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.