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We present "Diagrams of States", a way to graphically represent and analyzehow quantum information is elaborated during the execution of quantum circuits.This introductory tutorial illustrates the basics, providing useful examples ofquantum computations: elementary operations in single-qubit, two-qubit andthree-qubit systems, immersions of gates on higher dimensional spaces,generation of single and multi-qubit states, procedures to synthesize unitary,controlled and diagonal matrices. To perform the analysis of quantum processes,we directly derive diagrams of states from physical implementations of quantumcircuits associated to the processes. Complete diagrams are then rearrangedinto simplified diagrams, to visualize the overall effects of computations.Conversely, diagrams of states help to conceive new quantum algorithms, byschematically describing desired manipulations of quantum information withintuitive diagrams and then by guessing the equivalent complete diagrams, fromwhich the corresponding quantum circuit is obtained effortlessly. Relatedexamples and analysis of complex algorithms will be provided in future works,for whose comprehension this first tutorial offers the necessary introduction.

Diagrams of States in Quantum Information: an Illustrative Tutorial