Majorana zero modes emerge in Kitaev chains. We employ a neural network to estimate the relative Cooper pair splitting and tunneling rates from spectroscopic measurements. These estimates are then input into a gradient descent algorithm until the rates are balanced, and Majorana zero modes emerge. We present statistics on the algorithm’s performance and conclude that it is a vital tool in elevating Kitaev chains from the realm of fundamental study to quantum information.

We then propose a series of future experiments, based on our current findings. Notably, we explore the possibility of storing quantum information in the spin degree of freedom of a superconductor using Yu-Shiba-Rusinov states.

Superconducting circuits in cryogenic environments form an excellent material platform for the realization and study of quantum systems.
In this thesis, we continue the exploration of novel types of circuit elements which expand the circuit quantum electrodynamics toolbox to enable exotic, and potentially better circuit implementations. To this end, we combine the study of condensed matter systems and circuit quantum electrodynamics in what is called hybrid cQED experiments to arrive at the implementation of gate-tunable kinetic inductances for superconducting circuits. This discovery shed new light on the physics of gate-tunable kinetic inductances and enabled the observation of emergent phenomena in gate-tunable metamaterials, in particular the phase transition in a bosonic Su-Schrieffer-Heeger chain. Moreover, as gate-tunable kinetic inductances became available we realized tunable resonators and parametric amplifiers for enhanced control and readout of superconducting circuits.

Quantum technology is a developing field of sciencewhere devices possess novel and superior functionalities thanks to their quantum-mechanical behaviour at the nanometer scale. A typical example is a quantum computer, where information is stored in quantum states of its quantum bits. By manipulating entangled and superposition states of these qubits, quantumcomputers can achieve exponential speed-ups in calculation and therefore solve currently unsolvable problems within polynomial computational times. This powerful advantage of quantum computers is particularly difficult to achieve in practice, due to decoherence - a tendency of quantum objects to lose their quantummechanical properties when interacting with their environment. Obviously, qubit decoherence cannot be avoided because the control of a quantum computer inevitably causes couplings to the environment. To mitigate decoherence, fault-tolerant implementations of quantumcomputing need to be developed.

Topological quantum computing has been proposed to achieve fault-tolerance since its significant robustness to decoherence is inherent in the quantum-mechanical nature of topological qubits. Building units of a topological qubit are Majorana zero modes (MZMs) – zero-energy quasiparticles that possess the non-Abelian anyonic exchange statistics and are localized at the boundaries of a topological superconductor. In sufficiently large topological superconductors, MZMs exhibit no overlap and therefore can in pairs host non-local fermions. By braiding non-overlapping MZMs, the information stored in the non-local fermions is manipulated while being insensitive to local noise. In this way one can perform computation that is topologically protected against local sources of decoherence.

In 2010, III-V semiconductor nanowires proximitized by s-wave superconductorswere proposed as a suitable candidate platform for the realization of topological superconductors. Topological superconducting phase occurs in such a hybrid nanowire due to an interplay among the large spin-orbit interaction, s-wave superconductivity, controllable electron density and large Zeeman energy introduced by an externalmagnetic field. Consequently, the nanowire bulk undergoes a band inversion and two MZMs appear at the two nanowire ends. First signatures of MZMs were reported in 2012 and since then a lot of effort has been put in fully demonstrating them. Despite huge improvements in the materials and measurement techniques, conclusive evidence of MZMs in hybrid nanowires is still missing. This is because disorder in hybrid nanowires can also cause the observed signatures of MZMs and make the topological scenario indistinguishable from the trivial ones. Therefore, further improvements and more detailed studies are needed and this thesis shows some recent examples of these...

Superconducting qubits have seen a tremendous progress in the last two decades, and yet they remain unable to extract quantum advantage for application scenarios. While algorithms like Shor’s demonstrate quantum advantage in theory, they do not seem to fit modern noisy quantum processors. Then, in order to achieve quantum advantage either modern quantum processors catch up to their expected behaviour, or modern algorithms are tailored to fit the expected behaviour of modern chips.
This thesis focuses on the second approach, which is to explore the implementation of algorithms on modern quantum processors. Along all these implementations, we study the errors that cause these algorithms to derail from their ideal results. We attempt to understand, quantify and control these errors, in the hope that this provides useful insights into how to design algorithms for the modern hardware.
This thesis starts by introducing the topic of superconducting quantum processors and modern algorithms in the first two chapters. Then we move onto the three experiments, one chapter each, detailing our findings.
The first experiment cover an digital-analog implementation of a quantum simulation of light-matter interaction. We present the implementation that makes use of both digital (gates) and analog (evolution) blocks. The accuracy of the Trotterization technique is studied in detail, as well as the capability to study the photon population in the resonator. We manage to implement up to 90 Trotter steps and reproduce the behaviour in the ultra-strong coupling regime.
The second experiment presents an error mitigation technique, on an application of great interest to the field (molecular simulations). This application is a fully digital one, within the hot topic of variational algorithms for ground-state preparation. The mitigation technique, which is an invention of our own team (see referenced theoretical works) manages to reduce the algorithm error over an order of magnitude. In order to demonstrate this level of control, we quantify the error through accurate simulations of the quantum process and independent quantification of the parameters involved.
The third experiment presents another variational algorithm, this time to produce thermal states rather than ground states. Again, we pursue a detailed study of the many error mechanisms involved, in order to quantify and match the results obtained. We go beyond incoherent errors and add a coherent error mechanism common to our hardware architecture, the residual ZZ coupling.
Finally, we reflect on the final chapters about how to continue towards implementations that make the most out of modern, noisy, hardware.

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.

The technology of quantum computing is believed to solve certain computational problems significantly faster than classical computers, enabling classically inaccessible problems. However, the technology is still in its infancy and it is still too early to conclude which physical system(s) will form the basis of tomorrow's quantum computer. Small-scale quantum processors, built on the superconducting transmon qubit, demonstrated already the anticipated quantum speed-up. Despite this tremendous milestone, scaling up to a full-fledged quantum computer is far from trivial: with these qubits, the flux-control causes crosstalk between qubits and heating, the room-temperature microwave control is hardly scalable and comes with high energetic radiation, and most importantly, the loss of quantum information in time leads to computational errors. Recent advances in various hybrid semiconductor materials enabled novel voltage-controlled transmons, gatemons, which are less susceptible to heating and crosstalk. Even more exciting, gatemons can be designed to host Majorana zero modes in a way that renders the qubit inherently protected against decoherence. In order to induce Majorana zero modes in such nanowire systems strong magnetic fields are required. Problematically, magnetic fields destroy the superconductivity that these microwave circuits rely on. In this thesis we integrate three types of hybrid Josephson junctions in magnetic field compatible microwave devices. Chapter 4 demonstrates the first graphene-based transmon. Due to the mono-atomic thickness of graphene in combination with magnetic field resilient coplanar waveguide resonators, we are able to operate the transmon circuit at an in-plane magnetic field of 1 Tesla. Chapter 5 embeds an InAs-Al semiconducting nanowire Josephson junction in a high quality factor superconducting transmission line resonator, demonstrating on-chip microwave generation. The gate-controllable semiconducting platform lends itself for fast pulse control, providing a perspective for the coherent on-chip manipulation of artificial two-level systems, in particular superconducting qubits such as transmons. Chapter 6 continues the development of InAs-Al nanowire transmons. The offset-charge-sensitive regime, additional plunger gates and magnetic field compatibility prepares the platform for the detection of coherent coupling between Majorana zero modes, a phenomena which unfortunately still remains unobserved. Additionally, we realise the first InSb-Al gatemon. The higher spin-orbit coupling makes InSb to be a preferred material in the search for Majorana signatures. Chapter 7 reports on the dynamics of quasiparticle tunneling events in real-time across the InAs-Al nanowire junction in a transmon architecture. The magnetic field compatibility of our device up to 1 Tesla together with in-situ voltage-controlled quasiparticle trap engineering, allows us to measure the survival of the charge-parity lifetime up to strong magnetic fields. A result which is extremely important in the research field of topological quantum computing, where the qubit space is defined in the charge-parity.

Quantum technology is an exciting research area that has gained a lot of interest in the past few decades with the advances made in quantum computing. The quantum computer promises speedups that are impossible to achieve with classical computers. It does so by exploiting quantum mechanical properties such as entanglement and superposition with the quantum bit, or qubit, as its main building block.

Today, quantum computers are in their infancy and realizing a computer powerful enough to perform useful calculations poses major challenges. The fragility of qubits being the main difficulty. Approaches to mitigate this include implementing error correction schemes or alternative qubit designs. Topological qubits are part of the latter category and exploit the robustness of topologically invariant states to small perturbations to create more stable qubits.

In this thesis we explore semiconductor-superconductor hybrid nanowire structures and in particular the interaction of electron spins in quantum dots with superconductivity. When connected to superconductors, arrays of superconductor quantum dot hybrids can host Majorana states, a promising approach to realizing topological qubits. Creating Majoranas in quantum dots, as opposed to traditional methods, offers greater control over their properties. Additionally, understanding the interaction between spins in these quantum dots superconductor hybrids could enable new readout methods or coupling mechanisms between superconducting and spin qubits.

We start by investigating a nanowire SNS Josephson junction with signatures of Majorana states. A nanowire junction is capacitively coupled to an on-chip microwave detector made from a Josephson tunnel junction. We monitor the Josephson radiation frequency as a function of magnetic field and find a transition from a $2\pi$ to a $4\pi$-periodic Josephson current-phase relation, consistent with a topological transition.

In a different device, we investigate a multi-orbital double quantum dot Josephson junction. We measure the excitations between doublet and singlet states that arise in a quantum dot weakly coupled to a superconducting lead, also known as Yu-Shiba-Rusinov (YSR) states. With increased dot-lead coupling we observe a supercurrent and reveal its current-phase relation, both in the single and multi-orbit regime. We show that in the single-orbital regime the supercurrent sign follows an even-odd charge occupation effects. In the even charge parity sector, we observe a supercurrent blockade when the spin ground state transitions to a triplet -- demonstrating a direct spin to supercurrent conversion. For yet stronger dot-lead coupling we find a rectified current-phase relation at the transition between even and odd charge states. We investigate this apparent non-equilibrium effect and think about possible explanations.

To conclude, we discuss possible applications in spin qubit state readout and extensions of the device geometry towards realizing a Kiteav chain able to host Majorana states.

Of all parameters, determining the behaviour of a physical system in the laboratory, temperature is one of the most important, if not themost important. The study of solid matter at cryogenic temperatures revealed unexpected phenomena like superconductivity and was closely related to the verification of new and revolutionary concepts in solidstate physics in the last century. The nowadays pursued development of quantum effect devices is closely related to technologies of creating ultralow temperatures on the microand nanometerscale. Achievable electron temperatures in miniaturized electronic devices are currently limited to the millikelvin temperature regime, caused by the technical limits of 3He/4He dilution refrigeration in combination with hot-electron effects, due to a strongly weakening electron-phonon coupling strength in miniaturized electronic conductors with lowering the temperature. New physical and technological concepts, like the use of topological materials for quantuminformation processing, created an interest in reaching lower electron temperatures in nanoelectronic devices than currently possible. For this purpose, a bridge to classical ultralow temperature research, where microkelvin cooling of bulk solids is achieved for several decades, has to be built. This work is dedicated to the goal of enabling cooling of nanoelectronic devices to the yet unreached microkelvin regime. For enabling microkelvin refrigeration of nanodevices, methods for chipscale nuclear magnetic cooling are developed, in order to cool electrons on a chip to microkelvin temperatures by direct spin-spin thermalization with nuclear spins, bypassing the weak electron-phonon interaction. A decisive key for reaching a nuclear cooling power in miniaturized volumes, which is sufficient to refrigerate a nanoelectronic circuit to microkelvin temperatures, is the utilization of nonequidistant nuclear level splitting by nuclear quadrupole interaction in the nuclear refrigerant. The metal indium is proposed and utilized as nuclear refrigerant for this purpose, since it combines a strong quadrupolar interaction with a strong hyperfine interaction. The ultilization of indium for magnetic cooling on the micro- and nanoscale is studied by integrating electrochemically deposited indiumfilms onto a Coulomb blockade thermometer. Coulomb blockade thermometry is based on thermally activated single charge transport by tunneling between metallic islands and comprises an ideal and scalable solution for nuclear magnetic cooling and electronic thermometry on a combined, miniaturized platform. By combining indiummicrorefrigerators with an off-chip nuclear magnetic cooling stage, tailor made to couple the chip to an ultracold environment, cooling of a nanoelectronic device to microkelvin temperatures is demonstrated for the first time. With the cooling schemes for miniaturized electronic devices developed in this work, the foundation for quantum nanoelectronics at microkelvin temperatures is laid, opening the door to an experimentally unknown territory in physics.

Majorana bound states (MBSs) are novel particles predicted to be created when superconductor/semiconductor hybrid structures with strong spin-orbit coupling are subjected to strong magnetic fields. Expected to exhibit non-Abelian exchange statistics, they could form the basis of a new kind of quantum computer that is inherently protected from environmental noise, a common problem that has frustrated other quantum computing platforms. The current techniques used to measure these particles are highly sensitive, having provided the best evidence yet for their existence, but they are intrinsically too slow to form the basis of a useful quantum computer. To remedy this, this thesis integrates exotic materials into high frequency superconducting circuits that have been engineered to be resilient to strong magnetic fields, creating hybrid devices that potentially allow for fast and precise measurement and control of MBSs and their properties.

Several proposals to demonstrate the novel exchange statistics of MBSs use a specific type of superconducting qubit, the `transmon', for fast readout of the state of the MBSs. Problematically, the strong magnetic fields required to induce MBSs would destroy the superconductivity traditional transmons rely on, preventing them from operating as intended. To resolve this, the key constituent components of the transmon, the superconducting resonator and the Josephson junction have been engineered separately to become resilient to strong magnetic fields.

Chapter 4 explores how nanofabrication techniques and careful consideration of the properties of thin superconducting films can be used to engineer superconducting co-planar waveguide resonators that remain operational in strong parallel magnetic fields of \SI{6}{\tesla} and perpendicular magnetic fields of \SI{20}{\milli \tesla}, an order of magnitude greater than previously reported. Building on the results of Chapter 4, Chapter 5 utilises a graphene based Josephson junction, where the monoatomic thickness of the graphene provides an inherent protection against parallel magnetic fields, allowing us to demonstrate operation of a transmon circuit at a parallel magnetic field of \SI{1}{\tesla}.

Advances in nanowire material growth intended to improve the signatures of MBS are used in Chapter 6 to create a low power, highly coherent on-chip microwave source. With broad potential applications in superconducting circuits, it demonstrates a platform well suited for the detection of unique radiation that MBSs are predicted to emit. The thesis is concluded by Chapter 7, which describes the engineering and development of a nanowire based transmon qubit capable of measuring key properties of MBSs in the qubit's energy spectrum.

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.

Quantum cascade laser (QCL) technology has made a breakthrough in THz radiation sources, opening a new window into variety of applications. QCLs are compact, low-consumption and narrow linewidth lasers with relatively high output powers, capable to emit radiation across the whole super-THz (2-6 THz) range. These are all demanded for spectroscopy, which is so interesting in THz due to the fingerprint molecular rotational absorption/emission spectrums. Among many other potential applications of spectroscopy including chemical identification, security checking and biomedical diagnosis, high-resolution probing of celestial fine structured lines is prominent for addressing the human permanently staying curiosity about the origins of stars, galaxies and the Universe...

Majorana zero modes have been proposed as building blocks of intrinsically fault-tolerant quantum computers. Currently, externally applied magnetic fields are necessary to induce Majorana zero modes in carefully engineered systems. Topological qubit state readout is realized by parity sensing of Majorana islands. However, fast and high fidelity conventional cQED parity readout is incompatible with the magnetic fields needed for Majorana physics. In this thesis, magnetic field insensitive microwave CPW resonators with artificial Abrikosov vortex pinning sites have tested and implemented in a graphene based transmon qubit. It has been shown that these artificial pinning sites reliably trap vortices and are able to retain their zero field Q_i ~ 10⁵ up to perpendicular fields of 35 mT. By application of these resonators, we have described the successful continuous wave qubit spectroscopy of a graphene transmon qubit at B_|| = 1 T with a minimal linewidth of 166 MHz and demonstrated manipulation of the qubit frequency between 3.2-7 GHz with electric field. This is the first ever measured superconducting qubit that shows these properties at a magnetic field of 1 T.

Due to the collective behavior of electrons, exotic states can appear in condensed matter systems. In this PhD thesis, we investigate semiconducting nanowire Josephson junctions that potentially have Majorana zero modes (MZM) as exotic states. MZM are expected to form a robust quantum bit and quantum operations are done by interchange, otherwise known as braiding. The presence of MZM in a Josephson junction creates a topological junction, with properties which are drastically different from a normal Josephson junction. Understanding such topological junctions is of key importance in developing circuits for MZM braiding.

Similar to their charge, electrons also posses an intrinsic magnetic moment called spin. Whenmoving through an electric field, electrons experience and effective magnetic field in their restframe which will interact with the spin and influence its direction. This spinorbit interaction creates a measurable shift in the splitting of atomic energy levels and in the energy bands of solid state systems. Recently it has been proposed that systems with strong spin-orbit interaction can be used to engineer novel topological states of matter which are predicted to host non-abelian quasi particles. These could generate robust quantum states which are protected against decoherence. The research in this thesis focuses on indium antimonide (InSb) nanowires which combine exceptionally strong spin-orbit interaction with large g-factors and high electron mobilities. This makes them one of the most promising systems for realizing topological qubits based on Majorana zero modes (MZM).