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Community Detection in Quantum Complex Networks
Determining community structure is a central topic in the study of complex
networks, be it technological, social, biological or chemical, in static or
interacting systems. In this paper, we extend the concept of community
detection from classical to quantum systems---a crucial missing component of a
theory of complex networks based on quantum mechanics. We demonstrate that
certain quantum mechanical effects cannot be captured using current classical
complex network tools and provide new methods that overcome these problems. Our
approaches are based on defining closeness measures between nodes, and then
maximizing modularity with hierarchical clustering. Our closeness functions are
based on quantum transport probability and state fidelity, two important
quantities in quantum information theory. To illustrate the effectiveness of
our approach in detecting community structure in quantum systems, we provide
several examples, including a naturally occurring light-harvesting complex,
LHCII. The prediction of our simplest algorithm, semiclassical in nature,
mostly agrees with a proposed partitioning for the LHCII found in quantum
chemistry literature, whereas our fully quantum treatment of the problem
uncovers a new, consistent, and appropriately quantum community structure.Comment: 16 pages, 4 figures, 1 tabl
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