  Quantum time evolution exhibits rich physics, attributable to the interplay
between the density and phase of a wave function. However, unlike classical
heat diffusion, the wave nature of quantum mechanics has not yet been
extensively explored in modern data analysis. We propose that the Laplace
transform of quantum transport (QT) can be used to construct an ensemble of
maps from a given complex network to a circle $S^1$, such that closely-related
nodes on the network are grouped into sharply concentrated clusters on $S^1$.
The resulting QT clustering (QTC) algorithm is as powerful as the
state-of-the-art spectral clustering in discerning complex geometric patterns
and more robust when clusters show strong density variations or heterogeneity
in size. The observed phenomenon of QTC can be interpreted as a collective
behavior of the microscopic nodes that evolve as macroscopic cluster orbitals
in an effective tight-binding model recapitulating the network. Python source
code implementing the algorithm and examples are available at
https://github.com/jssong-lab/QTC.
