Topology in engineered quantum systems
Device design and artificial material implementation
G. Jin (TU Delft - Applied Sciences)
T. van der Sar – Promotor (TU Delft - Applied Sciences)
E. Greplová – Promotor (TU Delft - Applied Sciences)
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Abstract
Topological quantum matter offers robust, protected quantum states that could benefit quantum technologies. However, most work has focused on idealized systems rather than controllable platforms suitable for quantum information applications. This thesis investigates how topological features can be engineered in artificial quantum systems and what advantages they actually provide.
I study four questions through theoretical analysis and proposed experimental implementations: Can topological edge states stabilize quantum entanglement? How can topological phase transitions be controlled and measured? What are the practical limitations of topological protection in finite systems? How do topological quantum walks relate to quantum algorithms?
The results show that topological edge states do stabilize entangled Bell states against parameter fluctuations compared to trivial states. Real-time tuning of SSH arrays enables tracking of topological phase transitions and mid-gap state evolution. However, conventional topological invariants can mislead in finite systems, to which I propose a criterion bridging experimentally measurable quantities with real-space topology. Finally, discrete-time quantum walks on topological systems exhibit localization phenomena reminiscent of quantum search algorithms.
This work demonstrates that simple topological models can be implemented in realistic quantum hardware, revealing both the potential and limitations of topological protection in finite, noisy systems. The results inform future applications in quantum simulation and algorithm design while providing practical guidance for engineering topological features in quantum technologies.