Quantum State Assignment Flows

Jonathan Schwarz, Bastian Boll, Daniel Gonzalez-Alvarado, Dmitrij Sitenko, Martin Gärttner, Peter Albers, Christoph Schnörr

Abstract: This paper extends the assignment flow approach from categorial distributions to complex-valued Hermitian density matrices, used as state spaces for representing and analyzing data associated with vertices of an underlying graph. Determining the flow of the resulting dynamical system by geometric integration causes an interaction of these non-commuting states across the graph, and the assignment of a pure (rank-one) state to each vertex after convergence. Experiments with toy systems indicate the potential of the novel approach for data representation and analysis.