The distribution of multiple entangled pairs plays a vital role in various applications, such as quantum metrology, blind quantum computing, quantum key distribution, and quantum teleportation. While qubit-based protocols exist, they are often limited by short coherence times in quantum memories and the need for individual pair generation, leading to inefficiencies and reduced fidelity. To address these challenges, this thesis focuses on the development and analysis of a comprehensive theoretical framework for satellite-based entanglement distribution using high-dimensional qudits. By employing high-dimensional qudit encoding, which enables the simultaneous entanglement of multiple pairs, we aim to enhance the capacity and efficiency of entanglement distribution schemes.

The objectives of this research are twofold, first, to compare the performance of the qudit-based protocol with a similar qubit-based protocol, particularly in a satellite-based context, and second, to investigate the feasibility and potential advantages of employing high-dimensional qudit encoding for near-term long-range entanglement distribution. The theoretical framework encompasses various elements, including a single photon pair source, lossy transmission, mapping of qudit states to qubit memories, and heralding measurements.

Through various simulations, we evaluate the impact of different parameters on the performance of the proposed protocol. Our findings reveal that high-dimensional encoding significantly alleviates memory requirements, making it suitable for current technologies with low memory coherence times. Multiplexing techniques further enhance the achievable distances and transmission rates, highlighting their importance for realistic implementations. However, we note that higher-dimensional protocols introduce additional experimental challenges and errors, warranting further research and optimisation. Furthermore, we explore the effect of reducing dark count rates in detectors and analyse its influence on the overall performance. Our investigations underscore the need for substantial detector improvements, as current dark count probabilities are on the same order of magnitude as channel losses.

By advancing our understanding of satellite-based entanglement distribution using qudits, this research contributes to the development of practical and secure quantum communication networks. The results presented herein lay the groundwork for future advancements in quantum communication technologies, fostering the realisation of global-scale quantum networks.

For NP-hard optimisation problems no polynomial-time algorithms exist for finding a solution. Therefore, heuristic methods are often used, especially when approximate solutions can be satisfactory. One such method is quantum annealing, a method where some initial Hamiltonian is slowly perturbed to anneal towards a problem Hamiltonian. The annealing schedule should follow the adiabatic theorem of quantum mechanics and should therefore be slow to yield the most accurate results. Finding a schedule that is both fast and still accurate has been referred to as a 'black art' and is usually just guessed. In this thesis reinforcement learning (RL) is explored to see if it can help with finding the optimal quantum annealing (QA) schedules. The Hamiltonians used are of
the form of a transverse field Ising model. These are well studied Hamiltonians that can map to many NP-complete problems [1]. Finding a good balance between going both fast and being precise proved to be difficult and needs further research. Therefore this thesis mainly dealt with training an RL agent to find the most accurate QA schedule. The results show that the agent learns to find the most accurate (slowest) annealing schedule after 300,000 learning steps for a problem Hamiltonian with a single coupling constant J and no reward shaping. Annealing in an environment with a spin glass problem Hamiltonian proved to be difficult and has not shown good results in this thesis This needs further investigation. Nonetheless, the result on the single coupling constant Hamiltonian shows the potential of an RL agent for learning in a quantum annealing environment with very sparse rewards. This paves the way for further research into an RL agent that can find a schedule that is both fast and accurate on a wide range of problem Hamiltonians.