We start by briefly reminding the notion of uncertainty and superposition from quantum physics. Based on this, the concept of a quantum bit, the role of measurements, as well as the fundamental structure of a quantum algorithm are introduced. Next, quantum registers and entanglement are discussed. Operators to manipulate quantum registers are presented. The problem of decoherence is sketched. Next, the algorithm of Deutsch-Jozsa reveals the potential of exponential speedup by quantum algorithms. Algorithms to speedup unstructured search (Grover) and factorization (Shor) are sketched. Quantum cryptography is briefly addressed. A glimpse on quantum information follows. Finally, the possible mid term use of quantum computers is discussed.
Note: The talk assumes background knowledge in linear algebra.