Spin qubits in semiconductor quantum dots hold great promises for quantum information processing thanks to their small footprint, long coherence time, and similarities with classical transistors. However, such a new technology comes with new challenges and requires considering new metrics to develop proof-of-principle devices into a technological platform at scale.

Here, we study Si/SiGe heterostructures developed to host single electron spin qubits. We characterize the heterostructure and material stack using different structural techniques and measure the performances of multiple quantum devices with statistical significance. We use classical and quantum metrics to identify the performance-limiting mechanisms and improve them upon modification of selected parameters of the material stack to enable the next generation of spin qubit devices.

The first experiment is about the electrostatics of undoped Si/SiGe heterostructures. We study the semiconductor/dielectric interface between the epitaxial SiGe spacer and the SiOx and AlOx dielectrics. Against the mainstream approach, we grow heterostructures without an epitaxial Si cap. We find an improved interface from a structural characterization and in the two-dimensional electron transport at low temperatures.

The second experiment concerns the charge noise in few-electron quantum dots. We build on the previous results and focus our attention on the thickness of the Si quantum well. In thin quantum wells without a sacrificial Si cap, we find lower charge noise that we attribute to decreased density of remote impurities and misfit dislocations at the SiGe/Si and Si/SiGe interfaces arising from the local quantum well strain relaxation.

The third experiment finds the balance between disorder and the energy splitting of the nearly degenerate conduction band valleys (valley splitting) by fine-tuning the thickness of the Si quantum well. We challenge the apparent dichotomy between these two parameters and demonstrate heterostructures with simultaneously low disorder and high valley splitting. Besides, we give a quantitative estimation of the amplitude of the strain fluctuations in the quantum well arising from the virtual substrate.

The advancements reported in this thesis confirm the steady progress of the Si/SiGe platform towards realizing a full-scale quantum computer.
We summarize the results in the conclusion chapter, where we also highlight the general trends in the spin qubit community and suggest a few knobs to tweak to further improve the material platform.

The spin of a single electron or hole provides an attractive candidate for implementing a quantum bit when confined in a semiconductor quantum dot. Such a spin qubit is characterized by long coherence and short gate times. High-fidelity single and two-qubit operations have been demonstrated as well. Additionally, semiconductor quantum dots have a small footprint (~ 100 nm x 100 nm) and their fabrication employs techniques similar to processes commonly used in modern semiconductor technology foundries. This promises the realization of dense qubit arrays, leverage through industrial fabrication, and direct co-integration with classical control circuits.

Thus far, one-dimensional quantum dot arrays have been studied extensively. Yet, only by realizing two-dimensional quantum dot arrays the small footprint of quantum dots is fully exploited. Also, due to their small size quantum dots are extremely sensitive to their local environment and fabrication imperfections. In current devices, an individually tailored set of gate electrode voltages is required for each quantum dot to confine a single charge. The limited space available for routing these voltages on the device, coupled with the associated overhead in required voltage sources, presents a challenge in scaling quantum dot arrays, especially two-dimensional arrays.

This thesis focuses on two-dimensional quantum dot arrays and gate voltage uniformity. The first part (chapter 3 and 4) reports the realization of two-dimensional quantum dot arrays in a silicon/silicon-germanium (Si/SiGe) and a germanium/silicon-germanium (Ge/SiGe) heterostructure. Afterward (chapter 5 and 6), a novel all-electric method is presented to achieve increased homogeneity of the required gate voltages.

In chapter 3 a 2 x 2 quantum dot array in a Si/SiGe heterostructure is presented. It is tuned to be occupied by a single electron per quantum dot reaching the (1,1,1,1) charge state. Dedicated barrier gate electrodes on the device allow for controlling the interdot tunnel couplings between neighbouring quantum dots from about 30 ueV up to approximately 400 ueV as characterized through polarization line measurements.

In chapter 4 the focus is shifted towards a more scalable gate architecture for two-dimensional quantum dot arrays. It is inspired by random access architectures that are found in classical electronics. Specifically, a 4 x 4 quantum dot array in a Ge/SiGe heterostructure with shared gate electrode voltages is introduced. In this device, an odd charge occupancy is reached with either one or three holes in all 16 quantum dots simultaneously. Also, two shared barrier gate electrodes are placed between adjacent quantum dots. These enable selective control of the interdot tunnel coupling from less than 3 GHz to more than 10 GHz.

Spatial fluctuations in the electric background potential still limit the scalability of such a shared control array. Therefore, chapter 5 introduces a new method to increase the electrical uniformity in quantum dot devices. The presented method is based on applying stress voltages to the device gate electrodes. It enables the tuning of pinch-off voltages in quantum dot devices over hundreds of millivolts. Afterward, the new pinch-off voltages remain stable for hours at least. The method is used to homogenize the pinch-off voltages of the plunger gates in a linear array designed for four quantum dots. It reduces their spread by one order of magnitude from 153 mV to 20 mV.

Motivated by this demonstration, in the experiment presented in chapter 6 the stress voltage tuning method is applied to control the plunger gate voltages required to reach single electron occupation in a quantum dot array. In a double quantum dot, a stable (1,1) charge state is reached at identical and predetermined plunger gate voltage and for various interdot couplings. Finally, by applying stress voltages a 2 x 2 quantum dot array is tuned such that the (1,1,1,1) charge state is reached when all plunger gates are set to 1 V.

Quantum computers can solve specific problems with practical applications efficiently faster than classical computers. Spin qubits in semiconductor quantum dots are one of the most promising physical realizations of the quantum computers. This thesis aims to investigate the dynamics of semiconductor spin qubits in their actual environment. Specifically, we aim to understand how the actual environment of the spin qubits give rise to nonlinear response of the qubits to external driving, crosstalk, dephasing (T2 processes), and the temperature-dependence of the qubit frequency.
Chapter 3 reports on experimental observation of the nonlinear response of the spin qubits to external driving as well as the crosstalk effect, where the Rabi frequency of an adjacent qubit changes as the target qubit is driven. We propose a phenomenological model that relates the external drivings to the observed dynamics of the spin qubits. The physical mechanism that give rise to these phenomena could not be reproduced in our analysis.
Given the progress in reducing noise sources in the spin qubits environment, it is pertinent to investigate the dephasing of spin qubits in a sparse bath of defects. In Chapter 4, we theoretically investigate the qubit dephasing, as measured in the Ramsey and Hahn echo experiments, in a sparse bath of two-level fluctuators (TLFs) with 1/f spectral density. We find that although the spectral density remains approximately unchanged, the coherence times become more variable as the bath becomes more sparse. We also find that in a sparse bath the qubit decoherence is dominated by only a fraction of TLF defects. Removing these defects results in a significant improvement of the coherence times.
Chapter 5 explores the potential of a bath of TLFs in elucidating the frequency shifts of spin qubits with temperature and the temperature insensitivity of Ramsey and echo decay times. These effects have been observed in experiments. By tuning the bath parameters, we are able to replicate the observed qubit frequency shift. However, our simulations reveal a decrease in qubit decoherence with temperature, which is inconsistent with the experimental findings.
On the whole, Chapters 3 and 5 aim to refine the models that we use to describe the dynamics of spin qubit in their environment. On the other hand, the theoretical work in Chapter 4 is inspired by the experimental observation of the variability of qubit decoherence and offers suggestions to improve coherence times in certain parameter regimes.

For scaling up the qubits in silicon quantum computers, it is vital to determine crosstalk effects that can lower the fidelity of the computer.
In this computational project, we examine single-qubit gate-fidelities in the presence of crosstalk for uncoupled spin qubits that are driven with X-gates via electron dipole spin resonance (EDSR). We introduce two models: the first model introduces the AC Stark shift and the novel second model expands on this by adding a resonance frequency shift on top. We assume the latter resonance frequency shift to be due to heating effects. We optimize the gate-fidelity for a qubit coupled to up to six drives as a function of the overall driving time and -frequency of a single drive for both models using the Nelder-Mead algorithm.

Using the AC Stark shift model, we still obtain 0.99999 fidelity if we do not account for the crosstalk. However, when using the second model, the fidelity drops to 0.69 in the presence of two drives when we do not correct for the heating-induced resonance frequency shift and the AC Stark shift. Furthermore, the fidelity decreases linearly with the number of drives coupled to the qubit, implicating that the resonance frequency shift will become a significant problem for the scalability of silicon quantum computers. We find that we can correct for the resonance frequency shift entirely by using optimized driving time and -frequency, where most gain comes from optimizing the driving frequency. Moreover, we discover that there is a linearly increasing dependence of the resonance frequency shift at the theoretical driving time as a function of the total drives. Up to a translation factor of 0.5 MHz, we discover the same linear relationship for the correction needed on the theoretical driving frequency to hit maximum fidelity as a function of the total drives.

The discovery of the counter-intuitive laws of quantum mechanics at the beginning of the 20th century revolutionized physics. Quantum-mechanical properties, such as superposition and entanglement, can be harnessed to create quantum technology that opens a computing power far beyond the computing power that we know today. A quantum computer would enable efficient simulations of chemical reactions and material properties, which is expected to greatly impact healthcare and the energy transition. Practical quantum computation requires millions of qubits, either with neighbour-to-neighbour connectivity, or connected via quantum links. Spin qubits in electrically-defined silicon quantum dots are promising qubit candidates due to their small footprint and relatively long coherence time. The last decade meant a leap for the understanding and control of spin qubit systems with devices up to three quantum dots. Yet building systems capable of performing useful quantum calculations has proven difficult due to low sample yield, as well as challenges in controlling and scaling these systems. In this thesis, we explore quantum-dot-based spin qubits and their suitability for scaling to larger systems. This quest was threefold and can be summarized as: More, Distant, Industrial.
- More: Increasing the number of quantum dots and thus qubits to numbers greater than three was proven challenging, among others due to the the cross-capacitance that was posed upon quantum dots by the metallic gate electrodes of their neighbours. Here, we develop a material platform-independent method to individually control the chemical potential of each quantum dot and the number of electrons in it without affecting the quantum dots in their vicinity. We demonstrate the method by tuning up a linear array of eight GaAs quantum dots, containing exactly one electron each.
- Distant: Thereafter, we shift our focus to creating quantum links between distant quantum dots by shuttling electron spins across a chip. Given the superior spin coherence times, we moved to silicon quantum dots, which were not as far developed at the time. To improve our understanding of the material and allow for the fabrication of silicon arrays beyond two quantum dots, we formulate metrics that allow for sample comparison across material platforms and gate geometries, which allows us to examine samples and detect disorder and flaws to improve (uniform) sample fabrication. This enables the fabrication of a sample that can host an array of up to five quantum dots and tune it with the method described above. To mimic a quantum link, we shuttle an electron forth and back through four quantum dots of the array up to 1000 times, corresponding to a total distance travelled of approximately 80 _m. We observe that the spin orientation was preserved, forming a promising base for a quantum link.
- Industrial: Thirdly, in collaboration with Intel, we harness the experience of the semiconductor industry by industrially manufacturing quantum chips and controlling a qubit on these chips. By means of the metrics that we defined, we demonstrate that industrial manufacturing on 300-mm wafers allows for high yield and reasonable cross-wafer uniformity of the samples, while allowing for well-defined quantum dots and qubits with a performance that is comparable to state-of-the-art spin-qubit results. This high-yield fabrication without compromising qubit properties is crucial for scaling to the thousands of qubits that we need for practical quantum computation. The results in this dissertation provide perspective for scaling up silicon quantum dots and position the silicon spin qubit as a primary candidate for achieving quantum advantage with large-scale devices with millions of qubits.

Quantum computers promise an exponential speed-up over their classical counterparts for certain tasks relevant to various fields including science, technology, and finance. To unlock this potential, the technology must be scaled up and the errors at play must be reduced. As developments in scalable quantum computation devices advance, the demand for scalable benchmarking techniques that are able to reliably assess the fidelity – the complement of the error rate – of a device has increased significantly. Randomized benchmarking offers a single, concise number that reflects the average fidelity of multi-qubit operations performed on a quantum device. While this method is robust against state preparation and measurement errors, it still suffers from scalability issues. In this thesis, we present a protocol that efficiently predicts the multi-qubit fidelity obtained from randomized benchmarking by only benchmarking single- and two-qubit subspaces, greatly increasing the scalability. The protocol uses simultaneous randomized benchmarking with the aim of catching cross-talk effects while at the same time reducing the number of required benchmarking sequences. We have run numerical simulations of the protocol under two noise models, one depolarizing and one dephasing, to verify its performance. The results of these noisy simulations are promising and suggest that our protocol could offer a valuable tool on the road to developing large-scale quantum computers.

With continuous breakthroughs in quantum science and technology in recent years, the development of quantum computers is moving from pure scientific research to engineering realization. Meanwhile, the underlying physical structures also develop from the initial single qubit to multiple qubits or medium-scale qubit registers. Since qubits are operated by many sophisticated instruments under strict environmental conditions, people need a scalable solution to support many qubits working at the same time, so as to achieve high computing speed for a practical quantum computer.

More is more applies in particular to systems with interacting parts. These interactions enable the emergence of collective behaviour. Examples can be found among the behaviour of animals, such as the V-shaped formation of migrating geese and the flight of a flock of starlings. More examples are found among the electromagnetic properties of materials. For properties that rely on quantum-mechanical correlations it quickly becomes infeasible for classical numerical simulations to provide accurate results. An appealing alternative is to study these properties with quantum simulators, which mimic the material properties themselves. Besides being of scientific interest for the field of condensed matter physics, insights obtained from quantum simulations could in the future serve as input for the synthesis of novel materials. Developing quantum simulators requires the engineering of quantum systems. One such quantum system is that of electrons in gate-defined quantum dots, which are formed by three-dimensional confinement at the nano-scale. Experiments with quantum dots have already demonstrated measurement and coherent control of both individual charges and spins, and their operation as quantum bits. The first quantum simulation experiments with quantum dots have been performed in the last couple of years. Further development of quantum dots as platform for quantum simulations forms the overarching motivation for this thesis. The first experiment in this thesis describes the automated tuning of the tunnel coupling between quantum dots. This automation builds on previously developed automated tuning of double quantum dots. The automated tuning relies on image processing to extract parameters from measurement results. This step is part of a feedback loop in which the voltages on the gates are iteratively adjusted. This loop repeats until the target tunnel coupling is achieved. The second experiment further studies the tuning of tunnel couplings. For operation of gate-defined quantum dots it is common practice to independently control chemical potentials with so-called virtual gates. These virtual gates compensate for crosstalk effects due to cross-capacitances of the physical gates. The control of multiple tunnel couplings similarly suffers from crosstalk, but efficient compensation techniques were lacking. This chapter reports an efficient calibration scheme for such crosstalk, and demonstrates independent control of tunnel couplings with enhanced virtual gates. The third experiment demonstrates a method to measure charge and spin in large quantum dot arrays. The charge configuration of a quantum dot array is typically measured with a charge sensor, which is usually another quantum dot. To measure the spin configuration it is first mapped onto a charge configuration, which for singlet-triplet measurements is based on the Pauli exclusion principle. The charge measurement relies on Coulomb repulsion, which decays with distance, thus only charge and spin close to the sensor can be reliably measured. This chapter presents how, inspired by the effect of toppling dominoes, a cascade of hopping electrons induced by Coulomb repulsion can effectively convert the information about motion of a distant charge to the motion of a charge close to the sensor. The benefit of cascade-based readout is demonstrated by comparing singlet-triplet measurements with or without the cascade activated. The most involved experiment described in this thesis is a proof-of-principle quantum simulation of Heisenberg magnetism, which is one of the most famous models in condensed-matter physics. Specifically, this experiment demonstrates how a linear array of quantum dots can be operated as a Heisenberg spin chain. The first part of the experiment shows the characterization of the energy spectrum, which is based on degeneracies between spin states with different magnetization. From the energy spectroscopy the conditions are identified for which the exchange couplings are homogeneous. Next, the coherence is studied by inducing global exchange oscillations, and evolution in different subspaces of the Heisenberg Hamiltonian is demonstrated. The final step of the experiment consists of the adiabatic preparation of the low-energy global singlet state for a homogeneous chain, and its characterization with pairwise singlet-triplet measurements for each of the nearest-neighbours and correlations therein. These techniques and results form the basis for the operation of quantum dots to simulate larger spin systems and different lattice structures. The final experiment, shifts the focus from spin-spin interactions to electron-electron interactions. For gate-defined quantum dots, the Coulomb repulsion results in both on-site and inter-site interactions between electrons. The interaction is experimentally characterized with a linear array of six dots in which the tunnel couplings are tuned to be homogeneous. The decay of the interaction as a function of distance is modelled with both the method of image charges, where the gate metal acts as screening layer, and with a Yukawa type potential as a heuristic model. The latter provides an intuitive interpretation for the decay of the interaction in terms of a screening length. The characterization of the long-range electron-electron interaction is relevant for the operation of quantum dot arrays as hosts of spin qubits, but also for quantum simulations in which the charge degree of freedom and electron-electron interactions play an important role. Some examples of many-body physics for which long-range interactions are essential, are quantum chemistry, Wigner crystallization, and high-temperature superconductivity. Summarizing, this thesis reports novel techniques for the control and measurement of larger quantum dot arrays, the operation of such an array as quantum simulator of Heisenberg magnetism with control over the spin-spin interactions, and characterization of the electron-electron interactions. These results pave the way for future quantum simulations with quantum dots.

This dissertation describes a set of experiments with the goal of creating a super-conductor-semiconductor hybrid circuit quantum electrodynamics architecture with single electron spins. Single spins in silicon quantum dots have emerged as attractive qubits for quantum computation. However, how to scale up spin qubit systems remains an open question. The hybrid architecture considered here could provide a route to realizing large networks of quantum dot–based spin qubit registers. The first experiment in this thesis is aimed at achieving strong coupling between a single electron spin and a single microwave photon. The electron is trapped in a gate-defined double quantum dot in a Si/SiGe heterostructure and the photon is stored in an on-chip superconducting high-impedance NbTiN cavity. The photon is coupled directly to the electron charge, and indirectly to the electron spin, mediated through a synthetic spin-orbit field. We observe a vacuum Rabi splitting that depends on the spin-charge hybridization. The ratio of spin-photon coupling strength to decoherence rates of the spin and cavity combined is larger than unity, confirming the strong coupling regime has been reached. In addition, we find an optimal degree of spin-charge hybridization for which this ratio is maximized. The demonstration of strong spin-photon coupling not only opens a new range of physics experiments, but fulfills also a crucial requirement for coupling spin qubits at a distance via a cavity. The second experiment is focused on spin readout with the on-chip cavity. Instead of the direct dispersive readout of a single spin, we use the cavity to detect whether the electron is allowed to tunnel between the two dots or not. We benchmark the charge sensitivity and bandwidth of the detector and find that rapid detection of the electron charge with high SNR is possible. In the two-electron regime, electron tunneling is contingent on the total spin state (Pauli spin blockade). This spin-to-charge conversion scheme enables single-shot detection of singlet states with high-fidelity. The demonstration of single-shot spin readout with a cavity is an essential step towards readout in dense spin qubit arrays, such as the crossbar network, where it is not possible to integrate electrometers and accompanying reservoirs adjacent to the qubit dots. In the third experiment, we develop on-chip microwave filters to suppress microwave photon leakage from the cavity through the gate electrodes that are necessary to form quantum dots. We introduce a new cavity design that is compatible with long-distance connectivity between spins, but is also more susceptible to microwave leakage. We test and compare two low-pass filter variations in terms of performance, footprint and integrability. They use the same nanowire inductor, but different implementations of the capacitor: one with a planar interdigitated capacitor and one novel design with an overlapping thin-film capacitor. We find that both approaches are effective against microwave leakage. However, the large footprint of the interdigitated capacitor makes this solution inconvenient as the number of gate lines increases. The thin-film capacitor, with its much smaller footprint, is better suited for our devices. The final part of this dissertation contains concluding remarks and possible future directions are proposed.

Electron spins trapped in quantum dots have recently proven to be a promising technology for the implementation of qubits, already demonstrating high fidelity single- and two-qubits gates. The next step towards fault-tolerant quantum computing is to increase the number of so-called spin qubits on the processor. However, this poses several challenges, one of which being how to implement single-qubit gates in multi-qubit systems, with high fidelity. This work focused on two aspects. The first one was to identify the physical phenomena and limitations that hinder the realisation of high fidelity single-qubit gates in multi-qubit environments. The second objective was to investigate, implement and optimise methods in order to minimise the impact of these perturbing phenomena. The identified perturbing effects include unwanted driving between a pulse and the neighbouring qubits, as well as frequency shifts induced by drive-spin coupling and non-ideal pulse in experimental setups. Crosstalk was addressed using pulse shaping (i.e. amplitude or phase modulation of the driving pulse to tailor its spectral characteristics and reduce the energy transmitted at unwanted frequencies). The performance of shapes taken from both NMR and signal processing literature was investigated, for various pulse parameters, through an extensive grid search. In addition, a frequency correction algorithm was devised: off-resonant drive frequencies are selected so that the shifted qubits are resonantly driven. It currently accounts for two phenomena: the AC Stark and Bloch-Siegert shifts. The algorithm furthermore tracks the changes caused by the time-dependent characteristics of the shaped pulses. The proposed frequency correction algorithm was shown to almost entirely negate the effects of the considered shifts, leading to unitary fidelity improvements by up to 55%. In addition, pulse shaping was demonstrated to noticeably improve the fidelity of simultaneous single-qubit rotations compared to unshaped driving. Rotations with fidelities as high as 99.98% were obtained for pi/2 rotations on two-qubits systems. Moreover, shapes whose Fourier transform is narrow and sharp, associated with low Rabi frequencies, were demonstrated to generally provide the highest fidelities of the tested configurations. Lastly, the trends and guidelines highlighted by these results were shown to scale to systems with larger numbers of qubits. The correction techniques investigated in this work have proven promising for the implementation of high fidelity single-qubit gates in multi-qubit systems. In particular, the guidelines for selecting a well-performing pulse shape should also be useful for the design of optimised driving schemes, regardless of the number of qubits involved. Additionally, the proposed frequency shift correction algorithm is expected to be able to handle arbitrary shifts, and so to be easily adaptable to use in experiments.

To harness the potential of quantum mechanics for quantum computation applications, one of the main challenges is to scale up the number of qubits. The work presented in this dissertation is concerned with several aspects that are relevant in the quest of scaling up quantum computing systems based on spin qubits in silicon. Few-qubit experiments are maturing quickly, but simultaneously the lacuna between them and large-scale quantum computers is filled with a combination of science and engineering challenges. The challenges that are addressed in this dissertation are reliable and reproducible sample fabrication, qubit resilience to temperature, spatial correlations in the noise affecting the qubits, and co-integration of qubits with classical control electronics.

I start with describing the development of an integration scheme for silicon spin qubits in an academic cleanroom environment, as several research groups have demonstrated over the last years. This has allowed them to successfully fabricate and operate silicon spin qubit devices. The development of such a scheme is crucial for the fabrication of proof-of-principle devices, and the testing of several design variations for more and more complex qubit devices, before transferring the optimal designs to industrial foundries that are generally less flexible. Moreover, it is essential for performing paramount few-qubit experiments in the near term. The developed scheme has been successfully implemented in the next chapter of this thesis.

In the first experiment, we investigate the effect of temperature on the spin lifetime, as a first step towards higher temperature operation of silicon spin qubits. Spin qubit operation at elevated temperatures will be required to allow for co-integration of qubits with classical control electronics on a single chip, since the heat load associated with this electronics will be too much to deal with at the current qubit operation temperature of ∼10 mK. At a temperature of ∼1-4 K, significantly more cooling power is available (see for example CERN's Large Hadron Collider). Such co-integration would alleviate the interconnect bottleneck and facilitate the implementation of local control in large-scale devices. We find only a modest temperature dependence and measure a spin relaxation time of 2.8 ms at 1.1 K (still much longer than the record spin dephasing time measured in such a system). In addition, we present a theoretical model and use it in combination with our experimentally obtained parameters to demonstrate that the spin relaxation time can be enhanced by low magnetic field operation and by employing high-valley-splitting devices. Together with more recent work, this experiment demonstrates no fundamental limitations to prevent high-temperature operation of silicon spin qubits. Simultaneously, bringing classical control electronics to lower temperatures also is an active research area.

The second experiment uses maximally entangled Bell states of two qubits to study spatial correlations in the noise acting on those two qubits. Spatial correlations in qubit errors hinder quantum error corrections schemes that will be required for fault-tolerant large-scale quantum computers, as these schemes are commonly derived under the assumption of negligible correlations in qubit errors. Therefore, it is important to know to what extent the noise causing these errors is correlated. We find only modest spatial correlations in the noise and gain insight in their origin. The data is in accordance with decoherence being dominated by a combination of nuclear spins and multiple distant charge fluctuators coupling asymmetrically to the two qubits. We recommend to perform similar experiments in isotopically purified silicon to eliminate the effect of nuclear spins and in isolation study spatial correlations in charge noise. Furthermore, our insights show how correlations can be either maximized or minimized through qubit device design. For these reasons, the prospects for the development and implementation of quantum error correction schemes in fault-tolerant large-scale quantum computers are promising.

Finally, after having studied several aspects that are relevant to determine the suitability of silicon spin qubits for large-scale quantum computation in the preceding experiments, we propose a concrete physical implementation of co-integrated spin qubits with classical control electronics in a sparse spin qubit array. While the community usually claims compatibility of silicon spin qubits with conventional CMOS fabrication, existing proposals make assumptions that remain to be validated. Implementing quantum error correction protocols in a sparse array has been studied, but the description of a physical implementation was largely missing. The sparseness of the array allows for integration of local control electronics, as shown to be promising earlier in this thesis. Specifically, we propose to implement sample-and-hold circuits alongside the qubit circuitry that would allow to offset inhomogeneity in the qubit array. This enables individual local control and shared global control, resulting in an efficient line scaling. The scalable unit cell design fits 2²⁰ (≈10⁶) qubits in ∼150 mm².
We assess the feasibility of the proposed scheme, as well as its physical implementation and the associated footprint, line scaling and interconnect density.

In the last decade silicon has emerged as a potential material platform for quantum information. The main attraction comes from the fact that silicon technologies have been developed extensively in the last semiconductor revolution, and this gives hope that quantum dots can be fabricated one day with the same ease transistors are made today. However, building a large-scale quantum computer presents also complications that go beyond fabrication. The heat-dissipation challenge is one of these. As many other qubit platforms, also quantum dot qubits are cooled down at temperatures close to absolute zero in order to overcome the problem of decoherence. While this can be advantageous in few-qubit experiments, it becomes soon impractical as the qubit number increases. The first part of the thesis describes a series of experiments that demonstrate how Si- MOS quantum dot qubits can be successfully operated beyond one Kelvin, where the increase in cooling power is substantial. The first step is to demonstrate that electrons have sufficiently large energy scales to be properly isolated and controlled at these high temperatures. In the first experimental chapter of the thesis we demonstrate a highly uniform double quantum dot system at the temperature of 0.5 K. The on-chip single-electron-transistor (SET) shows very regular oscillations and an exceptional sensitivity to dot-reservoir and interdot transitions. The electrons in the quantum dot can also be completely decoupled from the reservoir, resulting in a fully isolated system. In order to performquantumoperations it is not only crucial to isolate electrons, but also to couple them. While this is routinely achieved in Si-SiGe heterostructures, it is usually more challenging in Si-MOS due to the larger disorder at the Si-SiO2 interface. However, we find that in the same device we can control the tunnel coupling between the electrons, in a range from below 1 Hz up to 13 GHz. This would allow to isolate the electrons for single-qubit operations and to couple them for two-qubit gates or readout using Pauli spin blockade. Part of the challenges concerning operation of ‘hot’ spin qubits lies in the temperature dependence of two parameters: the spin lifetime and the charge noise, which are thoroughly studied in chapter 4. The spin lifetime is usually very long in silicon, due to a weak spin-orbit coupling, and it can approach seconds at low magnetic fields. However, the temperature increases the excitations in the phonon bath and activates two-phonon transitions, which have a steep temperature dependence. These processes, which we experimentally find to start around 500 mK, can ultimately limit qubit performances. However, the spin lifetime can be significantly improved by working in a low magnetic field and high valley splitting regime. Si-MOS quantum dot qubits have a large valley splitting, usually of several hundreds of &eV, and a lowmagnetic field can be set by reading out the qubits with Pauli spin blockade. This guarantees that useful spin lifetimes can still be found at temperatures close to one Kelvin. In particular, in chapter 4 we measure values exceeding 1 ms at 1.1 K, and discuss how they can be further improved in case of a larger valley splitting.

We are entering the era of the second quantum revolution, where we aim to harness the power of quantum mechanics to create new technologies. Quantum technologies have the potential to revolutionize the fields of simulation, computation, communication, sensing, metrology, and many others. Here we discuss analog quantum simulation, which has attracted a lot of attention in the last few years from several platforms. Although arrays of gate-defined quantum dots exhibit significant potential for analog simulation, example experiments have been few and far between. This thesis focuses on simulating the Fermi-Hubbard model using two dimensional (2d) arrays of quantum dots.
The first experiment describes the creation and measurement of a 2x2 quantum dot array. Historically, most experiments with quantum dots have been performed with linear arrays due to the relative ease of fabrication. We introduce a bi-layer gate structure, facilitated by the lift-off of sputtered silicon nitride, to create the 2x2 dot array. This gate design enables us to achieve unprecedented tunability of the tunnel coupling between all nearest-neighbor pairs of dots in 2d arrays. We also demonstrate individual control over the chemical potential and the electron occupation of each dot along with accurate measurement of the on-site and inter-site interaction terms. The use of virtual gates significantly aids in the tuning of tunnel coupling and chemical potential. The demonstrated high degree of control of the system along with fast single-shot spin-readout achieved through Pauli spin blockade establish this dot array as a promising simulator of the Fermi-Hubbard model.
The 2x2 dot array is used to simulate Nagaoka ferromagnetism in the next experiment. This form of itinerant ferromagnetism arises from the Fermi-Hubbard model, and was first shown analytically in the limit of infinite interaction strengths and infinite lattices by Nagaoka in 1966. Nagaoka ferromagnetism has been a topic of rigorous theoretical studies ever since, but its experimental signature has eluded us for more than five decades. In this experiment, we load the four dot plaquette with three electrons and demonstrate the emergence of spontaneous ferromagnetism by measuring the spin correlation of two out of the three electrons. Changing the topology of the array to an open chain is shown to destroy the ferromagnetic signature, consistent with the Lieb-Mattis theorem. We also show indications that this ferromagnetic ground state can be destroyed by applying a perpendicular magnetic field, unlike most other forms of ferromagnetism. However, this ground state shows striking robustness to the offset in the local potential of any dot. This is the first experimental verification of Nagaoka’s prediction as well as the first simulation of magnetism using quantumdot arrays.
The final experiment takes a different approach to simulate the Fermi-Hubbardmodel with a large 2d array of quantum dots. The dot array is created using only three gates in a top-down approach. This allows for only global control over the electron filling and tunnel coupling of the dots, contrary to the previous experiments. The readout is performed with capacitance spectroscopy, which allows us to directly probe the density of states of the two-dimensional electron systems. We measure the disorder levels and optimize both substrates and gating strategies to induce periodic potential, sufficiently stronger than the disorder level, at the 2d electron gas. Although we demonstrate a novel platformfor the realization of artificial lattices of interacting particles, this effort is currently limited by the substrate inhomogeneity.

Interacting electrons on material lattices can build up strong quantum correlations, which in turn can lead to the emergence of a wide range of novel and potentially useful magnetic and electronic material properties. Our understanding of this physics, however, is severely limited by the exponential growth in complexity with system size, which leads all classical methods to fall fundamentally short. In this thesis, I show how artificial lattices of conduction band electrons in semiconductors, so-called quantum dot arrays, can be used to directly emulate and therefore elucidate such Fermi-Hubbard physics. To this end, I focus on two approaches. A top-down approach allows to scale easily, but lacks to ability to control or measure individual sites. A bottom-up approach on the other hand utilizes the small devices employed by the community for qubit experiments, in which the control of individual sites is both a blessing and a curse. We address the issue of control to the point where mapping to relevant models is possible and efficiently calibrating larger devices becomes feasible. These results open up the inherently well-suited and scalable platform of quantum dots to emulate novel quantum states of matter.