turkmath.org

Linear systems of equations over a finite field play an important role in quantum information theory. Instead of looking for solutions over the base field one can look for solutions (in a certain sense) over the unitary group, which are called operator solutions. The data of this system of equations can be expressed using a hypergraph and the operator solutions can be studied from a topological point of view by considering certain topological realizations of these hypergraphs. In this talk I will describe how homotopical methods provide a way to classify operator solutions of linear systems. Our basic approach is to interpret operator solutions as maps from a topological realization of the hypergraph to a certain classifying space first introduced by Adem-Cohen-Torres Giese.