  Borrowing ideas from the relation between simply laced Lie algebras and
Dynkin diagrams, a weighted graph theory representation of quantum information
is addressed. In this way, the density matrix of a quantum state can be
interpreted as a signless Laplacian matrix of an associated graph. Using
similarities with root systems of simply laced Lie algebras, one-qubit theory
is analyzed in some details and is found to be linked to a non-oriented
weighted graph having two vertices. Moreover, this one-qubit theory is
generalized to n-qubits. In this representation, quantum gates correspond to
graph weight operations preserving the probability condition. A speculation
from string theory, via D-brane quivers, is also given.
