Topological signal processing on quantum computers for higher-order network analysis

Abstract

Predicting and analyzing global behavior of complex systems is challenging due to the intricate nature of their component interactions. Recent work has started modeling complex systems using networks endowed with multiway interactions among nodes, known as higher-order networks. Simplicial complexes are a class of higher-order networks that have received significant attention due to their topological structure and connections to Hodge theory. Topological signal processing (TSP) utilizes these connections to analyze and manipulate signals defined on non-Euclidean domains such as simplicial complexes. Such analysis of higher-order network data is important for many real-world problems, such as..