Quantum State Assignment Flows.

This paper introduces assignment flows for density matrices as state spaces for representation and analysis of data associated with vertices of an underlying weighted graph. Determining an assignment flow by geometric integration of the defining dynamical system causes an interaction of the non-commuting states across the graph, and the assignment of a pure (rank-one) state to each vertex after convergence. Adopting the Riemannian-Bogoliubov-Kubo-Mori metric from information geometry leads to closed-form local expressions that can be computed efficiently and implemented in a fine-grained parallel manner.