  We explore the main processes involved in the evolution of general quantum
systems by means of Diagrams of States, a novel method to graphically represent
and analyze how quantum information is elaborated during computations performed
by quantum circuits. We present quantum diagrams of states for representations
of quantum states by density matrices, partial trace operations, density matrix
purification and time-evolution by Kraus operators. Following these
representations, we describe by diagrams of states the most general
transformations related to singlequbit decoherence and errors. Diagrams of
states prove to be a useful approach to analyze quantum computations, by
offering an intuitive graphic representation of the processing of quantum
information. They also help in conceiving novel quantum computations, from
describing the desired information processing to deriving the final
implementation by quantum gate arrays.
