E.Fermi School "Quantum Computers, Algorithms and Chaos"

Quantum computation is an emerging interdisciplinary field which takes advantage of concepts from both information theory and quantum mechanics. During the last decade a great progress was reached in the understanding of how quantum computing and quantum communications can be performed and efficient algorithms and communication protocols were developed. Due to massive parallelism of quantum evolution certain quantum algorithms demonstrate an exponential gain comparing to algorithms based on classical dynamics. In fact, a quantum computer represents a complex system of many coupled qubits which in general can be viewed as a many-body interacting quantum system. On the other hand, qubit or spin interactions have also been studied extensively in the field of quantum chaos, in which typical problems are decoherence and the quantum to classical transition, subjects that are also essential for any realistic implementation of a quantum computer. Understanding the connections between these fields may provide interesting cross fertilization of both fields. The aim of the school is to provide a background and to introduce participants to recent achievements in these rapidly developing directions of research. The main accent will be on the theory of quantum computer algorithms, error-correcting codes, decoherence and quantum chaos effects in the exponentially large Hilbert space of quantum computers. The understanding of these theoretical problems is vital for the ultimate technological succes of quantum computation.