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Quantum Physics
Title: Quantum walk on simplicial complexes for simplicial community detection
(Submitted on 1 Jan 2024 (v1), last revised 26 Apr 2024 (this version, v3))
Abstract: 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.
Submission history
From: E. Song [view email][v1] Mon, 1 Jan 2024 08:43:43 GMT (35kb,D)
[v2] Thu, 14 Mar 2024 03:43:23 GMT (35kb,D)
[v3] Fri, 26 Apr 2024 14:25:20 GMT (36kb,D)
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