Quantum computers hold great potential to solve complex physics and chemistry problems that are beyond the capabilities of classical computers. Unlike classical systems that use bits represented as deterministic 0s and 1s, quantum computers operate with quantum bits or qubits, which can exist in a superposition of states. In addition to superposition, quantum computers harness the power of entanglement and quantum interference that enable quantum computers to encode and process information in ways that classical systems fundamentally cannot. These properties allow quantum computers to explore vast solution spaces in parallel, solving certain computational problems far more efficiently than classical systems. This has numerous potential applications ranging from the factoring of large numbers, optimizing complex systems, computational chemistry, machine learning, cryptography, and artificial intelligence.

Yet, current quantum processors are fragile, noisy and fairly limited in both quantity and quality with tens of qubits and physical error rates of around 10-³. To realize practical quantum applications, however, error rates need to be below 10-¹⁵ across millions of qubits. To bridge this gap and fully harness the potential of quantum computers, quantum error correction (QEC) is essential. QEC codes are designed to protect quantum information by redundantly encoding it onto multiple physical qubits. This encoding allows for the detection and correction of local errors affecting individual qubits, e.g., through stabilizer measurements. Importantly, if the physical error rates are below a specific threshold, QEC codes can exponentially suppress logical error rates by increasing the number of physical qubits involved. This is essential for achieving fault-tolerant computations, which are key to unlocking the full potential of quantum computers…

Quantum computers hold the potential to revolutionize computation by harnessing the unique properties of qubits. However, qubits are highly susceptible to errors, posing a major challenge in building reliable quantum systems. To address this, the development of quantum error correction codes is essential. The surface code has become a well-known code, using a 2D square grid to encode qubits. However, its high qubit overhead may be improved by alternative codes with more efficient encoding schemes. This thesis focuses on the small stellated dodecahedron code, previously outperformed by the surface code, and proposes a new approach to optimize its performance by developing an algorithm that finds interleaved measurement schedules. The developed algorithm is tested on both the surface code and a code based on the Tetrahemi hexahedron, correctly providing interleaved schedules for both. Applying the algorithm to the small stellated dodecahedron reduces the number of time steps required from 10 to 6, significantly boosting error correction performance. Simulations under a depolarizing noise model confirm the fault tolerance of these new schedules and demonstrate a 2.6x improvement in the code’s pseudo-threshold compared to the original sequential schedule. While the surface code remains more effective at protecting against errors, performing 1.26 times better, the stellated dodecahedron code offers a compelling alternative for near-term research, requiring fewer qubits while maintaining strong performance.

Superconducting qubits are a leading platform holding potential for realization of fault-tolerant universal quantum computation. However, experimental demonstration of quantum fault tolerance may require scaling up to hundreds of physical qubits (Chapter 1).

The non-linearity of superconducting qubits emerges from current-phase relation in superconducting tunnel junctions, better known as Josephson junctions (Chapter 2). The transmon is a special case of the charge qubit with a large parallel shunt capacitance which results in suppression of charge noise sensitivity at the cost of reduced anharmonicity. The resonance frequency of a transmon depends on the charging energy contributed by the total capacitance of the circuit and the non-linear inductive energy of a Josephson junction. This inductance is in turn directly proportional to the room-temperature conductance of the tunnel junctions, determined by the junction area and thickness of the tunnel barrier. The manipulation of superconducting artificial atoms by strongly coupling to microwave photons is achieved using circuit quantum electrodynamics. In planar superconducting circuits, on­-chip transmission lines based on coplanar waveguide geometry is routinely employed to manipulate and readout the qubit states (Chapter 3).

The QuSurf architecture for a full-stack quantum computer features an extensible surface code comprising flux-tunable qubits with four-port connectivity to nearest neighbours. The first distance-3 logical qubit requires a 2D lattice of 17 qubits to perform quantum error correction. At the hardware level, we concurrently pursue a short-term low-overhead and a long-term high-overhead strategy with lateral and vertical input/output signal routing respectively (Chapter 3). The usefulness of a superconducting quantum processor depends on three main fabrication metrics, the physical yield of individual components, how well it matches the chip design specifications and its susceptibility to environmentally-induced decoherence (Chapter 4). Due to the nanometer-scale of Josephson junctions, it is particularly challenging to reliably target a desired qubit frequency within a margin of 50 MHz.

This thesis outlines the current fabrication bottlenecks which limit scalability with a focus on increasing the precision of qubit frequency targeting. The addition of through-silicon vias for vertical routing of signals and increasing the density of on-chip components add layers of complexity to this problem, which necessitates testing two variants of Josephson junctions with subtle differences in the fabrication process and its geometry. The primary objective is to systematically identify and quantify the sources of deviation affecting fabrication of the two Josephson junctions variants. To determine the causes of spread in Josephson junctions aside from intrinsic variations in the tunnel barrier, room-temperature conductance measurements are compared for thousands of test junction structures fabricated at waferscale. (Chapter 5). We also develop customized fabrication tools and techniques to achieve selective or global tailoring of qubit frequencies (Chapter 6). The thesis concludes with a summary on the factors identified in this work which impacts qubit frequency targeting, a reflection on the limitations of this work and an outlook on specific aspects of scalability of superconducting qubits in the near future (Chapter 7).

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.

One of the main components used in superconducting quantum chips is the Josephson junction. Currently when fabricating Josephson junctions, the resistance uniformity at wafer-scale is not optimal. It is also known that an annealing process can alter the junction resistance and with it the qubit frequency. However, laser annealing has only shown to be able to increase the junction resistance. An equally effective and minimally invasive technique to decrease junction resistance is necessary to have full control on frequency
targeting. Thermal annealing in a reducing environment is known to result in a global decrease in junction resistance. To get better control on frequency targeting the techniques could be combined. A die containing not-capped Manhattan type Josephson junctions has been annealed using forming gas at 200°C for 2 minutes, based on a non-linear least squares reciprocal function fit to the data an asymptotic lower bound of 467 μSμm^-2 for the change in conductance per unit area has been found. Smaller junctions with an area
of approximately 0.03 μm² undergo a bigger change in conductance per unit area of around 800 μSμm^-2. Annealing at higher temperatures such as 300 and 400°C results in a decrease of the conductance. There is no substantial change in yield of usable SQUIDs when using a rapid thermal annealing process.

This report introduces a customized software tool to enable automation of optical inspection optical and SEM images of a superconducting quantum processor during its fabrication. This is achieved by implementing image processing algorithms using the Python package OpenCV. This suite consist of three components; pyclq_base, pyclq_jj, pyclq_ab. The first component will template match the base layer to its CAD design. The second component will be a validation for the airbridges. These have 3D components and therefore can not be matched to their CAD design. The results had about twice as many false positives for, broken bridges, and no false negatives. The third component measures the width and overlap area for Manhattanstyle Josephson junctions using two different filtering methods; k-mean segmentation and thresholding. The results of these three components are used as a tool to understand the sources of spread in the conductance of Josephson junctions therefore optimizing the fabrication process.

In this thesis variations in the Josephson junction conductance across a 100 mm wafer are studied. For this study junctions fabricated with a Dolan bridge and with the Manhattan layout are used. These junctions are fabricated on a planar and a non-planar NbTiN base layer to characterise the uniformity. On a planar
base junctions fabricated with a Dolan bridge showed higher uniformity and yield than junctions with the Manhattan layout. On a non-planer base junctions fabricated with a Manhattan layout showed a higher uniformity
than the Dolan bridge junctions. This can be attributed to the through silicon vias, which affect the resist spinning required for the Dolan bridge.
Manhattan style junctions are fabricated on a Si base layer in an attempt to improve the uniformity across a 100 mm wafer. By fabricating junctions on Si overall fabrication complexity is reduced, while also reducing the fabrication time. These junctions are used to investigate the role of oxygen ashing prior to the junction deposition. We find that the ashing increase the uniformity of the junctions, however, further attempts to improve the uniformity using different ashing steps did not how any additional improvements. Finally, to explain the variations in Manhattan style junctions a geometric model is introduced. This model is based on the thickness of the top resist stack, which could potentially affect the width of the junction electrodes. The model is compared with SEM images and with the coefficient of variation. The model shows correspondence with the SEM data, but overestimates the variations when compared with the coefficient of variation.

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.

Superconducting-normalconducting-superconducting (SNS) transmons with 2-facet Al-shell nanowires are qubits compatible with magnetic fields above 10 mT. There are important correlations of the room temperature nanowire resistance with the chance of the qubit being measurable: at a resistance of 2−3 kΩ, the qubit is almost guaranteed to work. The chance of success halves every 2−3 kΩ increase. This information can be used to increase the yield. The flux noise power spectral density (PSD) of a model spin-1/2 fluctuator has been investigated as a function of the magnetic field using the Zeeman interaction. Not only the fluctuations parallel to the magnetic field contribute, but also the fluctuations perpendicular to the magnetic field. Cross-terms cancel out. The flux noise PSD of the SQUID is a linear combination of these spin PSDs when the spins are spatially uncorrelated. The magnetic field suppresses the parallel spin-axis noise PSD contribution as cosh^(-2)(μB/kBT). The magnetic field changes the perpendicular spin-axis PSD contribution due to the Larmor precession frequency peak 2fZ~μB, but does not influence the PSD contribution at frequencies higher that the Larmor precession frequency. When rotational asymmetry in the SQUID geometry is present, the PSD contributions of the perpendicular and parallel components can be separated. In our setup, a perpendicular coil is used to align the magnetic field with the transmon plane. The alignment procedure of maximizing the resonator frequency vs. the perpendicular coil field has been verified. To measure the flux noise, the perpendicular coil is first used to change the flux bias by large amounts. Then a dedicated flux bias is used to make a fine-grained sweep over the flux without flux-jumps, to calibrate the magnetic field at the SQUID. We have found a signal of the flux noise at zero field and at field. A flux noise amplitude of A~1000 μΦ_0 has been found at zero magnetic field.

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 computing may be the key to solving many of the problems our modern world faces today. Just as regular computers boosted our computing power to scales never imagined before, so too could quantum computers allow us to solve problems that we just do not yet have the computational power for. However, a properly functioning quantum computer that outclasses current classical computers is not yet a reality. Many di_erent platforms for quantum computing are being researched. Experiments are being done with diamond vacancies (see, for example, [1]), trapped ions [2], nuclear spins in NMR [3] and silicon quantum dots [4], to name a few. One of the most promising types of qubits is based on superconducting circuits [5]. The most widely studied and most promising superconducting qubit is the Transmon qubit [6]. One of the advantages of this type of qubit is that it can be fabricated using currently available lithographic patterning equipment. However, when fabricating Transmon chips, there is a problem of non-uniformity: when using the exact same method to make two chips, they can be vastly di_erent. As such, every chip needs to be characterised after fabrication. Characterising a chip means _nding speci_c important parameters for the qubits, such as their frequency and coherence times. For use in a quantum computer, qubit frequencies will have te be targeted with more precision than is currently possible [7] [8]. As such, a technique that allows change a qubit's frequency after its fabrication is very useful. In this thesis, such a technique is presented. The characterisation process of a Transmon chip is then explained. The data of the three chips that were subjected to the aforementioned technique is also presented.

In this work, the addition of a filtering resonator to protect against Purcell decay in the surface code implementation presented in [R. Versluis et al., 2017, Phys. Rev. Applied] is investigated.The requirements on single- and two-qubit gate operation as well as readout is outlined. We model the system with differential equations to optimize the coupling strengths and target frequencies for fast readout and minimized dephasing of untargeted qubits. The currently used qubit design is adapted to achieve these goals. A proof-of-concept chip, containing a subset of the surface code is implemented using these altered qubits, fabricated and characterized.On this device, state-of-the art readout fidelities of >98% within 450 ns are demonstrated. Back-action on untargeted qubits is measured and an upper bound is determined.

We generate entanglement between two transmon qubits each coupled to a readout resonator and located on different chips via engineering a half-parity measurement. This measurement does not distinguish |01> from |10>, thus if started in an initial full twoqubit superposition it will project the qubits to an odd Bell state 50% of the time. By post-selecting on measurement outcomes corresponding to |00> or |11> we have generated Bell-states of 51% (40%) concurrence or 75% (70%) Bell-state fidelity keeping 25% (50%) of the data. With a repetition rate of 5KHz based on state initialization by T1 this corresponds to a 1KHz generation rate. We show that changing the cavity frequencies with tuning qubits and by driving with a second compensation pulse in a weakly coupled port we can reduce residual distinguishability in the odd subspace, making the protocol robust to fabrication imperfections. By shaping the pulse of the compensation drive we also generate an even-parity Bell state of similar concurrence. We found that thermal excitation results in an overestimate of concurrence in state tomography and show a simple method to correct for this by assuming mixed calibration points. We find good agreement of unconditioned measurement dynamics with theory using a reduced two-qubit only master equation. A 45% measurement efficiency was found using a stochastic master equation to model final state concurrence conditioned on the measurement result. This protocol could be used in modular 2D quantum computing architectures where entanglement is distributed with itinerant photons.

For quantum computing with superconducting qubits, fabricating transmon qubits with increased coherence time is crucial, especially in view of multi-qubit quantum processors. The fabrication process, geometries and materials used to fabricate a transmon qubit are similar to the fabrication of CPW resonators. However, due to shorter fabrication time and straightforward measurement scheme of the latter, finding a way to increase the internal quality factor Q_i in a CPW resonator is a quick way to gain insight into methods to increase the coherence time of a transmon qubit. The main goal of this research is to characterize the Q_i at cryogenic temperature and single photon level of CPW resonators that are fabricated with novel surface treatments and etching techniques. The highest Q_i is observed for resonators etched using Deep Reactive Ion Etching and HDMS surface treatment, which reached ∼10⁶ at single photon level. This is comparable to the highest Q_i reported in literature so far.