Spin-Orbit Control of Spin Qubit Arrays in Germanium

Abstract

Is spin-orbit coupling a blessing or a curse? For the operation of spin qubits, the answer to this seemingly simple question is far from obvious. It provides convenient control mechanisms that are difficult to predict with precision, which leaves it unclear whether s-type electrons or p-type holes offer a simpler route to engineering quantum processing units.

At the start of my PhD, holes in germanium had only just established themselves as a promising alternative to electrons in silicon [1–5]. Prior experiments demonstrated that proof-of-principle quantum processors are feasible in germanium heterostructures, showing that spin-orbit interactions are not detrimental to device performance but can even be an important asset. While the potential of germanium quantum devices was clear, a pathway for scaling them up and a solid physical understanding of their behaviour were still missing.

Subsequent theoretical work [6–9] and experimental progress [10–13], including chapter 6, 7 and 9 of this thesis, have substantially advanced our understanding of hole spin qubit devices in germanium. The concept of spin quantisation axes has proved particularly effective in interpreting shuttle-induced dynamics and relating the g-tensor to spin evolution. This enabled hopping-based, high-fidelity single-qubit gates and the exploration of a ten-qubit array in chapter 6. In chapter 7,we tuned a ten-qubit array across several charge configurations, identified their driving mechanisms, and found promising operation points that support more reliable and local control at scale. Improved insight into the g-tensor also opened pathways to new qubit encodings and manipulation schemes, one of which is presented in chapter 9. Additional side gates shape the wave function and thereby tune the g-tensor, enabling access to distinct operation regimes. Experimental validation is ongoing.

Motivated by scalability challenges in large arrays, chapter 4 examines bichromatic driving, where two microwave signals applied to orthogonal lines locally mix to drive the qubit. This operation scheme is specifically designed for architectures with shared
control lines. In chapter 5, a unit cell of such a shared control architecture has successfully been realised by showcasing the charge tune-up of a quantum dot array with shared control lines. While we brought the full array into the odd-charge configuration for the
first time, device variability prevented progress toward qubit operation. In chapter 8, we explored qubit performance using an external magnet placed outside the dilution refrigerator. Despite the initially counter-intuitive idea of operating highly anisotropic spin qubits with a permanent magnet, we show that sufficient in- and out-of-plane tunability exists to reach favourable operating regimes, improve coherence times, and simplify system hardware.

In summary, we have demonstrated that spin-orbit coupling enables a wide range of opportunities for high-fidelity qubit control, from hopping-based gates to g-tensor engineering. We advanced germanium spin qubit devices from four-qubit systems to a
ten-qubit array, while also identifying and applying strategies to further enhance scalability. Germanium hole spin qubits controlled through intrinsic spin-orbit interaction remain at the forefront of scientific and technological advancement in the field of semiconductor-based quantum processing units.