Quantum computation in solid-state systems

In the last few years, as superconducting devices reached tens and later hundred qubits on a single chip, quantum computing has become a reality, tackling problems that would be prohibitively time-consuming even with the most powerful classical supercomputers. These early quantum computers (QC) are called noisy intermediate-scale quantum computers, since environmental noise cannot be efficiently counteracted in such small qubit arrays. While certain algorithms can indeed leverage the potential of hundreds of imperfect qubits, the great promises of quantum computing require perfect qubits that can be realized only in qubit arrays of much larger scales, using quantum error correction (QEC).
Spin qubits in semiconductors are the only platform to date that has the potential of reaching such scales, paving way for fault-tolerant quantum computing. Qubits hosted in quantum dots (QDs) have dimensions of few tens of nanometers, facilitating the integration of potentially millions of qubit on a single chip. Especially compelling candidates are spin qubits in silicon nanostructures. With decades of experience coming from the semiconductor industry, silicon is one of the most studied elements with the prosperity of uniquely advanced manufacturing techniques.
Electron spin qubits in silicon have immensely matured in the last few years reaching single- and two-qubit gate fidelities matching the error thresholds of QEC algorithms. However, the weak intrinsic spin-orbit interaction (SOI) in the conduction band necessitates the use of micromagnets to aid the all-electical qubit control. This additional complication presents new challenges in device design and fabrication. Hole spin qubits in silicon and germanium QDs, on the other hand, benefit from strong direct Rashba SOI accelerating qubit control speeds to several hundreds of megahertz, without the need to integrate additional elements in the device.
In this thesis, we start with an introduction and a brief overview of the field, in Chapter 1, where we discuss the fundamental physics of hole quantum dots and how they satisfy the stringent prerequisites of quantum computing. Furthermore, we take a glimpse at the various components of scalable architectures and the requirements on the qubit architecture posed by QEC codes. In the subsequent chapters we address the question how the enhanced anisotropy and SOI affect two-qubit gates in hole QDs. In particular, we discuss exchange anisotropy due to orbital effects of the magnetic field and crystalline anisotropy in Chapter 2. We also confirm the emergence of the zero-field splitting of triplet states in hole QDs numerically, and develop an analytical model linking the effect to the cubic Rashba SOI in Chapter 3. This work presents the first theoretical model to explain this recently observed effect in hole QDs. Afterwards, in collaboration with the Zumbühllab, we decipher the strong spin-orbit effects in an experiment on Ge/Si nanowire QDs, where we also identify the strong g factor renormalization caused by enhanced SOI (Chapter 4). Furthermore, we study the tunability of SOI in silicon FinFET devices in Chapter 5, identifying sweet spots where the qubit lifetime is greatly prolonged. Finally, we study the prospects of coupling distant spin qubits by a chiral magnon mode localized at the edge of a two-dimensional ferromagnet in Chapter 6.