Spectral bounds for the chromatic number of quantum graphs

Quantum graphs are a non-commutative generalization of classical graphs that have appeared in different branches of mathematics including operator algebras, non-commutative topology and quantum information theory. This talk reviews the different perspectives on quantum graphs and introduces a chromatic number for quantum graphs using a non-local game with quantum inputs and classical outputs. Many spectral lower bounds for chromatic numbers in the classical case (such as Hoffman’s bound) also hold in the setting of quantum graphs, via an algebraic formulation of quantum graph coloring and tools from linear algebra.