  Quantum walks have emerged as a transformative paradigm in quantum
information processing and can be applied to various graph problems. This study
explores discrete-time quantum walks on simplicial complexes, a higher-order
generalization of graph structures. Simplicial complexes, encoding higher-order
interactions through simplices, offer a richer topological representation of
complex systems. Since the conventional classical random walk cannot directly
detect community structures, we present a quantum walk algorithm to detect
higher-order community structures called simplicial communities. We utilize the
Fourier coin to produce entangled translation states among adjacent simplices
in a simplicial complex. The potential of our quantum algorithm is tested on
Zachary's karate club network. This study may contribute to understanding
complex systems at the intersection of algebraic topology and quantum walk
algorithms.
