Classical computers have long been the cornerstone of information processing, yet their capabilities are constrained by the limits of the classical laws of physics. Quantum mechanics offers a new spin on information processing, potentially providing immense speed-ups for some specialized problems. There are many approaches to building such a quantum computer, that leverages quantum mechanical principles. The most popular approach uses superconducting circuits to implement a qubit. This thesis, however, builds on the advances of the semiconductor industry. The miniaturisation of electronic devices in the last decades has enabled the fabrication of gate defined quantum dots. Such a quantum dot allows the isolation of a single charged particle that can be used to implement a qubit. More specifically this thesis employs electrons in Si/SiGe heterostructures. While most implementations so far rely on linear chains of quantum dots, scaling in a second dimension is crucial for building larger systems.

This thesis explores a 2x2 array as a proof of concept for a 2D array. This small-scale device demonstrates that charge-related properties, such as gate pitches and tunnel coupling control, remain similar when transitioning from one to two dimensions. We show that existing qubit control strategies using electric-dipole spin resonance (EDSR) and micromagnets can also be adopted for 2D arrays as long as the second dimension remains small. In larger 2D arrays, the magnetic field gradients achievable by micromagnets no longer meet the requirements for EDSR control. Additionally, the application of microwave bursts causes an unintended spin resonance shift that complicates qubit manipulation.

To address these challenges, this thesis also explores baseband control of single-spin qubits. In this scheme, single-qubit rotations are implemented using hopping gates, which use tilted quantisation axes in neighbouring quantum dots. In Si/SiGe this tilt is achieved using the strong spatial variation of the stray field of a nearly demagnetized micromagnet. Building on this, a nanomagnet-based architecture is proposed, integrating localized nanomagnets to provide magnetic field gradients for spin manipulation. This approach circumvents EDSR limitations, offering a more scalable pathway for 2D quantum dot arrays and advancing spin qubit technologies toward large-scale quantum computing.

In this thesis, we explore the physics and control protocols enabled by hopping spins in the quantum dot arrays. Our approach consists of experimental studies as well as numerical simulations. In chapter 2 we provide the background information relevant to the work in this thesis, including the theoretical description of spins in germanium quantum dots, as well as the measurement setup used in the experiments. In chapter 3 we study the control protocols for spin-spin exchange interactions, and quantify the individual coupling strength in a configuration of 2×2 array when all the nearest neighboring coupling are turned on. We can tune to a regime of equal coupling strength, in which the four-spin entangled states emerge as the resonating valence bond states. In chapter 4 we model the qubit frequency susceptibility to charge noise and predict the optimal magnetic field orientation for extended qubit coherence time. In chapter 5 we show multi-photon transitions in a two-spin system, and discuss opportunities to use this method for qubit addressability in large qubit array based on shared control architecture. In chapter 6 we demonstrate coherent spin qubit shuttling through quantum dots. We quantify the loss of the quantum information during the process. In chapter 7 we demonstrate high-fidelity baseband control of single qubit and two qubit gates, with extended coherence times by operating at low magnetic field. The single qubit gate is realized based on shuttling between the quantum dots, resembling the original spin qubit proposal by Loss and Divincenzo. The two-qubit CPhase gate achieves average fidelity 99.3% in the randomized benchmarking experiments. In chapter 8 we conclude and provide an outlook on the near future for germanium spin-qubits operations.

Quantum computers could solve certain problems exponentially faster than classical computers. Among the various physical implementations being explored, spin qubits in semiconductor quantum dots have emerged as a promising platform due to their potential scalability and compatibility with existing semiconductor manufacturing. Within semiconductor platforms, germanium has recently gained significant attention due to its strong spin-orbit coupling, absence of valley states, and compatibility with industrial processes. In this thesis, we explore several aspects key to advance germanium-based quantum computing technology. The work focuses on improving the material quality and understanding fundamental properties, developing new device architectures, and enabling hybrid superconductor-semiconductor systems. We begin by investigating the effective mass of holes in strained germanium quantum wells and its dependence on carrier density, confirming theoretical predictions of a remarkably light effective mass in compressively strained germanium. We then investigate the properties of a lightly-strained germanium quantum wells which can achieve holemobility exceeding 1×106 cm2/Vs while maintaining a remarkably low percolation density. Further, we achieve a major materials breakthrough by growing germanium quantum wells directly on germanium wafers, rather than the traditional silicon substrates. This novel approach reduces threading dislocation density of nearly an order of magnitude, resulting inmobility consistently exceeding 3×106 cm2/Vs. Building on our understanding of single quantum wells, we develop and characterize germanium double quantum well systems. Through magne to transport measurements, we demonstrate the formation of a high-mobility hole bilayer and study the coupling between the two layers. Leveraging this bilayer platform, we demonstrate the first vertical gate-defined double quantum dot in a strained germanium double quantum well, opening possibilities for three-dimensional quantum circuits. We further expand the germanium planar platformand create hybrid semiconductor superconductor systems by developing high-quality superconducting contacts to germanium. Using a germano silicide process formed through thermal reaction between platinum and the semiconductor, we achieve the first demonstration of a hard superconducting gap in germanium. This breakthrough enables the integration of quantum dots with superconducting elements for hybrid quantum devices. Finally, we present a qubit-array research platform for engineering and testing (QARPET). In a significant step toward testing scalability, we present a crossbar array approach for statistical testing of spin qubit tiles, each composed of one sensor and two quantum dots. The device with over 1000 potential spin qubits, achieves a quantum dot density of 2 million per mm2 while requiring minimal control lines and a single cooldown. This development represents a significant advance for characterizing quantum devices at scale. The results presented in this thesis establish planar germanium as a versatile platform for quantum devices, offering high-quality materials, novel three-dimensional architectures, and integration with superconductors. Altogether, these developments provide a foundation for scaling up the complexity of quantum devices.

Simulating the quantum properties of superposition and entanglement can be highly inefficient with digital computers. To allow for exploration and verification of complex quantum systems, a new tool must be developed. Quantum computers, leveraging discrete operations and error correction, offer potential speedups in factoring, unsorted database search and machine learning as well. However, quantum computers rely on large numbers of qubits that can be controlled with high accuracy to outperform classical computing and key challenges include managing interconnects, achieving uniformity and maintaining isolation from the environment.

Semiconductor spin qubits are promising because of their affinity for mass production and small footprint. However, a statistical understanding of the devices and materials is needed to ensure sufficient yield, which requires high measurement throughput. Additionally, the number of quantum dots per device must increase, transitioning from small linear systems to large 2D architectures which can support the millions of qubits required for fault-tolerant quantumcomputing.

Measurement throughput can be enhanced by mitigating bottlenecks in the feedback cycle through the development of a cryogenic multiplexing platform, using commercial off-the-shelf CMOS for sub-kelvin temperature measurements. This approach increases the number of wires available at cryogenic temperature, enabling efficient statistical characterization of mobility and percolation density in natSi/SiGe heterostructure Hall bars fabricated in an industrial CMOS fab.

The increased throughput enables systematic studies of performance-critical device parameters. Activation energy measurements reveal that conduction band valley energy splitting increases linearly with magnetic field but is independent of Hall density. Instead, it depends on incremental density changes across quantum Hall edge strips, aligning with theoretical predictions for a near-perfect Si quantum well top interface. By combining multiplexing with a crossbar architecture that offers quadratic scaling of unit cells with cryogenic interconnects, 648 narrow-channel field-effect transistors on an industrial 28Si-MOS stack are measured at 100% yield. The device scale allows for comparison between macroscopic pinch-off differences across the crossbar and local differences within each unit cell. These distributions can be converted to energy using addition voltages and compared to proposed 2D architecture uniformity requirements. Additionally, unit cell geometry variations can be used to characterize the impact of device design compared to intrinsic material stack variance.

Finally, the conclusion highlights how advances in this thesis contribute to both the quality and quantity of quantum devices, necessary for future quantum computers to solve real problems. Quality can be further improved with high throughput characterization of efficient measurement structures, using statistical data to deepen understanding viamodeling and exploration of alternative material stacks like Ge/SiGe heterostructures. Increasing quantity calls for further system integration and industry participation.

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.

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.

Spin qubit in semiconductor quantum dot arrays offers a promising platform for future scalable quantum computing with its small size and compatibility with modern semiconductor industry. To scale up the quantum dot arrays, one of the major challenges is the wiring bottleneck, as a high density of control lines might need to be integrated into a small chip. A proposal to solve this problem is using the shared control protocol, in which multiple qubits could be controlled by a shared line. For this, the most critical requirement is to realize uniformity across the quantum dot array, such that a single control signal could lead to an identical response in all dots involved. However, such uniformity is hard to achieve due to the variation of the device fabrication, and tackling this problem via materials and fabrication optimization only appears to be a daunting challenge.

In this thesis, we propose a potential solution to achieve uniformity of threshold voltage in such share-controlled systems. This solution is based on the hysteresis behavior of turn-on voltage in the heterostructure field-effect transistor (HFET) devices hosting the quantum dot array. In the Ge/SiGe HFET devices with hole as carrier, we found that the drift of turn-on voltage can be caused by population of 2DHG under negative gate voltage and reversed by applying positive gate voltage. We attribute this effect to trapping and detrapping processes on the dielectric surface of the device. Following this discovery, an automatic feedback control program was designed, in which gate voltage pulses are applied to control the trap filling level such that potential landscape in the device corresponds to the desired turn-on voltage. Using this program, we performed deeper investigations of the turn-on voltage shift including its relaxation and history-dependent stability. A hypothetical physical model for observations in these experiments is followed. For practical application of this effect, the feasibility to locally define and control the turn-on voltage is also demonstrated. Based on these results, we present a proposal for addressable manipulation of potential landscape in share-controlled quantum dot array, which might potentially realize the threshold voltage uniformity for scalable quantum dot array in the future.

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.

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.