Gate defined germanium spin qubits appear to demonstrate many attractive properties for building block of a future quantum computer. In this thesis we explore beyond the necessities, demonstrating three key results. In chapter4, a resonating valence bond is realised on a 2×2 qubit array, utilising precise control over the exchange interaction. The rich intrinsic physics provided by the spin orbit coupling gives many possibilities for controlling Ge spin qubits. While it can enable all electrical control using microwaves, we demonstrate that fast, high fidelity, and long coherence all electrical control can even be achieved with baseband pulses. Through the development of hopping based spin qubits, we exploit the g-tensor misalignment between quantum dots in order to produce quantum gates by diabatically and coherently shuttling spins between quantum dots. In chapter5 we show that the g-tensor anisotropy can be exploited for low power, baseband qubit control, with fast gate times and high fidelity. We obtain high single qubit gate fidelities, and measure two-qubit gate fidelities of FCZ = 99.3% using IRB, and FCZ = 98.1% using GST. It is certainly a step in the right direction; we don’t require strong magnetic fields, or microwave pulses, however this approach does depend on precise timing control, and more work is needed to determine how gates in a scaled computer would be timed.

In chapters 6, 7, 8, the toolbox of spin qubits is expanded once more and we show that spin qubits need not be confined to planar architectures, but can be scaled in the out of plane direction. Further to this, they support coherent spin physics. We establish methods to tune multi-well systems and realise a three-dimensional dot array. Bilayers promise higher connectivity and future research may indicate whether they can enable hopping-based qubits where the quantization axis can be consistently controlled by engineering the strain of the quantum wells. The extra tuning complexity introduced by additional layers may offset these gains; whether it would stand to benefit the community to adopt multilayer heterostructures remains an open question. When considering wiring bottlenecks this may reveal an efficient approach to circumventing the problem, and to achieve connectivities which can efficiently simulate natural systems it may be necessary to have three-dimensional quantum dot arrays.

Qubits that can be efficiently controlled are essential for the development of scalable quantum hardware. Although resonant control is used to execute high-fidelity quantum gates, the scalability is challenged by the integration of high-frequency oscillating signals, qubit cross-talk, and heating. Here, we show that by engineering the hopping of spins between quantum dots with a site-dependent spin quantization axis, quantum control can be established with discrete signals. We demonstrate hopping-based quantum logic and obtain single-qubit gate fidelities of 99.97%, coherent shuttling fidelities of 99.992% per hop, and a two-qubit gate fidelity of 99.3%, corresponding to error rates that have been predicted to allow for quantum error correction. We also show that hopping spins constitute a tuning method by statistically mapping the coherence of a 10-quantum dot system. Our results show that dense quantum dot arrays with sparse occupation could be developed for efficient and high-connectivity qubit registers.

Gate-defined quantum dots define an attractive platform for quantum computation and have been used to confine individual charges in a planar array. Here, we demonstrate control over vertical double quantum dots confined in a strained germanium double quantum well. We sense individual charge transitions with a single-hole transistor. The vertical separation between the quantum wells provides a sufficient difference in capacitive coupling to distinguish quantum dots located in the top and bottom quantum wells. Tuning the vertical double quantum dot to the (1,1) charge state confines a single-hole in each quantum well beneath a single plunger gate. By simultaneously accumulating holes under two neighboring plunger gates, we are able to tune to the (1,1,1,1) charge state. These results motivate quantum dot systems that exploit the third dimension, opening new opportunities for quantum simulation and quantum computing.

Gate-defined quantum dots in silicon-germanium heterostructures have become a compelling platform for quantum computation and simulation. Thus far, developments have been limited to quantum dots defined in a single plane. Here, we propose to advance beyond planar systems by exploiting heterostructures with multiple quantum wells. We demonstrate the operation of a gate-defined double quantum dot in a strained germanium double quantum well, where both quantum dots are tunnel coupled to both reservoirs and parallel transport occurs. We analyze the capacitive coupling to nearby gates and find both quantum dots to be accumulated under the central plunger gate. We extract their position and size, from which we conclude that the double quantum dots are vertically stacked in the two quantum wells. We discuss the challenges and opportunities of multilayer devices and outline some potential applications in quantum computing and quantum simulation.

Simulations using highly tunable quantum systems may enable investigations of condensed matter systems beyond the capabilities of classical computers. Quantum dots and donors in semiconductor technology define a natural approach to implement quantum simulation. Several material platforms have been used to study interacting charge states, while gallium arsenide has also been used to investigate spin evolution. However, decoherence remains a key challenge in simulating coherent quantum dynamics. Here, we introduce quantum simulation using hole spins in germanium quantum dots. We demonstrate extensive and coherent control enabling the tuning of multi-spin states in isolated, paired, and fully coupled quantum dots. We then focus on the simulation of resonating valence bonds and measure the evolution between singlet product states which remains coherent over many periods. Finally, we realize four-spin states with s-wave and d-wave symmetry. These results provide means to perform non-trivial and coherent simulations of correlated electron systems.