Scientific computing and applied mathematics enable the exploration of and, sometimes even, the simplification of complex systems through various optimized modeling and simulation methods. These fields create and utilize computational resources to do so. Many problems, however, are still unsolvable or very difficult to solve with current well-established methods – be it algorithms or computers. Quantum computers were theorized and are now being realized to extend computational abilities. Though commercially available and widely researched, quantum computers today are still more proof-of-concept than ”universally” applicable tools. A major part of the problem is these systems are riddled with noise, hence the phrase noisy intermediate scale quantum (NISQ) devices is commonly used to refer to current day devices. There are many approaches to mitigating the effects of noise in quantum systems from both hardware and software perspectives. This work focuses on optimizing the device hardware by combining aspects of two already well-explored systems – superconducting quantum integrated circuits and topological insulators.
The former are relatively easy to fabricate and have become one of the main focuses of today’s industry. The heart of superconducting quantum circuits is found in two circuit elements: the quantum bit (qubit) and the resonator. The qubit manages quantum information processing. The resonator is a simple inductor and capacitor (LC) in parallel and is a well understood classical circuit element. Resonators play a key role in this research. In contrast, topological quantum systems are incredibly difficult to fabricate. In theory, however, topological insulators promise a strong shield against noise across the device. By leveraging the simplicity and ease of simulating classical LC resonators and combining this with the noise-protection introduced in topological systems, this project lays the groundwork for developing a model supporting how such a hybrid hardware could process and protect quantum information. This thesis presents the characterization of how a two-dimensional array of LC resonators could behave similarly to a qubit when demonstrating edge modes, which are typically found in topological quantum systems. An approach for how to model such systems is proposed from the perspective of architecture, optimal control, and metrics.

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.