Weighted Automata – Theory and Applications Leipzig , March 27 – 31 , 2006

Quantum automata are, on one side, models of automata that go, in a natural way, beyond models of probabilistic automata and, on the other side, a natural way to get a deeper inside into the power of different quantum information processing features and phenomena. One can also say that, on one side, study of quantum automata is a natural way how to utilize further and sharpen techniques that have been successful at the study of the classical automata and, on the other side, a way of developing of techniques that can be useful not only in discovering potential of quantum information processing, but also for study of classical models of automata. In the first half of the tutorial, basics of quantum information processing and communication will be presented for pedestrians: why is QIPC interesting and important, what are specific resources and main models of QIPC and, finally, several very fundamental, but easy to demonstrate, results and limitations of QIPC will be introduced: no-cloning theorem, teleportation, non-locality boxes, Bell inequalities, quantum one-time pad, “classical” and unusual universal sets of quantum computational primitives. The main goal of this part of the tutorial is to show beauty, mystery, importance, main models and concepts as well as simplicity of the basic laws and limitations of QIPC. In the second half of the tutorial, at first several ways and main problems of “quantumization” of classical models of automata will be discussed. After that main models, computation modes, examples and results concerning power and succinctness of quantum finite automata will be introduced, discussed and analysed in some details. The main goal of this part of the tutorial is to show how to quantumize classical automata and what kind of old and new problems are of importance and interest at the study of such models.