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Complex topological matter (peculiar materials with different bulk and surface properties) has become the focus of both industrial and academic research because it is seen as a way to eventually make quantum computing more noise-free and robust. Today’s physical quantum computers are still noisy, and the protection of fragile quantum information against noises is a growing field of research. The goal of fault-tolerant quantum computing is to maintain its functionality in the presence of noise, which has driven investment into complex topological matter.