Spin Qubits in Germanium: Driving through Noise and Anisotropies

Quantum computers promise to revolutionise our approach to complex calculations by leveraging the unique properties of their fundamental information units: the qubits. Features such as superposition and entanglement - absent in classical computing - enable an exponential increase in processing power, unlocking faithful simulations of natural phenomena and faster solutions to combinatorial problems. However, engineering a physical system capable of storing fragile quantum information while allowing for precise manipulation presents an arduous challenge. Among the various contenders for the realisation of quantum processors, spin qubits in semiconductor quantum dots offer significant advantages.

In particular, hole spin qubits in germanium - the focus of this thesis - have recently gained substantial attention and are rapidly maturing as a promising quantum platform. The qubit computational basis states are encoded in the intrinsic spin states of a positive charge carrier, a hole. These holes are confined within a silicon-germanium heterostructure by an electrostatically defined quantum dot, a structure remarkably similar to the modern transistors, found by the billions in today's electronics. Beyond inheriting the general qualities of spin qubits, holes in germanium exhibit unique characteristics derived from the strong spin-orbit interaction. This intrinsic property allows for fast, all-electrical qubit control, but also introduces complex physics that must be understood and mastered.

In this thesis, we investigate the rich physics of hole spin qubits in germanium, moving from the material level to multi-qubit interactions, and exploring how their properties can be leveraged to advance quantum computing. We begin with the foundation of the quantum processor: the heterostructure that hosts the germanium quantum well where holes are confined. We characterise the material quality, focusing specifically on its susceptibility and response to applied potentials, which can cause drifts and instabilities that hinder the operation of large qubit registers. We then explore the properties of the qubits themselves, which are governed by the interplay between spin-orbit interaction and the tight confinement provided by the heterostructure and the quantum dot potential. This results in qubit characteristics that are highly dependent on the external magnetic field. We focus on qubit coherence - the ability to maintain stable quantum information - and demonstrate how this can be enhanced via operational sweet spots where coupling to noise sources is suppressed, reaching the longest coherence time for hole spin qubits up to date. Moreover, we investigate the exchange interaction utilised to implement multi-qubit operations, demonstrating that it is similarly governed by spin-orbit effects and the anisotropic properties of the qubit. By tuning the magnetic field vector, we effectively engineer the spin-spin coupling, unlocking two-qubit gates that are otherwise