Germanium heterostructures are frontrunners for semiconducting quantum information processing.
State-of-the-art double quantum dots are confined in monolayers of Germanium, however recent technological advances enable double quantum dots to be confined vertically in germanium bilayers, offering the opportunity to add the vertical degree of freedom to the qubit architecture.
This project consists in theoretically modelling the double quantum dot in a Germanium bilayer by finding an effective Hamiltonian of two interacting spins in the presence of spin-orbit interactions.
By analyzing the anisotropy of the Landé g-factors in the double quantum dot, the project aims to identify opportunities and challenges for two-qubit gates implemented in these structures.

The goal of quantum application scheduling is to enable the execution of applications on a quantum network. As the final step in the application scheduling process, program scheduling locally schedules execution of blocks of instructions on each node by defining so-called node schedules. In this thesis, we present a formal definition of program scheduling and propose success metrics to evaluate the quality of node schedules. We implement program scheduling using the framework of Resource-Constrained Project Scheduling Problem (RCPSP) and and simulate the execution of node schedules. By evaluating the performance of program scheduling on datasets with diverse quantum applications including quantum key distribution and blind quantum computing, we observe that heuristic-driven approaches achieve comparable results to optimal program scheduling while requiring fewer computational resources. Our work offers valuable insights into the translation of classical scheduling problems into the quantum domain, contributing to the advancement of quantum application scheduling.

Quantum computers promise an exponential speed-up over their classical counterparts for certain tasks relevant to various fields including science, technology, and finance. To unlock this potential, the technology must be scaled up and the errors at play must be reduced. As developments in scalable quantum computation devices advance, the demand for scalable benchmarking techniques that are able to reliably assess the fidelity – the complement of the error rate – of a device has increased significantly. Randomized benchmarking offers a single, concise number that reflects the average fidelity of multi-qubit operations performed on a quantum device. While this method is robust against state preparation and measurement errors, it still suffers from scalability issues. In this thesis, we present a protocol that efficiently predicts the multi-qubit fidelity obtained from randomized benchmarking by only benchmarking single- and two-qubit subspaces, greatly increasing the scalability. The protocol uses simultaneous randomized benchmarking with the aim of catching cross-talk effects while at the same time reducing the number of required benchmarking sequences. We have run numerical simulations of the protocol under two noise models, one depolarizing and one dephasing, to verify its performance. The results of these noisy simulations are promising and suggest that our protocol could offer a valuable tool on the road to developing large-scale quantum computers.

In recent years, Quantum Computing has gone from theory to a promising reality, leading to quantum chips that in a near future might be able to exceed the computational power of any current supercomputer. For this to happen, there are some problems that must be overcome. For example, in a quantum processor qubits are usually arranged in a 2D architecture with limited connectivity between them and in which only nearest-neighbour interactions are allowed. This restricts the execution of two-qubit gates and requires qubit to be moved to adjacent positions. Quantum algorithms, which are described as quantum circuits, neglect the quantum chip constraints and therefore cannot be directly executed. This is known as the mapping problem. This thesis focuses on the problem of mapping quantum algorithms into a quantum chip based on spin qubits, called the crossbar architecture. In this project we have developed the required compiler support (mapping) for making quantum circuits executable on the crossbar architecture based on the tools provided by OpenQL. Using this compiler, we have analyzed the mapping overhead of the crossbar architecture and studied how it relates to the characteristics of quantum algorithms. In addition, we have developed a verification program that checks the output of the compiler and provides a visualisation tool for debugging.